Science Porn

[Alex K]

Can somebody help me think/visualize about the 4th dimension as it applies here? Or maybe, point me to some good reading. Is the 4th dimension supposed to be thought of as directional or spatial in this context?

I can follow that '3d objects cast 2d shadows, so 4d objects cast 3d shadows', but why does this come to be a cube within a cube?

I've also seen this cube sort of undulating and inverting in a few animations, what is the significance of that? Is this meant to show the passage of time as being an added dimension?

On the "3d shadow", how is a 3d shadow different from a 3d object? Can it only be "cast" in a 4 dimensional realm, whatever that may be?

Hopefully math isn't the answer here, I don't speak that language very well.

Ok I'll try:
Imagine the usual scenario in one dimension less: a pointlike light source not too far away shines on a wireframe cube. The shadow it will cast on the wall is (roughly) something like two squares of different size inside each other, with the corners connected. In the shadow, you see that in each corner, three lines lead away which in the original object are all orthogonal on each other (but in the shadow, only two are orthogonal). In this method of projection, the third dimension is represented as a scaling: objects closer to the screen are represented smaller, objects closer to the light source larger. Hence, the cube face closer to the light source corresponds to the larger of the two squares in the shadow.
So much for the ordinary scenario.

The same can be generalized to one dimension more, where now the position in the fourth dimension is translated into a scaling: a pointlike lightsource casts a shadow of a 4D cube onto a three dimensional screen which we see as space. The further an elemwnt of the 4D cube is away from this "screen" in the new fourth dimension, the larger it gets represented in our 3D "shadow". In this case, both "faces" of the 4D cube are entire 3D cubes (compare: the faces of 3D cubes are squares, ie 2D cubes), and the "face" further from the screen gets represented as the larger 3D cube, the other as the smaller. Corners are now connected to four lines each, which are all orthogonal in 4D space, but in our 3D shadow, again one is not.

Always go to the analogy in one dimension less and try to draw comparisons one can generalize.

[DramaQueen]

I didn't understand anything

P.s I failed basic physics

[Alex K]

I didn't understand anything

P.s I failed basic physics

Do you understand the first part in 3D? If not, make the experiment!

[DramaQueen]

I just needed to read it slowly multiple times. It's in English

[Exian]

Thanks Alex. I had a feeling you'd be the one to take a stab at it.

[DramaQueen]

What's the avatar of Alex K?

[SteelCurtain]

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I get lost on this website.
http://what-if.xkcd.com

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The story of the three wise men got me wondering: What if you did walk towards a star at a fixed speed? What path would you trace on the Earth? Does it converge to a fixed cycle?

If the wise men leave Jerusalem and walk toward the star Sirius, day and night, even when it’s below the horizon, this is the path they follow over the surface:



If we allow a little theological confusion and assume the wise men can walk on water, they’ll eventually wind up going in an endless circle, 30 kilometers in diameter, around the South Pole.
But let’s be a little more realistic; the wise men are hardly going to walk toward the star while it’s behind the Earth. Let’s assume that they only walk toward the star when it’s in the sky and the Sun has set.
In that case, their path actually takes them through Bethlehem:



If they don’t stop there, after a few years, they wind up orbiting Botswana:



These paths are calculated using, among other things, PyEphem, which provides tools for determining the historical positions of astronomical objects.
It’s tricky to figure out exactly what the wise men would have been following. There aren’t very many good astronomical candidates for the Star of Bethlehem (Chinese records don’t show a supernova at the right time, and none of the other obvious candidates check out) and, furthermore, there’s a lot of historical and theological debate over Jesus’s date of birth (“4 BC” seems to be the closest thing to a historical consensus date). These charts are all calculated for a somewhat arbitrary departure date from Jerusalem of December 25th, 1 AD; different departure days would lead to different paths, but the overall picture would be the same.
What if the wise men followed a planet?
Planets move against the background of stars, so the paths they produce are more complex. Here’s where the Wise Men would’ve gone if they followed Venus:



And here’s their path for Mars:



If the three wise men had a hovercar that could move at highway speed over land and water (it’s in the gnostic gospels somewhere) and decided to follow Venus, they’d take a particularly weird path:



At one point, they wind up near the North Pole in October. There, the Sun and Venus spend months near the horizon, rising and setting, nudging the Magi into a month-long spiral around the pole, a chaotic strange Magi attractor around the North Pole which some argue provides the theological foundation for the story of Santa Claus [citation needed].
Sadly, the three wise men probably weren’t following Venus. It’s one of the most familiar objects in the night sky, and as the late Sir Patrick Moore observed, if the wise men mistook it for a new star, they couldn’t have been very wise.
But maybe they’re wiser than Sir Patrick gives them credit for. After all, if you pick a random star in the sky, point at the horizon, and predict that there’s a baby about to be born in that direction, statistics—and birth rates—are on your side.

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[ComradeMeow]

Am I the only person who is moist? Please tell me I am not alone

[vorlon13]

Moist as in tentacle pron moist ??

[Alex K]

What's the avatar of Alex K?

It's a Nasa false color photo of the sun in a pretty frequency, superimposed with a picture of the waxing moon I took with an old 300 mm telephoto lens a few weeks ago. The superposition is such that the sun comes through strongest where the moon is dark. That gives it the nice plasma moon look. No scientific value, just playing around with Gimp

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Am I the only person who is moist? Please tell me I am not alone

Not yet, the high tide siren just went off outside, so it's only a matter of time.