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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 15:10:12 -0700
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On 8/29/2024 3:01 PM, guido wugi wrote:
> 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".

Agreed. Now, I think we can convert any volumetric image into a 
hologram, right?

> 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.
>