Mathematical Challenges To Darwin’s Theory Of Evolution

Post Reply New Topic

Been away for a month. This seems like an interesting topic.

https://www.hoover.org/research/mathema ... -and-david



Based on new evidence and knowledge that functioning proteins are extremely rare, should Darwin’s theory of evolution be dismissed, dissected, developed or replaced with a theory of intelligent design?

Has Darwinism really failed? Peter Robinson discusses it with David Berlinski, David Gelernter, and Stephen Meyer, who have raised doubts about Darwin’s theory in their two books and essay, respectively The Deniable Darwin, Darwin’s Doubt, and “Giving Up Darwin” (published in the Claremont Review of Books).

Robinson asks them to convince him that the term “species” has not been defined by the authors to Darwin’s disadvantage. Gelernter replies to this and explains, as he expressed in his essay, that he sees Darwin’s theory as beautiful (which made it difficult for him to give it up): “Beauty is often a telltale sign of truth. Beauty is our guide to the intellectual universe—walking beside us through the uncharted wilderness, pointing us in the right direction, keeping us on track—most of the time.” Gelernter notes that there’s no reason to doubt that Darwin successfully explained the small adjustments by which an organism adapts to local circumstances: changes to fur density or wing style or beak shape. Yet there are many reasons to doubt whether Darwin can answer the hard questions and explain the big picture—not the fine-tuning of existing species but the emergence of new ones. Meyer explains Darwinism as a comprehensive synthesis, which gained popularity for its appeal. Meyer also mentions that one cannot disregard that Darwin’s book was based on the facts present in the 19th century.

Robinson then asks the panel whether Darwin’s theory of gradual evolution is contradicted by the explosion of fossil records in the Cambrian period, when there was a sudden occurrence of many species over the span of approximately seventy million years (Meyer’s noted that the date range for the Cambrian period is actually narrowing). Meyer replies that even population genetics, the mathematical branch of Darwinian theory, has not been able to support the explosion of fossil records during the Cambrian period, biologically or geologically.

Robinson than asks about Darwin’s main problem, molecular biology, to which Meyer explains, comparing it to digital world, that building a new biological function is similar to building a new code, which Darwin could not understand in his era. Berlinski does not second this and states that the cell represents very complex machinery, with complexities increasing over time, which is difficult to explain by a theory. Gelernter throws light on this by giving an example of a necklace on which the positioning of different beads can lead to different permutations and combinations; it is really tough to choose the best possible combination, more difficult than finding a needle in a haystack. He seconds Meyer’s statement that it was impossible for Darwin to understand that in his era, since the math is easy but he did not have the facts. Meyer further explains how difficult it is to know what a protein can do to a cell, the vast combinations it can produce, and how rare is the possibility of finding a functional protein. He then talks about the formation of brand-new organisms, for which mutation must affect genes early in the life form’s development in order to control the expression of other genes as the organism grows.

“Intelligent design” is something only Meyer agrees with, but Berlinski replies that as a scientific approach, one can agree or disagree with it, but should not reject it. Meyer talks about the major discovery in the 1950s and ’60s concerning the DNA molecule, which encodes information in a somewhat digital format, providing researchers with the opportunity to trace the information back to its source. Gelernter argues that if there was/is an intelligent designer then why is the design not the most efficient, rather than prone to all sorts of problems, including the mental and emotional.

Robinson quotes Gelernter: “Darwinism is no longer just a scientific theory but a basis of a worldview, and an emergency . . . religion for the many troubled souls who need one.” Gelernter further adds that it’s a fantastically challenging problem that Darwin chose to address. How difficult will it be for scientists to move on from Darwin’s theory of evolution? Will each scientist need to examine the evidence for his or herself? These are some of most important questions facing science in the 21st century.

Eh, evolutionary adaptation is proven fact. Self-replicating organisms can mutate and change to survive in different circumstances. This has been observed and even purposely generated on human timescales. The theory of evolution states that the diversity of life arose from this evolutionary adaptation. Give me a functional single celled organism, 2.5 billion years of random change with a selection pressure for positive changes, and I can believe you get all of life on earth.

I suppose the premise here is the origin of life, which is a major unknown as how to get to a functional cell from base chemicals is really really challenging. I know a guy at my university who is working on that right now by randomly mixing amino acids together and seeing if you get any self-promoting polymers. The generation of amino acids from a chemical reaction has already been famously demonstrated, so if you could get polymers that promoted their own formation you have an extremely primitive form of life.

As for modern evolution of say the whale evolving from land animals, the fossil record is pretty convincing on many of these transitions. Unless we're going through "the fossil record is a joke played by god." Whenever someone doubts that large changes in species can happen, remember that technically speaking a chihuahua and a St. Bernard are the same species of animal.

I'll check out what they say because the Hoover Institute is very reputable and likely has a good discussion going, and at least from the summary it seems like the guy they have is not a total crackpot.

Applying mathematics to a random, convoluted process? First, let's check the sources...

David Berlinski received his PhD in philosophy from Princeton University. He has taught philosophy, mathematics and English at Stanford University, Rutgers, the City University of New York and the Université de Paris. He was a research fellow at the International Institute for Applied Systems Analysis (IIASA) in Austria and the Institut des Hautes Études Scientifiques (IHES) in France.

David Hillel Gelernter is an American artist, writer, and professor of computer science at Yale University. He is a former national fellow at the American Enterprise Institute and senior fellow in Jewish thought at the Shalem Center, and sat on the National Endowment for the Arts. He publishes widely; his work has appeared in The Wall Street Journal, New York Post, Los Angeles Times, The Weekly Standard, Frankfurter Allgemeine Zeitung, and elsewhere. His paintings have been exhibited in New Haven and Manhattan. He is known for contributions to parallel computation and for books on topics including computed worlds (Mirror Worlds), and what he sees as the destructive influence of liberal academia on American society, expressed in his book America-Lite: How Imperial Academia Dismantled Our Culture (and Ushered in the Obamacrats).

Stephen C. Meyer (born 1958) is an American advocate of the pseudoscientific principle of intelligent design. He helped found the Center for Science and Culture (CSC) of the Discovery Institute (DI), which is the main organization behind the intelligent design movement. Before joining the DI, Meyer was a professor at Whitworth College. Meyer is a Senior Fellow of the DI and Director of the CSC. Meyer graduated with B.S. degrees in physics and earth science in 1981 from the Christian Whitworth College, then worked as a geophysicist for the Atlantic Richfield Company (ARCO) in Dallas from November 1981 to December 1985. Meyer then took up a scholarship from the Rotary Club of Dallas to study History and Philosophy of Science at Cambridge University in England. His 1990 dissertation was entitled "Of clues and causes: A methodological interpretation of origin of life studies." Meyer received his Ph.D. from Cambridge in 1991. In Fall 1990 he became an assistant professor of philosophy at Whitworth, where he was promoted to Associate Professor in 1995, and gained tenure in 1996. In Fall 2002 he moved to the position of professor, Conceptual Foundations of Science, at the Christian Palm Beach Atlantic University. He continued there to Spring 2005, then ceased teaching to devote his time to the intelligent design movement.

Not a single geneticist or evolutionary biologist in the group. Only philosophers, mathematicians, English teachers, artists, writers, computer scientists, physicists, and a wooist in "Intelligent Design".

It never ceases to amaze my how some people with expertise in one area of study will appropriate for themselves expertise in every other subject imaginable.

Lacking expertise in genetics and evolutionary biology behind the challengers to Darwin's Theory of Evolution, I think we can ignore their fake science, abject quackery, and self-serving publicity.

Yes this is the problem. They say Darwin is good for micro-scale evolution, but given what we learned from observing it on a human timescale and what is now known about genetic information and mutation rates, genetic code and all that - the maths says it is just improbable to the point of impossible that a few billion years could have produced the diversity we see today. The Cambrian explosion is even more troublesome as that implies a period of hyper-speed evolution on a small timescale. All of this is not to say that intelligent design and God's magic wand is the answer, just that we might need to go back to the drawing board for explaining the origin of species and the fossil record.



This shouldn't actually be too surprising if you know any biologists. Biologists generally suck at mathematics and it's from mathematics and information theory that this challenge comes.

I.e., it comes from people who generally suck at biology.

I'll have to watch the video to see what the mathematics of it are. I usually don't tout my background around here, but my graduate work is in the genetic engineering of microbes while my undergraduate degree is in chemical engineering. I have both the mathematical and biological expertise to critically evaluate their theses.

What I suspect is that they used a fixed mutation rate based on current observed average levels.

I couldn't say without reading the books, there's not a great deal of detail in the first video, it's pretty light on numbers. However I have heard a similar argument based on fixation rates from Vox Day (an economist by training hehe) when he debated some phd on youtube earlier this year. I'll dump the videos and relevant notes/posts I can find here. Much more to dig into compared to the first video if you're interested. I know I'm interested in your take(down?).

The debate:


It wasn't Vox at his best, but JF's primary objection of parallel propagation is wrongheaded, given that it was occurring in the Nature study and accounted for by the average.

Vox post debate:


Later notes: Possibly the most interesting thing about this debate was how it demonstrated the power of rhetoric to persuade those incapable of understanding dialectic. More than a few of JF's fans sincerely believe that he blew both me and my case away despite the obvious fact that he didn't even begin to address the latter. For example:

-He claimed that mutation rates rather than fixation rates were more relevant to my case, even though "the fixation probability is one of the cornerstones of population genetics."
-He failed to grasp that the 2009 Nature study specifically involved parallel gene fixation, thereby accounting for the entirety of his objection to my case. He thought my case assumed a successive-mutations regime even though the study obviously concerned a concurrent-mutations regime.
-He retreated to rhetoric and misdirection by bringing up that list of genome sizes and population mutation rates, neither of which said anything about actual fixation probabilities or time frames.
-The fact that there are "millions and billions of mutations" says absolutely nothing about how fast a single mutation propagates through an entire population, let alone provides part or all of the basis for a speciation event. The fact that each human child is born with an average of 70 mutations doesn't say anything about how long it took to fix the genetic structure of the human eye throughout the entire human population.

---

He's going to be suffering a lot more once people start explaining the difference between rhetoric and dialectic to him, to say nothing of the fact that he completely failed to understand that I specifically addressed the possibility - which is not at all the certainty that he assumes it to be - that fixation rates are considerably faster in mammals than in bacteria for a variety of proposed reasons that include the Fisher–Muller effect and the Ruby in the Rubbish effect, among others. And I did so in the debate, he simply did not understand that I had done so, and not only that, that I had done so in a manner extremely favorable to the orthodox perspective.

Remember, in my initial bacterial model, I utilized the observed average fixation rate of 1,600 generations. First notice that JF completely omits to mention that he incorrectly assumed that this was a successional-mutations regime and tried to claim that I was wrong because I was unaware of parallel mutations. However, it was a concurrent-mutations regime, which is why I pointed out in my post-debate analysis that JF was wrong and that particular objection was irrelevant.

Second, I directly addressed the possibility of faster fixation rates in mammals. In fact, I came up with a completely different fixation model which was built around the idea of a minimum viable population mutating into a recurring series of minimum viable populations. It should be conceptually impossible for fixation to occur any faster than this barring genetic engineering, even if we take asteroids, volcanoes, Biblical floods, and other possible catastrophes into account. This rate reduced the average fixed mutation propagation time from 1,600 to 15.7 generations, more than two orders of magnitude faster than the observed parallel fixation rate. And despite this average rate being considerably faster than any fixation event that has ever been observed or even seriously proposed, the recurring minimum viable population scenario still renders even the maximal evolutionary timelines highly improbable to the point of being considered a mathematical impossibility given the observed genetic differences.

And finally, his claim that fixation is a mathematical illusion is belied by the continued attempts of more serious and competent biologists to address that very issue.

I'm afraid I couldn't find the details of his other model that estimates the maximum possible fixation rate at 15.7 generations.

--

My thoughts having rewatched it: Without knowing much about the subject I can see where biologists might go with this without ditching the whole theory in the bin. You could, using similar maths to Vox try to estimate a necessary fixation rate given the time frame available and figure out the likelihood of being able to see and measure that on a human timeframe if were the rate of speciation/fixation assumed to be quite gentle and serene. Vox from his basic calculations said you might expect to have measured something by now. If that hasn't been measured or observed I guess you would rework the model of evolution into periods of relative stagnation and periods of insane evolution which would also happily make the Cambrian thing less strange. Still that idea rather unhelpfully raises more questions.

I remember reading Signature in the Cell back in 2009. As I remember there's a lot of focus on the shelf-life of the amines that make up the lattice of DNA and combinatorial problems that put self-assembly somewhere in the 1 in 10^-80's.

It's easy perhaps to say that how things got from one state to the next is incomplete. RNA world hypothesis is an interesting idea, ie. that RNA chains were forming before the first cells, lipids were forming bubbles, and eventually the two came together. All of this over a billion or so years going from free-floating precursors to the first prokaryote fits intuitively but if it were dead mechanism it still also offers no insight as to why there's any 'I' experience to be had. This is part of why panpsychism, dual-action monism, and idealism seem to be coming back.

I guess my question about intelligent design is - what's the goal? Would these men be okay if the best explanation in line with their observations was some sort of animism, pantheism, or polytheism? Would they be okay if it pretty much proved Daoism to be the most accurate religion or made us rearrange our Greek philosophers to put Heraclitus in a more renowned position? I would guess the evidence would show in how ecumenical they are in their travels, who they'll do research with, and how well they shoulder caustic criticism.

So I watched the Vox Day - JF debate and about 20 minutes of his post debate talk before I got bored. I think Vox Day asks some important questions, and it's important that scientific theories stand upto questioning.

In my opinion Vox makes a few crucial mistakes:

1) Over-reliance on a single laboratory study. Laboratory conditions for E. coli and Yeast are close to ideal as such selective pressure is very low. Selective pressure is what accounts for how fast a mutation can be fixed. An example of this is an antibiotic resistance. Certain antibiotic resistances can arise from a single mutation to an already functioning gene. If you bombard a population with antibiotics that mutation will be fixed in a single generation as every non-mutant dies. However, if you expose the bacteria to low levels of antibiotic that slightly slow their growth rate it will take hundreds are generations for it to become fixed. Vox's initial estimate off of ideal lab experiments was 33 billion fixed mutations. He refutes this by referencing real environmental generation times. However, the decrease in growth rate is offset by increase in selective pressure. The bacteria grow slower, because they are in a more challenging growth environment. Thus, the 33 billion fixed mutation estimate is the more likely of the two estimates. Combinatorially 33 billion mutations easily accounts for all prokaryote life on earth (the largest of whom have genomes of 13 million base pairs or 3 orders of magnitude ).

2) Not understanding the parallelization with regards to selective events. Vox assumes that because there is an average fixation rate that this accounts for parallelization. However, this fails to account for selective events. This fails to account for selective events. Say you have a single person with an extremely advantageous mutation. To the point that their mutation ensures them as common ancestor to the entire human race. (IF you think this is far-fetched look up mitochondrial eve). The fixation rate is not just of their mutation, but of all the accumulated mutations they acquired since the last common ancestor. Humans are born on average with 75 mutations. If there were say 10 generations between the last common ancestor of all humans and the second-last common ancestor of humans than there would be 750 mutations between the two. All 750 of those mutations become fixed by the common ancestor advantage. Thus the rate of mutation fixation is actually very close to the mutation rate per generation (there are some revertants back) when you factor in selective events. At 20 years per generation, needing 30 million mutations, and getting 75 per generation you can have the earliest human-chimp ancestor at 8 million years ago, which is within the estimates.

3) The "white skin" example. I'll have to admit to a little queasiness when Vox discussed this. His assumption is that white skin confers an advantage to the entire human race. This is obviously false as white skin is detrimental in some areas of the world while advantageous in others. He contends that white skin not being fixed in 8000 years is evident of it taking 400+ generations to fix a trait. Problem is mutlifold. First, white skin did fix in populations where it was advantageous. Find me a person with ancestry 100% from Russia, Scandinavia, or Great Britain without white skin today. Conversely find me a person with 100% ancestry from any equatorial society that does not have dark skin. These are divergent traits each of which holds predominance in a certain climate.

Absolutely 100% agree. I love these heretical science threads despite the appeals to authority that inevitably follow.



Selective events are what he made the second model for (which I still can't find on paper) where using overly generous assumptions in favour of the orthodox theory maximum fixation rate is calculated at 15.7 generations. He describes it as a model that has a species repeatedly experiencing selection events down to a minimum viable population over time, where that reduction in population is also assumed to increase the rate of fixation (again a questionable assumption, given what is observed today).

He also mentions it in this video at about 41:00



Rough transcription:

Let me point out the bottleneck issue. One retreat that they make is they claim "What if there is a catastrophe and then only the mutated individuals survive and then a whole bunch of mutations get fixed all at once. The problem there, the reason it doesn't work is the concept of the minimum viable population. What that have found in a declining population - one that gets subject to a bottleneck - that means that the species usually goes extinct. That's why environmentalists are so worried about so many of these species - because they are dropping well below the minimum viable population... They are not evolving much faster and becoming much more fit because they are experiencing severe population bottlenecks - they are just going extinct. While there may have been a couple that survived population bottlenecks ... in general their mutations tend not to increase fitness

There's also another problem with using the the chimp-human LCA. He uses the statistic that humans are 98% chimp. This is apparently an estimate based on the time needed for the species to diverge using the old evolution models. Now that the genomes are actually being mapped and compared : The true figure may be lower which puts extra pressure on the model.



Yeah Vox loves leaping over the politically correct line, I guess I'm used to it from him, but I don't recall him saying that. I think he was just pointing out that white skin does not homo sapiens make - it is not fixed in the human species as a whole, as part of his counter to JF's strange human-chimpanzee "spectrum" and his handwaving of fixation in favour of plain mutation.

Evolution stares us in the face.

Maybe not Darwin’s conception of it specifically....but evolutionary adaptations abound right before our eyes.

It's not a bottleneck issue its a mutation rate issue. Certain mutations are species defining. These are carried by common ancestors. In between the common ancestors are generations during which mutations accumulate. Natural selection, selects for the best of these mutations. Take a human-chimp example:

Gen 1: Last common ancestor between humans and chimps

Gen 2: 75 new mutations from the Last common ancestor between humans and chimps

Gen 3: 75 new mutations from gen 2, plus 75 inherited mutations (32.5 from each parent) from the last common ancestor between human and chimp for 150 total mutations

Gen 4: 225 total mutations (150 inherited, 75 new)

Now let's assume a low birth rate of 2.

Gen 1: 0 mutations selected from pool of 0 mutations (1 individual)

Gen 2: 75 best mutations selected from pool of 150 mutations (2 individuals)

Gen 3: 150 best mutations selected from pool of 300 mutations (4 individuals)

Gen 4: 225 best mutations selected from pool of 600 mutations (8 individuals)

As you can see over time the pool of potential mutations increases exponentially, while the number of accumulated mutations increases linearly. By the time you get to the next common ancestor you will have accumulated 75 times the number of generations. Natural selection and sexual recombination will select for the best of those mutations from the pool of potential mutations, but they must accumulate.

Seems a bit inane to me.

They aren't saying "evolution is wrong", and "Genesis is the literal truth, and the earth is only six thousand years old".

They are saying that the modern view that "evolution through natural selection" explains it all is only mostly right, but not totally right, and that God had to nudge natural selection along to get where we are. They don't seem to be denying evolution. Its only the "natural selection" part that they have a problem with.

Or that's what they SEEM to be saying. If not then I don't what they are claiming.

IF you're gonna claim that "the Cambrian Explosion shows this and that" then you are admitting that there WAS such a thing as the Cambrian Explosion, which means you're admitting that the Earth is old, and that living things have gradually changed over time (ie the definition of "evolution"), and that natural selection plays a role in the origin of species, and in the extinction of species. In defending God you have thrown your Young Earth Creationist allies under the bus by denying a young Earth. And your also playing around with "Christian Evolution" which is an actual heresy. Its worse than straight up Atheistic Darwinism.

Its also kinda like saying "that car crash you were in wasn't just an accident. God willed it. And I can prove it mathematically!". We cant know enough about your car accident to prove "mathematically" that it "wasn't an accident" and was willed by a "intelligent ruler of the Universe". So how could we do that with something in the fossil record?

If you're a hard core atheist then I suppose that you need to defend atheism from their claims. So folks on both extremes -Fundies/YECS,on one hand, and militant Atheists,on the other, will need to mobilize themselves against this guy's theory.

More mainstream thinkers in the middle who accept that some sort of evolutionary process occurred , and who are not necessarily atheists, are not really effected much in their thinking by this. Except for one crucial issue. It makes for a really BAD model for scientists to follow.

Science is driven by the need to seek naturalistic explanations for things. You investigate, say, the Cambrian Explosion, by postulating that it happened because of certain conditions on earth at the time. You don't investigate it by saying "god waved a magic wand and it just happened". That doesn't lead anywhere.








But not all folks who are not evolution deniers are atheists.

Yeah I think I'm seeing it. One very beneficial mutation could fix a ton of mutations in a relatively short time - it wouldn't be totally implausible for one common ancestor of an extant species to have fixed a million+ mutations in one shot, so to speak. 15 of that in one and 15 in the other of that over a few million years and you are there, though I doubt it's quite so chunky. Yeah I can see it, thanks.

From this you would not expect any kind of uniform rate of fixation, correct? Making a true average fixation rate both unobservable in the present and fairly useless going forward... I don't know if you watched the last video. Vox suggests comparing old human DNA (they found some pretty old stuff preserved somewhere) to new, then ascertaining the number of fixed mutations that have occurred and comparing that to what would be expected from a modeled average and evolution is therefore falsifiable. But I can see it is possible to find none at all or too many from such an experiment.

Yeah a uniform rate of fixation would not be expected at all, as its entirely dependent on the selection conditions. In fact I'd be very surprised if the mutation rate was constant either, as stressful environmental conditions increases mutation rates in bacteria and I would guess do the same in animals.

I'm not interested in arguments from improbability because they assume a limited number of trials whereas I believe that given enough time all physical possibilities will be actualized and so all improbable events are actually inevitable. I'll be interested once you determine that evolution or natural abiogenesis are actually 'impossible'.