摄影复发

—照片的复发是不可避免的？: 日期：2016年7月17日 11:50, 星期日; 作者： Jesse Riggs

Cover Photo

Meet Boltzmann

Boltzmann is a sentient being who materialized into existence, out of the void's thermal equilibrium, with a camera hung around his neck. After some contemplation, he concludes that his life's purpose is to take pictures of this universe in which he has found himself.

Shortly into his venture he takes a picture of a man named Fred. Fred finds Boltzmann's pictures to be intriguing. Each picture is a 2x2 grid of squares, with each square colored either black or white. “How does this camera work?” Fred asks.

Boltzmann explains “Light passes through the lens and lands on four photosensitive plates at the back of the camera. If the light is sufficient then a sensor will register that the plate is white; otherwise it is black. The signal from the plate is drawn to the picture as a pixel.”

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

How Many Paths?

“Each photograph has only four pixels, Mr. Boltzmann. How many unique photos could be taken with this camera?”

Boltzmann thinks for a moment and then says “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 is not already on the table, but if the photo is a duplicate, he discards it. 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 asks in an inquisitive tone.

Boltzmann uses his proficiency in maths to think of a way to show that there are only sixteen possible unique pictures. “Imagine yourself traveling down a road and 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 and one 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. Generally, we can say 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.”

Illustration 3: Two paths branch from each possible pixel state.

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 taken all sixteen possible photos, I will never be able to take 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 2⁶⁵⁵³⁶photos possible." says Fred. "But, the photos are quite grainy."

Boltzmann realizes that the photos are monochromatic (only two colors). He wonders if there is any way to make them more smooth. "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 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 which you could take; albeit a very large number of photos, 256⁶⁵⁵³⁶, by my calculations. But, if you were to live for an eternity, then eventually, you will run out of photos to take. 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 be 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 one of Margareta Thatcher tearing the ear from 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, they 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 just 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."