TRANSPARENT BUNDLES by Seth Goldstein

MEDIA FUTURES 2006: 2/5 ALGORITHM: History of Algorithm

An algorithm is a machine that can be used to reproduce a unique pattern of behavior.   The history of the word traces back to the Greeks and the instruments they used for mathematics; for example, the sieve.  In the context of Media Futures, imagine that algorithms are tightly woven filters that capture the full range of human Automata and slowly sift through them to produce the most meaningful, intentional gestures.

Ancient Algorithms

Finding its root in algorism, a reading of the name of Abu Ja’far Muhammad ibn Musa Al-Khwarizmi, the 9th century Persian mathematician who described a set of rules for solving both Linear and Quadratic equations, algorithm came to its present state by way of an 18th century European Latin translation and soon expanded its meaning to encompass all definite procedures for solving problems or performing tasks.  The very first algorithms are a part of the Babylonian mathematical legacy – a legacy which not only left us with algorithms for factorization, finding square roots and performing long division, but which also left us with the base 60 system that gives 60 minutes to an hour, 60 seconds to a minute, 360 degrees to a circle and 24 hours to a clock.  Babylonians were in fact able to calculate things with the same accuracy as Renaissance mathematicians due to their use of number tables, like the Plimpton Tablet, a table of Pythagorean Triples from about 1700 B.C.

While the Babylonians based their mathematical system in large part on algebra, the Greek system of mathematics was heavily based upon geometry.  It is speculated, though, that the founder of Greek science and mathematics, the philosopher Thales of Milet, visited Egypt and Babylon during his lifetime (634 – 546 B.C.) and brought back knowledge of their astronomy and geometry.  The Egyptians made great contributions in the fields of medicine, astronomy and applied mathematics, and while the former triumphs are well documented, there exist no records of the process by which they reached their mathematical conclusions.  Thales built on the knowledge brought back from his trips, inventing deductive mathematics and proving a number of theorems – a circle is bisected by a diameter; the base angles of an isosceles triangle are equal; and pairs of vertical angles formed by two intersecting lines are equal.

The foremost text on geometry came from fellow Greek Euclid, whose Elements put together former geometric knowledge with definitions, postulates and opinions – and, of course, Euclid’s elegant and rigorous proofs of the above.  In that text, he discussed the algorithm for finding the greatest common divisor of two numbers, which is today referred to as the Euclidean algorithm.  One hundred years later around 200 B.C., the world saw the next great algorithm – the Sieve of Eratosthenes, which was used to find prime numbers.

From Wikipedia: 

Sieve of Eratosthenes is a simple, ancient algorithm for finding all prime numbers up to a specified integer. It is the predecessor to the modern Sieve of Atkin, which is faster but more complex. It was created by Eratosthenes, an ancient Greek mathematician.

 

Another important site in the history of the algorithm was Alexandria, home to Hero, Ptolemy, and Diophantos.  Hero, whom we will remember as the inventor of the steam eolipile and other Automata, published widely on geometrics, optics and mechanics – as well as mathematics.  Though sources suggest his work is derivative of Archimedes and the work of the Babylonians, his Formula to calculate the area of a triangle in terms of its sides and his Method to extract a root are important contributions to the world of mathematics.  Ptolemy published widely on astronomy and geography and calculated the best approximation of ‘pi’ for his time.  And Diophantos, known as the ‘father of algebra’, wrote his thirteen-volume Arithmetica on the solution of algebraic equations and the theory of numbers and introduced the use of algebraic symbolism with an abbreviation for the unknown for which he was solving.

But Diophantos shares the title of the ‘father of algebra’ with the aforementioned Al-Khwarizmi, whose work was responsible for significant advances in the world of mathematics. 

It was Al-Khwarizmi’s work that promoted the use of Hindu-Arabic numerals that not only pushed forward the numeral system we use today, but that gives us the very term algorithm. From the very first algorithms of the Babylonians to those of Al-Khwarizmi – to John Napier’s 1614 method for performing calculations using logarithms to the 19th century work of Boole, Frege and Peano, which set out to reduce arithmetic to a series of symbols which could be manipulated by rules – to the work of Babbage, Lovelace and Turing, which took these rules and transformed them into agents of action in computing, these feats of problem-solving are instrumental in understanding man’s quest for a grasp of the workings of the world at large.      

Babbage and Turing

One great advantage which we may derive from machinery is from the check which it affords against the inattention, the idleness, or the dishonesty of human agents.
From Babbage’s 1832 work “On the Economy of Machinery and Manufactures”

In our discussion of rules that govern the Internet, we must turn to the work of Babbage and Turing, for it serves as the important foundation for computing at all.  Babbage’s work grew out in part out of a need for more accurate mathematical tables, which were essential calculating aids used in navigation and astronomy, insurance and civil engineering.  These tables were produced by human computers and by hand – and as such, they were prone to error in terms of computation and reporting.  Even the slightest errors in navigational or astronomical tables can be costly – so it is no surprise that in the years leading up to Babbage’s project, government sources were willing to fund projects that would minimize the costs of troubleshooting. 

For example, the British Nautical Almanac, the world’s first permanent table-making project – had a reputation for ever-improving accuracy since its inception in 1766.  But moving into the 19th century, that seaman’s bible swung into a dangerous territory of inaccuracy and error, and the British government recognized the promise of producing mathematical tables mechanically and typesetting them by the same machine. 

So Babbage set out, with financial support (and the admirals’ prayers) to improve the accuracy of those ever-important mathematical tables by constructing algorithm-driven machines.  It was a move that mechanized the production of thought, a move that would eliminate human folly in computation, transcription and typesetting.  The result would be better answers, answers which would in turn be used for giving new instructions, as inputs in other algorithms.   

Babbage never finished his Difference Engine – though, in 1832 his manufacturing engineer did construct a working portion of it, which measured two and a half feet high by two feet wide by two feet deep.  Babbage moved forward to conceptualizing what would be the world’s first programmable digital computer – the Analytical Engine.  Babbage’s designed the engine such that it would separate the sites of arithmetic computation from the storage of numbers.  The computation would be carried out through a series of steps recorded on punch cards, such as the ones used in the technology of the Jacquard loom. 

But however intriguing and important the technology seemed, Babbage’s Analytical Engine – due to factors financial and logistical – was never built.  It comes to us only through Ada Lovelace’s annotated translation of a French introduction to the machine – a piece of writing that established the algorithm for the computation of Bernouilli numbers, and a piece of writing that established the idea of computer programming.  Turing would later build on the work of Lovelace and Babbage, formalizing their concepts in the Universal Machine.

When Turing introduced the mathematical description of the Universal Machine in the 1936 paper “On Computable Numbers”, he set out to answer the Entscheidungsproblem, the third question left by mathematician David Hilbert.  Gödel had already answered Hilbert’s first two questions – No, mathematics was not complete, and it was not consistent.  Turing showed that mathematics was not decidable.  And that recipe to solve a particular problem, gave us an answer that begs the asking of a new set of questions.

Media Futures 2006: 1/5 Automata: The Human Computer

While the recent inventions of Web 2.0 and User Generated Content (UGC) seem to be radical departures from the computing culture we grew up in, their organic social metaphors are in fact rooted in the beginning of computer science.  In the 1940’s and 50’s work of Alan Turing, John Von Neumann and Norbert Weiner, most discussions of the future of computing evolve into a study of the brain.  The natural automata of human thought, the way in which our ideas express our independence, this is the machine intelligence that technologists tried to design into early computers.   

Alan Turing was fascinated by Automata and its relationship to natural human thought.  In his 1950 “Computing Machinery and Intelligence,” Turing outlined an experiment that was able to determine whether a computing machine could be defined as having the capacity to think.  The Turing test functions as follows: Human “X” and respondent “Y” take part in a teletype conversation, but X cannot know whether Y is human or a machine.   If, after a specified amount of time, X believes that Y has responded like a human, and Y is a machine, then Y can be defined as having that human capacity of thought.

In his biography of Turing, William Aspray writes that this:

“was among the earliest investigations of the use of electronic computers for artificial-intelligence research...He attempted to break down the distinctions between human and machine intelligence and to provide a single standard of intelligence, in terms of mental behavior, upon which both machines and biological organisms could be judged.   In providing his standards, he considered only the information that entered and exited the automata…Turing was moving toward a unified theory of information and information processing applicable to both the machine and the biological worlds.”

The fusion of machine and biology is promoted as a core computer architectural principle in the Interim Progress Report on the Physical Realization of an Electronic Computing Instrument:  Julian H. Bigelow, James H. Pomerene, Ralph J. Slutz and Willis H. Ware; Princeton: The Institute for Advanced Study; 1 January 1947.  This report was prepared for John Von Neumann, and the rest of the IAS authorities, on the development progress of a machine based entirely on mathematical equations.

Left to right: James Pomerence, Julian Bigelow, von Neumann and Herman Goldstine

Von Neumann had joined Princeton’s Institute for Advanced Study as a Mathematician in 1933.  About 10 years later he started concentrating on something less theoretical and more practical (which alienated many of his colleagues): building an electronic computing machine.  This project was a deep meditation on the act of creation.  Some of the greatest minds, across a variety of disciplines (math, biology, engineering, physics) converged in Princeton to help Von Neumann “physically realize” his ideas. 

IAS Report, 1947

According to the report, Organs are:  “portions or sub-assemblies of the machine which constitute the means of accomplishing some inclusive operation or function; as “arithmetic organ.”  Note how the processor in this case is able to extend its influence onto others in an “inclusive operation.”  The organ of social media was anticipated already then, in 1947, even without an Internet to enable it at scale.   

Von Neumann continued to extend his computer research towards an understanding of the human brain.  He described this specifically in his introduction to his 1958 work The Computer and the Brain:

In 1948, Norbert Weiner, the leader of cybernetics wrote Control and Communication in the Animal and the Machine.  His use of the word animal is different than Turing’s logic or Von Neumann’s brain, but he is similarly concerned with the organs of information and their ability to relay information between systems:

“It is a noteworthy fact that the human and animal nervous systems, which are known to be capable of the work of a computation system, contain elements which are ideally suited to act as relays.  These elements are the so-called neurons or nerve cells... The mechanical brain does not secrete thought <as the liver does bile>, as the earlier materialists claimed, nor does it put out in the form of energy, as the muscle puts out its activity.  Information is information, not matter or energy.”

Weiner, Control and Communication in the Animal and the Machine, 1947

In late 2004, the creator of del.icio.us Joshua Schachter described to me that tags were simply crystallized attention.  Both terms interested me: while attention has become my chief investigation, the transparent materialism expressed by “crystallized” has also been a key focus.  When you put these together, you get, in Weiner’s words, a “secretion” of passive behavioral data.

Seth Goldstein, April 2006

Just because a tag is a form of  information doesn’t mean that it lacks physicality  Without being matter or energy, can a tag be made of something else, something that comes closer in nature to mirror neurons?  Attentrons.  Remember that mirror neurons are a form of biological material.  These mirror neurons fire when the subject performs an action, but also when it observes somebody else performing an action.  In this latter case, the successful firing of a mirror neuron is based entirely on its ability to passively mimic the behavior of somebody else.  In this quiet absence of a human impulse, attention is full.

Media Futures 2006: 1/5 Automata: Industrial Automata: From Performance to Prosthesus

Automata evolved from acting like us to acting on behalf of us.  What if it was possible for an automaton to do the work of a human?   Would the stuff of Aristotle's ruminations come to pass, eliminating the need for servants and slaves?  To realize that fantasy – as Albertus Magnus supposedly did in the 13 th century, with the construction of a life-size human domestic servant automaton – is to eliminate the need for humans to pay Attention to certain aspects of work in the home.  These automata promised to give owners a surplus of energy and attention, but at a cost.

Scientists have long recognized, Sir Geoffrey Jefferson argued in his 1960 "The Mind of Mechanical Man", that aside from the mind, “both animal and human bodies were nothing more than a collection of pumps, reservoirs, bellows, fires, cooling and heating systems, tubes, conduits, kitchens, girders, levers, pulleys and ropes.”   (Clearly, as John Stewart points out, little has changed since)

In this model, automata do not have minds, hearts, or souls.  This was all the better, since those human aspects might have forced the automata into unnecessary error.  These perfect machines began to gain power over the very humans who operated them, a power which became even more threatening when humans wrestled with the possibility that their creations might actually come to life.  What, then, would these exploited classes do?   Embedded in their very name are the seeds of revolutionary threat: robot (as human-shaped automata are widely referred to) comes from the Czech robota, meaning forced labor, and it is a term that was first used in Karel Čapek's 1921 play Rossum's Universal Robots, or R.U.R. 

 

 

The questions raised by this term in Čapek's play are central questions in the discourse of modernity – questions of the nature of man and machine and of the boundaries between the two.   Human-like machines threaten to come to life and overpower the control of their former masters; machine-like humans threaten to destroy life, overpowering any sense of humanity and the body of humanity itself.   

 

(Picture: Georg Grosz. Republican Automatons.)

From the faceless figures in Georg Grosz's Republican Automata (above) with hooks for hands and gears for souls, to the orphaned machine of Francis Picabia's The Child Carburetor (born of the work of man but devoid of his agency) the machine-like human and the human-like machine confuse our sense of where us stops and the machine we created to stand for us begins.

 

(Picture: Francis Picabia. The Child Carburetor.)

In 1950, Norbert Wiener wrote in his 1950 work on cybernetics "The Human Use
of Human Beings":

When human atoms are knit into an organization in which they are used, not in their full right as responsible human beings, but as cogs and levers and rods, it matters little that their raw material is flesh and blood.  What is used as an element in a machine, is an element in the machine.  Whether we entrust our decisions to machines of metal, or to those machines of flesh and blood which are bureaus and vast laboratories and armies and corporations, we shall never receive the right answers to our questions unless we asks the right questions.

Let us bear this careful warning in mind, as we evaluate the visions being articulated now by our most noble leaders of the Internet.  Take for example the recent speech by Ray Ozzie, Chief Software Architect at Microsoft to an audience of financial analysts:

But beyond infrastructure services, what's most unique and valuable about a very large-scale services platform is what I'll refer to as optimization. By optimization I mean the monitoring and utilization of both collective end-user behavior and individual behavior to rank content for the user. That ranked content might be the order of advertisements in a search or e-mail window, or the order of relevant news items or playlists or video clips or items in a marketplace that are presented to the user...Optimization always respectful of a user's privacy will be increasingly key to delivering great user experiences, and it's already a key factor in the area of profitability, because the larger the number of users that are connected to any services platform, the more behavioral the data that can be generated. The larger the number of PCs and other devices that are connected to that platform, the more behavioral data that's available; the larger the number of applications connected to the platform, both Web apps and desktop apps, the better our optimizations will be and the more profitable it will be for us and for our partners.

It is remarkable the extent to which Ozzie seems to ignore the fundamental Web 2.0 premise that users are in control, and that just because behavioral data may be generated automatically, that does not mean that the companies enabling such data (ie Microsoft) have necessary dibs on it.

Over history, automata were at once objects calling for our attention – objects meant to enrapture us in spectacle – as well as objects that offered to do our work without requiring our Attention.   This represented the threat of triumph over human mastery: that these automata might take on lives of their own, rendering humans obsolete and placing us at the mercy of the machine which always acts without emotion, error or thought.  The power of choice manifests itself in one's ability to ask, in Weiner's words, "the right questions."  Right questions might be those queries specifically which elude their engine's best attempts at matching them to willing advertisers.