Using 3D+1T to look at 4D spatial space

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Using 3D+1T to look at 4D spatial space

Postby gonegahgah » Sat Sep 13, 2014 12:38 pm

3D+1T space has at times been used as an analogy to try to help people to understand 4D space.
An example is that a tesseract would exist as a cube that exists a finite time with a start time and finish time.

One of the things I just realised is the effect of 'turning' into time from our spatial dimensions.
We generally turn left or right sideways.
Generally we can consider that you would turn one direction into the time dimension.
You could spiral turn into time but that's fine for another story.

The interesting thing about turning into 'time' is that it mimics the effect of the tesseract existing through a time period. The difference is that initially we exist in the moment or in the current 3D space.

To turn into time - just as we turn into the 4th dimension - you would do so around a plane or cross section of ourselves. Now, how do you turn into time when there is nowhere to go except the 3D space that exists?

The answer is interesting in that you turn into the past and future. Everything on one side of the plane, that you are turning around, turns into the future and everything on the other side of the plane turns into the past.

Now if you don't actually move anywhere but stand in place and just turn into the time dimension a problem arises...

The part of you that turns into the past is trying to occupy space already occupied by your former self when you were standing unturned. There exists a problem of multiple things trying to exist simultaneously in the same location.

That was quite interesting to come to understand as a problem with using the 3D+1T space to model 4D space.

But it does show up something interesting. If you were angled into time and existed for but a single moment then to us you would appear as a cat scan going from one side to the other. Cool.
If you existed for more than a single moment and you started walking somewhere it would appear as if part of you started moving before the rest of you did. In a stretch-catch up kind of way. Cool too.
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Re: Using 3D+1T to look at 4D spatial space

Postby wendy » Sun Sep 14, 2014 12:11 pm

Using space-time to look at 4D space is not a good idea. It gives misleading results about both space-time and four dimensions. The geometries are fundamentally different too. A tesseract has no place in space-time.

In essence, space-time might be considered a stack of movie frames which one flicks through. You see the motion, but the pictures are static.

The best approach is to use wall-mounted images and maps (where things do and don't fall to gravity), and then use the room to represent pictures of 4D. The reason for using wall-mounted maps, is that if the room is a floor plan, the chair you poke up near the roof is not going to fall on you.

We don't see three-dimensional things by way of slices through two dimensions, and it is terribly misleading to apply the same thinking to four dimensions,
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Re: Using 3D+1T to look at 4D spatial space

Postby gonegahgah » Mon Sep 15, 2014 11:48 pm

As it turns out Wendy. Though you will come across this analogy being used on the internet.
For example: http://www.youtube.com/watch?v=MN4KC_zlW4g (gets into the time-4Dspace analogy comparison at 3:00 but worth watching the whole thing).
And the following compares space-time against 4D space: http://www.learner.org/courses/mathillu ... ook/03.php

There have also been 4D-space explanations that directly depict 4D-space objects using 3D+1T but I can't find them presently.
Whether it helps people to understand, to any degree or not, I don't know but it is interesting to see why it actually falls down.

It also does have some consequences for notions of time travel I would think so it is interesting to compare them.
To travel in our 3D space you have to follow a continuous path between two points to get from one to the other. That is without teleportation.
This seems to bare directly to notions of time travel. Unless we can first perfect teleportation spatially we can't expect to be teleporting backwards or forwards in time.
The motion through time has to be as continuous between two points in time as our motion is between two points in space...

At present all we can seek to do is animate slower (suspended animation) to get to the future.

However, also for the further reasons I have explained, it is problematic to try to incorporate time directly as a comparison due to co-location and the other weird effects.
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Re: Using 3D+1T to look at 4D spatial space

Postby gonegahgah » Tue Sep 16, 2014 11:17 pm

There are also some other interesting things that spring out of this.
For example, in our world you have 360° (or a circle) of directions that you can travel. In a 4D world you have a whole sphere of directions that you can travel.
If we applied the same idea to 3D+1T then you get some similar but interesting results.

Like in 4D where you can turn any sphere of directions; you could turn any sphere of directions in 3D+1T.
The could have your car stopped and start to move through space and time.
As your vision would effectively be partially backwards or forwards through time then this wouldn't be a problem.
You would still see a continuous landscape though there may be some stretching where things are moving.

You would see the hills undulating into the past in one direction and into the future in the other direction as you turned your head around in time.
In that one direction you would see the clock showing an earlier time and in the opposite direction you would see the clock showing a later time.
Clocks to either side would show the same time as yours.

If your a only partially turned into time then you will also have some direction in our 3D space over the time.
So moving forward would move your location both in our space and in time.
However accelerating in this partial direction would be less effective to travel in time because it would take longer to get to the past or future travelling at an angle to time.

Travelling directly in the time direction would be the fastest.
You could travel along at a steady pace and so travel at an even speed through the time dimension.
You could also accelerate and the landscape would then begin to change at different speeds before you.
Travelling foward in time everything would be animating faster the higher your speed.
Travelling backward in time things would eventually stop moving and then begin to animate backwards while you are going forward.

Although this may be fictitious it does add some reality to the time debate.
You would still need to travel from one location to another even if it is a time location.
Travelling takes 'time' and accelerating and maintaining motion requires continuous energy.

The notion of jumping about in time becomes more circumspect.
Until we perfect teleporting people about in space then the notion of teleporting people through time is no more real.

It is interesting to consider 3D+1T as a 4D space.
There seems to be some debate about this in the world of science.
Apparently we border on this with Minkowski space.
On the other side there are those who are arguing that time is not a dimension at all.

But, it is still beautiful to consider 3D+1T space if it behaved like 4D space.
Co-location, I'm thinking now, is no different to the situation we have in our 3D world.
If there is a post in the way you can't occupy the same space. If you have your twin next to you you can't occupy the same space.
Turning into the time direction would require moving around your former selves.
It's simply a matter of rolling around your former selves on your edge.
But, I guess this can quickly add up with multiple former selves so you might still be stuck trying to turn into time.

There are also the interesting aspects of time paradoxes.
If you go back in time and push yourself off a cliff then will your current self exist anymore to have pushed yourself off the cliff.
In 4D space at least their isn't a continuous self because it is actually 4D+1T space.
Even if you had a continuous object part of it could push another part of itself without any paradoxes occurring.

Ah well, it is still fun to explore 3D+1T as a 4D space and what the effects would be.
I think it helps to bring a little bit of reality to the problems associated with the notion of time travel.
Your former self can be a really big pain in the a#$3!
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Re: Using 3D+1T to look at 4D spatial space

Postby quickfur » Wed Sep 17, 2014 4:42 pm

Treating time as a spatial dimension is a clever device, but in order to really see it, one would have to step out of the time stream, otherwise, you can't experience anything because your personal time clock would be stopped! The only consistent way to see it, as long as you remain within the 3+1D space-time (i.e., not step out into 5D or beyond), is to consider the entire history of the universe, past, present, and future, already accomplished and calcified in "stone". Thus, the perspective of a being with full 4D freedom in 3D+1T space-time is one of examining a museum sculpture where everything has already been accomplished, and he sees it from an "external observer"'s POV ("external" not as in, lying in 5D outside the 3+1D space-time, but in the sense of being apart from the events that went into making that space-time universal history sculpture).

From this perspective, things like human beings and other organisms will be seen as very long snake-like extrusions, emanating from birth where they branch off from their parent, and tracing out a 4D path throughout their lives, possibly forking into children along the way, and eventually ending in death where they branch off into the ground where they are buried and splinter into fading threads as they decompose and become a part of the soil and/or part of other organisms that consume their remnant organic matter. All interactions between organisms will be seen as proximities between their respective snake-like extrusions, like a brief period of contact, or intertwining, before separating off again. Seen from "sideways", a human being would not look very much like a human being at all; you'd see, if you're 90° wrt to time, a long winding wall with various extended "folds" (i.e., extrusions of limbs over time). At less than 90°, you'd see an elongated stack of cross-sections, also wall-like except that it has visibly finite ends, and also with extended folds (limbs) along its length. Even hairs would not appear as hairs, but as wavy sheets representing the movement of individual hairs over time.

Furthermore, you can only see this from an observer's POV; it's not possible to interact with anything because time has "already passed" and history has "already been written". You wouldn't be able to interact with your past self -- if you can recognize yourself to begin with, from the time-rotated view! You would appear as a very long wall with folds -- as would everything else. Interaction is impossible because, well, time has "already happened", and without time, there is no action, progression, change, or interaction. (Neither is there movement -- everything because just pure static geometry -- but we'll let that slide for the sake of comprehensibility.)

The only way you can actually interact with your past self, is if time is greater than 1D. But that's where things become insanely complex, and it becomes incomprehensible to interpret such interactions because you wouldn't be just you, but you'd actually be infinite copies of yourself progressing through all positive paths in 2D (or greater) time, and each copy of yourself will be related yet independent, and at every point in time you are potentially forking into uncountably infinitely many copies of your future selves, each of which is a convergence from all negative paths in time... which then begs the question of how you could change your time trajectory in the first place! Anyway, it all devolves into infinite complexity from here, and there's really no intuitive way to grasp it. (What you see about time travel in the movies is almost always grossly oversimplified and critically inconsistent once you get down deep enough.)
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Re: Using 3D+1T to look at 4D spatial space

Postby gonegahgah » Mon Nov 03, 2014 1:09 pm

Sorry for the late reply quickfur.

It is interesting to consider a 4D being in this sense who exists in our 3D+1T space but has access to those dimensions as if they are all spatial.
As you say he would have to have his own time dimension to exist outside ours; except he would see our time dimension as just being a spatial dimension.
That fact that we change in time would only be looking at an object at one end and looking at it at the other end.
In our world one end of a cube might be yellow and the other might be blue. In their world one end would look like a baby and the other would look like an elderly person.

He could then theoretically take our life snake and push it around or even twist the whole thing if he can hold the whole thing.
The 4D creature wouldn't see each seperate time phase of us but would instead see it as a whole with the zygote visible at one end and the decayed body at the other.
The rest would form an amorphous continuity.

I just realised tonight, which is why I write, that it could be possible to turn into time - if it were possible - even though we have to turn against pre-existing existances of ourselves.
It could work if that when we turn into the time dimension this also causes our former selves to turn into the time dimension. In this fashion our former selves make way and space for our turning existing self.

Now, if you consider a 0 thin square trying to turn a cube that it is within - as we a 0 thin in the present of time - you can see that it it won't have much mass to turn the rest of the cube with it.
Fortunately if we continue to try to turn into time then our future existance will add to this effort giving us increasing mass to turn against our former self.
So given enough period of trying to turn into time we may start to achieve enough mass and some results and force our former selves to make way by them also turning into time. Pretty cool. That only dawned on me today.

The concept of time in this gets a little freaky. Although you are travelling the same distance when partially turned into time some of that distance is into time.
Just like air has to make way for trains trying to move through space; so do the substance of each time frame have to make way - by either moving aside or into the future or past - for any attempts of incursion into the future and past.
What's cool about this idea is the direct relation between travelling through time and travelling through space that it provides.

If you stand in place and turn into time forcing previous existances of yourself to turn into time then there shouldn't be a great deal of difference to other observers in those previous frames.
Wind blowing your hair may give some weird effects.
It is when you move spatially as well that you start to see some interesting developments. As I mentioned you will get elongation effects where a person seems to stretch as different parts of them are in your present time.
To the time traveler they remain altogether but you would see the nose which is futher back in time stretching ahead of the back of the head with the person stretching through time.

In our time only a slice of their present time is in our frame. We also have slices of their former and future selves and to us they seem to form a whole.
So, although to them they travel across the same amount of space while stepping - with normal time according to themselves - we actually see them moving slower through time.
We marvel at how they seem to be able to move - and animate - so slowly; in apparent defiance of gravity by our time sense. Really cool!
They in turn see the same effect when observing us.
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Re: Using 3D+1T to look at 4D spatial space

Postby wendy » Tue Nov 04, 2014 3:09 am

My main worry is that while you can map the ''w' coordinate onto t, to roll sections etc through a time sequence, space-time does not work like this.

Most people intuitively understand newtonian relativity (NR), but the usual meaning of the expression of space-time is GR (general relativity). There's also SR special relativity. Newtonian relativity is closest to 4D, but its really 3+1 dimensions, with no conversions. SR has conversions (x²+y²+z²-c²t²), and GR has curvature (those deep pits representing black holes. GR without gravity = SR, and SR with infinite speed of light = NR. Note the heaviside-jeffimenko gravity model does not implement gravity as curvature, and so is a model that works in SR.

The difference between NR and SR is visable as an anomaly, ie SR correctly places things that NR does not. Likewise the evidence for GR only comes if you suppose that gravity is a GR thing, and has

In any space-time, things are not objects, but have a continued existance in each frame. It is like one of those flick-animations, where for something to exist, it has a presence in each frame of the movie. So it's really that we are long hairs in space-time, which is not the round things that we are acustomed to.

If you make the analogy too heavy, you will create the false illusion that understanding one understands the other. For example, the scale of space time is l = ct, which means that something a foot in diameter would exist for a nanosecond, not several seconds.
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Re: Using 3D+1T to look at 4D spatial space

Postby Secret » Tue Nov 04, 2014 1:41 pm

In addition to Wendy's account on this, time also have a negative sign for hte metric signature, which means it transforms in an opposite way to space when you change frame of references

Or in English, changing your velocity relative to another event, if space looks compressed, time is dilated

There are also a lot of difference between space and time, even if you ignore the arrow of time

It might be very useful to model 4D objects in terms of cross sections, but that is as long you are in non relativistic conditions (so that spacetime don't do that hyperbolic rotation thingy significantly and distort the picture) and you cannot relate the lengths in the 4th dimension easily with the other 3 because of that factor of c to make time having a dimension of length (light second)

I would love people to point out more difference between space and time so we can learn more, particular in the mathematical way to formulate them, but I guess that's better left for another thread
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Re: Using 3D+1T to look at 4D spatial space

Postby gonegahgah » Wed Nov 05, 2014 10:24 pm

Hi Secret I think this is the perfect place to compare the two even if as Wendy says they don't compare exactly.
We can look at this is the context of a 2D person travelling through time if we consider each of their time frames being convertible to spatially sideways that they can turn towards.
If they turn into time and this forces their former self to turn into time then another observer in the original aligned frame would see different ages of the turner in their current frame.
They would see the younger nose of the person and the older back of their head.
Also whether the person turned towards the future or the past their angle of turn would mean that their nose is closer to the back of their head in the original alignment.
Turning in time would squash the 2D character, in the direction of turn, for observers who haven't turned into time.
For the turner he would see himself still animating the same speed.
For non-turners they would see the turner animating different speeds depending upon whether the turner's body moves towards forward or backwards in time with some movement in space.
Backwards in time would see the turner stretching longer and animating faster, forwards in time would see the turner moves squashing and them animate slower.
If the turner turned fully into time then one of our spatial dimensions would become fully their time dimension.
I like that the notion of speed of light can give some comparison between time and distance. Will have to explore that more...
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Re: Using 3D+1T to look at 4D spatial space

Postby anderscolingustafson » Sat Nov 08, 2014 4:48 pm

I have used the 3d+1t approach to learn about 4d before. Using that approach is how I learned that in 4d it's possible for sponges to pass through each other before joining this forum. I also used the 3d+1t approach to learn that it's possible to have two rings that have the same center and that are perpendicular to each other that do not intersect and from that, that it's possible to have a double rotation in 4d. I also tried using the 3d+1t approach to learn some about the toratopes so I can actually learn some basics about 4d simply from using time as the fourth dimension and manipulating the appropriate images in my head. Using time as the fourth dimension with images in my head to learn about the fourth dimension requires a lot of consentration and it has it's limits such as the fact that I haven't learned anything about many cell polytopes using this method. So I can not only visualize 4d using time as the fourth dimension but understand what I'm visualizing.
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Re: Using 3D+1T to look at 4D spatial space

Postby gonegahgah » Sat Nov 15, 2014 12:10 pm

Hi Anders, your post made me think about some things.

1. Mmmm, could someone help explain to me how a sponge passes through a sponge. Are we talking about two 3D kitchen variety sponges?

2. Two rings not touching is interesting and I was wondering how I would depict that using rotational projection. I guess it would be that if you can see one of the ring bands in front of you then the other ring band will appear as two squares opposite each other out from opposite centres of the ring with a purple shadow extending from them in a circular band that intersects with the visible band at two points. Being a purple shadow means it is off in the 4th dimension and not present in our 3D space. When you rotate these two rings at the same time, direction and speed into the 4th dimension they then both appear as these two purple shadows with two sets of opposing squares visible in our 3D space. These two sets of squares won't move if you are rotating into the 4th dimension. Once you have rotated 90° then the previously primarily purpled ring becomes solid in our 3D space and the other remains mostly purpled except for its two opposing squares. The same repeats if you rotate further until at a further 90° (=180° total) you get back to the original ring being visible but flipped in the 4th dimension. Might be an interesting object to have in the game for the player to play with or use?
I'm guessing at this stage that how the rings rotate before us will depend upon what angle they are rotated in 4d space relative to our orientation. The initial shadowed rings will either rotate around the axis of the two opposites, or the two opposites will move around the ring, or a combination of both, until they get to the top and the previous hidden ring appears solid. The other ring that was initially in our space will simply rotate around two opposite points leaving only those points visible (unpurpled).

3. The biggest pitfall of the 3D+1T approach is that people usually imagine that things still sit 'on the floor' so to speak in each time frame. However, to use the time analogy you have to realise that for true 4D space things can actually sit on the floor across each time frame and only exist as a plane shape in each time slot when turned into the 4th dimension. I certainly found that to be one of my initial stumbling blocks to overcome in my understanding. It is why things can rest on (not inside as we think) a 4D cubed floor.

The last point was the reason I wanted to point out the misconception usually created by the 3D+1T analogy of 4D space and to show how it would have to actually be conceived to make it comparable.

One of the things to remember is that just a 2Der's square is still a shape in our 3D space (ignoring how thin it is) our 3D volumes are still shapes in 4D space.
We can't get inside a 2Der's square anymore than a 4Der can get inside our cubes but we can still see the 2Der's objects from two sides (back and front) and 4Ders can indeed see our 'solids' from two sides also (again back and front).
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Re: Using 3D+1T to look at 4D spatial space

Postby ICN5D » Thu Nov 27, 2014 2:21 am

I'd also like to know how 4D sponges can pass by each other. Is it because of the flat rectangular shape, or the web-like consistency on the small scale?
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Re: Using 3D+1T to look at 4D spatial space

Postby wendy » Sat Nov 29, 2014 2:20 am

In four dimensions, tolines don't link.

Suppose you have a cunic array, of verties and edges. You can put a second one in there body centered. In three dimensions they are linked.

In four dimensions, you can have tesseractic arrays of vertices and edges, but when these project to 3d, the shadows fall on the v+e of the cubic.

When you push one of the cubics by half an edge in the w axis, the v+e turn into little spheres representing the half-way point of the edges between the verties on two different layers. In other words, it now becomes easy for a set of dots to fall out of the cubic monkey-bars they find themselves in.

Two lattices of vertices + edges are rigid things that can pass through each other,
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Re: Using 3D+1T to look at 4D spatial space

Postby ICN5D » Thu Dec 11, 2014 8:02 pm

I just found these excellent examples of a 1D + 1T universe. They're diagrams of a movie plot, that show where and how all the characters are grouped. If they had 1D of space, and 1D of time, then they would perceive a 2D space-time. As 3D beings, we can exist outside their spacetime, and look down on all of everything at once. We have no notion of their time, since all we see is space, a 2D plane. Not only that, but it's possible to fold this 2-plane into a sphere or torus, making space and time finite, yet unbounded. Our perception can freely travel to any point in their space and time at will.

So, by direct analogy, a 5D being will perceive a 3D+1T universe, from completely outside it. Imagine that, a 4D space wrapped up into a 5D toratope, that contains an entire universe, from start to finish. A 5D being could stroll past numerous, self-repeating toriodal universes, that contain an entire 3D+1T spacetime. There could be different universes, as a different toroidal shape, with alternate physics, yet the same outcome of life.

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