Renaissance for Information Theory in Biology

This year is the progenitor of what appears to be the biggest renaissance for the application of information theory to the area of biology since Hubert Yockey, Henry Quastler, and Robert L. Platzman’s “Symposium on Information Theory in Biology at Gatlinburg, Tennessee” in 1956. (I might argue it’s possibly even bigger than Claude Shannon’s Ph.D. thesis.)  It certainly portends to create a movement that will rapidly build upon and far surpass Norbert Weiner’s concept of Cybernetics and Ludwig von Bertalanffy’s concept of General Systems Theory.

This week John Baez has announced an upcoming three day workshop on “Entropy and Information in Biological Systems” to be hosted by the National Institute for Mathematical and Biological Synthesis in Knoxville, TN, tentatively scheduled for October 22-24, 2014.

Apparently unbeknownst to Baez, earlier this year Andrew Eckford, Toby Berger, and Peter Thomas announced a six day workshop on “Biological and Bio-Inspired Information Theory” to be hosted by the Banff International Research Station for Mathematical Innovation and Discovery scheduled for October 26-31, 2014 – just two days later!

What a bonanza!!

The BIRS workshop will be a bit more general in its approach while the NIMBioS workshop has a slightly tighter view specifically on maximum entropy as applied to biology.

Even more telling (and perhaps most promising) about the two workshops is the very heavy mathematical bent both intend to make their focus.  I have a theory that the bounds of science are held below the high water level of mathematics (aka are “bounded by” in mathematics-speak), so there is nothing more exciting than to see groups attempting to push the mathematics and its application further. It was both the lack of mathematical rigor and the general youth of biology (and specifically genetics and microbiology) in the 1950’s which heavily hampered the early growth of cybernetics as a movement. Fortunately this is no longer the case on either count. Now we just need more researchers who are more readily conversant in the two realms simultaneously.

Book Review: “Complexity: A Guided Tour” by Melanie Mitchell

Read Complexity: A Guided Tour by Melanie MitchellMelanie Mitchell (
Complexity: A Guided Tour Book Cover Complexity: A Guided Tour
Melanie Mitchell
Popular Science
Oxford University Press
May 28, 2009

This book provides an intimate, highly readable tour of the sciences of complexity, which seek to explain how large-scale complex, organized, and adaptive behavior can emerge from simple interactions among myriad individuals. The author, a leading complex systems scientist, describes the history of ideas, current research, and future prospects in this vital scientific effort.

This is handily one of the best, most interesting, and (to me at least) the most useful popularly written science books I’ve yet to come across. Most popular science books usually bore me to tears and end up being only pedantic for their historical backgrounds, but this one is very succinct with some interesting viewpoints (some of which I agree with and some of which my intuition says are terribly wrong) on the overall structure presented.

For those interested in a general and easily readable high-level overview of some of the areas of research I’ve been interested in (information theory, thermodynamics, entropy, microbiology, evolution, genetics, along with computation, dynamics, chaos, complexity, genetic algorithms, cellular automata, etc.) for the past two decades, this is really a lovely and thought-provoking book.

At the start I was disappointed that there were almost no equations in the book to speak of – and perhaps this is why I had purchased it when it came out and it’s subsequently been sitting on my shelf for so long. The other factor that prevented me from reading it was the depth and breadth of other more technical material I’ve read which covers the majority of topics in the book. I ultimately found myself not minding so much that there weren’t any/many supporting equations aside from a few hidden in the notes at the end of the text in most part because Dr. Mitchell does a fantastic job of pointing out some great subtleties within the various subjects which comprise the broader concept of complexity which one generally would take several years to come to on one’s own and at far greater expense of their time. Here she provides a much stronger picture of the overall subjects covered and this far outweighed the lack of specificity. I honestly wished I had read the book when it was released and it may have helped me to me more specific in my own research. Fortunately she does bring up several areas I will need to delve more deeply into and raised several questions which will significantly inform my future work.

In general, I wish there were more references I hadn’t read or been aware of yet, but towards the end there were a handful of topics relating to fractals, chaos, computer science, and cellular automata which I have been either ignorant of or which are further down my reading lists and may need to move closer to the top. I look forward to delving into many of these shortly. As a simple example, I’ve seen Zipf’s law separately from the perspectives of information theory, linguistics, and even evolution, but this is the first time I’ve seen it related to power laws and fractals.

I definitely appreciated the fact that Dr. Mitchell took the time to point out her own personal feelings on several topics and more so that she explicitly pointed them out as her own gut instincts instead of mentioning them passingly as if they were provable science which is what far too many other authors would have likely done. There are many viewpoints she takes which I certainly don’t agree with, but I suspect that it’s because I’m coming at things from the viewpoint of an electrical engineer with a stronger background in information theory and microbiology while hers is closer to that of computer science. She does mention that her undergraduate background was in mathematics, but I’m curious what areas she specifically studied to have a better understanding of her specific viewpoints.

Her final chapter looking at some of the pros and cons of the topic(s) was very welcome, particularly in light of previous philosophic attempts like cybernetics and general systems theory which I (also) think failed because of their lack of specificity. These caveats certainly help to place the scientific philosophy of complexity into a much larger context. I will generally heartily agree with her viewpoint (and that of others) that there needs to be a more rigorous mathematical theory underpinning the overall effort. I’m sure we’re all wondering “Where is our Newton?” or to use her clever aphorism that we’re “waiting for Carnot.” (Sounds like it should be a Tom Stoppard play title, doesn’t it?)

I might question her brief inclusion of her own Ph.D. thesis work in the text, but it did actually provide a nice specific and self-contained example within the broader context and also helped to tie several of the chapters together.

My one slight criticism of the work would be the lack of better footnoting within the text. Though many feel that footnote numbers within the text or inclusion at the bottom of the pages detracts from the “flow” of the work, I found myself wishing that she had done so here, particularly as I’m one of the few who actually cares about the footnotes and wants to know the specific references as I read. I hope that Oxford eventually publishes an e-book version that includes cross-linked footnotes in the future for the benefit of others.

I can heartily recommend this book to any fan of science, but I would specifically recommend it to any undergraduate science or engineering major who is unsure of what they’d specifically like to study and might need some interesting areas to take a look at. I will mention that one of the tough parts of the concept of complexity is that it is so broad and general that it encompasses over a dozen other fields of study each of which one could get a Ph.D. in without completely knowing the full depth of just one of them much less the full depth of all of them. The book is so well written that I’d even recommend it to senior researchers in any of the above mentioned fields as it is certainly sure to provide not only some excellent overview history of each, but it is sure to bring up questions and thoughts that they’ll want to include in their future researches in their own specific sub-areas of expertise.

Beauty, Melody, and Entropy are an Equivalence Class

Sir Arthur Stanley Eddington, OM, FRS (1882-1944), a British astronomer, physicist, and mathematician
in The Nature of the Physical World, 1927


Sir Arthur Stanley Eddington


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.

Page 51 of Melanie Mitchell's book "Complexity: A Guided Tour"
Page 51 of Melanie Mitchell’s book “Complexity: A Guided Tour” featuring Boltzmann’s tombstone in Vienna.

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.

Regard the World as Made of Information

John Archibald Wheeler (1911-2008), American theoretical physicist
[attributed by Jacob Bekenstein in “Information in the Holographic Universe” (Scientific American, 2007)]


John Archibald Wheeler

Rod, Can You Tell Our Contestant What She’s Won?

Possibly one of the oddest closing sentences of a technical book–and a very good one at that–I’ve ever read:

This pressure can be calculated by minimizing the Helmholtz function of the system. Details can be found in Fermi’s textbook on thermodynamics (Fermi 1956). But why does osmosis explain the behavior of a salted cucumber? This question is left to the reader as a parting gift.

André Thess in The Entropy Prinicple: Thermodynamics for the Unsatisified (Springer, 2011)


salted cucumber

John Battelle Review of James Gleick’s “The Information” and Why It’s a Good Thing

John Battelle recently posted a review of James Gleick’s last book The Information: A History, A Theory, A Flood. It reminds me that I find it almost laughable when the vast majority of the technology press and the digiterati bloviate about their beats when at its roots, they know almost nothing about how technology truly works or the mathematical or theoretical underpinnings of what is happening — and even worse that they don’t seem to really care.

I’ve seen hundreds of reviews and thousands of mentions of Steven Levy’s book In the Plex: How Google Thinks, Works, and Shapes Our Lives in the past few months, — in fact, Battelle reviewed it just before Gleick’s book — but I’ve seen few, if any, of Gleick’s book which I honestly think is a much more worthwhile read about what is going on in the world and has farther reaching implications about where we are headed.

I’ll give a BIG tip my hat to John for his efforts to have read Gleick and post his commentary and to continue to push the boundary further as he invites Gleick to speak at Web 2.0 Summit in the fall. I hope his efforts will bring the topic to the much larger tech community.  I further hope he and others might take the time to read Claude Shannon’s original paper [.pdf download], and if he’s further interested in the concept of thermodynamic entropy, I can recommend Andre Thess’s text The Entropy Principle: Thermodynamics for the Unsatisfied, which I’ve recently discovered and think does a good (and logically) consistent job of defining the concept at a level accessible to the average public.

Entropy Is Universal Rule of Language | Wired Science

Reposted Entropy Is Universal Rule of Language (Wired)
The amount of information carried in the arrangement of words is the same across all languages, even languages that aren't related to each other. This consistency could hint at a single common ancestral language, or universal features of how human brains process speech. "It doesn't matter what language or style you take," said systems biologist…

The research this article is based on is quite interesting for those doing language research.

The amount of information carried in the arrangement of words is the same across all languages, even languages that aren’t related to each other. This consistency could hint at a single common ancestral language, or universal features of how human brains process speech.

“It doesn’t matter what language or style you take,” said systems biologist Marcelo Montemurro of England’s University of Manchester, lead author of a study May 13 in PLoS ONE. “In languages as diverse as Chinese, English and Sumerian, a measure of the linguistic order, in the way words are arranged, is something that seems to be a universal of languages.”

Language carries meaning both in the words we choose, and the order we put them in. Some languages, like Finnish, carry most of their meaning in tags on the words themselves, and are fairly free-form in how words are arranged. Others, like English, are more strict “John loves Mary” means something different from “Mary loves John.”

Montemurro realized that he could quantify the amount of information encoded in word order by computing a text’s “entropy,” or a measure of how evenly distributed the words are. Drawing on methods from information theory, Montemurro co-author Dami??n Zanette of the National Atomic Energy Commission in Argentina calculated the entropy of thousands of texts in eight different languages: English, French, German, Finnish, Tagalog, Sumerian, Old Egyptian and Chinese.

Then the researchers randomly rearranged all the words in the texts, which ranged from the complete works of Shakespeare to The Origin of Species to prayers written on Sumerian tablets.

“If we destroy the original text by scrambling all the words, we are preserving the vocabulary,” Montemurro said. “What we are destroying is the linguistic order, the patterns that we use to encode information.”

The researchers found that the original texts spanned a variety of entropy values in different languages, reflecting differences in grammar and structure.

But strangely, the difference in entropy between the original, ordered text and the randomly scrambled text was constant across languages. This difference is a way to measure the amount of information encoded in word order, Montemurro says. The amount of information lost when they scrambled the text was about 3.5 bits per word.

“We found, very interestingly, that for all languages we got almost exactly the same value,” he said. “For some reason these languages evolved to be constrained in this framework, in these patterns of word ordering.”

This consistency could reflect some cognitive constraints that all human brains run up against, or give insight into the evolution of language, Montemurro suggests.

Cognitive scientists are still debating whether languages have universal features. Some pioneering linguists suggested that languages should evolve according to a limited set of rules, which would produce similar features of grammar and structure. But a study published last month that looked at the structure and syntax of thousands of languages found no such rules.

It may be that universal properties of language show up only at a higher level of organization, suggests linguist Kenny Smith of the University of Edinburgh.

“Maybe these broad-brushed features get down to what’s really essential” about language, he said. “Having words, and having rules for how the words are ordered, maybe those are the things that help you do the really basic functions of language. And the places where linguists traditionally look to see universals are not where the fundamentals of language are.”

Image: James Morrison/Flickr.

Citation:”Universal Entropy of Word Ordering Across Linguistic Families.” Marcelo A. Montemurro and Damián H. Zanette. PLoS ONE, Vol. 6, Issue 5, May 13, 2011. DOI: 10.1371/journal.pone.0019875.