What is the Fourth Dimension? (1884)
en.wikisource.org
en.wikisource.org
Technically speaking, we're talking about four dimensional space. It doesn't really make sense to call such a space "The Fourth Dimension", any more than real life space is "The Third Dimension", or a tabletop is "The Second Dimension". This sometimes trips people up into arguing over whether The Fourth Dimension "is" time, or whatever. For that matter, maybe the first dimension is time, and the second, third, and fourth dimensions are space. These things aren't ordered, and in fact you can't really distinguish between the three familiar spatial dimensions: imagine trying to point along dimension one, whatever that means.
The familiar three-dimensional space as we know it is three dimensional because you can put three straight lines to meet at right angles to each other, and no more. And you can label those lines x, y, and z if you like and pick their orientation. Four dimensional space allows you to cram another in. Two dimensional space only allows two, and one dimensional space is just a single line.
Similarly, if we were able to escape 3-space by moving into a 4th spatial dimension, what would you call it? If this hypothetical 4-space is Euclidean, then it contains exactly one dimension that is perpendicular to our familiar 3-space, so we would be perfectly justified in calling it The Fourth Dimension.
Hypothetically, if there are other (infinite) 3-spaces embedded in our 4D metaverse, then we either intersect them (which would cause all sorts of problems), or they are parallel and agree with our definition of The Fourth Dimension.
This would make the ana/kata vectors pointing outwards away from the universe where I am and the ana/kata vectors where you are not line up, and there wouldn't be any way to decide which ana/kata vector is the special one, even between different points inside our universe.
But really, my objection is mostly that "The Fourth Dimension" makes it sound like a "Dimension" is a kind of place, which is confusing.
However, we also talk about "curvature" of space-time, and people's intuitive first understanding of that is that space-time somehow gets bent from the perspective of a higher number of dimensions.
Curvature is very badly explained in physics, starting from the highly misleading rubber sheet analogy.
If you want more pet peeves for your collection, try every explanation of gravity that shows rubber sheets, and (for advanced peeving) rubber sheet diagrams of Schwarzschild black holes that put the event horizon partway down the well, instead of where the coördinate singularity actually places it (which is infinitely far down at a finite radius).
You can visualize (a static snapshot of) a 1-dimensional compression wave as the flattening of a 2 dimensional sine wave.
More generally, any n-dimensional space with varying "density" can be viewed an n+1 dimensional space, where the extra dimension is the "density" dimension. Maybe a "stretch".
A lot of religious/spiritual people will say that God or the metaphysical realm (some people agree, some disagree...just like certain ideas in physics) is where many higher dimensions can be found. Say what you want, but people's incorrect models of reality having more influence than "reality itself" isn't nothing (if it kills people, it's at least something[1]). Besides, almost everyone complains about it, they just don't consider it (thus it is not) dimensional, it's "just reality", kind of like how a lot of phenomena now understood due to science were(!) formerly "just reality".
Weirdly enough, there are big distinctions between three and four dimensions when it comes to geometry and topology. For example: “Four is the only dimension n for which R^n can have an exotic smooth structure. R^4 has an uncountable number of exotic smooth structures; see exotic R^4.” [0]
It turns out that having four dimensions really is magically different from having any other finite number.
[0] https://en.wikipedia.org/wiki/4-manifold#Special_phenomena_i...
Or in other words: People don't think it be like it is, but it do.
http://i0.kym-cdn.com/entries/icons/original/000/012/059/the...
There is also something mystical here (the "nothing"):
> there's nothing inherently mystical about...
What they may disagree on is which the third dimension is. But, so what? subjectivity isn't wrong. You can make the same argument to say that "right" and "left" don't exist because they are subjective.
It was even wrong by 1884 standards, although one could excuse a treatment of it at the novice level from explaining that not all subspaces of 4-dimensional spaces are necessarily parallel.
I have 4 children. You've met Amir, Carrie, and Dan. Benji is the 4th child you haven't met yet..
If I’m reading the first paragraph of Wikipedia right (surely an airtight source for a pedantic argument about advanced mathematics!) “dimensionality” is an adjective describing a space (a set?), so saying that we moved to “the fourth dimension” is about as meaningful as saying we moved to “The Euclidean” or “the big”. Rather than “a euclidean space” or “a big space”.
That said you’re colloquially absolutely correct, of course. If I was giving advice to fiction writers or journalists I’d definitely endorse your common-sense argument.
if we were able to escape 3-space by moving into a 4th spatial dimension
It makes a lot more sense to refer to time as "the fourth dimension" than to refer to all three spatial dimensions together as "the third dimension." Time is indeed one of the four dimensions that we're discussing here!
Of course you can quibble that the four dimensions are not in some fixed order, but in this context we're clearly referring to time as the fourth dimension because it's the one being introduced as an addition to the other three.
Further, dimensions being relative vs absolute makes more sense. In absolute sense, time is its own dimension T & point line cube are L, L^2 & L^3. A 3D object, a cube, has 2D object, plane, as its boundary & 1D object, lines, as its dimensional denotion. A square has 1D object as its boundary & n-2=0D objects, points, as its dimensions, relatively speaking. This is important because of the number of eyes? So basically, those 2D hypothetical characters in your physics are 1-eyed creatures, lol.
To continue in the spirit of your pedantry, it’s not really important that the lines meet at right angles; to say that space is three dimensional is just to say that a point in space can be uniquely expressed by specifying three numbers: the ‘coordinates’ of the point. What you say is true, but dimensionality in general doesn’t require the notion of ‘angle’ to make sense.
In vector space/linear algebra terms it’s to say that we live in three dimensional space because 3 is the size of a maximal linearly independent set of vectors, or alternatively the size of a minimal spanning set or vectors. They need not be orthogonal, but orthogonality does imply linear independence (it’s stronger).
"Right angle" isn't any kind of angle, it's the angle that means "perpendicular" . You don't necessarily need any other angles besides 0 (parallel) and right (perpendicular) in a system.
Well, yes. In a totally general vector space (in the mathematical sense of a vector space over a field; it’s the same notion as used in physics but perhaps more general) there’s no such thing as ‘perpendicular’ (aka ‘orthogonal’) — you need an inner product space for that. Of course, (at least in finite dimensions) you can always define such an inner product and you can certainly create orthogonal bases (see: Gram-Schmidt process), but my point was that the notion of dimension doesn’t require it to make sense. Indeed it’s not part of the usual definition; we only need to be able to talk about sets of vectors and their spans.
If I take a 1D space, I just need an orthogonal vector to find a 2D space (the second dimension).
If I take a 2D space, same...(3rd dimension).
So if I take a 3D space...? Needs a 4th vector (4th dimension) to find a 4 dimensional space?
?_? (wut?) is the pedantry really accurate here or is it sarcasm or should I go sleep..
Our 3D space uses all 3 dimensions interchangeably. It makes sense to talk about "the" 3 dimensions of space.
If you look at 3D + time, time acts differently than the other 3D.
- we only move through time in 1 direction, at a rate of pretty much 1 second per second.
- things break more easily than they go back together (ex. shattering a glass)
So time doesn't fit in with the other dimensions. Or does it? Einstein crammed it in there, and proved that time would be the same except we're being constantly pulled in the timewards direction by a really heavy object that we can't see. Or something like that.
I actually don't know what this means. You can certainly distinguish between the three spatial dimensions. Pointing along dimension one is irrelevant. Once you point in a direction, you can define the others given an orientation, and there are only two unique orientations on a three dimensional manifold.
A third party has no way to know whose choice of "1" is better for any reason related to the space itself, only by reference to some preferred object in the space, like the direction my pencil is pointing right now. Space itself has no such preferred object or direction.
I don't understand the point. What is the supposed consequence of that? As far as I can tell, it's an empty statement.
And as I said, there are only two orientations in three dimensions. For an orientation, which is an equivalence class of ordered bases, the order actually does matter. You can call them whatever you want, but once you've called them something, their order matters, which was my original retort.
Right and different "local cultures" in Flatland call them different things, so the order matters.
Orientation is a red herring. The same issue appears in 2-D manifolds inhabited by 1-D sub manifolds that one day "discover" the "other" dimension.
It does make sense to speak about a dimension. Say that some creatures in 2D space are ganging up from all sides on a creature which has access to 3D. As they close in, that creature can evade them by "disappearing into the third dimension". What it means is that it moves in such a way that its motion has a component that is orthogonal to the 2D plane, and only that component is relevant to the success of its escape. In the coordinate system in which that 2D plane makes up the first two dimensions, the orthogonal axis is "the third dimension".
What is the Fourth Dimension? (1884) - https://news.ycombinator.com/item?id=27329211 - May 2021 (45 comments)
He also wrote a book called "The 4th dimension" which explores the concept historically and in various ways.
What dimension is thought in?
I propose that thought is the fourth dimension and we are the shadows of our thoughts.
Shadows behave really differently to real objects. They disappear into nothing, they can move faster than light, they can fully overlap each other and then separate again.
Here's a Vsauce video about it:
Not only shadows can move faster than light. Any projection can. Take a laser pointer and aim for the moon, then flick your wrist back and forth. The point appears to move faster than light across the surface of the moon. The photons still travel in a straight line, at the speed of light; but you are sending new photons in a different direction. There really is no single photon actually moving across the surface of the moon; it is merely an image.
Even when an real object is moving, there isn't any single photon moving along with it that enables you to see it move.
Imagine an enormous black-body plane appears out of nowhere twenty light-seconds from the Sun, large enough to blot it out completely from Earth.
We would see that shadow eight minutes later.
If a planet orbits in, say, a day, its shadow will make a full circuit of the Dyson sphere in a day. Make the circumference of the Dyson sphere larger than a light-day, and now the shadow is "moving" faster than light.
What you're saying is like saying that vision is faster than light, because I can look at Sirius, and then look at Aldebaran a second later.
Nothing to stop others discussing the alternatives.
This is Euclidian geometry, much older and more 'accepted'.
I'm going to have to plead ignorance on this. Which will likely not surprise you.
I'll have more than the cursory read through the article in an attempt to educate myself.