Finite or Infinite Number of Possible Images on an LCD Display?

danshawen;
After this exercise in analysis to the nth degree, step outside the box and consider this.
Given a beautiful ballad played by a philharmonic orchestra, say "Spring is here" (at least we think it is).
Would you rather hear a 5 mln. rendition, or all the notes played simultaneously within a duration of 1/2 sec?

 

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Interesting question. If you could listen fast enough, it would make no difference. So perception is less about what's "out there" and more about what our senses allow us to perceive. Our senses do not show us what's out there; rather, our senses filter and limit what's out there. We see very little of what's actually going on in the universe. Huxley made this point in The Doors of Perception, which is where the band The Doors got their name.

http://en.wikipedia.org/wiki/The_Doors_of_Perception

 

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If you allowed for there to be 2 colors on the 2,000,000 pixel display, it could show 2,000,000! pictures. The modern calculator can only figure up to about 69!, because then you would end up getting close to over 100 decimal places (a google). 2,000,000! would be a number so large that it would shadow the total number of anything that exist in the universe all put together. I wouldn't even want to guess how big that number would be, because I would have to multiply all the numbers from 1 to 2,000,000 all together. It would be a big enough number to show a picture of everything in the universe along with every cartoon as well. Of course, a lot of small variations would be left out that didn't change the color of a single pixel from 1 out of 2 colors.

Now that I think about it, it would probably be more than that. Even two pixels could show 4 pictures instead of 2! pictures that would be 2 total. There would be; black black, black white, white black, and white white. Three pixels could show, black black black, black black white, white black black, black white black, black white white, white black white, white white black, white white white, and black white white, for a total of 9 pictures instead of 3! pictures that would only be 6.

Then, n > 2,000,000!

 

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I think the reason it goes over is because factorials do arrangements, but it doesn't count the pictures that started out as them being a different color. If there was two pixels, it wouldn't count black black and white white, or with three pixels it wouldn't count; black black white, white black black, and white white black. If it went on to 4 pixels it probably wouldn't count the variations that could branch off those orders either, by adding a white or black to the front and back of them. There could also be duplicates from sets that are included that copy sets not included. I would guess that the number of pictures excluded using factorials would be the same as the number of pixels used. For instance, 1! leaves out 1 picture (just black or white), 2! leaves out 2 pictures, 3! leaves out 3 pictures... ... 2,000,000! would then leave out 2,000,000 pictures.

Then the total number of pictures would be n = 2,000,000! + 2,000,000. Then a black and white TV that had a maximum of 1920 x 1080 resolution would actually use 2,073,600 pixels, so then the exact value for the number of pictures possible on that television would be n = 2,073,600! + 2,073,600.

 

If you watched a television that randomly changed pictures every second, you would only be able to see 435,827,520,000,000,000 pictures in the current lifetime of the universe. Even on a small black and white television with the lowest resolution could have 480,000! + 480,000 pictures. If 69! is as close to a google without going over, then the total number of seconds that have gone by in the universe isn't even close to this. That would be because the total amount of seconds in the universe only goes to about 18 decimal places. Inevitably, there will be a lot of things that could be seen on TV that we will never have time to watch. There wouldn't be enough time to watch a television that was 3 x 6 resolution to show every picture it could possibly have every second if you started watching it since the Big Bang itself, because 18! would go over the number of seconds in the universe.

 

It would still be a finite number.

 

The question is given in the context of common/normal behavior, without any modifications.
The point is, the value of music, movies, tours, gourmet meals, etc. is the intentional occurrence over a duration of time. These are non-technical examples of events considered by danshawn in his analysis, which did not include this aspect. I personally prefer it this way...what's the hurry.

 

I also think it's important not to confuse how many different images can be perceived or "input" by a finite brain, with how many images are possible. Especially the difference between mathematically and physically possible since the latter implies time.

 

I didn't mean to imply that it wouldn't be a finite number. It would be a finite number no matter how many pixels there were. Any scaled down version would have a finite number of pictures, so there would be no reason to assume that a larger version would go infinite. Then mathematically it should follow the same pattern no matter how many pixels are added.

From looking at the pattern of how much the numbers of pictures would increase for each pixel, it is surprisingly close to just using factorials to determine the possible number of arrangements. It would be like saying that 2,000,000 coins could be arrange in 2,000,000! ways, but if each coin could be heads or tails, it would only be 2,000,000 more ways they could be arranged. For how big 2,000,000! would be, adding 2,000,000 to that wouldn't be significant at all. It would have to be rounded long before then in decimal places. I am even having a hard time accepting that is all it would come out to, but that is the mathematical pattern that is created there.

I just added that other part, because I wanted to give an idea of how big that number would be. It seemed like from the other post that the answer would be so unimaginably high that it would have to be infinite. Then 2,000,000! would be unimaginably large as well. It would be bigger than adding everything in the visible universe all together. Then a TV normally displays at about 60 frames per second, so watching a random picture program could be 60 times faster than that. By showing that 18! could be unattainable in the lifetime of the universe for every second, then it just goes to show how big 2,000,000! would actually be.

 

That would be wild, a wild bear killing a salmon out in the wild...

It got me thinking that it wouldn't be that much larger than just using factorials, because it would be like using all of the same coin (instead of different ones) and determining if it is just heads or tails. Then you could say that n = x! + (a - 1) x, in that type of situation. If that statements was true, then you could find the number of alternate universes that are the same size as the observable universe. You could say n = multiverse, and x = (area of the observable universe/Planck Length), and a = number of fundamental particles + the absence of a particle. Then there could be (3.5 x 10^115)! + 2.135 x 10^82 combinations of possible alternate observable universes the same size as our own. It could actually be smaller than this, because not every particle could fit into a Planck Length. Then I guess they could just be microscopic black holes. That is still be over three and a half hundred trillion google factorial.

I got the figures from Wikipedia and I plugged them into Wolfram Alpha. It was also nice enough to calculate 2,000,000! to give the figure of it having 499,999 decimal places.

 

I don't know where I got the 82 from, but seemed strange that is a smaller number from multiplying. It was supposed to be 117 for the exponent of the second term, above. Funny how things like that always pop up, seemingly from nowhere...

 

This idea misses the point. See:

https://www.ted.com/talks/ramesh_raskar_a_camera_that_takes_one_trillion_frames_per_second

As Ramesh pointed out in his presentation of femtosecond photography, watching a video at frame normal speed of his video would require you to watch the movie of the laser pulse traversing the coke bottle for over a year. Believe me when I say, it is possible in principle to subdivide the time interval of the frame capture using the same technique Ramesh used virtually indefinitely.

And how long does it normally take for a light pulse to traverse a Coke bottle in real time? Much less time than it takes for you to begin to blink.

I don't care by what means some quantum physicists try to eliminate the variable time from their calculations. The infinity is there. It means, among other things, that quantities routinely treated as though they were finite are not actually either finite or discrete in any real sense. Interaction with matter makes absorption or emission of photons a discrete process, but this is by no means the rule in this universe, and time (and also energy) is the reason for that. So deal with it.

 

It doesn't sound like you want to have a discussion about this. It sounds more like your just demanding everyone adopt your same point of view. I could count the number of pictures of 1 to 3 pixels by stating all the possible number of combinations. At what number of pixels do you think the number would go infinite? What would be significant about that number that would make it different than all the other ones before it? The answer is there isn't such a number. The same pattern would evolve that would give a discrete number of combinations no matter how many pixels you added.

The reason why it would take longer to see a laser pulse video would be because time in the video had been slowed down. According to the Planck Scale, the maximum number of pictures that can be taken in a second would be about 10^34. If your television showed 60 frames per second, then it would take a very long time to see all those frames. (It is about only 60 frames per second, because that is about the rate the human eye cannot distinguish between.) It would take longer than the lifetime of the universe to view anything that happened in one second at the smallest possible interval at 60 frames per second, about 5.28 x 10^24 years.

If you took more pictures than that, you would end up getting duplicate pictures in a row, so there wouldn't be an infinite number of different pictures there either. Nothing would be able to travel fast enough to make a picture in an interval less than 10^-34 sec different from the picture before or after that picture, which would be measurable with a finite amount of energy. Then there would be no need to count pictures taken in an interval smaller than that. Besides, no one would have enough time to check precisely what happened at every instance in a second anyways. The frame rate of reality would just be too good to convert to a rate that the human eye could barely distinguish between.

 

All I really want is for folks like Brian Greene to think a little harder when he states that it is possible to see all of the images possible in this universe based on a simple discrete math calculation that is so restricted it is laughable, or equivalently, that the universe we are taking these finite images from is only one nanosecond old since the time of the BB.

Your analysis shows, even if all there was to see in this universe was a light pulse and a Coke bottle, there are a great deal more images possible than, as you say, there would be time within the age of this universe to view them all, even with something as limited as HDTV; even with a viewing instrument such as the human eye, designed with attributes other than resolution or speed in the forefront. If that isn't the definition of infinity, I don't know what is.

 

I don't think that's what Brian Greene is saying, at all.

The inevitable consequence of a display having a finite number of pixels is that it can display only a finite number of images; it doesn't matter "when" the images are displayed, this is mathematically irrelevant.

There are a finite (although very large) number of particles in the universe, from which follows the same logical argument which really has little to do with humans who can see or observe a very small amount of the total number of images at any time.

"And though the holes were rather small, they had to count them all . . ."

 

It isn't. Brian Greene couldn't even come up with a number that large for the possible number of universes. I just made it up from trying to solve the problem posted by the op in this thread, it just gave me an idea of a possible way to calculate it.

I think it would be true that most alternate universes would be the same size as our own universe in the many worlds interpretation (MWI) as it is perceived in quantum physics, but Brian Greene thinks there could be many different types of universes that could arise despite the MWI simply saying that it is caused by decoherence of particle waves. Then considering a quilted universe, it would mean that our doppelgangers would be at least (3.5 x 10^115)! observable universes away from us now, since the Planck Scale would essentially be the pixels of the real universe.

The thing is that I don't even believe in the MWI. It just seemed like an idea that I could toy around with at the time. If the multiverse was connected by every single little particle in the universe, there would be universes crashing into each other all the time. The expected outcome of that is seeing more universes being created or universes being created in our own universe, and that is just something that we don't ever see. Hyperspace would have to be mostly empty.

I think that is the core of your problem. Something is unimaginably large, and you just assume that it is infinite. They say that infinity is a number that can never be reached, but that is also with unlimited amounts of time. If you can't run the 100 meter dash in 9 sec that doesn't mean the track is infinitely long. To try to explain it in more detail to get you to understand it makes it laughable. It would take a certain amount of IQ points to be able to recognize that mathematical patterns continue the same way up the number line and that doesn't make them change, so it allows smaller examples to be used to describe unimaginably large concepts or ideas.

 

Right you are. Something that is "uncountably large" may be so either because it is infinite, or else because there literally is not enough time available to count it, at any practical rate of speed that could be applied to the counting.

The idea of this thread was not an original idea of mine, by the way. A graphic artist friend who frequents these forums started corresponding with me because he was distressed and obsessed with the idea that there would be no point in rendering his art if it were a fact that, as Brian Greene reportedly once said, there exists only a finite number of images possible to display on an n x n pixel display. The artist was, in fact, suicidal over the prospect that Greene's statement might actually be true. Eventually, we worked out the problem in the manner you have seen rendered here, and I also counseled him to see another therapist who takes such obsessions more seriously than the one he was seeing. I've seen many similar obsessions make folks in my mensa group very unhappy, for instance. Higher IQ types seem to be more susceptible to such depressions. Mine thankfully is only about 135 or so, barely enough to qualify. After reading Gould's "Mismeasure of Man", I'm actually ashamed and abashed at the misuses of such misinformed IQ rankings in venues such as mensa. I'm actually ashamed to admit such ideas ever appealed to me, not to put too fine a point on it.

I still have a similar obsession / depression over the limitations of our own cognition, but I'm very far from suicidal about it. The Brian Greene idea was merely something I found annoying because he had not clearly thought out what he was trying to say. You would need to impose too many limitations on the bandwidth of such images to make it work out to be something as discrete and limited as his limited imagination seems to be.

A universe composed of both matter and energy with intensive interaction between the two states is not something that could be described as finite in terms of any form of discrete mathematics, even in a much younger universe.

 

OK, in that case, all things considered, what is the thing on the eye then?

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jk

 

Shortly after discovery of the Higgs boson at the LHC in 2012, pictures of all sorts of things related to Higgs started appearing all over the internet. One of them showed actor Christopher Lloyd in his role as Doc Emit Brown in the 'Back to the Future' series, but with images of the Atlas particle detector at the LHC over both eyes, like a pair of goggles. I thought that was a little over the top, especially since any actor like Mr. Lloyd who is worth his salt knows that the eyes are possibly the most important expressive feature for acting. So I wondered how the same effect would look as a monocle, similar to what Jeri Ryan did in her role as the former borg Seven of Nine on the Star Trek Voyager series. The nano tech remnants over one of her eyes resembles a monocle.

I also gave myself red eye because it somehow looked better that way. The Atlas detector has been modified to make it resemble a borg implant. Now you know. Resistance is futile. You will be assimilated into the Higgs boson cult and synod, as soon as we finish reconstructing the enhanced venculum and power up the ZPM bank.

The new retina particle detectors at LHC this year are awesome, by the way. I pitched to a colleague the idea of modifying some of their proportional wire counters (a gas filled, layered bank of geiger counters, basically) into a superconducting equivalent last year also.

 

Just as I suspected!