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[futurebird]

Okay, this is blowing my mind, but I think, based on what I’ve read it’s true. Given two random lines whose length could be any real number the ratio of the lengths between these lines will be an uncomputable transcendental number ‘most of the time’ (that is, if every kind of real number is a possible length

Comments

[dangerzooey]

So, here's a question from a philosopher: Do you think that every real number is a possible length? (My intuitions say no, but I'm curious to hear yours.)

[futurebird]

WOW! That's a good question and a possible solution to my little conundrum. It seems the laws of the universe would dictate what lengths are possible (think of the structure of materials) --making all lengths calculatable.

This sounds good... but it feels dangerously newtonian.

[dangerzooey]

Yeah, I think the laws of the universe might dictate how we express numbers, but I worry that there are some numbers that are inexpressible (at least, in any non-arbitrary way) due to their nature.

I mean, I'd bet you've studied this before, but I'll get my thoughts out of my head while I have the chance. We can't make a list of all possible numbers, if you take this certain set of numbers to be possible. We can list whole numbers, easy. We can list rational numbers, easy.

What can't we list? Well, numbers with infinitely long, non-repeating decimals, (or for an alternative visualization, an infinite non-repeating sum of fractions). Pi might be such a number. I don't want to believe that there are such numbers, because I like closure. However, the evidence and the arguments make me question.

[jasonwentcrazy]

So uncomputable transcendental numbers, paintings, martinis, and Philip Glass? Another one of God's own prototypes, eh?

[futurebird]

He broke the mould... but I think He had His reasons.