Plus, I Got Religion

[Golden Applesauce]

Looking back at the wiki article, the problem isn't that mathematics is a poor map of reality, it's that a given branch of mathematics that accepts certain axioms is both the map and territory of a specific kind of set theory.  The theorem as proved has nothing to do with apples and suns, but subsets of three dimensional Euclidean spaces; there is no "cutting up and reassembling," there is taking disjoint subsets of set A and finding that they are identical except for translation and rotation to the same number of subsets in set B.

And in fact you couldn't do this to an actual apple, because an actual apple is discrete - you can't separate a point of apple from the rest of it; you can only do things in molecule-sized chunks.

The "problem" is that (some of) those presenting it claim it to be a model of the reality that we live in and make all these outrageous claims about suns and apples.  Reality isn't set theory - the best mathematics can ever say is "If reality follows all the rules we named 'axioms,' then and only then does our field of mathematics apply to it."

[Triple Zero]

there are also problems with discrete numbers. they're a bit harder to point out, but limiting yourself to discrete molecule-size chunks will not solve all problems between counting in reality and counting in mathematics.

i just pointed to the banach-tarski paradox because it's such a glaring discrepancy between reality and mathematics.

also it doesnt have anything to do with Euclidian spaces, the paradox appears for any set theory in which you accept the Axiom of Choice.

however, rejecting the Axiom of Choice yields other paradoxes incongruent with reality, catching us between a rock and a hard place.

this is really tricksy mathematics, and I dont understand it completely either, but as far as I know, fundamental mathematics is now looking at an entirely different way of "counting stuff" than set theory (at least one of my friends told me so).

the details are irrelevant, just take this home with you: not even mathematics is True.

[Golden Applesauce]

Of course mathematics is True.  It just isn't Real.

[Triple Zero]

No it's not, mathematical "Truth" (aka Logic) is chuckfull of paradoxes too.

besides, even fundamental logic starts out with posing True as an axiom and defining a negation operator to obtain False.

it's not really based on anything, it's built upon a castle in the sky, defining the existence of Truth as an axiom.

[Mesozoic Mister Nigel]

That's actually one of the things I really like about math... mathematicians acknowledge it as a construct that attempts to remain consistent within its logical framework. Adherents of most other constructs refuse to acknowledge themselves as such. Philosophers, for example.

[Triple Zero]

the really good theoretical physicists do too, btw. when i ask them, but really deep down when you look at it, what is it all based on? aand the honest ones will admit "well, nothing really", but they go ahead and research it anyway!!

[Aufenthatt]

but they go ahead and research it anyway!!

Its how we invented apple sauce.

[Urraco]

but they go ahead and research it anyway!!

Its how we invented apple sauce.

This is relevant.

[Jasper]

defining the existence of Truth as an axiom.

I sense an interesting train of thought in there somewhere.

[Aufenthatt]

but they go ahead and research it anyway!!

Its how we invented apple sauce.

This is relevant.

If I remove the perception sarcasm from the above point it captures my meaning.

[Ghoura Agur]

If a thing is real for you, then that is enough. Don't let others bug you.

Mmmm....You could run into some trouble there.  Any belief outside of...reality leads to...problems.

For instance, take the fellow who believes with all his might that he can fly, and so jumps off his roof.  He of course, cannot fly, and thus faces the consequences of his actions.

Or take that delightfully crazy "Brain in a bottle" bit of philosophical quandry, where, in fact, nothing we know can really be know.  We have to take it on faith.  After all, were all of us colorblind, the one fellow who wasn't would be a madman, Red and Blue would be unknowable to us.  And inconsequential.  Bad analogy.  Goodbye.

PS
I feel that believing there is more to reality that what we percieve is key to any...spiritual religion.  Belief in more than the material.  Because, quite simply, trying to cram the heavens into your head will make it split.  So please, simply be content to slip your head into the Heavens.

What does this fellow    mean?

[Aufenthatt]

Fnord

[Honey]

Visualizing geology by National Geographic - which is more like a textbook so it encompassing a lot of geology, never really going in depth in any of them. But has lots of pretty pictures

Supercontinent by Ted Neil - which is not a science book per say, but a real fun book to read and he goes through the creation of the earth to projected return of Pangaea in 250 million years

I actually could get more which aren't coming to mind from one of my profs when I see him tomorrow

Hey & thanks again, I still have yet to take a look at these.    & I was sorry to hear you had the flu - hope you're feeling better!

Just wanted to tell you I caught the tail end of this movie The Big Kahuna & it made me think of what you said here.  I don't know how good it is but Kevin Spacey is in it & I tend to like the movies he chooses.  Well, this is the quote:

Phil Cooper: It doesn't matter whether you're selling Jesus or Buddha or civil rights or 'How to Make Money in Real Estate With No Money Down.' That doesn't make you a human being; it makes you a marketing rep. If you want to talk to somebody honestly, as a human being, ask him about his kids. Find out what his dreams are - just to find out, for no other reason. Because as soon as you lay your hands on a conversation to steer it, it's not a conversation anymore; it's a pitch. And you're not a human being; you're a marketing rep.

Like this one too:

Phil Cooper: I'm saying you've already done plenty of things to regret, you just don't know what they are. It's when you discover them, when you see the folly in something you've done, and you wish that you had it do over, but you know you can't, because it's too late. So you pick that thing up, and carry it with you to remind you that life goes on, the world will spin without you, you really don't matter in the end. Then you will gain character, because honesty will reach out from inside and tattoo itself across your face.

[The Good Reverend Roger]

That's actually one of the things I really like about math... mathematicians acknowledge it as a construct that attempts to remain consistent within its logical framework. Adherents of most other constructs refuse to acknowledge themselves as such. Philosophers, for example.

Math isn't a construct, it's a language.

[Mesozoic Mister Nigel]

That's actually one of the things I really like about math... mathematicians acknowledge it as a construct that attempts to remain consistent within its logical framework. Adherents of most other constructs refuse to acknowledge themselves as such. Philosophers, for example.

Math isn't a construct, it's a language.

Language is a construct. It's communication built around a framework of concept.