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.

CONCEPTIONS OF πOne 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.

SQUARINGThe 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:

N.B.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:

ln

of

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

circle.- 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 e^{ln 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.

Well.... he's very distinguished looking.

This guy could be served by a course in basic algebra before anything else. From his expression "Q = (ln sqrt((e^ln(s))^2)/(ln(e^(ln(s))))/2," some simple simplification gives Q = 1/2. Doing the same thing to the later expression gives 4Q=4 or Q=1. Of course he can prove anything. He's got Q=1/2 and Q=1. From contradictory premises, it's trivial to prove anything. Watch:

(pi-good)*(Q-Q)=0

Q=1 and Q=1/2

=> (pi-good)*(1/2)=0

=> pi=good

But sadly, even this is too coherent for him...

Sorry, when I try to repeat your work, I get something different! I get:

(pi-good)*(Q-Q)=0 (So far we agree)

Q=1 and Q=1/2 (No problem)

=> (pi-good)*([1/2]-1) = 0

=> pi=-good !!

I get the

exact opposite!!Any attempt to actually verify his number totally fails.Not if you make your attempt in the fourth phase of a five phase multiverse with Pythagorean shift in the nth dimension!

You just lack imagination Mark!

I have been thinking of sending you that link a long time, but, as you, I believe we can make no fun of it.

I fear and foresee a new age of obscurity where the crackpots not only write nonsense, but write "nonsensely", definitively giving up grammar and syntax.

That will be a sad day (for entertainment).

Good gravy, there's 171 pages of the stuff!

And it's been through 4 published editions? You would think the publisher would have caught his or her mistake after the 3rd edition... (which was to print the book three times in the first place...)

Then again, his HP desktop printer is probably his primary publisher.

Why do bad books get published? The same reason bad anything gets produced. It's a dimple formula:

$profit > $revenue - $production_costs - $bad_PR - $lawsuits

This holds true for any situation where $profit is the driving factor. If Political or Social factors are driving it, then $profit is irrelevant.

And by 'dimple' I mean 'rosy cheeks'...

*stupid spell checker not knowing what I meant to type*grumble*

Maybe he can use this formula to derive your mom's phone number.

"Finally, how many per cent a circle cover its square’s

area and perimeter."

A circle touches "its square" in exactly four points if I understand what this guy means by "a circle's square". If each of those points is infinitesimally small, doesn't every circle cover "its square's perimeter" by exactly 0%? Am I guilty of trying to apply reason to the unreasonable?

Note to Ahmadinejad: One of your citizens is a genius! You should immediately appoint him as head of your military and reprogram all of your weapon trajectories with this new and correct value for π.

Normally I am able to see where a particular theory goes astray. In this case I'm dumbfounded. Would someone please try to explain why it's supposedly true that a circle's diameter is equal to the side of its superscribed square *only* when a value of 3.125 is used?

To me there is absolutely no need to even look at a formula. If you superscribe a square around a circle, it's plainly obvious that a line segment drawn from one point of intersection directly through the middle of the circle to the opposite point of intersection is "the diameter" of said circle. It is also plainly obvious that this line segment is identical in length to every side of that square.

I've been trying hard to figure this out and simply can't see where his brain jumped off track.

Clearly his brain never jumped off the track since it wasn't on track in the first place.

I have a tattoo of Euler's identity on my left shoulder. I am looking forward to when my son gets old enough to start asking what the various symbols mean. I feel like I should be able to explain Pi at a pretty young age by doing what you just said. i and e will probably have to wait a while...

I realize this is an old topic and may no longer be watched. If I get no reply here, I'll keep looking for a venue.

Here's my question. For a given encoding of text to number, is it possible to find the complete works of, say, Shakespeare in pi? If "Hamlet" were converted to a single (really huge) number, will that number appear as a sub-string in the digits of pi? How about the entire works of Shakespeare converted to a single vast number? Would that value appear somewhere in pi?

I guess what I'm trying to understand is whether the *structure* of the text might make it unlikely to appear. Or is is the case that any given sub-number, no matter its size, would be found in pi?