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Wednesday, 19 December 2007

Polkinghorne Quotes #5: Does the Math for Evolutionary Time even Work?

The fact that evolutionary mechanisms can physically account for the complexity of life on earth seems, well frankly, mind boggling if not preposterous. And there doesn’t seem to be any mathematical model that can explain how random mutations and natural selection results in, for starters, us. Here is how Polkinghorne put it:

"Three or four billion years may seem like a pretty long time for the coming to be of life and the formation of its evolved complexity, but incredibly intricate developments have to be fitted into that period. Someone like Richard Dawkins can present persuasive pictures of how the sifting and accumulation of small differences can produce large-scale developments, but, instinctively, a physical scientist would like to see an estimate, however rough, of how many small steps take us from a slightly light-sensitive cell to a fully formed insect eye, and of approximately the number of generations required for the necessary mutations to occur. One is only looking for an order of magnitude answer, comparable in crudity to the back-of-the-envelope calculations of early cosmologists, but our biological friends tell us, without any apparent anxiety, that it just can't be done. So much of evolutionary argument seems to be that 'it's happened and so it must have happened this way".

From Science and Christian Belief, page 16


So, is Polkinghorne just another mathematician type that doubts evolution? Should he just go take a biology class? Not so fast. Check out how Polkinghorne states the same idea with one important clarification.

"One of the serious questions that many physical scientists wish to ask about a purely Darwinian account of the evolution of life is whether there has been adequate time available to accommodate the amazing variety and complexity of change involved. Three to four billion years may seem a long period, but astonishing things have to have happened, not least in the rapid development of the hominid brain in the space of only a few million years. Is the patient accumulation and sifting of small genetic differences sufficient to accomplish this? Those who ask the question are not querying the idea that natural selection has a role to play, but they simply ask whether it is by itself totally adequate as an explanation. The questioners are not looking for a gap into which to insert the finger of divine intervention, but they may just be seeking a more comprehensive and persuasive scientific account. People like Paul Davies (The Cosmic Blueprint) are very impressed with the remarkable drive to complexity present in cosmic history. Dennett occasionally refers to this time-scale problem, but it seems that neither he nor any other evolutionary reductionist is able to offer a convincing answer to it."

From Polkinghorne's 1995 review of Dennett's "Darwin's Dangerous Idea"


So come on biologists, show us the equations!! You do get marks for the right answer, but unfortunately, to pass this exam you need to write your solution out in full.

Other Polkinghorne Quotes: [Introduction] [Previous] [Next]

13 comments:

Gordon J. Glover said...

Good point Steve. In my own mind, there is a huge disconnect between the fact of common descent, and the possible evolutionary mechanisms that account for it. I might be arguing from incredulity, but natural selection acting on random variation still doesn't cut the mustard. There has got do be much more going on than scientists can even fathom.

Take biogeography for instance. If a lake contains a population of fish, and the water level drops such that the lake divides into two separate bodies of water, the speices of fish become isolated and evolve along different paths.

The curious thing is that they both evolve and speciate to fill the same niches with similar looking species. So even though all the species in lake#1 are more related to eachother than than they are to the species in lake#2, the ones that fill the same niche in each lake appear to be more similar to eachother than to their original ancestor.

You can see this same effect in Austrailia and South America. All Aussie mammals have evolved from a common marsupial mammal, but similar species fill the same niches as their placental counterparts in South America. Yet the marsupial mole is more related to the kangaroo than it is to the placental mole, etc...

What this says to me is that evolution is "front-loaded" in some way. Perhaps genetically. And it's not totally random, but is somehow driven by the environment or by junk DNA in ways that we have yet to discover. Perhaps Behe is right and there is some divine tinkering, but I still think there is a material mechansim responsible for this. I just don't think we have a clue what it is.

If scientists can figure this out, and theologians can figure out what it means for Christian orthodoxy, then I think we'll be in good shape!

-GJG

elbogz said...

We mark a spot on a baseball field that 37.923 feet behind and 8.257 feet to the left of second base, and calculate the odds that you could hit the ball and have it land exactly in that spot. We find that number to be so close to impossible, that we say it would be impossible hit the ball and make it land there.

Yet, when we find the ball in that spot, we find nothing unusual about its presence there. In the words of the late Carl Sagan, we got here, because, we got here. If you look at the baseball sitting in center field it’s not amazing, but if you say, on the next pitch I’m going to hit the ball and have it land on that exact spot, then of course, you can use words like “impossible”

So here we are, sitting in the outfield. Was it impossible? Perhaps, but yet here we are. Explain that.

From a different perspective, when you say, the odd of us evolving are so small, that it is impossible, what does that say of the possibility of God? Compared to God, we are pretty insignificant creatures. For God to exist, then the odds of his being must be incalculable. So when you go down this path, you prove it even more impossible for there to be a God. Perhaps, then we are on the wrong path.

Siamang said...

"Yet the marsupial mole is more related to the kangaroo than it is to the placental mole, etc...

What this says to me is that evolution is "front-loaded" in some way. Perhaps genetically. And it's not totally random, but is somehow driven by the environment or by junk DNA in ways that we have yet to discover."

I think this shows how much our shape is driven by our environment.

Someone described it as this: natural selection is the process by which information passes from the environment into the genome. There's your front-loading. There's your programmer: the environment itself.

Steve:

I think plenty of time has gone by for the diversity of life we see around us. I just think humans are really, really bad at imagining just how long a billion years is!

Given the vast sweep of history, we still carry the same basic body-plan as fish. I can see how successive generations over billions of years take us from single-cell to full body humans, because in the womb a similar process takes only 9 months.

"One of the serious questions that many physical scientists wish to ask about a purely Darwinian account of the evolution of life is whether there has been adequate time available to accommodate the amazing variety and complexity of change involved."

The good reverend Dr. Sir Polkinghorne seems unaware of the sheer mind-boggling large search-space that can be covered by a massively parallel iterative, competitive, self-improving simulation.

How many "steps" to evolving the eye? You'll have to count the number of individual creatures worldwide who've ever had eyes, since the beginning of life on earth. And not just your and my ancestors, but all the failed bloodlines of creatures as well, for some of their eyes failed them, and in failure, provided our ancestors some lunch or kept them from being lunch. They failure of their eyes allowed our eyes, and so that is part of the simulation as well.

What is the order of magnitude of that simulation, for Polkinghorne?

Given that there's currently 63,000 species of chordates alone in the world... how many individual animals... is that anyone's guess? In a given year, how many animals with eyes are born? Ten trillion? Ten thousand trillion? I don't think were even close. One estimate states that there are one quadrillion ants in the world.

Let's just take fish. I've seen a wild-ass ballpark guess on the number of fish in the world as 10^12. Or 1,000,000,000,000 fish. Let's assume for generosity sake that that number is "fish born in a given year" though we know that most fish don't live as long as a year. (The real number may be an order of magnitude higher.)

Let's multiply that by the number of years since the Cambrian, five-hundred-fourty million, or 540,000,000. So that's 5.4^20 if I did my math right. We are approaching literally astronomical numbers, here. We're half way to the number of stars in the universe.

And realize, I'm JUST COUNTING FISH, nothing else with eyes.

Now realize that this is a learning simulation. Your eyes are getting better, but so are your predator's eyes, and your prey's eyes... here's where the massively parallel nature of the simulation requires ever better and better results. It's a learning simulation.. so multiply improvements by improvements every generation...

We're talking about a search space that is literally astronomical... all working together to make the eye.

If he thinks there hasn't been enough time to make an EYE, or any other structure we see in life around us, I don't know how deep he expects time to be, or how slowly he thinks evolution should work.

Does he really think evolution is running an order of magnitude or 10 too fast? Compared with what?

Steve Martin said...

Hi Gordon:

Good point Steve. In my own mind, there is a huge disconnect between the fact of common descent, and the possible evolutionary mechanisms that account for it. I might be arguing from incredulity, but natural selection acting on random variation still doesn't cut the mustard. There has got do be much more going on than scientists can even fathom.


Good distinction between the fact of common descent & the mechanisms that drive the change. I remember seeing a list of evolutionary mechanisms that was at least 30 long (eg. one very important one that I didn’t mention is genetic drift (http://www.talkorigins.org/faqs/genetic-drift.html)

re: front loading

Not sure if you’ve seen any of Simon Conway Morris’s work. He discusses the ability of evolutionary mechanisms to come up with similar solutions time and time again. Where Gould would say “rerunning the tape of life” would result in wildly different outcomes every time, Morris disagrees as he believes there is lots of evidence for convergence. Unfortunately my grasp of the technical details is so basic that I can barely understand the argument let alone try to determine who is right.

Siamang:


“Natural selection is the process by which information passes from the environment into the genome”

Now THAT is a very interesting idea. Never heard of it before. I think you are saying that Morris might be right that there has been convergence on earth BUT that our macro-environment is an important, if not the determining factor. So Morris could be right that if rewind the tape to certain points in time, we’d get a similar outcome. In this case I guess the implication is that the SETI folks should not necessarily expect anything similar if we ever discover life on another planet that is dissimilar to ours. (I know, an unrelated tangent – but I do like SF & thinking through the implications).

Re: Is Deep Time enough and “The good reverend Dr. Sir Polkinghorne seems unaware of the sheer mind-boggling large search-space that can be covered by a massively parallel iterative, competitive, self-improving simulation.”

1. Both quotes from Polkinghorne are from over a decade ago. A lot has happened in the last dozen years in both evolutionary theory & its interaction with software theory, and its use of computer technology. So it is possible he was “unaware” then but is not now (not sure if he’d say the same things today), but it is equally possible he hasn’t looked into this further. (Hey, he doesn’t even seem to use email yet .. check out http://www.polkinghorne.net/qanda.html … he appears to take questions through fax!).
2. I understand that anti-evolutionists (eg UcD) use the argument from incredulity all the time. Where I believe they make their mistake is moving from “preposterous” & “mind boggling” to “therefore untrue”. When you say that “humans are really, really bad at imagining just how long a billion years is!” I’d have to personally raise my hand and say “guilty as charged”. So to me, just like many of the claims made by quantum mechanics seem to be preposterous, (even the ones validated by experiments), the fact that evolutionary mechanisms can account for the physical changes seems preposterous as well. That doesn’t mean I think they are untrue.

3. But if the UcD et al are arguing from incredulity, isn’t the use of the big numbers in the example you are proposing just the flip side? Ie. with this much time ANYTHING can happen? Physicists and mathematicians are used to dealing with big numbers and discussing their implications. (Hey, they talk about “countable” vs “uncountable” infinities). Have you seen any studies / papers on this that would help? Maybe some simulations that have been run? (I suspect that given our current knowledge & technology, they’d need to be very, very crude).

Just before the first quote above in “Science and Christian Belief”, Polkinghorne begins the discussion with:

“Anyone expressing reservations about the total adequacy of the neo-Darwinian account of evolutionary history is apt to be looked at askance, as if he were a crypto-creationist seeking a gap into which to insert a pseudo-deity. Yet one can accept the insights of natural selection and still feel that one has not heard the full story.”

I guess that expresses my own (non-specialist, maybe not very well informed) view. I suspect that part of the problem is that not only are the coefficients in the equations speculative, but many of the parameters are still to be discovered. As we needed an Einstein to revolutionize Newtonian physics, maybe we need the same type of revolution for Darwinian evolution. (I guess you could argue that with genetics we’ve already done that).

siamang said...

"So Morris could be right that if rewind the tape to certain points in time, we’d get a similar outcome."

That depends, of course, on how far back you run the tape.

These shapes are conditional on the structures they built upon. All multicellular life on earth descended from the same stuff: cells.

Running all the way from the beginning, is it really clear that cellular life would form? Or would it be something we cannot imagine?

But yes, given a tetrapod vertebrate body plan, there are only so many ways you can be a swimming, hunting sea-animal... be you a shark, an ichthyosaur or a dolphin.


"But if the UcD et al are arguing from incredulity, isn’t the use of the big numbers in the example you are proposing just the flip side? Ie. with this much time ANYTHING can happen?"

Absolutely not. Impossible things cannot happen, no matter how much time you've got. By "impossible things" imagine a working eye that can see using photosensitivity when there's no light at all. Or a sonar system that can work in a complete vacuum. Or a stomach that can generate its own food from nothing. These impossible things remain impossible no matter what large numbers you throw at them.

The way I like to think about it is this: there are an infinte number of real numbers between 4 and 5. Yet none of them are greater than eleven.

In that way, I think I illustrate that even with infinite possibilities, there are still impossible things.


"When you say that “humans are really, really bad at imagining just how long a billion years is!” I’d have to personally raise my hand and say “guilty as charged”."

You know, a friend of mine gave a talk once and he just about cured me of my failure of imagination when talking about large numbers. He gives a talk about dinosaurs and tries to give children an idea of how long a million years is.

Actually, he just tries to give them an idea of how big a number one million is. This is how he did it. He has a piece of paper with one-million dots on it, each the size of the period at the end of this sentence.

He's mounted this piece of paper on cardboard, which he unfolds during his talk, and shows it to be a piece of cardboard about 4 feet by 5 feet. He has them focus on a tiny fraction of it, a small square of 100 dots, and tells them that if they're good and healthy and excersize and eat right and don't smoke or do drugs, they probably will live somewhere close to 100 years.

Now he says, the Dinosaurs lived 65 million years ago... so let's mentally imagine 65 of these all around this auditorium. And then we count up to 65, and we imagine these poster-boards covering the stage, covering the walls all around us, and going out into the hall and filling the lobby.

We don't get into trying to imagine one thousand of those.

geocreationist said...

Personally, I do not have a problem with how possible or impossible evolution appears to be, or how long it would take as a God-free process, because scripture does not describe a God-free process.

To me, it is this simple:

On Day 3, God said, "Let the land produce vegetation: seed-bearing plants and trees on the land that bear fruit with seed in it, according to their various kinds"

So on one hand, God didn't directly produce the seed-bearing plants; the land did, but God said to "let it" produce, implying the process needed His permission. Notice that He only mentioned seed-bearing plants, which are practically at the end of the evolutionary chain for plants, suggesting the evolutionary process that led up to seed-bearing plants is essentially what God commanded.

On Day 5, God said, "Let the water teem with living creatures, and let birds fly above the earth across the expanse of the sky."
This doesn't say there was no sealife or birdlife before, just that the water wasn't teeming and the sky wasn't full. Given the parallel with evolution 65 million years ago (after the dinosaur extinction), scripture reads to me like God is giving permission (once again) for the evolutionary process to occur.

On Day 6 He said, "Let the land produce living creatures according to their kinds", and notice that land mammals had a population explosion after the waters were teeming with sealife, after the birds filled the air, and after the giant sea animals (i.e., whales) of today evolved.

So, God said let the **land* produce... and it did, via evolution. And it was with God's permission.

"Let the land produce vegetation"
"Let the water teem"
"the air be filled"
"Let the land produce living creatures"

I'd say there was something preventing evolution from doing these things until God stepped in (tipping the first domino)... or perhaps there was nothing enabling evolution to occur without Him (empowering the dominoes). Is this a God of the Gaps argument? Not quite... because I am not using the gaps to prove God. On the contrary, the scripture is predicting both evolution **and** the gaps, lest God's creative statements prove unnecessary and the fossil record prove to be a hoax.

Anonymous said...

Gordon Glover wrote

All Aussie mammals have evolved from a common marsupial mammal, but similar species fill the same niches as their placental counterparts in South America. Yet the marsupial mole is more related to the kangaroo than it is to the placental mole, etc...

Siamang's answer is a good one: If you are an evolving species, the number of ways to "make a living" in the world is not infinite, and a given way of making a living involves similar physical constraints and pressures regardless of whether it's a marsupial mole evolving in Australia or a placental mole evolving in the Americas. Convergent evolution is a product of similar selective pressures operating on disparate lineages.

With respect to eyes, Nilsson and Pelger showed that it's about 500,000 generations from a simple light-sensitive patch to a camera eye like ours under very conservative assumptions. In species with generation times on the order of a couple of years, that's a geological eye blink or two.


Siamang wrote

We're talking about a search space that is literally astronomical... all working together to make the eye.

It's real important to remember when using a search metaphor for evolution (and it is a metaphor!) that the 'search' is not unconstrained. A reproducing population is already in a viable location in that humongous space, and it does not randomly sample from the whole space. Rather, it 'searches' nearby points in the space -- points near the population's present location -- where "nearby" is defined in terms of one application of a variation-generating operator (mutations of various kinds, recombination, etc.). Points that are near a viable location are more likely to also be viable living places than are randomly sampled points.

That's one reason the various creationist probability estimates of the formation of this or that phenotypic structure are bogus: the whole space of possible genotypes is not sampled by a given population, but only points near a known-to-be viable phenotype, know to be viable because it's reproducing! Evolution is descent with modification.

RBH

Steven Carr said...

POLKINGHORNE
'.....but, instinctively, a physical scientist would like to see an estimate, however rough, of how many small steps take us from a slightly light-sensitive cell to a fully formed insect eye, and of approximately the number of generations required for the necessary mutations to occur.'

CARR
Why doesn't Polkinghorne bother to read Dawkins books , where exactly such questions are answered?

Eye evolution

Siamang said...

Thanks, RBH


Yes, that's one aspect I should have described better... these are variations which are minor variations always on a successfully proven model... so that "search space" is in a local area of useful hits.

-Siamang

Steve Martin said...

Hi all,
Sorry for the delayed responses. My blogging break - which will continue for a few weeks yet - includes very intermittent comment checking.

Geocreationist:
I appreciate the difference between “using gaps to prove God” and your view that “scripture predicts the gaps”, but I really can’t swallow that. First, I think that sooner or later you will be boxed scientifically into a corner where “there is no domino to tip”. More importantly, I do not like the fact that “God had to step in”, as if he was ever absent from the process.

Siamang:
Re: big numbers anecdote. Yes, there are good ones – but I still find the brain short-circuits when I try to imagine the very big or the very small.

My statement that "Anything can happen" was a little misleading. I was not addressing impossible events, but complex possible events. Long periods of time are not some type of trump card that allows us to unilaterally solve the problem. For example, maybe using only the evolutionary mechanisms we currently understand some very complex combination of events / development should take around 100 billion years. This would most likely indicate that we haven't discovered or fully understood all the data or evolutionary mechanisms correctly.

RBH:
Excellent clarifying point re: the local search space. Thanks.

Re: With respect to eyes, Nilsson and Pelger showed that it's about 500,000 generations from a simple light-sensitive patch to a camera eye like ours under very conservative assumptions

Now THAT is interesting. Do you have some sources on this? When and where was it published - and how have the critics responded? This seems to be an estimate that is much better than the crudity of a back-of-the-envelope calculation. Also, note that last week Pharyngula had a nice post on the evolution of the eye in vertebrates (see: http://scienceblogs.com/pharyngula/2007/12/evolution_of_vertebrate_eyes.php).
Steven:
Accusing Polkinghorne of not engaging with those that disagree with him is not fair in my opinion – he is an extraordinarily well-read man and, from my perspective, seems to engage with a plethora of authors in many diverse areas of study. It is also ironic that you use Dawkins in your example. At least until a few years ago, it seems to me that he was the very epitome of a writer that did not engage in serious dialogue (eg. with Christian theologians & philosophers) and used only strawmen in his arguments. However, I also believe he has recently started to engage Christians in a more reasonable (at least less strident) way and that much of the Christian attack on Dawkins may no longer be valid (or parts of it may no longer be valid) – ie. we are responding to the old Dawkins & not the new Dawkins. The evolution of Dawkins is going to be very interesting.

geocreationist said...

I think that sooner or later you will be boxed scientifically into a corner where “there is no domino to tip”.
There only need to be 6 of them (1 per Creation Day), and all six are recorded in nature (though I've only documented 5 so far).

More importantly, I do not like the fact that “God had to step in”, as if he was ever absent from the process.
I agree God wasn't absent. In fact, He was there watching it (watching the dominoes fall if you may, which He set up). According to scripture, the Holy Spirit was hovering and the Son was there as the Father's master craftsman.

Also, recall that after watching the dominoes fall for a while, He often called it "good

RBH said...

Abstract of Nilsson & Pelger: http://tinyurl.com/2r6tbo

Dawkins' discussion of it:
http://tinyurl.com/3kzrq

Discussion of Berlinski's critique of it:
http://tinyurl.com/37a3xc

RBH

geocreationist said...

Nilsson and Pelger began with a flat retina atop a flat pigment layer and surmounted by a flat, protective transparent layer.
Assuming the article linked to has enough information to judge the study, the quote above describes a starting point that is both too much and not enough at the same time.

First of all, it assumes that every improvement can be taken advantage of. In other words, it assumes that the fish's brain will automatically evolve to exploit every improvement, every generation. (Don't misunderstand. I think the brain's evolution would keep up at some rate, but not necessarily in lockstep)

Furthermore, it assumes that taking advantage of the improvements results in more favorable selection 100% of the time.

But addressing these points in the model should not constitute a satisfactory response to an Old Earth Creationist, because the eye they started with is already too far along in the evolutionary process to diffuse an Intelligent Design argument.

To his credit, Dawkins states, "It would be nice, in the future, to do another computer model, this time at the level of the inside of the cell. to show how the first living photocell came into being by step-by-step modification of an earlier, more general-purpose cell."
Naturally, I would then want to go further back still, but this would take us in the right direction.

Of course, this stuff is only just registering on my radar, so if such advances have already occurred, I would be quite interested in the results.