Re: this is the time to pray

From: Beth (BethStone21_at_hotmail.NOSPICEDHAM.com)
Date: 02/02/05 

Date: Wed, 02 Feb 2005 15:00:14 GMT

Phil wrote:
> You seem to have forgotten that the average sexual creature procreates
> vastly more than once, amongst other things.

Not "forgotten"; Simplification..."isolation of the things of interest", so
to speak...

Admittedly, there is always a danger of "over-simplification"...I myself,
as you've seen, repeatedly caution about how "abstraction" can introduce
problematic issues, where it may start to "over-simplify" a situation...

It's Einstein, isn't it? "As simple as possible, but no simpler"...the
trick is not "overshooting the mark" when trying to make things "simple" or
practicing scientific "isolation of variables of concern"...there is always
the danger in a touch of "abstraction", that you accidentally "cut out" a
"minor detail", that, in fact, isn't "minor" at all (even more complicated
by "chaos"...something can look "minor" but when you're talking
evolutionary scales of time and the massive "unlikeliness" throughout it
all...well, this was, in a sense, what "hid" natural selection from view
until Darwin saw it...the principle is actually self-evident and,
technically, could have possibly be seen at _any_ point in time...but
"natural selection" itself depends on what appears a "minor detail" in a
specific instance - of some finch going to eat food or whatever (in
isolation, this hardly seems a "case" for an entire theory of the origin of
every species on the face of the planet, does it? Because, actually
watching this lone finch trying to get some fodd, it isn't easy to see the
"minor detail" hiding behind it all that "blows up", over massive periods
of time, as an explanation for it all :) - and, hence, making the same kind
of "mistake" again for another few centuries is, of course, a possibility
_every_ "scientist" or "pseudo-scientist" looking at the theory needs to
consider could also be applying to them)...I Hope I've not done so...but
you know different, then, please, let me know the specifics so I can
"correct" the mistake...

If there is a "mistake" here, then I assure you it's an honest one...also,
I did make clear to label this as "my personal theory", not anything from
the "established" memepool...so, I'm not claiming "correctness" to it but
merely "intriguing possibility"...indeed, knowing the "odds" of such
randomly invented "theories" from a complete non-expert like myself,
chances are that it _IS_ wrong...but, well, there is a school of thought
that there is no such thing as a "bad meme" because, even when it's wrong,
it can act as a "cautionary tale" and others refuting it demonstrates the
true facts...there's no harm in speaking it in that context...

> Having two sexes permits
> changes to propagate far quicker than when you only have one sex,
> unless the organism in question is incredibly simple (such as an AIDS
> virus). If you have a litter of 8, then there are on average 4 copies
> of every gene from each parent. Each of the 8 will be given a slighly
> different set of genes to cooperate with, and therefore you'd expect
> several will be in a better situation, genetically, than its parent.
> Your understanding is completely out of whack.

No, sorry...what you've spoken of is NOT "counter" to anything I said at
all...this is simply "additional" that it speeds propogation...it's not
"counter"...we ain't got a "mutual exclusion" situation here at all...the
fact that sexual reproduction also does this, is NOT a "counter" to what
I've stipulated because there is nothing inherently "mutual exclusive" with
the dual purposes of "faster propogation" _AND_ "second line of defence"...

Having more children with different sets of genes, as you mention, does NOT
in any way "counter" what I was talking about...indeed, it "propogates it
faster"..._helps_ it, not stops it...think it over some more...if the verb
is "average" then the final noun is "pre-destined" ahead of time, however
many "copies" you make...for example, using maths as a simple "model" (just
to have something actual to look at, to see how this works :), then it
doesn't matter _how many_ "clones" of the original number you make, the
"average" is always the same...

4 + 4 / 2 = 4

Let's "clone" that a few times:

4 + 4 + 4 + 4 / 4 = 4

Some more?

4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 / 8 = 4

"Population size" is _irrelevent_ to the _PROCESS_ of "averaging" in this
context...if they are all the same "clone" number then their "average" is
going to be the original number, NO MATTER how many of them you
"clone"...that, in a sense, is part and parcel of "averaging" itself and
why calculating an "average" is the way to get yourself a
population-size-neutral "representative" example...

But, yes, there is some "variation" here...BUT does this effect it either?
Actually, if the "odds" are equal for all possibilities, then, "on
average", no, this has _no effect_ on the final result either..."order" and
"chance" can effect the "running average" a little but not monsterously
so...indeed, the "averaging" more and more "irons out" these "outliers",
the greater the population (and, yes, "propogation" :) becomes...

There is, in a sense, an "attraction" towards the "mean average" of the
group..."outliers" are gradually "ironed out" by the "averaging" process
itself and then this "ironed out" version is what's propogated to
successive generations (or, indeed, works the same for "multiple
propogation" exactly the same: They are part of the "genepool" too),
further "ironing it out" even more...

This works, I'm thinking, in much the same way "natural selection" ends up
doing what it's doing...the finch going for the food in one particular
instance doesn't seem hardly like the grounds for the entire "origin of
species"...but it is because we're talking about such vast time
scales...the accumulation of "minor details", so to speak, explode in a
large-scale trend...what I'm thinking is that the _mechanism_ of "sexual
reproduction" working the way it does (half one parent, half the other) has
just such _another_ "minor detail" in it, which equally "explodes" over a
large-scale time scale...that of it being, in a manner of speaking, a
"running averaging" process, if we temporarily look at genes through more
mathematical eyes...

Well, there's one way to test my little theory, eh? Time to fire up
QuickBASIC, methinks:

----------------------------------------------

CONST nLen = 42 ' Chromosome length
CONST nPop = 250 ' Population size

DIM Parent(nPop, nLen)
DIM Child(nPop, nLen)

RANDOMIZE TIMER

CLS

' Juggle up a bunch of random genes for the
' initial population (code commented out
' puts in a "bias" delibrately to test the
' other aspect of the theory)...
'
FOR m = 0 TO nPop

  FOR g = 0 TO nLen

   Parent(m, g) = INT(RND(1) * 15) + 1

   ' IF (INT(RND(1) * 100)) <= 60 THEN
   '
   ' Parent(m, g) = 12
   '
   ' END IF

  NEXT g

NEXT m

DO

   LOCATE 1, 1

   ' Print first 41 members of the population
   '
   FOR m = 0 TO 40

      FOR g = 0 TO nLen

         COLOR Parent(m, g)
         PRINT CHR$(Parent(m, g) + 65);

      NEXT g

      PRINT

   NEXT m

   ' size of next generation (for simplicity)
   ' same size as last generation
   '
   FOR p = 0 TO nPop

      ' Select two "parents" randomly
      '
      ParA = INT(RND(1) * nPop)
      ParB = INT(RND(1) * nPop)

      ' for each "gene"...
      '
      FOR g = 0 TO nLen

         ' ...randomly select one or other of
         ' the "parents"...
         '
         d = INT(RND(1) * 2)

         ' ...and then copy that gene from parent
         ' to child to make up new generation
         '
         IF d = 0 THEN

            Child(p, g) = Parent(ParA, g)

         ELSE

            Child(p, g) = Parent(ParB, g)

         END IF

      NEXT g

   NEXT p

   ' Children become the new parents
   ' for next generation...
   '
   FOR p = 0 TO nPop

      FOR g = 0 TO nLen

         Parent(p, g) = Child(p, g)

      NEXT g

   NEXT p

' Repeat until user hits space
'
LOOP UNTIL INKEY$ = " "

----------------------------------------------

Okay, very, very simple "five minute" program here...it's basically a kind
of "genetic algorithm" _WITHOUT_ "mutation"...which I've left out because
we're only going to look at "sexual reproduction" alone..."mutations" and
"evolution" resulting from that is another topic again...

If you run this program, then every horizontal line across the screen is
the "genes" of one "person" in the population (due to screen limitations,
only the first 41 are actually shown on screen...I'm running in 80x50, if
you're wondering, so 41 lines doesn't go off the bottom of the screen...you
can "tweak" the gene length and amount shown to suit your screen display,
as you like :)...each "generation" overwrites the last one on screen, so it
"animates" before you...

And you'll notice that, every single time you run it, given enough time,
the entire "genepool" ends up with completely _identical_ genes...and the
initial "genepool" is completely random (straight from the random number
generator)...and the _ONLY_ process I am performing on the "genepool" - as
the code shows - is to pick two completely random "parents" (note: "random"
enough that the same parent _CAN_ be chosen more than once, hence this is
also covering your "propogation" point, as parents can have multiple
children in the next "generation"...indeed, umm, a parent can have children
with itself and "gender" is competely ignored...the program may need some
more "modifications" to be even more "realistic", granted ;)...

And, yet, every single time, the "genes" eventually settle with identical
patterns for the entire population...this can take a long time in
"generation" terms to get there, that's why I haven't put a single "delay"
in the program...it'll take long enough with the "genes" flashing by as
fast as possible on your screen...some "genes" take a lot, lot longer than
others to "settle"...but, eventually, they all "settle" with identical
genetic patterns for the entire population: _Exactly as predicted_...

And there is another thing I stipulated, which is what the commened out
code in the initial "genepool filling" loop is about...if you "uncomment"
this code, then what it does is that there's a 60% random chance of any
gene being _FORCED_ to "12" (bright red colour :)...

What's that all about? Ah, well...here's the _VERY_ interesting
thing...it's NOT a "precise science"...it varies and "wobbles"...BUT if we
"bias" the "genepool" to be roughly 60% "bright red" then let it run until
it settles...then - here's a little surprise that might astonish some - if
you count the amount of genes in the "settled" chromosome (they'll all be
the same for the entire population) then it _DOES_ vary and this is NOT a
"precise" thing at all (the "randomness" that entirely rules the process
_CAN_ "knock it off" the ideal value)...then count how many "bright reds"
you have in the "settled" chromosome...sometimes more and sometimes
less...but run it a few times and note that it's typically around 24...and
what's 24 "bright reds" as a percentage of the entire chromosome?

Why, just a fraction under 60%...wait a minute, didn't we force roughly 60%
of it to be "bright red" in the entire "genepool"...and, give or take the
"variances" in this process (for instance, it's not guaranteed to be 60%
"bright red" to begin with, just "on average"...and the "randomness" of the
process _can_ effect the final outcome to be "imprecise"), it is displaying
roughly that much in the final "settled" chromosome? Now, I bet you didn't
expect _THAT_, eh? ;)...

This little program you can run as many times as you like, change the
"population size" or the "gene length" (though, little old QuickBASIC has a
stupid 64KB array size limit...pop it into something else and try a
_massive_ "population size", if you like...I'd guess that the "settling"
would take much longer but, as the "settling" is _PART_ of the process - as
I'm contending - then it should always eventually happen)...play around
with it all...

And you're a programmer and can see that there's no "cheating" going
on...indeed, re-write your own version (just make sure to, of course,
perform the "process" in roughly the same way to be modelling the correct
thing :)...play around with it to your own satisfaction that, in fact, I
_am_ pointing out an actual "trend" here...

In fact, you're a very good mathematician, Phil, aren't you? Well, even
better placed than I to see what's going on, if you look closer at it,
probably...indeed, it surprises me that you didn't "intuitively" see that
what I was talking about _must_ happen from the very "averaging" process
itself (well, I worked it out "intuitively", anyhow...this program is the
first real program I've written to actually _test_ the idea and, happily
enough, the results are broadly as expected they would be from my "theory"
of what should happen :)...anyway, now you've got the program, you can mess
around with it and, indeed, please, try all possible combinations and sizes
and things you can think of...I've yet had not even a single "exception" to
what I predicted with running the program...

Other things can be thrown in..."gender" is missing...also, perhaps you
might want to add some "locality" to the "mating" (in simulation that
parents would actually have to physically meet up...hence, though there
would be the odd instance of a Thai bride and an American groom, there's a
"trend" towards some degree of "locality" in the choice of
"parents")...these will effect things but I'm going to stick my neck out
here (because I just did with the original "theory" and the results of the
program are exactly as predicted...so, perhaps I'm on a "winning streak"
here ;) and say that none of these things will prevent "settling" happening
eventually (may "postpone" it but, well, making the "parent selection"
process more limited I can't see would effect the "settling" phenomenon
because it's coming from the "50 / 50" split process itself, NOT from the
choice of parents at all...parents only define what is "average", but the
choice of parents _doesn't_ effect the fact that the "genepool" does have
this "trend" towards settling on the "average")...

"Mutation" is missing (as is "natural selection": The selection is utterly
random, as far as the PRNG will allow, anyway ;) but, of course,
_delibrately_ so...I'm talking of the "attraction to the average" from the
"sexual reproduction" process itself...so, I've left that out so it doesn't
effect us seeing this "attraction" taking place...if "mutation" happens,
then this will, of course, "skew" the average...BUT, as noted, if we
delibrately throw in 60% "bright red" genes at the beginning then,
generally speaking, we get around 60% "bright red" genes in the "settled
average chromosome"...hence, if there is just _one_ "gene mutation" and
this represents 0.1% of the chromosome, then - were this continuous - we'd
expect 0.1% in the "average"...except, nope: The process is
_DISCRETE_...hence, that lone "mutation" stands next-to-no-chance
whatsoever of surviving (that is, 0.1% of only 42 genes in integer terms?
Zero: Wiped out ;)...as noted: "stamped out" by the process
itself...although, indeed, it's not "precise science" and we do know that
some "mutations" fight those odds, per "evolution"...indeed, surmounting
those odds stacked against it is, in fact, what makes evolution so "slow
moving" (not "gradual", though, the process is _DISCRETE_, so it "jumps"
from one to the other state)...in fact, this is not "inevitable" in a
direct sense but a case of "Russian Roulette" (if you keep on playing
Russian Roulette over and over - a new person for each "round" - you
should, "on average", end up with a sixth of your "players" dead...it
_WILL_, of course, vary...sometimes just under a sixth, sometimes just over
a sixth but "on average" - and "averaging" _is_ what is effectively
happening here - then it'll do that whole "normal distribution" of odds
around the "mean" of a sixth ;)...

What was that you said again?

Phil wrote:
> If you have a litter of 8, then there are on average 4 copies
> of every gene from each parent. Each of the 8 will be given a slighly
> different set of genes to cooperate with, and therefore you'd expect
> several will be in a better situation, genetically, than its parent.
> Your understanding is completely out of whack.

What on Earth is a "better situation"? Please tell me this isn't "master
race" overtones or something..."better" is a _COMPARATIVE_ word..."better"
than what? Shorter height? Blue eyes? Longer nose? Is that always "better"?
Surely sometimes a longer nose is better, sometimes it's not, depending on
"environment"...

"Better" is a _RELATIVE_ word regards the _environmental conditions_ at the
time...there is NO ABSOLUTE "best" involved here...and, anyway, "natural
selection" does NOT guarantee "best solutions" NOR "linear
progression"...really, run the "simulations" yourself and go look...the
beginnings of evidence is but a BASIC computer program away, which I _know_
you're more than capable of writing (much better than my "five minute" job,
anyway ;)...

I've produced the program and it produces the results as I _predicted_
they'd fall out...that, I think, might not be "conclusive" (and I would not
contend so...just a "five minute" program and a few runs of it...NOT
"exhaustive", true enough :) but I have at least _some_ "evidence" in
favour of my "group evolution" hypothesis...I "predicted" on the strength
of my "hypothesis" alone and wrote a program to "simulate" it and the
predicted results from the hypothesis appeared on cue...

Is my understanding completely out of whack? Or is _YOUR_ understanding
what's completely out of whack?

Hint: I've done lots of work with genetic algorithms and neural networks in
a commercial research capacity...I've also given you a program to which you
can satisfy yourself that, without bias, the program spits out the results
that I _predicted_ it would...I've also given you all the necessary
details, I think, for you to - at your leisure - confirm that this stuff
really does go on exactly as I've said it would...yes, as I said, this is
"my little theory" and is not "established theory"...but, you know, every
once in a blue moon, it turns out the lone "mutant" was right all along...

Don't worry, nothing to worry about...it's just "evolution" taking
place...move along, move along...nothing to see here..."these are not the
droids you're looking for" and so forth ;)...

Beth :)

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