It seems to me that you have ignored some of the more difficult questions I put to you, — Luke

Fundamentally speaking, you're trying to illustrate a problem with the notion of a change-over-place as opposed to a change-over-time. Your questions can so far be classified into one of three types, which I'll just label here. Type A questions can be trivially addressed by a proper analog from place to time. Type B questions assert something that is ridiculous when applying the analog from place to time. Type C questions are non-analogous only in the sense that they apply particularly to change-over-time.

such as how a colour in Banno's image can "approach" the rightmost x-coordinate, — Luke

This is a Type A question. A time analog would be a video comprised of 1110 frames of 1x662 images. If we were to take the Euclidean distance of colors to the color at 1106 (0-based frame indexing) as they change-over-time in such a video and map the progression over-time, the graph would look like this:

...incidentally, this is the exact graph I showed you three days ago, which shows how the color's in the image approach the color at 1106 over-x-coordinate.

Unless you have an objection that the colors in the video approach the color at frame 1106, then all you're doing is begging the question.

or how an x-coordinate can increase. — Luke

This is a Type B question. Single points do not change, even in a change-over-time sense. You are trying to have your cake and eat it too. You're demanding that a single point change and then turning around and demanding there be multiple points in time.

"Motion by the way is change in position over change in time." — InPitzotl

Per this definition of motion, how can O move if "nothing is changing time"?
Analogously, how can O move if nothing is changing position? — Luke

Position here refers to the x,y,z coordinates. P1=(1,1,1) is an x,y,z coordinate. P2=(2,1,1) is an x,y,z coordinate. Statements like R1="O is at P1" are time-relative statements; we consider the truth value of such statements to change depending on the time of consideration. R1 is true at t=1; R1 is false at t=2.

A=(1,1,1,1) includes a time coordinate; this is equivalent to "P1 at t1". D=(2,1,1,2) likewise is equivalent to "P2 at t=2". The statement "O is at A" is thus equivalent to "O is at P1 at t=1". That is a time-fixed statement. The truth value of time-fixed statements do not change over time. If it is ever true that O is at P1 at t=1, it is always true. The past cannot change.

O does not move from A to D; O is always at A and always at D. O moves from P1 to P2 by virtue of having-been at P1 at some time, and then having-been at P2 at some different time. In the time-slice of t=1, O is at P1. In the time-slice of t=2, O is at P2. Those are different locations at different points in time, and that is what I said motion was... a change in position over a change in time.

Likewise, in Banno's image, in the coordinate slice x=850, the color is (253,216,218). In the coordinate slice x=900, the color is (253,204,155). There is no more anything moving from x=850 to x=900 here than there is something moving from (1,1,1,1) to (2,1,1,2); the color is always (253,216,218) at x=850 just as O is always at (1,1,1) at t=1, and the color is always (253,204,155) at x=900 just as O is always at (2,1,1) at t=2.

Perhaps you allow for an object to change in position — Luke

Sure. It changes position over time in the exact same fashion that Banno's image changes color over x coordinate.

It seems logical to me that if nothing is changing in time then nothing is changing in place, either. — Luke

But it is changing in time, just as Banno's image is changing in space. You're just misconceiving what a change is. The "thing" you're asking me to show moves from the left to the right is the "thing" you're assuming moves from the O at (1,1,1) at t=1 to the O at (2,1,1) at t=2, and that is the reified erroneous object you presume to exist that there is no such thing as. There is no such thing as that moving thing; there is only the O at (1,1,1) at t=1 and the O at (2,1,1) at t=2, and it is that thing that meets the criteria requisite to say O moved from (1,1,1) to (2,1,1).

Then nothing moves or changes (according to your definition of motion). — Luke

No, there's no such thing as Lukeian motion. It suffices for InPizotlean motion that the O-at-P1-at-t1 and the O-at-P2-at-t2 are in different places at different times; it's just the Lukeian concept of motion that requires this reified O-ghost to move through the O-at-P1-at-t1 into the O-at-P2-at-t2 for there to have been a motion of O. My definition makes no reference to this reified O-ghost.

such as how a colour in Banno's image can "approach" the rightmost x-coordinate,
— Luke

This is a Type A question. A time analog would be a video — InPitzotl

I’m asking you to explain this “approach” to the rightmost x-coordinate absent of time, so your analogy that includes time doesn’t help.

or how an x-coordinate can increase.
— Luke
This is a Type B question. Single points do not change — InPitzotl

You said earlier:

The colors are changing their distance to (252,176,65). The claim is equivalent to saying the color at an x coordinate approaches the color at the right as the x coordinate increases. That is equivalent to saying the color-distance of the color to the color at the right approaches 0. — InPitzotl

I’m looking for you to explain this “increase” in the x-coordinate. You said it, not me. I asked you what this change in the x-coordinate represents and how it increases.

You're demanding that a single point change — InPitzotl

No, I’m asking how can the x-coordinate “increase”, or how can any colour “approach” the colour on the right, given that there is no time and nothing changes position.

It seems logical to me that if nothing is changing in time then nothing is changing in place, either.
— Luke

But it is changing in time — InPitzotl

You said in your previous post that I was responding to:

When O moves from A=(1,1,1,1) to D=(2,1,1,2), nothing is changing time. — InPitzotl

Now you are saying that something is changing in time? Well, which is it?

go away marco :roll:

I got nowhere else to go... All people are against me...

:cry:

I’m asking you to explain this “approach” to the x-coordinate absent of time, so your analogy that includes time doesn’t help. — Luke

Not sure what you're looking for; if it's analogous, it's the same property. But okay.

Given an ordered sequence of values v₁, v₂, v₃, ..., v_n, and a distance metric D; if the sequence has the property that $i \lt j \Rightarrow D(v_j,v_n) \lt D(v_i,v_n)$, then we say that the sequence approaches v_n. (FTR, this is a simplification good enough for our purposes here).

Surely the statement refers to a change in the degree of difference of the color at a given x coordinate? — Luke
No, it refers to a change in degree of difference of the color over different x coordinates. — InPitzotl

"or how an x-coordinate can increase." — Luke
This is a Type B question. Single points do not change, — InPitzotl

You said earlier:
"...The claim is equivalent to saying the color at an x coordinate approaches the color at the right as the x coordinate increases. ..." — InPitzotl — Luke

I’m looking for you to explain this “increase” in the x-coordinate. You said it, not me. I asked you what this change in the x-coordinate represents and how it increases. — Luke

Consider three points: B1=(900,10), B2=(850,1), B3=(850,17); their colors are C1=(253,204,155), C2=(253,216,218) and C3=(253,216,218) respectively.

Given this particular set of points and associated colors, the statement above is describing the ordered sequence (253,216,218), (253,204,155). Each element in this sequence is "the color at an x coordinate". The sequence's order is specified by "as the x coordinate increases"; the order of said x coordinates is 850, 900. The statement is claiming that this sequence approaches the color on the right.

"But it is changing in time" — InPitzotl
You said in your previous post that I was responding to:
"When O moves from A=(1,1,1,1) to D=(2,1,1,2), nothing is changing time." — InPitzotl
Now you are saying that something is changing in time? Well, which is it? — Luke

Those look like different phrases to me. Refer to your quote here:

You are simultaneously asserting that nothing changes place while relying on a change of place (change of x-coordinate) in your calculation. — Luke

"Change time" without the "in" is used as an exact analog to "change place" in this quote. B2 doesn't change places to B1; B2 and B1 are merely different places on the same image. The "change" presumably involves a time at which something is at B1, followed by a time when it is at neither B1 nor B2 but traveling, followed by another time at which it is at B2 and not B1. O doesn't do that either. There's no such thing as a time when O is not at A.

"Change in time" with "in" contrasts with this; to me, this indicates a time relative view. O changes in time; as you change time coordinates, you get a change in position. Analogously, the color changes in x coordinates; as you change the x coordinate, you get a change in color.

Time is far nearer than distance.

Time is Now.

Describe Now.

Change in an x takes place with respect to something else, a y for instance. An image that displays change in color left-right, up-down, diagonally, or any other direction can be taken as change in color with respect to distance. However, a change in distance is always accompanied by a change in time. Otherwise division by zero $\frac{some \space distance}{0 \space time}$ ($\infty$ speed?)

Suppose the color im question is red and it changes at the rate from 10/cm where 10 is a measure of intensity of red. There's a speed here that comes with the cm (distance). Suppose this speed is 5 cm/s. What's the temporal rate of the color change? $\frac{10}{cm} \times \frac{5 \space cm}{s} = \frac{50}{s}$

Describe Now. — theRiddler

The now is constantly running from the past, fleeing towards the future. The past never catches up, the future always resides. We're caught in between.

Given an ordered sequence of values v1, v2, v3, ..., vn, and a distance metric D; if the sequence has the property that i<j⇒D(vj,vn)<D(vi,vn), then we say that the sequence approaches vn. — InPitzotl

Consider three points: B1=(900,10), B2=(850,1), B3=(850,17); their colors are C1=(253,204,155), C2=(253,216,218) and C3=(253,216,218) respectively.

Given this particular set of points and associated colors, the statement above is describing the ordered sequence (253,216,218), (253,204,155). Each element in this sequence is "the color at an x coordinate". The sequence's order is specified by "as the x coordinate increases"; the order of said x coordinates is 850, 900. The statement is claiming that this sequence approaches the color on the right. — InPitzotl

This doesn't tell me what the increase in the x-coordinate represents. I imagine it represents something in space?

I don't see why you've needed to introduce an ordered sequence of values, or why the sequence's order had to have been specified by "as the x coordinate increases".

O doesn't do that either. There's no such thing as a time when O is not at A.

"Change in time" with "in" contrasts with this; to me, this indicates a time relative view. O changes in time; as you change time coordinates, you get a change in position. Analogously, the color changes in x coordinates; as you change the x coordinate, you get a change in color. — InPitzotl

So you maintain that there is no time when O is not at A, that nothing moves or changes. Right? Or, as you expressed it earlier:

When O moves from A=(1,1,1,1) to D=(2,1,1,2), nothing is changing time. O moves because O is at A and is at D, D and A are at different times, and D and A are at different places (and more reasons which I'll ignore here for now). O never stops being at (1,1,1) at t=1. There's no such thing as a thing that moves from (1,1,1) at t=1 to (2,1,1) at t=2: — InPitzotl

This describes your view that nothing "changes time".

However, you also hold the view that things do "change in time"? I find these to be opposing views. The latter is, as you say, "the time relative view". According to this latter view, "as you change the x coordinate, you get a change in color". This is the view of change-over-space that you and Banno believe is possible without time? But in your view nothing "changes time"; nothing changes its x-coordinate or its t-coordinate. "O never stops being at (1,1,1) at t=1", like you said. So how can you hold both the time relative view where "you change the x coordinate" and the time absolute view where you don't?

Space $\uparrow$



Time $\uparrow$

To see what philosophy in modern times looks like, read some actual philosophy — SophistiCat

Yup. Some good recent books also, like Sebastian Rödl, Categories of the Temporal: An Inquiry into the Forms of the Finite Intellect, Harvard University Press, 2012, and Yuval Dolev, Time and Realism: Metaphysical and Antimetaphysical perspectives MIT Press, 2007.

This doesn't tell me what the increase in the x-coordinate represents. I imagine it represents something in space? — Luke

Are you trying to ask how the coordinates are laid out in graphics? The coordinates are labeled x and y thusly: (x,y). For any a and b, (a+1,b) is one pixel right of (a,b). (a,b+1) is one pixel down from (a,b). (0,0) is the coordinate of the leftmost topmost pixel.

I don't see why you've needed to introduce an ordered sequence of values, — Luke

Because that's what you asked me to do:

I’m asking you to explain this “approach” to the x-coordinate absent of time, so your analogy that includes time doesn’t help. — Luke

...Banno's image consists of an array of pixels. The x coordinates form a finite ordered sequence. The colors associated with the x coordinates form a corresponding finite ordered sequence. Approaching a value is a description of what ordered sequences do.

or why the sequence's order had to have been specified by "as the x coordinate increases". — Luke

Because that's the phrase under question:

The claim is equivalent to saying the color at an x coordinate approaches the color at the right as the x coordinate increases. — InPitzotl

So you maintain that there is no time when O is not at A — Luke

Correct. "O is at A" no matter what time you say it. "O is at A" is a time-fixed claim. "O is at A" is true at t=1, and "O is at A" is true at t=2.

However, you also hold the view that things do "change in time"? — Luke

Correct. "O is at P1" is a time relative claim. "O is at P1" is true at t=1. But "O is at P1" is false at t=2. "O is at P2" is false at t=1. "O is at P2" is true at t=2. Time relative claims have truth values relative to the time under consideration. P1 to P2 is a change in position of O over the change in time of O from t=1 to t=2.

I find these to be opposing views. — Luke

"View" is not the right word to apply here; these are manners of speaking.

According to this latter view, "as you change the x coordinate, you get a change in color". — Luke

Almost. This phrasing is x-coordinate relative, not time relative. "as you change the x coordinate" is telling you what it's relative to.

This is the view of change-over-space that you and Banno believe is possible without time? — Luke

It's not time relative; it does not matter when you say it. And it's not time fixed; it's not talking about a particular point in time. It is x-coordinate relative.

But in your view nothing "changes time"; nothing changes its x-coordinate or its t-coordinate. — Luke

Correct. There isn't an O-ghost that moves from O-at-A to O-at-D. There's just the O-at-A and the O-at-D. And there's no coordinate ghost that moves from 850 to 900. There's just a coordinate of 850 and a coordinate of 900.

So how can you hold both the time relative view where "you change the x coordinate" and the time absolute view where you don't? — Luke

They aren't views; they are manners of speaking. Our language is filled with relative and fixed references; "yesterday" is a time relative reference to a day, "Jan 27, 2022" is a time fixed reference. The fact that sometimes I use relative references and sometimes fixed references is not a conflict.

In the previous post I considered first B1 at time T1 let's say, then B2 at T2, then B3 at T3, where T1<T2<T3. But the x coordinate ordering here is (B2=B3) < B1. This demonstrates that the ordering has nothing to do with the ordering of consideration. What does it have to do with then? Exactly what it says on the tin... an increase of x coordinate values. If I remove the "at"'s in all of the above, I still get a time ordering with fuzzy time relative references ("first B1, then B2, then B3"), and it still has nothing to do with the x coordinate ordering, which is still the same ordering (B2=B3) < B1. So where is this alleged conflict you see?

This thread illuminates what it is to be a philosopher in modern times — jgill

No, it doesn't. To see what philosophy in modern times looks like, read some actual philosophy, e.g. here: https://philpapers.org/browse/time/ — SophistiCat

Since we are talking about time, glancing over some of the papers in the metaphysics of time (the truly philosophical area) much concerns the A-theory and the B-theory, and reading on one finds that subjects in physics, like relativity theory, come into play. Here the philosopher can only use popular versions of physics phenomena in their arguments - unless they have more in-depth knowledge of physics.

In the philosophy of mathematics it would appear that one becomes equally versed in foundation and set theory in order to make contributions. But I speculate. You may be right.

The problem of time can be reduced to the one way direction it goes on the macro level and the two way direction it flows at the micro level. All elementary particles motions are symmetric in time. The collective behavior is such that the particle patterns change unidirectional. But why all particles don't have an opposite velocity?
It are the collective motions and interactions that can be said to constitute time. The relations, the distances, between them, change and the time on a clock quantifies the process.

Are you trying to ask how the coordinates are laid out in graphics? — InPitzotl

No. I'm asking what the increase in the x-coordinate - that you mentioned earlier - represents. This applies equally to your hill example. What does an increase in the x-coordinate represent there? Again, I imagine it represents something spatial concerning the image or the hill, not something concerning an algorithm.

...Banno's image consists of an array of pixels. The x coordinates form a finite ordered sequence. The colors associated with the x coordinates form a corresponding finite ordered sequence. — InPitzotl

Why must the ordered sequence of the colours in the picture be from left to right? More to the point, why must the sequence approach "n" at all? Who or what is calculating the ordered sequence to "n" to enable the "approach"? In other words, what initiates the ordered sequence being followed?

or why the sequence's order had to have been specified by "as the x coordinate increases".
— Luke

Because that's the phrase under question:

The claim is equivalent to saying the color at an x coordinate approaches the color at the right as the x coordinate increases. — InPitzotl

That's circular. The x-coordinate increases because of the sequence's order and the sequence's order had to be specified by "as the x coordinate increases"...because that's what's in question? That's no explanation.

I find these to be opposing views.
— Luke

"View" is not the right word to apply here; these are manners of speaking. — InPitzotl

I was talking about your viewpoint(s) or opinion(s). I meant that I find them to be conceptually opposed; contradictory, incompatible.

According to this latter view, "as you change the x coordinate, you get a change in color".
— Luke

Almost. This phrasing is x-coordinate relative, not time relative. "as you change the x coordinate" is telling you what it's relative to. — InPitzotl

Sure, it's the space-relative view, analogous to the time-relative view. I understood that you were drawing an analogy. But you still hold these relative views and don't consider them to be problematic or incompatible with your opinion that nothing moves or changes position, right?

This is the view of change-over-space that you and Banno believe is possible without time?
— Luke

It's not time relative; it does not matter when you say it. And it's not time fixed; it's not talking about a particular point in time. It is x-coordinate relative. — InPitzotl

Like I said, "without time".

There isn't an O-ghost that moves from O-at-A to O-at-D. There's just the O-at-A and the O-at-D. And there's no coordinate ghost that moves from 850 to 900. There's just a coordinate of 850 and a coordinate of 900. — InPitzotl

But on the time-relative view that you endorse, which is analogous to the space-relative view, there is an O-ghost. The O-ghost on the space-relative view is the increasing x-coordinate.

And there's no coordinate ghost that moves from 850 to 900. There's just a coordinate of 850 and a coordinate of 900. — InPitzotl

What about the increasing x-coordinate(s) and their associated colour(s) "approaching" the colour on the right? Isn't 900 to the right of 850? Doesn't the colour at 850 "approach" the colours to its right, including the colour at 900?

The true mystery of time is not it's nature. Change in space and change in space go hand in hand. The comments here bear witness to that. The physical aspect seems to be clear. As the OP rightfully claimed, there are two kinds of physical time. Clock time, which is reversible ("let's turn back the clock"), and thermal time, which goes in one direction on the macro level.

The real mystery is the experience of time. Sometimes an hour seems passed in a second, sometimes a minute takes an hour... Why is that? Why the good things last so short and the bad things that long?

It is common nowadays for philosophers to have a second (or indeed first) degree in the discipline in which they specialize. I know of some prominent philosophers of physics with physics or math degrees: David Albert, David Wallace, Huw Price, Dennis Dieks.

Like I said, don't take us bullshitting on this forum as an indication of what's going on in academic philosophy.

As an acolyte of the doctrine of self-reliance, I frequently engage in proselytizing new members for the Dual Time Society (DTS). The enlightened disciples in this new age of pure enlightenment are strict followers of Dual Time Theorem (DTT), and in this new age of time awareness a strict following of this theorem is a welcome tool in the struggle of liberation from the bondages we are straightly jackened into by simplex-time implementation. It's time to smash the clock and break the watch.

DTT is a purely physical explanation of puzzles encountered in quantum mechanical and general relative approaches to time. It offers a coherent, self-consistent way out of the conundrums and paradoxes encountered in contemporary philosophy of time.

This doesn't tell me what the increase in the x-coordinate represents. I imagine it represents something in space? — Luke

The coordinates are labeled x and y thusly: (x,y). For any a and b, (a+1,b) is one pixel right of (a,b). (a,b+1) is one pixel down from (a,b). (0,0) is the coordinate of the leftmost topmost pixel. — InPitzotl

No. I'm asking what the increase in the x-coordinate - that you mentioned earlier - represents. — Luke

What do you mean by "no"? You asked me what an increase in x coordinates means in terms of space. I gave you a full specification of the coordinate system in an image, including the spatial relation you asked for. If you're looking for something else, I'm afraid you have to rephrase your question.

Why must the ordered sequence of the colours in the picture be from left to right? More to the point, why must the sequence approach "n" at all? Who or what is calculating the ordered sequence to "n" to enable the "approach"? In other words, what initiates the ordered sequence being followed? — Luke

I don't see any real questions here. This is just a giant chain of leading questions based on dubious premises.

"Because that's the phrase under question:
'The claim is equivalent to saying the color at an x coordinate approaches the color at the right as the x coordinate increases.'" — InPitzotl
That's circular. — Luke

No, it's reference. Surely you're not trying to make an argument against staying on topic in a thread? This is the example you're asking about, right?

You seem to be making an assumption that somebody claimed that only in this direction does a color approach another color. But you dreamed that claim up whole cloth, then leaned into it as if to prove someone wrong. It's downright Quixotic. The only special thing about increase in x coordinates here is that Banno posted an image and made a claim about a change of color from left to right.

But you still hold these relative views and don't consider them to be problematic or incompatible with your opinion that nothing moves or changes position, right? — Luke

Nope. I never said nothing changes or moves position; you said I said that.

Like I said, "without time". — Luke

That does not follow.

But on the time-relative view that you endorse, which is analogous to the space-relative view, there is an O-ghost. The O-ghost on the space-relative view is the increasing x-coordinate. — Luke

That's not an O-ghost (in my endorsed "view"); that's just O moving. Refer to this:

Under "reference", I show O moving from (1,1) to (2,1). O here is the yellow dot with the gray border.

Under "right", I show the same thing using a spatial coordinate for t. In this depiction O looks like a thick gray line, because it is smeared through all intermediate points, because if O is ever at some point (x_k,y_k,t_k), it is always at that point.

Under "wrong" there are two O's, and one of them doesn't belong. There's the O that actually traces a path in time; that is, the genuine O, the real deal. That is the thick gray line. And then there is that second O that moves through the genuine O from (1,1,1) to (2,1,2). That second O is the ghost that doesn't belong. That is the reified fictitious monster you keep trying to find in Banno's image that isn't there.

Incidentally, none of these depictions have to do with time-relative versus time-fixed references. I can describe points in both the left and the right images using both time-relative and time-fixed references.

What about the increasing x-coordinate(s) and their associated colour(s) "approaching" the colour on the right? — Luke

I was chocking this up to a mistake earlier and ignoring it, but you repeated it here. The increasing x-coordinates are not approaching the color on the right; they are just increasing, as it says on the tin. The colors are approaching the color on the right; but that phrase is an underspecification. Approaching is something an ordered sequence does, and we have to specify how the colors are ordered so we can meaningfully say it's approaching the color. That is what the phrase "as the x-coordinate increases" does... it imposes the order.

This was already explained to you.

All the same, this thread is embarrassing.

I know of some prominent philosophers of physics with physics or math degrees: David Albert, David Wallace, Huw Price, Dennis Dieks. — SophistiCat

Certainly doctorates in physics or math - especially theoretical physics - can place one in the borderlands of philosophy and science. That was my point. Thanks for the info.

in the borderlands of philosophy and science — jgill

Once upon a time...

This doesn't tell me what the increase in the x-coordinate represents. I imagine it represents something in space?
— Luke

The coordinates are labeled x and y thusly: (x,y). For any a and b, (a+1,b) is one pixel right of (a,b). (a,b+1) is one pixel down from (a,b). (0,0) is the coordinate of the leftmost topmost pixel. — InPitzotl

This does nothing but replace x-coordinates with a-pixels. None of this explains what the increase (a+1 or x+1) represents or why there is an increase. What is represented by the increase from a to a+1? You have used mathematics to demonstrate that there is an increase, but you then explain this increase as mathematical. I don't agree that there is any change over space without time. Where does this change come from? What, in spatial terms, does this change represent? Your explanation is circular, referring to the increase itself, not to what it represents.

It might be clearer if you could explain what the increase represents in terms of the hill. What does the increase in the x-coordinate represent there? Does it represent a change in position on the hill? If so, what has changed position on the hill? (Please do not say that the x-coordinate has changed position on the hill.)

The only special thing about increase in x coordinates here is that Banno posted an image and made a claim about a change of color from left to right. — InPitzotl

The claim is that there can be a change in colour over a change in space, absent of time. I am of the opinion that, absent of time, nothing changes in space. Therefore, I think you need to account for the assumed change in space (absent of time) and/or what such change represents or corresponds to. If your argument is that things can change in space (absent of time), then you can't simply assume that things do change in space (absent of time) in your argument. You want to say "as the x-coordinate increases, then there is a change in colour/height". But you first need to account for how the x-coordinate increases (absent of time), and what that increase represents. Otherwise, I think you are begging the question.

Nope. I never said nothing changes or moves position; you said I said that. — InPitzotl

You've said that nothing moves or changes position in various ways recently:

There's no such thing as a thing that moves from (1,1,1) at t=1 to (2,1,1) at t=2 — InPitzotl

O does not move from A to D; O is always at A and always at D. — InPitzotl

B2 doesn't change places to B1; B2 and B1 are merely different places on the same image. — InPitzotl

I was chocking this up to a mistake earlier and ignoring it, but you repeated it here. The increasing x-coordinates are not approaching the color on the right; — InPitzotl

Isn't each colour associated with an x-coordinate? If the colours are approaching the colour on the right, as you say, then I don't see how each x-coordinate isn't also approaching the colour on the right. You said that the x-coordinates were increasing, yes?

The increasing x-coordinates are not approaching the color on the right; they are just increasing, as it says on the tin. — InPitzotl

Why are the x-coordinates increasing?

The colors are approaching the color on the right; but that phrase is an underspecification. Approaching is something an ordered sequence does, and we have to specify how the colors are ordered so we can meaningfully say it's approaching the color. That is what the phrase "as the x-coordinate increases" does... it imposes the order. — InPitzotl

This is still circular: the x-coordinates increase due to the ordered sequence, and the ordered sequence is ordered due to the phrase "as the x-coordinates increase".

This thread has become nothing more than a conflation between verb and noun of the word "change"

You took the words right out of my mouth! There exist no space-like world lines in physics. Only time- and light-like. Both involve space and time. Every change in space is accompanied by a change in time.

Question to change over distance advocates. What causes change over distance?

I'll try to compress your wrongness here... Luke, you are very confused; possibly hopelessly so.

Exhibit A:

This does nothing but replace x-coordinates with a-pixels. — Luke

What the heck is an a-pixel? And what do you mean "replace x-coordinates"? a and b here are numbers; (a,b) expresses an x,y coordinate with x=a and y=b. 12+1=13; so (13,7) is one pixel right of (12,7), and (7,13) is one pixel down from (7,12). FYI, this is grammar school level competency.

Exhibit B:

You've said that nothing moves or changes position in various ways recently: — Luke

None of those things say "nothing moves"; none of them say "nothing changes". Incidentally, isn't this you?:
Exhibit B2:

Nothing about it has changed — Luke

...so I would like to know, Luke, if you're going to prefer to be consistent and claim that you are saying nothing changes, or honest and admit that you are just building straw men.

Exhibit C:

You have used mathematics to demonstrate that there is an increase, but you then explain this increase as mathematical. — Luke

...exactly what you would expect, if the increase is mathematical. That 5 is an increase from 3 ipso facto makes it an increase in value because it is that value being described by increase.

Exhibit D:

If the colours are approaching the colour on the right, as you say, then I don't see how each x-coordinate isn't also approaching the colour on the right. — Luke

This I believe is the first time in my life that I have seen a mathematical form of guilt by association fallacy. The fact that you don't see why this is wrong, I'm afraid, disqualifies you from having this conversation; it's basically a tacit admission that you don't understand what approach means. But to let you in on it, no. It doesn't work like that. We would never say given f(x)=x/2, that x approaches 5 as it approaches 10 because it is associated with a f(x) value; and that's a case where x and f(x) are both numbers in the first place. In Banno's image, x is a number and "f(x)" is a color.

It might be clearer if you could explain what the increase represents in terms of the hill. What does the increase in the x-coordinate represent there? — Luke

Coordinates are grammar school material, Luke. You shouldn't be confused in the first place.

I am of the opinion that, absent of time, nothing changes in space. — Luke

I think the main problem here is your own confusion.

Therefore, I think you need to account for the assumed change in space (absent of time) and/or what such change represents or corresponds to. — Luke

...I smell an epistemic double standard. The value of your opinion is proportional to the justification. You're not only lacking that; you're apparently so allergic to opposition, you invent straw men even on points you agree with (exhibit B).

So let's talk about that word change. That is an English word; used by English speakers. Applied to change-over-place, we can examine how people in the wild use that word. Here are some samples:

Progressive lenses are different in that they offer a gradual change in power from the top of the lens to the bottom, offering a smoother progression from one correction to the next. — Eye care specialists of Colorado

From here.

Gradients are used in places where you want a more natural change in color rather than using one solid color fill throughout the shape. — Amadine tutorial

From here.

Here are two examples of roof pitch expressed as horizontal run and riser vertical change in height (rise) for a roof with a 38 degree slope: — Inspectapedia, Roof Slope Calculation

From here.

The road changes width, offers poor sightlines, and sometimes offers no shoulder at all for pedestrians and bike riders. — Rockingham Planning Commission

From here.

The last reference (RPC) is similar to my early example of a "road narrows" sign, with the explicit use of the word "change" by Markatos-Soriano and Keeney. Here's an image:

Here, D1/D2 depict what a "road narrows" sign is trying to warn people about. The sign is up where a road does something like D1. That part of this image doesn't animate; i.e., there is no change in time here of the road. Roads simply don't do what's shown in B1/B2/C1/C2. And a road like A1/A2 would be described as not changing width.

Similarly:

...Banno's image is depicted here as E1. That is a gradient; it is what the Amadine tutorial calls a natural change in color as opposed to a solid fill. Just as D1 does not animate, E1 does not animate; i.e., there is no change in time of this coloring, in contrast with F1/F2/G1/G2, where there is such a thing. Still images, which is what Banno's image is, cannot do what F1/F2/G1/G2 does.

So here it is boiled down for you Luke. Do you agree that D1 and E1 do not animate? Do you have an alternate view of what Markatos-Soriano and Keeney are complaining about before the RPC, or what the Amadine tutorial is describing? Ostensively speaking, D1 and E1, especially opposed to B1/C1 and F1/G1 and friends, are changes that are not changes over time. By contrast, ostensively speaking, B1/C1 and F1/G1 show changes over time.

FYI, I'm not advancing any opinion on your stated opinion anyway (outside my sensitivity to epistemic double standards)... my point is only about the existence of changes other than change over time, as all of the quotes-in-the-wild above describe.

Impressive.

This should be overkill, but unfortunately it seems to be needed.

That 5 is an increase from 3 ipso facto makes it an increase in value because it is that value being described by increase — InPitzotl

The charm of TPF :roll:

What the heck is an a-pixel? And what do you mean "replace x-coordinates"? a and b here are numbers; (a,b) expresses an x,y coordinate with x=a and y=b. — InPitzotl

Right, x=a. My point was that a-pixels of a given value are no different to their associated x-coordinates of a given value, because they are both associated with the same colour. That is, the a-pixels of a given value form a vertical line of the same colour and they all cross the x-coordinate at the same point. Or, again, x=a. I asked you what the increase in the x-coordinate represented and you explained it in terms of a-pixels. My criticism was that this did not explain what the increase in the x-coordinate (or an increase in the a-pixels: from a to a+1) represented, and that you had merely expressed the same thing in a different way.

Exhibit B:

You've said that nothing moves or changes position in various ways recently:

There's no such thing as a thing that moves from (1,1,1) at t=1 to (2,1,1) at t=2
— InPitzotl
O does not move from A to D; O is always at A and always at D.
— InPitzotl
B2 doesn't change places to B1; B2 and B1 are merely different places on the same image.
— InPitzotl
— Luke

None of those things say "nothing moves"; none of them say "nothing changes". Incidentally, isn't this you?:
Exhibit B2:
— InPitzotl

Nothing about it has changed
— Luke

...so I would like to know, Luke, if you're going to prefer to be consistent and claim that you are saying nothing changes, or honest and admit that you are just building straw men. — InPitzotl

Yes, that's me. My position is that nothing changes without time. I thought you held the opposing view? But it seems you hold both views and think it's unproblematic.

Surely the first statement of yours quoted above (in bold) can be read as saying that nothing moves, or that there is no such thing as a thing that moves from one position at time t1 to another position at time t2? Do you also assert that there is something that moves from one position at t1 to another position at t2? Maintaining both statements is a contradiction.

...exactly what you would expect, if the increase is mathematical. That 5 is an increase from 3 ipso facto makes it an increase in value because it is that value being described by increase. — InPitzotl

I simply thought that the mathematics somehow linked back to the examples of Banno's image or the hill. I have asked numerous times what the increase in the x-coordinate represents but your only response has been that it represents the increase in the x-coordinate itself, not that it represents anything about Banno's image or the hill.

In Banno's image, x is a number and "f(x)" is a color. — InPitzotl

What does an increase in x represent in Banno's image (in terms of the image, but not in terms of the function/colour)?

It might be clearer if you could explain what the increase represents in terms of the hill. What does the increase in the x-coordinate represent there?
— Luke

Coordinates are grammar school material, Luke. You shouldn't be confused in the first place. — InPitzotl

I'm not confused; that's not why I asked.

The value of your opinion is proportional to the justification. You're not only lacking that; you're apparently so allergic to opposition, you invent straw men even on points you agree with (exhibit B). — InPitzotl

It's not a straw man to point out your contradictions.

So let's talk about that word change. That is an English word; used by English speakers. Applied to change-over-place, we can examine how people in the wild use that word. Here are some samples: — InPitzotl

I think that when the word "change" is used "in the wild", then it isn't typically assumed that time is absent, like we are assuming in this philosophical discussion. This is evident from your quoted examples. In the absence of time, what you call a "change", I would call only a "difference". There is no going or getting from left-to-right, top-to-bottom, or movement in any other direction. This is why I keep asking what the increase in the x-coordinate represents.

Do you agree that D1 and E1 do not animate? — InPitzotl

Yes, I agree.

Ostensively speaking, D1 and E1, especially opposed to B1/C1 and F1/G1 and friends, are changes that are not changes over time. — InPitzotl

What "road narrows" usually indicates is that the road gets narrower as you travel down the road. Absent of time, there can be no travel down the road.