the motion of 3D objects in the 4th dimension — Luke

This is your problem. 3D object move in three dimensions OVER a fourth (time). They’re not moving THROUGH a fourth, because that (hyper)motion would have to be OVER yet another dimension of hyper-time or something.

@Kenosha Kid I think you’re confusing Luke by using his language of “change of temporal position”. It’s clear to me that you mean we the observers attending to how things are at one time versus how they are at another time. Like with the ruler, we look at one end and see that the numbers are higher than at the other end: our attention is the only thing changing spatial position there, the ruler isn’t actually changing its spatial position (moving). Luke is talking about things moving through time, changing where they are in time, not just about them being different at one time than another. We, considering the object as it spans time, can attend to one temporal position or another, and note how the object’s features change between the two temporal positions, but you and I agree that the object is not changing its location in time, which is what Luke means by a change in temporal position.

Motion is an inevitable consequence of the geometry of 4D objects. — Kenosha Kid

Only if you assume it is. Otherwise, what are we discussing here? As I've said before, Eternalism without motion is equally conceivable.

This is where I see that things stand at the moment:

1. 'Change in temporal position' means the object moves from t to t' (which is not B-theory)
2. 'Change in temporal position' means the object does not move from t to t' (there is no motion)
3. 'Change in temporal position' means the object does not move from t to t' (but there is motion)

You need to explain how 3 can make sense. Namely, how does {change in temporal position from t to t'} not mean exactly the same thing as {the object has moved from t to t'}?

Things change in space with respect to time. — Pfhorrest

Yes. I agree. But if they don't really change then they don't really move.

Most people think of motion as something like a car travelling from point A to point B. But let's say that the car is already at point A and at point B simultaneously, with the same car also at every point in between. You wouldn't then say that the car could move from point A to point B, would you? The situation is no different with the same car being spread across the temporal dimension. Instead of a 3D car filling up the entire space (all spatial positions) from point A to point B, its a 4D car filling up the entire space (all spatiotemporal positions). The car exists at all temporal positions, and there is nothing which can move the car from one temporal position to the next. That is, the car can never change temporal position. Therefore, it does not move.

3D object move in three dimensions OVER a fourth (time). They’re not moving THROUGH a fourth — Pfhorrest

You still haven't explained the difference.

our attention is the only thing changing spatial position there — Pfhorrest

So much truth to this statement. That's all that ever moves in any of the 3D examples and 4D examples that have been given.

but you and I agree that the object is not changing its location in time, which is what Luke means by a change in temporal position. — Pfhorrest

How is "a change in location in time" NOT "a change in temporal position"? It's the same thing.

3D object move in three dimensions OVER a fourth (time). They’re not moving THROUGH a fourth — Pfhorrest

It's exactly this, but time instead of space:

car travelling from point A to point B. But let's say that the car is already at point A and at point B simultaneously, with the same car also at every point in between. You wouldn't then say that the car could move from point A to point B, would you? — Luke

A real car moves from spatial point A to spatial point B over time. It's not at both points at the same time: the car at point A is at time X, and the car moves to point B by time Y.

Nothing moves from temporal point X to temporal point Y, because in order to do that (rather than just spanning the two temporal points and all the times between them the way the weird hypothetical car just spans point A through B) it would have to be at time X at hyper-time P and then move to time Y by hyper-time Q.

In order for something to move through time, there must be some hyper-time for that motion to occur over. Otherwise, things can only span a duration of time, the way that your weird hypothetical car could only span a distance of space in a timeless world.

A real car moves from spatial point A to spatial point B over time. It's not at both points at the same time: — Pfhorrest

The 4D car is at all temporal points between A and B, just as the strange 3D car is at all spatial points between A and B. It cannot change position or move in either case and for the same reason.

In order for something to move through time, there must be some hyper-time for that motion to occur over. — Pfhorrest

No, this "hyper-time" would be required for the 4D object to move through, but we are talking about a 3D object (potentially) moving through/over the fourth dimension of time. That's just like a 3D car moving from point A to point B over time.

No, this "hyper-time" would be required for the 4D object to move through, but we are talking about a 3D object (potentially) moving through/over the fourth dimension of time. — Luke

It's just as much nonsense to talk about a 3D object moving through time with no hypertime as it is a 4D object.

Let's consider a variation of your car scenario for illustration:


Say instead of a real 3D car, we have a 2D cardboard cutout of a side-view of a car. In real life even cardboard cut-outs aren't actually 2D, but let's just pretend it is.

Call the direction down the road that the car is facing "x".

Call the direction from ground to sky "y".

Call the direction from the right side of the road to the left side of the road "z".

The car only spans the x and y dimensions, but it's in a 3D world with a z dimension too.


We could, in case [1], slowly move the car across the road, through the z dimension, over time. That would be normal motion as we usually mean it, through space, over time.

We could also, in case [2], instead have a kind of 3D shape made out of this 2D car, where there is another cut-out placed just down the road (in the x axis), offset a little bit across the road (in the z axis) each step of the way, so it can fit. This would make a 3D shape that runs diagonally down and across the road. It moves through the x dimension over the z dimension. But it's not moving anywhere over time. It's stationary over time. It's a big 3D thing laying diagonally across and down the road, just sitting there over time. But each 2D slice of it is at a different place in the x dimension for every step in the z dimension you look, so it moves through the x dimension over the z dimension. But not over time.


Now imagine instead that the whole space of this universe we're considering is just 2D. We can now imagine mapping time to a third dimension of that 2D universe, imagining time spread out where the z axis used to be. That's analogous to the eternalist view of time: it's just another dimension. By imagining the time of this 2D universe mapped out over a third dimension that we'd usually call "z", we're pretending to be eternalists in this 2D universe. There aren't just the two dimensions of space, there's a third dimension of time too, and other points in that third dimension of time are real.


In that kind of 2D-eternalist world, case [2] above with the funky 3D diagonal shape is motion through the x dimension over time. That's what happens when the car moves down the road, in the x dimension, in the normal way that we usually mean motion over time. The direction it's moving through is x, but that motion happens over time, which we're imagining visualized where we'd usually put z.

But in the 2D-eternalist version of case [1], the car is moving through time (across the road, where we'd normally put the z axis), over... what? How can you even make sense of this scenario? You could also try to imagine the funky 3D diagonal shape moving through time (across the road), but you'd hit the same problem. And you don't need to consider the 3D shape to hit that problem. Just an ordinary 2D car (of this 2D universe we're imagining) moving through the third dimension of time is impossible enough to make sense of, without some hyper-time for that motion to occur over.


Every kind of motion is through one dimension over another dimension. Normal literal motion as we usually mean it is motion through space over time. Motion through time would require something for it to be over, and would not be motion as we usually mean it, but some kind of weird time-travel.

Every kind of motion is through one dimension over another dimension. — Pfhorrest

I had assumed that "through" and "over" just meant the same thing for travelling in a dimension. I didn't realise this convention existed. If you want to be a stickler for that sort of usage, then fine. Take any of my former uses of these words to be synonymous with each other.

If you want to be a stickler for that sort of usage, then fine. Take any of my former uses of these words to mean the same thing. — Luke

Which thing? Usual motion that we talk about, like a car driving down the street, is motion over time. Eternalism doesn't deny that: it just says that other times are real, and objects span across them, four-dimensionally. Looking at that 4D picture from outside of it, nothing seems to be changing relative to something outside of the picture, because time is inside of that picture. A 3D object moving around through 3D space over a fourth dimension of time looks like a static 4D shape to someone not experiencing time in a timelike way but rather in a spacelike way, but that doesn't at all deny that things are moving over time.

Take any of my former uses of these words to mean the same thing.
— Luke

Which thing? — Pfhorrest

When I say an object moves "through time" I mean the same thing as you mean when you say an object moves "over time". Clear?

Only if you assume it is. — Luke

It's a direct consequence of its kinematic definition: dx/dt. Any continuous 4D object will have this property, even if its value is zero. Motion in 4D is geometry. This is not an opinion.

2. 'Change in temporal position' means the object does not move from t to t' (there is no motion)
...
You need to explain how 3 can make sense. — Luke

I don't, you do. (2) is meaningless garbage you insist upon to hold onto a conclusion you clearly do not understand but for some reason desperately need.

It's a direct consequence of its kinematic definition: dx/dt. — Kenosha Kid

Again, only if you assume motion in the first place. Otherwise there is no change. Which is what you keep saying.

Again, only if you assume motion in the first place. Otherwise there is no change. Which is what you keep saying. — Luke

No, I am assuming geometry and the kinematic definition of motion. Actually motion we get fir free. Unless you address that, I'm going to have assume you're not really interested in your own question.

Actually motion we get fir free. — Kenosha Kid

You don't say...

*Actual motion we get for free. Never post before coffee...

Yes, you still don't say.

I guess you're not going to address this question then:

Namely, how does {change in temporal position from t to t'} not mean exactly the same thing as {the object has moved from t to t'}? — Luke

I guess you're not going to address this question then:

Namely, how does {change in temporal position from t to t'} not mean exactly the same thing as {the object has moved from t to t'}?
— Luke — Luke

In translating phenomena from an eternalist viewpoint to that of subjective experience, the second is meaningful. It is meaningless in a purely eternalist viewpoint. That's been the problem throughout: you attempt to retain presentist ideas in eternalism. The only question that matters is: what does motion look like in eternalism. A: it looks like geometry.

In translating phenomena from an eternalist viewpoint to that of subjective experience — Kenosha Kid

I'm not asking for this. I'm just asking you to explain the difference between {change in temporal position from t to t'} and {the object has moved from t to t'}.

I'm just asking you to explain the difference between {change in temporal position from t to t'} and {the object has moved from t to t'}. — Luke

Because motion in 4D is not given by a time duration, it is given by the geometry of the 4D object over that time duration. If the 3D position of the object varies, it is moving. If it does not, it is not.

Because motion in 4D is not given by a time duration, it is given by the geometry of the 4D object over that time duration. If the 3D position of the object varies, it is moving. If it does not, it is not. — Kenosha Kid

Here's how I read what you're saying:

There is a time duration/interval with start and end points at t and t'.
If the 3D position of the object changes ("varies") from t to t', then it moves from t to t'.
---
However, you continually deny that the 3D position of the object changes from t to t',

If the 3D position of the object changes ("varies") from t to t', then it moves from t to t'. — Luke

No. It moves from position to position. In classical kinematics, a body at rest is not said to move from t to t'. In relativistic kinematics, it is.

However, you continually deny that the 3D position of the object changes from t to t', — Luke

No, I attest that it does, i.e. its position is time-dependent. I deny that this necessitates something moving from t to t' in order to do so. This is a presentist idea invading an eternalist domain where it cannot exist. In 4D, geometry is sufficient for motion.

No. It moves from position to position. In classical kinematics, a body at rest is not said to move from t to t'. — Kenosha Kid

Let's compare what you said and how I read it:

You: "If the 3D position of the object varies, it is moving."
Me: "If the 3D position of the object changes ("varies") from t to t', then it moves from t to t'."

I understand that a body at rest is not said to move. But in order for it to move, it needs to change both spatial and temporal position. Even a body at rest can still change temporal position, right? However, this is what you continually deny - that a body changes temporal position.

No, I attest that it does, i.e. its position is time-dependent. I deny that this necessitates something moving from t to t' in order to do so. — Kenosha Kid

If the body does not change temporal position, then it cannot change spatial position either. You are injecting motion into static Eternalism based on what? That wherever there is a spatial position there is a temporal position? Unless something moves from t to t' (without you importing it in as an assumption), then nothing is moving.

But in order for it to move, it needs to change both spatial and temporal position. — Luke

With respect to what? A moving body's position changes with respect to time: that is the very gradient that tells us it is moving. In 4D, it is not that a 3D slice moves from time to time -- a presentist idea -- it is that the 4D geometry of the object is that of a moving body.

If a body moves from t to t', it must be moving with respect to something. Relativity has this "something". Classical mechanics does not.

You could invert the equation, and say that a body moves through time with respect to position: dt/dx. Of course, this is no longer kinematics, and the "movement" through time is undefined for restful bodies.

A moving body's position changes with respect to time: that is the very gradient that tells us it is moving. — Kenosha Kid

As I understand it then, according to 4D geometry, a 3D body changes spatial position with respect to temporal position only, but it does not actually change either spatial or temporal position. And despite not actually changing either spatial or temporal position, the 3D body still moves (or there "is" motion). Have I understood that correctly?

As I understand it then, according to 4D geometry, a 3D body changes spatial position with respect to temporal position only, but it does not actually change either spatial or temporal position. And despite not actually changing either spatial or temporal position, the 3D body still moves (or there "is" motion). Have I understood that correctly? — Luke

Not completely. The gradient in 4D may be with respect to other spatial dimensions just as it can in 3D.

The 3D position changes with respect to time; the 4D object does not change with respect to anything.

The altitude of the mountain changes the closer to the summit you go, but a given position of the 3D mountain does not change. Equivalent statement, projected down a dimension.

Have I understood that correctly?
— Luke

Not completely. The gradient in 4D may be with respect to other spatial dimensions just as it can in 3D. — Kenosha Kid

I'll take that as a "pretty much".

I understand now why you and @Pfhorrest have been attributing a second dimension of time or "hyper-time" to my view. I don't know what a change in both spatial and temporal position would be with respect to.

However, your position is that a 3D body moves without changing either its spatial or its temporal position. That's quite a magic trick! Your 3D body moves as much as a cross section of a mountain ascends itself.

However, your position is that a 3D body moves without changing either its spatial or its temporal position. That's quite a magic trick! — Luke

Not from an eternalist viewpoint, where it's just a fixed 4D body in 4D spacetime. It's just that there's an element of translation in how we imagine motion to seem. It's no longer "It was there and now it's here," so much as "It's there and here" because all of time is laid out.

The best way to tackle it is graphically. If you've ever drawn a diagram where you plot something over time, you have laid out time a bit like an eternalist universe. You can point to this time or that, see durations as lengths on the page, and you know there's nothing moving along the time axis to get from one point to another. You can also see whether something is changing with time (a wiggly line) or not (a straight line parallel to the time axis). Its exactly the same thing in the 4D eternalist universe where the thing changing with time is position. But nothing's moving along the time axis; it's all just laid out.