The pendulum and the shape of the planet

The 'researchers' of the Internet, the climate clowns who cherry-pick data to prove their dopey obstructionist theories, commonly demonstrate how little they know of the ways that scientists can measure and discover things.

With the exception of the Flat-Earthers (and even climate clowns hate it when they are treated as latterday Flat-Earthers!), we all believe that the Earth is pretty much a sphere, but pretty much leaves wiggle room, and strange as it may seem, it was an upgraded version of a playground swing that revealed the precise shape of our globe, which some people likened to a watermelon stood on end, while others thought was more like a pumpkin.

This is the story of how they did it, almost three centuries ago.

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In some parts here, the main measurements have been converted to their modern equivalents. The unconverted unit called the ‘line’ is 1/4 of a barleycorn, a twelfth of an inch, or about 2 millimetres.

The barleycorn measurement turns up in the oddest of places. Edward I, King of England, decreed in 1305 that “three grains of barley, dry and round, make an inch”, and if you change from a size 7 shoe to a size 8 shoe, the difference in length is one barleycorn.

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Now to our story:

In 1672 Jean Richer reported that the period of a pendulum varied with latitude, and Isaac Newton said that Richer’s variation of pendulum was due to equatorial bulge, a comment offended the French. By this time, nobody thought the world was a perfect sphere any more, but France and England disagreed, and national honour was at stake.

Isaac Newton had proposed that the Earth was an oblate spheroid. If this were so, argued Newton, the precession of the equinoxes (we may or may not come to those later) could be explained. French scientists had taken some sloppy measurements, getting results which suggested that the Earth was more like a watermelon on its end than a pumpkin.

The French Académie set out to determine the truth of the matter by experiment, measuring a degree of latitude in Lapland and in Central America. Among those who went to Lapland was Pierre de Maupertuis, while the American group included Pierre Bouguer and Charles La Condamine.

Richer’s pendulum clock had been accurate in Paris but it lost two and a half minutes each day at Cayenne in Africa, closer to the equator. Clearly, more data were needed, and scientists were rushed to different places in 1735, mainly in South America, a mere 63 years after the comment. Newton had died in 1727, but the French still wanted to show him up, the insolent upstart!

We know Pierre Bouguer’s name today mainly in the form of Bouguer anomalies. This name commemorates his pioneering work in the Americas. When the acceleration due to gravity is measured very accurately, small local fluctuations can indicate equally local deposits of high or low density mineralisation — these fluctuations are the Bouguer anomalies.

Bouguer spent much of his life studying gravitational effects. In 1740, he estimated the value of G, the universal gravitational constant, using a mountain as an attracting mass. A method such as this can only be as accurate as the information the enquirer has about the interior of the mountain, and there were other problems which Bouguer could not have known about. We will ignore those for now, but the key word is isostasy, if you want to know more.

The French work in Central and South America between 1735 and 1743 was to measure the length of an arc of one degree of latitude at the Equator. Other scientists went to Lapland to measure a close-to-polar degree. Any difference in the lengths would reveal whether France or Britain had the right shape.

Inserted without comment.

Here, from the French Académie des Sciences Memoirs, is part of a letter from Bouguer to René de Réaumur in 1735, followed by part of Bouguer’s 1749 report of his findings.

I have made here [in San Domingo] a simple pendulum of steel which I have made as invariant as possible. It has a bob of [12 kilograms], about [12 centimetres] in diameter and [3 centimetres] deep. To keep it swinging true, I have put on the rod a crossbar of iron to serve as an axis, at right-angles to the rod. The instrument is mounted on a tempered steel knife-edge on two steel springs. These two springs are mounted on a copper plate in which there is a hole for the rod. The plate rests on a stool [1.5 metres] high, and is levelled by three screws…

We used the barometer that we set up to study the balance between the weight of the mercury and the air in all the accessible parts of the atmosphere. We saw how many feet we had to rise or descend to make the mercury change height by one line. It is then necessary to find the specific weight of air that balances other bodies. In this way, I have found by comparison with copper that on the top of Pichincha, there is a loss from unity of 1/11 000. Now it follows that the weight of my simple pendulum also loses 1/11 000 part of its weight. This loss produces a similar reduction in the restoring force, and naturally, I found the pendulum to be slow by 1/11 000. To correct this loss, it was necessary to adjust the pendulum’s length by 4/100 of a line…

Translation of the translation: Bouguer had an accurate pendulum, mounted on a wooden stand (the stool) and it was adjustable. He used a barometer as a way of measuring altitude. By timing the pendulum, he could get a measure of g at different heights above sea level.

The degree-measuring expeditions succeeded in proving Newton correct, but one of the more lasting effects came from La Condamine’s explorations while he was there, travelling over a large part of South America, and then 5000 km down the Amazon.

When he returned to Europe, La Condamine brought with him what the locals called cauchu, and the French still call caoutchouc. Thanks to Joseph Priestley, we still call it ‘rubber’, because it can be used to rub out pencil marks, and what is an eraser in some English-speaking countries is still called a rubber in others.

Benham's colourful tops.

 Charles E. Benham (1860-1929) was a journalist and inventor, and he deserves more than this, or what his Wikipedia entry, offers. I was triggered to go here this morning because of a comment Stew made about my last entry: there may be more, later.

When I first discovered the Benham disc, I was delighted, because I am colour-blind. The Benham disc is a black and white patterned circle, which looks coloured when it is spun around. I had heard of these things but I had never tried them, and I thought it would be interesting to see whether they had the same effect on a colour-blind viewer. Being colour-blind does not mean that you “see everything in black and white”, as David Brewster said. It simply means you see colours differently. It occurred to me to wonder if maybe I would see different colours in the disc from those other people see.

Benham described his illusion in an article published in Nature  back in 1894. In those days, if you wanted to see the disc, you would look for the design on a children’s top, known, predictably, as ‘Benham’s top’. The first account was a brief and anonymous one, noting that the ‘disc’ on the top was a black semi-circle, with the white half of the circle divided in four, and with black arcs painted in.

As the disc is rotated, people see different colours from the different black arcs. And, as the reporter noted, if “. . the direction of rotation is reversed, the order of these tints is also reversed. The cause of these appearances does not appear to have been exactly worked out.”

An ‘Artificial Spectrum Top’, devised by Mr. C. E. Benham, and sold by Messrs Newton and Co., furnishes an interesting phenomenon to students of physiological optics. The top consist of a disc, one half of which is black, while the other half has twelve concentric circles drawn upon it. Each arc subtends an angle of forty-five degrees. In the first quadrant there are three such concentric arcs, in the next three more, and so on; the only difference being that the arcs are parts of circles of which the radii increase in arithmetic progression. Each quadrant thus contains a group of arcs differing in length from those of the other quadrants. The curious point is that when this disc is revolved, the impression of different colours is produced upon the retina.

(Nature , 51 (1309), November 29, 1894, 113–114.)

There followed an animated correspondence, during which Benham stepped in. Illuminate the top with a bright sodium flame, he said, and you will see a very clear blue, and a very clear red. And now the controversy heats up: immediately underneath, in the same issue, Professor Liveing retorts that he has seen no such colours: the phenomenon is obviously a subjective one. Clearly there is room for more research here.

It is unclear whether Nature  thought so too, for they go on in the same column to publish next a letter from F. G. Donnan in Leipzig, suggesting that we need a new word in chemistry: ‘solute’, and the discussion seems to have died there. Well, as far as I can judge, I see the same colour effects as other people, which means we won’t learn anything about colour blindness from the Benham disc. But how about trying to learn about colour vision? What causes the colour effect as the disc slows down?

Most explanations seem to speculate rather than to explain, but here is the official version as found in psychology text-books. We have three kinds of light receptor in our eyes, in the same way there are three kinds of phosphor in a colour TV. Speaking crudely, these receptors, the cone cells, are all sensitive to just one of red, green and blue.

According to the theory, you need all three kinds of cone in the retina of your eye to see colours normally. Somehow, the cones which pick up one of the colours (red, for example) must react differently to flashing lights of a particular frequency. So with different size black bits on the disc, we get different frequency effects, and so our eyes are stimulated to ‘see’ different colours.

Well, that’s what the theory says. Some time in the future, a careful and critical look at it, will reveal once and for all whether and how this official explanation operates, and where it breaks down. There is probably a Nobel Prize in this for somebody, though they will need to acknowledge Gustav Fechner, and that's a hint.

The Birmingham Lunar Society

Once upon a time, they say, there was a wonderful Golden Age of scientific communication, an age when the most prominent scientists and admiring lay-people were in frequent contact, either with each other, or with each others’ works. To exist at all this age probably had to await the development of the railway, the telegraph, and machine type-setting.

I suspect this Golden Age came at the absolute height of public scientific interest and endeavour, a time when scientific creativity was pouring out all over the place, and discoveries sparked off other discoveries, almost at the speed of light. All that was required was the transmission of the original idea.

Calculating what destroyed the Golden Age is harder: it might be sufficient to blame television, but the era probably died earlier than that. Maybe there never was any Golden Age of science communication at all. One thing is certain, though: there was a definite Dark Ages for scientific communication, and they died out around 1800, when scientific journals were first published, including the journal which nearly robbed Alessandro Volta of his rightful credit.

If you were a scientist in provincial England in the late 1700s, or worse yet, in colonial Australia, tidings of new discoveries were an unconscionably long time coming, and much of the news came only in the form of private mail. This helps to explain why so many scientists banded together to share their news, but what I find harder to explain is why a few of these groups were so hugely successful. Groups like the Lunar Society of Birmingham, for example.

The ‘Lunatics’ got their name from their solution to the risks of travelling the dangerously rutted roads around Birmingham to get to their meetings. It was unsafe to travel those roads in the dark of a moonless night, so they would meet on the night of the full moon. The real problem with Birmingham was that it might have been a good place for building a factory, but it was the most dreadful starting place for a trip to London.

It wasn’t much better for getting to Edinburgh from either, the city where so many of the members had learned their science. They might as well have been in the colonies! For any sort of intellectual stimulation, they and their friends had to rely on what came to hand in their home town, or near to it.

They were a tightly interlinked and brilliant little group, and the Royal Society in London had nothing on them. The Royal Society’s members were a bunch of dullards and dilettantes by comparison. Upper Class twits, Tories, that sort of thing, nothing like the Birmingham mob at all.

And that brings us to one of the problems with the Birmingham Lunatics: they were seen as a mob of radicals, people who felt American and French Revolutions were Good Things and said so, which wasn’t a good idea, for the spirit of a former-day Senator McCarthy was alive and well in eighteenth century England.

At one point, the mob even burned down Priestley’s house to show what they thought of him. If ‘Congreves’ (the matches, that is, named because, like the incendiary rockets of Sir William Congreve, they set fire to things) had been invented back then, they might have got Joseph Priestley as well, but they had to send off for ‘some fire’, and Priestley made his escape. Recall, though, that while the members called themselves ‘Lunatics’, it was a real lunatic, Farmer George, King of England, who tried to get the Royal Society to reverse its stand on lightning rods, simply to contradict the American rebel, Benjamin Franklin.

You will find this story elsewhere. To its credit, the Royal Society refused the King’s demand, but Farmer George would never have tried the same stunt on the Lunar Society of Birmingham. After all, one of their corresponding members was that same villainous Ben Franklin, and one of the Society’s sources of inspiration (some call him a founder), William Small, had been the teacher of Thomas Jefferson in America, and had now come to Britain.

The other founders included a country doctor, Erasmus Darwin, who is fairly well-known as grandfather to Charles Darwin, but Erasmus was quite an intellectual giant in his own right. As we have seen, long before Charles got into the evolution business, Erasmus had proposed a Lamarckian sort of evolution, beating Jean-Baptiste de Lamarck to the idea by a number of years.

Charles’ other grandfather, Josiah Wedgwood was a member as well. So was William Withering, who discovered that the foxglove plant contained a steroid substance which we call digitalis, and use for heart disease.

It didn’t take long for other members to come rolling up, and the effectiveness of such a society soon became obvious. This was a time of breakthroughs and new ideas, a time for rapid development. It was also a time of simple apparatus to measure the extents of simple principles, so almost any participant could experiment further.

As I mentioned, they were mostly trained at that cradle of scientific education, the University of Edinburgh, and many of them were involved in manufacturing, so new problems arose quite frequently, nice knotty problems for the others to tackle.

But what would it take to establish a similar Golden Age of science and science communication and application today? Was there a magical formula, or was it just good fortune that so many people came together and sparked off each other? Was it because they were elitist, or only attracted an elite? As newsgroups, fora and email lists develop and mature on the Internet, will they begin to fill that role?

Only time can tell — but I think the email list is already dying away.

Water wheels

Left, an overshot waterwheel in Poland, right, an undershot waterwheel, Den Gamle By, Denmark.

The water wheel was the start of a whole, and rather serious set of simple machines, devices that used power. The water wheel gave more power more cheaply (once a mill was built), it helped feed a lot of people, but more importantly, it set people to thinking about the mechanical works of a mill.

Water mills probably started in Greece, some time before 80 BCE, because that was when a Greek poet called Antipater of Thessalonika mentioned young women being relieved of the work of operating a hand-mill, now water had taken over the hard work.

Soon, waterwheels began to spread into other areas where there was plenty of rainfall, all year round, places where slaves were hard to get. It was the first labour-saving device. The water wheel may have got its start, though, as a device used to raise water from a river to fields, high above the river bank, and that requires some explanation.

Today, if a moored paddle steamer sits in a current and the paddle wheel is disconnected from the engine, the wheel will turn. Something similar would happen to a water-raising wheel (usually powered by humans, working it as a treadmeill) when it sits in the current of the river. This is the simplest of water wheels, the undershot wheel, where water passes under the wheel, making it turn.

Then there is the more efficient overshot wheel where water drops onto the front side of the wheel and carries the front of the wheel down. Both the undershot and overshot wheel need at least two gear wheels to transfer the rotation through 90°.

Waterwheels were not as good at gathering energy as the efficient turbines in modern hydroelectric stations. Still, when there were no animals to feed, all you had to do was have a big enough mill, and enough fall to get enough energy from it.

This was a special problem with overshot wheels, where mill owners needed to take water out of the river, somewhere upstream, and run it through a channel that wound around the contours on a gentler gradient than the river bed.

Sometimes this would be helped out by a weir or a dam that raised the water level, but if there were several mills along a river, they would sooner or later start to interfere with each other. The Domesday Book was completed in England in 1086. This inventory of what the Normans had taken when they invaded England listed 5624 waterwheels in England, about one for every 50 households.

Bread was a staple food, and so mills were needed, all over the country. The Domesday book also records two mills in Somerset which paid their rent, before 1086, with blooms of iron, which makes it fairly clear that those mills were being used to forge iron. 

Cistercian abbeys in 12^th century France commonly used waterwheel power to grind grain, to sieve flour, to full cloth and to tan leather.

At other times, water power crushed olives and operated bellows for forges and the fires used to brew beer. A paper mill powered by water existed in Spain in 1238, and seven such mills were to be found in Italy by 1268. Paper was made by pounding linen, either by hand, or by foot, or by water power. Guess which one was more popular with the workers?

Water power was easier. when you could get it. In France, a tributary of the Seine River, the Robec, had two mills in the 10^th century, four in the 11^th, ten in the 13^th and twelve at the start of the 14^th century. Before long, the medieval world was running out of space for mills, and disputes began to break out as dams and weirs grew higher, backing water up to the next dam upstream, reducing the fall at the upper dam.

At peak times, the Garonne River at Toulouse in France has a flow of up to 9000 tons of water a second, about a fifth of a cubic mile or 780 megalitres of water a day. Damming something like that meant driving thousands of 6-metre oak logs into the river bed in two rows and then filling the gap between with rocks, gravel, oil and wood to make a water-tight wall.

There were three Garonne dams: Château-Narbonnais, La Daurade and Le Bazacle, and between 1278 and 1408, various acts of dam-raising led to lawsuits and orders to demolish dam extensions and pay damages that were mostly ignored. By 1408, the La Daurade company had ceased to exist, its last shares snapped up by the shareholders of Le Bazacle, ending the dispute.

In later times, windmills took over part of the task, simply because they could be located where there was no reliable flow of water, but windmills were not as powerful. The early Industrial Revolution grew up near rivers, but with time, the waterwheels were replaced by steam engines. The world was ready for them, because the mechanical skills needed to build and fix mills driven by water and wind were very much the skills needed to make early steam engines.

Paradoxes

In logic, a paradox is a contradictory or implausible conclusion which seems to follow by valid argument from true premises. Aside from Zeno’s paradox, and Maxwell’s demon, proposed by James Clerk Maxwell, Erwin Schrödinger’s cat and Olber’s paradox, all dealt with in other places, the most interesting paradoxes are all logical challenges.

The paradox of the Spanish barber concerns a barber who is asked how business is doing. “Not badly,” says the barber. “I shave everybody in the village who does not shave himself.” The problem: who shaves the barber?

Logicians with a smattering of Greek will
share my delight in this Athenian street sign.

Epimenides of Crete is credited with one of the simplest paradoxes: “All Cretans are liars”, meaning by implication that this statement (made by a Cretan) was necessarily untrue. But if it is untrue, then not all statements made by Cretans are liars, and so on.

There is a more complex form of this paradox, consisting of two sentences. “The next sentence is false” and “The previous sentence is true”. Or "there are two erors in this sentence".

The dilemma of the crocodile: a crocodile seizes a child, but promises to let the child go, if the father guesses correctly whether he will do so or not. If the father offers as his guess the opinion that the crocodile will not return the child, what should an honest crocodile do?

A lawyer is trained by a teacher who says “you must pay me for your tuition after you win your first case”. Several years go by, during which time the teacher gets annoyed because the lawyer has yet to win a case, and sues the lawyer, saying “If I win my case, you must pay me, but if I lose, you have won your first case and must pay me.”

“Not so fast”, says the young lawyer. “If I lose the case, I have yet to win a case and need not pay you. But if I win, then by the court’s judgement, I do not have to pay you.” Does the lawyer have to pay?

Some words describe themselves, so “short” is a short word, but “long” is not a long word, “English” is an English word, but “German” is not a German word, and so on. We call words which describe themselves as autological, while words which do not describe themselves are called heterological.

But what about the word “heterological” — does it describe itself or not? If “heterological” is heterological, then it describes itself, and so it is autological. But if the word is autological, then that means it is a word that does not describe itself … or something.

Paradoxes can be useful ways of extending our knowledge, or at least ways of finding the right questions to ask. Fermi’s conjecture, also known as Fermi’s paradox, was offered by Enrico Fermi. In simple terms, it asks why, if the Galaxy is filled with intelligent and technological civilizations, haven’t they come to us yet?

There are several possible answers to this question (good taste on the ETs’ part, distance, or a recognition that contact with a superior civilisation is damaging to the more primitive one), but as we only have the vaguest idea what the right conditions for life and intelligence in our Galaxy, this paradox probably has no ready answer.

Paradoxes are also useful as a form of the mathematical proof called reductio ad absurdum, an argument which comes to an absurd or contradictory conclusion, hence showing that an initial assumption must be wrong. This shows up well in the so-called grandfather paradox of relativity. Imagine that your grandfather has just built a time machine, which you then use to go back in time, to give your grandfather the plans, so he can later build the time machine.

You reach him at a time where he has yet to meet your grandmother, he refuses to believe you, and in an argument, he steps out into a road, and is run over and killed by a passing car. He has now died before he met your grandmother, so you do not exist, since one of your parents does not exist, and the time machine does not exist, so you cannot be there in any case.

This is one of the arguments physicists use to support their belief in the causality principle. Others say the fact that we have never met time travellers proves that there will never be any, but this is probably one of the most useless of paradox types.

Let's get back to more practical stuff!

Zeno's paradox

Zeno of Elea was a philosopher with a wicked imagination, and he made up a puzzle which can be simply described like this. Suppose you have a hundred-metre race between a man called Achilles and a tortoise. Assume that Achilles runs ten times as fast as the tortoise, and that he gives the tortoise a ten-metre ‘start’.

Zeno said that Achilles can never catch the tortoise for while the man runs the first hundred metres, the tortoise waddles ten metres, and is still ahead. The man runs the extra ten metres, but the tortoise gains an extra metre.

As the man sprints desperately across that metre, the tortoise sneaks a further tenth of a metre, and while Achilles is lunging across that tenth of a metre, the tortoise drifts another centimetre, and so the human can never catch the tortoise. The same argument can be used to show that a thrown spear can never reach its target!

Zeno’s aim was to prove that something we can see happening is impossible, from which it follows that since we can see the impossible happening, our senses must be faulty. In other words, his paradoxes were designed to make people think. Later, Aristotle would argue against Zeno’s ideas, and Zeno’s assumption that space and time were infinitely divisible would make Democritus try to resolve the problem by suggesting that matter was not infinitely divisible, finally coming up with the idea of atoms—and all because Zeno believed the senses could not be trusted —because even though Zeno had proved that Achilles could never catch the tortoise, we know that in real life, he can!

Other paradoxes can be more fun...

That is to say: to be continued

Finding iodine

There are thirty recognized isotopes of iodine, but only one of these, iodine–127, is counted among the stable isotopes, and is found in nature. Radioactive iodine-125 is routinely used in tracing problems with the thyroid gland, and another isotope, iodine-131 has been commonly used to treat overactive thyroid conditions. The “iodine” which is commonly used on small wounds is tincture of iodine, a solution of potassium iodide and iodine in ethanol.

Iodine is element number 53 in the periodic table, atomic weight 126.90. This element was first isolated in 1811 by Bernard Courtois (1777 - 1838). 

Like the Germans in the First World war, the French found themselves restricted by a British naval blockade which stopped them accessing American sources of potash during the Napoleonic wars.  The potassium carbonate was used to make potassium nitrate for French gunpowder, but the seaweed also contained a variety of other chemicals, one of which was an iodide.

In treating seaweed ash with acid to get rid of sulfur compounds, Courtois noticed a purple vapour, which condensed to make crystals of iodine. He later passed this information on to Sir Humphry Davy, who proposed the name “iodine”, from the Greek word for the colour violet, iodes. The credit for suggesting the name is sometimes given to Joseph Gay-Lussac, but this is incorrect.

As mentioned above, iodine is needed in the production of thyroxin, and a deficiency in dietary iodine leads to goitre, so that foods (especially table salt and bread) in many parts of the world now have traces of iodine added, although this is unnecessary in areas where seafood is available.

Part of the hormone ‘picture’ was already there in 1905, because a number of diseases were linked to disorders in particular glands: goiter and cretinism were associated with an enlarged thyroid gland, but this was rightly regarded as a deficiency disease caused by a lack of iodine. Many folk remedies used iodised salts or sea foods rich in iodine, even before we knew iodine existed (the element was detected in 1813). Its role in preventing goitre became more obvious after Eugen Baumann (1849–1896) showed in 1896 that iodine was only concentrated in the thyroid gland.

Curiously, Courtois also discovered that major fascination for undergraduates of a certain kind, nitrogen triiodide, which forms tremendously unstable crystals that will even explode when hot water falls on them.

I have no intention of revealing how I discovered this fact, as I conclude now that I had a lucky escape: Pierre Dulong  lost three fingers and an eye investigating this substance — which may explain why, when he was formulating what is now called “Dulong and Petit’s Law”, he chickened out, and did not investigate tellurium, fraudulently manufacturing the data for that and several other elements.

The reason is probably that when you handle tellurium, it is absorbed, and you get “tellurium breath “. Not to mince words, you stink of stale garlic for months after working with tellurium compounds. Dulong  either feared that, or perhaps he was attached to his remaining fingers and wished to stay that way.

Everything (other than Dulong's fingers, perhaps) is connected.

The art of estimation

Like the previous entry, this comes from my (now) out-of-print volume, The Speed of Nearly Everything.  I may get around to releasing it as an e-book, if enough people think it's a good idea.

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To a physicist, the notion of an immortal rabbit is quite acceptable. As a boy, my English teacher encouraged me to psychoanalyse Macbeth, even though I objected that we shouldn’t, since Freud hadn’t been invented when Shakespeare was writing. Ever a historically-minded cuss, I argued that it would be more relevant to look at the political situation in London, with a Scot sitting on the throne. Exasperated, he exhorted the class to engage in the willing suspension of disbelief.

And well he might, if he wanted us to accept some of the artifices and conceits of coincidence found in the 19th century novel, but we scientific types were subjected to much hardier fictional nonsense than that.

We routinely solved problems that involve a steel girder of negligible mass, suspended at its centre of gravity by a silken thread, and before we were too far advanced, we heard our first physics joke. It was about the three scientists who were trying to pick the winner of Australia’s premier horse race, the Melbourne Cup, which is held each November.

The mathematician gathers a wealth of data on weather, rainfall, wind, pollen counts and other possible influences, and three years in a row, fails dismally to pick a winner. At the end of those three years, the geneticist has just finished drafting a plan for a breeding program that should, in five generations, produce a winner, but the physicist has got it right, three times in a row.

The others ask him how he did it. He reaches into his pocket and produces an envelope which he turns over. Then he draws a circle on it. “Consider,” he says, “a spherical horse running in a vacuum…”

In fact a spherical cow or spherical horse can be a useful starting point to explore ideas, to get a first approximation that can be extended. Take the yarn about the bumblebee that was shown not to be able to fly: this is usually trotted out as evidence that scientists are thick, but there is a little more to it than that. In 1934, a French entomologist called Antoine Magnan tried to apply an engineer’s equation to bumblebees, and showed that according to that equation, designed for aircraft that did not flap its wings, the bee could not generate enough lift.

A bumblebee, coming in to land (or fall?)

There is a great deal of folklore wrapped around this “event” and who actually was involved, but it appears that the equation was worked out by André Saint-Lagué, and while the incident is often dressed up as “a scientist proving that bumblebees can’t fly”, all that was really shown was that the equation was inadequate to describe the flight of the bumblebee.

Magnan had shown that you can’t apply that particular equation to bumblebees, rather than proving that spherical bumblebees can’t fly, even if real ones, flapping their wings at 130 times a second, move happily along at 3 metres/sec, 11 km/hr or 7 mph. Like Zeno’s paradox (which will be in the next blog entry), Magnan’s calculation merely showed that there was a faulty assumption in there somewhere. The mathematical model was flawed.

When we escaped from the English classroom to the lab, we learned of marvels that could be done with simple apparatus. The muzzle velocity of a bullet could be measured with nothing more than a block of wood, a piece of string, a protractor and a measuring tape.

Our physics teacher, equally as at home with fiction as our English teacher, explained how, in the days of gunpowder and muzzle-loading firearms, slight variations in the ingredients, their amounts and proportions, could make a lot of difference. The most obvious measure was the speed at which a cannon ball or musket ball left the barrel of the gun, or in physics-speak, the muzzle velocity.

The idea was quite simple. You suspend a large block of wood and fire a bullet at it from close range. The bullet lodges in the block, and the energy of the bullet is transferred to the block, which swings like a pendulum. Then one simply has to measure the swing angle and calculate the height the block reaches.

This device even has a name: it is called the ballistic pendulum, and it has been around since the 1742, when it was invented by Benjamin Robins. From the swing, or so we were told, it is a fairly elementary calculation to estimate the energy and hence the velocity of the bullet. Unfortunately, this explanation ignores the 800-pound spherical horse which is rolling around the room.

Some of the energy goes into deforming the bullet and the wood, some is wasted as friction, and to do any calculations, we have to assume that the bullet stops instantaneously (which is as likely as a girder with negligible mass). Of course, if you are trying simply to compare different grades of gunpowder, rather than measuring the muzzle velocities, the losses will be similar in each case, and can be ignored. Whichever powder produces the biggest swing is the best, if everything else is kept constant — and in fairy physics, that always applies.

Robins was born to Quaker parents, but as a mathematician, he tried to make gunnery a science. Along the way, his ballistic pendulum probably showed that Indian saltpetre made the best gunpowder. He died in India in 1751, supervising the construction of forts, and a few years later, the British drove the French out of India, which let them have all that excellent saltpetre for their own use.

Curiously, the pursuit of novel sources for saltpetre during the Napoleonic wars led a French chemist, Bernard Courtois, to discover iodine, but that's another story...the next story, in fact.

That speedy botfly

I revived this excerpt from my out-of-print book The Speed of Nearly Everything when the image on the right turned up in my Facebook feed, coming from Science Humor.

In case you don't look out for details, the hole that the fly was caught in (or poked into) was actually made by a projectile coming from the other side, so the accompanying question about the fly's speed is, at the very least, just a bit misleading, but somebody is going to cite a legend.

When you enquire about fast animals, more often than not, you will read that the fastest animal of all is the deer botfly, which is credited with an amazing 1287 km/hr, though if you convert this to miles per hour, it comes out as a round 800 mph, a figure that smells a little bit like fudged science—and rightly so.

The story begins with a 1927 article by an entomologist called Charles Henry Tyler Townsend, who reported a speed like this in the Journal of the New York Entomological Society. He actually claimed that the fly was clipping along at 400 yards per second, which works out at 818 mph or 1316 km/hr in metric units. As we will see shortly, any preciseness in the conversion is hardly justified.

Townsend reasoned that these flies passed in a blur, and so must have been travelling very fast. On that scientific basis and no other, he credited them with a nice round 400 yards/second.

That story should have been questioned right away, but people wrote it down, passed it on, quoted it uncritically, and never stopped to wonder what would happen if flies were tearing around at supersonic speeds.

As we will see later (next entry in this blog), some people would stop to prove that the bumblebee could not fly, but nobody stopped to consider and demonstrate the impossibility of the botfly claim until 1938, when Irving Langmuir, a Nobel laureate in chemistry, having given it some thought, tested the assumptions.

First, the air pressure on the fly at that speed would be more than half an atmosphere, surely enough to crush it. The energy needed to maintain the flight would be 370 watts, half a horsepower, which would be quite an ask. Aside from anything else, the botfly would use up its own weight in fuel every second, so it would need to be a voracious feeder.

Next, Langmuir had been hit by these flies, and while it hurt, that weight of fly at 1300 km/hr would have left a significant hole, rather like that of a soft bullet, and the fly would have been mashed inside the wound. Instead, the fly bounced off.

Langmuir mocked up a model of the botfly, using solder to make a pellet that was 1 cm long and 0.5 cm wide. He attached this to a string, and whirled it around his head, timing it so he could work out its velocity. He reported that at 13 mph it was a blur, at 26 mph it was barely visible, at 43 mph an observer could not tell which way it was going, and at 64 mph, it was completely invisible.

He concluded that the blur Townsend had seen came from a fly travelling at 25 mph (40 km/hr). His results were published in Science and reported in Time magazine, but legends are tough things, even when they are debunked by Nobel Prize winners. So even today, the same old values keep emerging from the woodwork.

By a curious chance, Langmuir’s name crept into the record books in an entirely different way in 2006 when plasma physicists used a specially designed holographic-strobe camera to capture pictures of matter waves that were travelling at 99.997% of the speed of light.

Known as Langmuir waves, they are generated by intense laser pulses, and may one day lead to “tabletop” versions of high-energy particle accelerators. One step along the way was taking photographs of the waves to see if they behaved the way scientists thought they would. They did, which is more than we can say about the botfly's behaviour.

What is a day?

When does the day start? The ancient Greeks said the day began at sunrise, and ended at the next sunrise. The Babylonians held that the day began and ended at sunset, while up until 1925,

astronomers worked on a “day” which began and ended at noon, and so did the Royal Navy in the days of Captain Cook. Now the astronomers, like us, and the ancient Egyptians, have a day which commences at midnight. Islamic tradition has a day which begins at sunset.

By definition, noon is when the Sun is at its highest point in the sky, so it is always noon somewhere in the world, with a noon zone sweeping along through a degree of longitude every four minutes. Logically, you should be setting your clock forward or back by a minute for each 15-20 kilometres that you go east or west!

This would be far too confusing, and to make life easier, we have split the world into time zones, usually (but not always) 15 degrees across, where everybody keeps the same “official time”. If you are trying to set up a very accurate sundial, you need to make allowance for your position east or west of the true time in your zone.

Some points to ponder: Clockwise is a word used to describe the direction of the shadow of a northern hemisphere sundial. What way does the shadow travel in the southern hemisphere?

If you stop and think about it for a moment, you may be able to deduce where the word “dial” comes from, especially if you know anything about the Latin word dies. If you lack this knowledge, look up “dial” in a good dictionary, and find out where it comes from. From this knowledge, can you say what the most appropriate use of the word “dial” is?

We probably had the idea of the two ways, even before clocks. Widdershins is an old word meaning counter-clockwise. The equally old word which means “clockwise” is deasil.

Somewhere along the way, something happened to humans that made them start using art, that made them start communicating with each other, and generally showing signs of being human, rather than hominid. Could it have been the discovery of time which caused these changes?

It is probably time to look at the things we first used for time-keeping and calendars, the stuff that is out there, beyond our atmosphere, the stuff that even a century ago, people knew was forever unreachable — and rather hard to see in any case.

The barman says, “We don’t serve time travellers in here.”

A time traveller walks into a bar.

Brain size

I will studiously not comment on this next one, much as I would like to:

Bischoff, one of the leading anatomists of Europe, thrived some 70 years ago. He carefully measured brain weights, and after many years’ accumulation of much data he observed that the average weight of a man’s brain was 1350 grams, that of a woman only 1250 grams. This at once, he argued, was infallible proof of the mental superiority of men over women. Throughout his life, he defended this hypothesis with the conviction of a zealot. Being the true scientist, he specified in his will that his own brain be added to his impressive collection. The post-mortem examination elicited the interesting fact that his own brain weighed only 1245 grams.
— Scientific American, March 1992, 8, quoting from an unidentified and untraceable source in Scientific American, March 1942.

SMILE!

Corang River

Australia may be easily divided into two parts: the city and the bush.  Almost all of us live in what is loosely called ‘the city’ — while a smaller number live in ‘the bush’.  Any rural area, any wild or wilderness area, any quiet patch, even in the middle of the city, is ‘bush’.  There are patches of bush, just a kilometre from the Opera House in Sydney, and many larger patches dotted around the landscape.

We have a bush mythology, all about how Australians relate to it, but most of us are wholly city-bred and raised.  Even so, many Australians gain a great benefit from the bush and from bushwalking.  Each weekend, urban Australian may be seen wandering along well-worn tracks through urban bush, while others, rather better equipped, can be found far out in the wilderness of the Watagan ranges, the Blue Mountains, the Budawang Ranges, or some other favoured lonely place.  For my family, the preferred solution is to drive for four hours in the dawn to get to the Budawangs.

The Budawang basement rock was laid down in Devonian times, back 350 million years ago, when fishes ruled the earth, along with their cousins the early amphibians.  We can only guess at the rocks' history after that, but they must have been deeply buried and heated, for they are all now low-grade metamorphics, and that only happens with deep burial and light baking in the depths of the earth.

After baking and squeezing, the rocks were twisted and folded, then slowly revealed again.  The tops of the folds were carved off, leaving a series of tilted quartzite slabs.  These tough ribs of stone were shaped in the days of the early dinosaurs, which must have wandered over their surface, leaving not a trace.  By now, the rocks were 150 million years old, and due for burial once more.

They were covered over in a huge flood of mud and boulders that created massive conglomerates.  Some of the pebbles in this conglomerate are more than a metre across, and the beds stretch for kilometres.  But after the conglomerate had filled in around the old hills of Devonian rock, gentler conditions prevailed.  Sand was laid down over the top, through the Permian, then more Triassic sediments came on top of that.  Finally, the process reversed itself, and the Devonian rocks were brought back to the surface as the covering slowly weathered and eroded away.

The Devonian rocks are survivors.  They took all the world could throw at them before, and now they do so again.  When a river comes up against the uptilted ribs of tough metamorphic rock, the water is forced to fight to find a way through.  Where they can, the rocks dam up the water, creating swamps where the usual harsh dry conditions are replaced by harsh soggy conditions.  Where the river is strong enough, it carves down until it meets the truly immovable rocks: then it backs up to form a lagoon.

A little up the hill from such a place, we find the Permian conglomerate sitting uneasily on the tough Devonian ribs, making what the geologists call an unconformity, where one hand, spread on the cliff face, can span more than a hundred million years of history.  The base of the conglomerate falls apart easily, creating caves and rock shelters where campers can shelter when it rains.

The Budawang Ranges are full of places like this, but for my money, the best place to go in the whole area is the Corang River, at a place where the river backs up against tough tilted Devonian rocks, delayed for a couple of hundred metres.  This makes a pool which is refreshingly chill, even on the hottest day, where mists will rise off the river in the early morning, as the first small birds skim across, looking for insects to eat.

Around the edges of the lagoon, kangaroos thump around, looking for food at night.  It is not a place for those with a heightened imagination.  Wombats charge along their favourite tracks like small tanks, mopokes make dismal sounds in the dark, and possums scream at each other.  This is a good place to bring new chums, people who are marvellous victims when it comes to tall tales.  Here you can regale them with drop-bears, hoop snakes, fanged frogs, bush alligators, wombahs and more.

Out in the wilderness, such tales are believable.  Getting there means a drive of four hours, then a walk for three hours, so we usually camp overnight at the trail head, or drive down in the pre-dawn darkness on deserted roads.  Then we hike in, set up our tents, grab some firewood, and prepare for a couple of days of relaxing, reading and swimming.

Except, that is, when my adult son decides we should go exploring.  This is wild country, but we have been coming here for many years, and we know the land marks, so we elect to do a slightly risky thing, and wander off as a pair.  Strictly, we should take three people, one to stay by any injured person, and one to get help, but this is to be little more than a gentle stroll.

Famous last words!  It has been raining in the last few months, and all the swamps are topped up, trapped behind the quartzite dam walls.  When we decide to plunge into low-lying area for a short-cut, we become well and truly bogged down.  My son, I forgot to mention, is very stubborn: he must have inherited this from his mother, for I am never anything more than unswervingly determined.

Whatever the cause, we decide to push on, rather than going back and around the swamp.  Perhaps it is the range of unusual spiders you can find deep in a swamp: perhaps it is the hope of seeing some of the rarer sundews, small insectivorous plants that live in swamps like these, but we force our way, deeper and deeper, following the trails made by the wombats.  There is no plant alive that can withstand a wombat, which is good when we want a clear track, but wombats are very agile about jumping from tussock to tussock, which is not so good.

Cursing and grunting, we leap, slip and slide our way along.  We have done this sort of thing before, so we are still comparatively dry, but it is all very tiring.  We look around for somewhere to sit, but there is no dry dry place big enough or flat enough to sit on.

I recount the old paradoxical definition of an infinite regress, where a band of soldiers get tired in a swamp.  They form a circle, and each sits on the knees of the one behind, until they are rested.  Arguing the logic of this blunts our discomfort for a while as we slog along.  That and a complex disagreement about the differences between marshes, bogs, fens, swamps, swards and water meadows, which helps to keep our minds active as we go.

All good things come to an end, but so do bad things.  Suddenly, what I still insist is swamp, rises above the water table.  We stop, just at the edge of the mud, looking at the beautiful dry land in front of us.  ‘I've definitely learned one thing,’ he tells me.  Foolishly, I ask him what it was.

‘The fen is muddier than the sward’, he tells me.  Something inside me snaps.  One swift push and he learns the Zen lesson that one person cannot make an infinite regress.  Not in a swamp, anyhow.

Macedonio Melloni, a forgotten genius

This is just a filler to say I aten't dead yet. I'm just fairly busy.

Macedonio Melloni (1798 - 1854) is little-known, which is why this is a brief account. Still, what there is seems quite interesting, and it sets the scene for several other stories, so I will share it with you.

First, some background. William Herschel did many things in astronomy. Among other things, he took the temperature of different parts of the spectrum, and found that the hottest part of the Sun’s spectrum was beyond the visible range. Using a thermometer, he discovered the infrared part of the spectrum.

Now back to Melloni: if you heat a junction between two different metals, you generate a very small current. In order to be able to measure the current, you need to multiply it by linking a number of these junctions together, to make a battery of them, like the pile of cell units that Alessandro Volta made. This is why we call Melloni’s invention a thermopile.

Source: https://muxindia.wordpress.com/2014/11/06/passive-infrared-sensor-pir-sensor/

As well, Melloni developed ways of concentrating the heat from distant sources, and he found out how to use rock salt to make lenses to focus the heat rays, in the same way we use glass lenses to focus light rays. He established that the infrared rays were in every way like light: they could be refracted, reflected, polarised and made to interfere with each other, exactly like light.

Melloni really deserves to be better known, for while Herschel’s discovery of the infrared is a commonplace, few people realise that Melloni’s investigations laid a practical framework within which James Clerk Maxwell could propose the existence of a continuous electromagnetic spectrum.

Everything in science is connected, which is why we can usually spot fraudulent science at a glance. It doesn't connect with all the other bits...

Making predictions

Yes, it's been a bigger time gap than most, because in Covid-19 time, I have been clearing my back burner of partly done books. More of the current time-stealer in the near future.

* * * * * * * * * * * * * * * * * * * * * * *

Out there, somewhere, there is a discovery, an observation, a measurement that does not quite fit the present model for something. There is an idea, a notion, a hunch that will some day become a great discovery of science. I have no idea how long it will take for us to realise that it is both a discovery and a great discovery, but it will occur to us one day that we ought to have seen it coming.

I have no intention of trying to predict what it might be, because as Niels Bohr used to say, making predictions is problematical, especially about the future. Bohr always said he got it from Robert Storm Petersen, who apparently got it from somebody else.

Some people out there will already have predicted it: in 1906, rocket scientist Robert Goddard was thinking of the energy in a gram of radium and wondering if it could be used to power a rocket. In 1913, H. G. Wells was describing the dropping of an atom bomb, though he thought the target would be Berlin. Nobody paid attention.

Most predictions miss the mark. For the past hundred years, every depiction of the future has offered us food pills, flying cars and easy access to space, and none of those has happened.

Then again, remember Arthur C. Clarke’s First Law: When a distinguished but elderly scientist states that something is possible, he is almost certainly right. When he states that something is impossible, he is very probably wrong.

They say Thomas Watson, chairman of IBM, said in 1943: “I think there is a world market for maybe five computers.”

who could have guessed that two World War II developments, jet engines and computers, would lead to us booking our overseas holidays online in the 21st century?

When scientists get old, they often become fixed in their ways. They make dogmatic statements, and expect everybody to accept what they say, but more often than not, they turn out to be disastrously wrong. Take these examples:

• In 1797, farmers in America rejected a new cast-iron plough, saying it would stimulate weeds and poison the crops.

• The patent for the radio valve (the thermionic valve, the thing we used before the invention of the transistor) was not renewed when it ran out in 1907. Nobody could find a use for the Edison effect until a few years later.

• During World War II (when the first atom bombs were exploded), an admiral reassured the American vice-president: “Atomic bombs won’t go off, and I speak as an explosives expert.” (Even though H. G. Wells had predicted atomic bombs in his novel The World Set Free, as early as 1913!)

• A few years earlier, Ernest Rutherford, New Zealand’s greatest scientist, and one of the greatest scientists of this century, said “The energy produced by breaking down the atom is a poor kind of a thing. Anyone who expects a source of power from transformation of these atoms is talking moonshine.”

• Twelve years before the first moon landing, and just after the first Russian satellite was launched, the Astronomer Royal of Great Britain commented that generations would pass before people landed on the moon, and even if they did, there was little chance they would ever get back to earth. (In fairness, the Astronomer Royal was being political, as funds were being diverted into rocketry that he thought should have been going to astronomy.)

The moral of this list of disasters: keep an open mind, because things may change sooner than you think. And if you have to make a prediction, try to make sure nobody writes it down! But if you want to see science flourish, don’t let such fears stop you from making or drawing inferences.

Pneumatic transports of delight

No, this is not a reference to Brave New World, but to something that turned up in my FB feed this morning, concerning ways of getting cash away from the sticky fingers of shop assistants.

Some ran on wires, others ran through tubes, and as a small boy, these things made me aware that sometimes, rarely, Heath Robinson gadgets might work.

At the age of 8, I tried making Meccano versions of the run-on-wires models, without success. I knew about the pneumatic versions, but the Meccano sets had inconvenient holes, so I gave up.

In what follows, the pics are more detailed than they appear here: click on them to see them in all their glory.

As it happens, I wrote about such things in my Not Your Usual Clever Ideas, available on Kindle (it includes shoe guns, sharkproof suits and pile drivers powered by gunpowder and the 'rowing bike' seen on the left), but here's the detail on the stranger ways that things were moved by air pressure.

In 1868, all eyes were upon the new device, the pneumatic telegraph, which was going to revolutionise the world by allowing one to send actual documents hurtling to their destination. This was the pneumatic telegraph, which was all the rage in the 1860s.

The Pneumatic Dispatch Company in London declared its hand in 1861, when they set up a quarter of a mile (400 metres) of test tubing at Battersea, near the Victoria railway bridge. This included irregular curves and gradients to show that the terrain would be no obstacle to a working system. Carriages were introduced and air was drawn out in front of them to give a pressure differential of "seven to eleven inches of water".

Atmospheric pressure is taken today as 100 kilopascals, and it supports about 400 inches of water, so we are talking here of a pressure in the 2-3 kilopascal range, about the same difference as that between the top and bottom of a 300-metre building, so not that great. Still, this gentle difference was enough to accelerate the rail cars to 25 mph (40 km/hr), and the individual cast iron tubes were 9 feet (2.7 metres) long and about 850 mm high.

There was no seal, which would have caused frictional loss, so there was a small amount of "windage", and most importantly, Parliament had granted them the power to "open the streets", to lay the tubes that would no doubt soon link all of the post offices in the world's greatest metropolis.

By 1862, the company was meeting to vote on an increase in capital to fund extended works and to obtain new machinery, and a further £50 000 was subscribed, though several members opposed the motion, one of them declaring the system a financial failure which ought to abandoned. The details of the company are not very clear, but a 1929 enquiry mentioned "the Post Office Tunnel", constructed by the company in 1866, and found to be less than air-tight. The Post Office bought it in 1921, and the tunnel ended its days as a conduit for telephone cables.

By 1863, 110 mails passed through the pneumatic despatch tube from the station to the district post-office during each day, and, said a report in Scientific American, the occasional human was allowed to ride in the carts.

For some years, the system was used to carry parcels from the railway to the Post Office. In the USA, though, there were far more ambitious plans. By 1867, these extended to mail sorting systems that would carry letters in scurrying carts, hither and thither, under the streets of American cities.

That was nothing, though, to the grand plans of the Waterloos and Whitehall Pneumatic Railway Company which planned to send parcels under the Thames in a giant tube, 12 feet 9 inches (3.9 metres) in diameter. This would connect the various lines which were by then operating on either side of the river. The illustration shows sections of the tube being prepared on dry land before being lowered into the river.

The tube systems operated successfully in a few cities, but they had their greatest penetration in stores, where trusted cashiers, locked in cages, received cash and dockets by pneumatic tube, and sent receipts and change back, again by tube, to be handed to the customer.

If you want the original images, here are the sources.

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[1] Scientific American 5 October 1861, 209.

[2] Scientific American 5 January18 67, 1.

[3] Scientific American 16 March 1867, 165.  6

Magic, medicine and technology

This morning, I saw a picture of a truck on which the owner had painted "Jesus is my vaccine". I immediately began to write a piece that referenced this quotation:

Any sufficiently advanced technology is indistinguishable from magic.

— Clarke’s Third Law, Arthur C. Clarke, Profiles of the Future, 1973.

When I went to dig that out of my files, I recalled that I had written about this same matter at the start of my e-book, Not Your Usual Treatments, so I just plundered that. You don't need to read the book (though you'll never be the same if you do!). Here are the salient bits.

I use four different computing devices at different times, and for different purposes. Each uses a different sig file for emails, and right now, the message below appears under emails sent from my tablet:

Away from my desk, and using something with technology sufficiently advanced to pass for magic, given the right lighting. The fully indistinguishable bit will come with the next upgrade.

The sort of people I work and play with recognise that as a reference to Clarke’s Third Law. They probably also know the unofficial corollary: “Any technology distinguishable from magic is insufficiently advanced.”

My friends live in the world of logic, science and technology. They know what I know: that when we find “magic” being presented as real, rather than as entertainment, we’re in the presence of ignorance, or fraud, or both. Nearby, we will find charlatans and/or the gullible.

I first encountered “magic” when I was about 13. I had a severe rope burn on my leg, and my uncle had been dabbling with a new “religion”. He treated the burn using a neat trick taught to adherents of this movement. His sons, younger than me, mispronounced the trick as “touch and fix”.

Like most conjuring tricks, it was simple. He repeatedly touched my skin near the wound, asking each time if I could feel it, and in the end, according to my mother who watched the process, he was scraping his fingernail down the wound, quite hard — and I was reporting no pain.

Basically, this was desensitisation, a matter of overloading the pain receptors so they stopped sending strong pain signals. I was a scientifically-inclined child and I knew, even then, about desensitisation and deception. On the other hand, my mother, a life-long gullible, was impressed. Even though this was the first rope burn she had ever seen, she told all and sundry that no rope burn in history had ever recovered so quickly.

She was just about ready to sign us all up to join the group, which would have been a salutary experience for them, having me inside the tent and still aiming inwards, but my uncle realised they were dangerous, dropped them, and warned her off.

Desensitisation is easily explained by science. It is simple technology, but in the wrong hands, it can easily be packaged to look like something close to magic. In the wrong hands, it can wreak havoc, much as I would have done, inside the tent.

Almost anything in the wrong hands can wreak havoc.

In Lamb to the Slaughter, Roald Dahl showed us that the frozen leg of a fluffy lamb makes a grand club for braining somebody. The poison in 200 kg of potatoes will kill anybody persuaded to eat them, and a medicinal leech in a soldier’s drinking water may attach inside his throat and choke him to death. Any book, placed in a drum of cement, and tied to the ankle of a literary critic may be used, in damp environments of sufficient depth, to improve the human gene pool.

It’s all about context and intent. Medical havoc usually comes when a person lacks any basic knowledge of a technology, culture or set of procedures. Guided by a charlatan (or being a charlatan), the ignorant person adopts or constructs a nonsensical explanation of reality, and applies it without any thought, or hesitation.

In ignorant minds, analogy sounds as good as analysis, and by a false analogy with scurvy, cancers can be blamed on dietary deficiencies. It’s an easy slide, all the way down the slippery slope after that. Some users progress to believing that one can eliminate TB by rubbing the patient’s brow with crystals. Soon, the very same treatment is credited with fixing headaches, beating sunstroke, banishing syphilis and mending varicose veins.

Filled with excitement, the converts claim that eating worms mends broken bones, that a tea made from a noxious weed stops HIV in its tracks, or that snake bite is cured by injections of meerkat urine. These people enter a frauds’ universe where, while many things are still impossible, they, the victims, don’t know it. This is not magic, they parrot — just advanced and esoteric science that the listener could never comprehend.

To be fair, some of the frauds are the victims of self-delusion, but they are still a threat to public health. In 1709, Alexander Pope wrote in An Essay on Criticism, “A little learning is a dangerous thing”, though this is usually seen and heard as “A little knowledge is a dangerous thing”.

This book is about people with little knowledge or learning, and no inclination to find out — and about people with a great deal of knowledge of deception, and a strong inclination to find money.

I originally planned to look at Australian quacks, but I soon realised that context and intent are all-important, that most “quacks” were nothing of the sort — and that strange medicine knows no borders. In the end, I realised I simply had to spread the net wider, but there is still a strong emphasis on the Australian side of this story.

One generation’s orthodox medicine is seen by the next generation as out-and-out quackery, and the only thing that has changed is the dominant paradigm, the accepted model of what makes us ill.

Occasionally, a far-seeing practitioner has been denounced as a quack, before later being proven right. These rare examples of genius struggling along, unrecognised, are just what the frauds and charlatans need.

“They laughed at Einstein,” they jeer, trying on their Einstein wigs.

All the same, there is a difference between the medically trained lone-wolf pioneer and the fraud. The pioneer was merely working to a different paradigm, while the charlatan works only to a greed paradigm.