>>19
Numbers don't have to represent ``quantities''. Temperature isn't a quantity, but you can still measure it and make calculations based on that measurement. You could invent your own temperature system where sqrt 2 is the freezing point and pi is the boiling point. Your calculations won't round out nicely on paper but they'd be every bit as valid as if you used celsius or fahrenheit. The numbers we use are arbitrary. We base measurements on integers because they're convenient. We use base-10 so we can count the digits on our fingers. We use binary in computing because it's easy to represent with electronic signals. They're all arbitrary. Base-e occurs in nature, hence the natural logarithm, it's not arbitrary at all. Neither are pi and phi, they're real ratios that occur frequently in nature, every bit as real as 1/2 or even 1. You can have pi apples just as easily as you can have 1/2 an apple. 1/2 is abstract in it's own sense. Nothing in the physical world is ever exactly one half. You can halve an apple but those halves aren't exactly equivalent. You can have half a dollar, but that's just an arbitrary value we attach to it. We could have just as easily called it pi dollars. 1/2 is real to you because it's such a common part of your vocabulary, but in the grand scheme of the universe it's no more or less real or relevant as any irrational number.