What actually is a dimension?

  • Thread starter hivesaeed4
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  • #26
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No, in math we can describe a system using numbers. The more numbers you have the more "dimensions" you have. 100 tanks will require 100 different numbers to describe the heights. This is purely a mathematical dimension though, not a "real" one.

Physics is NOT math!!!!

Physics IS reality!!!

Besides, dimensions in math, per my understanding, constitute values which are to be multiplied against one another to describe the system (i.e., zero power (number 1, point in space/time), first power (one dimension, length of a line connecting two points (as in the fluid level of the contents of a tank), second power (two dimensions; multiple lines within a plane or a single-dimensional line whose length varies over time), third power (height, depth, breadth, or height and breadth changing shape over time, as in a television cartoon, or height or breadth and depth changing shape over time, which would make for a very boring cartoon much of whose motion would be invisible to you), fourth power (reality: the three observed spacial dimensions plus the single observed temporal dimension), whereas the differing levels of fluid within 100 tanks is purely an additive process, not involving the exponential mathematics which describe true dimensions.

By the way, gasses would tend to expand to fill any space which they occupy (losing heat in the process), so what is really meant in this case by "fluid levels" actually means "liquid levels", unless you're talking about some super-heavy gas lying on top of a much lighter gas.

***

Look, I know that I'm going to be banned from this forum for having dared to challenge a Mentor via my intervention in this thread, but I"m just doing what I'm doing in the hope that I might get through to someone who might cary on along the lines I've here proposed.


Sheesh!!
 
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  • #27
Drakkith
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Physics is NOT math!!!!

Physics IS reality!!!

Incorrect. A general definition of physics is: Physics is the general analysis of nature, conducted in order to understand how the universe behaves.

Physics is a branch of science, which has many different subfields and has many many tools to use to analyze the universe and try to accurately describe it. One of these tools is mathematics. Math has very specific rules and definitions that are required to make it function correctly. The dimensions of the water level in the 100 tanks is purely a mathematical way of representing them. It only corresponds to reality in that the numbers each represent the measured value of the height of the water in each tank in our 3 spatial dimensions. If I were to take more measurements later on and compare them, I could then also use time.

Besides, dimensions in math, per my understanding, constitute values which are to be multiplied against one another to describe the system (i.e., zero power (number 1, point in space/time), first power (one dimension, length of a line connecting two points (as in the fluid level the contents of a tank), second power (two dimensions; multiple lines within a plane or a single-dimensional line whose length varies over time), third power (height, depth, breadth, or height and breadth changing shape over time, as in a television cartoon, or height or breadth and depth changing shape over time, which would make for a very boring cartoon much of whose motion would be invisible to you), fourth power (reality: the three observed spacial dimensions plus the single observed temporal dimension), whereas the differing levels of fluid within 100 tans is purely an additive process, not involving the exponential mathematics which describe true dimensions..

Yes, this is pretty much how the 4 dimensions of spacetime are explained.


Look, I know that I'm going to be banned from this forum for having dared to challenge a Mentor via my intervention in this thread, but I"m just doing what I'm doing in the hope that I might get through to someone who might cary on along the lines I've here proposed.


Sheesh!!

There's nothing wrong with helping someone understand, but you need to be absolutely sure that what someone said was actually incorrect before calling them out on it. If you are unsure simply ask instead.
 
  • #28
Nabeshin
Science Advisor
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Physics is NOT math!!!!

Physics IS reality!!!
[...]

I don't know what your physics background is, but perhaps you've heard of phase space? If not, read up the wiki article. This is the general kind of dimension we're talking about, and the one that applies to a system with 100 different tanks with 100 (independent) levels.
 
  • #29
244
1
Physics is NOT math!!!!

Physics IS reality!!!
This reminds me of a Moral Orel quote.

"Well, Orel, drunk... IS... nature!"

Physics is the application of mathematical structures in an attempt to model observables.

Besides, dimensions in math, per my understanding, constitute values which are to be multiplied against one another to describe the system (i.e., zero power (number 1, point in space/time), first power (one dimension, length of a line connecting two points (as in the fluid level of the contents of a tank), second power (two dimensions; multiple lines within a plane or a single-dimensional line whose length varies over time), third power (height, depth, breadth, or height and breadth changing shape over time, as in a television cartoon, or height or breadth and depth changing shape over time, which would make for a very boring cartoon much of whose motion would be invisible to you), fourth power (reality: the three observed spacial dimensions plus the single observed temporal dimension), whereas the differing levels of fluid within 100 tanks is purely an additive process, not involving the exponential mathematics which describe true dimensions.
Dimensions don't have to be multiplied against each other.

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

A dimension is simply a value which can be measured independently from other values.

The level of one tank which is not connected to any other tanks is an independent value, that value ranges from some level to some other level, and that constitutes a dimension within the system of fluid filled tanks.
 
  • #30
195
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I don't know what your physics background is, but perhaps you've heard of phase space? If not, read up the wiki article. This is the general kind of dimension we're talking about, and the one that applies to a system with 100 different tanks with 100 (independent) levels.

Yes, I've heard of Phase Space, and I've applied the concept, and it requires no more dimensions than the three observed spatial and the one observed temporal to describe the energy state of any particle within a system.

Each particle with a given energy state within phase space is not a dimension; it is a particle moving within our observed dimensions, and, possibly (but not necessarily) others.

The Hamiltonians, although they foreshadow Quantum Mechanics (and I frankly think that Hamilton suspected that there was something else out there when he arrived at his equations), within themselves, require no dimensions beyond those of which he was aware.

If each particle is a dimension, then how can space be expanding faster than the maximum speed of the fastest known particle? How can gravitation act to warp dimensions only in response to mass, despite the fact that not all particles in our universe possess mass?
 
  • #31
195
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One more question:

Why are you working so hard to pound me down when you know I'm soon to be permanently banned from this forum for my having challenged a Mentor?
 
  • #32
244
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Why do you think challenging a mentor gets you banned?

I haven't seen that rule anywhere, as far as I can tell they've just got moderator privileges on the board software, they're not sanctified or anything. Don't be a jerk and you probably won't get banned.


Note, a particle can not be completely described with 3+1 dimensions.

You can say where it is, where it is going, but not what kind of particle it is, it's mass, it's spin, it's charge, all are dimensions in themselves.
 
  • #33
195
1
Why do you think challenging a mentor gets you banned?

I haven't seen that rule anywhere, as far as I can tell they've just got moderator privileges on the board software, they're not sanctified or anything. Don't be a jerk and you probably won't get banned.

Note, a particle can not be completely described with 3+1 dimensions.

You can say where it is, where it is going, but not what kind of particle it is, it's mass, it's spin, it's charge, all are dimensions in themselves.

Aaauw, man!

Why don't you read what I wrote?

What I write above was: "Each particle with a given energy state within phase space is not a dimension; it is a particle moving within our observed dimensions, and, possibly (but not necessarily) others."

Jeeze, you're pounding me now to the point of attributing arguments to me which I did not make.

And, I probably won't get banned? I challenged a Mentor, so bye bye Charley!
 
  • #34
201
4
I wanted to know what is the definition and what actually is a dimension. I mean I get that length, width and height story, but how does time fit in as a dimension. Then what about higher dimensions. Like if a certain system was defined in 7 dimensions what exactly would those dimensions be? 4 could be time, length width and height but what about the other 3?

When everyone is explaining dimension using Math, particles, motion. etc, let's try another way to interpret dimension.

Dimensions prove existence. Zero dimension means true nothingness.
If anything exists, it has a dimension and vice versa.
Interesting, this also proves empty space is not nothingness as some people think.
 
  • #35
195
1
OK, OK, I give up!

Each particle, together with its motion, is a dimension unto itself.

That means that, as gravitation affects the paths of photons, that photons are, in fact, massive particles, capable of response to immediate influence from gravitation.

That, in turn, means that, as each particle in the universe is a dimension unto itself, that the expansion of the observed spaciotemporal dimensions of the universe proceeds at precisely the speed of light in a vacuum.

And, in particular, that means that General Relativity is **** all.

***

Maybe you're right. Maybe I won't get banned after all, now that I've confessed myself back into the mould.
 
  • #36
Nabeshin
Science Advisor
2,205
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Hamiltonians, and in general Hamilton's equations, make no reference to dimensionality at all. You can apply them to an arbitrary system.

What we're trying to say is as simple as this: When calculating integrals in a phase space, for example of one particle with momentum, you integrate over three spatial coordinates and three momenta to perform the integral over all of phase space. This is a six-dimensional integral, everyone calls it that, and these are the 'Dimensions' that we're familiar with. They might not share the same status as the 3+1 that we know about, but they certainly serve a similar mathematical function, and that's why we use the same word for both.

Your final comment about space expanding and gravitation makes little sense, everyone (who understands GR) knows that spacetime is warped by stress/energy/momentum, not simply mass. And the phrase 'each particle is a dimension' was never uttered anywhere except for in your post, and I can not make anything of it.

Finally, indeed challenging a mentor is not grounds for immediate banning, as you seem to think. Being obnoxious and adversarial, however, is not going to contribute any brownie points. I suggest you spend less time complaining about your imminent ban and more time trying to understand.
 
  • #37
244
1
^Trufax.
 
  • #38
195
1
Hamiltonians, and in general Hamilton's equations, make no reference to dimensionality at all. You can apply them to an arbitrary system.

What we're trying to say is as simple as this: When calculating integrals in a phase space, for example of one particle with momentum, you integrate over three spatial coordinates and three momenta to perform the integral over all of phase space. This is a six-dimensional integral, everyone calls it that, and these are the 'Dimensions' that we're familiar with. They might not share the same status as the 3+1 that we know about, but they certainly serve a similar mathematical function, and that's why we use the same word for both.

Your final comment about space expanding and gravitation makes little sense, everyone (who understands GR) knows that spacetime is warped by stress/energy/momentum, not simply mass. And the phrase 'each particle is a dimension' was never uttered anywhere except for in your post, and I can not make anything of it.

Finally, indeed challenging a mentor is not grounds for immediate banning, as you seem to think. Being obnoxious and adversarial, however, is not going to contribute any brownie points. I suggest you spend less time complaining about your imminent ban and more time trying to understand.

What I'm saying is that Hamilton was definitely ahead of his time, and that he suspected that something else was out there beyond the physics of his own understanding.

The three spacial dimensions are obvious. The three moments I see as functions of the three spacial dimensions with respect to time. In other words, his calculations respected time as a dimension which interacts with space, even though he never phrased it in that manner. Moments necessarily imply motion, and, in the absence of time, there is no motion, only a dead stasis which makes nonsense of the Hamiltonians, as kinetic energy is impossible and potential energy is irrelevant. He was, in fact, describing space-time eighty years before Einstein, having access to more advanced knowledge than that available to Hamilton, formalized the concept.
 

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