A reply to: “a reply to ‘The Extinction of Pi: the short version'”

This week we’ll take a look at a critique of “The Extinction of π” from a guest author at Ex Falso named Dan. At first read, Dan appears to make a slam dunk with his two proofs against Mathis’ claim that π=4, (in kinematic situations.)

Although a closer examination reveals a major flaw in Dan’s application of those proofs to Mathis’ step method which Mathis himself lays out in the long version of his paper.


First, I want make it clear that I am not really writing this paper for Dan’s benefit. In reading his recent posts on this subject it seems that his mind may already be made up. Instead, I write this for others who might read it and be encouraged to take a look at Mathis’ work.

Second, in writing this paper I am assuming that the reader has read Dan’s paper and has a basic familiarity with the subject matter. That being said, I do want to thank Dan for taking the to time to analyze Mathis’ paper because it does deserve analysis. I only wish Dan had taken extra time to more carefully read the long version of this paper and realize that Mathis unequivocally states near the beginning of the paper:

More specifically, the π that I am correcting is the constant in the orbital equation v = 2πr/t.”

Unfortunately, Dan punted on that analysis near the end of his paper,

Dan wrote,

I can only assume what he means is that in a kinematic situation he feels the constant Pi = 3.14159265… is an inappropriate constant to use and the number 4 should be used in its place. I promise you that that is not that case, but a proof of that will have to come at another time.”

I am looking forward to that paper and I hope Dan will keep his promise.

That being said, it is important to remember that just like any other author’s work in physics, Mathis’ proof is only valid under strictly defined parameters. Since Mathis begins his analysis on Newton’s Lemmae it would follow that one would be speaking about a physical context or, in other words, a kinematic reference frame. This framework was used by Newton in the same manner and was subjected to a geometric vector analysis just as Mathis does in his paper on Newton’s Lemmae.

To summarize the paper:

Mathis, while studying one of Newton’s diagrams, discovered that Newton monitored the wrong angle while trying to find the limit of his data. Newton solved the problem with a flawed presumption, that being – that at the limit; the tangent, the arc and the cord are all equal in length. Mathis found instead that a second angle would have reached its limit before the one Newton monitored, invalidating Newton’s general assumption.

Mathis gives support for these assertions in his paper. He finds that because of this re-analysis he can prove that the tangent is normally longer than the arc at the limit and that the only time the tangent is equal to the arc is when the length of the tangent is equal to the radius. This means that the analysis that Newton did could only be done on one specific orbital diagram – the one that Mathis then analyzes. Since Newton used a flawed analysis for this and subsequent lemmae this affects most of Newton assumptions after that. These assumptions are what Mathis takes issue with.

(To get a clearer picture of what Mathis is proposing, please read the linked paper above.)

This quote sums up his discovery.

Mathis wrote,

…if we assign the tangent to the tangential velocity and the arc to the orbital velocity, as Newton did, we find they are equal not at the limit, but only when the tangent equals the radius. In fact, as I have shown, the tangent and the arc are NOT equal at the limit. At the limit, the tangent remains longer than the arc. And this means that the tangential velocity and orbital velocity are equal only when the length of the tangent is equal to the radius, or when the time is equal to 1/8th of the orbital period. An orbital velocity found by any other method will get the wrong answer. This is why 2πr/t is wrong: 2πr/8 is not equal to r.”

So this is what then brings the value of Pi, (the relationship of the orbits’ circumference to its diameter), into doubt in kinematic situations.

These are certainly bold assertions and they deal with a very specific orbital curve in Newton’s Lemmae. However, making specific assertions about specific curves does not necessarily invalidate Mathis’ proof nor does it make it some type of theoretical “cop-out” as some have implied. Mathis is very clear that Pi=4 only involves orbits and motion in the context noted above. In fact, Mathis’ proof relies on the “curve” being an orbit in kinematic terms where the length of the tangent is equal to the radius, or in other words, when the time is equal to 1/8th of the orbital period.

This discovery allows Mathis to find the length of the arc directly using the method he describes in “The Extinction of PI (the short version)”. In the longer version of the paper, Mathis explains his method of finding the length of the arc and the necessity of approaching that arc smoothy and evenly while using the method. We will come back to this issue later in this paper, but for now, let’s see how Dan sets the parameters for his proofs.

Dan made it very clear in his “Definition and Labels” that he is defining the function of a curve using two dimensions x and y. As if drawing a line on paper with a pencil. In other words, the function of the curve he is describing is using a two dimensional Cartesian grid for its values of x’s and y’s. Unfortunately, it does not adequately represent an orbit due to the fact that the curve is drawn all at once with no time factor assumed in the math. (At least it was never mentioned in the “Definitions and Labels”).

Dan wrote,

(think about drawing a curve above the x-axis where you never have to lift your pencil and above each x there is only one point on the curve and it never intersects itself)”

Even though Dan uses action words like “drawing a curve” and “never have to lift your pencil” There is no assumption of time in his definitions or diagrams. Since none of Dan’s analysis was done in kinematic terms or even in the context of vector analysis this quite invalidates both proofs from the very beginning.

Mathis specifically addresses some of the issues in the long version of the paper. He refers to the diagram below in the following quote.


…I showed that the centripetal force must pull down and back in order to take any object—either a pencil tip or an orbiting spacecraft—out of its original path and into a circular path. The simplest way to think of this is to think of the original velocity as AB. Then the centripetal force creates two other velocities: a velocity of size DB, which pulls the body back from B to D; and a velocity DC, which pulls the body down to its final destination of C. This is how we break down our curve into straight velocity vectors. The motion of the body from A to C is a summation of these three vectors. All three velocities happen over the same time interval, so we sum them. It is that simple.”

Note the non-zero time interval assumed in the drawing of the orbit and the mention of the velocity vectors of the object involved. Also note, Mathis describes the summation of three different velocity vectors – meaning they “add up” or “combine” to make the amplitude and direction of the orbit itself. There is also no claim of zigzag motion like others have misinterpreted Mathis as saying.

This leaves Dan’s curve functions without enough dimensions, (only having two and assuming no time dimension), to properly describe the orbit in question and thereby invalidates these proofs beginning with the first definition.

But let’s look for further problems with Dan’s proofs.

Dan begins the written portion of his first proof with a bit of grammatical slight of hand.

Dan writes,

Assume that Mathis is correct and the length of a curve can be approximated by considering the lengths of the horizontal and vertical line segments that make up the ‘steps’ in the diagrams. Mathis is correct, no matter how few or how many of these steps we subdivide the interval [0,1] into, the total of their lengths will remain constant. These steps can be made small, medium, large, evenly sized, or unevenly sized yet their total length will remain the same.”

Mathis is very specific in the long version of this paper that his step method approaches the curve in a very specific way.

Mathis wrote,

To make this method—which I have called exhaustion but which might just as easily be called approaching a limit—work, we have to push D toward the curve in a rigorous manner. In short, all of our steps have to be approaching the curve at the same rate, or the method will not work. For instance, if we draw a different curve from A to C, one that bulges out very near to D, and then we draw our steps, we will not be able to make those steps even. Or, to put it another way, we will not be able to push D toward the curve in an even manner. Our exhaustion will not “go to infinity” at the same rate all long the curve; therefore our method will not work, mathematically or physically. But it will work with the circle arc AC, and it works for the physical reason I have shown above: both the tangential velocity and the centripetal force are constant. The arc AC is created by a constant and unvarying process, therefore that arc can be approached by the (right) orthogonal vectors in a logical and rigorous manner. In fact, the arc AC is the only curve from A to C that can be exhausted in this manner , given AD and DC. All other curves are varying curves, and cannot be approached as a limit or exhausted in this direct way.”

Mathis states that he is talking about a very specific orbit and a very specific process. In fact am not even sure how Dan’s curve, (see picture below on right), applies to Mathis paper. It is obviously not a circle, not a circular orbit, nor even the curve that Mathis is analyzing. This is the whole thesis of Mathis’ paper.

Therefore, when Dan states the following,

Dan wrote,

Now consider the curve R and B in the right side of the diagram. They can be approximated by ‘steps’ as in the Mathis proof.”



Recall that Dan claims that Mathis’ method includes unevenly sized steps. Mathis specifically excludes this approach. As one can see in the diagram of R the steps do not evenly approach the curve as Mathis method requires.

Mathis wrote,

In short, all of our steps have to be approaching the curve at the same rate, or the method will not work. For instance, if we draw a different curve from A to C, one that bulges out very near to D, and then we draw our steps, we will not be able to make those steps even. Or, to put it another way, we will not be able to push D toward the curve in an even manner. Our exhaustion will not “go to infinity” at the same rate all long the curve; therefore our method will not work,”

and this quote form Mathis’ paper,

…you can approach the circle arc AC from the line AD + DC because those vectors created the arc AC to begin with. Those vectors physically created the curved path. They are not just orthogonal vectors, chosen because they were handy. They are THE orthogonal vectors that define the path of the curve. The arc AC is approached smoothly from D because it was in some sense created from D. D is the physical balance of O, given the interval AC and motion from A to C. D was guaranteed to approach the arc AC smoothly and evenly, which is why I use the method without explanation in my gloss of this paper.”

Therefore, Dan’s statements and diagram are obvious red herrings and simply do not represent Mathis’ method. This then further invalidates proof #1.

Also, note the curve that Dan chooses to use in his diagram across from Mathis’ diagram. I studied the diagram and I noticed something familiar about it – it is precisely the type of curve that Mathis gives us in his text as an example of a curve that will not work with his method!

It might be difficult to see at first because Dan has the diagram of his curve turned 90° counter-clockwise from Mathis’. I have edited Dan’s side of the diagram on the right and added the “D” to show you where it corresponds to Maths’ “D” in the diagram on the left.

Here’s the quote again,

Mathis wrote,

For instance, if we draw a different curve from A to C, one that bulges out very near to D, and then we draw our steps, we will not be able to make those steps even. Or, to put it another way, we will not be able to push D toward the curve in an even manner. Our exhaustion will not “go to infinity” at the same rate all long the curve; therefore our method will not work,”

So what Dan has really proven is that Mathis was correct in this analysis above and nothing more. Also note the blue line B in the diagram above. I will be referring to this line again when we examine Dan’s second proof.


Dan considers this right triangle and attempts to use the step method to measure the hypotenuse. Dan claims that AC is a curve in his definitions and in a general way he is correct. As it turns out, it happens to be a very specific curve. Namely a straight line. The 90° angle at B guarantees this. In fact, the line segment AC in Dan’s diagram directly corresponds to Mathis’ AC in his diagram. Dan’s hypotenuse is Mathis’ cord.

I have edited Dan’s diagram again, added an impression of a circle like in Mathis’ diagram, and added Mathis’ back on the left for comparison. The “D” right above Dan’s 90° was also added to again correspond to Mathis’ “D” in his diagram. I had to rotate the triangle 180° to make it correspond to the right triangle in Mathis’ side of the picture. Mathis’ cord is shown in red. It is clear to see that Dan’s hypotenuse acts exactly like Mathis’ cord AC in this case.



Mathis also makes it very clear in the long version of his paper how futile it is to measure the length of the cord or any straight line from D with his method. This includes Dan’s hypotenuse above and also includes line B in Dan’s other diagram. B also acts like a cord.

Mathis wrote,

To show why the chord AC cannot be approached like this, we use much the same analysis. At first look, it appears that you could draw steps along the chord AC in the same way, “exhaust” them in the same way by increasing the number of steps higher and higher, and find by this magic that the straight line AC was the same length as AD + DC. The reason you cannot do this is because once again you cannot approach the chord AC in an even manner from the point D. Therefore all your steps won’t go to the limit at the same rate, and your “method” won’t work.”

and this quote from the same paper,

The straight line is actually the most difficult thing to approach, and the impossibility of this approach is actually the easiest to discover. For instance, draw four equal steps along AC, then look at them from the point D. There isn’t any way you could have approached those four equal steps from D. In the method, you aren’t just drawing any steps you like. You are supposed to be drawing steps that would occur if you pushed the line AD + DC toward AC. Exhausting a process or going to a limit is not a willy-nilly process, it is a defined and rigorous process.”

and this quote,

…the distance of a line cannot be approached from off the line, because the line is already the distance itself. It is “even to start with”; therefore, it cannot be approached evenly (except by a parallel line of the same length).

It appears from this that Dan has actually proven Mathis’ analysis correct again!

In summary, at the very best, Dan is having trouble choosing the proofs that are relevant to Mathis’ theory. It is possible this was just a lack of reading comprehension or perhaps a lack of understanding of the material in question.

In the worst case scenario, Dan – reading these two examples of the “limitations” of Mathis’ method, (the only two that Mathis cites in the whole paper by the way), has knowingly attempted use them to “disprove” Mathis’ method. I hope this is not true because it would be very disingenuous to Dan’s readers.

I want to make it clear that I don’t dispute Dan’s proofs in isolation. I maintain that their application to Mathis’ method is faulty in this case. Therefore, Dan’s proofs fail to be relevant as to the veracity of Mathis’ procedure one way or the other.

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  1. #1 by artoffacts100 on November 30, 2010 - 10:49 PM

    Sleestack that was a great rebuttal. I enjoyed it very much, thank you for writing it. It was so needed. I’m looking forward to more posts and will check back often. I like the title of your blog by the way. Most appropriate.

    • #2 by AA “Proper Gander” Morris on September 14, 2016 - 2:04 AM

      pi = 4 is nothing but a nonsensical brainteaser

      The use of pixels or the so called step method is the incorrect way to model a circle, so it’s no surprise that the result is absurdly illogical. That method is a misleading magic trick and nothing more- a bit of intellectual sleight of hand.
      Drawing a circle as anything other than a circle is obvious nonsense. The resulting stair shape is not a circle but a pixelated version of one, like a low resolution bitmap graphic and not like an eps or postscript graphic, which is scalable.

      see:
      http://designinstruct.com/print-design/vectors-vs-bitmaps-printing/

      Various CAD and drawing programs draw circles using regular pi. 3d programs also make use of pi as 3.14…. not 4. We can make a 3d wheel turn the appropriate amount when a 3d car is moved forward by using a mathematical expression that links linear motion with rotation. Unwind a spool of thread or use another method- like that shown in the illustration linked – and you can prove pi is not 4 nor can it ever be.

      • #3 by tharkun on September 19, 2016 - 1:38 PM

        So your response is to show a geometric construction to disprove a kinematic one? Try again. Physically, the step method is the ONLY way to measure the circle because perfect circles only exist in abstract geometry. In kinematics, which is what pi = 4 applies to, curvilinear motion cannot be created with a single force. The application of those forces will always resolve into a step construction at a high enough resolution. Measuring a kinematic curve with a geometric straight line is illegal physically and mathematically. Line and curves aren’t equivalent kinematically or mathematically.

  2. #4 by Mark on April 12, 2011 - 7:34 PM

    After reading your post here I feel I should point out a couple things. First, you misunderstood Dan’s proof, completely. You also claim he somehow cheated by not clearly demonstrating that Pi = 3.1415…., He clearly explains where one can look to find those proofs using summation of power series representation of the tangent function.

    The point of his proof was that mathis’ method is flawed, for all curves. It yields contradictory results, and this any conclusions drawn from it is meaningless.

    You alse claim he fails to take into account that it is a kinemetic situation, that is actually completely irrelevant. The rules of plane geometry do not change simply because you are using them to model a kinematic situation, the rules of plane geometry are the rules of plane geometry, nad they do not change no matter what you are trying to model with it.

    Oh yeah, Mathis never does vector analysis either. Vector analysis is a branch of real analysis dealing with functions from R^m -> R^n, vector valued functions, vector fields, contour integrals, and more. I will tell you though that with relatively simple tools from vector calculus Mathis’s attempt at proof crumbles even faster. I could supply such a proof but would probably be wasting my time.

    • #5 by Sleestack VII on April 14, 2011 - 1:49 PM

      Thanks for commenting Mark. I will respond to your points of issue in order…
      you say that I misunderstand Dan’s proof completely but you give me no examples of what you mean. This gives me no way to respond to you on this point.
      Next you say that I require Dan to prove that Pi = 3.14 – but you never show me where I say that, nor can you, because it is not in the above post. So the fact that Dan tells me where to find this information is beside the point. The reason I never require Dan to prove that Pi = 3.14 is because in referring to plane geometry Mathis doesn’t dispute this either. Mathis is only referring to orbital mechanics. So again this seems to be added in as a red herring to muddle the issue.

      Next you say, “The point of his proof was that Mathis’ method is flawed, for all curves. It yields contradictory results, and this any conclusions drawn from it is meaningless”. – Again I do not dispute that that was the INTENT of Dan’s proofs. I maintain that Dan’s proofs are mis-applied in regard to what Mathis is describing. But again you give me no examples of how I may be incorrect in my analysis above. So other than to refer you back to the original counter-critique I don’t have much to respond to.

      The next part of your comment perplexes me. you say, “You also claim he fails to take into account that it is a kinemetic situation, that is actually completely irrelevant. The rules of plane geometry do not change simply because you are using them to model a kinematic situation, the rules of plane geometry are the rules of plane geometry, nad they do not change no matter what you are trying to model with it.”

      Never once did Mathis say that the rules of plane geometry have changed nor have I. But if you don’t use the tools of geometry correctly you will get the wrong answer and I agree with him.

      I will restate basically what Mathis is saying again if you missed it. In plane geometry the value of Pi ( 3.142 approx.) is the amount of times the diameter of a circle can be measured along the circumference of a circle. Mathis contends that in an orbital representation of this “circle” the diameter and the curcumference cannot be compared directly to each other in this way as in plane geometry. The reason, Mathis explains, is that the diameter here is a straight line velocity vector in our orbital diagram. It has units like meters/sec or x/t. On the other hand the path taken by the orbiting object takes a curved path. This must represent an acceleration in the diagram. He says that its a kind of velocity and acceleration combined as a type of complex acceleration. It has units like meters/sec/sec/sec or x/t³. So one would not expect to get the answer 3.142 even once the transform is applied to make the two directly comparable. All this is in Mathis article The Extinction of π . This explanation is near the bottom of the paper.

      This makes perfect sense to me, and it should be to you too, now that Mathis points it out. Using this and his discovery of errors in Newton’s Lemme allow him to determine the value for Pi in this case which equals 4. It would be helpful if you talked about these two fundamental points in Mathis’s papers, (which I contend Dan also failed to deal with), if we are to determine if there are problems with Mathis’ analysis.

      Mark, as you suspect, I am not a mathematician and so any liberal use of vector calculus jargon and symbols without detailed explanation would be a waste of both of our time.

      You should note that although Mathis did not use vector calculus in his papers for clarity’s sake, he does himself understand vector calculus and jargon and so if you submit your proof to him I’m sure he would respond to you in kind.

      I look forward to a response with more detail provided so that I may have more to respond to.

  3. #6 by Eric on April 24, 2011 - 5:47 PM

    Mathis entire argument fails at one very specific point. He speaks of planetary orbits, but then uses a circle as a model. Planetary orbits are elliptical not circular. So his method fails right of the bat.

  4. #7 by joetoe on February 9, 2012 - 7:59 PM

    “The reason you cannot do this is because once again you cannot approach the chord AC in an even manner from the point D. ” This seems to be the key, and I cannot make any sense of it. “In an even manner” … what does this mean?

    • #8 by Sleestack VII on March 6, 2012 - 6:10 PM

      What Mathis is talking about is a method of measuring the length of the arc of this particular orbit he is analyzing. (One where the length of the tangent is equal to the radius, or when the time is equal to 1/8th of the orbital period.) The idea is to measure the arc with an evenly spaced step method. In this case, the steps represent the vectors involved in creating the arc (in other words the path of the orbiting object) that is being measured. As the steps are made smaller, (the line segments are shortened and more segments added but each segment length is the same size and the total length of all the segments are kept the same), the “steps” will appear to get closer and closer to the arc being measured. In other words the steps or line segments will approach or get closer to the actual arc itself. That is all that Mathis is describing here.
      If you have any follow up questions Joetoe please reply to this post and I will try and respond in a much more timely manner.

      • #9 by Steve Urich on March 6, 2012 - 9:41 PM

        Mathis gets it right in the beginning, but stumbles at the end of his proof.

        Mathis is correct initially:
        AD + DC is the chord; i.e. the x and y components of the chord.

        He then goes to the limit; i.e. over an infinitely small interval the chord is approximately equal to the arc; but only when the interval is infinitely small.

        At this point, you must sum together all the infinitesimals; i.e. an integral is required (Integration). You can’t just return to the original lengths; the chord only approaches the arc when the interval is infinitely small. To finish out his proof, you must use Integral Calculus.

        The entire argument about 1/8 of the circle is invalid. The chord only approximates the arc when the interval is infinitely small. At 1/8 of the circle, the chord and arc aren’t even close to being similar in length.

        So, his proof is incorrect. Any Calculus textbook will show you the way to find the arc length of a curve using integration.

      • #10 by Sleestack VII on March 9, 2012 - 10:08 AM

        I think you have gotten to the heart of the matter with your comment Steve. Mathis describes in his paper on Newton’s Lemmae, ( http://milesmathis.com/lemma.html ) that Newton monitored the wrong angle when doing his analysis on this problem.

        This of course changed the conclusions that Newton would have arrived at. Mathis noticed that one of the other angles in the diagram reached a limit before the angle Newton was focused on, changing the solution to the problem.

        Quoted from the main post above –
        “…if we assign the tangent to the tangential velocity and the arc to the orbital velocity, as Newton did, we find they are equal not at the limit, but only when the tangent equals the radius. In fact, as I have shown, the tangent and the arc are NOT equal at the limit. At the limit, the tangent remains longer than the arc. And this means that the tangential velocity and orbital velocity are equal only when the length of the tangent is equal to the radius, or when the time is equal to 1/8th of the orbital period. An orbital velocity found by any other method will get the wrong answer. This is why 2πr/t is wrong: 2πr/8 is not equal to r.”

        So Steve all the textbooks would have the same erroneous conclusion that Newton gave us.

        Mathis also talks extensively about your second point of integration in the article linked above. I would encourage you to read it.

        Either Mathis’ analysis is correct or it isn’t. If it isn’t then you need to point that out to him so he can correct it.

  5. #11 by Steve Urich on March 10, 2012 - 1:58 AM

    I will address each of your arguments, one after another.

    “Mathis describes in his paper on Newton’s Lemmae, ( http://milesmathis.com/lemma.html ) that Newton monitored the wrong angle when doing his analysis on this problem.”

    This is simply not true. Mathis is wrong. Lemma 6 clearly states that the angle between the chord and the tangent will diminish as B approaches A. If you doubt my word, try it yourself. Simply move point B along the curve so that it approaches point A, and then redraw the chord (i.e. the straight line between A and B), and sure enough the angle between the tangent and the chord will diminish. This is easy to demonstrate. Mathis is flat out wrong.

    “Mathis noticed that one of the other angles in the diagram reached a limit before the angle Newton was focused on, changing the solution to the problem.”

    My best guess is that Mathis is now talking about Lemma 8; he appears to be mixing the two together (Lemma 6 and Lemma 8). He talks about moving a line; which applies to Lemma 8. But, the whole purpose of Lemma 8 is to demonstrate similar triangles, not diminishing angles. So, once again Mathis has it wrong. Newton’s first eight Lemma are all correct, regardless of what Mathis claims. Again, if you doubt my word simply look for yourself.

    “In fact, as I have shown, the tangent and the arc are NOT equal at the limit.”

    This is where Mathis performs his sleight-of-hand. The chord (AD + DC) was taken to the limit, not the tangent. Mathis substitutes the tangent into his proof, which is an illegal operation. Besides, the tangent can be any length at all; it’s not dependent upon the radius, nor was it ever taken to a limit. So, Mathis has preformed some illegal magic.

    “At the limit, the tangent remains longer than the arc. And this means that the tangential velocity and orbital velocity are equal only when the length of the tangent is equal to the radius, or when the time is equal to 1/8th of the orbital period.”

    The chord was taken to the limit, not the tangent. Also, what was the point of going to the limit? Mathis takes the chord to the limit, and then just ignores the result. He goes right back to 1/8 of the circle. What was the purpose of taking a limit, if its result is never used? As I said before, once you take the limit you must then sum together all the infinitesimals (integration); that’s the whole purpose of taking the limit. Mathis has left out an essential step. Finding the length of a curve requires Integral Calculus. Mathis is doing it all wrong!

    Also, it should be noted that Mathis claims that pi has two values: 3.14 and 4. This means that pi is no longer a constant; it has multiple values. How is pi defined? It can’t be defined as the circumference divided by the diameter; that definition will give you 3.14. Is pi time dependent? Is it velocity dependent? What determines pi’s value? Mathis never gives an explicit definition of pi. Look at it this way:

    4 – 3.14 = 0.86

    Where does this value of 0.86 come from? Pi has increased by 0.86. How? Where? We aren’t given any explanation. The number 0.86 just magically appears out of nowhere. Does 0.86 have something to do with time? It’s a big mystery! In fact, Mathis never even mentions 0.86.

    Mathis also claims that the radius is in fact a velocity. This is complete and utter nonsense. The radius is a length. It is defined as a length. To assign a velocity to the radius is ludicrous. What does it even mean? The velocity of what; your hand as it draws the radius? Suppose I told you that the distance between New York and Los Angeles was 7 miles per hour? Does that make any sense? It’s like claiming that the radius has a color, or a political affiliation; it’s complete lunacy. The radius is not a velocity, or a color, or a political party; it’s a length, and only a length!

    “Mathis also talks extensively about your second point of integration in the article linked above. I would encourage you to read it.”

    I have look through all of Mathis’ web site, and he has very little to say about Integral Calculus. Which is very strange, since he is dealing with a theory that involves the length of curves. If Mathis contends that Integral Calculus is wrong, then where is his equation for deriving the length of an arbitrary curve? For example, a parabola, a circle, an elipise, etc. This equation can be found in any Calculus texbook, but it can’t be found anywhere at the Mathis web site.

    “Either Mathis’ analysis is correct or it isn’t.”

    It isn’t!

    Note: For a complete analysis of Newton’s Dynamics, I recommend the following web sites:

    1) The Key to Newton’s Dynamics http://publishing.cdlib.org/ucpressebooks/view?docId=ft4489n8zn;brand=ucpress
    2) Isaac Newton: Principia
    http://www.17centurymaths.com/contents/newtoncontents.html

    • #12 by Steve Urich on March 24, 2012 - 2:11 AM

      “I show that in kinematic situations, π is 4. For all those going ballistic over my title, I repeat and stress that this paper applies to kinematic situations, not to static situations. I am analyzing an orbit, which is caused by motion and includes the time variable. In that situation, π becomes 4. When measuring your waistline, you are not creating an orbit, and you can keep π for that. So quit writing me nasty, uninformed letters.”

      A time variable, huh? Where in his proof do you see any time variables? Isn’t the short version proof in fact a static situation? I don’t see any mention of time or velocity.

      According to the quote above, pi only equals 4 when motion and time are involved? Do you see the obvious problem here? Mathis has preformed a static geometric proof, not kinematic, and yet he ends up with a value of 4. Mathis has in essence disproved his own theory!

      • #13 by Jack Sprite on March 25, 2012 - 4:45 PM

        If you draw a circle in the desert with the diameter one mile, and then you drive along its circumference, will your odometer read 3.14 miles or 4.0? If the result is 3.14, why? It is a “kinematic” situation, after all. If the explanation is that an odometer is capable of measuring the extra 0.86, what kind of instrument *would* be capable of measuring this quantity? (Certainly not a recalibrated odometer — recalibrating would mean that driving the length of the diameter would now give 1.27.) The purpose of having an unmeasurable quantity is unclear, and certainly not falsifiable.

  6. #14 by Steve Urich on March 14, 2012 - 1:05 AM

    I have a very simple question. Did anyone even bother to verify Mathis’ claim that Newton monitored the wrong angle? It appears that no one did. If you had you would have quickly discovered that the only one who has monitored the wrong angle is Mathis!

    At the very least, check and confirm everything Mathis claims. More often then not, it is Mathis who has gotten it wrong. In the case of Netwon’s first eight Lemma, Mathis is utterly, totally, and completely wrong! But don’t take my word for it, check it out yourself and see who’s right; Newton or Mathis?

    Hint: Newton was a genius; Mathis believes pi equals 4.

  7. #15 by John Miller on March 17, 2012 - 4:09 AM

    Miles major claims, are involved with the errors in “Physics”. Mathematics is a side issue showing
    the non-requirement for “curved” space mathematics to describe, as in Astronomy, visual data.
    The issue of 3.14 or 4 in the kinematic data is a red herring. As one viewer remarked “it’s an elipse anyway”.
    Which leads to an observation of our Solar System planetary “ellpses”, a closed figure with two separate points of focus. The Sun is not observed oscillating between two foci, creating an elliptical path, so how is Kepler’s ellipse derived? Planets are said to have constant straight line velocity, a vector. Gravity is also a vector. As illustrated in WEB pages this produces a circle.
    No two bits of data lead to a common conclusion?…?
    Plotting WEB data with Sun @ 220km/sec further muddies the maths, as currently expounded it looks like a sine wave.
    puzzled john

    • #16 by Steve Urich on March 17, 2012 - 11:53 AM

      The entire purpose of this thread is to discuss Mathis’ claim that pi equals 4. Elliptical orbits are an entirely different issue, and not germane to this discussion. Instead of shifting the focus to another topic, why don’t you comment on the erroneous claim by Mathis that the first eight Lemma of the Principia are wrong? Or, that Mathis’ proof that pi equals 4 contains illegal operations?

  8. #17 by Feng Jiahai on April 7, 2012 - 12:27 AM

    first of all, are you treating a velocity of a single object as 2 separate velocities? because after one instant, the inertia changes, and the horizontal component would be rotated and its magnitude changed. if that happens, it would not be a “staircase” motion, but a straight line.
    also, the “velocity” towards the centre isn’t constant. it has changing direction. how can you account for that, and at the same time preserve the horizontal and vertical “motion” of your orbit?

  9. #18 by Rob on June 19, 2012 - 7:51 AM

    The problem of the analyses of Mathis is that he doesn’t understand limits/infinitesimals, and fancys his own methods. Now from the example he gives it is clear that he is not in any real way approaching a limit that comes close to the real length of the arc. In fact what he calculates is some kind of ‘manhattan’ distance, which is defined as the metric for points (x,y) on a plane as:
    | y2 – y1 | + | x2 – x1 |. which reads as the absolute difference in the y coördinate plus the absolute difference in the x coördinate. Which is of course different then the usual metric for the length of a line segments between two points, which is SQRT( (y2-y1)^2 + (x2-x1)^2 ).

    As can be seen, the approach mathis takes, the length does not go to a limit, no matter how small you choose your ‘block’ size. So his method is simply wrong because the limit does not approach the length of the arc as you take smaller steps but keeps the same size.

    In the example of the circle, we can get a better approximation for pi by first drawing the point (1,1) which intersects with the arc at he point (1/2 sqrt(2), 1/2 sqrt(2). Now from that point draw the line to the point (1,0) and calculate the length of the line. It turns out to be sqrt(2-sqrt(2)).
    Multiply by 8 (you can fit 8 such segments on the circle) and you get an lower bound for pi reading 3.06146745892071817384.

    And of course you are now allowed to make better calculations by just everytime halving the line segment, draw a line from the origin through that point and see where it intersects the circle, draw a new line from that point to (1,0) and calculate the length (which now represents 1/16 of the length around the circle) and in each step you approach to a better value of pi.

    • #19 by Steve Urich on June 21, 2012 - 2:21 AM

      Rob,

      Bravo! You have honed in on the very crux of the problem; the Achilles heel of the entire ‘pi equals 4’ controversy. Your first two paragraphs are simple, succinct, and prove beyond doubt that Mathis is wrong. You have delivered the fatal blow. There is nothing left to say, except this: It’s time to sweep Mathis and his nonsensical theory into the ashbin of history!

  10. #20 by Joaquin on August 10, 2012 - 7:50 PM

    I am happy to see that talk about Miles Mathis and his absurd theories has dwindled dramatically on the internet since 2010. His two vanity-published books aren’t selling and all those insults against genuine scientists with which Mathis lards his essays have come back to bite him. His “papers” are laden with errors which are easily found with a little research and I think this is exactly what people have done with his essays. After the initial excitement they checked up on Mathis’ claims and have found him in error and have dropped him.

    Mathis is getting exactly what he deserves. He who sows the wind shall reap the whirlwind. Good riddance!

    • #21 by Sleestack VII on August 13, 2012 - 6:59 PM

      While all this back slapping and celebration of Mathis’ “demise” is going on here, Mr. Mathis is being published in science journals in Australia per his latest update of 08/07/2012. Perhaps it is the crack in the science establishment’s armor beginning to widen. It appears to me that Mathis isn’t going anywhere any time soon.

      • #22 by Steve Urich on September 1, 2012 - 5:38 PM

        Even if Mathis should manage to get one of his articles published in an obscure foreign newsletter, how does that add any credence to his assertion that pi=4? Clearly, it’s entirely irrelevant.

        And by the way, AIG decided to pull his article at the last minute. It was never published in their newsletter. Not that it matters one way or the other; this thread is about pi=4, not plate tectonics. Good grief, the twisted logic needed to defend Mathis and his half-wit theories is altogether stupefying.

  11. #23 by Joaquin on September 21, 2012 - 1:16 PM

    The AIG is not a peer-reviewed journal, but an informal newsletter so obscure that it takes great effort even to confirm its existence. That Mathis thought printing his musings in this newsletter was a career highlight is telling enough. By the way his Un-Unified Field book is ranked 2,218,148 on Amazon behind such great sellers as “Teach yourself Serbian, which is at 684,621.
    Mathis is so over.

  12. #24 by Kevin Bos on October 4, 2012 - 9:59 AM

    The author of this article’s refutations are completely irrelevant (“Mathis’ proof only works for this one specific curve”, “it only works in terms of velocities, not distances”, etc.). There is no mathematical reason given for why the even step size is a requirement; it seems the only real reason this condition was imposed was to restrict the geometry to one specific case that happens to *look* as though it works. Note also that while his steps are divided into equal size horizontally, their heights are uneven. This means that just by rotating the geometry by ninety degrees, a change that should have no bearing on the physics of the situation, Mathis’ condition is now violated.
    There is also no reason why it should make a difference whether you’re talking about orbits or just static curves, and nowhere in his proof does Mathis use this distinction as a necessary step. If he hadn’t explicitly stated it, there’d be nothing to indicate that this assumption was made, and so the assumption is irrelevant.
    But none of that matters, because even if we take these pointless assumptions and conditions for granted, the math is still wrong. Taking the limit of the line as it is bent into infinitely many right angles does *not* give a straight line. This is not immediately obvious because the area inside the shape does indeed approach the area of a circle, which is ironic, because if Mathis had based his proof on the formula for area instead of the formula for the circumference of a circle, he’d have gotten the proper result.

    All Mathis has done is proven that an arc length cannot be given by such a limit. I think that if a silver lining is to be had in any of this, then “Prove that the following limit does not give an accurate approximation of the arc length: …” should become a staple assignment problem for any educator teaching about limits.

  13. #25 by C. Takacs on November 16, 2012 - 12:18 AM

    I have learned that if you are even going to follow what Mathis is talking about (correct or incorrect), you cant just jump about in his articles randomly. He does lay out some of his fundemental arguments in earlier works, that then come in to play in later works, His article on time is excellent, and should be read by anyone who takes the measurement of time seriously. I’m not saying Mathis is always right, but I would suggest that anyone who studies the history of science and math in particular knows that “crackpots” comments include just about everyone who actually ever did make a contribution. Newton was into alchemy, Kepler was into Platonic solids etc. Often, someone gets something right.. and something wrong. If you disregarded any scientist or mathematican that was ever wrong, you would have no Einstein, Feynman, or Hawking, much less anyone from antiquity like Aristotle or Descartes. Each argument made should be considered, otherwise, you throw out everything with the bath water. I would also note, the vaunted establishment of academia now openly teaches mystical Platonism in the form of the mathematical universe hypothesis (MUH). If you subscribe to this, like almost everyone in Superstring Theory and most of quantum theory do, then you honestly don’t know the difference between math and the reality you are trying to measure anymore. Also, remember which side Copernicus (a crackpot of his time) was on with the epicycle debates with the establishment, and who ended up being correct. Being part of the establishment grants no favors of truth, or insights into reality. People who end up being right are rarely the of the herd mentality.

    • #26 by Kevin Bos on November 18, 2012 - 8:24 AM

      If the reader is required to have read a previous paper to be able to understand the proof, he should have included a reference.
      Secondly, the whole reason that the “crackpots of history”, as we’ll call them, are now celebrated as geniuses is that despite the initial reaction, their revolutionary conclusions were irrefutable. This is not the case with Mathis. If his “proofs” meant anything, people would have gotten over their initial shock at his results by now and lauded him as a genius. The derision that you see of Mathis by the scientific community is not the first reaction to a revolutionary idea. In the context of the historical analogy, Mathis is the modern-day equivalent of the alchemist or phrenologist. Worse, even.

  14. #27 by C. Takacs on November 28, 2012 - 11:38 PM

    @Kevin Bos in #24
    I find it surreal how many people respond emotionally to what Mathis says about math and physics without apparently taking the time to actually read what he says, and considering before responding. Notice I said ‘read’, and not speed skim and snark. Coming from a household full of mathematicians, I am very frequently and painfully reminded that ‘reading comprehension’ is often short shifted by those who are themselves mathematically gifted.
    If you had actually been to his site, you would have seen that he does have an organization to his chapters, and frequently does mention other chapters and provides hyperlinks to them. If you pick up any book and start reading several chapters in, it often can be confusing, doesn’t matter if the book is about biology, another language, quantum physics, or a Nancy Drew Mystery. As to your comment about geniuses, just google up ‘crackpots who were right’, once you read about the history of science you will see that ‘revolutionary conclusions’ are not always accepted even when right, this is taught in all basic science classes. Many who discover things of worth are not recognized in their own lifetime because of the prevailing trends or beliefs, or just that their contribution challenges the status quo. People who are often lauded as geniuses are also often wrong about some things; Einstein was wrong about all sorts of things, admitted to it, and changed his mind about some of his own conclusions. Mathis is actually very interesting to read because he isn’t afraid of stepping on mathematical dogmas or tenured toes in ivory towers, and he does know his mathematical history of how equations were derrived from previous equations. Mathis actually does have quite a few valid arguments about the math being screwed up foundationally, especially in the calculus, and in the definition of a physical versus a mathematical or graphed point.

    • #28 by Kevin Bos on November 29, 2012 - 11:15 AM

      “What right do you have to criticize the Emperor’s new clothes? You have not spoken with the world-class tailors who have sewn them, nor have you bothered to inspect the looms on which they were woven! How dare you be so critical of the Emperor’s new clothing after only such a cursory glance!?”

      For every “crackpot” in history that turned out to be right, I’ll show you a million who were dead wrong. Mathis belongs in the latter category.
      All of Mathis’ arguments pretty much stem from personal incredulity and mangling of definitions.

    • #29 by Steve Urich on November 29, 2012 - 11:28 AM

      If you are going to defend Mathis, please address the issue at hand. Long-winded diatribes that skirt the issue altogether is not a valid defense; it’s an artful dodge; an evasion.

      The topic under discussion is pi=4. The errors in the theory have been laid bare in the comments above. And, the “fundamental arguments in earlier works” have also been shown to be error ridden (Newton’s Lemma).

      Perhaps you should follow your own advice, and take the time to read the detailed and specific criticisms leveled at the pi=4 theory. Your desire to steer the discussion into unrelated topics is both shallow and transparent.

      • #30 by C. Takacs on December 5, 2012 - 2:05 AM

        @Kevin Bos,
        “What right do you have to criticize the Emperor’s new clothes?” Nice one Kevin, while showing a remarkable disdain for anothers honest comment. My right to criticize or not, is not dependent upon any sanctimonious authority, even one as lofty your own it would appear. Please put your indignation aside along with your pride. If you want to understand and critique someone else’s argument, it would help if you actually knew how they reach their conclusion instead of attacking their conclusion sans their argument for reaching it. So far as I can tell, your fantastic argument against Mathis’ conclusion is your appeal to expert authority, or to con-artist tailors trying to dupe emperors anyway, which is also not a good allusion to support your position.

        Both of you, Kevin, Steve,
        try reading HOW Mathis is reasoning his position on Pi in certain kinimatic situations. The fact that neither of you knows his actual argument is pathetic, and I’m not going to read his papers to you like you were both little children, you are both grownups…I assume.
        http://www.milesmathis.com/pi.html and http://www.milesmathis.com/pi2.html and http://www.milesmathis.com/pi4.html <–this should take you to his paper on Pi, Mathis knows your math quite well, thank you very much, and what you are doing with it. He makes a point about how Newton made certain assumptions based on previous classical assumptions concerning geometry and how it relates to movement. Both Nasa and the Russian space program did have problems making their orbital calculations work, and had to heuristically fudge equations to make their orbital calculations agree with data, which should not have been necessary if the use of Pi in a static diagramatic circle was mathematically equivalent to an orbit. The question is; do you see what he is saying about Pi, how it is used and why there is a problem with it in kinimatic situations? Can you see his argument? If you can see his argument and see where he is in error, could you so kindly point it out and explain why he is wrong? If you would please stop arguing from authority and arrogance, I'd appreciate it, because you both sound like indignant aristocrats kvetching about the commoners getting uppity.

        @Steve Urich,
        I assume you are attacking Mathis from the top down, thinking yourself in the stronger position from which to criticise, which is why your argument appears strange to me. Mathis is not attacking from above using high math to argue downards, he is attacking from below and working his way upwards, he is questioning the foundation of Pi, how it was derived and how it is used, and revealing there ARE some problems with the definitions and premises which underly the geometry and how it relates (and how it doesn't) to time and movement. If you don't know the man's argument, and merely critique his conclusion, you look silly. Mathis is being quite rigorous with his definitions, his terms, and how they are used in the math. Mathis is not saying Pi=4 in a timeless diagram construction like in geometry, which you would know if you actually READ his paper. He is saying that the real world works with actual time, movement, velocity and acceleration, and centripetal acceleration, that there are logical problems using a timeless static construction model and claiming it as mathematically equivalent to movement in actual reality. If you want to argue against this, Please, by all means, go for it, I would be glad to hear your counter argument, but you will actually have to read his stuff to rebut his argument and make yours. By argument, I mean your line of logical reasoning where you make the case that static geometric circular figures and constructs are (contrary to what Mathis argues) actually mathematically equivalent to actual circular physical movement, and not pointless posturing. If all you want to say is 'Myself and all really smart people in the 'know', just know Mathis is wrong because we disagree with him and we know better' then don't bother responding until you learn how to debate an idea.

  15. #31 by David on December 6, 2012 - 12:59 AM

    Sorry about the broken link. Apparently WordPress automatically creates pingbacks whenever you link to another WordPress blog. The fault was their’s, not mine. Anyway, the correct link is as follows:
    Miles Pantload Mathis (http://milespantloadmathis.wordpress.com/)

    • #32 by Kevin Bos on December 6, 2012 - 8:30 AM

      I’ll have a more comprehensive reply to this a little later, but at the moment I’m a bit busy. For the time being, I’d just like to point out that I think you’ve misinterpreted my Emperor’s New Clothes analogy. The quotation marks were meant to imply, somewhat sarcastically, that it was *you* who was speaking in such a way when you insist that we need to have read Mathis’ previous work to be able to pass judgement on his claims.
      As I said, I’ll have a more robust response at some later date.

  16. #33 by Steve Urich on December 6, 2012 - 11:22 PM

    C. Takas,

    “Say you have a curve and a line that are equal lengths, according abstract geometry or the string method. The curve will have more time embedded in it. Therefore, when you straighten it out, you should monitor both the distance and the time. If you do this, the time will add to the distance, and your curve will be appreciably longer than you expect. You can actually add the difference in time to the end of the line and get the correct answer, so thinking of time as embedded in the curve is not just a pretty visualization. It is mathematically true.” (The Extinction of Pi)

    Based on the above quote, please answer the following questions.

    I have a piece of string in front of me that is laid out in the shape of a parabola. I also have a stopwatch and a tape measure.

    According to the quote above, this piece of string has time embedded in it. I want to measure the length of the string and the amount of time embedded in the string.

    What procedure must I follow?

    Does it matter whether I straighten the string out slowly; or do it all in one quick instant?

    For instance: The piece of string is 3 meters long, and it takes me 5 seconds to straighten it out. So, how do I add 5 seconds of time to 3 meters of length? Is that possible?

    Now suppose I repeat the experiment, but this time it takes 45 seconds to straighten out the string. Will the same piece of string now be substantially longer than it was earlier? Is that possible?

    It should be self evident that the above quote has no basis in reality, and is meaningless nonsense. The theory is filled with sort of rubbish; practically from one paragraph to the next.

    • #34 by Sleestack VII on December 7, 2012 - 4:51 AM

      @Steve Urich,

      You can’t really be serious with this latest objection can you? Its obvious what Mathis is writing about is a well known technique. What is being measured with the string or any type of flexible measuring device is the length of the representations of the paths of the objects in question. Motion takes time and it is implied in the length of the string because you are measuring a physical event. Steve are you really asking us to believe that an object traveling a straight path vs a curved path at the same velocity will take the same time and that time factor won’t change the result of your measurement? Perhaps you just have trouble conceptualizing this type of stuff but I have a feeling you know exactly what Mathis is talking about and want to muddy the water with this type of pedantic nonsense. If I have misread your intentions then please clarify.
      You seem to be mostly focused on Mathis’ use of the term “embedded time” in his statement and then act like Mathis is giving this quality to the string and not the measurement of the string. I think this is where you run off the rails.
      Steve I would recommend you re-read Mathis’ paper on time. This will give you an idea of what Mathis is talking about. I hope this helps.

      • #35 by Steve Urich on December 7, 2012 - 1:45 PM

        Sure, I understand exactly why Mathis had to include the embedded time concept in the Pi theory. It’s an essential ingredient. You need a mysterious and magical quantity that can’t be measured or observed. Embedded time serves that purpose.

        When Pi is measured, either statically or kinematically, you always get the same value: 3.14. So how do you get pi equal to 4? Well, you do it by adding embedded time to the length of the circumference:

        “…time will add to the distance, and your curve will be appreciably longer than you expect.”

        Yet, Mathis never develops a general formula that applies to all curves. When measuring the length of an arbitrary curve, for instance a parabola, Mathis can’t tell us how much embedded time to add to that particular length. His theory only applies to the circumference of a circle.

        But an object moving along the path of a parabola (a ball tossed across the room, for instance) must also have embedded time and yield lengths that are “appreciably longer than you expect”. There is nothing unique about motion along a circular path; his theory must apply to all motion and every kinematic equation.

        So if you accept his “embedded time” premise, you must rewrite every equation that deals with a curve: a complete rewrite of integral calculus and all the laws of motion. Good luck with that.

  17. #36 by C. Takacs on December 8, 2012 - 2:43 PM

    @Steve Urich,
    In any case, you can’t compare a curve to a straight line where movement is concerned. A velocity along a straight line is possible. A velocity along a curve is not possible, by definition mathematically and in any high school math book(which Mathis points out over an over) a curve is an acceleration, and it is not remotely one dimensional like a straight line, it has to be two dimensional in order to even describe it mathematically… so when you compare a curve to a line you are comparing two dimensionally different things mathematically. In the school you went to, was an acceleration considered the same thing as a velocity, and were they interchangeble? Or did they tell you that a two dimensional object can be straightened into a one dimensional object and be considered mathematically and mechanically equivalent? I really am quite curious about how basic definitions in math seem to become quite optional with a mere turn of phrase whenever convenient.
    Your use of string as a measurement analogy is terrible. String is a three dimensional object (which even Super Sting people seem to miss on a regular basis) which can not be made into any shape you like without changing it’s length mechanically, the width, elasticity, and compression of the string will change as you bend it, or if you pull it taunt to ‘straighten’ it out euphemistically.

    Your comment about calculus is interesting as well, considering Mathis has written extensively about how calculus screws around with infinitesimals and infinities, and pretends measurements of velocity, time and distance can be calculated at a point instead of over a finite period of length. Mathis has actually written extensively about the corruption of calculus since the time of Newton, of why and how it works or doesn’t in some situations. Considering that Newton is known to have been wrong about certain assumptions he made about the speed of light, gravity, and motion, (he still was a genius working with the limits of knowledge of his time) it is not a valid argument to claim calculus is somehow excluded from possible error just because Newton invented it, or that it is old, or that it was taught to you in school like holy writ. I have learned first hand that students in math classes rarely question their teachers and rarely understand what they are taught, they are more concerned about ‘getting the grade’ or the ‘right answer’ that will get them the grade, as should be expected from the factory that is academia. I find it no mystery why great ideas do not come from the mainstream, and for certain, why revolutions of thought or understanding NEVER come from the mainstream.

    I take it your argument against Mathis is now that he can’t possibly be right because it would mean that too many other things you were taught would have to then logically be ‘not even wrong’. You should research the epicycle models that Copernicus overturned and simplified, the people who clung to them tightly had much the same argument as you use, good luck with that.

    • #37 by Steve Urich on December 8, 2012 - 4:39 PM

      I have searched the internet and checked all of my textbooks, and can’t find a definition for “embedded time”. It appears to be something Mathis has invented, though he doesn’t provide a detailed explanation.

      The way I understand it is this. The length of a curve can not be measured using a piece of string – which is our current method of measurement upon which integral calculus is based.

      Instead, time must be taken into consideration when measuring the length of a curve. All curves contain embedded time, and this embedded time adds additional length to the curve:

      “…time will add to the distance, and your curve will be appreciably longer than you expect.”

      This explains why the circumference of a circle is longer than its measured value; embedded time has been added to its length.

      Now, my question is this. If the measured length of a parabola (using a string) is 3 meters long, how much embedded time must be added to its length?

      Note: If it makes any difference, you can assume motion along a parabolic path at 1 meter per second; or any other necessary assumption.

      • #38 by Sleestack VII on December 9, 2012 - 10:52 PM

        @Steve Urich

        You asked the question, “If the measured length of a parabola (using a string) is 3 meters long, how much embedded time must be added to its length?”

        Mathis writes about this concept of using a string to act as a measure of a physical curve in his “extinction of pi” paper,

        “The number π is a relationship. We already know that. Currently we think it is a relationship between the diameter and the circumference. The problem is, we treat the diameter and the circumference as equivalent mathematical entities, when they are not. One is a line and one is a curve. If we study the line and the curve with a bit more rigor, we discover they aren’t directly comparable. To state it yet another way: we assume that we can straighten out a curve like a piece of string, measure it as a straight line, and then compare that new length to any line we like. Physically, this turns out to be a false assumption. The only place we can do that is in abstract geometry, where time does not exist, and where lines and curves can be “given”, rather than drawn or created in any physical sense.” (bold added)

        So Mathis rejects the concept as a whole which makes answering your first question (within Mathis’ theory) impossible.

        Your second question or caveat was,

        “Note: If it makes any difference, you can assume motion along a parabolic path at 1 meter per second; or any other necessary assumption.”

        This version of the question is a bit more to the topic that Mathis addresses but shows, by the way its structured, that you have forgotten that a curved path means acceleration.

        Since you’ve allowed me the freedom to make any necessary assumption let’s assume for a moment that you mean the object is moving at 1 m2/s2. Mathis maintains that if you treat a “straight line” on your graph as a simple distance, meters (m) in this case, then to correctly represent the complex acceleration of the “orbit” in your math one would need to use (m2/s2) and not just (m). Can you see now where the missing time variables are in the math?

        This is explained in more detail here.

        (It may be interesting to point out that the strict definition of an orbit would be a full circuit around a primary but the parabola in question, if considered to be part of the path of a body under gravitational influence, would escape the primary.) – see parabolic trajectory

        Mathis’ paper on celestial mechanics can be found here.

    • #39 by Ken NG on March 20, 2016 - 3:53 AM

      “ I have learned first hand that students in math classes rarely question their teachers and rarely understand what they are taught, they are more concerned about ‘getting the grade’ or the ‘right answer’ that will get them the grade, as should be expected from the factory that is academia. I find it no mystery why great ideas do not come from the mainstream, and for certain, why revolutions of thought or understanding NEVER come from the mainstream.”

      The above statement is right, people just fed the formulas into the brain without understanding and challenging the fundamental concepts,They are busy to get good grade to go to good university and earn big bucks (City boys!). I have seen this kind of example why people want to quickly apply the formulas and get A grade. That is it for the process of learning.

  18. #40 by Steve Urich on December 10, 2012 - 1:57 AM

    Which one of you guys is Mathis?
    a) C. Takacs
    b) Sleestack VII
    c) Steven Oostdijk
    d) All of the above

    It strains credulity that all of you can cite Mathis chapter and verse, and actually believe so much as a single word of it.

    On a side note: I regret saying “any necessary assumptions”; naturally that would open the door to this nightmare:

    “The circumference of any circle has the dimensions m^2/s^3, if written out in full.”

    • #41 by Sleestack VII on December 10, 2012 - 5:24 AM

      @Steve Urich,

      This is an often used technique of obfuscation on the internet where you accuse those who would disagree with you that they are, “in fact”, the author or primary architect of the argument to begin with. But, in and of itself, it is not an argument about the topic at hand.

      In a political context it is known as a “false flag”. It is used primarily by governments to blame their political enemies for a covert operation that they carry out themselves.

      In the context of this blog forum, which is informal and the identification of oneself voluntary, You must assume that everyone could be Mathis in disguise (both pro and con) For all I know you could be Mathis. It really makes no difference to the issue at hand.

      What does makes a difference to me is the analysis of the concepts that Mathis has actually laid out. This is what motivated me to start the blog in the first place! I read some critiques of Mathis’ work on another blog that misrepresented his theories so I was motivated to write this, “critique of a critique” at the top of this page. You see I didn’t think that Dan was being fair to Mathis by punting out of the gate, quoting Dan from above:

      “I can only assume what he means is that in a kinematic situation he feels the constant Pi = 3.14159265… is an inappropriate constant to use and the number 4 should be used in its place. I promise you that that is not that case, but a proof of that will have to come at another time.”

      Steve, do you think that is an appropriate way to argue in a debate? As C. Takas has alluded to, this is a well known logical fallacy or “debate technique” called, argumentum ad verecundiam or argument from authority. In this case Dan is his own authority. Recall he “assures” us with no evidence. This type of nonsense gets us nowhere and inundates the arguments made by Mathis’ detractors. Making them look foolish. But that doesn’t help us get to the truth of the matter (which I personally think Mathis is zeroing in on).

      In the last 6 years I have really been excited about only two new scientific theories/ideas Miles Mathis’ theories and the Electric Universe theory of the Thunderbolts team. I see evidence that they are one in the same theory. Miles works it from foundational theory upward and the Thunderbolts work it from a more macro effect-driven observable end but it is the same theory. I see promise that Mathis is now posting articles/podcasts from the Thunderbolts. I think that at least he sees that the thunderbolts project are open minded and in the pursuit of truth as I believe he is.

      As I said in one of my previous posts that at some point Miles should address the behavior of plasma and how his theory can help us penetrate its “mysterious” behavior. Since plasma makes up 99.99% of the viewable universe I am thinking Mr. Mathis will eventually get around to it. Hope springs eternal but I know he’s a pretty busy guy. I understand that plasma is very hard to model even with modern computers due to the complexity of it and the variables increasing exponentially very quickly. So perhaps it is even beyond accurate modelling but I think it is one of keys to the whole thing. Mathis’ treatment of Newton’s gravitational theorem, by including electro-magnetism makes this linkage to the Electric Universe idea necessary and foundational.

      Remember Steve, Mr. Mathis is only standing on the shoulders of Scientific giants as all others have in human history, including the ancient greeks, Copernicus, Newton, Euler, Kepler, Einstien and on and on. They were not gods, neither is Mathis. Just men. Men who should not be worshiped with any more reverence than their theories can explain what we observe. The standard model has left us with 94% unobservable “dark stuff” to fill the holes in the obviously flawed gravity-only theory. Perhaps you can begin to see how much we are missing and how much further we need to go. I see more and more evidence that both Mathis and the EU theorists are headed in the right direction.

      [As a bit of housekeeping – I never properly thanked Miles for linking to this blog from his pi papers. For that I thank him and am grateful that he thought my analysis was worth anyone’s time at all. If he reads this blog at all I hope he sees this forum post and considers EU ideas worth investigating as it relates to his theory. Especially the “electric comet” predictions that Wallace Thorhill has made and are featured in a recent Thunderbolts podcast.]

    • #42 by Kevin Bos on December 10, 2012 - 12:47 PM

      Haha, I wasn’t going to say it, but I’m glad that somebody else noticed. I’ve seen similar accusations made on other forums, and I agree that it seems very likely that there is some aliasing going on.
      And the way he talks about being curious of plasmas makes one suspect that we’ll definitely be seeing some papers by Mathis on that very same topic sometime soon, in much the same way that he tells us Mathis’ posting of content from these “Thunderbolts” folks has coincided with his own interest in them. Again, probably because they’re the same person.
      If it looks like a duck, swims like a duck, and quacks like a duck, it’s most likely a duck.
      Your reasoning is unassailable only because it is in fact some twisted form of unreason. It’s not unlike trying to disprove a supernatural claim: no matter how logically it is refuted, the claimant can always add another layer of mysticism to justify their story and confound rational discourse.

      Anyway…

      You say that any curve other than a straight line “is an acceleration”. To me, this implies that you’re saying that measuring the length of a curve can only be expressed in the context of some object traveling along it, but I may be wrong. Who the hell knows what you’re talking about.
      Consider this then: you have two curved metal blades connected at a pivot point (think of a pair of scissors, but the blades are curved instead of straight). Let’s say that one curved blade (blade 1) has a smaller radius of curvature than the other (blade 2) and that both blades’ convex sides face clockwise relative to the pivot point. Now rotate blade 1 clockwise around the pivot point until its convex side approaches the concave side of blade 2, and keep rotating it such that the blades begin to overlap near the pivot point. Rotating it further, the point at which the blades cease to overlap will move further along the concave edge of blade 2 from the pivot point The point of all of this is: in a Cartesian frame of reference, the equation of motion of the point between where the blades meet and where they separate (i.e., the point on the edge of blade 2 where the blades cease to overlap) describes a non-linear curve, and since the motion it’s describing does not belong to an object, but instead to some abstract point, how then do you measure the length along the edge of the blade over which that point has varied? Note that this is indeed a time-dependent physical situation.

      I chose this example because it clearly does not fall under the umbrella of “abstract geometry, where time does not exist, and where lines and curves can be ‘given’ “, and yet it is not strictly a “kinematic situation”. It is in fact something in between, and I’d like to know what you make of it.

      If my explanation of the situation isn’t clear enough, I’d be glad to provide clarification.

      • #43 by Steve Urich on December 10, 2012 - 4:57 PM

        Mathis rejects the entire premise of curve length. In his theory, the length of a curve doesn’t exist; so it’s impossible to measure.

        Lengths are velocities.

        Curves have dimensions of m^2/s^3.

        My best guess is that a curve is an area with a changing acceleration. But then, Pi is an acceleration. So a curve is… well, who knows?

      • #44 by Kevin Bos on December 10, 2012 - 5:05 PM

        @Steve Urich,

        I suppose as an anticipation to the sort of answer one might expect from Mathis, you’re probably right.
        However, a lot of his reasoning seems to boil down to the claim that abstract, dimensionless points do not exist in real life, because they cannot be drawn. I hope that my example at least illustrates that just because an infinitesimal point cannot be drawn with a pencil, it doesn’t mean that there are no physical situations involving such. All that’s required is that we consider something that is moving other than a tangible object.

      • #45 by C. Takacs on December 11, 2012 - 2:28 AM

        @Kevin Bos #41,
        “… I hope that my example at least illustrates that just because an infinitesimal point cannot be drawn with a pencil, it doesn’t mean that there are no physical situations involving such. All that’s required is that we consider something that is moving other than a tangible object.”
        Two things wrong with this statement, the drawing of the point not being either of them, nor the fact that you can’t name one single infintisimal thing that can be observed moving in reality.
        First, all things that move have a size or some measurable extension, if they didn’t, you would have no way of knowing they were moving, since there would be zero extension. If there is no extension, what pray tell is moving and how the heck are you observing it? Magic? Cosmic powers? Divine perception? You can imagine nothing moving I suppose, like a non physical abstract idea, but that has no bearing on what reality is or how it moves unless you also want to consider how many angels can dance on the head of a pin as observable phenomena. You might as well say, ‘if something that had no size moved it could happen’… How? If it has no size, it has no extension/period which is one of the requirements for movement, along with time and distance. If something has no size, it isn’t a thing that can physically move since there is nothing there to be moving. A physical point as defined has zero dimensions. A graphed or mathematical point has at least two dimensions (at least an x and y) or more. Right away you can see a mathematical point is not mathematically/dimensionally equivalent to a physical point.
        Second, any velocity you can calculate can not be at a physical or a mathematical point. v=d/t means literally that you have to have a non zero t in order to crunch your numbers with. In other words, you have a period of time over which you travel your distance from which you can calculate your velocity. If your distance is at a point/zero, you have traversed no distance, so you didn’t move or have zero velocity. If your time of movement is zero (a point or zero period of time) you are dividing by zero, which is a no no, besides, if you have no period of time over which you were traveling, you have no distance you could possibly cover. These are the reasons Mathis gives for jettisoning the point from physics and calculus. They make pretty good logical sense once you consider the operation you are logically and mathematically performing to make any calculation of velocity, distance, or time. Yes I know everyone is doing it with the damn points, but that doesn’t mean they are right. They are also renormalizing infinities (creating an infinite margin of error) and can’t figure out why the math is rebelling, consider contradiction and paradox “profound” and “mystical” design features and insights into higher math, and speculate about blackholes that exist in spacetime without mass with Ric=0, then get mystified why their equations can’t account for 98 percent of the mass in the universe and create dark fudge to smooth it over…lots and lots of fudge. My point is, Mathis has a good point about the point being a bad idea in calculus and physics.

      • #46 by Kevin Bos on December 11, 2012 - 10:50 AM

        You know, that certain debating tools, while technically logical fallacies, are still considered valid in practical use, right? For instance, someone’s credibility is something that in the real world should be called into question. But if you want to think of my taking note of popular opinion on Mathis as an ad hominem attack, then so be it. I’ve removed that line from my post, which is otherwise unaltered.

        “…you can’t name one single infintisimal thing that can be observed moving in reality.”
        Not a “thing”, per say, if by “thing” you mean a solid object of some kind, but certainly I think the example I’ve given adequately describes a moving infinitesimal point.
        You just have to stop thinking in terms of objects; that’s the whole point of the example I’ve described.

        “First, all things that move have a size or some measurable extension, if they didn’t, you would have no way of knowing they were moving, since there would be zero extension. If there is no extension, what pray tell is moving and how the heck are you observing it?”
        Since when has size been a requirement for movement? That seems to be something you’ve just made up. And you do realize that visual observation is not the only way of detecting and measuring things, right?
        How many times do people have to tell you that just because your #2 HB pencil can’t draw an infinitesimal point, it doesn’t mean that there is no such thing? The human mind is not good at considering infinities; they are outside of what we experience in normal life. But you know what? So is almost anything remotely interesting that’s happening in physics nowadays. We talk about things as small as atoms, and as vast as our universe, but how many people can actually conceive of such scales in earnest? It is beyond human experience. And yet we are able to study these things and create wonderful, working technologies from them, because people have learned to accept this incompatibility, this incomprehension, and get over it. The next step is to be able to consider infinities, and again, there is more good and proven science that works because of the concept of infinity than you can shake a stick at. You just need to get over the fact that it doesn’t “jive” with how we would normally think about our world, which we perceive only finitely and macroscopically.

        “Second, any velocity you can calculate can not be at a physical or a mathematical point. v=d/t means literally that you have to have a non zero t in order to crunch your numbers with. In other words, you have a period of time over which you travel your distance from which you can calculate your velocity. If your distance is at a point/zero, you have traversed no distance, so you didn’t move or have zero velocity.”
        Well, I *would* have an answer to this, if I didn’t already know that you’re just going to reject the concept of a limit.

        Next, I’d like to share something I stumbled across that happens to be written by good sir Steve Urich in the comments section of this site: http://scientopia.org/blogs/goodmath/2010/11/16/grandiose-crackpottery-proves-pi4/

        The following is a collection of quips and witticisms [a best of] taken directly from the Miles Mathis web site:

        “that solution looks like a fudge”
        “fudged from top to bottom”
        “a big fudge”
        “a blatant fudge”
        “a clear fudge”
        “a double and triple fudge”
        “a flagrant fudge”
        “a further fudge”
        “a highly successful fudge”
        “a horrible fudge”
        “a magnificent fudge”
        “a major fudge”
        “a massive fudge”
        “a mathematical fudge”
        “a new fudge”
        “a non-mechanical fudge”
        “a purposeful fudge”
        “a triple-decker fudge”
        “a virtual fudge”
        “embarrassing fudges”
        “the biggest cheats and fudges”
        “have to be fudged”
        “they had to be fudged”
        “is a fudge”
        “was just a fudge”
        “to fudge later”
        “fudged and false”
        “fudged as well”
        “both illegal and a fudge”
        “that manipulation was a fudge”
        “full of fudges”
        “must be fudged”
        “this is just one more fudge”
        “fudged corrections”
        “forced to fudge”
        “talk about a fudge”
        “to fudge over”
        “all the fudges”
        “the barycenter fudge”
        “the spring tide fudge”
        “the standard model fudge”
        “repeating a fudge”
        “to be fudged”
        “based on a fudge”
        “pushes and fudges”
        “an excuse to fudge”
        “correct their fudge”
        “fudge the math”
        “the moon’s orbit is fudged”
        “the whole thing is a fudge”
        “room to fudge”
        “forced to fudge”
        “fudged data”
        “that is a fudge”
        “there is even more fudge”
        “big fudged equations”
        “fudge any equation”
        “fudge your math”
        “another fudge”
        “remove all the fudge”
        “you fudge your fudge”
        “refudging the old fudges”
        “just one more fudge”

        This is only a partial list; there are many more!

        I came across Mr. Urich’s post (dated March 2012) just last night after our little discussion on this site lead me to do some more looking into opinions on Mathis. I bring it up now because I feel it’s relevant to the topic of whether Sleestack VII and/or C. Takacs are in fact Mathis aliases. Note that near the end of his post (#42), C. Takacs uses Mathis’ own trademark catchphrase twice. Also I just think it’s a hilarious little idiosyncrasy to point out.
        Obviously it’s virtually impossible to really prove that any of these users truly are Mathis, but I claim this as further indication that it is at least likely.

  19. #47 by Steve Urich on December 10, 2012 - 1:20 PM

    Sleestack VII,

    Avoiding the facts is also a debating technique. For instance, there has been no mention, or even an acknowledgement that the Mathis article on Newton’s Lemma is incorrect; a fact that plays a prominent role in your rebuttal to Dan:

    “Mathis, while studying one of Newton’s diagrams, discovered that Newton monitored the wrong angle while trying to find the limit of his data. Newton solved the problem with a flawed presumption, that being – that at the limit; the tangent, the arc and the cord are all equal in length. Mathis found instead that a second angle would have reached its limit before the one Newton monitored, invalidating Newton’s general assumption.” – Sleestack VII

    I have made frequent comments, and even wrote an entire article debunking this:

    http://milespantloadmathis.wordpress.com/2012/12/05/newtons-lemma/

    So far there has been nothing but silence from you. Have you conveniently turned a blind eye?

    On the subject of who is who? Steven Oostdijk, who was the chief mouthpiece and advocate for all things Mathis, has been suspiciously silent from the exact moment that you started this blog. Coincidence?

    • #48 by Sleestack VII on December 10, 2012 - 9:31 PM

      @Steve Urich,

      First off, let’s talk about this notion that I am avoiding the “facts” by not instantly responding to the article you wrote Steve Urich or David or whatever you are calling yourself today. How was I supposed to know you wrote the article if you used two different screen names? Are you posting as anyone else on this forum? Funny you accusing me of being someone I’m not while the whole time you are playing as (at least) two different posters. Rather sad really…

      Addressing the issue if I am Steven Oostdijk or Mathis all I can do is link you to the original Mathis thread at the thunderbolts forum that prompted me to start this blog. This way you can see the timeline for yourself. Anyway, the thread got locked down so I started this blog to rebut Dan’s critique and the rest is history. This should settle the issue so I won’t be addressing this again.

      Oh and Steve/David, I will need a little more time, but I plan to respond to both of your articles soon .

      • #49 by Steve Urich on December 10, 2012 - 9:53 PM

        If you check the posts above, you will see that I have been talking about Newton’s Lemma for the last 8 months. When you refused to respond, I wrote an article on the subject.

        Unlike Mathis, I readily admit that I have two accounts:
        Steve Urich and David. My full name is Steve David Urich. I never pretend to be someone I’m not, and if any asks (no one ever has) I am more than happy to reveal who I am.

        I am looking forward to reading your response to my article on Newton’s Lemma.

  20. #50 by Steve Urich on December 10, 2012 - 8:42 PM

    Mathis must be reading this blog. Look at what he just posted on his updates page:

    “PAPER UPDATE, 12/10/2012. The Extinction of Pi. In an important update, I show that my pi=4 metric is basically equivalent to Hilbert’s Taxicab or Manhattan metric, where pi also equals 4. This should silence my critics on this issue.”

  21. #51 by C. Takacs on December 11, 2012 - 12:28 AM

    @Steve Urich,
    (I’m not Mathis by the way, if I was, I probably wouldn’t bother talking to you considering your sophomoric insults in place of an actual argument…’milespantloadmathis’? oh please, how about calling him a ‘poopyhead’ for goodness sake, your debate skills leave much room for improvement.)
    Please read Mathis’ disclaimer at the beginning of his new paper you mention. Please note, Geometry is not suited to describe time and motion since it contains neither, contrary to reality which contains heaps of movement and time. In a way, as per the link from Mathis’ site to the interview with Stephan J. Crothers, it’s a lot like Einstein’s spacetime at Ric=0, completely useless at describing reality much less black holes or anything else.

    • #52 by Steve Urich on December 11, 2012 - 1:21 AM

      Alright Mathis, I’ll play along.

      We already knew that it was the Taxicab geometry; Rob pointed this out way back at post number 16, nearly 6 months ago. So I don’t see where this adds anything new to the conversation, or changes a thing.

      By the way, how did you like my article on Newton’s Lemma?

  22. #53 by tharkun on December 11, 2012 - 12:24 PM

    I love how Steve/David claims to disprove Mathis’ assessment of Newton’s lemma; but when searching for details on such disproof, we are given nothing but “try it yourself” and “look for yourself”.

    This quote, “Lemma 6 clearly states that the angle between the chord and the tangent will diminish as B approaches A” completely misses Mathis’ point. He doesn’t say that the angle will not diminish; he says that it is the wrong angle to monitor in the analysis.

    The rest of his analysis is so much misdirection and demonstration of not actually reading or understanding the argument, that it is of no value as a valid criticism.

    • #54 by Steve Urich on December 11, 2012 - 2:28 PM

      “I assert that the angle BAD [generated] by the chord and tangent, would be diminished indefinitely and would ultimately vanish.” — Isaac Newton

      Let me help you with your reading comprehension. The key phrase is the angle “generated by the chord and the tangent”. What do you suppose that means?

      I also gave two sources. The other author phrased it this way: “the angle contained within the chord and the tangent”. What do you suppose that means?

      Basic reading 101.

      • #55 by tharkun on December 11, 2012 - 3:43 PM

        Perhaps you should apply some of that ‘Basic Reading 101′ to Miles’ actual papers. It is clear that you have neither understood or even attempted to understand his analysis.

        The fact that he posits that Newton monitors the wrong angle (which he describes in detail and the reasons why, btw), does not mean that the angle between then tangent & the chord does not diminish at all. But regardless it cannot go to zero and still apply to a real-world situation.

        It doesn’t matter if lemma 8 was purely geometric from Newton’s point of view. The geometric analysis was used to develop the calculus and the calculus can be used to analyze the motions in question. But we can’t assume that there is a 1-to-1 correspondence between geometry and kinematics. And we know, in fact, that there is no such correspondence.

        You cannot dismiss time from consideration just because geometers do when creating and analyzing their abstract figures. Motion requires time, there is no such thing as instantaneous velocity or acceleration. Because real motions, in the real world require real time, we cannot use time when we want,and ignore it when it gets in our way.

  23. #56 by C. Takacs on December 11, 2012 - 12:31 PM

    @Kevin Bos #43,
    Kevin, I’m not sure why you being so obtuse about points. Insults aside, the biggest part of your argument was about ‘fudge’. Yes, I am using the term as Mathis does. I like his use of the term and I adopted it, since “mathematical bullsh*t” is not as polite a term when discussing math with or about someone who is well regarded professionally, historically, or otherwise. I’m still not Mathis, and using the term ‘fudge’ doesn’t logically make me him any more than it makes me you for speaking in english with you about mathematical fudges.
    As to the damn points. This is what you said… and I can’t quote everything you say…but I can’t just sum over your infintisimal points so easily. You say, and I’m trying not to take it out of any context…

    ” Since when has size been a requirement for movement? That seems to be something you’ve just made up. And you do realize that visual observation is not the only way of detecting and measuring things, right?
    How many times do people have to tell you that just because your #2 HB pencil can’t draw an infinitesimal point, it doesn’t mean that there is no such thing? The human mind is not good at considering infinities; they are outside of what we experience in normal life. But you know what? So is almost anything remotely interesting that’s happening in physics nowadays. We talk about things as small as atoms, and as vast as our universe, but how many people can actually conceive of such scales in earnest? It is beyond human experience.”

    I’m saying: Physical movement requires an object with extension or what are you observing? Everything we CAN measure, from atoms to the galaxy we live in has a size, by that I mean it has some extension that can be comparitively measured in this universe. If you imagine an infintisimal with no extension or size, you are not going to be able to measure it with any kind of relation to anything we can observe, either with our physical senses or instrumentation. You are talking about metaphysics or a study of what is outside objective experience if you want to play around with sizeless objects moving or interacting in abstraction. Once again, this has nothing to do with the size of your pencil (sorry, that sounded bad). Something small or tiny is comparitively measureable to something else with extension, either another object or meter of some kind. You can not compare something with no physical extension with something that does have physical extension in any kind of ratio.
    As to the “The human mind is not good at considering infinities; they are outside of what we experience in normal life.” statement eventually followed up by “It is beyond human experience”, well, my awe of ‘Big and Infinite’ Vs. ‘Small and finite’ arguments died a long time ago after I got tired of endless big-banged exponentially accelerated and inflated cosmically silly-stringed assertions in science journals. The universe is big and I am comparitively small, so what? Small is still something quite measurable and not in any way infinitesimal in a physical or philosophical sense. Not that you are correct, since you go on about infinite math, which implies you are considering what you speculate to be infinity. By your statement you are either not human, or you have painted yourself into a corner of paradox. Anything remotely interesting in actual physics had better well relate to what is within human experience so we can observe and measure it, or you aren’t doing physics, you are playing with yourself metaphysically and confusing complex math with reality. Atoms and galaxys DO have extension, size, and can be compared, and evaluated, and relate to one another. If you want to go play with infinity at the bottom of a mathematical artifact that lives in a massless fantasy with the resulting associative paradoxes, go for it, just don’t confuse it with science or physics or reality in general. Ok, I’m hungry now, time for some actual Christmas fudge.

    • #57 by Kevin Bos on December 11, 2012 - 10:50 PM

      @ C.Takacs #55
      When I spoke of atoms and universes, I didn’t mean that those were examples that directly related to the issues Mathis takes with infinitesimal points. I simply meant that immense (or immensely small) scales and infinites are somewhat similar in that they are very difficult to envision, so I thought some parallels could be drawn between how an understanding of each concept is obtained. It wasn’t meant to relate to any of the specific points of debate.
      As I’ve said before, I feel like too much of Mathis’ reasoning is based on personal incredulity and intuition, rather than on doing actual math. I wouldn’t be the first to remark that his papers tend to have more rhetoric/verbal explanations and less math than your typical math/physics paper. And so my previous post was meant to address not the specifics of Mathis’ theories, but his way of thinking in general.

      And again, I think you’re taking it for granted that something without size cannot be observed. For instance, if an electron truly is a point particle, then we can’t possibly see the thing, but we still know it’s there because of its electric field.

      • #58 by C. Takacs on December 15, 2012 - 10:13 AM

        @Kevin Bos,
        Mathis actually does discuss what you are referring to in “Why so Angry?” Considering the reception I myself have received from asking simple questions from ‘experts’ who show themselves to be anything but calm and rational themselves, while hiding their own lack of curiosity under degrees, conceits and smugness, I can understand why Mathis is ticked off sometimes. I can also say that emotion is not bad when it drives us to overcome adversity, just imagine a coach, CEO, director, general, president saying ‘don’t feel anything, remain emotionless, yet somehow feel inspired to follow me or try hard and overcome difficulty’? Maybe in robot land, but not in the ranks of humanity.
        Funny you should bring up point particles, because it is one of the causes against points being in math that Mathis champions. If you read his works you would know that. I think it strange in your line of argument to state that I take it for granted that something without size cannot be obeserved why you make a huge assumption that an electron is a point particle. Once again you show you have not read Mathis, or you would not be using this example. I would ask you to read about Mathis’ papers about the radius of an electron. Yes, I do believe electrons have radius, which is a prerequisite for it being there to have a ‘field’ in the first place. To state that an electric field exisits at a point without something to generate it is…silly, much like saying a black hole is a singularity, having immense gravity, yet having no physical extension to allow it density or mass. Once again, you can not assign gravity, mass, density, inertia, movement or anything else besides a statement like ‘there it is’ to a physical point in reality. I think it is you who is making the logical error of trying to turn a mathematical artifact with zero physical extension into something that can exist in reality and interact with real objects that do have physical extension. In reality, numbers must be applied to actual things, like distances and velocities, size measurements, time elapsed, etc. You can’t just start hanging sizeless abstractions like numbers in the void and say they have physical presence to interact with actual energy and matter without the messy details of having physical extension, if you know otherwise, please provide examples to consider, just remember, point particles are abstract mathematical objects that exist in the field of math, not reality.

      • #59 by Kevin Bos on December 15, 2012 - 8:18 PM

        @ C. Takacs #55

        I wasn’t referring to Mathis being “ticked off sometimes”, I was referring to his habit of trying to justifying his claims with words rather than simply let his math speak for itself.
        You say that an electron couldn’t have an electric field “without something to generate it”. This perfectly illustrates a very telling misconception. If a particle has no size, it does not mean that it is not there. Having no size is not the same as “not being there”.
        Your comment about black holes belies a fundamental confusion. Black holes are only approximated as point masses in calculations and models. In reality, given any mass, one can calculate the finite and non-zero size to which that mass must be compressed in order for it to become a black hole. So you’re right: for a proper calculation of density, a non-zero size is required. But there’s no parameter for size in any equation of motion. All you’ve done is keep repeating that “you cannot assign gravity, mass, density, inertia, movement or anything else […] to a physical point in reality”, but you never bother to explain just why that is other than that it seems counter-intuitive. News-flash: physics doesn’t have to work according to your intuition.
        I don’t think that it is making a “huge assumption” to entertain the possibility of point particles. In fact, the assumption that they cannot exist simply out of some “common sense” argument is much more dangerous. Speaking of assumptions, there was no need to condescend to me about whether or not I’ve familiarized with Mathis’ papers. I knew that Mathis rejects the idea of point particles. That’s why I chose that example.
        Not that it would matter anyway. You seemed to have missed the point of my analogy when I made it earlier, so I’ll restate it: One needn’t have been trained by master invisible-clothesmakers or learned the intricacies of the invisible loom in order to tell you that the Emperor has no clothes.

      • #60 by C. Takacs on December 16, 2012 - 6:37 AM

        @Kevin Bos #56,
        Having exchanged multiple comments with you now, I see your concept of a debate is typical of someone who had no intention of debating. You are merely running down the clock or trying to tire out your opponent, which is a sad tactic lacking any skill, merit, or substance. I’ve tried to be methodical with your points of contention, if I nail down one, you change the subject to another point of contention. Your “Nailing Jello to the wall” defense is lame, I regularly laugh at women who try to use it to wear out their husbands and boyfriends to get what they want, and then I suggest to those boyfriends and husbands that they inform their female ‘partner’ to make up their minds what they want to complain about, or stop wasting their breath. Just because I’m curious about your next response, lets try another round.

        Point 1. Can you or can’t you give me an example of anything in this universe we know of that can interact with any other thing in the universe that does not have a relative size? I’m not ‘limiting’ my conceptual faculties or taking anything for granted in any way by actually asking for evidence of anything outside of abstract mathematical spaces that can interact with other actual things without some relative scale required to #1 observe such an interaction or even know where to look, and #2 make any kind of testable prediction of what should or should not happen by this interaction. If you want to even talk about physics, you had better remember length, volume, and density are related and required, and yes, size does matter in the interaction of these things. If you say otherwise, I ask ; what things are you talking about interacting that have no extension? Have a density?, you’ve got extension through volume and mass. Have a velocity? you’ve got extension of distance and time, and how mass relates to that velocity. Got mass? you have extension of volume and density, and thus size.

        If you don’t know why you can’t assign dimensions or properties to a physical point, you don’t understand that a physical point is zero dimensional by definition (please look it up if you like), or what zero dimensional means, and you must be missing the fact that a mathematical point is not a physical point. Also, your mathematical point can not ever leave the abstraction of the graph and become a physical point in reality, by definition of what it is. Ask yourself, how many dimensions does a graphed point have? If it’s in a graph, it can’t have zero dimensions. Assigning any quality to a physical point other than euphemistic location makes as much sense logically and definitionally as asking what the tensile strength of a one dimensional line is (like superstring theory does all the time) or asking how heavy a radius is, or asking how many pieces a square breaks into when it crashes into another square.

        Point 2. You have more than a tad of gall to bring up black holes and talk about my fundamental confusion concerning them. Hah. Technically, everyone is confused. Neither you, or Hawking (much less Einstein) really know anything about black holes, you can only guess or speculate based on assumptions based on speculation ad nausea. Black holes exist in speculation in mathematical spaces like spacetime at Ric=0 in general relativity where people like you pretend gravity can exist without matter to influence, and mass can exist without an extension of volume to calculate density. Mathematical artifacts that exist by their own definition in mathematical spaces that do not have any relation to the measurable properties of our own physical universe are not exactly useful in figuring out how our universe works.

        Point 3. My common sense and intuition depends upon logical definitions to navigate concepts both real and abstract and imagined. When mathematicians and physicists forget that their precious symbols are abstractions that must be clearly defined, they become next to useless and ‘undefined’, and what follows is the absurdity of pardox and contradiction passing itself off as reason. I believe that if your logical ‘intuition’ had not been suspended by whatever it is that you have replaced it with, you would have remembered that in physics, numbers represent actual things, and have the limitations/properties of those things, both logically and definitionally. Remember anything about the ‘eureaka’ moment in the bath tub? no…? An apple falling out of a tree? still drawing a blank? I hope Feynman isn’t your role model in this, he liked to brag about how the universe was irrational, and wouldn’t make sense to us, yet he mysteriously continued to collect a paycheck while claiming his solution to making QED work was a ‘dippy process’…ok. Jettison your intuition if you like, I’ll keep mine alive and healthy to help me to make up my own mind.

        Point 4. You want to attack Mathis about using too many words to explain his ideas instead of writing only pure mathematical equations down? Are you serious? You single him out for this as an actual argument? Do you even know how many pages of math some superstring meanderings continue on for? Even Newton used considerable human language to describe his ideas, as did Einstein, You must be joking or are unaware of how quantum mechanics texts still require lengthy explanation not to mention the numerous pages of the Copenhagen Interpretation just to be considered and it still can’t fully explain what is going on and be agreed upon throughout the physics community. I’m freezing this piece of your jello argument strategy with liquid nitrogen and punting it out the window.

        Point 5. I have no idea why you keep bringing up things Mathis talks about when you don’t take the time to read and debate his conclusions. You don’t want to examine his ideas, you just want to mock them with very poorly constructed arguments. Ok, I figured that out. I know this because most of your arguments are arguments Mathis himself makes in many of his papers… then answers them carefully. Most of your statements resemble a poor gloss reading, like the kid who thinks his cliff notes will get him through the test on Hamlet in fifteen minutes. I also figured out you haven’t carefully questioned much of what you believe, and seem very unwilling to examine your mathematical assumptions and the philosophical foundation they rest upon. You also seem to have difficulty with basic term and concept definitions, and treat them as esoteric noise that can be hand waved away if they get in the way of your greater intent.

        Point 6. Why choose the example of point particles if you read Mathis’ argument against them? You made no argument as to why Mathis might be considered wrong, you only stated it was a ‘huge assumption’ to entertain the idea, yet offered no explanation as to why, and certainly as of yet to provide an example of your point particle in the real world. I do doubt you have one, If you find an example please provide it, I would be interested.

        Point 7. Assumptions are actually right sometimes. Your statement about there being no need to ‘condescend’ to you about being familiar with Mathis papers is misdirection so you are incorrect. There was a reason to condescend, namely, you were being dishonest. You aren’t familiar with Mathis’ papers. I’m no math genius, but I am quite good at reading comprehension, good enough to recognize when someone is skimming a paper or article they don’t want to read. Your constantly shifting points of contention reveal you are not following the logical argument before you critique, you are merely reacting with contention every place your eye falls across. Cursory reading will only get you the vaguest outline of the subject material, and when you have contempt for the author it makes comprehension far more difficult.

        Point 8. I have no idea what analogy you are making about the Emperor’s New Clothes at this point. The analogy certainly does not fit my position in the argument, since I am not the one buying invisible clothing or unsupported arguments based upon an appeal to authority, mass hysteria, peer pressure, or just the general fear of not being cool. I don’t see Mathis as the groupthink sort, or fearful of other’s disapproval and I think he would laugh if you tried to portray him as the ‘deluded emperor’, since he is the one basically saying ‘what a load of garbage’ about the mainstream. I would also see the honesty of the childs perception of the emperor’s true state of dress as a demonstration that truth has nothing to do with what most people think or an elite consensus.

      • #61 by Kevin Bos on December 20, 2012 - 11:35 AM

        @ C. Takacs #57

        You denigrate my style of debate, and then spend a good portion of your post doing little more than snidely insulting me. Bravo. I don’t see how you can say my arguments have been all over the place. My last post was composed so as to respond directly to things that you’d said in your previous post. I even made sure to quote you in various places so that you’d know which specific point I was addressing.
        Regardless, how about I even respond to your points in similar format. Will that make you happy?

        1. ” I ask ; what things are you talking about interacting that have no extension? Have a density?, you’ve got extension through volume and mass. Have a velocity? you’ve got extension of distance and time, and how mass relates to that velocity. Got mass? you have extension of volume and density, and thus size.”

        Yes, you require mass and volume for density. But you can’t have it both ways by then saying that you require volume and density to have mass. You determine the density by mass/volume, but mass is intrinsic. It is only equal to volume times density in the case where either of these things exist. (Somewhat) analogously, just because you can write t=d/v for some object, it doesn’t mean that no time has passed if v is zero. And again on the subject of size being required for movement, you say “you’ve got extension of distance and time”. But neither time nor distance traveled have anything to do with the actual extension of the object itself. As I said previously, there is no parameter for size in any equation of motion. A point can travel along a continuum just as easily as an interval.
        Obviously I would be arrogant to say with absolute confidence that we know for sure that certain fundamental particles have no size. In my experience, even experts in the field would probably only go so far as to say that “it seems that way, as best we can tell”. But even if I were to outright tell you, “no, I cannot give you an example of anything in the universe that has zero size”, that would only mean that such a thing has not been seen yet, not that it cannot exist. No existence proof ever went like “we don’t know of any, therefore they cannot exist”. Furthermore, even if one were to somehow formally prove that in fact they cannot exist, that wouldn’t necessarily invalidate all math that relies on infinitesimals and limits, which makes the whole thing rather irrelevant.

        “Also, your mathematical point cannot ever leave the abstraction of the graph and become a physical point in reality, by definition of what it is. Ask yourself, how many dimensions does a graphed point have? If it’s in a graph, it can’t have zero dimensions.”

        Again, you’re inventing properties that aren’t included as part of the actual definition. The proper definition of a point is, as you say, that it is zero-dimensional, but that is all. Nothing in the definition dictates whether it can or cannot exist in reality. As there is currently no way of proving that an infinitesimal point cannot exist, we have to assume that it can. It is simply more prudent that way. And then you pull the classic Mathis and try to base an argument on not being able to draw a point on a graph, which is a position that has already been refuted about a thousand times by now.

        “Assigning any quality to a physical point other than euphemistic location makes as much sense logically and definitionally as asking what the tensile strength of a one dimensional line is (like superstring theory does all the time) or asking how heavy a radius is, or asking how many pieces a square breaks into when it crashes into another square.”

        Or saying that a circumference has units m^2/s^3 ?

        2. You’re right that the details of black holes aren’t understood. However, it really isn’t that hard to understand the very basics of it and why scientists believe they exist. For someone who claims that I’ve been avoiding the issues, you don’t seem to have responded very directly to my statement that black holes do indeed have size and that your concerns about them being approximated as point masses should therefore be resolved.

        3. As a physics student, I’ve been beaten over the head a million times with the importance of thinking about the significance of the calculations and what they represent in physical reality. The professors really put a lot of emphasis on it, and I’d say that that’s probably the case at virtually every school. That’s a bit at odds with your vision of a bunch of starchy old scholars mindlessly grinding through calculations without any consideration for their meaning.
        The real problem arises when you try to intuit an answer to your problem before even having done any of the work. When that happens, you find yourself inventing things like “embedded time” to get your answer to what you think it should be.

        4. In most math/physics papers, explanatory text is usually restricted to doing exactly what you claim physicists don’t do: interpreting how the math corresponds to physical reality. Sometimes this can take up some space, but most authors aim to be concise. The results, though, are almost always arrived at in a mathematical, stepwise fashion.
        Mathis on the other hand, doesn’t limit himself to simply interpreting results via text. He actually will write multiple paragraphs to act as a stand-in for what should be a lengthy calculation. That is just sloppy and highly susceptible to error.

        5. The problem is that Mathis’ answers to the arguments he anticipates are often ludicrous. Therefore the questions bear repeating. For example, take his paper “Music from Jupiter: A song of the Charge Field” (very fanciful title, Mathis, you’re a real poet). The footnote about multiplying by c instead of dividing is to be laughed at.
        Also in your paragraph headed as “point 5” you criticize the quality of my debating, which is not the same as refuting a point, and serves only to denigrate your opponent, which, normally I wouldn’t even mind, except that in the same paragraph you invent a number of personality traits that you project onto me, which I think demonstrates that your own debating tactics aren’t so high above mine after all.

        6. Because Mathis’ argument against them is flawed, and I feel as though I’ve addressed the main objections in #1, above. And I’ve already given an example of a particle that is thought to have zero size: the electron. In fact, all fermions are thought to be this way. Maybe my wording here (“thought to have”) will put to rest your eagerness to peg all mainstream academics as believing that they are privy to absolute and unchanging truth. I think I’ve stated before that virtually any physicist would tell you that we think fermions have no size, but few would tell you that we know it for sure. Indeed, the possibility that no real thing can have zero size is perfectly reasonable. But it would be foolish to claim that it is true for reasons that I think I’ve addressed in point 1, above.

        7. If your argument that Mathis’ detractors simply haven’t read his repertoire of work thoroughly enough is to be accepted, then you might as well have decided beforehand that you win every argument you’ll ever have on the subject. Obviously people like you, who support his claims, will be much more familiar with his papers than people who do not. Pointing that out is just clouding the issue. This isn’t helped by the fact that a debate about a specific paper, “The Extinction of Pi” has now been mutated into a debate over Mathis’ entire repertoire (a topic in which you have a distinct advantage because, as I’ve just pointed out, it’s inevitable that you’ll be more familiar with it). But of course that was bound to happen because, as we’ve been told time and time again, “to understand Mathis you have to have read all of his past work”. In other words, a barrier has been set up with which to easily turn away detractors with a wave of the hand. If you effectively declare that you won’t accept any argument against Mathis unless the detractor has read his whole life’s work, then you have the ultimate trump card, because virtually no one in their right mind has the patience to slog through that much bull simply to argue against the notion that pi=4.

        8. In a way, you have subverted the “appeal to authority” and turned it into a weird sort of logical fallacy in which anyone who argues from what you see as the accepted view must be wrong. And I don’t see how you having turned this debate into a contest of “I’ve read more Mathis than you, therefore I know better” (as per point 7, above), is very much different than someone doing the same thing for mainstream scientific literature.
        Regardless, the analogy wasn’t meant to refer so much to the aspect of “group-think” or “peer pressure” in the story of the Emperor’s new clothes, but simply to the fact that every one of the citizens knew that the Emperor was naked, and they needn’t have known anything about the claims made by invisible-clothiers in order to have said so. At the climax of the story, a child points out that the Emperor has no clothes, and nobody has to ask her to prove it.
        Similarly, nobody needs to have read all of Mathis’ papers to be able to tell you that pi is not equal to 4, and asking them to prove it is a waste of everybody’s time.
        …Which really makes me wonder why I’ve wasted so much of mine arguing with you.

      • #62 by C. Takacs on December 25, 2012 - 4:36 AM

        @Kevin Bos,
        “But even if I were to outright tell you, “no, I cannot give you an example of anything in the universe that has zero size”, that would only mean that such a thing has not been seen yet, not that it cannot exist. No existence proof ever went like “we don’t know of any, therefore they cannot exist”. Furthermore, even if one were to somehow formally prove that in fact they cannot exist, that wouldn’t necessarily invalidate all math that relies on infinitesimals and limits, which makes the whole thing rather irrelevant”

        Kevin, If that was an argument, I don’t think it was supporting your side of the discussion. “We don’t know of any,…” is the true part of your proof so far, Which is what Mathis has been talking about. In physics, or science, If you don’t know of any examples or have physical evidence of whatever you are speculating about, like black holes or superstrings, you lack evidence to support the likelihood of your speculation. This is not a good time to be claiming that your opponents must prove anything other than that you don’t have any actual evidence to support your claims.
        Mathis was talking about the physics of actual things and how they move in reality, which is what physics is about, actual things with extension which move, not ‘sizeless’ hypothetical mathematical point particles which you do not seem to be able to provide any example of in actual existence. Once again this goes back to the problem of measurement which you keep dancing around. Why on earth would you claim any kind of physics on things which can not be observed has validity? based on what? My argument was quite simply “you can’t be calculating properties of things you can’t measure and call it physics (or science for that matter)”. I think you are making a huge error in reasoning to use the “You can’t disprove my imaginary unicorns, therefore they could exist” argument. I do not need to prove that your sizeless ‘unicorns’ do not exist, I only have to state the obvious, that you can’t give a single example or proof of one of your sizeless unicorns that actually does exist, and can be observed by any known means to confirm its existence. The burden of disproof is not on me, the burden of proof is on you. Good luck with finding or detecting your ‘point particle’, I will be waiting with baited anticipation to see how you might accomplish this, outside of your imagination.
        I really think you should drop the Emperor’s New Clothes elaboration, you just keep making it worse. You yourself just made the argument that just because I couldn’t see or detect your ‘Emperor’s sizeless outfit’ (nor anyone else for that matter), that he ‘could’ still be wearing one …theoretically, even though not even you can see or detect it either.
        I would say you haven’t been hit over the head enough yet with the importance of “..thinking about the significance of the calculations and what they represent in physical reality” when you want to make statements about things in reality having mass without volume. If you have no extension of volume, what is your mass connected to? In reality I mean? What are you hanging your mass on? Do you also think lines, circles, and squares have mass?? How about things like two dimensional objects? because you can fit an infinite number of sizeless points on a finite area that isn’t zero, so how would you calculate its mass? Do you believe you can even measure gravity without something for it to be acting upon, say another physical object?
        1.You acknowledge the whole black-hole baliwick is based on…well, speculation and mathematical spaces which in no way ressemble reality but are supposed to be equivalent in someway to reality. What point am I missing about how there is zero empirical information about actual black holes outside of mathematical spaces? And that these mathematical spaces only produce a mathematical artifact? If the math you are going to use to prove a black hole has any validity, it is going to have to resemble reality, reality is not empty space without objects that somehow contains huge amounts of mass, which is what Einstein goofed around with, look it up. Mr. Rodger’s Land of make-believe had far more in common with our reality than Einstein’s Ric=0 spacetime does.

        2. If you don’t know why size is related to movement, LOOK UP. Have you have never really studied actual objects moving? Mind you, I said actual, not imaginary, or in your textbooks. Look up at the stars, see how they appear to move? Now look at the planets. See how they seem to move? Does size have anything to do with the planets? Like perhaps how we calculate their mass, their density, apparent distance and orbit, rate of movement? How large they appear to us? Look at the sun. Does its apparent size to us have anything to do with it’s distance from us? When objects like dust which appear small move slowly across our field of vision, we do not think their velocity or speed is very great. When you view actual distant planets moving across the sky, do you evaluate their speed of movement by the same criteria as the dust? Does their size and distance from us have anything to do with evaluating their speed of movement, and allowing us to comprehend that while the planets would appear to be moving much more slowly than dust floating in the air, because planets and stars are considerably larger, much farther away, it explains why even if moving at considerable speed would appear to be moving quite slowly? You really have not thought this one out at all, I can give many examples of size being entirely relevant to evaluate distance, speed and mass. You can not provide a single example beyond conjecture without physical foundation for point particles outside of your mathematical spaces. Please look up the definition of sloppy, seriously, look it up before you evaluate anything else. It is your reasoning faculties that would appear to be sloppy by your refusal to even consider your own argument by it’s own merits, not the authority of your instructors. I do not think you honestly understand the difference between abstraction (numbers, lines, planes, symbols) and actuality (atoms, planets, stars, people), and I don’t think you care. If you did care, you would realize, that unless you know the size of what you are looking at, and at what distance, you really have no way to determine how fast it is moving, nor how much mass it would have because of it’s volume, which will be a factor in how it moves in relation to other things. Nothing that physically moves can have zero size because you would have no way to relate it to any background meter from which to determine it’s rate of movement.
        I studied art (among other things) in college and was taught about perspective and how it relates distance, size, proportion, geometry, and apparent movement. A good artist learns that nothing can be accurately depicted or modeled without a scale for the subject to relate to, Maybe you should learn this too before you talk about sloppy arguments or complain about how explanatory text is used. You don’t like Mathis, ok. Big whoop. It’s about the only thing you’ve made clear in your statements that is self evident, which is a shame, but ok. If you ever have an argument besides, ‘Mathis is wrong because everyone knows blah blah blah, I don’t need to argue or prove my point because its obvious that blah blah blah, Mathis uses too many words which means he’s wrong blah blah blah…’ let me know, otherwise, save your precious time and spend it on doing something more important to you. I’m sure you can find that the textbooks you study are brimming over with people who broke new ground and made major advancements and discoveries in their respective fields by agreeing with their instructors and following the mainstream.

  24. #63 by Steve/David on December 11, 2012 - 7:33 PM

    @tharkun,

    Nice try. Who knows, you might succeed at convincing someone; don’t hold your breath.

    What’s so hilarious is that this is Chapter 2 of the Un-Unified Field; a published book. Ouch! You may want to revisit your stance on peer-review.

    I will leave to the readers to decide who’s right. These are the two articles for side-by-side comparison:

    1) Newton’s Lemma
    http://milespantloadmathis.wordpress.com/2012/12/05/newtons-lemma/

    2) A Disproof of Newton’s Fundamental Lemma
    http://milesmathis.com/lemma.html

    • #64 by tharkun on December 12, 2012 - 1:57 PM

      And a typical response from a naysayer…nothing of substance, don’t address the issues and points made just deflect with hyperlinks and ad hominems.

      • #65 by Steve/David on December 12, 2012 - 8:29 PM

        I appreciate the feedback. I am certain I can improve the article; polish it up, so to speak. I will add some Mathis quotes, and of course more ad hominems; a lot more.

      • #66 by Kevin Bos on December 12, 2012 - 9:59 PM

        @tharkun

        All attempts at addressing the issue have been promptly hand-waved away. As I said before, not unlike trying to disprove mysticism or supernatural claims, every argument against Mathis is just countered with some new layer of contrivance, with no end in sight, and after having gone on for long enough, it inevitably reaches a point where one is arguing a point so self-evident that one doesn’t take the argument seriously anymore.
        It has reached that point.

      • #67 by Steve/David on December 13, 2012 - 1:19 AM

        @ Kevin Bos,

        I completely agree. Each time a valid argument is put forth, it’s knocked down with nonsense like this:

        – You didn’t take time into consideration
        – Lengths don’t exist, only velocities
        – Curves have units of m^2/s^3
        – There are no points, only intervals
        – Pi is an acceleration
        – And so on…

        This is so far removed from reality that no one can follow it. We might as well be discussing unicorns or fairy dust.

        By the way, I want to compliment you on the Amazon book review. Well done!

      • #68 by Sleestack VII on December 13, 2012 - 9:32 AM

        I completely agree with you tharkun. Many Mathis critics I’ve noticed have very little in way of argument and complain about personality issues or Mathis’s writing style as if that was relevant to the physics he talks about. It’s not! Others like to put words in this mouth. Still others use unjustified name calling. This is usually a sign that the author has already lost the logical argument and is resorting to school yard bullying or a type of tabloid style. In other words, sensationalism for its sake alone. The bottom line is this; if they put half their time in just reading what Miles actually writes instead of posturing and embracing willful ignorance, they might begin to question the things they thought they understood – and that scares the hell out of them.

  25. #69 by Steve/David on December 12, 2012 - 9:10 PM

    Sleestack VII,

    This blog of yours is over two years old. Do you ever plan on starting additional threads? I enjoy the Pi=4 discussions, but would also like to address other issues. For instance: Differential and Integral Calculus. Any chance of you adding new threads to the blog?

    • #70 by Sleestack VII on December 13, 2012 - 8:12 AM

      Yes, I am planning to do more with this blog in the near future. First off I will be publishing a counter-critique of Steve/David’s article on Newton’s Lemma. So stay tuned for that. After that I plan to, once-a-month, feature a different Mathis article for discussion. I have not decided specifically how I want to do it yet. But since Miles has ten years plus of papers written I will likely never run out of material to feature. Begin to look for the new features here in early 2013.

  26. #71 by Lee on December 14, 2012 - 11:30 PM

    I think this proves Mathis’s pi = 4
    The cycloid is what a point on a circle traces out relative a flat surface.
    It is motion.
    The arc length S of one arch is given by: since i can’t copy the equation please refer to
    Wikipedia – cycloid -arc lenght

    So this is the transform of the arc length to a radius in an orbit.
    With time inserted the orbit is now in motion relative to an imaginary plane
    With a distance of 2pi = diameter.

    • #72 by Kevin Bos on December 15, 2012 - 9:30 AM

      @Lee #63

      Is this the page you mean?
      http://en.wikipedia.org/wiki/Cycloid#Arc_length

      A cycloid is traced out by a rolling circle, as illustrated by the .gif on the Wikipedia page, however the curve that is traced out is not circular or even a segment of a circle. Therefore the result S = 8r is really quite irrelevant.
      Furthermore, since one of the steps in the derivation of the arc length depends on the value of sin(pi), I’d be interested to know if Mathis considers his redefinition of pi to have any effect on the angular definition (that is, pi = 180 deg). In other words, if pi =4, does sin(pi) still equal zero, and does cos(pi) still equal -1, etc.?
      Lastly, wouldn’t you say that trying to use a mathematical derivation that depends on integral calculus to defend someone who rejects the whole concept kind of counter-intuitive?

      • #73 by Steve/David on December 16, 2012 - 4:40 AM

        @Kevin Bos #66

        You bring up a valid point. The pi=4 theory would require two sets of trig tables: one for static, and one for kinematic.

        Also, how would this new trig table be derived? The radius is constantly changing due to the stair-steps around the circle. How would you ever know when you are on the curve, or off the curve and onto one of the stair-steps?

        Further, when you transition for one stair-step to the next, is that an instantaneous transition? And does it occur at a point? If it is an interval, as Mathis claims, does that interval begin at a point?

        Where is the mathematical formalism for any of this? It’s all cloaked in nebulous phrases of time and motion, without any actual equations. The whole theory contains just one equation: C=8r. That’s all there is; stair-steps, hand-waving and one equation.

    • #74 by Steve/David on December 15, 2012 - 5:21 PM

      That is a fascinating article. Huygens discovered a relationship between the arc length of an arch (S), and the radius of a circle (r):

      S=8r

      It’s the same value Mathis got for the circumference of a circle (C):

      C= 8r

      However, Huygens uses a value of pi=3.14 in his integral to calculate the arc length of the arch.

      If you substitute pi=4 into Huygens integral, the arc length of the arch will change, and will no longer equal 8r.

      The Huygens solution requires a value of pi equal to 3.14. And, his computed arc length is measured in meters.

      On the other hand, the Mathis solution requires stair-steps drawn around a circle. And, the computed circumference has units of m^2/s^3.

      It is an interesting coincidence though, that both solutions yield a value of 8r.

    • #75 by Ken NG on March 20, 2016 - 4:55 AM

      This is right and Mr. Miles Mathis had been added it in his paper. The truth sets us free.

  27. #76 by Lee on December 15, 2012 - 8:18 PM

    Kevin—Yes that is the page.

    Please keep in mind this equation transforms the circumference from
    flat geometry to motion.

    Interesting note: Galileo thought the fastest path
    of decent due to gravity was the arc of a circle.
    It was recognized in his time the cord did not give the least time of decent.

    Ironic — the brachistochrone curve is the actual least time. This was solved by Newton as a challenge. So he developed the transform but didn’t connect the dots!
    Had he, the name Einstein is not what it is today in physics.
    The brachistochrone curve is an inverted cycloid

    • #77 by Kevin Bos on December 16, 2012 - 8:44 AM

      “Please keep in mind this equation transforms the circumference from flat geometry to motion”: Okay, but it’s still not circular and therefore can’t be compared to Mathis’ result which was strictly for the case of a circle. Unless Mathis feels fit to expand his proof for all curves, that is.

      • #78 by tharkun on December 18, 2012 - 2:04 PM

        See here where Mathis shows that his conclusion of pi = 4 in circular motion is equivalent to Hilbert’s Manhattan Metric.

        http://milesmathis.com/manh.pdf

        Let’s see if the naysayers care to argue about their beloved Hilbert!

        Note also that Miles expands his construction to any curve such that final path length (kinematic, not static!) is the sum of the orthogonal vectors.

  28. #79 by Lee on December 17, 2012 - 2:00 PM

    Kevin,
    Mathis is not addressing a point on a spinning stationary wheel which conforms to 2* pi* R.
    Place the wheel on the ground and the point now traces out a cycloid = 8R. The wheel is now in motion.

    A comment on Mathis.

    One has to read his papers with an open mind. I’ve found he proceeds with precise, concise, and logical progression along with a god given gift for analyzing complex motion and to write in the KISS language which enables me to follow along.

    A final comment.

    Science has become arrogant. They have used their time and talent on undermining the foundation of religion (God, creation, the beginning etc.) without checking on their own foundation because of either blind faith or the inability to do the analysis.

    Mathis is doing it for them and much of their foundation is being reduced to rubble.

    Arrogance leads to destruction.

    • #80 by Kevin Bos on December 20, 2012 - 11:40 AM

      Tharkun,

      Regardless, something traveling a circular path, which is what Mathis addressed in his pi=4 paper, is not the same as the movement of a point on a circular object, and so it still is irrelevant to compare the two.

  29. #81 by Steve David Urich on December 19, 2012 - 12:48 AM

    @tharkun,

    “Again, the proof that the tangent and chord don’t approach equality is in my paper titled “A Disproof of Newton’s Fundamental Lemmae”. You have to go there to get the proof, since I can’t include everything I know in every paper I write.” – Miles Mathis (The Manhattan Metric)

    Proof? Misreading Newton’s Lemma and confusing one with another, hardly qualifies as a formal proof.

    Bringing Newton’s Lemma into the pi=4 theory was guaranteed to bite you in ass; big mistake. There is no way to hand-wave your way out of this.

    The following paper gives a full and thorough rebuttal to the notion that pi’s value of 4, and Newton’s Lemma are somehow related:

    “Newton’s Lemma”

    (This post edited by Sleestack VII to create the link that appears in this post. No actual content was changed.)

    • #82 by tharkun on December 19, 2012 - 11:23 AM

      What a bogus ‘rebuttal’! The author doesn’t ‘understand’ Mathis’ proposition by his own admission and that somehow disproves Mathis’ assertion?!? You’ll have to do better than that.

      Newton’s own diagrams in Lemma 6 and 8 are identical so there is no confusion on what is being referred to. Mathis simply redraws Newton’s own diagram in his paper. How is that confusing?

      Given that the lemmas build upon each other to make Newton’s case, how is it somehow a disproof of Mathis’ theory that appeals to each as well (he also mentions lemma VII)? If Mathis had only referenced one lemma, we would be hearing complaints of how Miles ignored the later devopement in subsequent lemma!

      And not a single ‘rebuttal’ has touched on the crux of Mathis argument: you cannot assume that geometry and kinematics are equivalent! One ignores time, the other does not! While the tangent, the arc and the chord may go to equality at the limit per Newton, that limit CANNOT apply to any real world stuation or measurement. Not DOES NOT, CANNOT! If you have motion, you necessarily have time; you cannot measure velocity at a point, you must have an interval. That being so, the chord will ALWAYS be shorter than arc. You cannot have have a zero or negative time interval and claim to be doing real physics.

      Newton’s method is strictly geometric (though he wants to apply it to kinematics). The problem is that he left kinematics behind when he went to the limt and this compromised the derivation as Mathis shows.

      It is no good appealing to a GEOMETRIC construction of the circle (or any curve) and thereby claim that because we can construct a circle with only the hypoteneuses of the inscribed polygons, that those hypoteneuses have anything to do with the actual motions in the real field of motion. Real circular motion is composed of real vectors and there is no vector along the hypoteneuse in circular motion.

      Even if you want to create a vector along the hypoteneuse, you then have to add additional vectors to explain how the hypoteneuse continually changes its angle to result in the final orbit. At this point, you are deep into kinematics and have left the road of geometry altogether. You can’t create kinematic vectors to create your orbit and then do a bait and switch at then end and claim that it’s only geometry and therefore pi always equal 3.141….

      • #83 by Steve David Urich on December 19, 2012 - 3:36 PM

        @tharkun,

        To disprove the first 8 Lemma, you must go through each one individually, and demonstrate where and why it fails. Disproof by fiat or decree is unacceptable science. The majority of the first 8 Lemma are never mentioned at all in the Mathis article. The reader has no idea why the first 5 Lemma, for instance, are invalid. Mathis just claims they have been disproved without any explanation whatsoever.

        Further, the rebuttal gives a demonstration of the validity of Lemma 6, proving that it is true: the angle between the chord and the tangent does in fact diminish as point B approaches point A, exactly as Newton claimed.

        To disprove Lemma 6, Mathis would have to show that the angle between the chord and tangent doesn’t diminish as point B approach’s point A; he never does this, nor could he since it isn’t true.

        Also, Mathis refers to triangles and line RBD when discussing Lemma 6. These only apply to Lemma 8, and are entirely irrelevant to Lemma 6. Mathis has confused one Lemma with another.

        And finally, Mathis never labels his angles so the reader can tell which angle is which. For instance, which angle is ABD, and which angle is BAD? No one knows this for sure, except Mathis. That is his oversight, not mine.

        All in all, the Mathis article was an underhanded attempt to drag Newton’s Lemma into the pi=4 fiasco. The two are unrelated and have nothing to do with one another.

  30. #84 by tharkun on December 20, 2012 - 3:30 PM

    “The reader has no idea why the first 5 Lemma, for instance, are invalid. Mathis just claims they have been disproved without any explanation whatsoever.”

    Please provide a citation for this statement. I have read Miles’ paper many times and have never seen where he states this.

    “To disprove Lemma 6, Mathis would have to show that the angle between the chord and tangent doesn’t diminish as point B approach’s point A; he never does this, nor could he since it isn’t true.”

    This is a false understanding of Miles’ argument. Of course he’s not going to argue that the angle between the chord and tangent doesn’t diminish. His own analysis SHOWS the angle diminishing. What he points out rather is that the angle BAD (between the chord and tangent) is the WRONG angle to monitor as the point B goes toward point A at the limit. The angle he says must be monitored is ABD. ABD must go to 90° before BAD goes to 0 at the limit. First because in any real motion analysis (and that’s what Newton’s aim is) you cannot go past 90° for BAD because that means you are in a zero or negative time interval. You cannot postulate a zero or negative interval and claim to be studying motion that is dependent on positive time intervals. Second, BAD cannot go to zero because angle ADB would have to be 90° as well. But you can’t have two angles of 90° and still have a triangle.

    Since the limit of ABD is 90° and cannot go past 90°, the tangent and the chord are not equal at the limit; the tangent is always longer than the chord.

    “Also, Mathis refers to triangles and line RBD when discussing Lemma 6. These only apply to Lemma 8, and are entirely irrelevant to Lemma 6. Mathis has confused one Lemma with another.”
    As I pointed out last time, both Lemma 6 & 8 use the same diagram provided by Newton so if there is irrelevant information in the diagram, it is provided by Newton and not Miles. However, as Mathis clearly states in his paper, he refers to line RBD only to help readers who have been confused on visualizing the motion of B towards A. Quote:

    “I have added this paragraph after talks with many readers, who cannot visualize the manipulation here. It is very simple: you must slide the entire line RBD toward A, keeping it straight always. This was the visualization of Newton, and I have not changed it here. I am not changing his physical postulates, I am analyzing his geometry with greater rigor than even he achieved.”

    Note that he is PRESERVING Newton’s own visualization, so your objection does not stand up to scrutiny.

    “And finally, Mathis never labels his angles so the reader can tell which angle is which. For instance, which angle is ABD, and which angle is BAD? No one knows this for sure, except Mathis. That is his oversight, not mine.”

    And this too is false; he provides a labeled diagram within the third paragraph as can clearly be seen. So it seems the oversight is yours and not Miles.

    “All in all, the Mathis article was an underhanded attempt to drag Newton’s Lemma into the pi=4 fiasco. The two are unrelated and have nothing to do with one another.”

    This statement seems to clearly show that you have neither read nor comprehended Miles argument at all. Given that several of your objectives above (including this one) are demonstrably false by even a cursory reading of Miles’ paper, it makes me wonder if you have actually read the paper or are you just reading a critique of the paper?

    • #85 by Steve David Urich on December 20, 2012 - 10:32 PM

      1) The following quote is posted on the main page of the Mathis web site (milesmathis.com):

      “Newton’s first 8 lemma from the Principia are shown to be false.”

      According to Mathis, the first 8 Lemma are false. Or more accurately, shown to be false.

      2) When reading Newton’s version of Lemma 6, you won’t find any mention of the following:

      – time
      – triangles
      – negative time intervals
      – line RBD
      – angle ABD
      – right angles
      – acute angles
      – and so on…

      This has all been added by Mathis. The man suffers from an overactive imagination.

      • #86 by tharkun on December 21, 2012 - 12:09 PM

        Ok, so he says, the first 8 lemma are false. If you’ve understood and read his papers on the calculus, he shows that it is flawed from the beginning. You don’t need to go to ‘zero’ for that calculus to work, you only need to go the constant subinterval. Your ‘citation’ doesn’t actually come from a paper, so it’s hardly worthy of being called a ‘citation’.

        Reagarding Miles’ “addition” of things – I suppose he went back in time added this diagram to Leema VI in Newton’s Principia?

        http://archive.org/stream/newtonspmathema00newtrich#page/n101/mode/2up

        Triangles, line RBD, angle ADB, right angles, acute angles are all clearly drawn in Newton’s own diagram. The time intervals are IMPLIED logically becasue Newton is attempting use his geometric analysis to investigate a kinematic event. Time is axiomatic when analyzing REAL motions. He doesn’t have to say “I’m using time here”. It’s a pre-requisite for analyzing real motion.

        There is nothing substantive to your criticisms at all.

      • #87 by Steve David Urich on December 22, 2012 - 7:04 PM

        @tharkun

        Lemma 6 is a geometry problem. There aren’t any forces acting upon point B, moving it along the arc in a specified time interval. And even if there were, the angle between the chord and the tangent would still diminish.

        Also, Lemma 6 is not an analysis of triangles; that’s Lemma 8. Mathis has combined the two Lemma (6 and 8) into a confused, incoherent mess. Line RBD only applies to Lemma 8; it’s never mentioned in Lemma 6.

        Funniest of all, Mathis claims that point B can never reach point A. No joke! There must be an invisible force field (hey, maybe it’s the charge field) preventing point B from reaching point A.

        Mathis should spend more time reading Newton, and less time churning out these silly, error-ridden articles.

  31. #88 by Steve David Urich on January 6, 2013 - 2:44 PM

    @tharkun,

    “Your citation doesn’t actually come from a paper, so it’s hardly worthy of being called a citation.” – tharkun

    Okay. I don’t agree with you, but let’s assume for the sake of argument that a citation must come directly from a paper in order to qualify as a worthy citation. Then the following quote most certainly meets that criteria:

    “The second paper proves that Newton’s first eight lemmae or assumptions in the Principia are all false.” – Miles Mathis (The Extinction of Pi)

    Mathis claims to have proved that the first 8 Lemma are all false; not just one, but all eight.

    As my rebuttal shows, Mathis never disproved any of the first 8 Lemma. He merely misread Lemma 6, and then leapt to the preposterous and unsubstantiated claim that he had disproved 8 of Newton’s Lemma. It’s an outlandish claim that doesn’t hold up to even a cursory inspection; but it does clearly demonstrate the caliber of science that Mathis routinely practices.

    The rebuttal can be found at the following web site:

    Newton’s Lemma

    • #89 by tharkun on February 19, 2013 - 4:54 PM

      So I finally got around to analyzing your supposed ‘rebuttal’, and, as I expected, it is as vapid as your claims here have been.

      On a first glance, I wondered why, if Mathis is so wrong about Newton’s analysis, that you found it necessary to create (or borrow) your own drawings to insert into your ‘rebuttal’. After all, the Principia is widely available online and I myself have linked to it in these discussions.

      But then I realized that, Newton’s own drawings (that Mathis copied) actual refute some of your statements. ‘Right angles’ and angle ‘RBD’ are clearly seen in Newton’s own drawing (though you would have the reader belive otherwise), and anyone who can read can follow Mathis analysis. Yours is an intentional misrepresentation of the diagrams in order to manufacture evidence for your ‘rebuttal’.

      I don’t mind discussing with an honest critic; but seeing that you are demonstrably not honest….well….enjoy the Kool-Aid.

      • #90 by Steve David Urich on March 1, 2013 - 1:22 PM

        ”Newton’s own drawings (that Mathis copied)…” — tharkun

        Let’s set the record straight. Mathis created his own diagram too; it’s not an exact copy of Newton’s.

        The key point is that my diagram accurately depicts Lemma 6, and Lemma 6 only. Whereas, Mathis’ diagram doesn’t accurately depict any of Newton’s Lemma; it contains too much information for Lemma 6, yet not enough for Lemma 8 – which is the root of his confusion.

  32. #91 by Steve David Urich on February 18, 2013 - 4:32 PM

    “Yes, I am planning to do more with this blog in the near future. First off I will be publishing a counter-critique of Steve/David’s article on Newton’s Lemma. So stay tuned for that. After that I plan to, once-a-month, feature a different Mathis article for discussion.” – Sleestack VII (December 13, 2012)

    What has happened here, have you closed up shop? There hasn’t been any activity for two months now. I’m still waiting for the counter-critique to Newton’s Lemma, as promised. Also, when are you going to implement the once-a-month Mathis article for ridicule… oops, make that discussion?

  33. #92 by Lee on February 22, 2013 - 5:01 PM

    Mathis and the Manhattan metric.

    Take a ball and roll it on the floor a distance of D feet. With no losses due to friction nor air resistance the ball rolls past D without any loss in velocity.

    Construct a staircase that connects between floors D feet apart. The staircase is pitched at 45 degrees. Take the ball and give it the same velocity as on the floor again no friction nor air resistance and the ball possess no bounce. Roll the ball down the stairs. To confirm Mathis the ball velocity at the bottom of the staircase is the same as at the top and equal to the velocity of the ball rolling on the floor.

    Next lay a plank down the steps the length of the staircase. Roll the same ball with the same velocity down the plank To refute Mathis the ball must roll with the same velocity at the bottom as it had on top.

    As I see it Mathis is correct, The Manhattan metric imparts no acceleration to the ball and halfway down the stairs the ball has traveled a distance D, which equates to his assertion that the radius, tangent, and distance traveled are equal at 1/8 of a circle. One can imagine four such staircases with gravity at center, the ball is then in perpetual motion or in ORBIT.

    The slanted plank or the slanted vector is acceleration as he points out.

    • #93 by Kevin Bos on February 25, 2013 - 2:29 AM

      I’m sure that somebody else might think of much better ways of refuting that ridiculous analogy, but I’ll start by simply pointing out that you haven’t even shown the minimal amount of rigor required of high school physics students, in that if you’d taken the trouble to draw a free-body diagram, or maybe even just think for a second, you’d have realized that the situations can’t even be compared.

      In the staircase example, each step provides a normal force that arrests the downward velocity to which the ball has been accelerated by gravity after rolling beyond the edge of the previous step. The reason that the ball will have a greater speed at the bottom of the staircase after having rolled down a plank than after a series of drops is that the normal force provided by the plank is not directly opposite the acceleration of gravity.
      So in the case of an orbit, what is providing the normal force (or its analogue)? An orbiting body is subject only to the force of gravity, whereas the example you gave has the body subject to gravity as well as to a normal force. The differences you note between the two cases of the stairs vs. the plank arise entirely from the differences in the direction of the normal force, which I’ve just pointed out does not even exist in the situation you’re trying to analogize.

      Furthermore, you suggest that we imagine 4 staircases formed around some center point towards which gravity is pointing. It seems you haven’t actually thought that through yourself. An object traveling counter-clockwise around the edge of such a pixelated circle executes a series of alternating left and right 90-degree turns. At four equally-separated points on the edge, though, the object will have to make two consecutive left turns, before returning to the alternating left-right-left-right sequence. Draw it and see for yourself. Given the system that you suggest, as the ball approaches one of these “left-left” points, gravity will actually be acting more and more opposite to the motion of the ball, whereas in the single staircase analogy, gravity is always acting perpendicular to the steps. In fact, there are only two ways that your “four staircases glued together” analogy works: A) if gravity points in one of four perpendicular directions depending on which quarter of the “circle” that the ball is traveling, or B) if the steps are rounded such that gravity always acts normal (inward) to their surface. Option A is ridiculous, because no such conspicuously discontinuous gravitational field is possible, let alone observed, and option B goes against your claim that the object can only move in 90-degree zig-zag motions.
      Lastly, you’ve done nothing to address the corresponding extension of your analogy as it applies to the continuous surface. Imagine a continuous surface (our plank), but curved around the gravitational well. As I’ve stated before, no such surface should be (and indeed it isn’t) required for our object to maintain orbit around a gravitational well. But, for argument’s sake, let’s say that such a surface is required to provide a normal force. In other words, let’s say that our ball’s tangential velocity is not enough to keep it in orbit, and so the only thing keeping it from plummeting into the center of the gravitational well is the continuous curved surface (or whatever analogue we can conjecture to provide a normal force). In this case, the ball’s motion does follow a proper orbital trajectory around the gravitational well, much unlike your proposed quadruple staircase.
      So, to recap: your analogy fails because it relies on a normal force that does not act on a body undergoing centripetal motion, and even if it did, the “staircase scenario” would still fail terrifically, whereas if the conjectured constraint force is continuously normal to the gravitational well, we see the motion that we’d expect and that is observed in real life.

      I’d like to point out that Mathis’ co-opting of the Manhattan metric fails outright when you consider that the choice of orthogonal axes is completely arbitrary. If you can make the claim that all non-linear motion is a composite of many small 90-degree turns, then you can also make the claim that it is composed of similar small 90-degree turns, but in a Cartesian coordinate system that is rotated, say, 45 degrees from the first. Does Mathis claim that there is one single, universal Cartesian coordinate system, according to which all motion is restricted to the three axes?

      Finally I’d just like to ask any Mathis supporters why they continue to buy into his shtick that the mainstream scientific community is intentionally disingenuous, fraudulent, etc., when he himself seems so steadfastly determined never to admit to an error or make a retraction even in the face of mountains of evidence and logical refutations proving him wrong?

      • #94 by Steve David Urich on February 25, 2013 - 8:04 PM

        I completely agree with your analysis; as usual, it’s dead-on accurate. Rolling a ball down stair-steps has two obvious problems. First, there isn’t any curvature at all. And second, the ball will just bounce out of control.

        Christiaan Huygens attached a string to the ball, and let it swing back and forth like a pendulum; thus, creating motion along the arc. But then he wasn’t trying to determine pi’s value; that had already been accomplished nearly two thousand years earlier by Archimedes.

        And by the way, Huygens experiments were all “kinematic”. Maybe the conspiracy to conceal pi’s real value of four was originally hatched by Huygens back in the 1600’s? Yeah, that’s the ticket.

      • #95 by Kevin Bos on February 25, 2013 - 9:04 PM

        @ Steve David Urich,

        Well, to be fair, he did specify that the ball, and presumably the steps, had no bounce to them (unrealistic, of course, but let’s take it at face value), and we might as well do him the favor of making the assumption that the ball will always land on a flat part of each step, and not on the corner where it will be liable to be deflected at some unusual angle. The point is that the analogy fails completely even after making all of these concessions.

      • #96 by Kevin Bos on February 25, 2013 - 9:12 PM

        By the way, I’ve recently made a contribution to Michael Norris’ “Mathis-watch” in the comments section of his Amazon.com review of Mathis’ book. Please feel encouraged to check it out.

  34. #97 by tharkun on February 26, 2013 - 3:33 PM

    While I agree with the above analysis that the ‘staircase’ analogy fails, that in no way disproves Mathis argument on the Manhattan metric and its application to orbital motion. Mathis’ argument is not built upon gravitational forces and normal forces, so the entire argument amounts to an extended strawman. You’ve knocked down something that someone else built up, not Mathis.

    The statement that Miles claims that all non-linear motion is a composition of many 90-degree turns is out right false. No citation was given for support of such a statement, nor can there be one for his argument is not based on such. Yes, the Manhattan metric and Miles’ own analysis of ‘pi’ in kinematic situations can be DRAWN as such 90 degree turns. But Miles’ argument clearly spells out that the ‘stair step’ picture is the RESULT of decomposing both the centripetal acceleration and the tangential velocity into two resultant vectors that determine the overall path length that the orbiter travels. Once again, the critics have willingly or unwillingly failed to comprehend the argument. Therefore the ‘arbitrary axes’ rebuff fails as well.

    Miles argument is entirely based on real motions in time, and in the case of uniform circular motion, two different motions superimposed over the same time interval. You cannot have a velocity or acceleration over a zero time interval; therefore the arc, the chord and the tangent CANNOT be equal at the limit. Any orbiter has two motions: one due to gravity (an acceleration) and one due to the orbiter’s ‘innate motion’ (a velocity). That’s THREE units of time if you’re keeping count. But orbital ‘velocity’ only has one unit of time. Where are the other two? Nowhere according to current theory; they don’t exist! Newton built a kinematic case from a geometric foundation, but failed to recognize the necessary difference between geometry (that can ignore time intervals) and kinematics (which cannot).

    So again, we’re left wanting when it comes to actual arguments against Miles theories; but loaded up with strawman arguments, red herrings and ad hominems.

    • #98 by Kevin Bos on February 26, 2013 - 9:17 PM

      A short note of personal defence:
      If it had been me who had introduced the argument that I refuted, then I would be knocking over a strawman. But I think it’s hardly fair to say that I am doing so when the point I was addressing was brought up by someone other than myself. I was simply responding to their input. Furthermore, I never once said “Mathis’ analogy fails because…”; what I said was that Lee’s analogy fails.

      Anyway, you say that “the Manhattan metric and Miles’ own analysis of ‘pi’ in kinematic situations can be DRAWN as such 90 degree turns. But Miles’ argument clearly spells out that the ‘stair step’ picture is the RESULT of decomposing both the centripetal acceleration and the tangential velocity into two resultant vectors that determine the overall path length that the orbiter travels.” Sounds like somebody skipped a day or two of their high school physics class. Vector addition/decomposition does not work like that: the magnitude of a vector is not equal to the sum of the magnitudes of its components. So even IF the velocity and the acceleration had anything to do with the path length, summing their components as scalar quantities is still wrong.

      I’ll end this reply with a disclaimer: you’re entirely right that I’ve failed to comprehend Mathis’ argument. You will say that it’s because I am misguided, but I believe that it’s because the argument makes absolutely no sense whatsoever and in fact cannot be comprehended by anyone logical. So there’s no need to say that I have failed to understand the argument. No one is denying it. What we disagree on is whether the argument can even be understood at all.

      • #99 by tharkun on March 1, 2013 - 4:28 PM

        Given that you admit to not understanding Miles’ argument (or appear to have even read it closely from what I can tell), it’s difficult to respond. His decomposition is not in contradiction to vector addition that any high school student learns, and he clearly spells it out in his papers. Of course velocities and accelerations have something to do with path lengths! Without a velocity or acceleration you would have no path because you would have no circular motion. It’s hard to believe that I even need to type something so blatantly obvious.

        Summing the scalars in a strictly LINEAR situation would be wrong; but we aren’t in a strictly linear situation, we are in the special situation of curvilinear motion created by the superposition of three different motions over the same time interval. Orbital ‘velocity’ is not a velocity, and orbiters never travel along the hypoteneuse of the geometric construction. There are no vectors along the hypoteneuse, so the hypoteneuse cannot be used to determine the path length.

        The fact that you admit that you cannot understand the argument is only an admission of your own limitations (willing or no) and not evidence that Mathis argument is flawed. To do that you would have to at least be able to repeat his argument as presented (whether you believe it or not). You could at least try to answer what has happened to the other two units of time that magically dissapear from the derivation of orbital ‘velocity’. That might be a start.

      • #100 by Kevin Bos on March 2, 2013 - 1:28 PM

        Well, you’re right that I misspoke when I said that velocity and acceleration have nothing to do with path length. Specifically, integrating over the velocity gives the distance traveled. But that’s not what Mathis is doing. Not even close. From what I can tell, he doesn’t even subscribe to the idea of integral calculus.

        Just as you can’t add units of heat with units of charge, nor units of mass with units of time, Mathis is just going to have to accept that you can’t add units of distance with units of velocity and acceleration, no matter how much “embedded time” you conjure up to make the unit analysis work. The whole concept smacks of “ex post facto” to it’s very core.

        I don’t understand his argument in the same way that I don’t understand the statements “8:00 PM is colored blue”, or “the number 4 is sad”. I could certainly rebuke such statements by pointing out that they make no sense and that the person saying them is describing things by properties that they cannot possibly have, but from my experience arguing with you, that doesn’t seem to work. In other words, don’t read too much into it when I say that I don’t understand Mathis’ arguments.

        Most of Mathis’ ideas, including the whole “embedded time” thing, if true, would merit a lifetime of study, and yet Mathis devotes no more than a paragraph to it in his original pi=4 paper. If he wants to be taken more seriously, perhaps he should slow waaaaay down and flesh out his ideas a bit more.

        Lastly, you’re going to have to get used to the fact that not everyone is able to cite Mathis chapter and verse. At this point, all you’re doing is insinuating that anyone familiar enough with Mathis’ papers should agree with him and that the only reason not to is if you’ve not paid close enough attention. Never mind the possibility that someone might actually be very familiar with Mathis’ writings and still disagree with him. More importantly, you don’t even consider that one might not need to read nearly 2500 pages of material to come to an informed conclusion on a single paper. No matter what, you’ll always be able to make the claim that the person disagreeing with you simply isn’t familiar with Mathis’ papers, but it’s obvious to everyone that it’s an evasion argument, so you might as well just come off it.

    • #101 by Steve David Urich on February 26, 2013 - 11:12 PM

      “But Miles’ argument clearly spells out that the ‘stair step’ picture is the RESULT of decomposing both the centripetal acceleration and the tangential velocity into two resultant vectors that determine the overall path length that the orbiter travels.” – tharkun

      If the stair-steps are merely the x and y components, and not the actual path followed, then the circumference cannot be equal to 8r.

      • #102 by tharkun on March 1, 2013 - 4:33 PM

        That would only be true if the stair-step picture were as presented above at a strictly 45 degree angles ot x and y. But Miles’ construction does not do this (as hi paper shows), in which case the sum of the x- and y- components are the path length and C does = 8R.

        The difference bewteen geometric Pi and kinematic Pi is that Geo-pi is based on a limit from the inside that follows the diminishing chord (hypoteneuse). Kine-Pi follows the actual vectors and motions involved that create the orbit. There are no vecotrs along any hypoteneuse, so the Geo-pi is not applicable to any real motion. The tangent and arc are ALWAYS longer than the chord.

    • #103 by Steve David Urich on February 27, 2013 - 2:47 PM

      ”You cannot have a velocity or acceleration over a zero time interval; therefore the arc, the chord and the tangent CANNOT be equal at the limit.” — tharkun

      That is a misinterpretation of Newton’s dynamics. Newton never claimed that there is motion over a zero time interval. He claimed that the chord, arc and tangent will approach equality at the limit; that is, as the time interval diminishes indefinitely but never actually becomes zero.

      ”If when I discuss quantities, in advising about things to be considered vanishing or final; you may understand the quantities are determined with great care, but always to be thought of as diminishing without limit; in the sense that they are finite and getting smaller, and keep on doing so.” — Isaac Newton (Book 1, Section 1, Scholium)

      • #104 by tharkun on March 1, 2013 - 4:15 PM

        Approaching a limit and hitting a limit are two different things. The only way the tangent, chord and arc are equivalent is AT the limit. Which is ZERO, which means you have no time or space intervals on which to have a velocity or acceleration. Which means there is no such thig as an instantaneous velocity or acceleration. In any real motion, the tangent, arc and chord are never equivalent.

      • #105 by Steve David Urich on March 2, 2013 - 3:51 PM

        @tharkun,

        ”The only way the tangent, chord and arc are equivalent is AT the limit.” — tharkun

        Not only have you misinterpreted Newton, but now you are also contradicting Mathis:

        “The tangent can never equal the chord, not when approaching the limit and not when at the limit.” — Miles Mathis (A Disproof of Newton’s Fundamental Lemmae)

        The correct interpretation, of course, is the one given by Newton himself in the first Lemma at the very beginning of his book. Pay close attention to the key words ‘finite’, ‘before’, and ‘approach’:

        ”Quantities, and so the ratios of quantities, which tend steadily in some finite time to equality, and before the end of that time approach more closely than to any given differences, finally become equal.” — Isaac Newton (Book 1, Section 1, Lemma 1)

        In other words, the final values of the chord, arc and tangent, just before vanishing, is that of equality. If you allow the values to shrink all the way to zero (hitting zero, using your parlance), then the chord will disappear entirely and can no longer exist; not even as a point on the curve. The chord, by its very definition, requires a finite distance:

        Chord = a straight line connecting two points on a curve.

        Also, when evaluating limits it is the ‘approach’ that is taken into consideration; not the “hitting” of a limit. That is why an arrow is used, instead of an equal sign.

        And finally, you have also misinterpreted instantaneous velocity. It does not mean the velocity over a zero time interval. It means as the time interval diminishes indefinitely.

  35. #106 by Syfek on April 16, 2013 - 6:32 AM

    Where is Sleestack’s rebuttal of Ulrich’s disproof of Mathis’ disproof of Newton’s Lemma ?

  36. #107 by tom arnall on July 15, 2013 - 7:01 PM

    i don’t get it. if you wrap a string around a bottle and mark where the end of the string which rests on the bottle touches the string after the wrap, you have marked a piece of string which is much closer in length to 3.14 than to 4.0. what am i missing?

    • #108 by Sleestack VII on July 16, 2013 - 6:53 AM

      Tom, if you read the Mathis paper on pi its specifically addresses your question.
      http://milesmathis.com/pi2.html

    • #109 by Kevin Bos on July 16, 2013 - 9:01 AM

      Don’t worry, you aren’t missing a thing. The circumference is always pi*diameter, regardless of “embedded time” or whether it’s a measurement of a static or kinematic path, or whatever other sophistry Mathis can come up with.

      • #110 by Steve David Urich on July 16, 2013 - 10:25 PM

        Mathis has told us that circular motion has embedded time. But what about an ellipse? The planets are moving in elliptical orbits. Hey, what happened to their embedded time? His article “Explaining the Ellipse”, doesn’t even mention it. Apparently it’s only required when computing the value of pi. For all other curves, embedded time can just be ignored. Yeah, uh huh; makes perfect sense.

      • #111 by tharkun on July 18, 2013 - 3:32 PM

        Do you actually read his papers, or just keep assuming what you want to believe about them? You’re comparing apples and oranges. He doesn’t mention it in his ellipse paper because it has nothing to do with the critique. He’s not calculating a path length in the ellipse paper; he’s showing that the mainstream gravity-only theory cannot explain the resulting orbital ellipses. You can’t create an ellipse with only one field; you must have two fields in vector opposition. But if you’d actually read the papers you would know that. Since you implied that you have, you’re either willingly ignorant or deliberately dishonest.

      • #112 by tharkun on July 17, 2013 - 2:02 PM

        Don’t worry about Kevin either, he hasn’t comprehended the argument and doesn’t understand that physics is about mechanics first and that the mechanics determines the math and not the other way around. He seems to think a geometric construction is identical to a kinematic one.

  37. #113 by tom arnall on July 15, 2013 - 7:03 PM

    oops! i meant ‘closer in length to 3.14 x the diameter of bottle than to 4.0 x the diameter of bottle’

    • #114 by tharkun on July 16, 2013 - 3:51 PM

      Tom, Miles is strictly talking about kinematics and not a static measurement. The specific velocities that produce the curve have to be examined and not just the abstract geometric equivalent that ignores the forces and time involved to create the final path. The kinematics is driven by three different velocities driven over the same time interval to produce the curve; but when you ‘straighten’ the line out to measure it, you’ve dropped two of those velocities out of the window, and hence lost some of the measurement as well.

      Basically, there are two ways to measure the circumference of a circle statically; we can go to the limit internally by summing the chords, or we can go to the limit externally by summing the ‘x’ & ‘y’ legs. Only one method matches the kinematics involved that produce real circles in real time, the summation to the external limit. But if we do that, pi must equal 4 and not 3.141…. But, again, this only applies to kinematics situations, not geometric ones (like measuring an area or whatever.)

  38. #115 by tom arnall on July 16, 2013 - 10:18 PM

    “It is not a personality contest. The majority has nothing to say about it, since the majority knows nothing about the question at hand.”

    I am astounded when people talk about Mathis’ arrogance. He’s one of the funniest writers I know of, and I enjoy reading his stuff sometimes just for the humor. If you think he is outrageous, read some of Mark Twain’s essays. Or of Poe’s! I suspect it is self-importance and not much else which is wounded by Mathis’ barbs.

    HOWEVER, I regret that he used the term “poor bastard” when he referred to a writer at Wikipedia in his essay on lift (lift.pdf at his site). An impoverished spirit and pitiable, for sure, but “poor bastard” betokens a lack of compassion which is beneath Mathis’ dignity.

  39. #116 by Steve David Urich on July 21, 2013 - 5:43 PM

    Tharkun,

    Alright, let’s examine the facts and then decide who is guilty of being “deliberately dishonest”, as you put it.

    According to Mathis, gravity creates two velocities: “one which pulls the body back; and a velocity which pulls the body down”. And it is this backward velocity that creates the embedded time. That’s where it comes from, and that’s why Mathis invented embedded time. He contends that gravity is pulling down and back. Therefore, the length of the curve is longer than expected: “the curve will have more time embedded in it. Time will add to the distance, and your curve will be appreciably longer than you expect.” And he expresses it mathematically this way: AB – BD + DC. The embedded time comes from the backward velocity vector BD.

    However, when Mathis discusses elliptical motion, not only does he ignore the backward velocity and embedded time, but he tells us that it is impossible for gravity to cause a backward velocity: “there is no possible way to generate a perpendicular force from the center of a spherical or elliptical gravitational field.”

    So, for circular motion, gravity pulls down and back. But for elliptical motion, Mathis claims that it is impossible for gravity to pull down and back; it can only pull downward. It’s a glaring contradiction. Here are the full quotes from his two articles:

    “The centripetal force must pull down and back in order to take any object—either a pencil tip or an orbiting spacecraft—out of its original path and into a circular path. The centripetal force creates two velocities: one which pulls the body back; and a velocity which pulls the body down… In other words, gravity must pull down and back. If it just pulled down, no circle or orbit would be created. Because the spaceship is moving forward, gravity must pull down and back.” — The Extinction of Pi

    “There is no mechanism to impart tangential velocity by a gravitational field. Both Newton and Einstein agreed on this. Einstein’s tensor calculus shows unambiguously that there is no force at a perpendicular to the field, and Einstein stated it in plain words. How could there be? The force field is generated from the center of the field, and there is no possible way to generate a perpendicular force from the center of a spherical or elliptical gravitational field.” — Explaining the Ellipse

    Mathis invented the embedded time concept soley as an explanation for his pi equals 4 theory. It isn’t used anywhere else, and by Mathis’ own admission gravity can’t supply the mechanism that will produce embedded time. So he has two conflicting theories; one for circular motion, and one for elliptical motion. Circular motion has embedded time, and elliptical motion doesn’t. Which means that Mathis has created two contradictory explanations for motion along a curve and its associated embedded time.

    • #117 by tharkun on July 26, 2013 - 4:15 PM

      Seriously?!? You’ve shifted the goalposts and gotten the critique wrong in the same post! We were discussing the value of pi in geometry vs. kinematics in which you incorrectly apply a path length to his analysis of the ellipse – an analysis which is a discussion about the kinematics (forces) that create the ellipse and not the path length any orbiter takes. The ignored embedded time is a problem for the calculated path length and not the forces that create the path.

      So having pointed that out to you, you ignored the fact that you were comparing apples and oranges and now have quote mined his papers looking for a contradiction. And look, you found something! Well, maybe………..actually, no, you didn’t find anything. If you had read the full Extinction of Pi paper, you would know that the statement about gravity pulling back is in his analysis of the standard model’s explanation of the creation of orbits. The orbital ‘velocity’ is always less than the tangential velocity, so gravity must be pulling back against the tangential velocity in order for the gravity-only model to work. But Miles’ model is not a gravity-only model, so he doesn’t have this contradiction in his model.

      Honestly, if you would actually read the papers fully and not stop when you think you’ve proven him wrong, you wouldn’t post critiques that are so easy to disprove. But, either way, I have shown which of us is either willingly ignorant or deliberately dishonest; that I can agree with.

  40. #118 by Steve David Urich on July 27, 2013 - 2:30 PM

    Mathis has more than one theory of gravitation (expansion of matter, and univeral stacked-spins). But neither of those can account for a backward velocity. So where is this backward velocity coming from? To be mechanical, the velocity must have a source. This is the equation that Mathis uses in his pi=4 theory:

    arcAC = AB – BD + DC

    Hence:
    arcAC is the motion along a circular path
    AB is the innate tangential velocity
    BD is the backward velocity due to gravity
    DC is the downward velocity due to gravity

    So the question is, what force is causing this backward velocity BD? Is it gravity? And if so, which theory of gravity (he has more than one)? Without a valid explanation for this backward velocity, his pi=4 theory is baseless.

    • #119 by tharkun on July 30, 2013 - 2:04 PM

      You have once again misunderstood his argument. He is not saying that there is a backwards component to gravity in that analysis. The backwards component is required IF we accept the concept of ‘orbital velocity’ because the ‘orbital velocity’ is ALWAYS less than the tangential velocity component. How does the mainstream explain this? It doesn’t, it ignores it. Because if we use the tangential velocity, pi = 4 by straight logic. All he has done in your statement is break the gravity vector into its Cartesian components in order to match the math to the actual mechanics and vectors that create the final path. He broke up the segments to show how the orbit is built, but both motion occur over the same interval of time, so there is no backwards component to gravity as he has stated many times. Those segments are what it would take to build the motion piece wise.

      • #120 by Steve David Urich on July 31, 2013 - 2:13 PM

        “There is no backwards component to gravity as he has stated many times.” — Tharkun

        Alright, let’s examine the facts. Here are just a few Mathis quotes taken from his Extinction of Pi article:

        “Gravity must pull down and back”

        “Gravity must have some backward component”

        “Gravity tends to diminish the tangential velocity”

        “Gravity tends to pull you back slightly”

        “Gravity is not strictly perpendicular; there is a component of force backward along the line of the tangent”

        “The centripetal force creates two velocities: one which pulls the body back; and a velocity which pulls the body down”

      • #121 by tharkun on July 31, 2013 - 4:43 PM

        Steve, the more you write, the more you prove that you don’t read what people actually write. The backwards component of gravity is a part of the PHONY concept of orbital ‘velocity’, not Miles own theory! He’s doing an analysis of the standard model’s orbital ‘velocity’. What part of this do you not understand? It is the orbital ‘velocity’ that requires a backwards component to gravity because the value of the orbital ‘velocity’ is ALWAYS less than the tangential (true) velocity.

        Yes, he is stating that gravity must pull backwards in different ways (I never said that he didn’t type the words in his analysis as per your quote mining); but he’s saying that because that is the ONLY force that could possibly reduce the tangential velocity’s value to the orbital ‘velocity’ value IF we accept the concept of an orbital ‘velocity’, which Miles clearly does not. This is a CRITIQUE, he is examining orbital ‘velocity’ in view of the mainstream’s mechanics, not his own! The body CANNOT change it’s own tangential (true) velocity (the innate velocity per Newton). That’s the whole point of the analysis. Orbital ‘velocity’ as a concept is a farce; it cannot be what we have been told it is with the mechanics we have been told create it. Gravity cannot work at the tangent but the concept and mechanics of orbital ‘velocity’ demand that it must.

        And again, his breaking of gravity into it’s components is to demonstrate the proper method of calculating the path length in conjunction with the tangential (true) velocity and not demonstrate the actual motion that the body takes. A body doesn’t move per the tangential velocity in one interval and then per the centripetal acceleration in the next interval to create the arc. It does BOTH over the same interval. The component motion against the tangential velocity is only necessary if you deconstruct the actual motion to show how the body would necessarily have to move to create the ultimate path if the component motions took place over DIFFERENT subsequent time intervals. Since the true mechanics create the summed motion over the same interval, there is no backwards component to gravity in reality. Either way, there are NO velocities along the chord in reality, so using the chord to calculate the path length (and therefore concluding pi=3.141.. in any real motion) is false per the actual velocities involved.

  41. #122 by C.Takacs on September 22, 2013 - 5:22 AM

    @Tharkun,
    While I do appreciate what you are doing by trying to explain Mathis’ ideas, I don’t think there is any chance of you convincing someone who isn’t even willing to read the articles and ask questions in good faith. Steve is using some kind of text editor I believe to find key words, which he then jumps upon with “I gotcha!” without even bothering himself to read the context of what he is reacting to. When you make your argument to him, he side steps it, then responds as if you had no argument. I continue to READ Mathis’ papers, I’m hoping as time passes, and people get tired of magic black holes, super silly string, and ‘firewall problems’ ad nausea, that some traction will be possible to move physics back to reality. Until then, I have to just roll my eyes at the latest hype describing an imaginary new particle or quantum event that only exists in a computer simulation of some other universe that isn’t like ours.

    Take care,
    C.Takacs.

    • #123 by tharkun on September 23, 2013 - 1:22 PM

      Thanks, C.

      I don’t actually expect to change Steve’s mind; I post for lurkers and those who are analyzing Miles’ arguments on their own so that they can see that are answers to many of the critiques and alleged ‘contradictions’ in Miles’ ideas. Many people will read a supposed problem and never read the original papers as I have; I just want them to know that the critics by-and-large either have not understood the argument, or have ignored the context in most cases. Most critics cannot even repeat Miles’ theories correctly, so how can they claim to have a valid critique?

      Besides, I’ve ‘dialogued’ with Steve in different guise on forums other than this one, and his tactics at least are consistent – he repeats the same faulty arguments and understanding on other boards as well. And you’re right – he does a quick search through a document looking for a single word or phrase, ignores the context and how Miles uses those words or phrases, compares it to mainstream theory and thinks he has proven Miles wrong. I even caught him posting a phony diagram of his own making (or copying, I don’t know which), using it as if it was Miles’ diagram and then claiming that Miles’ diagram and explanation didn’t match! Last I checked it was still on his blog even after I pointed it out to him. Sad to be so desperate to prove somebody wrong that you resort to flat out lying on your own blog. I’m all for genuine criticisms, but I’ve seen little of that from Steve.

  42. #124 by Ken NG on March 20, 2016 - 5:47 AM

    It is obvious that pi = 4 is right now after reading these comments above,

    Great for cycloid proof, manhattan matrix, and also Mathis added “Proof from NASA that π is 4.” real world experimental result. This one is so obviously it is a proof.

    The truth (pi = 4 in kinematic situation) sets us free.

  43. #125 by AA “Proper Gander” Morris on September 14, 2016 - 2:06 AM

    “Mathis is only referring to orbital mechanics. So again this seems to be added in as a red herring to muddle the issue.”

    pi = 4 only for orbits? This is absurd. So when I draw or move around a circle pi is 3 but if I measure a Euclidean circle pi is somehow 3.14…..

    this is obvious nonsense.

    • #126 by tharkun on October 6, 2016 - 1:46 PM

      Geometry and Kinematics are not equivalent physically or mathematically. Pi = 3.14.. only in geometry, not in kinematics where time a consideration. You can’t claim to be doing physics, which necessarily involves intervals of time, and then apply a geometric solution completely ignoring time.

      See this video here for experimental proof:

      • #127 by Sleestack VII on October 7, 2016 - 3:54 AM

        Thanks tharkun for linking this incredible video! We all owe Steven Oostdijk some kudos for spending the time and effort in creating the experiment and video. I hope it is becoming increasingly clear that Pi=4 when time is considered just like Mathis has been writing about for years.

  44. #128 by AA “Proper Gander” Morris on September 14, 2016 - 2:11 AM

    “Tom, Miles is strictly talking about kinematics and not a static measurement. The specific velocities that produce the curve have to be examined and not just the abstract geometric equivalent that ignores the forces and time involved to create the final path. The kinematics is driven by three different velocities driven over the same time interval to produce the curve; but when you ‘straighten’ the line out to measure it, you’ve dropped two of those velocities out of the window, and hence lost some of the measurement as well.

    Basically, there are two ways to measure the circumference of a circle statically; we can go to the limit internally by summing the chords, or we can go to the limit externally by summing the ‘x’ & ‘y’ legs. Only one method matches the kinematics involved that produce real circles in real time, the summation to the external limit. But if we do that, pi must equal 4 and not 3.141…. But, again, this only applies to kinematics situations, not geometric ones (like measuring an area or whatever.)”

    Nonsense. This makes no sense. If pi is 4 when I draw or run around a circle, how then can I measure the geometric circle pi as being 3.14…. ? The track itself has pi at 3.14… but if you move around it the same circle’s circumference is now longer. This is absurd. Changing a circle into pile art is not a good way to measure its circumference. This is just Bait and switch brain teasing silliness.

    http://designinstruct.com/print-design/vectors-vs-bitmaps-printing/

  45. #129 by Alex on September 26, 2016 - 4:57 AM

    I find it interesting, seeing the same names and the same comments popping up everywhere anyone’s discussing this guy. Mathis, I mean.

    And I ask myself, “Why?”

    Why would anyone go to so much trouble, invest so much time, to “debunk” that which they claim is so patently absurd even a child could understand its error? If an idea is so ludicrous that it cannot be seriously countenanced for even a moment, then why would it need to be “debunked” at all? And why would it require a concerted effort by a consistent group of individuals, all following one another from site to site, blog to blog, repeating the same things over and over again? And why would the personality, character or habits of the proponent of said “bunk” theory have anything whatsoever to do with the theory itself? Is the theory “bunk” or not?

    If it is, then any discussion of the character, etc. of the proponent appears superfluous at the least, when not outright malicious and, hence, disingenuous. And if it isn’t, then the personal attacks appear as little more than misplaced anger which adds little or nothing to whatever substance the “debunking” may have.

    Putting aside the details of the story so far, when I look at the *process* it appears senseless if viewed as some kind of natural, organic outcome. To explain:

    Assume Mathis is a total nut/whacko/con-man/whathaveyou…

    1. Nutjob with tiny, tiny audience writes something nutty.
    2. Some people agree with nutjob, some don’t.
    3. Small group of people who disagree create numerous web pages devoted solely to promoting their contention that Nutjob is a Nutjob.
    4. The same people also, while maintaining these sites/blogs, visit every other site they can find that mentions Nutjob, and repeat their assertions ad infinitum.

    Personally it’s 3 and 4 that I have trouble with, in the above scenario. That human beings will disagree with one another isn’t in dispute. That humans will campaign against one another isn’t either. But to me 3 and 4 are misplaced. They’re the equivalent of t.v. ads attacking Gary Johnson, Libertarian candidate for President.

    Why don’t you see such ads? Because Gary’s a fucking nobody as far as politics go. He’s going nowhere. No one feels threatened by Gary in the least, so no effort needs to be expended to “combat” him.

    Yet Mathis, who according to his detractors is at least as un-important as Gary is to the two-party establishment, and is just as much of a threat to his sphere as Gary is to the political reality, must be combatted and “debunked” wherever his name is spoken. You know. For the children, or something.

    If we postulate that Mathis may be *correct* then we are presented with a very different interpretation of the story.

    1. Person with tiny, tiny audience writes something true.
    2. Some people agree, some don’t.
    3. A small group of people engages in a concerted campaign to smear said Person, creating web-sites for the sole purpose of doing so, and spreading their message everywhere said Person and their truth are discussed, said message largely being composed of personal attacks against the Person which have nothing whatsoever to do with the theory proposed.

    So which is it, fellas? Are you a group of shining white knights, defenders of the realm, upholders of truth and virtue who spend so much time, so much effort, and not a little money making all those sites, all so you can save the future’s children from the evil and pernicious theory of P = 4 Kinematically? All because you just can’t stand to see “bad science” taught, even if it’s being “taught” by a virtual no-one with an audience you could fit in a matchbox?

    How noble.

    Forgive me for feeling that the second scenario seems more likely.

    • #130 by tharkun on October 6, 2016 - 1:49 PM

      Alex, you hit the nail on the head. If Miles’ ideas were so inconsequential, there would be no need to for the other side to so actively pursue and harass his followers. The moment they get personal, you know they don’t have a real argument, and either haven’t understood Miles’ arguments, or have understood them and can’t afford to adjust their reality.

      Miles has documented several times that mainstream websites were altered immediately after the publication of one of his papers. Now why would that be?

  46. #131 by Noah on September 28, 2016 - 6:42 PM

    This all appears to be a circular argument.

  47. #132 by Belinda Bauer on January 25, 2017 - 12:04 AM

    Is Mathis right? Go to YouTube and search for “For circular motion does pi=4?”. This experiment proves he is right. No one has debunked the experiment so far, and I don’t see how it can be. The long blond hair guy that the youtube algorithm always puts next claims it is friction, but gives no justification. And it’s easy to prove friction is neglible in the experiment (figure it out, it’s easy).
    Therefore the emphasis needs to be why he is right, not if he is right.

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