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.
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
January 13 – March 24
11 meetings total
Class will not meet on one Tuesday to be annouced.
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.
[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.”
Not only a great quote, but an interesting way to view the subjects.
Designer/Artist William Morris once said, “Have nothing in your house that you do not know to be useful, or believe to be beautiful.” My Zojirushi stainless steel mug is one of the few things I’ve ever owned that I feel truly meets both of these criteria.
The design, materials, manufacturing and workmanship of the mug are nothing short of outstanding; the aesthetics and heft in the hand are truly fantastic. I really could not want for more out of such a product. I love looking at it, I love holding it, and I love using it.
I hope one day to come back and write a review worthy of how truly great this travel mug is, but for now, suffice it to say that I’m in love. I spent a LOT of time reading reviews on Amazon and elsewhere, and searching stores and vendors to find the best thermos/mug on the planet and settled on this one. Not only is it easy and intuitive to take completely apart and wash thoroughly (too many I’ve come across are impossible to take apart and clean properly, if at all), but it seals completely and doesn’t spill.
Even better it keeps my beverages piping hot or cold for far longer than I wish it would. There have been days that I’ve filled it with hot coffee or tea and come back several times to drink it hoping that it had cooled a bit only to find it still too hot to consume. After several rounds with this over an eight hour span, I finally opened it up and put in some ice so I could finally drink my coffee. Now I often just leave the cap open (or off) to let it cool a bit more quickly, although even this is a fairly slow process. Now I try to put my beverages in at the temperature I want to drink them knowing that that’s generally the temperature they’ll be when I get around to drinking them.
I love the fact that the cap is designed with a two stage opening mechanism (which probably won’t be noticed by most users because it’s so subtle). One pushes the button and the top opens just a few millimeters. Then letting go of the button allows the top to spring back and click neatly into place so that it doesn’t fall forward and bonk one on the nose when attempting to take a drink.
When I first came across it, I will admit I was a bit reticent at it’s relatively high price (particularly in comparison with cheaper mugs on the market, many of which I’ve tried and been highly disappointed with), but the Zojirushi is certainly worth ever penny; I would not hesitate for a moment to buy more of these.
As a small aside, I will mention that due to physics and the design of the mug that it can occasionally leak a bit when filled with carbonated beverages and then shaken. Doing this creates additional interior pressure that pushes up the internal seal mechanism on the cap that allows a small amount of liquid to escape. Beyond this small category of fluids, which I infrequently use with the mug (and I’m sure others probably won’t either), it has been absolutely airtight and worry-free.
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.