## Logical proof the universe cannot be infinite

• 626
Imagine an empty digital photo, say with resolution of 900x900 pixels and 900 colours. It potentially can hold a picture of every planet, star and galaxy that ever was and will ever be, at any arbitrary given time, from every possible angle, every possible altitude. It can hold every photo and movie frame that was ever taken and will be taken, every scene that was ever seen and will be seen, dreamt or imagined by every human or alien that ever was and will ever be. It can also contain every page of every book that existed, exists, and will ever exist... it potentially contains a picture of anything that was and can ever be, a picture of everything that can possibly be, both in reality or imagination, and yet the number of those pictures is not infinite.

Therefore, the universe, along with the number of things, actions, or concepts, is not, and cannot be infinite, not even potentially. Right?
• 7k
Interesting, tempting, but no. Your number of pictures is finite. And that simply forecloses on consideration of the universe. And then there is what "infinite" means in this context.
• 1k
and yet the number of those pictures is not infinite.

The number of picture tokens is (presumably, but it's your rules) equal to the number of pictured scenes.

But the number of picture types is 900^810000, and therefore eventually less than the number of scenes.

It's like, the natural numbers are infinite, but modulo 12 they are 12. And modulo 900^810000 they are 900^810000.

Funny how so much information woo rests on confusing tokens and types; seeing as they were invented by its patron saint.

No offence, @Zelebg, I always enjoy quoting your last word on panpsychism.
• 626

And then there is what "infinite" means in this context.

Infinity here refers to the maximum possible number of different or unique things or concepts that can possibly exist, ever. For example, the number of unique human faces is not infinite, or the number of unique living things or beings, or the number of unique actions they can perform, thoughts or feelings they can have, it is not infinite.

Or, in the scale of the universe, the number of unique planets, including everything that happens and will ever happen on them, that number is not infinite. So, I am talking about infinity that actually matters, because infinity that at some point starts to repeat is not true infinity, if you ask me.
• 626

But the number of picture types is 900^810000, and therefore eventually less than the number of scenes.

How is it eventually less, what scenes are not included within the total number of all the pictures that photo can potentially hold?
• 560
Imagine an empty digital photo, say with resolution of 900x900 pixels and 900 colours.
...or possibly imagine an empty digital photo, with a resolution of 1x1 pixel and 2 colors.
• 1k
what scenes are not included within the total number of all the pictures

The question is only, what scenes are not assigned their exclusively own personal picture (type). Some at least will have to share.
• 626

Heh, yeah, the logic doesn't seem to scale that way, and that baffles me. I mean, just exactly at what resolution the logic starts to fail, and why there, what does that particular resolution has to do with the universe? I feel there is something profound to be learned here, or not, who knows. Who knows!
• 626

Don't understand.

Do we agree this logic with empty photo and all the possible pictures it can hold means there is only a finite number of unique book pages that can be written?
• 2.1k
Therefore, the universe, along with the number of things, actions, or concepts, is not, and cannot be infinite, not even potentially. Right?

The universe that is the model in our minds can not be, because we cannot list an infinity of things. That does not mean that that which is ontologically real (whatever it is) cannot possibly infinite, though it is of course not possible to imagine what that would mean.
• 4k
Go to the beach with bucket. Walk out into the ocean till the water is waste high. Plunge the bucket down to your feet and drag it along for some sand, shells, weeds and maybe some bottom-feeders. Take the bucket of ocean water and detritus back to the shore and climb up on the rocks so the sun can warm you. Now study the bucket without dumping its contents back into the surf. One day, maybe, you'll write a dissertation titled "All There Is" on the entirety of the ocean you'd once observed in a bucket full of briny water, sand & shells. Of course it's not infinite.
• 626

Of course it's not infinite.
Your "of course" surprises me since I do not know of any other argument or reasoning that even comes close to be as convincing. What convinced you that it is not infinite?
• 5.4k
Imagine an empty digital photo, say with resolution of 900x900 pixels and 900 colours. It potentially can hold a picture of every planet, star and galaxy that ever was and will ever be, at any arbitrary given time, from every possible angle, every possible altitude.

I don't get this. How could a 900x900 pixel image show the entire universe or even a small part of the universe?
• 626

Perhaps the best way to explain it is to ask what part of the universe it can not show?
• 2.4k
Perhaps the best way to explain it is to ask what part of the universe it can not show?

Itself, of course. It could not show itself in full detail.
• 10k
I don't want to spoil it for you but, if you ask me, an image isn't the object it's an image of or as @180 Proof might've said, the map isn't the territory.
• 4k
:up:
Irony, no doubt, is lost on you.
• 626

Itself, of course. It could not show itself in full detail.
What part, what detail could it not show? For example, could it show every single square millimetre of Earth, Moon, Jupiter, and Mars? And so on... could there possibly be a planet in the whole universe whose every single square millimetre it could not show?
• 626

What does that have to do with anything I said?
• 50
Therefore, the universe, along with the number of things, actions, or concepts, is not, and cannot be infinite, not even potentially. Right?

If the frame has an infinite number of pixels then the possible images are even more infinite than the number of pixels. If it is1x1 with 2 colors it can only have 2 possible images.
• 626

Irony, no doubt, is lost on you.
Your irony is a waste of time until you make clear what your opinion is and explain your reasoning.
• 2.4k
What part, what detail could it not show? For example, could it show every single square millimetre of Earth, Moon, Jupiter, and Mars? And so on... could there possibly be a planet in the whole universe whose every single square millimetre it could not show?

Your digital photo is a thing in the universe. It lives in a piece of silicon memory in a computer. We think of software as ethereal or nonphysical, but an electrical engineer can measure the electric charges of the bits in a memory chip. Computer memory is a physical thing and the data stored therein is likewise physical. It requires energy to maintain.

If your photo perfectly images everything in the universe, it must image itself in every detail. You have an infinite regress problem in your thought experiment. All simulation arguments do.

But of course that leads to the refutation of your argument. At some level of detail, we must only approximate the world. You can't perfectly image the image of the universe. You must necessarily omit some level of detail. Likewise you must necessarily omit some level of detail about everything. Just like a movie isn't reality even though we see people moving around. It's one still frame after another, and the retention of our eye/brain system fills in the blanks and creates the illusion of motion.

At best you have an approximation of reality. The interesting parts are everything your approximation fails to capture.
• 626

If you would please answer the question: could there possibly be a planet in the whole universe whose every single square millimetre it could not show (and even with arbitrary given magnification / zoom in, that is unlimited detail)?
• 2.4k
If you would please answer the question: could there possibly be a planet in the whole universe whose every single square millimetre it could not show (and even with arbitrary given magnification / zoom in, that is unlimited detail)?

All of them. The detail of the universe far exceeds what you can represent. You couldn't even fully represent a grain of sand ... for the reason that we don't fully understand a grain of sand. What holds the quarks together? Gluons. Why does that work? Why does the binding energy of the quarks create mass and thereby distort the fabric of spacetime, creating the illusion of gravity? We don't know these things. You don't know these things.

Of course you are right, you can indeed represent a picture of a physical object that's perfect up to the resolving ability of the human eye. But that's not much of a standard. It puts us back in the era before we knew about microbes and the germ theory of disease. There's a lot more to the world than we can see.

The artistic movement of pointilism comes to mind. Your image is only an approximation to a certain level of detail.

• 626

It is the other way around, the number of possible images my empty photo or your computer screen can represent far exceeds the possible details of the universe, because any given detail can not only be represented as a photograph, but also as a diagram and also with words written descriptions, in every language too.

Whatever detail there can possibly be, known or unknown, visible or not, as long as it can be described with pictures or words, or whatever symbols and diagrams, there is an empty space on your computer screen waiting and ready to represent it, in more than one way.
• 2.4k
as long as it can be described with pictures or words, or whatever symbols and diagrams, there is an empty space on your computer screen waiting and ready to represent it, in more than one way.

So you agree that you can only represent computable phenomena. You can't, for example, solve the Halting problem. But it's not known whether the universe is computable or whether the universe can solve the Halting problem. Some people believe so, but there's no proof, nor is it even clear what would constitute proof.

But how can you be certain there are no levels of detail below the resolution of your $(900 \times 900)^{900}$ universe? After all that's a finite number. It's large by everyday standards, but it's very small compared to Skewes's number, Graham's number, Tree(3), the larger Busy Beaver numbers, and other ginormous (Sean Carroll's word) large positive integers studied by mathematicians and computer scientists.

Those numbers may not have physical existence in terms of planets or molecules. But they have undeniable mathematical existence. Where does mathematics fit in your universe?

What scientific principle limits the universe to only that many distinct states, large though your number may be? Wolfram Alpha gives your number as approximately $4.33 \times 10^{5317}$. There are more decimal digits of pi than that. How would you represent them?

And to reiterate my earlier concern; if you can perfectly replicate the universe in your grid, you would need to replicate the grid itself, right? Your grid is a physical thing in the universe. Wouldn't that give you a bit of an infinite regress problem?

Or as William Blake said:

To see a World in a Grain of Sand
And a Heaven in a Wild Flower
Hold Infinity in the palm of your hand
And Eternity in an hour

https://www.poetryfoundation.org/poems/43650/auguries-of-innocence
• 626

So you agree that you can only represent computable phenomena.
I don't see why involve computation/simulation in this. For whatever problem we do not yet know the answer to, your computer screen will be able to represent description of the solution if it exist.

So, I am talking about describable phenomena, and I do not know what is indescribable phenomena or can such thing exist.

But how can you be certain there are no levels of detail below the resolution of your (900×900)900 universe? After all that's a finite number. What scientific principle limits the universe to only that many distinct states, large though it may be?
Because finite resolution is no limit for the amount of detail or zoom factor, so your monitor can show whole Earth from far away, but it can also zoom in and show microscope images of tiny bacteria from up close, and further down it can show electrons and protons, and whatever else as CGI, as illustration, diagram or other kind of symbolic representation.

This holds true for any past, present and future planet and its every square nanometer we zoom in on. Your monitor can show it all, and then some.
• 4k
Your irony is a waste of time
Apparently. :yawn:

:100: :up:
• 2.4k
I don't see why involve computation/simulation in this. For whatever problem we do not yet know the answer to, your computer screen will be able to represent description of the solution if it exist.

You need to look at the Wiki page I linked on the Halting problem. It's an easily stated problem that no computer can possibly solve. It was discovered by Turing in his famous 1936 paper in which he outlined the notion of computation.

I
So, I am talking about describable phenomena, and I do not know what is indescribable phenomena or can such thing exist.

it potentially contains a picture of anything that was and can ever be, a picture of everything that can possibly be, both in reality or imagination, and yet the number of those pictures is not infinite.

Therefore, the universe, along with the number of things, actions, or concepts, is not, and cannot be infinite, not even potentially. Right?

You are clearly talking about everything that is.

But now you say you are only talking about everything that is describable. By whom? By human beings on earth? Well the number of things that could be verbally described by all the human beings who have ever existed is a very small number compared to the size of your grid. So in that case I would grant your premise.

But please note that you have now entirely changed your claim from saying that your grid can represent everything in the universe, to only that which is "describable," a term you haven't bothered to define. And that switcheroo makes a huge difference.

Because finite resolution is no limit for the amount of detail or zoom factor, so your monitor can show whole Earth from far away, but it can also zoom in and show microscope images of tiny bacteria from up close, and further down it can show electrons and protons, and whatever else as CGI, as diagrams or other kind of symbolic representation.

Only to the limit of your memory to know what's there. You can zoom in on a map because the map's database already holds the data. All the zoom is doing is giving you a different view of the data that already exists in the computer's memory. Likewise you can only zoom in on detail that you already have in your grid; and the information capacity of your grid is limited.

So I repeat my question. By what scientific principle do you claim that the amount of information in the universe is less than the limited size of your grid?

This holds true for any past, present and future planet and its every square nanometer we zoom in on. Your monitor can show it all, and then some.

Only if you have the data stored first. And you have not demonstrated that the total amount of data in the universe is below the limits of your grid.

After all if you have the entire state of the universe stored in memory (which is impossible, because of the infinite regress problem I've already pointed out), you could use a conventional laptop screen to represent parts of it at any zoom level. You are confusing view resolution with the resolution of your stored data.

You should really think about how zooming into a map actually works. The data has to already be there in order for the screen to give you that view.

If you go to Google earth or Google maps and keep zooming in, what happens? Eventually you can't zoom in any more. Why not? Because you've reached the limit of the data that they store. Your viewer would have the same problem. You can only zoom in to the limits of the data you store.
• 1.3k
I don't get this. How could a 900x900 pixel image show the entire universe or even a small part of the universe?

The OP essentially assumes the conclusion, then attempts to "prove" it. :roll:
• 626

What a finite resolution image can potentially show has nothing to do with computers and memory limitations.

It's a simple logic exercise. There is no planet in the universe that your monitor could not show a photograph of, from far away, down to every single square nanometre of it. And since finite resolution monitor can only show finite number of different screens, it means the number of unique planets in the universe cannot be infinite.

If this one point is not yet clear, I'm afraid any further discussion is pointless.
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