Randomness
From Maze
Contents[hide] |
Chapter Outline
I. Brief, General Introduction to the Power of Randomness
Quickly, in a paragraph or two, summarize the power of randomness in computational and aesthetic realms.
II. Randomness and Aesthetics, Pre-Computing
The role of randomness in creating patterns and designs, using analog methods of random generation. Burroughs and Cage will figure prominently here, but there are earlier examples, most notably, the 18th century Dominican priest Sebastien Truchet, whose randomly generated Truchet patterns eerily prefigure that pattern produced by 10 PRINT.
Note from Casey: I haven't put my notes into prose yet, but I have basic material here and more forthcoming here Randomness_in_the_Arts
III. The emergence of Randomness in Computing
The RND command is the algorithmic heart of 10 PRINT, its flip-flip-flopping beat powering the creation of the maze. It is also a paradox. The function of the RND token in 10 PRINT is immediately known yet its output is entirely unknown. Unpredictable. A cipher, the manifestation of a much deeper latent content, operating underneath the surface of the machine.
An obvious question to ask about randomness is why bother at all? Why have the ability in the first place to generate random numbers? Computers are supposed to calculate with exactitude. Computers are supposed to order the world. Computers are supposed to sift through reams of data and model possible outcomes, possible futures.
But it turns out that it’s impossible to function as any kind of calculating machine or simulation without taking into account randomness, a defining feature of life—and the universe for that matter.
Quite simply, randomness is required for any statistical endeavor needing random sampling or tests of probability. And one or two random numbers are not enough. Large-scale statistical calculations or simulations require large batches of random numbers. In her history of humans’ quest for randomness--which Bennett suggests goes as far back as ancient Babylonia (17)--Bennett highlights one the early and largest set of random numbers, the RAND Corporation’s A Million Random Digits with 100,000 Normal Deviates (135). Generated in 1955 “by random frequency pulses of an electronic roulette wheel,” the RAND’s set of random numbers was an important contribution to any study of probability and is still in use today. As the forward to the undated online edition of the table notes:
The tables of random numbers in the book have become a standard reference in engineering and econometrics textbooks and have been widely used in gaming and simulations that employ Monte Carlo trials. Still the largest known source of random digits and normal deviates, the work is routinely used by statisticians, physicists, polltakers, market analysts, lottery administrators, and quality control engineers. (RAND Corporation)
These seemingly benign uses aside, the RAND report ominously explains that its one million random numbers were originally “prepared in connection with analyses done for the United States Air Force” (RAND Corporation). Like so many other advances in computing, randomness, it turns out, is intimately linked to Cold War military strategies. In fact, most of the early work on computer-based random number generation was performed under the auspices of the U.S. Atomic Energy Commission (see, for example, Rotenberg’s work in the late fifties) or the U.S military (such as Green et al’s work at MIT, with joint support of the U.S. Army, Navy, and Air Force).
As Donald Knuth relates in The Art of Computer Programming, John von Neumann was the first to propose the idea of harnessing a computer to generate random numbers (Knuth 3). It was around 1946 and von Neumann was fresh off the Manhattan Project and soon to begin his lead work on the hydrogen bomb. Von Neumann’s solution, for which a computer was to be used, was called the middle-square method. It worked by squaring an initial random number and extracting the middle digits; this number was then squared again, and the middle digits provided a new random number. The disadvantage of this method soon became apparent: because each number is a function of the one before it, the sequence, as Knuth explains, “isn’t random, but it appears to be” (3)--a phenomenon known today as “pseudo-randomness,” which arguably describes any human or machine attempt to generate random numbers.
Knuth gamely admits that his own attempts to generate random numbers through software algorithms—using what he hoped to be a “’super random’ number generator”--failed, though it’s worth noting that he wanted his machine language program “to be so complicated that a man reading a listing of it without explanatory comments would not know what the program was doing” (Knuth 5). It does not take a leap of imagination to see in Knuth’s desire for obscure code an early version of the same kind of mystery residing in 10 PRINT.
IV. The emergence of computational randomness in aesthetic design
An early example of this is a 1960 teleplay "written" by a computer at MIT, and then performed on CBS.
V. The C64 and RND
In this section we finally discuss the RND function in the context of the C64. How the number is actually generated, the reliability of the randomness, and alternative methods of finding randomness within the C64.
We also synthesize some of the previous sections, and discuss the aesthetic qualities of the 10 PRINT pattern in terms of randomness.
- Prg in User guide demo of biasing randomness
- Use to explin to reader how randomness orks, what it's good for
- Use multiple seeds, then SID register random
- Is this similar to how it sounds? Visual equivalence
- Develop three or four one-liners
- User/programmer side
- Two note example
- Point Out that psuedo randomness is not bad or inferior
- How it could be used to teach someone randomness/probability
A Working Bibliography
Bennett, Deborah. 1998. Randomness. Cambridge Mass.: Harvard University Press.
Ekeland, Ivar. 1996. The Broken Dice, and Other Mathematical Tales of Chance. University of Chicago Press, June 15.
Felder, H. 1968. The GPSS/360 random number generator. In Proceedings of the second conference on Applications of simulations, 21–28.
Green Jr, B. F, J. E. Smith, and L. Klem. 1959. Empirical tests of an additive random number generator. Journal of the ACM (JACM) 6, no. 4: 527–537.
Isida, Masatugu, and Hiroji Ikeda. 1956. Random number generator. Annals of the Institute of Statistical Mathematics 8, no. 1 (12): 119-126. doi:10.1007/BF02863577. http://www.springerlink.com/content/02510157q12768k4/.
Knuth, Donald E. 1969. The Art of Computer Programming. Vol. 2. Reading, Massachusetts: Addison-Wesley.
Lord, E. A., and S. Ranganathan. 2006. Truchet tilings and their generalisations. Resonance 11, no. 6 (6): 42-50. doi:10.1007/BF02838881. http://www.springerlink.com/content/w1577r5g78rx2033/.
Neumann, John von. 1961. Various Techniques Used in Connection with Random Digits. In Collected Works: Design of Computers, Theory of Automata and Numerical Analysis, ed. A.H. Taub, 5:768-769. Oxford: Pergamon Press.
Pfeiffer, John E. 1962. The thinking machine. Lippincott.
RAND Corporation. 1955. A Million Random Digits with 100,000 Normal Deviates. http://www.rand.org/pubs/monograph_reports/MR1418/index2.html.
Rotenberg, A. 1960. A new pseudo-random number generator. Journal of the ACM (JACM) 7, no. 1: 75–77.
Smith, Cyril Stanley, and Pauline Boucher. 1987. The Tiling Patterns of Sebastien Truchet and the Topology of Structural Hierarchy. Leonardo 20, no. 4: 373-385.
