Category Archives: Bad Geometry

Silly φ and π crackpottery

Over time, I’ve come to really, really hate the number φ.

φ is the so-called golden ratio. It’s the number that is a solution for the equation (a+b)/a = (a/b). The reason that that’s interesting at all is because it’s got an interesting property when you draw it out: if you take a rectangle where the ratio of the length of the sides is 1:φ, then if you remove the largest possible square from it, you’ll get another rectangle whose sides have the ratio φ:1. If you take the largest square from that, you’ll get a rectangle whose sides have the ratio 1:φ. And so on.

The numeric value of it is (1+sqrt(5))/2, or about 1.618033988749895.

The problem with φ is that people are convinced that it’s some kind of incredibly profound thing, and find it all over the place. The problem is, virtually all of the places where people claim to find it are total rubbish. A number that’s just a tiny bit more that 1 1/2 is really easy to find if you go looking for it, and people go looking for it all over the place.

People claim it’s in all sorts of artwork. You can certainly find a ton of things in paintings whose size ratio is about 1 1/2, and people find it and insist that it was deliberately done to make it φ. People find it in musical scales, the diatonic and pentatonic scales, and the indian scales.

People claim it comes up all over the place in nature: in beehives, ant colonies, flowers, tree sizes, tree-limb positions, size of herds of animals, litters of young, body shapes, face shapes.

People claim it’s key to architecture.

And yet… it seems like if you actually take any of those and actually start to look at it in detail? The φ isn’t there. It’s just a number that’s kinda-sorta in the 1 1/2 range.

One example of that: there’s a common claim that human faces have proportions based on &phi. You can see a bunch of that nonsense here. The thing is, the “evidence” for the claim consists of rectangles drawn around photographs of faces – and if you look closely at those rectangles, what you find is that the placement of the corners isn’t consistent. When you define, say, “the distance between the eyes”, you can measure that as distances between inner-edges, or between pupils, or between outer edges. Most of these claims use outer edges. But where’s the outer edge of an eye? It’s not actually a well-defined point. You can pick a couple of different places in a photo as “the” edge. They’re all close together, so there’s not a huge amount of variation. But if you can fudge the width a little bit, and you can fudge other facial measurements just a little bit, you’ve got enough variation that if you’re looking for two measurements with a ratio close to φ, you’ll always find one.

Most of the φ nonsense is ultimately aesthetic: people claiming that the golden ratio has a fundamental beauty to it. They claim that facial features match it because it’s intrinsically beautiful, and so people whose faces have φ ratios are more beautiful, and that that led to sexual-selection which caused our faces to embody the ratio. I think that’s bunk, but it’s hard to make a mathematical argument against aesthetics.

But then, you get the real crackpots. There are people who think φ has amazing scientific properties. In the words of the crank I’m writing about today, understanding φ (and the “correct” value of π derived from it) will lead humanity to “enter into a veritable Space Age”.

I’m talking about a guy who calls himself “Jain 108”. I’m not quite sure what to call him. Mr. Jain? Mr. 108? Dr 108? Most of the time on his website, he just refers to himself as “Jain” (or sometimes “Jain of Oz”) so I’ll go with “Jain”).

Jain believes that φ is the key to mathematics, science, art, and human enlightenment. He’s a bit hard to pin down, because most of his website is an advertisement for his books and seminars: if you want to know “the truth”, you’ve got to throw Jain some cash. I’m not willing to give money to crackpots, so I’m stuck with just looking at what he’s willing to share for free. (But I do recommend browsing around his site. It’s an impressive combination of newage scammery, pomposity, and cluelessness.)

What you can read for free is more than enough to conclude that he’s a total idiot.

I’m going to focus my mockery on one page: “Is Pi a Lie?”.

On this page, Jain claims to be able to prove that the well-known value of π (3.14159265….) is wrong. In fact, that value is wrong, and the correct value of π is derived from φ! The correct value of π is \frac{4}{\sqrt{\phi}}, or about 3.144605511029693.

For reasons that will be soon explained, traditional Pi is deficient because historically it has awkwardly used logical straight lines to measure illogical curvature. Thus, by using the highest level of mathematics known as Intuitive Maths, the True Value of Pi must be a bit more than anticipated to compensate for the mysterious “Area Under The Curve”. When this is done, the value, currently known as JainPi, = 3.144… can be derived, by knowing the precise Height of the Cheops Pyramid which is based on the Divine Phi Proportion (1.618…). Instead of setting our diameter at 1 unit or 1 square, something magical happens when we set the diameter at the diagonal length of a Double Square = 2.236… which is the Square Root of 5 (meaning 2.236… x 2.236… = 5). This is the critical part of the formula that derives Phi \frac{1+\sqrt{5}}{2}, and was used by ancient vedic seers as their starting point to construct their most important diagram or ‘Yantra’ or power-art called the Sri Yantra. With a Root 5 diameter, the translation of the Phi’s formula into a geometric construct derives the royal Maltese Cross symbol, concluding that Phi is Pi, that Phi generates Pi, and that Pi must be derived with a knowledge of the Harmonics of Phi. When this is understood and utilized, we will collectively enter into a veritable Space Age.

How did we get the wrong value? It’s based on the “fact” that the computation of π is based on the use of “logical” straight lines to measure “illogical” curvurature. (From just that one sentence, we can already conclude that Jain knows nothing about logic, except what he learned from Mr. Spock on Star Trek.) More precisely, according to Jain:

In all due good respects, we must first honour Archimedes of Syracuse 2,225 years ago, who gave the world his system on how to calculate Pi, approximated to 22÷7, by cutting the circle into say 16 slices of a pizza, and measuring the 16 edge lengths of these 16 triangular polygons (fig 3), to get a good estimate for the circumference of a circle. The idea was that if we kept making the slices of pizza smaller and smaller, by subsequently cutting the circle into 32 slices, then 64, then 128 then 256 slices, we would get a better and more accurate representation for the circumference. The Fundamental Flawed Logic or Error with Archimede’s Increasing Polygon Method was that he failed to measure The Area Under The Curve. In fact, he assumed that The Area Under The Curve, just magically disappeared. Even in his time, Archimedes admitted that his value was a mere estimate!

This explanation does a beautiful job of demonstrating how utterly ignorant Jain is of math. Archimedes may have been the first person from the western tradition to have worked out a mechanism to compute a value for π – and his mechanism was a good one. But it’s far from the only one. But let’s ignore that for a moment. Jain’s supposed critique, if true, would mean that modern calculus doesn’t work. The wedge-based computation of π is a forerunner of the common methods of calculus. In reality, when we compute the value of almost any integral using calculus, our methods are based on the concept of drawing rectangles under the curve, and narrowing those rectangles until they’re infinitely small, at which point the “area under the curve” missed by the rectangles becomes zero. If the wedge computation of π is wrong because it misses are under the curve, then so will every computation using integral calculus.

Gosh, think we would have noticed that by now?

Let’s skip past that for a moment, and come back to the many ways that π comes into reality. π is the ratio of the diameter of a circle to its radius. Because circles are such a basic thing, there are many ways of deriving the value of π that come from its fundamental nature. Many of these have no relation to the wedge-method that Jain attributes to Archimedes.

For example, there is Viete’s product:

\frac{2}{\pi} = \left(\frac{\sqrt{2}}{2}\right)\left(\frac{\sqrt{2 + \sqrt{2}}}{2}\right)\left(\frac{\sqrt{2 + \sqrt{2 + \sqrt{2}}}}{2}\right)(...)

Or there’s the Gregory-Leibniz series:

\frac{\pi}{4} = 1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \frac{1}{9} - ...

These have no relation to the wedge-method – they’re derived from the fundamental nature of π. And all of them produce the same value – and it’s got no connection at all to φ.

As supportive evidence for the incorrectness of π, Jain gives to apocryphal stories about NASA and the moon landings. First, he claims that the first moon landing was off by 20 kilometers, and that the cause of this was an incorrect value of π: that the value of π used in computing trajectories was off by 0.003:

NASA admitted that when the original Mooncraft landing occurred, the targeted spot was missed by about 20km?
What could have been wrong with the Calculations?
NASA subsequently adjusted their traditional mathematical value for Pi (3.141592…) by increasing it in the 3rd decimal by .003!

Let’s take just a moment, and consider that.

It’s a bit difficult to figure out how to address that, because he’s not mentioning what part of the trajectory was messed up. Was it the earth-to-moon transit of the full apollo system? Or was it the orbit-to-ground flight of the lunar lander? Since he doesn’t bother to tell us, we’ll look at both.

π does matter when computing the trajectory of the earth-to-moon trip – because it involves the intersection of two approximate circles – the orbit of the earth around the sun, and the orbit of the moon around the earth. (Both of these are approximations, but they’re quite useful ones; the apollo trajectory computations did rely on a value for π.

Let’s look at earth-to-moon. I’m going to oversimplify ridiculously – but I’m just trying to give us a ballpark order-of-magnitude guess as just how much of a difference Mr. Jain’s supposed error would cause. THe distance from the earth to the moon is about 384,000 kilometers. If we assume that π is a linear factor in the computation, then a difference in the value of pi of around 1 part in 1000 would cause a difference in distance computations of around 384 kilometers. Mr. Jain is alleging that the error only caused a difference of 20 kilometers. He’s off by a factor of 15. We can hand-wave this away, and say that the error that caused the lander to land in the “wrong” place wasn’t in the earth-moon trajectory computation – but we’re still talking about the apollo unit being in the wrong place by hundreds of kilometers – and no one noticing.

What if the problem was in the computation of the trajectory the lander took from the capsule to the surface of the moon? The orbit was a nearly circular one at about 110 kilometers above the lunar surface. How much of an error would the alleged π difference cause? About 0.1 kilometer – that is, about 100 meters. Less than what Jain claims by a factor of 200.

The numbers don’t work. These aren’t precise calculations by any stretch, but they’re ballpark. Without Jain providing more information about the alleged error, they’re the best we can do, and they don’t make sense.

Jain claims that in space work, scientists now use an adjusted value of π to cover the error. This piece I can refute by direct knowledge. My father was a physicist who worked on missiles, satellites, and space probes. (He was part of the Galileo team.) They used good old standard 3.14159 π. In fact, he explained how the value of π actually didn’t need to be that precise. In satellite work, you’re stuck with the measurement problems of reality. In even the highest precision satellite work, they didn’t use more that 4 significant digits of precision, because the manufacturing and measurement of components was only precise to that scale. Beyond that, it was always a matter of measure and adjust. Knowing that π was 3.14159265356979323 was irrelevant in practice, because anything beyond “about 3.1416” was smaller that the errors in measurement.

Mr. Jain’s next claim is far worse.

Also, an ex-Engineer from NASA, “Smokey” admitted (via email) that when he was making metal cylinders for this same Mooncraft, finished parts just did not fit perfectly, so an adjusted value for Pi was also implemented. At the time, he thought nothing about it, but after reading an internet article called The True Value of Pi, by Jain 108, he made contact.

This is very, very simple to refute by direct experience. This morning, I got up, shaved with an electric razor (3 metal rotors), made myself iced coffee using a moka pot (three round parts, tight fitted, with circular-spiral threading). After breakfast, I packed my backpack and got in my car to drive to the train. (4 metal cylinders with 4 precisely-fitted pistons in the engine, running on four wheels with metal rims, precisely fitted to circular tires, and brakes clamping on circular disks.) I drove to the train station, and got on an electric train (around 200 electric motors on the full train, with circular turbines, driving circular wheels).

All those circles. According to Jain, every one of those circles isn’t the size we think it is. And yet they all fit together perfectly. According to Jain, every one of those circular parts is larger that we think it should be. To focus on one thing, every car engine’s pistons – every one of the millions of pistons created every year by companies around the world – requires more metal to produce than we’d expect. And somehow, in all that time, no one has ever noticed. Or if they’ve noticed, every single person who ever noticed it has never mentioned it!

It’s ludicrous.

Jain also claims that the value of e is wrong, and comes up with a cranky new formula for computing it. Of course, the problem with e is the same as the problem wiht π: in Jain’s world, it’s really based on φ.

In Jain’s world, everything is based on φ. And there’s a huge, elaborate conspiracy to keep it secret. Any Jain will share the secret with you, showing you how everything you think you know is wrong. You just need to buy his books ($77 for a hard-copy, or $44 for an ebook.) Or you could pay for him to travel to you and give you a seminar. But he doesn’t list a price for that – you need to send him mail to inquire.

It's MathematicS, not Mathematic

As you may have noticed, the crank behind the “Inverse 19” rubbish in my Loony Toony Tangents post has shown up in the comments. And of course, he’s also peppering me with private mail.

Anyway… I don’t want to belabor his lunacy, but there is one thing that I realized that I didn’t mention in the original post, and which is a common error among cranks. Let me focus on a particular quote. From his original email (with punctuation and spacing corrected; it’s too hard to preserve his idiosyncratic lunacy in HTML), focus on the part that I’ve highlighted in italics:

I feel that with our -1 tangent mathematics, and the -1 tangent configuration, with proper computer language it will be possible to detect even the tiniest leak of nuclear energy from space because this mathematics has two planes. I can show you the -1 configuration, it is a inverse curve

Or from his latest missive:

thus there are two planes in mathematics , one divergent at value 4 and one convergent at value 3 both at -1 tangent(3:4 equalization). So when you see our prime numbers , they are the first in history to be segregated by divergence in one plane , and convergence in the other plane. A circle is the convergence of an open square at 8 points, 4/3 at 8Pi

One of the things that crackpots commonly believe is that all of mathematics is one thing. That there’s one theory of numbers, one geometry, one unified concept of these things that underlies all of mathematics. As he says repeatedly, what makes his math correct where our math is wrong is that there are two planes for his numbers, where there’s one for ours.

The fundamental error in there is the assumption that there is just one math. That all of math is euclidian geometry, or that all of math is real number theory, or that real number theory and euclidian geometry are really one and the same thing.

That’s wrong.

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Loony Toony Tangents

As I’ve mentioned before, one of the pitfalls of writing this blog is that I get a lot of mail from crazy christians. I’m not sure why it’s just the christian crazies that come after me, but that’s the way it is.

Anyway, yesterday, I got a fresh one which is really quite bizarre. I can’t figure out what the heck the dumbass is trying to get at, so I thought I’d share.

It all starts yesterday at 2:30 or so, when I got the following, under the title “To Marcus From a Christian Physician Mathematician”. I put it in a pre-format region, in order to give you the full experience. This is exactly how it appeared in my inbox. I’ve done my best to preserve the exact formatting, so that you get the full sense of looniness.

 Mark ,

 The Lord has helped me and all I need from you is to
help write a manuscript in math language. I have
developed a new mathematics -1 tangent, very hard to
communicate and very difficult , but by a simple
computer program we have placed and sieved all
 prime numbers ( Please examine our site )

. Basically the mathematics creates a tangent over the
 original primordial universe , tangents used are 1/6
and 5/ 6 at Inverse 19  and if you can solve
this simple equation a help from my lord from my
 lord then work with me. No PHDs
 have been able to solve this, and no one has been
 able to understand the
mathematics. My papers were accepted as
assignment by the worlds top Physics
journal , and they said they have a hard time
understanding the tangents, write it better

X- 0.5=(0.5X)/10        ( The lord parted the waters)
What is the rational value of X ( Least whole number ratio)

 You may  write  these papers with us in the grace of
 our Lord Jesus Christ. We
will give you that site if you
acknowledge our Lord Jesus Christ that stilled
the waters.

My first thought was the usual annoyance at being pestered by one of these twits. My second was “perhaps the reason why no one has been able to understand the mathematics is because you’re making absolutely no sense at all. And my third was to be really annoyed, because the moron sent me a request to “look at his site”, without even bothering to give me a URL!

So… I responded. I know that I shouldn’t have, but I can’t resist a good crank. A couple of quick and mostly nonsensical exchanges occured, which just aren’t worth the effort of copying. But one thing that I did say to him was:

If you send me your stuff, I’ll take a look at it. But you should understand that if, as I suspect, it turns out to be nothing but garbage, then I’m going to post it on my blog, with an appropriate amount of mockery of you and your work.

There were a couple of stupid back and forths… including his explaining that the reason that he sent this to me was because I’ve written about christian mathematicians on by blog. From this, I conclude that the guy’s reading comprehension is about as good as his writing, because the only times that I’ve mentioned the religion of anyone (except myself) that I’ve written about, it’s to mock them. (Like, for example, I’ve frequently mocked Dembski’s, and the way that he substitutes christian apologetics for actual math.)

Anyway, the first thing with any actual substance to it in our exchange, was this:

What ever , is fine, my Paper as I say was accepted as assigned by the AIP Journals and it is not accepted for publication because it is sloppy and poorly written in different mathematics. The reason I will only give you the prime number placement and the Computer program because you will not understand -1 tangent or some of the mathematical statements like ” A divisor of Space must be 2* a tangent ( a tangent always has a midline. Divisor 19 is exactly 1:3 (1/6+1/6) . That is it , do you solve or understand X-0.5= (0.5X)/10

Attached is a very tiny snippet slow prime number sieve/placement Program that no one has seen or understood yet but “each prime number is connected to each prime number and is continuous program” so unlike all the yobos prime number sieve out there , this one is different . It does not need a proof . We have done a billion and it is already copywrited to our site . Attached is the source code and the sample prime numbers by gaps and placement. It is my gift to you, and if you understand this then I will show you the rest of the mathematics, and why I can help you and you me .

Dont you dare call it Garbage, because then I can do the same to you , what is garbage is current mathematics understanding of prime numbers etc. I have a Phd education too, so it do not matter, I am a fellow of the royal college of Surgeons . See only the rest at your risk , you will not get it, because it is -1 tangent mathematics. It is copy righted ten times over.


Along with this, he included a PDF file that had Fortran-77 source code superimposed on background images…

Now, I have no idea of just what this twit is trying to get at. But he did at least send me a link to his website. He’s created his own “research institute” called hope research. And it’s an absolute gem of almost time-cube caliber insanity. He’s got a picture of a file of rocks, with a metal plaque on a pole above them, reading:

AT 1 AND MINUS 1(0.999.), IN 2009-2010


OF 1 AND -1. 1=MUN 1(0.999.) AT NATURAL 1/3(1/6 + 1/6)
SPACE 1,-1 AND 0.000166666667 (1/6X1/1000)

Try to make sense out of that, eh?

Looking at his web-page a bit, it’s an amazing jumble of incoherent rubbish. Most of it is just pure incoherence. But, as near as I can figure it out… the nugget, the basic idea at the center of it all, is:

CURRENT MATHEMATICS THEORY is wrong because it is based on a single square plane with a squared center, “a circle can never be squared”, vice versa, by a single mathematical plane, the mistake of Riemann, Euclid, Archimedes, and Einstein.

In somewhat more coherent terms: he believes that our number system is fundamentally defined by a square plane, and that all sorts of errors come from the fact that we always analyze things in terms of a “square space”. He believes that there are actually two overlapping spaces – one square, and one circular.

The “circle can never be squared” bit is really quite interesting, because it’s something that cranks constantly bring up, without ever bothering to understand what it means.

There’s an old traditional of geometry dating back to the ancient Greeks, which looks at things you can do using nothing but a straight-edge and a compass. You can do a lot of interesting things; for example, you can construct a perfect square without needing to measure any lengths or angles. Below is an animation of the process, from wikipedia.

Squaring a circle is a straight-edge and compass problem: if I give you a circle, can you draw a square which has the same area as that circle using nothing but a straight-edge and a compass? And the answer is: No, you can’t. When someone talks about “squaring a circle”, that’s all that they’re talking about: you can’t draw a square and a circle with the same area using nothing but a straight-edge and a compass.

People like our incoherent friend here believe that it means something much, much stronger: that you can never convert between circles and squares; that things that are round, and things that have right angles are completely, fundamentally incompatible. This is utter nonsense.

In fact, given a plane, we can identify points in the plane in two different ways: by picking a line and an arbitrary 0 point, we can then measure its distance from the origin in two directions (the rectangular coordinate), or we can measure its angle and distance from the origin and baseline (the polar or circular coordinate). And we can freely convert back and forth between those two representations.

He doesn’t understand that at all. He believes that the cartesian plane is actually rectangular, and believes he’s made some brilliant discovery by inventing a circular form of a plane. (A plane isn’t rectangular or circular. It’s a plane.)

As far as his prime number stuff goes… I can’t make head or tail out of it. He seems to be using the word “tangent” in a novel way, and I can’t figure out what his definition of the word is. Without that, there’s no hope of rendering his babble into anything meaningful.

But for your entertainment… He claims that he’s got this program which somehow demonstrates his prime discovery. For you, my loyal readers, I have actually copied it out of his PDF file. This appears to some version of BASIC.. it’s amusing; his programming is just as incoherent as his english. I mean, look at it: there’s no way that this program can work. None. Nil. Zero.

I doubt that it’s even valid syntax. I can’t say that for certain, because there are so many different variants of BASIC, and so many of them are so wacky. But even if the syntax, by some miracle, is actually valid in some version of basic, it doesn’t work.

How can I say that? Just look at the program – you don’t need to look very far. Look at the line with line number 10: 10 IF PRIME(X)=0 THEN GOTO 1009. There is no line 1009. There are jumps to line 1014; there is no line 1014. There are statements that jump to line 2002; there is no line 2002.

5 A = A + 1
7 AA=0





1999 AA=AA +1
2000 X=0



2001  GOTO 2003


BB =BB +6
 BA =BA +6





C=C+A              'NUMBER OF LOOPS

                   ' START NEXT LOOP




open "LOOP" for text as #1
  print #1, "NUMBER OF LOOPS "; C
  PRINT #1, "X ";E;" Y ";F

  confirm "DO YOU WISH TO CONTINUE?"; answer$

  if answer$ = "no" then [END]







I wanted to give you folks a version of this that actually ran… to at least see if this was, in any way, shape, or form a prime number generator. I tried to translate it into Python… But I can’t make any kind of sense out of it. Even with all of the obscure and deliberately pathological languages I’ve learned, I can’t make this make sense. For example, BA and [BB] seem to branch targets. But they also seem to somehow be used as variable prefixes. I’m not sure what, if anything, that’s supposed to mean.

If you know the variant of BASIC that this is written for, and you can explain it to me, I’ll be glad to make another stab at rewriting it into a runnable program in Python.

To conclude.. Why should I bother to do this? According to my loony correspondent:

I feel that with our -1 tangent mathematics, and the -1 tangent configuration , with proper computer language it will be possible to detect even the tiniest leak of nuclear energy from space because this mathematics has two planes. I can show you the -1 configuration, it is a inverse curve

I reluctantly give you the raw very primitive site of the mathematics without the calculus , it is not written in modern math language,but we are sure of it the mathematics and the numbers placement. DO NOT ridicule us, and if you can help find a partner to write this mathematics with us , let us know, we will teach you the calculus

Yes, we’ll be able to detect the tiniest leak of nuclear energy using his prime number sieve! (Which, in so far as I can understand it, isn’t even a sieve.) And I’d better not ridicule him. Oops, too late.

Oh, and according to him, π is exactly 22/7.

Grandiose Crackpottery Proves Pi=4

Someone recently sent me a link to a really terrific crank. This guy really takes the cake. Seriously, no joke, this guy is the most grandiose crank that I’ve ever seen, and I doubt that it’s possible to top him. He claims, among other things, to have:

  1. Demonstrated that every mathematician since (and including) Euclid was wrong;
  2. Corrected the problems with relativity;
  3. Turned relativity into a unification theory by proving that magnetism is part of the relativistic gravitational field;
  4. Shown that all of gravitational/orbital dynamics is completely, utterly wrong; and, last but not least:
  5. proved that the one true correct value of pi is exactly 4.

I’m going to focus on the last one – because it’s the simplest illustration of both his own comical insanity, of of the fundamental error underlying all of his rubbish.

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Too Crazy to Be Fun: Pi Crackpottery

I always appreciate it when readers send me links to good crackpottery. But one of the big problems with a lot of the links that I get is that a lot of them are just too crazy. When you’ve got someone going off on a time-cube style rant, there’s just no good way to make fun of them – the stuff just doesn’t make enough sense to make fun of.

For example, someone sent me a really… interesting link recently, to a book by a guy who claims to have proved that pi=3.125. Let me quote the beginning of his book, to give you an idea of what I mean. I’ve attempted to reproduce the formatting as well as I can, but it’s frankly worse that I can figure out how to reproduce with HTML.


One conception of π is the value 3.141… that is used for calculations, involving geometrical figures containing circles.

Another conception is that the number 3.141… is only an approximation. I interpret

π in this book as the relationship between a circle and its diameter, and not as the irrational number 3.141…

I have attempted to find a value that will result in exact calculations of circles.


The word “squaring” is used for the following:

A. The square with side of 4 u.l. so-called square squaring form

B. A circle with the diameter of 4 u.l., the circle squaring form

C. The only cylinder that has been produced by a square and two circles, from which come the cylinder squaring form

I identify the characteristics found in figures that I call square squaring, circle squaring and cylinder squaring and the principles behind these figures. I refer to three figures:

1. Square

2. Circle

3. Cylinder

It’s not particularly easy to make fun of that, because it’s so utterly and bizarrely nonsensical.

It’s pretty hard to get through his drek… But he’s got this way of characterizing different kinds of squares, and then different kinds of circles based on the different kinds of squares. The ways of characterizing the squares are based on screwing up units. There are three kinds of squares: squares where the number of length units in the perimeter are larger than the number of area units in the area; squares where the number of length units in the perimeter are smaller than the number of area units in the area; and squares where they’re equal.

That last group contains only one element: the square who’s sides have length 4. He concludes that this is a profoundly important square, and says that a square whose side-length is four of some unit is the “square squaring form” of the square. This is a really important idea to him: he goes out of his way to write a special note in extra large font:


Squares with sides of 4 u.l. have a perimeter of 16 u.l. and an area of 16 u.a. Perimeter = 16 u.l. and area = 16 u.a. What I immediately observed was the common number for the perimeter and the area.

As you can see, we’re dealing with a real genius here.

From there, he launches into a description of circles. According to him, every circle is defined by a square, where the circle is inscribed in the square. It makes no sense at all; this section, I can’t even attempt to mock. It’s just so damned incoherent that it’s not even funny. The conclusion is that for magical reasons to be explained later, the circle with diameter 4 is special.

Then we get to the heart of the matter: what he calls “the circle squaring form”. This continues to make no sense. But it’s got some interesting typography. It starts with:



the logarithm e

For no apparent reason. Then he goes on to start presenting the notation he’s going to use… And to call it insane is kind. In includes two distinct definitions: “Logarithm e = log e” and “Logarithm ln of e = log ln”. I have no clue what this is supposed to mean.

From there, he goes through a bunch of definitions, leading up to a set of purported equations describing the special circle related to the special square whose sides are 4 units long. What are the equations going to show us?

The formulae will define a circle that shows relation to;

  • Its diameter to its circumference and area.
  • Circles relation to its square.
  • Its relation of the shaded area that is not covered by the
  • Finally, how many per cent a circle cover its square’s
    area and perimeter.
  • Also relations to the cylinder.

So he gets to the equations, which are defined in terms of “ln of logarithm e”. His first equation, presented without explanation, is:

Q = (ln sqrt{(e^{ln s})^2}/ln e^{ln s})^2/2

What in the hell that’s supposed to mean, I don’t know. He doesn’t define Q. s is the length of the side of a square. Where eln s comes from, I have no idea… but he gets rid of it, replacing it with s. Apparently, this is supposed to be a meaningful step – we’re supposed to learn something really important from it! He goes through a bunch of steps, ending up with “Relevant Formula: ⇒ 4Q = ( ln sqrt{s^2 *2}/ln s)^2*2“, which supposedly defines “the relationship between area, circumference, and diameter of a circle”.

I’ll stop here. I think by now you can see my problem. How can you make fun of this in an entertaining way? There’s just nothing that I can say about this stuff beyond “huh? what in the bloody hell is he trying to say here?”

He offers a cash prize to anyone who can prove him wrong. I think he’s pretty safe in not needing to worry about paying that prize out; you can’t prove that something nonsensical is wrong. Yeah, sure, π=3.2 or whatever in his universe: after all, for any statement S, bot Rightarrow S. Hell, 4Q = ( ln sqrt{s^2 *2}/ln s)^2*2, therefore the moon is made of green cheese!

What kills me about this is how utterly, insanely, ridiculously wrong it is… My daughter, who is in fifth grade, did experiments last year in math class where they roll a circle along a piece of paper to get its diameter, and then compare that to its length. A bunch of fourth graders can easily do this accurately enough to show that the ratio of the circumference to the diameter is around 22/7. Any attempt to actually verify his number totally fails. But it would seem that in his world, when reality conflicts with theory, reality is the one that’s wrong.

Euclid? Moron!

A coworker of mine at Google sent me a link this morning to an interesting piece of crackpottery: a guy who calls himself “the Soldier of the Truth” who claims to have proved Euclid’s parallel postulate; and that therefore, all of non-Euclidean geometry, and anything in the realms of math and science that in any way rely on non-Euclidean stuff, is therefore incorrect and must be discarded. This would include, among numerous other things, all of relativity.

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