Bumblebee Aerodynamics

There is a hackneyed saying to the effect that “scientists have proved that bumblebees can’t fly”, or alternatively “according to the laws of physics, it’s impossible for a bumblebee to fly”. You only have to look at a bumblebee flying (as in this video I filmed yesterday) to see the statement is patently false. Who says bumblebees can’t fly? Scientists say it! The laws of physics say it! If you want to prove that scientists and the laws of physics are dull-witted imbeciles, you only have to whip out the bumblebee quote.

Despite being such valuable ammunition for the technophobes and pseudoscientists of the world, there is actually no such thing as the non-flying bumblebee theorem. From a Google search, it’s clear that no-one really knows where the quote originated. My own theory is that it’s a mangled version of a subtly different statement: that “the equations of aerodynamics can’t be solved for the case of a flying bumblebee”. This latter statement is perfectly true – or at least it was when the myth of the non-flying bumblebee emerged in the 20th century.

The fundamental equations of aerodynamics are called the Navier-Stokes equations. These are non-linear partial differential equations, and they’re notoriously difficult to solve even with a modern computer. In fact they can’t be solved at all, in any general sense – they can only be approximated if you make additional simplifying assumptions relevant to the specific cases of interest. During the 20th century, the main “cases of interest” were manned aircraft. While still not easy, the Navier-Stokes equations could at least be made tractable with the aid of a number of simplifying assumptions – such as considering steady-state flow only, and restricting viscous effects to a thin boundary layer.

But these assumptions simply aren’t applicable to a bumblebee. The flow of air around such a tiny insect is highly viscous and anything but steady-state. If you tried to apply equations tailored for a 50-metre long, Mach 0.8 airliner to a bumblebee you might well calculate that the latter couldn’t fly – but the result would be meaningless, because the equations were applied way beyond their range of validity. 20th century aerodynamicists simply weren’t interested in developing the correct set of equations for bumblebees. The situation these days is different, with a lot of current research going into insect-sized “micro air vehicles”. Some of the devices emerging from science laboratories are described as bumblebee-sized – making it more ludicrous than ever to claim that scientists have "proved" that such things can’t fly!

Another historical myth-conception

A recent Mensa newsletter contained a letter from Malcolm Burn in which he says “History itself (or rather, the version of history which most people who are not professional historians think they know) is full of [...] myths. Sometimes people become so attached to them that, even when an historian has explained to them why a particular story is a myth, they dismiss the true version and still cling to the old familiar one.” I couldn’t have put it better myself – this is an old hobby-horse of mine. I mentioned it most recently in Chronological Snobbery. But the example given by Malcolm is one I hadn’t realized was a mythconception – I have to admit I always believed it myself!

The essence of the “myth” is that when the British government switched from the Julian to Gregorian calendar in 1752, entailing the skipping of 11 days, hordes of ordinary people took to the streets with placards demanding “Give us back our eleven days”. Like many historical myths, people are inclined to believe this because it’s amusing, and it’s always presented as hard fact. But when you stop to think about it, the idea is pretty ludicrous. Why should “ordinary people” be so bothered by such an abstract item of government policy? According to Malcolm’s letter, the case has been thoroughly debunked by a historian named Robert Poole, who hasn’t found a single shred of evidence for popular protests on the subject anywhere in Britain during the course of 1752. Ordinary people are by and large sensible – they protest about things like taxes and working conditions, not calendar reform!

The true origin of the phrase “Give us our eleven days” makes a lot more sense when you know the context. I’ve mentioned the great artist William Hogarth before (Paranormal investigation, 18th century style). There is no-one before or since quite like Hogarth. He produced fine-art paintings and engravings which, rather than dealing with the usual timeless subjects of high art, were satirical treatments of the fashions and politics of his time. The closest comparison in modern terms is with a satirical cartoonist, although few modern-day cartoonists can expect to be remembered 250 years after their death, as Hogarth is.

In 1754—two years after the calendar change—Hogarth produced a series of paintings called Humours of an Election. The aim was to make fun of the various goings on behind the scenes at a parliamentary election – an easy target for satire in those days just as it is today. The first picture in the series, "An Election Entertainment", shows a gathering of the Whigs (liberals) while their rivals the Tories (conservatives) cause trouble outside. The characters depicted in the scene aren’t “ordinary people”—as the “eleven days” protesters are imagined to be in the mythical version of events—but hard-line party faithful. They don’t think like “ordinary people” – they’re only interested in bringing down the other party. So there on the floor, amidst the Whig gathering, is a placard saying “Give us our eleven days” – the significance being that the calendar reform two years earlier was the work of the Tories.

What Hogarth is doing is satirizing the way members of one political party will mindlessly oppose each and every policy of their opponents. The idea is that, if the Whigs had won the election, they would have reversed the Tory decision to switch to the Gregorian calendar. But that has nothing to do with the real world – it just came out of Hogarth’s imagination. Perhaps it’s a testament to his satirical genius that people continue to believe it really happened to this very day!

Chronological Snobbery

I’ve got another letter in this month’s Fortean Times! This one touches on a favourite hobby horse of mine, “chronological snobbery” – the widespread belief that people of the past were intrinsically inferior to people of the present. An example of this is the smug assertion that “people were much smaller in the old days”, as discussed by Mat Coward in the 150th instalment of his Mythconceptions column (FT284, February 2012). One piece of evidence often put forward to support this is the short length of the four-poster beds you see in English Stately Homes (“Gosh, these people had all that wealth and power, yet they were shorter than I am!”). The fallacy of this, as my letter in FT287 points out, is that people used to sleep propped up on pillows against the headboard rather than lying flat. The picture sort of illustrates my point (I know the people in the bed aren’t sleeping, but it was the best I could find).

There was another sentence in my letter that didn’t make it into print: “People often point out that King Charles the First was a very short person, at just five foot four... but they neglect to mention that his grandmother, Mary Queen of Scots, was five foot eleven!”

Galileo wasn’t always right...

Present-day fringe theorists often cite the case of Galileo (1564–1642) as proof that they’re right and the authorities are wrong. It’s true that Galileo was constantly in conflict with the intellectual establishment of his time, and that history has proved him to be on the winning side on all the big issues. The Earth really does move around the Sun, and heavy objects really do fall at the same rate as light ones. But is Galileo really such a good role model? Unlike the armchair scientists and internet cranks of today, Galileo didn’t always get it right.

To start with, it’s worth dispelling a couple of tenacious myths about Galileo. The first myth is that he set out to disprove the Bible. In fact, it’s clear from his Selected Writings that he had no problems at all with the Bible: “Holy Scripture can never lie or be in error... nonetheless some of its interpreters or expositors can.” All of Galileo’s arguments are aimed not at the Bible but at the Greek philosopher Aristotle—who was held by the Church to be second only to the Bible in authority.

Galileo used the Biblical story of Joshua, where God caused the Sun to stand still in order to lengthen the day, as evidence that the Aristotelian earth-centred model is wrong, and the Copernican sun-centred model is correct: “This passage of scripture clearly demonstrates the impossibility of the Aristotelian and Ptolemaic world system, and on the contrary fits perfectly well with the system of Copernicus.” Galileo argues (correctly) that making the Sun stand still in the Aristotelian view would actually shorten the day, not lengthen it (since the length of the day is set by the Primum Mobile, and the Sun moves backwards relative to this). What you actually need to do is freeze up the whole Solar System. Galileo had observed the Sun to rotate on its own axis, and believed (wrongly) that this rotation was the source of all the motion in the Solar System—hence he argued it was this rotation that God halted in the story of Joshua.

Another myth-conception is that the Church prohibited Galileo from writing about the Sun-centred theory, and that his ‘crime’ was to defy this prohibition. Actually, the Church encouraged him to write about the theory... as long as he ended up debunking it, or at least showing that the truth couldn’t be proved one way or the other. What he was prohibited from doing was offering any concrete proof that Copernicus was right and Aristotle was wrong. But that’s what he did, and that’s what got him into trouble.

The hilarious thing (and now I’m finally getting to the point of the article) is that Galileo’s proof was rubbish. At the time, no-one knew what caused sea tides—Galileo’s fellow Copernican Kepler believed they were due to the influence of the Moon, but Galileo dismissed this as mystical mumbo-jumbo (“Of all the great men who have speculated on this marvellous effect of nature, the one who most astonishes me is Kepler... he had grasped the motions attributed to the Earth, and yet he still listened and assented to the notion of the Moon’s influence on the water, and occult properties, and similar childish ideas.”) Galileo was convinced the tides were a direct result of the Earth's motion, in the same way water sloshes around in a vase when you move it. But Galileo was wrong about this... and he was wrong about the Moon having nothing to do with the tides!

You might think that, having upset the Irish nation last week by suggesting that St Patrick was British, I’ve now lurched on Boris Johnson style to insult the Italians—by pointing out the single occasion on which Galileo made a mistake. But it’s worse than that... he made another mistake as well! Galileo believed that orbits had to be perfectly circular (again, this was a disagreement with Kepler). This created a problem in the case of comets, which are on manifestly non-circular orbits. Galileo’s solution was to dismiss comets as not really existing at all—merely an illusion caused by the Sun reflecting off the upper layers of the atmosphere!

The Einstein Misconception

A few months ago I submitted a “Mythconception” to Fortean Times concerning what I described at the time as “a very tenacious myth about Einstein”. After much conferring, they decided it was too abstruse and too open to debate to go into the magazine. They were probably right -- but I still think my original point was valid, so I’m going to inflict it on the world anyway.

As I originally stated it, the Mythconception concerns “the idea that Einstein’s 1905 theory of relativity, with its famous equation E = mc², laid the theoretical groundwork for the atomic bomb -- which, the myth claims, works by converting small quantities of matter (atoms) into large quantities of energy. This view is repeated ad nauseam by the media, but it’s wrong. There is no annihilation of matter in a nuclear weapon, only the release of nuclear binding energy.”

To be even more pedantic, E = mc² doesn’t describe the conversion of one thing into another, but the absolute equivalence of energy and mass... with c² as the constant of proportionality. A cannonball may have a mass of 10 kg when it’s sitting in the cannon, but when it’s flying through the air it has a very slightly greater mass due to its additional kinetic energy. This extra energy/mass came from the chemical binding energy released by the exploding gunpowder. If you could collect all the combustion products together again, their combined mass would be just slightly less than that of the original gunpowder.

So even a mediaeval cannon obeys E = mc² -- you don’t need an atom bomb! You might argue that a nuclear weapon is qualitatively different from a cannon, but it isn’t really. There’s a quantitative difference, in that the “slight” changes in mass in the case of a cannon are so slight as to be immeasurable, whereas they’re appreciably bigger in the nuclear case. But they’re still very small. The difference is that the energy released in this case is nuclear binding energy, not chemical binding energy.

The basic nuclear reaction involves the fission of an unstable heavy nucleus (such as Uranium 235) into lighter nuclei. This is commonly described as “splitting the atom”, which is accurate, and “annihilation of the atom”, which is journalistic bollocks. Nothing is annihilated. The fission products have just as many nucleons (protons and neutrons) as there were to start with. But because they’re stable, they have less binding energy -- hence less total mass. That missing energy/mass went into the X megatons of explosive energy.

The archetypal Cold War weapon was a “thermonuclear” device that produced additional energy from the fusion of heavy hydrogen into helium. Again, the number of nucleons remains the same, and the energy released comes from binding energy. If people want to say that matter is “destroyed” in a fission reaction, then they might as well say it is “created” in a fusion reaction!

I know I’m being pedantic -- it all comes down to what you mean by “matter”. I’m using the term to mean “nucleons”... and what I’m saying is that nucleons are neither created or destroyed in a nuclear reaction. But if by “matter” you mean the rest-mass of a macroscopic chunk of matter, then a measurable part of that comes from the nuclear binding energy, some of which is lost (in both fission and fusion reactions). But—coming back to Einstein—that’s a consequence of quantum theory, not the theory of relativity! E = mc² merely describes one effect of the nuclear reaction, not its ultimate cause.

When you get down below the scale of nucleons, things get even more blurred. Protons and neutrons are made up of three quarks each, but if you could separate the quarks out they’d hardly have any mass at all -- most of the mass you’re aware of in the real world is the binding energy holding the quarks together!

Hyperbolic Orbit

On 5 May 1961, as the result of a short trip on the end of a rocket, Alan Shepard became an instant celebrity and one of the greatest American heroes of the twentieth century. But was he really the first American in space? Personally I think it's an exaggeration to claim this... a Myth-conception created by a mixture of Cold War politics and the media's ignorance of science. If you're going to talk about space travel, you need at least a basic understanding of Newton's Law of Gravitation.

Shepard's trajectory in May 1961 was parabolic, the same as a ball thrown into the air, or any other object which is launched upwards with less than orbital velocity V_o. To enter Earth orbit (as Yuri Gagarin's Vostok spacecraft did three weeks before Shepard's flight), the trajectory must be an ellipse, which requires the speed to be somewhere between V_o and escape velocity V_E = √2V_o. If the speed is greater than V_E the object will escape the Earth altogether on a hyperbolic orbit.

The adjective "hyperbolic" can also mean "of exaggerated importance" (from the noun hyperbole, normally shortened to hype). In this sense, Alan Shepard's flight was hyperbolic as well as parabolic!

I don't mean to belittle Shepard personally -- after all, he was just doing a job, and had no control over how that job was presented to the world by NASA or the news media. Arguably, his flight required far more courage than Gagarin's had, since the latter had the benefit of a well-designed, well-engineered spacecraft that virtually flew itself, and was always well within its operational envelope. Soviet cosmonauts were never bothered by Shepard's oft-quoted worry that "every component was built by the lowest bidder"!

The Redstone rocket used for Shepard's mission (and Gus Grissom's similar flight a couple of months later) was designed in the early 1950s as a short-range ballistic missile, and was (in engineering terms if not in visual appearance) only a slight modification on the German V-2 rocket of World War 2. Test flights of captured V-2s in the late 1940s achieved similar altitudes to Shepard's flight, yet no-one at the time described them as "flights into space". Some of these flights even carried monkeys and other animals as passengers, with no great media fanfare. Under normal circumstances, I'm sure that Alan Shepard's mission would have been seen as "just another test flight"... if it hadn't been for the exigencies of Cold War politics, which demanded an instant U.S. response to Gagarin's flight into space!

Eventually, in February 1962, an American did make it into orbit: John Glenn, boosted into space by an Atlas rocket which was far more powerful than the Redstone. As a space-obsessed but scientifically ignorant schoolboy in the 1960s (from which period the postcard above dates), Alan Shepard was one of my great heroes, and I could never understand why grown-ups made such a fuss about John Glenn... after all, he was only the third American in space, wasn't he? And if the Americans really believed that Alan Shepard's flight was on a par with Gagarin's, they wouldn't have made a fuss about John Glenn either!

From Myth to Reality

Like most people, the editors of Fortean Times generally ignore everything I say (presumably because most of what I say is indistinguishable from the ravings of a lunatic). However, this month's issue, FT275, does contain a letter from me... the first since FT187 way back in September 2004! The subject isn't particularly Fortean, but it's an interesting example of the way a long-standing "myth" can eventually become reality.

In this case, the myth in question concerns the great architect Sir Christopher Wren (1632 - 1723), who was supposed to have installed columns to support the ceiling of the Sheldonian Theatre in Oxford because his patrons insisted they were necessary. However, because Wren knew the columns were not in fact necessary, he built them so they stopped just short of the ceiling and didn't support it at all. This story was featured in FT271 (February 2011) in the "Mythconceptions" department, and can be read online here.

When I saw this, it rang a bell because I remembered hearing something very similar on a TV programme a few months earlier. Here is the text of my letter:

Another example of redundant architectural columns cropped up in the "Climbing Great Buildings" series shown on BBC2 last year. In the episode dealing with the Glasgow School of Art (aired 20 September 2010), it was revealed that the wooden pillars that appear to hold the roof up are not actually supporting anything. The capitals which supposedly form the top of the pillars are in fact hanging from the roof, while the pillars themselves are purely decorative. The architect in this instance was Charles Rennie Mackintosh, who the programme's presenter Jonathan Foyle describes as a "joker" and a "showman" whose aim here was "to have fun with traditional architectural styles".

Charles Rennie Mackintosh (1868 - 1928) is more famous today as a furniture designer of the Art Nouveau school, but in his early years he was also an architect. The Glasgow School of Art was Mackintosh's first major work, as the Sheldonian Theatre had been Wren's more than two hundred years earlier.

Here is the relevant clip from Climbing Great Buildings (thanks to Paul Jackson for help in locating and extracting it).

Dorset myth-conception

As readers of Fortean Times know, the world is full of "myth-conceptions" which sound so credible they get repeated ad nauseum, even though there is no truth to them. Here is one that has just been pointed out to me by Paul Jackson, concerning the Drax Estate's prominent "Stag Gate" on the A31 (the main route from Dorchester to the M27). The Stag is famous for having five legs -- and everyone in Dorset "knows" the reason for this. But they're wrong, as Paul explains:

"It seems that it has often been assumed (by me too) that the Stag was given a fifth leg to ensure that it looked like it had four legs when viewed from the road. Presumably when it only had four legs, it appeared to have three! However, when reading the Drax estate website I noticed that: Although the stag appears to have five legs, the 'fifth leg' is actually a 'tree stump' originally incorporated into the sculpture to add strength, as can be clearly seen in the photos [reproduced at left]. There are quite a few comments on-line and in publications that the stag has five legs so that it appears to have four when viewed from any angle, which is clearly imaginative but incorrect."