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This article, soon to be published by Springer in the Serge Lang Memorial Volume cites the following:

Section 7 of Preprint “Artin Formalism, for Kleinian Groups, via Heat Kernel Methods”:


This interactive graphic of the fundamental domain studied in Section 2 of the paper:


README for the graphics:

  1. To run: download onto a Windows computer (tested on Windows 7).  Run .exe.  Sorry, no binary yet for linux.  Coming soon!  (Write me if you want the source, which required openGL and GLUT libraries for C++ to compile).
  2. General description: axes x,y,z and real, imaginary, plus j (quaternionic) in upper-half-space model of the hyperbolic 3-space.  The fundamental domain F(G) in the paper, is the region INSIDE the moccasin-colored triangular prism (going up to infinity, although it is only shown to a finite height of about 20) and OUTSIDE the red-colored sphere (centered at z=1 and of radius square root 2).
  3. Controls:
  • Mouse: primary-key clicking with shift button depressed changes the viewpoint (the point the observer is looking at), without shift button the standpoint (the point the observer’s eye is located).  Secondary key closes the graphics window (exits the app).
  • Arrow keys: up-down arrows with shift button depressed moves the standpoint into/out of screen, without shift button moves the viewpoint into/out of screen.  Left/right rotates the “up” vector.

Coming soon: text labels.

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Book 2 of "World Made by Hand" Series

Book 2 of the "World Made by Hand" series

…and I like it!

James Howard Kunstler may be best known for his social commentary in such books as The Long Emergency (2006), and, my enduring favorite, The Geography of Nowhere (1994).  However, he evidently remains at heart a novelist, or as he puts it in interviews “a prose stylist”.  He has devoted his last two book-length efforts to exploring, in novel form, the consequences of the “Long Emergency”, an series of apocalyptic events and shortages he envisions for America, focusing on one small town in the real Washington County of Upstate New York.  Although all his books are filled with humor (sometimes overlooked by professional reviewer), this turn away from nonfiction towards speculative fiction would probably be viewed as an unexpected departure for most writers on urban theory and resource economics/politics.  But it should not come as such a surprise to his long-time readers. Not only did Kunstler find his original calling as a fiction writer* (though more as a satirist of contemporary mores than a speculator about the future), but attentive readers of his earlier books, even those who only have read his nonfiction books of the last two decades, would recognize a commonality: cultural and (in the broadest sense) spiritual concerns underly his critique of society and its resource issues, not the other way around.  In other words, Kunstler, in his original journey from novelist to the “political” writer of The Long Emergency and his popular blog, was originally motivated by his observations of dysfunction in American social structure and his deep-held belief in the spiritual impoverishment of American life.  In searching for the causes of this impoverishment, he was first led to look at the way Westerners, and particularly Americans, have degraded public space (The Geoegraphy of Nowhere, 1994).  Next, in searching for and proposing solutions (Home from Nowhere, 1998, and The City in Mind, 2002) he was led to consider what future arrangements people might make in urban living, particularly fixing his attention on the New Urbanist movement.  Finally, at some point in the research and thinking for these books, it seems that he was led to believe that resource scarcity and societal collapse would overwhelm the best laid plans, and that more primal forces such as basic concerns for survival would ultimately determine the future of American living arrangements, rather than well-intentioned movements such as the New Urbanists.

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Meltdown: A Free-Markey Look at Why the Stock Market Collapsed, the Economy Tanked, and Government Bailouts Will Make Things Worse, Thomas E. Woods, Jr., Regenery, Washington D.C., 2009.

ECONned: How Unenlightened Self Interest Undermined Democracy and Corrupted Capitalism, Yves Smith, Palgrave Macmillan, New York, 2010.

I would have never come across the first book under review, Meltdown…, had it not been for an argument I’d had with a self-described “anarcho-capitalist” acquaintance, concerning economic systems.  It ran roughly as follows,

Me: If liberatarianism/anarcho-capitalism is really kicks the butt of every other economic system ever devised, how come we’ve never seen it tried out anywhere in the world?

Him: It was in medieval Iceland.

Me:  Well, that’s one very isolated, long-ago example.  Can you think of an economically modern and sophisticated country which has made a serious attempt to implement Austrian economics.

Him: The early U.S. economy, prior to the “reforms” of Progressivism and the advent of the Federal Reserve System, approximated a free-market Austrian model most closely.  And just look at the unparalleled success and growth of the U.S. from 1776 to 1913!  Right up to the time the elites decided to abandon this model and establish the Fed, which has created the boom-and-bust cycle since.

Me:  I have my doubts about this version of history.  First of all, isn’t it well documented that the U.S. DID have booms and busts before 1913, ones even more severe than the ones since?  Second, if that laissez-faire system was working so well for the economy, why would the elites abandon it and substitute something much worse in its place?  Sure, bankers and evil, but they also aren’t dumb, wouldn’t simple “evolutionary” considerations argue against the idea that they would do something harmful to their own interests?

Him: I don’t have time to debunk all the misconceptions in that last statement of yours.  Go and read Meltdown, by Thomas Woods, Jr., and get back to me when you have.

While I wanted to come back to him someday and say “I read what you asked so now you have NO excuse not to debate me!” I doubted my ability to get through a whole book of what, at the time, I figured would be nothing more than Propaganda for Plutocrats.  So I decided to pair my reading of the supposedly arch-Right laissez-faire capitalist Meltdown with a much more (to me) congenial-seeming left-of-center book on the financial crisis, namely ECONned, by Yves Smith, the blogger at naked capitalism, whose work I followed and admired for some time already.

To say the least, the results of this experiment were a little different from what I had expected.

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As much as the Democrats may “deserve” to win this next Presidential election on the merits, given the personal nature of US politics, they still are going to lose to McCain unless they select a more popular nominee.  Here are the head-to-head match ups of the two leading Dem candidates against McCain, via The Votemaster:

Finally, Cook/RT Strategies just released some head-to-head polls for the general election. Here they are.

Democrat Pct Republican Pct
Clinton 41 McCain 45
Obama 45 McCain 43
Clinton 48 Romney 42
Obama 50 Romney 41

If McCain is the GOP nominee, he beats Clinton but loses narrowly to Obama.

Not only that, but in the electoral college vote, which is the only thing that counts anyway, all indications are that Obama’s advantage, vis-a-vis Clinton, would be magnified.  Why?   A glance at the new color-coded maps at Electoral-Vote.com shows that Hillary’s big victories have been in safe Democratic states like NY and California, while Obama has been triumphing all over the place in battleground states like Missouri, Iowa, and Minnesota.  This would allow Obama to convert his popular vote advantage more easily into an electoral-vote advantage, and head-off a repeat of the disastrous 2000 Bush-Gore situation.  Further, Obama, not Clinton, has been winning in all the traditionally Republican bastions such as the Deep South.  This would also help because McCain would be forced to devote resources to shoring up his support in those states, thereby diverting those resources from swing states.

And note that all these numbers are before the Republican attack machine gears up.  So if you want any chance of defeating the GOP in Nov. and you’re a dem primary voter, it’s pretty clear who to vote for.  Just for the record, I think Obama is no saint or savior, I’m just saying for informational purposes…

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I’m filing this one away for activation after I make my first billion…

It turns out there’s an almost entirely abandoned city only 30 miles from The Loop on the shore of Lake Michigan.  What a far-sighted someone needs to do is buy up the center of the city and redevelop it into the Model City for the 21st century. First step would be to put in an express rail line to downtown Chicago.  Since trains in Europe are now running at well over 120 miles per hour, you could cut the commute to Chicago to a little over 15 minutes.  The trains would run around the clock and be serviced by group taxi-vans at the Gary end–this would be the main initial investment.  Now, redevelop some of those crumbling buildings into condos for white collar Chicagoans priced out of the urban market there and use the sale of them to finance the rest of the project.  Here are a few principles to observe:

  1. Have the New Gary run entirely off the regional electricity grid.  Cover every new building with solar panels, build a solar-thermal power generation plant where some of the abandoned parking lots are now.  Put in a wind farm on the edge of Lake Michigan, or wherever around there winds are most dependable.
  2. Strive for relatively high density, i.e. no useless grassy yards around buildings. But devote some lots on each and every downtown block to intensive community gardening
  3. Start a whole new school system from scratch, private if necessary, with all schools being within walking distance of the houses that they serve.  Invite anyone from the surrounding community to enroll for free in the new, small schools, provided they are willing and able to maintain a certain minimum academic standard.
  4. The schools would be just one of several methods the developers would have to adopt to win the good will of the previous city residents, who would no doubt initially view the project with suspicion if not downright hostility.  Others would be a special effort to hire from the city whenever possible, and perhaps a guaranteed job within the development corporation for anyone from the city who finished the course of study in the “new” school system.
  5. Eventual long-term goal would be to found a graduate-level university specializing in environmental, energy, and urban development and politics.

But this doesn’t have to wait until I get rich, because any day now, some religious cult might buy up the city and put it to more nefarious uses.  Thus, I issue a call for bored billionaires reading this to leave a comment with their contact info.  Let’s get to work!

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This is the film that I now want to project onto the sides of buildings in public squares.

I wouldn’t have expected to find out that the BBC showed a three-hour documentary on the telly that covered many of the topics I’ve been thinking about and kicking around in discussion with friends for the past 10 years, but there you have it.* In addition to the philosophy, game theory, economics, politics, it was most interesting to me the way they interwove psychiatry and surveys in the first two episodes (I’m still working on the third episode). The Ladd-Lipset Survey of the American Professorate and how that came about in the late 70s, although it was not mentioned in the documentary, would have also fit into this context. Mathematical measurement of dubious value was a lietmotif of those times.

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Here’s a little puzzle about Fuchsian groups. [A collaborator came up with it and we’d like to use it to simplify a proof in a paper, but I think it’s a question that may have totally independent interest.] Is any Fuchsian group $latex \Gamma_1$ of the first kind with at least one cusp contained as a subgroup of finite index in another Fuchsian group $latex \Gamma$ such that $latex \Gamma$ has exactly one cusp?

If one is more comfortable with this terminlogy, “Fuchsian group of the first kind with at least one cusp” equals “nonuniform lattice in $latex \mathrm{PSL}(2,\mathbf{R})”$.

For example, obviously if $latex \Gamma_1$ is a congruence subgroup of any sort, then obvserving that $latex \Gamma_1\leq\mathrm{PSL}(2,\mathbf{Z})$ suffices. This gives me the feeling if there’s a counter-example to be found, it would be among non-arithmetic lattices, but I’ve never had any sort of handle on those.

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Good place to start for the basics: Wikipedia articles on solar cells, solar power, photovoltaics.

Some blogs I’ve come across that might be worth following on this (and other renewable energy resources): The Energy Blog, Alternative Energy Blog, a guy who calls his site
“The War Against Oil” (how could I pass up linking to a title like that?).

Other organizations and companies to look at: the solar energy page of the National Renewable Energy Laboratory (which I’d never even heard of until a few days ago), a company that makes quantum dots and has some flash presentations explaining them in simple terms.

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Edward Aldwell

Checking up on what Aldwell was up to these days–I remembered hearing something vague about his working on some new recordings–I found out that he died in an ATV accident a few months ago. Turns out he was getting ready to record the English Suites, but now we’ll never get to find out to find out what his interpretation might have been like, which is a real shame. Amazon lists about 6 CD albums, belonging to him, all but one of them Bach. There must be others recorded on LP and not remastered, and I’d be interested to find out what those might be. Continue Reading »

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Tao Times

The Times has this article up on the life and work of Terence Tao. Unfortunately, they mis-state the Green-Tao Theorem:

Dr. Tao and Dr. Green proved that it is always possible to find, somewhere in the infinity of integers, a progression of prime numbers of any spacing and any length.

If this were the theorem, it would imply the twin prime conjecture. The correct statement (as well as a link to the paper of Green and Tao) can be found here. The difference between that and what the Times article is that, for a given k, you cannot specify the spacing you want your arithmetic progression of primes of length k to have. The theorem says that a suitable spacing can be found for each k, and this spacing may never be 2, as far as the theorem itself says.

Nevertheless, Green and Tao’s work is huge progress towards the twin prime conjecture, even if it doesn’t solve it outright (yet).

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