Probability of intelligent design

Draft 4

How might we calculate the probability that a very primitive organism occurs randomly? Herewith is an approach:

Let us grant that any organism is a machine that changes a set of inputs into a set of outputs.

In that case such an organism can be modeled by either a Turing machine or Boolean circuit (it is easy to show that Turing machines require Boolean logic gates).

In that case we can choose some economical numbering scheme for any Turing machine or Boolean circuit. Perhaps we'll use Godel numbering as a bookkeeping measure to keep track of the order of the gate numbers. So we can string a sequence of gate numbers together as one number that represents the organic machine.

Supposing that we are using binary numbers, the probability of any one string occurring randomly (with each digit independent and equiprobable) is 2^-m, where m is the length of the digit string.

Now the probability that a particular machine does not occur is given by the complement 1 - 2^-m. So then the probability that the machine's string does not occur in a string of n digits is given by (1 - 2^-m)ⁿ.

Of course, perhaps the gates are not equiprobable and yet our method only varies probability by string length. However, there must be in that case some primitive components of the gates that can be written as simple digit strings where 0 and 1 are equiprobable (there seems no good reason not to make those digits equiprobable in virtually all cases).

Using an artificially low example, a string of 2^-16 digits has a probability of occurring in a string of 10⁶ digits of 0.999999764, or virtually certain.

But the ratio 2^-16/10⁶ = 1.526 x 10^-11 does not seem unreasonable on the face of it. In fact, one might expect much lower ratios.

Of course by abstracting out all the physical data, we may well be overlooking an important consideration.

Still, once physical factors are taken into account, one would expect this approach to be useful.

An interesting concept: Take the typical information value of a virus code to obtain a string of n bits. Then establish a software program that concocts strings of length n randomly. We grant the program considerable computational power -- perhaps it uses a network of parallel processors -- and determine how many bits per second it can process. Without actually running the program, we can then determine the probability that a particular virus code will emerge randomly in some specific time interval.

(We could notionally add something to each string that allows it to "escape" into the internet. However, only a virus string will continue past the first receiever.)

A possible physical approach: atoms of each element have a probability of combining with atoms of another over some temperature range and depending on density of each in some volume. Compound molecules likewise. These atoms and molecules can be numbered, according to the scheme outlined, and probability of a primitive cell might be worked out.

Of course, we should posit a plausible environment: sufficient heat and a good mix of chemicals in a small enough volume over a large enough time. In principle, one should be able to test whether the probability is acceptable or not for life to emerge from an inorganic stew.

I realize that probabilities have been used to try to assess such a happenstance. And complexity theory has been developed in large part to address the issue of emergent order (negative entropy). In other words, emergent order implies that in some cases conditional probabilities are to be used. However, when a sample size is large enough, we can often ignore conditional probabilities and treat events as independent, as the central limit theorem tends to show.

Emergent order implies that conditional probabilities become predominant at the level of pattern recognition (emergence). However, before that level, the component events can usually be treated independently, if not as equiprobable.

Some numbers
Cray's Red Storm supercomputer has exceeded the 1 terabyte per second mark and Cray talks of a bandwidth capacity of 100 terabytes per second.

If we guess that a string of code that not only self-replicates but self-defensively morphs must have a minimum of 256 bits and put to work a 100 terabyte-per-second processor spitting out binary strings of 256 digits, we obtain:

10¹⁴(2³) = 8 x 10¹⁴ bits per second versus 2²⁵⁶ = 1.16 x 10⁷⁷.

The probability that the specific string will be generated randomly corresponds to an average time interval between hits of 1.45 x 10⁶⁶ seconds, or 4.59 x 10⁵⁹ years, with the age of the cosmos being on the order of 10¹⁰ years.

How many strings of length 256 would replicate and morph? It's hard to believe the number would exceed 10⁶ -- because various substrings follow specific permutations in all cases -- and the difference in probability is negligible.

What is design?
But, when we detect a computer virus, why do we infer design? Because we know that such code IS designed non-randomly. We can say that in 99.999etc. percent of cases investigation reveals a human agent. So we have a frequency or assumed frequency for a nonrandom cause for comparison.

Similarly, we may compare a digit string of length n to "common" strings of that length. For example, if we see the first nine digits of pi"s decimal extension, we compare the randomness probability of 10^-9 with the fact that that sequence is associated with a set of human-discovered algorithms. We can guess that the number of practical algorithms for producing nine-digit sequences is low by comparison with 10⁹. (By practical, we mean an algorithm that is used often in math, science or engineering.)

Now when it comes to an organism at stage 0 of evolution, we may find an amazingly low probability of random occurrence. But we should not ask WHY SHOULD such an event have occurred but rather WHY NOT? If a grammatical (functioning) logic gate string is one of a set of equiprobable strings, then, absent further information, there is no reason to deny that the string occurred randomly. On the other hand, if we ask, "what is the chance that such an event WILL happen," the probability tells us not to hold our breath waiting.

Now modeling a stage 0 organism as a machine represented with a blueprint of logic gates, we may ask, when is a machine designed rather than a consequence of random forces? A machine is determined to have been designed if a human-devised algorithm for its construction can be found and if experience shows that the system rarely if ever is seen naturally. Suppose we camouflage the machine such that immediate sensory clues are of little importance. So we examine the machine's operation and draw up a description, using appropriate symbolism, to see whether the description matches some subset of known human-derived algorithms or blueprints. If so, we infer design based on the higher frequency of designed machines to randomly generated machines.

So then, in order to infer design of a stage 0 organism, we would need to have available at least one human-discovered formula. But if we had that, it would radically alter the entire debate.

So how would a higher power design a stage 0 organism? No answer is given since, perhaps on the assumption that the human mind could not fathom such a design. That may be true. However, one cannot show a strong probability of design without a reference base, and there are no divine blueprints that can be examined for comparison.

It should be noted that if it were argued that lifeforms had emerged spontaneously on several occasions at a rate higher than what would be expected randomly, then we would have a basis for believing that a non-random force was at work within some confidence interval. However, one emergence gives little basis for drawing conclusions.

That said, one may agree that the apparent startlingly low probability associated with life's origin may well stir much inner reflection.