

Douglas Hofstadter-Intertwined Patterns of Integers&Patterns OfThought Processes - vampirebat
http://vimeo.com/album/3082332/video/109139374

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vampirebat
From the abstract:

Abstract: As a math-loving teen-ager, I got swept up into an intense and
almost indescribably intoxicating binge of mathematical exploration, all of
which was centered on the discovery (or invention?) of integer sequences. The
very first discovery in this binge came out of an empirical exploration of the
way in which triangular numbers intermingle with squares, and the discovery of
the strange hidden order in the sequence that reflected their intermingling
was extremely unexpected and exciting to me.

This huge burst of joy instantly gave rise to the desire to repeat the
experience, which meant to recreate essentially the same phenomenon again, but
in a new "place", which meant to generalize outwards, and I carried out this
generalization by exploring all sorts of "nearby" analogues, where the words
"place" and "nearby" of course suggest (at least to mathematically inclined
folk!) some kind of metaphorical, but perhaps objective, space of ideas, and
in it, some kind of metaphorical metric.

Over the next few years, analogies and sequences came to me in wondrous
flurries, giving rise to all sorts of discoveries, some very rich and
inspirational to me, some of course less so, but in any case, these coevolving
discoveries constantly pushed the envelope of richly-interconnected ideas
outwards, revealing new and unsuspected caverns in this mysterious idea-space
that I had stumbled upon. Some of my explorations gave rise to patterns that I
could fully understand and prove, whereas others gave rise to mysterious,
chaotic behaviors that were far too deep for me to fathom, let alone prove.
After a while, I started hitting up against the limits of my own imagination,
and thus, sadly, I gradually ran out of steam, but the several-year voyage had
been incredible one of the greatest voyages in my life.

The talk will thus be all about the very human, intuition-driven, analogy-
permeated nature of mathematical discovery, invention, and exploration not at
the immensely abstract level of great mathematicians, to be sure but
hopefully, the essence of the mental processes mediating the modest
meanderings of a middling, minor mathematician is more or less the same as
that of those that mediate the marvelous and majestic masterstrokes of a
major, mature mathematician.

