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"?
— Luke

Its own temporal axis. — Kenosha Kid

How is this not the 4D object moving wrt the 4D universe (an idea you reject)? The temporal axis is the fourth dimension. If the 4D object moves with respect to its own temporal axis, then surely it moves with respect to the fourth dimension or wrt the 4D universe.

Likewise, motion in 4D is manifest as a deviation from, say, a purely cylindrical shape (for the case of a 3D ball). — Kenosha Kid

Is it a 3D or a 4D object that moves?

How is this not the 4D object moving wrt the 4D universe (an idea you reject)? The temporal axis is the fourth dimension. — Luke

But moving wrt the 4D universe would be moving wrt a fifth dimension. The 3D (2+1) representation I posted from Huw Price's talk would, if the 4D object moved wrt the 4D block, be an animation, i.e. changing with a time that wasn't already in the picture.

Is it a 3D or a 4D object that moves? — Luke

They're the same object and it's the same motion, just different representations. The 3D object changes position with time: this is our everyday experience of motion. The 4D object changes shape with time: motion in 4D is geometry. They're not describing two different things but the same thing as two different representations.

But moving wrt the 4D universe would be moving wrt a fifth dimension. — Kenosha Kid

Exactly, which is why I'm questioning your statement that a 4D object "sometimes moves".

The 3D (2+1) representation I posted from Huw Price's talk would, if the 4D object moved wrt the 4D block, be an animation, i.e. changing with a time that wasn't already in the picture. — Kenosha Kid

How is the animation supposed to work? What moves and how? Huw Price's talk contains only still pictures.

They're the same object and it's the same motion, just different representations. The 3D object changes position with time: this is our everyday experience of motion. The 4D object changes shape with time: motion in 4D is geometry. They're not describing two different things but the same thing as two different representations. — Kenosha Kid

How can that be? A 3D object would be defined by a dimensionless point on the timeline, or a slice of the timeline. No 3D point or slice moves from one time or space to another. All points/slices exist at all times of the 4D object. A 3D slice cannot move from t to t' because different 3D slices (i.e. different 3D objects) exist at both times. The slice at t never leaves t, which means the 3D object at t does not move or go anywhere. You appear to simply assume that it goes from t to t'. If t and t' are the start and end points of a gradient, then surely you are talking about a 3D object moving from/between t to t', especially if the 4D geometry is but two different representations of the same thing.

Exactly, which is why I'm questioning your statement that a 4D object "sometimes moves". — Luke

Then you are defining motion in 4D to be 5D, which is not standard kinematic motion. (We're going round in circles here.)

How can that be? — Luke

I don't think this demands explanation. You are perfectly familiar with 3D objects changing position with time. That is everyday experience.

If you're asking how it can be the same thing as geometry in 4D, do the maths: v=dx/dt in both representations. In 3D, 'dt' does not refer to a dimension. In 4D, it does, making motion a geometric feature.

Then you are defining motion in 4D to be 5D, which is not standard kinematic motion. (We're going round in circles here.) — Kenosha Kid

What? You have said both that a 4D object "sometimes moves" wrt "its own temporal axis", and that a 4D object "moving wrt the 4D universe would be moving wrt a 5th dimension". As I pointed out earlier, you've contradicted yourself.

If you're asking how it can be the same thing as geometry in 4D, do the maths: v=dx/dt in both representations. In 3D, 'dt' does not refer to a dimension. In 4D, it does, making motion a geometric feature. — Kenosha Kid

"dt" is a change in temporal position. In your view, does any part of a 4D object change its temporal position?

What? You have said both that a 4D object "sometimes moves" wrt "its own temporal axis", and that a 4D object "moving wrt the 4D universe would be moving wrt a 5th dimension". As I pointed out earlier, you've contradicted yourself. — Luke

No, motion is the gradient from a hyper-cylindrical (for a sphere) 4D geometry. You are conflating this gradient with movement with respect to the 4D block.

If you are understanding me as you claim to, then you have read me as saying that a mountain literally lifts up from the horizon, rather than grading up wrt it. And yet somehow this goes unmentioned by you.

As I've suggested many times now, your approach fails to address the principle problem it faces even obliquely: that motion in 4D is an inevitable feature of geometry, that you cannot have shape in 4D without kinematic motion.

Your approach instead is very clearly about getting someone to explain the same thing over and over and over again in an as many different ways as they can muster in good faith, then claiming those difference approaches to be contradictions according to some bizarre logic.

If you face the actual problem head on, there is a discussion to be had. But this is just 17 pages of utterly pointless repetition.

So... how can a 4D object have geometry and not kinematic motion? How can dx/dt be zero or undefined?

No, motion is the gradient from a hyper-cylindrical (for a sphere) 4D geometry. You are conflating this gradient with movement with respect to the 4D block. — Kenosha Kid

No, I'm correcting you where you said that the 4D object "sometimes moves" wrt "its own temporal axis". I never asserted this. And you have identified the problem with that statement yourself: it would require a 5th dimension.

Since motion of a 4D object does not make sense without invoking a 5th dimension - which neither of us want to invoke - then we can only be talking about the motion of a 3D object over time (over the 4th dimension). Right?

If you are understanding me as you claim to, then you have read me as saying that a mountain literally lifts up from the horizon, rather than grading up wrt it. And yet somehow this goes unmentioned by you. — Kenosha Kid

I don't understand what you mean when you say "a mountain literally lifts up from the horizon, rather than grading up wrt it." I'm here to discuss Eternalism, not geometry. But I am willing to go along with your talk of geometry anyway.

that motion in 4D is an inevitable feature of geometry, that you cannot have shape in 4D without kinematic motion. — Kenosha Kid

Are you familiar with begging the question?

Your approach instead is very clearly about getting someone to explain the same thing over and over and over again in an as many different ways as they can muster in good faith, then claiming those difference approaches to be contradictions according to some bizarre logic. — Kenosha Kid

Demonstrate how it's bizarre logic. You barely address my arguments, which I've also had to repeat constantly. All I get from you is that motion is assumed in the 4D geometry or gradient without any supporting argument. The closest you have come to an argument is this:

... how can a 4D object have geometry and not kinematic motion? How can dx/dt be zero or undefined? — Kenosha Kid

I've already provided an answer to this question, which is the argument I keep repeating: the measurement of v=dx/dt assumes that the motion (v) is of an identical 3D object between t and t', but in 4D geometry there exist two non-identical 3D objects at t and t' (and at all times in between). Therefore, the assumption of an identical object moving or having motion between two times in Eternalism is false. In short, you can't calculate the motion of a 3D object between t and t' if it's not the same object at t and t'.

In Presentism, an identical 3D object is assumed to leave t and travel to t', so it does not have this problem. You are attempting to insert this same Presentist motion into a 4D object, but it's just not there, either logically or physically. Motion is a Presentist notion. A cylinder cannot travel from one end of its length to the other.

in 4D geometry there exist two non-identical 3D objects at t and t' (and at all times in between) — Luke

In Eternalism, a 3D sphere becomes a D hypersphere which is a geometric object. That geometric shape has a well-defined dx/dt. That dx/dt is called motion. It doesn't go away because you like to think of the hypersphere as being compromised of a plenum of 3D spheres. It's still there in the 4D geometry.

It doesn't go away because you like to think of the hypersphere as being compromised of a plenum of 3D spheres. — Kenosha Kid

Yes, I suspected that you might make this move. It's quite a departure from what you said just a day or two ago:

They're the same object and it's the same motion, just different representations. The 3D object changes position with time: this is our everyday experience of motion. The 4D object changes shape with time: motion in 4D is geometry. They're not describing two different things but the same thing as two different representations. — Kenosha Kid

But I guess thinking of them as "a plenum of 3D spheres" must just be my crazy idea. And I guess you're also back to talking about the motion of a 4D object without any qualms that this requires a 5th dimension.

It's quite a departure from what you said just a day or two ago — Luke

Can you pin down where you think the inconsistency is? These are not contradictory statements. The first says that it doesn't matter for motion whether you think of a 4D object as one thing or a continuum of different things. The second says that the concept of motion is the same in presentism and eternalism, they are just represented differently, which they are: time is not a dimension in presentism, so motion is not a gradient.

But I guess thinking of them as "a plenum of 3D spheres" must just be my crazy idea. — Luke

I'm not arguing against it, it's just not the killer blow for motion you assume it to be.

And I guess you're also back to talking about the motion of a 4D object without any qualms that this requires a 5th dimension. — Luke

I never left.

Can you pin down where you think the inconsistency is? These are not contradictory statements. The first says that it doesn't matter for motion whether you think of a 4D object as one thing or a continuum of different things. — Kenosha Kid

You said: "It doesn't go away because you like to think of the hypersphere as being compromised of a plenum of 3D spheres". I think you meant "comprised". Nevertheless, the implication is that I "like to think of" a 4D object this way, whereas you do not.

But I guess thinking of them as "a plenum of 3D spheres" must just be my crazy idea.
— Luke

I'm not arguing against it, it's just not the killer blow for motion you assume it to be. — Kenosha Kid

My argument is not merely that you can think of a 4D object as comprised of 3D parts. Perhaps you would care to address my actual argument.

And I guess you're also back to talking about the motion of a 4D object without any qualms that this requires a 5th dimension.
— Luke

I never left. — Kenosha Kid

Motion of a 4D object means moving wrt the 4D universe. As you said: "moving wrt the 4D universe would be moving wrt a fifth dimension." If this is what you have been talking about all along, then we have been talking about different things.

Motion of a 4D object means moving wrt the 4D universe. — Luke

Then this is not kinematic motion e.g. dx/dt which merely requires a gradient of position wrt time.

I'm done. You have a fundamental contradiction in your argument and your preference is clearly to run around in circles forever lest you approach it. Your continued "Ah, but YOU said" approach, coupled with imagined contradictions between compatible statements, is tiresome, unproductive, and in bad faith. 17 pages of it are more than sufficient to satisfy me that you have absolutely no interest in the subject of your OP. Farewell!

Then this is not kinematic motion. — Kenosha Kid

Bloody hell, I know that. I'm trying to get you to disavow motion of a 4D object in the fifth dimension. But then you'd have to actually address my argument instead of just repeating your assumptions. Bye.

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

That's really interesting!

Do you view it as:

(1) The block has slices.
(2) The slices have temporal (1d) and spatial (3d) parts.
(3) The slices are all distinct. The time index ensures they are.
(4) Objects at t are subsets of a spacetime slice at t.
(5) Objects at t all include the time stamp t. They are space-time objects.
(6) In order for an object to move, they need to move in time.
(7) Objects include the time stamp, so cannot move in time.
(8) Objects cannot move in time.

?

In this block universe view, objects are all spacetime objects, and individuated by both their spatial and temporal parts. Because objects are individuated by their temporal parts, a spacetime object which is characterised as moving from t to t' is actually changing identity over that time period. There's not "a spacetime object in motion".

If you want to define "motion" in terms of an entity's 3d parts changing with respect to time but still hold that objects are spacetime slice subsets that must include time, that actually looks to dodge the issue created by throwing the temporal parts into the individuating conditions of objects.

Sound about right?

Hi @fdrake, yes that all sounds about right.

Because objects are individuated by their temporal parts, a spacetime object which is characterised as moving from t to t' is actually changing identity over that time period. There's not "a spacetime object in motion". — fdrake

Yes, and since each 3D temporal part exists at its own spacetime location, then no part can move to another spacetime location that isn't occupied.

Before this discussion exits to oblivion, I just wanted to add the (now probably rhetorical) question: What does motion mean in Eternalism?

Eternalists can't say that something "has moved", "is moving", or "will move"; these are A-theory or Presentist designations which presuppose temporal passage. Without temporal passage, B-theory Eternalists can only say that "there is motion" at (or over?) a given time period, or length of time. But what does "there is motion" mean?

One would assume it means the same as what Presentists mean by it: that a 3D object moves from here to there or changes spatial position over time (or wrt a change in temporal position). However, nothing changes temporal or spatial position in Eternalism. So, what is this mysterious motion of Eternalism? Earlier in the discussion, I was informed that such motion is represented by a gradient running away from the temporal axis, in contrast to a line running parallel to the temporal axis that represents no motion. However, the line running parallel to the temporal axis does not signify that a 3D object changes temporal position any more than a gradient running away from the temporal axis signifies that a 3D object changes spatial position. The line doesn't "run" at all.

For the sake of argument, let's allow the Eternalists their motion. If we accept that there is motion between, e.g., t1 and t2, despite the fact that no 3D object moves or changes spatiotemporal position between t1 and t2, then how is this motion supposed to work? Will there forever be motion between t1 and t2? Does everything move "on the spot" or at each spatiotemporal position - without changing position? What is Eternalist motion if it is not a 3D object moving from here to there over time? Isn't this Presentist view of moving from here to there over time, or of changing spatiotemporal position, the only meaning that there can be of the word "motion"? What is Eternalist motion if not this?