
Computational Complexity Theory - sonabinu
http://plato.stanford.edu/entries/computational-complexity/
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Sharlin
No discussion of philosophy and complexity theory is complete without the
thought-provoking paper by Aaronson [1].

[1] Aaronson, Scott. Why Philosophers Should Care About Computational
Complexity.
[http://www.scottaaronson.com/papers/philos.pdf](http://www.scottaaronson.com/papers/philos.pdf)

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gnudon
The posted URL adds a greater than sign breaking the link.

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Sharlin
Doh, thanks, fixed.

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paulpauper
I noticed that this is posted on the Stanford philosophy portal. Does anyone
else think philosophy should be considered a STEM subject (or tangentially
related)? The work of Godel, Turing, and Cantor blur the lines between
philosophy and mathematics. I've also noticed an immense increase in interest
mathematical-philosophy in the past few years, online especially.

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unabst
At the highest level, philosophy already is part of the STEM subject. At lower
levels, it's up to the teacher, but in my experience the best teachers would
make me think and juggle abstract ideas, which is pretty much philosophy in a
nutshell.

Philosophy as a lone subject is rather broad and less relevant, as most
scientific philosophy has already transferred to STEM courses with real
scientists doing a better job incorporating them in their classes.

Here is a course description lifted straight from MIT's CS course list:

> 6.833 The Human Intelligence Enterprise

> Analyzes seminal work directed at the development of a computational
> understanding of human intelligence, such as work on learning, language,
> vision, event representation, commonsense reasoning, self reflection, story
> understanding, and analogy. Reviews visionary ideas of Turing, Minsky, and
> other influential thinkers. Examines the implications of work on brain
> scanning, developmental psychology, and cognitive psychology. Emphasis on
> discussion and analysis of original papers. Requires the completion of
> additional exercises and a substantial term project. Enrollment limited.

[http://student.mit.edu/catalog/m6c.html](http://student.mit.edu/catalog/m6c.html)

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jhanschoo
Adding on, paraphrasing from Anthony Kenny in an introduction to a volumen of
his book A New History of Philosophy, philosophy is affectionately called the
mother of sciences. When a philosophical question, e.g. what is free will, and
is there free will, develops a well-defined approach to an answer, it often
splits off into its own scientific field. For example, for the question of
free will, we can investigate it as politics, and examine the structures of
coercion by power, as behavior and psychology, and as biological processes.

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zitterbewegung
Another good resource for computational complexity theory is the computational
complexity zoo
[https://complexityzoo.uwaterloo.ca/Complexity_Zoo](https://complexityzoo.uwaterloo.ca/Complexity_Zoo)
. If you are just starting out you might want to start here:
[https://complexityzoo.uwaterloo.ca/Petting_Zoo](https://complexityzoo.uwaterloo.ca/Petting_Zoo)

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Cieplak
I wonder how many people are arbitraging proofs of P = NP. If it were a solved
problem, which I suspect it is, surely folks wouldn't talk about their
solutions when they could rather print money :)

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daveFNbuck
In all likelihood, if P = NP (which most people don't think is true) it won't
be in a way that allows for practical algorithms. You won't be able to get
more money by hiding such a proof than by sharing it.

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Cieplak
Gödel's theorem implies that Turing machines are not complete. The problems of
floating point numbers exemplify this. Our existing machine architectures
operate on a discrete silicon substrate (ℤ), but we live in a continuously
differentiable spacetime continuum (ℝ). I don't think this has any deep
implications for P = NP, though; it's just a tooling issue.

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jon_richards
That site kills my scroll wheel.

