🚀 go-pugleaf

In article <1992Nov7.214329.24552@galois.mit.edu>, jbaez@riesz.mit.edu (John C. Baez) writes:
> Dave Griffiths writes:
> 
> >There is no such thing as infinity. Physicists are going to have to bite
> >the bullet and develop a discrete TOE at some time or other. To do so
> >may require going right back to basics to develop an information based
> >theory. But with so much momentum in current theories, so much resistance
> >to the radically new, so little money to be made from such a reformulation,
> >I wonder if it will ever happen.
> 
> This is what computer scientists often say.  We eagerly await the day
> when one of them actually does some physics.  :-)  Do physicists go
> around saying that present-day computers are inadequate for physics
> because they are digital and not analog?  Maybe some do, but
> that would be equally misguided.  
> 
> The main point is that "there is no such thing as infinity" is an
> extremely vague and misleading statement.  Is there such a thing as a
> universal Turing machine?  (I've never seen one.)  Is there such a thing
> as the square root of minus 1?  All these things are mathematical
> constructs which can play an important role in modeling reality - all
> three can also be misused.  

This is misleading. The difference between the potential
and completed infinite is an old and well defined one in mathematics.
At one point it was the consensus among mathematicians that the completed
infinite did not make sense. As mathematicians got better
at using infinities in their reasoning and avoiding inconsistencies
they got carried away to the point of believing that there is 
a platonic heaven in which completed infinite totalities exist. This
view is falling out of fashion among some mathematicians today. 

Our universe, in contrast to mathematician's platonic heaven, does exist.
For completed infinite totalities to have physical existence is problematic.
Some of the problems physicists face (such as singularities and the
inconsistency between general relativity and quantum mechanics) are related
to these problems.

> Secretly, my theory about computer scientists' love of discrete physics
> is that it's a still poorly-understood side-effect of staring at pixels
> all day.  I have long had a humorous battle with Nate Osgood over this
> issue, replete with such slogans as "Wreck the rectangle!" (which I
> stole from Zippy the Pinhead), "Crush the continuum!" and "Death to the
> discrete!"  

Let me suggest another theory. The reasons for rejecting the completed
infinite in physics are more intuitive than intellectual.
Younger disciplines, such as computer science, tend to attract more
people whose primary strength is intuition. As a discipline matures
dominance in it tends to shift from the intuitive people who created
it to those who are better at developing and refining it. One thing I
was stuck by in Pais's excellent biographies of Einstein and Bohr was
how different these men were. Bohr was the extrovert and Einstein
the introvert. Yet one thing they had in common was that
their greatest strength was not a powerful intellectual grasp of
mathematical techniques. It was their powerful physical intuition.

> ...
> Work in discrete physics *is* proceeding nicely, *not* because some
> folks hope the universe is just like a computer, but because it's nice
> to understand the sort of quasi-physical processes that a digital
> computer can simulate exactly.

Of course it is not a question of the universe being just like a computer.
Most important to me it is that there are no physical effects that require
continuous models. Thus it would be an extreme violation of Ockham's
razor if nature employed continuous structures in creating such effects.

Paul Budnik