(Referring to Sektor) That makes two people not reading, eh?
3D space is already a combination of 3 spacial dimensions, plus time (but that's a given). In terms of four spacial dimensions, that would include, length, width, height, 4D 'breadth', and time.
But on other notes, I've never gotten a proper explanation of the space-time thing of looking at space and duration as being lumped together. Most books just dish out analogies to fabric and curves and leave it at that.
Spanky, this is one of those things that requires actual work that goes beyond reading laybooks about science. In order to understand spacetime, you must understand tensors and manifolds, which requires junior-level diffeQ, vector and tensor calculus, and differential geometry. In "diffyG", you derive a general form for tensors and by the end of the course you will understand the ground form. Unfortunately, if you go for a year after that without doing it, you'll forget how to explain the ground form and be stumped in a thread while discussing your favorite subject DiffyG is the class you take if your next goal is to read Einstein.
To truly understand spacetime, you need the math. Things that are valuable require work to attain.
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I have being given A's for depleting Dragon ball Z the way it should be.
We are not talking about time. We are talking about a hypothetical (there's that word again ) fourth spatial dimension. Why is this so hard to understand?
What the hell do I have to do with this? All I said is that I find the concept of 4D Space and terms like "Surface Volume" to be mindblowing, not that I didn't understand them.
Vorlon: I think we're refering to a fourth spatial dimention, not the Fourth Dimension: Time.
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Spanky The Dolphin wrote:What the hell do I have to do with this? All I said is that I find the concept of 4D Space and terms like "Surface Volume" to be mindblowing, not that I didn't understand them.
I thought you had said you weren't able to find any books that talked abt spacetime very well, that just talked abt "fabric" and such.
I have being given A's for depleting Dragon ball Z the way it should be.
I was under the impression that in the theory of the Worldline, a 3D object which moves and changes over time can be thought of as a 4D Super-Object: every point along this line is a cross-section, a slice, representing the object "now". Theis "now" travels along the super-object along the worldline, into the future (the 4th dimension) at the speed of light.
Masochist to Sadist: "Hurt me."
Sadist to Masochist: "No."
That could be one way of looking at measurable dimensions. But there's still the separate theory that an object could have 4 spatial dimentions in addition to time. I don't see how or why it's flying over so many people's heads.
EDIT: Why the heck would it's duration travelling at a the speed of a spatial measurement? That's like saying my shirt's measurement in time is 27 centimeters. It's kinda fudging up units, if I'm reading it properly.
Well, think of it this way: suppose a particle has a life of only one second, a duration between the creation in a particle collider and the particle's ultimate decay.
During that one second of existence, it's worldline has traveled through the fourth dimension a total of 299,292,458 meters.
Masochist to Sadist: "Hurt me."
Sadist to Masochist: "No."
Perhaps it's "flying over our heads" bec there hasn't yet been a satisfactory explanation of a 4th spatial dimension; ie, address the issue of linear dependence and what "kata/ana" really mean. Or, what use a 4th spatial dim would have.
I have being given A's for depleting Dragon ball Z the way it should be.
That'd be hard to do, Malecoda. Obviously, it would be like trying to explain height to a Flatlander, when he insists 'all you need is length and width'. All we can really do is observe the representations of 3D space in 2D space, and make a step up to 4D space represented in 3D space.
Did ya know a 4D sphere passing through 3D space will appear from out of 'nowhere', expand from a size of nothing to it's maximum diameter, and then shrink back into 'nothing'. A 4d hypercube would simply 'pop' in instantly and then 'pop' out once it passed through. It's not too weird if you think about it.
And Enola, I think you'd need to explain alot more of the worldline theory in order to expalin why (when measuring an object's duration) it's using measurements for spacial dimensions when describing movement in time. As it is, I can picture the reverse situation; applying measurements for time for spacial measurements (some particles exists for a few seconds, etc.), but otherwise it sounds absurd.
Malecoda wrote:Perhaps it's "flying over our heads" bec there hasn't yet been a satisfactory explanation of a 4th spatial dimension; ie, address the issue of linear dependence and what "kata/ana" really mean. Or, what use a 4th spatial dim would have.
I don't know what you mean by "linear dependence," but I believe kata/ana was referred to as the fourth dimensional equivalents of "up/down."
See, in three dimensions, we use the following descriptors of direction:
up/down
left/right
backwards/forwards
So if you add a fourth you need another pair of descriptors: kata/ana. I like these, they sound cool.
ANd a fourth spacial dimension is essentially what the "hyperspace" in many SF universes can be explained as. Particularly in the Cultureverse, although their 4th dimension is strangely finitely (and apparently relatively closely) bounded by the energy grid.
I grasp most of this relatively easily, though the actual math would fly so far over my head I couldn't see it with a telescope, being only in calc one.
Malecoda wrote:mmm, hmm. yup. so you would write a 4-dimensional spatial equation... how? See, it's different. What I said is true. What you said is true. They're not contradictory, they're merely different. But I noticed that there are no ground forms for 4 spatial dimensions.
I understand that the various versions of the String Theory require more than ten spatial dimensions. They represent them as currently "folded" at quantum level, so they can never interact with the three macroscopical ones. Mathematically, you can have them..
There are 4 dimensions "open" that we experience. 3 spatial and 1 temporal. According to Superstring Theory, there are 6 additional spatial dimensions which have shrunk down to the Plank length and cannot be directly measured. However, they still manifest matter, energy, and the four fundamental forces.
But on other notes, I've never gotten a proper explanation of the space-time thing of looking at space and duration as being lumped together. Most books just dish out analogies to fabric and curves and leave it at that.
Simple. All macroscopic phenomenon can be measured this way: depth, length, breadth, and duration.
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It is an arbitrary enumeration. I can go to the store and buy a CD, and I'll say it was the 1st disc I had bought. Then I'd buy another one and it would be the 2nd. Then the 3rd and 4th. Could I buy a new one and say "I want this to be my -1th disc", or my "minus fourth CD", and it wouldn't make any sense. Could I have bought the 4th before the 3rd? Yes, but then they would be reversed, the 4th becoming the 3rd. It's not like there's a label in the store on every CDs enumerating them from 1 to 1000 and that I have to buy them in that order.
That's not really what I was asking in terms of comparison, but nevermind.
I've already understood the 'a duration's past and future can be measured' since I was 7 (who didn't watch The Time Machine by that age?), and re-heard it in this thread several times, but forget my question about comparing space and time together. I'll just stick to 'it's curves in fabric' and not put another thought into the comparisons.
Surface volume. Brilliant. But wait, what is the next step up from volume? Length, area, volume, ...?
Oh, oh! Does this make any sense? You got lines tangent to circles, and planes tangent to spheres, so would you have platonic solids tangent to hyperspheres?
"Heaven is an American salary, a Chinese cook, an English house, and a Japanese wife. Hell is defined as having a Chinese salary, an English cook, a Japanese apartment, and an American wife." -- James H. Kabbler III.
It makes perfect sense, Cthulhu-chan. Good to hear another person say it.
Don't know any 4D terms other than 'tesseracted' (4D equivalant to 'squared' or 'cubed'), and the Kata/ana thing for both directions on a 4D axis. Need to know what the words equivalent to 'volume' and 'width' for my quest to be complete, though.
Oh, and a 2D square can be interesced by a 1D line, a 3D cube intersected by a 2D plane, and a 4D hypercube intersected by a 3D cube. A cube could be a insignificant wedge of a 4D hypercube; not a very complete representation to an object with far more mass than what's in the cube section.
You know how a sphere's represented on paper? It's a circle with an oval directly inside it, which becomes wider or thinner depending on what 3D angle we're supposed to be looking at it.
You know how to represent a hypershpere in 3D space? It's a sphere with a 3D oval (sorry, my 3D terminology is starting to short out) directly inside the sphere. And it's shape probably widens and narrows depending on what 4D angle we're supposed to be viewing it from.
Oh, and imagine a 3D rendering of a 4D cone: a 3D cone that 'morphs' into a sphere as you rotate it 90 degrees 4th dimentionally.
And y'know, technically a 4D cyllinder would be a rectangular cube that's wrapped around a sphereical shape 4th dimensionally, with a sphere capping each end.
Last edited by Utsanomiko on 2003-01-31 03:03am, edited 1 time in total.
"Heaven is an American salary, a Chinese cook, an English house, and a Japanese wife. Hell is defined as having a Chinese salary, an English cook, a Japanese apartment, and an American wife." -- James H. Kabbler III.
Cthulhu-chan wrote:Surface volume. Brilliant. But wait, what is the next step up from volume? Length, area, volume, ...?
Oh, oh! Does this make any sense? You got lines tangent to circles, and planes tangent to spheres, so would you have platonic solids tangent to hyperspheres?
We can go the old SF route and call it hypervolume!
DiffyG is the class you take if your next goal is to read Einstein.
