Every art and every inquiry, and similarly every action and pursuit, is thought to aim at some good; and for this reason the good has rightly been declared to be that at which all things aim.
–Aristotle

The moment has arrived. Weve invoked the laws of thermodynamics, probability and the law of large numbers; we can now state the Universal Law of Life. We define a utility function for all living systems:

max E([α – α_c]@t | F@t-1)

E is expected value. α is alpha, the equation for which I gave in Part 2. α_c, or alpha critical, is a direct analogue to wealth_c in Part 5. If you’ve ever played pickup sticks or Jenga, you know there comes a point in the game where removing one more piece causes the whole structure to come tumbling down. So it is for any Eustace. At some point the disruptive forces overwhelm the stabilizing forces and all falls down. This is alpha critical, and when you go below it it’s game over.

F is the filtration, and F@t-1 represents all of the information available to Eustace as of t – 1. t is the current time index.

You will note that this is almost identical to the wealth maximization equation given in Part 5. We have simply substituted one desirable, objective, measurable term, alpha, for another, wealth. In Alphabet City or on Alpha Centauri, living systems configured to maximize this function will have the greatest likelihood of survival. Bacteria, people, and as-yet undiscovered life forms on Rigel 6 all play the same game.

To maximize its sustainability, Eustace must be:

• alphatropic: can generate alpha from available free energy. Living organisms are alphatropic at every scale. They are all composed of a cell or cells that are highly coordinated, down to the organelles. The thermodynamic choreography of the simplest virus, in alpha terms, is vastly more elaborate than that of the most sophisticated machined devices. (This is an experimentally verifiable proposition, and alpha theory ought to be subject to verification.)
• alphametric: calibrates “appropriate” responses to fluctuations in alpha. (I will come to what “appropriate” means in a moment.) In complex systems many things can go wrong — by wrong I mean alphadystropic. If a temperature gauge gives an erroneous reading in an HVAC system, the system runs inefficiently and is more prone to failure. Any extraneous complexity that does not increase alpha has a thermodynamic cost that weighs against it. Alpha theory in no way states that living systems a priori know the best path. It states that alpha and survivability are directly correlated.
• alphaphilic: can recognize and respond to sources of alpha. A simple bacterium may use chemotaxis to follow a maltose gradient. Human brains are considerably more complex and agile. Our ability to aggregate data through practice, to learn, allows us to model a new task so well that eventually we may perform it subconsciously. Think back to your first trip to work and how carefully you traced your route. Soon after there were probably days when you didnt even remember the journey. Information from a new experience was collected, and eventually, the process was normalized. We accumulate countless Poisson rules and normalize them throughout our lives. As our model grows, new information that fits cleanly within it is easier to digest than information that challenges or contradicts it. (Alpha theory explains, for example, resistance to alpha theory.)

Poisson strategies or “Poisson rules” are mnemonics, guesses, estimates; these will inevitably lead to error. Poisson rules that are adapted to the filtration will be better than wild guesses. The term itself is merely a convenience. It in no way implies that all randomness fits into neat categories but rather emphasizes the challenges of discontinuous random processes.

There are often many routes to get from here to there. Where is there? The destination is always maximal alpha given available free energy. To choose this ideal path, Eustace would need to know every possible conformation of energy. Since this is impossible in practice, Eustace must follow the best path based on his alpha model. Let’s call this alpha quantity α* (alpha star). We can now introduce an error term, ε (epsilon).

ε = |α – α*|

Incomplete or incorrect information increases Eustace’s epsilon; more correct or accurate information decreases it. “Appropriate” action is based on a low-epsilon model. All Eustaces act to maximize alpha star: they succeed insofar as alpha star maps to alpha.

This is an extravagant claim, which I may as well put extravagantly: Alpha star defines behavior, and alpha defines ethics, for all life that adheres to the laws of thermodynamics. Moral action turns out to be objective after all. All physiological intuitions have been rigorously excluded — no “consciousness,” no “self,” no “volition,” and certainly no “soul.” Objective measure and logical definition alone are the criteria for the validity of alpha. There is, to be sure, nothing intuitively unreasonable in the derivation; but the criterion for mathematical acceptability is logical self-consistency rather than simply reasonableness of conception. Poincaré said that had mathematicians been left in the prey of abstract logic, they would have never gone beyond number theory and geometry. It is nature, in our case thermodynamics, that opens mathematics as a tool for understanding the world.

Alpha proposes a bridge that links the chemistry and physics of individual molecules to macromolecules to primitive organisms all the way through to higher forms of life. Researchers and philosophers can look at the same questions they always have, but with a rigorous basis of reference. To indulge in another computer analogy, when I program in a high-level language I ultimately generate binary output, long strings of zeros and ones. The computer cares only about this binary output. Alpha is the binary output of living systems.

The reader will discover that alpha can reconstitute the mechanisms that prevailed in forming the first large molecules — the molecules known to be the repositories of genetic information in every living cell throughout history. In 1965 the work of Jacob, Monod, and Gros demonstrated the role of messenger ribonucleic acids in carrying information stored in deoxyribonucleic acid that is the basis of protein synthesis. Then American biologists Tom Cech and Sidney Altman earned the Nobel Prize in Chemistry in 1989 for showing that RNA molecules possess properties that were not originally noticed: they can reorganize themselves without any outside intervention.

All of this complexity stems from the recursive application of a simple phenomenon. Alpha’s story has never changed and, so long as the laws of thermodynamics continue to hold, it never will. But recursive simplicity can get awfully complicated, as anyone who’s ever looked at a fractal can tell you. Remember that t and t – 1 in the maximization function change constantly; it’s a fresh Bernoulli trial all the time. Human beings calculate first-order consequences pretty well, second-order consequences notoriously badly, and the third order is like the third bottle of wine: all bets are off. This is why we need alpha models, and why we can maximize only alpha star, not alpha itself. Alpha is not a truth machine. It is one step in the process of abstracting the real fundamentals from all the irrelevant encumbrances in which intuition tangles us. There is a lot of moral advice to be derived from alpha theory, which I will get around to offering, but for now: Look at your alpha model. (Objectivists will recognize this as another form of “check your premises.”)

But for those of you who want some cash value right away — and I can’t blame you — the definition of life falls out immediately from alpha theory. Alpha is a dimensionless unit. Living systems, even primitive ones, have an immensely higher such number than machines. Life is a number. (We don’t know its value of course, but this could be determined experimentally.) Erwin Schrödinger, in his vastly overrated book What Is Life?, worried this question for nearly 100 pages without answering it. Douglas Adams, in The Hitchhiker’s Guide to the Galaxy, claimed that the meaning of life is 42. He got a hell of a lot closer than Schrödinger.

In the next few posts, well subsume Darwin into a much more comprehensive theory and we’ll consolidate — or as E.O. Wilson would say, consiliate — the noble sciences into a unified field in a way that might even make Aristotle proud.

Part 1
Part 2
Part 3

Watch a drop of rain trace down a window-pane. Being acquainted with gravity, you might expect it to take a perfectly straight path, but it doesn’t. It zigs and zags, so its position at the bottom of the pane is almost never a plumb drop from where it began.

Or graph a series of Bernoulli trials. Provided the probability of winning is between 0 and 1, the path, again, will veer back and forth unpredictably.

You are observing Gaussian randomness in action. All Gaussian processes are Lipschitz continuous, meaning, approximately, that you can draw them without lifting your pencil from the paper.

The most famous and widely studied of all Gaussian processes is Brownian motion, discovered by the biologist Robert Brown in 1827, which has had a profound impact on almost every branch of science, both physical and social. Its first important applications were made shortly after the turn of the last century by Louis Bachelier and Albert Einstein.

Bachelier wanted to model financial markets; Einstein, the movement of a particle suspended in liquid. Einstein was looking for a way to measure Avogadro’s number, and the experiments he suggested proved to be consistent with his predictions. Avogadro’s number turned out be very large indeed — a teaspoon of water contains about 2x10E23 molecules.

Bachelier hoped that Brownian motion would lead to a model for security prices that would provide a sound basis for option pricing and hedging. This was finally realized, sixty years later, by Fischer Black, Myron Scholes and Robert Merton. It was Bachelier’s idea that led to the discovery of non-anticipating strategies for tackling uncertainty. Black et al showed that if a random process is Gaussian, it is possible to construct a non-anticipating strategy to eliminate randomness.

Theory and practice were reconciled when Norbert Wiener directed his attention to the mathematics of Brownian motion. Among Wiener’s many contributions is the first proof that Brownian motion exists as a rigorously defined mathematical object, rather than merely as a physical phenomenon for which one might pose a variety of models. Today Wiener process and Brownian motion are considered synonyms.

Back to Eustace.

Eustace plays in an uncertain world, his fortunes dictated by random processes. For any Gaussian process, it is possible to tame randomness without anticipating the future. Think of the quadrillions of Eustaces floating about, all encountering continuous changes in pH, salinity and temperature. Some will end up in conformations that mediate the disruptive effects of these Gaussian fluctuations. Such conformations will have lower overall volatility, less positive entropy, and, consequently, higher alpha.

Unfortunately for Eustace, all randomness is not Gaussian. Many random processes have a Poisson component as well. Unlike continuous Gaussian processes, disruptive Poisson processes exhibit completely unpredictable jump discontinuities. You cannot draw them without picking up your pencil.

Against Poisson events a non-anticipating strategy, based on continuous adjustment, is impossible. Accordingly they make trouble for all Eustaces, even human beings. Natural Poisson events, like tornadoes and earthquakes, cost thousands of lives. Financial Poisson events cost billions of dollars. The notorious hedge fund Long-Term Capital Management collapsed because of a Poisson event in August 1998, when the Russian government announced that it intended to default on its sovereign debt. Bonds that were trading around 40 sank within minutes to single digits. LTCM’s board members, ironically, included Robert Merton and Myron Scholes, the masters of financial Gaussian randomness. Yet even they were defeated by Poisson.

All hope is not lost, however, since any Poisson event worth its salt affects its surroundings by generating disturbances before it occurs. Eustaces configured to take these hints will have a selective advantage. Consider a moderately complex Eustace — a wildebeest, say. For wildebeests, lions are very nasty Poisson events; there are no half-lions or quarter-lions. But lions give off a musky stink and sometimes rustle in the grass before they pounce, and wildebeests that take flight on these signals tend to do better in the alpha casino than wildebeests that don’t.

Even the simplest organisms develop anti-Poisson strategies. For example, pH levels and salinity are mediated by buffers while capabilities like chemotaxis are a response to Poisson dynamics.

A successful Eustace must mediate two different aspects of randomness: Gaussian and Poisson. Gaussian randomness continuously generates events while Poisson randomness intermittently generates events. On the one hand, Gaussian strategies can be adjusted constantly; on the other, a response to a Poisson event must be based on thresholds for signals. Neither of these configurations is fixed. Eustace is a collection of coupled processes. So in addition to external events, some processes may be coupled to other internal processes that lead to configuration changes.

We will call this choreographed ensemble of coupled processes an alpha model. Within the context of our model, we can see a path to the tools of information theory where the numerator for alpha represents stored information and new information, and the denominator represents error and noise. The nature of this path will be the subject of the next installment.

Part 1
Part 2

We’ve established that thermodynamics is based on two fundamental empirical laws: the first law (conservation of energy) and the second law (the entropy law). Any systematic scheme for the description of a physical process (equilibrium or non-equilibrium, discrete or continuous) must also be built upon these two laws. Here we employ a simplified but instructive model of probability that captures our reasoning without overwhelming us with details.

Eustace, our thermodynamic system, hops off the turnip truck with $100 and walks into a casino. The simplest and cheapest games are played downstairs. The complexity and stakes of the games increase with each floor but in order to play, a guest must have the minimum ante.

The proprietor leads Eustace to a small table in the basement and offers him the following proposition. He flips a coin. For every heads, Eustace wins a dollar. For every tails, Eustace loses a dollar. If Eustace accumulates $200, he gets to go upstairs and play a more sophisticated game, like blackjack. If he goes broke he’s back out in the street.

How do we book his chances? Depends on the coin, of course. If it’s fair, then the probability of winning a single trial, p, is .5. And the probability of winning the $100, P, also turns out to be .5, or 50%. Which is just what you’d expect.

But in Las Vegas the coins aren’t usually fair. Suppose the probability of heads is .495, or .49, or .47? What then? James Bernoulli, of the Flying Bernoulli Brothers (and fathers and sons), solved this problem, in the general case, more than three hundred years ago, and his result might save you money.

One round
0.5000
0.4950
0.4900
0.4700

Chance to win $100
0.5000
0.1191
0.0179
0.000006

Average # rounds
10,000
7,616
4,820
1,667

Unreal. A lousy half a percent bias reduces your chances of winning by a factor of 4. And if the bias is 3%, as it is in many real bets in Vegas, such as black or red on the roulette wheel, you may as well just hand the croupier your money. There is a famous Las Vegas story of a British earl who walked into a casino with half a million dollars, changed it for chips, went to the roulette wheel, bet it all on black, won, and cashed out, never to be seen in town again. This apocryphal earl had an excellent intuitive grasp of probability. He was approximately 80,000 times as likely to win half a million that way as he would have been by betting, say, $5,000 at a time.

Bernoulli trials, the mathematical abstraction of coin tossing, are one of the simplest yet most important random processes in probability. Such a sequence is an indefinitely repeatable series of events each with the same probability (p). More formally, it satisfies the following conditions:

• Each trial has two possible outcomes, generically called success and failure.
• The trials are independent. The outcome of one trial does not influence the outcome of the next.
• On each trial, the probability of success is p and the probability of failure is 1 – p.

Now, what this has to do with α theory is, in a word, everything: Eustace’s thermodynamic state changes can be modeled as a series of Bernoulli trials. Instead of tracking Eustace’s monetary wealth, we’ll track his alpha wealth. And instead of following him through increasingly luxurious levels of the casino, we’ll follow him through increasing levels of complexity, stability and chemical kinetics.

Inside Eustace molecules whiz about. Occasionally there is a transforming collision. We know that for each such collision there are thermodynamic consequences that allow us to calculate alpha. When the alpha of a system increases, its complexity and stability also increase. The probability of success, p, is the chance that a given reaction occurs.

Each successful reaction may create products that have the ability to enable other reactions, in a positive feedback loop, because complex molecules have more ways to interact chemically than simple ones. It takes alpha to make alpha, just as it takes money to make money.

At each floor of the casino, the game begins anew but with greater wealth and a different p. Enzymes, for example, which catalyze reactions, often by many orders of magnitude, can be thought of simply as extreme Bernoulli biases, or increases in p.

If you’ve ever wondered how life sprang from the primordial soup, well, this is how. Remember that Eustace is any arbitrary volume of space through which energy can flow. Untold numbers of Eustaces begin in the basement — an elite few eventually reach the penthouse suite.

Richard Dawkins, in The Blind Watchmaker, describes the process well, if a bit circuitously, since he spares the math. Tiny changes in p produce very large changes in ultimate outcomes, provided you engage in enough trials. And we are talking about a whole lot of trials here. Imagine trillions upon trillions of Eustaces, each hosting trillions of Bernoulli trials, and suddenly the emergence of complexity seems a lot less mysterious. You don’t have to be anywhere near as lucky as you think. Of course simplicity can emerge from complexity too. No matter how high you rise in Casino Alpha, you can always still lose the game.

Alpha theory asserts that the choreographed arrangements we observe today in living systems are a consequence of myriad telescoping layers of alphatropic interactions; that the difference between such systems and elementary Eustaces is merely a matter of degree. Chemists have understood this for a long time. Two hundred years ago they believed that compounds such as sugar, urea, starch, and wax required a mysterious “vital force” to create them. Their very terminology reflected this. Organic, as distinct from inorganic, chemistry was the study of compounds possessing this vital force. In 1828 Friedrich Wohler converted ammonia and cyanate into urea simply by heating the reactants in the absence of oxygen:

NH4 + OCN –> CO(NH2)2

Urea had always come from living organisms, it was presumed to contain the vital force, and yet its precursors proved to be inorganic. Some skeptics claimed that a trace of vital force from Wohler’s hands must have contaminated the reaction, but most scientists recognized the possibility of synthesizing organic compounds from simpler inorganic precursors. More complicated syntheses were carried out and vitalism was eventually discarded.

More recently, scientists grappled with how such reactions that sometimes require extreme conditions can take place in a cell. In 1961, Peter Mitchell proposed that the synthesis of ATP occurred due to a coupling of the chemical reaction with a proton gradient across a membrane. This hypothesis was quickly verified by experiment, and he received a Nobel prize for his work.

I claimed in Part 2 that changes in α can be measured in theory. Thanks to chemical kinetics and probability, they can be pretty well approximated in practice too. Soon, very soon, we will come to assessing the α consequences of actual systems, and these tools will prove their mettle.

One more bit of preamble, in which it will be shown that all randomness is not equally random, and we will begin to infringe philosophy’s sacred turf.

Tomorrow. Did I say tomorrow? I meant the last syllable of recorded time.

Now where were we? Oh yes: nowhere. Philosophy to date has yielded no explanations, no predictions, no tools unless we classify logic generously, and very little practical advice, much of it bad. And then from “cogito ergo sum,” or “existence exists,” philosophers expect to explain the world, or at least a good chunk of it. Tautologies unpack only so far. No matter how much you cram into a suitcase, you cannot expect to fill a universe with its contents.

I was a little unfair to the Greeks in Part 1. They didn’t have 300 years of dazzling scientific advance to build on. What they had was nothing at all, and as Eddie Thomas pointed out in the comments, you have to start somewhere. But 2500 years later, do we have to start from nothing all over again? In what follows I will take for granted that the external world exists, that we are capable of knowing it, and doubtless many other truths of metaphysics and epistemology that everyone knows but philosophers still hotly dispute. If you want to argue that stuff, the comments are still raging on Part 1.

I propose to begin with the First and Second Laws of thermodynamics. You can follow the links for some helpful refreshers, but in brief, the First Law states that energy is always conserved. It is neither created nor destroyed, merely transferred. And since we know, from relativistic physics, that matter is merely energy in another form, we conclude that everything that ever happens is an energy transfer.

This profound fact about the universe has gone almost entirely unnoticed by philosophers, whether from ignorance or indifference I cannot say. But it leads almost immediately to two other profound facts. First, all events are commensurable at some level. They are all instances of the same thing. Second, all events are measurable, at least in theory. We need only to be able to measure each thermodynamic consequence, and add them all up.

Now let’s set up a little thermodynamic system. Call it Eustace. Eustace need not be biological, or at all fancy; it is best to think of him as just a cube of space. Eustace would be pretty dull without a few things going on, so to liven up matters we will assume that at least something in the way of atomic state change is going on. Particles will dart in and out of our little cube of space.

To describe Eustace, we have recourse to the Second Law. As ordinarily formulated, it states that energy, if unimpeded, always tends to disperse. Frying pans cool when you take them off the stove. Water ripples outward and fades to nothing when you throw a pebble in a still lake. Iron rusts. Perpetual motion machines run down. Rocks don’t roll uphill.

Vast quantities of ink have been spilled in attempts to explain entropy, but really it is nothing more than the measure of this tendency of energy to disperse.

The Second Law is, fortunately, only a tendency. Energy disperses if unimpeded. But it is often impeded, which makes possible life, machines, and anything that does work, in the technical as well as the ordinary sense of the word. The lack of activation energy impedes the Second Law: some external force must push a rock poised atop a cliff, or take the frying pan off the fire. Covalent bond energy impedes the Second Law as well, which is why solid objects hang together. The Second Law has been formulated mathematically in several ways. The most useful for describing Eustace is the Gibbs-Boltzmann equation for free energy, which states:

ΔG = ΔH – TΔS

This is one of the most important equations in the history of science; it has been shown to hold in every context that we know of. The triangles, deltas, represent change. Gibbs-Boltzmann compares two states of a thermodynamic system — Eustace in our case, but it could be anything. As for the terms: G, or free energy, is simply the energy available to do work. The earth, for example, receives new free energy constantly in the form of sunlight. Free energy is the sine qua non; it is why I can write this and you can read it. It does not, unfortunately, necessarily become work, as no one knows better than I. Let alone useful work: this depends on how it is directed. I do work when I paint your car and work when I scratch it.

H is enthalpy, the total heat content of a system. We are interested here in changes (Δ), and since we know from the First Law that energy is neither created nor destroyed, that nothing is for free, any increase in enthalpy has to come from outside the system. T is temperature, and S is entropy, which can be either positive or negative. Negative entropy is, again, good; it leads to more free energy by subtracting a negative from a negative. Positive entropy is what you lose, and one of the consequences of the Second Law is that you always lose something.

To return to Eustace, we know from the First Law, in the terms of the equation, that ΔG >= 0. We will also assign Eustace a constant temperature, which isn’t strictly necessary but simplifies the math a bit. So we have:

ΔH – TΔS >= 0

We are dealing here with sums of discrete quantities here. Not one big thing, but many tiny things. Various particles are darting around inside Eustace, each with its own thermodynamic consequences. Hess’s Law states that we can add these up in any order and the result will always be the same. So we segregate the entropic processes into the positive and the negative:

ΣH – TΣS negative – TΣS positive >= 0

From here it’s just a little algebra. We take the third term, the sum of the positive entropies, add it to both sides, and then divide both sides by that same term, yielding:

α = (ΣH – TΣS negative) / TΣS positive >= 1

And there we have it. Alpha (α) is just an arbitrary term that we assign to the result, like c for the speed of light. The term TΣS negative (the sum of the negative entropy) is always negative, so the higher the negative entropy, the larger the numerator. And alpha is always greater than or equal to 1, as you would expect. One is the alpha number for a system that dissipates every last bit of its enthalpy, retaining no free energy at all.

Alpha turns out to have several interesting properties. First, it is dimensionless. The numerator and denominator are both expressed in units of energy, which divide out. It is a number, nothing more. Second, it is calculable, at least in principle. Third, it is perfectly general. Alpha applies to any two states of any system. Fourth, it is complete. Alpha accounts for everything that has happened inside Eustace between the two states that we’re interested in.

Which leaves the question of what α is, exactly. It can be thought of as the rate at which the free energy in a system is directed toward coherence, rather than dissipation. It is the measure of the stability of a system. And this number, remarkably, will clear up any number of dilemmas that philosophers have been unable to resolve. Not to get too far ahead of ourselves here, but I intend, eventually, to establish that the larger Eustace’s α number is, the better.

Next (I do not say tomorrow): From physics to ethics in one moderately difficult step.

Update: Edited for clarity. So if you still don’t understand it, imagine what it was like before.