Still in operation, NASA’s SOHO (Solar and Heliophysical Observatory) spacecraft orbits the sun (not the Earth)
in step with the Earth, by slowly orbiting around the First Lagrangian Point (L1), where the combined gravity of the Earth and Sun keep SOHO in an orbit locked to the Earth-Sun line. The L1 point is approximately 1.5 million kilometers away from Earth (about four times the distance of the Moon), in the direction of the Sun. There, SOHO enjoys an uninterrupted view of our daylight star. (source)
One of the instruments on board is the Coronal Diagnostic Spectrometer (CDS), which was designed to study the atmosphere of the sun spectroscopically,* i.e., to look at characteristic wavelengths in the light put out by the corona, from which one can deduce quite a bit about the physical processes going on there.
On 26 March 2002 the CDS took a “quiet-sun” spectrum of the corona (meaning there were no particular disturbances, solar flares, or coronal discharges going on, just a normal, quiescent (such as it is) solar atmosphere. Below is the spectrum (shown one half above the other). The spectrum was taken in the extreme ultraviolet (EUV), so this red is dramatic false coloring. There are quite a few spectral lines visible, demonstrating the range and resolution of the CDS.
Evidently I am not the only one who thinks this spectrum is quite beautiful. It seems that the designers of this natatorium also thought so.
I want one.
———- * Here is the official description of the CDS. It’s like scientific pornography for us experimentalists. Just let the words flow over you:
CDS consists of a Wolter II grazing incidence telescope which has a focus at a slit assembly which lies beyond a scan mirror. Light stops define two telescope apertures which feed, simultaneously into two spectrometers beyond the slit assembly. One portion of the beam hits a grating in grazing incidence and the spectrum is dispersed onto four 1-D detectors placed around the Rowland circle. This is the grazing incidence spectrometer or GIS. The other portion is fed through to a twin grating in normal incidence and the resulting spectrum is viewed by a 2-D detector system. This is the normal incidence spectrometer or NIS.
The GIS grating is spherical. The system is astigmatic, i.e. there is no spatial focus. Thus, one would use “pinhole” or square slits and build up images by rastering in two directions over the Sun’s surface. The rastering is performed by rotating the scan mirror (E-W rastering; i.e. by presenting different portions of the Sun to the slit) and by scanning the slit (N-S rastering). The four detectors sit at specified, fixed locations around the Rowland circle and thus detect the EUV spectrum in four fixed wavelength ranges.
The NIS gratings are toroidal, resulting in a stigmatic system. Thus, we may use long, thin slits and can image, spatially along the slits. Images of the slit are dispersed on the NIS detector producing an image, effectively, of wavelength against a spatial dimension. As a result, one can produce rastered images very quickly by rastering in only one dimension with the scan mirror. Since the NIS spectrum is dispersed by two gratings, slightly angled with respect to one another, two spectral ranges are viewed on the one 2-D detector.
This is birthday boy Charles Robert Darwin (1809-1882), born 200 years ago on 12 February 1809. This photograph (which I have cropped) was taken in 1882 by the photographic company of Ernest Edwards, London.*
Many people call Darwin’s great idea, common descent through evolution by means of natural selection, the greatest scientific discovery ever. Maybe. It’s certainly big. My hesitation is merely a reflection of my feeling that it’s really difficult to prioritize the great ideas and discoveries of science and math into a hierarchy that would assign the top position to one idea alone. No doubt it’s the over cautious precision of my inner scientist asserting itself.
Almost since the pages of Origin of Species were first sewn into a book there has been a cottage industry of trying to “disprove Darwin”. So strongly associated is his name with the big idea that “Darwin” and “Darwinism” serve as effigies for those who revile the idea so much that they expend considerable energy looking for anything that might weaken the authority of the idea so that it can be toppled from its scientific pantheon.
Unfortunately for their efforts, they sorely misunderstand how science works and, therefore, how futile their efforts are. Detractors seem to believe they are operating under junior debating-society rules where locating any hint of a logical inconsistency in the “theory”, or any modern deviation from what they think is Darwinian orthodoxy, is certain to be a fatal blow to the hated “theory”. Alas, they hope to disprove Darwin but can only disapprove and look silly and naive.
The biggest impediment to tearing down the edifice of “Darwinism”, of course, is reality. Scientists believe that reality has a separate, objective existence that affords no special place to humans. One corollary to this is that objective reality is what it is regardless of our most fervent desires, regardless of our prayers to a supernatural deity to change it, regardless of the stories we tell ourselves over and over about how we would like it to be. Deny reality for your own psychological benefit as needs must, but you will not alter reality by doing so.†
But, suppose there are chinks in the armor of “Darwinism”–isn’t that fatal? Well, no. Great ideas that flow into the vast river of science stay if they are useful ideas. Depending on utility they may change, grow, even evolve over time, but they’re frequently treated as the same idea. Creators do not have veto power over how their scientific ideas are used, nor how they are changed or updated, although they continue to get the credit for great ideas. The way we understand and describe gravity is nothing recognizable to Newton, but he continues to get credit as the discoverer of “universal gravitation”.
But aren’t wrong theories, those that have been “disproven” by logical errors or deviations from precise descriptions of reality, immediately discarded as useless? Oh no, far from it. See the aforementioned Newtonian theory of gravity for but one ready example.‡
This is the trade-off: a somewhat inaccurate (or “wrong”) but productive theory is of far more use to science than a correct but sterile idea. By “productive” I refer to ideas that lead one to new ideas, new experiments, and new understandings. Compare that notion with what some would have you believe is the undeniable perfection of revealed truth from a divine creator: it is an investigative dead end, it leads to no new ideas whatsoever, it affords no solution beyond the parental disclaimer, “because”.
“Why” is the path science follows, not “because”. I believe that “why” is the more interesting and the more valuable path to follow, at least when it comes to understanding how the universe works. One may feel free to disagree on its value and utility, of course, but denying its reality is futile.
———- * The photograph is part of the wonderful collection of “Portraits of Scientists and Inventors” from the Smithsonian Institution, which we have sampled here before and undoubtedly will again and again, photographs they have contributed to the Flickr Commons Project. (The Flickr page; the persistent URL)
† This is probably the source of the calm, know-it-all demeanor that atheists tend to exhibit, and that so inflames those who would consign us prematurely to the flames of hell: all the evidence we see about how the world really operates fails to suggest that a creator-deity exists–not to mention a personal-coach-deity–and no amount of wishful thinking can change reality.
‡ Sometime we’ll talk about the contingent nature of scientific “truth” and how uncomfortable that idea is for those with an absolutist predilection.
This is Sir William Thomson, Baron Kelvin* (1824 – 1907) or, simply, Lord Kelvin as he’s known to us in the physical sciences. This is the same “Kelvin” as in the SI unit “Kelvins”, the degrees of the absolute thermodynamic temperature scale.
The photograph was taken c. 1900 by T. & R. Annan & Sons. I love the title given the photograph by the National Galleries of Scotland: “Sir William Thomson, Baron Kelvin, 1824 – 1907. Scientist, resting on a binnacle and holding a marine azimuth mirror”.
A binnacle, Wikipedia tells me, is a box on the deck of a ship that holds navigational instruments ready for easy reference. One reason Kelvin might be leaning on one is suggested by this bit from the article on “binnacle”
In 1854 a new type of binnacle was patented by John Gray of Liverpool which directly incorporated adjustable correcting magnets on screws or rack and pinions. This was improved again when Lord Kelvin patented in the 1880s another system of compass and which incorporated two compensating magnets.
Kelvin also patented the “marine azimuth mirror” (see the description of “azimuth mirror” from the collection of the Smithsonian National Museum of American History), so the photograph has narrative intent. It seems that Kelvin was an active and successful inventor.
I like this understated biography of Kelvin from the National Galleries of Scotland website (link in first footnote), where it accompanies the photograph:
A child prodigy, William Thomson went to university at the age of eleven. At twenty-two he was appointed Professor of Natural Philosophy in Glasgow where he set up the first physics laboratory in Great Britain and proved an inspiring teacher. He primarily researched thermodynamics and electricity. On the practical side he was involved in the laying of the Atlantic telegraph cable. He was also the partner of a Glasgow firm that made measuring instruments from his own patents.
“He primarily researched thermodynamics and electricity” is a bit of an understatement! Around the time this photograph was taken (c. 1900), Kelvin was pretty much the scientific authority in the world, the great voice of science, the scientist whose opinion on every matter scientific was virtually unassailable.
That unassailability was a huge problem for (at least) Charles Darwin and his theory of common descent by means of natural selection. The crux of the problem was the answer to this question: how old is the Earth?
These days we are quite accustomed to the idea that the Earth is around 4.5 billion years old. At the beginning of the 19th century is was very commonly believed that the Earth was only several thousand years old: Bishop Usher’s calculated date of creation, 23 October 4004 BC, was seen at the time as a scholarly refinement of what everyone already pretty much knew to be true.
Perhaps the big idea growth during the 1800s was the dawning realization of the great antiquity of the Earth. This was accompanied by the realization that fossils might actually be animal remains of some sort; the emergence of geology as a science; and the concept of “uniformitarianism” (an interesting article on the topic), so central to geology, that geological processes in the past, even the deep past, were probably very much like geological processes in action today, so that the geological history of the Earth–and of fossil remains!–could be made sense of.†
Throughout the 19th century discovery after discovery seemed to demand an ever-older Earth. I can imagine that an element of the scientific zeitgeist that precipitated Darwin’s ideas on natural selection as a mechanism for evolution was this growing realization that the Earth might be very, very, very old and that something so remarkably slow as he knew natural selection would be, might be possible. In fact, his ideas went further out on the intellectual limb: he realized that it was necessary that the Earth be much, much older than was currently thought.
In fact, he staked his reputation on the great antiquity of the Earth. This was the critical prediction of his theory, really: the Earth must be vastly older than people thought at the time or else his theory of common descent by natural selection was wrong. It was a bold, seemingly foolhardy claim that he seemed certain to lose.
He was right, of course, but things looked grim at the time and his reasoning was not vindicated by physics until well after his death.
The biggest roadblock to widespread acceptance of the idea of an Earth old enough to allow evolution of humankind through natural selection was none other than Lord Kelvin.
Calculating the age of the Earth looked at the time to be a very challenging problem. But, if there was one thing Kelvin knew, it was that the Earth could not be older than the Sun, and he believed he could calculate the age of the Sun. He was the master of physics, particularly thermodynamics, so all he had to do was add up the sources of energy that contributed to the energy we saw coming from the Sun and figure out how long it might have been going on.
But what were the sources of the Sun’s heat? Kelvin quickly concluded that it could not be any sort of chemical burning, like coal in a fireplace. There simply could not be enough coal. To keep this long story short, Kelvin finally settled on two leading possibilities. One was the energy that came from gravitation contraction of the primordial matter that formed the sun, in which case the sun heated up a great deal originally and then spent eons radiating away its heat. The other possibility that might contribute was the gravitational energy of meteors falling into the sun. (Here’s an interesting and brief exposition of the arguments: S. Gavin, J. Conn, and S. P. Karrer, “The Age of the Sun: Kelvin vs. Darwin“.)
Kelvin published his thoughts in an interesting, and very readable paper, called “On the Age of the Sun’s Heat” , Macmillan’s Magazine, volume 5 (March 5, 1862), pp. 288-293. (html version; pdf version) In the conclusion to that paper Kelvin wrote:
It seems, therefore, on the whole most probable that the sun has not illuminated the earth for 100,000,000 years, and almost certain that he has not done so for 500,000,000 years. As for the future, we may say, with equal certainty, that inhabitants of the earth can not continue to enjoy the light and heat essential to their life for many million years longer unless sources now unknown to us are prepared in the great storehouse of creation.
What an irritant for Darwin! That was not nearly enough time!
These days it is a clichéd joke to say of something that “it violates no known laws of physics”, but that’s the punchline for this entire controversy. Kelvin, naturally, had to search for sources of the Sun’s heat that violated no known laws of physics as they were known at the time, but there were new laws of physics lurking in the wings.
Darwin published On the Origin of Species in 1859. Kelvin published his paper in 1862. Radioactivity was only discovered by Henri Becquerel in 1896. The radioactive decay of elements was not recognized for some time as a possible source of solar energy, but as understanding advanced it was realized that the transmutation of one element into another through radioactive decay involved a loss of mass–the materials before and after could be weighed.
The next domino fell in 1906, a year before Kelvin’s death, when Einstein published his famous equation, , a consequence of his special theory of relativity. Understanding dawned that the loss of mass was related to a release of energy through the radioactive decay.
Our modern knowledge that the sun is powered by nuclear fusion through a process that releases enormous amounts of energy via fusion cycles (interesting, mildly technical paper on its discovery and elucidation) that consume hydrogen atoms to create helium atoms, and then consume those products to produce some heavier elements, was still decades in the future (generally credited to Hans Bethe’s paper published in 1939).
But the message was clear: here was a possible new source of energy for the sun that Kelvin knew nothing about but that could vastly increase the likely age of the Sun.
To finish this part of the story, here is an excerpt from John Gribbin’s The Birth of Time : How Astronomers Measured the Age of the Universe. (New Haven : Yale University Press, 1999. 237 pages.), a fascinating page-turner of a popular science book. (Book note forthcoming.)
If the whole Sun were just slightly radioactive, it could produce the kind of energy that we see emerging from it in the form of heat and light. In 1903, Pierre Curie and his colleague Albert Laborde actually measured the amount of heat released by a gram of radium, and found that it produced enough energy in one hour to raise the temperature of 1.3 grams of water from 0°C to its boiling point. Radium generated enough heat to melt its own weight of ice in an hour–every hour. In July that year, the English astronomer William Wilson pointed out that in that case, if there were just 3.6 grams of radium distributed in each cubic metre of the sun’s volume it would generate enough heat to explain all of the energy being radiated from the Sun’s surface today. It was only later appreciated, as we shall see, that the “enormous energies” referred to by Chamberlin are only unlocked in a tiny region at the heart of the sun, where they produce all of the heat required to sustain the vast bulk of material above them.
The important point, though, is that radioactivity clearly provided a potential source of energy sufficient to explain the energy output of the Sun. In 1903, nobody knew where the energy released by radium (and other radioactive substances) was coming from; but in 1905, another hint at the origin of the energy released in powering both the Sun and radioactive decay came when Albert Einstein published his special theory of relativity, which led to the most famous equation in science, , relating energy and mass (or rather, spelling out that mass is a form of energy.) This is the ultimate source of energy in radioactive decays, where careful measurements of the weights of all the daughter products involved in such processes have now confirmed that the total weight of all the products is always a little less than the weight of the initial radioactive nucleus–the “lost” mass has been converted directly into energy, in line with Einstein’s equation.
Even without knowing how a star like the Sun might do the trick of converting mass into energy, you can use Einstein’s equation to calculate how much mass has to be used up in this way every second to keep the Sun shining. Overall, about 5 million tonnes of mass have to be converted into pure energy each second to keep the sun shining. This sounds enormous, and it is, by everyday standards–roughly the equivalent of turning five million large elephants into pure energy every second. But the Sun is so big that it scarcely notices this mass loss. If it has indeed been shining for 4.5 billion years, as the radiometric dating of meteorite samples implies, and if it has been losing mass at this furious rate for all that time, then its overall mass has only diminished by about 4 percent since the Solar System formed.
By 1913, Rutherford was commenting that “at the enormous temperatures of the sun, it appears possible that a process of transformation may take place in ordinary elements analogous to that observed in the well-known radio-elements,” and added, “the time during which the sun may continue to emit heat at the present rate may be much longer than the value computed from ordinary dynamical data [the Kelvin-Helmholtz timescale].” [pp. 36--38]
Kelvin was not always right.
———- * I’ve taken this image from the Flickr Commons set uploaded by the National Galleries of Scotland, and cropped it some from the original: Source and National Galleries page.
† The history of these ideas in the context of geology as an emerging science is very ably traced in Simon Winchester’s The Map that Changed the World : William Smith and the Birth of Modern Geology (my book note).
All sorts of stuff has been going on up in the sky lately. There’s just so much to look at.
For instance, NASA sent word today (SpaceWeather for 6 December 2008) that the SOHO spacecraft, the orbiting solar observatory,* has only hours ago taken this picture (like this one, which I’ve cropped quite a bit; full-sized source here) of a massive solar prominence. They also link to some additional amazingly beautiful photographs of the prominence taken by other people with solar telescopes: from Mark Walters of Four Crosses, Powys, Wales, UK; from Emiel Veldhuis of Zwolle, the Netherlands; from Robert Arnold of Isle of Skye, Scotland; from M. Ugro et al. of South Portland, Maine.
Now, you may remember the giant meteorite that made an appearance last week over British Columbia. There’s been another (a “superbolide”), this time in Colorado. From the same SpaceWeather page as above:
Astronomer Chris Peterson photographed the event using a dedicated all-sky meteor camera in the town of Guffey, near Colorado Springs.
“In seven years of operation, this is the brightest fireball I’ve ever recorded,” says Peterson. “I estimate the terminal explosion at magnitude -18, more than 100 times brighter than a full Moon.”
Finally, more pretty pictures. There was some excitement earlier this week on Monday (1 December 2008), when there was, at sunset, a beautiful conjunction of Venus, Jupiter, and a crescent moon. We had clear, cold skies that evening and beautiful viewing of the event, which really was remarkably pretty. NASA has a “Conjunction Gallery” of very lovely photographs of the event submitted astronomy enthusiasts. Visit when you have some time to look and ooh and aah.
__________ *About SOHO’s orbit, from the project page at NASA:
SOHO is in orbit between the Earth and the Sun. It is about 150,703,456 kilometers (92 million miles) from the Sun and only about 1,528,483 Kilometers (1 million miles) from the Earth (three times farther than the moon). This orbit is around a mathematical point between the Earth and the Sun known as the Lagrange point or the L1 point. The L1 point is a point of [gravitational] equilibrium between the Earth’s and Sun’s gravitational field, that is to say that the pull is equal from both the Sun and the Earth. The L1 point is a point of unstable equilibrium (like a bowl round side up with a marble balanced on it). As a result, we have to compensate for perturbations due to the pull of the planets and the Earth’s moon. Every few months we use a little fuel to fine tune our orbit and keep it from getting too far off track. This is known as “station keeping manoeuvres”
No spacecraft is actually orbiting at the L1 point. For SOHO there are two main reasons: the unstable orbit at the L1 point and facility of communication in a halo orbit. If SOHO was sitting directly at the L1 point, it would always be right in front of the Sun. The trouble is that the Sun is very noisy at radio wavelengths, which would make it very difficult to tune into the radio telemetry from the spacecraft. By putting it into a halo orbit, we can place it so that it’s always a few degrees away from the Sun, making radio reception much easier.
This beard belongs to Mr. Spock, the venerable half-Vulcan who served as the science officer aboard the Enterprise in “Star Trek”, the original television series. It is thought that he has another name that is unpronounceable by humans. In grade school I identified quite a bit with Mr. Spock. Personally I hoped to develop the cool, rational demeanor and analytical outlook he displayed; outwardly, it was because my ears were too big for my head and looked vaguely pointy.
It seems that this episode in which Spock had this beard (“Mirror, Mirror“), is the only time Spock was ever portrayed with a beard (and, in fact, the bearded version is a mean, anti-Spock in a parallel universe–his beard kept viewers clued in about which universe events were happening). I think that’s too bad because he looks quite dashing in a beard, but apparently NBC already found the Spock character too “sinister” looking to begin with, and everyone knows beards make men look more sinister.
“Spock’s Beard” is also the name of a progressive rock band I’d never heard of until this morning. Isn’t it splendid to learn new things?
Surely, in addition to the main characters, one of the most recognizable things from the “Star Trek” series was the theme song. Last night, for reasons we may or may not get to, the conversation happened to turn on the question whether the familiar and unusual timbre of the melody was 1) a woman singing; or 2) a theremin, which sounded like a woman singing?
Coloratura soprano Loulie Jean Norman imitated the sound and feel of the theremin for the theme for Alexander Courage’s theme for the original Star Trek TV series. Soprano Elin Carlson sang Norman’s part when CBS-Paramount TV remastered the program’s title sequence in 2006.
I was relieved. I had always thought it was a woman singing, but it did sound remarkably like a theremin. And now we’ve arrived at my real object for this piece: Theremin and his theremin. (He never had a beard, it seems, but I would not be thwarted!)
Léon Theremin (1896–1993), born in Russia, started out as Lev Sergeyevich Termen. His name is familiar to many people these days because he invented the “theremin” (here’s an interesting short piece about the theremin; or course there’s Wikipedia on the theremin, not to mention Theremin World). Theremin invented the instrument in 1919 when he was doing research on developing a proximity sensor in Russia. Lenin loved it. Some ten years later Theremin ended up in New York, patented his instrument, and licensed RCA to build them.
The theremin (played by a “thereminist”) is generally deemed to have been the first ever electronic instrument. It also claims the distinction that it is played by the thereminist without being touched. Instead, the thereminist moves her hands near the two antennae of the instrument, one of which controls pitch and the other of which controls volume; capacitive changes between the antennae and the body of the thereminist affect the frequency of oscillators that alter the pitch and volume of the generated tone.
It is a very simple device and the musical sound is not very sophisticated, and yet there’s something beguiling in watching a good thereminist perform, and something haunting about the sound.
Most people have heard a theremin and typically haven’t recognized it. Most popularly, perhaps, is its appearance in the Beach Boys’ “Good Vibrations”, by Brian Wilson (YouTube performance), although this appears to be a modified theremin played by actually touching it!
My favorite theremin parts are in the score Miklós Rózsa wrote for the Hitchcock film “Spellbound“–fabulous film, fabulous music, for which Rózsa won an Academy Award. (In a bit, a link where you can hear the “Spellbound” music, with theremin). This movie was the theremin’s first outing in such a popular venue–”Spellbound” was the mega-hit, big-budget, highly marketed blockbuster of its day. Later on, of course, the theremin was widely used in science-fiction movies, famously The Day the Earth Stood Still and Forbidden Planet. (On the use of the theremin in film scores, here’s a fascinating article by James Wierzbicki: “Weird Vibrations: How the Theremin Gave Musical Voice to Hollywood’s Extraterrestrial ‘Others’ “).
There seems to have been a resurgence of interest in the theremin in the past few years, or else I’ve just noticed other people’s interest more–the internet can make such things much more visible and seemingly more prevalent. One recent development: a solar-powered theremin that fits in an Altoids box. (Heard, by the way, in the radio program mentioned below.)
Some claim that the new interest began following the release of Steven M. Martin’s 1995 documentary, “Theremin: An Electronic Odyssey“. I don’t know about that, but we did watch this film a few weeks ago (we got a copy for rather few dollars–we couldn’t pass it up because of the rather lurid cover art more suitable for something like “Plan Leon from Outer Space” perhaps), and it is an outstanding documentary. It’s about Theremin and the theremin, and the story is very, very engaging. There’s a lot of weird stuff that went on in Theremin’s very long life, like the time in the 1930s (I think) when he was snatched from his office in New York City by Russian agents and spirited away to the Soviet Union. Friends thought he was dead, but he reappeared years later. He’d been forced to work for the KGB developing small listening devices.
A few people of interest also show up in the film: Brian Wilson (enjoy watching him try to finish one thought or get to the end of a sentence), Nicolas Slonimsky, Todd Rundergren, Clara Rockmore, and Robert Moog (of the Moog Synthesize–he started out making theremin kits). Of particular interest, I thought, was Clara Rockmore (1911–1998), thought of as probably the greatest thereminist of all time. Listening to her talk in the film is interesting, but more interesting is watching and listening to her play the theremin. Check out her technique! It’s great stuff.
Now for one last treat. Here is a link to a 90-minute radio program (and information about it), called “Into the Ether“, presented by a British thereminist who performs under the name “Hypnotique”. The program is nicely done and filled with audio samples of theremin performances in a wide variety of genres. If you don’t have the time for the entire thing, I’ll point out that the “Spellbound Concerto”, by Miklós Rózsa, from his music for the film, is excerpted at the very beginning of the program and that’s a must-hear for thereminophiles, whether new or seasoned.
This is Euclid (c. 365 BCE — c. 275 BCE) of Alexandria, Egypt, possibly one of the earliest celebrities to use only one name. Euclid is famous, of course, for writing Elements, his 13-book exposition on geometry and the earliest mathematical textbook and second only to the Bible in the number of editions published through history.
Invoking Euclid’s name is a ruse. Although there are any number of things related to Euclid and the Elements that we could discuss, what I’ve really been thinking about lately is , and I needed a pretext. In fact, it wasn’t even exactly that I’ve been thinking about so much as people’s relationship with the idea of .
It’s a trivial thing in a way, but I was perplexed to discover that some googler had reached a small article I had written (“Legislating the Value of Pi“, about the only actual case in history of an attempt to do so–in Indiana) by searching for “accepted value of pi”.
That disturbed me, although I’m finding it difficult to explain why. Let’s talk for a moment about the difference between physical constants and mathematical constants.
In physical theory there are any number of “physical constants”, numbers (with no units) or quantities (with units) that show up in physical theories and are generally presumed to be the same everywhere in the universe and often described as “fundamental” because they can’t be reduced to other other known values. Examples that might be familiar: “c”, the speed of light in a vacuum; “G”, Newton’s universal constant of gravitation; “e”, the charge of the electron; “”h”, Planck’s constant, ubiquitous in quantum mechanics; the list is lengthy. (You can find a long list and a bunch about physical constants at a page maintained by NIST the National Institute of Science and Technology.)
Fundamental physical constants are measured by experiment; that is the only way to establish their value. Some have been measured to extraordinary accuracy, as much as 12 decimal places (or to one part in one-million-million). The NIST website has an “Introduction to the constants for nonexperts“, which you might like to have a look at. (I never quite made it to being a fundamentals-constant experimentalist, but I did do high-precision measurement.)
Now, contrast the ontological status of fundamental constants with mathematical constants, things like ““, the ratio of the circumference to the diameter of a circle; “e”, the base of the natural logarithms; ““, the “golden ratio”, and numbers of that ilk. These are numbers that are perfectly well defined by known and exact mathematical relationships. (I once discussed a number of mathematical equations involving “” in “A Big Piece of Pi“.)
Now, it may be something odd about the way my mind works (that would be no real surprise), but to me there is a difference in status between fundamental physical constants, which must be measured and will forever be subject to experimental limitations in determining their values, and mathematical constants, which can always be calculated to any desirable precision (number of digits) using exact mathematical expressions.
To me, one can reasonably ask about the “current accepted values” of fundamental physical constants–indeed, you’ll see a similar expression (“adopted values”) on the NIST page–but that “accepted value” makes no sense when used to describe mathematical constants that simply have not been calculated as yet to the precision one might desire. And so, asking about the “accepted value” of seems like an ill-formed question to me. Your mileage is almost certain to vary, of course.
Well, now that you’ve made it through that ontological patch of nettles, it’s time for some entertainment. In the aforementioned article I had already discussed some of the fascinating mathematical equations involving , so we’re just going to have to make do with something a little different, even though it is still an equation involving you know what.
The problem of “Buffon’s Needle” was first put forward in the 18th century by Georges-Louis Leclerc, Comte de Buffon. I like the way Wikipedia states it (or find another discussion here):
Suppose we have a floor made of parallel strips of wood, each the same width, and we drop a needle [whose length is the same as the width of the strips of wood] onto the floor. What is the probability that the needle will lie across a line between two strips?
Worked it out yet?
You can always measure an approximate value of the probability for yourself with a needle and a sheet of paper on which you have ruled parallel lines separated by the length of the needle. Drop the needle on the paper a whole bunch of times. Divide the number of times the needle lands on a line by the total number of times you dropped the needle. What value do you get closer to the more times you do the drop the needle?
The title of the film, “Fabrication d’une lampe triode” (“Build a triode vacuum tube”) may sound unusually recherché or highly metaphorical, but it is meant literally. M. Claude Paillard is an amateur radio enthusiast with an interest in historic radio equipment (or, poetically in the original: “Amoureux et respectueux des vieux et vénérables composants”). As far as I can make out from the page about this film and M. Paillard — my French is getting rusty and the Google translator is useful but not nuanced — he was involved in a project to restore an old radio station and needed to build some triode vacuum tubes.
This film illustrates how he did this from scratch. It amazes me. He demonstrates so many skills and techniques that simply are not called upon much anymore and are largely being forgotten. It all makes me feel rather dated just because I know what a vacuum tube is.
But the beauty of this film, which is almost entirely nonverbal and requires no skills in French, is that watching it will fill you in on exactly what a vacuum tube is. Okay, it won’t tell you how it works or why that’s useful in electronic circuitry, but you’ll get a remarkably tangible understanding of what’s inside, and seeing its manufacture by hand, by someone actually touching all the pieces, shaping them and putting them together to make a functional whole, is a remarkable learning experience.
I recently finished reading The Carbon Age : How Life’s Core Element has Become Civilization’s Greatest Threat, by Eric Roston (New York : Walker & Company, 2008. 308 pages). I very much enjoyed the act of reading it, but it was only when I was writing about it that I realized that is really an excellent book on all counts. My book note is here.
In this case I think what I admired the most was the author’s scienticity, which is how we refer to a scientific / rational / analytical / naturalistic perspective combined with the fortitude to integrate science moments into a larger cultural context. Mr. Roston did an excellent job of it, making it entertaining and informative without being the least bit silly or imprecise. As you may recall, I’m easily irritated by authors writing about science who do not take the trouble to be precise and thoughtful in their scientific exposition, but I had no such reaction here. If my memory is correct, I thought there was one explanation, out of the 300 pages, where the concept being explained was slightly befuddled–not a bad record!
But, our purpose here is to provide a place for a few excerpts that just didn’t fit into the book note for some reason or that I marked specially for blogging. (It’s true! Sometimes there are bits of the text that I think are a must-share but they don’t share the tone of a book note, so it’s lucky you!)
In this first excerpt, we’re in the midst of a long discussion about carbon’s place in the origins of life and how its central role may have come about. One of the great steps forward happened very, very early in the process. In a world of one-celled life, one cell managed to trap another cell inside it and the two continue to reproduce together to this day. Eukaryotes are organisms, including humans and most everything we think of as life except bacteria, whose cells are complex systems containing a nucleus and other parts, including mitochondira, which produce the energy the cell runs on by breaking down (“burning”) carbohydrates. I liked this terse, elegant, and altogether sensible paragraph about that moment.
The capture and integration of one cell by another is called endosymbiosis. Nearly all eukaryotes have little organs (“organelles”) called mitochondria. These cellular energy centers descend from purple sulfur bacteria, inhabitants of stomatolites in Shark Bay. This class of bacteria has made its living for as long as 3 billion years by using oxygen to burn carbohydrate fuel. Deep in the evolutionary past, some oxygen-breathing bacteria became engulfed within anaerobic cells, which needed help thriving in an atmosphere of increasing oxygen. These bacteria are the ancestors of our cellular power plants. The evidence is that bacteria and mitochondria share much of the same DNA. [p. 73]
In this next short excerpt, Roston comments on the familial culture of experimental scientists. I’ve known this phenomenon myself. I started out in low-temperature physics, an experimental discipline that appeared early in the 20th century when Heike Kamerlingh Onnes, the Dutch physicist, first liquefied helium in 1908. We were a small community and everyone could trace their lineage; there are only a couple of major branches of the family. I don’t think I’ve seen this written about elsewhere and I thought Roston’s observations were very perceptive.
Labs are structured as intellectual family fiefdoms. A professor “raises” his graduate students, who grow up and fan out across the world of research universities and private industry. Virtually everyone’s intellectual ancestors [in chemical synthesis] can be traced back to J.J. Berzelius, the Swedish chemist who first called carbon “C”. Every generation tends the repository of knowledge, weeding out its predecessor’s bad ideas, answering some of their questions, and asking many of their own. [p. 135]
The name of this extraordinary film is “SX-70″; it was made by Charles and Ray Eames. (Whether you should watch first or read first I can’t say; if you have the time, watch then read then watch again.)
Some of us will be old enough to remember the Polaroid SX-70 camera and how exciting and modern it was. Such advanced technology! As the narrator says near the beginning:
Since 1947, Edwin Land and Polaroid have pursued a central concept, one single thread: the removal of the barriers between the photographer and his subject. [Title: "SX-70"] And now, a compact, folding, electronically controlled, motor-driven, single-lens reflex camera, capable of focusing from infinity down to ten inches, has been developed to exploit integral self-processing film units which, when exposed, are automatically ejected from the camera, with no parts to peel or discard, and whose final images emerge without timing, in daylight, where the viewer can see them materialize within the same transparent protective plastic cover through which the film was originally exposed.
The SX-70 looked like no other camera before or after, and worked like no other camera, either. The film was the culmination of this dream of Edwin Land’s, and the camera’s design and engineering gave the distinct impression that it had been thought about without preconceptions of how a camera should look.
But this isn’t just about the camera, which is a marvel. I’m more interested right now in this film about the camera, and the film itself is a marvel.
Presentation of the revolutionary SX-70 Land camera and its aesthetic potential that becomes a meditation on the nature of photography. A tour-de-force of filmmaking that gives the audience a real understanding of the workings of the camera. Filmmakers: Charles and Ray Eames Sponsor: Polaroid Composer: Elmer Bernstein Narrator: concluding statement by Philip Morrison Date: 1972
Charles and Ray Eames were the remarkably creative and remarkably influential husband-and-wife design team working mostly from the 40s through the 60s (a quick biographical survey). Many of their designs have become so iconic that they are recognizable by countless people who have never heard of the Eames. There is just so much that I can’t begin to organize my thoughts about them here, where my focus is on this one film anyway. When you have time, explore Charles & Ray Eames: A Legacy of Invention.
Next in the credits is Elmer Bernstein, noted composer of many, many famous film scores like those for “To Kill a Mockingbird”, “The Ten Commandments”, “The Blues Brothers”, and “Ghostbusters”, to name a small fraction. The score is just a few instruments, nothing that’s going to take a lot of time assembling and orchestrating, but nevertheless thoughtfully written and quite suitable for the film.
Then there’s Philip Morrison, whose distinctive voice appears near the end, where he takes over from the anonymous narrator in the rest of the film. Morrison, who died in 2005, was a physicist of some renown, but I think his more important contribution was as an explainer and popularizer of science, as he did with his remarkable television series (and book), “The Ring of Truth” (1987). Then there was the “Powers of Ten” project (1977), the justly famous film of which he worked on with the Eames (watch the nine-minute film). He had also been the main reviewer of books for Scientific American since 1965, a remarkable legacy.
But this list of luminaries would contribute empty celebrity if the film itself weren’t brilliant, and it is. It was shown originally at a Polaroid shareholders meeting and subsequently used internally as a sales tool. It was not made for average viewers, perhaps, and wouldn’t be the right tone for a television advertisement, but it’s not intended for a predominantly technical audience, either. Instead, it’s made for viewers of some intelligence who are willing to give it their attention and learn some amazing things.
I am particularly delighted at how the language is kept clear and understandable, particularly as it’s supported by the visuals, without being patronizing or gratuitously simplified. Amidst the poetical and metaphysical thoughts about photography as an art form, watch for the exposition about the camera, how it operates, and all the technical advances it contains. Pay attention: it’s all too easy to be drawn into the narrative without realizing that all that technical information is entering your mind with relative ease.
As you might expect, there are plenty of people taking pictures with the camera, demonstrating what fun it is and how it is used and its various special features. But look at what they’re taking pictures of: several appear to be scientists, or even amateurs of science, documenting the natural world. Of course, there are also proud parents taking pictures of their children, but they’re just part of the panorama. But even while we see the parents photographing their kids, we are also shown that the SX-70 has a fast lens, a short focal length, a quick shutter that can stop action, and the ability to take exposures in quick succession. The Eames are not merely marketing the SX-70 in this film, they are demonstrating its capabilities and technologies and making that look easy.
I love the attitude that includes the scientific as part of the cultural, a film that combines poetry and philosophy and technical explanations and kids and nature into one amazing whole that’s so amazing one hardly notices that all that’s going on. I like how the technical specifications of the camera are explored and shown rather than explained–before the narrated explanation (beginning at about the 4:15 mark) of the internal workings of the camera–assuming a viewer without special technical knowledge but sophisticated enough to absorb the ideas.
Then, when you do get to the technical narrative, notice how crisp and concise the narration is, and how it’s so beautifully documented by the combined animation and live action (done in the days before CGI). I don’t think it hurts anyone to hear the word “aspheric”, even if it’s not a familiar word–yet. And while we’re there, let’s not overlook the achievement of the Eames’ documenting the internal mechanisms of the camera. There are as many shots in there as Hitchcock used in that famous murder scene in “Psycho”.
Amazing. It inspires me and intimidates me at the same time, which I expect is a good thing.
I recently finished reading the book Hydrogen : The Essential Element, by John S. Rigden (Cambridge, MA : Harvard University Press, 2002. vii + 280 pages). Here’s my book note. It’s a book I can recommend.
As I mentioned in the book note, the “hydrogen” of this book is the physicist’s “hydrogen”,* the simple atom of electron + proton (with some isotopic variations) that is the simple test case for all physical theories that deal with things atomic: if it doesn’t work for hydrogen, it’s not going to work.
Hydrogen is overwhelmingly the most abundant atomic species in the universe, making up about 74% (by weight) of the matter we can see. It is the predominant fuel that stars burn through fusion (to make helium nuclei). Hydrogen is the earliest element in the cosmos, protons condensing from a universe of quarks when the temperature finally became low enough, in the period (the “hadron epoch”) between one microsecond to one second after the big bang.† It was some time longer before the universe cooled enough (some 380,000 years!) for the protons to capture and hold onto electrons, thus becoming actual atoms of hydrogen (Of course, there had to be electrons to capture; they condensed around one second ABB.#)
Anyway, the history of our modern understanding of the hydrogen atom, and the efforts to gain that understanding, is virtually identical to the history of “modern physics”, by which we loosely mean all that physics stuff from the early twentieth century: quantum mechanics and its friends. Lots of other interesting things get thrown in, too, from all the attention the hydrogen atom got. A couple of the more interesting: the development of the hydrogen maser and very high precision time keeping (i.e., “atomic clocks”, leading to the GPS), and the invention of a technique known to physicists as NMR (nuclear magnetic resonance), which in recent decades developed into the familiar MRI (magnetic-resonance imaging‡).
Anyway, that’s book-note stuff. What we’re all about here is a couple of leftover quotations from the book that go under the heading: “Physicist’s and their Strange Sense of Humor”. The first two quotations reveal things that physicists find almost knee-slappingly funny but may remain inscrutable to nonscientists (and I wouldn’t worry about that either, if I were you–you’re not missing all that much).
Paul Dirac was a[n] unusual person. Perhaps because Dirac’s father demanded that his young son use French rather than his native English to converse with him, the young Dirac adopted the habit of silence during his childhood simply because he could not express his thoughts in French. Whatever the reason, the adult Paul Dirac was a a man of silence. Dirac’s silence was so intense that it inspired a little levity among physicists. In physics, the units given to physical quantities like time or length are important. Physicists, clearly in jest [!], have defined the unit of silence as the dirac. [p. 89]
For this second joke, I might mention that it was Ed Purcell who pioneered the NMR technique, and that the technique uses magnetic properties of the hydrogen atom, which moves much like a gyroscope when magnetically disturbed (hence the reference to “precessing”**).
I remember, in the winter of our first experiments, just seven years ago, looking at snow…around my doorstep–great heaps of protons quietly precessing in the earth’s magnetic field.
–Edward M. Purcell [quoted on p. 137]
Finally, this one goes into that file where we put really bad predictions of what the future might hold.
In 1952, neither Purcell nor Bloch could have predicted the ways their discovery would advance understanding of solids, of the structure of chemical molecules, and even more. In fact, a representative from Dupont Chemical Company visited Purcell soon after the paper announcing the discovery was published. The Dupont scientist asked Purcell what the practical applications of NMR might be. Purcell responded that he could see no practical applications. In this, Purcell was very wrong. [p. 147]
———- * Rather than, say, a chemist’s “hydrogen” with discussions of interesting molecules and acids and reducing reactions and carbohydrates, etc. Nor is it an engineer’s “hydrogen”, nor a politician’s “hydrogen” (as in “hydrogen economy”). They’re all stories for another book for someone else to write. What a publishing opportunity!
† I just read this the other day about the big bang and the origin of the cosmos (and now I forget who gets the attribution): “In the beginning there was nothing, then it exploded.”
# We could just say “it happened at one second”, since the current understanding has it that time (whatever it is besides a whole other story) began with the big bang.
‡ I’m sure I’ve expressed my peevishness before about how the perfectly good word “nuclear” had to be expunged before MRI could be a commercial success.
** When some body, like the Earth or a hydrogen nucleus, rotates about an axis, and that axis is tilted relative to some other axis about which the tilted axis itself executes a (generally much slower) rotation (a kind of wobble), that latter motion is referred to as “precession”. The precession of the Earth’s axis takes about 26,000 years. Hydrogen atoms do it at about 500 megahertz (or 500,000,000 times each second).
This is birthday boy Charles Robert Darwin (1809-1882), born 200 years ago on 12 February 1809. This photograph (which I have cropped) was taken in 1882 by the photographic company of Ernest Edwards, London.*
This is Sir William Thomson, Baron Kelvin* (1824 – 1907) or, simply, Lord Kelvin as he’s known to us in the physical sciences. This is the same “Kelvin” as in the SI unit “Kelvins”, the degrees of the absolute thermodynamic temperature scale.
, a consequence of his special theory of relativity. Understanding dawned that the loss of mass was related to a release of energy through the radioactive decay.
All sorts of stuff has been going on up in the sky lately. There’s just so much to look at.
This beard belongs to Mr. Spock, the venerable half-Vulcan who served as the science officer aboard the Enterprise in “Star Trek”, the original television series. 
This is Euclid (c. 365 BCE — c. 275 BCE) of Alexandria, Egypt, possibly one of the earliest celebrities to use only one name. Euclid is famous, of course, for writing Elements, his 13-book exposition on geometry and the earliest mathematical textbook and second only to the Bible in the number of editions published through history.
, and I needed a pretext. In fact, it wasn’t even exactly 
“, the “golden ratio”, and numbers of that ilk. These are numbers that are perfectly well defined by known and exact mathematical relationships. (I once discussed a number of mathematical equations involving “
. Exactly.
