
The Generalist – On Alexander Grothendieck - benbreen
http://www.thebigquestions.com/2014/11/17/the-generalist/
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westoncb
I've been devoting myself for a while now to an approach to thinking that
seems along the lines of Grothendieck's project (as described in the blog),
where difficulty should only come in defining the framework to work within,
while work within the framework is easy.

In defining a framework, fundamentally you are coming up with a set of types
and describing how things of these types are able to interact with one
another; if it's a framework that's easy to work with, the number of types,
relations, and operations is small (relative to other formulations). If this
framework is concise, but the universe of things described by it is large,
then the types must be very general. Therefore, using an approach of finding
an elegant framework, rather than mastering the complexity of an inelegant
framework, relies heavily on one's ability to generalize.

My issue with spending a lot of time thinking this way is that it gives me a
sort of uneasy feeling... What are these super abstract generalizations? From
what I can tell, this mostly comes from wondering whether with all this
'zooming out' we are getting closer to truths about the universe, or our own
minds—and the latter possibility feels a little suffocating.

Anyone know any books, essays, whatever taking up that issue?

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dsfsdfd
I spend a lot of my time thinking about how to construct the universe in as
general a way as possible. Every now and then I feel like I 'level up' and the
picture becomes clearer. Then usually about the same time I learn something
new from mathematics that shows me I am following a path already travelled. Or
in this case following a path closely related to a path well travelled. I
think the truths about our own minds are intimately connected with truths
about the universe. I suspect the mystery of consciousness is very similar to
the mystery of the universe. Understand one and you understand the other. For
me the ultimate mystery is explaining why there is pattern rather than no
pattern. Why is there self similarity, why is the universe compressible? Why
is it that within everything there is a place where this exists and why does
'this' have the structure it does. Can we invoke the anthropic principle,or is
there something like population dynamics within totality. I am currently
following an interesting line, starting from the thought experiment - If you
recorded every moment of the universe on a physical representation, a hard
drive for instance with perfect fidelity. Would there be any difference
between the representation and the universe itself? I don't think there would.
This is leading me to try to recast what I know of mathematics without the
notion of process, to visualise it all it terms of structure only. And to to
truly grok that our notion of computing is a method for finding a piece of the
internal structure of a larger structure. Within a structure constructed from
self similar elements. Just ramblings, sure it's non sense, or perhaps
trivially obvious, but am trying to connect with someone :)

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westoncb
Your project makes a lot of sense to me—same kind of questions I've been
wondering on: why patterns, why self-similarity, etc. I'm westoncb[at google's
mail service] if you want to discuss sometime.

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auntienomen
Lovely writing. This is better than most of what popular science writers have
produced on the subject.

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tel
Can anyone who understands sheaves clarify the whole "point is a place where
all functions are constant" analogy?

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vzcx
You actually don't need all the machinery behind sheaves to understand this!
The general concept is that of a terminal object in a category. In the
category of sets, the terminal objects are the singletons: given a set S,
there is only one function f:S -> {a}... send everything in S to a! In the
category of topological spaces, the terminal objects are the single-point
spaces.

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tel
That was my first thought as well, but the author directly linked this notion
to sheaves and also was talking about mapping _from_ points.

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qcoh
I guess this is because the structure sheaf of the spectrum of a field is a
constant sheaf.

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SteveLandsburg
Yes, this is exactly what I intended.

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elliptic
"What else falls when you drop it?" A duck!

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terrn
Exactly! So logically if Grothendieck also fell when dropped he was a witch!

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dbtc
[http://en.wikipedia.org/wiki/Duck_typing](http://en.wikipedia.org/wiki/Duck_typing)

