Do you know the difference between duration and a clock’s “12 O’Clock”?
Do you know the difference between saying 12 O’Clock and 265 Hours?
“How many still images there are in the film” is a quantity. “The set of all places” is NOT a quantity.
True. But note that words very often have multiple meanings. The word “time” is no exception. It is often used to refer to temporal length a.k.a. duration (which is no more than the number of temporal points that exist between two temporal points) but it is also used to refer to the set of all places in the filmstrip that is the universe itself. The term “point in time” testifies to this. It suggests that time is a container made out of points / places.
“100 seconds” would contain a greater number of still images than “1 second”. The number of still images wouldn’t be the same. “1 2 3” and “1 1 1 2 2 2 3 3 3” are quite similar in many ways but they are not identical.
I said that time is the set of all places in the filmstrip. The word “place” does not mean the same thing as “still image”. It refers to a slot where a still image of any sort can be inserted. Still images occupy places – they are not places themselves. A place is more like a potential.
A single still image occupies time. It’s not time itself. And yes, it occupies a period of time – that period being the smallest period a.k.a. point / place in time.
You seem to be saying that if a period of time is made out of zero elements that it is nothing and that it therefore refers to non-existence. I agree. The thing is that, the word “point in time”, as I use it, does not refer to a period of time that is made out of zero elements. It is indeed a stretch, as you say. I understand the word is also used to refer to something that has no temporal length i.e. position / address. Position is merely a reference to how some place can be accessed from another place which is why it is often said that it has “zero size” or “no size”.
It depends on what “infinitely divisible” means. What does it mean? Let’s be a bit more abstract to cover some cases that might arise at one point or another.
A set of elements is said to be indivisible if it cannot be split into more than one non-empty set. ({1}) is an obviously indivisible set. You can’t split it into more than one non-empty set because it has exactly one element.
On the other hand, a set of elements is said to be divisible if it can be split into more than one non-empty set. ({1, 2}) is a divisible set because you can split it into ({1}) and ({2}).
From there, it’s easy to deduce that a set of elements is said to be infinitely divisible if it can be split into an infinite number of non-empty sets. ({1, 2}) is clearly not infinitely divisible but the set of all natural numbers ({1, 2, 3, \dotso}) is because you can split it into ({1}), ({2}), ({3}) and so on.
See? We just infinitely divided a set and ended up with indivisible sets.
When we say that a portion of space is infinitely divisible, we mean that it consists of an infinite number of parts that are arranged in a particular way and that would require us to infinitely zoom into them in order to see them all. It doesn’t mean that there are no indivisible components – that would actually mean that there are no parts at all and that we’re talking about nothing at all (similar to a set that is made out of two subsets that are made out of two subsets that are made out of two subsets and so on.) It merely means there’s an infinity of parts.
As you zoom into these infinitely many parts, you get to see more and more of them. Albeit, due to the way observation works, you generally won’t see them individually; instead, you will see their average. It’s similar to down-scaling an image. If you’re down-scaling by 50%, every 2x2 group of pixels will be replaced with their average. If two pixels are black and the other two are white, you’ll end up with a gray pixel. And in reality, the black and white pixels themselves would be an average of some other pixels you are not seeing. In general, what this means is that you will never see with your own eyes – though you may be able to do it using your brain – the “real pixels”. And none of that means that reality is smudgy / blurry / smeary / fuzzy nor that these perceptions are illusions (they are only illusions if you’re misinterpreting them.)
I suggest defining the word “vagueness”. I’d argue it’s a subjective term referring to things that exist within minds. In other words, it’s not a term you can use to describe reality outside of minds without doing so metaphorically.
You are right in that if a physical object, or a period of time, has no size then it’s equivalent to non-existence. However, there are concepts that have no property called “size” but that can nonetheless be found in reality. As an example, colors have no property called “size”. They are, in this particular sense, without size. Yet, they exist. The thing is that “no size” is sometimes used to mean “no property called size” rather than “it has a property called size and it’s zero” (a subtle but important distinction.) What about ghosts? Ghosts exist in time and space but they have no material existence – they have no physical bodies, and thus, they are not physical objects. Nonetheless, even though they do not exist, they can exist just fine. They would NOT constitute non-existence. It’s quite a bit of a mistake to think that only physical objects can exist. Lots of things that aren’t physical objects can and do exist: change, movement, laws, values, justice, beauty, morality, abilities, potentials, etc. And some of these things that aren’t physical objects even have size e.g. aspirations, problems, desires, etc.
I have a film with 250 images and a different film with 500 images.
The film with 250 images runs at 5 images per second and takes 50 seconds to run from start to end.
The film with 500 images runs at 20 images per second and takes 25 seconds to run from start to end.
The film with less images takes more time!
You were saying? Oh that’s right, I forgot, you were talking nonsense!
The whole point is that it’s a bad example, because frames in a film strip refer to stretches. So you still need a viable example illustrating the static point you are attempting to define.
But you misunderstand what element means. element is a mathematical convenience. an element, containing number 0. If the element contains a number 0, refering to time, it means there was 0 time. The element still exists in the notation, but there is no actual point in time, because 0 means 0 points in time.
The position is important. Because a position needs location, and to designate a location, you need to indicate where it is. To indicate where it is, you have to define it as existing, thus giving it quantity, thus a range.
Otherwise, not to harp, where is it? Exactly?
Infinitely divisible means the process of dividing it never ends. Everytime you have a product, a division ensues. If no division ensues, the progress ends, and is thus not endless, thus not infinite.
In this case, the number of elements (not the numbers represented by the elements) is not infinitely difisible, but finitely divisible.
Right, that set is infinitely divisible if you start from an infinite position. That is, the whole set, which is endless, is divisible. The moment you select an arbitrary finite portion of the set, and divide it, it will not be infinitely divisible. Like how you were mentioning before that the endless part can be in front or in back or in middle, this one is in front.
If time is actually infinite in quantity, then the entirety of time can be infinitely divided. But that is an absurdity. However, a single finite stretch, such as ten time points, we will imagine it constitutes a millionth of a second, is not infinitely divisible, if time is in fact, as you say, composed of single finite points. Indivisible means the same thing as finite.
You argue incorrectly.
Vagueness means the lack of distinction, contrast, and clarity - the lack of finite fixed boundaries or absolute “here - not there” definition.
Points are a convenience of the mind’s effort to map reality - but like Newton’s laws of motion - fall short when it comes to the extremes. And like Newton’s laws - many years are wasted by those who cannot see the short coming as they argue their absolute faith in ideas that are already proven invalid.
Points of location in space or in time - do not exist – not only as physical objects but not even as reality concepts. The matrix or grid of lines imagined to be able to map position and location are not applicable to the extremely small – such perfectly straight lines cannot exist physically and also cannot accurately represent reality on infinitesimal levels.
That imagined grid is actually a fuzzy blurred grid when seen at Plank levels. There is no straightness. There is no point where a straight crosses another straight. It is all a primitive imagined ontology of the mind - like the flat Earth - but not actually real. Straightness does not exist.
If you stack “1, infinite zeroes, 2, infinite zeroes, …” — you have only 1.0.
No progress at all can be made from adding even an infinity of nothing to anything.
But not really. That’s just in notation. If you want to know what it says, you look at the notation. The first one says one. Ok, that occupies a space of one. The next notation says an infinity of zeroes. Ok, that occupies no space. then the notation says 2. Ok, that has a quantity of 2, so after 1 there is 2.
The elements aren’t themselves accounting for what is referred to. They account for the quantity of what is being referred to. If there are a million elements referring to the quantity 0, then the total quantity is 0, occupying nothing. The notation occupies something, but what the notation describes occupies nothing.
Infinite zeroes cannot even be written, what you notate is a process whereby you postulate the rpetition of the notation of zero without end. You know that, no matter how many times this happens, even endlessly, the quantity will still be zero.
You appear to be arguing both sides –
I agree that the notation is not the subject - but rather what the notation represents.
The notation “1” represents a location - a point (in my original discussion). It doesn’t matter how many zeroes are added – still only a location point “1”. Add the notation “2” then both “1” and “2” become the same location point with two labels. Add more zeroes – still only have one location point “1” or call it “2” now if you like – still merely a single point.
I am afraid you’ve lost me. Maybe if you write it more formally in notation. That way I think I will better understand what you mean the numbers to mean.
I am certain that you agree with what I actually mean - so no need to go into details. 
“Lack of distinction” means “lack of difference”. The same goes for “lack of contrast”. They mean no more than “sameness”. There are indeed things that are the same e.g. the species you belonged to yesterday is the same as the species you belong to today. You are, in other words, still a human being. Albeit, if you think that literally everything changes, then thinking that reality lacks distinction is a contradiction. Of course, in reality, there are things that change and there are things that do not change (similar to what Aristotle argued.) “Everything is change” (Heraclitus) and “Change is an illusion” (Parmenides) are both false.
The word “clarity” means “the state of being clear”. The word “clear” means “easy to perceive, understand or interpret”. Of course, it goes without saying that some things are easier to perceive than others. Perceiving the laws that govern the entire universe is a lot more difficult than perceiving the laws that govern a small portion of time and space. But is that what you really mean? I don’t think so.
“Here” and “there” refer to portions of reality. If when you say “here”, you don’t know the exact boundaries of the portion of reality you’re talking about, it merely means that the concept that you attach to the word “here” is either not fully understood by you or that it is not fully defined. It has absolutely nothing to do with reality itself and everything to do with definitions that are either misunderstood or that are incomplete and require further work. If when you say “here” to refer to some region of space, there are regions of space for which you do not know whether they belong to “here” or not, it means that you either do not understand the concept that you attached to the word “here” or that the concept isn’t fully formed. So called “gray areas” come into existence when you can’t tell whether any given portion of reality can be represented by some word you’re using (indicating that you either do not fully understand the word you’re using or that the word is not fully defined i.e. defined with respect to every conceivable thing.) I suspect that many human concepts aren’t fully formed which is why “gray areas” exist. None of that has to do with reality itself. It all has to do with human ability and human tendency to project inability onto the universe itself.
Yes, as I said, every point in time is a stretch i.e. a period of time. “Point in time”, as I use the term, does not refer to something that has no temporal length. It refers to the smallest period of time. It refers to a single place in the sequence that we call time. That place is not zero in size.
Yes.
You don’t have to start from “an infinite position” assuming that by “infinite position” you mean the last element in the sequence (there is no such thing after all.) You start with the first element in the sequence. You take the first element out of it and place it in its own group. Then you take the second element out of it and place it in its own group. And so on. The result of that is an infinite number of indivisible sets. The same would happen if you infinitely zoomed into an infinitely divisible region of space. It’s just that, due to the way observation works, you wouldn’t be able to see the individual elements with your own eyes, merely their average.
That’s all true, but unfortunately for you, you’re using the word “image” in a different way than you’re supposed to (entering the territory of equivocation.) You’re talking about an actual film strip consisting of 250 images. I’m talking about metaphorical film strip that is time itself.
I don’t think that is true.
You are presuming that clarity exists and we have only the need to discover it. I am explaining that is a false assumption. I am explaining that the clarity isn’t there to be discovered - every location is a “blur” - a “smear” in the general shape of that bell curve (a single wave) - every point layered upon the next - each a smear of existence overlapping those others it is immersed in and a part of - affecting their affect and being affected by them - existing within each of them only slightly less than others further distant.
If talking about conceptual zero-wide points - each physical location is at both point A and at point B at the same time - and at point C also though slightly less so.
At the extreme low level - existence is not a dichotomy (not “either here or there” - existent or not) - locations and “points in time” are not totally separate. They only appear to be that way in the macroscopic world.
Quantum mechanics describes positions as probability waves. I disagree with the use of that word “probability”. The reality seems to be that QM’s “probability wave” is the actual position itself - a wave/blur/smear - not just a probability of where something might be found but a description of the location itself.
Physical existence does not come in zero-widths.
What’s impossible in concept is also impossible in reality. The reverse isn’t true. Thus, if motion is impossible in concept, it is also impossible in reality.
That’s why we don’t have to check every single shape in the world – or at least, as many shapes as possible – in order to determine whether or not square-circles exist. It’s enough to look at the concept that is “square-circle” and realize that absolutely nothing can be represented with it.
First, you will have to define what you mean when you say “clarity”. As I already said, normally, the word “clarity” means “the state of being clear”. And the word “clear”, in turn, means “easy to perceive”. Thus, the word “clarity” means “the state of being easy to perceive”. It’s typically used with respect to statements. “This statement is lacking clarity” and “This statement is clear”. They mean “This statement is difficult to understand” and “This is statement is easy to understand”, respectively. But I guess it can also be used, and that is sometimes used, with respect to any other portion of reality with the aim to describe how easy it is for someone to perceive the contents of it. It’s obviously a relative term. What is easy to perceive for one is not necessarily easy to perceive for another. Assuming that the Earth is round, it is obviously the case that there are people who find it difficult to perceive its roundness (the Earth being round is not clear to them) and others who don’t (the Earth being round is clear to them.) How easy it must be for a portion of reality to be perceived by someone in order for it to be said to have clarity? Where do you draw the line? Place it high enough and you’d be able to correctly state that nothing has clarity. But then, what’s the point?
But that is MY definition. And not merely mine, that’s how most people use the term “clarity”. What is yours? What does it mean for clarity to exist? What does it mean for a thing to have clarity?
Which I’m not.
What is a metaphorical film strip that is time itself?
Ah, ok, this is good to clear up.
But that’s really a process of addition or multiplication more than division, it’s a reverse engineereed division. Because the ultimate amount of repetition of points will be infinite, that is what would divide into all the points, infinity, which is not really a quantity.
If points in time are indivisible, the total set of all stretches of time of any given size can be infinite, but any specific section of time cannot be infinitely divisible.
To use your operation above, if we take exactly 100 elements from the set ALL OF TIME, that is a specific stretch composed of 100 indivvisible portions, and is so not infinitely divisible.
Time can either be composed of indivisible points, or be infinitely divisible for any given finite section, not both.
That is not always true - Zeno’s paradox is an example. Things do actually move so the concepts being expressed in the paradox are obviously flawed (that is why it is a paradox). What is flawed about it is the ontology it presumes - that the universe can be described to a perfect degree by a straight line location grid. In reality there are no straight lines.
It means that despite any confusion about the matter - the actual truth is discretely black or white - that objects exist in reality either here or there but not both. That clarity in reality is not true. As it turns out - objects on that Plank level really do exist in multiple places at the same time (although only extremely close places (>=10^{-35}m)).
It is similar to the idea that velocities can be simply added. In Newton’s ontological understanding - simple addition is sufficient. As it turns out - velocities at extreme speeds, close to speed of light cannot be simply added to reveal a final velocity. What was clear to Newton was a false image of the structure of reality. Einstein points that out.
Similar is true about the extremely small distances or durations - they cannot be merely added with simple arithmetic.