## God Could Have Caused Birds to Fly With Their Bones Made of Solid Gold

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## Beauty, Melody, and Entropy are an Equivalence Class

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## How to Sidestep Mathematical Equations in Popular Science Books

In the publishing industry there is a general rule-of-thumb that every mathematical equation included in a book will cut the audience of science books written for a popular audience in half – presumably in a geometric progression. This typically means that including even a handful of equations will give you an effective readership of zero – something no author and certainly no editor or publisher wants.

I suspect that there is a corollary to this that every picture included in the text will help to increase your readership, though possibly not by as proportionally a large amount.

In any case, while reading Melanie Mitchell’s text Complexity: A Guided Tour [Cambridge University Press, 2009] this weekend, I noticed that, in what appears to be a concerted effort to include an equation without technically writing it into the text and to simultaneously increase readership by including a picture, she cleverly used a picture of Boltzmann’s tombstone in Vienna! Most fans of thermodynamics will immediately recognize Boltzmann’s equation for entropy, $S = k log W$, which appears engraved on the tombstone over his bust.

I hope that future mathematicians, scientists, and engineers will keep this in mind and have their tombstones engraved with key formulae to assist future authors in doing the same – hopefully this will help to increase the amount of mathematics that is deemed “acceptable” by the general public.

## Book Review: Gregory Chaitin’s “Proving Darwin: Making Biology Mathematical”

Gregory Chaitin’s book Proving Darwin: Making Biology Mathematical combining biology, microbiology, mathematics, evolution and even information theory is directly in my wheelhouse. I had delayed reading it following a few initial poor reviews, and sadly I must confirm that I’m ultimately disappointed in the direct effort shown here, though there is some very significant value buried within. Unfortunately the full value is buried so deeply that very few, if any, will actually make the concerted effort to find it.

This effort does seem to make a more high-minded and noble attempt than what I would call the “Brian Greene method” in which an academic seemingly gives up on serious science to publish multiple texts on a popular topic to cash in on public interest in that topic through sales of books. In this respect Chaitin is closer to Neil deGrasse Tyson in his effort to expound an interesting theory to the broader public and improve the public discourse, though I would admit he’s probably a bit more (self-) interested in pushing his own theory and selling books (or giving him the benefit of the doubt, perhaps the publisher has pushed him to this).

Though there is a reasonable stab at providing some philosophical background to fit the topic into the broader fabric of science and theory in the later chapters, most of it is rather poorly motivated and is covered far better in other non-technical works. While it is nice to have some semblance of Chaitin’s philosophy and feelings, the inclusion of this type of material only tends to soften the blow of his theoretical work and makes the text read more like pseudo-science or simple base philosophy without any actual rigorous underpinning.

I’m assuming that his purpose in writing the book is to make the theories he’s come up with in his primary paper on the topic more accessible to the broader community of science as well as the public itself. It’s easy for a groundbreaking piece of work to be hidden in the broader scientific literature, but Chaitin seems to be taking his pedestal as a reasonably popular science writer to increase the visibility of his work here. He admittedly mentions that his effort stems from his hobby as his primary area is algorithmic information theory and computer science and not biology or evolution, though his meager references in the text do at least indicate some facility with some of the “right” sources in these latter areas.

Speaking from a broad public perspective, there is certainly interest in this general topic to warrant such a book, though based on the reviews of others via Amazon, Goodreads, etc. the book has sadly missed it’s mark. He unfortunately sticks too closely to the rule that inclusion of mathematical equations is detrimental to the sale of ones books. Sadly, his broader point is seemingly lost on the broader public as his ability to analogize his work isn’t as strong as that of Brian Greene with respect to theoretical physics (string theory).

From the a higher perspective of a researcher who does work in all of the relevant areas relating to the topic, I was even more underwhelmed with the present text aside from the single URL link to the original much more technical paper which Chaitin wrote in 2010. To me this was the most valuable part of the entire text though he did provide some small amount of reasonable detail in his appendix.

I can certainly appreciate Chaitin’s enthusiastic following of John von Neumann but I’m disappointed in his lack of acknowledgement of Norbert Weiner or Claude Shannon who all collaborated in the mid part of the 20th century. I’m sure Chaitin is more than well aware of the father of information theory, but I’ll be willing to bet that although he’s probably read his infamous master’s thesis and his highly influential Bell Labs article on “A/The Mathematical Theory of Communication”, he is, like most, shamefully and wholly unaware of Shannon’s MIT doctoral thesis.

Given Chaitin’s own personal aim to further the acceptance of his own theories and work and the goal of the publisher to sell more copies, I would mention a few recommendations for future potential editions:

The greater majority of his broader audience will have at least a passably reasonable understanding of biology and evolution, but very little, if any, understanding of algorithmic information theory. He would be better off expounding upon this subject to bring people up to speed to better understand his viewpoint and his subsequent proof. Though I understand the need to be relatively light in regard to the number of equations and technicalities included, Chaitin could follow some of his heroes of mathematical exposition and do a slightly better job of explaining what is going on here. He could also go a long way toward adding some significant material to the appendices to help the higher end general readers and the specifically the biologists understand more of the technicalities of algorithmic information theory to better follow his proof which should appear in intricate glory in the appendix as well. I might also recommend excising some of the more philosophical material which tends to undermine his scientific “weight.” Though I found it interesting that he gives a mathematical definition of “intelligent design”, I have a feeling its intricacies were lost on most of his readership — this point alone could go a long way towards solidifying the position of evolution amongst non-scientists, particularly in America, and win the support of heavyweights like Dawkins himself.

I’ll agree wholeheartedly with one reviewer who said that Chaitin tends to “state small ideas repeatedly, and every time at the same shallow level with astonishing amount of redundancy (mostly consisting of chit-chat and self congratulations)”. This certainly detracted from my enjoyment of the work. Chaitin also includes an awful lot of name dropping of significant scientific figures tangential to the subject at hand. This may have been more impressive if he included the results of his discussions with them about the subject, but I’m left with the impression that he simply said hello, shook their hands, and at best was simply inspired by his having met them. It’s nice that he’s had these experiences, but it doesn’t help me to believe or follow his own work.

For the technically interested reader, save yourself some time and simply skim through chapter five and a portion of the appendix relating to his proof and then move on to his actual paper. For the non-technical reader, I expect you’ll get more out of reading Richard Dawkins’ early work (The Selfish Gene) or possibly Werner R. Loewenstein’s The Touchstone of Life: Molecular Information, Cell Communication, and the Foundations of Life.

Though I would certainly agree that we could use a mathematical proof of evolution, and that Chaitin has made a reasonable theoretical stab, this book sadly wasn’t the best one to motivate broader interest in such an effort. I’ll give him five stars for effort, three for general content, but in the end, for most it will have to be at most a 2 star work overall.

This review was originally published on June 17, 2013.

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## Book Review: Jared Diamond’s “The World Until Yesterday: What Can We Learn from Traditional Societies?”

I’m honestly shocked that no one else has written a book similar to The World Until Yesterday: What Can We Learn from Traditional Societies prior to now. It’s certainly a wonderful synthesis and a fantastic resulting thesis based on an incredibly broad array of areas of study over a lifetime of work.

I personally don’t think that it is as significant as Guns, Germs, and Steel: The Fates of Human Societies was, though perhaps it should be just as (if not more) ground shaking for modern society. As a long-time student of evolutionary biology and other fields related to this work, I’m not as impressed with the effort as I might otherwise be since most of the overarching thesis is second nature to me. It does however have some superb anecdotes and broad reviews of large areas of literature to provide some excellent motivation that I might not otherwise have spent the time to find thus giving it some excellent value to me.

As for others in the general public, I highly recommend it for it’s simple and clear examples and the ultimate thesis which are exceptionally worth reading (and implementing) into one’s life as well as into broader areas of modern society. If nothing else, it points out how drastically life has changed for human societies even in the last 150 years, much less the last 10,000.

For those in the field or with an interest in Big History, this is certainly a must-read and possibly an excellent place to start for those without any background at all.

Based on my own personal background, I’d give this 3 stars (in terms of it’s direct value to me), but for the general public it’s easily a 5 star work. I do wish that it had been more traditionally and extensively footnoted, but for a broader audience I certainly understand Dr. Diamond’s reasons for publishing it as he did.

## Review of “Major Transitions In Evolution” by Anthony Martin and John Hawks

Overall this series of 24 video lectures from The Teaching Company as part of their Great Courses series is a great introduction to evolution and many of its interdisciplinary sub-fields. I particularly enjoyed seeing the perspective of a geologist/paleontologist to start things off and then the tag-team to cover human evolution from primates.

I especially loved the philosophical conceptualization of “deep time” (in analogy with “deep space”) particularly as one considers the even broader idea of “Big History“. Though the professors here don’t delve into Big History directly, they’re covering a large portion of the cross-disciplinary and inter-disciplinary studies which underpin a large portion of the field. More specifically taking the general viewpoint of “transitions” in evolution underlines this conceptualization.

Though the transitional viewpoint seems to be a very natural and highly illustrative one to take, I would be curious in seeing alternate presentations of evolution from a pedagogical standpoint. It was nice to hear a bit of alternate discussion in the final lecture as well as discussion of where things might “go from here.”

I do wish that there were additional follow-on lectures that covered additional material in more depth. It would also have been nice to have included a handful of lectures from a microbiologist’s viewpoint and background to give some additional rounding out of the material and this could have been done either in the early parts of the material or certainly around the discussions of primate evolution. Overall all though, these are wonderfully self-contained and don’t require a huge prior background in material to understand well.

It’s always great to see lecturers who truly love their fields and have the ability to relate that through their lectures and infect their students.

From a purely technical standpoint, I’m glad to see that The Teaching Company only offers a video version of (as opposed to their usual additional offering of audio-only) as having pictures of the fossils and organisms under discussion and their relative physiological structures was very helpful. Additionally having the recurring timecharts of the portions of geological time under discussion was very useful and generally reinforcing of the chronology. Somewhat monotonous from a visual perspective was the almost programmatic back and forth pacing between two cameras during the lectures which at times became distracting in and of itself. Certainly including a third camera would have added some variety as would having had camera operators to zoom in or move the camera around while the lecturers stand relatively stationary. (Though the production value here is exceptionally high, small details like this over the span of several hours of watching become important. As an example of better execution, I prefer Glenn Holland’s “Religion in the Ancient Mediterranean World” as a model – though there wasn’t as much additional visual material there, the lectures were simply more “watchable” because of the camera work.)

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## Axiom of Choice? “Would you rather be deaf or blind?”

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## Some Brief Thoughts on Cliodynamics and Big History

As an electrical engineer (in the subfields of information theory and molecular biology), I have to say that I’m very intrigued by the articles (1, 2) that Marc Parry has written for the Chronicle in the past few weeks on the subjects of quantitative history, cliometrics/cliodynamics, or what I might term Big History (following the tradition of David Christian; I was initially turned onto it by a Chronicle article). I have lately coincidentally been reading Steven Pinker’s book “The Better Angels of Our Nature” as well as Daniel Kanheman’s “Thinking, Fast and Slow”. (I’ll also mention that I’m a general fan of the work of Jared Diamond and Matt Ridley who impinge on these topics as well.)

I’m sure that all of these researchers are onto something in terms of trying to better quantify our historical perspectives in using science and applying it to history. I think the process might be likened to the ways in which methods of computed tomography, P.E.T., S.P.E.C.T, et al have been applied to the areas of psychology since the late 70’s to create the field of cognitive neuropsychology which has now grown much more closely to the more concrete areas of neurophysiology within biology, chemistry, and medicine.

I can see both sides of the “controversy” which is mentioned in the articles as well as in the comments in all of the articles, but I have a very visceral gut feeling that they can be ironed out over time. I say this as areas like behavioral economics which have grown out of the psychology work mentioned in Kahneman’s book become more concrete. The data available for application with relation to history will be much more useful as people’s psychological interactions with their surroundings are better understood. People in general are exceptionally poor at extrapolating statistical knowledge of the world around them and putting it into the best use. For example, although one can make an accurate calculation of the time-value of money, most people who know it won’t use it to determine the best way of taking a large lottery payout (either a lump sum or paid out over time), and this doesn’t even take into consideration the phenomenal odds against even playing the lottery in the first place. Kahneman’s system 1 and system 2 structures in conjunction with more historical data and analysis of the two in conjunction may be a far better method than either that of historians’ previous attempts or that of the quantitative method separately. Put into mathematical terms, it’s much more likely the case that human interactions follow a smaller local min-max curve/equation on a limited horizon, but do not necessarily follow the global maxima and minima that are currently being viewed at the larger scales of big history. We’ll need to do a better job of sifting through the data and coming up with a better interpretation of it on the correct historical scales for the problem at hand.

Perhaps, by analogy, we might look at this disconnect between the two camps as the same type of disconnect seen in the areas of Newtonian and quantum physics. They’re both interlinked somehow and do a generally good job of providing accurate viewpoints and predictions of their own sub-areas, but haven’t been put together coherently into one larger catch-all theory encompassing both. Without the encouragement of work in the quantitative areas of history, we’ll certainly be at a great disadvantage.

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