An important part of describing something is to quantify how "big" it is. But we need to use different notions of "bigness" depending on the object being described and the purpose we have in mind. The need to understand how these notions of "bigness" are related, and which is most suitable in a particular case, leads to ideas in dimension theory, information theory, entropy theory, and other areas, which are all fundamentally connected.

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Fractal dimension from Wikipedia	The AMY1 gene from Wikipedia

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