
Programs are made of ideas - acangiano
http://lukepalmer.wordpress.com/2010/09/24/programs-are-made-of-ideas/
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10ren
My old supervisor, an acm fellow, admonished me: stop thinking about the
theory! _Look at the data!_

Henri Poincaré said, _C'est par la logique qu'on démontre, c'est par
l'intuition qu'on invente._ (It is by logic that we prove, but by intuition
that we discover) <http://www-history.mcs.st-
and.ac.uk/Printonly/Poincare.html>

Implicit in this idea is that there is some kind of search going on - some way
of thinking about the problem - which is not logic, and which is beyond
notational reasoning; and indeed, mathematicians create new mathematics and
notation at the drop of a hat (even if, or sometimes it seems, especially if,
someone else's notation already exists. They are like Lispers - or, perhaps,
lispers are like them.)

Now, the truth is that our thoughts and ideas are also constrained by a system
- our own minds, by which I mean both the specific development of a particular
mind at a given time; and also the biological constraints of our thought.

Obviously, there are thoughts which a specific person cannot yet conceive,
because they simply don't have the background: consider great geniuses of the
past, born before crucial mathematics had been invented, or before crucial
facts about the world were known.

But are there thoughts that are _biologically_ impossible for humans to think?
I think so. For example, it is very difficult for humans to understand complex
ideas without hierarchy. All our systems are founded on hierarchies, or layers
of abstractions, because our short-term memory - even of the best of us - is
limited. I'm sure this has been discussed academically, but I'm only aware of
a couple of science-fiction writers who have mentioned this: Niven/Pournelle's
Motie Engineers, who effortlessly improvised simple solutions that
participated in solutions to many problems at once; and Vinge's Rider design (
_clearly of Transcendental origin_ , apparently simple, even mechanical
operational, but with extraordinary emergent properties.)

As the old joke goes: _any problem can be solved by another layer of
abstraction, except for the problem of too many layers of abstraction._

