Q: How many dimensions are there? A: ?
January 22, 2018 9:05 AM   Subscribe

The History and Future of Dimensions. Science writer Margaret Wertheim has written a whirlwind essay on the idea of 'dimension' that encompasses Aristotle, Renaissance artists, Cartesian geometry, relativity, and the strange constructs of string theory.
posted by storybored (20 comments total) 42 users marked this as a favorite
 
37 & 3/7th's
posted by sammyo at 9:29 AM on January 22, 2018


Twenty. Same as in town.
posted by Naberius at 9:34 AM on January 22, 2018 [10 favorites]


This touches on a sort of pet theory of mine (which I absolutely do not have even close to the maths or physics training to properly explore, so is almost certainly hot garbage on some very obvious level). So the question of What even is a dimension comes up and there is one definition that seems to make sense to me. I'll see if I can put my thought in words.

Ok, so if you have a line (1 dimension) with a dot on it, you can't add another dot in the same place. The first dot is in the way. If you add a second dimension, so you have a plane, you can add another dot in the same place as the first just offset slightly.
So, you can describe that as an X/Y system, a third dimension (up and down) means you can now put a dot which has the same x and y coordinates, and a different z coordinate.
Again, add another dimension (which we call time). You can have a different dot in the same place in X, Y and Z so long as it's later or earlier.

So if we look at the actual universe, at the quantum level you can, in fact, have things with the same x, y and z coordinate at the same time.
If you look at an electron it can be in the same place at the same time as another electron, so long as at least one of its quantum numbers (Principal, Angular Momentum, Magnetic and Spin) is different. That, to me, starts to look very much like the same behaviour as the set of four dimensions we're used to. They're just not called dimensions (so far as I know).
posted by Just this guy, y'know at 9:53 AM on January 22, 2018 [8 favorites]




The Three-Body Problem trilogy by Cixin Liu does a great job of explaining dimensions, IMO. But like Just this guy, y'know, I'm not a physicist, so I could be completely incorrect.
posted by Lyme Drop at 10:26 AM on January 22, 2018 [1 favorite]


Great article for the layperson (me). Thanks. Also, that Sean Carroll guy has a lot of fun stuff to read ... from FPP:

Carroll writes that, from a quantum perspective, the Universe ‘evolves in a mathematical realm with more than 10(10^100) dimensions’ – that’s 10 followed by a googol of zeroes, or 10,000 trillion trillion trillion trillion trillion trillion trillion trillion zeroes. It’s hard to conceive of this almost impossibly vast number, which dwarfs into insignificance the number of particles in the known Universe. Yet every one of them is a separate dimension in a mathematical space described by quantum equations; every one a new ‘degree of freedom’ that the Universe has at its disposal.

As unbelievable and unfathomable at that concept is, based on the scope of our known universe (so far), 10(10^100) feels a lot more reasonable than 5, 10, 11, or 26.
posted by mrgrimm at 10:30 AM on January 22, 2018 [3 favorites]


Nice article, going over some familiar subject matter, but with some fresh details, like this bit about Theodor Kaluza:
Kaluza, however, was not a man easily deterred. He believed in his fifth dimension, and he believed in the power of mathematical theory, so he decided to conduct an experiment of his own. He settled on the subject of swimming. Kaluza could not swim, so he read all he could about the theory of swimming, and when he felt he’d absorbed aquatic exercise in principle, he escorted his family to the seaside and hurled himself into the waves, where lo and behold he could swim. In Kaluza’s mind, the swimming experiment upheld the validity of theory and, though he did not live to see the triumph of his beloved fifth dimension, in the 1960s string theorists resurrected the idea of higher-dimensional space.
posted by crazy_yeti at 10:43 AM on January 22, 2018 [6 favorites]


Kaluza could not swim, so he read all he could about the theory of swimming, and when he felt he’d absorbed aquatic exercise in principle, he escorted his family to the seaside and hurled himself into the waves, where lo and behold he could swim. In Kaluza’s mind, the swimming experiment upheld the validity of theory

Okay...sure, why not? You can swim after reading how to do it, therefore...higher dimensions.
posted by Naberius at 10:46 AM on January 22, 2018 [9 favorites]


Kaluza-Klein unifying gravity!
posted by Talez at 10:50 AM on January 22, 2018


Kaluza could not swim, so he read all he could about the theory of swimming, and when he felt he’d absorbed aquatic exercise in principle, he escorted his family to the seaside and hurled himself into the waves, where lo and behold he could swim. In Kaluza’s mind, the swimming experiment upheld the validity of theory and, though he did not live to see the triumph of his beloved fifth dimension

He must have not studied up enough on the theory of how to get back out of the ocean again.
posted by Atom Eyes at 11:09 AM on January 22, 2018 [5 favorites]


Centuries before Aristotle, Leucippus and Democritus had posited a theory of reality that invoked an inherently spatialised way of seeing – an ‘atomistic’ vision, whereby the material world is composed of minuscule particles (or atoms) moving through a void.-Obvious time travelers, or remnants of older civilization's information destroyed by ? What I don't get, and try not to judge me, if x=1, and y=1, and z=1, then when you add them together, why don't you get 3, as opposed to 1? Why is the answer to the equation x x x +y x y+ z x z=1; If the values of x, y, and z are each 1?
posted by Oyéah at 11:35 AM on January 22, 2018


I like the idea that the quantum fuzz gives us more dimensions because we asked for them.
posted by Annika Cicada at 12:25 PM on January 22, 2018 [1 favorite]


Just this guy, y'know: This touches on a sort of pet theory of mine ...

I have a fair bit of mathematical education, and I think your intuition is good.

Oyéah: Why is the answer to the equation x x x +y x y+ z x z=1; If the values of x, y, and z are each 1?

I think this is just a case where the author used a notation whose meaning was obvious to her and she forgot that it could use a sentence or two of explanation for others. When people write something like "a circle with a radius of 1 can be described by the equation x^2 + y^2 =1" what this really means is something like: "out of all possible pairs of points x and y, the circle of radius 1 is characterized by being equal to exactly those pairs for which the equation x^2 + y^2 = 1 is true". So in your example, since the point with x =1 and y=1 does not satisfy the equation, it does not lie on the circle of radius 1.
posted by jomato at 12:33 PM on January 22, 2018 [2 favorites]


livered through a wormhole.
posted by grumpybear69 at 2:03 PM on January 22, 2018


This message has been de
posted by grumpybear69 at 2:04 PM on January 22, 2018 [4 favorites]


Epicycles, man. Epicycles.

M-Theory is probably wrong, even if it works, because nature is elegant, and M-Theory ain't.
posted by Xyanthilous P. Harrierstick at 3:21 PM on January 22, 2018 [2 favorites]


What I don't get, and try not to judge me, if x=1, and y=1, and z=1, then when you add them together, why don't you get 3, as opposed to 1? Why is the answer to the equation x x x +y x y+ z x z=1; If the values of x, y, and z are each 1?

In two dimesions (i.e. the unit circle), x and y cannot both be 1. If X=1 then Y must equal 0. This applies in three dimensions as well.

Frankly, dealing with circular phenomena is where cartesian coordinates gets all sorts of messy. Polar coordinates make much more sense.

And really, then, the whole notion of "dimensions" starts to come to life when you start scheming of other ways to identify a point. Different models for mapping out a location in space. For example - you could define an arbitrary point in a library using either Cartesian or polar coordinates.

Or, you could define it as Floor, Row, Shelf, Book, Page, Sentence, Word, Letter.

Well, you say, why would you ? In real life, such a model might not be much use, but that multi-dimensional property is very useful for structuring a database model of that library.

And really - that's what we're doing is creating models to represent a reality. Different models will have strengths and weaknesses*, but my point is that it is the models we use that define our understanding. The 3D+t model is intuitive, but deeply limiting. Subatomic particles don't exist in a place - they're events, really - so it's sort of wrong to think about them in a 3D+t sense. So if you're having trouble grasping something, sometimes it really pays to change the way you think about it.

*"All models are wrong, some are useful"
posted by Pogo_Fuzzybutt at 4:09 PM on January 22, 2018 [3 favorites]


Yes, a dimension is just an abstraction to measure something, up, left, depth are arbitrary depending on where you're standing. But it's (better) worse, a sphere is only, take a beat, TWO dimensions! The AI/big data folks use thousands of dimensions, that just means that a bunch of messy tables (matrix's) make measuring what everyone buys the week before the holidays computable. Among all the amazing things in the world (universe) the attraction forces of magnets, gravity and the strong and weak forces are just like magic to us limited sensory animals, finding a way to measure that very stuff of the world will be very complex and then simplified when another step is well understood. I'm still betting on 37.42857142857 dimensions but it'll probably end up 42.
posted by sammyo at 4:26 PM on January 22, 2018


I think the idea of "dimensions" as abstract things is easy for some people and a leap for others. She does a good job explaining with the hypersphere notation it but I honestly think I "got it" the very first time I encountered the idea, which makes it hard to explain to others.

I was recently trying to explain to someone at work that we describe molecules in 2^32 dimensions for some problems. It's totally abstract--each dimension is assigned basically by hashing a string, they don't really mean anything chemical, and only a tiny fraction of them are non-zero. But then you do this fairly simple math in this ridiculously large space and you get all these results that make sense. I get excited by this stuff, but alas I could tell they were eager not to have to deal with any of this in detail ever.
posted by mark k at 9:36 PM on January 22, 2018 [1 favorite]




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