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Jeremiah Dyke Posted: Thu, Dec 2 2010 10:45 AM

Anyone frequent any science or physics forums/groups i could pose these types of questions to?

Read Flatland, reading Flatterland right now and have a question. To a cluster of 2d creatures, could the third dimension be considered time (or more specifically duration)?

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Metus replied on Thu, Dec 2 2010 10:58 AM

If the third dimension is time, why not? Time has certain properties that space does not have, thus you can distuingish both. There nothing beyond convention that makes "time" the 4th (or in Flatland 3rd) dimension. Of course, this is mathematically speaking.

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what would time itself be considered?

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I. Ryan replied on Thu, Dec 2 2010 11:23 AM

Jeremiah Dyke:

To a cluster of 2d creatures, could the third dimension be considered time (or more specifically duration)?

For one frame of consciousness of a 2D creature, it wouldn't see anything but a group of colored pixels arranged in 1 dimension. It would see a bunch of colored pixels arranged in a line. For example, it might see a row of 10 black pixels, then a row of 20 white one, and so on, until it reached the limit of its visual field.

But where would its idea of 2D objects come from?

It wouldn't come up with the idea of 2D objects until it were to experience a sequence of 1D frames, and systematically were to group them into specific categories as to form its idea of 2D objects. Just like we can't think of a 3D object without imagining a sequence of 2D appearances, it wouldn't be able to think of a 2D object without thinking of a sequence of 1D appearances.

In that sense, for a 2D creature, I would say that the sequence of 1D appearances (time) wouldn't supply them their 3rd dimension, but would supply them their 2nd dimension!

(If this doesn't make any sense, I can expand on a lot of these points.)

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Clayton replied on Thu, Dec 2 2010 12:15 PM

I think that's the implication of the Flatland analogy but I don't buy it. Time is a lot harder problem than just saying "it's another dimension!" A "dimension", mathematically speaking, is any independent variable. Depending on how you slice it, your phone number is a 4-dimensional object - country code, area code, prefix and suffix. Do each of these "dimensions" have their own real existence? Who knows, maybe they do!

The problem is that we are abusing language. The world, as we experience it, is a holistic blob of states of affairs that we experience in a movie-like flow and in which all the frames of the movie are clearly causally related to one another. If you think about it, space is as mysterious as anything else, we just feel pretty comfortable taking it for granted. The unique problem of time is that it is entangled with causation - we believe that the present state of affairs is the sum result or effect of all previous states of affairs. But, really, we believe that the distant past doesn't matter to the present... it can be neglected for the sake of analysis. All that matters to understanding the present state of affairs is the immediately prior state of affairs. Then, we can apply a regressive argument to say that the state of affairs at each "moment of time" is dependent solely on its immediately prior state of affairs. But what is the meaning of "immediately prior" in a continuous variable?? What is the number immediately prior to pi, for example?

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I. Ryan replied on Thu, Dec 2 2010 12:29 PM

Clayton:

I think that's the implication of the Flatland analogy

No, it isn't.

Isn't what we call "time" just the sequence of frames?

If we are supposing that the 2D creature already has the idea of 2D objects, we are supposing that it already experiences sequences of 1D frames. And, if we need the sequence of 1D frames to build its idea of 2D objects, how could we have anything left over after we build its idea of 2D objects which would add a "3rd dimension" that we could call "time"?

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Clayton replied on Thu, Dec 2 2010 1:19 PM

Isn't what we call "time" just the sequence of frames?

What frames?

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I. Ryan replied on Thu, Dec 2 2010 1:22 PM

Clayton:

What frames?

Let me state it another way.

For one moment of our consciousness, we don't see anything but a bunch of colored pixels arranged in 2 dimensions.

So, for one moment of the consciousness of a 2D creature, it wouldn't see anything but a bunch of colored pixels arranged in 1 dimension.

Just like we need to experience a sequence of 2D "pictures" to experience a 3D object, they would need to experience a sequence of 1D "pictures" to experience a 2D object.

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baxter replied on Thu, Dec 2 2010 1:30 PM

>To a cluster of 2d creatures, could the third dimension be considered time (or more specifically duration)?

Edit: I think I misunderstood your question. Yes, 2D creatures constrained to a 2D membrane in our universe could experience, measure, and think about time as their third dimension.

At first I thought you were asking whether a third spatial dimension could be interpreted by them as a kind of time. I think that's not possible.

For that dimension to be called "time", these creatures must have some kind of device (a "clock") for measuring it. Simply imagining an extra dimension is entirely different from being able to measure it.

Also, to be similar to our concept of "time", I think there must be some kind of statistical macroscopic arrow of time. For us, it is our proximity to a boundary condition (the Big Bang) that gives us an arrow of time. For the 2D creatures, there doesn't seem to be any difference between opposite directions along a third spatial dimension.

Finally, time is not simply another space dimension but, due to the hyperbolic geometry of the universe, is radically different from space dimensions. In special relativity, the metric tensor n = ((-1 0 0 0) (0 1 0 0) (0 0 1 0) (0 0 0 1)) meaning the interval (squared length) of a 4-vector is not vv=xx+yy+zz+tt, but it is vv = vnv = xx+yy+zz-tt. (I'm not sure how to write it in text, but there is a distinction made between contravariant and covariant vectors). This is why we have a 4D light-cone and not a "light hypersphere"  Even if the 2d creatures somehow imagined a third space dimension, it wouldn't necessarily be anything like our "time".

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I. Ryan replied on Thu, Dec 2 2010 1:36 PM

baxter:

Also, to be similar to our concept of "time", I think there must be some kind of statistical macroscopic arrow of time. For us, it is our proximity to a boundary condition (the Big Bang) that gives us an arrow of time. For the 2D creatures, there doesn't seem to be any difference between opposite directions along the third dimension.

For time, where does our idea of the direction come from?

It comes from the fact that there is a regularity in the life-cycle of things growing and then detiorating.

(I can expand on that if it wasn't clear enough.)

But why couldn't the 2D objects in a 2D world not be subject to the same kind of thing?

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baxter replied on Thu, Dec 2 2010 1:39 PM

>why couldn't the 2D objects in a 2D world not be subject to the same kind of thing?

I see no reason why they couldn't. As my edit explained, I misunderstood the question. I was pointing out that it doesn't make a lot of sense to call additional, inaccessible spatial dimensions "time".

I think it's physically possible - but not technologically yet - to create a 2D membrane on which are constrained 2D sentient beings who can perceive and contemplate time. Virtual reality would probably be an easier way to do this.

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I. Ryan replied on Thu, Dec 2 2010 1:42 PM

baxter:

For that dimension to be called "time", these creatures must have some kind of device (a "clock") for measuring it. Simply imagining an extra dimension is entirely different from being able to measure it.

If there is a regularity in the sequence of 1D appearances, it would be possible to measure it.

(And, if there weren't a regularity, they wouldn't be able to come up with the idea of 2D objects anyway.)

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I. Ryan replied on Thu, Dec 2 2010 1:45 PM

baxter:

I see no reason why they couldn't. As my edit explained, I misunderstood the question. I was pointing out that it doesn't make a lot of sense to call additional, inaccessible spatial dimensions "time".

Ah, I see.

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I. Ryan replied on Thu, Dec 2 2010 1:47 PM

baxter:

Yes, 2D creatures constrained to a 2D membrane in our universe could experience, measure, and think about time as their third dimension.

What exactly would it mean for "time" to be their "3rd dimension"?

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czelaya replied on Thu, Dec 2 2010 1:48 PM

I.Ryan brings up a fascinating and interesting point about the thermodynamical properties of time. Specifically, entropy and the laws of thermodynamics. Either way, time seems to be a property of thermodynamics.

The equations of general relativity and Newtonian physics are symmetrical temporal. It's only when we introduce thermodynamics into the physical equations that we see the arrow of time.

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baxter replied on Thu, Dec 2 2010 1:51 PM

>What exactly would it mean for "time" to be their "3rd dimension"?

When asked what directions there are, they will reply west and east, north and south, and before and after.

Unless they say before and after, west and east, north and south. Then time will be their 1st dimension :)

 

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baxter replied on Thu, Dec 2 2010 1:56 PM

"It's only when we introduce thermodynamics into the physical equations that we see the arrow of time."

True for most purposes. But even at a microscopic level, in some exotic cases, the universe shows a bias between the two directions in time. From http://en.wikipedia.org/wiki/CP_violation "This discovery showed that weak interactions violate not only the charge-conjugation symmetry C between particles and antiparticles and the P or parity, but also their combination... a violation of the CP symmetry is equivalent to a violation of the T symmetry... The kind of CP violation discovered in 1964 was linked to the fact that neutral kaons can transform into their antiparticles (in which each quark is replaced with the other's antiquark) and vice versa, but such transformation does not occur with exactly the same probability in both directions"

 

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I. Ryan replied on Thu, Dec 2 2010 2:06 PM

baxter:

When asked what directions there are, they will reply west and east, north and south, and before and after.

Unless they say before and after, west and east, north and south. Then time will be their 1st dimension :)

Hm, interesting.

But would it be useful to reserve the same word - "dimension" - for all of those 3 parameters?

Just wondering if you have any thoughts on that.

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czelaya replied on Thu, Dec 2 2010 2:17 PM

Introduction of quantum mechanics into the dynamics of time adds a boat full of more considerations that are far too bizarre. The Dirac equation still blows my mind. There is so much to say on the matter.

I've had very little exposure to quantum chromodynamics but the Lagragian formalism it still the same as in non-relavistic quantum mechanics and quantum field theory. Quantum chromodynamics digs way deep into the cosmos, and as you go deeper things become more bizarre, including C-P violations. However, just like every quantum theory, as you begin to move to larger spatial scales, fluctuations in space(fields in this case bc of quantum topology)-time begins to cancel out and emerge into smooth geometries and basic Newtonian physics. Well for the most part.

I will read more on C-P violations.

Either way, time experienced on cosmological and quantum scales introduce new views of time that the human mind have difficulty in understanding.

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baxter replied on Thu, Dec 2 2010 2:18 PM

>But would it be useful to reserve the same word - "dimension" - for all of those 3 parameters?

Yes, only because it's easiest to do special and general relativity (SR/GR) with bunches of numbers called vectors (for us, 4-vectors). Even though time is fundamentally different as shown by the metric tensor of Minkowski space, it's still convenient to lump it together with the spatial coordinates and do math on them. (Edit: FYI vectors are more than just bunches of numbers because they obey certain transformation rules. It's not meaningful to count a quantity of apples and a quantity of oranges and just form a vector out of it.)

You can also choose different coordinate systems, including crazy ones where time and space are mixed together. (The simplest such mixing is akin to adopting the point of view of a moving observer). If done cleverly this has the benefit of allowing some of the coordinates to be neglected while solving a particular problem.

Another good reason for calling time a "dimension", is that time is conceptually similar to spatial directions in that it supports the idea of orthogonality. I can imagine myself "moving" back and forth in time while not moving left or right, just like I can imagine myself moving up and down while not moving left or right.

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baxter replied on Thu, Dec 2 2010 2:25 PM

>fluctuations in space(fields in the case bc of quantum topology)

It's hard to say much about this, because it's all highly speculative and unproven :(

 

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czelaya replied on Thu, Dec 2 2010 2:40 PM

That depends on how deep you want to go. I'm assuming you're talking about the geometry dealing within the Plank scales (ie string theory, LQG, and so forth).

There are indeed topological considerations involving the Schrodinger equation, quantum electrodynamics (tensor analysis, fiber bundles: U(1), and other areas where Hamiltonian and Lagrangian dynamics can be formulated with differential geometry), chromodynamics, and, of course, molecular quantum mechanics.

A fundamental quantum topology, if ever discovered, is going to involve something very radical that hasn't been postulated by any of theories currently in quantum gravity.  

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"Time" is not a dimension. Time is not orthogonal to length, width and height and is thus not a dimension. Dimension refers to structure and is a static concept. Time is an abstract concept (you referred to duration which is a dynamic concept.)

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Clayton replied on Thu, Dec 2 2010 3:32 PM

For one moment of our consciousness, we don't see anything but a bunch of colored pixels arranged in 2 dimensions.

I don't know what a "moment of ... consciousness" is. Also, I've never experienced pixelated vision.

So, for one moment of the consciousness of a 2D creature, it wouldn't see anything but a bunch of colored pixels arranged in 1 dimension.

Just like we need to experience a sequence of 2D "pictures" to experience a 3D object, they would need to experience a sequence of 1D "pictures" to experience a 2D object.

I understand the analogy. I just don't think it gets us anywhere. Saying that we're "really" seeing timeless 4-D objects smeared through 3-D space+time, even if true, doesn't help us reach any better understanding of the nature of time. And I think it's silly to say the world is actually comprised of 4-D objects.

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Clayton replied on Thu, Dec 2 2010 3:36 PM

"Time" is not a dimension. Time is not orthogonal to length, width and height and is thus not a dimension. Dimension refers to structure and is a static concept. Time is an abstract concept (you referred to duration which is a dynamic concept.)

At "normal" speeds, time is, indeed, orthogonal to length, width and height. My bookshelf does not get narrower as I slide it across the floor to the other side of the room.

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I. Ryan replied on Thu, Dec 2 2010 3:45 PM

Clayton:

I don't know what a "moment of ... consciousness" is.

I'm not sure how else to explain it.

Well, let's just try to take an example here.

A tiger running across your field of vision is fundamentally a sequence of "pictures".

(For vision, one moment of your consciousness is a 2D picture.)

Clayton:

Also, I've never experienced pixelated vision.

Well, it's just an analogy.

Switch "colored pixels" to "colored points", if that makes it clearer.

(By the way, are you experiencing a pixelated Mises forum page right now?)

Clayton:

I understand the analogy.

Evidently not.

(See below for why.)

Clayton:

Saying that we're "really" seeing timeless 4-D objects smeared through 3-D space+time, even if true, doesn't help us reach any better understanding of the nature of time. And I think it's silly to say the world is actually comprised of 4-D objects.

Really I have no idea what you are talking about.

(I didn't say anything about 4D objects, space-time, smearing things, or whatever else.)

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@Clayton, Time is orthogonal to Length, Width and Height?!?!?

If that is true, can you please point your finger in the direction of Time?

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I. Ryan replied on Thu, Dec 2 2010 4:06 PM

baxter:

Another good reason for calling time a "dimension", is that time is conceptually similar to spatial directions in that it supports the idea of orthogonality. I can imagine myself "moving" back and forth in time while not moving left or right, just like I can imagine myself moving up and down while not moving left or right.

But you have to imagine at least something moving left/right, up/down, or forward/back.

(Whereas can't you imagine something moving left/right without imagining anything else moving up/down?)

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baxter:

Another good reason for calling time a "dimension", is that time is conceptually similar to spatial directions in that it supports the idea of orthogonality. I can imagine myself "moving" back and forth in time while not moving left or right, just like I can imagine myself moving up and down while not moving left or right.

 

They are most certainly not conceptually similar. Length, Width and Height are conceptually static, they are a photograph. Time is abstract, when referring to an object in motion moving left or right, it is conceptually dynamic and necessarily refers to multiple locations in the universe, it is like a movie.

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Metus replied on Thu, Dec 2 2010 4:43 PM

I don't even understand what you want to say, Orthogonal. A dimension is simply an independent variable, charge or mass for example can be considered dimensions too but do not appear as often as time and space which, after all, are the basis of our thinking. Time and space are conceptually different in non-relativistic physics but this difference gets washed away in relativistic theories because it depends on the observer what he perceives as time and what as space, similar to the transformation of magnetic fields and electric fields.

Of course I am not able to point in the direction of time (or direction of charge for that matter) since "pointing in the direction of" is a concept of space. But that does not mean that time is something completely different from space.

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Clayton replied on Thu, Dec 2 2010 5:12 PM

I can't point my finger in the direction of the fourth dimension of any orthogonal vector space because I simply cannot visualize a four dimensional vector space.

I may be misremembering my relativistic physics, but as I recall, spacetime is just a four-dimensional, orthogonal vector space (with time a complex dimension).

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Clayton replied on Thu, Dec 2 2010 5:18 PM

A tiger running across your field of vision is fundamentally a sequence of "pictures".

Is it? I'm not trying to be obtuse - I simply think that you're asking me to assume with you that time is comprised of a series of "moments".

I like to think of it this way. Imagine your tiger running across the field as an ordinary sequence of movie frames. Now, stack those discrete movie frames one on top of the other like a deck of cards. Now, take a specially designed lighter that "melts" the frames into one another so that if you were to slice the solid block of celluloid at any cut point, you'd see a well-defined picture of the cat in motion at that point in time. This is how we experience time. It is this indivisible, continuous thing that has a causal relation between "earlier" and "later".

Switch "colored pixels" to "colored points", if that makes it clearer.

No, it doesn't, because points are just infinitely small pixels. The problem is that even if you pack infinitely many points into a plane, you still do not have enough points to cover the plane.

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Metus replied on Thu, Dec 2 2010 5:21 PM

Clayton,

Your first objection is invalid, since in a two-dimensional space you could very well visualise a three-dimensional space-time. But even there you are not able to point your finger in the direction of time, or any other non-space-like dimension for that matter.

Spacetime is a four-dimensional real vectorspace with a pseudo-metric, the Minkovski-metric, or a four-dimensional complex vectorspace with an actual metric, the Euclidian. In the latter case you loose much mathematical elegance and possibilities to generalise principles, in the first case you loose all the properties of vector spaces with scalar products. Though in both models of space-time, time and space dimensions are distuingishable in the metric or definition, they do not retain their 'classical' meaning. Two points seperated by time or space for one observer are not seperated for an other observer. The invariant distance between two points of space-time is the world-line, a mixture of space and time. But the mixture is observer-dependant.

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I. Ryan replied on Thu, Dec 2 2010 6:04 PM

Clayton:

No, it doesn't, because points are just infinitely small pixels. The problem is that even if you pack infinitely many points into a plane, you still do not have enough points to cover the plane.

If what makes up a 2D appearance isn't a bunch of indivisible, colored points, then what is it?

Clayton:

Is it?

As far as I can tell, that's how my vision works.

Clayton:

I like to think of it this way. Imagine your tiger running across the field as an ordinary sequence of movie frames. Now, stack those discrete movie frames one on top of the other like a deck of cards. Now, take a specially designed lighter that "melts" the frames into one another so that if you were to slice the solid block of celluloid at any cut point, you'd see a well-defined picture of the cat in motion at that point in time. This is how we experience time. It is this indivisible, continuous thing that has a causal relation between "earlier" and "later".

Sorry, but I lost you at "slice the solid block of celluloid at any cut point".

(By the way, if this has anything to do with that you are talking about, we know through experience that "trailing" indicates motion, but trailing is still nothing but a bunch of colored points arranged in 2 dimensions as to form what we call "trailing".)

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Permit the interjection...

Just because we humans perceive time as indivisible does not mean it is not quantised...so too for space. i.e. space-time...

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I. Ryan replied on Thu, Dec 2 2010 6:14 PM

nirgrahamUK:

Just because we humans perceive time as indivisible does not mean it is not quantised...so too for space. i.e. space-time...

Can you explain?

(I'm not sure what you mean, and don't have enough information to make a good assumption.)

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'plank time' is often referred to as smallest 'meaningful' unit of time, the issue of whether there are smaller 'unmeaningful/unmeasurable' units is then kind of metaphysical...

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I. Ryan replied on Thu, Dec 2 2010 6:42 PM

nirgrahamUK:

'plank time' is often referred to as smallest 'meaningful' unit of time, the issue of whether there are smaller 'unmeaningful/unmeasurable' units is then kind of metaphysical...

What's it mean to be a "meaningful" unit of time?

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by analogy in an abstract computer whose memory is stored in arrays of 1's and 0's (bits) ... a meaningful unit of memory is a bit... 

Where there is no property there is no justice; a proposition as certain as any demonstration in Euclid

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I. Ryan replied on Thu, Dec 2 2010 7:03 PM

nirgrahamUK:

by analogy in an abstract computer whose memory is stored in arrays of 1's and 0's (bits) ... a meaningful unit of memory is a bit...

For vision, I see a sequence of groups of points arranged in 2 dimensions.

(I remember a bunch of 2D appearances, and arrange them in an order from "earlier" to "later".)

I don't understand what your argument is against that, or whether there's even supposed to be one.

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