Re: are Real Numbers evil? The answer(?).

Claudio Grondi wrote:

Someone out there is going to want to transform their model by an amount
smaller than your available transformations or rotations. Then you will
have aliasing and error yet again.



With this above you probably arrived at
one of the vital core points in this thread.

What if _there is_ a finite number of
directions and a smallest amount of
movement which can't be decreased
any more? What if experimental
evidence of it could be found?


I don't see a point in tying 3D graphics implementation issues to the quest for the Unified Field Theorem. Such evidence isn't going to come from a computer model, it's going to come from a laboratory experiment. Such experiments are big engineering projects in and of themselves; building and using cyclotrons ain't cheap! Certain answers, you don't get from the back of an envelope.

You will get a lot more done if you stop chasing the impossible / silly and just implement some really really really precise reals. Make 'em 1K bits apiece or something, and get some time on a supercomputer. Your going to need supercomputers to handle super high precision on sizable datasets. There's probably a literature on such approaches. But you're going to have to start looking at such problems as *practical* problems of computation, not theoretical ones. You aren't going to get anything done in this kind of theoretical physics by just scribbing on paper, hoping for some perfect answer that 100,000 researchers have overlooked. Not for something as basic as numerical representation. It's a simple case of you get what you pay for. In terms of storage, in terms of computational time. Someone paid for that cyclotron too, they had to pay to play. Atom bombs cost lotsa money. Etc.

There's a disease among the theoretically inclined, of which I'm nominally a member: the aesthetic desire to find elegant, closed form solutions. Often these solutions do not exist. We want them really really badly, and we stay up late driving ourselves nuts trying to come up with them. Learn how to recognize a negative result, a theory of untheorizability. You need to develop good instincts about when it's time to give up. This is one of those times. Embrace your Inner Engineer and move on.

But how the experimental evidence of it
can be found if there is _no model_ ,
no theory you can check against the
facts?


WTF precision do you think your real physical measurement equipment has? All you need is a model that's more precise than your measuring equipment. You're under the delusion that finite math is the limiting bottleneck to such research. It isn't.

What you are asking for is impossible.


I think it's not impossible, even if maybe
not easy, especially when thinking in terms
of what many have learned at school
about 3D space and the XYZ cartesian
coordinate system.


No, impossible! You're still believing in your accounting tricks. Finite is finite! I don't care if it's finite distance, finite angles of rotation, finite numbers of axial spans....

--
Cheers,                     www.indiegamedesign.com
Brandon Van Every           Seattle, WA

20% of the world is real.
80% is gobbledygook we make up inside our own heads.
.