Category Archives: Autobiographical

It’s Solstice Time Again!

We are deep in what is commonly called the holiday season. For personal reasons I don’t celebrate Christmas and as I explained in this post starting the New Year on 1 January on the Gregorian Calendar is/was a purely arbitrary decision. I wrote there that I consider the winter solstice to be the best choice to celebrate the end and beginning of a solar cycle in the northern hemisphere.


Stonehenge Winter Solstice

Today at 22:23 UTC the sun will turn at the Tropic of Capricorn and begin its journey northwards to the Tropic of Cancer and the summer solstice.  Tropic comes from the Latin tropicus “pertaining to a turn,” from Greek tropikos “of or pertaining to a turn or change.”

I wish all of my readers a happy solstice and may the next 365 days, 5 hours, 48 minutes and 45 seconds bring you much light, joy, peace and wisdom. We can only hope that they will be better than the last 365 days, 5 hours, 48 minutes and 45 seconds (length of the mean tropical or solar year).


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Filed under Autobiographical, Odds and Ends, Uncategorized

Don’t criticise what you don’t understand!

I was pleasantly surprised by the level of positive support my latest anti-Ada polemic received on Twitter, I had expected much more negative reaction to be honest. But I did receive two attacks that I would like to comment on more fully here. The first came from a certain Yael Moussaieff (@sachaieff) and reads as follows:


It still blows my mind how convinced mediocre men are that they’re not mediocre and that their opinions are in fact urgent and needed.

I’m not really sure in what sense here I am supposedly mediocre: my intelligence, my expertise, my abilities, all three, in all aspects of my existence? And how does Ms Moussaieff (I assume she is a she) know this, never having met me, on the basis of one, what I consider to be a fairly reasonably argued, blog post on the evaluation of the contributions of one Victorian woman to computer science. If she had brought some counter arguments to demonstrate the mediocrity of my thought processes or the mediocrity of my understanding of the historical period or the mediocrity of my abilities as a historian of computing (and I am one, see the reply to the next comment) then perhaps I could understand the intension or meaning of her criticism but for the moment I remain perplexed. Maybe my inability to comprehend is, in itself, a sign of my mediocrity.

Peter Robinson (@PeterRobinson76) chose a different line of attack:

We also love to put down anyone that dares to have popularity. Even long dead women.

To which I spontaneously responded:

There is a difference between a put down and a reasoned argument based on facts. I formally studied and researched both Babbage and Lovelace long before the current Lovelace hagiography started, as a professional historian of logic and computing. What are your qualifications?

For his benefit I would like to elucidate and explain my claim to professionalism in this matter. Some or even most of what I am now going to relate ought to be already known to those who have been reading this blog for a number of years for newer readers it might prove instructive.

Throughout the 1980s and the early 1990s I studied as a mature student at the Friedrich-Alexander University of Erlangen & Nürnberg. The first two and a half years I studied mathematics with philosophy as my subsidiary. I then changed to philosophy with English philology and history as my subsidiaries. The emphasis of my studies was always on the history and philosophy of science. During this time I worked for ten years as a paid research assistant in a major research project into the history of formal/symbolic/mathematical logic under the supervision of one of the world’s leading logic historians. This means that somebody, who is considered knowledgeable in these things, thought me competent enough to appoint me to this position. The fact that I was still there ten years later shows that he still believed in my competence. Possibly because I was the only English native speaker in the research team, my main area of research was nineteenth century British algebraic logics, which means I was researching Boole, Jevons, De Morgan, Venn, Cayley, McColl and others including the Americans working together with Peirce. Because algebraic logic was just a small part of the much wider field of abstract algebras emerging in the nineteenth century, I also researched Peacock, John Herschel, Babbage, Cayley, Sylvester, William Rowan Hamilton and various others. Calculating machines was also a part of our remit so Babbage and his computers along with the good Countess Lovelace came in for extensive study on my part.

Now ten plus years might seem a rather long time to study as a student but as I said I was a mature student without grant or parental support, which meant I had to earn money to do silly things like pay the rent or even on occasions eat and the pittance paid to research assistants in those days did not cover my daily living costs, so I also worked outside of the university. I had virtually finished my studies with just my master thesis to complete and my final exams to write–not a very big deal, as there was in those days a strong emphasis on continual assessment–when I crashed out with serious mental health problems. You can only burn the candle at both ends for a limited period of time until the two flames meet in the middle. Coming out of the loony bin I chucked my studies because being a qualified historian of science was never going to pay those pesky bills.

When I quit I had completed the entire research for both my master’s thesis and my doctoral thesis. I had written about 50–70% of my master’s thesis and a complete, highly detailed outline for my doctoral thesis. Now it might seem strange that I was writing both theses at the same time but my original master’s thesis, a wide-ranging study of the entire English speaking nineteenth century algebraic logic community, had grown far too big to be a master’s thesis, so I had cut out one section, on the life and work of Hugh McColl, to be my master’s thesis and turned the main project into a potential doctoral thesis. I recently, whilst clearing out some old cartons, came across all the material for that doctoral thesis. I was stunned at how far I had got with it, having in the intervening years forgotten most of the work I had invested. I sat and stared at it for three days then threw it all away.

So you see, if I say that I have researched and studied Babbage and Lovelace in a professional capacity it is simply the truth. I should point out that if I write about either of them now, I don’t rely on my memory of work done long ago but go back and read the original sources that I sorted out and studied then, modifying if necessary my views, as my knowledge has grown over the intervening years. In more recent years I have been paid by reputable, educational institutions to hold public lectures on Mr Babbage and his computing engines, so yes through preparing those lectures my knowledge has grown.

Let us return to my critics. Over the years battling the Ada hagiography I have come to the conclusion that the majority of her acolytes don’t actually bother to look at the sources at all. It seems some of them have read a blog post or an article in a non-academic Internet magazine, highly biased and based on dubious secondary sources rather than primary ones (and yes I am aware of the irony of writing that on a blog post). The rest have only ever read a short précis of those blog posts/articles posted on one or other of the Internet’s social media, which parrot the inaccurate accounts of their sources. This majority continue to parrot this ‘fake news’ without bothering to check whether it is historical accurate. The result is that we now have a major Ada myth industry.

If I had the chance to discuss with Yael, Peter or any of the acolytes who have criticised and attacked me over the years I would ask them the following questions:

Which Ada biography have you read?

 I have read five of which I have what I regard as the two best ones standing on my bookshelf.

What about Babbage? Have you read his autobiography?

It’s actually a fascinating piece of literature covering much more than the computing engines for which Babbage is famous.

Maybe you have instead read the more modern and objective biography contained in Laura Snyder’s “The Philosophical Breakfast Club”?

A wonderful book, as I wrote in my review of it for the journal Endeavour

Have you read his 9thBridgewater Treatise, in which Babbage discusses religion and expands on his theory that one could explain miracles by unexpected changes in computer programmes?

An interesting if slightly bizarre  argument.

Or perhaps, you have read his On the Economy of Machinery Manufactures, the result of his extensive research into automation?

Babbage’s interest in automation drove much of his studies including his work on computing and computers. His On the Economy was a highly influential book in the nineteenth century.

Maybe you have read his unpublished writings on abstract algebra, now in the British Library, that are thought to have inspired George Peacock’s “Treatise on Algebra”?

 I will admit that I haven’t but it’s on my bucket list. I have however read Peacock’s book, fascinating and an important milestone in the history of mathematics,

Maybe you’ve read up on the Analytical Society, the student group Babbage and Herschel created in Cambridge to convince the university to introduce continental methods of analysis to replace Newton?

I stumbled across this intriguing piece of maths history during my research; it shows the dynamic that drove Babbage even from an early age.

This might seem like an intellectual pissing contest but if you wish to criticise me and maybe show me that I have erred, that I am mistaken or that I’m just plain wrong then I expect you to at least do the leg work. I actually like being shown that I am wrong because it means that I have learnt something new and I love to learn, to improve and to expand my knowledge of a subject. It is what I live for. I am a historian of science with a good international reputation that I have worked very hard to earn. I also work very hard to get my facts right. If you criticise me and hold a different opinion on some topic that I have written about but treat me with respect then I will treat you with respect even if I know that you are wrong. If, however, you just gratuitously insult me, as, in my opinion, Yael and Peter have done then I will treat you with disdain and if the mood suits me with a generous portion of sarcasm.





Filed under Autobiographical, History of Computing, Uncategorized

A Newtonian Refugee

Erlangen, the Franconian university town, where I (almost) live and where I went to university is known in German as ‘Die Hugenottenstadt’, in English the Huguenot town. This name reflects the religious conflicts within Europe in the 17thcentury. The Huguenots were Calvinists living in a strongly and predominantly Catholic France. Much persecuted their suffering reached a low point in 1572 with the St Bartholomew’s Day massacre, which started in the night of 23-24 August. It is not know how many Huguenots were murdered, estimates vary between five and thirty thousand. Amongst the more prominent victims was Pierre de la Ramée the highly influential Humanist logician and educationalist. The ascent of Henry IV to the French Throne saw an easing of the situation for the Huguenots, when he issued the Edict of Nantes confirming Catholicism as the state religion but giving Protestants equal rights with the Catholics. However the seventeenth century saw much tension and conflict between the two communities. In 1643 Louis XIV gained the throne and began systematic persecution of the Huguenots. In 1685 he issued the Edict of Fontainebleau revoking the Edict of Nantes and declaring Protestantism illegal. This led to a mass exodus of Huguenots out of France into other European countries.

Franconia had suffered intensely like the rest of Middle Europe during the Thirty Years War (1618-1648) in which somewhere between one third and two thirds of the population of this area died, most of them through famine and disease. The Margrave of Brandenburg-Bayreuth, Christian Ernst invited Huguenot refugees to come to Erlangen to replace the depleted inhabitants. The first six Huguenots reached Erlangen on 17 May 1686 and about fifteen hundred more followed in waves. Due to the comparatively large numbers the Margrave decided to establish a new town south of the old town of Erlangen and so “Die Hugenottenstadt” came into being.


The earliest known plan of New Erlangen (1686) Attributed to Johann Moritz Richter Source: Wikimedia Commons

In 1698 one thousand Huguenots and three hundred and seventeen Germans lived in Erlangen. Many of the Huguenot refugees also fled to Protestant England establish settlements in many towns such as Canterbury, Norwich and London.


Town plan of Erlangen 1721 Johann Christoph Homann Source: Wikimedia Commons

In the early eighteenth century Isaac Newton, now well established in London at the Royal Mint, would hold court in the London coffee houses surrounded by a group of enthusiastic mathematical scholars, the first Newtonian, eager to absorb the wisdom of Europe’s most famous mathematician and to read the unpublished mathematical manuscripts than he passed around for their enlightenment. One of those coffee house acolytes was the Huguenot refugee, Abraham de Moivre (1667–1754).


Abraham de Moivre artist unknown

Abraham de Moivre the son of a surgeon was born in Vitry-le-François on 26 May 1667. Although a Huguenot, he was initially educated at the Christian Brothers’ Catholic school. At the age of eleven he moved to Protestant Academy at Sedan, where he studied Greek. As a result of the increasing religious tension the Protestant Academy was suppressed in 1682 and de Moivre moved to Saumur to study logic. By this time he was teaching himself mathematics using amongst others Jean Prestet’s Elémens desmathématiquesand Christiaan Huygens’ De Rationciniis in Ludo Aleae, a small book on games of chance. In 1684 he moved to Paris to study physics and received for the first time formal teaching in mathematics from Jacques Ozanam a respected and successful journeyman mathematician.

Although it is not known for sure why de Moivre left France it is a reasonable assumption that it was Edict of Fontainebleau that motivated this move. Accounts vary as to when he arrived in London with some saying he was already there in 1686, others that he first arrived a year later, whilst a different account has him imprisoned in France in 1688. Suffering the fate of many a refugee de Moivre was unable to find employment and was forced to learn his living as a private maths tutor and through holding lectures on mathematics in the London coffee houses, the so-called Penny Universities.

Shortly after his arrival in England, de Moivre first encountered Newton’s Principia, which impressed him greatly. Due to the pressure of having to earn a living he had very little time to study, so according to his own account he tore pages out of the book and studied them whilst walking between his tutoring appointments. In the 1690s he had already become friends with Edmund Halley and acquainted with Newton himself. In 1695 Halley communicated de Moivre’s first paper Methods of Fluxions to the Royal Society of which he was elected a member in 1697.


Edmund Halley portrait by Thomas Murray Source: Wikipedia Commons

In 1710 de Moivre, now an established member of Newton’s inner circle, was appointed to the Royal Society Commission set up to determine whether Newton or Leibniz should be considered the inventor of the calculus. Not surprisingly this Commission found in favour of Newton, the Society’s President.

De Moivre produced papers in many areas of mathematics but he is best remembered for his contributions to probability theory. He published the first edition of The Doctrine of Chances: A method of calculating the probabilities of events in playin 1718 (175 pages).


Title page of he Doctrine of Chances: A method of calculating the probabilities of events in playin 1718

An earlier Latin version of his thesis was published in the Philosophical Transactionsof the Royal Society in 1711. Although there were earlier works on probability, most notably Cardano’s Liber de ludo aleae(published posthumously 1663), Huygens’De Rationciniis in Ludo Aleaeand the correspondence on the subject between Pascal and Fermat, De Moivre’s book along with Jacob Bernoulli’s Ars Conjectandi(published posthumously in 1713) laid the foundations of modern mathematical probability theory. There were new expanded editions of The Doctrine of Chance sin 1738 (258 pages) and posthumously in 1756 (348 pages).

De Moivre is most well known for the so-called De Moivre’s formula, which he first

(cos θ + i sin θ)n = cos n θ + i sin n θ

published in a paper in 1722 but which follows from a formula he published in 1707. In his Miscellanea Analytica from 1730 he published what is now falsely known as Stirling’s formula, although de Moivre credits James Stirling (1692–1770) with having improved his original version.

Although a well known mathematician, with a Europa wide reputation, producing much original mathematics de Moivre, the refugee (he became a naturalised British citizen in 1705), never succeeded in obtaining a university appointment and remained a private tutor all of his life, dying in poverty on 27 November 1754. It is claimed that he accurately predicted the date of his own death.








Filed under Autobiographical, History of Mathematics, Newton, Uncategorized

The Renaissance Mathematicus – A users guide

It occurred to me that over the recent months and years I have acquired a whole new crop of readers, who I have not welcomed or explained the house rules and so to rectify this omission, I have written this post.


First off, if you are new around here then welcome and I hope you enjoy yourself reading my humble scribblings. If you want to know more about me then go here. There is really only one house rule: I am the god of this blog and what I say goes! Although open to the public, this is not a public forum but my private, personal space for expressing my thoughts on the histories of science, mathematics, technology and medicine. I write those thoughts down, in the first instance, for myself and for nobody else and do not consider a potential audience when writing. However, anybody who wishes to do so is welcome to read those thoughts but remember this is my place so don’t piss on the carpet. As the name of my blog would suggest I write mostly about the mathematical sciences during the European Renaissance but I reserve the right to write about any other topic that might interest me. A more detailed account can be read here.

Trigger warnings:

1) Bad language!

I am an Englishman and whilst I don’t use swear words as punctuation like some of my fellow Brits or indeed swear like the proverbial drunken sailor, I do on occasions, when I feel like it, use so called strong or bad language. I have even used the f-word in a blog post title because I thought it was appropriate. I still do. If you strongly object to such language don’t complain, nobody is forcing you to read my blog.

2) Bad grammar and terrible orthography

If you are one of those who gets their nickers in a twist about split infinitives and misspelt words then be warned I suffer from dysgraphia, which means that on a bad day a blog post can be liberally sprinkled with typos and grammatical horrors.Or to put it another way I’m an orthographic anarchist. In fact, as I once wrote in a post, one of the reasons I started blogging was to overcome my fear of writing caused by my dysgraphia and the English school system. I have over the years made quite a lot of progress but I sure as hell ain’t perfect. If you severely criticise my orthographic failings out of some sort of feelings of moral superiority (and yes it happens!) I will simply delete your comments and block you. Remember, I am the god of this blog! However, I regard my readers as my unpaid copy editors or proofreaders and if you point out any errors that you spot, either in the comments or per email, in a friendly manner, I will be grateful and thank you.

The comments:


I actually welcome comments. I even welcome being told that I am wrong by somebody, who is better informed than I am and many, many people are better informed than I am. Being shown that I am wrong means that I have learnt something and I love learning things. For the same reason I also enjoy further or new information on the topic of my post. However, if your complaint is a matter of opinion, with which I disagree, you can expect me to fight my corner. If you try to use my comments as a pulpit for your own shit, whatever that might be, I will delete your comments and I will block you. Remember, I am the god of this blog!


Welcome aboard and I hope you enjoy the ride.



Filed under Autobiographical, Uncategorized

Imre and me – a turning point

Today is once again the anniversary of the day I started this blog nine years ago. Nine years‽ I have difficulty believing that I have really churned out blog posts on a regular basis, with only minor breaks, for nine years now. It has become something of a tradition that on my blog anniversary I post something autobiographical and I have decided this year to maintain that tradition and explain why, when asked, I always name Imre Lakatos’ Proof and Refutations not just as my favourite book but as the most important/influential book in my life.

As regular readers might have gathered my life has been anything but the normal career path one might expect from a white, middle class, British man born and raised in Northeast Essex. It has taken many twists and turns, detoured down one or other dark alleyway, gone off the rails once or twice and generally not taken the trajectory that my parents and school teachers might have hoped or expected it to take.

In 1970 I went to university in Cardiff to study archaeology but after one year I decided that archaeology was not what I wanted to do and dropped out. I however continued to live in Cardiff apart from some time I spent living in Belgium and but that’s another story. During this period of my life I earned my living doing a myriad of different things whilst I was supposedly trying to work out what it was that I actually wanted to do. As I’ve said on several occasions I became addicted to the history of mathematics at the age of sixteen and during this phase of my life I continued to teach myself both the history of maths and more generally the history of science.

In 1976 my life took another left turn when I moved to Malmö in Sweden.


Image of Malmö (Elbogen) in Scania, Southern Sweden from a German book (Civitates orbis terrarum, Vol. IV, by G. Braun & F. Hogenberg) .1580 Source: Wikimedia Commons

This was not my first attempt to move to Sweden there had been another abortive attempt a couple of years earlier but that is also another story. This time the move was not instituted by me but by my then partner K. K was a qualified nursery nurse and had applied for a job looking after the children of a pair of doctors in Malmö and her application had been successful. The couple agreed to my accompanying K on the condition that to pay my part of the rent of the flat (that went with the job) I would look after their garden until such time as I found work.

So after witnessing the rained out but brilliant Bob Marley open air in Cardiff football stadium in the summer of 76, we set of for a new life in Malmö. Not having employment my role was to do the cleaning, shopping, cooking and looking after the garden, all things I had been doing for years so no sweat. This left me with a lot of spare time and it wasn’t long before I discovered the Malmö public library. The Swedes are very pragmatic about languages; it is a country with a comparatively small population that lives from international trade so they start learning English in kindergarten. The result in that the public library has lots and lots of English books including a good section on the history and philosophy of mathematics and science, which soon became my happy hunting ground. Card catalogues sorted by subject are a great invention for finding new reading matter on the topic of your choice.

At that point in life I was purely a historian of mathematics with a bit of history of science on the side but in Malmö public library I discovered two books that would change that dramatically. The first was Stephan Körner’s The Philosophy of Mathematics–mathematics has a philosophy I didn’t know that–and the second was Karl Popper’s collection of papers, Conjectures and Refutations: The Growth of Scientific Knowledge. Both found their way back to our flat and were consumed with growing enthusiasm. From that point in my life I was no longer a historian of mathematics and science but had become that strange two-headed beast a historian and philosopher of mathematics and science.

Given the fundamental difference between empirical science and logically formal mathematics my next move might seem to some to be somewhat strange. However, I began to consider the question whether it would be possible to construct a Popperian philosophy of mathematics based on falsification. I gave this question much thought but made little progress. In 1977, for reasons I won’t expand upon here, we returned to the UK and Cardiff.

In Cardiff I continued to pursue my interest in both the histories and philosophies of mathematics and science. In those days I bought my books in a little bookshop in the Morgan Arcade in Cardiff.


Morgan Arcade Source: Wikimedia Commons

One day the owner, whose name I can’t remember but who knew my taste in books said, “I’ve got something here that should interest you” and handed me a copy of Imre Lakatos’ Proofs and Refutations: The Logic of Mathematical Discovery[1]. I now for the first time held in my hands a Popperian philosophy of mathematics or as Lakatos puts it a philosophy of mathematics based on the theories of George Pólya, Karl Popper and Georg Hegel, a strange combination.


This is still the copy that I bought on that fateful day in the small bookshop in the Morgan Arcade forty plus years ago

Lakatos was born Imre Lipschitz in Debrecen, Hungary in 1922. He studied mathematics, physics and philosophy graduating from the University of Debrecen in 1944. Following the German invasion in 1944 he formed a Marxist resistance group with his girlfriend and later wife. During the occupation he changed his Jewish name to Molnár to avoid persecution. After the War he changed it again to Lakatos in honour of his grandmother, who had died in Auschwitz. After the War he became a civil servant in the ministry of education and took a PhD from the University of Debrecen in 1948. He also studied as a post doc at the University of Moscow. Involved in political infighting he was imprisoned for revisionism from 1950 to 1953. One should point out that in the post War period Lakatos was a hard-line Stalinist and strong supporter of the communist government. His imprisonment however changed his political views and he began to oppose the government. Out of prison he returned to academic life and translated Georg Pólya’s How to Solve It[2] into Hungarian. When the Russians invaded in 1956, Lakatos fled to the UK via Vienna. He now took a second PhD at the University of Cambridge in 1961 under R.B. Braithwaite. In 1960 he was appointed to a position at the LSE where he remained until his comparatively early death at the age of 51 in 1974.


Library of the London School of Economics and Political Science – Professor Imre Lakatos, c1960s Source: Wikimedia Commons

The book that I had acquired is a large part of Lakatos’ 1961 PhD thesis, published in book form posthumously[3], and extends Popper’s philosophy of logical discovery into the realm of mathematics. In his seminal work The Logic of Scientific Discovery, (which I had read shortly after discovering his Conjectures and Refutations) Karl Popper moved the discussion in the philosophy of science from justification to discovery. Most previous work in the philosophy of science had been devoted to attempting to justify the truth of accepted scientific theories; Popper’s work was concerned on a formal level at how we arrive at those theories. The same situation existed in the philosophy of mathematics. Philosophers of mathematics were concerned with the logical justification of proven mathematical theorems. Lakatos turned his attention instead to the historical evolution of mathematical theorem.

Proofs and Refutations is written in the form of a Socratic dialogue, although the discussion has more than two participants. A teacher and his class, the students all have Greek letters for names, who are trying to determine the relationship between the number of vertices, edges and faces in polyhedra, V-E+F = 2; a formula now known as the Euler characteristic or Euler’s Gem[4]. The discussion in the class follows and mirrors the evolution in spacial geometry that led to the discovery of this formula. Lakatos giving references to the historical origins of each step in the footnotes. The discussion takes the reader down many byways and cul de sacs and on many detours and around many corners where strange things are waiting to surprise the unwary reader.

The book is thoroughly researched and brilliantly written: erudite and witty, informative on a very high level but a delight to read. I don’t think I can express in words the effect that reading this book had on me. It inspired me to reach out to new heights in my intellectual endeavours, although I knew from the very beginning that I could never possibly reach the level on which Lakatos resided. Before reading Proofs and Refutations, history of mathematics had been a passionate hobby for me; afterwards it became the central aim in my life. I applied to go back to university in Cardiff to study philosophy, having already matriculated six years earlier to study archaeology this meant a one to one interview with a head of department. I completely blew the interview; I always do!

In 1980 I moved to Germany and in 1981 I applied to go to university in Erlangen to study mathematics, which I was able to do after having spent a year learning German. I wanted to choose philosophy as my subsidiary, which meant an interview with a professor. The man I met was Christian Thiel, a historian of logic and mathematics although I didn’t know that at the time, who was just starting his first year as professor, although he had earlier studied in Erlangen. We clicked immediately and although he no longer remembers on that day we discussed the theories of Imre Lakatos. As I documented here Christian Thiel became my mentor and is indirectly more than somewhat responsible for this blog

I have read a lot of books in my life and I continue to do so, although now much more slowly than in the past, but no book has ever had the same impact on me as Proofs and Refutations did the first time I read it. This is why I always name it when asked questions like, what was the most important book you have read or what is your all time favourite book.


[1] Imre Lakatos, Proofs and Refutations: The Logic of Mathematical Discovery, eds. John Worrall and Elie Zahar, CUP, Cambridge etc., 1976

[2] How to Solve It is a wonderful little volume describing methods for solving mathematical problems; its methodology can also be used for a much wider range of problems and not just mathematical ones.

[3] Part of the thesis had been published as a series of four papers paper under the title Proofs and Refutations in The British Journal for the Philosophy of Science, 14 1963-64. The main part of the book is an expanded version of those original papers.

[4] I recommend David S. Richeson, Euler’s Gem, University Press Group Ltd., Reprint 2012

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Filed under Autobiographical, History of Mathematics, Uncategorized

Normal service will be resumed as soon as possible


I am currently engaged in copyediting the English translations of a collected volume of history of science papers. The translations are mostly crappy and the English more than somewhat dubious. The result is that it is difficult, irritating, exasperating and at time down right shitty. The official deadline was 30 September but I am not to blame, as I had not even received the majority of the typescripts by then!

Add to this the fact that I am trying to cope with three different moderately serious physical health problems. The end result of all this is that my mental health is starting to deteriorate. I am currently even more of an aggressive, obnoxious arsehole than usual.

Conserving my mental health has been the number one priority in my life for a number of years now, so I have decided that I need to reduce the stress in my life. This means that I will not be blogging for the next couple of weeks. I am planning on being back for my usual Christmas trilogy if all goes well.

To keep you occupied in my absence you can offer your opinions on the following thoughts. The man who more than anyone else in responsible for the existence of this blog the Albino Aussie Anthropoid,TM John Wilkins, has once again tackled the problem of those that say , evolution is ‘just’ a theory.

I personally think that scientists and science communicators are themselves partially to blame. A theory is actually what the denialists think it is, a point of view, an idea, a standpoint, as in, “I don’t know why she left him but I have a theory.” The theory of evolution and all other scientific theories are just that they are scientific theories and not just theories; a scientific theory being a tested hypothesis that explains the given scientific facts. Scientist and science communicators need to stop being lazy and start saying scientific theory and not just sloppily saying theory.


Filed under Autobiographical

School days

It is the middle of August and also the middle of what in German is known as Saure-Gurken-Zeit, in English as the silly season and in American as the dog days. It’s that time when parliaments are in recess, the politicians on holiday and the press is full of silly man bites dog stories. Even the history of science community is in a sort of half sleep with little happening and many of its members conspicuous by their absence. This being the case I though I would write a somewhat frivolous post this week before I too disappear off on holiday or a gathering of the clan in the beautiful city of Bath to be more precise.

It is common practice for schools to boast about the famous politicians, sports persons and show business celebrities who once, as snotty nosed kids, ran screaming through their corridors but what about the scientists? Which notable or significant scientist got their education at the pedagogical institution where you acquired the ability to write grammatical sentences and to find the derivatives of simple trigonometrical functions? To start the ball rolling I shall tell you of my historical scientific school chums and I hope you will tell me of yours in the comments.

I will admit to having an advantage as the grammar school that I attended has a somewhat more than eight hundred year history giving them lots of time to have educated one or other scientific luminary. From September 1963 till July 1969 I was a pupil of Colchester Royal Grammar School (CRGS) for boys, one of England’s most elite state schools; the first four years as a day boy, the last to as a boarder. Founded at the beginning of the thirteenth century, 1206 to be precise, and adorned with not one but two royal charters, Henry VIII (1539) and Elizabeth I (1584), it has boasted one of the highest Oxbridge entrance rates and best A-level averages almost every year since the WWII. It would be very surprising if this august educational institution had not thrown up a notable scientist over the centuries and in fact it can boast at least three.

School House CRGS pre-1908. The first floor window to the left of the main entrance in the middle was my bedroom for two years.
Source Wikimedia Commons

CRGS’s first and possibly most famous scientist (if you’ll excuse the anachronistic use of the term) was William Gilbert (1544–1603). Born in Colchester he followed his time at the school by becoming one of those Oxbridge statistics in 1558, St. John’s College Cambridge to be precise, where he graduated BA in 1561, MA in 1564 and MD in 1569. He moved to London where he followed a successful medical career. Elected a Fellow of the Royal College of Physicians he became their president in 1600. He became personal physician to Elizabeth I in 1601 and to James IV and I and 1603 the year of his death.

William Gilbert (1544–1603) artist unknown.
Source: Wellcome Library via Wikimedia Commons

Gilbert is of course most famous for his De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure (On the Magnet and Magnetic Bodies, and on That Great Magnet the Earth) published in London in 1600, regarded as one of the first ‘modern’ science books. This legendary scientific publication was much admired in its time and exercised a great influence on the development of experimental physics in the first half of the seventeenth century. Galileo praised it but thought it had too little mathematics and Kepler based his theory of a planetary force holding/driving the planets in their orbits on a magnetic monopole theory derived from Gilbert’s book. Based on his false belief that a terrella (a spherical magnet) revolves on its axis and his correct assumption that the earth is a large spherical magnet, Gilbert hypothesised a diurnal rotation for the earth. His theory had a major influence on the acceptance of a helio-geocentric system with diurnal rotation (as opposed to one without) in the first half of the seventeenth century.

There is a certain irony in the fact that although Gilbert is thought to have attended CRGS, as his name is attached to another school in Colchester, The Gilberd School. Gilberd is an alternative spelling of the family name.

We fast-forward almost a century to CRGS’s next scientific luminary, Francis Hauksbee (1660-1730). Not as famous as Gilbert, Hauksbee is still a notable figure in the history of science. Also a born Colcestrian, Hauksbee original apprenticed as a draper to his older brother in 1678 but at some point he became an assistant to Isaac Newton. In 1703 he became Robert Hooke’s successor as curator, experimentalist and instrument maker at the Royal Society.

From 1705 onwards he concentrated his experimental efforts on the phenomenon of electricity, a word coined by Gilbert in his De Magnete, publishing his investigations in his Physico-Mechanical Experiments on Various Subjects in 1709. In 1708 he independently discovered Charles’s law of gasses. Being something of an unsung hero of science it is fitting that in 2009 the Royal Society created the Hauksbee Awards to recognise “the unsung heroes of science, technology, engineering and maths for their work and commitment.”

We now spring into the nineteenth century to a scientist who whilst probably not as well known as Gilbert was truly one of the giants of science in his time, George Biddle Airy (1801– 1892).

George Biddell Airy (1801-1892)
John Collier / 1883
Source: Wikimedia Commons

Born in Alnwick in Northumberland he attended CRGS after an elementary school in Hereford. Like Gilbert he went up to Cambridge University, in his case Trinity College, in 1819. He graduated senior wrangler in in 1823, became a fellow of Trinity in 1824 and became Lucasian professor of mathematics, Newton’s chair, in 1826. He moved to the Plumian chair of astronomy in 1828 and was appointed director of the new Cambridge observatory. The list of Airy’s appointments and scientific achievements is too long for this light summer post – he published 518(!) scientific papers in his long live – but he was most notably Astronomer Royal from 1835 until his retirement in 1881.

George Biddell Airy caricatured by Ape in Vanity Fair Nov 1875
Source: Wikimedia Commons

As you can see CRGS can boast a trio of notable scientist in its long history, what about your alma mater? I do have to admit that I was expelled from CRGS in 1969 and finished my schooling at Holland Park Comprehensive in the school year 69–70. Much younger than CRGS, Holland Park was in my time as famous as the older establishment, as the flag ship educational establishment in the Labour government’s scheme to turn the English school system into a comprehensive one. I must admit that I know of no famous scientists who have emerged from Holland Park and my own memories of my one year there are largely of getting stoned and dropping acid; come on it was the late 60s and Notting Hill Gate!


Filed under Autobiographical, History of Astronomy, History of Physics, History of science