The genetic algorithm is one method of solving problems in computer science. Although it comes in many flavors, for the purposes of this article I’ll focus on a simple example.

Imagine you have a multiple choice test with 20 questions. Each question can be answered by choosing one of four choices. A compete answer to the test consists of a string of 20 characters, each of which is chosen from the set {A, B, C, D}. The solution to the test is an answer string where every answer is correct.

A valid, but not necessarily correct, answer string would look like this:

ABDCBDABDBCABDCCBABD

How many possible answer strings are there? Well, each position in the string can take on 4 different values, and there are 20 of them, so there are 4^20 = 1,099,511,627,776 possible ways to answer the test. That’s “just” over 1 trillion (over by 99 billion, that is). To give you a sense of perspective, that’s about as many seconds as there are in 35,000 years. Yeah, that’s a lot.

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My wife turned up this post, in which a blogger goes on a bit of a rant in regards to attractiveness and weight. I’d like to throw my two cents into the pot and comment on two specific things she touches on briefly.

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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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