Instagram filter used: X-Pro II
As many may know or have already heard, Dr. Mike Miller, a retired mathematician from RAND and long-time math professor at UCLA, is offering a course on Introduction to Lie Groups and Lie Algebras this fall through UCLA Extension. Whether you’re a professional mathematician, engineer, physicist, physician, or even a hobbyist interested in mathematics you’ll be sure to get something interesting out of this course, not to mention the camaraderie of 20-30 other “regulars” with widely varying backgrounds (actors to surgeons and evolutionary theorists to engineers) who’ve been taking almost everything Mike has offered over the years (and yes, he’s THAT good — we’re sure you’ll be addicted too.)
Even if it’s been years since you last took Calculus or Linear Algebra, Mike (and the rest of the class) will help you get quickly back up to speed to delve into what is often otherwise a very deep subject. If you’re interested in advanced physics, quantum mechanics, quantum information or string theory, this is one of the topics that is de rigueur for delving in deeply and being able to understand them better. The topic is also one near and dear to the hearts of those in robotics, graphics, 3-D modelling, gaming, and areas utilizing multi-dimensional rotations. And naturally, it’s simply a beautiful and elegant subject for those who have no need to apply it to anything, but who just want to meander their way through higher mathematics for the fun of it (this will comprise the largest majority of the class by the way.)
Whether you’ve been away from serious math for decades or use it every day or even if you’ve never gone past Calculus or Linear Algebra, this is bound to be the most entertaining thing you can do with your Tuesday nights in the fall. If you’re not sure what you’re getting into (or are scared a bit by the course description), I highly encourage to come and join us for at least the first class before you pass up on the opportunity. I’ll mention that the greater majority of new students to Mike’s classes join the ever-growing group of regulars who take almost everything he teaches subsequently. (For the reticent, I’ll mention that one of the first courses I took from Mike was Algebraic Topology which generally requires a few semesters of Abstract Algebra and a semester of Topology as prerequisites. I’d taken neither of these prerequisites, but due to Mike’s excellent lecture style and desire to make everything comprehensible, I was able to do exceedingly well in the course.) I’m happy to chat with those who may be reticent. Also keep in mind that you can register to take the class for a grade, pass/fail, or even no grade at all to suit your needs/lifestyle.
As a group, some of us have a collection of a few dozen texts in the area which we’re happy to loan out as well. In addition to the one recommended text (Mike always gives such comprehensive notes that any text for his classes is purely supplemental at best), several of us have also found some good similar texts:
Given the breadth and diversity of the backgrounds of students in the class, I’m sure Mike will spend some reasonable time at the beginning [or later in the class, as necessary] doing a quick overview of some linear algebra and calculus related topics that will be needed later in the quarter(s).
Further information on the class and a link to register can be found below. If you know of others who might be interested in this, please feel free to forward it along – the more the merrier.
I hope to see you all soon.
MATH X 450.6 / 3.00 units / Reg. # 249254W
Professor: Michael Miller, Ph.D.
Start Date: 9/30/2014
Location UCLA: 5137 Math Sciences Building
September 30 – December 16, 2014
11 meetings total (no mtg 11/11)
Register here: https://www.uclaextension.edu/Pages/Course.aspx?reg=249254
A Lie group is a differentiable manifold that is also a group for which the product and inverse maps are differentiable. A Lie algebra is a vector space endowed with a binary operation that is bilinear, alternating, and satisfies the so-called Jacobi identity. This course, the first in a 2-quarter sequence, is an introductory survey of Lie groups, their associated Lie algebras, and their representations. This first quarter will focus on the special case of matrix Lie groups–including general linear, special linear, orthogonal, unitary, and symplectic. The second quarter will generalize the theory developed to the case of arbitrary Lie groups. Topics to be discussed include compactness and connectedness, homomorphisms and isomorphisms, exponential mappings, the Baker-Campbell-Hausdorff formula, covering groups, and the Weyl group. This is an advanced course, requiring a solid understanding of linear algebra and basic analysis.
Nature: “Iranian is first woman to nab highest prize in maths”
Also includes coverage of the Gauss Prize for research that has had an impact outside mathematics, which was awarded to Stanley Osher of the University of California at Los Angeles.)
Artur Avila – A Brazilian Wunderkind Who Calms Chaos
Manjul Bhargava – The Musical, Magical Number Theorist
Martin Hairer – In Noisy Equations, One Who Heard Music
Maryam Mirzakhani – A Tenacious Explorer of Abstract Surfaces
Subhash Khot – A Grand Vision for the Impossible
Terry Tao (previous Fields Medal Winner): Avila, Bhargava, Hairer, Mirzakhani
Entropy and Information in Biological Systems (Part 2)
• 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. The deadline is 12 November 2014.
Financial support for travel, meals, and lodging is available for workshop attendees who need it. We will choose among the applicants and invite 10-15 of them.
Information theory and entropy methods are becoming powerful tools in biology, from the level of individual cells, to whole ecosystems, to experimental design, model-building, and the measurement of biodiversity. The aim of this investigative workshop is to synthesize different ways of applying these concepts to help systematize and unify work in biological systems. Early attempts at “grand syntheses” often misfired, but applications of information theory and entropy to specific highly focused topics in biology have been increasingly successful. In ecology, entropy maximization methods have proven successful in predicting the distribution and abundance of species. Entropy is also widely used as a measure of biodiversity. Work on the role of information in game theory has shed new light on evolution. As a population evolves, it can be seen as gaining information about its environment. The principle of maximum entropy production has emerged as a fascinating yet controversial approach to predicting the behavior of biological systems, from individual organisms to whole ecosystems. This investigative workshop will bring together top researchers from these diverse fields to share insights and methods and address some long-standing conceptual problems.
So, here are the goals of our workshop:
- To study the validity of the principle of Maximum Entropy Production (MEP), which states that biological systems – and indeed all open, non-equilibrium systems – act to produce entropy at the maximum rate.
- To familiarize all the participants with applications to ecology of the MaxEnt method: choosing the probabilistic hypothesis with the highest entropy subject to the constraints of our data. We will compare MaxEnt with competing approaches and examine whether MaxEnt provides a sufficient justification for the principle of MEP.
- To clarify relations between known characterizations of entropy, the use of entropy as a measure of biodiversity, and the use of MaxEnt methods in ecology.
- To develop the concept of evolutionary games as “learning” processes in which information is gained over time.
- To study the interplay between information theory and the thermodynamics of individual cells and organelles.
For more details, go here.
If you’ve got colleagues who might be interested in this, please let them know. You can download a PDF suitable for printing and putting on a bulletin board by clicking on this:
Since the beginning of January, I’ve come back to regularly browsing and using the website Rap Genius. I’m sure that some of the education uses including poetry and annotations of classics had existed the last time I had visited, but I was very interested in seeing some of the scientific journal article uses which I hadn’t seen before. Very quickly browsing around opened up a wealth of ideas for using the platform within the digital humanities as well as for a variety of educational uses.
Briefly, the Rap Genius website was originally set up as an innovative lyrics service to allow users to not only upload song lyrics, but to mark them up with annotations as to the meanings of words, phrases, and provide information about the pop-culture references within the lyrics themselves. (It’s not too terribly different from Google’s now-defunct Sidewicki or the impressive Highbrow, textual annotation browser, but has some subtle differences as well as improvements.)
Users can use not only text, but photos, video, and even audio to supplement the listings. Built-in functionality includes the ability to link the works to popular social media audio services SoundCloud, and Spotify as well as YouTube. Alternately one might think of it as VH1’s “Pop-up Video”, but for text on the Internet. Ultimately the site expanded to include the topics of rock, poetry, and news. The rock section is fairly straightforward following the format of the rap section while the poetry section includes not only works of poetry (from The Rime of the Ancient Mariner to the King James version of The Bible), but also plays (the works of William Shakespeare) and complete novels (like F. Scott Fitzgerald’s The Great Gatsby.) News includes articles as well as cultural touchstones like the 2013 White House Correspondents’ Dinner Speech and the recent State of the Union. Ultimately all of the channels within Rap Genius platform share the same types of functionality, but are applied to slightly different categories to help differentiate the content and make things easier to find. Eventually there may be a specific “Education Genius” (or other) landing page(s) to split out the content in the future depending on user needs.
On even its first blush, I can see this type of website functionality being used in a variety of educational settings including Open Access Journals, classroom use, for close readings, for MOOCs, publishing in general, and even for maintaining simple-to-use websites for classes. The best part is that the ecosystem is very actively growing and expanding with a recent release of an iPhone app and an announcement of a major deal with Universal to license music lyrics.
To begin with, Rap Genius’ YouTube channel includes an excellent short video on how Poetry Genius might be used in a classroom setting for facilitating close-readings. In addition to the ability to make annotations, the site can be used to maintain a class specific website (no need to use other blogging platforms like WordPress or Blogger for things like this anymore) along with nice additions like maintaining a class roster built right in. Once material begins to be posted, students and teachers alike are given a broad set of tools to add content, make annotations, ask questions, and provide answers in an almost real-time setting.
Given the rapid growth of the MOOC-revolution (massively open online courseware) over the past several years, one of the remaining difficulties in administering such a class can hinge not only on being able to easily provide audio visual content to students, but allow them a means of easily interacting with it and each other in the learning process. Poetry Genius (aka Education Genius) has a very interesting view into solving both of these problems, and, in fact, I can easily see the current version of the platform being used to replace competing platforms like Coursera, EdX, Udacity and others in a whole cloth fashion.
Currently most MOOC’s provide some type of simple topic-based threaded fora in which students post comments and questions as well as answers. In many MOOCs this format becomes ungainly because of the size of the class (10,000+ students) and the quality of the content which is being placed into it. Many students simply eschew the fora because the time commitment per amount of knowledge/value gained is simply not worth their while. Within the Poetry Genius platform, students can comment directly on the material or ask questions, or even propose improvements, and the administrators (the professor or teaching assistants in this case) can accept, reject or send feedback request to students to amend their work and add it to the larger annotated work. Fellow classmates can also vote up or down individual comments.
As I was noticing the interesting educational-related functionality of the Rap Genius platform, I ran across what is presumably the first MOOC attempting to integrate the platform into its pedagogical structure. Dr. Laura Nasrallah’s HarvardX course “Early Christianity: The Letters of Paul,” which started in January, asks students to also create Poetry Genius accounts to read and comment on the biblical texts which are a part of the course. The difficult portion of attempting to use Poetry Genius for this course is the thousands of “me-too” posters who are simply making what one might consider to be “throw-away” commentary rather than the intended “close reading” commentary for a more academic environment. (This type of posting is also seen in many of the fora-based online courses.) Not enough students are contributing substantial material, and when they are, it needs to be better and more quickly edited and curated into the main post to provide greater value to students as they’re reading along. Thus when 20,000 students jump into the fray, there’s too much initial chaos and the value that is being extracted out of it upon initial use is fairly limited – particularly if one is browsing through dozens of useless comments. It’s not until after-the-fact – once comments have been accepted/curated – that the real value will emerge. The course staff is going to have to spend more time doing this function in real time to provide greater value to the students in the class, particularly given the high number of people without intense scholarly training just jumping into the system and filling it with generally useless commentary. In internet parlance, the Poetry Genius site is experiencing the “Robert Scoble Effect” which changes the experience on it. (By way of explanation, Robert Scoble is a technology journalist/pundit/early-adopter with a massive follower base. His power-user approach and his large following can drastically change his experience with web-based technology compared to the common everyday user. It can also often bring down new services as was common in the early days of the social media movement.)
Typically with the average poem or rap song, the commentary grows slowly/organically and is edited along the way. In a MOOC setting with potentially hundreds of thousands of students, the commentary is like a massive fire-hose which makes it seemingly useless without immediate real-time editing. Poetry Genius may need a slightly different model for using their platform in larger MOOC-style courses versus the smaller classroom settings seen in high school or college (10-100 students). In the particular case for “The Letters of Paul,” if the course staff had gone into the platform first and seeded some of the readings with their own sample commentary to act as a model of what is expected, then the students would be a bit more accepting of what is expected. I understand Dr. Nasrallah and her teaching assistants are in the system and annotating as well, but it should also be more obvious which annotations are hers (or those of teaching assistants) to help better guide the “discussion” and act as a model. Certainly the materials generated on Poetry Genius will be much more useful for future students who take the course in future iterations. Naturally, Poetry Genius exists for the primary use of annotation, while I’m sure that the creators will be tweaking classroom-specific use as the platform grows and user needs/requirements change.
As a contrast to the HarvardX class, and for an additional example, one can also take a peek at Cathy Davidson’s Rap Genius presence for her Coursera class “The History and Future (Mostly) of Higher Education.”
In my mind, this type of platform can easily and usefully be used for publishing open access journal articles. In fact, one could use the platform to self-publish journal articles and leave them open to ongoing peer review. Sadly at present, there seems to be only a small handful of examples on the site, including a PLOS ONE article, which will give a reasonable example of some of the functionality which is possible. Any author could annotate and footnote their own article as well as include a wealth of photos, graphs, and tables giving a much more multimedia view into their own work. Following this any academic with an account could also annotate the text with questions, problems, suggestions and all of these can be voted up or down as well as be remedied within the text itself. Other articles can also have the ability to directly cross-reference specific sections of previously posted articles.
Individual labs or groups with “journal clubs” could certainly join in the larger public commentary and annotation on a particular article, but higher level administrative accounts within the system can also create a proverbial clean slate on an article and allow members to privately post up their thoughts and commentaries which are then closed to the group and not visible to the broader public. (This type of functionality can be useful for Mrs. Smith’s 10th grade class annotating The Great Gatsby so that they’re not too heavily influenced by the hundreds or possibly thousands of prior comments within a given text as they do their own personal close readings.) One may note that some of this type of functionality can already be seen in competitive services like Mendeley, but the Rap Genius platform seems to take the presentation and annotation functionalities to the next level. For those with an interest in these types of uses, I recommend Mendeley’s own group: Reinventing the Scientific Paper.
A Rap Genius representative indicated they were pursuing potential opportunities with JSTOR that might potentially expand on these types of opportunities.
Like many social media related sites including platforms like WordPress, Tumblr, and Twitter, Rap Genius gives it’s users the ability to self-publish almost any type of content. I can see some excellent cross-promotional opportunities with large MOOC-type classes and the site. For example, professors/teachers who have written their own custom textbooks for MOOCs (eg. Keith Devlin’s Introduction to Mathematical Thinking course at Stanford via Coursera) could post up the entire text on the Poetry Genius site and use it not only to correct mistakes/typos and make improvements over time, but they can use it to discover things which aren’t clear to students who can make comments, ask questions, etc. There’s also the possibility that advanced students can actively help make portions clear themselves when there are 10,000+ students and just 1-2 professors along with 1-2 teaching assistants. Certainly either within or without the MOOC movement, this type of annotation set up may work well to allow authors to tentatively publish, edit, and modify their textbooks, novels, articles, journal articles, monographs, or even Ph.D. theses. I’m particularly reminded of Kathleen Fitzpatrick’s open writing/editing of her book Planned Obsolescence via Media Commons. Academics could certainly look at the Rap Genius platform as a simpler more user-friendly version of this type of process.
I’m personally interested in being able to annotate science and math related articles and have passed along some tips for the Rap Genius team to include functionality like mathjax to be able to utilize Tex/LaTeX related functionality for typesetting mathematics via the web in the future.
Naturally, there are a myriad of other functionalities that can be built into this type of platform – I’m personally waiting for a way to annotate episodes of “The Simpsons”, so I can explain all of the film references and in-jokes to friends who laugh at their jokes, but never seem to know why – but I can’t write all of them here myself.
Interested users can easily sign up for a general Rap Genius account and dig right into the interface. Those interested in education-specific functionality can request to be granted an “Educator Account” within the Rap Genius system to play around with the additional functionality available to educators. Every page in the system has an “Education” link at the top for further information and details. There’s also an Educator’s Forum [requires free login] for discussions relating specifically to educational use of the site.
Not only a great quote, but an interesting way to view the subjects.
My rating: 4 of 5 stars
This series of 12 audio lectures is an excellent little overview of Augustine, his life, times, and philosophy. Most of the series focuses on his writings and philosophy as well as their evolution over time, often with discussion of the historical context in which they were created as well as some useful comparing/contrasting to extant philosophies of the day (and particularly Platonism.)
Early in the series there were some interesting and important re-definitions of some contemporary words. Cary pushes them back to an earlier time with slightly different meanings compared to their modern ones which certainly helps to frame the overarching philosophy presented. Without a close study of this vocabulary, many modern readers will become lost or certainly misdirected when reading modern translations. As examples, words like perverse, righteousness, and justice (or more specifically their Latin counterparts) have subtly different meanings in the late Roman empire than they do today, even in modern day religious settings.
My favorite part, however, has to have been the examples discussing mathematics as an extended metaphor for God and divinity to help to clarify some of Augustine’s thought. These were not only very useful, but very entertaining to me.
As an aside for those interested in mnemotechnic tradition, I’ll also mention that I’ve (re)discovered (see the reference to the Tell paper below) an excellent reference to the modern day “memory palace” (referenced most recently in the book Moonwalking with Einstein: The Art and Science of Remembering Everything) squirreled away in Book X of Confessions where Augustine discusses memory as:
Those interested in memes and the history of “memoria ex locis” (of which I don’t even find a reference explicitly written in the original Rhetorica ad Herrenium) would appreciate an additional reference I subsequently found in the opening (and somewhat poetic) paragraph of a paper written by David Tell on JSTOR. The earliest specific reference to a “memory palace” I’m aware of is Matteo Ricci’s in the 16th century, but certainly other references to the construct may have come earlier. Given that Ricci was a Jesuit priest, it’s nearly certain that he would have been familiar with Augustine’s writings at the time, and it’s possible that his modification of Augustine’s mention brought the concept into its current use. Many will know memory as one of the major underpinnings of rhetoric (of which Augustine was a diligent student) as part of the original trivium.
Some may shy away from Augustine because of the religious overtones which go along with his work, but though there were occasional “preachy sounding” sections in the material, they were present only to clarify the philosophy.
I’d certainly recommend this series of lectures to anyone not closely familiar with Augustine’s work as it has had a profound and continuing affect on Western philosophy, thought, and politics.
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.
I remember using volume III in Dr. James Martino‘s class many moons ago and enjoying its style. I do however have to credit all my facility in the subject to Dr. Richard Joseph who taught it to me by means of the steepest gradient possible – that of electromagnetic theory.
Given the technical nature of what Nate Silver does, and some of the early mentions of the book, I had higher hopes for the technical portions of the book. As usual for a popular text, I was left wanting a lot more. Again, the lack of any math left a lot to desire. I wish technical writers could get away with even a handful of equations, but wishing just won’t make it so.
The first few chapters were a bit more technical sounding, but eventually devolved into a more journalistic viewpoint of statistics, prediction, and forecasting in general within the areas of economics, political elections, weather forecasting, earthquakes, baseball, poker, chess, and terrorism. I have a feeling he lost a large part of his audience in the first few chapters by discussing the economic meltdown of 2008 first instead of baseball or poker and then getting into politics and economics.
While some of the discussion around each of these bigger topics are all intrinsically interesting and there were a few interesting tidbits I hadn’t heard or read about previously, on the whole it wasn’t really as novel as I had hoped it would be. I think it should be required reading for all politicians however, as I too often get the feeling that none of them think at this level.
There was some reasonably good philosophical discussion of Bayesian statistics versus Fisherian, but it was all too short and could have been fleshed out more significantly. I still prefer David Applebaum’s historical and philosophical discussion of probability in Probability and Information: An Integrated Approach though he surprisingly didn’t mention R.A. Fisher directly himself in his coverage.
It was interesting to run across additional mentions of power laws in the realms of earthquakes and terrorism after reading Melanie Mitchell’s Complexity: A Guided Tour (review here), but I’ll have to find some texts which describe the mathematics in full detail. There was surprisingly large amount of discussion skirting around the topics within complexity without delving into it in any substantive form.
For those with a pre-existing background in science and especially probability theory, I’d recommend skipping this and simply reading Daniel Kahneman’s book Thinking, Fast and Slow. Kahneman’s work is referenced several times and his book seems less intuitive than some of the material Silver presents here.
This is the kind of text which should be required reading in high school civics classes. Perhaps it might motivate more students to be interested in statistics and science related pursuits as these are almost always at the root of most political and policy related questions at the end of the day.
For me, I’d personally give this three stars, but the broader public should view it with at least four stars if not five as there is some truly great stuff here. Unfortunately a lot of it is old hat or retreaded material for me.
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.
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.