The Black Vault

by **khanster** » Sat Jan 01, 2011 3:22 am

at1with0 wrote:
But what is more "self evident" just might be what's more apparently obvious. Some people would say that X=X is more apparently obvious.

That is called major brain fog... :lol:

by **at1with0** » Sat Jan 01, 2011 3:28 am

I like taking ideas and running with them. I'm a thought stealer. Like an Illithid from D&D

by **bionic** » Sat Jan 01, 2011 3:40 am

what's apparently obvious can sometimes be nothing but illusion
Magicians come to mind.

That pic reminds me of the 'beast/god' you (via morbid angel)go on about sometimes.

I think Kahn is really onto somethign with x only being equivalent to x

no two things can take up the same space
even if they seem to..they'd be in different dimensions

by **at1with0** » Sat Jan 01, 2011 3:50 am

I'm confused. I thought khan was suggesting that it is not self-evident that X=X.

by **khanster** » Sat Jan 01, 2011 4:24 am

at1with0 wrote:I'm confused. I thought khan was suggesting that it is not self-evident that X=X.

X = X in a limited sense for abstract mathematical purposes.

But in the physical world there are two different things with another thing in between them.

IF you are looking for the isomorphism between abstract reality and physical reality then you need to search for a fractal mathematics and not see math as a game.

X is not equal to not-X

is a good start...

by **at1with0** » Sat Jan 01, 2011 4:38 am

Physical reality can be seen as a set.

by **khanster** » Sat Jan 01, 2011 4:48 am

at1with0 wrote:Physical reality can be seen as a set.

http://en.wikipedia.org/wiki/Ultimate_e ... _responses

Tegmark's response in [8] (sec VI.A.1) is to offer a new hypothesis "that only Godel-complete (fully decidable) mathematical structures have physical existence".

by **at1with0** » Sat Jan 01, 2011 4:52 am

Great, a new hypothesis!

What is unclear is how he defines 'physical'.

by **khanster** » Sat Jan 01, 2011 5:03 am

Physical reality cannot be defined as a set if set theory itself contains undefined notions... :shock:

http://planetmath.org/encyclopedia/SetTheory.html

Axiomatic set theory
I will informally list the undefined notions, the axioms, and two of the ``schemes'' of set theory, along the lines of Bourbaki's account. The axioms are closer to the von Neumann-Bernays-Gödel model than to the equivalent ZFC model. (But some of the axioms are identical to some in ZFC; see the entry ZermeloFraenkelAxioms.) The intention here is just to give an idea of the level and scope of these fundamental things.

...There are three undefined notions:

1. the relation of equality of two sets

2. the relation of membership of one set in another (xy )

3. the notion of an ordered pair, which is a set comprised from two other sets, in a specific order.

by **at1with0** » Sat Jan 01, 2011 5:14 am

Nothing can really be defined.

What is a true definition?

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