/sci/ - Science & Math

>I) For motion to exist in one dimension, it seems that one higher dimension must exist.

This can be proven wrong by taking a line segment and drag it along in the direction it was already pointing.

>>5021921
"If you want a point to have more freedom of movement you have to add another dimension" derp.

>For motion to exist in one dimension, it seems that one higher dimension must exist.
what do you mean dimensions? real life doesn't have dimensions, we dont work with voxels or have X Y Z.
>Basically if you want a point to move up and down a line (a 2 dimensional system) you can't do that in 2 dimensions- you need 3
yeah, no. you only need 2 dimensions to move 360x1 ways.
stopped reading these because it doesn't look like it's going anywhere.

>>5021932
>knows how to sage
>doesn't know how to greentext
what kind of being are you ?

>>5021932
That's actually true. You do need an extra dimension to allow for more freedom.

i think that dimensions and time are separate:
for a point/line/anything to move in its dimension it requires time, so it doesn't look like time would be its own dimension

>>5021966
Spacetime is 4-dimensional space with the 4th dimension being time.

>>5021977
thats theoretical

>>5021966
Stop using the word 'dimension' when you mean 'spacial dimension'.
lrn2linearalgebra.

(Flatland is a pop-math book about trivial geometry for retards btw.)

>>5021983

Anything talking about dimensions is theoretical. A dimension is a mathematical object, it doesn't actually exist.

Your petty mathematical Euclidean geometry disgusts me. It's much more fun in Lorentzian geometry (where it makes sense to think of multiple time dimensions)

>>5021991
Are you fucking retarded?

So up and down do not exist?

>>5022048

Up and down can exist but left and right are meaningless.

>>5022048
Stop calling other people retarded if you don't even understand what a dimension is.

That guy tells you a dimension is a theoretical mathematical object (which it is) and you somehow extrapolate from that that 'up and down do not exist'..
You are talking about the spacial dimensions. Which it just one of the many examples of where we can apply that mathematical object.

>>5022048
up and down exist as much as a number 4 exists. we use it to describe, and identify things but you can't show me an "up" or "4" in life.

>mathematicians trying to understand physics

>>5021921

Time travel is a logical impossibility if by "time travel" you mean "sending something back in time".

The problem becomes clearer if you think about information. If you build something that can send information back in time (not only letters, but even photons at will) you could know things that you didn't know when you send that information back in time.

That would mean that information cannot travel back in time (at least in a useful way). Therefore you can't send back a person or an object, because it contains a lot of information (structure, DNA, etc).

I think that every scientist worth the name would agree with this point of view or would say that if something travels back in time it wouldn't get back in time in "our" universe but in a copy of it (implying the existence of a Multiverse that contains every possible universe).

About the 5th dimensional machine... think in what is saying >>5022080
If a 5th dimension exists, how do you know that you are "out of it"? We exists in every dimension in which matter exist, so a machine made of matter would have the same properties... then it doesn't make sense to say "to build a 5 dimension machine" if you are going to use matter.

On the other hand, according to string theory there are multiple dimensions that we don't experience; but this dimensions are compact (they are curled up in themselves).

If you want to think about something really mind blowing, learn some (a lot really) String Theory and get to the point where some scientist justify the existence of a second line of time independent of the one that we experience but that it's as real as this one.

>>5022144
I'm sorry to say this, but you didn't clarify anything. You just regurgitated the original thought by renaming matter as information, while at the same time still talking about matter.

>>5022144
Are you really madsci?

>>5022056
>Stop calling other people retarded if you don't even understand what a dimension is.
I know precisely what the mathematical definition of 'dimension' is, you arrogant aspie.

In the case of a generalized vector space X, it's the cardinality of some set over V such that it is free.

For a manifold, you can either define it via the local isomorphism to Cartesian space, the eigenvalues of the metric, or the number of coordinates in the bilinear form.

>Anything talking about dimensions is theoretical.
Space-time is a smooth manifold, therefore by definition it has orthogonal structure and therefore a soldering form for each dimension.

http://en.wikipedia.org/wiki/Direction

So the concept of direction does not exist? I mean it's surely mathematical and does yield a theoretical basis.

Also, it's spelled 'spatial', btw.

>>5022080
Then tell me how relative directions such as up and down do not exist. Without these navigation would be impossible and subatomic particles would not have any degrees of freedom. Or admit that your idiotic laymen definition of dimension sucks and you're in fact an uneducated highschooler who has to take his first linear algebra course yet.

>>5022168
>Then tell me how relative directions such as up and down do not exist.
If they do not exist, Anon cannot tell you how they do not exist, because to not exist means to have no properties. Are you even considering what you are asking.
Up and down are conventions that are agreed upon and that is it. They do not exist.
>Without these navigation would be impossible
Navigation does not depend on the conventions of language
>Subatomic particles would not have any degrees of freedom
The freedom of subatomic particles does not depend on the conventions of language

I guess you can consider yourself successful now?

>>5022182
How old are you? 12? 13?

What you're saying is total gibberish, I don't think you have even taken a high school physics course. You are arguing over philosophical nonsense such as the definition of "existence". Do you even know what translational invariance is?

>If they do not exist, Anon cannot tell you how they do not exist, because to not exist means to have no properties. Are you even considering what you are asking.

>Up and down are conventions that are agreed upon and that is it. They do not exist.
>The freedom of subatomic particles does not depend on the conventions of language
Confimed for troll. Do you know what a "degree of freedom" is?
http://en.wikipedia.org/wiki/Degrees_of_freedom_(mechanics)


You should read this!

http://math.ucr.edu/home/baez/crackpot.html

>>5022182
>If they do not exist, Anon cannot tell you how they do not exist, because to not exist means to have no properties.
Nobody asked you about the conventions of language or the philosophical definition of property/existence. Don't post irrelevant and unrelated things nobody ever asked for.
>Are you even considering what you are asking. Up and down are conventions that are agreed upon and that is it. They do not exist.
Restating your point over and over again does not make it more true.
>Navigation does not depend on the conventions of language The freedom of subatomic particles does not depend on the conventions of language
Directions and dimensionality are not a language, they are a physical property that translations and rotations in space are dependent on. If this were not true, the homogeneity of space would not hold, and without this the conservation of momentum would not work. Consider taking elementary school physics to see this. Do you have any testable predictions to conclude that mechanical bodies do not have a specific number of translational/rotational degrees of freedom? Extra degrees of freedom would imply that the photons hitting your eyes would allow you to see through buildings. Just admit that you were wrong. Can't be that hard on an anonymous board.

>>5022211
You're trying too hard.

>>5022256

>>5022271
You can continue to insult me but that does not change physics.

>>5022279
I could, yes, because clearly your insult-worthiness would allow for it, but as it happens, you are right: it does not change physics. This makes me glad.

>>5022302
>your insult-worthiness
Mind pointing out what exactly is wrong with my post instead of resulting to ad hominem attacks?

>>5022302
>your insult-worthiness
Mind pointing out what exactly is wrong with my post instead of resorting to ad hominem attacks?

>>5022309
Your posts are irrelevant, because you seem to think physics ceases to accurately describe the world if 'up' is 'down' and 'down' is 'up'.

>>5022335
-->
>>5022316
Yeah, that went wrong somehow.

>>5022309
your missing the point completely.
up and down DO exist, they do not exist ABSOLUTELY they are RELATIVE to the orientation of the OBJECT which we are talking about.

i believe this is the source of the confusion here.


>>5022168
this is the post he was replying to, and it completely misses the point too, assuming that the lack of an absolute up and down restricts movement lol without considering that they might be relative to a reference point.

>>5022335
That's a fine strawman. Note the usage of "relative" direction. Obviously this implies no preferred observes. A sense of dimensionality does not at all infer a preferred frame. A sense of dimensionality implies coordinate transformations between frames of reference. Are you really 12 like the other guy said?

Show me where the physical concept of degrees of freedom imply this.

next argument: left and right exists without a refrence point for a 'front'

This thread.

>>5022352
>>5022350
Let's talk about a Galilean coordinate system for simplicities' sake.

This is defined as a 5-tuple <span class="math">G=(\mathcal{B}^4,\mathbb{R}^4,\mu,t,(,))[/spoiler] where <span class="math">(\mathcal{B}^4,\mathbb{R}^4,\mu)[/spoiler] is some affine space, <span class="math">t:\mathbb{R}^4\to\mathbb{R}[/spoiler] is a linear map, and <span class="math">(,):\mathrm{ker} t \times \mathrm{ker} t \to \mathbb{R}_{\geq 0}[/spoiler] is a inner product on the vector space <span class="math">\mathrm{ker}t[/spoiler]. <span class="math">\mathcal{B}^4[/spoiler] are events. The time interval between events is defined as <span class="math">t(b-a)[/spoiler], while the space interval for some fixed events <span class="math">a,a'[/spoiler] with a time interval equal to 0 is defined as
<div class="math">||a'-a||=\sqrt{(a'-a,a'-a)}</div>
There is a map <span class="math">A:\mathcal{B}^4 \to \mathcal{B}^4[/spoiler] called a Galilean transformation which preserves this 4 dimensional structure.

A Galilean manifold <span class="math">M[/spoiler] equipped with Galilean structure has tangent vectors in a tangent space <span class="math">v\in TM[/spoiler] which, by the defnition of a vector, have time/space orientation. This gives "up", "down", "left", "right" at every point <span class="math">x\in M[/spoiler].

You can generalize this to the Lorentzian case.

>>5022390
To add: this is what I mean. I do not understand how you can get the impression that the physical existence of direction/dimensionality implies a preferred frame.

>>5022350
Also, to add once more (I'll sage this time):
>your missing the point completely.
I stated in
>>5022168
>relative directions

Again, I don't understand how this came about. The argument was over
>>5022182
Whereas he stated
>They do not exist. Navigation does not depend on the conventions of language. The freedom of subatomic particles does not depend on the conventions of language

>>5022390

laymans terms plz?

>>5022410
Wait, what? That's some hardcore linking and quoting. I don't get it.