gregor

I believe in evolution. The only way for me to believe in God is if I can believe that God created the natural evolution. This, of course, is not completely obvious.

I would like to use this thread to explain the reasons for my belief and hopefully discuss the issues with other debaters. I have a website on this, but I prefer stepwise advances starting with the traveling salesman problem.

The salesman should visit a number of towns, one at a time, and wants to know in what order they should be visited in order to make the tour as short as possible.

Suppose that the number of towns is = 60. For a random search process, this is like having a deck of cards numbered 1, 2, 3, ... 59, 60 where the number of permutations is of the same order of magnitude as the total number of atoms in the universe. If the hometown is not counted the number of possible tours becomes 60*59*58*...*4*3 (about 10 raised to 80, 10^80, (i. e. a 1 followed by 80 zeros).

Suppose that the salesman does not have a map showing the location of the towns, but only a deck of numbered cards, which he may permute, put in a card reader - like in the childhood of computers - and let the computer calculate the length of the tour. The probability to find the shortest tour by random permutation is about one in 10^80 so, it will never happen. So, should he give up?

No, by no means, evolution may be of great help to him; at least if it could be simulated on his computer. The natural evolution uses an inversion operator, which - in principle - is extremely well suited for finding good solutions to the problem. A part of the card deck - chosen at random - is taken out, turned in opposite direction and put back in the deck again like in the figure below with 6 towns. The hometown (nr 1) is not counted.

If this inversion takes place where the tour happens to have a loop, then the loop is opened and the salesman is guaranteed a shorter tour. The probability that this will happen is greater than 1/(60*60) for any loop if we have 60 towns, so, in a population with one million card decks it might happen 1000000/3600 = 277 times that a loop will disappear.

I have simulated this with a population of 180 card decks, from which 60 decks are selected in every generation (using MATLAB, the language of technical computing). The figure below shows a random tour at start

After about 1500 generations all loops have been removed and the length of the random tour at start has been reduced to 1/5 of the original tour. The human eye can see that some improvements can be made, but probably the random search has found a tour, which is not much longer than the shortest possible. See figure below.

In a special case when all towns are equidistantly placed along a circle, the optimal solution is found when all loops have been removed. This means that this simple random search is able to find one optimal tour out of as many as 10^80.

This random process is also similar to evolution in the sense that it uses random variation and selection in cyclic repetition. This also means that the cyclic repetition of random variation and selection of individuals is a very important principle for creating a huge amount of information. So generally, there is no reason to distrust random developmental processes.

So, why should God hesitate to use random search?

ironman

You must understand that God can't be explained by science, and trying to do is futile. Faith and reason are very opposite neighbors, faith is believing in something that reason tells you is unbelievable. Whenever you decide to have Faith in God, you leave the scientific method behind you.

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gregor

Sorry, I don’t understand your logic.

The theorem of Gödel states that there will always exist true statements that can never be proved and in such statements we can have faith or no faith. This means that I may believe in God on Sunday but not on Monday also because my nervous system is not a deterministic system. There is randomness in the system according to the entropy law.

According to Martin Luther (the founder of protestantism) we have no free will because God is omnipotent and does not play dice. I think he was right in the sense that there can’t be any freedom of choice in a deterministic system. As i see it, the only way to have some freedom of choice, imagination and creativity is to include some random uncertainty into the system. Since our nervous system is a physical system totally ruled by previous history and the omnipotent laws of nature including the entropy law, which solely is about chance, probability and disorder, this may be a credible possibility.

analog

I've said for a while that I believe in evolution, and that doing so has nothing to do with believing or not believing in God, which I do.

Even if we can prove- and I mean absolutely prove, down to the very first instance of the existence of EVERYTHING, that there is a scientific step-through the way right up to the very words i'm typing right now, that still does not disprove to me, or change my faith, that God created everything.

As I believe in God, I believe that He is omnipotent and omniscient, and that more than allows for faith to exist, based on the ideal that WHATEVER actually spawned everything that has ever existed, it was all started by Him.

My example is usually something like having a kid. We have the ability to reproduce- does that mean we will a child into existence? No. We fertilize an egg through sex or other insemination, and then we sit back and wait for the growing process to complete. "Creating" a child does not make us Gods, nor does proof of the steps of creation of the child, all the way back to the first components, mean that we didn't make it happen ourselves.

roachboy

within a judeo-christian framework, there is no problem.
god is infinite.
evolution a process within time.
the first register is not in any way negated by the characteristics of the second.
augustine said in the confessions (bk 11) that god had set time into motion, but was not within the time that was set into motion.
same logic.
another way: the tension/contradiction between infinite and finite is at the source of much of the paradox(es) of the incarnation (jesus).


to the extent that there is a problem with this, it arises for those variants of protestantism that choose to read the bible "literally"...whatever that really means...personally, i figure that these folk develop one-dimensional readings of an extremely complex, heterodox text and so create the problems for themselves that they attribute to the notion of evolution.

so there is no problem.
not to worry.

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SirLance

The difficulty fundamentalists have with evolution arises from their treatment of Genesis as a literal description, rather than a theology. As roachboy correctly points out, Augustine's argument shows that God could have set the ball in motion without having to direct it's course.

There are two aspects to the debate on evolution. First, people seem to forget that evolution's factual component, observed in the universe and validated, is that species evolve and change. They do.

Second, the theoretical component, describes the mechanism of that change and names that mechanism "natural selection." This theory correctly predicts observations, and so it is considered accurate. It could be disproved, but no one thinks that likely. When you say you believe in evolution, I assume it is the theoretical component you are speaking of.

I am deeply religious, and I agree that the theory of evolution offers the best explanation for the observed facts. I point out my religious nature because I think it is important to note that being religious doesn't mean someone automatically discounts evolution, or any other theory.

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Willravel

You can't say God created evolution because you can't say that God exists in a scientific context. You can have faith in God and believe that evolution happens, but saying that God created evolution is like mixing oil and water, or fact and fantasy. If I were to say that Don Quixote founded Newtonian Physics, you'd think I was silly, right?

Yakk

God could have created evolution. The God hypothesis, in it's most general (broad) form, is not disproveable hypothesis. No feature of the world, perception or thought can disprove the existance of the broadest defined God. So any percievable feature, thought or world could have been created by God.

Are you talking about a narrower God? (ie, do you want a God with particular features to have created evolution?)

Or, do you want evidence that God created evolution? There is no need for the broad God hypothesis to explain evolution.

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Dilbert1234567

I would go with: Evolution created god(s).

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loganmule

It seems that the OP assumes, first, that God exists and, second, that God opted for evolution. One can accept this on faith, but there is no scientific method to prove or disprove it. ironman said it all...accept (or not) on faith and believe that which cannot be objectively shown to be true or false.

gregor

Thanks for many informative posts!

In the “threads regarding evolution/creationism” I noticed that this issue is perhaps not very popular, but a point #9 in a post by tecoyah points to a creationist argument as a misunderstanding of the entropy law. I think there may be more misunderstandings here.

“9. The Second Law of Thermodynamics says that systems must become more disordered over time. Living cells therefore could not have evolved from inanimate chemicals, and multicellular life could not have evolved from protozoa. This argument derives from a misunderstanding of the Second Law. If it were valid, mineral crystals and snowflakes would also be impossible, because they, too, are complex structures that form spontaneously from disordered parts. The Second Law actually states that the total entropy of a closed system (one that no energy or matter leaves or enters) cannot decrease. Entropy is a physical concept often casually described as disorder, but it differs significantly from the conversational use of the word. More important, however, the Second Law permits parts of a system to decrease in entropy as long as other parts experience an offsetting increase. Thus, our planet as a whole can grow more complex because the sun pours heat and light onto it, and the greater entropy associated with the sun's nuclear fusion more than rebalances the scales. Simple organisms can fuel their rise toward complexity by consuming other forms of life and nonliving materials.”

I prefer a simplified version of the entropy law. “A physical (biological) system occupies its possible states in proportion to their probability of occurrence.” I also prefer the simplest possible definition of disorder, which may be calculated for any probability density function. Thus, the sun is hardly needed in a simplified debate on evolution.

Evolution is defined as random variation followed by selection in cyclic repetition where random variation produces disorder, while selection may produce order. Creationists are right in the sense that random variation does not produce order. But an enormous amount of disorder represented by millions of different species and billions of different individuals in certain species has been produced, in agreement with the entropy law because a more widespread gene pool is more disordered. When DNA-messages increase in length there will be more room for disorder. The order in the biosphere was biggest when the first living organism ruled the roost.
The illusion of order in the biosphere may be due to the fact that only a very tiny little fraction of all possible DNA-messages may manifest themselves as living organisms. Thus, the disorder becomes restricted (by selection), and this restricted disorder is interpreted as order (complexity) by both creationists and biologists. Intuitively, this may be understood, if we observe that the duality order-disorder is like cold-warmth. From a scientific point of view there is no cold, only limited warmth. Likewise (in the biosphere), there is no order, only limited disorder.

I agree that God can never be fully understood, but if science is a tool by which we may reach more knowledge about God, why must God and science necessarily be separated? If He/She created everything, then He/She also created the entropy law, which seems to be a very important tool in evolution.

SirLance

Sure I can. I just can't offer any proof.

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Willravel

*If* we reach knowledge about God through science eventually, then the discussion will change, but why frame a discussion about something that hasn't happened yet and there's no evidence that will happen?

You're still framing questions in the 'if God exists' hypothetical. I say, Why bother with that hypothetical if there is absolutely no proof of God's existence? It's like posing a hypothetical questions around faries or Zeus. It's an exercise in futility.

Isn't that called fiction?

1010011010

Gods created evolution to the same extent that gods have created anything.

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Ourcrazymodern?

If God, then on course he, she, or it did. Evolution is a kind of compelling fact-based "theory". It happens. So if God created the framework in which it happens, God must have created it as well? I, personally, don't personalize where our existence came from, but God is easier to say than Our Universe, so when I'm feeling lazy, I use the one syllable. The quasi-religionists in my life it tends to piss off: I'm sure the universe doesn't mind. Good God!

SirLance

No, my friend. It is called faith.

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Ourcrazymodern?

Futility for the futile.
Faith for the faithful.
Reality for the real?
Evolution for the evolved?
Tilted forum for the tilted.
Love is for lovers. LYA!

Willravel

That's true. What I mean to suggest is that faith and science often work in opposition, much as fiction and fact work in opposition. I'm not in any place to say God doesn't exist exactly, but I think it needs to be said that we have no proof of God's existence and therefore basing science on his existence doesn't make sense.

Xera

I've always believed that God exists in tandem with science. I understand those that can only see one side of that balance. I understand it, I do not however, agree with it.

God is who, science is how.

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Yakk

Willravel, it isn't that there is no proof of God. Proof is a rather high standard to hold a hypothesis up to.

It is that there is no evidence.

Let's take a hypothesis. "This coin is a fair coin".

What kind of predictions can I make? Well, if the coin was fair, and I flipped it 100 times...

We'll, I'd predict that a 95% of the time, we'd get between 40 and 60 heads.

So if I did a trial and ended up with 45 heads, that would be evidence that the coin is fair. It wouldn't be proof.

If you flipped a coin and got 45 heads, in a way the simplest explaination would be "the coin is fair".

Proving it was a fair coin can't be done by merely flipping it. Because no matter how many times you flipped it, the coin could be "almost fair".

Now, you could "prove" that the coin "is no more unfair than X" -- by prove, I mean "provide extremely strong evidence".

You could also "prove" that the coin was fair by analyzing it's physical makeup.

But what is lacking about the god hypothesis isn't proof. It is evidence.

There isn't an observation whose simplest explaination is "Omnipotent Omniscient Benevolent Being, Alpha and Omega".

There are possible observations that would require the "OOBB,A&O" God as the simplest hypothesis.

However, the same holds true of the Invisible Pink Unicorn. Lacking these observations...

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Intense1

God exists... because mankind strives.

If mankind didn't strive for something more, there would be no God.

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gregor

It may be that the headline is wrong, and that the thread should perhaps be closed, but since there are debaters who may have a different meaning, we may perhaps leave to each individual debater to judge.
In my first post a combinatory problem was described. The next post about my background will be about a parametric problem. It will result in a theorem capable of solving a very difficult problem, in principle dependent of the number of degrees of freedom. At the first glance, the normal distribution seems to be the result of a random process. But this distribution has many remarkable theorems attached to it. Is a designer needed for the theorems?
In the middle of the 60-ties, I worked at a Swedish telephone company with analysis and optimisations of signal processing systems. Formerly such systems consisted of interconnected components such as resistors, inductors and capacitors. I retired in 1993.

In the late 60-ties my boss formulated a technical problem: “Try to find system solutions that are insensitive to variations in parameter or component values due to the statistical spread in manufacturing” he said. This means that he wanted the manufacturing yield maximized.

If we have only two components - each having a parameter value – the problem is very simple. Let the first parameter value be the shortest distance to the left edge of a picture (below) while the second value is the distance to the bottom edge. Then, if the interconnection is given, a point in the picture represents the system unambiguously.

Suppose now that all points inside a certain triangle (region of acceptability, marked by red edge) will meet all requirements according to the specification of the system, while all other points does not, and that the spread of parameter values is uniformly distributed over a circle (green). Then, if the circle touches the three sides of the triangle, the centre of the circle would be a perfect solution to the problem.

But if we have 100 parameters, then the number of possible parameter combinations becomes super-astronomical and the region of acceptability will not possibly be surveyed. I begun to think that the man was not all there.

The problem was almost forgotten until a system designer entered my room about half a year later. He wanted to maximize the manufacturing yield of his system that was able to meet all requirements according to the specification, but with a very poor yield.

Oh, dear! I would not like to get fired immediately. So, we wrote a computer program in a hurry, using a random number generator giving Gaussian (normally) distributed numbers according to the bell curve to the left in the figure below. A cluster of points in two dimensions - where each pair of two normally distributed parameters is represented by a point - is seen to the right.

The system functions of each randomly chosen system were calculated and compared with the requirements. In this way we got a population (generation) of about 1000 systems from which a certain fraction of approved systems was selected. For the next generation the centre of gravity of the normal distribution was moved to the centre of gravity of the approved systems and this process was repeated for many generations.

After about 100 generations the centres of gravity reached a state of equilibrium. Then the designer said “but this looks very god”. And we were both astonished, because we had only put some things together by chance. A closer look revealed that there is a mathematical theorem valid for normal distributions only stating:

If the centre of gravity of the approved systems coincides with the centre of gravity of the normal distribution in a state of selective equilibrium, then the yield is maximal.

This gave an almost religious experience. Here a mathematical theorem solved a difficult problem without our knowledge and independently of the structure of the region of acceptability. But in order to fulfil the theorem exactly, infinitely many random points must be generated, which is of course impossible. Nevertheless the solution was good enough for our technical purposes. Our very simple process was also similar to the natural evolution in the sense that it worked with random variation and selection in cyclic repetition.

SirLance

I don't disagree, but to my tiny little mind, the opposition is perceived and not actual. Science attempts to chart the workings of the universe using a well defined methodology. Faith cannot work in such rigid parameters, because by definition, faith is not necessary in the presense of proof. Faith attempts to address what science cannot. What happens to our self when we die? Is there a unity to the universe? Something from which all things spring?

The religious fundys maintain that science and faith are opposed, and they clearly understand neither science nor faith. I think you maintain that science and faith are opposed because you want to apply the same guidelines to both, and you can't. Faith is not the result of, nor subject to, the scientific method.

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Willravel

I don't think the thread should be closed at all.

I found your story really facinating. I do love when there is equilibruim in nature, as it contradicts the idea that the universe is chaotic by it's nature (something that just doesn't sit well with me). I'm not trying to put words in your mouth, so I have to ask: are you suggesting that it's possible that coincedences and/or occourances of equilibruim in nature are evidenec of an intelligent design? I've heard that suggested before, without any real connection between the evidence, be it physical or mathematic, and an intelligence beyond simply the "who else could have done it" or "what are the odds" arguments. I'm left wondering if there might be a more simple explaination: that's just how things work. Instead of suggesting a Judeo-Christian diety or Flying Spaghetti Monster is responsible for coincedences or equilibruim in nature, isn't it more practical and reasonable to suggest that is simply how nature works?

The more common argument made is our very existence. Without having information on another planet with life, people suggest that the odds of life, let alone intelligent life, developing are astronomical and it's easier to suggest that an intelligence designed us (ID) than to say we are the result of a random set of coincedental happenings (evolution). I think that this thread is an attempt to appease both sides by playing the middle: yes, God exists, Yes evolution exists. I'm fine with people believing that, but to frame the existence of a supernatural being in science is fundamentally flawed. Something supernatural cannot, by definition, be explained by science. We can guess, without evidence, that God might exist. People have been doing that for thousands of years and they will continue to do so for thousands more, I would guess. The problems start when the supernatural enters the world of science.

I died once, nothing happened. It depends on what meaning of unity you're using. We all came from the big bang.
I agree completly. Philosophy, in my mind, is an interesting way to try and bridge science and religon or spirituality, but at the end of the day, science has rules that faith can't follow, so faith has to wait outside.
That's exactly what I'm thinking. Science doesn't fit in with the rules of faith because science would be too limited. Likewise, faith does not fit in science because it refuses to follow all the rules.

SirLance

Which makes me curious.... we are in agreement that science and faith can't be reconciled. Are others? Show of hands?

And, that being the case, why do we continue to try to reconcile science and faith...? Our nature?

I suppose if we keep asking questions, we'll eventually hit on the right ones!

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gregor

O. k., in the following I will continue my believing-in-evolution-story.

Our artificial process was climbing an artificial landscape defined by the math-model of the signal processing system. A corresponding phenotypic landscape would be defined by the fitness of the individual, defined by Hartl as the probability s(x) that the individual having the n characteristic parameters xT = (x1, x2, ..., xn) – where xT is the transpose of x - will survive, i. e. become selected as a parent of new individuals in the progeny.
Hartl, D. L. A Primer of Population Genetics. Sinauer, Sunderland, Massachusetts, 1981.

From my point of view it was an issue of interest if the natural evolution was able to make use of the theorem of Gaussian (normal) adaptation for the maximisation of mean fitness. So, I looked in some textbooks of biology and noted that many phenotypes were Gaussian distributed in a large population, or nearly so. There was also a strong indication that the ontogeny was a modified stepwise replay of the phylogeny and the central limit theorem stating that the sum of many steps tends to become Gaussian distributed.

If m is the centre of gravity of the Gaussian and m* is the centre of gravity of phenotypes of survivors, could evolution make the centers of gravity, m and m*, coincide for the maximization of mean fitness?

Yes, if mating is random, then the Hardy Weinberg law seemed to do the job. The law states that If mating takes place at random, then the allele frequencies in the next generation are exactly the same as they were for the parents. Thus we would expect m = m* in every generation. Selection will move m*, but the process will always strive towards a selective equilibrium with m = m*, thus mean fitness will be maximized as far as Gaussian phenotypes are considered.

Thus, Gaussian adaptation seemed to be a fairly good model of evolution.

MuadDib

Not being able to prove faith or God in scientific terms doesn't mean you cannot prove either faith's or God's works in scientific terms.

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gregor

Well, I have sometimes been thinking that intelligent design is the same thing as evolution. But I have noticed that this is not accepted by ID:ers.

Lasereth

I really don't think Evolution and God can even be compared. God is faith and religion. Evolution is proving how we came to be. Proving. You can't prove that God exists, but we can prove that evolution happened. Tying the two together is inherently flawed. Like it or not, there is no way to prove religion. This is starting to remind me of the Ghost Debate® so I think I'll stop before I go off on a tangent.

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florida0214

I believe that Evolution was part of Gods plan. Not the we came from monkeys evolution. I believer people adapt and evolve. Not only people but everything. Evolution was all part of the plan. kind of like the big bang. Thebible oly says that god made it happen. It has no detail as to how he made it happen. The scientist's may just have it right, except for the one fact that God started it all with his words. Anyway Just my .02

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Dilbert1234567

Evolution does not say we came from monkeys... evolution says monkeys and us have a common ancestor.

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Willravel

We came from things that are similar to today's primates. I think that's what people mean when they say we came from monkeys or apes.

Ourcrazymodern?

We might as well call it our universe then, and do what we must, and if Invisible pink unicorns blow your skirt up...well? All is well. Religion and politics are two things we kept private {meaning within ourselves - we didn't talk about them, even within our "place"} when I was growing up, though there were obvious inconsistencies:
1)not only were we required to go to Sunday school, I'm pretty sure my mom and step-father used the time wisely !
2)always there was noise about "the way things are",
3)none of it was discussed with the chidren.
Well. you catch my drift. No specific citations, no vague citations, no citations at all. I am believing (y'allmightunderstand)!
Time will tell

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roachboy

i thought the question posed in the op was in itself religious.
from any other viewpoint, the makes no sense.

gregor: your posts are interesting. i confess, though, that i can't quite figure out how the demonstrations you provide either do or do not speak to anything to do with evolution in a darwinian sense. they seem to speak more to questions of modalities of change. which isn't the same thing, simply as a function of the time-frame involved and the imputing of a directedness to very long-term biological processes (an imputing that may or may not be a massive example of a teleological fallacy, there is no way to know).

but it seems that you have a set of assumptions about the formal language of mathematics and the kind of information about the world that it can generate that i find curious--the sort of thing that make some physicists imagine that there is are theological dimensions to string theory. this is itself a religious question because it only functions when you cross frames of reference. but it's a bit hard to tell: can you explain how you understand the relation between mathematics, its formal expressions, and theology or theological questions?

the obvious response would probably be that you see mathematics are a device that lets you describe the underlying rationality of physical phenomena even as it is itself a type of metaphysics (the language and its procedures). but it'd be better if you could explain it a little.

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hiredgun

I think that both 'intelligent design' and 'God' are each operating in two different modes here.

1) ID posed as an explicit challenge to the scienctific fact and theory of evolution is poppycock.

2) ID in the sense of the OP, posed simply as an explanation (or even justification) for what might be considered 'irreducible complexity' - that for which we currently have no physical explanation - is not poppycock, but as far as its material implications, it collapses completely into scientific evolution.

3) Conceptually, God is doing two things here as well. First of all, he exists. Secondly, God is employed as an explanatory tool; the observable facts of the world are linked to His will or Design.

These two aspects of God are logically quite separate. It is possible to have faith in God's existence without bothering to link particular facets of the world with heavenly design. So yes, there is no internal contradiction in stating - from inside a perspective of faith - that God created evolution. It is problematic only, as rb pointed out, in the context of a literal defense of the Bible [this falls under (1) above].

gregor

Well, at a first glance, the only connection to Darwinian evolution is that Gaussian adaptation (GA) uses random variation and selection. It is an example of “simulated evolution” using a computer with a Gaussian random number generator. Assuming that the rules of genetic variation – such as crossover, inversion etcetera - may serve as a random number generator for phenotypic parameters (morphological polygenic characters or even mental parameters as IQ, for example), GA would serve as a fairly good second order statistical approximation of the natural evolution.

According to the fundamental theorem of biology (due to Fisher, 1930) evolution, like the GA-model, strives to a maximum in mean fitness. Briefly, the theorem states that: the rate of increase of mean fitness of any organism at any time is equal to its variance at that time. And a process that maximises something is goal seeking and may therefore be directed towards a maximum or a goal.

There is a difference, however, between the fundamental theorem and GA. In Fisher’s case the mean is determined over the set of genes in a large population assuming that a gene may have a fitness of its own and be a unit of selection. References may be found in
http://www.evolution-in-a-nutshell.se/references.htm
In the GA-case the mean is determined over the set of individuals leading to a different result. I think that GA is better off, because it is the selection of individuals that rules the selection of genes.

According to the fundamental theorem of biology (due to Fisher, 1930) evolution, like the GA-model, strives to a maximum in mean fitness. Briefly, the theorem states that: the rate of increase of mean fitness of any organism at any time is equal to its variance at that time. And a process that maximises something is goal seeking and may therefore be directed towards a maximum or a goal.


I can only explain the mathematics used in the GA-model. If s(x) is the probability that an individual having the phenotypes x (an n-dimensional vector) and N(m – x) - where m is the mean of N - is the distribution of phenotypes in a large population, then
P(m) = integral s(x) N(m – x) dx is the mean fitness.

If x is only one parameter it is easily verified (high school level) that m = m* is a necessary condition for a maximal P. In a high-dimensional case matrices must be used for the proof and university level is recommended.

But it is also possible to maximise the disorder/mean information/diversity (all the same) keeping P at a suitable level. m = m* is the same condition of optimality as before. A new condition of optimality is M proportional to M* for the moment matrix of the Gaussian. These conditions are necessary to maximise disorder, keeping P constant.

This shows the difference between Fisher’s theorem and GA. Our interpretation is that GA maximises both mean fitness and phenotypic disorder simultaneously. The maximisation of disorder seems to have been missed in Fisher’s theorem. For more details see:
http://www.evolution-in-a-nutshell.s...adaptation.htm
My interpretation is that the GA-model explains both good things (maximum mean fitness) and evil things caused by the disorder, which stands for imagination and creativity, but which also is a reverse of the medal.

Ourcrazymodern?

Philosophy, in my mind, is an interesting way to try and bridge science and religon or spirituality, but at the end of the day, science has rules that faith can't follow, so faith has to wait outside.
This is so amazing willravel! Cogent cum cool. Do you think the day will come when faith gets let in, or will it be kicked to the curb and left for the dustman? Can philosophy become more common in our species when education isn't working as well as it used to? I'm thinking math has nothing to do with evolution, but I don't understand very much math. I tell the kids that only God is awesome, whenever they say the word awesome as an off-hand adjective, even though I don't have anything other than my own personal relationship with my universe. What a miraculous thing is our living, thinking, and doing. Why doesn't everbody feel uber-blessed?

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roachboy

the fundamental theorem of biology?
that's quite a title.
what is "fitness" according to this?
what does it mean to "strive" in this context?
i do not understand the equivalence you note between "fitness" and "variance"
the definition of "goal seeking" seems to me somewhere between tautological (you observe a particular pattern. you note the pattern appears to be directed. you then impute that directedness to the pattern itself--when it seems to me that the notion of "goal-seeking" is more about the observer's viewpoint and perspective on what is observed than it is about the data)

what i really dont understand is the time-frame. it sounds like you are modelling emergent characteristics within complex systems. that may provide a way to think about evolution (there is a ton of recent work influenced by notions of biological autonomy that uses this kind of information in this way--but as a metaphor, a conceptual device that you would use to rethink what you are looking for/considering when you try to research evolution/emergence--not as a model for evolution itself)
if you collapse questions of emergent characteristics/properties into evolution in general, you end up recapitulating something like lamarck.

this all seems terribly problematic when you try to move from the mathematical simulation to a viable modelling of biological evolution.

but maybe i am still not understanding--so.
seems to me like the fundamental theorem

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gregor

Yes, it is a magnificent title, but it is a little out of place, because the premise that evolution selects genes is doubtful – not because Fisher’s calculations are wrong.

Sorry, I got my quotation wrong. “Variance” should be “genetic variance”. So a better formulation of the theorem should be: The rate of increase of mean fitness of any organism at any time is equal to its genetic variance at that time.
In the Fisher case, fitness is a mathematical measure of the ability of a gene to contribute to survival. Or according to Maynard Smith: ”Fitness is a property, not of an individual, but of a class of individuals – for example homozygous for allele A at a particular locus. Thus the phrase ’expected number of offspring’ means the average number, not the number produced by some one individual."
This definition is certainly useful in breeding programs. But unfortunately, a theory based on this is completely useless as a basis of a model of an evolution selecting individuals, because the selection of individuals rules the selection of genes. For more details see Maynard Smith in my references (I forgot to tell that this is my reference to the theorem).
http://www.evolution-in-a-nutshell.se/references.htm
From a mathematical expression Fisher calculates the mean value of fitness over the set of all genes of a large population. The result is – what is called - the fundamental theorem. This way of thinking has inspired biologists since 1930, leading to the opinion that egoism is a law of nature. An example is Dawkins: The selfish gene. See also
http://www.evolution-in-a-nutshell.se/egoism.htm

As long as the genetic variance (variability) is > 0, mean fitness will increase and therefore the process strives or converges towards a maximum in mean fitness. On the other hand – as Maynard Smith points out – evolution may reach a state of selective equilibrium, in which case there will be no increase in mean fitness, even though the genetic variance is > 0. This contradicts the theorem.

The theorem of Gaussian adaptation may be formulated in a similar manner. Say that the gradient of mean fitness is grad[ P(m) ] is a measure of increase in mean fitness P. Then the theorem of GA states:
grad[ P(m) ] = inverse-of(M)* P ( m* – m ), where M is the moment matrix of the Gaussian distribution, m and m* defined as before. I should perhaps not use the word fundamental, but the GA-theorem is fundamental in the sense that it is valid for all regions of acceptability of any structure.

In contrast to the fundamental theorem due to Fisher, this result seems more reliable, because in a state of selective equilibrium, we have m* = m and consequently no increase in P. But the phenotypic variance (disorder) – displayed by M - must not be equal to zero.

It is also possible to maximize the logarithm of the determinant of M (proportional to the disorder of the Gaussian) keeping P constant using Lagrange multipliers. The condition of optimality will be the same, m = m*, meaning that GA effectuates a simultaneous maximization of men fitness and disorder.
I have never observed any data. My interpretation is purely mathematical philosophical. The basis of this philosophy is according to the following six theorems.
http://www.evolution-in-a-nutshell.se/six-theorems.htm
I hope the theorems are correctly proved. But of course, their application to natural evolution can always be questioned. They constitute a second order approximation of what may happen to the mean fitness and the phenotypic disorder in large populations, nothing more. But the approximation may still be good. Evolution is viewed as a statistical optimisation algorithm. See for instance Kjellström, 1996, in references.


I dont understand what you mean by time-frame. In natural evolution there will be millions of years. In simulated evolution some hours, days or months perhaps. It has nothing to do with Lamarck.

Ourcrazymodern?

All this math and theory flying over my head is making me dizzy! Does anybody here really have their heads around the span of time since the Big Bang? We are a mote in god's eye. Frog odd's sake, buy me a firkin pint!
Almost 14 billion years, and here we sit quibbling. LYA!

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