Wednesday, December 19, 2012

Funny thought experiment about information density

What are the human constraints of comprehension of numbers?  I think I have an idea of mine.  There are some cavernous mental pitfalls when thinking about information density.  This one regards the application of context (which always matters but is always stored outside of the data itself).

How many sentences, words, and sounds can be spoken in five minutes?  In any number of languages.  Is there an infinite possible number of languages and combination of languages itself?

Intuitively I do think of all the possibilities as infinite.

Some more thinking proves my intuition wrong.  Let's look at the problem from a different angle.  How much data is stored in that five minutes?

60 * 5 = 300 = length of recording (in seconds)
128 = bitrate (in kilobits per second)
z = file size (in kilobytes)
(300 * 128) / 8 = z
38,400 kilobits / 8 = 4,800 kb = 4.8mb

4.8mb of information is nowhere near infinite.  It's actually pretty damn small.  My intuition was dead wrong... or was it?

Maybe my intuitive perception of infinite languages is due to same sounds being perceived differently in context.  That's the infinite; it's in there somewhere but it's completely based on the infinite context of the same sounds.