The Photographic Recurrence

—Is the recurrence of photos inevitable?: Published: Sunday, July 17 2016 11:50; Written by Jesse Riggs

Cover Photo

Meet Boltzmann

Spontaneously materialized into existence, from thermal equilibrium deep within the void, with a camera-sidekick, Boltzmann is a fully conscious sentient being. After some introspection, he concludes that his life's purpose must be to photograph this universe in which he has found himself. It's not long before Boltzmann encounters a new face.

Stooped upon his philosophizing perch, a man named Fred becomes the first object of this man's art. Fred becomes mutually intrigued by Boltzmann's photographing machine. Each photograph is a 2x2 grid of squares, with each square colored either black or white. “How does this 'camera' work?” Fred asks.

“Observe! As light passes through this lens and lands on four photosensitive plates behind the shutter. If the light is of some sufficient luminosity then a sensor will register that the plate is white; otherwise it is black. The signal from the plate is drawn onto a picture screen as a 'pixel'.”

Illustration 1: Light reflecting off of Fred, passes through lens, striking photo plate.

How Many Paths?

“As elating as this technology may be, each photograph, Mr. Boltzmann, has only four pixels. How many unique photos could even be taken with this camera? I shouldn't imagine that I could venture too far into eternity before I find myself back here, at this very photo.”

Boltzmann ponders for a moment before responding, “I will count the number of photos that I have taken.” He proceeds to count the number of unique photos. He places each photo on a table, if it's not already on the table, but smashes the photo if it is a duplicate. Soon he is left with sixteen photos.

Illustration 2: Table containing Boltzmann's 16 photos.

“There are only sixteen pictures here. But, could there be more?” Fred inquires.

Utilizing his most proficient skills in maths, Boltzmann finds a path to show that there are only sixteen unique photographs. “Imagine yourself meandering down a road when you come to a fork. You have two options, you can either go left ( black ) or you can go right ( white ). This fork is like the first pixel in a photo, there are two possible options.

"After the color of the first pixel has been determined, there comes a second pixel to be decided. This second pixel is represented by two more forks: one at the end of the left road, the other at the end of the right road. Each fork is another two options; doubling the total number of options. The third pixel will place eight more forks into this road; again, doubling the number of possibilities. Finally, our path will end by the color of the fourth pixel being determined; again, doubling the number options.

I can see that there are 2x2x2x2 = 2⁴ = 16 possible photos that could be taken with this camera. We could generalize that there are 2ⁿ possible photos, where n is the number of pixels. To show that this is correct, we can draw all paths and then count them.”

Boltzmann's Interactive Tree Of Decision

Colour a picture, and then trace its path through the decision tree. Are there ways to color this image that do not exist in the decision tree?

A New Approach

"This means that if I were to capture 17 photos, at least two of them would be exactly the same. No mater what the object of the photo may be, once I have exhausted all sixteen possible photos, I will never be able to capture another unique photo." So, Boltzmann gets an idea to rebuild his camera with more photosensitive plates so that the pictures will contain more pixels. He increases the picture size to 16, 64, 4096, 16384 and 65536 pixels.

Illustration 4: Increasing grid size to 256 x 256.

"This will make 2⁶⁵⁵³⁶ photos possible." says Fred. "But, the photos are quite grainy."

Boltzmann realizes that the photos are monochromatic (only two colors). He ponders a way in which to smooth the images. "Each sensor can detect one of two states, depending on the level of light which strikes the plate. We could add another state to each sensor so that it can detect some shade of gray. We could continue to add more states, perhaps as many as 256, so that we may see a seamless image."

Illustration 5: Gradient showing new possible shades.

After some modifications, Boltzmann's camera is able to take a clear picture of his new friend.

Illustration 6: Increasing possible shades to 256.

A Startling Revelation

"Now, you have some interesting photos." says Fred "However, there are still only a countable number of photos that can be taken; albeit a very large number of photos, 256⁶⁵⁵³⁶, by my calculations. But, if you were to live for an infinitesimal fraction of an eternity, then, eventually, you will run out of new photos to capture. Once this number of photos have been taken, no mater where you go in the universe, you will never be able to take a photo that you have not yet taken. The eternal Etch-A-Sketch of photography is turned upside down again and again, and you with it, speck of dust!"

"If we were to pick, arbitrarily, a path down this long road," says Boltzmann, "we could see one of any image that we could imagine, though most of them would make no more sense than mere static on the television. I could only imagine what pictures would arise from this set of images. Certainly there would be one of Mike Tyson drinking tea with The Queen, and another where Margareta Thatcher tears the ear from the face of Evander Holyfield, with her teeth. Any story that we could tell could be told with images that could be taken by this camera."

"But," Fred speculates "if any one of these images could be photographed more than once, would any of the duplicates be required to entail the same story? No, their meanings are but illusions. Like clouds in the sky, we will see only what our minds can imagine. Perhaps the only true limits are those of our imaginations. Perhaps even this image, which I imagine to be of myself, is no more than random static."

"Possibly," Boltzmann conjectures "but it's more probable that these images embody actual objects, existing in some state which evolved from a complex series of simple events."

"Precisely," Fred says, "life is change."

"I will explore the universe, in search of all that can be seen. But, when I have see it all, do I gnash my teeth and curse my existence? If I have seen all that could ever have been, what's left for me to ponder or long for? How will I know to what I can compare my elation and suffering? if all that I have for comparison is all that I know? What could I suffer but to know all things? But, to become all things, I could know my place in the universe, and suffer anything. I bid you farewell."

And, like that, Boltzmann disappeared into the vast universe.