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.)
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:
- Stillwell, John. Naïve Lie Theory. (Springer, 2008) ISBN: 9780387782157
- Baker, Andrew. Matrix Groups: An Introduction to Lie Group Theory (Springer, 2002) ISBN: 9781447101833
- Tapp, Kristopher. Matrix Groups for Undergraduates (AMS, 2005) ISBN: 0821837850
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
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.
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Marginalia and Revision Control
At the end of April, I read an article entitled “In the Margins” in the Johns Hopkins University Arts & Sciences magazine. I was particularly struck by the comments of eminent scholar Jacques Neefs on page thirteen (or paragraph 20) about computers making marginalia a thing of the past:
I actually think that he may be completely wrong and that current technology actually allows us to keep far more marginalia! (Has anyone heard of digital exhaust?) The bigger issue may be that many writers just don’t know how to keep a better running log of their work to maintain all the relevant marginalia they’re actually producing. (Of course there’s also the subsequent broader librarian’s “digital dilemma” of maintaining formats for the future. As an example, thing about how easy or hard it might be for you to read that ubiquitous 3.5 inch floppy disk you used in 1995.)
A a technologist who has spent many years in the entertainment industry, I feel compelled to point everyone towards the concept of revision control (or version control) within the realm of computer science. Though it’s primarily used in tracking changes in computer programs and is often a tool used by large teams of programmers, it can very easily be used for tracking changes in almost any type of writing from novels, short stories, screenplays, legal contracts, or any type of textual documentation of nearly any sort.
Example Use Cases for Revision Control
As a direct example, I’m using what is known as a Git repository to track every change I make in a textbook I’m currently writing. I can literally go back and view every change I’ve made since beginning the project, so though I’m directly revising one (or more) text files, all of my “marginalia” and revisions are saved and available. Currently I’m only doing it for my own reference and for additional backup not supposing that anyone other than myself or an editor possibly may want to ever peruse it. If I was working in conjunction with otheres, there are ways for me to track the changes, edits, or notes that others (perhaps an editor or collaborator) might make.
In addition to the general back-up of the project (in case of catastrophic computer failure), I also have the ability to go back and find that paragraph (or multiple pages) I deleted last week in haste, but realize that I desperately want them back now instead of having to recreate them de n0vo.
Because it’s all digital, future scholars also won’t have problems parsing my handwriting issues as has occasionally come up in differentiating Mary Shelley’s writing from that of her husband in digital projects like the Shelley Godwin Archive. The fact that all changes are tracked and placed in a tree-like structure will indicate who wrote what and when and will indicate which changes were ultimately accepted and merged into the final version.
Screenplays in Hollywood
One particular use case I can easily see for such technology is tracking changes in screenplays over time. I’m honestly shocked that every production company or even more likely studios don’t use such technology to follow changes in drafts over time. In the end, doing such tracking will certainly make Writers Guild of America (WGA) arbitrations much easier as literally every contribution to a script can be tracked to give screenwriters appropriate credit. The end results with the easy ability to time-machine one’s way back into older drafts is truly lovely, and the outputs give so much more information about changes in the script compared to the traditional and all-too-simple (*) which screenwriters use to indicate that something/anything changed on a specific line or the different colored pages which are used on scripts during production.
I can also picture future screenwriters using services like GitHub as platforms for storing and distributing their screenplays to potential agents, managers, and producers.
Redlining Legal Documents
Having seen thousands of legal agreements go back and forth over the years, revision control is a natural tool for tracking the redlining and changes of legal documents as they change over time before they are finally (or even never) executed. I have to imagine that being able to abstract out the appropriate metadata in the long run may actually help attorneys, agents, etc. to become better negotiators, but something like this is a project for another day.
In addition to direct research for projects being undertaken by academics like Neefs, academics should look into using revision control in their own daily work and writings. While writing a book, paper, journal article, essay, monograph, etc. (or graduate students writing theses) one could use their own Git repository to not only save but to back up all of their own work not only for themselves primarily, but also future scholars who come later who would not otherwise have access to the “marginalia” one creates while manufacturing their written thoughts in digital form.
I can easily picture Git as a very simple “next step” in furthering the concept of the digital humanities as well as in helping to bridge the gap between C.P. Snow’s “two cultures.” (I’d also suggest that revision control is a relatively simple step one could take before learning a particular programming language, which I think should be a mandatory tool in everyone’s daily toolbox regardless of their field(s) of interest.)
Start Using Revision Control
“But how do I get started?” you ask.
Know going in that it may take parts of a day to get things set up and running, but once you’ve started with the basics, things are actually pretty easy and you can continue to learn the more advanced subtleties as you progress. Once things are working smoothly, the additional overhead you’ll be expending won’t be too much more than the old method of hitting Alt-S to save one of your old Word documents in the time before auto-save became ubiquitous.
First one should start by choosing one of the myriad revision control systems that exist. For the sake of brevity in this short introductory post, I’ll simply suggest that users take a very close look at Git because of its ubiquity and popularity in the computer science world and the fact that it includes a tremendously large amount of free information and support from a variety of sites on the internet. Git also has the benefit of having versions for all major operating systems (Windows, MacOS, and Linux). Git also has the benefit of a relatively long and robust life within the computer science community meaning that it’s very stable and has many more resources for the uninitiated to draw upon.
Once one has Git installed on their computer and has begun using it, I’d then recommending linking one’s local copy of the repository to a cloud storage solution like either GitHub or BitBucket. While GitHub is certainly one of the most popular Git-related services out there (because it acts, in part, as the hub for a large portion of the open internet and thus promotes sharing), I often recommend using BitBucket as it allows free unlimited private but still share-able repositories while GitHub requires a small subscription fee for keeping one’s work private. Having a repository in the cloud will help tremendously in that your work will be available and downloadable from almost anywhere and because it also serves as a de-facto back-up solution for your work.
I’ve recently been playing around with version control to help streamline the writing/editing process for a book I’ve been writing. Though Git and it’s variants probably seem more daunting than they should to the everyday user, they really represent a very powerful tool. I’ve spent less than two days learning the basics of both Git and hosted repositories (GitHub and Bitbucket), and it has been more than well worth the minor effort.
There is a huge wealth of information on revision control in general and on installing and using Git available on the internet, including full textbooks. For the complete beginners, I’d recommend starting with The Chronicle’s “A Gentle Introduction to Version Control.” Keep in mind that though some of these resources look highly technical, it’s because many are trying to enumerate every function one could potentially desire, when even just the basic core functionality is more than enough to begin with. (I could analogize it to learning to drive a car versus actually reading the full manual so that you know how to take the engine apart and put it back together from scratch. To start with revision control, you only need to learn to “drive.”) Professors might also avail themselves of the use of their local institutional libraries which may host small sessions on learning such tools, or they might avail themselves of the help of their colleagues or students in the computer science department. For others, I’d recommend taking a look at Git’s primary website. BitBucket has an excellent step-by-step tutorial (and troubleshooting) for setting up the requisite software and using it.
What do you use for revision control?
I’ll welcome any thoughts, experiences, or additional resources one might want to share with others in the comments.
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:
- 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
- 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
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.
Deadline for manuscript submissions: 28 February 2015
Special Issue Editors
Dr. Christoph Salge
Adaptive Systems Research Group,University of Hertfordshire, College Lane, AL10 9AB Hatfield, 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
Dr. Georg Martius
Cognition and Neurosciences, Max Planck Institute for Mathematics in the Sciences Inselstrasse 22, 04103 Leipzig, Germany
Phone: +49 341 9959 545
Interests: Autonomous Robots; Self-Organization; Guided Self-Organization; Information Theory; Dynamical Systems; Machine Learning; Neuroscience of Learning; Optimal Control
Dr. Keyan Ghazi-Zahedi
Information Theory of Cognitive Systems, Max Planck Institute for Mathematics in the Sciences Inselstrasse 22, 04103 Leipzig, Germany
Phone: +49 341 9959 535
Interests: Embodied Artificial Intelligence; Information Theory of the Sensorimotor Loop; Dynamical Systems; Cybernetics; Self-organisation; Synaptic plasticity; Evolutionary Robotics
Dr. Daniel Polani
Department of Computer Science, University of Hertfordshire, Hatfield AL10 9AB, UK
Interests: artificial intelligence; artificial life; information theory for intelligent information processing; sensor Evolution; collective and multiagent systems