Every possible 1080p image

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Shivoa

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#1  Edited By Shivoa

A cc of a response to an email on the latest bombcast:

An aside

Your comments about copyright, while amusing, miss one of the great things about almost all copyright legislation: independent creation. If we both, independently, create exactly the same work then we both have copyright claims to it and the other cannot be infringing. The burden of proof is obviously high if you claim this when it looks like you copied someone else's work and the chances of it happening are low but this is a safety valve in copyright. The lack of a similar provision for patents is one of the reasons why everything is so messed up for patent law.

Think of a number. No bigger than that

Source: Wikipedia.
Source: Wikipedia.

But on to that TV that will show you every possible image: even moving to SD or 320x240 is not going to help you. The problem is how quickly the numbers blow up.

As the original emailer mentions, each pixel is just an R G B triple and with a standard TV the brightness of each sub-pixel ranges from 0 to 255. So there are 256 different brightnesses for each sub-pixel. 256 to the power 3 (which is 256*256*256, 256^3) is about 16.7 million; the number of different colours possible for a single pixel to display.

Lets scale that up to an 8 by 6 screen, not 800 by 600 but just 8 pixels wide by 6 pixels high. There are now 8*6*3 = 144 sub-pixels taking a range of 256 values. 256^144 is approximately equal to a 6 with 346 zeros after it and before the decimal point.

If this 8 by 6 screen was to show a brand new image 60 times a second, standard 60Hz, then it would take a 3 followed by 337 zeros of years to display all possible images. With the default zoom/font on GB (on Chrome on my PC) this 8 by 6 screen has about as many pixels are there are inside a single 0 in this text. Not big enough to render the entire 0, just the void in the middle. It's not a very good screen.

30​0​0​0​0​0​0​0​0​0​0​0​0​0​0​0​0​0​0​00​0​0​0​0​0​0​0​0​00​0​0​0​0​0​0​0​0​00​0​0​0​0​0​0​0​0​00​0​0​0​0​0​0​0​0​00​0​0​0​0​0​0​0​0​00​0​0​0​0​0​0​0​0​00​0​0​0​0​0​0​0​0​00​0​0​0​0​0​0​0​0​00​0​0​0​0​0​0​0​0​00​0​0​0​0​0​0​0​0​00​0​0​0​0​0​0​0​0​00​0​0​0​0​0​0​0​0​00​0​0​0​0​0​0​0​0​00​0​0​0​0​0​0​0​0​00​0​0​0​0​0​0​0​0​00​0​0​0​0​0​0​0​0​00​0​0​0​0​0​0​0​0​00​0​0​0​0​0​0​0​0​00​0​0​0​0​0​0​0​0​00​0​0​0​0​0​0​0​0​00​0​0​0​0​0​0​0​0​00​0​0​0​0​0​0​0​0​00​0​0​0​0​0​0​0​0​00​0​0​0​0​0​0​0​0​00​0​0​0​0​0​0​0​0​00​0​0​0​0​0​0​0​0​00​0​0​0​0​0​0​0​0​00​0​0​0​0​0​0​0​0​00​0​0​0​0​0​0​0​0​00​0​0​0​0​0​0​0​0​00​0​0​0​0​0​0​0​0​00​0​0​0​0​0​0 years. (I am preparing to hit the edit and put some breaks in that if it doesn't automatically get broken up by the forum engine)

We should put that in context: After 1 followed by 14 zeros of years (100000000000000 years) the universe will no longer be forming new stars, the beginning of the end. Much much later, about 1 followed by 100 zeros of years later then even the supermassive black holes (potential mass: 100 billion solar masses) will have completed evaporated.

Maybe 1 followed by 150 zeros of years after now, there will be "a state of no thermodynamic free energy to sustain motion or life", the heat death of the Universe. In any case, at this theoretical point in time there would still be 3 followed by 337 zeros of years left before the 8 by 6 screen finished showing all possible images, so little progress would have been made that the percentage change can only sensibly be approximated to 0.<lots of zeros>% progress. None, not a sausage. The expected lifespan of the universe as a place where things occur is but an instant compared to how long that 8 by 6 screen would take to show all the possible images made up of RGB sub-elements when running at 60Hz. A billion expected lifespans of the universe in a row would be nothing compared to how long this 8 by 6 screen would take to display all images.

So moving from 1080p to SDTV or EDTV would not help. The bigness of the numbers involved is basically impossible to comprehend, our brains are just not able to deal with it. Every pixel you add to the display makes it take 16.7 million times longer to finish displaying all possible images. And that's just with normal 8 bits per sub-pixel TVs, at some point before the head death of the Universe we might have to start again and use a wide gamut (maybe xvYCC) colour space and deep colour (maybe 12 bits per sub-pixel).

Edit: I wanted to add some zero width space chars to that long number so it should break reasonably well for all views but we can't drop HTML into our text so experimented with pasting them in (Edit 2: seems to work).

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nightriff

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So you are saying the math was wrong on the bombast? Shocking. But a really interesting read, nice work.

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BisonHero

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#3  Edited By BisonHero

OK, but what if we go full Cave Johnson on this, and find multiple alternate universes full of screens, devoted to covering all possible configurations, and we here on Earth Prime just cash in on their billennia of hard work.

Loading Video...

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SgtSphynx

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Crazy thought, what would happen if you upped the refresh rate?

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Shivoa

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#5  Edited By Shivoa
@sgtsphynx said:

Crazy thought, what would happen if you upped the refresh rate?

To what? Moving from 60Hz to 600Hz (where it would be a blur you couldn't really make out anything on) would only make it improve by a factor of 10. 3 followed by 336 zeros of years. What about 6 BILLION Hz (a long way from any even speculative technology we might have to make a refreshing display)? Now it will only take 3 followed by 328 zeros of years. A massive improvement, but still basically infinite for all practical terms (and in vs lifetime of the universe terms, which are far from practical).

Think of a number. No bigger than that. The problem is we really can't really think of how long this time time span is. We can't reasonably think about how long the universe will continue to tick over for and that's nothing compared to how long this will take. Again, for an 8 by 6 pixel display only using standard colour depth.

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49th

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What if we had 2 screens though? Or 3?

Cool math though, thanks for calculating this stuff.

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damodar

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It's an interesting thought experiment and the exponential growth is quite astounding.

Some other interesting things, displaying the gamut of one pixel at 60Hz would take about 3 days and doing it with two pixels would take about 150,000 years.

In these examples, each pixel is capable of displaying 16.7 million different colours. If we take the screen of the original Game Boy, a 160x144 display with each pixel only capable of displaying 4 different values, at the system's natural refresh rate of 59.7Hz, it would take around 150 million years to display all possible variations. This would require about 235 billion AA batteries, at which point, buying some Eneloops starts to seem pretty sensible.

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bhurnie

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From this thread yesterday, I bothered to find the number of combinations for a full-size screen. It's not that printable here, at nearly 15 million digits, but is approximately 1.5 × 10^14981179. Knock off about 7 decimal places for the number of years required at 60Hz. The start of the full number below:

No Caption Provided

There's probably not much point trying to put it in perspective.

@damodar: How do you get 150 million years for your example? I get 4^(160*144) = 3E13871 and even including the refresh rate that's still far off. Given 150 million years at 60Hz is about 2.83E17, and 4^29 = 2.88E17, you'd only need a tiny fraction of the gameboy screen to take that long. Have I missed something obvious?

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awesomeusername

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#9  Edited By awesomeusername

All the numbers made me faint. Thanks a lot nerd. (No it didn't. I love you. You're not a nerd. (Yes you are.))

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GERALTITUDE

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I love you people so, so much.

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ltsmash

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#11  Edited By ltsmash

Did I visit Tested by mistake?

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MEATBALL

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All of this is basically the greatest thing.

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audiosnow

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I haven't even listened to that portion of the Bombcast, so I have no idea if what I'm saying is relevant:

Images have to be dissimilar enough to be considered unique. The human eye can't see the entire range (or even most of the range) of a screen pixel, and the brain does a good job of approximating. Take two identical images and add a single tier of red to each pixel in one of them, and while it would technically be a different image, it would absolutely be the same image.

But like I said, I don't even know what this is about.

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SgtSphynx

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I am curious how the math changes if you take all those sub-pixels and made them binary, so instead of each sub-pixel having 256 levels it only has 2. It would still technically be able to show every viewable image, but should take exponentially less time.

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csl316

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"You guys get close enough."

When they started talking about this, I was ready to pull over and just start shaking because of the shear massiveness of the idea.

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swimbuff

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Way to shit on everyone's hopes and dreams, guy.

Just kidding, this is great work! I wonder how long it would take if we only considered black & white images.

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damodar

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#17  Edited By damodar

@bdhurkett: I think I did the total number of pixels to the power of 4 rather than 4 to the power of the total number of pixels. Apologies, it was very late :P So yes, you missed something obvious. You missed that I'm an idiot. Or I guess you didn't.

@swimbuff said:

Way to shit on everyone's hopes and dreams, guy.

Just kidding, this is great work! I wonder how long it would take if we only considered black & white images.

If you keep the range of 256 but only have greyscale, it becomes a lot more managable. The 8x6 pixel grid would then only take 20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 years. Which is a muuuuuch smaller amount of time. I believe that could actually be done before the complete heat death of the universe.

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Vuud

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It was a really dumb question anyway.

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Christoffer

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A really fun read for a friday.

I wonder how long the editing process would be after all that. If you want to put together something coherent you have a lot of raw material to go through. But on the plus side, you could put together a n y t h i n g !

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Shivoa

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U.G.L.Y. images

I am curious how the math changes if you take all those sub-pixels and made them binary, so instead of each sub-pixel having 256 levels it only has 2. It would still technically be able to show every viewable image, but should take exponentially less time.

Well it would be able to show every image made up of only pixels that were fully saturated: RGB (white), RG (yellow), GB (cyan), RB (purple), R, G, B, & black. 2^3 = 8 different colours per pixel. Almost all of the viewable images on your TV wouldn't be visible on it or even reasonably approximable. It's better than an actual black/white binary pixel but way worse than a grayscale (what we refer to as black & white TV) image for giving good images to look at, especially with our 8 by 6 pixel grid that is killing any concept of detail (or pixel adjacency blurring into an effectively lower res image with more colours).

That does make the maths a lot smaller. 2^144 (our good old 8 by 6 screen; also 8^48 if you consider pixels rather than subpixels, maths is the same) is about 2 followed by 43 zeros of distinct images, that's 1 followed by 34 zeros of years. If we start right now then apparently the period of "stellar remnants escape galaxies or fall into black holes" will have long ended and we'd be deep in the period of "nucleons start to decay" but at least the time when "effectively, all baryonic matter will have been changed into photons and leptons" will not have arrived.

I can never find the shot I want

I wonder how long the editing process would be after all that. If you want to put together something coherent you have a lot of raw material to go through. But on the plus side, you could put together a n y t h i n g !

"tiny Mariachi band playing inside his mouth"

I bet Sony Vegas would give you an import error. But seriously, this actually becomes an interesting* insight into a search problem. Not a practical one, but indicating why search can be an issue even if creation becomes trivial. Once we've got all our images captured, we have every possible image and we can say we have the raw material to create every possible scene and, in those scenes, every possible shot. I use shot here to simply mean a scene with no cuts, each frame follows the previous in what a normal person would consider a fluid transition, but possibly using the most magical of CG so we could move the camera to space without a cut if we made the sequence look like a satellite eye transition.

So you grab your video editor and you see infinite possible images that are the first frame of each shot you captured, that's a search problem right there. But say you had a frame already in mind. Due to having every possible image on file you then have every possible viable transition from that frame available under that one thumbnail of the starting frame. Every shot that you can conceive of (and many others you couldn't even imagine until you saw it happen in front of you) are there for you. From that point, you have every shot where anything can happen. It's all in the database. How do you possibly find the right one? You start with a shot of Jeff, roughly facing camera, on the studio chair but while searching for the 5 second clip where he mouths to camera (we have no audio yet - we'll add it in post), "You're typing a lot over there." the search keeps coming back with the one where that happens but there's a tiny Mariachi band playing inside his mouth that you can see whenever he opens it, or the one where the camera zooms to Cool Baby and it mouths the line, or the one where Jeff realistically melts for no apparent reason while mouthing the line. All of those sequences of images are there too, and anything else you can think of as a single shot starting with that one frame. Literally everything that could possibly happen and everything that couldn't (!) would be shown in shots starting at that frame.

I wouldn't want to be the UX guy working out how to design that search tool; whatever precision the user specified, short of exact pixel-by-pixel details of every frame in the sequence, would return many more shots they didn't want than the narrow parameters of what they did want and nothing else. But here's the lesson in all this: the user would need to be taught to settle for 'good enough', when searches become too hard because there's to much data then providing the exact thing desired in the data set isn't viable, but providing something that is close enough will be the best case. Insert commentary on expansive government snooping and the expectation of generating faulty intelligence framing an innocent person here.

* YMMV.

Thanks

Thanks for all the positive messages guys, glad you enjoyed my bit of calculator spam.

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ElixirBronze

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@shivoa: Good read! thanks alot. A big number you say? Have you ever heard of Graham's Number? How about a number that is so high, there aren't even enough space in the universe to properly print it out? I find it really fascinating to read about.

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geirr

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Ow.

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ildon

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#23  Edited By ildon
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Shivoa

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Presenting, PANOPTITRON.

(I don't actually know if this works anywhere other than my computer with my browser.)

*applause*

Bravo sir! That is marvellous.

Working fine in Unity for me here.

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AMyggen

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@shouldice: You should make a new thread with that link, duder. Doesn't deserve to get buried in this thread!

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shouldice

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#27  Edited By shouldice
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ildon

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I've been working on my version a bit. I realized shortly after I posted it that as I had done it randomly rather than sequentially, it would eventually show the same image twice. I'm working on fixing that right now, but here's a version that runs much much faster (60 fps, can reach 200 fps but my monitor is only 60 hz so I'd be missing frames) and actually has functional web hosting that shouldn't 404 an hour later.

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granthinds

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My brain is too small.