according to this article,
.
so, what are these dimensions? what is a dimension anyways?
From what I have read, these extra dimensions can be shown mathematically (whatever that means), but even the people doing the math cannot imagine what these dimensions can be, what they’re like, etc.
i just read an article i found on Google that was talking about the eighth dimension having somethin to do with empty space in an atom that enables solids to pass through each other if done in perfect timig. it said that some guy had driven some kind of car through a mountain… doesn’t sound very credible to me. if this were possible, then why don’t we fall through our beds periodically at night?
First of all, I don’t think Institute for Creation Research, the originator of the article, is a good place to learn about physics (or evolution).
That being said, the current versions of string theory (M-Theory) predict eleven dimensions. Catch it on TV:
NOVA: The Elegant Universe. Oct 28 at 8pm on PBS.
Here’s a great quote from the NOVA website:
“The kind of physics that my community engages in – trying to understand the most fundamental structure and issues for our
universe – is a birthright for all of us. For me there is a personal joy in participating in that adventure. It belongs to everybody, just like great art and great music belongs to everybody. Great science belongs to everybody.” - Dr. James Gates Jr.
Another thread got me interested in dimension theory, I read the book Flatland, suggested by a poster to that thread. I’ve come to the conclusion that “they” are full of poop, and that there only exist three or more dimensions. Not two, not one, but a minimum of three. More is ok.
Two dimensional line my butt.
A dimension is simply a limitation.
Peace,
mangeorge
The DEX and KAREN article is helpful as far as it goes, but I’m not sure it DOES go very far, and it might be a good idea to get a handle on that aspect of the thing.
“Dimension” is a word. It is an adaptation of a Greco-Latin term which I believe suggested something like “laying down a measure”–basically, the act of measuring something. By the usual process, this came to mean the thing-measured, abstractly considered. (In other words, not just the sofa-length and the car-width, but that which widths and lengths and heights have in common–the “measurable,” so to speak).
If people want to compare the shape-extent of various objects, they need a general rule specifying exactly how to “lay down the measure.” It does no good to indifferently measure various diagonals and curves on two distinct things, and then try to compare them. Therefore common sense and common practice leads to measuring things along their “lines of greatest mutual difference.” (“Lines” means “straight-lines.”)
Consider a flat surface, like a piece of floor tile. Draw a straight line across it. (We won’t worry for now about how to select which of the infinite possible directions across its surface to choose for the initial line–this is the separate problem of “orientation.”) Now the task is to find some other line on that surface, which both (a) crosses the first line, and (b) has the absolute least in common with the first line, direction-wise. (Why? Because we’re setting up parameters for reference purposes, and they are most efficient to the extent that they are as different as possible–ie, that they don’t “overlap.”)
It is quickly apparent that the line meeting these requirements will be the line that is perpendicular to the first.
The exact same rule applies in setting the measurement parameters (the “metric frame”) of a cube, or other full-figured solid. The line with the least in common with both the first AND the second line will be the line perpendicular to both. (For simplicity we let line 3 intersect 1 and 2 at the same place the latter have already intersected–it’s now a three-line junction.)
That, then, is the traditional geometrical understanding of what a dimension is: the direction taken by (one or another of the) mutually-perpendicular (right-angled) measuring lines.
Imagination tends to extend this concept into a sort of half-seen “picture” of real space being chock-full of all these lines and planes–something like the planes of fracture in a crystal. Thus, we lazily think of “space” as being “made of” the dimensions that we use in measuring it. So, reversing it, one might say that a dimension “is” simply SPACE (ie, extension) considered in terms of how many “kinds” of direction its inner nature permits.
A 1-space (“linear extent,” measured as “length”) allows only one kind of direction (“this way, or that”–think right/left) with two modes or polarities (the aforesaid right vs. left).
A 2-space (“areal/planar extent,” measured as “length, and breadth”) allows two kinds of direction (“right/left” AND “foreward/back”) each with their two modes.
A 3-space (“voluminal extent,” measured as “length, and breadth, and height”) allows three kinds of direction (adding “up/down” to the preceding ones).
These are the traditional dimensions.
It occurred to thinkers that there is another measurable with two “modes” that is ever-present in real objects and thus might be treated as yet another dimension, namely the (hypothetical) direction along which perduration occurs–which we call “time”. This was given the same sort of right-angle treatment (you can do it mathematically, though you can’t “see” it as a separate angle). Einstein and many others found that if you take this idea seriously it leads to further ideas that prove to be useful.
Here we pause a bit. Note that the first three dimensions have a kind of reality in human experience that the proposed fourth dimension lacks. We actually see and touch and move-around in those dimensions. The objects with which we deal allow us to explore them along those dimensions. But the fourth dimension, Time, is quite different. And not MERELY because we “can’t move in it freely” or “only move one way.” We simply don’t “see” the durational extent of an object as an aspect of its shape. We sense time-lengths imperfectly and indirectly; and most of what we say about dimension four is derived through abstraction.
With me so far?
Higher dimensions are more of the same. They are even LESS sensed and MORE abstracted than Time-as-a-dimension. From a certain point of view and a certain logic, a fifth dimension ought to measure the “distance” between “alternate-history worlds”; the sixth, something to do with different ways of ARRANGING those alternate-history worlds with respect to one another. If those analogies are valid, I can sort of “get” dimension 5, but dimension 6 means just about nothing to me beyond some vague words. And those yet higher are even worse.
But!–some scientists believe that certain observed physical processes can be most simply explained if we treat them as if parts or phases of them “move” along those ultra-high directions. Whether those dimensions are “really real” or just convenient crutches for calculation is not presently known.
A few final notes from earlier explorers:
Superman’s impish adversary, Mr. Myxyzptlk, hails from a world separated from ours by a fifth-dimensional distance.
Rod Serling taught that there is a fifth dimension “not of sight or sound, but of mind.”
Will Robinson encountered some “invaders from the sixth dimension”–basically free-floating heads in a space vehicle larger on the inside than the outside.
Anyone know of references in fiction to higher-yet dimensions?
We live in a universe of three spatial dimensions. There cannot be more spatial dimensions because things as basic as orbits become unstable in more than three spatial dimensions. That’s why the six other dimensions needed to make M-theory work are usually described as being rolled up into balls too small to make their presence felt on anything larger than basic forces.
The Nova Elegant Universe series is based on the book The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory, by Brian Greene.
It is simply the best book on the subject for the non-scientist, taking you from the very basics to concepts that will spin your head right off your body in clear, yes, elegant, prose and understanble metaphors and explanations.
The Fifth Dimensions are up, up, and away.
I’m sceptical about pop-science books. The last one I looked at had Umberto Eco opining about ‘the death of ethics’ because some Italian girls were idolising fashion models. I don’t think the study of morality is going to give up the ghost just because some kids like clothes, but anyway.
Just a minor point, but maybe that idea about the fifth dimension being the ‘distance’ between alternate worlds is going to commit you (or whoever’s suggesting it) to a rather problematic ontology. I used to think intuitively that possibility was where the fifth dimension was at, but it turns out that there are least just as good arguments for postulating that possible worlds are either abstract constructs or combinatorial creations made out of real worldly objects. (Like a the ways you can restitch a patchwork quilt or something.) Well, there are problems with all three accounts, but if possible worlds (or less pseudo-science: alternative states of affairs) don’t exist in the typical sense then I’d imagine it to be quite awkward trying to get even a theoretical distance between them over a fifth dimension.
But nonetheless, possibility of some description seems to be as likely candidate as anything recognisable for #5. If we’re going to go with that, I am flippantly inclined to think that doxastic possibility has a separate realm from logical possibility since you can perfectly well have incoherent belief sets being true for your doxastic alternatives in #6 but you certainly can’t have that for the logical alternatives swanning around in #5. (That is, I suppose there’s sort of this dimension of unreal variance around the possible worlds.) But I don’t have a clue, really, about what #6 is and certainly no idea about the others. I haven’t really thought about it (not that it would help).
But I bet that when someone realises what’s going on with these dimensions, it’ll turn out that we’ve been using them all in our day to day lives since the first caveman clobbered his dinner.
Literary Reference: There was a Sonic the Hedgehog novel called ‘Sonic in the Fifth Dimension’. Or was it fourth? It was basically some never ending metal building outside of reality which was full of ineffecient police that goverened time. They had to fight all the possible beings that didn’t really exist but wanted to. The unreal beings were determined to destroy time if they weren’t allowed to exist. Let’s quantify over those non-actuals, baby.
Oh, I think Richard Feynman (or someone else) once said he could conceive of a five dimensional shape. Dubious and handily unverifiable claim, but maybe he’s special like that.
-James
gypsymoth3,
Are you talking about Buckaroo Banzai?
The first point is that you shouldn’t try to figure out which dimension is which number. Even in the familiar three dimensions, this breaks down: Is length the first dimension, or is width? You can perfectly consistently say that, of the 10+1 dimensions of M theory, length, witdth, and height are the seventh, third, and tenth, respectively (or any other choice of numbers you want).
The second point is that the “extra” dimensions of string theory are hypothesized to be ordinary spatial dimensions, just on a scale too small to detect (or possibly just too small to detect by any means other than gravity). In this case, they’re most assuredly not the dimension which separates alternate universes (if that phrase even has any meaning at all, which is debateable), nor are they likely to be new interpretations of anything we’re familiar with.
Point the third, is that you can have whatever dimensions you like, in a more mathematical sense. I can, for instance, describe a single particle moving at constant speed by six numbers, for its x, y, and z position at some time, and the x, y, and z components of its velocity. I can then say that the set of all such particles occupy a six dimensional space, with the components of position and velocity being the dimensions (this is generally called phase space). Phase space also illustrates the point that a space need not be “metric”: You can’t say how “far apart” two points are in phase space. And in some spaces, you can’t even say how far apart the components of a point are.
As for Feynman’s claim, it’s easy to conceive of a shape in an arbitrary-dimesional space, but it’s another matter entirely to visualize one. But I can easily visualize a four-dimensional object, and in moments of extreme lucidity, I can occasionally get a “glimpse” of a five-dimensional one, so I wouldn’t be surprised to hear that Feynman could routinely do five.
Just a couple things:
The “no higher spatial dimensions because it would make orbits unstable” objection requires a further assumption that the higher dimensions do not resist entry. Being itty-bitty is one way to resist entry, but does not exhaust the possibility.
I too do not believe in sci-fi’s “alternate history parallel worlds” model. But the spread of possibilities fanning out around a particular point-event (OK, smudge-event) need not be presumed to link up with other such spreads to constitute a coherent “world.” Nevertheless, one could conceive the fifth dimension as the direction along which said spread is extended (and leave out the “worlds” bit).
no the assumption is reasonable as proposing an extra force is a far bigger assumption.
Not Sci-Fi, the many-worlds theory was proposed by the physicist Hugh Everett and is mathematically correct, the arguments against it are ontological.
The many-worlds interpretation of quantum mechanics postulates the creation of new universes, not new dimensions.
I’m afraid I find the notion that alternate worlds or even possibilities spreading out along a fifth dimension to be lacking in any physical meaning I can understand.
And the original statement:
sounds more like something out of a R. L. Fanthorpe novel than anything remotely resembling math or physics.
Imagining higher-dimensional shapes isn’t that difficult.
4D is pretty easy. 5D is a lot harder, but even I can manage some basic geometry.
The 8th Dimension is sort of an interdimentional prison. Rocky. possibly electrically filled, and contains several forms of living matter (including exiled beings from other planets). An experiment was conducted in the in the desert in Texas some time ago to try to enter this 8th dimension. Using a device dubbed the “Oscillation Overthruster” which was first developed at Princeton University in the 1930s, the so-called “Jet Car” passed through the mountain in Texas and even returned with a sample of some form of 8th Dimension life. The experiment was performed and overseen by the Banzai Institute for Biomedical Engineering and Strategic Information in conjunction with the United States Department of Defense.
Further information (including a texual account of the experiment, as well as information regarding the docu-drama) can be found at: http://www.banzai-institute.com
<g> War in the 8th Dimension, indeed.
Does anyone mind if I do the lower-dimensional analogies thing?
Imagine something moving in a plane. You can describe it’s position with 2 numbers (eg. x and y coords), so this is a 2d world. (simplification alert)
Now imagine something moving on a sphere. It’s 2d again, (eg. lat. and long.) but it’s different - for instance, you can go all the way round and come back to where you started, and the angles in a triangle don’t add up to 180. However, locally, it looks like the first example.
According to General Relativity our universe is 3d, but not ‘flat’.
Now imagine a moving on a (straight) line. This is 1d.
Now imagine moving on the surface of a wire! This is 2d (x=distance along, theta=angle round). However it has a lot in common with the line. For instance, you are almost certain to bump into someone if you’re at the same x. Theta is a hidden sort of dimension.
String theorists postulate 4 ‘big’ dimensions (3 space and 1 time) and several more Theta-like ‘small’ ones. We only see 4, the same way on the wire only x was really noticable. They assure us this makes more sense mathematically.
MC MASTER:
“…1) no the assumption is reasonable as proposing an extra force is a far bigger assumption…”
I didn’t say it WASN’T reasonable; just noting that mini-curls are not the only possible answer.
Hmmm. I agree that there are non-SciFi proponents of “many worlds.” To Everett (and Hugh Wheeler?) I would add the philosopher David Lewis. I don’t know what to make of the statement that Everett’s theory is “mathematically correct” or that the arguments against it are “ontological.” Far as I’m concerned, the arguments against are (a) logico-semantic, a la Putnam, and (b) moral/religious (or perhaps ethico-religious).
Incidentally, IMHO, the very first story to deal with “alternate histories” was Dickens’ “Christmas Carol.”
It tell’s us something though about he nature of these higher dimensions, i.e. that they must be radically different from the normal three spatial dimensions.
By mathematically correct, I mean is that it doesn’t conflict with the mathematics of QM and by ontological, I mean the same as you when you say “logico-semantic”.