> It's nonsensical that a single die roll takes 2.58 bits, but it's perfectly believable that 100 die rolls could fit in 258 bits. It takes 3 bits to code for

> It's nonsensical that a single die roll takes 2.58 bits, but it's perfectly believable that 100 die rolls could fit in 258 bits. It takes 3 bits to code for six values, but that is clearly a loose bound, since 2^3 = 8. But by taking the base-2 logarithm, you can get the exact number of bits required. That's how I rationalize it. The 258-bits-in-100-die-rolls is a nice trick though. This is why the logarithm is my favorite mathematical function -- it's not just an operation on a number, but it also describes various properties of the number itself. Depending on how you use the log, it can describe the number of digits the input has, or how much "information" can be contained in the input, and so forth.