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
Likewise, motion in 4D is manifest as a deviation from, say, a purely cylindrical shape (for the case of a 3D ball). — 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. — Luke
Is it a 3D or a 4D object that moves? — Luke
But moving wrt the 4D universe would be moving wrt a fifth dimension. — Kenosha Kid
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
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
Exactly, which is why I'm questioning your statement that a 4D object "sometimes moves". — Luke
How can that be? — Luke
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
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
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. — Kenosha Kid
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
that motion in 4D is an inevitable feature of geometry, that you cannot have shape in 4D without kinematic motion. — Kenosha Kid
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
... how can a 4D object have geometry and not kinematic motion? How can dx/dt be zero or undefined? — Kenosha Kid
in 4D geometry there exist two non-identical 3D objects at t and t' (and at all times in between) — Luke
It doesn't go away because you like to think of the hypersphere as being compromised of a plenum of 3D spheres. — Kenosha Kid
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
It's quite a departure from what you said just a day or two ago — Luke
But I guess thinking of them as "a plenum of 3D spheres" must just be my crazy idea. — Luke
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
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
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
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. — Luke
Then this is not kinematic motion. — Kenosha Kid
Except that no 3D part ever changes its temporal or spatial position. — Luke
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
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