| Subject: yep - profundities abound... |
Author:
Duane
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Date Posted: 09/12/04 4:44am
In reply to:
Damoclese
's message, "Long time, no see." on 09/11/04 11:47pm
Hey everyone...
Firstly, welcome back, Don - long time no read. Good to see you're back.
Now to the meat.. er.. gristle. erm... "mechanically separated chicken parts"
>>Well days and years are nothing but place holders in a
>>counting system, as math is, that exist only in the
>>mind of man as far as we know. If aliens can count I
>>supose you have to show an alien first. See any aliens
>>around lately?
Well, days and years are tools we use to mark the passage of time. Of course they're constructs of a sentient mind, but your point is well taken, and I agree. In fact, I'd even go further and say that time's "arrow," the direction of time, is a fundamental part of our experience.
>I've fought around with this idea for quite some time,
>actually. I can't decide whether or not math is some
>fundamental constituent of reality, or just merely a
>human convenience.
Yeah - that's a doozy. My opinion is that math is a construct of the human mind. 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.
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.)
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.
>I'm inclined to think that if some
>alien civilization came along and they had something
>like math, (if it even be a requisite) that the pieces
>may be more advanced, but would contain derivations of
>what we've found.
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.
>It really is more a question of "Does reality continue
>to exist when everybody is dead?" and I find that to
>be a difficult one to answer. It seems like nature
>ought to persist indepedent of us, but if we die and
>we are the deciders of reality to each of ourselves
>(and reality is a little different to each person)
>then I'm not sure that reality does exist, or even if
>we ever had it in the first place.
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.
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.)
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.
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?
Mathematics stems from our naturally occurring concepts of cardinality (if I have three cows, would I trade them for your two cows?) And set theory tried to define reality axiomatically (and it did a pretty good job)
OK. We should continue the discussion, "Why do we have math." It seems pretty interesting. But I have to sleep now - discuss later.....
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:"...
It won't be for a few weeks (maybe a month?).
Duane
Duane
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