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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: 4D Visualisierung
Date: Thu, 29 Aug 2024 11:47:34 -0700
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On 8/29/2024 7:56 AM, guido wugi wrote:
> Op 29-8-2024 om 00:31 schreef FromTheRafters:
>> guido wugi explained :
>>> 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,
>>>>> [...]
>>>>>
>>>>> Actually, it's impossible to visualize a true tesseract in 3d space?
>>>>>
>>>>
>>>> A question I have is where do I plot a 4d point, say:
>>>>
>>>> (0, 0, 0, 1)
>>>>
>>>> in a 3d space? Humm...
>>>
>>> How do you plot a photo of a 3D scene?
>>
>> Oh, now you're projecting. :)
>>
>> Sorry, couldn't help myself. In another group they all think that they 
>> are psychologists.
> 
> Most "3D" renderings of math objects are done in 2D, whether on paper or 
> on screen.
> As for surfaces and curves, which is what we do, there is no difference 
> in rendering 3D or 4D ones. The main problem is having a coherent 
> coordinate projection base (conserving spherical rotation symmetry). 
> Which I've had to resolve the last couple of weeks :)
> 

I don't think you can truly project a _true_ 4d object into a 3d space. 
We can get some insights, but the projection does not really represent 
the 100% true 4d object... It does not capture all of the information? 
Actually, this kid did an interesting explanation, well at least to me: :^)

https://youtu.be/eGguwYPC32I

What do you think?