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(Quanta Magazine)   Mathematicians struggle to explain and understand dimensions, a weirdly undefinable notion that n-dimensional math depends on. "All of us are slaves to the prejudices of our own dimension"   (quantamagazine.org) divider line
    More: Weird, Dimension, Euclidean space, notion of dimension, two-dimensional plane, zero dimensions, three-dimensional space, n degrees of freedom, four-dimensional equivalent of a cube  
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321 clicks; posted to STEM » on 14 Sep 2021 at 12:46 PM (5 days ago)   |   Favorite    |   share:  Share on Twitter share via Email Share on Facebook



25 Comments     (+0 »)
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5 days ago  
11 dimensions makes higher math work. If a person can understand √-1 exists somewhere they should be able to grasp multiple unseen dimensions exist.
 
5 days ago  

eurotrader: 11 dimensions makes higher math work. If a person can understand √-1 exists somewhere they should be able to grasp multiple unseen dimensions exist.


Well, that's certainly an opinion.
 
5 days ago  

HugeMistake: eurotrader: 11 dimensions makes higher math work. If a person can understand √-1 exists somewhere they should be able to grasp multiple unseen dimensions exist.

Well, that's certainly an opinion.


You can use i, j, k instead of x, y, z to denote three dimensions in some kinds of math. But I'm not sure how that helps people understand traveling across the 8th dimension.
 
5 days ago  
Old joke:

An engineer and a mathematician go to a physics lecture on a proposed 9-dimensional string theory. At the end, the engineer was kind of wincing but the mathematician thought it was lovely.

"How does 9-dimensional space make sense to you?" the engineer asked.
"Oh, I just visualize it." The mathematician replied.
"How can you possibly visualize something with 9 dimensions?"
"That's easy: I just visualize n dimensions, then let n go to 9."
 
5 days ago  
The history in TFA is alright, but the clickbaity headline implies that implies that n-dimensionality is poorly understood *now*, as opposed to well understood for centuries.

Also, article fails for not mentioning Emmy Noether.
 
5 days ago  

ArkPanda: HugeMistake: eurotrader: 11 dimensions makes higher math work. If a person can understand √-1 exists somewhere they should be able to grasp multiple unseen dimensions exist.

Well, that's certainly an opinion.

You can use i, j, k instead of x, y, z to denote three dimensions in some kinds of math. But I'm not sure how that helps people understand traveling across the 8th dimension.


My friend, I'm going to set you free right now. You can use any variable names you want in EVERY kind of math.

(v1, v2, v3) is better for building up the intuition that you can just... keep going.
 
5 days ago  

Martian_Astronomer: Old joke:

An engineer and a mathematician go to a physics lecture on a proposed 9-dimensional string theory. At the end, the engineer was kind of wincing but the mathematician thought it was lovely.

"How does 9-dimensional space make sense to you?" the engineer asked.
"Oh, I just visualize it." The mathematician replied.
"How can you possibly visualize something with 9 dimensions?"
"That's easy: I just visualize n dimensions, then let n go to 9."


I hadn't thought about original string with 10 and super gravitational with 11 for some time. An engineer being able to follow was funny though.
 
5 days ago  
"We're working in 5 and 6 dimensions, so we're able to 'manifest' stuff and better understand the co-creation process. It's no big deal when we go over to the 'other side' since we're already co-creating.

You still have to wade through 3 and 4 dimensions to make your thoughts a reality, but you're starting to see past the matrix a bit."

i.imgur.comView Full Size
 
5 days ago  

Algebrat: The history in TFA is alright, but the clickbaity headline implies that implies that n-dimensionality is poorly understood *now*, as opposed to well understood for centuries.

Also, article fails for not mentioning Emmy Noether.


Username checks out, but you already knew that.
 
5 days ago  
I actually wrote a program that generates 5 dimensional fractals recently. The extra 3 dimensions are RGB. It uses an iterative approximation, so it's not an efficient algorithm or anything, but it spares me having to figure out how to convert complex plane geometries to 5-d geometries, because I'm bad at math.

But a lot of the work I do, even when it's in low dimensions, I'm often working in weird eigenvectors anyway, so visualizing weird dimensionality is a thing I'm pretty used to. The easiest thing to remember is that no matter what dimensionality your space has, points are points, two points define a line or a sphere, three points define a plane. Using those, you can slice, rotate, and traverse the higher dimensional space pretty easily.
 
5 days ago  

ArkPanda: HugeMistake: eurotrader: 11 dimensions makes higher math work. If a person can understand √-1 exists somewhere they should be able to grasp multiple unseen dimensions exist.

Well, that's certainly an opinion.

You can use i, j, k instead of x, y, z to denote three dimensions in some kinds of math. But I'm not sure how that helps people understand traveling across the 8th dimension.


Ironically, your reply is completely orthogonal to anything in the headline, my comment, or the article. If thtat was what you aiming for, well done.
 
jbc [TotalFark]
5 days ago  

Algebrat: Also, article fails for not mentioning Emmy Noether.


You misspelled Marilyn McCoo.
 
5 days ago  

jbc: Algebrat: Also, article fails for not mentioning Emmy Noether.

You misspelled Marilyn McCoo.


By building the mathematical framework that made General Relativity possible, Emmy's advancements were the true dawning of the age of Aquarius.
 
5 days ago  
If just handing out love and respect Ernest Rutherford deserves a great deal.
Fark user imageView Full Size
 
5 days ago  
Fark user imageView Full Size
 
5 days ago  
Alpha Centauri Quotes: Intro and Tech's 0-24
Youtube 24OXzIRIiMQ
 
5 days ago  
res.cloudinary.comView Full Size
 
5 days ago  

t3knomanser: I actually wrote a program that generates 5 dimensional fractals recently. The extra 3 dimensions are RGB. It uses an iterative approximation, so it's not an efficient algorithm or anything, but it spares me having to figure out how to convert complex plane geometries to 5-d geometries, because I'm bad at math.

But a lot of the work I do, even when it's in low dimensions, I'm often working in weird eigenvectors anyway, so visualizing weird dimensionality is a thing I'm pretty used to. The easiest thing to remember is that no matter what dimensionality your space has, points are points, two points define a line or a sphere, three points define a plane. Using those, you can slice, rotate, and traverse the higher dimensional space pretty easily.


Radial sphere or diametral?
 
5 days ago  

ajgeek: Radial sphere or diametral?


I mean, either, but it makes the most sense for one point to be the center, and the other to be the surface, so radial. Of course, if you've got two points, you can also make an ellipsoid.
 
5 days ago  
VR amusement ride marketers are way ahead of mathematicians then: https://theride7d.com/

But seriously, you can basically think of dimensions as any quantifiable attribute. A D&D character sheet is a six-dimensional object. (Or more, if you include the skill points and whatnot.)
 
5 days ago  
So has anyone serious ever looked at whether UAPs could be objects from a 4th spatial dimension poking through our three dimensional space?
 
5 days ago  

Raoul Eaton: So has anyone serious ever looked at whether UAPs could be objects from a 4th spatial dimension poking through our three dimensional space?


It's just Dr. Who popping in for a visit. The TARDIS has a feature that lets it project any shape it wants.
 
5 days ago  
I'm developing a 4-dimensional expansion of a field of music theory that can be used for generative purposes, so I'm getting a kick.
 
5 days ago  

austerity101: I'm developing a 4-dimensional expansion of a field of music theory that can be used for generative purposes, so I'm getting a kick.


Ah, that's funny, I was taking some of that 5-d fractal logic and attempting to use it for composition. It didn't work so great, but I applied it to a 300 dimensional analysis of english words, and got a thing that generates interesting poetry.
 
5 days ago  

Raoul Eaton: So has anyone serious ever looked at whether UAPs could be objects from a 4th spatial dimension poking through our three dimensional space?


Yes. it's one of the primary theories
 
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