Over the past year I have very much enjoyed posting almost 70 articles on this blog. I have also been happy to see the comments, likes, and post reblogging, and want to say thanks to all of the followers and other readers of the Book of Works.

It is summer time, and though I am quite busy with some deadlines, and ongoing work on long term projects, I am hoping to take some time off soon. So from today I am on blogcation, and will not be posting here for a few weeks.

I hope everyone has a great and relaxing rest of the summer, and I hope to see you back here in September.   Peace and joy to all.

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The Reasonable Ineffectiveness of Mathematics in the Biological Sciences


(With apologies to Wigner)

The fact that biology is not rich in theory is well known. Of the theories that do exist (such as Darwin’s theory of evolution), many have never been formulated into mathematical laws. Physics envy is a well-known propensity of those biologists who desire to be working on a more general understanding of whole fields (like cellular biophysics or regulation of gene expression) rather than on uncovering details of particular subsystems.

I used to be certain that the lack of mathematical rigor in biology was the fault of biologists, who generally are unable to grasp the fundamentals of even simple math. But that canard may be less true than it used to be (if it ever really was). With the explosion of systems biology and the development of algorithms for data mining, there are plenty of biologists around who are perfectly familiar with the manipulation of equations and concepts of theoretical formulation.

Certainly for some areas of biological science, good mathematical minds (taking a break from physics) have attempted for quite some time to apply their skill to producing the kind of laws that are (as Wigner put it) “true everywhere on the Earth, was always true, and will always be true.” And yet, success in these attempts has been limited at best.

Evolutionary biology is a good example. We certainly have a wonderful theory, one that has been well formulated, improved upon and expanded over the years to include data and concepts from many disciplines, and that has been supported beyond question as to its truthfulness. And yet, where is the law of evolution? Why can we not formulate a mathematical treatment of the evolutionary process, including inheritance of genotype, selection of the fittest phenotype, and fixation of that genotype in the population?

Of course, there are equations that can approximate some of the steps fairly well, but not the whole process. Is this because biologists are too stupid or lazy to come up with the right answers? Of course not, and even if they were, physicists have fared no better at the task, and not for want of trying.

So, what is the problem? I think the answer might be that biology is, unlike physics, simply not amenable to mathematical description. This is certainly not a new thought; biologists have been saying this for generations, although I have never believed it. The whole point of making a theory is to tame what seems to be a wild, complex mess of unconnected data into a tidy manageable package. But what if tidy manageable packages are something alien to biology? What if there is a fundamental truth behind the enormous difficulty of reducing biology to math?

Of course, mathematics doesn’t describe the real physical world very well, either. What it does is describe models of the real world perfectly, and the best laws for the models are used for real-world calculations. If the model is very good, the laws work well in the real world also.

Perhaps this is the problem. Perhaps there aren’t any really good biological models. In evolution, for example, one can develop a model, but as soon as we have one that can be predicted by an equation, we run into major difficulties. How can we define fitness so that it can be mathematically described? We cannot say that we will determine fitness by the number of offspring produced, because that leads to a circular argument. Fitness is a characteristic that cannot be quantitated a priori . But if we cannot assign a value of fitness to a characteristic, how can we model the process of natural selection?

The fitness issue is only one example of the problems facing the theoretical biologist in the construction and use of models. Take the cell. Or better, any functional cellular component, like ribosomes or chloroplasts. We know a great deal of the detail of the molecular mechanisms of protein synthesis, and we can make impressive videos or elaborate cartoons, but how can such a process be mathematically modeled with any degree of accuracy?

Actually the problem is much worse. There are very few biological entities or concepts that can be defined mathematically with sufficient precision to allow for making models. Even the idea of a species turns out to be very fuzzy. One definition of a species is a group of animals that can produce viable offspring only by mating with each other. The problem is, there are too many exceptions to this rule to make it mathematically precise.  And what about the majority of living species that don’t actually mate (like all the bacteria, and other monists)?

Sharing the same exact DNA sequence doesn’t really work, because individuals within a species don’t share their exact complete sequences, and it is impossible to draw the line between who is in the species and who isn’t on this basis. It seems that the idea of species is useful, but not very exact, and very hard to pin down.

So, it might be necessary, in order to make any mathematically based theoretical progress in biology, to either: 1. Invent some new kind of mathematics or formalism that is conducive to describing biological reality (as was done a number of time for physics); or 2. Give up on a mathematical treatment, and use something completely different. And no, I do not know what that might be, but it might need to stretch what we call science and methodological naturalism a bit. We might even need philosophy to get somewhere!. I can write this scientific heresy here, because this is my blog, and I can write anything I want. If you are reading this, you can also, and I would love to read what you think about this idea.

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My Talk on Evolutionary Biology

Here is the link to my recent talk at the American Scientific Affiliation Washington DC Metro Chapter, on June 24, 2016. Its a bit dark, and its long, but about half of the video is discussion from the audience, which is worth hearing.

Among the voices in the Discussion (the camera didnt move, so you cant see them) are Mike Beidler, Keith Furman, Anna Rich, Tom Burnett, Paul Arveson, Langston McKee, and a number of guests whose names I didnt write down.


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It’s in our DNA

Genes are amazing things. They are storehouses of information. They are also able to copy themselves (with some help), and they are the reason I am here typing. In the 1970s, evolutionary biologist Richard Dawkins had an insight that propelled him to write a book called The Selfish Gene. It was a brilliant, carefully thought-out theoretical and philosophical breakthrough in biology. It was also badly misunderstood. In the years and decades that followed publication, people who had not actually read the whole book complained that genes are not really selfish, since they have no minds to entertain such notions, and anyway, the term selfish is a negative one, and it makes evolution seem like an evil doctrine (which creationists already agreed it was).

The book makes it quite clear that our concept of selfishness has nothing to do with the point. What Dawkins is saying is that genes are the key components of the evolutionary process that involves selection of the most fit varieties of life. And since genes are the ultimate controllers and determinants of all the characteristics of all living organisms, what we end up with are genes that create the best possible cellular structures and features to allow those genes to keep on existing.

In other words, the selfish gene concept was actually a distilled and targeted demonstration of the root mechanism of evolution – natural selection. This is possible because genes do two things extremely well, and these happen to be the two most important things in biology: they replicate themselves with a very high degree of accuracy, and they code for all of the phenotypic characteristics of the cell that are the target of natural selection.

Think of a school board that is trying to decide between two textbooks. They do an experiment in which one class of students uses one text, and another class uses the other text. The students who used the first book do better on an exam than did those who used the second. So the School Board decides to order more of book 1. The books are the genes, the students’ knowledge are the phenotypes, the exam is the environment, and the school board is natural selection. Textbook 1 (which the school board didn’t even read) survives and becomes the only book in use. Nothing selects the genes themselves, but when the information in the genes is translated into the phenotype of the cell, the selection of the better phenotype leads to the selection of the better gene.

Dawkins’ view is that while the bird with the better eyesight might be better adapted and outcompete its rivals, what is successful is really the gene in that bird that coded for the better protein that produced the better eyesight. The phenotype (including later, the extended phenotype) is only a means to the gene’s ability to survive and continue to prosper.

It really is a very nice, consistent, logical and convincing idea. It’s also probably wrong.

At least that is the conclusion I have recently come to. I have always been pretty much a gene-centric kind of guy. As I said in my last post, I took the side of the replicator-first faction in origin-of-life discussions. I worked with genes and DNA, and I loved the way all of biology seemed to make good scientific sense if one simply ignored all the rest of life and just focused on genes. But alas, I can no longer support that view.

Part of the reason I am undergoing a conversion to a non-gene-centric view is the kind of new data and concepts about the extended evolutionary synthesis that I have discussed here before. Another part is that the idea of the gene as the absolute master of all of biology is just too simple, and biology is never, ever simple. The resurgence of the Lamarckian heresy; the importance of epigenetic effects, which can even be inherited (more heresy); and all of the results on niche construction, genomic engineering, and, of course, gene expression, have exerted their influence on my thinking.

I am not comfortable with all of this non-genic stuff. It makes everything more complicated and a lot harder. But if it is actually true that there is more to life than genes, I suppose there is no avoiding this. I have more to say about the whole subject, and I will in a later post. Meanwhile, it might be time to retire that well-known phrase “He has to do it that way. It’s in his DNA”. The big question now is, what do we replace it with?

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The “Brothers” Shapiro

Well, they aren’t brothers – they just share the same last name. I don’t think they knew each other. I don’t even know if they even knew the other existed. One of them, James is alive and well; sadly the other, Robert, died a few years ago. But in addition to their last name, they have something else in common. Both were scientists who changed my mind about evolution.

Bob Shapiro was a friend and a colleague of mine at NYU, where he was a Professor of Chemistry. For two semesters we co-taught a course in the School of Journalism on science for journalists. Bob was older than me, and senior in rank and reputation. We worked in similar areas related to the interactions of chemical carcinogens with cells and biomolecules. But Bob had started to become famous for something quite different -the science of the origin of life.

After teaching (we each lectured for about a half hour), we would go to a coffee shop in the Village near the campus and talk about science and life. At that time, I had no interest in Bob’s passion for the origin of life, but I was willing to listen to anything he had to say. With his quiet insistence he told me about his ideas and the state of the controversy that has always been at the heart of all scientific theories about the origin of life.

Life as we know it depends on two overarching characteristics: metabolism, which is the sum of all the chemical reactions that go on in cells, and genetic replication and expression, wherein the information that controls all of those reactions is copied and translated. Not surprisingly, the central controversy in the origin of life is about which of these two systems arose first. The replicator-first crowd will tell you (Richard Dawkins is the leading proponent) that replicating genes made of nucleic acids are the key and original components of living cells, and metabolism is a later invention, developed mostly to aid in the preservation and maintenance of the genes. The metabolism-first faction counters that nucleic acids need enzymes and other metabolic reactions in order to replicate, and life began as more or less automatic hypercycles of chemicals.

Bob Shapiro was one of the most convincing and outspoken advocates of the metabolism-first scenario. He published articles and spoke against the possibility that either DNA or RNA could have possibly been formed before life existed. I did not agree. I loved genes and DNA and was working on many aspects of genetics at that time (and later). I strongly admired Dawkins, and I was firmly in the replicator-first camp. But I didn’t argue with Bob; I cherished my time with him, and tried to learn as much as I could. Once the course ended, we saw each other rarely, working on different campuses and in different fields as he devoted more and more time and effort to his “hobby” of the origin of life.

I have not met James Shapiro, and had never heard his name until a few years back, when a friend suggested I look at some of his papers to gain an understanding of some new and interesting trends in evolutionary biology that is called the Extended Evolutionary Synthesis (EES). (That friend, btw, is an occasional commenter on this blog). Reading James Shapiro’s papers was an eye-opener for me. Like Bob, James is not a passionate fan of genes as the masters of all creation. In fact, James Shapiro is one of the leading architects of the EES, which is trying to replace neo-Darwinism as the standard model for evolutionary theory. According to James Shapiro, genes and their cellular and extracellular environments are engaged in a two-way interaction, with each having strong effects on the other. James calls this natural genetic engineering, and believes that a great deal of evolution that could not be easily explained by the traditional neo-Darwinian paradigm of gradual change from random mutations can in fact be due to rapid and dramatic changes brought on by the re-engineering of the genome by things like transposons, horizontal gene transfers, and large-scale amplifications.

I agree with James Shapiro. I have written about the EES in this blog and elsewhere (see “New Ideas in Evolutionary Biology, Parts 1 to 3, from August 2015), and am now working on some aspects of it. And I have recently decided that I also agree with my departed, dear friend, Robert Shapiro, that genes are not the be-all and end-all of life (although I still think genes are fantastic!). I have even come to the understanding that genes are not even essential for life (although they probably are for evolution. More on this later).

So thank you, Dr. Shapiro and Dr. Shapiro for your wise instruction, and may one of you continue to prosper and teach us, and may the other rest in well-deserved peace.

More on the subject of genes and their importance is coming. Watch this space.


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The Right Answer

Several decades ago, I welcomed a new graduate student to my lab. She had just graduated summa cum laude from a major Ivy League college, and she was as smart as can be. I put her to work on a project with happy anticipation of seeing wonderful results. I told her all about the project, which was to confirm a theory I had that the expression of two genes were linked in way to produce a specific phenotypic outcome. She spent several weeks learning the techniques and quickly mastered them. My technician, who was working with her, told me she was a quick learner, and her lab skills were great.

And then, I heard nothing from her. I asked her how things were going, and she just shrugged. My technician told me she was still working, repeating some experiments over and over, and she seemed depressed. One day I asked her to see me and tell me her progress. She came to my office reluctantly. After I asked her a few questions, she burst into tears. “What is it?” I asked her. “It didn’t work,” she told me. “I can’t get it to work”. This seemed strange to me. One of the secrets of scientific research is that most lab work doesn’t work. Not the first time. But her experiments were using techniques that we had mastered long ago, and based on what I had heard and seen, it didn’t seem likely that she had forgotten to add a crucial reagent, or had made a pipetting error, or set the temperature too high, or anything like that.

So for the next two days, I went over everything she had done in detail. It looked like all the experiments had gone just fine, and the results were clear But not at all what I had been hoping for. There was no correlation between the expression of the two genes and the phenotype. In other words, she felt she had failed because she had gotten the “wrong” answer.

I understood the problem. My student had only just finished a long, highly successful career of learning a gigantic quantity of facts and ideas, and she knew the right answers to any question one might ask her. What she didn’t understand was that when we do research, the right answer is anything that we find out, not what the Professor thinks the right answer should be. I tried to explain this to her, and she seemed to understand, and kept working. Pretty soon, she had found out why the original idea was wrong, and what the real mechanism was to explain the phenotype. I was thrilled, and we published several papers on the subject. But despite this success (and having her name on some pretty good papers), she never really recovered from her disappointment, and eventually left my lab.

I have always said that our educational system is not geared at all to the research enterprise. First, students are taught nothing about failure, which is the most common experience of all researchers. Failure is not a bad thing – it’s an opportunity to learn. When things go wrong, there is a reason. Usually the reason is just that somebody goofed, or the water wasn’t pure enough or something mysterious happened. And sometimes the failure is actually a hidden success waiting to be found.

Once, a postdoctoral fellow in my lab showed me a photo of DNA bands with one of the spots in the completely wrong place. We chalked it up to some kind of experimental mistake. But then we found it again, and realized that this was actually a new discovery – we had found a brand new allele of an important gene, never seen before.

I was reminded of this two weeks ago when I met Professor Stuart Firestein of Columbia University at a workshop I had organized. Firestein has a TED talk that I highly recommend, ( and has written popular books on the subjects of ignorance and failure in science. He got the idea for the books and talk from a course he developed and taught called “ignorance”. He had scientists come in and lecture on what was not known in their fields.

In addition to the problem that ignorance and failure are not properly treated in our educational systems, there is, I believe, a profound philosophical and perhaps theological aspect to the subject of ignorance in the sciences. This relates to a deceptively simple question – How much can we know? More about that in a future post.

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Tweeting and God

My busy two weeks of meetings and deadlines is now past, and I can devote myself to important stuff like lying on the hammock, watching the garden grow, and blogging.

I recently started using Twitter to expand my social network life. I generally tweet a link whenever I put up a new post here or publish something. But more recently I have begun just tweeting stuff that I think of. Doing this in 140 characters is a challenge for me (as my regular readers can imagine), but I have managed a few times.

I don’t have many followers as yet (still learning the system), but a couple of recent tweets did get some attention. This was one.

  1. What would you say if science learned how life began, what caused the Big Bang, and why all constants are fine-tuned? A: Praise God.

If we knew ALL that happened through purely natural means, wouldn’t God be “redundant” (Dawkins)?

Nope, because “purely natural means” are the methods by which God creates. Without God there is no nature. This idea removes any force from the well-worn atheist argument that science can explain the world better than religion can. Of course its true that science explains how things work What many atheists cannot seem to fathom is that religion’s purpose is not to explain the world, but to understand the divine in human beings, and God’s purposes for us.

Atheists keep telling us that our “claim” that God exists requires extraordinary evidence. Why? We are not claiming to prove that God exists. Instead we witness to our belief in God. To the question, “what evidence do you have for the existence of God?”, there are several equally valid answers, among which is “none”. Other answers can range from purely subjective emotional experience (which are generally dismissed as psychological ephemera) to metaphysical views about the universe, which are generally dismissed as God of the Gaps, soon to be overturned by science.

The truth is that science “explains” nothing, it isn’t supposed to. What it does do is illuminate the laws and mechanisms by which things work, and events happen. It doesn’t tell us why things happen that way, or how they should happen, or what’s behind it all. Likewise, religion isn’t supposed to elucidate physical or natural mechanisms. When it used to do that, it was only because religion was the only organized thought system around at the time, so people turned to it for explanations.

The other tweet that garnered some interest in the form of retweets and likes is related to the same discussion on my views of how science and faith are related.

Science discovers and describes natural laws. Natural laws come from God. So how could science displace God? Science is distilled doxology.

I like that last 4 word sentence, and I thought it was worth reposting here.


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