Information is a precise concept that can be defined mathematically, but its relationship to what we call "knowledge" is not always made clear. Furthermore, the concepts "entropy" and "information", while deeply related, are distinct and must be used with care, something that is not always achieved in the literature. In this elementary introduction, the concepts of entropy and information are laid out one by one, explained intuitively, but defined rigorously. I argue that a proper understanding of information in terms of prediction is key to a number of disciplines beyond engineering, such as physics and biology.
Comments: 19 pages, 2 figures. To appear in Philosophical Transaction of the Royal Society A
Subjects: Adaptation and Self-Organizing Systems (nlin.AO); Information Theory (cs.IT); Biological Physics (physics.bio-ph); Quantitative Methods (q-bio.QM)
Cite as:arXiv:1601.06176 [nlin.AO] (or arXiv:1601.06176v1 [nlin.AO] for this version)
Yesterday, via a notification from Lanyard, I came across a notice for the upcoming conference “The Information Universe” which hits several of the sweet spots for areas involving information theory, physics, the origin of life, complexity, computer science, and microbiology. It is scheduled to occur from October 7-9, 2015 at the Infoversum Theater in Groningen, The Netherlands.
I’ll let their site speak for itself below, but they already have an interesting line up of speakers including:
Erik Verlinde, Professor Theoretical Physics, University of Amsterdam, Netherlands
Alex Szalay, Alumni Centennial Professor of Astronomy, The Johns Hopkins University, USA
Gerard ‘t Hooft, Professor Theoretical Physics, University of Utrecht, Netherlands
Gregory Chaitin, Professor Mathematics and Computer Science, Federal University of Rio de Janeiro, Brasil
Charley Lineweaver, Professor Astronomy and Astrophysics, Australian National University, Australia
Lude Franke, Professor System Genetics, University Medical Center Groningen, Netherlands
For those in attendance or participating by watching the live streaming video (or even watching the video after-the-fact), please feel free to use the official hashtag #entropyWS, and I’ll do my best to include your tweets, posts, and material into the story stream for future reference.
Those participating in the workshop are also encouraged to take a look at a growing collection of researchers and materials I maintain here. If you have materials or resources you’d like to contribute to the list, please send me an email or include them via the suggestions/submission form or include them in the comments section below.
I’m giving a short 30-minute talk at a workshop on Biological and Bio-Inspired Information Theory at the Banff International Research Institute. I’ll say more about the workshop later, but here’s my talk: * Biodiversity, entropy and thermodynamics. Most of the people at this workshop study neurobiology and cell signalling, not evolutionary game theory or…
I’m having a great time at a workshop on Biological and Bio-Inspired Information Theory in Banff, Canada. You can see videos of the talks online. There have been lots of good talks so far, but this one really blew my mind: * Naftali Tishby, Sensing and acting under information constraints—a principled approach to biology and…
John Harte is an ecologist who uses maximum entropy methods to predict the distribution, abundance and energy usage of species. Marc Harper uses information theory in bioinformatics and evolutionary game theory. Harper, Harte and I are organizing a workshop on entropy and information in biological systems, and I’m really excited about it!
John Harte, Marc Harper and I are running a workshop! Now you can apply here to attend: * Information and entropy in biological systems, National Institute for Mathematical and Biological Synthesis, Knoxville Tennesee, Wednesday-Friday, 8-10 April 2015. Click the link, read the stuff and scroll down to “CLICK HERE” to apply.
There will be a 5-day workshop on Biological and Bio-Inspired Information Theory at BIRS from Sunday the 26th to Friday the 31st of October, 2014. It’s being organized by * Toby Berger (University of Virginia) * Andrew Eckford (York University) * Peter Thomas (Case Western Reserve University) BIRS is the Banff International Research Station,…
How does it feel to (co-)write a book and hold the finished product in your hands? About like this: Many, many thanks to my excellent co-authors, Tadashi Nakano and Tokuko Haraguchi, for their hard work; thanks to Cambridge for accepting this project and managing it well; and thanks to Satoshi Hiyama for writing a nice blurb.
You may have seen our PLOS ONE paper about tabletop molecular communication, which received loads of media coverage. One of the goals of this paper was to show that anyone can do experiments in molecular communication, without any wet labs or expensive apparatus.
[My comments posted to the original Facebook post follow below.]
I’m coming to this post a bit late as I’m playing a bit of catch up, but agree with it wholeheartedly.
In particular, applications to molecular biology and medicine are really beginning to come to a heavy boil in just the past five years. This particular 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.
Upcoming/recent conferences/workshops on information theory in biology include:
I’ll note in passing, for those interested, that Claude Shannon’s infamous master’s thesis at MIT (in which he applied Boolean Algebra to electric circuits allowing the digital revolution to occur) and his subsequent “The Theory of Mathematical Communication” were so revolutionary, nearly everyone forgets his MIT Ph.D. Thesis “An Algebra for Theoretical Genetics” which presaged the areas of cybernetics and the current applications of information theory to microbiology and are probably as seminal as Sir R.A Fisher’s applications of statistics to science in general and biology in particular.
For those commenting on the post who were interested in a layman’s introduction to information theory, I recommend John Robinson Pierce’s An Introduction to Information Theory: Symbols, Signals and Noise (Dover has a very inexpensive edition.) After this, one should take a look at Claude Shannon’s original paper. (The MIT Press printing includes some excellent overview by Warren Weaver along with the paper itself.) The mathematics in the paper really aren’t too technical, and most of it should be comprehensible by most advanced high school students.
For those that don’t understand the concept of entropy, I HIGHLY recommend Arieh Ben-Naim’s book Entropy Demystified The Second Law Reduced to Plain Common Sense with Seven Simulated Games. He really does tear the concept down into its most basic form in a way I haven’t seen others come remotely close to and which even my mother can comprehend (with no mathematics at all). (I recommend this presentation to even those with Ph.D.’s in physics because it is so truly fundamental.)
For the more advanced mathematicians, physicists, and engineers Arieh Ben-Naim does a truly spectacular job of extending ET Jaynes’ work on information theory and statistical mechanics and comes up with a more coherent mathematical theory to conjoin the entropy of physics/statistical mechanics with that of Shannon’s information theory in A Farewell to Entropy: Statistical Thermodynamics Based on Information.
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, , 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.
Information Theory and Evolution
Non-fiction, Popular Science
January 1, 2003
This highly interdisciplinary book discusses the phenomenon of life, including its origin and evolution (and also human cultural evolution), against the background of thermodynamics, statistical mechanics, and information theory. Among the central themes is the seeming contradiction between the second law of thermodynamics and the high degree of order and complexity produced by living systems. This paradox has its resolution in the information content of the Gibbs free energy that enters the biosphere from outside sources, as the author shows. The role of information in human cultural evolution is another focus of the book. One of the final chapters discusses the merging of information technology and biotechnology into a new discipline — bio-information technology.
This is a fantastic book which, for the majority of people, I’d give a five star review. For my own purposes, however, I was expecting far more on the theoretical side of information theory and statistical mechanics as applied to microbiology that it didn’t live up to, so I’m giving it three stars from a purely personal perspective.
I do wish that someone had placed it in my hands and forced me to read it when I was a freshman in college entering the study of biomedical and electrical engineering. It is far more an impressive book at this level and for those in the general public who are interested in the general history of science and philosophy of the topics. The general reader may be somewhat scared by a small amount of mathematics in chapter 4, but there is really no loss of continuity by skimming through most of it. For those looking for a bit more rigor, Avery provides some additional details in appendix A, but for the specialist, the presentation is heavily lacking.
The book opens with a facile but acceptable overview of the history of the development for the theory of evolution whereas most other texts would simply begin with Darwin’s work and completely skip the important philosophical and scientific contributions of Aristotle, Averroes, Condorcet, Linnaeus, Erasmus Darwin, Lamarck, or the debates between Cuvier and St. Hilaire.
For me, the meat of the book was chapters 3-5 and appendix A which collectively covered molecular biology, evolution, statistical mechanics, and a bit of information theory, albeit from a very big picture point of view. Unfortunately the rigor of the presentation and the underlying mathematics were skimmed over all too quickly to accomplish what I had hoped to gain from the text. On the other hand, the individual sections of “suggestions for further reading” throughout the book seem well researched and offer an acceptable launching pad for delving into topics in places where they may be covered more thoroughly.
The final several chapters become a bit more of an overview of philosophy surrounding cultural evolution and information technology which are much better covered and discussed in James Gleick’s recent book The Information.
Overall, Avery has a well laid out outline of the broad array of subjects and covers it all fairly well in an easy to read and engaging style.
Information theory provides a constructive criterion for setting up probability distributions on the basis of partial knowledge, and leads to a type of statistical inference which is called the maximum-entropy estimate. It is the least biased estimate possible on the given information; i.e., it is maximally noncommittal with regard to missing information. If one considers statistical mechanics as a form of statistical inference rather than as a physical theory, it is found that the usual computational rules, starting with the determination of the partition function, are an immediate consequence of the maximum-entropy principle. In the resulting "subjective statistical mechanics," the usual rules are thus justified independently of any physical argument, and in particular independently of experimental verification; whether or not the results agree with experiment, they still represent the best estimates that could have been made on the basis of the information available.
It is concluded that statistical mechanics need not be regarded as a physical theory dependent for its validity on the truth of additional assumptions not contained in the laws of mechanics (such as ergodicity, metric transitivity, equal a priori probabilities, etc.). Furthermore, it is possible to maintain a sharp distinction between its physical and statistical aspects. The former consists only of the correct enumeration of the states of a system and their properties; the latter is a straightforward example of statistical inference.