If one endorses the view that everything flows, an endpoint doesn't exist - everything is an in-between. Since you seem to ascribe a tangible existence to some, any, endpoint, it follows, because all such endpoints are actually in-between states, that in-between state are as real/unreal as what consider endpoints.

Just as orange is "traversed" when going from red to yellow, yellow is "traversed" going from orange to green. Ergo, in terms of being "traversed" there's no difference between orange and yellow. If one has a certain quality, the other too possesses the same quality and if one is missing something, the other too is missing that thing.

If one endorses the view that everything flows, an endpoint doesn't exist - everything is an in-between. — TheMadFool

Yes, if 'everything flows' is taken broadly as a principle in reality, then there are no end-points, I completely agree. But I feel like given a particular frame of reference, where there is a flow between two end-points and not before and beyond that, there has to definitely be a difference in the nature of the thing that is in the middle of the flow and the nature of the end-points. Maybe this is plainly theoretical on my part and not empirical. But, when you say "yellow keeps flowing" and then say "orange keeps flowing," then the referenced entity that keeps flowing are different in each of your statements, the point being that 'every thing,' ie each individual thing, flows, rather than 'All is one flow.' So, a similar question still stands: how does the nature of the flowing entity change from yellow flowing to orange flowing to finally red flowing in a given process? If orange was just an elusive middle phase, we would not have seen it, whether as a stable thing or as a flow, and there would have been no way to say it was "orange" flowing. Rather, we would say this process of becoming is yellow-to-red [a 'digital' kind of process] and not yellow-to-orange-to red [a process of becoming]. The question is how do we have the name and reference of an entity called orange when it is a middle-phase, regardless, I think, of whether it is a flowing middle phase or a static middle phase. We would not have it if its nature was to be completely elusive. I think we have the reference because it exists as a distinct thing, again distinct either as flowing or static, but then gets broken up in a particular flow that has red as its end-point. As for the process of becoming in my mind, I am thinking of the end-points as already pre-determined, in the sense that the end-point red is an absence of yellow and the end-point yellow is an absence of red. Now, for me, the middle-point orange is not an absence of both yellow and red, which would make it elusive. Rather, it is definitely there, for a definite duration, but it gets broken up in the flow of becoming because its nature is fragility. This is of course not a scientific fragility, like it was made of a weaker 'substance and form' than yellow or red, and I really do not know why it is fragile, only that, if it is the middle phase and yet is not elusive, it has to be considered fragile. Maybe this gets to the Buddhist-ic idea of a thing being neither A nor B and both A and B as well. Both these options are not satisfying, to me, because they ultimately paint that thing as elusive, as not having some kind of identity of its own. This is not empirically satisfying when orange is clearly there and is clearly identifiable with a label or a name: orange. So, I would say the Buddhist 'neither A nor B' and 'both A and B' are the language of elusiveness, when the more empirically satisfying language has to be the language of fragility--orange is fragile if it is the middle stage in a flow of becoming. Again, this raises all kinds of problems for the idea of becoming or flow--for any continuity between yellow and red is not there if orange, the middle point, is broken up completely. Yellow would be yellow and red would be red, with no concept of becoming to explain a relation between them, because even if yellow became orange, let's say, if that orange is fragile, it cannot possibly have become red.

What real world example of "something in between" being overlooked or trivialized provoked you to ask the question? — Gnomon

There is not any thing like that to be honest :smile: . But the problem is that it is difficult to say that the idea of a 'continual progression' is 'not in the human mind' whereas the idea of digitized 'a series of steps' is. I don't see why 'continual progression' should be any more empirically established in the real world, whereas our digitized categorizations of reality is not. Why do you think so?

If I were to think about what makes me talk about the 'something in between,' I would say the names and presence of entities themselves: that in a theoretical A-to-B-to-C flow, there is a label, a name, B, and it looks a certain, unique way, and so the question of why it is there, what its nature is, and what happens to it, such that C is possible after it, is raised. To continue with the color example, if a hypothetical animal changes color from yellow to orange to red in the exact same place on its skin, what is the philosophical status of that orange, and why is the transformation to red possible in the first place if orange could have been an obstacle that prevented it? Why would things not simply have been 'digital' in the sense of shifting one step from yellow to red, and not passing something else in between yellow and red in at least three [but maybe infinitely many] steps? But yes, maybe it is a question for science and not philosophy, but to take the idea of becoming or continuity as a given is also a philosophical position, and one which I am trying to argue against here.

I don't see why 'continual progression' should be any more empirically established in the real world, whereas our digitized categorizations of reality is not. Why do you think so? — SaugB

Actually, my view is BothAnd. Our world is both a Holistic System that works as a unit, and a swarm of Holons that work independently. The "holistic view" is top-down, while the "holon view" is bottom-up. The bottom-up view is basically that of reductive pragmatic Science, but the top-down view is more like a philosophical objective perspective from outside the universe. Perhaps, what Thomas Nagel called "The View From Nowhere".

Your original question may be motivated by a scientific desire to slice the "flow" of Change (cause & effect) into ever smaller increments. For example, the study of Phase Transitions has not yet revealed any intermediate steps between liquid water and ice. But scientists continue to carve that instantaneous "traversal" into a series of middle stages. They may, in part, want to dispel the mystery in order to make it look less like "presto change-o" magic. Yet immaterial Energy remains a mysterious force for change that can't be dissected into particles. My guess is that It may be more like bits & bytes of mental Information.

The scientists probably expect, like Zeno, to find an almost infinite sequence of smaller causes and effects between Water & Ice. But I'm not so sure. The process of EnFormAction (causal energy) may actually be more like magic than our materialistic worldviews allow. But then, I don't believe in Magic, at least not in the Real physical world. :cool:

Both/And Principle :
My coinage for the holistic principle of Complementarity, as illustrated in the Yin/Yang symbol. Opposing or contrasting concepts are always part of a greater whole. Conflicts between parts can be reconciled or harmonized by putting them into the context of a whole system.
http://blog-glossary.enformationism.info/page10.html

Objective View : https://en.wikipedia.org/wiki/The_View_from_Nowhere

Intermediate Phases : https://pubs.rsc.org/en/content/articlelanding/2017/cp/c7cp01468f#!divAbstract

Your original question may be motivated by a scientific desire to slice the "flow" of Change (cause & effect) into ever smaller increments. — Gnomon

No, I don't think my question was motivated by that; it was actually about 'in-between-ness' in becoming as such. A cup of tea is 'sliced' such that it is felt as hot for two minutes, cool for 24 hours and frozen for 2 minutes afterwards, let's say. Science can investigate very small increments and tell me why that change happened in terms of particles, room temperature, the external climate etc. But I am asking why it is possible for that 'change' of temperature to happen, for there to be 'in-between-ness' in reality. Basically, I am asking why there can be made at the very least three slices to any 'thing,' as this idea of becoming I have in mind seems to have it.

For someone who strictly believes in becoming, to know hot did not become cold, slices have to be made to the thing, and in those slices an observation has to be made that coldness is elusive or absent. This can be the only application of the concept of elusiveness or absence in becoming; ie, when the sought out attribute [here, cold] is completely irrelevant to the slices. So, elusiveness cannot work as an attribute for anything present in a given becoming is my basic point, and the only viable alternate option for an attribute I can apply to the middle phase is 'fragility,' which is such a concept that, if it is accepted, there can really be no becoming at all.

The Planck scale gives us a pretty dialectical answer on the notion of instants and distance. — apokrisis

This certainly gives Planck time a new spin in my thinking. — jgill

Quantum Hegelianism.

It's curious, but I remain unconvinced.

It's curious, butI remain unconvinced. — Banno

As if you have ever checked out the maths of the Planck constants and understood their reciprocal relations. :lol:

It’s Saturday morning. Time for Banno to run around piddling on lampposts, marking his territory.

It’s Saturday morning. Time for Banno to run around piddling on lampposts, marking his territory. — apokrisis

:rofl:

Such choice prose. But so defensive.

I'm just pointing out that for the rest of us, and I include the physics community, the issue remains unsettled. Your Nobel Prize is not yet in the mail - that being the way I presume such things are done these days.

Nah. You’re just demonstrating you know fuck all about physics again. And you have a weak bladder. :hearts:

So, a similar question still stands: how does the nature of the flowing entity change from yellow flowing to orange flowing to finally red flowing in a given process? — SaugB

That's a different line of inquiry but, as I said, if everything flows each point in the flow is both a destination (enpoint) AND a transit point (traversed point). Your distinction is empty - has no basis.

Basically, I am asking why there can be made at the very least three slices to any 'thing,' as this idea of becoming I have in mind seems to have it. — SaugB

Maybe you are questioning how the human mind can analyze seemingly unbroken processes of change into smaller bits. Plato proposed the metaphor of "carving nature at its joints", but in practice, scientists have found those "joints" elusive (as in defining a species). Yet, if you are asking about a metaphysical issue, modern psychology should be able to shed some light on our tendency to divide ongoing processes into arbitrary "beginning, middle & end". Unfortunately, I'm not aware of studies that analyze "analysis". But you might find something on Google if you look beyond the first page.

If your concern is more physical than metaphysical, then you might profit from reading Into The Cool, by Dorian Sagan. It analyzes how the natural laws of Thermodynamics cause all change in the world. On the macro scale, Energy Flow seems to be continuous, but in our imagination we can zoom-in to look at smaller & smaller pieces of that fluid process. At the very bottom limit of our mechanically-assisted perception though, that flowing stream of causation begins to break-down into the physical bits we call "quanta". At that point, philosophers will ask if reality is inherently continuous or discontinuous. This may sound disingenuous, but I think it's BothAnd. :nerd:


Carving Nature at Its Joints : https://philarchive.org/archive/SLAILF

Into The Cool : Scientists, theologians, and philosophers have all sought to answer the questions of why we are here and where we are going. Finding this natural basis of life has proved elusive, but in the eloquent and creative Into the Cool, Eric D. Schneider and Dorion Sagan look for answers in a surprising place: the second law of thermodynamics. This second law refers to energy's inevitable tendency to change from being concentrated in one place to becoming spread out over time. In this scientific tour de force, Schneider and Sagan show how the second law is behind evolution, ecology,economics, and even life's origin.
https://www.amazon.com/Into-Cool-Energy-Flow-Thermodynamics/dp/0226739376

Continuity and Infinitesimals : https://plato.stanford.edu/entries/continuity/

Maybe you are questioning how the human mind can analyze seemingly unbroken processes of change into smaller bits. — Gnomon

I think the human mind does not just "analyze" unbroken processes of change into smaller bits, because the eyes can actually 'see' reality [or nature: I use reality and nature interchangeably, if you don't mind] as broken into smaller bits. I see a piece of metal as non-rusty one day at 12 noon, a little rusty at night at 12 AM, and then the next day I see it as fully rusty 12 noon. If you really get down to looking 'microscopically' at the change by observing it continuously rather than at 12 o'clocks only [this continuous observation, by the way, would show a subjective engagement with reality, given how the periods of observation themselves have first been increased from being discrete to a status where they seem continuous], I can guess there is no joint in between, but I could at least imagine it in my mind as being a very obvious joint-based becoming of that piece of metal--like flipping a switch from "no rust" to "middle rust" to "full rust" at the three 12 o'clocks I observed them. Even if reality itself is a continuum, and the sight of smaller, joint-based parts of it is an illusion, I would now ask, inside that realm of illusion, how the middle phase is traversed. Your denial of joints in reality/nature has not denied the joints for the eyes, as I see it. As I see it, the point of asserting that reality is continuous has the implicit message that the eyes do not see it as continuous and the mind does not process it as continuous. So, what is the 'truth value' of those optic and mental perceptions and analyses; what to make of the joints therein? As for the science, I know I am probably completely wrong about all that! I was sincerely asking from the metaphysical side of things. In sum, if nature was continuous, or a flow, I would have gotten the sense of its continuity even if I observed it now, and then ten years from now, and then twenty years from now, if continuity was really its independent nature. But I am sure that if I took three photos of these three temporally distant observations of nature, and put them side by side, at least my eyes and my mind will convincingly be able to identify joints in there, though they may not be really present in that nature itself.

I apologize for sliding into some irrelevance up there, but more will follow! Your point is a really interesting point, but how are the no sound point in a volume dial and the max sound point in a volume dial transit points? Are they rather not 'interior limits' to how soft/loud the sound can become? The sound becomes 12 dB loud, but does not go beyond, so it cannot be a transit point, and has to be the interior end point, as I see it. I was actually thinking of systems like that when I made my post.

If you say 'everything flows,' it is as if my loud song always already exists at 12dB and that that loud song is only a transit point in something getting louder. But before my turning the dial approaches that loudness of 12dB, my song at that loudness does not even exist, so how can it flow from there? I am a little suspicious that my example of sound here might not be scientifically founded, but I am asking philosophically.

I apologize for sliding into some irrelevance up there, but more will follow! Your point is a really interesting point, but how are the no sound point in a volume dial and the max sound point in a volume dial transit points? Are they rather not 'interior limits' to how soft/loud the sound can become? The sound becomes 12 dB loud, but does not go beyond, so it cannot be a transit point, and has to be the interior end point, as I see it. I was actually thinking of systems like that when I made my post.

If you say 'everything flows,' it is as if my loud song always already exists at 12dB and that that loud song is only a transit point in something getting louder. But before my turning the dial approaches that loudness of 12dB, my song at that loudness does not even exist, so how can it flow from there? I am a little suspicious that my example of sound here might not be scientifically founded, but I am asking philosophically. — SaugB

You have to prove that some things don't change, are endpoints, and can't be just another stage in the process of flow. Your volume example is a physical limit imposed by the capacity of a particular brand of player you happen to own. A different stereo system may have a different volume setting.

To be fair though, to my reckoning, the total amount of energy contained in the universe is finite and that means there's an upper limit to how loud a speaker can get.

If your concern is more physical than metaphysical, then you might profit from reading Into The Cool, by Dorian Sagan. It analyzes how the natural laws of Thermodynamics cause all change in the world. On the macro scale, Energy Flow seems to be continuous, but in our imagination we can zoom-in to look at smaller & smaller pieces of that fluid process. At the very bottom limit of our mechanically-assisted perception though, that flowing stream of causation begins to break-down into the physical bits we call "quanta". At that point, philosophers will ask if reality is inherently continuous or discontinuous. This may sound disingenuous, but I think it's BothAnd. — Gnomon

:up: Top book.

You might like Stan Salthe’s more technical treatment in his two hierarchy theory books.

On the discrete vs continuous issue, he highlights how we can imagine reality as being composed in hierarchical fashion by levels of “cogency”.

So all entities in reality are regarded as differing scales of an integrative process. Some act of thermalisation which achieves the stability of reaching a statistical equilibrium (where micro change persists, but that changing doesn’t make a macro state difference).

A molecule might be an example of such stability. The atoms still jitter, but are sufficiently bound so that the molecule form a stable level of entification.

Now the point is that reality builds up as levels of such complexity. So say we are focused on the River Thames as our focal level of interest. That is the scale of entification we seek to understand. We then need to look to the lower and higher scales of being in which our focal scale is embedded.

These will form boundary conditions - an appearance of continuity - while also being themselves composed of discrete entities (remembering that entities are self organised coherent processes, not “things”).

So the Thames is composed of a flow of water molecules. At that scale, it is a collection of discrete entities. But for the river itself, the water blurs into the continuity of a fluid flow. If you look downwards form the scale of the river, you see just the emergent macro property which is H2O being watery. The spatiotemporal scale of the molecular action is so fast in terms of its integration that none of that internal dynamics is apparent from the distance at which we want to describe the dynamics of a river.

So looking downwards, the dynamics blur into a generality, a continuity, that covers over the detail.

Then looking upwards to the larger scale of spatiotemporal integration, the River Thames is embedded in the much greater “cogent moment” that is geological time and its punctate events. Plate tectonics is shifting the earth’s crust about to ease thermodynamic pressures. The climate is changing over lond cycles.

So the Thames exists as a stable solution to a hydrodynamic problem set by a landscape during some particular era. From the point of view in which we see the Thames as a stable entity, this is possible because those larger thermodynamic flows in which it is embedded are so large in scale that now a single whole moment fills our vision. We can’t see how the landscape was once very different, and how eventually it will be very difference again, as the earth’s crust continues to convulse and erode.

Look upwards and the big changes aren’t visible. We are inside the continuity of some very large event. Look downwards and the small changes aren’t visible. We see only the continuity of their collective behaviour.

So hierarchy theory gives a natural account of how it is BothAnd.

In sum, if nature was continuous, or a flow, I would have gotten the sense of its continuity even if I observed it now, and then ten years from now, and then twenty years from now, if continuity was really its independent nature. — SaugB

Nature is contrast. So it is both continuous and discrete ... these two ideal states describing the limits towards which it can tend, but never fully reach as “independent” states.

Continuity as a contrasting concept depends on discreteness in the sense that it is a measurable lack of sharp breaks. While discreteness depends likewise on a relative lack of continuity. The two limits are thus mutually dependent and neither could have had independent, stand alone, identity.

I think the human mind does not just "analyze" unbroken processes of change into smaller bits, because the eyes can actually 'see' reality [or nature: I use reality and nature interchangeably, if you don't mind] as broken into smaller bits. . . . Your denial of joints in reality/nature has not denied the joints for the eyes, as I see it. — SaugB

As you suggest, the mind perceives that physical objects can be broken-down into smaller pieces, and then it conceives (in imagination) that metaphysical processes can be analyzed likewise. Processes (the flow of time) are indeed natural, but they don't have obvious "joints" to guide our cutting. So, we slice & dice them as desired.

You could say that the Planck scale of Time is a "joint", but it's a human creation, not natural. So, my point is that Natural Time is continuous, but Artificial Time is discrete. Yet, no one can deny that Time is imagined by humans in terms of hours, minutes & seconds. But even those increments derived from sun cycles, are relative to our little corner of the universe, and not absolute. Even the standardized frequency of atomic clocks is an arbitrary choice from an infinite range. Beginning, Middle & End and Past, Present, & Future are human concepts, not natural increments. Are you thinking otherwise? Is there some inherent logic to a trilogy? :cool:


Time is a river : Time is a construct with which humans have struggled throughout history. Although physics after Einstein's relativity theory has somewhat taken over conceptualizing time, and generally holds that there is no such thing as that "passage" of time, and that all events are equally real, humans have traditionally seen time as consisting of past, present, and future.
https://www.quora.com/What-is-the-meaning-of-time-is-a-river

Discrete Time : In mathematical dynamics, discrete time and continuous time are two alternative frameworks within which to model variables that evolve over time.
https://en.wikipedia.org/wiki/Discrete_time_and_continuous_time

PS__BothAnd Principle implies that what you "see" depends on how you look at it, not necessarily on how it is essentially.

Beginning, Middle & End and Past, Present, & Future are human concepts, not natural increments. Are you thinking otherwise? — Gnomon

Yes, I agree that they are human concepts. Let's say a person hallucinates a river, and so, it is completely that person's river, a 'human' river. My question is, how is it possible to conduct and operate with quite plausible analysis of that hallucinated river using concepts of Beginning, Middle and End, regardless of the truth that any river is not in fact broken into such steps? Why can any statement on that river not necessarily have to reference its true nature of flow at all? How come the discrete view is not very irrelevant, in the manner in which if someone asked that person, "what's the weather like outside?" that person replied "it smells like a white light"? The discrete view has to correspond accurately to something, whether in nature or in the imagination. Even if the middle phase is a content of a human's consciousness assuming things are discrete, and not really 'out there' in nature, it is thus still a middle phase somewhere, even if it is within the thought image in an assumption. In short, the discrete view is not as lacking of a correspondence as 2+2=5 is. If someone hallucinates a river, and then says to you "I hallucinated a discrete river" you wouldn't think that river looked in their eyes any different from a real, natural river, right? If someone said, "I am beside a huge flooding river, but I view it as discrete" you would still warn them to run away from the flooding river, for you would know they were talking about a natural river, and not an 'unnatural' river with joints. That means the discrete view has some strange credibility where it is perfectly capable of corresponding to a real object, ie, the river. Really hope this made sense!

One who abides by your view still needs to make a switch from the discrete view to the continuous view and vice versa, I am assuming. But is that switch convincing when we go from discrete to continuous in some cases? For example, in some systems of length measurement, if one erases the set of discrete marks from a given reality, there are still the erasure marks themselves the still designate a discrete measure, and one only assumes that the marks are gone and one is perceiving things continuously now. For example, if you use an eraser to erase marks from a map, those white gaps signifying your erasure are still marking the map discretely. So, it is only a matter of assumption that the discrete view has been 'switched off' and the continuous view is now valid, in my given example. You might think that this example is too random and too particularly about the type of eraser I have, but I feel like my operating with one particular eraser is sufficient reason for me to think the discrete view has validity. The permanence of those discrete marks, such that their absence is itself a notable absence, means that the discrete-ness of reality cannot really ever be overcome, and in this sense it is more relevant to reality than the continuous view, which is like a reaction dependent on whether you choose to identify the gaps of erasure as discrete marks or not. The discrete is there whereas the continuous is an 'argumentative leap' based on an assumed definition of erasure. One can only go so far as to assume for the sake of some function one wants to do that the discrete marks are not relevant, but they are never any less real, in my example. Even if you physically remove a concrete entity from the fabric of reality, to vividly demonstrate the continuous view to someone, that hole where that entity was is still a discrete, concrete hole. In this sense, at least, the discrete-ness of reality seems a permanent feature, and making the switch to a continuous view is a rather 'arbitrary' project. Even if a flow completely fills that hole you have made by removing a discrete item, like let's say when you remove a big rock from the middle of a river and the river fills the hole with its own flowing water, a discrete function is seen to be active, because the river is filling a discrete hole, the river is engaging with a discrete-ness. Even if you think that rock was continuous to begin with, I think you have come to that conclusion based on the erasure of discrete marks you first made from it, which, I am trying to say, is not ever that convincing, as the gaps of erasure are themselves discrete markings, and could readily be used for a discrete measurement or process. So, discrete-ness is basic, as a point of departure for the assumption of continuity. It has to thus be a little more real, a little more true, at least. I hope this made some sense at least.

My question is, how is it possible to conduct and operate with quite plausible analysis of that hallucinated river using concepts of Beginning, Middle and End, regardless of the truth that any river is not in fact broken into such steps? — SaugB

I don't know that there is any authoritative answer to your interesting question. But in my own imagination, I can speculate. First, there is a significant difference between Reality and Ideality. Reality is limited by the laws of nature, while Ideality is limited only by the loose constraints of imagination in a physical body that evolved as an adaptation to physical laws. The human mind has gone way beyond the pragmatic limitations of the physical brain. So, it can create mental models of things that "never were" but could be. Human culture --- architecture, language, technology, etc --- has broken loose from the constraints of Nature, in part by imagining Super-Nature : something better, more ideal. In other words, we are free to create un-real ideas (Utopias, Gods, Virgin Birth, etc), and then to vainly pursue them in reality. Hence, it's possible to analyze wholes into any number of parts, because humans can "see" things that are not there --- in imagination, we have X-ray vision. But, our flights of fancy remain "plausible" to the extent that we can convince others to see them too.

None of that explains our tendency to divide things into three parts. Since bi-lateral symmetry is an important feature of our world, often related to living things, we may simply be more likely to notice things with a left, right, and axis . And that tripartite imagery may incline us to imagine invisible immaterial processes with Beginning & End boundaries, plus an indefinite Middle or well-defined Axis. Or it may be simply a handy way to think of groups (wholes) that consist of more than one item : solo, duo, trio, quartet, quintet, etc . Or, It may have something to do with brain structure, or it may be simply that the number of parts gets unwieldy when you go beyond Three. The river can be easily imagined as left bank & right bank; or left, middle, & right; or as oxygen & hydrogen, or as all the millions of things swimming or dissolved in water. I'm just riffing here --- what difference does it make to you? :joke:

Bilateral Symmetry with three parts, one imaginary :

One can only go so far as to assume for the sake of some function one wants to do that the discrete marks are not relevant, but they are never any less real, in my example. — SaugB

So all you are saying that a continuum only makes sense to us if we can imagine stepping along it in discrete steps.

That is my point. We can’t really imagine (or measure) the one without the other. So rather than focus on the apparent contradiction, appreciate the fundamental mutuality of the metaphysical dichotomy which is the discrete~continuous.

So rather than focus on the apparent contradiction, appreciate the fundamental mutuality of the metaphysical dichotomy which is the discrete~continuous. — apokrisis

They might certainly be fundamentally mutually established as you say, but all sorts of value systems come in when we start using one with the other. For a start, which one does the philosopher or scientist use first, the discrete or the continuous, in their analysis? This might influence a lot of their analysis.

But my main point was that in any flow, I can easily make discrete marks, by shifting some of the flow away. But once those discrete marks have been made, I cannot really erase them at all--they are permanent, their shell remains even if their content is erased. Even if I want to make a flow where I have made discrete marks, those discrete marks end up existing in form. Since all flow can be shifted, but all discrete marks are permanent, as an analytic tool at least, discreteness is more reliable than continuity.

Since all flow can be shifted, but all discrete marks are permanent, as an analytic tool at least, discreteness is more reliable than continuity. — SaugB

Don’t flows wash away discrete marks? How do you mark the surface of a river?

Hegel I believe was the first thorough process philosopher in the West. He still has something discreet at the end of the process: the Absolute. When he writes on the continuous and discrete, he is rightfully perhaps wary of calculus, perhaps having read The Analyst. And he puts the discrete and continuous side by side and says they work together. Along with the OP, I've felt that objects (even rivers) have an irrational merging of the discrete with the continuous within them. This is likely to be confusing for humans well into the future. Zeno is not dead

If you remove a big rock from a river all at once, some of the water fills the gap that is left, and so the water that filled it becomes discrete upon completely filling that gap. This discreteness is impermanent not because of that water's own tendency to flow, but because there is a whole river of flow pushing up against it. So, that initial 'block of water' is moved by the force of the flow of water behind it, and another block takes up the space of that previous block for itself, and again, becomes discrete, because the previous block of water was discrete, but again for a brief duration because of more flow behind it. The newer water takes up the space of the previous water incrementally, but in the final step it has taken no more space than the initial block, that initial bit of discreteness. So, in a sense, whichever block of water that comes 'there' becomes discrete because that gap has an origin and a 'history' of discreteness. Same goes for pressing a piece of wood upon the surface of the river, I feel, for a particular region of water comes to fill it once you remove the wood, and that region of water can be thought of as having become discrete for a bit before the rest of the flow also comes to become discrete there. So, the tendency towards discreteness is in the flow, because there is no other way, since discreteness, once established, is permanent, in the sense of constantly having a 'chain-reaction' type of history.

So, in a sense, whichever block of water that comes 'there' becomes discrete because that gap has an origin and a 'history' of discreteness. — SaugB

But the very idea of this gap involves an interval. The hole is not a dimensionless point. It is a continuous length of river bed itself.

So again, the discrete and the continuous are concepts that are opposed in a relative sense. Neither is primary. They are each needed as the measure of the "other". The contrast boils down to that between the shortest imaginable interval vs the longest imaginable interval. The infinitesimal vs the infinite.

The infinitesimal vs the infinite. — apokrisis

Isn't is really the FINITE vs the infinitesimal? The infinitesimal is infinite in it's own right. It's interesting that you say that the continuous and discrete measure each other though

But maths treats infinity as a "discrete" whole. You have infinities of many different "sizes".

Everyone complains this is paradoxical. However really it only shows that you can't escape the need for the dialectic of the discrete and the continuous. The relation between two opposing extremes is the irreducible fact.

It's interesting that you say that the continuous and discrete measure each other though — Gregory

They are reciprocal. A lack of one is the measure of the presence of the other.

I think Duns Scotus's principle of "less than a numerical unity", and the "principle of explosion" ( see Wikipedia), are relevant here (although we have to take caution), if anyone happens to know anything about these principles on this forum

↪Gregory
But maths treats infinity as a "discrete" whole. You have infinities of many different "sizes". — apokrisis

This certainly seems to be true of areas of math concerned with sets and/or foundations, and probably valid in other areas of modern, abstract mathematics including analysis. Although in my subject of classical complex analysis a specific point on the Riemann sphere identifies with infinity, I've never had to deal with a discrete whole infinity and think of unboundedness in the complex plane instead.