Hence the mountain that gets smaller with altitude even though it stays the same size with time; the pipe along its side that gains altitude as it moves westward, even though it’s not moving with respect to time; the abstract line that moves in a y-ward direction over the x-ward direction, even though it too doesn’t move with respect to time. — Pfhorrest
Allow me to fix the ambiguity:
Motion in (3D + time) = geometry in 4D. — Kenosha Kid
Some measure in the first n-1 dimensions changes over the last dimension. In the case of the mountain it’s diameter over altitude. — Pfhorrest
In the case of the mountain it’s diameter over altitude. In the case of me it’s height over time. — Pfhorrest
I am an eternalist, I've read the views of other eternalists plenty, and none of us deny that change or motion happen. — Pfhorrest
How can you give the diameter of a mountain without specifying at which altitude you mean? The mountain has different diameters at different altitudes. — Pfhorrest
You (and MU) seem to think that that sign is lying. "The road doesn't actually get narrower. — Pfhorrest
And I'm asking what justifies your assumption that such change/motion does happen? — Luke
You've been talking about a change in altitude/diameter. — Luke
I don't deny that it "gets" narrower over time — Luke
That I see it happen, and nobody's presented a good reason to doubt that. I remember things being different at earlier times than they are now. That's what change over time is. — Pfhorrest
A change in diameter over altitude. — Pfhorrest
The mountain isn't changing its altitude. Over the dimension of altitude, the mountain changes its diameter. — Pfhorrest
You believe that temporal passage is real? Perhaps you are a Moving Spotlight Theorist instead of an Eternalist. — Luke
The virgule was intended to signify "or", not division. — Luke
So nothing actually changes? It's merely comparative? — Luke
Moving Spotlight is nonsense; if something "moved" to give the perception of time, it would have to be over time, and so would appear static from a perspective outside of time — Pfhorrest
Nothing moves through time, and time itself doesn't move past anything. Saying that either of those things happens is nonsense. Things move through space over time. — Pfhorrest
They can also move through one dimension of space over another dimension of space, without bring time into anything at all. — Pfhorrest
All change is comparative. Something changes in one dimension with respect to another dimension. The road to my house changes its altitude in respect to its latitude (it gets higher the further north it goes). — Pfhorrest
What does a gradient have to do with motion? It's just an assumption that there is motion in the gradient. — Luke
I was shorter as a child than I am now. That child and the adult I am now are the same person. How can one person possibly be shorter or taller than themselves? The same way a mountain can be smaller at the top: we’re talking about an n-1 dimensional section of an n-dimensional whole. Some measure in the first n-1 dimensions changes over the last dimension. In the case of the mountain it’s diameter over altitude. In the case of me it’s height over time. — Pfhorrest
You may think it’s a weird way of talking, but understanding that way of talking is necessary to understand what eternalists mean, and if you don’t, then you’re not talking about the same thing as them at all. — Pfhorrest
It is the definition of velocity in kinematics. If position depends on time, position has a gradient with respect to time in the exact same way altitude has a gradient with respect to radius (and angle, for non-isotropic mountains :) ). In eternalism, position does depend on time, et voila: motion. — Kenosha Kid
Firstly, thank you for taking the time to try and clarify this matter for me. — Luke
I think that my argument is really more to do with the change in time that underpins motion. I don't understand what difference there is between the change in time found in Eternalism and the temporal passage of Presentism. — Luke
Kinematics holds in eternalism and presentism. That is, it doesn't care how you conceive of a change in time, whether it's a length or an evolving 'now'. Eternalism is more general and complete insofar as it both allows for and does not require motion forward in time to have motion in space. Presentism has a more tenuous position because it does need such a thing, be it a spotlight or whatever. — Kenosha Kid
position has a gradient with respect to time in the exact same way altitude has a gradient with respect to radius — Kenosha Kid
neither does the temporal position of the object change — Luke
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
However, in relativistic kinematics, an object does have a velocity in the temporal direction and so can be thought of, at any given time, as changing temporal position in a reference frame with respect to temporal position in its own rest frame. This is true at all times and requires no particular 'now'. Nor does motion completely depend on it, since photons have no temporal velocity and yet move pretty nippily.
We have been discussing the former, but happy to discuss the latter, or QM. — Kenosha Kid
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