Go and Chess are generally considered to be the paradigm of strategy games and pure intellectual pursuit. But not many people have heard of Go in the western world, at least not compared to Chess. Anyone that likes chess is doing themselves a grave disservice by not at least trying out Go. I learned how to play Go approximately 6 years ago, but only played sporadically until approximately 2 years ago, when i started to play any chance i could. These days, i try to play at least 4 or 5 games a week, and have seen my strength rise dramatically as a result. Frustrated by a lack of people to play against, this is a small attempt of mine to introduce the game to people, in the hopes of increasing its popularity.
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Go
Or, You Can’t Know What You Don’t Know You Can’t Know.
This is an interesting result from modal logic that I will try to sketch here. The upshot of the result, depending on which side of a divide you fall into, is either that there are some truths that are logically impossible to know, or that every truth is already known by someone.
The dividing line in this case is whether you are a realist or anti-realist. The realists posit that there is an external reality that has certain definite properties. The anti-realist deny that such an external reality exists (or, in some cases, that we can have access to it). I’ll get more into this distinction after I sketch the proof. If you find logic boring, feel free to skip the proof and scroll to the end for a brief discussion on the implications of this result.
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Logic, Philosophy
XKCD posted a logic program titled Blue Eyes: The Hardest Logic Puzzle in the World. The problem got posted to reddit, and of course a large argument erupted in the comments thread about how the question doesn’t make sense, the solution doesn’t make sense / doesn’t work / is flawed / etc. etc. etc.
Rather than futilely attempt to make myself heard above the din, I’m writing this post which explains what the solution is, how you get to the conclusion, why it is in fact correct, and why the guru’s statement is necessary.
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Evolution, Logic
In mathematics, a fixed point is a value of a function that maps to its self. In other words, x is a fixed point of a function f if f(x) = x.
According to Kleene’s recursion theorem, fixed points exist in every programming language; i.e. in every programming language, there is at least one program (actually infinitely many, trivially different from each other.) the output of which is an exact duplicate of the program.
Attached you will find a fixed point program written in perl.
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Computer Science, Programing
At a philosophical discussion last night, we read “Jipi and the Paranoid Chip” by Neal Stephenson (Which, I just noticed, was posted to reddit 9 days ago, and got 1 up vote and 1 down vote. WTF?). If you’ve never read anything by him, I suggest you stop right this moment, go out and buy Cryptonomicon, Snowcrash and the Baroque Cycle, and do nothing until you’ve read them all.
The story is about a piece of software that was evolved to be indistinguishable from a paranoid schizophrenic. In the course of discussing the plot, someone asked if the paranoid schizophrenic chip would pass the Turing Test, with their inclination being no, it couldn’t.
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Computer Science, Metaphysics, Philosophy
The paradox of the heap, also known as the Sorities Paradox (from the Greek word for heap), is a paradox revolving around the problem of vagueness.
In its classical formulation, the paradox is expressed as follows:
One grain of sand is not a heap.
If one grain of sand is not a heap, adding one grain of sand will not make it a heap.
So two grains of sand are not a heap.
So three grains of sand do not make a heap.
…
X grains of sand do not make a heap.
Therefore, 10,000 grains of sand do not make a heap.
The form of this argument boils down to:
X grains of sand are not a heap.
If X grains of sand are not a heap, adding 1 grain of sand will not make it a heap.
(Some arbitrary large number of grains of sand) do not make a heap.
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Computer Science, Evolution, Musings, Philosophy, Vagueness
You’ll have to forgive me, as the first part of this is reconstructed from memory, from a paper I read several months ago.
Lets do a little thought experiment.
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Mathematics, Musings
Cognitive Daily has an interesting discussion going on about whether or not an artificial intelligence requires a body. There are some interesting posts in the discussion, but as with most of these discussions, it quickly turned into a matter of “what does it mean to be intelligent?”
To drop my two cents in on the matter, I must say that the answer to the question is obviously yes; but we have to define “body.”
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Computer Science, Musings