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

> 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?
But how the experimental evidence of it
can be found if there is _no model_ ,
no theory you can check against the
facts?
You always need the model _prior_ to
perform your experiments confirming it.

What makes you assuming, that you
can split any distance or rotation into
smaller ones?
The fact, that you can imagine it?
The experience that you can do it
with most macroscopic things?


> you're worried far too much about theory
> and not enough about real applications.

With nanotechnology arriving at the
limits of miniaturization it makes in
my eyes sense to take a look at it
not only for fun or for theoretical reasons,
but also aiming a serious impact on real
applications.

> 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.

Claudio

"Brandon J. Van Every" <mylastnameruntogether@xxxxxxxxxxxxxxxxx> schrieb im
Newsbeitrag news:ds0oe.13295$M36.7285@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> Claudio Grondi wrote:
>
> >- applying any sequence of translations
> > and rotations doesn't change the
> > geometrical shape of the set
> > of the elements if compared to some
> > initial or intermediate shape if the
> > geometrical orientation of the set
> > is the same as the orientation
> > at the initial or intermediate state.
> >
> >
> What you are asking for is impossible. You want a discrete
> representation of space. That means when you perform operations at a
> granularity smaller than the discrete quantum, you will have aliasing.
> Sorry, you cannot have your cake and eat it too. All you can do, is
> reason about what level of error is acceptable to you.
>
> Saying that you're going to accept only a finite number of
> transformations or rotations is just an accounting trick on your part.
> 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.
>
> Finite is finite. Worry about acceptably approximating the infinite. I
> know this is comp.theory, and I'm sure theorists abound, but all
> evidence to date is you're worried far too much about theory and not
> enough about real applications.
>
> --
> 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.



.

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