I was rejecting the idea that the 4D object moves wrt the 4D universe, an idea that would require some other dimension of time to make sense of. — Kenosha Kid

You have said that the 4D object does "sometimes move". Since you reject "the idea that the 4D object moves wrt the 4D universe", then with respect to what universe (3D? 5D?) does the 4D object "sometimes move"?

I frequently said that if the 4D object has slopes or wiggles, "it is moving", i.e. has motion, i.e. is sometimes moving. — Kenosha Kid

Is it the 4D object moving or a 3D part/s?

Refer to my previous explanation of how motion is recovered without assuming the 3D object at t' is the same as that at t, if you're interested — Kenosha Kid

You previously provided the same argument in about three different ways as far as I can tell, including this one:

motion may still be recovered in this eternalism, even if we assume the object at t' to be different to the object at t, so long as there exists another continuity connecting the objects at t and t'. This is at least sensible: we do not see an object disappear then be replaced by a different but indistingushable object.

Then we can define a new kinematics over that continuity, identical in mathematical form to the previous kinematics except maybe from some replacement of dummy variables (e.g. t -> i), and giving exactly the same net result. This thing would look identical to what motion looks like in normal eternalism, where the object at t' is just another part of the same object at t. — Kenosha Kid

My response is that: If the objects at t and t' are different, then you are no longer talking about the motion of a single object from t to t'. What's moving in that case? Given that the 4D object can be infinitely divided into 3D parts, then no single 3D part ever moves. Maintaining that they are different objects at t and t' doesn't help to prove that an object has motion from t to t' (or between t and t'), because it's not the motion of the same object (or 3D part) from one point to another (or between one point and another).

It is exactly in concord. "has motion", "is sometimes moving" appear to be equivalent expressions. — Kenosha Kid

You didn't say "has motion". You were apparently mocking the idea that a 4D object moves, saying it would require a "higher-dimensional space that would be hard to conceive of." You're now saying that a 4D object "sometimes moves", but this seems like an attempt to avoid the issue I've raised regarding the existence of different 3D parts vs. your assumption of a single 3D object changing position over time. I'm not trying to "catch you out", I'm arguing for my position.

The 4D shape is not moving. In what sense are the different 3D slices moving?
— Luke

It is, as in "it is sometimes moving". — Kenosha Kid

This contradicts your earlier statement:

It is not a condition in eternalism that a 4D object need move within a 4D space to have motion, since that would be a new kind of motion (hypermotion, I guess) in an even higher-dimensional space that would be hard to conceive of. — Kenosha Kid

TL;DR version: the concept of motion is recoverable even without continuity of identity — Kenosha Kid

How so? (I trust that your explanation will be about continuity of identity, rather than just saying "the gradient!" ("first base!")).

Having a gradient appears to mean no more than that a 3D part has a different spatial position than the spatial position of its temporal (3D part) predecessor. That they are the same 3D part (they're not) or that there is some sort of change/motion between parts (there isn't) is what you and @Pfhorrest appear to have simply assumed without argument.

If that shape is not just comprised of the same 3D slice for all times, it is moving. — Kenosha Kid

The 4D shape is not moving. In what sense are the different 3D slices moving?

In the same way, a mountain is not comprised of the same 2D slice at all altitudes and thus has a spatial gradient. — Kenosha Kid

Are the 2D slices moving?

I think you are a presentist in denial. You insist on presentist notions being true in 4D for motion to occur. — Kenosha Kid

That's irrelevant if we agree to a definition of motion.

The other thing I think you are both illicitly assuming is that it is the same 3D object/part over time.
— Luke

Yes, but that is true of any kinematics. — Kenosha Kid

It may be true and even required for motion, but that doesn't mean it's true or possible in Eternalism.

The other thing I think you are both illicitly assuming is that it is the same 3D object/part over time.

Basically, motion requires that an object changes its temporal position, but this does not and cannot occur in an Eternalist 4D universe. The object needn't change its temporal position with respect to anything else; it simply changes temporal position (or "moves over time"). You and @Kenosha Kid are both assuming that a 3D part of the 4D object changes temporal position and/or that the same 3D part changes spatial position, but it doesn't really.

It moves relative to time, which you would be perceiving as another spatial dimension. — Pfhorrest

The same way that radius moves along a mountain relative to altitude?

Pick a particle. Step outside of time and look down at a 4D model of the universe. That particle will look like some crazy string zig-zagging its wave through the universe. — Pfhorrest

Or it will look like a motionless string merely existing at all points.

At some point in time, that string is at one point in space. At other points in time, it is at other points in space. But there is no meta-time across which they can "previously" have been at one place at time t, but "now" they're in a different place at the same time t. — Pfhorrest

In other words, it doesn't move.

Given that motion is by definition with respect to time, just as spatial gradients are by definition with respect to space, you can't use them interchangeably any more than you can measure the radius of a mountain and say that's how tall it is. — Kenosha Kid

But you say that the radius changes wrt altitude (in a 3D object) just as spatial position changes wrt time (in a 4D object). They both "change" in the same respect, and time is just another spatial dimension, so why is there no motion in the mountain?

So what you're suggesting is about generalising the concepts of 3D shape and motion to a higher-order concept that encompasses both. — Kenosha Kid

I don't believe so. I'm saying that if there is motion within a 4D object, then there should also be motion within a 3D object, given that time is just another dimension like space (time is "space-like"). That is, I'm asking about generalising from 4D to 3D.

So you have a change in position over time. That’s exactly what motion is. — Pfhorrest

Except that no 3D part ever changes its temporal or spatial position.

Do the 2D cross-sections of a 3D mountain move? Is there motion in the 3D mountain?
— Luke

On geological timescales, sure. On hiker timescales, not so much. — Kenosha Kid

I may have been unclear. Here you are talking about motion of the mountain over time (over the fourth dimension), whereas I was asking about motion of the mountain in three dimensions only (over the third dimension).

You stated that: "4D is a generalisation of 3D that implements time as a dimension like space." If time is space-like, or to be treated as another spatial dimension, then it seems reasonable that space is also time-like (i,e. they are the same type of dimension). You also stated that: "Everything that is true about mountains in 3D is true about mountains in 4D", so it seems reasonable that the converse is also true. My question was intended to be whether there is motion in a mountain in three dimensions only.

It is merely x that need differ. The value at one time being different to that at another. This does not depend on something moving wrt something else along either x or t. — Kenosha Kid

Sounds like there is motion even though nothing moves.

This is worth clarifying: it is not an analogy. Everything that is true about mountains in 3D is true about mountains in 4D.

4D is a generalisation of 3D that implements time as a dimension like space. That which is true of space in 3D remains true of spacetime in 4D. Just as a mountain has a slope in altitude wrt radius in 3D, it does so in 4D. It may also have a slope in altitude wrt time (erosion or formation). — Kenosha Kid

Do the 2D cross-sections of a 3D mountain move? Is there motion in the 3D mountain?

Change which temporal position you're asking about, and the corresponding spatial position will be different. — Pfhorrest

Asking about it causes it to change?

the main road has a higher elevation in the north than it does in the south...So its elevation changes with latitude — Pfhorrest

Elevation might change wrt latitude, but nothing about the (3D) road changes at a time, including the position of any of its 2D cross-sections (per elevation).

But the road isn't moving north over time, and the 4D object isn't moving later through... something. — Pfhorrest

That's not analogous. In the case of your 3D road, it's the elevation of 2D cross-sections of the road changing wrt latitude/length. In the case of a 4D object, it would be (some attribute of) 3D cross-sections of the 4D object changing wrt time. It is not analogous for the 4D object to change/move. We are only considering the motion of a 3D object over time.

According to Eternalism, a 3D object does not move from here to there over time; it is always here and there over time. This is no different to the 2D cross-sections of your road, which do not change position either.

Sorry, I can't leave this alone.

But nothing's moving along the time axis; it's all just laid out. — Kenosha Kid

Motion or change along the time axis is required by the definition of motion (v=dx/dt). If there is no change in temporal position, then there is no motion. This is not according to a Presentist view of motion, but according to the definition of motion.

To repeat my argument against the 3D-4D analogy, a 2D cross-section of a mountain cannot change/move in the 3rd dimension, and neither can a 3D cross-section change/move in the 4th dimension. You might say that the radius of a 2D cross-section of a 3D mountain changes wrt altitude, and, likewise, that the spatial position of a 3D cross-section (body) of a 4D object changes wrt time. But none of this implies any motion of a 2D or 3D cross-section. By analogy, if there is motion in the 4D object, then there is motion in the mountain. I trust you would agree that there is no motion in the mountain.

I still think you're just reading motion into that graph that isn't necessarily there.

However, I don't think there's much more to say on the subject. Thanks for taking the time. I have very much enjoyed it. :smile: :up:

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.

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?

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.

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',

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'}.

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

Actually motion we get fir free. — Kenosha Kid

You don't say...

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.

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?

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.

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.

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.

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.

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.

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.

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'}?

If time is like a ruler, as per Eternalism, then there is no motion.

Then your definition of motion depends on temporal passage, which kinematics does not. — Kenosha Kid

If time is continuous, what else could change in temporal position of the object mean except that the object moves from one time to the next , i.e., temporal passage?

If you are happy with a ruler having length without changing position, you have no reasonable objection to a 4D object having duration without changing temporal position. — Kenosha Kid

If it doesn't change temporal position then it can't change spatial position. Motion = 0.

Either the object moves from t to t' and there is temporal passage (not B-theory).
Or the object does not move from t to t' and there is no motion.

How can a change in the temporal position of the object from t to t' not mean that the object has moved from t to t'?

And if the object has not moved in time, then the object has not moved.

You keep oscillating between these.

And you've agreed that the object has moved from t to t'.

If so, are you satisfied that a 3D part at time t' may differ from the 3D part a time t? — Kenosha Kid

Yes, representing a change in temporal position of the object. That is, the object has changed its temporal position.

It is not a condition in eternalism that a 4D object need move within a 4D space to have motion, since that would be a new kind of motion (hypermotion, I guess) in an even higher-dimensional space that would be hard to conceive of. — Kenosha Kid

No. I've only ever been talking about the motion of 3D objects in the 4th dimension; that is, 3D parts of the 4D object. This is what you consider with your temporal interval and this is what we mean when we talk about the motion of an object. I have not been talking about anything different.

To reiterate what's at stake here:

Motion has been defined as change in spatial position over change in temporal position (or dx/dt)

@Kenosha Kid states that: "A "change" in temporal position, as referred to by myself, meant nothing more than an interval of time over which we can consider different positions of the same object, i.e. it is a length of a section of the 4D object. It is not something the object does in classical kinematics."

@Kenosha Kid needs to remain consistent with B-theory Eternalism, in which the entire (4D) object exists at all times and time does not pass. Objects do not really travel through time according to the B-theory. Therefore, @Kenosha Kid does not want to say that the object actually moves from t to t'. So he maintains that a change in temporal position is no more than "an interval of time over which we can consider different positions of the same object".

However, if an object does not actually change its temporal position, then it cannot actually change its spatial position either. And if an object does not actually change its spatial position, then it doesn't actually move. According to the above definition of motion, that is.

@Kenosha Kid appears to be saying that an object both does and does not change its temporal position.