I know there are 4dimensions (front and back,leftside and rightside,up and down).But are there more dimensions than these.If there are any, could you explain.....
Stardust,
This may help:
http://en.wikipedia.org/wiki/Dimensions Regards,
Blacknad.
Nice find, Blacknad. Thanks for posting.
the truth is, there are infinite dimentions but to describe any shape, you only need to use 3.
Rob wrote:
"the truth is, there are infinite dimentions but to describe any shape, you only need to use 3."
No Rob that is not the truth. That is something you made up in your head that has no relevance to the universe in which you live any more than does the invisible purple rhinoceros.
It also is untrue that any shape can be described using only 3.
"No Rob that is not the truth. That is something you made up in your head that has no relevance to the universe in which you live"
Well in that case, it is also untrue that 1+1=2 but let's not get philosophical now.
I am dying to hear you explain how "it is also is untrue that any shape can be described using only 3".
Rob said "Well in that case, it is also untrue that 1+1=2 but let's not get philosophical now."
Unfortunately, you started the philosophy with the following statement:
"the truth is, there are infinite dimentions"
How can you know this except by philosophical conjecture?
Blacknad
The same way I know there are infinite numbers.
"The same way I know there are infinite numbers."
REP: And what way is that, that would also apply to dimensions? How is one connected to the other?
Blacknad.
"And what way is that"Well Blacknad, once again I will take time out of my day to explain the obvious to someone. Let's look over some of the most basic mathematics in the whole world. Shall we look at the line y=x. The gradient is one, which means that you go 1 place in the y direction, and one place in the x direction to get the next point on the line. Now, measure the distance between 1 on the y-axis and the corresponding point on the line y=x. It is 1 unit isn't it? Now look at the point 2 on the y-axis. The point on the line now is 2 spaces away. Do the same for the x-axis and you will see that the nth term formula for finding the distance from the axis to the line... -heck, forget this! The mere
fact that an nth term formula
exists implies that there are infinite numbers. The fact that there is a
symbol for infinity its self USED IN MATHS (∞) should be enough to prove that there are infinite numbers. The fact that if you realise the rule to get the next number when counting upwards in 1's is n+1 you can just see straight away that there are infinite numbers. If there was a limit, what would n(being the limit)+1 be? Please tell me! ANY answer you give me would be in direct violation of some mathematical law. Go on! I dare you! Tell me an answer.
Not enough evidence?
Go here:
http://en.wikipedia.org/wiki/Infinity http://en.wikipedia.org/wiki/Counting SURPRISE! SURPRISE!
When I search for things like 'number limits in maths' and 'biggest number in maths' nothing of much relevance comes up.
Look, if you have any more questions of that kind to ask I suggest you consult a primary school teacher since they are trained to answer those kinds of questions.
So that's how I can be sure that there are infinite numbers. Now how would it apply to dimensions? Well, even though we say there are 360 degrees about a point there are actually infinite degrees about a point. How do I know that? See above. Let us imagine a dimension as a line through that point. Well, there, you can blatantly see that there are infinite dimensions. Got any problems with this? Take it up with the universe, not me. I'm just a humble soul who doesn't have time to be explaining why 1+1=2 and so on.
Rob,
Your arrogance is exceeded only by your density.
Oh is it now? Find one flaw in my logic and I may consider conversing with you. My original point, that there is an infinite amount of numbers connects to dimentions in a way that has nothing to do with an x-axis and a y-axis. The fact that I started to use a graph as an example to point out the abundancy of numbers is an unfortunate coincidence. So, let me take you through it again using consecutive bullet points that contain simple words. Hopefully this time you will understand.
- imagine a point in a 3D world with lines petruding from it at angles x, y and z
- now you can plot any other point in space relative to this point, can't you?
- another point could be said to be at point (1,1,1,) relative to the point (which could be said to be the origin)
- now, add as many dimentions as you like. Have lines coming out of every angle of the 3D point (origin). Each of these lines is another axis and therefore another dimension.
- Now the same point (1,1,1) could be written as (1,1,1,a,b,c,d,e,f,g,h...). It makes no difference how accurately you wish to describe the position of this point as long as you use a minimum of 3 dimentions, x, y and z.
If you still don't understand, there is no hope for you.
Rob wrote:
"now you can plot any other point in space relative to this point, can't you?"
Given your assumption that the only axes are x, y, and z yes. But you've not established that.
One of the latest insights in string theory concerns the concept of holography. According to this surprising conjecture, first put forward by G. 't Hooft, our three dimensional space may be fully described by a theory that lives on a two dimensional projection. The motivation comes from the Bekenstein-Hawking results for black holes where it is known that the entropy of a black hole grows with the area of its horizon. As a consequence one can deduce an entropy bound for any physical system. The result is that the maximum entropy does not grow with the volume but rather with the area. 't Hooft and others have proposed that this insight carries an important clue to the secrets of quantum gravity.
Want to argue with G. 't Hooft be my guest. But right now all I see of substance in your post is the undeserved insult.
Please name one shape that cannot be described using 3 dimentions and 3 dimentions only.
A Kline bottle.
Want to try again? ;-)
Try describing a Hypercube in 3d...
http://en.wikipedia.org/wiki/Tesseract euklid "proved" that there are only three dimensions thus:
If you have three lines that are at righjt angels to each other, you cant find a fourth line that is also at right angles with the other three and not one of the three itself.
His error is that he can only imagine 3 dimensions, thus he is handicapped. but you actually can find a fourth (or nth) line.
I liked all the replies.
Remember for the majority 4D world is sufficient.
Rest remain wrapped within its own defnition i.e. it is self-enlosed.Infact the Entire History of Universe can be travelled without caring for the Huge Distance which us seperated by such huge distances..
Time as dimension as I have explained already...
Originally posted by dkv:
Infact the Entire History of Universe can be travelled without caring for the Huge Distance which us seperated (sic) by such huge distances..
You lost me here. I can't figure what you are trying to say. A history is a line of time linked causally together by some definable thread or cause. Are you suggesting that time travel is possible?
Oh, and by the way, the word is "separated".
DA Morgan,
Sure, I want to try again. Never heard about a KLINE bottle, is it related to the famous actor? Is he more than three-dimensional?
;-) ;-) ;-)
However, if you are talking about the KLEIN bottle, you are wrong. The Klein bottle can locally be described by using three coordinates, so it is a three-dimensional (non-orientable) manifold. However, it cannot be embedded in three space dimensions - but requires at least four - so in that limited sense you are right.
Kline bottles are physically and logically impossible in three spatial dimensions: Try again.
dvk wrote:
"I am not talkin English"
Why would anyone expect anything else from you?
Weren't you going to go to some other URL and share your profound gift for inarticulate sentences?
DA Morgan: wrong again... a Klein bottle can locally be described using three coordinates, hence as a manifold it is three-dimensional.
This answers the question about the dimension of a Klein bottle.
But it is non-orientable and cannot be covered by a single three-dimensional map. And it cannot be embedded in three spatial dimensions.
You should try to read about the Klein botttle in the wikipedia or some other place.
To make a Moebius strip you start with a two-dimensional sheet (say, a square piece of paper). You then glue two ends together with a 180 degree twist - the Moebius strip is still locally described using two numbers.
To make a Klein bottle, you start with a Moebius strip (or a sheet of paper again) and glue the remaining sides - now you need three local coordinates.
Here is an analogy: a string is an extended object; you need only one coordinate to specify a point on a string. But a string does not really move in one dimension, but in two or more....
A mathematician named Klein
Thought the M?bius band was divine.
Said he: "If you glue
The edges of two,
You'll get a weird bottle like mine.
I wonder? Is there a
real world object that has the shape of the Klein bottle?
Oh, by the way have a look at this:
http://www.kleinbottle.com/index.htm Neat, het!
Kasper Olsen, Ph.D.'s inability to quote correctly notwithstanding I will repeat my original statement ... Klein bottles can not be constructed in anything less than four physical dimensions.
1 dimentional objects cannot exist
2 dimentional objects cannot exist
Do you agree with the above statements?
I will continue if the answer is yes
Based on what you wrote I would say, without hesitation, you are incorrect.
You see the problem is that strings and branes, thought by many highly qualified mathematicians and physicists to exist or at least to be possible solutions ... are precisely what you are asking me to say do not exist.
That I can not do.
Rob said: "Please name one shape that cannot be described using 3 dimentions and 3 dimentions only." And you, DA Morgan, said: "A Kline bottle.
Want to try again? ;-)"
and later: "Klein bottles can not be constructed in anything less than four physical dimensions."
Your last statement is correct - at least if you make precise what you mean by "constructed".
But your former statement is wrong. The Klein manifold is three-dimensional in a precise mathematical sense. Roughly it can locally be covered by the real space R^3 - in this sense it is three-dimensional.
The question about embedding the Klein bottle in R^n is another thing. Let's talk about embedding a manifold M, of dimension m, in the space R^n.
How large must n be, in terms of the dimension m of M? The so-called Whitney embedding theorem states that n = 2m is enough. For example the real projective plane of dimension 2 requires n = 4 for an embedding and the Klein bottle of dimension 3 requires n = 6, but can actually be embedded with n = 4.
You are confusing m with n above.