I love this place. At first I said to myself, "Duh!" Then I was like, there's a trick involved... :) Perhaps I can reward a thought with a thought... isn't it also true that a pound of feathers will weigh more? ;)

I'm an artist, and believe that any two given individuals will not share an identical color perception.

Being an artist has nothing to do with the accuracy of this belief.

I've always had issues with infinity and transcendental numbers. For instance, pi is said to be transcendental as it cannot be expressed as the ratio of two integers; yet, in a sense, is the ratio of two numbers - the circumference over the diameter.

There are two problems here. First, irrational numbers are the ones that cannot be expressed as a fraction of integers. Transendentals are defined as numbers that are not algebraic. All transcendental numbers are irrational, but the converse does not hold.

Second, pi is defined as the ratio of circumference to diameter, true. This would only be a contradiction if both the circumference and diameter could be integers at the same time, which is impossible.

This got me to thinking about numbers as mere concepts. Numbers that we count on our fingers and toes have a greater "reality" than such oddballs as radical two and i, yet those oddballs seem to me much more useful.

You are confused about what numbers actually are. Some classes of numbers are useful for certain tasks, but there is no sense in which one class is more 'real' than another. I recommend Mathematics, Queen & Servant of Science by Eric Temple Bell for a wonderful overview of mathematics. Chapter 2, "Mathematical Truth", is relevent to this discussion. Also, see Godel, Escher, Bach, Chapter 11: "Meaning and Form in Mathematics".

Don't mind me. I just found "Less Wrong" recently, and I'm here to learn things. I say that this is a great post as it makes me think. I've yet to find the directions to this place to know if any "higher purpose" is idealized, or if conducting electricity into thought is its own reward.

I'm an artist, and believe that any two given individuals will not share an identical color perception. For that reason, I have argued in the past that color did not exist until the widespread use of the computer. Rather than debate teal, blue, or green, I could just use a hexadecimal.

I'm also a mathematician. (Not necessarily a very good nor learned one, but since it is oft defined that mathematics is what mathematicians are doing, I qualify. :) ) I was looking into the Continuum Hypothesis because I've always had issues with infinity and transcendental numbers. For instance, pi is said to be transcendental as it cannot be expressed as the ratio of two integers; yet, in a sense, is the ratio of two numbers - the circumference over the diameter. This got me to thinking about numbers as mere concepts. Numbers that we count on our fingers and toes have a greater "reality" than such oddballs as radical two and i, yet those oddballs seem to me much more useful.

Is conception so very cluttered? I think so. I imagined creating a set of numbers (the stupid number set) that were just one, two, three - got to thinking of forming axiom and method - and lo and behold! How much geometry did they sneak into my pure mathematics?

I'm currently waiting to get the funding for a complete collection of graduate-level mathematics textbooks to informally "finish my degree" as it were (because I'm not supposed to be a "mathematical theorist" as a forty-one year old former construction worker, but the whole world may be wrong and I may be right ;) ) and I mention this here because I believe this very post set me off a week ago. What I know of QM I could probably fit in a spoon, but from here to a single night of learning stuff; to drawing a picture the next day - and now I know I must learn a whole bunch of math. Because now I "believe" in quantum decoherence.

So! Even if I'm not helping you, you've helped me. Thank you.

Synchronicity: this is one of the best things I have ever read in life, yet my life had to come to this point in order to appreciate what I was reading. Thanks muchly. :)