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Recorded at brunch on 6/17/12 at Mijares Mexican Restaurant, Pasadena, CA.
Artin very wisely identifies these matrix groups as more fundamental–and they are. They come up much more in mathematics. Linear algebra is the central subject of mathematics. You cannot learn too much linear algebra. That’s the basic principle for all of you going on in mathematics.
Linear algebra is presented as sort of stupid stuff, [but] you cannot learn too much linear algebra.
Benedict Gross, Ph.D., George Vasmer Leverett Professor of Mathematics, Harvard University
in Abstract Algebra, Lecture 2 at 14:25 via Harvard Extension
Replied toFeed Your Research by Ellen Keith (The Sheridan Libraries Blog)
All props to the graduate student in Sociology who alerted me to this wonderful time saver. I knew that researchers could set up RSS feeds and e-mail alerts for tables of contents, but I wasn’t practicing what I preached. I’ve got my e-mail alerts set up for tables of contents of favorite library science journals (an oxymoron, I know), but truth be told, those were starting to feel a little old school. I’ve got RSS feeds set up in Google Reader for all my favoritelibraryblogs (NOT an oxymoron). But, although we promote this, I hadn’t set up any RSS feeds from our databases. When a student in the Soc department asked me a question about his RSS feed, I finally set one up myself to see what he was seeing.
You can do this in almost any database but my example above is from two databases we get via ProQuest: Sociological Abstracts and International Bibliography of the Social Sciences. These databases can be searched simultaneously and an RSS feed set up for their combined results. New citations that match my search show up in my feed reader, and as a bonus, the feed results import Find It links so if the articles are in full-text, I’ve got immediate access to them. Best of all, my time is saved by setting up this feed. I’m not constantly checking these databases for new articles on my topic. Instead, they’re delivered to me!
To take it a step further is there an easy way to integrate it into other social tools like Instapaper, ReadItLater, et al or to have the full journal article results emailed to my Kindle’s address so that the papers all show up for instant reading on my Kindle, tablet, e-reader?!
Quite often in science we get a bit ahead of ourselves and begin theorizing wildly, which can very often be an excellent thought experiment in and of itself. But without some data to give proof to our theorems, we can be easily sidedtracked. Never have I read a statement so poetically phrased to admonish against it as I have recently:
So, we’d better bridle our speculations, lest we run the risk that someone like LeCarre’s Smiley asks us one day: ‘What dreams did you cherish that had so little of the world in them?’
Possibly one of the oddest closing sentences of a technical book–and a very good one at that–I’ve ever read:
This pressure can be calculated by minimizing the Helmholtz function of the system. Details can be found in Fermi’s textbook on thermodynamics (Fermi 1956). But why does osmosis explain the behavior of a salted cucumber? This question is left to the reader as a parting gift.
To establish a place of work where engineers can feel the joy of technical innovation, be aware of their mission to society, and work to their heart’s content.
Masara Ibuka (—), co-founder of Sony Corporation
on the first “Purposes of Incorporation” of Sony
Popular physics has enjoyed a new-found regard. Now comes a brave attempt to inject mathematics into an otherwise fashionable subject
This review of Brian Cox and Jeff Forshaw’s forthcoming book The Quantum Universe: Everything That Can Happen Does Happen sounds intriguing. I’m highly impressed that so much of the review focuses on the author’s decision to include a more mathematical treatment of their subject for what is supposed to be a popular science book. I always wish books like these at least had the temerity to include much more in the way of the mathematical underpinnings of their subjects; I’m glad that the popular press (or at least The Economist in this case) is willing to be asking for the mathematics as well. Hopefully it will mark a broader trend in popular books on scientific topics!
Fundamental physics
Big bang
Popular physics has enjoyed a new-found regard. Now comes a brave attempt to inject mathematics into an otherwise fashionable subject
PREVIOUSLY the preserve of dusty, tweed-jacketed academics, physics has enjoyed a surprising popular renaissance over the past few years. In America Michio Kaku, a string theorist, has penned several successful books and wowed television and radio audiences with his presentations on esoteric subjects such as the existence of wormholes and the possibility of alien life. In Britain Brian Cox, a former pop star whose music helped propel Tony Blair to power, has become the front man for physics, which recently regained its status as a popular subject in British classrooms, an effect many attribute to Mr Cox’s astonishing appeal.
Mr Cox, a particle physicist, is well-known as the presenter of two BBC television series that have attracted millions of viewers (a third series will be aired next year) and as a bestselling author and public speaker. His latest book, “The Quantum Universe”, which he co-wrote with Jeff Forshaw of the University of Manchester, breaks the rules of popular science-writing that were established over two decades ago by Stephen Hawking, who launched the modern genre with his famous book, “A Brief History of Time”.
Mr Hawking’s literary success was ascribed to his eschewing equations. One of his editors warned him that sales of the book would be halved by every equation he included; Mr Hawking inserted just one, E=mc2, and, even then, the volume acquired a sorry reputation for being bought but not read. By contrast, Mr Cox, whose previous book with Mr Forshaw investigated “Why does E=mc2?” (2009), has bravely sloshed a generous slug of mathematics throughout his texts.
The difficulties in explaining physics without using maths are longstanding. Einstein mused, “The eternal mystery of the world is its comprehensibility,” and “the fact that it is comprehensible is a miracle.” Yet the language in which the world is described is that of maths, a relatively sound grasp of which is needed to comprehend the difficulties that physicists are trying to resolve as well as the possible solutions. Mr Cox has secured a large fan base with his boyish good looks, his happy turns of phrase and his knack for presenting complex ideas using simple analogies. He also admirably shies away from dumbing down. “The Quantum Universe” is not a dry undergraduate text book, but nor is it a particularly easy read.
The subject matter is hard. Quantum mechanics, which describes in subatomic detail a shadowy world in which cats can be simultaneously alive and dead, is notoriously difficult to grasp. Its experiments yield bizarre results that can be explained only by embracing the maths that describe them, and its theories make outrageous predictions (such as the existence of antimatter) that have nevertheless later been verified. Messrs Cox and Forshaw say they have included the maths “mainly because it allows us to really explain why things are the way they are. Without it, we should have to resort to the physicist-guru mentality whereby we pluck profundities out of thin air, and neither author would be comfortable with guru status.”
That stance might comfort the authors, but to many readers they will nonetheless seem to pluck equations out of thin air. Yet their decision to include some of the hard stuff leaves open the possibility that some readers might actually engage in the slog that leads to higher pleasures. For non-sloggers alternative routes are offered: Messrs Cox and Forshaw use clockfaces to illustrate how particles interact with one another, a drawing of how guitar strings twang and a photograph of a vibrating drum. A diagram, rather than an equation, is used to explain one promising theory of how matter acquires mass, a question that experiments on the Large Hadron Collider at CERN, the European particle-physics laboratory near Geneva, will hopefully soon answer.
The authors have wisely chosen to leaven their tome with amusing tales of dysfunctional characters among scholars who developed quantum mechanics in the 1920s and beyond, as well as with accounts of the philosophical struggles with which they grappled and the occasional earthy aside. Where the subject matter is a trifle dull, Messrs Cox and Forshaw acknowledge it: of Heinrich Kayser, who a century ago completed a six-volume reference book documenting the spectral lines generated by every known element, they observe, “He must have been great fun at dinner parties.” And they make some sweeping generalisations about their colleagues who pore over equations, “Physicists are very lazy, and they would not go to all this trouble unless it saved time in the long run.”
Whether or not readers of “The Quantum Universe” will follow all the maths, the authors’ love for their subject shines through the book. “There is no better demonstration of the power of the scientific method than quantum theory,” they write. That may be so, but physicists all over the world, Messrs Cox and Forshaw included, are longing for the next breakthrough that will supersede the claim. Hopes are pinned on experiments currently under way at CERN that may force physicists to rethink their understanding of the universe, and inspire Messrs Cox and Forshaw to write their next book—equations and all.
How do we search for alien life if it's nothing like the life that we know? Christoph Adami shows how he uses his research into artificial life -- self-replicating computer programs -- to find a signature, a "biomarker," that is free of our preconceptions of what life is.
Adami’s work is along similar lines to some of my own research. This short video gives an intriguing look into some of the basics of how to define life so that one can recognize it when one sees it.
