Thursday, March 28, 2013

biology and information theory

One sign of a highly technical theory's influence and profundity is the improbable attention it receives in seemingly unrelated if not inappropriate contexts. Information theory certainly qualifies. Unfortunately one of these peripheral contexts is abstract arguments against biology.

The argument based on information theory follows the template of a more popular argument based on the Second Law of the theory of thermodynamics: "Biology cannot increase in orderly complexity because the Second Law states that disorder increases over time." The variant using information theory is "Biology cannot increase in orderly complexity because information theory states that the result of random modifications of an orderly message is nothing more than an unintelligible message. These random modifications are the noise of the corresponding information channel, and the noise reduces its optimal information rate."

However, the intuitive appeal of either argument relies on ignorance of the extraordinary scale of biology's abundant populations and prolonged time periods. Regardless of an event's slim probability, a sufficiently massive number of trials actually implies that it's more likely that the event will happen. In merely 13 die rolls, the probability of never rolling 6 is less than 1 in 10. Perhaps many biological changes are destructive like the metaphors of thermodynamic disorder or noisy information, and the candidates that experience those changes are worse-off. Yet the multitude of candidate organisms throughout epochs can still yield the event of a comparatively rare constructive change, and thereafter the change spreads through reproduction of that singular beneficiary. (Although according to the, y'know, facts, occasionally the constructive events have indeed occurred too rarely to compensate for rapid changes in circumstances—mass extinctions.)

Furthermore, this application of information theory prompts more questions. If it were accurate to analyze biology as an information channel in which all organisms were messages, and all modifications to organisms were noise, then how would the first noise-free organisms originate? Presumably from "The Great Communicator"...but the usual name for theoretical message senders is "Alice". Assuming all the first organisms were perfectly communicated messages from Alice, then later organisms could only have become more noisy or less perfect. Isn't this implied distinction between "message" and "noise" so narrow that it verges on nonsensical? Given all the actual differences between the first organisms and organisms in the present, is it apt for all these differences to qualify as increases in noise, i.e. always relative degradation? Is it accurate to suppose that every grandparent were a more precise expression of Alice's original message than every grandchild? Are the implications of this proposition consistent with human interactions with reality? In other words, is it true in the pragmatic sense?

In contrast, real biology's ambiguity of "message" and "noise" is closer to something else in information theory. Extreme information ambiguity is a defining feature of the unbreakable encryption strategy of a one time pad. The "pad" itself contains a long encryption key that's strongly random: no portion of the key/pad can be calculated from any other portion. Then sequential portions of this key are used to encrypt sequential small portions of a message. In effect, the key from the pad acts like the worst possible kind of communication noise. The key's "noise" affects each small portion of the message and the "noise" is always unpredictably different for each. It's like sending numerous tiny encrypted "micro-messages" and using a separate independent key for each micro-message. This is secrecy by brute-force. Hence the strength of this strategy is also its weakness. The large quantity of random and therefore incompressible key information must itself be exchanged over a sufficiently secure and efficient channel. But if a superior channel meets these requirements then it should communicate the message instead! (The strategy could still be appropriate if the superior channel for the key, e.g. handing over a literal pad in-person in the past, differs from the inferior channel for the secret message, e.g. series of short radio broadcasts in the future.)

Consequently, depending on how closely biological information matches the metaphor of a one time pad, nobody should be surprised by the difficulty of disentangling its "messages" from its "noise". Inquisitive humans are the interceptors of the channel. The recipient of the channel is the organism, and the sender of the channel is the organism's ancestor(s). The biological information has flowed over a staggering number of channels or generations. In doing so, it has absorbed noise coming from an ever-changing key on the one time pad commonly known as the universe.

At the same time, the environment of the organism is ever-changing. This means that the definition of sensible biological information is also ever-changing, since biological information is sensible insofar as it corresponds successfully to an environment—oxygen-breathing organisms aren't sensible in an oxygen-deprived environment. Unlike the phantasmal perfection of first organisms communicated by a non-biological Alice, this concept of environmental sensibility is inescapably relative and limited. Metaphorically speaking, the "message" consists of biological information with environmental sensibility, and the rest is "noise". Due to environmental changes, the same bits of biological information can change from message to noise and back. Correct answers cease to be correct when the questions transform.

The inherent uncertainty of a one time pad forces an ignorant interceptor to admit that any possible message could result in any possible encrypted message. The one time pad causes the sender's input message to diverge into a random output message. In the context of restrictive human communication, the recipient is displeased by receiving any other message than the sender's. But in the context of biology, a descendant organism that receives innovative information could thereby surpass the ancestor in the broad criterion of environmental sensibility, if only by a little. To use an overstretched analogy, this biological case is more like a sender who sent the message "The meeting is at 3:30," and then the message changed along the way to "The meeting is at 3:00"...while the meeting was rescheduled to 3:15 anyway.

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