>"How Many Decimals of Pi Do We Really Need?" Here's the thing about the transcendental numbers, of which Pi is one of, all of them contain information. All o

>"How Many Decimals of Pi Do We Really Need?" Here's the thing about the transcendental numbers, of which Pi is one of, all of them contain information. All of them (and if someone knows of an exception, please let me know) seem to be able to be generated by functions, iterated functions, where the result of one iteration of the function is fed back into the equation (aka algorithm, aka function, aka "series of repeated steps") for future iterations... In that respect -- all transcendental numbers -- can be thought of as fractals. Think of it this way, Nature herself has a way of indexing a whole bunch of fractal algorithms via numbers that have a decimal after the integer component, and an infinite series of digits after that decimal! Which also seems to imply (via reversal of cause and effect) that infinite information -- can be stored in the proper fractal equation -- although, that's just a personal hypothesis at this point with no real proof to back that claim up... Anyway, math people out there, feel free to correct me on any or all of this (I claim Socratic ignorance in my reasoning process! <g>) -- but please cite concrete examples to back your specific claim... You know what someone needs to do? Look at the number gaps between multiple transcendental numbers... I don't mean like the number gap between pi and phi, or e and phi, or pi and e -- I mean like you take an algorithm for a transcendental, and you bump it (inside of its algorithm) by an integer value of one, then two, etc. If you still get another transcendental, then what is the gap between those transcendentals? In fact, what is the smallest gap between two transcendentals, and why is this so? Also, what kind of information -- does that gap represent? ?