# virus: Evolution (was Sexuality )

ken sartor (*sartor@visidyne.com*)

*Wed, 18 Sep 1996 13:16:40 -0500*

At 12:09 AM 9/18/96 -0500, zaimoni@ksu.edu wrote:

*>*

*>*

*>On Tue, 17 Sep 1996, ken sartor wrote:*

*>*

*>> At 09:14 AM 9/17/96 -0500, zaimoni@ksu.edu wrote:*

*>*

*>> >Let me add one of my own:*

*>> > IF random-mutation-based biological evolution is to be mathematically*

*>> >coherent, [as far as I know], one must have either the many-worlds*

*>> >interpretation of quantum mechanics, or a steady-state universe. [Roger*

*>> >Penrose's ideas ARE a steady-state universe.] The currently-inferrable*

*>> >space-time is woefully inadequate, and cannot even account for the*

*>> >Von-Neumann minimal life-form. [1500 bits, one-shot 10^(-450) against]*

*>> >[For reference: the smallest biological virus is larger than a*

*>> >Von-Neumann minimal life-form. The smallest computer virus I have data on*

*>> >DOES go under--by 4 BITS! This isn't really enough to make an impact on*

*>> >the calculations. There is not much difference between 10^(-250) against*

*>> >and 10^(-248) against. Besides, whether a computer virus is*

*>> >self-contained is an interesting question--biological life doesn't have*

*>> >the 'copy codon'!]*

*>> > All of which can be escaped by simply not requiring the mutations to*

*>> >be random. Saying that the mutations are random imposes a mathematical*

*>> >structure which allows numerical calculation. [Note that natural*

*>> >selection doesn't really alter these results. First, because whether*

*>> >pruning occurs immediately or later has no effect here. Second, because*

*>> >I'm talking about getting to the point where one has a sufficiently alive*

*>> >life-form to evolve!]*

*>> *

*>> I don't know how one can reasonably compute the probabilities you*

*>> have stated here. However, seeing that life is here changes *

*>> everything. The probability of life arising in this universe is*

*>> 1. Interesting data would be on seeing how prevalent it*

*>> is in the universe (and how diverse).*

*>*

*>Of course the probability of life arising in this universe is 1. It then*

*>requires more faith [Virian definition] than I have to insist that*

*>originating methods with amazingly low a priori chances of results must be*

*>preferred to originating methods whose a priori chances are NOT*

*>measurable. [The a priori chance IS an experiment!]*

*>*

*>The Von Neumann limit is 1950's material--mathematics, so it's not going*

*>to change fast. In particular, it doesn't really care about HOW the*

*>DNA/RNA/etc. is implemented. 1500 bits means just what it sounds like in*

*>CIS; it selects an event of 1 in 2^1500=(2^10)^150. The latter is bounded*

*>below by (10^3)^150 i.e. 10^450. [Thus the 10^(-450) for one-shot.]*

*>*

*>Note that redundancy reduces the information content. The technical*

*>definition is to take a ground set of states S_i, compute their*

*>probabilities P_i of occuring, and then take -log_2(P_i) to be the*

*>information content of state S_i. [The i must match, and there should*

*>only be a finite number of ground states.] Thus [using ACGT as our ground*

*>set], it will take at least 750 bases i.e. 250 codons to specify a Von*

*>Neumann minimal virus, but it can take more. [Does anyone have recent*

*>enough data on biological virus sizes to contradict this? Exclude*

*>prions--no DNA or RNA, and it's controversial whether they exist. The*

*>smallest instance I recall finding a reference to is ~260 codons.]*

*>*

*>Information, as defined above, is very close to an inverse of entropy, in*

*>quantum-mechanical terms.*

*>*

*> Besides the domain question [to be dealt with below], I*

*>am presuming that:*

*> 1) We are interested in life based on conventional matter.*

*> 2) We are restricted to the apparently-observable universe*

*>[many-worlds violates this trivially, as does infinite-time i.e.*

*>steady-state. That's why I excluded them.]*

*> 3) Such life must contain at least one electron per organism.*

*>Thus, I cannot possibly have more organisms around than electrons [the*

*>latter number IS fuzzy--I used 10^130, above.] [The point is to*

*>deliberately favor success.]*

*> 4) For each candidate, I [Nature] am allowed to replace it at most*

*>only once per second. Note that until a functional candidate occurs*

*>[self-reproducing in a suitable environment], that natural selection*

*>will reject all others equally--we need something that replicates before*

*>any normal evolution kicks in. For conventional-matter life, this seems*

*>extremely fast. [Again, the point is to deliberately favor success.]*

*> 5) We need an estimate for observable space-time, of course. The*

*>big-bang limit is a first guess. Pick your favorite estimate, and convert*

*>to seconds. [The most liberal estimate I've seen is around 20 trillion*

*>[AMERICAN; read as 20*10^12] years, back in the 1950's. This gives*

*>10^70 seconds, to 1 decimal place. Shorter estimates give lesser numbers*

*>of seconds, although not that much shorter; anything below 10^60 seconds*

*>would be blatantly inconsistent with conventional cosmology. *

*> The sample size then is (# of electrons in estimate)*(# of seconds in*

*>estimate). For the numbers I used, this is 10^200. You may recompute*

*>with your own numbers.*

*> We now must decide on a method of generating our sample. [Note that*

*>partial match detection would speed this up a LOT--but the natural*

*>selection is assumed to not be able to distinguish between various total*

*>failures, so it won't notice partial matches. The Von Neumann limit*

*>doesn't presume 100% accurate copying.]*

*> We could, of course, use an exponential model--sampling with*

*>duplication. This gives worse numbers than the one I quoted.*

*> [If our sample size was 10^450, we still would have only 1/e chance*

*>of making it [e=2.718281828....] This is basic AFTER one has understood a*

*>700-level analysis course [i.e., Calc 700]. Since we are short by a*

*>factor of 10^(-250), the number computed is e^(-(10^250)), which is MUCH*

*>smaller than the 10^(-250) I named. It's bounded above by 2^(-(10^250))*

*>i.e. (2^(-10))^(10^249) i.e. (10^-3)^(10^249)--and now I'm looking at*

*>some leading decimal place beyond 10^249 instead of decimal place*

*>250<10^3....]*

*> Sampling without duplication is easier to compute: simply divide*

*>one's sample size by the total sample space. This gives the 10^(-250) I*

*>cited. It is clearly a gross overestimate.*

*> In other words, the numbers I mentioned were highly biased in favor*

*>of the hypothesis I was computing the a priori chances of.*

*>*

*>> Note as a side issue that _random_ mutation may be considered a*

*>> reserved phase. I.e., it is restricted by the laws of chemistry*

*>> and physics and hence not totally random...*

*>*

*>Certainly, one must always state the environment from which one picks a*

*>'random' variable. I actually want more restricting than just 'the laws*

*>of chemistry and physics'--I need something that will let the candidates*

*>survive long enough to do something interesting. [The surface of the sun *

*>is restricted that way, and it's not going to work.] I am assuming that*

*>we are not allowed to change the interpreter to match whatever happened to*

*>come up [For a full-blown cellular organism, we must bootstrap an*

*>interpreter within the coding. For a virus-type organism, the interpreter*

*>is given to us.]*

*>*

*>I'm not assuming a particular representation--I don't really care about*

*>the exact nucleic acid setup, or whether I'm looking AT carbon-based*

*>life. I am presuming that each attempt has some sort of defined*

*>ground-set for the DNA-analog. I am also presuming that, on a macroscopic*

*>scale, that there are no special choices of sequence that show up*

*>unusually often [or unusually rarely] according to various statistical*

*>tests, compared to the self-replicating one we are trying to construct.*

*>[Clearly, once we have our life-form, this assumption is violated.]*

*>*

Hmmmm.... ok these are interesting tricks of math that i am probably

not going to research throughly enough to despute. However, i do not

think that the starting assumptions are reasonable. For instance,

what is the chances in the above formulism that worlds with water

can exist? Is the number time dependent? Does it say anything about

the ratio of various elements to each other (e.g., hydrogen to

helium ratio - relavant because if all we have is electrons or hydrogen,

very little interesting chemistry is going to take place).

When interesting chemistry takes place, random chance is supplanted

by chemistry and physics - some reactions form stable compounds that

can combine further to make even more interesting compounds. Certain

environments tend to foster such chemistry much more than others (i

know, this is obvious, but somewhere in the above formulism there has

to be an accounting of this and i don't think there is).

I guess i am trying to say that if by random you mean all patterns are

equally likely, i agree, life did not arise that way. Certain patterns

are much more likely to arise than others and once formed, to

continue to exist. These patterns are not truely random, rather they

are mightly influnced by the laws of physics and chemistry.

ken

BTW - von Neumann also 'proved' that we are alone in the universe.

Cool proof but never struck me as convincing - perhaps you

have seen it?