Michaelos comments on Counterfactual Calculation and Observational Knowledge - Less Wrong

11 Post author: Vladimir_Nesov 31 January 2011 04:28PM

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Comment author: [deleted] 01 February 2011 07:08:23PM *  -1 points [-]

It seems like one answer to "Why isn't anything you can think of evidence?" might be that "anything you can think of" becomes incomputable very quickly.

Let's say you were to ask a computer to consider "Anything you can think of" with respect to this problem. Imagine each unique hard drive configuration is a thought, And it can process 1 thought per second per hertz. Let's make it a 5ghz computer.

It can think of anything on a 32 bit drive in a bit less then 1 second since 2^32 is 4,294,967,296, which is less then 5 billion.

The problem is, in uncompressed Ascii where you would need 8bits for a character, you can't even fit the thought "32bit" onto a 32 bit harddrive, since it's 5 bytes/40 bits long.

If we double the harddrive to 64 bits to give ourselves more room for longer thoughts, our 5ghz computer goes from being able to calculate all possible thoughts in less then a second to being able to calculate it in around a human lifetime, because of the exponential growth involved. (At least, assuming I've made no math errors.)

We actually have computers do this when we try to have them crack passwords with brute force. A computer trying to brute force a password is essentially trying "Anything it can think of" to open the password protected data.