Ohm Sweet Ohm

This is the story of two brothers born into the working class in a small town in Germany in the late eighteenth century. Both of them were recognised as mathematically gifted whilst still teenagers and went on to study mathematics at university. The younger brother was diligent and studious and completed his doctorate in mathematics with a good grade. There followed a series of good teaching jobs before he obtained a lectureship at the then leading university of Berlin, ten years after graduating. In due course, there followed positions as associate and the full professor. As professor he contributed some small but important proofs to the maths cannon, graduated an impressive list of doctoral students and developed an interesting approach to maths textbooks. He became a respected and acknowledged member of the German mathematical community.

The elder brother’s life ran somewhat differently. He started at the local university but unlike his younger brother he was anything but studious preferring a life of dancing, ice -skating and playing billiards to learning mathematics. His father a hard working craftsman was disgusted by this behaviour and forced him to leave the university and take up a teaching post in Switzerland. On the advice of his mathematics professor he taught himself mathematics by reading the greats. He returned to his home university and obtained his doctorate in the same year as his brother. There then followed a series of dead end jobs first as a badly paid university lecturer with little prospect of promotion and then a series of deadbeat jobs as a schoolteacher. In the last of these he had access to a good physics laboratory and began a series of investigations in a relatively new area of physics. At the age of thirty-eight, something of a failure, he published the results of his investigations in a book, which initially failed to make any impact. At the age of forty-four he obtained an appointment as professor at a polytechnic near to his home town and things began to finally improve in his life. At the age of fifty-two his work received acknowledgement at the highest international levels and finally at the age of sixty-three he was appointed professor for physics at a leading university.

The younger brother whose career path had been so smooth, fairly rapidly disappeared from the history of mathematics after his death in 1872, remembered by only a handful of specialists, whereas the much plagued elder brother went on to lend the family name to one of the most frequently used unit of measure in the physical sciences; a name that can be found on multiple appliances in probably every household in the western world. The two bothers of my story are Georg Simon Ohm (1789–1854), the discover of Ohm’s Law, and his younger brother, the mathematician, Martin Ohm, who was born on 6 May 1792 and the small German town where they were born is Erlangen where I (almost) live.


The Ohm House, Fahrstraße 11, Erlangen Source: Wikimedia Commons

The Ohm House, Fahrstraße 11, Erlangen
Source: Wikimedia Commons

Georg Simon and Martin were the sons of the locksmith Johann Wolfgang Ohm and his wife Maria Elizabeth Beck, who died when Georg Simon was only ten. Not only did the father bring up his three surviving, of seven, children alone after the death of their mother but he also educated his two sons himself. The son of a locksmith he had enjoyed little formal education but had taught himself philosophy and mathematics, which he now imparted to his sons with great success. As Georg Simon was fifteen he and Martin were examined by the local professor of mathematics, Karl Christian von Langsdorf, who, as already described above, found both boys to be highly gifted and spoke of an Erlanger Bernoulli family.

Plaque on the Ohm House

Plaque on the Ohm House

The plaque reads: The locksmith Johann Wolfgang Ohm (1753–1823) brought up and taught in this house as a true master his later famous sons

Georg Simon Ohm (1789–1854) the great physicist and Martin Ohm (1792–1872) the mathematician

I’ve already outlined the lives of the two Ohm brothers so I’m not going to repeat myself but I will fill in some detail.

Martin Ohm Source: Wikimedia Commons

Martin Ohm
Source: Wikimedia Commons

As above I’ll start with Martin, the mathematician. He made no great discoveries as such and in the world of mathematics his main claim to fame is probably his list of doctoral students several of whom became much more famous than their professor. It was as a teacher that Martin Ohm made his mark, writing a nine volume work that attempted a systematic introduction to the whole of elementary mathematics his, Versuch eines vollkommenen, consequenten Systems der Mathematik (1822–1852) (Attempt at a complete consequent system of mathematics); a book that predates the very similar, but far better known, attempt by Bourbaki by one hundred years and which deserves far more attention than it gets. Martin Ohm also wrote several other elementary textbooks for his students. In his time in Berlin Martin Ohm also taught mathematics for many years at both the School for Architecture and the Artillery Academy.

I first stumbled across Martin Ohm whilst researching nineteenth-century algebraic logics. When it was first published George Boole’s Laws of Thought (1864) received very little attention from the mathematical community. With the exception of a small handful of relatively unknown mathematicians who wrote brief papers on it, it went largely unnoticed. One of that handful was Martin Ohm who wrote two papers in German (the first works in German on Boole’s logic). Thus introducing Boole’s ground-breaking work to the German mathematical public. Boole had written and published other mathematical work in German so he was already known in Germany. Later Ernst Schröder would go on to become the biggest proponent of Boolean logic with his three volume Vorlesungen über die Algebra der Logik (1890-1905). It is perhaps worth noting that Boole like the Ohm brothers was the son of a self-educated tradesman who gave his son his first education.

Martin Ohm has one further claim to notoriety; he is thought to have been the first to use the term “golden section” (goldener Schnitt in German) thus opening the door for hundreds of aesthetic loonies who claim to find evidence of this wonderful ration all over the place.


Georg Simon Ohm

Georg Simon Ohm

We now move on to the man in whose shadow Martin Ohm will always stand, his elder brother Georg Simon.

House in Erlangen just around the corner from their birth house, where both Georg Simon and Martin worked as poorly paid lecturers for physics Photo: Thony Christie

House in Erlangen just around the corner from their birth house, where both Georg Simon and Martin worked as poorly paid lecturers for physics
Photo: Thony Christie

Plaque on house Photo: Thony Christie

Plaque on house
Photo: Thony Christie

The Plaque reads: In this house the physicist Georg Simon Ohm (1789–1854) taught physics in the years 1811 to 1812 and the mathematician Martin Ohm (1792–1872) in the years 1812 to 1817

The school where Georg Simon began the research work into the physics of electricity was the Jesuit Gymnasium in Cologne, which even granted him a sabbatical in 1826 to intensify his researches. He published those researches as Die galvanische Kette, mathematisch bearbeitet (The Galvanic Circuit Investigated Mathematically) in 1827. It was the Royal Society who started his climb out of obscurity awarding him the Copley Medal, its highest award, in 1842 and appointing him a foreign member in the same year. Membership of other international scientific societies, such as Turin followed. Georg Simon’s first professorial post was at the Königlich Polytechnische Schule (Royal Polytechnic) in Nürnberg in 1833. He became the director of the Polytechnic in 1839 and today the school is a technical university, which bears the name Georg Simon Ohm. Georg Simon ended his career as professor of physics at the University of Munich.

The town of Erlangen is proud of Georg Simon and we have an Ohm Place, with an unfortunately rather derelict fountain, the subject of a long political debate concerning the cost of renovation and one of the town’s high schools is named the Ohm Gymnasium. The city of Munich also has a collection of plaques and statues honouring him. Ohm Straße in Berlin, however, is named after his brother Martin.


Statue of Georg Simon Ohm at the Technical University in Munich Source: Wikimedia Commons

Statue of Georg Simon Ohm at the Technical University in Munich
Source: Wikimedia Commons

Any fans of the history of science with a sweet tooth should note that if they come to Erlangen one half of the Ohm House is now a sweet shop specialising in Gummibärs.






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Filed under History of Mathematics, History of Physics, Local Heroes, University History

Unsung? I hardly think so

Recently, New Scientist had an article about Emmy Noether because 2015 is the one hundredth anniversary of Noether’s Theorem. I’m not going to link to it because it’s behind a pay wall. A couple of days later they had an open access follow up article entitled, Unsung heroines: Six women denied scientific glory. This is the latest is a fairly long line of such articles in the Internet, as part of the widespread campaign to increase the profile of women in the history of science. Now in general I approve of these attempts and from time to time make a contribution myself here at the Renaissance Mathematicus, however I think the whole concept is based on a misconception and also the quality of the potted biographies that these post contain are often highly inaccurate or even downright false. I will deal with the particular biography that inspired the title of this post later but first I want to address a more general issue.

Such posts as the New Scientist one are based on the premise that the women they feature have slipped through the net of public awareness because they are women, although this might be a contributory factor, I think the main reason is a very different one that not only affects female scientists but the vast majority of scientists in general. I call this the Einstein-Curie syndrome. The popular history of science is presented as a very short list of exulted geniuses who, usually single-handedly, change the course of (scientific) history. If you ask an averagely intelligent, averagely educated person, who is not a scientist or historian of science, to name a scientist chances are near to certain they will say either Galileo, Newton, Einstein or Stephen Hawking or maybe Darwin and I seriously think even Darwin is a maybe. Alternatively they might name one of the high profile television science presenters, depending on age, Carl Sagan, David Attenborough, Neil deGasse Tyson or Brian Cox. Almost nobody else gets a look in. If you were to specify that they should name a female scientist almost all will respond Marie Curie. In fact the last result has led various women writers to protest that we have much too much Marie Curie as role model for women in STEM. It is not that women in the history of science get ignored, it’s that almost all scientist in the history of science get ignored in favour of the litany of great names.

If we take a brief closer look at this phenomenon with respect to the revolution in physics in the first half of the twentieth century then good old Albert cast a vast shadow over all his contemporaries. He is not just the most well know scientist, he is one of the iconic figures of the twentieth century. Most non-scientists will probably not know where to place the name Max Planck, although here in Germany they might have heard of it because the official German State research institutes are named after him. Schrödinger might fare a little better because of his cat but beyond awareness of the term ‘Schrödinger’s cat’ you would probably draw a blank. The same is true of Heisenberg and his ‘uncertainty principle’, of which the questioned Mr or Mrs Normal will almost certainly have a false conception. Throw in Louis de Broglie, who after all was a Nobel laureate, and you will just provoke a blank stare. People are not ignorant of women in the history of science; people are ignorant of the history of science.

I now want to turn to that which provoked this post and its title, the article in question starts with a potted biography of the great Austrian physicist Lise Meitner, to call Lise Meitner unsung is a straight up abuse of language, which I will come back to later. I first want to deal with some serious inaccuracies in the article and in particular the all too oft repeated Nobel Prize story and why the version that usually gets peddled is highly misleading.

Lise Meitner in 1906 Source: Wikimedia Commons

Lise Meitner in 1906
Source: Wikimedia Commons

The potted biography starts reasonably OK:

As with Noether, Meitner’s career was blighted by discrimination, and not just because of her sex. Meitner studied physics at the University of Vienna, then in the Austro-Hungarian Empire, before moving to Berlin, Germany, to further her education. She attended a series of lectures by Max Planck – the first woman to be allowed to do so – and became his assistant.

It neglects to mention that Meitner got a PhD in physics in Vienna in 1906 as only the second woman to do so. She went to Berlin in 1907, after one year post-doc in Vienna. In Berlin she was only allowed to study as a guest as women were first allowed into the Prussian universities in 1909. She served as Planck’s assistant from 1912 till 1915. In the next paragraph the biography goes for pathos rather than fact: She later began to work with chemist Otto Hahn, but was refused access to his laboratory and was forced to work in a broom cupboard. When Hahn’s research group moved to a different institute, Meitner was offered an unpaid job as his “guest”. The situation for young academics at German universities in the late nineteenth century or early twentieth century was not very rosy no matter what their sex. On the whole you either had rich parents, a rich sponsor or you were the proverbial destitute student. Meitner had wealthy parent, who were prepared to pay for her efforts to become a physicist. Both Meitner and Hahn worked as unpaid guest in the former carpentry shop (not a broom cupboard) of the Chemistry Institute of the Berlin University. In 1912 they got their own research section at the Kaiser Wilhelm Institute for Chemistry although initially Meitner remained an unpaid guest.

Lise Meitner and Otto Hahn in their laboratory. Source: Wikimedia Commons

Lise Meitner and Otto Hahn in their laboratory.
Source: Wikimedia Commons

In 1913 she became a paid member of staff. From 1914 to 1916 she served as a nurse in the First World War. In 1916 she and Hahn returned to the Kaiser Wilhelm Institute and resumed their research work. In 1918 Meitner was appointed head of her own department at the Kaiser Wilhelm Institute. As you can see a slightly different story to the one offered in New Scientist and it doesn’t end here. In 1922 Meitner habilitated on the University of Berlin thus qualifying to be appointed professor and in 1926 she was appointed the first ever female professor of physics at a German university. When the Nazis came to power in 1933 Meitner, a Jew, lost her position at the university but retained her position at the Kaiser Wilhelm Institute until 1938 when she was finally forced to flee the country, greatly assisted by Hahn. She made her way to Sweden where she obtained a position at the Nobel Institute. Meitner was an established physicist who had held important academic teaching and research posts in the thirty years before she fled Germany. She and Hahn had made many important discoveries and had produced a significant list of publications. She was a leading nuclear physicist with an international reputation, not quite the picture that the New Scientist biographer imparts. After she had left Germany she and Hahn continued to work together by post. We have now reached that ominous Nobel Prize story:

In 1938, because of her Jewish heritage, Meitner was forced to leave Nazi Germany. She eventually fled to Sweden, with Hahn’s help. Hahn remained in Germany, but he and Meitner continued to correspond and in 1939 they discovered a process they called nuclear fission. In possibly the most egregious example of a scientist being overlooked for an award, it was Hahn who received the 1944 Nobel prize for the discovery. She was mentioned three times in the presentation speech, however, and Hahn named her nine times in his Nobel lecture.

A clear-cut case of prejudice against women in science, or? Actually if you look at the full facts it isn’t anyway near as clear-cut as it seems, in fact the whole situation was completely different. In 1938 Otto Hahn and Fritz Strassmann carried out a series of experiments in Berlin that led to nuclear fission, at that time completely unknown, Hahn realised that fission must have occurred but could not clearly explain the results of his experiment.

Nuclear Fission Experimental Apparatus 1938: Reconstruction Deutsches Museum München Source: Wikimedia Commons

Nuclear Fission Experimental Apparatus 1938: Reconstruction Deutsches Museum München
Source: Wikimedia Commons

Hahn corresponded with Meitner who together with her nephew Otto Frisch worked out the theory that explained nuclear fission. Hahn published the results of his experiments in a joint paper with Strassmann in 1938. Meitner and Frisch published the theory of nuclear fission in 1939. In 1944 Otto Hahn alone was awarded the Nobel Prize in chemistry for his experiment, which demonstrated the existence of nuclear fission. Meitner had no part in these experiments and so should not have been included in the prize as awarded. Strassmann, however, contributed both to the experiments and the subsequent publication so it is more than justified to ask why he was not included in the award of the prize. It is not unusual in the history of the Nobel Prize for the prize to be jointly awarded to the theory behind a discovery and the discovery itself, so it would also be justified to ask why the Nobel committee did not chose to do so on this occasion. However if they had done so then not only Meitner but also Frisch should have been considered for the prize. If on this assumption we add together all of those who had a right to the prize we come to a total of four, Hahn & Strassmann, and Meitner & Frisch, which of course breaks the Nobel Prize rule of maximal three laureates pro prize. Who gets left out? It would of course also be legitimate to ask why Meitner and Frisch were not awarded the Nobel Prize for physics for the theory of nuclear fission; they had certainly earned it. This is a question that neither I nor anybody else can answer and the Nobel Prize committee does not comment on those who do not receive an award, no matter how justified such an award might be. Whatever, although Meitner can be considered to have been done an injustice in not being awarded a Nobel, she didn’t have a claim on the prize awarded to Hahn in 1944 as is so often claimed by her feminist supporters. We now come to the title of this post.

The New Scientist article claims that Lise Meitner is an unsung heroine who was denied scientific glory. This statement is pure and absolute rubbish. Lise Meitner received five honorary doctorates, was elected to twelve major academic societies, she was elected Woman of the Year in America in 1946.

Lise Meitner 1946 Source: Wikimedia Commons

Lise Meitner 1946
Source: Wikimedia Commons

She received the Max Planck medal of the German Physical Society, the Otto Hahn Prize of the German Chemical Society, the peace class of the Pour le mérite (the highest German State award for scientists), the Enrico Fermi Award of the United States Atomic Energy Commission, awarded personally by President Lyndon B. Johnson and there is a statue of her in the garden of the Humboldt University in Berlin. On top of this she received numerous awards and honours in her native Austria. Somehow that doesn’t quite fit the description unsung. Just to make the point even more obvious an institute at the University of Berlin, a crater on the moon, and another crater on venus, as well as an asteroid all bear the name Meitner in her honour.

Can it be that people put too much emphasis on Nobel prizes, for which Meitner was nominated numerous times but never won? The disproportionality of this way of thinking is shown by Meitner last and greatest honour. Element 109 is named Meiterium in her honour. There are 118 know elements of which 98 are considered to occur naturally and the other twenty are products of the laboratory. Only ten of the elements are named after people so this honour is in every way greater than a mere Nobel Prize. Strangely the New Scientist article mentions this honour in a very off hand way in its final sentence, as if it was of little significance. Otto Hahn does not have an element named after him.

Added 5 May 2015:

Over on his blog John Ptak has a post about a wonderful American comic book that mentions Lise Meitner and her role in the history of the atomic bomb. With John’s permission I have added the the comic panel in question below.

Source: Ptak Science Books

Source: Ptak Science Books

If you don’t already visit Mr Ptak’s delightful Internet book emporium you should, it’s a cornucopia of scientific and technological delight.


Filed under History of Physics, History of science, Ladies of Science, Myths of Science

Abraham Ortelius and the 16th century information age.

The sixteenth century saw the evolution of modern cartography emerge out of a renaissance in Ptolemaic cartography. In the second half of the century the Netherlands played a leading role in this process. I have already blogged twice about Gerard Mercator the man most closely associated with the modern cartography, here and here, and also about his teacher Gemma Frisius, so today I want to turn my attention to Mercator’s friend and rival Abraham Ortelius.


Abraham Ortelius by Peter Paul Rubens Source: Wikimedia Commons

Abraham Ortelius by Peter Paul Rubens
Source: Wikimedia Commons

He was born Abraham Ortel (as we most Renaissance scholars there are numerous variant spellings of the family name) in Antwerp on 14 April 1527, to where his grandfather William had moved the family from Augsburg in Southern Germany in 1460, supposedly because of religious persecution. The son of a merchant who died whilst he was still young, in about 1535. Ortelius studied mathematics, Latin and Greek as a youth and apprenticed as an engraver of maps and entered the Antwerp guild of map illuminators in 1547. He set a shop trading in books, prints and maps with his sister and became an engraver for the highly influential Plantin publishing house. Through his various activities as a trader Ortelius came to travel extensively throughout Europe, visiting all the regions of Germany, Italy, France, England and Ireland.

He met and became friends with Gerard Mercator at the Frankfurt book Fair in 1554. In 1559-1560 he accompanied Mercator on his cartographical expedition through Trier, Lorraine and Poitiers. It was during this trip that Mercator is supposed to have persuaded his friend to not just engrave and colour other people’s maps but to become a cartographer in his own right.

Following the example of his mentor, Ortelius started out producing single maps sold as prints. His first effort was an eight-sheet world map produced in 1564. This was followed by a two-sheet map of Egypt (1565), a single-sheet map of the Holy Land in 1566, a two-sheet map of Asia (1567) and a six-sheet map of Spain (1570). Ortelius’ entry into the map business was a success. Gemma Frisius, Mercator and Ortelius were all cartographers and businessmen. However, whereas it is safe to say that Gemma Frisius and Mercator were cartographers first and businessmen second in the case of Ortelius it was the other way round; he was very much a businessman first and a cartographer second.


Ortelius' World Map 1564 Source: Wikimedia Commons

Ortelius’ World Map 1564
Source: Wikimedia Commons

Given the massive increase in international trade and the travel involved in it, there was a strong increase in the demand for good maps. To save themselves the trouble of carrying around large bundles of loose maps various people had started collecting together maps from various sources and binding them together in a book. However, the maps in such collections were of different styles, varying qualities and highly varying usefulness. Ortelius and his business partners came up with the idea of printing and publishing a comprehensive collection of maps of uniform size all in the same style and containing the most up to date geographical data available. Published by Ortelius and printed by Egidius Coppens van Diest the first edition of Ortelius’ Theatrum orbis terrum (the first modern atlas!?) containing fifty-three maps appeared in 1570.


Theatrum Orbis Terrarum Title Page Source: Wikimedia Commons

Theatrum Orbis Terrarum Title Page
Source: Wikimedia Commons

Ortelius didn’t produced the maps from scratch himself but relied on the maps of other cartographers, modifying and improving them as he reproduced them in his uniform style oft incorporating elements of several maps into his finished product. This method of working was not new but had been employed by the leading cartographers throughout the sixteenth century, where Ortelius differed was in that he included a Catlogus cartographorum, a list of eighty-seven cartographers whose work he had used to compose his Theatrum. The Theatrum was a major success going through forty editions between 1570 and 1624. As well as numerous Latin editions there were also several editions each in German, French, Italian, Spanish and English. The Theatrum was very definitely a sixteenth-century bestseller.


Map of the Persian Empire from the Theatrum Orbis Terrarum Source: Wikimedia Commons

Map of the Persian Empire from the Theatrum Orbis Terrarum
Source: Wikimedia Commons

One of the most important features of the Theatrum was its evolution. Each new edition would be modified and updated with as much new information as Ortelius could obtain.

Starting with 53 maps in 1570, it grew to 70 maps in 1573, 93 maps in 1579, 122 maps in 1584 and in the final edition prepared by Ortelius and published in 1590, one year after his death, 134 maps. Plantin had been involved in marketing and selling the Theatrum from the very beginning and took over printing it in 1579 uptil his own death in 1589.

Of interest is a pocket sized version, or epitome, of the Theatrum that was published by Philips Galle and printed by Plantin beginning in 1577. Like the original this too went through many editions in several different languages, the first edition having been in Dutch.

The evolution of the Theatrum between its birth in 1570 and Ortelius’ death in 1589 is a wonderful example of the so-called Republic of Letters in operation in the Early Modern Period. Ortelius had connections all over Europe and even further afield amongst the scholars of his day. Through correspondence they supplied him with the information he needed to update and modernise his maps. Also supplying the geographical and historical information with which he annotated later editions of his magnum opus. This information network worked in both directions with Ortelius passing on information he had received from one member of the network to others he thought might be interested. This correspondence did not only deal in matters geographical and cartographical but also included much information from all the various branches of natural history. An impression of Ortelius’ correspondence network can be gained from his Album Amicorum (friendship book), which he maintained from 1574 to 1596. It has 130 entries that read like a who’s who of the European intellectual elite of the period.


Maris Pacifici, 1589, the first dedicated map of the Pacific to be printed Source: Wikimedia Commons

Maris Pacifici, 1589, the first dedicated map of the Pacific to be printed
Source: Wikimedia Commons

Ortelius’ second major geographical work was his Synonymia Geographica sive Popularum, Regionum, Insularum, Urbium… Appelationes et Nomina, originally an appendix in the Theatrum but then published in expanded form as a separate volume beginning in 1578. This is a list of classical place names identifying their modern locations based on Ortelius’ own historical research, an important research tool for anybody studying classical works.

Another minor claim to fame possessed by Ortelius is that he appears to be the first person to have suggested a theory of continental drift based on his recognition that the continents surrounding the Atlantic basin seemed to fit together. He suggested that the Americas had been torn away from Europe and Africa by earthquakes and floods. His theory fell on deaf ears in his own times.

We still have one rather important linguistic question to clear up. If the ‘first modern atlas’, was entitled the Theatrum orbis terrum by Ortelius, its creator, then why do we call a collection of maps an atlas?

Almost at the same time as Ortelius, his friend Mercator embarked on a very similar project if his motivation was somewhat different. I have blogged about Mercator’s map collection, which he called an atlas already here so I won’t repeat the story now. Mercator’s book only appeared in full, bearing for the first time the title Atlas, posthumously in 1595, twenty-five years after the first appearance of the Theatrum. Although Mercator’s work was without doubt superior to Ortelius’, the later was already a well-established best seller and the larger more complex work of Mercator failed to seriously challenge the market leader. Had the situation remained as it was, we would probably still refer to a bound collection of maps as a theatre. In case you are wondering Ortelius’ original title translates as something like view of the earthly globe. However at the end of the 1590s things changed. Ortelius died and although his Theatrum continued to appear until 1624 nobody took the trouble to update it. On the other hand Mercator’s son died in 1599 and Jodocus Hondius a cartographical publisher and globe maker from Amsterdam bought up the rights to Mercator’s Atlas. Hondius did update and modify Mercator’s work and so took over dominance in the market. In 1624 Hondius’ biggest rival Willem Janszoon Blaeu bought the rights to Ortelius’ Theatrum incorporating it into his own map book that he titled an atlas in imitation of Hondius. And so it is that we now call a bound collection of maps an atlas and not a theatre.









Filed under History of Cartography, Renaissance Science

Asterisms and Constellations and how not to confuse them with Tropical Signs.

If you are going to write about something, especially if you intend to lay bare somebody else’s ignorance, it pays to actually know what you are talking about otherwise you could well end up looking like a total idiot, as does Anna Culaba in her article on the RYOT website, The Stars and Your Astrological Signs Have Been Lying to You This Whole Time. I should point out that Ms Culaba is by no means the first person to publically embarrass themselves pontificating on this subject, in fact it’s a reoccurring theme much loved by scientists and science fans who want to take a cheap shot at astrology. Indeed, as we will see later Ms Culaba, in her article, is in fact just regurgitating the content of a BBC website. So what exactly does our intrepid science fan say in her blog post?

My horoscope for today (I’m a Virgo) according to Astrology.com reads, “Today, explore an aspect of an unfamiliar religion or culture. Today is a day to make plans and aim high.” There are only two things that are keeping me from leaving work right now: one, I don’t really believe that the stars can determine what will happen in my life and two, I wasn’t really born under the star sign that the world told me I was born into. According to the BBC, about 86 percent of people are actually born under a different sign than the one they think. This is because 2,000 years ago, when the Ancient Greeks first created the zodiacs, the star signs corresponded to the position of the sun relative to the constellations that appeared in the sky the day people were born. Unfortunately, during that time people didn’t know of the phenomenon known as the precession. Live Sciences reports that the precession is when the Earth continually wobbles around its axis in an almost 26,000-year cycle thanks to the gravitational attraction of the moon. Thanks to this phenomenon, the constellations some people live and die by have actually drifted away from us. This means that constellations are now actually off by a month. So if you were born between August 11 to September 16 you’re not the picky and critical Virgo that you thought you were — you’re really an ambitious Leo whose strength of purpose allows you to accomplish many, many things. And if you’re astrological world hasn’t been rocked enough, if you thought you had your star sign wrong, wait until some of you realize that there’s actually a 13th zodiac sign known as the Ophiuchus. According to the BBC, the Ancient Greeks deliberately left out the original zodiac so that ancient astrologers would be able to divide the sun’s 360 degree path into 12 equal parts. Where does Ophiuchus fit into the zodiac calendar? It goes between Scorpio and Sagittarius, so if you were born between November 30 and December 18 consider yourself an Ophiuchus. You’re probably very secretive and good at hide and seek.

I have reproduced the whole of Ms Culaba’s screed here to save me having to quote it in little bits, merely removing the links from the original. If you read it through you what will discover is the central claim that astrologers were too stupid to realise the astronomical phenomenon of precession and so you were not actually born under the star sign that they claim you were. There are two general points to be made here, firstly astrologers were well aware of precession and secondly Ms Culaba and the source she is quoting don’t know the fundamental difference between constellations and tropical signs. So for the benefit of Ms Culaba and all others who are confused by the topic we will have a Renaissance Mathematicus guide to asterisms, constellations, the zodiac and tropical signs.

If you go out on a dark night with a clear sky in an area with little or no light pollution (and if you have never done so you should, it’s awesome) and look up in the heavens you will see a myriad of stars looking down on you in a vast blue black vault. If you are not a trained astronomer you will probably find no means of orienting your gaze in this confusion of twinkling lights. This problem was confronted by all human cultures since the dawn of human existence. The human brain seems to be programmed for pattern recognition and so, like children with a join up the dots picture book, all cultures started to create pictures by imagining lines joining up or outlining eye-catching groups of stars and giving these pictures names. These pictures, and they exist in all human cultures, are known technically as asterisms. These asterisms help the observing eye gain orientation when traversing the vast dome of the night sky and early astronomers started compiling lists of the most prominent such join-up-the-dots-pictures or asterisms in order to use them as a scaffolding for mapping the heavens. Those asterisms contained in such formal lists are called constellations. Our modern, western list of constellations has its origins in ancient Babylonian astrology/astronomy and comes down to us via the ancient Greeks and the medieval Islamic astronomers. In his Syntaxis Mathematiké, Ptolemaeus lists 48 constellations by name. Currently, the International Astronomical Union (IAU) recognises 88 named constellations. We now need to turn our attention to the origins of the zodiac.

Viewed from the earth, and before the beginning of the so-called space age that was the only way possible to view the heavens, the sun appears to orbit the earth once every year. In fact the year is defined as the time it takes for the sun to orbit the earth. The path the sun follows on its way around the earth is called the ecliptic and is tilted at approximately 23 degrees to the earth’s equator. This tilt, known as the obliquity of the ecliptic, is the reason why we have seasons on the earth. The six planets visible to the naked eye and know in antiquity – Moon, Mercury, Venus, Mars, Jupiter and Saturn – all appear to orbit the earth in the plane of the ecliptic making this imaginary belt around the heavens very important for the study of astronomy. The earliest known mapping of the ecliptic is contained in a set of Babylonian clay tablets known as the MUL.APIN, which date from around 1000 BCE. Here the path of the moon’s orbit is described or mapped with 17 or 18 (the text is somewhat ambiguous) constellations and stars. The moon’s orbit is tilted at about five degrees to the ecliptic. This mapping was still in use around 700 BCE. By around 500 BCE the 17/18 constellations/stars had be replaced by twelve constellations of varying sizes. Circa 420 BCE the Babylonians had replaced those twelve constellations with twelve equal divisions of the ecliptic comprising 30° segments. These segments were named after the constellations they replaced and form the zodiac that was taken over by the Greeks and made its way down to us. Those segments are known technically as tropical or sun signs, form the basis of zodiacal astrology and are abstract geometrical segment of the ecliptic and not constellations. The constellations slowly circle the heavens due to precession, the tropical signs do not! If an astrologer says you were born under the sign Virgo it means that the sun was in the 30° segment of the ecliptic that bears the name Virgo at the moment of your birth. This has nothing apart from the name in common with the constellation Virgo.

It is not the astrologers who display ignorance of the precession of the equinox, to give the phenomenon its full name, but Ms Culaba who displays total ignorance of both astronomy and astrology. This is not a very good situation to be in if you are going to write about the history of science and yes we are talking about the history of science here, the zodiac with its tropical signs was originally conceived for astronomical purposes. Ms Culaba might be excused because she did not originate this particular piece of history of science rubbish but is merely regurgitating false information from what she obviously thought was a reliable source, the BBC.

Here we have the presenter of Stargazing Live, a high prestige BBC science programme, Dara O Brian presenting the world with high-grade bullshit under the BBC’s banner. O Brian and his co-presenter Brian Cox should know better and I find it a total disgrace that the fee payers money is being wasted on such rubbish under the guise of educational television, both the presenters and the Beeb should be thoroughly ashamed of themselves.


Filed under History of Astrology, History of Astronomy, Myths of Science

The worst history of technology headline of the year?

The Guardian website produced a couple of articles to announce the publication of Sydney Padua’s graphic novel, The Thrilling Adventures of Lovelace and Babbage: The (Mostly) True Story of the First Computer. I strongly suspect that despite Padua’s qualifying ‘mostly’ in her subtitle what we will be presented with here bears very little relation to the historical facts. However, not actually having read the book, it is not the subject of this brief post but rather the Guardian article. This article is crowned with the following headline:

Ada Lovelace and Charles Babbage designed a computer in the 1840s.

A cartoonist finishes the project.

 Can you spot the major howler in the very brief first sentence? Who designed a computer? Charles Babbage designed a computer. Ada Lovelace wrote a puff piece about that computer, which was in all probability largely ghost-written by Babbage. Just in case you should think that this was an inadvertent slip of a subeditor’s thumb on his computer keyboard the claim is repeated even more emphatically in the title of an illustration to the article.

200 years after Ada Lovelace’s birth, the Analytical Engine she designed with Charles Babbage is finally built, thanks to the imagination of Sydney Padua. Illustration: The Observer

In case you should still think that the writer of the piece could or should be excused of all blame, embarrassed by the hyperbolic flights of fancy of that technology history ignorant subeditor, we find the following in the main body of the article.

Brought up to shun the lure of poetry and revel instead in numbers, Lovelace teamed up with mathematician Charles Babbage who had grand plans for an adding machine, named the Difference Engine, and a computer called the Analytical Engine, for which Lovelace wrote the programs.

Where to begin? First off both the Difference Engine and the Analytical Engine are computers. The former a special purpose computer and the latter a general purpose one. Babbage would have been deeply offended having his mighty Difference Engine denigrated to a mere adding machine, although all computers are by name adding machines; computer coming, as it does, from the Latin computare which means to reckon/compute/calculate, sum/count (up). As a brief aside, when the word computer was coined in the 17th century it referred to a person employed to do calculations. Second, and in this context most important, Lovelace did not write the programs for the Analytical Engine. The afore mentioned puff piece from her pen contained one, note the singular, specimen program for the Analytical Engine, which she might possibly have written, although it seems more probable that Babbage wrote it. All the other programs for the Analytical Engine, and there were others were written by, you’ve guessed it, Charles Babbage.

The deification of Ada Lovelace marches on a pace with the honest historian of the computer barely able to keep pace with the waves of mythology that pour out of the unsavvy media almost every day it seems.


Filed under History of Computing, Myths of Science

There is no such thing as Greek science.

I’m pretty certain that a fair number of people reading the title of this post will be going, ‘what the hell is he talking about? We heard all about Greek science at primary (grade) school, secondary school, high school, college, university” or “I’ve read about Greek science in that popular history of science book, popular science journal, that website, on Wikipedia, in that magazine at the hairdressers!” “Of course there is such a thing as Greek science you can hear/read about it all over the place. Has he gone barmy or something?” Others are probably thinking he’s about to go on about how the word science when used for the ancient Greeks is anachronistic and we shouldn’t call it science but … This chain of thought is in fact correct but is not the topic of this post. In fact for the moment I’m quite happy to use the word science in this context as a shorthand way of describing all of the intellectual disciplines practiced by the ancient Greeks that are related to the disciplines that we call the sciences today, even if this usage is more than somewhat anachronistic. What I’m objecting to, in fact rejecting is the whole term ‘Greek science’ it doesn’t exist has never existed and its usage leads to a series of dangerous misconceptions; dangerous that is for our understanding of the history of western science. Why do I say this and what misconceptions?

The usage of the term Greek science implies that there is a coherent, albeit, abstract object that can be indicated by this term, no such object has ever existed. This becomes very obvious if one takes the time to look closely at what is usually labelled Greek science.

If we look at the time dimension we are talking about a set of activities that begins some what earlier than six hundred BCE with the earliest of the so-called pre-Socratic philosophers i.e. Thales and co. It carries on in the western world until the death of the last of the so-called encyclopaedists Isidore of Seville in 632 C. That is a time span of more than twelve hundred years. Just to put that in perspective, if we go back twelve hundred and fifty years from today Pippin the Short, the first of the Carolingians to become King of the Franks, was on the throne. His son Karl der Große, or Charlemagne, as the English call him, might be better known to you. Twelve hundred years is a lot of human history and a lot can happen in a time span that long.

A geographical examination yields a similar result. The pre-Socratics lived in what became known as Asia Minor and is now part of Turkey. It stretches over the Greek island and mainland in its development to Southern Italy. It took in the whole of the Hellenistic Empire of Alexander the Great and later the whole of the Roman Empire. Our last representative Isidore, as his name tells us, lived in Seville in Spain. Up till now I’ve not mentioned the final Greek Empire, Byzantium, which begins when the Roman Emperor Constantine moved his capital from Rome to Constantinople and ended with the fall of that noble city to the Turks in 1453. It occupied a large part of what is now Turkey. Geo-politically over our twelve hundred plus years we progress from ancient Greek culture through Hellenistic culture, on to Romano-Hellenistic culture and finishing up in post-classical Roman late antiquity or the Early Medieval period. It should be clear by now that to refer to Greek science is a fairly pointless exercise from the point of view of time, geography, and politics and culture. It’s about as meaningless as referring to European science and using the term to designate some sort of coherent whole beginning with Charlemagne and going up to the present and encompassing the whole of the continent of Europe. That coherent whole simply doesn’t exist.

Of course the time, special and politico-cultural dimensions are only part of the problem and not even the most important part. Despite the vast diversity that we have just sketched people still insist in talking about a single coherent science and it is here that the real damage caused by misconception takes place. Let us start with one typical example to illustrate what I mean. In popular presentations of the study of the theory of optics I constantly stumble across statement of the type, ‘the Greeks believed that we see by beams projected from the eyes to the objects perceived’. Such standpoint is know technically as an extramission theory of vision and is indeed one of the theories of vision proposed and discussed by the ancient Greeks. The important phrase here is ‘one of the theories’; the various groups in ancient Greece proposed at least five different contrasting, conflicting and contradictory theories of vision over a number of centuries that they investigated and discussed. These theories were then taken up and debated further by both the Islamic and the European scholars in the Middle Ages. We don’t have a case of ‘the Greeks thought/believed this’ but rather the Atomists believed this, the Platonists believed this, the Aristotelians believed this, the Stoics believe this and the mathematical optical theorists believed this. In other words we have conflicting competing theories presented by different schools of thought each of which was different at different times and often in different areas during those twelve hundred years that Greek culture existed. Those who just present the extramission theory as being what the Greeks thought seem to be motivated by presenting the Greeks in a bad light. Look how stupid the Greeks were, they actually believed that the eyes send out rays of fire enabling people to see.

One could of course argue that this is one example and doesn’t necessarily represent the whole of Greek science but it does. The list of groups that I named as holding differing theories of vision is basically the list of principle schools of thought within ancient Greek culture who developed and presented views on a multitude of scientific topics throughout the Greek cultural period. They are others who didn’t necessarily have views on optics, such as the Pythagoreans, but did develop theories in other areas. Each of the named schools came into being and enjoyed a period of prominence as their ideas were shiny new and stimulating then falling somewhat into the background as new schools emerged with other shiny new ideas.

A second example is provided by the disciplines of astronomy and cosmology. It is a commonplace that the Greeks believed the heavens to be divided into two spheres, the sublunar and the supralunar, the latter being perfect and the former corruptible. They, the Greeks, also believed that comets being corruptible inhabit the sublunar sphere. These views are not the views of the Greeks but of Aristotle and the Aristotelians. Another school of thought the Stoics regarded the entire heavens to be of one nature with no division and comets to be phenomena of the supralunar region. The Stoics and there cosmology were in general more dominant in later antiquity than the Aristotelians.

The opinion that the views of the Aristotle were those of the Greeks comes from adoption of those views by Europeans in the High Middle Ages and the misconception that they and they alone dominated European thought until deposed by the ‘modern’ astronomy in the Early Modern Period. In fact modern research into the history of astronomy has revealed that a renaissance of the Stoic cosmology in Europe in the fifteenth and sixteenth centuries played a significant role in the so-called astronomical revolution.

I could go on producing examples from every branch of Greek knowledge that display the diversity of Greek thought across the centuries. Even the much-quoted Greek mathematics was in reality a varying range of diverse and oft conflicting schools. The two most famous Greek mathematicians Euclid and Archimedes represent two conflicting approaches to the subject, Euclid synthetic, Archimedes analytical. These two fundamentally different approaches resurfaced in conflict with each other during the seventeenth century following the renaissances of synthetic Euclidian mathematics in the fifteenth century and analytic Archimedean mathematics in the sixteenth century.

Any extensive in depth survey of science carried out in the Greek language in the Mediterranean region in antiquity should convince anybody that there never was anything that could reasonably be called Greek science and we should all endeavour to stop using the term and instead talk about the Platonic theory of vision, Aristotelian cosmology, Euclidian geometry or whatever label correctly identifies the topic under discussion. By pure chance Mary Beard, a leading British classicist, tweeted the following statement during the week that perfectly sums up the message of this post in 140 characters:


Afraid I bridle at generalising “did THE GREEKS think?” M Finley always said “which Greeks? when?” Not unitary culture – @wmarybeard



Filed under Myths of Science

Emmy the student and Emmy the communist!

Emmy Noether’s birthday on 23 March saw her honoured with a Google Doodle, which of course led to various people posting brief biographies of Erlangen’s most famous science personality or drawing attention to existing posts in the Internet.

Emmy Google Doodle

Almost all of these posts contain two significant errors concerning Emmy’s career that I would like to correct here. For those interested I have written earlier posts on Emmy’s family home in Erlangen and the problems she went through trying to get her habilitation, the German qualification required to be able to teach at university.

The first oft repeated error concerns Emmy’s education and I quote a typical example below:

Today she is celebrated for her contributions to abstract algebra and theoretical physics, but in 20th-century Bavaria, Noether had to fight for every bit of education and academic achievement. Women were not allowed to enrol at the University of Erlangen, so Noether had to petition each professor to attend classes.

As a teenager Emmy displayed neither an interest nor a special aptitude for mathematics but rather more for music and dance. She attended the Städtische Höhere Töchterschule (the town secondary girls’ school), now the Marie-Therese-Gymnasium, and in 1900 graduated as a teacher for English and French at the girls’ school in Ansbach. In 1903 she took her Abitur exam externally at the Königlichen Realgymnasium in Nürnberg. The Abitur is the diploma from German secondary school qualifying for university admission or matriculation. Previous to this she had been auditing some mathematics courses in Göttingen as a guest student with the personal permission of the professors whose courses she visited, hence the claim above. However she had become ill and had returned home to Erlangen. In 1903 the laws were changed in Bavaria allowing women to register at university for the first time. Emmy registered as a regular student at the University of Erlangen in 1903 and graduated with a PhD in mathematics in 1907, under the supervision of Paul Gordon, in invariant theory. She was only the second woman in Germany to obtain a PhD in mathematics. In 1908 she became a member of the Circolo Matematico di Palermo and in 1909 a member of the Deutschen Mathematiker-Vereinigung. In 1909 Hilbert and Klein invited her to come to the University of Göttingen, as a post-doc researcher. It was here in 1915 that Hilbert suggested that she should habilitate with the well know consequences.

Emmy remained in Göttingen until the Nazis came to power in 1933. She held guest professorships in Moscow in 1928/29 and in Frankfort am Main in 1930. She was awarded the Ackermann-Teubner Memorial Prize for her complete scientific work in 1932 and held the plenary lecture at the International Mathematical Congress in Zurich also in 1932. In 1933 when the Nazis came to power she was expelled from her teaching position in Göttingen and it is here that the second oft repeated error turns up.

On coming to power the Nazis introduced the so-called Gesetz zur Wiederherstellung des Berufsbeamtentums, (The Law for the Restoration of the Professional Civil Service). This was a law introduced by the Nazis to remove all undesirables from state employment, this of course meant the Jews but also, socialists, communists and anybody else deemed undesirable by the Nazi Party. Like many of her colleges in the mathematics department at Göttingen Emmy was removed from her teaching position under this law. In fact the culling in the mathematics department was so extreme that it led to a famous, possibly apocryphal, exchange between Bernhard Rust (and not Hermann Göring, see comments) and David Hilbert.

Rust: “I hear you have some problems in the mathematics department at Göttingen Herr Professor”.

Hilbert: “No, there are no problems; there is no mathematics department in Göttingen”.

The Wikipedia article on the history of the University Göttingen gives the story as follows (in German)

Ein Jahr später erkundigte sich der Reichserziehungsminister Bernhard Rust anlässlich eines Banketts bei dem neben ihm platzierten Mathematiker David Hilbert ob das mathematische Institut in Göttingen durch die Entfernung der jüdischen, demokratischen und sozialistischen Mathematiker gelitten habe. Hilbert soll in seiner ostpreußischen Mundart (laut Abraham Fraenkel, Lebenskreise, 1967, S. 159) erwidert haben: „Jelitten? Dat hat nich jelitten, Herr Minister. Dat jibt es doch janich mehr.“

The source here is given as Abraham Fraenkel in his autobiography Lebenkreise published in 1967.

This translates as follows:

One year later [that is after the expulsions in 1933] the Imperial Education Minister Bernhard Rust, who was seated next to the mathematician David Hilbert at a banquet, inquired, whether the Mathematics Institute at Göttingen had suffered through the removal of the Jewish, democratic and socialist mathematicians. Hilbert is said to have replied in his East Prussian dialect” Suffered? It hasn’t suffered, Herr Minister. It doesn’t exist anymore”

It is usually claimed that Emmy lost her position because she was Jewish, a reasonable assumption but not true. Emmy lost her position, like many other in Göttingen, because the Nazis thought she was a communist. Like many European universities in the 1920s and 30s Göttingen was a hot bed of radical intellectual socialism. Emmy had been a member of a radical socialist party in the early twenties but changed later to the more moderate SPD, who were also banned by the Nazis. However it was her guest professorship in Moscow that proved her undoing. Because she reported positively on her year in Russia the Nazis considered her to be a communist and this was the reason for her expulsion from the university in 1933.

Initially Emmy, after her expulsion, actually applied for a position at the University of Moscow but the attempts by the Russian topologist Pavel Alexandrov to get her a position got bogged down in the Russian bureaucracy and so when, through the good offices of Hermann Weyl, she received the offer of a guest professorship in America at Bryn Mawr College she accepted. In America she taught at Bryn Mawr and the Institute of Advanced Studies in Princeton but tragically died of cancer of the uterus in 1935.


Filed under History of Mathematics, Ladies of Science