ellenjanuary comments on How to think like a quantum monadologist - Less Wrong

-14 Post author: Mitchell_Porter 15 October 2009 09:37AM

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Comment author: meanerelk 23 October 2009 04:26:23AM 6 points [-]

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".

Comment author: ellenjanuary 23 October 2009 05:57:05AM 0 points [-]

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. :)

Comment author: RobinZ 27 October 2009 05:33:42PM 2 points [-]

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."

I apologize for the belated reply, but did you sincerely believe this at the time at which you said it, and do you sincerely believe it now?

Comment author: ellenjanuary comment score below threshold [+] (2 children)

Comment author: ellenjanuary 01 November 2009 05:35:02PM -5 points [-]

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, <i>A New Kind of Science</i>, 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. ;)

Comment author: Zack_M_Davis 01 November 2009 07:46:13PM 5 points [-]

Your passion is admirable, but you would seem to have much more to learn before you are ready to make your greatest contribution. (As do we all, of course.) For instance, the mathematical community at large actually does consider zero to be a number; this is not really in contention.

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,

Here at Less Wrong, we prefer focused, previously-researched posts: probably this partially explains the downvotes you've been getting. Have you considered getting your own blog? Keep studying, and I hope to see your work in the future.

Comment author: RobinZ 01 November 2009 11:27:38PM 3 points [-]

Elaborating on Davis's remarks: what you have to consider is that mathematics is something of a game, something of an art, and something of a science - to become a mathematician is not to be declared such, but to develop the skill of mathematics.

On the point of zero: just to begin with, consider subtraction. Subtraction is a simple operation, the inversion of addition - because one plus one is two, two minus one is one. When we consider this operation, we discover that there is nothing to prevent us from subtracting a number from itself unless we make a rule such - and why should we? The only reason to make such a rule is to appease an idea of numbers which does not include those less than zero, and that is no reason at all.

So, we call this number - one less than one, two less than two, etc. - zero. We find it behaves as the other numbers do - it may be added, subtracted, multiplied just as other numbers, and that it cannot be divided by suggests a host of new ideas.

Calling zero a number pays dividends. Therefore zero is a number. Quod erat demonstrandum.

ellenjanuary comments on How to think like a quantum monadologist - Less Wrong

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