Neither the process nor that it has begun was focus of my point, but infinite set the process is assembling and the fact that it can never be complete, by definition. Infinite set will never be complete, therefore infinite set will never exist. There is no such thing as infinite past, it's simply a self-contradiction.

the collection of events cannot add up to an infinite collection in a finite amount of time, but they do so add up in an infinite amount of time. And since it is coherent to suppose that in relation to any present an infinite amount of time has elapsed, it is also coherent to suppose that in relation to any present an infinite collection of past events has already been formed by successive addition.
— Smith, Infinity and the Past

Starts with fallacy, continues with assumption, ends with paradox.

...if by that you mean an infinite number of material objects

Infinity is not a number. No logically valid statement can account for uncountable.

A washing machine is assembled in ordered steps. If these are known then each step is a stage in the construction of the washing machine. Similarly the simple process of adding 1 to a preceding number as in 0,1, 2, 3,... is a buildup to infinity.

Process describing a thing that will never be completed, that will never exist.

It is no more ‘located in the brain’ than actors are located inside televisions. Rather a rational mind is able to recognize such concepts which however are not dependent on being recognized in order to be real.

It is located in the brain just like simulated crocodile is located inside the computer and just like representations of actors are located inside a TV set. It's a virtual or mental kind of existence, a form of abstraction. i.e. representation.

Infinity exists for the simple reason that if you were to task me to write down all the natural numbers then that would be an instantiation of infinity in the real world.

You are referring to the concept of infinity that can not actually exist, by definition. The concept does not represent a thing to exist or not exist, nor it represents a collection or set of things. It represents an unfinished process of counting, and as such whatever it is accounting for can not exist because it is in perpetual state of becoming, just like you can not say a washing machine exists while its parts are still on assembly line and has not been put together yet.

We can talk about infinity in percentages though. For example, if time and space are infinite, would there be more planets that are completely identical or those that are different in some way? There will be more identical ones. So chances are there is Earth clone planet in the neighbourhood and there your clone is reading this same sentence right now. Don’t you two have anything better to do?

As for your conceptual anti-infinitist argument, this is an old and surprisingly persistent confusion. Quentin Smith had a nice analysis of this and several other such arguments in a 1987 paper Infinity and the Past.

Involving infinity neither side of the argument can be semantically valid. One side wants to count from the beginning where there is no beginning, and the other side has to say something like “infinite amount of events actually occurred”.

Infinite events could not have occurred, semantically, they would have to be still occuring, just like infinite future events can not ever occur by some point in future time and instead would have to still be occurring at every point in time, by definition.

Infinity is a concept defining indefinite, there is no reason to expect any logical / semantic manipulation of such a concept can squeeze some definite or meaningful answer out of it. We need to be asking other kinds of questions, it seems, if there is any actual answer to be found at all.

Yes, I have agreed as much. The problem is that Tegmark is making a contentious premise in his argument, and therefore, we cannot be sure of his conclusion.

Right. So if we don’t make any assumptions and instead choose arbitrary resolution and size we can make conclusions related to that specific resolution and size, like: there is only finite number of planets that look unique as seen from the altitude where they maximally occupy the given screen area.

Then we do smaller, lakes and mountains, then plants and animals, and everything else. And while you can argue there can always be some difference further you zoom in down below the decimal point, once we pass the size of an atom those differences are insignificant compared to the more general point.

Sure, but so what? Nothing interesting results from this.

Of you want to get to the interesting question, let's take Max Tegmark's argument that in our Hubble Sphere, there are only a finite number of possible states.

Now this is funny. Don't you see that is exactly what I'm saying? All I have to do is set my arbitrary resolution to planck scale and define the arbitrary given size as that of the universe to match Tegmark.

I’m not sure if that article makes one interesting distinction about the abstraction algorithm called “visual perception”. There are colors, clearly an abstraction of who knows what order, but then, there are lines and shapes, and countable discrete things, not quite abstracted, but rather mapped kind of directly.

That sort of thing hints that geometry may hold the truth and perhaps even all the answers, but unfortunately along also comes everything else with all the non-answers included.

Faces can differ in details that are smaller than the resolution that can be captured with an electron microscope. Also, different faces, even if they look the same in a particular pair of photographs, can move very differently from each other, which can completely alter our perceptions of what those faces look like.

And I am not arguing what you are refuting. I want to set up a basic unambiguous premise we can all agree with and thus have some starting point.

So, for some arbitrary given resolution and some arbitrary given size of an object, such that it maximally occupies the whole screen, say 800x600 resolution and passport style photographs of human faces - there exist a finite number of possible human faces for that particular specified size and resolution. Yes?

Your may want to rephrase your qestion?

Can any information be digitally encoded? The answer is yes, and to arbitrary given precision. My monitor can indeed represent any and every possible information.

I was referring to that fact that infinity is not a number that is mapped to. That fact doesn't entail an upper bound.

While it is true that abstract concepts only exist in minds as mental entities, minds themselves have no other source of information than the actuality of the external world, so they are all ultimately grounded or abstracted from the real world and are really only extrapolations and variations on the theme provided by the universe itself.

In more poetic language you could say that all we do or think can only be just a reflection of what the universe does and what the universe is. To put it bluntly, a bunch of abstract, meaningless symbols like: 0 = -x + x, can actually have a true metaphysical implication and might be our only way to answer the hardest questions of all, such as “why is there something rather than nothing”, and all about continuity / discreteness and infinity of both time and space.

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?

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?

Abstractions do not exist (not in the real world), they are mental devices that we create via The Way of Abstraction. They reflect types of objects that share some common properties. For example, the abstract object triangle does not actually exist (not in the real world) but triangular objects exist - they are instantiations of the abstraction.

Yes.

Numbers are abstractions, some of which are instantiated in the real world.

As far as we can see integer numbers are instantiated or mapped to the real world, how do you find it reasonable to assume this relation abruptly stops above some very large number or below number one?

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?

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?

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.

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.
.

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.

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?

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.

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.

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.

I think I see a way to turn around this argument that infinity does not exist into argument that infinity does actually exist. Damn! Reconsidering...

I'm not sure. If those are anything like Zeno's paradoxes, then yes, and that does seem related from the perspective of spatial continuity - analog vs. digital "space grid".

Doesn't it bother you that the number of distinct things in the universe is limited by an arbitrarily chosen resolution of your camera?

It bothers me. However, whatever new information that mystery holds, I do not see how it can possibly disprove what we can conclude with some standard monitor resolution, but then again, it does feel very strange, so let us think about it...

It does not seem the resolution sets the limit, it’s like the limit is already set pretty low and we only stumble over the limit at some specific resolution. Consider your monitor and Google Earth, you can zoom in and out, so you can encode all the information in sequential images to represent something that is much bigger than the screen.

So we make monitor resolution smaller and smaller, and at what point Google Earth can no longer represent the Earth, if there is such a point? But surely an image with only one pixel and just two colors is meaningless to us, and here we are in the domain of binary encoding, so when and how did we get here, where have we been before, where was the critical point where it broke, and what does it all mean… I’m not quite sure yet. What do you make of it?

It is not a "proof" as meant by proof theory.
For that purpose, you first need to list the axioms in your theory.

You are mistaking mathematics for a self-evident logical fact. In other words, the whole proof is an axiom, what part can you possibly doubt?

But that's just a quantitative difference that doesn't bear on the problem with your argument.

I’m not sure if you are saying there is a problem with my argument or not. If there is, point to which statement of mine is supposed to be unwarranted.

Last but not least, you would not be able to prove anything about infinity in the physical universe, because you cannot prove anything at all about the physical universe.

I just proved the number of unique things that can or will ever exist, both physical and imaginary, is finite. What part of the proof can you possibly doubt?

So, taking your "proof" to its logical conclusion, if you could encode all the information in the universe with a digital dataset - that is to say, a sequence of zeros and ones - then all you would end up with would be a bunch of zeros and ones. And since any zero or one is just like any other zero or one, it follows that there are only two distinct things in the universe, which repeat many times over. Brilliant!

There is a significant difference between full color, grayscale, and a picture that can only show black / white pixels. It doesn’t follow ‘there are only two distinct things in the universe’ from the ability to ‘encode all the information in the universe with a digital dataset’. You are obfuscating delimiters between different binary strings encoding many different things. What follows is just that any information can be encoded with a minimal set of only two bits, nothing more follows.


On the other hand, at the core of it all there might be just two things that make up everything, and in some way it is true. Attraction and repulsion for example, plus-minus, things either move apart or come closer together, that is all things really do.

Coincidently, I do have a theory everything is made of only positrons and electrons, but never imagined these two topics would come together, and I do not think there is actually any meaningful connection.

It's simply about the set of all the possible combinations of pixels. It has nothing to do with time and taking photos, that was only to illustrate how enormously huge the number is, and yet it is finite.

Colors are properties, and properties exist.

Aha. Forget I said anything, I'm out of here.

This is fun. You realize snakes see colors right?

Sorrry, I did not know you are insane.

This line of reasoning leads to madness. You end up with nothing but quantum probability waves existing and nothing else.

It's a simple logical fact. What is your objection exactly?

You are not talking about what the question is supposed to be.

The point is colors do not actually exist, and that is a fact in the sense that in the outside 3d person empirical reality there are only electric and magnetic fields, and they are transparent. There is no field of purple or substance of green. Therefore, we do not see colors, we "see" something else as colors. For example, colors could be mapped to magnetic density or electric voltage scales, or different orientation of molecules, or even symbols and numbers in some higher order representation mapping.

The existence of conscious minds is the most surprising thing about this universe, I think. It needs an explanation and science is failing spectacularly at providing one.

I already told you, are you broken? The explanation for the existence of things that do not actually exist, such as unicorns or qualia, is virtual existence.

That is not it. I guess I failed to formulate the question properly.

The point is colors do not actually exist, and that is a fact in the sense that in the outside 3d person empirical reality there are only electric and magnetic fields, and they are transparent. There is no field of purple or substance of green. Therefore, we do not see colors, we "see" something else as colors. For example, colors could be mapped to magnetic density or electric voltage scales, or different orientation of molecules, or even symbols and numbers in some higher order representation mapping.