Monday, December 18, 2006

Mathematical Delusions

It's early in the morning, the moon is still up, and I lie awake in bed dreaming of infinite compression and actually believe that it is possible. Which it isn't (if you need 4 bits to represent something, you need 4 bits -- and when compressing, you can't assume that something is useless). So... why, every so often, even though I'm aware that it is impossible, I have the urge to study the math, try to find a way to get infinite compression?

Why is this interesting? I'm wondering why I'm interested in attacking a problem that is impossible. Why must I keep on going and try to find a solution? To always try it again, and again, always hopeful that a positive result emerges.

Anyhow, what is the idea behind this infinite compression? It's simple -- re-think of the data as being stored in a highly inneficient manner, and then restore it as efficiently as possible. That is, take a binary number, view it in it's decimal equivalent, and then recompress the decimal value by decomposing it in tenths, etc. One decomposition might be superiour (which is not the case).

Wonderful delusions!

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