Why Aren’t Math Textbooks More Straightforward?

Math textbooks often seem difficult, obtuse, and often incomprehensible. Here are some hints and tips for making the situation better for all students.

Some General Advice for Math Students of All Ages

I recently saw the question “Why aren’t math textbooks more straightforward?” on Quora.

In fact, I would argue that most math textbooks are very straightforward!

The real issue most students are experiencing is one of relativity and experience.  Mathematics is an increasingly sophisticated, cumulative, and more complicated topic the longer you study it. Fortunately, over time, it also becomes easier, more interesting, and intriguingly more beautiful.

As an example of what we’re looking at and what most students are up against, let’s take the topic of algebra. Typically in the United States one might take introductory algebra in eighth grade before taking algebra II in ninth or tenth grade. (For our immediate purposes, here I’m discounting the potential existence of a common pre-algebra course that some middle schools, high schools, and even colleges offer.)  Later on in college, one will exercise one’s algebra muscles in calculus and may eventually get to a course called abstract algebra as an upper-level undergraduate (in their junior or senior years).  Most standard undergraduate abstract algebra textbooks will cover ALL of the material that was in your basic algebra I and algebra II texts in about four pages and simply assume you just know the rest! Naturally, if you started out with the abstract algebra textbook in eighth grade, you’d very likely be COMPLETELY lost. This is because the abstract algebra textbook is assuming that you’ve got some significant prior background in mathematics (what is often referred to in the introduction to far more than one mathematics textbook as “mathematical sophistication”, though this phrase also implicitly assumes knowledge of what a proof is, what it entails, how it works, and how to actually write one).

Following the undergraduate abstract algebra textbook there’s even an additional graduate level course (or four) on abstract algebra (or advanced subtopics like group theory, ring theory, field theory, and Galois theory) that goes into even more depth and subtlety than the undergraduate course; the book for this presumes you’ve mastered the undergraduate text and goes on faster and further.

A Weightlifting Analogy

To analogize things to something more common, suppose you wanted to become an Olympic level weightlifter.  You’re not going to go into the gym on day one and snatch and then clean & jerk 473kg! You’re going to start out with a tiny fraction of that weight and practice repeatedly for years slowly building up your ability to lift bigger and bigger weights. More likely than not, you’ll also very likely do some cross-training by running, swimming, and even lifting other weights to strengthen your legs, shoulder, stomach, and back.  All of this work may eventually lead you to to win the gold medal in the Olympics, but sooner or later someone will come along and break your world record.

Mathematics is certainly no different: one starts out small and with lots of work and practice over time, one slowly but surely ascends the rigors of problems put before them to become better mathematicians. Often one takes other courses like physics, biology, and even engineering courses that provide “cross-training.”  Usually when one is having issues in a math class it’s because they’re either somehow missing something that should have come before or because they didn’t practice enough in their prior classwork to really understand all the concepts and their subtleties.  As an example, the new material in common calculus textbooks is actually very minimal – the first step in most problems is the only actual calculus and the following 10 steps are just practicing one’s algebra skills. It’s usually in carrying out the algebra that one makes more mistakes than in the actual calculus.

Often at the lower levels of grade-school mathematics, some students can manage to just read a few examples and just seem to “get” the answers without really doing a real “work out.” Eventually they’ll come to a point at which they hit a wall or begin having trouble, and usually it comes as the result of not actually practicing their craft.  One couldn’t become an Olympic weightlifter by reading books about weightlifting, they need to actually get in the gym and workout/practice. (Of course, one of the places this analogy breaks down is that weightlifting training is very linear and doesn’t allow one to “skip around” the way one could potentially in a mathematics curriculum.)

I’m reminded of a quote by mathematician Pierre Anton Grillet: “…algebra is like French pastry: wonderful, but cannot be learned without putting one’s hands to the dough.” It is one of the most beautiful expressions of the recurring sentiment written by almost every author into the preface of nearly every mathematics text at or above the level of calculus. They all exhort their students to actually put pencil to paper and work through the logic of their arguments and the exercises to learn the material and gain some valuable experience.  I’m sure that most mathematics professors will assure you that in the end, only a tiny fraction of their students actually do so. Some of the issue is that these exhortations only come in textbooks traditionally read at the advanced undergraduate level, when they should begin in the second grade.

Patissiere puts their hands to a pie crust in a rustic kitchen
“Algebra is like French Pastry: wonderful, but cannot be learned without putting one’s hands to the dough.” -Pierre Anton Grillet

“It’s Easy to See”

A common phrase in almost every advanced math textbook on the planet is the justification, “It’s easy to see.” The phrase, and those like it, should be a watchword for students to immediately be on their guard!  The phrase is commonly used in proofs, discussions, conversations, and lectures in which an author or teacher may skip one or more steps which she feels should be obvious to her audience, but which, in fact, are far more commonly not obvious.

It’s become so cliche that some authors actually mention specifically in their prefaces that they vow not to use the phrase, but if they do so, they usually let slip some other euphemism that is its equivalent.

The problem with the phrase is that everyone, by force of their own circumstances and history, will view it completely differently.  A step that is easy for someone with a Ph.D. who specialized in field theory to “see” may be totally incomprehensible for a beginning student of algebra I in the same way that steps that were easy for Girgory Perelman to see in his proof of the Poincaré conjecture were likewise completely incomprehensible for teams of multiple tenured research professors of mathematics to see. (cross reference: The Poincaré Conjecture: In Search of the Shape of the Universe by Donal O’Shea (Walker & Co., 2007))

How to Actively Read a Math Text

The Problem

So how are students to proceed? It will certainly help to see a broader road map of what lies ahead and what the expected changes in terrain will look like. It will also help greatly if students have a better idea how to approach mathematics for themselves and even by themselves in many cases.

In my opinion, the most common disconnect occurs somewhere between high school mathematics and early college mathematics (usually a calculus sequence, linear algebra) and then again between linear algebra/differential equations (areas which usually have discussion followed by examples and then crank-out problems) and higher abstract mathematical areas like analysis, abstract algebra, topology (areas in which the definition-theorem-proof cycle of writing is more common and seemingly more incomprehensible to many).

The first big issue in early college mathematics is the increased speed at which college courses move. Students used to a slower high school pace where the teachers are usually teaching to the middle or lower end of the class get caught unaware as their college professors teach to the higher ability students and aren’t as afraid to leave the lower end of the spectrum behind. Just like high school athletes are expected to step up their game when they make the transition to college and similarly college athletes who go pro, mathematics students should realize they’re expected to step up their game at the appropriate times.

Often math students (and really any student of any subject) relies on the teacher assigning readings or problems from their book rather than excersizing their curiosity to more avidly and broadly explore the material on their own.  If they can take the guidance of their teacher as well as that of the individual authors of books, they may make it much further on their own.  High school teachers often skip sections of textbooks for time, but students should realize that there is profitable and interesting material that they’re skipping.  Why not go and read it on their own?

Earlier I mentioned that an average undergraduate abstract algebra textbook might cover the totality of a high school algebra textbook in about three pages.  What does this mean for upper level mathematics students?  It almost always means that the density of material in these books is far greater than that of their earlier textbooks.  How is this density arrived at?  Authors of advanced textbooks leave out far more than they’re able to put in, otherwise their 300 page textbooks, if written at the same basic level as those that came before would be much more ponderous 1000+ page textbooks.  What are they leaving out?  Often they’re leaving out lots of what might be useful discussion, but more often, they’re leaving out lots of worked out examples. For example, a high school text will present a definition or concept and then give three or more illustrations or examples of problems relating to the concept.  The exercises will then give dozens of additional drill problems to beat the concept to death.  This type of presentation usually continues up to the level of calculus where one often sees massive tomes in the 800+ page length. Math texts after this point generally don’t go much over 300 pages as a rule, and it’s primarily because they’re leaving the examples out of the proverbial equation.

The Solution

How does one combat this issue?  Students need to more actively think back to the math they’ve taken previously and come up with their own simple examples of problems, and work though them on their own.  Just because the book doesn’t give lots of examples doesn’t mean that they don’t exist.

In fact, many textbooks are actually presenting examples, they’re just hiding them with very subtle textual hints. Often in the presentation of a concept, the author will leave out one or more steps in a proof or example and hint to the student that they should work through the steps themselves. (Phrases like: “we leave it to the reader to verify” or “see example 2.”) Sometimes this hint comes in the form of that dreaded phrase, “It’s easy to see.” When presented with these hints, it is incumbent (or some students may prefer the word encumbering) on the student to think through the missing steps or provide the missing material themselves.

While reading mathematics, students should not only be reading the words and following the steps, but they should actively be working their way through all of the steps (missing or not) in each of the examples or proofs provided. They must read their math books with pencil and paper in hand instead of the usual format of reading their math book and then picking up paper and pencil to work out problems afterwards.  Most advanced math texts suggest half a dozen or more problems to work out within the text itself before presenting a dozen or more additional problems usually in a formal section entitled “Exercises”. Students have to train themselves to be thinking about and working out the “hidden” problems within the actual textual discussion sections.

Additionally, students need to consider themselves “researchers” or think of their work as discovery or play.  Can they come up with their own questions or exercises that relate the concepts they’ve read about to things they’ve done in the past? Often asking the open ended question, “What happens if I…” can be very useful.  One has to imagine that this is the type of “play” that early mathematicians like Euclid, Gauss, and Euler did, and I have to say, this is also the reason that they discovered so many interesting properties within mathematics.  (I always like to think that they were the beneficiaries of “picking the lowest hanging fruit” within mathematics – though certainly they discovered some things that took some time to puzzle out; we take some of our knowledge for granted as sitting on the shoulders of giants does allow us to see much further than we could before.)

As a result of this newly discovered rule, students will readily find that while they could read a dozen pages of their high school textbooks in just a few minutes, it may take them between a half an hour to two hours to properly read even a single page of an advanced math text. Without putting in this extra time and effort they’re going to quickly find themselves within the tall grass (or, more appropriately weeds).

Another trick of advanced textbooks is that, because they don’t have enough time or space within the primary text itself, authors often “hide” important concepts, definitions, and theorems within the “exercises” sections of their books.  Just because a concept doesn’t appear in the primary text doesn’t mean it isn’t generally important.  As a result, students should always go out of their way to at least read through all of the exercises in the text even if they don’t spend the time to work through them all.

One of the difficult things about advanced abstract mathematics is that it is most often very cumulative and even intertwined, so when one doesn’t understand the initial or early portions of a textbook, it doesn’t bode well for the later sections which require one to have mastered the previous work.  This is even worse when some courses build upon the work of earlier courses, so for example, doing well in calculus III requires that one completely mastered calculus I. At some of the highest levels like courses in Lie groups and Lie algebras requires that one mastered the material in multiple other prior courses like analysis, linear algebra, topology, and abstract algebra. Authors of textbooks like these will often state at the outset what material they expect students to have mastered to do well, and even then, they’ll often spend some time giving overviews of relevant material and even notation of these areas in appendices of their books.

As a result of this, we can take it as a general rule: “Don’t ever skip anything in a math textbook that you don’t understand.” Keep working on the concepts and examples until they become second nature to you.

Finally, more students should think of mathematics as a new language.  I’ve referenced the following Galileo quote before, but it bears repeating (emphasis is mine):

Philosophy is written in this grand book, the universe which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the letters in which it is composed. It is written in the language of mathematics, and its characters are triangles, circles and other geometric figures without which it is humanly impossible to understand a single word of it; without these, one wanders about in a dark labyrinth.

Galileo Galilee (1564–1642) in Il saggiatore (The assayer)

Though mathematical notation has changed drastically (for the better, in my opinion) since Galileo’s time, it certainly has its own jargon, definitions, and special notations.  Students should be sure to spend some time familiarizing themselves with current modern notation, and especially the notation in the book that they choose.  Often math textbooks will have a list of symbols and their meanings somewhere in the end-papers or the appendices. Authors usually go out of their way to introduce notation somewhere in either the introduction, preface, appendices, or often even in an introductory review chapter in which they assume most of their students are very familiar with, but they write it anyway to acclimate students to the particular notation they use in their text.  This notation can often seem excessive or even obtuse, but generally it’s very consistent across disciplines within mathematics, but it’s incredibly useful and necessary in making often complex concepts simple to think about and communicate to others. For those who are lost, or who want help delving into areas of math seemingly above their heads, I highly recommend the text Mathematical Notation: A Guide for Engineers and Scientists by my friend Edward R. Scheinerman as a useful guide.

A high school student may pick up a textbook on Lie Groups and be astounded at the incomprehensibility of the subject, but most of the disconnect is in knowing and understanding the actual language in which the text is written.  A neophyte student of Latin would no sooner pick up a copy of Cicero and expect to be able to revel in the beauty and joy of the words or their meaning without first spending some time studying the vocabulary, grammar, and syntax of the language.  Fortunately, like Latin, once one has learned a good bit of math, the notations and definitions are all very similar, so once you can read one text, you’ll be able to appreciate a broad variety of others.

Actively Reading a Mathematics Text Review:

  • Work through the steps of everything within the text
  • Come up with your own examples
  • Work through the exercises
  • Read through all the exercises, especially the ones that you don’t do
  • Don’t ever skip anything you don’t fully understand
  • Math is a language: spend some time learning (memorizing) notation

Exceptions

Naturally there are exceptions to the rule. Not all mathematics textbooks are great, good, or even passable.  There is certainly a spectrum of textbooks out there, and there are even more options at the simpler (more elementary) end, in part because of there is more demand.  For the most part, however, most textbooks are at least functional.  Still one can occasionally come across a very bad apple of a textbook.

Because of the economics of textbook publishing, it is often very difficult for a textbook to even get published if it doesn’t at least meet a minimum threshold of quality. The track record of a publisher can be a good indicator of reasonable texts. Authors of well-vetted texts will often thank professors who have taught their books at other universities or even provide a list of universities and colleges that have adopted their texts. Naturally, just because 50 colleges have adopted a particular text doesn’t necessarily mean that that it is necessarily of high quality.

One of the major issues to watch out for is using the textbook written by one’s own professor.  While this may not be an issue if your professor is someone like Serge Lang, Gilbert Strang, James Munkres, Michael Spivak, or the late Walter Rudin, if your particular professor isn’t supremely well known in his or her field, is an adjunct or associate faculty member, or is a professor at a community college, then: caveat emptor.

Since mathematics is a subject about clear thinking, analysis, and application of knowledge, I recommend that students who feel they’re being sold a bill of goods in their required/recommended textbook(s), take the time to look at alternate textbooks and choose one that is right for themselves.  For those interested in more on this particular sub-topic I’ve written about it before: On Choosing Your own Textbooks.

Parting Advice

Often, even with the best intentions, some authors can get ahead of themselves or the area at hand is so advanced that it is difficult to find a way into it. As an example, we might consider Lie groups and algebras, which is a fascinating area to delve into. Unfortunately it can take several years of advanced work to get to a sufficient level to even make a small dent into any of the textbooks in the area, though some research will uncover a handful of four textbooks that will get one quite a way into the subject with a reasonable background in just analysis and linear algebra.

When one feels like they’ve hit a wall, but still want to struggle to succeed, I’m reminded of the advice of revered mathematical communicator Paul Halmos, whose book Measure Theory needed so much additional background material, that instead of beginning with the traditional Chapter 1, he felt it necessary to include a Chapter 0 (he actually called his chapters “sections” in the book) and even then it had enough issueshewas cornered into writing the statement:

…[the reader] should not be discouraged, if on first reading of section 0, he finds that he does not have the prerequisites for reading the prerequisites.

Paul Halmos in Measure Theory(1950)

This is essentially the mathematician’s equivalent of the colloquialism “Fake it ’til you make it.”

When all else fails, use this adage, and don’t become discouraged. You’ll get there eventually!

 

Algebra is Like Pastry: Wonderful!

Pierre Anton Grillet (1941 – ), algebraist
in preface to Abstract Algebra, Second Edition (Springer, 2007)

 

The Postdoctoral Experience (Revisited)

Bookmarked The Postdoctoral Experience Revisited (2014) (The National Academies Press)
The Postdoctoral Experience Revisited builds on the 2000 report Enhancing the Postdoctoral Experience for Scientists and Engineers. That ground-breaking report assessed the postdoctoral experience and provided principles, action points, and recommendations to enhance that experience. Since the publication of the 2000 report, the postdoctoral landscape has changed considerably. The percentage of PhDs who pursue postdoctoral training is growing steadily and spreading from the biomedical and physical sciences to engineering and the social sciences. The average length of time spent in postdoctoral positions seems to be increasing. The Postdoctoral Experience Revisited reexamines postdoctoral programs in the United States, focusing on how postdocs are being guided and managed, how institutional practices have changed, and what happens to postdocs after they complete their programs. This book explores important changes that have occurred in postdoctoral practices and the research ecosystem and assesses how well current practices meet the needs of these fledgling scientists and engineers and of the research enterprise. The Postdoctoral Experience Revisited takes a fresh look at current postdoctoral fellows - how many there are, where they are working, in what fields, and for how many years. This book makes recommendations to improve aspects of programs - postdoctoral period of service, title and role, career development, compensation and benefits, and mentoring. Current data on demographics, career aspirations, and career outcomes for postdocs are limited. This report makes the case for better data collection by research institution and data sharing. A larger goal of this study is not only to propose ways to make the postdoctoral system better for the postdoctoral researchers themselves but also to better understand the role that postdoctoral training plays in the research enterprise. It is also to ask whether there are alternative ways to satisfy some of the research and career development needs of postdoctoral researchers that are now being met with several years of advanced training. Postdoctoral researchers are the future of the research enterprise. The discussion and recommendations of The Postdoctoral Experience Revisited will stimulate action toward clarifying the role of postdoctoral researchers and improving their status and experience.

The National Academy of Sciences has published a (free) book: The Postdoctoral Experience (Revisited) discussing where we’re at and some ideas for a way forward.

Most might agree that our educational system is far less than ideal, but few pay attention to significant problems at the highest levels of academia which are holding back a great deal of our national “innovation machinery”. The National Academy of Sciences has published a (free) book: The Postdoctoral Experience (Revisited) discussing where we’re at and some ideas for a way forward. There are some interesting ideas here, but we’ve still got a long way to go.

Book cover of The Postdoctoral Experience Revisited (2014)
The Postdoctoral Experience Revisited (2014) | National Academies Press

Introduction to Lie Groups and Lie Algebras (Part 2) | UCLA Extension

Dr. Mike Miller has just opened up registration for the second course in the series. His courses are always clear, entertaining, and invigorating, and I highly recommend them to anyone who is interested in math, science, or engineering.

Dr. Mike Miller, who had previously announced a two quarter sequence of classes on Lie Groups at UCLA, has just opened up registration for the second course in the series. His courses are always clear, entertaining, and invigorating, and I highly recommend them to anyone who is interested in math, science, or engineering.

Philosophy is written in this grand book, the universe which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the letters in which it is composed. It is written in the language of mathematics, and its characters are triangles, circles and other geometric figures without which it is humanly impossible to understand a single word of it; without these, one wanders about in a dark labyrinth.

Galileo Galilee (1564–1642) in Il saggiatore (The assayer)

Prior to the first part of the course, I’d written some thoughts about the timbre and tempo of his lecture style and philosophy and commend those interested to take a peek. I also mentioned some additional resources for the course there as well.  For those who missed the first portion, I’m happy to help fill you in and share some of my notes if necessary. The recommended minimum prerequisites for this class are linear algebra and some calculus.


Introduction to Lie Groups and Lie Algebras (Part 2)

Math X 450.7 / 3.00 units / Reg. # 251580W
Professor: Michael Miller, Ph.D.
Start Date: January 13, 2015
Location: UCLA, 5137 Math Sciences Building
Tuesday, 7-10pm
January 13 – March 24
11 meetings total
Class will not meet on one Tuesday to be annouced.

Register here: https://www.uclaextension.edu/Pages/Course.aspx?reg=251580

Course Description

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 is the second in a 2-quarter sequence that offers an introductory survey of Lie groups, their associated Lie algebras, and their representations. Its focus is split between continuing last quarter’s study of matrix Lie groups and their representations and reconciling this theory with that for the more general manifold setting. Topics to be discussed include the Weyl group, complete reducibility, semisimple Lie algebras, root systems, and Cartan subalgebras. This is an advanced course, requiring a solid understanding of linear algebra, basic analysis, and, ideally, the material from the previous quarter.Internet access required to retrieve course materials.

Recommended Textbook

Hall, Brian. Lie Groups, Lie Algebras, & Representations (Springer, 2004) ISBN: 9781441923134

 

A photograph of Sophus Lie's very full and bushy beard.
“I wouldn’t lie to you. This is Sophus’s beard.”

 

BIRS Workshop on Biological and Bio-Inspired Information Theory | Storify Stream

Over the span of the coming week, I'll be updating (and archiving) the stream of information coming out of the BIRS Workshop on Biological and Bio-Inspired Information Theory.

Over the span of the coming week, I’ll be updating (and archiving) the stream of information coming out of the BIRS Workshop on Biological and Bio-Inspired Information Theory.

Editor’s note: On 12/12/17 Storify announced they would be shutting down. As a result, I’m changing the embedded version of the original data served by Storify for an HTML copy which can be found below:

BIRS: Biological and Bio-Inspired Information Theory

A 5 Day workshop on Biology and Information Theory hosted by the Banff International Research Station

  1. Wishing I was at the Gene Regulation and Information Theory meeting starting tomorrow  http://bit.ly/XnHRZs  #ITBio
  2. Mathematical and Statistical Models for Genetic Coding starts today.  http://www.am.hs-mannheim.de/genetic_code_2013.php?id=1  @andreweckford might borrow attendees for BIRS
  3. Mathematical Foundations for Information Theory in Diffusion-Based Molecular Communications  http://bit.ly/1aTVR2c  #ITBio
  4. Bill Bialek giving plenary talk “Information flow & order in real biological networks” at Feb 2014 workshop  http://mnd.ly/19LQH8f  #ITBio
  5. #ITBio http://t.co/Ty8dEIXQUT"/>

    CECAM Workshop: “Entropy in Biomolecular Systems” starts May 14 in Vienna.  http://jhu.md/1faLR8t  #ITBio pic.twitter.com/Ty8dEIXQUT
  6. Last RT: wonder what the weather is going to be like at the end of October for my @BIRS_Math workshop
  7. @JoVanEvery I’m organizing a workshop in Banff in October … hopefully this isn’t a sign of weather to come!
  8. Banff takes its name from the town of Banff, Scotland, not to be confused with Bamff, also Scotland.
  9. Good morning from beautiful Banff. How can you not love the mountains? http://t.co/mxYBNz7yzl

    Good morning from beautiful Banff. How can you not love the mountains? pic.twitter.com/mxYBNz7yzl
  10. “Not an obvious connection between utility and information, just as there is no obvious connection between energy and entropy” @BIRS_Math
  11. Last RT: a lot of discussion of my signal transduction work with Peter Thomas.
  12. Live now: Nicolo Michelusi of @USCViterbi on Stochastic Model for Electron Transfer in Bacterial Cables  http://www.birs.ca/live  #ITBio
  13. Nicolo Michelusi (University of Southern California), A Stochastic Model for Electron Transfer in Bacterial Cables  http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410271450-Michelusi.mp4 
  14. Listening to the always awesome @cnmirose talk about the ultimate limits of molecular communication.
  15. “Timing is fundamental … subsumes time-varying concentration channel” @cnmirose @BIRS_Math
  16. Standard opening quote of these talks: “I’m not a biologist, but …” @BIRS_Math
  17. Stefan Moser (ETH Zurich), Capacity Bounds of the Memoryless AIGN Channel – a Toy-Model for Molecular Communicat…  http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410271610-Moser.mp4 
  18. Weisi Guo (University of Warwick), Communication Envelopes for Molecular Diffusion and Electromagnetic Wave Propag…  http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410271643-Guo.mp4 
  19. .@ChrisAldrich @andreweckford @Storify @BIRS_Math Sounds like a fascinating workshop on bioinformation theory in Banff.
  20. Toby Berger, winner of the 2002 Shannon award, speaking right now. @BIRS_Math
  21. Naftali Tishby (Hebrew University of Jerusalem), Sensing and acting under information constraints – a principled a…  http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410281032-Tishby.mp4 
  22. “…places such as BIRS and the Banff Centre exist to facilitate the exchange and pursuit of knowledge.” S. Sundaram  http://www.birs.ca/testimonials/#testimonial-1454 
  23. We’re going for a hike tomorrow. Many thanks to Lukas at the @ParksCanada info centre in Banff for helpful advice! @BIRS_Math
  24. Alexander Dimitrov (Washington State University), Invariant signal processing in auditory biological systems  http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410281416-Dimitrov.mp4 
  25. Joel Zylberberg (University of Washington), Communicating with noisy signals: lessons learned from the mammalian v…  http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410281450-Zylberberg.mp4 
  26. Robert Schober (Universitat Erlangen-Nurnberg), Intersymbol interference mitigation in diffusive molecular communi…  http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410281549-Schober.mp4 
  27. Rudolf Rabenstein (Friedrich-Alexander-Universitat Erlangen-Nurnberg (FAU)), Modelling Molecular Communication Cha…  http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410281627-Rabenstein.mp4 
  28. THis week @BIRS_Math ” Biological and Bio-Inspired Information Theory ” @thebanffcentre #biology #math @NSF
  29. “Your theory might match the data, but the data might be wrong” – Crick @BIRS_Math
  30. So information theory seems to be a big deal in ecology. @BIRS_Math
  31. Tom Schneider (National Institutes of Health), Three Principles of Biological States: Ecology and Cancer  http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410290904-Schneider.mp4 
  32. “In biodiversity, the entropy of an ecosystem is the expected … information we gain about an organism by learning its species” @BIRS_Math
  33. Seriously, I’m blown away by this work in information theory in ecology. Huge body of work; I had no idea. @BIRS_Math
  34. I encourage @BIRS_Math attendees at Biological & Bio-Inspired Information Theory to contribute references here:  http://bit.ly/1jQwObk 
  35. Christoph Adami (Michigan State University), Some Information-Theoretic Musings Concerning the Origin and Evolutio…  http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410291114-Adami.mp4 
  36. #ITBio http://t.co/VA8komuuSW"/>

    .@ChristophAdami talk Some Information-Theoretic Musings Concerning the Origin of Life @BIRS_Math this morning #ITBio pic.twitter.com/VA8komuuSW
  37. ICYMI @ChristophAdami had great paper: Information-theoretic Considerations on Origin of Life on arXiv  http://bit.ly/1yIhK2Q  @BIRS_Math
  38. Baez has a post on Tishby's talk "Sensing &  Acting Under Information Constraints" http://t.co/t1nPVI1pxa @BIRS_Math http://t.co/dFuiVLFSGC

    Baez has a post on Tishby’s talk “Sensing & Acting Under Information Constraints”  http://bit.ly/1yIDonR  @BIRS_Math pic.twitter.com/dFuiVLFSGC
  39. INFORMATION THEORY is the new central ...

    INFORMATION THEORY is the new central …
  40. I’m listening to a talk on the origin of life at a workshop on Biological and Bio-Inspired Information Theory. …  https://plus.google.com/117562920675666983007/posts/gqFL7XY3quF 
  41. Now accepting applications for the #Research Collaboration Workshop for Women in #MathBio at NIMBioS  http://ow.ly/DzeZ7 
  42. We removed a faulty microphone from our lecture room this morning. We’re now fixing the audio buzz in this week’s videos, and reposting.
  43. Didn’t get enough information theory & biology this week @BIRS_Math? Apply for NIMBioS workshop in April 2015  http://bit.ly/1yIeiWe  #ITBio
  44. Amin Emad (University of Illinois at Urbana-Champaign), Applications of Discrete Mathematics in Bioinformatics  http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410301329-Emad.mp4 
  45. Paul Bogdan (University of Southern California), Multiscale Analysis Reveals Complex Behavior in Bacteria Populati…  http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410301401-Bogdan.mp4 
  46. Lubomir Kostal (Institute of Physiology, Academy of Sciences of the Czech Republic), Efficient information transmi…  http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410301534-Kostal.mp4 
  47. Banff ☀️❄️🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲❤️
  48. @conservativelez I’m a big fan of your dad’s research & was reminded of much of it via a workshop on Biological Information Theory
  49. @conservativelez Though he may not have been able to attend, he can catch most of the talks online if he’d like  https://www.birs.ca/events/2014/5-day-workshops/14w5170 
  50. Depressed that @BIRS_Math Workshop on Biological & Bio-Inspired Information Theory is over? Relive it here:  http://bit.ly/1rF3G4B  #ITBio
  51. A few thoughts about that workshop while I wait for my flight back to Toronto.
  52. 1/ Everyone I talked to said it was the best workshop they’d ever been to, and they’d like to do a follow-up workshop @BIRS_Math
  53. 2/ There is an amazing diversity of work under the umbrella of “information theory”. @BIRS_Math
  54. 3/ Much of this work is outside the IT mainstream, and an issue is that people use different terms for related concepts. @BIRS_Math
  55. 4/ Some community building is in order. I think this workshop was a good first step. @BIRS_Math
  56. 5/ Many many thanks to @BIRS_Math and huge kudos to @NGhoussoub for excellent service to the Canadian scientific community. BIRS is a gem.
  57. 6/ Also many thanks to the participants for their excellent talks, and to @ChrisAldrich for maintaining a Storify.


See Leopold. See Molly. Hear Molly’s Soliloquy.

October 22, 2014 (10:50 am)

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Information Theory is the New Central Discipline

Replied to Information Theory is the new central discipline. by Nassim Nicholas Taleb (facebook.com)

INFORMATION THEORY is the new central discipline. This graph was from 20y ago in the seminal book Cover and Thomas, as the field was starting to be defined. Now Information Theory has been expanded to swallow even more fields.

Born in, of all disciplines, Electrical Engineering, the field has progressively infiltrating probability theory, computer science, statistical physics, data science, gambling theory, ruin problems, complexity, even how one deals with knowledge, epistemology. It defines noise/signal, order/disorder, etc. It studies cellular automata. You can use it in theology (FREE WILL & algorithmic complexity). As I said, it is the MOTHER discipline.

I am certain much of Medicine will naturally grow to be a subset of it, both operationally, and in studying how the human body works: the latter is an information machine. Same with linguistics. Same with political “science”, same with… everything.

I am saying this because I figured out what the long 5th volume of the INCERTO will be. Cannot say now with any precision but it has to do with a variant of entropy as the core natural generator of Antifragility.

[Revised to explain that it is not *replacing* other disciplines, just infiltrating them as the point was initially misunderstood…]

Nassim Nicholas Taleb via Facebook

[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:

At the beginning of September, Christoph Adami posted an awesome and very sound paper on arXiv entitled “Information-theoretic considerations concerning the origin of life”  which truly portends to turn the science of the origin of life on its head.

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.

For the advanced readers/researchers interested in more at the intersection of information theory and biology, I’ll also mention that I maintain a list of references, books, and journal articles in a Mendeley group entitled “ITBio: Information Theory, Microbiology, Evolution, and Complexity.”

Venn Diagram of how information theory relates to other fields.
Figure 1.1 [page 2] from
Thomas M. Cover and Joy Thomas’s textbook Elements of Information Theory, Second Edition
(John Wiley & Sons, Inc., 2006) [First Edition, 1991]

Announcement: Special issue of Entropy: “Information Theoretic Incentives for Cognitive Systems”

Dr. Christoph Salge asked me to cross-post this notice from the Entropy site here.

Editor’s Note: Dr. Christoph Salge asked me to cross-post the following notice from the Entropy site here. I’m sure many of the readers of the blog will find the topic to be of interest.


 

Logo for the journal Entropy

 

Dear Colleagues,

In recent years, ideas such as “life is information processing” or “information holds the key to understanding life” have become more common. However, how can information, or more formally Information Theory, increase our understanding of life, or life-like systems?

Information Theory not only has a profound mathematical basis, but also typically provides an intuitive understanding of processes, such as learning, behavior and evolution terms of information processing.

In this special issue, we are interested in both:

  1. the information-theoretic formalization and quantification of different aspects of life, such as driving forces of learning and behavior generation, information flows between neurons, swarm members and social agents, and information theoretic aspects of evolution and adaptation, and
  2. the simulation and creation of life-like systems with previously identified principles and incentives.

Topics with relation to artificial and natural systems:

  • information theoretic intrinsic motivations
  • information theoretic quantification of behavior
  • information theoretic guidance of artificial evolution
  • information theoretic guidance of self-organization
  • information theoretic driving forces behind learning
  • information theoretic driving forces behind behavior
  • information theory in swarms
  • information theory in social behavior
  • information theory in evolution
  • information theory in the brain
  • information theory in system-environment distinction
  • information theory in the perception action loop
  • information theoretic definitions of life

Submission

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. Papers will be published continuously (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are refereed through a peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed Open Access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1200 CHF (Swiss Francs).

Deadline for manuscript submissions: 28 February 2015

Special Issue Editors

Guest Editor
Dr. Christoph Salge
Adaptive Systems Research Group,University of Hertfordshire, College Lane, AL10 9AB Hatfield, UK
Website: http://homepages.stca.herts.ac.uk/~cs08abi
E-Mail: c.salge@herts.ac.uk
Phone: +44 1707 28 4490
Interests: Intrinsic Motivation (Empowerment); Self-Organization; Guided Self-Organization; Information-Theoretic Incentives for Social Interaction; Information-Theoretic Incentives for Swarms; Information Theory and Computer Game AI

Guest Editor
Dr. Georg Martius
Cognition and Neurosciences, Max Planck Institute for Mathematics in the Sciences Inselstrasse 22, 04103 Leipzig, Germany
Website: http://www.mis.mpg.de/jjost/members/georg-martius.html
E-Mail: martius@mis.mpg.de
Phone: +49 341 9959 545
Interests: Autonomous Robots; Self-Organization; Guided Self-Organization; Information Theory; Dynamical Systems; Machine Learning; Neuroscience of Learning; Optimal Control

Guest Editor
Dr. Keyan Ghazi-Zahedi
Information Theory of Cognitive Systems, Max Planck Institute for Mathematics in the Sciences Inselstrasse 22, 04103 Leipzig, Germany
Website: http://personal-homepages.mis.mpg.de/zahedi
E-Mail: zahedi@mis.mpg.de
Phone: +49 341 9959 535
Interests: Embodied Artificial Intelligence; Information Theory of the Sensorimotor Loop; Dynamical Systems; Cybernetics; Self-organisation; Synaptic plasticity; Evolutionary Robotics

Guest Editor
Dr. Daniel Polani
Department of Computer Science, University of Hertfordshire, Hatfield AL10 9AB, UK
Website: http://homepages.feis.herts.ac.uk/~comqdp1/
E-Mail: d.polani@herts.ac.uk
Interests: artificial intelligence; artificial life; information theory for intelligent information processing; sensor Evolution; collective and multiagent systems

A Mathematical Symphony

Robert B. Ash, mathematician
in A Primer of Abstract Mathematics (The Mathematical Association of America, 1998)

 

A Primer of Abstract Mathematics by Robert B. Ash
A Primer of Abstract Mathematics by Robert B. Ash

 

Proofing Bread

Leave it to a mathematician to get a proof out of everything - including bread!
Leave it to a mathematician to get a proof out of everything - including bread!
Leave it to a mathematician to get a proof out of everything – including bread!

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Introduction to Lie Groups and Lie Algebras | UCLA Extension

Looking for some serious entertainment on Tuesday nights this fall? Professor Mike Miller has got you covered!

Exercise Your Brain

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.)

“Beginners” Welcome!

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.

My classes have the full spectrum of students from the most serious to the hobbyist to those who are in it for the entertainment and  ‘just enjoy watching it all go by.’

Mike Miller, Ph.D.

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.


Introduction to Lie Groups and Lie Algebras

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
Tuesday, 7-10pm
September 30 – December 16, 2014
11 meetings total (no mtg 11/11)
Register here: https://www.uclaextension.edu/Pages/Course.aspx?reg=249254

Course Description

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.

Recommended Textbook

Hall, Brian. Lie Groups, Lie Algebras, & Representations (Springer, 2004) ISBN: 9781441923134

 

Portrait of Sophus Lie (1842-1899)
Sophus Lie (1842-1899)

If I had a dollar for every time someone invited me to a Lie Algebra class, I’d be a…

 

Lie Groups, Lie Algebras, and Representations by Brian C. Hall

Because wouldn't you start with an elementary introduction?

Because wouldn't you start with an elementary introduction?

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2014 Fields Medal and Nevanlinna Prize Winners Announced

Here's some of the best coverage I've seen about yesterday's awards.

The 2014 Fields Medal and Nevanlinna Prize winners were announced yesterday.

General announcement

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.)

Great personal profiles with short videos via Quanta Magazine

Artur AvilaA Brazilian Wunderkind Who Calms Chaos

Manjul BhargavaThe Musical, Magical Number Theorist

Martin HairerIn Noisy Equations, One Who Heard Music

Maryam MirzakhaniA Tenacious Explorer of Abstract Surfaces

Subhash KhotA Grand Vision for the Impossible

Technical explanation of their work

Terry Tao (previous Fields Medal Winner): Avila, Bhargava, Hairer, Mirzakhani

 

 

Workshop Announcement: Entropy and Information in Biological Systems

I rarely, if ever, reblog anything here, but this particular post from John Baez’s blog Azimuth is so on-topic, that attempting to embellish it seems silly.

Entropy and Information in Biological Systems (Part 2)

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. 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.

The idea
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:

Rap Genius, a Textual Annotation Browser for Education, Digital Humanities, Science, and Publishing

Since the beginning of January, I’ve come back to regularly browsing and using the website Rap GeniusI’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.

Rap Genius logo

Overview of Rap Genius

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.

General Education Use

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.

Screen capture from Poetry Genius featuring The Great Gatsby

MOOC Use Cases

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.”

Open Access Journal Use

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.

Publishing

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.

Other Uses

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.

Are there particular (off-label) applications you think you might be able to use the Rap Genius platform for? Please add your comments and thoughts below.