### The End of Photography?

Originality in art, and photography specifically, is a difficult thing to maintain within a culture as image-saturated as ours, and so it becomes inevitable to wonder if there exists some finite limit upon how many original photographic images can be created. The rise of sampling and derivation within music and the visual arts further muddies the question of what defines originality, since so many new works are presumed to be inspired from earlier works, to varying degrees.

Within the genre of photography we can at the very least begin to answer this question based on limitations imposed by the technology itself, by placing an upper limit upon the total number of possible unique photographs, considering uniqueness as being defined by image variation at the pixel level.

Once we have agreed upon certain preconditions, it becomes obvious that there are only so many photographs possible, a finite amount. Once they’re all made, photography as a creative art-form is closed, dead-ended. Were this to happen, what then?

I don’t believe anyone has ever seriously considered there to be an upper limit to how many unique oil paintings or drawings that can be created. Talent might be harder to find, and the art world’s tastes might seem to seriously challenge one’s credibility at times, but there does not seem to exist any intrinsic technical limit upon these media. Medium, form, tone, color and texture seem to be infinitely variable, even within a fixed canvas size, such that painting appears to remain open, in the mathematical sense.

Consider that branch of mathematics called Game Theory, wherein the game of Checkers is closed (all possible variations of play having been worked out mathematically), while Chess (at least for the time being) remains open. It is much easier to see that Tic-Tac-Toe is closed (counter a center or corner move with a move to the opposite corner), while it is much less obvious that photography, represented as images formed from grids of discrete pixels at a finite variety of tonal intensities, is also a game of sorts, and one that is mathematically closed in that there are a finite and calculable number of image variations within any specifically defined resolution size.

Let us permit ourselves to be limited photographically to discussing images that can be viewed by a web browser and display monitor of contemporary resolution. Assuming that the typical Internet-based image is rarely displayed larger than 800 pixels wide, let us presume to limit our discussion to images 800 by 800, or 640,000 pixels in size, with a color depth of 8 bits, an image of finite spatial resolution with finite tonal variation, as are all photographs.

Given that 8-bit graphics yields 256 variations in tone, and an 800 by 800 image space yields 640,000 pixels, there are therefore 256^640,000 possible images within that space, a huge number on the surface, one that might seem limitless but is in fact quite finite and calculable.

However, 8-bit graphics are monochrome. What about 24-bit color images? Here the numbers get even more ridiculously huge at 16,777,216^640,000. That’s over 16 million raised to the 640,000 power.

Normally we are used to seeing large numbers like these expressed in scientific notation, as 10 raised to some exponent. In doing the conversion to scientific notation I discovered that, although this number is finite, it is still very large, so large in fact that Google thinks of it as being near enough to infinity so as to decline an answer, as does my old Hewlett Packard scientific calculator. So, I had to dust off my old secondary school maths and run the numbers myself.

5.42E4,623,820 is the shorthand way of expressing this number, or 5.42 times 10 raised to the 4,623,820 power. In simpler terms, it’s 542 followed by 4,623,818 zeroes. You’d be hard pressed to view that many photographs in your lifetime (as we shall see), or even be able to write the number down on paper with all of its trailing zeroes. In fact, writing down the number at the rate of one trailing zero every second would require nearly 54 days, and reams of paper, absent the benefits of using scientific notation.

But let’s try a thought experiment. Let’s say a person lives for 80 years, and is connected to a machine that takes care of all their bodily functions such that they are free to view photographs for their entire life. (Wait - don’t we already do that?) Think of this person as the ultimate Flickr or Instagram viewer, the ultimate Internet surfer. The question is, how many images could this person view in their lifetime if they flicked through 1 image every second? The answer amounts to 80 times 365 times 24 times 60 times 60, or 2,522,880,000 images. In scientific notation, that’s roughly 2.52E9. It hardly makes a dent in the total number of possible photographs, however.

Perhaps we need more participants in our thought experiment, many more of them hooked up, rapidly viewing photographs at a rate of one per second, in order for all possible photographs to be viewed. We do seem to be growing more and more Internet viewers every day, don’t we? How many more participants would we need? As a comparison, the current global population is around 5 billion, which is 5 followed by 9 zeroes. In order to successfully complete our thought experiment, we would require 4.29E4,623,801 planet earths full of people at our present population, every one of them connected into our imaginary photo viewing machine, going full tilt for 80 years. You are unlikely to find that many people, any time soon, to participate in your experiment.

But let’s limit ourselves to just this one planet’s worth of people, and say the Internet grew and grew until a vast majority of the earth’s population (say 5 billion people) did nothing but continuously click through photos, one per second. At the rate at which the Internet is taking over people’s lives, this might not seem so farfetched. How long would it then take to view all possible images? It would take 1.08E4,623,811 seconds, or 2.96E4,623,803 years. How long of a time is that? The universe is presumed to be about 14 billion, or 1.4E10 years old, and therefore you would require 2.11E4,623,793 universe lifetimes for those 5 billion Internet surfers to complete their mission of viewing every possible photograph. That’s a long time, for certain.

I think it is safe to say that we will not run out of new photographs to view any time soon, although I would argue about the originality of many of them. For instance, there would be 1.07E13 different variations on Ansel Adams’ “Moonrise Over Hernandez, New Mexico,” where each version differed by just one pixel in position and/or tone, hardly original in the cultural sense, although each one might be mathematically unique.

There would also be countless photographs composed of mere random fields of noise with no discernible pattern at all, like what us oldsters remember from tuning in to a blank analog broadcast television channel, before the advent of the 8VSB DTV system in the United States, and before televisions were designed to mute a blank channel with a blue screen. I often wondered, sitting in front of a dead channel, late at night, whether it was possible, if for but a brief second, the random variations in electronic noise to suddenly form themselves into some coherent image, like out of a Stephen King novel. For all of the blank T.V. screens I’ve looked at (I used to be a T.V. repairman), I’ve never seen such a phantom image (that I know of).

Another way to look at the question of originality in art is to consider legal precedent. Although case law is in constant flux, there is no simple guideline for determining a percentage within which sampling would remain legal, since legal appropriation is usually considered to require recontextualization of the sampled work. However, in order to make some simplistic mathematical calculations I will presume the legal appropriation of others’ works to remain within a limit of around a 10% sampling rate, within which a new work is considered original. Thus, if 90% of Adam’s "Moonrise" were discarded, and 10% retained as derivative, the new image would be considered original under my presumed limits. So, discarding 90% of our total image count results in 5.42E4,623,819 original photographic images, still astronomical in magnitude.

Let us attempt to get this problem under control, by reducing the requirements of our experiment further. We shall consider viewing mere thumbnails rather than full screen-sized images, say at a resolution of 100 by 100 pixels. Crunching the numbers, how large of an image space results? Again at a 24-bit tonal scale, there remains 1.58E72,247 possible thumbnail images, hardly as massive as previously but still unwieldy in size.

Let us reduce even further our image requirements, simplifying our 100 by 100 pixel thumbnail images down to a crude 1-bit tonal resolution of black or white only pixels, resulting in 2^10,000, or 2E3010 possible images, smaller yet but still requiring 6.3E3002 years to view by one person.

If we then consider reducing our image size even further, down to a mere 10 by 10 pixel size of 1-bit tonal scale, small enough to no longer represent photographic images but rather to resemble typographical characters, we are still left with 2^100, or 1.27E30 unique characters, requiring about 2.72E12 universe lifetimes to complete viewing at a rate of one character per second.

Whew!

It is interesting that, although photographic uniqueness can be calculated mathematically as being finite yet practically limitless, cultural (and even biological) restrictions impose many more such restrictions upon our sense of perceived newness and originality within the photographic genre. Page after page of monotonous vacation snapshots lend proof to the notion that, like the proverbial boring slideshow, what is required to grab and hold our attention is much more ethereal and difficult to define than by simplistic mathematical presumptions.

Although I find these kinds of hypothetical calculations fun to work with, there exists a more serious lesson hidden within. As technological improvements increase tonal and spatial resolution to photographic images over time, tending to merely increase the theoretical limits of photography to even more ridiculous extremes, the limits to the practical art are defined less by megapixels and bit depth and more by those intangible elements found through human perception and intelligence of insight, a well-developed personal aesthetic and photographic vision, which no mathematical formulae can easily fathom.

Though science continues to probe with increasing resolution the mechanics of the human brain, the center of wisdom and creative insight remains thankfully well-concealed, to be revealed only in fleeting glimpses provided by those skilled practitioners of the ephemeral arts, whose voice and vision all civilizations would do well to heed at their own peril. The numbers, though they in this case be enormous, otherwise reveal little outside of the domain of the artist.

Performing thought experiments such as these has been a pastime of mine since the early 1970s, when I developed an interest in those new gadgets called electronic pocket calculators. I wish that I still had some of them, many of which had fluorescent tube displays, and whose batteries only lasted but a few hours at best. I still have several HP calculators, the oldest being an HP 21, with it's red LED display. Regarding the image, it is a self portrait, onto silver gelatin paper, from an early prototype of the Pixelator camera, a pinhole camera that incorporates a diffuser screen and pixelator grid to create analog pixelated images. I'm slowly working on a newer version with much finer resolution.

Within the genre of photography we can at the very least begin to answer this question based on limitations imposed by the technology itself, by placing an upper limit upon the total number of possible unique photographs, considering uniqueness as being defined by image variation at the pixel level.

Once we have agreed upon certain preconditions, it becomes obvious that there are only so many photographs possible, a finite amount. Once they’re all made, photography as a creative art-form is closed, dead-ended. Were this to happen, what then?

I don’t believe anyone has ever seriously considered there to be an upper limit to how many unique oil paintings or drawings that can be created. Talent might be harder to find, and the art world’s tastes might seem to seriously challenge one’s credibility at times, but there does not seem to exist any intrinsic technical limit upon these media. Medium, form, tone, color and texture seem to be infinitely variable, even within a fixed canvas size, such that painting appears to remain open, in the mathematical sense.

Consider that branch of mathematics called Game Theory, wherein the game of Checkers is closed (all possible variations of play having been worked out mathematically), while Chess (at least for the time being) remains open. It is much easier to see that Tic-Tac-Toe is closed (counter a center or corner move with a move to the opposite corner), while it is much less obvious that photography, represented as images formed from grids of discrete pixels at a finite variety of tonal intensities, is also a game of sorts, and one that is mathematically closed in that there are a finite and calculable number of image variations within any specifically defined resolution size.

Let us permit ourselves to be limited photographically to discussing images that can be viewed by a web browser and display monitor of contemporary resolution. Assuming that the typical Internet-based image is rarely displayed larger than 800 pixels wide, let us presume to limit our discussion to images 800 by 800, or 640,000 pixels in size, with a color depth of 8 bits, an image of finite spatial resolution with finite tonal variation, as are all photographs.

Given that 8-bit graphics yields 256 variations in tone, and an 800 by 800 image space yields 640,000 pixels, there are therefore 256^640,000 possible images within that space, a huge number on the surface, one that might seem limitless but is in fact quite finite and calculable.

However, 8-bit graphics are monochrome. What about 24-bit color images? Here the numbers get even more ridiculously huge at 16,777,216^640,000. That’s over 16 million raised to the 640,000 power.

Normally we are used to seeing large numbers like these expressed in scientific notation, as 10 raised to some exponent. In doing the conversion to scientific notation I discovered that, although this number is finite, it is still very large, so large in fact that Google thinks of it as being near enough to infinity so as to decline an answer, as does my old Hewlett Packard scientific calculator. So, I had to dust off my old secondary school maths and run the numbers myself.

5.42E4,623,820 is the shorthand way of expressing this number, or 5.42 times 10 raised to the 4,623,820 power. In simpler terms, it’s 542 followed by 4,623,818 zeroes. You’d be hard pressed to view that many photographs in your lifetime (as we shall see), or even be able to write the number down on paper with all of its trailing zeroes. In fact, writing down the number at the rate of one trailing zero every second would require nearly 54 days, and reams of paper, absent the benefits of using scientific notation.

But let’s try a thought experiment. Let’s say a person lives for 80 years, and is connected to a machine that takes care of all their bodily functions such that they are free to view photographs for their entire life. (Wait - don’t we already do that?) Think of this person as the ultimate Flickr or Instagram viewer, the ultimate Internet surfer. The question is, how many images could this person view in their lifetime if they flicked through 1 image every second? The answer amounts to 80 times 365 times 24 times 60 times 60, or 2,522,880,000 images. In scientific notation, that’s roughly 2.52E9. It hardly makes a dent in the total number of possible photographs, however.

Perhaps we need more participants in our thought experiment, many more of them hooked up, rapidly viewing photographs at a rate of one per second, in order for all possible photographs to be viewed. We do seem to be growing more and more Internet viewers every day, don’t we? How many more participants would we need? As a comparison, the current global population is around 5 billion, which is 5 followed by 9 zeroes. In order to successfully complete our thought experiment, we would require 4.29E4,623,801 planet earths full of people at our present population, every one of them connected into our imaginary photo viewing machine, going full tilt for 80 years. You are unlikely to find that many people, any time soon, to participate in your experiment.

But let’s limit ourselves to just this one planet’s worth of people, and say the Internet grew and grew until a vast majority of the earth’s population (say 5 billion people) did nothing but continuously click through photos, one per second. At the rate at which the Internet is taking over people’s lives, this might not seem so farfetched. How long would it then take to view all possible images? It would take 1.08E4,623,811 seconds, or 2.96E4,623,803 years. How long of a time is that? The universe is presumed to be about 14 billion, or 1.4E10 years old, and therefore you would require 2.11E4,623,793 universe lifetimes for those 5 billion Internet surfers to complete their mission of viewing every possible photograph. That’s a long time, for certain.

I think it is safe to say that we will not run out of new photographs to view any time soon, although I would argue about the originality of many of them. For instance, there would be 1.07E13 different variations on Ansel Adams’ “Moonrise Over Hernandez, New Mexico,” where each version differed by just one pixel in position and/or tone, hardly original in the cultural sense, although each one might be mathematically unique.

There would also be countless photographs composed of mere random fields of noise with no discernible pattern at all, like what us oldsters remember from tuning in to a blank analog broadcast television channel, before the advent of the 8VSB DTV system in the United States, and before televisions were designed to mute a blank channel with a blue screen. I often wondered, sitting in front of a dead channel, late at night, whether it was possible, if for but a brief second, the random variations in electronic noise to suddenly form themselves into some coherent image, like out of a Stephen King novel. For all of the blank T.V. screens I’ve looked at (I used to be a T.V. repairman), I’ve never seen such a phantom image (that I know of).

Another way to look at the question of originality in art is to consider legal precedent. Although case law is in constant flux, there is no simple guideline for determining a percentage within which sampling would remain legal, since legal appropriation is usually considered to require recontextualization of the sampled work. However, in order to make some simplistic mathematical calculations I will presume the legal appropriation of others’ works to remain within a limit of around a 10% sampling rate, within which a new work is considered original. Thus, if 90% of Adam’s "Moonrise" were discarded, and 10% retained as derivative, the new image would be considered original under my presumed limits. So, discarding 90% of our total image count results in 5.42E4,623,819 original photographic images, still astronomical in magnitude.

Let us attempt to get this problem under control, by reducing the requirements of our experiment further. We shall consider viewing mere thumbnails rather than full screen-sized images, say at a resolution of 100 by 100 pixels. Crunching the numbers, how large of an image space results? Again at a 24-bit tonal scale, there remains 1.58E72,247 possible thumbnail images, hardly as massive as previously but still unwieldy in size.

Let us reduce even further our image requirements, simplifying our 100 by 100 pixel thumbnail images down to a crude 1-bit tonal resolution of black or white only pixels, resulting in 2^10,000, or 2E3010 possible images, smaller yet but still requiring 6.3E3002 years to view by one person.

If we then consider reducing our image size even further, down to a mere 10 by 10 pixel size of 1-bit tonal scale, small enough to no longer represent photographic images but rather to resemble typographical characters, we are still left with 2^100, or 1.27E30 unique characters, requiring about 2.72E12 universe lifetimes to complete viewing at a rate of one character per second.

Whew!

It is interesting that, although photographic uniqueness can be calculated mathematically as being finite yet practically limitless, cultural (and even biological) restrictions impose many more such restrictions upon our sense of perceived newness and originality within the photographic genre. Page after page of monotonous vacation snapshots lend proof to the notion that, like the proverbial boring slideshow, what is required to grab and hold our attention is much more ethereal and difficult to define than by simplistic mathematical presumptions.

Although I find these kinds of hypothetical calculations fun to work with, there exists a more serious lesson hidden within. As technological improvements increase tonal and spatial resolution to photographic images over time, tending to merely increase the theoretical limits of photography to even more ridiculous extremes, the limits to the practical art are defined less by megapixels and bit depth and more by those intangible elements found through human perception and intelligence of insight, a well-developed personal aesthetic and photographic vision, which no mathematical formulae can easily fathom.

Though science continues to probe with increasing resolution the mechanics of the human brain, the center of wisdom and creative insight remains thankfully well-concealed, to be revealed only in fleeting glimpses provided by those skilled practitioners of the ephemeral arts, whose voice and vision all civilizations would do well to heed at their own peril. The numbers, though they in this case be enormous, otherwise reveal little outside of the domain of the artist.

**Post-Script:**Performing thought experiments such as these has been a pastime of mine since the early 1970s, when I developed an interest in those new gadgets called electronic pocket calculators. I wish that I still had some of them, many of which had fluorescent tube displays, and whose batteries only lasted but a few hours at best. I still have several HP calculators, the oldest being an HP 21, with it's red LED display. Regarding the image, it is a self portrait, onto silver gelatin paper, from an early prototype of the Pixelator camera, a pinhole camera that incorporates a diffuser screen and pixelator grid to create analog pixelated images. I'm slowly working on a newer version with much finer resolution.

## 1 Comments:

Thanks for the number crunching. I enjoyed reading this post, as I work with vast amounts of data and probabilities and enjoy thinking about this kind of stuff.

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Have a comment? I'll post your comment after I read it.

~Joe

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