Remember that the maths was developed to deal with idealised point objects. So the Zeno-style paradox of jumping to the first next point to get moving is an artefact of that maths. — apokrisis

The problem applies to the movement of any object. If the object is at rest, then accelerates, there must be infinite acceleration in this time period. What this indicates is that this interaction cannot be properly accounted for with this conceptual scheme. Even if we theoretically break the object down into fundamental particles, the problem persists because it is inherent within the concept of energy.

Energy is conceptualized as the property of an object related to its existence in space and time. That energy transfers from one object to another is evident. How energy transfers from one object to another is an unresolvable problem. This indicates that the concept of energy is deficient, inadequate for a complete understanding of an object's existence in space and time, because it leaves us with an unresolvable problem.

If we took the arrow in flight analogy. I do want to freeze frame it, just like the paradox. But I want to swap it out for an arrow that is not in flight:One that I pull out of my quiver. When I release time again, the swapped out arrow will drop lifelessly to the ground while the in flight arrow will continue its flight. — MikeL

This is a good representation of the problem. If you "freeze frame" the moving object, you assume a point in time where the object is at X location. But this assumption automatically denies that time is continuous. The two are incompatible premises. If there are points in time then time is not continuous.

Energy is a property which is based in the premise of a continuous time. So if you assume a point in time when you might switch out the arrows, you also deny the applicability of the concept of energy. This allows you to claim, in your example, that you have robbed the arrow of its energy, invisibly switching it for one with no energy. By saying that you could "freeze frame" time, you've rendered the concept of energy inapplicable.

As both arrows are identical in appearance, it is my contention that the difference between the two arrows must have to do with a difference in the energy fields of the atoms within the arrow. Could it be that an asymmetry in the energy field of an atom (pulling all the energy fields in a singular direction like a magnet) is creating the motion. — MikeL

The difference between the two arrows can be very simply understood now. The flying arrow is conceptualized as existing in a continuous time, and the evidence for this is the claim that it has energy. The arrow which you replace it with is conceptualized as existing in a time which consists of points, i.e. it is not continuous. The freeze framing of time is the premise which allows you to bring in that arrow. So the difference is that one is conceptualized as existing in a continuous time while the other is conceptualized as existing in a non-continuous time.

If we can accept this assumption then we can elaborate on it further to say, an initial change in the direction of the energy field creates acceleration. The restoration of the energy field thereafter maintains a velocity at the point of release, a further tug will cause further acceleration.

That being said, I can envisage a futuristic programmer typing a value and direction of the energy field into an object and causing it to spontaneously leap into a state of acceleration. — MikeL

The problem cannot be resolved in this way because you now utilize two distinct, and contradictorily incompatible concepts of time, one which conceives of time as continuous and the other which allows for points in time.

If we adhere to the idea that time is continuous, allowing for the concept of energy, then we must dismiss the idea that the energy passes from one object to another at a point in time because there are no points in this continuous time. So this must occur over a period of time. But this will reduce our capacity to conceive of energy as the property of objects. That is because if energy is transferred from object A to object B in such a transaction, we must now assume a time period when the energy is neither the property of object A, nor the property of object B.

It appears like the difficulty may be due to our conceptualization of "objects", so we reduce the problem by assuming parts of the object, and allow that in the period of time when energy is transferring from A to B it is the property of the parts of the object. But this does not resolve the problem because each part is itself an object which is subject to the same unresolvable problem. So the problem is really intrinsic to how we conceive of time and energy.

Being able to switch the balls. I'm not sure if being able to divide motion in such a way is possible, but the thought experiments exist. — JupiterJess

The mind divides motion for practical purposes which is why the mind invented symbolic representations. It is a way of freezing so multiple minds can share. But actual observation will reveal that duration (real time) and motion is continuous. This is again confirmed by Heisenberg's Principle and wave mechanics.

If we took the arrow in flight analogy. I do want to freeze frame it, just like the paradox — MikeL

I do not believe it is possible possible to develop an ontologically sound metaphysics that is premised on divisibility of duration and motion. It's a brick wall and you are inviting in all kinds of problems, infinities, infinitesimals, and paradoxes, etc. But as an exercise, go for it. Learning is by doing.

I do not believe it is possible possible to develop an ontologically sound metaphysics that is premised on divisibility of duration and motion. It's a brick wall and you are inviting in all kinds of problems, infinities, infinitesimals, and paradoxes, etc. But as an exercise, go for it. Learning is by doing. — Rich

The problem is, that to have an ontology which has the capacity to act as the basis of an epistemology, it is required that the ontology is premised on the divisibility of duration and motion, contrary to what you state here.

This is what you say in the prior post:

The mind divides motion for practical purposes which is why the mind invented symbolic representations. It is a way of freezing so multiple minds can share. — Rich

The multiple minds sharing which you refer to, is justification, which is essential to knowledge. So the problem you have here is that the cut and dried divisions, and static states of descriptions, which are required by the fundamental laws of logic, in order that we can have such a thing as knowledge, are exactly what you claim are a "brick wall" to an ontologically sound metaphysics.

Now you need to face the fact that either there is something fundamentally wrong with the laws of logic, by which we describe things, or there is something fundamentally wrong with your assertion that the divisibility of duration and motion is ontologically unsound.

The problem is, that to have an ontology which has the capacity to act as the basis of an epistemology, it is required that the ontology is premised on the divisibility of duration and motion, contrary to what you state here. — Metaphysician Undercover

Ontology describes what is and how one derives knowledge varies. Science at times may require divisibility for practical problem solutions, but such efforts have nothing to do with the ontological underpinnings. It is a super-huge error to elevate measurement solutions, such as Special Relativity, to ontological statements about nature, but for those who worship science that is what they do and all of a sudden you get backwards time travel. As far as I can tell there is no way to divide space and duration, but if one insists on trying, go for it.

which are required by the fundamental laws of logic, — Metaphysician Undercover

There are no such thing as the laws of logic and more so than the laws of nature, laws of physics, or laws of God. However, it sounds good, and gives it lots of gravitas. Who's to argue with Laws. In and case, the matter is not complicated and doesn't require laws and never has. The universe is indivisible, but humans, for various practical reasons have developed symbolic representations that can be manipulated as if it was divisible. There are no boundaries between this and that. It is a complete continuum. There is no such thing as the beginning and end of something.

I do agree that an acknowledgement of such an ontology does crash and burn lots of symbolic constructs that are suppose to provide paths to the Truth: e.g. logic, mathematics, scientific method, etc. But then again, I never put much into the notion of Truth.

Another question would be, is it the ball that shatters the window, or is it the individual atoms that collectively shatter the window? Is the ball an epiphenomenon?

Nothing it's shattering anything. The interference patterns are changing. The pattern for the ball will be deformed in some manner but not nearly as much as the ones for the window. One thing for sure, the ball land window are not in the brain. What is in the mind is some memory of the event, also stored as an interference pattern outside of the brain in the holographic universe.

The problem applies to the movement of any object. — Metaphysician Undercover

You are confusing a problem of maths with a problem of reality. Calculations break down when they arrive at a singularity - a point of circular self-reference. But that's just calculations for you. Don't conflate the map with the territory.

What is in the mind is some memory of the event, also stored as an interference pattern outside of the brain in the holographic universe. — Rich

We know how a hologram can be recorded in a material medium. How is it recorded in an immaterial one?

If we are to grant Bergson some subtlety of thought, then he was a holist taking a constraints-based view of temporal duration. He generalised the notions of time and memory so that the past is an accumulation of constraining information that conditions the present so that it has now its well defined degrees of freedom that constitute its future.

It is an organic and hierarchical model of why time unfolds with an entropic direction and a "cogent moment" spatiotemporal structure. The speed of light means that every event is constrained by a lightcone structure. The sun may have disappeared seven minutes ago. It is only now that its heat and gravity are a loss we can suddenly notice.

So sure, Bergson can be understood as another telling the systems science tale. But even he would be horrified by the mechanical crudeness of this hologram analogy. And if you aren't just taking that analogy literally, you will be able to say in what sense an interference pattern is being stored or recorded, without that being a claim that the mind or mentality is some kind of (im)material substance.

You are confusing a problem of maths with a problem of reality. Calculations break down when they arrive at a singularity - a point of circular self-reference. But that's just calculations for you. Don't conflate the map with the territory. — apokrisis

If mathematics is what we apply to reality in an attempt to understand it, and there is a problem with the mathematics which renders the reality incomprehensible, then there is a problem with the conceptual scheme. That's what I was saying, there is a problem with the way that we conceptualize these things. I wasn't saying that this is a problem of reality, whatever that might mean.

Ontology describes what is and how one derives knowledge varies. — Rich

We derive knowledge from others, so our principles of communication dictate how we derive knowledge.

Science at times may require divisibility for practical problem solutions, but such efforts have nothing to do with the ontological underpinnings. — Rich

This is not true, because "what is", which is what you describe as the ontological underpinnings, is itself a division. It is a division between what has been (past) and what may be (future). So this point in time, which we call the present, which is also a necessary assumption to support the idea of "what is", and the basis for ontology, has "division" inherent within as the divider. Since division is inherent within the ontological underpinnings, then what is implied by this is that divisibility is an essential aspect of reality. In order that reality is actually divided, as it is between past and future, it is necessary that it is divisible.

The universe is indivisible, but humans, for various practical reasons have developed symbolic representations that can be manipulated as if it was divisible. There are no boundaries between this and that. It is a complete continuum. There is no such thing as the beginning and end of something. — Rich

This is an assertion which is totally unfounded. As I explained, reality is fundamentally divided between past and future. Furthermore, it is quite obvious that there are boundaries between things, and this is what allows me to pick up some food and eat it without eating the entire universe. Your claim of "no boundaries" is completely untenable.

But mathematical physics makes simplifying assumptions to allow tractable calculation. Understanding is then demonstrated because the equations make predictions that match observation.

If you want to "understand" the landscape you want to cross, you could chose an oil painting as your guide, or you might buy a map. Whatever you do, it's still a story about reality and not reality.

So no. Mathematical physics is smart in that it knows what it can leave out. It is not ignorant about what it then leaves out. It has already thought about the issue much more deeply.

That was Newton's very great genius. He knew what to leave out when everyone else - like Aristotle or Descartes - was saying you couldn't possibly.

The others were saying nothing could move unless there was something to actually there as a force to push it along the whole time. Newton said just accept inertial motion. And then when it came to gravity, throw away local pushing entirely. Just have action at a distance. Newton was as torn as anyone by this apparent lack of "philosophical" commonsense. But as a simplification it worked.

Ever since, science has understood the game. Anything we can conceptualise in a metaphysical sense is merely a mental crutch for the real business of model building. The intuitive images we have of waves or billiard balls or fluctating strings or whatever are just an aid to thought. We shouldn't start believing our own "free creations of the mind", as Einstein put it.

So sure, Newtonian mechanics might have a hole in the calculations right where at the instant where a force acts and a motion changes. But that was an inconsequential kind of hole - a necessary shortcut for the maths. The real holes in Newtonian mechanics were the ones later tackled by special and general relativity, and also quantum mechanics. There were consequential holes as well. Which were worth fixing.

We derive knowledge from others, so our principles of communication dictate how we derive knowledge — Metaphysician Undercover

Sharing it ideas is helpful in providing direction and clue, but ultimately one must rely on direct observation and intuition. This is how the Daoists accumulated their vast knowledge. Without direct experience too much is lost including that which cannot be communicated in any fashion and certainly b not via words or math.

It is a division between what has been (past) and what may be (future). — Metaphysician Undercover

No such division exists. It is a continuum. The division is artificial since duration continues without interruption. Call it b what you wish, it is all arbitrary with no hard boundary. It is for this reason that any symbolic approach will utterly fail and the search for truth and facts will equally fail. All is in continuous flux and cannot be frozen. You can try but then the infinities and infinitesimals will start popping up all over.

food and eat it without eating the entire universe — Metaphysician Undercover

Try finding the boundary between the fruit, you, and the universe. Impossible. But keep trying.

Thanks guys, a lot to think on.
For the time being though: Motion is relative, which is a good thing, because on both arrows I placed a tracker that is recording all the atomic information of the arrow. To the tracker the arrows are not in motion. The tracker is beaming information to a teleporter which through the trackers activates the teleportation of both arrows. When they materialise at the new destination I suspect the arrow in motion will continue to fly while the other won't. Is this a feasible work around for the pointilism vs continuous problem of time? If so, how can we account for the movement of the arrow in flight, or do you think they will both drop lifelessly to the ground?

That was Newton's very great genius. He knew what to leave out when everyone else - like Aristotle or Descartes - was saying you couldn't possibly. — apokrisis

The op is a question concerning what is left out. Sure you can say that as long as you can predict what will happen, it doesn't matter how it happened, but prediction does not provide an understanding of what is happening, and philosophers want to understand. Ancient people using mathematics could predict where on the horizon the sun would rise and set each day, as well as many things concerning the motions of the moon and planets, but they did not understand these motions. Modern physicists using mathematics can predict many things concerning the motions of electrons and photons, but they do not understand these motions.

It is this very attitude which you refer to, the attitude of leaving things out, because predictions can be made without resolving these little paradoxes, which moves us forward into a realm of misunderstanding and self-deception. It is self-deception because some believe that because predictions can be made, the phenomenon is understood, and others such as yourself seem to believe that understanding the phenomenon is unimportant so long as predictions can be made. But the philosophical spirit does not stop with the pragmatic of making predictions, it is the desire to understand. So things which appear as unimportant to the pragmatist, which one might be inclined to "leave out", are very important to the philosopher, because unraveling these little problems, these little paradoxes, is like working on a little puzzle which hides the mysteries of the universe.

Sharing it ideas is helpful in providing direction and clue, but ultimately one must rely on direct observation and intuition. This is how the Daoists accumulated their vast knowledge. Without direct experience too much is lost including that which cannot be communicated in any fashion and certainly b not via words or math. — Rich

But observation is dependent on words. To observe is to "notice", or take note of what is happening. This implies a description of what occurs. We can remember what has happened with mental images, but this is not very useful toward knowledge. So the capacity to accumulate vast knowledge relies on the power of description, which is a use of words.

And, I would go even further, to say "that which cannot be communicated in any fashion" cannot be understood. It is a necessary requirement of understanding, to be able to put what is understood into words. If you cannot put it into words, you do not understand it. And this points to the issue which apokrisis brings up with mathematics. Apokrisis seems to think that to model a phenomenon with mathematics such that predictions can be made, is all that is required in order to understand that phenomenon. I disagree because the things which the mathematical model leaves out are critical to understanding.

I agree that the subjective element, the direct observation and intuition which you refer to, is the most fundamental, because it is always an individual being who knows and understands. But referring back to the individual is inconsistent with your fundamental principle that there is no boundaries and therefore no individuals. The individual person's ability to understand the complexities of physical processes is capacitated by what is derived from others, communicated. We always build upon existing principles.

No such division exists. It is a continuum. The division is artificial since duration continues without interruption. Call it b what you wish, it is all arbitrary with no hard boundary. It is for this reason that any symbolic approach will utterly fail and the search for truth and facts will equally fail. All is in continuous flux and cannot be frozen. You can try but then the infinities and infinitesimals will start popping up all over. — Rich

Are you claiming that the present, as the division between future and past, is an artificial division? How do you account for the fact that what has happened has happened, and cannot be changed, yet things which have not yet happened can be prevented from happening, or induced to happen? According to your direct observation and intuition, which seems to be of the utmost importance to you, do you not notice that there is a very real, and non-artificial division between past and future? I think your claim that "duration continues without interruption", and that time is a continuum, is what is artificial. because our direct observation and intuition tells us that time is a divide between past and future. How could such a division be a continuum?

Try finding the boundary between the fruit, you, and the universe. Impossible. But keep trying. — Rich

I have no problem finding a boundary between the fruit and the rest of the universe. This boundary is what allows me to pick up the fruit and move it this way and that way, in relation to other things. It exists as a separate and distinct entity and therefore must have a boundary or else I could not move it in this way as a separate entity. What is impossible, and untenable, is your claim that this boundary does not exist. Such a boundary must exist or else I could not move the fruit in that way, as an individual entity. What do you think you see when you see an object? Are you not seeing a boundary?

But observation is dependent on words. To observe is to "notice", or take note of what is happening. — Metaphysician Undercover

Hellen Keller was able to sense way before she learned the words. Words are for sharing. I can observe a structure (a tree) and create a new rendition of that structure without naming it anything. Symbolism is not required to observe. What is required is memory of the observation. In fact, many times a memory, e.g. a dream, is indescribable. It is a feeling.

Actual direct one observation and intuition is all that an artist needs. A picture is worth a thousand words. Even music and dance can communicate feelings that words can never hope to describe. This is why I suggest that all philosophers who are truly interested in understanding the nature of nature, as opposed to understanding what Plato or Kant may or may not have meant, study the arts not the books.

Books makes one a slave of words and mathematics a slave of numbers. That is not nature. Nature is in sound, movements, and images.

It is this very attitude which you refer to, the attitude of leaving things out, because predictions can be made without resolving these little paradoxes, which moves us forward into a realm of misunderstanding and self-deception. It is self-deception because some believe that because predictions can be made, the phenomenon is understood, and others such as yourself seem to believe that understanding the phenomenon is unimportant so long as predictions can be made. But the philosophical spirit does not stop with the pragmatic of making predictions, it is the desire to understand. So things which appear as unimportant to the pragmatist, which one might be inclined to "leave out", are very important to the philosopher, because unraveling these little problems, these little paradoxes, is like working on a little puzzle which hides the mysteries of the universe. — Metaphysician Undercover

I think that is a stupendously good piece of writing that highlights the differences between science and philosophy. However, I think the issue of thinking about the mysteries of inertial motion could perhaps be fruitful to science - it's a "boundary" issue between science and philosophy, I would say.

For the time being though: Motion is relative, which is a good thing, because on both arrows I placed a tracker that is recording all the atomic information of the arrow. To the tracker the arrows are not in motion. The tracker is beaming information to a teleporter which through the trackers activates the teleportation of both arrows. When they materialise at the new destination I suspect the arrow in motion will continue to fly while the other won't. Is this a feasible work around for the pointilism vs continuous problem of time? If so, how can we account for the movement of the arrow in flight, or do you think they will both drop lifelessly to the ground? — MikeL

Let me see if I understand what you're asking. You have assumed a teleporter which positions the arrows at a particular place at each moment of time. One arrow would be positioned at each moment so as to appear as a continuous flight through the air, and the other arrow would be positioned so as to be dropping to the ground without any forward momentum. So you have described discrete, non-continuous motion. The arrows appear like still-frames at each moment of time, which give the illusion of continuous motion.

The still-frame of the arrow in its position constitutes a moment in time when the physical world exists in such and such a state. Between each moment in time, the teleporter is active preparing the next physical position of the arrow. So time is passing because the teleporter is active but no physical activity is occurring. The teleporter behind the scenes is active so time must be passing, yet no physical change is occurring. This activity of the teleporter constitutes continuous time, but the arrow only has physical existence at one moment and the next.

If I understand then, your question is how does the arrow get from one point to the next.

. But referring back to the individual is inconsistent with your fundamental principle that there is no boundaries and therefore no individuals. — Metaphysician Undercover

Individuals would be analogous to waves in an ocean. They are no hard boundaries but they are all there.

Are you claiming that the present, as the division between future and past, is an artificial division? — Metaphysician Undercover

Yes. The present doesn't exist as it continuously moves into memory (the past). There is no way to freeze it. The future is an image in memory (the past) of some possible actions (Bergson's virtual actions).

I have no problem finding a boundary between the fruit and the rest of the universe. This boundary is what allows me to pick up the fruit and move it this way and that way, in relation to other things. — Metaphysician Undercover

The boundary is a cloud. There is no hard boundary though there is a continuum of substantiality. Physicists have acknowledged this in their research of particles. In fact, everything seems to be connected, even non-locally. Daoists arrived at the same idea but observing the macro and how everything flows from one to the other. I flow directly into the rest of the universe. There is no nothingness floating in between me and everything else.

Similarly time flows continuously. One cannot freeze it. This is what Zeno's paradox is all about. To create an ontology around freezing creates unresolvable paradoxes. Bohm once wrote where there are paradoxes there is something that needs to be looked at in an entirely new way. Spacel and time had to be looked at as indivisible, otherwise paradoxes abound.

Symbolism is not required to observe. What is required is memory of the observation. — Rich

Since the memory, is not the occurrence itself, then the memory is a symbol of the occurrence and memory is symbolism.

However, I think the issue of thinking about the mysteries of inertial motion could perhaps be fruitful to science - it's a "boundary" issue between science and philosophy, I would say. — Jake Tarragon

I agree, and believe there are many such boundary issues. Resolution of these issues requires speculation and hypotheses (philosophy), as well as empirical trials (science). The nature of time, and the issue of continuous versus discrete motion, which MikeL appears interested in, is one such key issue.

The future is an image in memory (the past) of some possible actions (Bergson's virtual actions). — Rich

How can the future be in the memory? That doesn't make sense.

The boundary is a cloud. — Rich

But a boundary doesn't have to exist as a non-dimensional line, X on one side, Y on the other. Such a boundary would be unreal, artificial, because it would consist of nothing but an ideal. A real boundary between X and Y would consist of something which is neither X nor Y, but prevents the two from mixing. The piece of fruit, does not mix with the surrounding air to become a homogenous thing because the chemistry of these two keeps them separate. So "the chemistry" whatever that refers to, is neither the fruit nor the air, but is something else, the boundary which prevents the two from mixing.

If I understand then, your question is how does the arrow get from one point to the next. — Metaphysician Undercover

I've been thinking a lot about your pointilism problem, and it seems like an easy fix. First, here's what I think the problem is. Between each interval there are an infinite amount of intervals. So 0.9 can become 0.99 can become 0.999 but never reach one. In a nut shell is that it? That an infinite amount of time would be required to transverse the infinite number of intervals?

If so, the easy fix would be to make time a quanta. Give it a fixed value, then you can summate it.
Yes? No?

Since the memory, is not the occurrence itself, then the memory is a symbol of the occurrence and memory is symbolism. — Metaphysician Undercover

Memory is fundamental. The words we use to attempt to describe it (always inadequately and too late) are our symbolic ways to sharing.

I agree, and believe there are many such boundary issues. Resolution of these issues requires speculation and hypotheses (philosophy), as well as empirical trials (science). — Metaphysician Undercover

Philosophically the way to resolve paradoxes is to flip ideas on their head. Zeno's paradoxes are resolved by simply observing that motion and time are indivisible. In other words the problems are created by giving divisibility ontological status. Ditto for paradoxes arising out giving Special Theory of Relativity ontological status and it is the reason (philosophically speaking) why STR can never be resolved with QM. STR it's designed to resolve measurement questions not ontological issues. Hence the Twin Paradox and all of the others (e.g. moving train in a barn).

The heart of Begson's philosophy is continuity of duration and space, which is why DeBroglie have him credit for quantum ideas that predated QM by several decades.

. A real boundary between X and Y would consist of something which is neither X nor Y, but prevents the two from mixing. The piece of fruit, does not mix with the surrounding air to become a homogenous thing because the chemistry of these two keeps them separate. — Metaphysician Undercover

There is no boundary here. There is a gradual and not so gradual fall off in substantiality or compactness if energy. Food moves from substantial to unsubstantial via the digestive process which begins with the bite. What is left behind is still embedded in the energetic universe that surrounds us. It is a continues flow like a cloud forming rain (insubstantial to substantial) and the rain then melting into the ground. Never a hard boundary in this process of conversion.

The nature of time, and the issue of continuous versus discrete motion, which MikeL appears interested in, is one such key issue. — Metaphysician Undercover

I think the root issue of the OP is not about discrete vs continuous motion per se, rather it is motion itself - and I think MikeL has sort of acknowledged that. It's something that "bothers" me from time to time - the way I phrase it is "what the heck is the difference between two objects that move differently besides the motion itself?" Psychologically speaking, it seems that there should be some way of knowing the velocity of an object (moving in an inertial reference frame, for the sake of simplifying) by isolating the object and getting "intrinsic" information from it. This "information" would represent a "cause" of the motion. The object moving in space would be the "effect".

One angle of attack might be to think about Lorentz contraction. One could argue that the measured length is an "intrinsic" property of the object, and gives away the velocity. The measurement would have to be made over a short time of course, as in a photographic snap, say. But the information gleaned - the length of the object, is not a direct measurement of the velocity. Or is it?....

I've been thinking a lot about your pointilism problem, and it seems like an easy fix. First, here's what I think the problem is. Between each interval there are an infinite amount of intervals. So 0.9 can become 0.99 can become 0.999 but never reach one. In a nut shell is that it? That an infinite amount of time would be required to transverse the infinite number of intervals? — MikeL

That's not exactly the problem, but it's an acceptable analogy. In theory, if two points are separate then there is an infinite number of points between them. In practise it is impossible to measure an infinite number of points. So as you point out there is a discrepancy between the way things are in theory and the way thing are in practise. That, I believe is your rendition.

If so, the easy fix would be to make time a quanta. Give it a fixed value, then you can summate it.
Yes? No? — MikeL

I don't think that this solves the problem because you would then say that a quantum of time passes, and value this quantum according to some physical change. But unless such a valuation could be supported by some real evidence, of real quanta of change, it would be purely arbitrary. So within each quantum of change, there would still be continuous change occurring which would have to be accounted for by some other means, and the states referred to at each point, constituting the quanta, would be completely arbitrary and artificial.

So for instance, suppose the motion or change which we are quantifying is my breathing. We could arbitrarily assume that each time I completely inhale, this constitute one quantum of change. So we have a series of states, at each point my lungs are full, and this repetition of similar states validates the assumption of the arbitrarily determined one quantum. However, we still have all the intermediary activity, and all the possible definable states in between these arbitrary designated points.

So any time we give time a fixed value like that, say X amount of time is equivalent to Y oscillation, it is an arbitrary quantum of time which is artificially designated. within that quantum there is still change occurring, and therefore time passing. Unless you can empirically determine that there is state, then no physical change for a certain period of time, followed by a different state, with no activity between, you have no empirical support for the assumption of a quantum of time. In other words, the assumption of a quantum of time is completely arbitrary and useless unless it is supported by physical evidence of such. But so far, it appears like physical evidence points to a continuous time like Rich argues for.

The logic indicates a need for quantized time, but until the evidence is provided for real physical quanta of time, any such designation is purely arbitrary and useful only according to the purposes for which it assigned (my breathing for example), and not representative of any real quanta.

There is no boundary here. There is a gradual and not so gradual fall off in substantiality or compactness if energy. Food moves from substantial to unsubstantial via the digestive process which begins with the bite. What is left behind is still embedded in the energetic universe that surrounds us. It is a continues flow like a cloud forming rain (insubstantial to substantial) and the rain then melting into the ground. Never a hard boundary in this process of conversion. — Rich

A gradual boundary is still a boundary, and I think you are speaking nonsense calling this a "compactness" of energy. The energy cannot be compacted unless something compacts it, and this would be the boundary.

I think the root issue of the OP is not about discrete vs continuous motion per se, rather it is motion itself - and I think MikeL has sort of acknowledged that. It's something that "bothers" me from time to time - the way I phrase it is "what the heck is the difference between two objects that move differently besides the motion itself?" Psychologically speaking, it seems that there should be some way of knowing the velocity of an object (moving in an inertial reference frame, for the sake of simplifying) by isolating the object and getting "intrinsic" information from it. This "information" would represent a "cause" of the motion. The object moving in space would be the "effect". — Jake Tarragon

I agree that the inertial information concerning an object is the information which is intrinsic to that object, but ironically this is the information which relates the object to its environment. So by describing in completion, the surroundings of the object, we actual provide a complete description of the object itself, and this is its spatial-temporal reality. We can conclude that this information exists within the object, as the object itself, or that the object actually is the information which describes its surroundings.

But that leaves us with the question of "in what form does this information really exist?". If we say that it exists as the object, we are just going around in circles. So we must plunge further into the object itself, until we have reduced it as near as possible to a non-dimensional point (apokrisis will deride this as reductionism) and then determine what is at this point. What is at this point is the same thing as "a description of its surroundings" but what is that?

A gradual boundary is still a boundary, and I think you are speaking nonsense calling this a "compactness" of energy. The energy cannot be compacted unless something compacts it, and this would be the boundary. — Metaphysician Undercover

There is a difference between continuity of substantiality and boundary. A wave is continuous with no point of demarcation. It continuously flows from one to another the difference being, shall we say, the amplitude. This is, btw, the essence of Bohm's quantum potential. The potential works via form not distance.

There is a difference between continuity of substantiality and boundary. A wave is continuous with no point of demarcation. — Rich

But "wave" refers to an activity of a substance, and that substance must consist of particles, and space between the particles in order that the wave can move. So the concept of a wave requires a duality of substance and space and a necessary boundary between these two. The wave itself may be described as continuous (assuming that it has no point of origin or completion), but the medium in which the wave exists cannot be continuous.

But "wave" refers to an activity of a substance, and that substance must consist of particles, and space between the particles in order that the wave can move. — Metaphysician Undercover

I have to say this, but such a description is anachronistic Newtonian. While I don't agree with Whitehead's analysis, on the basis of quantum mechanics and his own studies of Bergson, he did endeavor to eliminate the notions of particles and space and such and replace it with processes (activities). One way to think of electrons are as wave perturbations (large amplitudes). Such electrons do not occupy a definite space or time but are in constant in and out flux. This marries well with current understanding of particle theory.

The medium, if one can call it such, is interwoven with that which emerges from it. Bohm referred to it as the Implicate/explicate Order while ac simple analogy would be a wave emerging from an ocean, the ocean being the mind/consciousness.

This video posted in another thread discusses, near the end, the nature of processes and waves as opposed to particles.


https://youtu.be/6Uy5-mOGgC8

I have to say this, but such a description is anachronistic Newtonian. While I don't agree with Whitehead's analysis, on the basis of quantum mechanics and his own studies of Bergson, he did endeavor to eliminate the notions of particles and space and such and replace it with processes (activities). One way to think of electrons are as wave perturbations (large amplitudes). Such electrons do not occupy a definite space or time but are in constant in and out flux. This marries well with current understanding of particle theory. — Rich

You may utilize wave analogies to describe things like electrons, as "wave-like", but that doesn't change what a wave is. A "wave" still abides by the same description, despite that description being anachronistic Newtonian. But it is wrong to refer wave-like things as an example of what a wave is, because these things aren't waves, they simply have some wave-like characteristics..

But it is wrong to refer wave-like things as an example of what a wave is, because these things aren't waves, they simply have some wave-like characteristics.. — Metaphysician Undercover

If one wishes to begin to form some sort of image in their mind of what the nature of nature might be, one must begin to think of the substrate as a continuity of wave forms as opposed to particles separated by .... what? The wave nature of the universe reveals itself everywhere in everything we observe and do. In dance and drawing and music, waves of rhythm are fundamental. Even the double helix is a wave. There are no points and there are no boundaries. However, we arbitrarily choose boundaries, e.g. the beginning and end of a bone or muscle, for the sake of sharing ideas but in reality the body is continuous. A problem at any point can create a problem anywhere else. This is the heart of holistic medicine - indivisible continuity.

If one wishes to begin to form some sort of image in their mind of what the nature of nature might be, one must begin to think of the substrate as a continuity of wave forms as opposed to particles separated by .... what? — Rich

The problem, as I said already, is that I think of a wave as a bunch of particles interacting in a certain way which produces the form of a wave, like a sound wave, or a wave in water. So there is no such thing as thinking of "wave forms as opposed to particles" because a wave form is a form that a group of particles has.

There are no points and there are no boundaries. — Rich

How could there be a wave form without points and boundaries?