Re: probability and apologetics

glenn r morton (Glenn.Morton@oryx.com)
Wed, 6 Sep 95 08:39:25 CDT

Abstract: I show that Brian Harper's objection to the fall of the
probability argument is based upon ignoring the CONTAINED shorter
sequences in the phase spaces of the larger ones. These contained
sequences can be cut out of the longer sequences by random cuts
with a probability of around 1/10000 to cut it in the correct
place.

Brian Harper wrote:

"Not only could one read falacy and understand that fallacy was
intended, one could do the same for all of the following:

falllacy, faalacy, falicy, faallaaccy, falllaci etc. etc.

The problem then is the combination of English phrases with an
intelligent interpretor is probably muchmore flexible in
retaining function (meaning) than in a protein sequence."<<

I am not sure that I could do with an English sentence what Terry
said was done with the Lambda receptor, namely take one sentence
of 100 letters long, and mutate it in 10^55 ways and still retain
meaning. The first sentence above written as "Hot only could une
bead falacy and kndervtand tzar fallacy yas intended, one could
do the same for all the following." That is only 8 mutations and
meaning is almost gone! Proteins have lots of locations in which
almost any amino acid can go without hurting its meaning.
English is not quite so flexible.

Brian Wrote :
>>Another point though is that when you start to consider other
sequences that convey the same meaning, these sequences are for
the most part all of different length chaning the associated
probabilities. For example, there are several different ways of
saying the same thing. The total number of sequences of the same
length is given in [brackets] following each phrase.

a) if pick nose get warts [10^31]

[...snip]

i) When a digit is inserted into a nostril the finger produces
calloused bumps [10^107]

My point hwere is that your adding up all the different ways of
producing a particular meaning is not really fair."<<
*****endquote*****

First, I am not merely "adding up all the different ways". You
have not understood what I am saying in my argument. This is
evident from your later statement,

>>As noted above, Yocky found that there were 10^93 functional
sequences of length 110. According to what you wrote above there
are 10 known sequence lengths for cytochrome c. Let's suppose
there are also 10^93 functional sequences for each of these
lengths. This seems pretty generous to me in view of your
suggestion of trillions above, 10^93 is literally trillions of
trillions ;-). But we note that we have only increased the
number
of functional sequences by a factor of 10, now we have about
10^94.<<<

Herein lies your misunderstanding. I have, by this method, not
merely increased the chances by a factor of 10. Let me diagram
this for you. Consider a 112 length sequence and a 111 length
sequence. The phase space of the 112 length sequence contains
several examples of the 111 length sequence in it. The 112
length
sequence can be made by adding one amino acid to either end.


[111]* or *[111]

where [111] is the 111 length sequence and * is
the additional amino acid. Since any of 20 amino acids can go
into this * position, there are 20 +20=40 copies of any given 111
sequence in the phase space of the 112 sequence. By merely cutting
off one end, I have the increased the probability not by 10 but
by 40 to find a [111].

Consider other lengths factor increase is in {}.

[110]** + *[110]* + **[110] = {3 x 2^20=3145728

[109]*** + *[109]** + **[109]* + ***[109] {4 x 3^20=13.9 billion}

[108]****+*[108]***+**[108]**+***[108]*+****[108] {5 trillion}

etc. etc.

If each length has 10^93 functional permutations, then there are
10^12 x 10^93 = 10^105 functional [108] in the phase space of the
[112]. These [108] can be obtained by merely cutting the [112].
To cut it in the proper place is (1/112)^2=1/12544.

In support of the concept that this type of cut is to be expected
I will quote from a well known creationist. He says,

"But, according to the laws we have just been studying,
reaction time in reversible reactions will also increase still
more the possibility of degradation (randomness) of already
synthesized
molecules, that is, if their entropy is lower than that of the
starting materials. It is so easy to forget that the possibility
of decomposition in reversible reactions increases with time just
as the chance of synthetic processes does." A.E. Wilder-Smith,
Man's Origin, Man's Destiny, p. 67.

Brian, you are not dealing with the CONTAINED functional sequences.
This is a BIG hole in all probability calculations. Assuming your
10^93 usable functions for each of the sequences from 111 down to
103 in length, then the phase space of the [112] sequence has
40 x 10^93 [111]'s + 3,145,728 x 10^93 [110]'s + 13,900,000,000 x
10^93 [109]'s + 5,000,000,000,000 x 10^93 [108]'s.

The largest contributor to that sum is the last term. And there
can not be 10^93 functional sequences in short sequences which
don't have 10^93 permutations, but subject to that limitation,
there are lots of functional permutations CONTAINED in a longer
sequence.

We are not dealing with the independent production of sequences of
103,104,105... but with the independent production of 112's and
the volume of contained 103's, 104's 105's.... This is a very
different problem than what is normally presented.

Brian wrote:
>>This seems to me to be just wild speculation. Perhaps a
possible length of a protein that could perform some nontrivial
function? Is it even remotely conceivable that something as
simple as leu-ser could perform the function of cytochrome c?<<

I was using the ser-leu as an illustration of the mathematics of
the phase spaces of contained sequences. I am NOT making the
claim that ser-leu could perform that function. All I wanted to
show was that a short sequence has LOTS of copies in a longer
sequence and this I successfully showed.

If my memory does not fail me, oxytocin is only 8 residuals long.
I bet you could find a longer sequence which would perform that
function, but you might have to search a long time.

glenn