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From: guido wugi <wugi@brol.invalid>
Newsgroups: sci.math
Subject: Re: 4D Visualisierung
Date: Fri, 30 Aug 2024 00:01:21 +0200
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Op 29-8-2024 om 20:47 schreef Chris M. Thomasson:
> 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?

I find it obvious that we can project from 4D space into 3D space in the 
same way that we can, and do (everytime you look at a photograph;), 
project 3D into 2D. What we can't do really, is project 
3D-volumes/manifolds. But projecting surfaces and curves works just fine.

Of course the projected image isn't the "real [4D] thing". But then a 
photograph isn't the real 3D world it depicts either. Still we like 
looking at and interpreting photographs/pictures and find them 
interesting. So how for heaven's sake could one not find 4D-to-3D 
projected images equally interesting, I ask you???

So then, my renderings aren't "true 4D" objects alright, but they are 
"true 4D" projections.
Just as the ubiquitous pictures of the Tesseract are already.
But contrary to the usual 3D extractions of complex functions, like 
Re(w), Im(w) etc, which are effectively cutting off a 4th dimension.

-- 
guido wugi