AI and cognitive psychology rant (getting more and more OT - tell me if I should shut up)

[Michele Simionato]

"Andrew Dalke" <adalke at mindspring.com> wrote in message news:<KdSob.350$qh2.208 at newsread4.news.pas.earthlink.net>...
> On the fourth hand, Wolfram argues that cellular automata
> provide such a new way of doing science as you argue.  But
> my intuition (brainw^Wtrained as it is by the current scientific
> viewpoint) doesn't agree.

Me too ;)

> Or it means that asking those questions is meaningless.  What's
> the charge of an electron?  The bare point charge is surrounded
> by a swarm of virtual particles, each with its own swarm.  If you
> work it out using higher and higher levels of approximation you'll
> end up with different, non-converging answers, and if you continue
> it onwards you'll get infinite energies.  But given a fixed
> approximation you'll find you can make predictions just fine, and
> using mathematical tricks like renormalization, the inifinities cancel.

I would qualify myself as an expert on renormalization theory and I would
like to make an observation on how the approach to renormalization has 
changed in recent years, since you raise the point.

At the beginning, quantum field theory was - more or less universally - 
regarded as a fundamental theory. Fundamental theory means that asking 
the right questions one must get the right answers. 
Nowadays people are no more so optimistic. 

Quantum field theory is hard: even if the perturbative renormalizability
properties you are referring to can be proved (BTW, now there are easy 
proofs based on the effective field theory approach; I did my Ph.D. on 
the subject) very very little can be said at the non-perturbative level. 
Also, there are worrying indications. It may be very well possible that 
QFT does not exists as a fundamental theory: i.e. it is not mathematically
consistent. For instance, perturbation theory in quantum electrodynamics 
is probably not summable, so the sum of the renormalized series (even if 
any single term is finite) is not finite. In practice, this is not bad, 
since we can resum even non-summable series, but the price to pay to make
finite an infinite sum is to add an arbitrarity (technically, this
is completely unrelated to the infinities in renormalization, they
only seems similar). Now, one can prove that the arbitrarity is
extremely small and has no effect at all at our energy scales: but
in principle it seems that we cannot determine completely an observable, 
even in quantum electrodynamics, due to an internal inconsistency of the
mathematical model. 

Notice that what I am saying is by no means a definitive statement:
there are no conclusive proofs that the standard model is 
mathematically inconsistent. But it could be. And it would not be 
surprising at all, given the experience we have with simpler models.  

> The latter argument was an analogy that the tools (formalisms) affect
> the shape of science.  With that I have no disagreement.  The science
> we do now is affected by the existance of computers.  But that's
> because no one without computers would work on, say, fluid dynamics
> simulations requiring trillions of calculations.  It's not because the
> science is fundamentally different.

Yes, and still a lot of science is done without computers. I never
used a computer for my scientific work, expect for writing my papers
in latex ;)
 
> The other solution is to know everything about everything, and, well,
> I don't know about you but my brain is finite.  While I can remember
> a few abstractions, I am not omnipotent.
> 

we are not omnipotent nor omniscient, but still we may learn something ;)