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Thursday, November 30, 2006
New Serial Feature: Lignières: Then and Now
Comparing images, some taken more than a century ago, of Fourmilab's home in Switzerland with contemporary photos from the same viewpoints provides a transtemporal perspective on the evolution of a rural village in Western Switzerland. You can start with the introduction to the project, embark upon a walking tour of the village, or pick a viewpoint from the graphical index based on a map of the village. Those interested in undertaking such a project themselves may wish to read the tips on the craft of “then and now” photography gleaned during the production of these pages. This project was launched today as a new Fourmilab serial feature, in conjunction with the publication on December 14th of the Lignières history book for which these historical images were collected. A new “then and now” image will be posted every Friday until all are available on-line. Bookmark this week's image to view new images as they are released. This entire document tree is produced in XHTML 1.0 using the “Strict” Document Type Definition. It demonstrates that even within that strait-laced dialect, it is nonetheless possible to implement hovering thumbnail images, targeted links, and pages which gracefully degrade when JavaScript is absent or disabled. If your pages have been afflicted by the floating link bug in Microsoft Internet Explorer 7, which causes a link floated to the right or left of text which happens to be set in italics not to function, take a look at the <table> based document footer in these pages. While it's less elegant than a pure CSS solution, it has the merit of dodging the flaw in the legacy foolscap browser, while continuing to work correctly in its competently-implemented competition and maintaining strict compliance with XHTML 1.0.Posted at
23:25
Thursday, November 23, 2006
Reading List: Stretch: The World of Panoramic Photography
- Meers, Nick. Stretch: The World of Panoramic Photography. Mies, Switzerland: RotoVision, 2003. ISBN 2-88046-692-X.
- In the early years of the twentieth century, panoramic photography was all the rage. Itinerant photographers with unwieldy gear such as the Cirkut camera would visit towns to photograph and sell 360° panoramas of the landscape and wide format pictures of large groups of people, such as students at the school or workers at a factory or mine. George Lawrence's panoramas (some taken from a camera carried aloft by a kite) of the devastation resulting from the 1906 San Francisco earthquake and fire have become archetypal images of that disaster. Although pursued as an art form by a small band of photographers, and still used occasionally for large group portraits, the panoramic fad largely died out with the popularity of fixed-format roll film cameras and the emergence of the ubiquitous 24×36 mm format. The advent of digital cameras and desktop image processing software able to “stitch” multiple images more or less seamlessly (if you know what you're doing when you take them) into an arbitrarily wide panorama has sparked a renaissance in the format, including special-purpose film and digital cameras for panoramic photography. Computers with high performance graphics hardware now permit viewing full-sphere virtual reality imagery in which the viewer can “look around” at will, something undreamed of in the first golden age of panoramas. This book provides an introduction to the history, technology, and art of panoramic photography, alternating descriptions of equipment and technique with galleries featuring the work of contemporary masters of the format, including many examples of non-traditional subjects for panoramic presentation which will give you ideas for your own experiments. The book, which is beautifully printed in China, is itself in “panoramic format” with pages 30 cm wide by 8 cm tall for an aspect ratio of 3¾:1, allowing many panoramic pictures to be printed on a single page. (There are a surprising number of vertical panoramas in the examples which are short-changed by the page format, as they are always printed vertically rather than asking you to turn the book around to view them.) Although the quality of reproduction is superb, the typography is frankly irritating, at least to my ageing eyes. The body copy is set in a light sans-serif font with capitals about six points tall, and photo captions in even smaller type: four point capitals. If that wasn't bad enough, all of the sections on technique are printed in white type on a black background which, especially given the high reflectivity of the glossy paper, is even more difficult to read. This appears to be entirely for artistic effect— there is plenty of white (or black) space which would have permitted using a more readable font. The cover price of US$30 seems high for a work of fewer than 150 pages, however wide and handsome.
Posted at
19:58
Tuesday, November 21, 2006
Reading List: Symmetry and the Monster
- Ronan, Mark. Symmetry and the Monster. Oxford: Oxford University Press, 2006. ISBN 0-19-280722-6.
-
On the morning of May 30th, 1832, self-taught mathematical genius and
revolutionary firebrand
Évariste Galois
died in a duel in Paris, the reasons for which are forgotten; he was twenty
years old. The night before, he wrote a letter in which he urged that
his uncompleted mathematical work be sent to the preeminent
contemporary mathematicians Jacobi and Gauss; neither, however, ever
saw it. The work in question laid the foundations for
group theory,
an active area of mathematical research a century and three
quarters hence, and a cornerstone of the most fundamental
theories of physics: Noether's
Theorem demonstrates that conservation laws and physical
symmetries are two aspects of the same thing.
Finite groups,
which govern symmetries among a finite number of
discrete items (as opposed to, say, the rotations of a sphere,
which are continuously valued), can be arbitrarily complicated,
but, as shown by Galois, can be decomposed into one or more
simple
groups whose only normal subgroups are
the trivial subgroup of order one and the improper subgroup
consisting of the entire group itself: these
are the fundamental kinds of symmetries or, as this book
refers to them, the “atoms of symmetry”, and
there are only five categories (four of the five
categories are themselves infinite). The fifth category
are the sporadic
groups, which do not fit into any of the other categories.
The first was discovered by Émile Mathieu in 1861, and
between then and 1873 he found four more. As group theory continued
to develop, mathematicians kept finding more and more
of these sporadic groups, and nobody knew whether there were
only a finite number or infinitely many of them…until
recently.
Most research papers in mathematics are short and concise.
Some group theory papers are the exception, with two hundred
pagers packed with dense notation not uncommon. The
classification
theorem of finite groups is the ultimate outlier; it has
been likened to the Manhattan Project of pure mathematics. Consisting of
hundreds of papers published over decades by a large collection of
authors, it is estimated, if every component involved in the proof were
collected together, to be on the order of fifteen thousand
pages, many of which are so technical those not involved in the work
itself have extreme difficulty understanding them. (In fact, a
“Revision project” is currently underway with the goal
of restating the proof in a form which future generations
of mathematicians will be able to comprehend.) The last part of the
classification theorem, itself more than a thousand pages in length,
was not put into place until November 2004, so only then could one
say with complete confidence that there were only 26 sporadic
groups, all of which are known.
While these groups are “simple” in the sense of not being
able to be decomposed, the symmetries most of them represent are
of mind-boggling complexity. The
order of a
finite group is the number of elements it contains; for example,
the group of permutations on five items has an order of 5! = 120. The
simplest sporadic group has an order of 7920 and the biggest, well,
it's a monster. In fact, that's what it's called, the
“monster
group”, and its order is (deep breath):
808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000 = If it helps, you can think of the monster as the group of rotations in a space of 196,884 dimensions—much easier to visualise, isn't it? In any case, that's how Robert Griess first constructed the monster in 1982, in a 102 page paper done without a computer. In one of those “take your breath away” connections between distant and apparently unrelated fields of mathematics, the divisors of the order of the monster are precisely the 15 supersingular primes, which are intimately related to the j-function of number theory. Other striking coincidences, or maybe deep connections, link the monster group to the Lorentzian geometry of general relativity, the multidimensional space of string theory, and the enigmatic properties of the number 163 in number theory. In 1983, Freeman Dyson mused, “I have a sneaking hope, a hope unsupported by any facts or any evidence, that sometime in the twenty-first century physicists will stumble upon the Monster group, built in some unsuspected way into the structure of the universe.” Hey, stranger things have happened. This book, by a professional mathematician who is also a talented populariser of the subject, tells the story of this quest. During his career, he personally knew almost all of the people involved in the classification project, and leavens the technical details with biographical accounts and anecdotes of the protagonists. To avoid potentially confusing mathematical jargon, he uses his own nomenclature: “atom of symmetry” instead of finite simple group, “deconstruction” instead of decomposition, and so on. This sometimes creates its own confusion, since the extended quotes from mathematicians use the standard terminology; the reader should refer to the glossary at the end of the book to resolve any such puzzlement.
246×320×59×76×112×133×17×19×23×29×31×41×47×59×71
Posted at
22:27
Saturday, November 18, 2006
Reading List: 1915: The Death of Innocence
- Macdonald, Lyn. 1915: The Death of Innocence. London: Penguin Books, [1993] 1997. ISBN 0-14-025900-7.
- I'm increasingly coming to believe that World War I was the defining event of the twentieth century: not only a cataclysm which destroyed the confident assumptions of the past, but which set history inexorably on a path which would lead to even greater tragedies and horrors as that century ran its course. This book provides an excellent snapshot of what the British people, both at the front and back home, were thinking during the first full year of the war, as casualties mounted and hope faded for the quick victory almost all expected at the outset. The book does not purport to be a comprehensive history of the war, nor even of the single year it chronicles. It covers only the British Army: the Royal Navy is mentioned only in conjunction with troop transport and landings, and the Royal Flying Corps scarcely at all. The forces of other countries, allied or enemy, are mentioned only in conjunction with their interaction with the British, and no attempt is made to describe the war from their perspective. Finally, the focus is almost entirely on the men in the trenches and their commanders in the field: there is little focus on the doings of politicians and the top military brass, nor on grand strategy, although there was little of that in evidence in the events of 1915 in any case. Within its limited scope, however, the book succeeds superbly. About a third of the text is extended quotations from people who fought at the front, many from contemporary letters home. Not only do you get an excellent insight into how horrific conditions were in the field, but also how stoically those men accepted them, hardly ever questioning the rationale for the war or the judgement of those who commanded them. And this in the face of a human cost which is nearly impossible to grasp by the standards of present-day warfare. Between the western front and the disastrous campaign in Gallipoli, the British suffered more than half a million casualties (killed, wounded, and missing) (p. 597). In “quiet periods” when neither side was mounting attacks, simply manning their own trenches, British casualties averaged five thousand a week (p. 579), mostly from shelling and sniper fire. And all of the British troops who endured these appalling conditions were volunteers—conscription did not begin in Britain until 1916. With the Regular Army having been largely wiped out in the battles of 1914, the trenches were increasingly filled with Territorial troops who volunteered for service in France, units from around the Empire: India, Canada, Australia, and New Zealand, and as the year progressed, Kitchener's “New Army” of volunteer recruits rushed through training and thrown headlong into the killing machine. The mindset that motivated these volunteers and the conclusions drawn from their sacrifice set the stage for the even greater subsequent horrors of the twentieth century. Why? Because they accepted as given that their lives were, in essence, the property of the state which governed the territory in which they happened to live, and that the rulers of that state, solely on the authority of having been elected by a small majority of the voters in an era when suffrage was far from universal, had every right to order them to kill or be killed by subjects of other states with which they had no personal quarrel. (The latter point was starkly illustrated when, at Christmas 1914, British and German troops declared an impromptu cease-fire, fraternised, and played football matches in no man's land before, the holiday behind them, returning to the trenches to resume killing one another for King and Kaiser.) This was a widely shared notion, but the first year of the Great War demonstrated that the populations of the countries on both sides really believed it, and would charge to almost certain death even after being told by Lord Kitchener himself on the parade ground, “that our attack was in the nature of a sacrifice to help the main offensive which was to be launched ‘elsewhere’” (p. 493). That individuals would accept their rôle as property of the state was a lesson which the all-encompassing states of the twentieth century, both tyrannical and more or less democratic, would take to heart, and would manifest itself not only in conscription and total war, but also in expropriation, confiscatory taxation, and arbitrary regulation of every aspect of subjects' lives. Once you accept that the state is within its rights to order you to charge massed machine guns with a rifle and bayonet, you're unlikely to quibble over lesser matters. Further, the mobilisation of the economy under government direction for total war was taken as evidence that central planning of an industrial economy was not only feasible but more efficient than the market. Unfortunately, few observed that there is a big difference between consuming capital to build the means of destruction over a limited period of time and creating new wealth and products in a productive economy. And finally, governments learnt that control of mass media could mould the beliefs of their subjects as the rulers wished: the comical Fritz with which British troops fraternised at Christmas 1914 had become the detested Boche whose trenches they shelled continuously on Christmas Day a year later (p. 588). It is these disastrous “lessons” drawn from the tragedy of World War I which, I suspect, charted the tragic course of the balance of the twentieth century and the early years of the twenty-first. Even a year before the outbreak of World War I, almost nobody imagined such a thing was possible, or that it would have the consequences it did. One wonders what will be the equivalent defining event of the twenty-first century, when it will happen, and in what direction it will set the course of history? A U.S. edition is also available.
Posted at
21:47
Wednesday, November 15, 2006
One-Time Pad Generator: Version 1.2 Released
Fourmilab's one-time pad generator, which has been available on the Web as C source code since 1996 and as a JavaScript utility which runs within the user's browser since 1997, has been updated to version 1.2. The C source code has been converted to ANSI C and now compiles with GCC 4.1.1 at the “-Wall” level with no warnings. The ready-to-run Windows console application included with the source distribution is now a Win32 binary compiled with Microsoft C 7.0 (previously it was a 16-bit application built with Visual C 1.52). When generating a random seed on a Unix system, entropy from the /dev/random device file, if present, is stirred into the mix. The JavaScript generator page and the HTML documentation are now XHTML 1.0 Strict DTD compliant, and use Unicode entities for special characters such as left and right double quotes. This version is 100% compatible with all earlier releases in that if run with a fixed seed of a given value, identical output will be produced. This means that users who generate one-time pads from shared seeds need not ensure they're using the same version of the program. If you're using Microsoft Internet Explorer 7.0 and wonder why the XHTML validation buttons in the one-time pad generator documents don't do anything, that's the good old floating links bug which was reported against the 7RC1 release in these pages and to Microsoft on September 8th, 2006, and remains broken in the final production release of that putative browser.Posted at
17:42
Tuesday, November 14, 2006
Reading List: America Alone
- Steyn, Mark. America Alone. Washington: Regnery Publishing, 2006. ISBN 0-89526-078-6.
-
Leave it to
Mark Steyn to write a funny book about the
collapse of Western civilisation. Demographics are destiny, and
unlike political and economic trends, are easier to extrapolate
because the parents of the next generation have already been born: if
there are more of them than their own parents, a population is almost
certain to increase, and if there are fewer, the population is
destined to fall. Once fertility drops to 1.3 children per woman or
fewer, a society enters a demographic “death spiral” from
which there is no historical precedent for
recovery. Italy, Spain, and Russia are already below this level,
and the European Union as a whole is at 1.47, far below the
replacement rate of 2.1. And what's the makeup of this shrinking
population of Europe? Well, we might begin by asking what is the most
popular name for boys born in Belgium…and Amsterdam…and
Malmö, Sweden: Mohammed. Where is this going? Well, in the
words
of Mullah Krekar of Norway (p. 39), “We're the ones who
will change you. Every Western woman in the EU is producing an
average of 1.4 children. Every Muslim woman in the same countries is
producing 3.5 children. By 2050, 30 percent of the population in
Europe will be Muslim. Our way of thinking…will prove more
powerful than yours.”
The author believes, and states forthrightly, that it is the purest
fantasy to imagine that this demographic evolution, seen by many of
the élite as the only hope of salvation for the European
welfare state, can occur without a profound change in the very nature
of the societies in which it occurs. The end-point may not be
“Eutopia”, but rather “Eurabia”, and the
timidity of European nations who already have an urban Muslim
population approaching 30% shows how a society which has lost
confidence in its own civilisation and traditions and imbibed the
feel-good but ultimately debilitating doctrine of multiculturalism ends up
assimilating to the culture of the immigrants, not the other way
around. Steyn sees only three possible outcomes for the West
(p. 204):
- Submit to Islam
- Destroy Islam
- Reform Islam
Posted at
11:49
Sunday, November 12, 2006
Fourmilab: New Backup Configuration in Production
The transition to the new in-house server at Fourmilab is now complete with its assuming complete responsibility for backups of all on-site machines. Backups are made to LTO Ultrium 3 tapes with a Dell PowerVault 124T tape changer with one LTO-3 drive and support for two magazines of 8 tapes each, for a total on-line capacity of 6 Tb uncompressed, reserving one slot for a cleaning cartridge; that's what, in marketing, we call “the feature”. The benefit is that I can go out of town for an extended period without shutting down the regular backup cycle since there's more than enough capacity in the tape changer to handle an absence longer than I'm comfortable leaving the site unattended. The tape changer includes a bar code reader, which permits automatic labelling and recognition of tapes regardless of which physical slot they occupy.
For years, Fourmilab backups have been entrusted to Bacula, the open source enterprise-class network backup solution. With the migration to the tape changer on the new server, the server and all clients have been updated to the current 1.38.11 release of Bacula, using the distribution-supplied release 5.0.22 of MySQL on the server. Bacula fully supports automatic tape changers using the MTX utility, and can handle configurations far more ambitious than this (multiple drives, some reserved for restores, hundreds of slots, etc.).
Installation of the hardware and deployment of the new version of Bacula across all of the Fourmilab hosts went without the slightest hitch. You need to read the Bacula manual carefully to get everything right, but if you do, you can be quite confident it will behave as documented.
Posted at
22:29
Saturday, November 4, 2006
Astronomy: mercredi le 8 novembre
In Latin, the seven days of the week were named after the seven principal celestial bodies, or “luminaries”: the five planets known in antiquity (Mercury, Venus, Mars, Jupiter, and Saturn), plus the Sun and Moon. Many other languages around the world name days of the week in the same manner, while in other languages the names of weekdays are derived from their numerical order in the week, usually starting on Sunday or Monday. Modern Romance languages such as French, Italian, and Spanish retain the Latin-derived names for all of the days except Sunday, renamed the “Lord's day”. In French, for example, Wednesday is “mercredi”—Mercury's day. Next Wednesday, mercredi le 8 novembre, will indeed be Mercury's day, for observers in the Western Hemisphere, Pacific, East Asia, Australia, and New Zealand will be treated to the spectacle of a transit of Mercury across the disc of the Sun, the second in the pair of transits which began with the May 2003 transit, and the last such event until May 9th, 2016. I posted a heads up here on October 17th, encouraging folks in areas from which the transit will be visible to outfit their telescopes with a safe solar filter, as that is by far the best way to observe the event. (Unlike a transit of Venus, which is visible to the unaided eye with “eclipse specs” or a similar filter, Mercury in a November transit subtends only 10 arc-seconds and requires optical assistance: a magnification between 50 and 100 diameters is best.) If you have suitable telescope but lack a solar filter for it, it's probably too late by now to obtain one before the transit, but you can still glimpse the event by using eyepiece projection onto a piece of white cardboard held some distance from the eyepiece; hold the cardboard perpendicular to the light emerging from the eyepiece and move it back and forth until the Sun's disc is in focus. The focal length of the eyepiece will determine the size of the image produced by this method. If your telescope has a finder scope, be sure to leave its objective lens covered (or cover it with aluminium foil if you don't have a lens cap for it), to avoid accidentally burning yourself with the intense light emerging from it. You can aim the telescope at the Sun without need of a finder simply by moving it until the shadow of the telescope tube on the ground is as small as possible. I've never had a problem using eyepiece projection to view sunspots before I had a full aperture solar filter, but some people warn that the intense sunlight passing through the eyepiece may heat it sufficiently to cause damage; it's wise to use an inexpensive eyepiece and not keep the telescope aimed at the Sun for too long. Also, never leave the telescope unattended, even for a moment, as some kid might look directly through it and be instantly blinded. If you don't have a telescope, or aren't in a location from which the transit will be visible, you can still observe the event as it occurs via the Webcasts planned from Kitt Peak, Arizona and several sites in Hawaii. Clear skies!Posted at
15:37
Friday, November 3, 2006
HotBits: Redundant Servers in Production
Posted at
20:49