alt Hacker NewsTake the approximate number of subatomic particles in the universe, call it Ω. Define the largest number as Ω² and the smallest number as -Ω², and define the number of decimal numbers between each integer number as Ω², evenly spaced. That should be more than enough numbers. Redefine Ω with each new discovery in physics.
If this seems too conservative to you, like if for some reason you want to talk about the volume of the universe in terms of the width of an up-quark or whatever, feel free to tack on some modifier to my proposed number system.
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At the bottom end we have the Planck length. How many cubic Planck lengths in the visible universe ? Anyone ? To paraphrase Bill Gates (allegedly), "(PlanckLengths/widthOfUniverse)*3 ought to be enough for anybody."
This system breaks down when you start looking at permutations; there are Ω! ways to arrange your subatomic particles, and that's just in 1 dimension.
I want to count the number of possible permutations of the particles. We’ve now got a “larger” number than Ω will ever be able to represent by definition (even Ω² is minuscule by comparison).