The science of physical infinities is much less developed than the science of mathematical infinities. The main reason is simply that the status of physical infinities is quite undecided.

Although some have speculated that three-dimensional space is infinite, cosmologists generally believe that the universe is curved in such a way as to make it finite but unbounded—akin to the surface of a sphere.

In the light of the big-bang model of the origin of the universe, cosmologists generally believe that the universe has a finitely long past; whether it might have an endless future is an open question.
— Encyclopedia Brittanica on physical infinities

Is anything infinite in the physical world? Although the concept of infinity has a mathematical basis, we have yet to perform an experiment that yields an infinite result.

The universe could be infinite, both in terms of space and time, but there is currently no way to test whether it goes on forever or is just very big. — NewScientist on physical infinity

Infinity is a principle that arises while reasoning from first principles, such as in mathematics, but not while experimental testing, such as in science. Furthermore, the models for number theory and set theory are never the physical universe. These models are collections of formal language strings. They are 100% abstract only.

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. We do not have a copy of the Theory of Everything of which the physical universe is a model. Hence, there is no syntactic entailment ("proof") from theoretical axioms possible about the physical universe.

We would never finish writing down the natural numbers.

This is a guess...ONLY A GUESS...

...but chances are humans are kidding themselves in thinking they have an inkling of what actually IS in the REALITY of existence.

We sit here on this tiny rock circling a not especially impressive star in a not especially impressive galaxy...supposing our musings about the REALITY...are of great value.

If all that can be known about what exists were a yardstick...what we humans know may be nothing more than the first atom on that stick.

Fun to muse. We all do it...and probably should be encouraged to do more of it.

But to suppose that we are even close to "proving" anything like "infinity does not exist" or "infinity does exist"...is laughable.

Your argument is implicitly circular. You assume you could take these photos in a finite period of time. If the universe is infinite, your photography expedition will never end.

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.

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!

Being 1 being infinite do not go hand in hand. We think infinity contains 1. It is one, and everything in a set growing harmoniously for infinite source. Infinity would be that because a abyss of lines can exist, there is this really advanced line form which can go on forever. Can/Does/Will. Does infinity exist? Yes, but it is a wider but not necessarily taller concept than per se, harmony.

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.

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. — Zelebg

Yeah, that was the point of the reductio. One black/white pixel can encode one bit. 800x600 24-bit pixels can encode 11.5 million bits. But that's just a quantitative difference that doesn't bear on the problem with your argument.

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?

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? — Zelebg

It is not a "proof" as meant by proof theory.

For that purpose, you first need to list the axioms in your theory. Next, you need to show that what you have said syntactically entails from these axioms.

Therefore, it is a problem with (the lack of) formalisms that you use.

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.

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?

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. — Zelebg

Doesn't it bother you that the number of distinct things in the universe is limited by an arbitrarily chosen resolution of your camera? With an 800x600 24-bit pixel camera you can register at most ~8*10¹² distinct things. If instead you used an 800x600 16-bit pixel you would register at most ~3*10¹⁰ distinct things. And with a 1x1 1-bit pixel camera you would register only 2 distinct things. Haw can this be?

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

Hi Zelebg!

Have you considered the concept of time and eternity from Gödel (self-reference), and Turing? Or even the paradox of time itself?

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?

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".

Have you considered the concept of time and eternity from Gödel (self-reference), and Turing? Or even the paradox of time itself? — 3017amen

Could you please summarize what you have in mind as "the concept of time and eternity from Gödel (self-reference), and Turing," as well as "the paradox of time itself"? Thanks in advance.

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...

Sure, no problem. Gödel and Turing taught us about mathematics being incomplete & incomputable, and never ending, similar to irrational numbers and the modal logic paradox. For instance in modal logic (or if you prefer the liar's paradox/self-reference):

Socrates: What Plato is about to say is false
Plato: Socrates has just spoken truly

With respect to time, another paradox of trying to define time also appears incomplete in its 'eternal way' of trying to measure same. You may have seen this before:

Gödel and Turing taught us about mathematics being incomplete & incomputable, and never ending, similar to irrational numbers and the modal logic paradox. — 3017amen

I still do not see what those mathematical results have to do with "the concept of time and eternity."

With respect to time, another paradox of trying to define time also appears incomplete in its 'eternal way' of trying to measure same. — 3017amen

Sorry, I do not understand this sentence.

You may have seen this before: — 3017amen

Thanks for the video. To me, the paradoxes identified by Aristotle and McTaggart are resolved by recognizing that the principle of excluded middle only applies to individuals, while time is continuous and therefore general. There are no discrete instants within time itself, they are artificial creations that we impose for the purpose of marking and measuring time. The present moment is always indefinite, blending seamlessly into the immediately past and future moments, yet itself neither past nor future.

I still do not see what those mathematical results have to do with "the concept of time and eternity." — aletheist

Eternity equals no resolution.

Sorry, I do not understand this sentence. — aletheist

I explained earlier what the definition of abstract time is viz the concept of eternity.

There are no discrete instants within time itself, they are artificial creations that we impose for the purpose of marking and measuring time. The present moment is always indefinite, — aletheist

Is that then, abstract and/or eternal?

Eternity equals no resolution. — 3017amen

Eternity usually means timelessness, or perhaps infinite time. I still see no connection with incompleteness and incomputability.

I explained earlier what the definition of abstract time is viz the concept of eternity. — 3017amen

Not in this thread, as far as I can tell.

Is that then, abstract and/or eternal? — 3017amen

What do you mean by "abstract" in this context? The present is certainly not eternal.

or perhaps infinite time. I — aletheist

Correct. Otherwise, explain eternity to us?

What do you mean by "abstract" in this context? The present is certainly not eternal. — aletheist

Time itself.. Can you explain time in better terms? Maybe in less abstract terms, your choice.

Otherwise , it's ok, since you could not grasp my analogy (which is often used in theoretical physics), perhaps you have one that makes better sense?

(If you don't mind, maybe re-post it in different terms with the appropriate analogies so we can all understand.)

Tick toc tick toc LOL

Can you explain time in better terms? Maybe in less abstract terms, your choice. — 3017amen

I am attempting to spell out my Peirce-inspired ideas about time in another thread, so I suggest that we continue this conversation over there.

What do you make of it? — Zelebg

Well, first it is unclear what it is that you claim to have proven. The question you claim to answer is "How many distinct things can there be in the world?" But the answer will depend not only on how the world is, but also on how you cut it at its joints, so to speak: what kind of things are you looking for? Distinct geometrical shapes? Distinct species of animals? Distinct entities posited by fundamental physics? The answer to your question will depend on the chosen mereology, and here the problem is that a priori, without knowing anything about the world, we can hardly even decide on an appropriate mereology. And even if we do know something about the world, our idea of what the proper mereology ought to be can change as we learn more about it. On the other hand, with a trivial choice of mereology (e.g. "Everything is either Donald Trump or not Donald Trump") we can get a pretty good answer without doing any work at all.

But the most glaring problem with your approach is that the answer to your inquiry is completely depended on your instrument of choice. If your instrument cannot register something, then that thing does not exist. If it cannot distinguish between two things, then they are the same thing. The result therefore is bogus: it tells you nothing about how the world really is, it just tells you about the limitations of your method.

Yet the number of all those possible photos is not infinite. — Zelebg

Faulty hypothesis. :yawn:

Faulty hypothesis — jgill

Well, no, the number of distinct digital photos of a given resolution is finite. But so what? He might as well have said: I am going to count the number of distinct things in the world using the fingers on my right hand. Let's see... Tree, house, shoe, smartphone... oops! Only one finger left - I better lump everything else into one remaining thing. There! The number of distinct things in the world is five!