/sci/ - Science & Math

>>3155120
http://www.youtube.com/watch?v=UnURElCzGc0

Sagan.

>>3155126
I've already seen that, I'm more interested in the higher ones.

Am I the only one reminded of timecube when I look at OP's image?

>>3155150
It's Internet pseudoscience, but there's a whole lot of Internet pseudoscience that is not Time Cube.

so that's it? No one is interested in discussing what the higher dimensions are like?

>>3155133
It's the same concept. You just add more directions perpendicular to the ones you already have.

Degrees of freedom. The ones in most superstring theory are compactified and assumed to be scaled down to the point they are not observable.

I basically think of them as being extra local information at every point in the observable universe that can only be seen when it influences the main 4.

I also happen to think it's bullshit cheating and that superstring theory isn't science.

>>3155133
Sagan goes on about flatland for six and a half minutes, but that's just a primer for the explanation of 4D he gives afterwards. It really is the most elegant explanation ever.

>>3155198
OP here. I've heard the 4th dimension is time, then I've heard it isn't. Anyone care to explain the truth?

>>3155156
eh? They're like our dimensions, except they're all tiny n shit

>>3155205
Time is just a way to represent the 4th dimension since we can't visualize it. You can also represent the 3rd dimension as time when you are working in the second dimension.

>>3155205
Time is one of the four dimensions of spacetime in special and general relativity. Now there is a difference between spacelike and timelike dimensions. Which is not to say that time is not geometrical in nature; it is. But there are some differences between it and the spatial dimensions.

>>3155225
That's the idea... they pretty much assumed the extra dimensions because they needed them to get the math to work out and then spent ten years getting around the fact that we don't see 7 extra dimensions.

>>3155205
Time is a temporal dimension, not a spatial dimension. When people talk about shapes like hypercubes they are talking about shapes that can exist in four spatial dimensions. Time is called the fourth dimension because of spacetime, which contains both spatial and temporal dimensions.

>>3155259
OP here
Brain = fucked

>>3155269
The technical difference between a timelike and spacelike dimension is that they enter into the distance formula with the opposite sign:

ds^2 = dx^2 + dy^2 + dz^2 - c^2 dt^2

>>3155275
Formulas not helping
I just don't get how a dimension can NOT be spatial... For that matter, how many temporal dimensions are there? And which temporal dimension are we in?!

>>3155247
OP needs to realize that the whole 'time as a dimension' concept requires understanding higher-dimensional space as well as understanding *non-Euclidean* space. I can visualize n-dimensional geometry in Euclidean space in some abridged cognitive way (slices, degrees of freedom, perpendicular directions, etc.) and I can even understand curvature and manifolds, but Lorentzian and other manifolds with negative metric signature I cannot grasp with my natural spatial intelligence yet, though I can follow along mechanistically and symbolically with local timelike/spacelike/null directions (i.e. the causal structure) despite the inability to visualize it. It makes me think that's how most people view advanced math. Anyway, I'm ranting now.

The idea that first helped me understand four-dimensional space was the thought experiment of being an omni God with the universe, from beginning to end, as an editable digital file for me to play with, plus the assumption the universe is completely Euclidean. I can step into any timeslice of the universe and exist in an infinitesimal duration of time. If I put myself in a box, I can move (say) forward in time to when the box is something else, then move out of the box, then move backward in time and I'm right where I started but magically displaced from inside the box - as if I went through it or "around" it like a ghost. I can also "point" to the future, so that most of my body exists in one timeslice sans for my arm, my elbow exists a few seconds in the future in the location my shoulder is currently occupying, and my hand in the same location a few more seconds in the future, and the tip of my finger something like a full 10 seconds after the time slice my main torso occupies.

>>3155248
Granted, some of the math is (apparently) elegant, and you know what they say about beauty and truth when it comes to mathematics...

>>3155120
>>3155120
Where are you getting this bullshit from?
The only "dimensions" used in science are the 3-space, and 1-time. All the other nonsense you listed is complete and utter bullshit!

>>3155302
derp

>>3155277
>I just don't get

You mean an underage child can't grasp advanced physics concepts? OMFG...CALL THE PRESS....THIS IS HEADLINE NEWS

"UNDERAGE FAGGOT CANNOT COMPREHEND ADVANCED PHYSICS"

>>3155277
You tell your aunt where to meet you (some position in spatial dimensions). She goes there but does not find you. You were there earlier in the day and left already. You should have also specified a position in the temporal dimension.

>>3155277
"spacelike" not "spatial"
Time is still a part of geometry, just in some formulas there's a sign change for the piece in the time direction.
There's only one timelike dimension as far as we know.

>>3155302
Not all scientists take string theory seriously, but its still something "used in science", and it indicates eleven spatial dimensions. Spatial dimensions beyond three also come up a lot in mathematics, because mathematicians don't always care if their proofs are useful or not .

itallmakessensenow.jpg

>>3155277
I'm not that anon, I'm >>3155295, but I'll try to express it as best I can. The metric that anon wrote out (<span class="math">ds^2 = dx^2 + dy^2 + dz^2 - c^2 dt^2[/spoiler]) means that the "interval" between two events increases as they are further apart in spacelike directions but actually decreases as they are further apart in timelike directions. The shortest path between two events in spacetime is defined as the path which minimizes the total "interval" accumulated on the path. This is what precipitates time dilation, length contraction, invariant speed of light under changing frame of reference, and other special relativistic effects.

Essentially, it's a geometry (the whole of spacetime that is) which has properties unlike normal all-spacelike geometries, hence it being what's called a <span class="math">pseudo[/spoiler]-Riemannian manifold: it is an object with points and intervals between them, but the intervals' mathematics is unlike what we would typically attribute to our naive notions of "space".

Remember the xy-plane? Where you had things like (2,3) and (0,4)? Each one of those was a coordinate? Well, that's two-dimensional because it has two coordinates. The xyz-space has points that look like (0,2,0) and (1,4,5) and such; this is three-dimensional because it has three coordinates.

Well, what is 4-dimensional then? It just has four coordinates. There are a lot of interpretations about this, but, mathematically, this is what it comes down to.

(For other mathfags, note that these coordinates need not even be "linearly independent"; we may consider things which are three dimensional as higher-dimensional objects by simply injecting them into higher-dimensional spaces. The lower-bound on such constructions is generally defined to be the "dimension" of the figure, or the minimal immersion dimension, or a dozen different other names.)

When people talk about four "spacial" dimensions, they mean a vector space (like the xy-plane or the xyz-space) which has FOUR linearly independent basis vectors. This is difficult to imagine and it took me many years before I was comfortable with thinking about anything in 4D. The best ways I find to do it are to think of things as a "red-shift", where an object is sitting in 3D and simply becomes whiter as it approaches negative infinity on the 4th basis vector's span, and redder as it approaches positive infinity. It plays out like a video. Similarly, you may think of it as a time-lapse where each part is a cross-section of the 4D object at time t. This is the "flatland" interpretation which is popular.

Spatial dimensions are stupid because there's no reason we wouldn't have eleventy dimensions or whatever also.

You can't even hold a 4th dimension it's as fake as music.

I also just wanted to note here that, while string theory is interesting and potentially intoxicating to you young math and science people, it is not a great field to work yourself into. Don't just take my word for it (as I have not officially worked in any main branch of string theory) but picking up any journal on string theory (or even modern physics) shows a significant amount of back-peddling and attempts to make things fit by approximations assuming all sorts of ridiculous things.

BUT, do not be put off because string theory requires a number of "unseen" dimensions; this type of thing happens frequently in science. It may seem unsettling, but sometimes adding more dimensions makes things significantly nicer. For example, when I was an undergraduate, my professor told me a "potential solution" to the double slit experiment which he didn't regard as a legitimate answer but more of a thought experiment to show us that more dimensions isn't necessarily more complicated: imagine light, instead of in a particle (or wave) form, but, rather, as a cross section of a 4-dimensional object that sort of looks like two pairs of pants sewn together at the feet. Then sometimes we will see one particle (when we are seeing a cross section of the "waist" of the pair of pants) and sometimes we will see two particles (when we are seeing a cross section of the "legs" of the pants) and these sections will obviously be related in many significant ways because of the way the pants are put together. It's a nice thought.

Understanding dimensions in general does not require truly comprehending spatial dimensions.

For example, I can imagine a cost function of cans of soda that depends on (say) number of cans, diameter of cans, height of cans, thickness of cans, and percent aluminum in the alloy to make them. Each variable in this function is a "dimension" in the mathematical sense, but is perfectly easy to understand. So we have a five-dimensional function describing a perfectly mundane (and indeed overly simplistic) scenario.

But more than three spatial dimensions is much harder to imagine. Many theories stretching back to the first part of the century have proposed extra spatial dimensions, but none have given a satisfactory way of envisioning them. Worse still, the size and shape of those dimensions varies tremendously between the theories. In some versions, most extra dimensions are not even accessible to us (except via gravity)!

Suffice it to say that there is currently no evidence that spacetime contains more than three spacelike dimensions and one timelike dimension (it is hard to imagine how one could even have more than one timelike dimension). Some theories which proposed extra dimensions have been falsified while others still remain, but any dimensions beyond the ordinary four must be so small that even our most precise nuclear measurements have so far failed to detect them.*

*Actually, if what we observe to be our entire "universe" is merely a 3-brane, then any extra dimensions could be somewhat larger, perhaps even as large as ~0.05 mm. But any larger than that and they would need to be extremely curved or we would have detected them with sub-millimeter gravitational experiments.

>>3155459

I just want to note something here, though everything you've said is correct. When you say there is no significant evidence for higher dimensionality, there is also no significant evidence to support 4-dimensionality except that it how we experience the world on a day-to-day; of course, as quantum physics as well as general relativity have shown us, what we see isn't always exactly what we get.

Also, when you say "falsified" I'm assuming you mean string theories. Unfortunately, these theories are not falsified (this is one of the huge problems with string theory) but merely "ruled out" based on current experimental evidence.

Also, there are a number of ways to imagine 4D space which are employed by those who study geometry and topology, though, as you note, they are not entirely elementary, and they cannot help one imagine more than those shapes which are made by gluing disjoint cross sections of 3-space figures together.

>>3155527
When I said "falsified" I was referring to several theories, including the likes of early Kaluza-Klein theory (which originally could not explain the weak interaction at all, now a requirement for any theory describing EM) or loop quantum gravity. Whether they were technically "falsified" I guess is a semantic question, but the important thing is that they were not (exactly) correct.