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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: 4D Visualisierung
Date: Thu, 29 Aug 2024 16:15:24 -0400
Organization: Peripheral Visions
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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,
>>>> [...]
>>>>
>>>> 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...
>> 
>> I've been doing that for a few decades by now ;o)
>> 
>
> 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.
>
> 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.