| Subject: and sometimes with profundities come headaches |
Author:
Damoclese
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Date Posted: 09/13/04 1:53am
In reply to:
Duane
's message, "yep - profundities abound..." on 09/12/04 4:44am
In fact, I'd even go further and say that
>time's "arrow," the direction of time, is a
>fundamental part of our experience.
Perhaps if we lived in a more multi-time-dimensioned world it wouldn't be. But soon, we'll end up conversing about string theory, and the sheer number of dimensions it proposes already gives me headaches.
>
>Yeah - that's a doozy. My opinion is that math is a
>construct of the human mind.
I think the rules which are set are definitely less "real" in order to keep the system internally logically consistent for us. The bits and pieces that have come more from observation though, well, that's the one that keeps slapping me on the head.
But the interesting part
>of all this is that set theory and the concept of
>'classes' (which is part of the more complicated way
>we now define set theory) are efforts to ground
>mathematics in the "real" world.
Yeah, set theory has come a long way from what it once was, and I like the idea of having a definition of what comprises a class and what rules things must follow in order to be of that class.
On the other hand, I think efforts to try to "ground mathematics into reality" are always going to end with someone in a fetal position weeping. The problem as I see it is that numbers aren't ... uh... necessarily real. I can define 1 as two or 20 as 1 or whatever I like. They just act as placeholders for something I observe, and within more theoretical domains require some divination to even figure out what it is they are supposed to be representing.
I don't think this problem is ever going to be overcome, or at least I don't see a way for it to be overcome.
>
>For example, number theory gives no real meaning to
>numbers. It defines how to generate and manipulate
>them, but it doesn't give "one" it's property of
>"one-ness" or "two" it's "two-ness" Sets and classes
>are our most recent attempt to define cardinality
>(which is a way of saying that "the symbol we use for
>"six" refers to a set of items of which there are
>"six" of them.)
Exactly! We ended up in nearly the same place here. Again I still have problems with sort of tautologically defining the number six. Here are some items that are six is still not quite satisfactory to me in a definitional way. Oh, how I wish we could lasso some forms via my quasi-enemy Plato.
>
>The nifty way that set theory does this is by saying
>that the idea of "one" defines all sets containing
>"one" item - one dog, one person, one symbol, one
>snotball, etc. And that the idea of "two" defines a
>property of all sets containing two dogs, two cats,
>two beers, etc.
Which is certainly a nice feature.
>
>
>I agree with you. Cardinality is something ALL living
>organisms MUST deal with in order to survive. For
>example, "I want to explore this cave I just found,
>but bears live there. I saw some bears go into it a
>while ago, and just now some bears came out. Did ALL
>the bears come out? Or are there still some left
>inside?"
>
>You can see how the ability to "count" might confer a
>survival advantage.
Yes, or something very much like cardinality.
As a tangetially related thing though, I know that the Aborigine cultures never really had cardinality in the sense of direction. "Four miles" to them was all contained in a song about the place, which overlapped with pieces of everybody elses songs. I suppose when you found a new place, you added to the already existing elements of the song by composing your own little ditty.
So maybe it's possible that an alien culture could sing about the bears or something.
>>
>Well, we can make a choice. Now, let's assume a few
>things (and these are pretty weak assumptions - By
>"weak," I mean that they're not assuming much - not
>that they're probably false. An example of a "strong"
>assumption would be the assumption underlying
>Intelligent (i.e. Deceptive) Design - that a sentient,
>fairly powerful being exists who designed the inner
>workings of our cells.)
>
>So these assumptions are:
>
>1) The majority of humans "experience" (sense) the
>same things - color, light, smells, tactile
>sensations, etc. in very much the same way as the
>majority of other humans do.
I'm fairly comfortable with this assumption.
>
>2) Since most of us experience these things in the
>same way, we'll assume that they really do "exist."
>(i.e., we define our reality by consensus.)
This one makes me highly antsy. The reason it makes me antsy is because this assumption relies on an ad populum approach. This is also the one that drives me bat shit.
>
>3) We'll use our senses to observe this "Reality" and
>figure things out about it. And that's the best we
>can hope for.
And this one feels like a warm bath.
>
>So I think it's either assume these things, or pretty
>much just give up on thinking and understanding
>anything, since if there's no reality, what's the
>point?
I generally choose to postpone my thinking of the problem itself. This may all be an illusion, but illusions to brains have all the properties of realness, and so, whatever it is, I've got to deal with it. I guess you might call this the "pragmatic philosophy".
>
>OK. We should continue the discussion, "Why do we
>have math." It seems pretty interesting. But I have
>to sleep now - discuss later.....
I should be slumbering also, but I've opted to torture my body instead. I figure I'll teach it a thing or two.
>
>By the way, I should be installing a multiuser chat
>room on our lab's web server soon - could everybody
>who might be interested in participating in live
>discussions let me know? We could set up times and
>"meet:"...
Sounds good to me. Is it an open source chat? Sometimes the pings on those things are slow as hell. You hit "submit" and nothing seems to happen until five minutes later.
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