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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: 4D Visualisierung
Date: Sun, 15 Sep 2024 12:28:04 -0700
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On 9/15/2024 2:11 AM, guido wugi wrote:
> Op 15-9-2024 om 02:17 schreef Chris M. Thomasson:
>> On 9/14/2024 5:10 PM, Chris M. Thomasson wrote:
>>> On 8/28/2024 12:30 PM, guido wugi wrote:
>>>> Hallo,
>>> [...]
>>>
>>> This is your artificial 4d axis, right?
>>>
>>> https://i.ibb.co/rMqqp9k/image.png
> 
> Exactly. I called them (x,y,z,v) here, but (x,y,u,v) for complex 
> functions. The positions are initiated by the six angle controls for 
> coordinate plane rotations (or four angle controls for "spherical" 
> coordinate rotations).

Okay. I see. Thanks.


>> To be quite honest, 4d kind of freaks me out a little bit... If 3d is 
>> comprised of infinite 2d planes, then 4d is comprised of infinite 3d 
>> planes...
> 
> Yes, 3D-manifolds aren't much indicated for visualisation of course.
> It's all about *surfaces and edges*:
> Pure surfaces and their parameter curves as for complex functions.
> Or border edges of border surfaces, of (border) volumes of 4D-volumes, 
> as for the tesseract.
> If you want 3D-volumes in 4D, that's another pair of sleeves (as we say 
> in Dutch:-).

Yeah. That's an interesting one for sure. So, a 3d volume would be one 
3d plane out of the infinity of them in the 4'th dimension? Humm...

Btw, I have created a lot of 3d volumes. Even in DICOM format. They are 
all good candidates for holograms... :^)

Check these out if you can get to the link:

https://www.facebook.com/share/p/n2nMhW5G2PhRzyfx

They can all be 3d printed. Humm... Sometimes I think that a 3d 
"observer" would only be able to see 2d. As in a 3d scene projected onto 
a 2d plane with lights and shadows, ect... However, a 4d observer would 
be able to see in pure 3d. Make any sense? Thanks.