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Taking the airs.

The eighteenth century was the century of the pneumatic chemists and of the discovery of gases or as they termed it different kinds of air. Following the invention of the pneumatic trough by Stephan Hales it became possible for researchers to produce, isolate and study gases. To quote an early post:

Most European eighteenth-century chemist accepted and worked within the framework of the phlogiston theory and produced a great deal of new important chemical knowledge. Most notable in this sense are the, mostly British, so-called pneumatic chemists. Working within the phlogiston theory Joseph Black (1728–1799), professor for medicine in Edinburgh, isolated and identified carbon dioxide whilst his doctoral student Daniel Rutherford (1749–1819) isolated and identified nitrogen. The Swede Carl Wilhelm Scheele (1742–1786) produced, identified and studied oxygen for which he doesn’t get the credit because although he was first, he delayed in publishing his results and was beaten to the punch by Joseph Priestley (1733–1804), who had independently also discovered oxygen labelling it erroneously dephlogisticated air. Priestley by far and away the greatest of the pneumatic chemists isolated and identified at least eight other gases as well as laying the foundations for the discovery of photosynthesis, perhaps his greatest achievement.

Henry Cavendish (1731–1810) isolated and identified hydrogen, which he thought for a time might actually be phlogiston, before going on to make the most important discovery within the framework of the phlogiston theory, the structure of water.


Joseph Priestley (1733-1804) – Frontispisce of Experiments and Observations on Different Kinds of Air Pneumatic trough, and other equipment, used by Joseph Priestley Source: Wikimedia Commons

Perhaps the highpoint of all this gas activity or at least the most bizarre outgrowth of it was the Pneumatic Institute set up in Bristol by Thomas Beddoes in 1799 to study the medical effects of the recently discovered and isolated gases.


Thomas Beddoes, pencil drawing by Edward Bird Source: Wikimedia Commons

Beddoes was born in Shropshire on 13 April 1760 and after being educated at Bridgnorth Grammar School and Pembroke College Oxford he entered the University of Edinburgh to study medicine in the 1780s, where he study chemistry under Joseph Black.


Mezzotint engraving by James Heath after Sir Henry Raeburn Source: Wikimedia Commons

He took his medical degree at Pembroke in 1786. After 1786 he visited Lavoisier in Paris. Beddoes was appointed professor of chemistry at Oxford University in 1788. His lectures were very popular but he was regarded as a political radical because of his sympathy for the French Revolution. He resigned from Oxford in 1792.

Between 1793 and 1799 he ran a clinic for the treatment of tuberculosis in Bristol. This led to him setting up the Pneumatic Institute in 1799 to investigate the treatment of diseases with gases. At first Beddoes’ idea might seem a little bizarre given how recent the discovery of most gases had been and basically how little was actually known about them. However, two strong indications inspired Beddoes’ lines of inquiry. Firstly carbon dioxide was known to prevent decay in organic materials. This led to trials by the navy in dosing seamen with carbonated water, invented by Priestley, to try and prevent scurvy. Today, in our age of worldwide trade, fresh fruit and vegetables are transported in a carbon dioxide atmosphere to prevent spoilage. The other was the known effects of oxygen. Priestley had amply demonstrated the life sustaining properties of oxygen and also recorded the mild high obtained from breathing the pure gas. Lavoisier and Simon Laplace had demonstrated experimentally the role that oxygen plays in mammalian respiration. On the basis of this primary knowledge Beddoes set out to see if other gases possibly possessed medical properties.

L0001624 Bristol Pneumatic Institute.

Bristol Pneumatic Institute Source: Wellcome Institute via Wikimedia Commons

Beddoes could not afford to finance his planned institute himself and failed to find a single sponsor so he took a route that now seems very 21st century. We see crowd funding as a product of the Internet age but it existed already in the eighteenth century under the name subscription. Beddoes found enough subscribers under his circle of friends to finance his endeavour. Amongst the principle subscribers were several members of the Birmingham Lunar Society to whose wider circles Beddoes belonged. James Watt, like Beddoes, was a protégé of Joseph Black and Joseph Priestly shared Beddoes’ political views. Watt designed and built the technical equipment for the Institute.


Apparatus designed by James Watt in preparation of the Pneumatic Institution Source: Wikimedia Commons

The Watt family provided assistance in another way as well. Beddoes needed a superintendent/laboratory assistant for his Pneumatic Institute and Watt’s son Gregory recommend his friend Humphry Davy (1778-1829), a young self taught chemist for the post. Beddoes was impressed by Davy’s, at that point unpublished, researches and appointed him to the post just twenty-one years old; a decision he possibly came to regret.


Sir Humphry Davy, Bt, by Thomas Phillips Source: National Portrait Gallery via Wikimedia Commons

Davy was a fearless practical researcher and set out to investigate the effects of various gases by testing them on himself, writing detailed protocols of the results of these experiments. He proceeded to test the effects of inhaling the recently discovered carbon monoxide. Now we know that carbon monoxide is highly poisonous but Davy didn’t and his career as a professional chemist almost ended before it had really begun. He inhaled pure carbon monoxide, which resulted in his becoming comatose. Fortunately he had taken the precaution of filling several balloons with pure oxygen and instructed his assistant to revive him if he should lose consciousness. Revived he wrote a detailed report of the experiment and its results, and then he proceeded to repeat it. The young Davy knew how to live dangerously.

His next experiment was considerably less dangerous but would prove far more fateful. He began to test the properties of nitrous oxide, known colloquially as laughing gas, a name coined by Davy. Nitrous oxide was one of the gases discovered and investigated by Joseph Priestly. Davy inhaled pure nitrous oxide and got high! In fact he got very high and he liked it. He liked it very much. Davy effectively became addicted to nitrous oxide inhaling it several times a day, everyday. He also began to subject other people to nitrous oxide highs and recording their reactions and behaviour whilst under the influence. Things got a little out of hand.

Davy, a very talented young man, was not just a chemist but also a recognised romantic poet well connected to Robert Southey and Samuel Taylor Coleridge. Davy invited his poetical friends down to Bristol for what were, in reality, drug parties. These drug orgies combined with the fact that Davy experimented with nitrous oxide on female subjects led to the ruin of the Institute’s reputation and the end of the whole of Beddoes research programme. There were accusations of impropriety with the female subjects; what had taken place whilst they were under the influence?

Beddoes faded into the background but Davy was able to rescue his reputation and get appointed to the post of assistant lecturer in chemistry, director of the chemical laboratory, and assistant editor of the journals of the recently established Royal Institution in London in 1801, where he went on to become one of the greatest research scientists of the nineteenth century. Although Gillray’s legendary cartoon from 1802 show that his laughing gas reputation had not been forgotten.


1802 satirical cartoon by James Gillray showing a Royal Institution lecture on pneumatics, with Davy holding the bellows and Count Rumford looking on at extreme right. Dr Thomas Garnett is the lecturer, holding the victim’s nose. Source: Wikimedia Commons

One probably other casualty of Davy’s drug trips was the medical use of nitrous oxide. Although Davy had, in his protocols, recorded the anaesthetic effects of the gas it had become so disreputable that it would be another fifty years before it was actually used as an anaesthetic.



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From decimal fractions to sand yachts – the unbelievably fertile mind of Simon Stevin

Of all the people who contributed to the evolution of modern science at the beginning of the seventeenth century and who have disappeared from popular perception under the over dimensioned shadow cast by Galileo, one of the most fascinating is the Netherland’s engineer Simon Stevin. Stevin is usually referred to as an engineer but in reality he was a jack-of-all-trades, mathematician, physicist, astronomer, engineer, inventor, music theorist, political advisor and army quartermaster.


Simon Stevin Source: Wikimedia Commons

Simon Stevin was the illegitimate son of Antheunis Stevin and Cathelijne von van der Poort probably born in Bruges around 1548. This and the fact that he seems to have come from an affluent background and was apparently well educated are all we know about his origins. In 1571 he became a merchants clerk in Antwerp and between 1571 and 1577 he travelled to Prussia, Poland, Denmark, Norway and Sweden. In 1577 he returned to Bruges where he was appointed city clerk a position he held until 1581 when he moved north to Leiden. It is not known why Stevin left Bruges for Leiden; his motive might have been religious, political or something else altogether. In Leiden he enrolled in a Latin school in 1581 and then the university in 1583 where he stayed until 1590 but appears never to have graduated. At the university he became friends with Maurits of Nassau the son of Willem I, Prince of Orange, who led the Dutch revolt against the Spanish Habsburgs. Maurits, who later became Stadtholder of the Dutch Republic and commander of the Dutch army, and Stevin remained close friends until Stevin’s death in 1620 and Stevin became Maurits’ technical and scientific advisor and tutor. Initially he was simply engineer but in 1604 he was appointed quartermaster-general of Dutch army.


Portrait of Maurits, Prince of Orange-Nassau School of Michiel Jansz. van Mierevelt Source: Wikimedia Commons

For Maurits he wrote textbooks on a wide range of mathematical and technical subjects, as well as organising and setting up a school of engineering at the university in Leiden. He wrote original scientific works as well as general surveys of the science and technology of the age. His published works include books on mathematics, mechanics, astronomy, navigation, military science, engineering, music theory, civics, dialectics, bookkeeping, geography and house building. He wrote his books in the vernacular and in doing so coined much of the necessary Dutch vocabulary for science and technology, some of which has been replaced since his times but much of which is still in use. However, much of his work was translated into Latin and/or French and was so available and known to other researchers in Europe.

Probably his most well known work is De Thiende (Tenths), a twenty-nine-page booklet in which he explained how to use decimal fractions. He did not originate the concept, Chinese and Islamic mathematician had already been using decimal fractions for several centuries before Stevin but he did introduce and make popular the idea in Europe. In mathematics he also wrote interesting forward-looking textbooks oh arithmetic and algebra, as well as linear perspective.


In physics he worked on statics some fifty years before Galileo developing and continuing the work of Archimedes. His most famous discovery here was the law of the inclined plane, which he demonstrated using a chain of wreaths. His demonstration shows that the effective component of gravity is inversely proportional to the length of the inclined plane. What Stevin is in principle using here is the theory of the parallelogram of forces, something learnt in schools today using vector algebra but Stevin is using it a couple of centuries before vector algebra existed.


Stevin’s proof of the law of equilibrium on an inclined plane, known as the “Epitaph of Stevinus”. Source: Wikimedia Commons

Of historical interest is that Stevin, unlike Galileo, actually did drop balls from a church tower and also hypothesised that objects in a vacuum would fall at the same rate irrespective of weight.

Having dealt with statics, Stevin next turned to hydrostatics, another discipline that he inherited from Archimedes, and here he was the first to demonstrate the so-called hydrostatic paradox i.e. that the pressure in a liquid is independent of the shape of the vessel and the area of the base, but depends solely on its depth. This discovery is often falsely attributed to Blaise Pascal.

In his book on astronomy published in 1608, Stevin revealed himself to be an unconditional supporter of Copernican heliocentricity at a time when very few were prepared to make such a commitment. He also accepted that the tides were caused by the moon, also a forward-looking commitment for the times. Being a Dutchman he of course wrote on the principles of navigation giving a clear explanation of steering a ship along a loxodrome or rhumb line as originally propagated by the Portuguese mathematician Pedro Nunez and used by Mercator in his famous Mercator projection.

As an engineer Stevin wrote on military fortification. Of course, as a Netherlander he also wrote on hydraulic engineering designing new types of sluices and locks, as well as better windmills for drainage work. In many areas his work was of a very practical nature but always looking for ways to improve machines or find better solutions for mechanical tasks.

In music theory, a very hot topic at the time, Stevin rejected a couple of thousand years of highly emotional debate on the subject of the intervals of the scale and proposed what is now known as equal temperament. He was not the first to do so, he was anticipated by Galileo’s father Vincenzo amongst others, but was almost certainly not aware of the fact.

On a somewhat more frivolous level he designed and built sand or land yachts (Zeilwagen) for Maurits. Wind driven carriages had existed in China for a thousand years before Stevin built his and illustrated in the Theatrum Orbis Terrarum of Abraham Ortelius in 1584 and in Mercator’s Atlas slightly later and it can be assumed that this was the source of inspiration for Stevin’s own vehicles.


Wind chariot or land yacht (Zeilwagen) designed by Simon Stevin for Prince Maurice of Orange (Engraving by Jacques de Gheyn). Source: Wikimedia Commons

Stevin collected all of his mathematical writings into his two volume Wisconstighe Ghedachtenissen in 1608, which were published simultaneously in both French and Latin; the latter translation being carried out by Willebrord Snel. A modern edition of The Principle Works of Simon Stevin in 5 volumes was published in Amsterdam 1955–1968.

Stevin wrote extensively over a very wide ranch of scientific, mathematical and technological subjects. His writings were always lucid, up to date and very often-contributed new concepts, ideas, methods and discoveries, some of which were very significant. He was in his own lifetime highly influential, both of the Snels knew him personally and Willebrord did much to spread his work. Isaac Beeckman consulted his unpublished papers from which he much profited.

I have one personal puzzle concerning Stevin’s work. When Hans Lipperhey demonstrated his newly invented telescope to Maurits in The Hague in September 1608, Simon Stevin had already been Maurits’ scientific advisor for more than twenty years and was without doubt the leading scientific and technological authority in the young Dutch Republic, but I know of no reaction, comment, statement or whatever from Stevin on this sensational new discovery. For me as a historian of the telescope his silence is deafening.




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Send me back to Silicon Valley II – Gratitude


I am flabbergasted, deeply touched, humbled and overwhelmed by the unbelievable generosity of all those who have already contributed to my GoFundMe. These wonderful, awesome people have already donated more than €900 in less than twenty-four hours; to say thank you seems somehow totally inadequate.

I thought about asking my Internet community for financial help with my travel cost to SciFoo for a long time before finally taking the plunge. I set a target of €1500 because GoFundMe requires you to set a target, and this is roughly my total travel costs for the trip I’m planning. Whilst contemplating taken this step I had daydreams of maybe raising €500 but dismissed them as fantastical. More realistically I though I might manage €200 to €300, which for my financial situation would be quite a lot of money and for which I would be very grateful. On bad days I thought I would raise €3,40 and a couple of bottle tops and that only because some confused soul contributed to the wrong GoFundMe appeal. Yes, since you ask, I am a pessimist; the glass in not only half empty but somebody also spat in it.

I want all of the people, who have responded so quickly and so generously, to know that I am eternally grateful for their kindness and cannot thank all of you enough.



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Send me back to Silicon Valley

Some of my readers might remember that in 2015 I, for reasons that I couldn’t comprehend, got invited to the mega, invitation only, elite, unconference in the Googleplex in Mountain View, SciFoo. Being the poverty stricken bum that I am, I realised that there was no way that I could afford the airfare from Bavaria to California so I politely declined this amazing invitation. Somewhat later I received the astounding news that the organisers were, under the circumstances, prepared to pay my airfare. So borrowing the money I needed to live on against my testament (I have a very large music collection, which is one of the reasons that I have no money that and books) I jetted off to California and had the time of my life, almost literally.

Imagine my surprise some weeks ago when I got invited back for SciFoo 2018. Either I had done something right last time I was there or they need a clown for some light entertainment between the sessions. If anything my general financial situation is now worse than it was in 2015, so I decided that I would again have to decline the invitation and with little hope that they would stump up for my airfare a second time.

However due to some copyediting that I have been doing on the English version of our Simon Marius book, I do have some money that I had intended to put on the high shelf for times of trouble. Naturally I was very tempted to take that money and say hell to it and go to SciFoo but I was determined to do what I saw as the sensible thing. Strangely enough the people whose wise advice I trust, and who knowing my profligate habits usually advise me to financial caution, all said don’t be silly take the money and go! You are not getting any younger and who knows if you will ever get such an invitation again. I didn’t need to be told twice I accepted the invitation and am now going to attend SciFoo 2018 as your friendly neighbourhood Renaissance Mathematicus.

Having taken the plunge, by the time I have paid my airfare and the money I need to live on in California I shall once again be pretty much broke. This being the case I have decided after much hesitation and serious struggle with my conscience decided to hold out the virtual begging bowl. My initial thoughts were why should anybody give me money to attend an unconference in California, what have I ever done to deserve that?

Well, I have been writing this blog for the general entertainment of my readers, without charge for almost nine years now. I also managed the monthly #histSTM blog carnival On Giants’ Shoulders for about five years and single-handedly produced the weekly #histSTM Internet journal Whewell’s Gazette for three years both again without charge. I have also, for several years now, been the #histSTM megaphone on Twitter collecting and distributing all things #histSTM for several thousand followers. When I look at all these things I feel less guilty about asking the #histSTM community and in particular my readers for a small contribution to my SciFoo travel costs.

It is normal in such circumstances for those asking for contributions to offer something in exchange. If collecting towards the publication of a book, for example, the donors name on the book or for those who donate more a free copy of the book. I have nothing tangible to offer but I will post a list here on the blog of all those who donate and who don’t wish to remain anonymous. I intend this time to hold a session at SciFoo on the use of #histSTM in STEM education and I will open that session with a slide of that list stating quite clearly that I owe my presence in Mountain View to the generosity of the people on that list. If anybody is mad enough to contribute €30 or more then they will earn themselves the right to negotiate the topic of a future blog post here at RM. I say negotiate and not choose, because there are many topics that I do not consider myself qualified to write about but should the donor choose a topic about which I can write then I will gladly do so.

I have set up a GoFundMe where you can make your donations; please don’t feel obliged to contribute if you don’t wish to do so. I shall continue to blog for everybody for free in the future without any reservations. If you do decide to contribute something no matter how little I will be eternally grateful. Each according to their means and desires, remember the widow’s mite is as important as the rich man’s…




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Getting Galileo wrong yet again

As a history of science blogger, whose reputation is built to a large extent on my playing Whac-A-Mole with crappy pieces of history of science, I should be eternally grateful for Galileo, the gift that keeps on giving. Actually Galileo is not the problem, it is the people who choose to write about him. What is most frustrating is that there is a vast amount of accessible literature written by historians of science that the offenders could consult to get their pieces about Galileo correct but they don’t seem to think that they need to do so. So who is the latest offender? Alan Lightman has published an essay in the online journal Nautilus with the title, When the Heavens Stopped Being Perfect: The advent of the telescope punctured our ideals about the nighttime sky. In fact it’s a part of his newly published book, Searching for Stars on an Island in Maine.

Alan Lightman is according to his Wikipedia page an ex astrophysicist turned novelist, who has published an impressively long list of both fact and fiction books. He also has an almost as long list of honorary doctorates. One could expect that such an author would know how to consult historical sources, primary and or secondary, and thus get his facts right, apparently not!

In his essay Lightman wishes to pay tribute to Galileo’s first major publication the Sidereus Nuncius, which is in and of itself a good thing as it is to quote Lightman, “one of the most consequential volumes of science ever published.” So far so good.


Title page of Sidereus nuncius, 1610, by Galileo Galilei Source: Wikimedia Commons

In his introductory biographical sketch Lightman write:

Unable to discharge his financial responsibilities on his academic salary alone—he had to pay the dowries of his sisters in addition to supporting his three children by a mistress—he took in boarders and sold scientific instruments.

As head of the family following the death of his father, he did indeed have to pay the dowries for his sisters a financial burden that he could have lived without. However, Galileo was also a bon vivant, who almost certainly lived beyond his means, so his financial problems were certainly aggravated by his life style. Taking in the student sons of rich families as boarders was a common practice amongst Renaissance university professors, as it provided a nice extra income and good connections to the influential parents. This is something Galileo would probably have done with or without financial problems and not something he was forced to do. The same applies to his instrument making. Designing, making and selling mathematical instruments was again a very common practice amongst Renaissance professors of mathematics and medicine and something in which Galileo excelled, so once again voluntary and not a burden. We now arrive at the telescope:

In 1609, at the age of 45, he heard about a new magnifying device just invented in the Netherlands. Without ever seeing that marvel, he quickly designed and built a telescope himself, several times more powerful than the Dutch model. He seems to have been the first human being to point such a thing at the night sky. (The telescopes in Holland were called “spyglasses,” leading one to speculate on their uses.)

The story that Galileo built his first telescope purely by here say, without having seen one, a claim which he set in the world, has been largely debunked. He almost certainly saw one through the offices of Paolo Sarpi, who first drew his attention to the instrument. Also Galileo took surprisingly long between first hearing of the telescope and actually building one. Eileen Reeves thinks that before he actually saw one he thought it had something to do with mirrors rather than lenses and thus lost time on a wild goose chase. He was definitively not the first person to point one at the night sky, as I have written on a number of occasions. To quote myself:

Galileo was not the first person to turn a telescope to the skies. Already in the last week of September 1608 as Hans Lipperhey demonstrated his new invention to the assembled prominence in The Hague it was turned to the skies “and even the stars which normally are not visible for us, because of the scanty proportion and feeble sight of our eyes, can be seen with this instrument.” The quote is taken from Embassies of the King of Siam Sent to his Excellency Prince Maurits, Arrived in The Hague on 10 September 1608, the French newsletter that carried the news of the advent of the telescope throughout Europe. If instead he meant the first astronomer/astrologer/mathematician/natural philosopher or whatever then that honour goes to Thomas Harriot and not to Galileo. There is fairly strong but not conclusive evidence that Simon Marius also turned his telescope to the heavens before Galileo.

Galileo ground and polished his own lenses. His first instruments magnified objects a dozen or so times. He was eventually able to build telescopes that magnified a thousand times and made objects appear 30 times closer than they actually were.

Remember those instruments? Galileo employed a full time instrument maker, although he did work in the workshop himself. I mention this because his instrument maker, Marc’Antonio Mazzoleni rarely gets the credit he deserves. Galileo’s first instruments, such as the one he demonstrated to the Senate of Padua, magnified nine times. His later observational instruments varied between twenty and thirty times magnifications. The problem with Dutch or Galilean telescopes is the higher the magnification the smaller the field of view, anything above thirty is practically useless. A Galilean telescope, which magnified a thousand times is pure fantasy! That would really have been a sensation! Lightman, an astrophysicist remember, here falls into a trap that Galileo laid out for the careless reader. If a telescope magnifies the sides of a square thirty times then it magnifies the area of the square thirty times thirty, equals nine hundred or approximately one thousand!

Lightman now indulges in a bit of fairy tale telling:

Many people were skeptical, questioning the legitimacy of the device and thus the validity of its findings. Some regarded the strange tube as magical, not of this world, as if a cell phone were presented to someone in the year 1800. Galileo himself, although a scientist, did not understand exactly how the thing worked.

We should recall that belief in magic, sorcery, and witchcraft was widespread in Europe in the 16th and 17th centuries. In just those two centuries, 40,000 suspected witches, most of them women, were burned at the stake, hung from the gallows, or forced to put their heads on the chopping block. In 1597, King James VI of Scotland (who in 1603 became James I of England) complained about the “fearefull abounding at this time [and] in this Countrey, of these detestable slaves of the Divel, the Witches or enchaunters.” It was believed that sorcerers could cast spells by damaging a strand of hair or a fingernail of an intended victim. Was the Italian mathematician’s device a bit of sorcery?

I have read a vast amount of literature about the early use of the telescope both by Galileo and by all of the other early users. I have read all of the objections, the discussions, the rejections and the acceptances but not once have I ever come across a reference that people thought the telescope or the observations made with it were magic or sorcery. Lightman seems to have extracted this little piece of ridiculousness out of his…

Within a couple of months of the publication of Sidereus Nuncius, Galileo became famous throughout Europe—in part because the telescope had military and commercial value as well as scientific. (From “the highest bell towers of Venice,” Galileo wrote to a friend, you can “observe sea sails and vessels so far away that, coming under full sail to port, 2 hours and more were required before they could be seen without my spyglass.”) Word of the invention traveled by letter and mouth.

Maybe I’m not reading this paragraph correctly but as I read it Lightman is saying that the spread of news of the telescope was due to Galileo’s publication. This is rubbish, the news of the new invention spread like wildfire after the first demonstration in The Hague in September 1608. This was largely due to the Embassies of the King of Siam Sent to his Excellency Prince Maurits, Arrived in The Hague on 10 September 1608, the French newsletter that carried the news of the advent of the telescope throughout Europe. However it was also due to the fact that Maurits van Nassau sent telescopes as gifts to many of the crowned heads of Europe including the Pope. For example, the Jesuit astronomers of the Collegio Romano were already making telescopic astronomical observations well before Galileo published his Sidereus Nuncius. It was this widespread knowledge of the telescope that first led Galileo, in far away Padua, to hear of the telescope.

In his book, Galileo exhibits his own pen-and-ink drawings of the moon seen through his telescope, showing dark and light areas, valleys and hills, craters, ridges, mountains. He even estimates the height of the lunar mountains by the length of their shadows.

The illustrations of the Moon are not pen-and ink drawings but washes, i.e. monochrome watercolour paintings.

All of which supported the proposal of Copernicus, 67 years earlier, that the sun, rather than the earth, is the center of the planetary system. These were quite a few new ideas to pack into such a little book. And with no apologies to Aristotle or the Church.

Altogether now in chorus, the telescopic discoveries published in the Sidereus Nuncius neither refute the Ptolemaic geocentric astronomy nor do they support the Copernican heliocentric astronomy. They merely shred the Aristotelian cosmology.

All of it supposedly constructed out of aether, Aristotle’s fifth element, unblemished and perfect in substance and form, what Milton described in Paradise Lost as the “ethereal quintessence of Heaven.” And all of it at one with the divine sensorium of God. What Galileo actually saw through his little tube were craters on the moon and dark acne on the sun.

Lightman doesn’t seem to be aware that the discovery of the sunspots cannot be found in the Sidereus Nuncius, they came later.

Galileo’s announcement of dark spots on the sun was an even greater challenge to the divine perfection of the heavens. We now know that “sunspots” are caused by temporary concentrations of magnetic energy in the outer layers of the sun. Being temporary, sunspots come and go. In 1611, Christoph Scheiner, a leading Jesuit mathematician in Swabia (southwest Germany), procured one of the new gadgets himself and confirmed Galileo’s sightings of moving dark spots in front of the sun. However, Scheiner began with the unquestioned Aristotelian premise that the sun was perfect and unblemished, and he went from there to proposing various precarious arguments as to why the phenomenon was caused by other planets or moons orbiting the sun rather than the sun itself.

Note, Galileo constructed his own telescope, whereas according to Lightman Christoph Scheiner merely “procured one of the new gadgets.” Actually Scheiner like Galileo constructed his own telescope and was in fact very good at it. Scheiner did not confirm Galileo’s sightings of moving dark spots in front of the sun. When Marcus Welser published Scheiner’s Three Letters on Sunspots, Galileo had not published anything on the subject and was caught, so to speak, with his pants down. This of course explains his violent reaction, somebody was poaching on his territory, he, and he alone, was the great telescopic discoverer of marvels in the heavens. Of course both Scheiner and Galileo were blissfully unaware that Thomas Harriot had made the discovery before either of them or that Johannes Fabricius had already published a booklet on the subject. Scheiner did indeed initial suggest that the sunspots were the shadows of satellites orbiting the sun. This actually spurred Galileo on to prove that they were really on the surface of the sun, something he had not done before being goaded by Scheiner. Scheiner accepted Galileo’s proof with grace and then went on to devote several years to intensive solar astronomy producing much new information.

When Galileo’s observations became known, churchmen reacted with skepticism. On March 19, 1611, Cardinal Robert Bellarmine, head of the Collegio Romano, wrote to his fellow Jesuit mathematicians:

I know that your Reverences have heard about the new astronomical observations by an eminent mathematician … This I wish to know because I hear different opinions, and you Reverend Fathers, being skilled in the mathematical sciences, can easily tell me if these new discoveries are well founded, or if they are apparent and not real.

 Although the Church mathematicians argued about the details of Galileo’s findings, they unanimously agreed that the sightings were real. Nevertheless, Galileo’s telescopic findings and his support of the heliocentric model of Copernicus were considered an unpardonable attack on theological belief. For that offense, Galileo, a pious Roman Catholic who had once seriously considered the priesthood, was eventually tried by the Inquisition, forced to recant most of his astronomical claims, and spent the later years of his life under house arrest.

The astronomers of the Collegio Romano had begun their efforts to confirm Galileo’s discoveries, with Galileo’s active assistance, well before Bellarmine asked their opinion on the matter. Almost everybody was of course sceptical of Galileo’s quite extraordinary claims. They, after some effort, confirmed the findings and held a banquet in Galileo’s honour to celebrate the discoveries. Galileo’s telescopic findings played absolutely no role in his trouble with the Inquisition or his subsequent trial.

I want to focus now not on the displacement of earth as the center of the cosmos but on the newly conceived materiality of the heavens. Because it was that materiality, that humbling of the so-called heavenly bodies, that struck at the absolute nature of the stars.

 Here Lightman goes off on a long excurse evoking Kepler’s Somnium and Giordano Bruno amongst other on the materiality of the stars. He writes:

Once Galileo and others had declared the stars to be mere material, their millennia were numbered— because all material things are subject to the law of the conservation of energy.

Lightman wants his readers to believe that there was a direct link between the discovery of sunspots and the acceptance that the sun is just another star and that all stars are material. This is historically simple not true, Galileo never declared the stars to be mere material and it took quite a long time for this chain of thought to establish itself in the world of astronomy. If I were a university teacher grading Lightman’s essay in an introductory history of astronomy course, I would give it a big fat F.


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Marine chronometer, lunar distance method or something else altogether?

Trying to find a method to determine longitude at sea was one of the greatest technical problems of the Early Modern Period. Quite a wide-range of ideas were floated of which the most were either totally impractical or simply false. In the end the two main competitors were: on the one hand the attempts to develop a clock reliable enough to carry time from a given starting point accurately enough through all the vicissitudes of a long sea voyage to be then compared with local time and thus to determine longitude, i.e. the marine chronometer. Or on the other to develop accurate tables of the Moon’s orbit respective a set of given fixed stars in order to be able to use the Moon’s position at any given time as a clock with which to calculate longitude, i.e. the lunar distant method. Both of these concepts were first presented in the sixteenth century but it took until the middle of the eighteenth century before they could be realised.

Around 1760, Tobias Mayer succeeded in delivering up a set of tables of the lunar orbit accurate enough to be used for determining longitude using the lunar distance method. Shortly after this John Harrison showed with his H4 that a solution with a chronometer was also possible. Unfortunately even with the naval almanac produced by Nevil Maskelyne to simplify the calculations the lunar distant method was mathematically difficult to execute. As I have written elsewhere although Harrison’s H4 showed that a chronometer solution was possible, the clock itself was too complex and too expensive to provide a real solution to the longitude problem. It would take well into the nineteenth century before enough affordable, accurate chronometers were available to make this a viable mass method. Many sources claim that in the mean time navigators used the lunar distant method, but did they?

It would appear that for the first fifty or so years following those breakthroughs seafarers relied on a mixture of navigational methods to help determine their longitude. Principally they relied on the old tried and trusted method of dead reckoning. This is the process of calculating the ships new position from a previous one based on compass direction, ship’s speed based on log line measurements, and knowledge of currents. In the period we are talking about, many navigators checked their dead reckoning results against chronometer or lunar distant determinations. Given the lack of reliability of the available chronometers the navigators often carried several watches, comparing or even averaging the results. Sometimes the lunar distant method was only used by landfall to correct or control the longitude determined by dead reckoning. In general it seems that the well-established dead reckoning was the principle method used, supplement by one or other or both of the new methods, although neither of them was really trusted by the navigators.

For a more detailed picture of the navigational methods used from the middle of the eighteenth century to the middle of the nineteenth by the various European sea going nations I can recommend Navigational Enterprises in Europe and its Empires, 1730–1850 (1) edited by Richard Dunn (@Lordoflongitude) and Rebekah Higgitt (@beckyfh) a set of academic papers that supplement their more popular, excellent Finding Longitude.


After an excellent general introduction to the subject by the editors follow eleven papers covering a wide range of aspects of the subject, all of which maintain a very high level of scholarship.



My only real quibble with the book is the unfortunately usual high price putting it beyond my humble resources and probably those of most others interested in reading and learning from this highly informative volume.

(1) Ricard Dunn & Rebekah Higgitt eds., Navigational Enterprises in Europe and its Empires, 1730–1850, Palsgrave Macmillan, 2015


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Dangerous Twaddle

Someone on Twitter drew my attention to a BBC4 television documentary by David Malone from 2007 about mathematics. Interested I thought I would give it a whirl, I wish I hadn’t. It’s a sort of biography of Georg Cantor, Ludwig Boltzmann, Kurt Gödel and Alan Turing so what could go wrong? It’s called Dangerous Knowledge but Dangerous Twaddle would have been more appropriate.

In my opinion it starts off with a real humdinger: atmospheric images with the following dramatic voice over:

Beneath the surface of the world are the rules of science but beneath them there is a far deeper set of rules. A matrix of pure mathematics, which explains the nature of the rules of science and how it is we can understand them in the first place.

Ignoring the fact that I don’t actually agree with this piece of trite metaphysics, the author completely blows it in my opinion because another even more dramatic voice over follows this with the following quote:

To see a World in a Grain of Sand

And a Heaven in a Wild Flower

Hold Infinity in the palm of your hand

And Eternity in an hour

This is of course one of the most well known quotes by William Blake taken from his Auguries of Innocence. Malone is obviously ignorant of Blake’s opinion of the mathematical description of the world.

God forbid that Truth should be confined to Mathematical Demonstrations! (Written as a marginal note to Reynolds’ Discourses.)

Before we get down to the real reason that I’m writing this a couple of things that annoyed me whilst watching this documentary. The author-narrator mispronounces the names of both Leibniz and Dedekind. One would think that if somebody is making a documentary about mathematics and mathematicians they would at least take the trouble to get the names of famous mathematicians right. At the end of the section about Cantor he describes him as the greatest mathematician of his century! Regular readers of this blog will know that I intensely dislike such superlatives in the history of science. Even if I didn’t, is Cantor really the greatest mathematician of the nineteenth century? There’s an awful lot of competition. In the section on Gödel, we get told about his friendship with his fellow Austrian mathematician, Albert Einstein.


Two Austrian Mathematicians!? Albert Einstein und Kurt Gödel in Princeton, circa 1948, Foto: Oskar Morgenstern; mit freundlicher Genehmigung des Shelby White and Leon Levy Archives Center, Institute for Advanced Study, Princeton, NJ, US

Now, I know that trying to keep track of Einstein’s nationality is rather difficult for the non-historian; he had a total of eight different ones including being stateless for five years. However, he was only a citizen of the Austrian Empire from April 1911 to July 1912, as professor at the University of Prague. Eleven months out of a life of 76 years hardly justifies calling him an Austrian.

My real beef with the documentary is contained in a further piece of voice over from the introduction:

… pursued the questions to the brink of insanity and over it.

Basically Malone spends eighty minutes telling the world that if brilliant mathematicians think outside the box it can and will drive them insane! This is quite simply bullshit!

He devotes the largest part of the documentary to Georg Cantor and the invention of set theory. I found his explanations of what Cantor achieved and why he did it totally opaque and I spent quite a lot of time at university studying and understanding it. Malone gives a totally bogus explanation of the continuum hypothesis, which suggests very strongly that he simply doesn’t understand it, and then goes on to explain that it was Cantor’s inability to prove the continuum hypothesis drove him insane. I will return to this.


Georg Cantor, around 1870 Source: Wikimedia Commons

We then move on to Ludwig Boltzmann and his championing of a probablistic atomic theory when the majority of physicists and philosophers opposed the real existence of atoms. Once again Malone tells us that it was Boltzmann’s science that drove him mad and led him to commit suicide.


Ludwig Boltzmann Source: Wikimedia Commons

Although it is always dubious to make historical diagnoses of illnesses, in particular mental ones, Both Cantor and Boltzmann displayed all of the symptoms of a severe bipolar disorder. Bipolar disorder is not caused by mathematical research or any other work for that matter. A stressful working situation might well aggravate an existing bipolar disorder it won’t cause it. This is as I said, dangerous twaddle.

Malone now accelerates his gallop into the realm of total crap with his segment on Kurt Gödel. Following the usually incorrect statement of Gödel’s incompleteness theorem. People almost invariably leave off the very important final “within the system” in their accounts. What Gödel showed in that we cannot produce a formal logical system within which all true mathematical statements are provable. However this does not mean that the statements that are unprovable within the given system are fundamentally unprovable, as Malone claims in his statement of Gödel. However this is a minor quibble compared to Malone’s central claim. He states that Gödel took up the continuum hypothesis and because he like Cantor was unable to prove it, he too went insane. Now, it is well known that Gödel displayed serious symptoms of mental illness that got increasingly worse as he got older, until he quite literally starved himself to death due to his paranoid belief that somebody was trying to poison him. I’m not a clinical psychiatrist, but I’m more that willing to state that Gödel’s ability or lack of it to solve the continuum hypothesis did not cause his mental illness. Malone, however, seem to be totally unaware that Gödel in fact showed the continuum hypothesis was consistent, i.e. cannot be proved false, with the axioms of Zermelo-Fraenkel set theory. This is one of the major breakthroughs in the history of set theory; far from being frustrated by the continuum hypothesis Gödel produced one of his most important results with it.


Kurt Gödel Image Credit

Malone closes out his trip through the insane and suicidal mathematical geniuses with none other than Alan Turing. Following up on the usually false claim that Turing invented the computer and a very confusing explanation of Turing’s achievements in meta-mathematics, Malone takes us forward to Turing’s death. He has the British secret service responsible for Turing’s chemical castration following his conviction for indecency, which is just simply crap. Turing was offered a choice between a prison sentence or probation with the hormonal treatment as a condition by the court. He freely chose the later. I’m not even going to enter the discussion of whether he committed suicide or not and if he did why. There has already been enough ink spilt on that particular topic.


Alan Turing Source: Wikimedia Commons

Malone made a documentary about four major figures in the history of mathematics, logic and mathematical physics and presents the quite honestly laughable thesis that it was their intellectual audacity and the opposition that they experienced to their theories that drove them insane. This is quite simple put, bullshit. As someone who has experienced, at time quite serious, mental illness I find it quite frightening that an organisation such as the BBC is not only prepared to air such crap but to finance it with obviously comparatively large sums of money. We live in a society where it is extremely difficult to explain to people what mental illness is and such pseudo-psychological bullshit as Malone’s documentary does nothing to help with this problem.




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