Jun 252005

Fifteen years ago I walked into the Phoenix, a poetry bookshop on Jones Street that no longer exists, and asked what they had by Yvor Winters. The proprietor went to the back and returned with several items from the library of Glenway Wescott (1901-1987), a distinguished novelist and a friend and contemporary of Winters. I promptly relieved him of them for more than I could readily afford.

Among the items was a typescript of two poems, “The Hermit” and “To a Coyote,” signed by Winters, with a note by Wescott: “I found this with poems of my own not later than the summer of 1920? (I think)”. To judge by the style he is correct. Winters’ first book of poetry, The Immobile Wind, was published in 1920, and these obviously belong to him, and to that period. They have appeared nowhere in print to my knowledge.

Winters took considerable pains with his literary estate. He issued a Collected Poems in 1952, revised it, adding two later poems, in 1960, and collected his early poetry in 1966. He was very definite about what he wanted to keep, as he was about most matters. In the introduction to The Early Poems of Yvor Winters, 1920-28, he wrote as follows:

I publish this book to provide an authorized edition of my early and “experimental” work. Some one would do this in any event, and probably some one who would sweep all of my uncollected work into a single volume, with no indication of what I had considered my best work at the time I was writing and publishing it. I include three small books [The Immobile Wind, The Magpie’s Shadow, and The Bare Hills], a group of four poems previously uncollected from magazines, and two later groups of some size… Any other uncollected material is rubbish.

Some one else has done this, regardless, although Winters has been fortunate in his editors so far. In 1978 Donald Davie published The Poetry of Yvor Winters, which included everything from Winters’ own two collections and only fifteen additional pages of what he wished to throw away. In 2000 R.L. Barth put out a fine selection of Winters’ verse, along with a well-edited Selected Letters, which are amusing and harrowing by turns.

The Complete Poetry of Yvor Winters, with the usual trappings, critical detritus, and library pricing, is surely in our future. Sooner or later an academic with more diligence than talent will get around to exhuming Winters’ literary remains. He will want to see my typescript.

I will not reproduce “The Hermit” and “To a Coyote” here. They are, in fact, rubbish. The typescript gives me great joy to possess, and I will not let it go until I die. The question is, what then? Should I donate it to a library and put the poems in the public domain? Or should I burn it? You tell me: I honestly don’t know.

Jun 212005

In ordinary discourse a “dated” work of art is old-fashioned, no longer pertinent, a back number. But this is imprecise. The truly dated work can be traced to the moment it was made.

The 40s: Gentleman’s Agreement (1947)

The 40s are remembered, cinematically, as the era of gangsters and gun molls, of crooked cops and desperate double-crossing dames, all pursued by gumshoes who dangle a cigarette out of one side of their mouths and deliver snappy patter out of the other. This is known as “realism.”

Whatever it was, the audience had a taste for something else. The top ten grossing movies of the decade were Bambi, Pinocchio, Fantasia, The Best Years of Our Lives, The Bells of St. Mary’s, Duel in the Sun, Sergeant York, Mom and Dad (not quite so wholesome as it sounds), Meet Me In St. Louis, and Easter Parade.

Somewhere between the 30s and 40s journalists in the movies went from raffish ambulance chasers to plumed crusaders for truth. Maybe Ernie Pyle is to blame, maybe more journalists starting getting screenwriting jobs, I don’t know, but when Gregory Peck is cast as a journalist you know the party’s over. In Gentleman’s Agreement he plays his customary straight arrow with that deer-in-the-headlights look that he didn’t manage to lose until The Boys from Brazil. Anti-semitism is exposed with all the investigative grit of Eddie Murphy’s seminal “White Like Me” sketch on Saturday Night Live. Does this movie date? Well, let’s just say that 1947 was about the last year that even senile lounge lizards thought they could keep the money in the country club and the Jews out.

The 50s: Rebel Without a Cause (1955)

Here we have a case of overdetermined dating. Psychology: until the 1950s it did not occur to psychologists, not always the sharpest tools in the shed, that juvenile delinquents weren’t always from the slums. Mise-en-scène: teen angst without music, garish Technicolor, homoerotic subtext (did I really just write “subtext”?), pegged jeans, chicken runs. Acting style: James Dean slouches and shambles, stumbles and mumbles, shrieks and stammers, and generally Methods up a storm. Bonus: the climax takes place in a planetarium.

The 60s: Guess Who’s Coming To Dinner? (1967)

Poitier glowers! Hepburn quavers! Tracy blusters! Miscegenation shocks white liberals!

Of course the movie was released in 1967, but when? It’d have to be after the summer (of Love); I estimate September 23rd, 4:33 EST. Give or take ten minutes.

The 70s: Carnal Knowledge (1971)

It would be cheating to draw any inference from the fact that this movie stars Art Garfunkel, though inferences from Garfunkel’s hair, not to mention Carol Kane’s, are admissible. It’s when Jack Nicholson sits himself down in one of those praying-mantis lounge chairs and treats Kane and Garfunkel to a slide show of his erotic life that we know we’re in that early 70s netherworld between Godspell and disco. Plus Garfunkel describes Kane as his “love teacher.”

The 80s: Wall Street (1987)

Oliver Stone is no accountant. Anacott Steel, according to the wise old broker, has “no fundamentals,” while according to the corporate raiders it has a breakup value of 80 a share when it’s selling at 45. So maybe you figure there are a few fundamentals in there somewhere.

Oliver Stone, God help us, is a screenwriter. Daryl Hannah says to Charlie Sheen, “I want to do for furniture what Laura Ashley did for fabric.” “And I’ll take you public,” Sheen says. “You will?” she squeals. (Her next line, “Oh goody!”, apparently survives only in the director’s cut.)

Charlie Sheen says to Daryl Hannah, “So what do you want?” “I want…a Turner. A perfect Canary diamond. World peace. The best of everything.” Not necessarily, one surmises, in that order. 1987’s on the phone. He says it’s OK, you can keep his dialogue.

Honorable mention: Flashdance (1983). What a feeling.

The 90s: Jerry Maguire (1996)

Writer/director Cameron Crowe is really, truly sorry about the 80s, and he promises they won’t happen again. This abject apology for the previous decade is, to my knowledge, the first, and one hopes the last, movie to feature a sports agent, which dates it with precision. Before 1995 nobody knew what a sports agent was; after 1996 nobody cared. Jerry Maguire is of course best known for bequeathing to subnormals that most 80s of all slogans, “Show me the money!” This bitter irony for Crowe was assuaged, in part, by a tall, cool stack of cash. The movie grossed over $150 million in the US alone.

The 00s:

Ask me in ten years.

Jun 202005

There is bridge blogging, as in “check out my culture, it’s even worse than yours,” which is copious, and then there is bridge blogging, as in the game, which is scarce. Me, I prefer the latter: my own damn culture gives me enough tzuris. Unfortunately, if we except the occasional bridge entry at Floyd McWilliams’ Declarer, there were, as of last week, no decent bridge blogs at all. Now there is one: Squeezing the Dummy, by my friend Justin Lall, the best player in America under 30 and a great system theoretician. He also writes frankly, and in complete sentences. You Gee Chronicles refugees will want to have a look.

(Update: After three weeks of excellent daily blogging, he took it down. Never mind.)

Jun 092005

Now is the time on God of the Machine when I play nice with the other blogchildren, who must be exasperated by my philoso-scientific treatises. I have been tagged for a game by Agenda Bender, who sustains, practically single-handledly, my diminishing belief that homosexuals are, in fact, witty. I will indulge him.

1. Number of Books I’ve Owned: Lifetime, a few thousand, more than five and less than ten. Like Alfred Jay Nock in Memoirs of a Superfluous Man — which I own — I owe a great deal of my education to reading the spines of books. My apartment has room for only 1,500 or so, and henceforward each arrival necessitates a departure.

2. Last Book Bought: The Greeks and the Irrational, by E.R. Dodds. See last book read.

3. Last Book Read: The Origins of Consciousness in the Breakdown of the Bicameral Mind, by Julian Jaynes. I picked this up a few years ago and brought it to work, intending it for subway reading. My boss spotted it and called me “a Julian Jaynes homosexual.” I had to put the book down so I could think about how to punctuate that.

Jaynes’s book is interesting, if a bit off the wall, and he cites Dodds favorably, which prompted me to buy it. The portion of my education not due to book spines I owe to my habit of reading the books that the authors I admire read. A book without footnotes and bibliography is like a day without sunshine.

4. Five Books That Mean a Lot to Me: I just gave a reading list, and I hate reading lists. Instead you will get a reading history.

In my adolescence I had no mind to speak of. I read indiscriminately, remembered little and understood less. I assiduously studied Fowler’s Modern English Usage, utterly failed to discern its spirit, and became a pedant. The only books I thoroughly absorbed were about games: Bobby Fischer’s My 60 Greatest Games, Louis Watson’s The Play of the Hand, and The Baseball Encyclopedia.

At 20 my sneaking suspicion that I had been fed an awful lot of shit was confirmed by Ayn Rand, which helped to make me insufferable for the better part of a decade. Fortunately I was already a bit too old; Hazlitt and von Mises convinced me about economics before Rand made a dent. It usually begins with Ayn Rand, and usually ends there too.

At 25 I was browsing the back of the book in The New Republic and came across a reference to Yvor Winters as “being opposed to everything the 20th century stood for” or something like that. Not true — Winters believed that the 20th century is poetry’s greatest in English — but there, I thought, is the critic for me. After two years of immersion in Forms of Discovery and its accompanying anthology, Quest for Reality, I fancied myself a poet; after five, a poetry critic.

At 30 I took up computer programming. I learned how to think about programming problems from George Pólya’s various books about mathematical heuristic, especially How to Solve It; how to design complex systems from Christopher Alexander’s The Timeless Way of Building and A Pattern Language; and how to develop reasonable coding habits from Code Complete by Steve McConnell and Refactoring by Martin Fowler. For any bugs in my current code these four men are entirely responsible.

Now I patch the holes in my defective education as best I can. Since I forget faster than I read, I keep falling further behind, in the manner of Uncle Toby in Tristram Shandy, who needs half an hour to write fifteen minutes of his life. And there we are.

The culturati are going at it hot and heavy over the burden of consumer choice. So much food, so much art, so little time! Jon Hastings sympathizes; Virginia “Eternal Sunshine” Postrel is having none of it:

Since different people care intensely about different things, only a society where choice is abundant everywhere can truly accommodate the variety of human beings. Abundant choice doesnt force us to look for the absolute best of everything. It allows us to find the extremes in those things we really care about, whether that means great coffee, jeans cut wide across the hips, or a spouse who shares your zeal for mountaineering, Zen meditation, and science fiction.

True, sometimes, I guess, though one wonders in passing which supermarket Postrel bought her husband at. I will readily stipulate that there are markets, like mattresses or deodorants, in which people who “really care about” sleep or smelling fresh will not be any better served than the rest of us by the hundreds of indistinguishable products on offer. Point is, the mattresses and deodorants are all pretty good, for exactly the same reason that there are so many of them. Here our choices are limited: high quality and profusion, or neither.

Also, Anne Bancroft died. I exempt myself from my recent strictures on the grounds that I often talked about her but never got around to writing, and besides, I feel like it. She triumphed as Annie Sullivan and equally, in a completely different way, as Mrs. Robinson, in a dated and overrated movie that lives only when she is on screen (excepting Buck Henry’s neat turn as the hotel desk clerk). She also managed to stay married to Mel Brooks for forty years and keep her mouth shut in public. A working definition of adulthood is the day you watch The Graduate and not only find Anne Bancroft more alluring than Katharine Ross but wonder how you could have ever thought otherwise.

(Update: Colby Cosh comments. Alan Sullivan comments.)

Jun 022005

What is entropy, exactly? First try an easier one: What is gravity? Suppose you had never heard of gravity and asked me what it was. I answer the usual, “attraction at a distance.”

At this point you are as badly off as you were before. Do only certain objects attract each other? How strong is this “attraction”? On what does it depend? In what proportions?

Now I give a better answer. Gravity is a force that attracts all objects directly as the product of their masses and inversely as the square of the distance between them. I may have to backtrack a bit and explain what I mean by “force,” “mass,” “directly,” “inversely,” and “square,” but finally we’re getting somewhere. All of a sudden you can answer every question in the previous paragraph.

Of course I am no longer really speaking English. I’m translating an equation, Fg = G*(m1*m2)/r2. It turns out that we’ve been asking the wrong question all along. We don’t really care what gravity is; there is some doubt that we even know what gravity is. We care about how those objects with m’s (masses) and r’s (distances) act on each other. The cash value is in all those little components on the right side of the equation; the big abstraction on the left is just a notational convenience. We write Fg (gravity) so we don’t have to write all the other stuff. You must substitute, mentally, the right side of the equation whenever you encounter the term “gravity.” Gravity is what the equation defines it to be, and that is all. So, for that matter, is alpha. The comments to the previous sections on alpha theory are loaded with objections that stem from an inability, or unwillingness, to keep this in mind.

In a common refrain of science popularizers, Roger Penrose writes, in the preface to The Road to Reality: “Perhaps you are a reader, at one end of the scale, who simply turns off whenever a mathematical formula presents itself… If so, I believe that there is still a good deal that you can gain from this book by simply skipping all the formulae and just reading the words.” Penrose is having his readers on. In fact if you cannot read a formula you will not get past Chapter 2. There is no royal road to geometry, or reality, or even to alpha theory.

Entropy is commonly thought of as “disorder,” which leads to trouble, even for professionals. Instead we will repair to Ludwig Boltzmann’s tombstone and look at the equation:

S = k log W

S is entropy itself, the big abstraction on the left that we will ignore for the time being. The right-hand side, as always, is what you should be looking at, and the tricky part there is W. W represents the number of equivalent microstates of a system. So what’s a microstate? Boltzmann was dealing with molecules in a gas. If you could take a picture of the gas, showing each molecule, at a single instant–you can’t, but if you could–that would be a microstate. Each one of those tiny suckers possesses kinetic energy; it careers around at staggering speeds, a thousand miles an hour or more. The temperature of the gas is the average of all those miniature energies, and that is the macrostate. Occasionally two molecules will collide. The first slows down, the second speeds up, and the total kinetic energy is a wash. Different (but equivalent) microstates, same macrostate.

The number of microstates is enormous, as you might imagine, and the rest of the equation consists of ways to cut it down to size. k is Boltzmann’s constant, a tiny number, 10-23 or so. The purpose of taking the logarithm of W will become apparent when we discuss entropy in communication theory.

An increase in entropy is usually interpreted, in statistical mechanics, as a decrease in order. But there’s another way to look at it. In a beaker of helium, there are far, far fewer ways for the helium molecules to cluster in one corner at the bottom than there are for them to mix throughout the volume. More entropy decreases order, sure, but it also decreases our ability to succinctly describe the system. The greater the number of possible microstates, the higher the entropy, and the smaller the chance we have of guessing the particular microstate in question. The higher the entropy, the less we know.

And this, it turns out, is how entropy applies in communication theory. (I prefer this term, as its chief figure, Claude Shannon, did, to “information theory.” Communication theory deals strictly with how some message, any message, is transmitted. It abstracts away from the specific content of the message.) In communication theory, we deal with signals and their producers and consumers. For Eustace, a signal is any modulatory stimulus. For such a stimulus to occur, energy must flow.

Shannon worked for the telephone company, and what he wanted to do was create a theoretical model for the transmission of a signal — over a wire, for the purposes of his employer, but his results generalize to any medium. He first asks what the smallest piece of information is. No math necessary to figure this one out. It’s yes or no. The channel is on or off, Eustace receives a stimulus or he doesn’t. This rock-bottom piece of information Shannon called a bit, as computer programmers still do today.

The more bits I send, the more information I can convey. But the more information I convey, the less certain you, the receiver, can be of what message I will send. The amount of information conveyed by a signal correlates with the uncertainty that a particular message will be produced, and entropy, in communication theory, measures this uncertainty.

Suppose I produce a signal, you receive it, and I have three bits to work with. How many different messages can I send you? The answer is eight:


Two possibilities for each bit, three bits, 23, eight messages. For four bits, 24, or 16 possible messages. For n bits, 2n possible messages. The relationship, in short, is logarithmic. If W is the number of possible messages, then log W is the number of bits required to send them. Shannon measures the entropy of the message, which he calls H, in bits, as follows:

H = log W

Look familiar? It’s Boltzmann’s equation, without the constant. Which you would expect, since each possible message corresponds to a possible microstate in one of Boltzmann’s gases. In thermodynamics we speak of “disorder,” and in communication theory of “information” or “uncertainty,” but the mathematical relationship is identical. From the above equation we can see that if there are eight possible messages (W), then there are three bits of entropy (H).

I have assumed that each of my eight messages is equally probable. This is perfectly reasonable for microstates of molecules in a gas; not so reasonable for messages. If I happen to be transmitting English, for example, “a” and “e” will appear far more often than “q” or “z,” vowels will tend to follow consonants, and so forth. In this more general case, we have to apply the formula to each possible message and add up the results. The general equation, Shannon’s famous theorem of a noiseless channel, is

H = – (p1log p1 + p2log p2 + … pWlog pW)

where W is, as before, the number of possible messages, and p is the probability of each. The right side simplifies to log W when each p term is equal, which you can calculate for yourself or take my word for. Entropy, H, assumes the largest value in this arrangement. This is the case with my eight equiprobable messages, and with molecules in a gas. Boltzmann’s equation turns out to be a special case of Shannon’s. (This is only the first result in Shannon’s theory, to which I have not remotely done justice. Pierce gives an excellent introduction, and Shannon’s original paper, “The Mathematical Theory of Communication,” is not nearly so abstruse as its reputation.)

This notion of “information” brings us to an important and familiar character in our story, Maxwell’s demon. Skeptical of the finality of the Second Law, James Clerk Maxwell dreamed up, in 1867, a “finite being” to circumvent it. This “demon” (so named by Lord Kelvin) was given personality by Maxwell’s colleague at the University of Edinburgh, Peter Guthrie Tait, as an “observant little fellow” who could track and manipulate individual molecules. Maxwell imagined various chores for the demon and tried to predict their macroscopic consequences.

The most famous chore involves sorting. The demon sits between two halves of a partitioned box, like the doorman at the VIP lounge. His job is to open the door only to the occasional fast-moving molecule. By careful selection, the demon could cause one half of the box to become spontaneously warmer while the other half cooled. Through such manual dexterity, the demon seemed capable of violating the second law of thermodynamics. The arrow of time could move in either direction and the laws of the universe appeared to be reversible.

An automated demon was proposed by the physicist Marian von Smoluchowski in 1914 and later elaborated by Richard Feynman. Smoluchowski soon realized, however, that Brownian motion heated up his demon and prevented it from carrying out its task. In defeat, Smoluchowski still offered hope for the possibility that an intelligent demon could succeed where his automaton failed.

In 1929, Leo Szilard envisioned a series of ingenious mechanical devices that require only minor direction from an intelligent agent. Szilard discovered that the demon’s intelligence is used to measure — in this case, to measure the velocity and position of the molecules. He concluded (with slightly incorrect details) that this measurement creates entropy.

In the 1950s, the IBM physicist Leon Brillouin showed that, in order to decrease the entropy of the gas, the demon must first collect information about the molecules he watches. This itself has a calculable thermodynamic cost. By merely watching and measuring, the demon raises the entropy of the world by an amount that honors the second law. His findings coincided with those of Dennis Gabor, the inventor of holography, and our old friend, Norbert Wiener.

Brillouin’s analysis led to the remarkable proposal that information is not just an abstract, ethereal construct, but a real, physical commodity like work, heat and energy. In the 1980s this model was challenged by yet another IBM scientist, Charles Bennett, who proposed the idea of the reversible computer. Pursuing the analysis to the final step, Bennett was again defeated by the second law. Computation requires storage, whether on a transistor or a sheet of paper or a neuron. The destruction of this information, by erasure, by clearing a register, or by resetting memory, is irreversible.

Looking back, we see that a common mistake is to “prove” that the demon can violate the second law by permitting him to violate the first law. The demon must operate as part of the environment rather than as a ghost outside and above it.

Having slain the demon, we shall now reincarnate him. Let’s return for a moment to the equation, the Universal Law of Life, in Part 6:

max E([α – αc]@t | F@t-)

The set F@t- represents all information available at some time t in the past. So far I haven’t said much about E, expected value; now it becomes crucial. Eustace exists in space, which means he deals with energy transfers that take place at his boundaries. He has been known to grow cilia and antennae (and more sophisticated sensory systems) to extend his range, but this is all pretty straightforward.

Eustace also exists in time. His environment is random and dynamic. Our equation spans this dimension as well.

t- : the past
t : the present
t+ : the future (via the expectation operator, E)

t+ is where the action is. Eustace evolves to maximize the expected value of alpha. He employs an alpha model, adapted to information, to deal with this fourth dimension, time. The more information he incorporates, the longer the time horizon, the better the model. Eustace, in fact, stores and processes information in exactly the way Maxwell’s imaginary demon was supposed to. To put it another way, Eustace is Maxwell’s demon.

Instead of sorting molecules, Eustace sorts reactions. Instead of accumulating heat, Eustace accumulates alpha. And, finally, instead of playing a game that violates the laws of physics, Eustace obeys the rules by operating far from equilibrium with a supply of free energy.

Even the simplest cell can detect signals from its environment. These signals are encoded internally into messages to which the cell can respond. A paramecium swims toward glucose and away from anything else, responding to chemical molecules in its environment. These substances act to attract or repel the paramecium through positive or negative tropism; they direct movement along a gradient of signals. At a higher level of complexity, an organism relies on specialized sensory cells to decode information from its environment to generate an appropriate behavioral response. At a higher level still, it develops consciousness.

As Edelman and Tononi (p. 109) describe the process:

What emerges from [neurons’] interaction is an ability to construct a scene. The ongoing parallel input of signals from many different sensory modalities in a moving animal results in reentrant correlations among complexes of perceptual categories that are related to objects and events. Their salience is governed in that particular animal by the activity of its value systems. This activity is influenced, in turn, by memories conditioned by that animal’s history of reward and punishment acquired during its past behavior. The ability of an animal to connect events and signals in the world, whether they are causally related or merely contemporaneous, and, then, through reentry with its value-category memory system, to construct a scene that is related to its own learned history is the basis for the emergence of primary consciousness.

The short-term memory that is fundamental to primary consciousness reflects previous categorical and conceptual experiences. The interaction of the memory system with current perception occurs over periods of fractions of a second in a kind of bootstrapping: What is new perceptually can be incorporated in short order into memory that arose from previous categorizations. The ability to construct a conscious scene is the ability to construct, within fractions of seconds, a remembered present. Consider an animal in a jungle, who senses a shift in the wind and a change in jungle sounds at the beginning of twilight. Such an animal may flee, even though no obvious danger exists. The changes in wind and sound have occurred independently before, but the last time they occurred together, a jaguar appeared; a connection, though not provably causal, exists in the memory of that conscious individual.

An animal without such a system could still behave and respond to particular stimuli and, within certain environments, even survive. But it could not link events or signals into a complex scene, constructing relationships based on its own unique history of value-dependent responses. It could not imagine scenes and would often fail to evade certain complex dangers. It is the emergence of this ability that leads to consciousness and underlies the evolutionary selective advantage of consciousness. With such a process in place, an animal would be able, at least in the remembered present, to plan and link contingencies constructively and adaptively in terms of its own previous history of value-driven behavior. Unlike its preconscious evolutionary ancestor, it would have greater selectivity in choosing its responses to a complex environment.

Uncertainty is expensive, and a private simulation of one’s environment as a remembered present is exorbitantly expensive. At rest, the human brain requires approximately 20% of blood flow and oxygen, yet it accounts for only 2% of body mass. It needs more fuel as it takes on more work.

The way information is stored and processed affects its energy requirements and, in turn, alpha. Say you need to access the digits of π. The brute-force strategy is to store as many of them as possible and hope for the best. This is costly in terms of uncertainty, storage, and maintenance.

Another approach, from analysis, is to use the Leibniz formula:

Π/4 = 1 – 1/3 + 1/5 – 1/7 + 1/9 – …

This approach, unlike the other, can supply any arbitrary digit of π. And here you need only remember the odd numbers and an alternating series of additions and subtractions.

Which method is more elegant and beautiful? Which is easier?

Human productions operate on this same principle of parsimony. Equations treat a complex relation among many entities with a single symbol. Concepts treat an indefinite number of percepts (or other concepts). Architects look at blueprints and see houses. A squiggle of ink can call up a mud puddle, or a bird in flight. The aim, in every case, is maximal information bang for minimal entropy buck.

In an unpredictable environment, decisions must be made with incomplete information. The epsilon of an alpha model depends on its accuracy, consistency and elegance. An accurate model corresponds well to the current environment, a consistent model reduces reaction time, and an elegant model reduces energy requirements. Everything, of course, is subject to change as the environment changes. The ability to adapt to new information and to discard outdated models is just as vital as the ability to produce models in the first place.

Thus Eustace generates his alpha* process, operating on some subset of F@t- where t is an index that represents the increasing set of available information F. As Eustace evolves, the complexity of his actions increases and his goals extend in space and time, coming to depend less on reflex and more on experience. He adapts to the expected value for alpha@t+, always working with an incomplete information set. As antennae extend into space, so Eustace’s alpha model extends into a predicted future constructed from an experienced past.