Category Archives: Myths of Science

Did Isaac leap or was he pushed?

In 2016 2017 it would not be too much to expect a professor of philosophy at an American university to have a working knowledge of the evolution of science in the seventeenth century, particularly given that said evolution had a massive impact on the historical evolution of philosophy. One might excuse a freshly baked adjunct professor at a small liberal arts college, in his first year, if they were not au fait with the minutiae of the history of seventeenth-century astronomy but one would expect better from an established and acknowledged expert. Andrew Janiak is just that, an established and acknowledged expert. Creed C. Black Professor of Philosophy and Chair of Department at Duke University; according to Wikipedia, “Duke is consistently included among the best universities in the world by numerous university rankings”. Janiak is also an acknowledge expert on Isaac Newton and author of Isaac Newton in the Blackwell Great Minds series, so one is all the more dumbfounded to read the following in his article entitled Newton’s Leap on the Institute of Arts and Ideas: Philosophy for our times website:

Newton_-_1677.jpeg

Isaac Newton 1677 after Peter Lely Source: Wikimedia Commons Comment from CJ Schilt (a Newton expert) on Facebook: On another note, that picture is probably not Newton, despite what Finegold thinks.

 

But wait a minute: what could be more amazing than a young man discovering a fundamental force of nature while sitting under a tree? For starters, we have to recognize how foreign Newton’s ultimate idea about gravity was to philosophers, astronomers and mathematicians in the era of the Scientific Revolution. Newton provided an answer to a question that hadn’t even been asked yet. The problem with understanding the distant past is that we take our twenty-first century ideas and attitudes for granted. We think, for example, that the following is obvious: if the planets, like the Earth and Jupiter, regularly orbit the Sun, there must be something that causes them to follow their orbits. After all, if nothing caused them to orbit the Sun, they would fly off into deep space. [my emphasis]That seems so obvious to us, it’s hard to imagine that for centuries, the world’s leading thinkers, from Aristotle to Ptolemy and onwards, did not have that idea at all. Instead, for many generations, leading philosophers and mathematicians thought this: the circle is a perfect mathematical form, and the planetary orbits are circular, so they are ever-lasting aspects of the natural world. To them, the orbits were so perfect that nothing caused them to occur. They simply were. [my emphasis] The question of what caused the planetary orbits was not even on the table for astronomers in those days. [my emphasis] Down on earth, apples fell from trees throughout history just as they do now. But philosophers and mathematicians didn’t have any reason to think that whatever causes apples to fall to the ground might somehow be connected to anything going on in the heavens. After all, the heavens were thought to be the home of everlasting motions, of perfect circles, and were therefore nothing like the constantly changing, messy world down below, where worms eat through apples as they rot on the ground.

So what is wrong with this piece of #histSTM prose? Let us start with the second of my bold emphasised segments:

Instead, for many generations, leading philosophers and mathematicians thought this: the circle is a perfect mathematical form, and the planetary orbits are circular, so they are ever-lasting aspects of the natural world. To them, the orbits were so perfect that nothing caused them to occur. They simply were.

Whilst it is true that, following Empedocles, Western culture adopted the so-called Platonic axioms, which stated that celestial motion was uniform and circular, it is not true that they claimed this motion to be without cause. Aristotle, whose system became dominant for a time in the Middle Ages, hypothesised a system of nested crystalline spheres, which working from the outside to the centre drove each other through direct contact; a system that probably would not have worked due to friction. His outer-most sphere was moved by the unmoved mover, who remained unnamed, making the theory very attractive for Christian theologians in the High Middle Ages, who simple called the unmoved mover God. Interestingly the expression love makes the world go round originates in the Aristotelian belief that that driving force was love. In the Middle Ages we also find the beliefs that each of the heavenly bodies has a soul, which propels it through space or alternatively an angel pushing it around its orbit.

All of this is all well and good but of course doesn’t have any real relevance for Newton because by the time he came on the scene the Platonic axioms were well and truly dead, killed off by one Johannes Kepler. You might have heard of him? Kepler published the first two of his planetary laws, number one: that the planetary orbits are ellipses and that the sun is at one focus of the ellipse and number two: that a line connecting the sun to the planet sweeps out equal areas in equal time periods in 1609, that’s thirty-three years before Newton was born. Somewhat later Cassini proved with the support of his teachers, Riccioli and Grimaldi, using a heliometer they had constructed in the San Petronio Basilica in Bologna, that the earth’s orbit around the sun or the sun’s around the earth, (the method couldn’t decide which) was definitely elliptical.

Part of the San Petronio Basilica heliometer.
The meridian line sundial inscribed on the floor at the San Petronio Basilica in Bologna, Emilia Romagna, northern Italy. An image of the Sun produced by a pinhole gnomon in the churches vaults 66.8 meters (219 ft) away fills this 168×64 cm oval at noon on the winter solstice.
Source Wikimedia Commons

By the time Newton became interested in astronomy it was accepted by all that the planetary orbits were Keplerian ellipses and not circles. Kepler’s first and third laws were accepted almost immediately being based on observation and solid mathematics but law two remained contentious until about 1670, when it was newly derived by Nicholas Mercator. The dispute over alternatives to Kepler’s second law between Ismaël Boulliau and Seth Ward was almost certainly Newton’s introduction to Kepler’s theories.

Turning to the other two bold emphasised claims we have:

 Newton provided an answer to a question that hadn’t even been asked yet. The problem with understanding the distant past is that we take our twenty-first century ideas and attitudes for granted. We think, for example, that the following is obvious: if the planets, like the Earth and Jupiter, regularly orbit the Sun, there must be something that causes them to follow their orbits. After all, if nothing caused them to orbit the Sun, they would fly off into deep space.

And:

The question of what caused the planetary orbits was not even on the table for astronomers in those days.

I’m afraid that Herr Kepler would disagree rather strongly with these claims. Not only had he asked this question he had also supplied a fairly ingenious and complex answer to it. Also quite famously his teacher Michael Maestlin rebuked him quite strongly for having done so. Kepler is usually credited with being the first to reject vitalist explanations of planetary motion by souls, spirits or angels (anima) and suggest instead a non-vitalist force (vir). His theory, based on the magnetic theories of Gilbert, was some sort of magnetic attraction emanating from the sun that weakened the further out it got. Kepler’s work started a debate that wound its way through the seventeenth century.

Ismaël Boulliau, a Keplerian, in his Astronomia philolaica from 1645 discussed Kepler’s theory of planetary force, which he rejected but added that if it did exist it would be an inverse-square law in analogy to Kepler’s law of the propagation of light. Newton was well aware of Boulliau’s suggestion of an inverse-square law. In 1666 Giovanni Alfonso Borelli, a disciple of Galileo, published his Theoricae Mediceorum planetarum ex causis physicis deductae in which he suggested that planetary motion was the result of three forces.

Famously in 1684 in a London coffee house Christopher Wren posed the question to Robert Hooke and Edmond Halley, if the force driving the planets was an inverse-square force would the orbits be Keplerian ellipses, offering a book token as prize to the first one to solve the problem. This, as is well known, led to Halley asking Newton who answered in the positive and wrote his Principia to prove it; in the Principia Newton shows that he is fully aware of both Kepler’s and Borelli’s work on the subject. What Newton deliberately left out of the Principia is that in an earlier exchange it had in fact been Hooke who first posited a universal force of gravity.

As this all too brief survey of the history shows, far from Newton providing an answer to a question that hadn’t been asked yet, he was, so to speak, a Johnny-come-lately to a debate that when he added his contribution was already eighty years old.

The Institute of Arts and Ideas advertises itself as follows:

So the IAI seeks to challenge the notion that our present accepted wisdom is the truth. It aims to uncover the flaws and limitations in our current thinking in search of alternative and better ways to hold the world.

Personally I don’t see how having a leading philosopher of science propagating the lone genius myth by spouting crap about the history of science fulfils that aim.

 

 

 

 

 

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Filed under History of Astronomy, History of science, Myths of Science, Newton

Galileo, The Church and that ban

Quite Interesting @qikipedia is the Twitter account of the highly successful British television comedy panel game QI (Quite Interesting). For those who are not aficionados of this piece of modern television culture it is described on Wikipedia thus:

The format of the show focuses on Davies and three other guest panelists answering questions that are extremely obscure, making it unlikely that the correct answer will be given. To compensate, the panelists are awarded points not only for the right answer, but also for interesting ones, regardless of whether they are right or even relate to the original question, while points are deducted for “answers which are not only wrong, but pathetically obvious”– typically answers that are generally believed to be true but in fact are misconceptions. These answers, referred to as “forfeits”, are usually indicated by a loud klaxon and alarm bell, flashing lights, and the incorrect answer being flashed on the video screens behind the panelists. [my emphasis]

Given the section that I have highlighted above the Twitter account should have points deducted to the sounds of a loud klaxon and an alarm bell accompanied by flashing lights for having tweeted the following on 12 September

It wasn’t until 1992 that the Catholic Church finally admitted that Galileo’s views on the solar system were correct – @qikipedia

Portrait of Galileo that accompanied the @qikipedia tweet

 

This is of course complete rubbish. In what follows I will give a brief summary of the Catholic Church’s ban on heliocentrism, as propagated by Galileo amongst others.

The initial ban on propagating heliocentrism as a proven theory, one could still present it as a hypothetical one, was issued by the Inquisition in 1616. Interestingly whilst the books of Kepler and Maestlin, for example, were placed on the Index of Forbidden Books, Copernicus’ De revolutionibus was not but merely banned temporarily until corrected, which took place surprisingly rapidly; correction meaning the removal of the very few passages where heliocentricity is presented as a fact. By 1621 De revolutionibus was back in circulation for Catholic astronomers. Galileo’s Dialogo was placed on the Index following his trial in 1632.

A title page of the Index of Forbidden Books 1758
Source: Linda Hall Library

Books openly espousing heliocentricity as a true fact, which was more that the science of the time could deliver, were placed on the Index by the Catholic Church, so all good Catholics immediately dropped the subject? Well no actually. The ban had surprising little effect outside of Italy. Within Italy, astronomers kept their heads below the parapet for a couple of decades but outside of Italy things were very different. Protestant countries, naturally, totally ignored the ban and even astronomers in Catholic countries on the whole took very little notice of it. The one notable exception was René Descartes who dropped plans to publish his book Le Monde, ou Traite de la lumiere in 1633, which contained his views supporting heliocentricity, the full text only appearing posthumously in 1677. Quite why he did so was not very clear but it is thought that he did it out of respect to his Jesuit teachers. However, Descartes remained the exception. Galileo’s offending Dialogo quickly appeared in a ‘pirate’ edition, translated into Latin in the Netherlands, where later his Discorsi, would also be published. I say pirate but Galileo was well aware of the publication, which had his blessing, but officially knew nothing about it.

Title page of the 1635 ‘pirate’ Latin edition of Dialogo
Source: The History of Science Collections of the University of Oklahoma Libraries

Within Italy once the dust had settled Catholic astronomers began to publish books on heliocentricity that opened with some sort of nod in the direction of the Church along the lines of, “The Holy Mother Church has in its wisdom condemned heliocentricity as contrary to Holy Scripture…” but then continued something like this “…however it is an interesting hypothetical mathematical model, which we will now discuss.” This face saving trick was accepted by the Church and everybody was happy. By the early eighteenth century almost all astronomers in Italy, with the exception of some Jesuits, were following this course.

In 1758 the ball game changed again as the then Pope basically dropped the ban on heliocentricity, although this was done informally and the formal prohibition stayed in place. The publication of a complete works of Galileo was even permitted with a suitable preface to the Dialogo pointing out its faults. From this time on Catholic astronomers were quite free to propagate a factual heliocentricity in their publications.

This was the situation up till 1820 when an over zealous Master of the Sacred Palace (the Church’s chief censor), Fillipo Anfossi, refused to licence a book containing a factual account of heliocentricity by Giuseppe Settele. Settele appealed directly to the Pope and after deliberations the ban on heliocentricity was formally lifted by the Church in 1821. The next edition of the Index, which didn’t appear until 1835, no longer contained books on heliocentricity. Anfossi and Settele only feature in the history of science because of this incidence.

So to summarise, the Church only banned factual claims for the heliocentric system but not hypothetical statements about it, so this is how Catholic astronomer got around the ban. In 1758 the Pope informally lifted the ban clearing the way for Catholic astronomers to write freely about it. In 1821 the ban was formally lifted and in 1835 books on heliocentricity were removed from the Index, so where did QI get their date of 1992 from?

In 1981 the Church constituted the Pontifical Interdisciplinary Study Commission to re-examine the Galileo trial, which came to rather wishy-washy conclusions. In 1992 the Pope held a speech formally closing the commission and saying that the whole affair had been rather unfortunate and that the Church had been probably wrong to prosecute Galileo.

 

 

 

 

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Hyping the history of mathematics

A while back the Internet was full of reports about a sensational discovery in the history of mathematics. Two researchers had apparently proved that a well know Babylonian cuneiform clay tablet (Plimpton 322), which contains a list of Pythagorean triples, is in fact a proof that the Babylonians had developed trigonometry one thousand years before the Greeks and it was even a superior and more accurate system than that of the Greeks. My first reaction was that the reports contained considerably more hype than substance, a reaction that was largely confirmed by an excellent blog post on the topic by Evelyn Lamb.

Plimpton 322, Babylonian tablet listing pythagorean triples
Source: Wikimedia Commons

This was followed by an equally excellent and equally deflating essay by Eduardo A Escobar an expert on cuneiform tablets. And so another hyped sensation is brought crashing down into the real world. Both put downs were endorsed by Eleanor Robson author of Mathematics in Ancient Iraq: A Social History and a leading expert on Babylonian mathematics.

Last week saw the next history of mathematics press feeding frenzy with the announcement by the Bodleian Library in Oxford that an Indian manuscript containing a symbol for zero had been re-dated using radio carbon dating and was now considered to be from the third to fourth centuries CE rather than the eight century CE, making it the earliest known Indian symbol for zero. This is of course an interesting and significant discovery in the history of mathematics but it doesn’t actually change our knowledge of that history in any really significant way. I will explain later, but first the hype in the various Internet reports.

A leaf from the Bakhshali Manuscript, showing off Indian mathematical genius. A zero symbol has been highlighted in the image.
Courtesy of the Bodleian Library

 

We start off with Richard Ovenden from Bodleian Libraries who announced, “The finding is of “vital importance” to the history of mathematics.”

Bodleian Library Carbon dating finds Bakhshali manuscript contains oldest recorded origins of the symbol ‘zero’

The Guardian leads off with an article by Marcus Du Sautoy: Much ado about nothing: ancient Indian text contains earliest zero symbol. Who in a video film and in the text of his article tells us, “This becomes the birth of the concept of zero in it’s own right and this is a total revolution that happens out of India.”

The Science Museum’s article Illuminating India: starring the oldest recorded origins of ‘zero’, the Bakhshali manuscript, basically repeats the Du Sautoy doctrine,

Medievalists.net makes the fundamental mistake of entitling their contribution, The First Zero, although in the text they return to the wording, “the world’s oldest recorded origin of the zero that we use today.”

The BBC joins the party with another clone of the basic article, Carbon dating reveals earliest origins of zero symbol.

Entrepreneur Cecile G Tamura summed up the implicit and sometimes explicit message of all these reports with the following tweet, One of the greatest conceptual breakthroughs in mathematics has been traced to the Bakhshali manuscript dating from the 3rd or 4th century at a period even earlier than we thought. To which I can only reply, has it?

All of the articles, which are all basically clones of the original announcement state quite clearly that this is a placeholder zero and not the number concept zero[1] and that there are earlier recorded symbols for placeholder zeros in both Babylonian and Mayan mathematics. Of course it was only in Indian mathematics that the place-holder zero developed into the number concept zero of which the earliest evidence can be found in Brahmagupta’s Brahmasphuṭasiddhanta from the seven century CE. However, this re-dating of the Bakhshali manuscript doesn’t actually bring us any closer to knowing when, why or how that conceptual shift, so important in the history of mathematics, took place. Does it in anyway actually change the history of the zero concept within the history of mathematics? No not really.

Historians of mathematics have known for a long time that the history of the zero concept within Indian culture doesn’t begin with Brahmagupta and that it was certainly preceded by a long complex prehistory. They are well aware of zero concepts in Sanskrit linguistics and in Hindu philosophy that stretch back well before the turn of the millennium. In fact it is exactly this linguistic and philosophical acceptance of ‘nothing’ that the historian assume enabled the Indian mathematicians to make the leap to the concept of a number signifying nothing, whereas the Greeks with their philosophical rejection of the void were unable to spring the gap. Having a new earliest symbol in Indian mathematics for zero as a placeholder, as opposed to the earlier recorded words for the concept of nothingness doesn’t actually change anything fundamental in our historical knowledge of the number concept of zero.

There is a small technical problem that should be mentioned in this context. Due to the fact that early Indian culture tended to write on perishable organic material, such as the bark used here, means that the chances of our ever discovering manuscripts documenting that oh so important conceptual leap are relatively low.

I’m afraid I must also take umbrage with another of Richard Ovenden’s claims in the original Bodleian report:

 Richard Ovenden, head of the Bodleian Library, said the results highlight a Western bias that has often seen the contributions of South Asian scholars being overlooked. “These surprising research results testify to the subcontinent’s rich and longstanding scientific tradition,” he said.

Whilst this claim might be true in other areas of #histSTM, as far as the history of the so-called Hindu-Arabic numbers system and the number concept zero are concerned it is totally bosh. Pierre-Simon, marquis de Laplace (1749-1827) wrote the following:

“It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it has lent to computations put our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of the achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.”

I started buying general books on the history of mathematics more than 45 years ago and now have nine such volumes all of which deal explicitly with the Indian development of the decimal place value number system and the invention of the number concept zero. I own two monographs dedicated solely to the history of the number concept zero. I have four volumes dedicated to the history of number systems all of which deal extensively with the immensely important Indian contributions. I also own two books that are entirely devoted to the history of Indian mathematics. Somehow I can’t see in the case of the massive Indian contribution to the development of number systems that a Western bias has here overseen the contributions of South Asian scholars.

This of course opens the question as to why this discovery was made public at this time and in this overblown manner? Maybe I’m being cynical but could it have something to do with the fact that this manuscript is going on display in a major Science Museum exhibition starting in October?

The hype that I have outlined here in the recent history of mathematics has unfortunately become the norm in all genres of history and in the historical sciences such as archaeology or palaeontology. New discoveries are not presented in a reasonable manner putting them correctly into the context of the state of the art research in the given field but are trumpeted out at a metaphorical 140 decibel claiming that this is a sensation, a discipline re-defining, an unbelievable, a unique, a choose your own hyperbolic superlative discovery. The context is, as above, very often misrepresented to make the new discovery seem more important, more significant, whatever. Everybody is struggling to make themselves heard above the clamour of all the other discovery announcements being made by the competition thereby creating a totally false impression of how academia works and how it progresses. Can we please turn down the volume, cut out the hype and present the results of academic research in history in a manner appropriate to it and not to the marketing of the latest Hollywood mega-bucks, blockbuster?

[1] For those who are not to sure about these terms, a placeholder zero just indicates an empty space in a place value number system, so you can distinguish between 11 and 101, where here the zero is a placeholder. A number concept zero also fulfils the same function but beyond this is a number in its own right. You can perform the arithmetical operations of addition, subtraction and multiplication with it. However, as we all learnt at school (didn’t we!) you can’t divide by zero; division by zero is not defined.

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The Great Man paradox – A coda: biographies

This is a follow up to my last post that was inspired by an interesting discussion on Twitter and by the comment on that post by Paul Engle, author of the excellent Conciatore: The Life and Times of 17th Century Glassmaker Antonio Neri.

It is clear to me that biographies, particular popular ones, play a very central roll in the creation of the great men and lone genius myths. Now don’t misunderstand me I am not condemning #histSTM biographies in general; I have one and a half metres of such biographies on my bookshelves and have consumed many, many more that I don’t own. What I am criticising is the way that many such biographies are written and presented and I am going to make some suggestions, with examples, how, in my opinion such biographies should be written in order to avoid falling into the great man and lone genius traps.

The problem as I see it is produced by short, single volume, popular biographies of #histSTM figures or the even shorter portraits printed in newspapers and magazines. Here the title figure is presented with as much emphasis as possible on the uniqueness, epoch defining, and world-moving importance of their contribution to the history of science, technology or medicine. Given the brevity and desired readability of such works the context in which the subject worked is reduced to a minimum and any imperfections in their efforts are often conveniently left out. In order to achieve maximum return on their investment publishers then hype the book in their advertising, in the choice of title and/or subtitle and in the cover blurbs. A good fairly recent example of this was the subtitle of David Loves Kepler biography, How One Man Revolutionised Astronomy, about which I wrote a scathing blog post.

The authors of such works, rarely themselves historian of science, also tend to ignore the painfully won knowledge of historians and prefer to repeat ad nauseam the well worn myths handed down by the generations – Newton and the apple, Galileo and the Tower of Pisa and so on and so forth.

#histSTM biography does not have to be like this. Individual biographies can be historically accurate, can include the necessary context, and can illuminate the failings and errors of their subjects. Good examples of this are Westfall’s Newton biography Never at Rest and Abraham Pais’ Einstein biography Subtle is the Lord. Unfortunately these are doorstep size, scholarly works that tend to scare off the non-professional reader. Are there popular #histSTM works that surmount this problem? I think there are and I think the solution lies in the multi-biography and the theme-orientated books with biographies.

A good example of the first is Laura J Snyder’s The Philosophical Breakfast Club: Four Remarkable Friends Who Transformed Science and Changed the World. Despite the hype in the subtitle this book embeds its four principal biographies in a deep sea of context and because all four of them were polymaths, manages to give a very wide picture of Victorian science in the first half of the nineteenth century.

Another good example is Jenny Uglow’s The Lunar Men: The Friends Who made the Future, once again a terrible subtitle, but with its even larger cast of central characters and even wider spectrum of science and technology delivered by them we get a true panorama of science and technology in the eighteenth and nineteenth centuries. Neither book has any lone geniuses and far too many scrambling for attention for any of them to fit the great man schema.

Two good examples of the second type are both by the same author, Renaissance Mathematicus friend and Twitter sparring partner, Matthew the Mancunian Maggot Man, aka Matthew Cobb. Both his books, The Egg and Sperm Race: The Seventeenth Century Scientists Who Unravelled the Secrets of Sex, Life and Growth

and Life’s Greatest Secret: The Race to Crack the Genetic Code

deal with the evolution of scientific concepts over a relatively long time span. Both books contain accurate portraits of the scientists involved complete with all of their failings but the emphasis is on the development of the science not on the developers. Here, once again, with both books having a ‘cast of millions’ there is no place for lone geniuses or great men.

These, in my opinion, are the types of books that we should be recommending, quoting and even buying for friends and relatives not the single volume, one central figure biographies. If more such books formed the basis of peoples knowledge of #histSTM then the myths of the lone genius and the great man might actually begin to fade out and with luck over time disappear but sadly I don’t think it is going to happen any day soon.

Having mentioned it at the beginning I should say something about Paul Engle’s Conciatore.

This is a single volume, one central figure biography of the seventeenth-century glassmaker Antonio Neri, who was the first man to write and publish a book revealing the secrets of glassmaking. His revealing of the trade secrets of a craft marks a major turning point in the history of technology. Up till the seventeenth century trade secrets were just that, secret with severe punishment for those who dared to reveal them, including death. Later in the century Joseph Moxon would follow Neri’s example publishing a whole series of books revealing the secrets of a whole range of trades including the first ever textbook on book printing his Mechanical Exercises or the Doctrine of Handy-Works. Paul’s book is a biography of Neri but because of why he is writing about Neri it is more a history of glassmaking and so sits amongst my history of technology books and not with my collection of #histSTM biographies. Here the context takes precedence over the individual, another example of how to write a productive biography and a highly recommended one at that.

 

 

 

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A mini-pre-vacation rant roundup

I don’t seem to have provoked anyone for quite sometime, so I thought I would set up a quick Hist­_Sci Hulk triple threat match before I disappear off on holiday. What follows are three things that irritated me on the Internet in recent days.

The major scientific theme of the day has been, of course, Monday’s total eclipse over America. In the lead up we have seen a lot on the Internet about eclipse maps. Eclipse maps are maps that show/predict the shadow path of the eclipse usually differentiating between those areas experiencing a full eclipse and those only experiencing various degrees of partial eclipse. On 17 August the website Atlas Obscura had an article on eclipse maps with the title How Edmond Halley Kicked Off the Golden Age of Eclipse Mapping that featured Halley’s 1715 eclipse map. Now this title contains a serious history of astronomy error and Atlas Obscura were unfortunately not the only ones to make it in the lead up to Monday’s great solar event.

Halley’s 1715 Eclipse Map

Edmond Halley did not kick off the Golden Age of Eclipse Mapping, the seventeenth-century mathematician and astronomer Erhard Weigel (1625–1699) (who you can read about here) did with an eclipse map published in 1654 sixty-one years before Halley’s effort.

Weigel’s 1654 Eclipse Map

Halley wasn’t even second in the eclipse map stakes as Weigel’s student Johann Christopher Sturm (1635–1703) (who you can read about at the Weigel link) published one 1676, thirty-nine years before Halley.

Sturm’s 1676 Eclipse Map

Both Weigel and Sturm were known to the Royal Society, of which Halley was both a member and for a time an employee, and Sturm was also a member, so there is a strong possibility that Halley knew of the efforts of his German colleagues and cannot even be regarded as an independent inventor.

If you want all of the dope on eclipse maps then I highly recommend the excellent Eclipse-Maps website, which can fill all of your eclipse map desires whatever they might be. It is the source of the three eclipse maps shown here.

Another eclipse related false claim is the one presented below:

Now Ibn al-Haytham (c.965–c.1040) is one of the most important figures in the history of optics and he put the pinhole camera effect to very good use in his optical researches but he can’t be said to have invented it. You don’t actually have to build a ‘camera’ to display the pinhole camera effect and there are plenty of images on the web of people projecting images of the eclipse onto some sort of background through a hole in a hat, through a colander, through the holes in a salt cracker etc., etc.

The earliest known description of the pinhole camera effect can be found in the so-called Chinese Mozi writings, which date from the fifth century BCE, so about one and a half thousand years before Ibn al-Haytham lived. A description of the pinhole camera effect can also be found in the writings of Aristotle (384–322). In his Problems Aristotle wrote:

Why is it that an eclipse of the sun, if one looks at it through a sieve or through leaves, such as a plane-tree or other broadleaved tree, or if one joins the fingers of one hand over the fingers of the other, the rays are crescent-shaped where they reach the earth? Is it for the same reason as that when light shines through a rectangular peep-hole, it appears circular in the form of a cone?

 As you can see he’s even describing using the effect to view a solar eclipse. As a small bonus, the name camera obscura for the pinhole camera (the origin of the term camera) was coined by Johannes Kepler.

My third rant of the day leaves the direct field of history of science and moves into the sphere of science communication and philosophy of science. Also provoked by the eclipse several different versions of the following meme have been circulating in the Internet over the last few days. I don’t know who originated it but Neil deGrasse Tyson has been aggressively tweeting a shorter version.

Now I’m a one hundred per cent supporter of science and the scientific method (whatever that might be) and the results that they produce in their attempts to explain our world but I find the analogy drawn here simplistic, naive and anything but helpful. I will endeavour to explain my thoughts on the matter.

Put very simply people are making the mistake here of comparing apples with oranges. A solar eclipse and its scientific explanation are of a very different type to the science of evolution or vaccines and all the other things that denialists reject.

First of all there is a time dimension. Already in the second half of the first century BCE Babylonian astronomers were pretty good at explaining solar and lunar eclipses and could predict lunar ones accurately and at least predict when a solar eclipse could theoretically take place. This knowledge was acquired through many centuries of astronomical observation. So, we are talking about more than two thousand years for people to digest and accept the science behind solar eclipses. In contrast to this, the theory of evolution and the scientific explanation for vaccines are both products of the nineteenth century and less than two hundred years old, far less time for people to digest and accept.

The second factor and the more serious one is complexity. Once you accept that the sun, the moon and the earth are just three balls rotating through the heavens, something accepted in Europe around five hundred BCE, – whether your model is geocentric or heliocentric doesn’t make any real difference to the explanation – then the scientific explanation of an eclipse is, to put it mildly, trivial. In fact it can be easily demonstrated in any classroom using a powerful torch (that’s a flashlight for Americans), a basketball and a large inflatable terrestrial globe. I’ve even seen it demonstrated using a torch and three children as the sun, the moon and the earth. There is not an awful lot you have to understand.

If we now turn to evolution or vaccines we are in a wholly different ball game. The theory of evolution is a highly complex scientific theory based on a vast amount of scientific material. The same can be said of the science behind the theories of disease and the use of vaccines to combat some of them. These are not scientific results that can be lucidly explained by a simple classroom demonstration in a couple of minute.

A third factor is personal involvement. There is a certain distance between a human being and the object of astronomy. It is true that we are dependent on the sun for our existence but on the whole we don’t connect to celestial objects on a very personal level. Things are very, very different with both the theory of evolution and vaccines. The theory of evolution says very directly where we as a species come from and that people have difficulty getting their heads around the fact that we are, over a long period of time, descended from some sort of proto-ape-like creature, in fact from the very same proto-ape-like creature as chimpanzees and gorillas shouldn’t come as a surprise. Remember that infamous Victorian quip, “You might think that your grandfather was an ape, sir but your grandmother!” It’s very easy to mock but it’s a hell of a long stretch to convince people to believe the theory of descent. Add to this the complexity of the actually mechanisms of evolution and that you are going to have problems convincing people to accept them shouldn’t surprise anybody.

All the above can be repeated for the theory of disease and the explanations for the function of vaccines; it’s all very, very complex and difficult to swallow for many people. Add to this the fact that vaccine damage is a reality. Before anybody tries to teach me how to suck eggs, I am well aware of the fact that the risk of any given child suffering vaccine damage is by several factors lower than the risk of death or serious brain damage, from say measles, for a child in a non-vaccinated population. But this statement has two problems, firstly ‘my child’ could be damaged by the vaccine, people are emotional, and secondly people don’t understand statistics. Any scientific explanation that involves statistics is likely to set the recipient in a state of panic.

As science communication, or spreading the science gospel, I find the meme above underwhelming to say the least. To say in an arrogant, sneering tone that if you accept the scientific explanation for, trivial phenomenon, A then you have to accept the scientific explanation for, anything but trivial, B is in my opinion anything but helpful and is more likely to antagonise than convince.

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The West’s intellectual birthright!

The American cultural magazine, The Atlantic recently published an article by Daniel Foster entitled, In Defense of ‘The West’. This was a political article questioning the speech that Donald Trump had made in Warsaw and what the author sees, as what The Trump White means when they talk of ‘The West’. Amongst many other things the article contains the following paragraph encapsulating the authors view of what he sees as The West’s intellectual birthright in the history of science:

Likewise, Egypt hosted the first great repository of Western knowledge—the library at Alexandria—and for a millennium or so following that library’s destruction, it was Muslim metaphysicians who kept lit the flame of Greek ideas. The West’s intellectual birthright, then, was reborn in Latin and French and German and English because it was vouchsafed in Arabic, in the dark interregnum between Charlemagne and the Renaissance.

These sixty-six words made my hair stand on end, or would have done if I had any, for several different reasons that I shall attempt to explicate in what follows.

We will start off with the expression The West’s intellectual birthright. What is meant here is of course Greek science, which doesn’t actually exist and never did. However, how is Greek science The West’s intellectual birthright? The article’s author is trying to argue against a view of the West as being white and bordering the North Atlantic and he could start right here. Even the Greek’s were quite happy to admit that their scientific endeavours were based on those of their predecessors in Egyptian and Babylon, whereby Babylon is shorthand for the various cultures that occupied the so-called fertile crescent in antiquity. So why is Greek science not the intellectual birthright of North Africa or the Middle East, the areas that laid its foundations? Greek science is nobody’s intellectual birthright; the various schools of intellectual thought who developed scientific and proto-scientific ideas within Greek culture in the period between roughly 600 BCE and 600 CE sowed seeds in various cultures throughout the world some of which blossomed and some of which withered and the cumulative developments out of those seeds belong to the whole of humanity.

The author tries to argue against a white North Atlantic West by pointing out that it is geographically and culturally intertwined with much outside of this narrow concept viewed historically and so the opening sentence of the paragraph is supposed to imply a non European source for that intellectual birthright. This ignores the fact that although Alexandria lies in Egypt it was a Greek city and the library was a Greek institution and not an Egyptian one. The next problem is that the library in Alexandria was not the first, and by no means the only, great repository of Western knowledge and was not in any meaningful sense destroyed but declined over several centuries probably disappearing from the world stage around 300 CE. For full details of this story I direct you to Tim O’Neill’s recent excellent essay on the subject.

We now stumble over the next problem; Muhammad first fled from Mecca to Medina in 622 CE, this being the formal date of the establishment of Islam. The establishment of Islam as an intellectual culture begins first in the 8th century CE, so more than 400 years after the final collapse of the library of Alexandria. The Muslims, Christians, Jews and Zoroastrians who established the intellectual culture within the Islamic Empire collected their science and philosophy not only from various Greek sources but also from Persian, Indian and Chinese ones, so they are not just keeping the flame of Greek ideas lit but a melange of ideas from numerous sources. Even more important, they didn’t just keep a flame lit but analysed, criticised, commented upon and improved and expanded the knowledge that they had collected from those other cultures. They were not simply guardians of the flame but added fuel of their own to make it burn brighter.

This knowledge came back into Europe through the boundaries between the Islamic Empire and Christian Europe in Spain and Sicily in the 12th and 13th centuries through the efforts of the so-called translators. These were Christian scholars who worked together with Arabs and Jews to translate the Greek, Latin and Arabic works from Arabic into Latin. This means that the Islamic Empire had only had ‘exclusive’ access to this conglomeration of knowledge for five hundred years and not a millennium as claimed above. Note that this knowledge returned to Europe only in Latin and not also in French German and English as claimed. The introduction of the use of the vernacular for scientific texts only really began in the seventeenth century long after this knowledge had become established in Europe.

We now turn to the final and by far and away the worst piece of shoddy history in this strange paragraph, its final clause: in the dark interregnum between Charlemagne and the Renaissance. When I read this the first time I did more than a double take. I seriously couldn’t believe what I had just read. Let us be clear. We are not talking here about the Early Middle Ages, long known as The Dark Ages, a term that historians now shun but about the period that represents the emergence from the Early Middle Ages into what is generally known as the High Middle Ages and this is according to our author a ‘dark interregnum’. Sorry but this is just simple wrong.

There was a definable intellectual decline within the Roman Empire that begins gradually in the middle of the 2nd century CE and can be regarded as complete by around 400 CE with the collapse of the Western Empire. Over the next approximately 400 years there is little of no intellectual activity in Europe and it is first with Karl der Große (that’s Charlemagne) and the so-called Carolinian Renaissance that this situation begins to change. Far from being the start of a dark interregnum Charlemagne marks the end of one and the gradual climb out of the intellectual darkness into the sunshine of knowledge. Starting with Charlemagne’s own intellectual reformer, Alcuin of York, there is a long chain of medieval scholars including the translators mentioned above, the Oxford Calculatores, the Paris Physicists and many others who laid the foundations for the Renaissance and the so-called Scientific Revolution.

The rich world of medieval science and technology has been well documented beginning with the work of Pierre Duhem in the 19th and early 20th centuries over the substantial contributions of Alistair Crombie, Marshall Clagett, Edward Grant, John Murdoch, Toby Huff and David Lindberg amongst others. With the work of James Hannam and John Freely there are even two good popular books on the subject available for those who don’t want to plough through heavy academic texts, so there is really no excuse for the piece of arrant bullshit presented by Daniel Foster.

The scant paragraph that I have eviscerated above is unfortunately typical for the type of history of science, although to even call it history is a misnomer, that gets presented all too often by journalists, a collection of random myths, legends, clichés and ignorance that they have picked up somewhere down the line. Checking their facts or even consulting an expert on the subject seems to be too much trouble for these people, what does it matter, it’s just history of science seems to be their creed and that really pisses me off.

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Did Eratosthenes really measure the size of the earth?

Last Thursday was Summer Solstice in the Northern Hemisphere and The Guardian chose to mark the occasion with an article by astrophysicist turned journalist and novelist, Stuart Clark, who chose to regale his readers with a bit of history of science. The big question was would he get it right? He has form for not doing so and in fact, he succeeded in living up to that form. His article entitled Summer solstice: the perfect day to bask in a dazzling scientific feat, recounted the well know history of geodesy tale of how Eratosthenes used the summer solstice to determine the size of the earth.

Eratosthenes of Cyrene was the chief librarian at the great library of Alexandria in the third century BC. So the story goes, he read in one of the library’s many manuscripts an account of the sun being directly overhead on the summer solstice as seen from Syene (now Aswan, Egypt). This was known because the shadows disappeared at noon, when the sun was directly overhead. This sparked his curiosity and he set out to make the same observation in Alexandria. On the next solstice, he watched as the shadows grew small – but did not disappear, even at noon.

The length of the shadows in Alexandria indicated that the sun was seven degrees away from being directly overhead. Eratosthenes realised that the only way for the shadow to disappear at Syene but not at Alexandria was if the Earth’s surface was curved. Since a full circle contains 360 degrees, it meant that Syene and Alexandria were roughly one fiftieth of the Earth’s circumference away from each other.

Knowing that Syene is roughly 5000 stadia away from Alexandria, Eratosthenes calculated that the circumference of the Earth was about 250,000 stadia. In modern distance measurements, that’s about 44,000km – which is remarkably close to today’s measurement of 40,075km.

Eratosthenes also calculated that the tilt of the Earth’s polar axis (23.5 degrees) is why we have the solstice in the first place.

Illustration showing a portion of the globe showing a part of the African continent. The sunbeams shown as two rays hitting the ground at Syene and Alexandria. Angle of sunbeam and the gnomons (vertical pole) is shown at Alexandria, which allowed Eratosthenes’ estimates of radius and circumference of Earth.
Source: Wikimedia Commons

Whilst it is correct that Eratosthenes was chief librarian of the Alexandrian library one should be aware that the Mouseion (Shrine of the Muses, the origin of the modern word, museum), which housed the library was more akin to a modern academic research institute than what one envisages under the word library. Eratosthenes was according to the legends a polymath, astronomer, cartographer, geographer, mathematician, poet and music theorist.

From the information that during the summer solstice the sun was directly overhead in Syene at noon, and cast no shadows and that a gnomon in Alexandria 5000 stadia north of Syene did cast a shadow, Eratosthenes did not, and I repeat did not, realise that the Earth’s surface was curved. Eratosthenes knew that the Earth’s surface was curved, as did every educated Greek scholar in the third century BCE. Sometimes I get tired of repeating this but the first to realise that the Earth was a sphere were the Pythagoreans in the sixth century BCE. Aristotle had summarised the empirical evidence that showed that the Earth is a sphere in the fourth century BCE, in writings that Eratosthenes, as chief librarian in Alexandria, would have been well acquainted with. Put simply, Eratosthenes knew that he could, using trigonometry, calculate the diameter of the Earth’s sphere with the data he had accumulated, because he already knew that it was a sphere.

The next problem with the account given here is one that almost always turns up in popular version of the Eratosthenes story; there wasn’t just one measure of length in the ancient Greek world known as a stadium but quite a collection of different ones, all differing in length, and we have absolutely no idea which one is meant here. It is in the end not so important as all of them give a final figure with 17% or less error compared to the true value, which is for the method used quite a reasonable ball park figure for the size of the Earth. However this point is one that should be mentioned when recounting the Eratosthenes story. Eratosthenes may or may not have calculated the tilt of the Earth’s axis but this is of no real historical significance, as the obliquity of the ecliptic, as it is also known, was, like the spherical shape of the Earth, known well before his times.

An astute reader might have noticed that above I used the expression, according to the legends, when describing Eratosthenes’ supposed talents. The problem is that everything we know about Eratosthenes is hearsay. None of his alleged many writings have survived. We only have second hand reports of his supposed achievements, most of them centuries after he lived. This raises the question, how reliable are these reports? A comparable situation is the so-called theorem of Pythagoras, well known to other cultures well before Pythagoras lived and only attributed to him long after he had died.

The most extreme stance is elucidated by historian of astronomy, John North, in his one volume history of astronomy, Cosmos:

None of Eratosthenes’ writings survive, however, and some have questioned whether he ever found either the circumference of the Earth, or – as is often stated – the obliquity of the ecliptic, on the basis of measurements.

So what is our source for this story? The only account of Eratosthenes’ measurement comes from the book On the Circular Motions of the Celestial Bodies by the Greek astronomer Cleomedes and with that the next problems start. It is not actually known when Cleomodes lived. On the basis of his writings Thomas Heath, the historian of Greek mathematics, thought that text was written in the middle of the first century BCE. However, Otto Neugebauer, historian of ancient science, thought that On the Circular Motions of the Celestial Bodies was written around 370 CE. Amongst historians of science the debate rumbles on. North favours the Neugebauer date, placing the account six centuries after Eratosthenes’ death. What exactly did Cleomodes say?

The method of Eratosthenes depends on a geometrical argument and gives the impression of being slightly more difficult to follow. But his statement will be made clear if we premise the following. Let us suppose, in this case too, first, that Syene and Alexandria he under the same meridian circle, secondly, that the distance between the two cities is 5,000 stades; 1 and thirdly, that the rays sent down from different parts of the sun on different parts of the earth are parallel; for this is the hypothesis on which geometers proceed Fourthly, let us assume that, as proved by the geometers, straight lines falling on parallel straight lines make the alternate angles equal, and fifthly, that the arcs standing on (i e., subtended by) equal angles are similar, that is, have the same proportion and the same ratio to their proper circles—this, too, being a fact proved by the geometers. Whenever, therefore, arcs of circles stand on equal angles, if any one of these is (say) one-tenth of its proper circle, all the other arcs will be tenth parts of their proper circles.

Any one who has grasped these facts will have no difficulty in understanding the method of Eratosthenes, which is this Syene and Alexandria lie, he says, under the same mendian circle. Since meridian circles are great circles in the universe, the circles of the earth which lie under them are necessarily also great circles. Thus, of whatever size this method shows the circle on the earth passing through Syene and Alexandria to be, this will be the size of the great circle of the earth Now Eratosthenes asserts, and it is the fact, that Syene lies under the summer tropic. Whenever, therefore, the sun, beingin the Crab at the summer solstice, is exactly in the middle of the heaven, the gnomons (pointers) of sundials necessarily throw no shadows, the position of the sun above them being exactly vertical; and it is said that this is true throughout a space three hundred stades in diameter. But in Alexandria, at the same hour, the pointers of sundials throw shadows, because Alexandria lies further to the north than Syene. The two cities lying under the same meridian great circle, if we draw an arc from the extremity of the shadow to the base of the pointer of the sundial in Alexandria, the arc will be a segment of a great circle in the (hemispherical) bowl of the sundial, since the bowl of the sundial lies under the great circle (of the meridian). If now we conceive straight lines produced from each of the pointers through the earth, they will meet at the centre of the earth. Since then the sundial at Syene is vertically under the sun, if we conceive a straight line coming from the sun to the top of the pointer of the sundial, the line reaching from the sun to the centre of the earth will be one straight line. If now we conceive another straight line drawn upwards from the extremity of the shadow of the pointer of the sundial in Alexandria, through the top of the pointer to the sun, this straight line and the aforesaid straight line will be parallel, since they are straight lines coming through from different parts of the sun to different parts of the earth. On these straight lines, therefore, which are parallel, there falls the straight line drawn from the centre of the earth to the pointer at Alexandria, so that the alternate angles which it makes arc equal. One of these angles is that formed at the centre of the earth, at the intersection of the straight lines which were drawn from the sundials to the centre of the earth; the other is at the point of intersection of the top of the pointer at Alexandria and the straight line drawn from the extremity of its shadow to the sun through the point (the top) where it meets the pointer. Now on this latter angle stands the arc carried round from the extremity of the shadow of the pointer to its base, while on the angle at the centre of the earth stands the arc reaching from Syene to Alexandria. But the arcs are similar, since they stand on equal angles. Whatever ratio, therefore, the arc in the bowl of the sundial has to its proper circle, the arc reaching from Syene to Alexandria has that ratio to its proper circle. But the arc in the bowl is found to be one-fiftieth of its proper circle.’ Therefore the distance from Syene to Alexandria must necessarily be one-fiftieth part of the great circle of the earth. And the said distance is 5,000 stades; therefore the complete great circle measures 250,000 stades. Such is Eratosthenes’ method. (This is Thomas Heath’s translation) 

You will note that Cleomedes makes no mention of Eratosthenes determining the spherical shape of the Earth through his observations but writes very clearly of great circles on the globe, an assumption of spherical form. So where does Stuart Clark get this part of his story? In his article he tells us his source:

I first heard the story when it was told by Carl Sagan in his masterpiece TV series, Cosmos.

The article has a video of the relevant section of Sagan’s Cosmos and he does indeed devote a large part of his version of the story to explaining how Eratosthenes used his observations to determine that the Earth is curved. In other words Stuart Clark is just repeating verbatim a story, which Carl Sagan, and or his scriptwriters, made up in 1980 without taken the trouble to verify the accuracies or even the truth of what he saw more than thirty years ago. Carl Sagan said it, so it must be true. I have got into trouble on numerous occasions by pointing out to Carl Sagan acolytes that whatever his talents as a science communicator/populariser, his history of science was to put it mildly totally crap. Every week he pumped his souped-up versions of crappy history of science myths into millions of homes throughout the world. In one sense it is only right that Neil deGasse Tyson presented the modern remake of Cosmos, as he does exactly the same.

 

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