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 π**

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.

__SQUARING__

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:

__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.