Re: 4D Visualisierung

On 8/29/2024 1:15 PM, FromTheRafters wrote:

Chris M. Thomasson submitted this idea :

On 8/28/2024 12:55 PM, guido wugi wrote:

Op 28-8-2024 om 21:49 schreef Chris M. Thomasson:

On 8/28/2024 12:38 PM, Chris M. Thomasson wrote:

On 8/28/2024 12:30 PM, guido wugi wrote:

Hallo,

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Actually, it's impossible to visualize a true tesseract in 3d space?
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A question I have is where do I plot a 4d point, say:
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(0, 0, 0, 1)
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in a 3d space? Humm...

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I've been doing that for a few decades by now ;o)
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You can't just create another axis in 3d space and say its 4d because this axis exists in 3d space. Now, with some of my n-ary field work I can add a 4d point (a non-zero 4d component of a vector) to the field and see how it effects it, but I cannot actually plot a 4d point. I can just see how the 4d field point mutates the results.
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The true 4d axis is not visible... ;^)

 There is, in a way, a way to imagine it though. We can't really draw a cube on a piece of paper, but if a cube were backlit in a way which casts a shadow on the plane of paper - we must move it in time to ascertain its shape. Sometimes it looks square and sometimes a hexagon. Consider now your mental image of a cube, and imagine it being a cube in 4D, just a projected shadow the actual object, that you must see in motion to ascertain its shape.
 That having been said, mathematically it doesn't matter that we can't get a clear mental 4D image.

Fair enough. We can try to get some ideas about it, but even the shadow implies a light source. We will never get to see its full 4d beauty. Actually, sometimes I think of an alpha channel wrt transparency as being kind of like the 4'th dimension. We can see through things... Think about being able to walk in the middle of things. Say a big boulder. Well, if your 4'd component was non-zero, then you could walk into the middle of the boulder because the boulder is in the 3d and you with your non-zero 4d component is off axis. So, you can walk through walls and shit. ;^) What that too far off the rails? Sorry.
Say if your standing on Earth and went into the off axis, the 4d with a non-zero 4d component. You would be able to look down through the Earth and out into space on the other side?