VLVL(6) - Questions: Group Theory

[Howard, Jesse]

I'm still trying to research this, but here is the context in which I formed
the thought:
1)In reading Hofstadter's Godel, Escher, Bach, I have seen the thoroughgoing
failure of formal logical systems.  In particular, many of the ideas of
group theory which arose as a result of Godel's theorem are presented as
being idealizations of "real world" mathematics (if such a distinction can
be made).
2)What little I know of chaotic systems suggests to me that the study of
dynamic systems requires a mindset and mathematical tools which defy
conventional logic and number theory.  I am assuming this also extends to
include this "idealized" world of group theory - but I could be wrong.
3)A research mathematician friend of mine once made a comment, in passing,
that "group theory is dead."  He went on to mention that chaotic systems had
made hash of what was once considered to be the hot, new math.  I haven't
been able to get ahold of him to ask him what he meant, but his comment got
me thinking that there may have been some conflict between those wanting to
embrace the chaotic nature of the "real world" and those wanting to make
progress with their idealized functions.  But I really need to learn more
about this before I can say more - I am fishing.

Of other passing interest was a tidbit I turned up when researching group
theory on the web, which was located on a website for some encryption
software.  The notes by the software company said that they used a "one-way
zeta function" in their encryption algorithm, which according to group
theory cannot be cracked except by trying every possible permutation in the
solution set (or meta-set).  Again, I need to research one-way Zoyd
functions?

Any mathematicians out there want to help?  I only do ancient stuff.

jch

On Friday, December 11, 1998 8:23 AM, Peter Petto [SMTP:ppetto at apk.net]
wrote:
> At 02:41 PM 12/7/98 -0800, Howard, Jesse wrote:
> 
> > which brings to mind the tug of war between group theory and chaos
> > mathematics that was beginning to appear in the mid-to-late sixties
> 
> Could you say a little more about this? What was this war?