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The entirety of mathematics is a hologram.

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Postby at1with0 » Wed Dec 29, 2010 3:39 am

Pick the conjunction of all axioms ever to be employed. This set can be broken down into finitely many groups of axioms where two axioms/statements are in the same group if they imply each other.

Take the consequence hull (or closure) of that set of statements. (The smallest set of all consequences of those statements, say)

That is all of mathematics.

Thus, mathematics is a hologram.
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Postby Tairaa » Wed Dec 29, 2010 1:50 pm

Is that break-down-able into more simple terms? :P
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Postby at1with0 » Wed Dec 29, 2010 3:14 pm

The axioms math is based on generates all of math.

The axioms are akin to the film and the "all of math" is like the image, in a hologram.

Or, at least, there is some self-similarity like a fractal.

Could be wrong though. It's happened before numerous times! :P
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Postby at1with0 » Wed Dec 29, 2010 3:24 pm

by self-similar, I mean like an image that contains a smaller part of itself and that smaller part is the whole image.

http://en.wikipedia.org/wiki/Self-similarity

Image

Image

Image
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Postby at1with0 » Wed Dec 29, 2010 3:26 pm

If reality is mathematical, then it too is akin to a hologram.
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Postby Tairaa » Wed Dec 29, 2010 3:31 pm

Trippy.

Math isn't my thing, but my graphics program uses it a LOT.
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Postby at1with0 » Wed Dec 29, 2010 3:36 pm

Which program, one traveler to another?
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Postby Tairaa » Wed Dec 29, 2010 3:40 pm

3ds max.


Tinkering away right now as a matter of fact. Can you tell my why my Boolean commands don't work so hot on complex objects, even if they match one another in general complexity both overall and local?

I've worked ways around this problem (which is probably a problem with the operator) of course, but knowing why... WHY!?! Would be nice. :P
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Postby at1with0 » Wed Dec 29, 2010 3:50 pm

Tairaa wrote:3ds max.


Tinkering away right now as a matter of fact. Can you tell my why my Boolean commands don't work so hot on complex objects, even if they match one another in general complexity both overall and local?

I've worked ways around this problem (which is probably a problem with the operator) of course, but knowing why... WHY!?! Would be nice. :P


My guess would be that a subtle exclusion (like NAND or XOR) is there when it shouldn't be or not there when it should be. Something in the complex object is not getting caught correctly by the boolean operator so I would think that the only way to fix it is to take a look at which boolean expression you're using and what is hanging it up in the complex object, though I'm sure that would be time consuming. Exactly how to do that would take knowledge of your program environment, your code, and the complex object.

It's probably similar to how on this board you used to not be able to write union without your post getting screwed up and eaten. Some clause in the boolean expression wasn't tweaked perfectly and union is a common phrase (at least in meaning) in programming.
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Postby Tairaa » Wed Dec 29, 2010 4:09 pm

I would think that the only way to fix it is to take a look at which boolean expression you're using and what is hanging it up in the complex object, though I'm sure that would be time consuming.


I used to do this, and it works. I perform the boolean and it doesn't work properly, I take note of the problem area, undo the boolean, and tweak the area(s) prior to the boolean and that typically works after some effort. Alas, I have much more efficient methods now. Procedurally speaking I like to keep my boolean commands to a minimum after I add complexity to my objects. Instead I find it easier, for unions of complex objects anyway, to simply attach and weld manually. Works exactly how I want it every time. :P

Do you use a graphics program?
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