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.
Chance can mean the free association works of the surrealists (automatism) or allowing things to happen (paint to drip). It can also be a more strict/technical definition of 'random'.
When scientific predictions are made, such as whether a meteor will destroy the planet, or whether a new drug will help people, surveys are made, and noise, or random events must be separated.
As observant creatures, we remember and perceive, combing through each others' experiences and stories to thrive. In the process of acquiring that culture, randomness often causes surprise, which is how it so effectively accesses our emotions.
Randomness heightens every other emotion, because, like Bruce Schneier has observed of technology, it obscures perception, and mandates further observation and investment.
"Practice random acts of kindness" suggests that when combined with generosity, surprise makes something even better.
Perceptually, random visual images can alert us to previously undiscovered compositions. Musically, random sound works the same. It can re-order sonic events or even produce original ones. which satisfy our need for emotion.
Yet surprise elements have existed in music well before computers. Consider blues music - a genre which invites improvisation. It might be imagined as a personal music, in which the performer surprises himself though taking random chances in the notes played on an instrument. Imagine an evening's performance, a guitarist onstage, struggling to connect his inner feelings with the motion of his hands and the sound his instrument produces. As playing gets more intense, the body couples tightly to the instrument, and perhaps due to a bit of perspiration, a brief index finger slip near the 14th fret leads to a random “wrong note” which the player's and listeners' ears quickly detect. Yet, the skilled player perceives it not as a "wrong note," but an unexamined slice of his story, and incorporates the new pitch into the melody. Working the note back into the fold, the player relives that surprise moment with every pluck until it no longer becomes a surprise.
Randomness implies a relationship between expectation and surprise, a violation of anticipation as well as a notion of temporariness and release. This notion of violated predictability is key to some modern musician's playing and composing styles, leading many to create “generative music,” such as Autechre (http://www.soundonsound.com/sos/apr04/articles/autechre.htm) who produce music using precisely-chosen strands of random numbers.
When used in art and performance, the surprise which random moments produce may even be contagious: Imagine the story in the previous paragraph from the perspective of a potential romantic couple:
In that moment of tension after the performer stuck the random note, the whole roomed breathed in together. Instead of resolving it, the guitarist let the silence of the room suffuse. This delighted two shy listeners. As they simultaneously smiled, they mutually recognized the expressions from the corners of their eyes and took it as a cue to move closer together. In their first conversation, one of them revealed, "I wasn't even supposed to be here, I took the wrong train. It was an accident..." Their conclusion is that fate brought them together. While their biological systems may have primed them for the experience, it was the accumulation of random events which produced the perceptible event.
In this theoretical example, the randomness played only a small role in the story. In some artworks, as in 10Print, randomness plays a much larger role.
For example, Duchamp's 3 Standard Stoppages and their use in the Large Glass.
3 standard stoppages = alternate views of what the meter could have been. Resulted in 3 meterstick-like objects with curvy edges... each a meter long, but "undermining the rational basis" made by dropping a thread from the air, allowing it to hit randomly, yet keeping it a permeant part (On Line: Drawing Through the Twentieth Century November 21, 2010–February 7, 2011)
Large Glass: http://en.wikipedia.org/wiki/The_Large_Glass
One of Duchamp's last works. Involves alternate physics. Notable materials for their longevity and craftiness (copper wire, glass). mysterious physical apparatus powered by previously designed curvy metersticks? "The Greenbox," DuChamp's explanation is no more revealing. but the piece has been described as a hilarious, erotic encounter between a bride in the upper half and her suitors below. The piece was inspired by a performance of the stage adaptation of Roussel's novel Impression of Africa which Duchamp attended in 1912
Must discuss Cage and Zen Buddhism and his influence.
Cage in Experimental Music, 1958 [Iversen 51] " Those involved with the composition of experimental music find ways and means to remove themselves from the activities of the sounds they make. Some employ chance operations, derived from sources as ancient as the Chinese Book of Changes, or as moderns as the tables of random numbers used also by physicists in research. " In a world in which surprise is available as a commodity, e.g. entrance to the fairgrounds, Cage's observation may be interpreted as a criticism on the over-reliance of chance-determined processes to "produce" surprise on demand.
"Dada wished to destroy the reasonable frauds of men and recover the natural, unreasonable order. Dada wished to replace the logical nonsense of the men of today with an illogical nonsense. "
Marcel Duchamp and John Cage have been the most influential. Duchamp influenced Cage and Cage influenced many more across a range of fields.
Gabrielle Buffet-Picabia quoted in Chance Imagery by George Brecht [Iversen 38] Chance-Imagery here: http://www.robertspahr.com/courses/ela/brecht_chance.pdf quote in question: “Dada wished to destroy the reasonable frauds of men and recover the natural, unreasonable order. Dada wished to replace the logical nonsense of the men of today with an illogical nonsense. That is why we beat the Dadaist bass drum with all our might and trumpeted the praises of unreason. . . . Dada like nature is without meaning. Dada is for infinite meaning and finite means.” (Gabrielle Buffet-Picabia, 1949, ref. 8.)
I imagine the relevant part of the Buffet-Picabia quote is "infinite meaning and finite means," referring to the projection of meaning into the maze, and the limited resources of the computer's tiles??????
Sometimes, it is not merely a single random event, but an accumulation of them which really makes the world run, at least according to a theory science fiction writer Douglas Adams repeatedly referred to called "Infinite Improbability."
… " This means each performance of such a piece of music is unique, as interesting to its composer as to others listening. It is easy again to see the parallel with nature, for even with leaves of the same tree, no two are exactly alike. The parallel in art is the sculpture with moving parts, the mobile. "
"Art, Cage remarked, is not 'self expression but self alteration.'" [Iversen 92]
Fluxus was important in promoting the ideas further.
Note from Noah: I have edited the first half of the randomness_in_the_arts, combined it with a few paragraphs about random music and pasted them here.
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.
With so many variables in the real world like late buses, misdialed numbers, and slippery fingers dropping grilled cheese sandwiches into french fry oil (the legendary origin of the Monte Cristo sandwich!), one of randomness's opposites, order, becomes a valued commodity. Clocks, calendars, safety standards, and style guides suffuse our culture to protect us.
Yet, in a computer, it is quite the opposite. Computer chips differ greatly from the outer world in their orderliness. Unlike our beaches or the bumpy landmasses with weather on which we build our houses, the world inside chips is meticulously fabricated, symmetrical, isolated and predictable. In fact, its basis is one massive crystal grown from purified silicon. It is so perfect that it is difficult to create unanticipated behavior.
As randomness in the home computer market transitioned from being a mere source of artificial surprise into practical security applications, computer chips were designed with modules designed to encourage random amounts of heat energy to influence their silicon junctions to hasten the creation of unpredictable data. This is part of the essence of encryption - the production of obscurata.
But normally, digital orderliness is the rule. It is at least true for the chip (MOS6510) running the Commodore 64’s BASIC interpreter, as well as the chip running the original BASIC interpreter at Dartmouth.
- Prg in User guide demo of biasing randomness
intrestingly enough, they thought this would be a good idea to teach in the C64 User Guide.
- Use to explain to reader how randomness works, what it's good for
In my own memories from 1984 and beyond, RND was most often used to improve the quality of games. For example, in my endless clones of Breakout!, RND chose where the ball would drop into the game, how much it would wiggle through the air, and helped make the sound of the bricks exploding. It made the game a little bit different each time and more challenging
- How the number is actually generated,
Rnd(0) Uses the timer as the random number generator
rnd(1) is a deterministic sequence of random numbers it is a linear congruential generator with some extra byte-swapping taking place.
The original BASIC manual shows that Dartmouth Basic (the first BASIC), had a similar specification for the RND(x) function. It generated a single stream of pseudorandom numbers. Interestingly, it recommends throwing away the first "115" or so numbers. (reference: BASIC_Oct64.pdf, page 45 of PDF, page -39- of original document)
- reliability of the randomness,
The linear congruential generator (LCG) was proposed by Lehmer in 1949.
Patterns in these data are way behind the abilities of humans to predict in our heads, and are even difficult for many computers to suss out.
- Point Out that psuedo randomness is not bad or inferior
- alternative methods of finding randomness within the C64.
Assembly routine (Ian)
Rand8 lda random ; get seed (must be non-zero) asl ; shift byte bcc Rand8.no_eor ; branch if carry flag not set after left shift eor #$CF ; otherwise EOR with literal $CF Rand8.no_eor sta random ; save number as next seed
It was possible on the C64 to get random values from the Sound Interface Device (SID) chip. Reading from register 27 (decimal) returns the current value of oscillator 3. If it's set to noise, you get a random number generator.
5 rem init sid for noise 6 poke 54272+wave, noise 10 print chr$(209.5+peek(54272+osc3read));goto 10
- Use multiple seeds, then SID register random
- How it could be used to teach someone randomness/probability
- Is this similar to how it sounds? Visual equivalence
- Develop three or four one-liners
- User/programmer side
- Two note example
We also synthesize some of the previous sections, and discuss the aesthetic qualities of the 10 PRINT pattern in terms of randomness.
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.
