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). — Luke
Change which temporal position you're asking about, and the corresponding spatial position will be different. — Pfhorrest
the main road has a higher elevation in the north than it does in the south...So its elevation changes with latitude — Pfhorrest
But the road isn't moving north over time, and the 4D object isn't moving later through... something. — Pfhorrest
Motion or change along the time axis is required by the definition of motion (v=dx/dt). — Luke
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. — Luke
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
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
Asking about it causes it to change? — Luke
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). — Luke
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. — Luke
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). — Luke
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. — Luke
Except that no 3D part ever changes its temporal or spatial position. — Luke
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
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
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
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. — Luke
The other thing I think you are both illicitly assuming is that it is the same 3D object/part over time. — Luke
If that shape is not just comprised of the same 3D slice for all times, it is moving. — Kenosha Kid
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
I think you are a presentist in denial. You insist on presentist notions being true in 4D for motion to occur. — Kenosha Kid
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
The 4D shape is not moving. In what sense are the different 3D slices moving? — Luke
Are the 2D slices moving? — Luke
It may be true and even required for motion, but that doesn't mean it's true or possible in Eternalism. — Luke
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
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
This contradicts your earlier statement: — Luke
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. — Luke
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." — Luke
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. — Luke
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
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
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
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
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
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'. — Luke
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