From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: Warm and Fuzzy?  Koalas vs. Math
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Mon, 14 Sep 92 03:49:33 GMT

matmcinn@nuscc.nus.sg (Mcinnes B T (Dr)) inquires:

>By the way, John, what IS the best flavour of ice cream?

It should be easy to calculate once we work out the bugs in our Theory
of Everything.

In the meantime, I've been studying a little string theory.  I
recommend Kaku's Introduction to Superstrings, in part because it is
a good exposition, and in part because he is honest, even listing the
pros and cons of string theory quite honestly.  Heck, I'll list 'em,
just to prove I am not alone in my criticisms.  [Slightly abridged.]

Pros:

1)  The gauge group includes E8 x E8, which is much larger than the
minimal group SU(3) x SU(2) X U(1).  There is plenty of room for
phenomenology in this theory.

2)  The theory has no anomalies... the symmetries of the superstring
theory, by a series of "miracles," can cancel all of its potential
anomalies.  

3)  Powerful arguments from the theory of Riemann surfaces indicate
that the theory is finite to all orders in perturbation theory
(although a rigorous proof is still lacking).

4)  There is very little freedom to play with.  Superstring models are
notoriously difficult to tinker with without destroying their
miraculous properties.  Thus, we do not have the problem of 20 or more
arbitrary coupling constants.

5)  The theory includes GUTs, super-Yang-Mills, supergravity, and
Kaluza-Klein theories as subsets.  Thus, many of the features of the
phenomenology developed for these theories carry over into the string
theory.  

Cons:

1)  It is impossible experimentally to reach the tremendouw energies
found at the Planck scale.  Therefor, the theory is in some sense
untestable.  A theory that is untestable is not an acceptable physical
theory. 

2)  No one shred of experimental evidence has been found to confirm
the existence of supersymmetry, let alone superstrings.

3)  It is presumputous to assume that there will be no surprises in
the "desert" between 100 and 10^19 GeV.  New, totally unexpected
phenomena have always cropped up when we have pushed the enrgy scale
of our accelerators.  Superstring theory, however, makes predcitions
over the next 17 orders of magnitude, which is unheard of in the
history of science.

4)  The theory does not explain why the cosmological constant is zero. 
Any theory that claims to be a "theory of everything" must surely
explain the puzzle of a vanishing cosmological constant, but it is not
clear how superstrings solves this problem.

5)  The theory has an embarrassment of riches.  There are
apparently *thousands* of ways to bread down the theory to low
energies.  Which is the correct vacuum?  Although superstring theory
can produce the minimal theory of SU(3) x SU(2) X U(1), it also
predicts many other interactions that have not yet been seen.  

6)  No one really knows how to break a 10-dimensional theory down to 4
dimensions.   

Towards the end of the book, he adds, tongue in cheek, that "The
biggest drawback to the superstring theory, however, is that particle
accelerators able to probe down to the Planck length are prohibitively
expensive."  

Some readers might enjoy the "physicist's proof" of the Atiyah-Singer 
index theorem in this book.  

As a quiz - what are these numbers:

496
18883584

and for extra credit, what is the next number in the series?  (I can't
do it myself.)  
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