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 May 9th, 2017, 05:51 PM #2 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,838 Thanks: 653 Math Focus: Yet to find out. Relax... Keep working on your sim, but make yourself some clear objectives of what you want it to do, predict the results, and then go from there..
 May 10th, 2017, 05:22 AM #3 Member   Joined: Dec 2016 From: United States Posts: 53 Thanks: 3 Math Focus: Abstract Simulations The things I'm reaching for can only be 100% implemented in a 2.0 version. Exploring higher concepts has helped me solidify what needs to be done with a simpler version. I do have code, it works. I promise you I'm not entirely crazy. Am I just wasting my time? Maybe. The fact that I know the 4th dimension is a weird place for spheres, tells me something I should look out for when casting shadows down to the 3rd dimension. I think it's valuable to have these nuggets of information. This is the projection involving a 4-dimensional object called a dodecaplex. Image crated by Paul Nylander Last edited by InkSprite; May 10th, 2017 at 06:08 AM.
May 10th, 2017, 07:03 AM   #4
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Quote:
 Originally Posted by InkSprite The fact that I know the 4th dimension is a weird place for spheres, tells me something I should look out for when casting shadows down to the 3rd dimension.
you might enjoy a short story by Greg Bear called "Tangents".

It's about a kid that can see and to some extent interact with the 4th dimension.

 May 11th, 2017, 06:56 AM #5 Banned Camp   Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 126 Infinite dimensional point: $\displaystyle p=\lim_{n\rightarrow \infty}(x_{1},x_{2},x_{3},...,x_{n})$ Infinite dimensional line: $\displaystyle p=p_{1}+k(p_{2}-p_{1})$ Infinite dimensional plane: $\displaystyle \lim_{n\rightarrow \infty}a_{0}(p-p_{0})+a_{1}(p-p_{1})+a_{2}(p-p_{2})+...+a_{n}(p-p_{n})=0$ Infinite dimensional circle: $\displaystyle \lim_{n\rightarrow \infty}(x_{1}^{2}+x_{2}^{2}+x_{3}^{2},...,x_{n}^{2 })=r^{2}$ There is nothing mysterious about a 4-dimensional circle. It is simply a definition: $\displaystyle x_{1}^{2}+x_{2}^{2}+x_{3}^{2}+x_{4}^{2}=r^{2}$ If $\displaystyle (x_{1}, x_{2}, x_{3})$ are space coordinates and $\displaystyle x_{4}$ is time t, then it describes a spherical shell contracting from r. $\displaystyle x_{i}, k, r, a_{i}$, real
May 12th, 2017, 04:48 AM   #6
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Quote:
 Originally Posted by zylo There is nothing mysterious about a 4-dimensional circle. It is simply a $\displaystyle x_{i}, k, r, a_{i}$, real
That's not what I gathered from this link
https://plus.maths.org/content/richard-elwes

They say that they don't know how many "spheres" the 4th dimension has. It just has a question mark.
15 dimensions has 16256 spheres. 7 dimensions, 28. There's something weird about the 4th dimension I don't quite understand.
Quote:
 The realm which remains the most mysterious, even today, is 4-dimensional space. No exotic spheres have yet been found here. At the same time no-one has managed to prove that none can exist. The assertion that there are no exotic spheres in four dimensions is known as the smooth Poincaré conjecture. In case anyone has got this far and is still not sure, let me make this clear: the smooth Poincaré conjecture is not the same thing as the Poincaré conjecture! Among other differences, the Poincaré conjecture has been proved, but the smooth Poincaré conjecture remains stubbornly open today.
oh... "exotic" spheres. not regular ones.

Last edited by InkSprite; May 12th, 2017 at 04:57 AM.

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