Thread: Infinite possibilities?

Hi all,

Wondering if anyone else sees the paradox in this scenario...

An LCD screen has a certain number of individual pixels, each of which can display a certain number of colours. This means that every LCD screen has a finite number of unique images that can be displayed. Certainly a very large number in the case of a modern full HD screen, but finite nonetheless.

Now consider a digital camera that captures images at the same resolution and colour depth as a nominated reference screen. Because the screen that will display the images can only display a limited number of images, it follows that there is a limited number of unique photos that could be taken with our camera. If our photographer had unlimited time and could travel the entire universe there would be a limit to the number of unique photos he or she could take?

Or, another way to look at it. If we set an image generator running that would output all possible screen combinations (assuming infinite storage and infinite time to produce and/or review the images) the resultant image set would contain all information that is capable of being rendered visually at the nominated resolution. A picture of the screen you're looking at now might be image number 1033924932849, but the collection of images from which it is drawn must be finite.

Thoughts?

I don't understand your point, if your suggesting with a finite number of pixels only a finite number of images could be shown on the screen then yes thats correct, but equally the same limitation would apply to your digital camera, it would always just translate what ever picture you took into an image within capability parameters. Thus meaning whatever information you put into either device they would always be limited to what they could recreate. But that is not a paradox it's just a limitation on the ability of the technology.

Thats an interesting thought.

So does that mean that if there are infinitely many planets then infinitely many of them will be identical (since there are only finitely many photographs to go around)?
or does that show somehow that the universe is finite?

Originally Posted by Chrisgorlitz

I don't understand your point, if your suggesting with a finite number of pixels only a finite number of images could be shown on the screen then yes thats correct, but equally the same limitation would apply to your digital camera, it would always just translate what ever picture you took into an image within capability parameters. Thus meaning whatever information you put into either device they would always be limited to what they could recreate. But that is not a paradox it's just a limitation on the ability of the technology.

Agreed.

You haven't presented a paradox, you answered your own question. The amount of unique images a screen can display is finite, thats it.

Hi Danz, you might have to elaborate. I don't really understand what the supposed paradox is supposed to be. In a simple statement, could you say where exactly the contradiction/problem/mislogic is in this situation?

Clearly I haven't explained what I see as the paradox very well.

The paradox is that in an infinite universe should not there be an infinite number of potential images that can be displayed?

My camera example was intended to illustrate this, as was the image generator scenario.

It seems paradoxical to assert that every image that can potentially be created (past, present and future) can be represented by one of the finite number of images that our screen can display.

"You haven't presented a paradox, you answered your own question. The amount of unique images a screen can display is finite, thats it."

If we accept that the unique images that the screen can display is finite, then we must accept that every image that can potentially be rendered on the screen fits within a finite set. This includes every possible potential image in the entire universe (past, present, future). That's what I see as a the paradox.

Originally Posted by DanNZ

"You haven't presented a paradox, you answered your own question. The amount of unique images a screen can display is finite, thats it."

If we accept that the unique images that the screen can display is finite, then we must accept that every image that can potentially be rendered on the screen fits within a finite set. This includes every possible potential image in the entire universe (past, present, future). That's what I see as a the paradox.

Originally Posted by KALSTER

Originally Posted by Chrisgorlitz

I don't understand your point, if your suggesting with a finite number of pixels only a finite number of images could be shown on the screen then yes thats correct, but equally the same limitation would apply to your digital camera, it would always just translate what ever picture you took into an image within capability parameters. Thus meaning whatever information you put into either device they would always be limited to what they could recreate. But that is not a paradox it's just a limitation on the ability of the technology.

Agreed.

The limitation of the technology isn't the point in it's own right. The limitation of the camera was intended to support my point. If the screen can only display a finite number of images, then the camera can only take a finite number of unique pictures. In an infinite universe this seems paradoxical.

Trying to think of other ways to explain why I think there's a paradox here. If I take a photo and display it on the TV I'm looking at, the static image on the screen might be (for the sake of argument) image 10 million or 100 trillion possibilities (numbers plucked from the air but not relevant so long as you accept that it's a finite number). You could take a photo of your living room, and when displayed on my TV it might be image 900 million of 100 trillion possible. An alien life form 1000 light years away takes a picture of its sleeping pod and it might be image 30 billion of 100 trillion. By accepting that there there 100 trillion possible pictures, we have to accept that it's only possible for 100 trillion unique pictures to exist.

Originally Posted by DanNZ

If the screen can only display a finite number of images, then the camera can only take a finite number of unique pictures. In an infinite universe this seems paradoxical.

Why is this paradoxical ? All it means is that the camera is incapable of reproducing projections of the universe at large, and that's simply because the the camera is a digital device trying to capture an analogue system.

Originally Posted by DanNZ

Trying to think of other ways to explain why I think there's a paradox here. If I take a photo and display it on the TV I'm looking at, the static image on the screen might be (for the sake of argument) image 10 million or 100 trillion possibilities (numbers plucked from the air but not relevant so long as you accept that it's a finite number). You could take a photo of your living room, and when displayed on my TV it might be image 900 million of 100 trillion possible. An alien life form 1000 light years away takes a picture of its sleeping pod and it might be image 30 billion of 100 trillion. By accepting that there there 100 trillion possible pictures, we have to accept that it's only possible for 100 trillion unique pictures to exist.

Actually you may have a point if you are suggesting the idea that trying to come up with only a finite number of photo's could only ever be displayed from a 'potentially' unlimited number of possibilities of different photo, whilst again from our perspective it's easy to equate the idea that our technology will always only ever be capable of reproducing a finite number of different photos, it does present a problem in as much as that any finite number taken in comparison to infinity will not logically compute.

This is simply because the idea that infinity and also any part of infinity must always equal the same amount and there is always the possibility to make any finite number larger where as infinity must always remain the same.

We are constantly surrounded by things have a finite size and thus are not and cannot be infinite, so that leaves us with to quandries: Does infinity indeed exist? and if so how indeed to have anything else that is finite?

So if this is what you are suggesting as a paradox then you may be correct, because it leaves us with this problem that the universe has the potential to contain infinite space, and thus infinite possibility for different photographs, but also the fact that must equally well contain infinitely 'filled space' leaving no room for any possibility to take any photographs.

This I suppose comes very much down to whether you subscribe to the theory that something indeed anything can exist within something infinite.
I ,though personally, find this idea very difficult to accept as it does not seem logical. The reason being that any object within an infinite space must also occupy an inifite space within it, because when taken out it would leave a void a void that is part of the infinite space, remember all values for infinity or parts of infinity must equal the same, therefore to occupy an infinite space any object must also be infinite.

However there may well be others who can provide a perfectly logical explanation of indeed just how a finite object can exist within infinity, I for one will be just as interested in understanding that if it does actually prove possible.