Dec 072004

Although alpha itself is simple enough at the molecular level, the derivation is complicated, its exposition has been spaced out over several posts and, alas, several months, and a summary is in order. Besides, the girlfriend wants one. Now 100% formula-free!

In Part 1: Starting From Zero
The history of philosophy, ethics in particular, was reviewed and found wanting. It continues to stink of vitalism and anthropocentrism, despite the fact that the idea of a “vital force” was thoroughly discredited by the 1850s. No ethics to date has managed to improve on moral intuition, or explain it either.

What fun is a game with no rules? There must be some common structure to all living systems, not just human beings, and based on its track record, it is science that will likely discover it.

In Part 2: Rules — The Laws of Thermodynamics
We sought rules that are precise and objective without indulging dogmatism. The laws of thermodynamics are the most general we know. They are independent of any hypothesis concerning the microscopic nature of matter, and they appear to hold everywhere, even in black holes. (Stephen Hawking lost a bet on this.) Thus they seemed a good place to start. We postulated a cube floating through space and called it Eustace, in an ill-advised fit of whimsy. A little algebraic manipulation of the Gibbs-Boltzmann formulation of the Second Law produced a strange number we called alpha, which turns out to be the measure of sustainability for any Eustace, living or dead, on Earth or in a galaxy far, far away.

In Part 3: Scoring — The Alpha Casino
We laid out a scoring system for Eustace built entirely on mathematics using alpha, a dimensionless, measurable quantity. Alpha measures the consequences of energy flux. All is number. Along the way we explained, via Bernoulli trials, how complexity emerges from the ooze. The dramatic effects of probability biases of a percent or less are dwarfed by the even more dramatic biases afforded by catalysts and enzymes that often operate in the 10E8 to 10E20 range.

In Part 4: Challenges — Gaussian and Poisson Randomness
We introduced two general (but not exhaustive) classes of random processes. Gaussian (continuous) randomness can be dealt with by a non-anticipating strategy of continuous adjustment. Relatively primitive devices like thermostats manage this quite nicely. Poisson (discontinuous) randomness is a fiercer beast. It can, at best, only be estimated via thresholds. Every Eustace, to sustain itself, must constantly reconfigure in light of the available information, or filtration. We introduced the term alpha model to describe this process.

In Part 5: Strategy — Strong and Weak Solutions
Increasingly complex organisms have evolved autonomous systems that mediate blood pressure and pH while developing threshold-based systems that effectively adapt filtrations to mediate punctuated processes like, say, predators. We introduced strong and weak solutions and explained the role of each. Weak solutions do not offer specific actionable paths but they do cull our possible choices. Strong solutions are actionable paths but a strong solution that is not adapted to the available filtration will likely be sub-optimal. Successful strong solutions can cut both ways. Paths that served us well in the past, if not continuously adapted, can grow confining. An extreme example, in human terms, is dogmatism. Alpha models must adapt to changing filtrations. Each generation must question the beliefs, traditions, and fashions of the generations that preceded it.

In Part 6: The Meaning of Life
We finally arrived at the universal maximization function. We introduced the concept of alpha*, or estimated alpha, and epsilon, the difference between estimated and actual alpha. Behavior and ethics are defined by alpha* and alpha, respectively. All living things maximize alpha*, and all living things succeed insofar as alpha* approximates alpha. From here we abstract the three characteristics of all living things. They can generate alpha (alphatropic). They can recognize and respond to alpha (alphaphilic). And they can calibrate responses to alpha to minimize epsilon (alphametric).

That’s it. An ethics, built up from thermodynamics and mathematics, in 700 words. The entire derivation from premise to conclusion was presented. Can anyone find fault with the sums?

(Update: Jesus von Einstein comments.)

Dec 042004

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.

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 – αc]@t | F@t-1)

E is expected value. α is alpha, the equation for which I gave in Part 2. αc, or alpha critical, is a direct analogue to wealthc 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.