## Tuesday, September 20, 2005

### Rational geometry

I wonder what you think about this news that was pointed out to me by Olda Klimanek. An associate professor of mathematics in Australia, Dr. Norman Wildberger, has figured out that the angles, sines, and cosines essentially do not need to exist and irrational functions should be eliminated from math by replacing angles by new concepts of "spreads" and "quadrances". Students won't have to learn any functions beyond the rational ones. I wonder whether you have an explanation what this means and whether there is a reason why this bizarre news appears in tens of newspapers.

#### 4 comments:

1. I really meant 1-(A.B)^2/(A.A)(B.B) of course. Please assume that I made an honest typo...

Lubos seems to have disabled the Haloscan comments.

2. Dear Lumos,

Perhaps this guy has an system which is mathematically equivalent to that which is already used, but does not have the vast array of interrelated trig functions to confuse people (sin, cos, tan, cosec, cot, sec, arctan, etc., etc.)

To remember the sin=opposite/hyp, cos=adjacent/hyp and tan=opposite/adjacent we were forced to remember 'Some Old Hens Can't Always Hide Their Old Age' which gives SOH CAH TOA, enabling the definitions of sin, cos and tan to be decoded without confusion. It would be nice if this guy has really simplified things.

It would be nice, too, to know if the Kaluza-Klein model (for unifying general relativity with Maxwell's equations) works in 10/11-D M-theory with the 6/7 extra dimensions forming the compressed manifold? The different models of string theory look contradictory.

The Klein suggestion that an extra dimension is curled up into a Planck-length circle is so vague it beggars belief that it passes for a physical idea. Why not, for sake of argument, have the string size the size of a black hole for the mass in question, so the string radius is 2MG/c^2 instead of the Planck size?

The Planck length has no more physical support as normally stated than Eddington's suggestion that the gravitational coupling constant is smaller than that for electromagnetism by 10^-40 times 'because' the square root of the number of particles in the universe, 10^80, gives the right number, which is astronomical and therefore should have an astronomical origin.

There is plenty of speculation around, what is missing is physics. I tried to point out on Peter Woit's blog that Eddington's square root factor can be obtained physically from causal electromagnetism.

The gauge bosons emitted by all electric charges cause attraction since opposite charges shield one another and get pushed together, while similar charges exchange gauge bosons and thus recoil apart.

When you add up the electric field strength in the universe, it is zero along any straight line because of equal charges of either sign. But a zig-zag exchange of gauge bosons is possible between similar charges is possible, which adds up statistically like a drunkard's walk. The result, when you use a working version of the LeSage gravity mechanism, is that electromagnetism is stronger than gravity by the square root of the number of charges. So Eddington was right after all, despite being dismissed as a crackpot.

Best wishes,
Nigel

3. Nigel,

You cannot discard length scales.

As much as it seems that Lisa Randall would not think we are capable of viewing these abstractions, I would try my imput to help organized such revisions in thinking. Although, it may not be correct, I hope it is so.

We spoke of temperatures as a measure of this. This is only one way in which to view it, and on Bekenstein bound, CFT is another.

From layman apprehensions such attempts boggle my mind, yet it is there for us.

4. Dear Plato,

I'm not arguing to discard scale lengths. I'm just asking what the physical justification for using the Planck length, about 10^-35 m, as the string size.

It is an arbitrary scale length.

Why not have a string radius equal to 2GM/c^2 where M is the rest mass?

If every fundamental particle is a string of the fixed Planck size, then the string tension must be varied to give different amounts of mass-energy for different fundamental particles.

However, if the string size is not fixed by the Planck scale, but is equal to the black hole size for equivalent energy, then the string tension will vary in a different way.

For the electron mass, the black hole radius is 6.8 x 10^-58 m, far smaller than the Planck scale length. This makes me wonder whether the reliance on Planck dimensions makes any sense at all.

Best wishes,
Nigel