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Sir, yes sir! But I'm hardly an expert, college dropout and all that. (Community college even. ;) ) So, where do I get off claiming to be a mathematician? Why, the scientific method, of course. The zero is not as "concrete" concept as his material other half, the one; but concepts of a symbolic language is all they are. A guy on Youtube made me a mathematician. He was arguing for the establishment of a new symbology to replace the zero; a "blank" that was more computer friendly, as it were. To me, that's not the point. I mean, that old, round fellow is all but a number to most but the nit-pickers like me. I see it as a type of warning. Here there be dragons. Zero is the face of infinity that has become contemptible by its familiarity, yet the wise men of the East have long knew something all our vaunted Western technology is just discovering. The legendary kingdom of heaven is not beyond the sum total of everything, the nearer doorway is through the absence of anything.
What is empty space? Far more than nothing, it would seem. I was watching Stephen Wolfram discuss his book, A New Kind of Science, the other day. Since I missed genius by a couple of points, I couldn't quite follow how computational irreducibility is other than deterministic chaos in a new suit; but I'm sure the stupid brain will do further research one day. But it was drifting, thinking about how I don't know jack about QM but quantum decoherence sounds like a winner; and he's showing patterns of cellular automatia, rule 110, I think it was. A nearly "random mess" in the first line, but as successive iterations display... particles, from the stuff of nothingness. He even mentioned how it resembled particle interaction towards the end. Like sixteen lines of code that display the sum total of the Julia sets, twenty years and three hundred pages of Gaston Julia's life. Elegant, as we say in the field.
But I love this place. I still have to go back and research half of this very post to decode what is actually being said, but "yes, no, and maybe" sure seem to be covered by the three infinities; positive, negative, and zero. ;)
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? ;)
First of all, thank you for your reply. Honestly, I'm here because I love this place. I guess one is required to figure out the rules as one commiserates, hmmm? ;)
1) I agree. Being an artist does not validate the belief, it is merely shorthand for the formation of the belief.
2) Thank you for the definition of transcendentals. I'm a passionate writer more than an accurate one. That shall improve, and is part of the reason why I am here. The contradiction formed in my mind due to "skipping a couple of steps" and concluding that "all infinities converge at infinity." I agree that there is no contradiction.
3) We're going to have to agree to disagree in this area. Previously I was told I was "confusing the referent for the symbol" when I sat on a thread and took all comers with the proclamation that "zero is not a number, it is a concept." Glory days in the mind of a mathematician. (Yes, we are strange. ;) ) Irrelevant. I fully intend to dedicate the next four years on discovering the reality of concepts, and I will be sure to look into what you have recommended. The bookstore on the corner had the last tome; if it is still there in two weeks, that baby is mine. Thanks.
PS. In writing "thank you for the definition of transcendentals," it occurs to me that it sounds sarcastic. It is not. Previously, the stupid brain did not have a concise definition; and now it does. I fully intend to be polite, courteous, and respectful in all discussion on this blog. If I am not, please let me know. Thanks again. :)
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. :)