Well, no, the number of distinct digital photos of a given resolution is finite. But so what? — SophistiCat

Of course. The entire process is faulty. The assumption that every aspect of the universe can be so pixeled assumes his conclusion.

You don't get it, you can zoom in as much as you wish in arbitrary small steps. You can also forget photographs and imagine all the knowledge there is about everything that will ever be is simply written in English words, with illustrations and diagrams.

You are not addressing the problem. What part of the universe you could not potentialy see on your monitor? You can either name what kind of object or information it is that your monitor can not visually convey, or you have to admit your monitor can convey any and every possible information.

The assumption that every aspect of the universe can be so pixeled assumes his conclusion. — jgill

In other words, there is no actual infinity of discrete objects; but this does not rule out real continuity in the universe, such as that of time and space, which are not composed of distinct parts.

You are not addressing the problem. What part of the universe you could not potentialy see on your monitor? You can either name what kind of object or information it is that your monitor can not visually convey, or you have to admit your monitor can convey any and every possible information. — Zelebg

A pixellation of something is a map of it to a finite set of polygons that cover it . Let's say they're squares. It doesn't matter what you apply the pixellation to, it ends up finite. You can throw squares on the unit square $[0,1]\times [0,1]$ by dividing it into 4 squares along its non-diagonal lines of symmetry, but the unit square is uncountably infinite. That is, an object having a finite pixellation is not sufficient for it being a finite object (specifically, of finite cardinality).

I think you're confusing the necessary finiteness of the pixellation with the finiteness of the pixellated object.

Of course. The entire process is faulty. The assumption that every aspect of the universe can be so pixeled assumes his conclusion. — jgill

Do you know what kind of properties a space would need to have so that every subset of it could be covered by a finite set of polygons?

You don't get it, you can zoom in as much as you wish in arbitrary small steps. — Zelebg

Wow! So there are an infinite number of pixels in each photo. You're correct. Guess I don't get it.

You can also forget photographs and imagine all the knowledge there is about everything that will ever be is simply written in English words, with illustrations and diagrams. — Zelebg

There are a finite number of existing English words, but if there is no limit on the length of a word you could be speaking of infinities. There are 26 letters, so how many "words" could be constructed, of any length? Of two letters: 676. It goes up from there. 26^n. n increases without bound. Also, there could be an infinite number of diagrams.

Is the map the territory?

Wow! So there are an infinite number of pixels in each photo.

You are on the right track now, just wrong side of the equation. The number of pixels is finite and so is the number of their combinations, that part of the equation is known. But for the equation to be equal the number on the other side must be finite too, and that number represents every possible information your monitor can represent. Therefore, the total number of unique bits of information is finite, or there is some kind of information your monitor can not display, for some reason.

I think you're confusing the necessary finiteness of the pixellation with the finiteness of the pixellated object.

Can you explain that by describing a type of object or information that can not be visually represented on a computer monitor?

Can you explain that by describing a type of object or information that can not be visually represented on a computer monitor? — Zelebg

Yes.

A pixellation consists of a finite number of finite pixels arranged in some sort of grid that cover an object.

So I took an object which has infinitely many things in it, all the points contained in a square whose side lengths are 1 and gave it a finite pixellation, four squares defined by its non-diagonal lines of symmetry.

Such a square has infinitely many points, but it nevertheless has a finite pixellation. So an object having a finite pixellation doesn't prove that the object is finite.

What information is lost? Imagine that you're trying to specify your position on the monitor's image - you can represent this as the position of a pixel (its centre). If you move right one pixel, you move a distance according to the length of the pixel. You can't specify any within pixel coordinate just using pixels.

If instead you want to be able to move right by any distance at all, you're already dealing with an infinite object (at least something like the rational numbers, the fractions, which have a coordinate between every pair of coordinates, no matter how close they are).

Therefore, the total number of unique bits of information is finite, or there is some kind of information your monitor can not display, for some reason. — Zelebg

Say each piece of information is a string of alphabet symbols. Since the length of these strings is unbounded, so is the amount of information. We're not talking about computer programs that terminate.

Do you know what kind of properties a space would need to have so that every subset of it could be covered by a finite set of polygons? — fdrake

Compactness? Are your "polygons" abstract entities? Topological spaces or what? Compactness in TS if you adjoin limit points, I suppose. :nerd:

Such a square has infinitely many points, but it nevertheless has a finite pixellation. So an object having a finite pixellation doesn't prove that the object is finite.

It’s not about size. Infinitely large square we can scale down to arbitrary small size without omitting any information, or even fully describe it just by a single word. It’s about unique features, so ultimately it is about compressibility and randomness.

Forget the images, let’s just take black&white monitor, just two colors and only English words, symbols and numbers from ASCII set. Is there any part of the universe, any law, property, force, event or phenomena, any planet, star, or galaxy, that can not be fully and extensively described on such a monochrome monitor with just ASCII?

For the amusement take a note with the above example we used only a tiny portion of all the available potential space. There are still many empty screens waiting that can hold all that information written in every other language, current, past and future, also all the alien languages included, plus much, much, much more unused space waiting and we have already described every possible thing many times over.

Compactness? — jgill

This was my thought too. If covers need not have a finite subcover, then something like a pixellation couldn't exist for sets that fail to have finite subcovers.

My other intuition was that: open covers having finite open subcovers in some topology (of a suitable object) would probably let you "push" any open set in that topology into an open set in the plane through a continuous injective function, then you could cover the open set in the plane with a grid of polygons; composing the continuous injection with the point->polygon grid assignment would give an association between the points of any open set in the first object with a pixel, then you 'pull' the point back through the composition. I didn't check if this preserves the grid like properties on the first space (maybe small open sets in the first space can be guaranteed to hit multiple pixels).

Are your "polygons" abstract entities? — jgill

I was imagining closed plane figures with straight line edges.

Topological spaces or what? — jgill

Yes!

Compactness in TS if you adjoin limit points, I suppose. — jgill

What is TS?

Guess a grid on an object in a more general topology would be a collection of disjoint closed (or open?) sets that cover the object.

Maybe this will be easier to think about, and it's also about 'time' this time. Imagine there exists an encyclopedia of all the particles in the universe for all the time as far as it goes.

On every page there is a description of a single particle, where it is, what is doing at the given time. Collectively all that information describes everything that exists and will ever exist.

The question is whether this encyclopedia of everything has infinite number of pages or not. The answer is no, because there is no reason why your monitor could not display any of those pages, and the number of pages your monitor can display is finite.
.

What is TS? — fdrake

Topological space.

On every page there is a description of a single particle, where it is, what is doing at the given time. Collectively all that information describes everything that exists and will ever exist. — Zelebg

Let's say particle alpha is under consideration. We measure time in seconds. Page 1, present time. Page 2 , 1 second from now. Page three, 2 seconds from now, etc. Page N, N-1 seconds from now. You would have to assume time stops at some point in the future in order to secure your "proof." So you would postulate that time is finite. But this seems to be part of what you wish to prove.

I must be missing some important debate points here, in my old age. :gasp:

Maybe time just goes in circles? It's not my goal to prove anything, it's all the same to me. I just like mysteries and here is some mystery it's not even quite clear what the mystery actually is. Mysterious mystery is the best mystery of all.

You are not addressing the problem. What part of the universe you could not potentialy see on your monitor? You can either name what kind of object or information it is that your monitor can not visually convey, or you have to admit your monitor can convey any and every possible information. — Zelebg

If your monitor - or, say, any device or method for identifying distinct objects - can only register a limited number of objects, due to the way in which it is constructed, and you have registered that many objects, then all that you can say is that there exist at least that many distinct objects. This is the point that you fail to grasp.

Suppose, for example, that your device can register only up to five distinct things, and suppose that the world has more than five distinct things. What conclusion do you draw from this: too bad for your device or too bad for the world?

This idea, that your device or method can bias, limit or even fully determine what what you can observe is known as observation selection bias or observation selection effect.

The question is whether this encyclopedia of everything has infinite number of pages or not. The answer is no, because there is no reason why your monitor could not display any of those pages, and the number of pages your monitor can display is finite. — Zelebg

Perhaps you will realize your mistake if you reduce the size of the page to the extreme (although a similar exercise with reducing the number of pixels on the monitor failed to convince you). If you only have one character on the page, and there are, say, 100 letters, digits and other signs that you can depict with one character, does this mean that there cannot be more than 100 distinct entities in the world?

If your monitor - or, say, any device or method for identifying distinct objects - can only register a limited number of objects, due to the way in which it is constructed, and you have registered that many objects, then all that you can say is that there exist at least that many distinct objects. This is the point that you fail to grasp.

You keep avoiding the question. If my monitor is limited to show only some of all the possible objects, what is it about those remaining objects that prevents my monitor from showing information about them, why can it show object A but not object Z?

Perhaps you will realize your mistake if you reduce the size of the page to the extreme (although a similar exercise with reducing the number of pixels on the monitor failed to convince you). If you only have one character on the page, and there are, say, 100 letters, digits and other signs that you can depict with one character, does this mean that there cannot be more than 100 distinct entities in the world?

Does it not bother you every time instead of addressing the question directly you always make up your own interpretation and end up answering your own question instead of mine? -- What is the reason why my monitor could not display any of those pages from the encyclopedia of everything?

How about instead of petulantly demanding answers to stupid questions you use your own head? You demand to know why a device like a monitor, camera or book can only store a limited amount of information. Did you already forget that this was the very premise of your stupid argument?

Ugh, why do I even waste my time on this...

I’m repeating the question so you don’t fool yourself that you have answered it.

You demand to know why a device like a monitor, camera or book can only store a limited amount of information. Did you already forget that this was the very premise of your stupid argument?

No. You claimed there are objects that my monitor can not represent, I’m asking what is it about those objects that prevents my monitor from showing information about them, why can it show object A but not object Z?

Imagine an empty digital photo, say 800x600 pixels. You could take a camera and potentially go to every single point in the universe and take as many photos from any point in any direction, even using a telescope and microscope, and infrared, ultraviolet, any filter you like… and you can also add to that every frame of every movie ever made, and every page of every book that was written, that will be written, and even those pages that will never be written… also add to that illustrations of every thought and dream, and every scene every man has seen and will ever see....

That single empty photo potentially contains all there is, was, and all that will ever be, and more, even things that can not and will never be. Yet the number of all those possible photos is not infinite. Therefore, if the universe / space is infinite, it can only be due to repetition since the number of unique things that can exist is apparently finite. — Zelebg

I'm not saying your wrong, but something to note when you change the space between two particles or two eye balls you also change the appearance and also the behaviors of that object/ball of mass/or human face. The structures of atoms is effected by distances (as well as other things) between any given "sub" particles or sub atomic particles that make it up. So once again i'm not saying you are wrong however when you change a pattern even slightly or change distances even slightly you are also changing alot of other things. So it is possible for an infinte different variations or patterns.

Ugh, why do I even waste my time on this... — SophistiCat

You are clearly a glutton for punishment!

You can bring a horticulture, but you can't make him think.

|>ouglas

On every page there is a description of a single particle, where it is, what is doing at the given time. — Zelebg

You can't fit all the required information about even a single particle on any finite-sized pixelated page because some of the values associated with the particles would be represented by Real numbers not Integers or Rationals, and a Real number contain an infinite amount of information in it. I.e., you cannot encode an infinite amount of information on a page that can only hold a finite amount of information.

|>ouglas

That is not the answer, just refusal to accept the premise of the question, and is beside the point since the bottom resolution can be fixed to arbitrary size and precision. Say, human faces. My monitor can show every possible human face at least down to a scale and precision of an electron microscope. Therefore, there is only a finite number of unique human faces. Yes?

Therefore, if the universe / space is infinite, it can only be due to repetition since the number of unique things that can exist is apparently finite. — Zelebg

Simple proof that your theory is false:

Let's assume that the space is infinite and physical manifestation is limited to a finite (not infinite) number of possible arrangement.

Let 's further assume, that A represents the number of possible configurations, B represents any configuration, and C represents a subconfiguration to B.

In this case all you have to do is add C to B, and you got an additional number, A+1, to represent the possible configurations of matter. Obviously A+1 is a number greater than A, and B union C is a unique, new representation.

Now let's assume A' is A+1 and B' is B union C. Repeat the experience, and you realize this experience can be repeated without any ending, and with forever producing A' from A and getting a larger number every time, and with forever producing B' from B without repeating the same configuration.

A little help to understand my prevous post: B is not the same as BuC, and BuC is not the same as BuCuC, .... and no configuration of B (n* uC) is the same as b ((n-1)* uC).

B here is a given configuration of matter, C is a subconfiguration of B, and BuC means B union C, because u means union (as in set theory) and n is any positive integer greater than 1.

Simple proof that your theory is false:

The question is, can my monitor represent information about every possible object or it can not. What is your answer?

Your monitor has a capacity to represent only a limited amount and thus a finite amount of different combinations. Your monitor, however, can not represent all possible combinaitons that can be otherwise present in the same area as your monitor shows or is.

But that's not my point. Even with a finite number of combinations, you can present double the amount of combinations if you add another screen or monitor. And triple it with adding a third screen. ETC.

can my monitor represent information about every possible object or can it not. — Zelebg

To give a straight answer, no, it cannot, if the information is to be complete, exhaustive and precise.

However, information may mean "limited but pertinent knowledge" or it can also mean "scanty knowledge".

Your may want to rephrase your qestion?