Thursday, July 30, 2015

31

These musings provide the basis for estimating, very generally, the amount of data required to describe a universe of things. A single bit can, in fact, describe a universe, in some sense, and even something in it. It is always the case that a bit, or a number, has the meaning assigned to it, so we could assign the value 30 billion light years to the number 1, and, say, one half that number to the number 0, and one bit would then convey information, in some sense, about a volume of space the size of our visible universe.

This represents the extreme lower extreme of detail, represented by one bit and the values assigned to its two possible states. How many bits, then, would be required to describe a universe at something approaching the extreme upper extreme of detail? To begin, let us assign to the unitary distance between the four equidistant points that define a universe the value 1 light year. How many bits would be required to locate a point anywhere in a universe the size of our visible universe to an accuracy of one light year?