That's a great short story. It reminds me of the movie Pi, in which a man obsessively searches for a secret number, to the point of debilitating paranoia. If you enjoyed this short story even slightly, then I highly recommend watching Pi.
I've always thought about stuff like this; a numerals system based upon quantities appearing in nature. 3.1415... is silly. Make that 1 or 4, and see where everything else "fits", or something similar based on a universal constant as the base.
But, in your number system where π is 4, what is e?
More to the point, we aren't just making up numbers here to enjoy infinite decimal expansions; the reason is that you can wrap the radius of a circle around its circumference more than 3 times (or, if you don't like numerals, as many times as letters in 'pie'), but fewer than 4 (not as often as letters in 'easy')—and no changing of units is going to get around that.
