Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin. —John von Neumann
States of Sin is an artist monograph with 70 prints of random walks, made with a pen plotter and my Ludus programming language.
The statement on the first page reads as follows:
John von Neumann and Stanilaw Ulam, in the course of the Manhattan Project, invented the Monte Carlo method. At the time, it was not possible to simulate all the particles in a nuclear chain reaction; it was far too computationally expensive to do so. They discovered that they could achieve satisfactory results by approximating the reaction through random sampling. Getting enough truly random numbers into the computer, however, was itself expensive. At one point, the RAND corporation had a roulette wheel attached to a computer. Silicon Graphics, for a while, had a camera pointed at lava lamps as a source of randomness. It became necessary to use computers themselves to generate randomness.
The computer, as a calculating machine, gets its value from its determinism. How could a determinism machine produce something random? Von Neumann, discussing in 1952 his novel technique for producing something like random numbers—what we now call a pseudorandom number generator—offered the quip that is this book’s epigraph: “Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin.”
The world we live in functions in no small part through living in this state of sin. Cryptography depends upon the production of very nearly random numbers. Contemporary pseudorandom number generator algorithms produce sequences of numbers that are very nearly indistinguishable from truly random numbers. Perhaps more to the point, the generative in generative artificial intelligence system depends on random number generation. The indeterminacy of LLMs and other generative AI systems depends on not just predicting something, but in diverging from predictability. Some of the more asinine techbros in Silicon Valley believe that their generative AI is about to give rise to “superintelligence.” We may soon give birth to a new god in the form of a chatbot. Thus the calamitous divine enters the world through randomness.
Collected in this book are 70 random walks. These are visualizations of randomness: a line whose contour is determined by randomness, constrained in various ways. Random walks, however, are important for simulating any number of social or natural processes in evolution, finance, economics, physics. In these drawings, using Seymour Papert’s famed “turtle graphics,” it is the turtle who walks randomly.
The first sheath draws its visual language from British mathematician John Venn (famous from his diagrams). In 1866, he published a single line that represented the first 707 digits of pi. Irrational numbers, like pi, must necessarily have random digits. To visualize pi, he represented each digit, from 0 to 7, as a step in a direction: north, northeast, east, southeast, etc.; he ignored 8 and 9. I have used his visualization technique here to visualize computational randomness.
The other random walks here are driven, instead, by aesthetic concerns. How might randomness be made manifest as a force? One criterion: randomness can only be felt when manifest serially. I present 10 exemplars of 7 different algorithms for random walks. Each of these is only a single line, whose contour is determined by the pseudorandom number generator in my web browser.
Documentation
I've provided documentation in three formats for States of Sin: Ludus code to run, live, in your browser; sample SVGs; and sample images.
Algorithmic
Each of these links to a live Ludus page with the algorithms that make up the random walks in States of Sin. They will load the code in the left-hand pane. To make a drawing, click the RUN button at the top right. You will likely have to adjust the view to see the whole drawing.
- 1: In the style of John Venn.
- 2: With many circles.
- 3: Hashmarks upon hashmarks.
- 4: In the style of Calder.
- 5: A zigzag, which reminds me of comic books.
- 6: Scribbled wildly.
- 7: Organic lines, with occasional murmurations.
SVG
Each of these links will open an SVG file with a single run of each algorithm.
- 1: In the style of John Venn.
- 2: With many circles.
- 3: Hashmarks upon hashmarks.
- 4: In the style of Calder.
- 5: A zigzag, which reminds me of comic books.
- 6: Scribbled wildly.
- 7: Organic lines, with occasional murmurations.
Photo
Perfectly cromulent amateur photo documentation is available as a single (large) PDF.