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Geometry from Another Universe

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Re: Geometry from Another Universe

#31

Post by asxd »

echelon wrote: post #13
pavel_lishin wrote: post #10

If you're interested in this, you may be interested in Hyperbolica, which is a whole game about this concept: https://store.steampowered.com/app/1256230/Hyperbolica/ https://www.youtube.com/watch?v=EMKLeS-Uq_8

These are great! (There's also miegakure: https://www.youtube.com/watch?v=uWsBnVtl8tA ) I can't wait for these games to start being built for VR. Maybe it'll be possible to develop a sense for higher dimensionality intuitively using our senses. Maybe young mathematicians and physicists can explore higher dimensions in VR to get accustomed to it, which might help with their theorizing and explorations.

Looks like 4D toys is VR-supported: https://store.steampowered.com/app/619210/4D_Toys/

Re: Geometry from Another Universe

#32

Post by jvanderbot »

all2 wrote: post #17
ryandrake wrote: post #14

Earlier quoted context omitted.

Wow, if you’re having these dreams without the aid of substances, I envy you. The most intellectual dreams I seem to be able to come up with “unenhanced” are falling off buildings and being late to college exams while having no pants on.

My favorite are the dreams I have before a semester starts: it is the end of the semester, and I've just discovered I've forgotten about an entire class for most of the semester. Then I wake up.

I still have those dreams -- except now I know they are going to take away my degree, and thus job.

Re: Geometry from Another Universe

#33

Post by jonsen »

all2 wrote: post #17
ryandrake wrote: post #14

Earlier quoted context omitted.

Wow, if you’re having these dreams without the aid of substances, I envy you. The most intellectual dreams I seem to be able to come up with “unenhanced” are falling off buildings and being late to college exams while having no pants on.

My favorite are the dreams I have before a semester starts: it is the end of the semester, and I've just discovered I've forgotten about an entire class for most of the semester. Then I wake up.

As a student or teacher? I've had exactly this recurring dream, forgetting to teach a class. What a nightmare when they are not ready for the exam.

Re: Geometry from Another Universe

#34

Post by p1mrx »

zackmorris wrote: post #19

Does anyone know of a good visualization of a hypercube? Specifically, I'd like to be able to rotate it around various axes to see what its shadow looks like in 3D. On that note, a VR rendering might help since a 2D projection overcomplicates the shadow. It's easy to construct, just build a point, extrude the point out to make a line, extrude the line out to make a square, extrude the square out to make a cube, then…

Stella4D free demo: https://www.software3d.com/Stella.php#stella4D

Re: Geometry from Another Universe

#35

Post by mekal »

mark_l_watson wrote: post #3

I had a dream a year ago in which I was traveling at very high speed towards an edge of our universe. In the dream I entered a null space before entering the next universe in which all star systems obeyed solid state physics type laws: stars formed an outer lattice and planets in small lattices around stars. After traveling through the second universe in my dream, I then entered a third universe that was more compact…

Have you read the Three-Body Problem trilogy? There's some stuff in the third book (Death's End) that sounds a lot like your dream. Specifically the different dimensions of space. If your dream didn't come from that book, perhaps you should consider writing some science fiction!

Re: Geometry from Another Universe

#36

Post by jerf »

all2 wrote: post #17
ryandrake wrote: post #14

Earlier quoted context omitted.

Wow, if you’re having these dreams without the aid of substances, I envy you. The most intellectual dreams I seem to be able to come up with “unenhanced” are falling off buildings and being late to college exams while having no pants on.

My favorite are the dreams I have before a semester starts: it is the end of the semester, and I've just discovered I've forgotten about an entire class for most of the semester. Then I wake up.

I'm in my 40s. For a good long while, my recurring school dream was that my high school discovered that I didn't actually finish correctly, and because that invalidates my college degrees (in dream logic land), I can't do my job until I go back and finish high school properly.

For some reason in the last six months to a year it has shifted to the idea that I signed up for a full semester's worth of courses, while still trying to work my full time job, and I'm flunking all of them because I keep going to work and never attending the classes or doing the homework.

Either way, coming up on nearly 20 years since I've been in any kind of school and my subconscious is still freaked out about it, one way or another.

By contrast, my subconscious appears to not give a flip about whether I'm doing my paying job correctly. Don't tell my boss.

Re: Geometry from Another Universe

#37

Post by jerf »

Jeff_Brown wrote: post #11
melissalobos wrote: post #7

Earlier quoted context omitted.

> everything was happening in lower dimensional manifolds curving through that space where “all the action was.” I feel like this would have to be true in a very high dimensional space, since an infinite dimensional orange is all skin. > systems obeyed solid state physics type laws: stars formed an outer lattice and planets in small lattices around stars. This sounds really fun, could you try explaining a bit more ab…

> an infinite dimensional orange is all skin Huh?

As you increase the dimensionality of a sphere, an ever-increasing proportion of the sphere is within epsilon of the surface.

This 3Blue1Brown video addresses enough related stuff that the rest should become reasonably comprehensible: https://www.youtube.com/watch?v=zwAD6dRSVyI This particular result is tossed in as a side note around 23:25, so it's not addressed directly, but it'll help.

Re: Geometry from Another Universe

#38

Post by bckr »

mark_l_watson wrote: post #3

I had a dream a year ago in which I was traveling at very high speed towards an edge of our universe. In the dream I entered a null space before entering the next universe in which all star systems obeyed solid state physics type laws: stars formed an outer lattice and planets in small lattices around stars. After traveling through the second universe in my dream, I then entered a third universe that was more compact…

Thanks for sharing this. I love dreams like this. Flying, space travel, and alternate physics are some of the most fun. This actually makes me want to go to sleep and have a nice dream.

Does anyone know of any communities specifically for sharing awesome dreams? DreamerNews?

Re: Geometry from Another Universe

#39

Post by corysama »

zackmorris wrote: post #19

Does anyone know of a good visualization of a hypercube? Specifically, I'd like to be able to rotate it around various axes to see what its shadow looks like in 3D. On that note, a VR rendering might help since a 2D projection overcomplicates the shadow. It's easy to construct, just build a point, extrude the point out to make a line, extrude the line out to make a square, extrude the square out to make a cube, then…

https://apps.apple.com/de/app/the-fourth-dimension/id5042017...

https://www.theverge.com/2012/3/29/2912766/the-fourth-dimens...

Re: Geometry from Another Universe

#40

Post by ck45 »

all2 wrote: post #17
ryandrake wrote: post #14

Earlier quoted context omitted.

Wow, if you’re having these dreams without the aid of substances, I envy you. The most intellectual dreams I seem to be able to come up with “unenhanced” are falling off buildings and being late to college exams while having no pants on.

My favorite are the dreams I have before a semester starts: it is the end of the semester, and I've just discovered I've forgotten about an entire class for most of the semester. Then I wake up.

This is extremely common, I googled a lot about it some years ago. I have it in two versions, the first one is that I have to repeat a maths course in school, being aware about the age difference with the other students, the other one is missing a course in university and not having graduated. The latter one feels so real that in the beginning I had to remind myself about having been at the graduation ceremony :)
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