Blurb: Nick Lomb’s Transit of Venus

Nick Lomb’s Transit of Venus 1631 to the Present is the best illustrated astronomy book for general readers since Terence Dickinson and Alan Dyer’s The Backyard Astronomer’s Guide.  Everything about Lomb’s book from its eye seizing cover, rarely seen historic photographs and charming well researched commentary is first class. Transit is the type of work you steal[1] from and frankly, there is no better endorsement than that.  I’m not the only reader to reach this conclusion check out this and this and this.

When prowling our few remaining bookstores I often skip illustrated works. Usually they’re dumbed-down rehashes of familiar material but, in Transit’s case, I learned something on my first randomly browsed page. The chapter introduction for Venus of the South Seas reads:

Sometimes scientific expeditions have unintended consequences. The desirability of observing the 1769 transit from the South Seas began a chain of events that would lead to the founding of the colony of New South Wales by the British in January 1788. In effect, modern Australia owes its existence to a celestial event.

How about that history haters. I knew why astronomers cared about transits of Venus. In 1677 Edmond Halley, of Halley’s Comet fame, described a method for calculating the astronomical unit from transit of Venus timings. Venus is close enough to the Earth that its track over the Sun differs for widely separated terrestrial observers. This is the familiar parallax effect.  From this small difference you can determine the astronomical unit and if you know the astronomical unit Kepler’s third law tells you the distance of every planet in the solar system.  This was a huge payoff for 17th, 18th and early 19th century astronomers. This is what got Cook out in the Pacific. It’s a great story and Lomb’s telling is the best you will find.

[1] I’ve picked up a few page design ideas.

2012 Venus Transit and Annular Eclipse

I’m gearing up for two big eminent celestial events. On May 20th I’ll be near Page Arizona observing an annular eclipse of the Sun and on June 5th, weather permitting, I’ll be in St. Louis watching Venus creep on the disc of the Sun for the last time in my lifetime.

Eclipses and transits are spectacular events for amateur astronomers and innocent bystanders. Of the two eclipses offer the greater spectacle. In fact, for sheer unbridled awesomeness, it’s hard to beat a total eclipse of the Sun! You can add up all the World Cups and Super Bowls ever played and they would barely register on the logarithmic total solar eclipse spectacle scale. The one total solar eclipse I saw easily ranks as the greatest thing I’ve ever seen and I’m including the births of my children. The May 20th solar eclipse is annular so it’s not in the same galaxy as a total but annular’s have their charms. At maximum eclipse the Sun appears like a perfect blazing ring of light. In Page it will be 10 degrees above the north-western horizon: a good altitude for composing solar landscape pictures.

By comparison the June 5th transit of Venus will not be a big show. Without proper equipment you won’t be able to see it at all. During transit Venus looks like a little black dot on the Sun. The best way to see this event is with telescope or binocular projection. Under no circumstances should you look directly at the Sun without proper eye protection!  For safe transit viewing techniques look here. In 2004 I used binocular projection to view the last transit of Venus from Ottawa Canada. Transits of Venus come in pairs, eight year apart, followed by over a century before the next pair.  After 2012 you will have to wait until 2117 to see another transit of Venus. This is our last chance people. Yeah mortality seriously blows.

2004 transit of Venus from Ottawa Canada. I used 10x50 binoculars to project an image of the Sun. The little dark spot on Sun's limb is the planet Venus.

Mike Brown Punts Pluto

As a longtime amateur astronomer I appreciate good science writing and Mike Brown’s little book How I Killed Pluto and Why It Had It Coming is a wonderful example of the genre. When Pluto was tossed from the pantheon of planets I didn’t care. I knew that in previous centuries, when asteroids were first discovered, that they were briefly counted as planets. Eventually asteroids lost their planet status; there were too many of them and they were all dinky compared to real planets. Brown notes this bit of astronomical history by pointing to 19th century textbooks with high planet counts. The same holds for Pluto, Eris, Sedna, Quaoar and all the other known baby ice balls that make up the Kuiper belt. Real planets are massive enough to clear their orbits of crap. By this standard Mars barely qualifies and Pluto does not.

The emotional hysterics that greeted Pluto’s demise are still playing out. Some reviews posted here castigate Brown in terms rightly applied to suicide bombers and Obama voters. When Pluto bulks up and starts bullying its neighbors like all manly planets do we’ll talk until then I’d advise the puerile Pluto partisans to plumb up their pie holes otherwise we’ll have to toss you in the crank bin with the creationists and cold fusion nitwits.

cross posted on Goodreads.

Old white guys look at the sky!

Last Friday I joined the Saint Louis Astronomical Society (SLAS). In the last twenty years I have been a member of two chapters of the Royal Astronomical Society of Canada, Kingston and Ottawa, the Forth Worth Astronomical Society in Texas, the Minnesota Astronomical Society in Saint Paul and the Orange County Astronomers in southern California. No matter where I go I can see the sky and I can find people who share my interest in it. The SLAS is very similar to other clubs. If you were to walk into a typical astronomy club meeting your overwhelming impression would be: old white guys like looking at the sky!  

The undeniable old whiteness of astronomy clubs is a concern because it tells you something about the health of our culture.  If you think I am pulling your leg or being sarcastic consider the following.

  1. Club members have strong noncommercial or unprofessional interests in science.  Most are not professional astronomers or even scientists. Few derive any income from their interests in astronomy and many spend insane amounts of time and money building telescopes, observing  the sky and keeping up with findings in astronomy and related sciences. What’s the point? Wouldn’t these people be better off devoting the time they “waste” on astronomy to more productive pursuits?  Mind you the same applies to unprofessional artists and hobbyists of all types that “waste” comparable amounts of time on their own “pointless” pursuits.  Astronomy club members love what they do, and, in my experience, it’s a constant and enduring love that never dims or goes away. Anyone with a real passion knows what I’m talking about.
  2. Astronomy club members respect, understand and value scientific arguments. We are constantly reading depressing assessments of the public’s dismal understanding of science. For example, 44% of the US public accepts that, “God created man pretty much in his present form at one time within the last 10,000 years.”  Only 5% of scientists accept this nonsense and even 5% seems to high for my skeptical ass.  Astronomy club members will poll more like scientists than the general public on this question. A society that depends on science yet harbors ignorant masses that do not grasp or appreciate basic scientific findings will not hold.
  3. Club members welcome anyone with an interest in astronomy. I have belonged to half a dozen astronomy clubs and without exception they welcome anyone with an interest in the subject. I have never seen somebody turned away, or discouraged, for reasons of race, age, sex, sexual orientation, political or religious affiliations, or social class. Astronomy clubs are about as egalitarian as it gets! It gets better. Most clubs nurture and cherish the youngsters in their midst’s. This is partly because we don’t see a lot of youngsters and by youngster I mean anyone under thirty!

So why are astronomy clubs in North America old and white? Do people think you need expensive telescopes and other pricey gadgets to enjoy amateur astronomy?  I’ve looked at the sky for decades primarily with binoculars. They are still the best way to learn the sky. Has the public’s interest in science declined during the last forty years? Is elementary science education worse than it was when I was a child? Is the XBox’ed and Avatar’ed generation bored with looking at faint smudges in the sky? Finally, do we smell?  I don’t know why astronomy clubs are old and white but I do know that I will probably be associated with one until the day I die.

PIP News: Isabelle is Up!

Before my fall I launched a PIP (Perpetual Impossible Project).  PIPs are long-range risky undertakings that cannot be finishedPIPs contradict and subvert the very notion of tightly controlled corporate style projects: hence their manifest appeal to recusants like myself.

I won’t go into details about my particular PIP. Let’s just say it captures every delusional notion I have ever entertained. Part of my project involved installing a few Proof Assistants. Proof assistants are programs that verify formal mathematical proofs. There are many proof assistant programs available. These programs are not mathematical magic bullets. They don’t prove theorems and they don’t make the job of “theorem proving” easier. To use a programming analogy: a traditional proof is like pseudo code while a formal proof is like an assembly language program.  If you have ever written a nontrivial assembly language program you have some idea of the sheer effort required to produce a formal proof.

So, if formal proof only makes mathematics more difficult, why bother? This is like asking, so if implementing pseudo code only makes programming more difficult, why bother?

Isabelle 2011 on my Ubuntu box.

A screen shot of Isabelle 2011 on my Ubuntu machine. To install this program I had to convert a Windows machine to Ubuntu and install a host of Linux tools. Reaching this point represents a lot of water under the software bridge.

Open Source Hilbert for the Kindle

David Hilbert

David Hilbert

While searching for free Kindle books I found Project Gutenberg. Project Gutenberg offers free Kindle books but they also have something better! Would you believe \LaTeX source code for some mathematical classics.

The best book I’ve found so far is an English translation of David Hilbert’s Foundations of Geometry. Hilbert’s Foundations exposed some flaws in the ancient treatment of Euclidean geometry and recast the subject with modern axioms. Because it is relatively easy to follow, compared to Hilbert’s more recondite publications, this little book exercised disproportionate influence on 20th century mathematics. We still see its style aped, but rarely matched, in mathematics texts today.

I couldn’t resist the temptation of compiling a mathematical classic so I eagerly downloaded the source and ran it through \LaTeX.  Foundations compiled without problems and generated a nice letter-sized PDF. Letter-size is fine but I was looking for free Kindle books! I decided to invest a little energy modifying the source to produce a Kindle version. Project Gutenberg makes it clear that we are free to modify the source. Isn’t open source wonderful!

Converting Foundations was simple. The main \LaTeX file included 52 *.png illustrations with hard-coded widths in \includegraphics commands. I wrote a J script that converted all these fixed widths to relative \textwidth‘s. This lets \LaTeX automatically resize images for arbitrary page geometries. When compiled with Kindle page dimensions this fixed most of the illustrations. I had to tweak a few wragfig‘s to better typeset images surrounded by text. The result is a very readable Kindle oriented PDF version of Hilbert’s book. There are still a few problems. The Table of Contents is a plain tabular that does not wrap well and one table rolls off the right Kindle margin. Neither of these deficiencies seriously impair the readability of the text.  If these defects annoy you download the Project Gutenberg source with my modifications and build your own version.

This little experiment convinced me that providing free classic books, in source code form, is a service to mankind.  Not only does it allow you to “publish” classics on new media it also fundamentally changes your attitude toward books. Hilbert was one of the great mathematical geniuses of the 19th and 20th century. It’s hard to suppress we are not worthy moments and maintain a sharp critical eye when reading his “printed” works.  You don’t get the same vibe when reading raw \LaTeX.  Source code puts you in a, it’s just another bug infested program, frame of mind. You expect errors in code and you typically find them. This is exactly the hard-nosed attitude you need when reading mathematics.

C. K. Raju: Genius or Crank (Part 1)

Euclid's first proposition

Euclid’s first proposition

Lately I have been amusing myself by working through Euclid’s Elements. Despite studying mathematics in university, teaching it in high school and occasionally using it in my software-soaked day job I never got around to reading Euclid.

Euclid is routinely lionized as the wellspring of axiomatic mathematics. Before The Elements mathematicians were clearly out of control!  They were running around developing useful methods, (counting, fractions, roots),  and — gasp — making unjustified assertions!

Fortunately, The Elements put an end to all that and ushered in the endless age of rigorous axiomatic mathematics. I admire mathematical rigor but my tiny brain can only take so much of it before an all-pervading fog of befuddlement sets in. When I’m all fogged up there are only a few options:

  1. Reread and rework until the fog clears.
  2. Press on and review later.
  3. Give up and abase self.
  4. Take a break.

I’m a lazy S.O.B. so option (4), take a break, comes up more often than it should.  One of my favorite ways to  break away from mathematics is to read about it’s long history.  While tracing the history of The Elements I came across the writings of C. K. Raju.

C. K. Raju has written a fascinating book: (the) Cultural Foundations of Mathematics: The Nature of Mathematical Proof and the Transmission of the Calculus from India to Europe in the 16th c. CE. Raju’s book is a bit hard to get your hands on.  It’s not on Amazon but you can use World Cat to find a copy near you.

Raju’s thesis consist of these major points:

  1. Significant portions of the calculus developed in India long before Newton and Leibniz and Indian methods, particularly series expansions, came into Europe via 16th century Jesuit missionaries.
  2. European notions of rigorous mathematical proof evolved from the needs of  the Catholic Church to convert Muslims with impressive iron-clad logical arguments.  The old baffle them with bullshit tactic.  Raju claims this theological attitude worked it’s way into mathematics and resulted in the bizarre western view that deduction is superior to observation, experience and induction.
  3. The ultimate source of eastern secular knowledge, (mostly Arab and Indian), was systematically suppressed and “Hellenized” by the Catholic Church.  The church claimed  all the “good stuff” in Arab texts originated with the ancient Greeks and had been merely preserved by Arab copycats. It just wouldn’t do to credit hated, (remember the crusades),  enemies for their good ideas.
  4. Insisting on rigorous proof when teaching mathematics, especially to children, is sterile and stupid.

All of this reads like a mathematical Dan Brown novel and oddly the Catholic Church is once again the villain.  I was enjoying Raju’s account until this passage about Kepler:

Why, after all, was Tycho so secretive about his papers, not even allowing his trusted assistant Kepler to see them?  In any case, on Tycho’s sudden death, Kepler obtained not just Tycho’s observations but also the rest of his papers which contained the underlying theory. Being inclined towards heliocentrism, Kepler transformed Nilakantha’s “Tychonic” orbits to a heliocentric frame (a simple transformation). This made Nilakantha’s variable epicycles come out as ellipses. Being a professional astrologer, Kepler was good at making up stories, and he made up the story about how he had arrived at his results using Tycho’s data.

In other words Kepler is a fraud and he ripped off one of the major discoveries in astronomy, the elliptical orbits of planets, from Indian astronomers. It’s one thing to spin plausible stories about how parts of calculus may have seeped into Europe from unacknowledged sources it’s another thing to posthumously accuse someone of fraud.

What would it take to make Raju’s case?  How about some hard evidence! What about Tycho’s secret papers, do any of these documents survive and do they contain references to Nilakantha?   Now that would be a smoking gun.  Of course we don’t know of any such papers but that doesn’t mean they didn’t exist. Proof by conspiracy is a very powerful inference rule — 9/11 troofers and ufologists swear by it!  What about the claim that the transformation from Nilakantha’s variable epicycle Earth centered system to a Sun centered elliptical orbit system is “a simple transformation.”   I rather doubt it’s as simple as claimed and even if the transformation was, to use the most abused word in mathematics — trivial, it still misses the point.  The major shift was to abandon all pretense of Earth centered systems no matter how mathematically sophisticated!  Before Kepler astronomers and mathematicians, in many cultures, toyed with the idea that planets orbit the sun.  After Kepler everyone had to grow up.  Planets do orbit the sun deal with it!

And it was precisely how Newton dealt with it that made calculus something worth fighting over.  Newton’s unprecedented and monumental proof that elliptical orbits are a mathematical consequence of the inverse square law of gravity is the dividing line between modern and early science.   Nothing like it had ever been done before and even today physics and mathematics students are given to chanting we are not worthy when presented with this brilliant argument. Without Newton’s use of the calculus nobody but a few anal mathematicians would give a rat’s ass about who invented calculus.

In a later post I will argue that Raju discounts the importance of independent and coequal mathematical discovery in his account.