Exponential Dracula

Herewith, from the popular press, an excellent example of geometric (exponential) growth and its implications:

WASHINGTON (AP) — It may be the season for vampires, ghosts and zombies. Just remember, they’re not real, warns physicist Costas Efthimiou.
[...]
Efthimiou takes out the calculator to prove that if a vampire sucked one person’s blood each month [only 1 meal a month!] — turning each victim into an equally hungry vampire [exponential growth!] — after a couple of years there would be no people left, just vampires. He started his calculations with just one vampire and 537 million humans on January 1, 1600 and shows that the human population would be down to zero by July 1602.

[Associated Press, "Count Dracula not in the numbers, physicist says",^* cnn.com, 27 October 2006.]
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^* Evidently the headline writer was tired; a more obvious choice: “Count Numbers, not Dracula”.

Fairy-Tale Astronomy

In a way it’s hardly worth the bother to describe the background to this tidbit, which is a headline to a “Search and Discovery” item in this month’s Physics Today.* The story concerns type Ia supernovae, which are white dwarf stars that make their startling brightness by accreting enough mass to ignite the fusion of carbon in their core, vaporizing the star. But, along the way, accreting mass may simply ignite in a smaller fusion explosion on the surface of the star and blow away from it — this is a plain nova, and they’re much more frequent occurences.

It might seem like a challenge for the white dwarf to find mass to swallow up, but it’s not so hard because many of them are in binary-star arrangements, and they can take mass from their companion star. One such nova outburst was seen recently. Here’s a bit of the background from the story:

Stargazers have noticed novae since antiquity. But only 10 novae, RS Ophiuchi among them [the interesting star system that's the subject of the article], have ever been caught in outburst more than once. RS Ophiuchi flared up in 1985, 1967, 1958, 1933, and 1898 and possibly in 1944 and 1902. Hiroaki Narumi and Kiyotaka Kanai of Japan spotted the new outburst on 12 February and promptly alerted their fellow astronomers.

From the previous outbursts, astronomers identified RS Ophiuchi as a symbiotic binary: a white dwarf and red giant orbiting their mutual center of mass. [...] The pairing is unusual. So far, only about 200 symbiotics have been cataloged in our galaxy.

What Narumi and Kanai witnessed was the thermonuclear explosion on the white dwarf surface. As the burning layer lifts off, it expands adiabatically and cools. By March, the ejecta’s optical flux had plunged to one thousandth of its 4.5-magnitude peak.

Anyway, the whole point of my mentioning it was to assert that — occasionally — even physicists display their sense of humor, although it might not always be recognizable to others. It was the title of the article that caused me to chortle:

White dwarf is caught hurling its outer layers at its red giant companion

Make of it what you will.
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^*Unfortunately it’s subscriber only, but for reference, here’s the link.

Medieval Astronomy

Isaac and I have both recently finished reading Tycho & Kepler, by Kitty Ferguson, and we thoroughly enjoyed it. (There’s more about the book in our Science Besieged Book Note.) Thus it happens that this beard and rather extravagent mustache belongs to the Danish astronomer Tycho Brahe.

Tycho, active in the second half of the 16th century, is often described as the greatest naked-eye astronomer in history. The biggest reason for this is that the telescope was just being invented — it was only in 1610 that Galileo discovered the moons of Jupiter in one of the earliest astronomical uses of the telescope. Think for a moment of what it must have been like to try to do science when, as Ms. Ferguson pointed out, geometry was the most advanced mathematics known. Calculus would not be invented by Newton & Leibnitz for nearly another century.

Regardless, he created some magnificent and clever instruments with which he made observations of unprecedented precision. In particular, he measured the orbits of the planets with enough accuracy that, just after Tycho’s death, Kepler finally hit on his (Kepler’s) 3 Laws of Planetary Motion and announced that the planets followed eliptical orbits. (The eccentricity of the orbits, which is to say the amount by which they are elliptical rather than circular, was very small and barely discernable.)

These portraits of Tycho do not represent his reddish-blond beard and quite remarkable mustache too clearly, but Ms. Ferguson’s description makes it clear that he was physically rather to my taste:

Tycho had just turned twenty-nine [in 1575] and was an experienced courtier, polished by his travels and attendance at many courts. Garbed appropirately with flowing cape, feathered hat, and sword, he was an imposing figure, barrel-chested, elegant, and of distinctly noble bearing. His eyes were light-colored, and his hair, beard, and substantial mustache were reddish blond. In portraits, his false nose looks a fairly successful imitation, close to flesh-colored — though an astute portrait painter would have made it so in any case. [p. 72]

[from: Kitty Ferguson, Tycho & Kepler : The Unlikely Partnership That Forever Changed Our Understanding of the Heavens. New York : Walker & Company, 2002.]

Oh, about the nose: in his youth Tycho got a substantial portion of his nose cut off during a rather pointless duel. Although it is true that he had an ersatz nose fashioned of gold alloy, it was for special occasions only. For everyday use he had a copper and tin alloyed nose. He had made both noses himself.

Farewell to James Van Allen

Physics^* tends to carry around all manner of homages to its creators and discoverers. Vast numbers of units of measure, constants, concepts, equations, effects, principles, and laws are named for famous scientists: Galilean Relativity, Newton’s Laws of Motion, Kepler’s Laws of Planetary Motion, Bernoulli’s Equation, Euler’s Equation, Laplace’s Equation, Boltzmann’s Constant, Planck’s Constant, Hubble’s Constant, the Compton Effect, the Zeeman Effect, Kelvins, Celsius degrees, Curies…. Obviously the list is not strictly endless, but it does go on quite a bit.

I’ve always found it a humanizing influence to acknowledge scientific pioneers this way, and a useful way for students of physics to learn some of its history as they go, which I also think is a good thing. I also find that it helps me remember which equation, constant, or effect is which — just imagine the mental chaos if all our equations and constants were simply numbered!

One thing that virtually all these nominal designations have in common is that the person after whom they are name is dead. There are a few exceptions, of course, for those that are associated with phenomena discovered more recently.

One such was the Van Allen radiation belts around the earth. They had been discovered in 1958 by James Van Allen. Van Allen and his team had built Explorer I, the first satellite launched by the US. The satellite carried only one instrument: a Geiger counter^#. The instrument’s readings led Van Allen to deduce the existence of regions of high-energy charged particles trapped by the Earth’s magnetic field. ^**

I went to college in Iowa (Cornell College, in Mt. Vernon, Iowa) in the late 70s. I knew about the Van Allen Belts, but hadn’t quite caught on to the fact that they had been discovered after I was born (albeit in my extreme youth: I was 2 years old). Thus, I thought of them as named for an historic scientist — if I thought of it at all back then.

Imagine my surprise then when I learned not only that Van Allen was a living, working physicist, but that he was also living and working at the University of Iowa, a mere 30-minute drive south through the corn fields from me! It was probably the only time I would be young enough and naive enough to react to something like that with such profound surprise — I had never imagined something like that! It seemed almost mystical at the time, since I was certainly still in awe of anyone who had something like that named for him. Since then I have met physicists with things named for them and they seemed like … people.^## It’s just as well, though, that I never met James Van Allen since, for me, he had mytical status and I’m sure I would have been embarrassingly tongue-tied.

James Van Allen died this past Thursday, news that seems surprising to me since — in my mind — he is immortal.

Here’s what Bob Park had to say in today’s “What’s New“:

JAMES VAN ALLEN: THE FIRST AMERICAN SPACE HERO, DEAD AT 91.

Almost nothing was known about conditions beyond the ionosphere when the US launched Explorer I on 31 Jan 58. The Cold War was at its peak, and the Soviets seemed to own space. Sputnik I, launched 4 Oct 57, carried no instruments. Sputnik II, a month later, could only send back Geiger counter readings taken when it was in sight of the ground station. In June, however, at a conference in the USSR, James Van Allen, a physics professor at the University of Iowa, announced that Explorer I had discovered the first of the two “Van Allen radiation belts.” Soviet space scientists were crushed; the “space age” was not a year old and already the U.S. had taken the lead in science. Two years ago I visited Prof Van Allen in his office at the U. Iowa. At 89 he was down to a 7-day work week. He showed me an op-ed he was sending to the NY Times in which he described human space flight as “obsolete” http://bobpark.physics.umd.edu/WN04/wn072304.html. I don’t believe they used it. Van Allen said using people to explore space is “a terribly old fashioned idea.”

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^*I’m sure this is true of many other fields, but I’m a physicist, so I’m talking about physics.

^#Named for Hans Geiger, one of its inventors in 1908.

^**Here are two pieces about the radiation belts: one more technical, one less technical; also, an article with lots of pretty pictures — be sure to scroll down past the section “Reading to be Informed Questions” to see them.

^##With maybe one exception (although we didn’t actually meet). The background is this: there was a famous textbook in quantum mechanics written by Eugen Merzbacher that was known to any physics student at the time; not surprisingly, given the familiarity of his name, Merzbacher also had a status that exceeded mere personhood. Once, when I was at a meeting of the American Physical Society, Merzbacher was there: I happened to stand in line next to him at a McDonald’s for breakfast. To this day it fascinates me to have heard someone of such exhalted status say: “I will have an Egg McMuffin, please.”

Three New Things

Three items in this week’s issue of “What’s New”, by Bob Park,^* amused me enough to share. That I found these amusing may tell you more about me than anything.^#

1. ABC PRIMETIME: WAKE UP ABC, IT’S THE TWENTY-FIRST CENTURY!
Here’s the scene: Adam Dreamhealer is a normal 19 year-old, who wears an earring, has a tattoo, pumps iron, and all that stuff. A regular guy, except he has this gift. It came from a 4-foot tall blackbird he encountered on a strange island. The bird downloaded all the world’s knowledge into Adam’s head. Now Adam goes into trances in dark rooms to manipulate quantum holograms with his hands. (Tom Cruise in Minority Report?) It enables Adam to cure cancers that haven’t been verified by biopsy. How does it work? “Quantum mechanics.” An over-the-hill physicist said scientists “groan” at that explanation. He said more but it was cut. Dr. Edgar Mitchell of Apollo 14 fame came on and agreed with Adam that it must be quantum mechanics. It was Mitchell who carried out ESP experiments from space, and now worries about all of these UFO visits. He is the author of Quantum Holography: A Basis for the Interface Between Mind and Matter. Why am I telling you this? Because I was the “over-the-hill physicist” who allowed himself to be used. I will perform any penance WN readers feel is appropriate. I really should have known better: http://bobpark.physics.umd.edu/WN05/wn021105.html.

2. DOUBLE BLIND: WHAT THE MEDIA JUST CAN’T SEEM TO UNDERSTAND.
Feynman once described science as “what we have learned about how not to fool ourselves.” The most important discovery in medicine is the randomized, double-blind, placebo-controlled test, by means of which we learn what works and what doesn’t. When I was first contacted by ABC about Adam Dreamhealer, a producer asked how I would respond to Adam’s claims? “I would ask for the test results,” I replied. But of course, there are no test results. That’s the point. And it’s the only point ABC needed to make.

4. SOUL SEARCHING: ZYGOTES, PEOPLE, AND THE TWIN PARADOXES.
Several readers commented on last week’s science v. religion story that, if a zygote is assigned a soul, identical twins would have to share a soul. One reader noted that in the very rare case of chimerism, which involves the fusion of two paternal twin zygotes, one person would have two souls. Identical twins, however, as we all know, are not identical. Many connections in the brain, mostly dealing with language, are still not completed at birth. In the sense that our “essence” is our “soul,” the soul keeps changing throughout life.

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^* Archive at http://www.bobpark.org. Bob: when are you going to start the “What’s New Blog”?

^# It should go without saying that physicists often have an inscrutible sense of humor, particularly when it comes to physics jokes; that is to say, there are things that physicists find knee-slappingly funny that makes no sense to others.

The Sun & The Moon

I have a friend upon whom I can rely to send me, with some regularity, unbelievable photos and incredible stories, most of which turn out in the end to be fabricated photos and urban legends. Someplace in the forwarding of these things, someone will often add a wishy-washy “I don’t know if this is true, but….” and then carry on anyway.

Sure enough, the last photo I got from him was a beauty: an arctic landscape with a bright, tiny sun hovering on the horizon and, above it, an enormous crescent moon. It was quite a lovely image. The text with it said

This is the sunset at the North Pole with the moon at its closest point. And, you also see the sun below the moon. An amazing photo and not one easily duplicated. You may want to save this and pass on to others.

“…not easily duplicated” is correct! While the image is pretty, it’s a complete fabrication, and I’d like to think that should have been obvious to anyone seeing it. But then, I’d like to think a lot of things that turn out to have nothing to do with reality.

Happily, snopes.com says plainly that the photograph is a fabrication, created digitally by a German astrophysics student. (Follow the link for the details and to see the image.)

However, Snopes missed their chance to state the obvious: the photograph could not possibly be a real image of “sunset at the North Pole” for one simple reason that everyone should be able to spot — the image of the moon, compared to the image of the sun, is far, far too large.

But how could anyone be expected to know this^*, you ask? Well, I claim, nearly everyone knows the cause of total solar eclipses, even if they’ve never seen one: the moon passes between the Earth and the sun and exactly covers the disk of the sun for a short time.

The simple deduction, then, is that the apparent size of the moon, as seen from the Earth, is very nearly the same as the apparent size of the sun. Thus we know that this image, in which the moon is some 20 times the size of the sun, must be a fabrication.
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^* This is an interesting question, particularly since in films, night scenes are often created with a looming, full moon shot with a telephoto lens; the same is rarely done for the sun, unless it is near the horizon into which the movie’s heroes are riding. People often seem ready to accept that the apparent size of the moon is substantially larger than it is in reality, whereas they seem to imagine the apparent size of the sun to be rather smaller than it actually is. These mistaken notions are exploited in the north-pole “sunset” image.

Mystical Time

Not to harp on the innumeracy thing (although — plug time! — it is part of the mission of Ars Hermeneutica), but I’m a little irritated.

You see, I keep seeing people for the last few days pointing out, in e-mail and on their blogs^*, that on 5 April something unusual is going to happen. Namely, the time and date at one moment in the wee hourse will be

01:02:03 04/05/06

“This will never happen again!” is trumpeted along with the observation.

Of course, this is incorrect for two contradictory reasons: 1) it isn’t really happening in the first place; and 2) it will happen again.

Dispensing with #2 first, a moment’s reflection quickly shows that because only the last two digits of the year are used in the mystical rendering, this “reading” will happen precisely every 100 years, give or take depending on leap seconds or other adjustments; we could say it will happen exactly every 100 nominal years.

Now, for #1. It should come as no surprise that I am always troubled by mystical malarky like this, but I find it more troubling when it is so arbitrary, depending as it does only on accidents of the way we count time and keep track of days.

For most Europeans, the revelation won’t make any sense because they tend to write the day number before the month, 05/04/06, so clocks won’t get all mystical for them until 4 May. But should the mystical power depend so critically on using only two digits for the date? Oh dear, but 04/05/2006^# just doesn’t do it, does it? All this without even mentioning the different calendars and years observed by different cultures (China, say, or Orthodox Christians or Jews). Also not to mention that it depends on the fact that we divide the day up into 24 hours, and each hour in 60 minutes of 60 seconds each — like that’s natural and deeply meaningful!

I am not, however, totally immune to these accidental coincidences of digits. For instance, I find it useful — as a mnemonic — that Ars Hermeneutica’s incorporation was recorded in the Maryland Department of State at 11:11 on 11 November. Surely that must mean something!

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^* For example, Shakespeare’s Sis mentions it here.

^# Update added barely one hour before the mystical event here in the Central-Daylight-Time timezone: I just realized with some excitement that if only we more generally used a 24-hour clock and wrote our dates euro-style, we could look forward, in just a couple of months, to 20:06 20/06/2006, which is guaranteed never to happen again with our current Gregorian calendar.

But Is It Science?

It is not often that I laugh out loud while reading court decisions. True, I may smile at a clever argument or an adept turn of phrase, or maybe chuckle over displays of willful stupidity; however, cackling is not a common response for me.

Today I’m finally giving a first read to Judge Jones’ decision in Kitzmiller v Dover, the case last fall concerning the Dover, PA school-board’s decision to demand inclusion of so-called intelligent-design creationism in the curriculum of the biology classroom.^*

I’ve just gotten through the important first half in which the judge gives his rationale for finding that actions taken by the school board had been in violation of the Constitution’s establishment clause. Just before he takes up the question of “Whether ID is Science” (section 4, p. 64), he offers the following justification. I think his tone is well indicated by his use of the word “traipse”, which I don’t think I’ve ever seen before in a judicial opinion (in case the reference to judicial waste of time hadn’t been clear enough).

We have now found that both an objective student and an objective adult member of the Dover community would perceive Defendants’ conduct to be a strong endorsement of religion pursuant to the endorsement test. Having so concluded, we find it incumbent upon the Court to further address an additional issue raised by Plaintiffs, which is whether ID is science. To be sure, our answer to this question can likely be predicted based upon the foregoing analysis. While answering this question compels us to revisit evidence that is entirely complex, if not obtuse, after a six week trial that spanned twenty-one days and included countless hours of detailed expert witness presentations, the Court is confident that no other tribunal in the United States is in a better position than are we to traipse into this controversial area. Finally, we will offer our conclusion on whether ID is science not just because it is essential to our holding that an establishment Clause?violation has occurred in this case, but also in the hope that it may prevent the obvious waste of judicial and other resources which would be occasioned by a subsequent trial involving the precise question which is before us.

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^* Much useful information, including a copy of Jones’ opinion, can be found on this ACLU web page.

All In Perspective

From a report about Exxon’s latest record earnings^*, this extraordinary statement

For the full year, net income surged to $5.71 per share from $3.89 per share in 2004. Annual revenue grew to $371 billion from $298.04 billion.

To put that into perspective, Exxon’s revenue for the year exceeded Saudi Arabia’s estimated 2005 gross domestic product of $340.5 billion, according to statistics maintained by the Central Intelligence Agency.

Now, I’m not talking about the statement about Exxon’s revenues, which is extraordinary, but about the helpful “putting into perspective” that the revenues were about the same as the GDP of Saudi Arabia.

Does the average reader know more — or have more perspective on that number — knowing that it’s comparable to the GDP of a country whose economics are not terribly familiar? Please! That’s about as helpful as saying the earnings in dollars is about the same as the number of miles in a light-week, or the number of sperm the average man produces in a year (about 390 billion). Even saying that it’s nearly 5% of the US national debt is more revealing. (It is, however, only about 50% greater than Wal*Mart’s yearly revenues.)

How about something that really gives a sense of how big such a number is. Something like: imagine that you were able to spend $10,000/hour, 24/7, 365.25 days a year, a pretty breathtaking pace — for perspective, that’s over 4 new Hummer H2s each day (use the surplus to buy the gas) . It would take you over 42 thousand years to spend Exxon’s yearly revenue.

Or, suppose we were to use the money to pay out to people an amount equal to the median US income in 2004: $44.4 thousand. Exxon’s yearly revenues would pay the median income to 8.3 million workers. For perspective, that’s about 11 workers for every mile between Earth and the Sun.

To my mind, either of these comparisons gives quite a bit more “perspective” than the GDP of Saudia Arabia
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^* Steve Quinn, “Exxon Mobil Posts Record Profit for 2005“, Associated Press / Yahoo! News, 30 January 2006.

Two Physics Questions

Angry Professor at “A Gentleman’s C” asked two questions that caught my attention:

• Is there a difference between an electromagnetic field and an electromagnetic wave?
• Why does the addition of particle detectors in the two-slit experiment cause the collapse of the wavefunction?

Good, physics type questions. Naturally I started thinking about answers. I was finally provoked to write the answers down, though, through irritation. My irritation was at the willingness of the people in her comments to provide “answers” who didn’t really understand at all what they were talking about. It reminded me of my early days with Usenet newsgroups when (and this is still prevalent, of course) person A would ask a question and persons B-ZY would say that, although the didn’t know anything about the subject and had no idea about the answer, they’d be happy to offer their ill-informed opinions anyway. Person ZZ would invariably point out to person A that person A should really be interested in an entirely different question and was wasting time asking this one.

So, on the off chance that anyone might be intereted, here are my answers as I wrote them in Angry’s comments:

EM fields and EM waves are really two distinct, but intimately related concepts. A field in general is just a mathematical concept that assigns numbers to every point in space. They may be scalar fields or M-dimensional vector fields, continuous or not, static or time varying. Hydrodynamic fields specify a fluid’s velocity throughout space. EM fields specify the EM force as a function of spatial variables and time.

Stationary electric charges are the sources of static electric fields. Electric currents (steadily flowing electric charge) are the sources of magnetic fields. This connection between E and M is why they’re called EM fields. EM fields are completely described by Maxwell’s equations: four, first-order partial differential equations.

EM waves are time-dependent, propagating disturbances in the EM field, if you want to think of them that way. Propagating means that they travel in some direction and carry energy in the direction of travel. They are created by accelerating electric charges and are solutions of the second-order, partial differential equation, the “wave equation”, which is impicit in Maxwell’s equations. In modern thought, EM waves are identified with photons (just as “gravitons” are identified with the waves that presumably propagate through gravitational fields when masses accelerate).

The results of the double-slit experiment have nothing to do with interactions with photons from the detectors — this is some sort of mistaken impression [that was mentioned in the original question, but I cut it out]. It is an entirely quantum-identified effect. In short, the surprising result was that with one slit there was no interference effect; with two slits there was. This was thought to demonstrate the unequivocal wave-nature of light because how could a particle “know” which slit to go through? Waves, having spatial extent, can sense the presence of the second slit, provided the spacing of the slits is near the wavelength of the waves. The experiment was first done with light, but it can also be done with particles with suitable “slits”.

The answer to the conundrum from quatum mechanics is that the “particle” is really a “probability wave” that can sense both slits when they are present. According to the “Copenhagen Interpretation” of QM, the probability wavefunction has physical reality while the “particle” it represents has none until the act of observation, which instantaneously “collapses” the wavefunction and localizes the particle (in accordance with Heisenberg’s Uncertainty Principle) due to the act of detection itself. However, this result has nothing to do with the nature of the detector, and certainly nothing to do with interacting photons.

The Copenhagen Interpretation is not part of QM; the mathematical formalism works fine without it. It is, indeed, an interpretation of physical processes, and not everyone who uses QM believe the CI. It is claimed as the source of all those new-age ideas about how our minds alter the universe by “observing it”, ideas that demonstrate more clearly a lack of understanding of QM than an understanding of the universe.