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> So shifting the dimensions up we get a cube on the first 3d section of
> this "4d table leg" with each cube being curved more than the previous
> and the last 3d section is a perfect sphere.
FWIW I think an equation for such an object might be:
x^(1/w) + y^(1/w) + z^(1/w) < 1 and 0 < w <= 0.5
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On Thu, 25 Jul 2013 09:11:03 +0200, scott <sco### [at] scott com> wrote:
>> So shifting the dimensions up we get a cube on the first 3d section of
>> this "4d table leg" with each cube being curved more than the previous
>> and the last 3d section is a perfect sphere.
>
> FWIW I think an equation for such an object might be:
>
> x^(1/w) + y^(1/w) + z^(1/w) < 1 and 0 < w <= 0.5
>
Ingenius! =)
I will give that a try. I want to make an image that will depict how a 4
dimensional object can look totally different depending on where it is
sliced.
--
-Nekar Xenos-
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Now for the part that I don't understand at all:
I have heard it mentioned in scientific news that scientists have found
the fourth dimension and measured it.
How can you measure a dimension? I don't understand that. If the 4th
dimension has a "thickness", what then is the thickness of the 3rd
dimension. It makes absolutely no sense to me at all.
--
-Nekar Xenos-
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Am 25.07.2013 19:24, schrieb Nekar Xenos:
> Now for the part that I don't understand at all:
>
> I have heard it mentioned in scientific news that scientists have found
> the fourth dimension and measured it.
> How can you measure a dimension? I don't understand that. If the 4th
> dimension has a "thickness", what then is the thickness of the 3rd
> dimension. It makes absolutely no sense to me at all.
Those news actually make no sense for yet another reason: Scientists
around the world should know better than to call a newly discovered
dimension the "4th dimension", as the term is already firmly associated
with time.
But yes, there is some sense to measuring a dimension: Imagine the
universe was made up of only one spacetime dimension, and one additional
dimension curled up in a small loop; the universe would then have the
shape of a cylinder surface stretching into infinity(*) along the
spacetime dimension. But the other dimension would be finite, and could
probably be measured.
(*Alternatively, spacetime might also be finite, but on a much larger
scale, in which case we'd get a torus surface.)
String theory postulates that there are indeed - AFAIR - about half a
dozen extra dimensions, and it is suggested that they may indeed all be
curled up in this manner, with sizes roughly on the scale of sub-atomic
particles.
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>> FWIW I think an equation for such an object might be:
>>
>> x^(1/w) + y^(1/w) + z^(1/w) < 1 and 0 < w <= 0.5
>>
> Ingenius! =)
Thinking about it, there should probably be a modulus function around
x,y,z (to get the absolute value), otherwise x=-5,y=5,z=0,w=0.2 is part
of the solid (which it shouldn't be).
> I will give that a try. I want to make an image that will depict how a 4
> dimensional object can look totally different depending on where it is
> sliced.
Slicing it along one of the coordinate axes will be easy, the hard (and
more interesting) bit will be taking angled slices :-)
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On 26/07/2013 05:16 AM, clipka wrote:
> String theory postulates that there are indeed - AFAIR - about half a
> dozen extra dimensions, and it is suggested that they may indeed all be
> curled up in this manner, with sizes roughly on the scale of sub-atomic
> particles.
More fully: Some formulations of string theory suggest that the universe
has as many as 11 spatial dimensions. The obvious question is then "so
why can't I see any of them?", and the only answer anybody has come up
with is "well, maybe they're really tiny..."
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Nekar Xenos <nek### [at] gmailcom> wrote:
> I have heard it mentioned in scientific news that scientists have found
> the fourth dimension and measured it.
You are probably confusing it with something else.
--
- Warp
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On Fri, 26 Jul 2013 09:36:45 +0200, Orchid Win7 v1 <voi### [at] devnull> wrote:
> On 26/07/2013 05:16 AM, clipka wrote:
>> String theory postulates that there are indeed - AFAIR - about half a
>> dozen extra dimensions, and it is suggested that they may indeed all be
>> curled up in this manner, with sizes roughly on the scale of sub-atomic
>> particles.
>
> More fully: Some formulations of string theory suggest that the universe
> has as many as 11 spatial dimensions. The obvious question is then "so
> why can't I see any of them?", and the only answer anybody has come up
> with is "well, maybe they're really tiny..."
That one is easy. Simply because our eyes can only see in 2d. We can
perceive 3d images because of the stereoscopic effect of having 2 eyes.
I think it is possible that this universe itself may be 4d or even more
dimensions, but we can only perceive a 3d slice of it.
If a 4d being has only 2d and 3d "perceptors", how will it know that it is
4d?
--
-Nekar Xenos-
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On Fri, 26 Jul 2013 06:16:05 +0200, clipka <ano### [at] anonymousorg> wrote:
> Am 25.07.2013 19:24, schrieb Nekar Xenos:
>> Now for the part that I don't understand at all:
>>
>> I have heard it mentioned in scientific news that scientists have found
>> the fourth dimension and measured it.
>> How can you measure a dimension? I don't understand that. If the 4th
>> dimension has a "thickness", what then is the thickness of the 3rd
>> dimension. It makes absolutely no sense to me at all.
>
> Those news actually make no sense for yet another reason: Scientists
> around the world should know better than to call a newly discovered
> dimension the "4th dimension", as the term is already firmly associated
> with time.
>
> But yes, there is some sense to measuring a dimension: Imagine the
> universe was made up of only one spacetime dimension, and one additional
> dimension curled up in a small loop; the universe would then have the
> shape of a cylinder surface stretching into infinity(*) along the
> spacetime dimension. But the other dimension would be finite, and could
> probably be measured.
>
> (*Alternatively, spacetime might also be finite, but on a much larger
> scale, in which case we'd get a torus surface.)
>
> String theory postulates that there are indeed - AFAIR - about half a
> dozen extra dimensions, and it is suggested that they may indeed all be
> curled up in this manner, with sizes roughly on the scale of sub-atomic
> particles.
>
It still doesn't make sense to me ...
--
-Nekar Xenos-
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On Fri, 26 Jul 2013 12:35:45 +0200, Warp <war### [at] tagpovrayorg> wrote:
> Nekar Xenos <nek### [at] gmailcom> wrote:
>> I have heard it mentioned in scientific news that scientists have found
>> the fourth dimension and measured it.
>
> You are probably confusing it with something else.
>
It may be more dimensions and not just the 4th dimension.
--
-Nekar Xenos-
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