The issue of probabilities and evolution of intelligence
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First let me clarify my motives. I believe in the realm of evolution. I also
believe that what one believes in should be critisized by one self. Some of
you may think that critisizing evolution will have as a concequence that
souls are lost to the creationist side, and therefore should be avoided.
While this is sad, I strongly believe that the quest for knowledge of our
world weighs stronger than confusing and losing some souls to fundamentalist
beliefs such as creationism. By critisizing one's own beliefs, one opens up
the possiblity to refine one's knowledge, that would not be possible in a
defensive view of one's beliefs. Additionally, and this is a strong point,
by openly declare that one critsizes one's view of the world, one distances
oneself from those who do not critisize their own view, such as
creationists. By openly declaring a critical onlook on one's own beliefs, my
view is that such an onlook will have more crediblity than onlooks which
lack self critisism, all in the eyes of thinking bystanders (the one's we
are concerned with, anyway). Therefore we should not be afraid of exposing
weaknesses in evolutionary theories.
>From the headline, you will notice that this post will address the topic of
probability, and the topic of evolution of intelligence. Therefore I will
here define my view of probabilty, as well as intelligence.
In previous posts, when the issue of probablity has been addressed, I have
concluded that the word probabilty implies the chance of some *future* event
to happen. Now what if an event already has happened, can we talk of
probablity of something other than equal to one, then? Probably not.
Therefore I define a new word, pre-probability. Pre-probability is defined
as follows:
"Given all possible states that possibly *could* happen with each a certain
probability *before* it happened, what was the probability of this state we
have arrived at, *before* we arrived at this state."
I will give an example to clarify matters. Suppose a dice is to be rolled.
Before the dice is rolled, the probability of getting a one is 1/6. After
the dice is rolled, and a one appears, then the probablity is eqaual to one
of that we got a one, but the pre-probability is 1/6, given that we would
not ask a simlilar question for other results of the roll, eg if we got a
two, then we would not ask what is the chance of getting a two, but would
still ask, what was the pre-probability of that we got a one, which still is
1/6, while the probability of getting a one is zero, since it did not occur.
Now let me define intelligence. I will make it really simple, and simply
pose this condition:
If one can *possibly* ask one self the following question, then one is
concidered intelligent, otherwise, one is not concidered intelligent:
"What is the pre-probability that this question will be posed?"
The core idea behind this question is that only intelligent beings can ask
themself this question, and thus also at the same time wonder about their
origins.
Now, as we have defined pre-probability and intelligence, let us move
further and see if we can answer the question posed previously.
First, when one quickly looks at the concept of evolution, one is hit by its
shear elegance and simplicty. At its fundamentals, evolution is simply the
following: "Successful tests of survivability gets inherited further down in
future species, and therfore all species that exist in any time has a
history of ancestors that all have passed the test of fitness of past
conditions, and therefore have inherited information that is beneficiary to
survival", or simply "the survival of the fitest". Further, the historic
records of archeology more or less proves evolution as a concept. Even
further, noticed gradual buildup of resistance of insects to pesticides, or
noticed buildup of resistance of disease causing agents to pharmaceuticals
more or less proves evolution in present time.
However, when one looks at the details of evolution, many (even well known
evolutionists) have been amazed at the improbability of evolution occuring
as fast as it actually does. To look at the details requires atleast a basic
understanding of genetics.
I will here give a basic introduction to genetics.
The reason a species (such as humans) grow the way they do from egg to grown
up, is because there exists information on how to build a species. This
information is chemicly stored in DNA, that acts as a memory, that is read
and written to by chemical means. The DNA is composed of a series of
base-pairs, and each base pair can hold one of four possibly states. For
example the human DNA is composed of approximately 3*10^9 base pairs, of
which approximately 150*10^6 base pairs are conciderd relevant to the build
up and functioning of a human. How much information does this represent?
Well, 150*10^6 base pairs means 4^(150*10^6) possibly combinations, which is
10^(90*10^6) or 2^(300*10^6). Therefore to store the entire relevant DNA in
a computer memory would require 35,8 Mbyte of memeory (each byte is 8 bits,
and each Megabyte is 1024*1024 bytes). This just for you to get a feel of
the information content.
Now to the core of analyzing pre-probabilites of intelligent species
evolving.
The basic function of the DNA is to provide information on how to build
protiens. Proteins are in turn composed of a number of amino acids. An amino
acid is one of twenty possible. Each amino acid requires three base pairs
for coding. A typical protein requires about 1000 base pairs for coding.
Now, for intellgient species to evolve (so that they can possibly pose the
question above), one requires the relevant proteins for a brain, and for
proteins for receiving signals from the brain such as nerve cells attached
to muscles. This system requires several proteins to function. For
simpliciy, let us say that two proteins are required, one for the brain and
one for the receptors at the muscles. Now each protein cannot develop on its
own, since that will not give any evlutionary advantage, both has to be
available at the same time for a species to take advantage of this new
function. Thus 1000*2 base pairs has to be developed "in an instant".
This development of DNA "in an instant" we see evidence in "punctuated
equibilums" in fossil records of species. A species develops in discrete
steps, it seems, like a stair case going upwards. The punctuated equilibria
can be explained by a combintaions of proteins being invented by evolution
"in an instant", and once it is available, it gives instant selective
advantage to the species.
Now what is the probability of "in an instant" development of proteins.
Well, let as say, from above, 2000 base pairs need to be invented "in an
instant". These 2000 base pairs has a combinational space of 4^2000 or
10^1204. Now build up of DNA sequences, such as these 2000 base pairs occur
at random, therfore, there are 10^1204 paths of evolution for a build up of
this sequence, concidering one base pair at a time in each generation
multiplied by the number of available population. Now it does not matter if
one or many base pairs are added at each generation; the number of
combintations remain the same regardless. Each combination requires a test
to see if the new sequence is functioning advantageoulsy to a species.
Now let us define a "test". A test is an actual organisms with a specific
DNA that is being tested for survival/extinction.
Now the issue here, is how many test are available, for a species. Let us
assume we have an evolution of a non-brain species to a brain species. Let
assume that this non-brain species is available 1*10^9 years ago. Therefore
evolution has one billion years available for development. Let as calculate
the number of available tests of the new gene sequence. Assume we have a
generation time of 1/10000th of a year (52 minutes, compare to 1 hour, the
typical cell divistion rate of ecoli), let us assume the average population
is 10^39 (this is a gross over estimate, the earth's volume, for example is
10^39 cubic micrometers; typical bacteria range in sizes from 1 micrometer
to 10 micrometers).
>From the assumptions above we have that there have been availble
10^39 * 10^9 * 10000 tests = 10^52 tests.
Now compare this number to the number of tests that we needed: 10^1204. The
pre-probability that intelligent life should evolve is thus 10^52/10^1204 =
10^(-1152).
This calculation means to me that evolution is a big mystery to me. Yet it
seems that punctuated equilibrium developments occur in much less time space
than one billion years. Furhter, mutations occur also as damaging, infact
the vast majority of mutations are either damaging or have no impact on
evolution; this furhter makes beneficiary mutations as calculated above less
likely. Further we only concidered two dependent proteins. What if more
proteins are interdependent?
Further, evolution occurs in steps, in quantum units. What this smallest
quantum is in terms of base pairs, is very important to the calculation. I
assumed 2000 base pairs. If it is much less, then a completely different
result will appear. A typical protein needs base pair code in the range of
300 to 3000 base pairs. Hemoglobin, for example is coded with 438 base
pairs. Now in the calculation above I assumed only one variant of a working
protein, in reality there is a whole class of proteins having the same
function. When taking this into account, the number of combinations are
less. For example if there are an allowance of 100 base pairs (allowing for
4^100 variations) that can differ, then the corresponding combinations for a
1000 base pair protein is 4^900. Still, even taking this variation into
account will still produce a very small pre-probability for intelligent
life.
Now one factor that is interesting to include is the estimated number of
planets in the universe that has acceptable life conditions. Let us say
there are 100*10^9 galaxies, and each galaxy has 10^12 stars, assume each
star has a planet with acceptable life conditions; then we arrive at 10^11 *
10^12 = 10^23 planets. Therfore the pre-probability for life to evolve
anywhere in the universe is 10^(-1152)*10^23 = 10^(-1129).
Finially, let us assume that the universe as experience a sequence of big
bangs for an infinite time. Then, with this assumption, evolution of
intelligent life becomes likely.
Still, for now, evolution is a big mystery to me.
