Category Archives: Autobiographical

Death don’t have no mercy.

Normal service is being suspended as I have to write an obituary for a friend.

Anybody who has read the autobiographical fragments on this blog will know that I have led a far from the normal life that is expected of a child from a middle-class English family–school, university, career, family, retirement. My path through life has been a chaotic labyrinthian path, with the feeling that for much of the route my legs were tied together, and I was wearing a blindfold. Along the way a handful of people have had a massive influence on the direction my wanderings have taken, one of those was Michael J “Mike” Pearson, also known to me as Mr P, who I have just discovered from a Guardian obituary has died. I’m devastated!

Before I can introduce Mr P, I need to go back to four years before I met him. As I already explained in an earlier blog post, my mother died of a massive heart attack on Christmas eve in 1966, just after I turned fifteen. An event that scarred me for life. In the school year 67-68 my father entered me as a boarder at the grammar school I had been attending for the previous four years. We had moved from the rural Essex village, where I grew up to London, and he thought it would be better not to interrupt my education by moving me to a new school. It was a mistake. I was miserable, lost and didn’t give a fuck. 

The following year the school acquired a new headmaster, who took the adage “a new broom sweeps clean” very seriously. By the second term of what was my first year sixth, it was obvious to everybody that I was failing miserably, and I was summoned to the headmaster’s study. He asked me what I wanted to study at university, they assumed you would go to university, it was that sort of school. I answered truthfully, history. He then, not unnaturally, asked “why then was I doing science A-levels”–maths, physics, and chemistry? I, “because that’s what I’m good at”. He trying to be helpful gave the matter some thought and suggested that I could study archaeology with science A-levels. I initially rebelled against the idea, my father was an archaeologist, but during the Easter holidays I was packed off to my first archaeological excavation, a small Roman site in Chelmsford. I loved it and a very beautiful lady, called Jenny, persuaded me to go to the big Roman excavation in Usk, in South Wales, in the summer of 69. 

Having been expelled from my illustrious grammar school at the end of the school year, I duly trundled off to Usk and the world of Cardiff University archaeology. I had a ball and immediately booked to return for the digging season the following summer, 1970. 

I spent the school year 69–70 at, the then infamous, Holland Park Comprehensive, consuming vast amounts of drugs and basically not giving a fuck about anything. I naturally screwed up my A-levels, despite prognoses from my teachers that I was destined to get three straight ‘As’, I was good at bluffing. But I still got a place to study archaeology at Cardiff through indirect nepotism, one of the lecturers was trying to suck up to my father, a big name in those days in the world of anthropology. So, in the summer of 1970, I set off for a full season of digging in sunny Usk, knowing that I would be going up to Cardiff to study archaeology in the autumn. This is when Mr P entered my life.

The Lesson of Anatomy by Mike Pearson I built the set for the original version of this piece

In the late 1960s early 1970s the archaeological excavation at Usk were one of the largest in the UK. Each summer about 150 “volunteers” laboured away at the pink clay revealing the remains of a 55-acre Roman fort. A large number of those who worked there were Cardiff University archaeology students fulfilling part of the eight-week practical experience requirement of their degrees. Mike was one of the Cardiff University conscripts, a student at the end of his second year. A big lad, with thick blond locks from near Scunthorpe in Lincolnshire. We hit it off immediately. I need to introduce two other figures from that summer at Usk. Mike introduced me to his mate Steve, a Cardiff drop out turned printer and graphic designer, who came to visit him one day. I also met for the first time, Dave, who would go on to become my best friend, a Cardiff conscript at the end of his first year, who had never dug before and who was given into my tender care with the instruction, “teach him how to dig”! Having discovered that we had both come to Usk via the Bath Festival of Blues and Progressive Music in Shepton Mallet, Dave and I also hit it off immediately. 

On a large archaeology site there is always a team of mostly lightly insane people, who take on the construction tasks that occur on such sites, building scaffolding photographic towers, or creating spoil heaps, these have to take up as little space as possible but the paths up to the top have to have a gradient that a volunteer pushing a wheelbarrow full of heavy soil can still negotiate them. At Usk I was a member of that team. 

Having become friends, Mike knew that I would be going up to Cardiff in the autumn and spoke to me about a project he was planning. It turned out that he was the driving force behind a student theatre group and was planning a production of Euripides’ The Trojan Women for the autumn term, to take to the NUS Student Theatre Festival in Southampton over the Christmas vacation. He envisioned a stage set constructed of scaffolding and ask me if I could construct it for him? Somewhat naively, I said yes.

In the autumn I set off to my student digs in Cardiff wondering what lay ahead of me. Mike P was sharing a flat with Dave and another Mike, Mike B, and I went to visit and to find out what I was going to have to construct. Today, with smartphones, blue tooth, and Airpods, it is easy to forget the time when music was consumed from vinyl albums on that high altar of hippie existence, the stereo system. Now, I, Dave, and both Mikes all had record collections but none of us owned a stereo system. I owned a fairly good quality turntable, for which I had built the plinth myself and which I had wired up mono into my valve radio at home. None of us had the wherewithal to acquire a fancy stereo system, so Mike P bought a serviceable stereo amplifier and a cheap set of do-it-yourself loudspeakers boxes, which I put together. Together, we now had a functioning stereo which resided on the sideboard in the living room of their flat, with our four record collections inside the sideboard. This meant that I spent a lot of time in that flat.

But back to The Trojan Women. By the time I got to Cardiff, Mike had abandoned his scaffold set concept and he and I together with other members of the cast worked out a new staging concept. There were four figures representing the four women of the play. These were open frame wooden pyramids with an approximately one and a half metre square base and standing about three metres tall, constructed out of planed two by one deal. I constructed these and they were dismantlable for transit. On top of the pyramids were papier-mâché heads about one metre high made by a member of the cast. Below the heads were two metre long one inch diameter rods thrust through as arms on which hung hands made of plaster of Paris filled plastic gloves. All-in-all, very impressive but also very grotesque figures. These were arranged facing inwards in the corners of a square, about the size of a boxing ring, that was surrounded by coils of barbed wire. It’s a play about war!

This set was placed, not on a stage, but on the floor in the middle of a large room surrounded by rows of stools for the audience on all four sides. The set was lit with four, five-hundred-watt Fresnel spotlights mounted on floor stands, which I also constructed, which were focused on the head of the diagonally opposite figure casting vast shadows on the walls and ceiling. I mention all this in detail because I was then eighteen years old and had never done anything remotely like any of this in my entire life. It was a case of make it up as you go along and hope it works. Did I mention that I’m good at bluffing.

Mike had reduced Euripides’ text to word fragment in a sort of vocal concrete poetry. This was recorded on tape by four actresses representing the four Trojan women. It was recorded in the universities small recording studio. Steve, who had some experience, was supposed to engineer the session but backed out at the last moment. He gave me a five-minute introduction to audio engineering and left me to it. Something new everyday 

For the performance itself the recording was played, whilst the four actresses, dressed totally in black, sat motionless on their heels inside the barbed wire on the four sides of the square. In the middle, Mike, also dressed in black, with a lightning flash drawn in artificial blood across his face, mimed out the story, as the universal soldier. I sat at the back of the audience running the tape deck and turning the lights on and off depending on which of the women was featured in that moment.

Come the Christmas vacation we, Theatre in Transit, drove up to Southampton in a Ford Transit (pun intentional). Once there, I was in charge of putting up the set and sorting out the sound equipment, which the people in Southampton had arranged for us. Over the evening, I learned a lot about earthing loops and mains hum, finally getting the assorted heap of shit to work at about three o’clock in the morning. The performance was well received, all the effort seemed worthwhile, and I was now a bona fide stage carpenter and theatre technician.

A couple of years after this all began Dave, Steve, Mike, and I all lived in the same house. Dave and I in the first floor flat and Mike and Steve in the second floor flat. I would spend several years working on theatre projects with Mike under various different company names. Ritual and Tribal Theatre (RATT), Scarab, Cardiff Laboratory Theatre and whatever, as set and prop designer and builder, and as light designer and operator. By the time I stopped working with Mike, probably around, 1976, he was already am established name in Welsh alternative theatre or performance art as he preferred to call it. He would go on to become a major figure in European performance art.

Mike P, Mike B and Steve were all heavily involved in the Cardiff Students Union, and I slotted in there as well, working for the Union Events as a stagehand. As a theatre lighting technician, I also provided the light for a couple of concerts put on by the Students Union in Cory Hall, an old temperance hall from the nineteenth century. I did the lights for Loudon Wainwright III and Pentangle. 

I dropped out of the university at the end of the academic year 1970-71, having decided that I didn’t want to be an archaeologist. What I really wanted to be was a historian of science, but I didn’t know then that it was even possible.  However, I continued working with Mike and for the Students Union. I also worked as a stagehand for the Welsh National Opera and as either a lighting or a sound technician for the university’s Sherman Theatre when they were short a man. I was even theatre manager, that’s general dog’s body, in Chapter Arts for six months, an episode that ended badly. I toured Wales with a Welsh Language theatre company and learnt first-hand about the discriminatory and racist attitude that many of the English-speaking population have towards the Welsh speaking minority. I toured the South of England with a small independent opera company doing the lights for a Harrison Birtwistle opera with a really cool group of musicians, which included the cellist from Keith Tippett’s Ark, a wonderful lady, who took me aside to smoke a joint to calm me down, when I lost patience with a local BBC news crew, whose filming was preventing me from completing setting up the lights in a very narrow time frame. 

In between working for Mike, I still took part in archaeological excavation at Easter and during the summer. Mike joining me for one final delightful summer at Usk, when we both needed the money. For Mike I worked at venues all over England and in the early seventies at what was then one of the biggest theatre festivals, the Festival Mondial du théâtre de Nancy, where the then current French Minister of Culture took Mike and I to tea in a vey posh café one afternoon. 

Mike’s interpretation of the Rhyme of the Ancient Mariner, that’s him chocking at the end of the rope. I built the set, which was conceived by Mike and I together and the photo is by Steve

Through Mike I became part of the professional world of theatre and music and when I left the UK and moved to Germany at the beginning of the 1980s, I drew on that experience to find my feet in my new home. I worked as a stagehand for big concert promoters, managed a jazz club for ten years, was evening manager of a culture centre for about fifteen years and was a sound and lighting technician for live music in that centre for most of that time. 

Mike and I stayed loosely in touch over the decades and in the last couple of years that contact has been Mike first informing me that Steve had died and then last year that Mike B had also died. We talked about the fact that we should meet up again in person before one of us dies. Now, it is too late, and my heart is broken. 

Mike’s simple question, asking if I could erect some scaffolding for him, inadvertently set me on the path that would shape a very large part of my adult life.  

Mike apparently died at the end of May but I only found out on Monday through the Guardian obituary, which Dave posted on FaceBook. There is another much longer obituary from the Welsh theatre community here.

Normal service will be resumed next week!


Filed under Autobiographical


Today the Renaissance Mathematicus officially became a teenager, although I think it’s been one since it first emerged into the digital world thirteen years ago, snotty-nosed, stroppy, belligerent, argumentative, anti-authority, whilst at the same time oscillating between bursting with energy and sloth like behaviour. Did I mention self-opinionated and convinced it knows better than everybody else?

Thirteen is, in the Germanic languages, the first number with a compound name, three plus ten, eleven and twelve having single names. It is the sixth prime number and the second two-digit prime forming a twin prime with eleven, the first two digit prime. 

In some countries, including the UK and the USA, thirteen is considered an unlucky number, with people going as far as to not having a thirteenth floor in a building or a room 13 in a hotel. This superstition has been given the wonderful name Triskaidekaphobia from the Ancient Greek treiskaídeka for thirteen and phóbos meaning fear. There are various attempts to explain the historical origins of this phobia but none of them can actually be substantiated. Friday 13th is considered particularly unlucky in these cultures and has the equally splendid name paraskevidekatriaphobia from the Greek Paraskevi for Friday, reiskaídeka for thirteen, and phóbos meaning fear. In the Gregorian calendar, Friday 13th occurs at least once every year and can occur up to three times. Although there is evidence of both Friday and thirteen being considered unlucky, the earliest reference to Friday 13th as unlucky is in the nineteenth century. Once again, the origin of the superstition is a mater of speculation. 

One common occurrence of the number thirteen in the English language is the baker’s dozen. Whereas a dozen is a group of twelve, a baker’s dozen is a group of thirteen. The term dates back to the fifteenth century and refers to the habit of baker’s selling their wares in units of thirteen rather than twelve as the law required. As bakers could be fined for selling their wares underweight, it is thought that they included an extra item to avoid the risk of a fine.

As usual the Renaissance Mathematicus blog anniversary is an occasion for reflection, looking inward and questioning, a period of introspection. Why do I do this at all? What is my motivation? What do I hope to achieve? 

I’ve actually been thinking about these questions for sometime now. I am a self-confessed music junkie, who has spent a large part of my life working as a very small cog in the music business, as a stagehand, club live sound man, jazz club manager and chief cook and bottle washer. I also possess an obscenely large album collection, which I relativise by pointing out that other music junkies I know have much larger collections. One of my favourite rock guitarists is Robert Fripp, the genius behind King Crimson. Fripp is very philosophical for a rock musician and one of his sayings is, “don’t become a professional musician unless you can’t do anything else.” This statement is of course ambiguous. It could mean, if you are physically or mentally incapable of doing anything else or on the other hand you are so obsessed that nothing else comes into question. 

I prefer the second interpretation and it neatly sums up my relationship to history in general and the history of science in particular. I have been addicted to history for as long as I can remember, history in general, history of mathematics, history of science, history of food… What ever else I’ve done in my life, I’ve always studied history simply because. However, as I have revealed in the past, I am an AD(H)Dler and this means I tend to get easily distracted in my studies, research, and readings. Oh look, there’s another aspect I could follow up over there and isn’t this fact interesting, maybe I could find out something about that! This means I have in my life a strong tendency never to get anything finished, because there are always twenty other different pathways I want to go down first. Forcing myself to write a weekly blog post helps me to stay focused, to concentrate, and get at least one thing finished.  When I’m not writing blog posts my mind still wanders off in twenty different directions at once, but that’s OK; that’s have I come up with new topics for blog posts. 

All of the above basically covers the first two of my questions, why and motivation and there isn’t really any other explanation. This still leave the third question open; what do I hope to achieve? I don’t really have a general answer to this. I don’t actually think I want to achieve anything in particular. Initially, as I have said in the past, I wanted to teach myself to write, and I think I fulfilled that aim some time ago. I wrote my, The emergence of modern astronomy – a complex mosaic series to prove to myself that if I wrote in slices; I could write a book. Another aim that I think I successfully fulfilled. I might even get around to turning it into a proper book manuscript and trying to find a publisher this summer! The Renaissance Science series was just, you’ve written one long series, what could you write a second one about? 

On the whole I try not to think about potential readers but to write just for myself. This is a safety mechanism to stop me putting myself under any sort of pressure, will I fill my readers expectations!? Of course, I’m happy that people do read my scribblings and some of them even appear to enjoy them. Truth be told, the actual number of people who regularly read this blog scares me somewhat, in particular the successful professional historians of science, who I know do so. Imposter syndrome, what moi? As I have been known to say on occasions, even my imposter syndrome has imposter syndrome. One very concrete thing that I have aimed to achieve with my scribblings since the day I started this blog, is to try and clear away at least some of the myths that plague the popular perception of the history of science. It’s a Sisyphus task but it helps to keep me motivated and focused. 

Having mentioned my readers, I will close this anniversary post by saying I’m grateful for every person, who takes the time to read my weekly outpourings and I hope they gain something for the time taken. I’m also grateful to all those, who take the time to provide feedback, through comments: I thank all of you both readers and commentors and hope you stay on bord for the next twelve months.


Filed under Autobiographical, Myths of Science

Rants, Rage, Rudeness, and Respect

A man that I’ve never come across before, Brett Hall, has taken me to task in, what he terms, a newsletter on YouTube for being rude to Neil deGrasse Tyson. Before somebody drew my attention to his comments, I had absolutely no idea who or what Brett Hall was. It appears he is an Australian, who, it seems, studied about seventeen degrees, I might be exaggerating somewhat, I lost count somewhere down the line in his litany of all the wonderful things he had studied. Anyway, if I understand him correctly, he now regards himself as a science communicator and has a podcast where he explicates and propagates the philosophies of Karl Popper and David Deutsch. He also has a blog and apparently, has recently added a newsletter, in the first edition of which he chose to criticise me. 

I am well acquainted with the works of Karl Raimund Popper, he being one of my first two introductions to the philosophies of mathematics and science, the other was Stephen Körner. I read my first philosophy of science books by both of them in the same week many, many moons ago. I read a large amount of Popper’s oeuvre and a decade later studied him at university. Popper led me to Imre Lakatos, the biggest influence on my personal intellectual development. 

I must admit, because I gave up trying to keep up with all the developments in modern physics quite some time ago, that until about two weeks ago I had never heard of David Deutsch. So that you don’t have to go look, he’s a big name in quantum physics and especially in the theory of quantum computing. Purely by chance, the German news magazine, Der Spiegel, had a long interview with him a couple of weeks ago about his views on epistemology and what he sees as the correct approach to the future and development of scientific thinking. Mr Hall will probably come down on me like a ton of bricks for saying this but, for me, it came across as fairly vacuous, a lot of waffle and pie in the sky. But I’m probably just too stupid to understand the great maestro!  

But back to Mr Hall and good old Neil deGrasse Tyson. Mr Hall bemoaned what he saw as increasing rudeness in debate in the Internet age, a common and widely spread trope, and cited my latest diatribe against NdGT, as an example, misquoting the title of my piece, claiming that I had said that Tyson “knows nothing”, whereas I in fact wrote “knows nothing about nothing”, a wordplay on Tyson’s topic the history of zero. There is a substantial difference between the two statements. He then went on to quote correctly that I accused Tyson of “spouting crap.” Strangely, Mr Hall calls me a science historian, whereas the correct term is historian of science. There is a whole debate within the discipline, as to why it’s the latter and not the former. Even more bizarrely, he states that he is not going to name me and then provides a link to the post on my blog that of course contains my name! I have no problems in being named, I’m old enough and ugly enough to defend myself against all comers.

Mr Hall goes on to explain that he also does not always agree with the theories of NdGT, but that there is no reason not to treat him with respect when stating your disagreement. I have no objection to this statement; however, it misses the point entirely. NdGT is not stating a theory in astrophysics, which is, or rather was, his academic discipline. If he had, I almost certainly would not have commented in any way whatsoever, as I’m not an astrophysicist and so not qualified to pass judgement. No, NdGT was doing something entirely different. On a commercial podcast, for which, given his popularity, he is almost certainly extremely well paid, he was mouthing off extemporaneously about the history of mathematics, a topic about which he very obviously knows very little. He was, as I put it, and there really is no polite way to express, spouting crap, with all the assurance and authority that his prominent public persona gives him. He was literally lying to his listeners, who, I assume, mostly not knowing better believe the pearls of wisdom that drip from his lips. That is serious abuse of his status and of his listeners and deserves no respect whatsoever. 

I would also point out that he is a serial offender and regularly delivers totally ignorant speeches about the history of science and/or mathematics. For example, he regularly repeats, with emphasis, that Newton invented calculus in a couple of weeks, on a dare, which, not to put to finer point on it, is total codswallop. Newton developed his contribution to the evolution of calculus over several years having first read, studied, and digested the work of Descartes, Fermat, Wallace, and Barrow. One can point these things out to NdGT but he simply ignores them and carries on blithely spreading the same tired out falsehoods. He has long ago wilfully squandered any right to be treated with respect, when talking about the history of science and/or mathematics.

Returning to Brett Hall’s basic thesis that academics have jettisoned common decency, politeness, and good manners in the computer age as a result of social media, he expounds on this for the whole of his newsletter, claiming that this behaviour from academics put young people off from entering academia to study the sciences. Like NdGT, Mr Hall appears to have very little knowledge of the history of science. Academics/scholars/scientists, or whatever you want to call them, have been slagging each other off, both publicly and privately, since the first Egyptians put brush to papyrus and the first Babylonians wedge to clay.

Just to take the era in which I claim the most expertise, the emergence of modern astronomy in the Early Modern Period. The two Imperial Mathematici, Tycho Brahe and Nicolaus Reimers Baer laid into each other in a way that makes the HISTSCI_HULK look like a cuddly kitten. A half generation later the next generation, Kepler and Longomontanus, attacked each other with slightly less expletives, but just as much virulence. Galileo laid into anybody and everybody, that he perceived as his enemies and there were many, with invective that would cause a drunken sailor to blush. Moving to the other end of the seventeenth century. Isaac Newton, Lucasian Professor, treated John Flamsteed, Astronomer Royal, like a doormat. In turn, Flamsteed refused to even utter the name of Edmond Halley the Savilian Professor of geometry. Newton and Robert Hooke, demonstrator of experiments at the Royal Society, abused each like a couple of fishwives. Hooke had blazing public rows with virtually every notable scientist in Europe. You get the picture?

In case Mr Hall should argue that modern academics weren’t like that before the advent of the Internet, I could entertain him for hours with anecdotes about the invectives that leading academic archaeologist launched at each other in the early 1970s. One stated that an excavation report by another was about as useful of a mid-Victorian museum guide. The offended party then opened legal proceedings for libel but withdrew them when the offender expressed joy at the prospect of being able to prove his statement under oath in a court of law. I could go on but…

Let us return to myself and my alter ego the HISTSCI_HULK, why do I launch my notorious rants? 

One of my favourite musicians, Robert Fripp, says that one shouldn’t become a professional musician unless one can’t do anything else. This statement is, to say the least, ambiguous. It could mean you lack the ability to do something else, or the compulsion to create music is so great that nothing else comes into question. I have always assumed he intended the second meaning, and this is exactly why I’m a historian of science. The fascination with numbers, number systems, and their origins started very early, at most about five years old, and has simply grown ever since. I can’t explain rationally why I’m fascinated, intrigued, even obsessed by the history of science, I simply am. I have a compulsion to investigate, discover and learn about the history of science so great that nothing else comes into question. 

On a personal level I have always been taught, more by example than anything else, that if one is going to do something then learn to do it properly and then do so. I am from nature a pedant, and I don’t regard pedantry as bad, and a perfectionist. Over the years I have had the good fortune to meet and learn from several excellent teachers, who have helped me to channel that pedantry and perfectionism into my studies and not to accept anything but the best possible.

The history of science is very much a niche discipline within the academic hierarchy and has to battle constantly to justify its existence. There have been and are many excellent historians of science, many of whose books line the walls of my humble abode and nourish my unquenchable thirst for a depth of understanding in the history of science. As I have documented elsewhere, I have a multiple addictive personality and my greatest addiction is without doubt the history of science.

The commercial world of books and television is not interested in the complex and difficult web that is the real history of science, but pop history of science sells well, so they commission not historians of science but scientists to produce pop books and television programmes about the history of science. I mean, after all they are scientists so they must know about the history of their discipline. The results are all to often a disaster. There are exceptions, my friend Matthew Cobb is a professional scientist, who also writes excellent history of science books, several of which adorn my bookshelves. However, the majority of popular history of science books and television programmes are badly researched, shallow perpetuators of myths and inaccuracies–in the Middle Ages the Church opposed science and people believed the world was flat, Newton had an Annus mirabilis and created calculus, and modern optics, physics and astronomy all in one year during the plague, Galileo was persecuted by the Church because he proved that the Earth goes around the Sun, which contradicted the Bible, Ada Lovelace created computer science, and, and, and… A classic example was the original Cosmos television programme from Carl Sagan in which his presentation of the history of astronomy and cosmology was a total and utter cluster fuck, which influenced his tens of million viewers in a very bad way. Whenever I say this on the Internet, I get screamed at by Sagan groupies.

Because I love and live for the discipline, the abuse that it suffers at the hands of these popularises hurts my soul and sets me in a rage causing the HISTSCI_HULK to emerge and go on a rampage. One of the reasons that I do this is because established historians of science are very reluctant to subject these perversions of their discipline to public review. Somehow, they seem to think it is beneath them to engage and point out that the product in question is so much bovine manure. Nobody pays me to be a historian of science, I have no position, no status, and no academic reputation to lose, so I weigh in with all guns blazing and say what I really think. I have a message for Mr Hall and anybody else, who feels offended by my approach, nobody says you have to read it! 


Filed under Autobiographical, Myths of Science

Winter solstice comes but once a year and with it comes the Renaissance Mathematicus New Year

As I have explained over the years, being a historian of astronomy, for me, the year does not end and restart on the very arbitrary 31 December/1 January, but, in the Northern Hemisphere, with the Winter Solstice, when the Sun reaches the furthest point on its journey southwards, turns, and begins the slow climb towards the north and the summer solstice. 

Obligatory Stonehenge winter solstice image

I wish all of my readers a happy solstice and may you enjoy whatever seasonal events you participate in. I personally don’t celebrate any of them. I thank all of you for your engagement, for reading my verbal outpourings, for your comments and your criticisms and hope you will continue to do so in the year to come. 

There will be no normal blog post on Wednesday, because on Saturday we start with another established tradition, the Renaissance Mathematicus Christmas Trilogy. For any new readers, who have found there way here in the last twelve months, they can find out what this is here and at the same time catch up on twelve years of previous trilogies! 

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Filed under Autobiographical

The days of my years

Today, according to the Bible, I have reached the end of a normal life span:

The days of our years are three-score years and ten;
and if by reason of strength they be fourscore years,
yet is their strength labour and sorrow;
for it is soon cut off, and we fly away.

Psalms: Chapter 90 Verse 10

Of course, with the developments in medicine, the introduction of modern plumbing, and the improvements in nutrition, the average life span has increased since that Bible verse was written sometime between the nineth and fifth centuries BCE, although not as much as some might think. According to the WHO, in 2019 the average life expectancy for a German was 81.7 and for a Brit 81.4 years. For a man, and the last time I looked I was one, this drops to 78.7 for Germany and 79.8 for the UK; women live longer. The Bible’s three-score years and ten is, however, not average life expectancy but the age it was possible to reach if one didn’t die by the age of thirty or so. The estimates of the paleodemographers, isn’t that a lovely word, for the Bronze and Iron Ages, is that if one had reached the age of fifteen, one might expect to live to between twenty-eight and thirty-three years. 

As it seems with all things, the Bible estimate turns up in Shakespeare, in Macbeth to be precise, in a play full of people getting knocked off before their time had come.

Three-score and ten I can remember well: 
Within the volume of which time I have seen 
Hours dreadful and things strange; but this sore night 
Hath trifled former knowings. 

Macbeth: Act 2, Scene 4

As a historian of mathematics, I am, of course, fascinated by the use of the word score to mean twenty. This is an indication of a base twenty number system some time in the past, as are the French quatre-vingt for eighty and quatre-vingt-dix for ninety. It turns out that a lot of languages have of had a vigesimal or base-twenty number system. Perhaps, the most notable was the Mayan number system in which the names for the powers of twenty are: 

kal (20), bak (202 =400), pic (203 =8,000), calab (204 =160,000), kinchil (205 = 3,200,000) and alau (206 = 64,000,000). 

The word score itself is interesting as it appears, at first glance, to have several meanings in English. They are however all closely related. The etymology of score is:

Score (n.):– late Old English scoru “twenty,” from Old Norse skor “mark, notch, incision; a rift in rock,” also, in Icelandic, “twenty,” from Proto-Germanic *skur-, from PIE root *sker (1) “to cut.”

So, to score something in the sense of making a scratch or a notch is the same as score meaning twenty. This almost certainly comes from people tallying or counting something making a notch in a tally stick for every twenty counted in a vigesimal number system. To keep score or the score obviously derives from the same sense of counting or tallying. Interestingly the word tally means virtually the same as score. 

Tally (n.) mid-15c., “stick marked with notches to indicate amount owed or paid,” from Anglo-French tallie(early 14c., Old French taille “notch in a piece of wood signifying a debt”), Anglo-Latin talea (late 12c.), from Medieval Latin tallia, from Latin talea “a cutting, rod, stick”

Score first appears in English in the simple sense of counting up in the seventeenth century and in the sense of the final score in a game or match in the eighteenth century. The score also referred to the final bill in a tavern inn and settling the score originally meant to pay the bill. The score in music derives from the scored lines on the stave. 

We will just have to wait half-a-score-years to see if I have the strength to notch up fourscore years! 

Addendum: It appears that I have now reached the age where one gets an official birthday card from the leader of the local parish council. However, I don’t think I’m every going to get that telegram from the Queen.


Filed under Autobiographical

Internet Superstar, who are you, what do you think you are?

He’s back!

After his stupendously, mind-bogglingly, world shattering success rabbiting on about the history of astronomy on the History for Atheists YouTube channel, he can now be heard going on and on and on and on and on and on…  about the history of astronomy from Babylon to Galileo Galilei on the monumental, prodigious, phenomenal Subject to Change podcast, moderated by sensational Russell Hogg and available on so many different Internet channels you’ll need a week to decide where to listen. 


Filed under Autobiographical, History of Astrology, History of Astronomy


Sometime back I revealed on Twitter that I am having serious problems walking. I have had back problems, which have got steadily worse, for more than twenty years that make walking unpleasant but, as long as I don’t overdo it, can be mostly ignored. However, since about five or six months, whenever I start to walk my legs feel tired and heavy, a feeling which gets progressively worse as I continue to walk. A kilometre is about the limit of my mobility at the moment and at the end of that kilometre I’m fucked!

After various visits to doctors, my orthopaedist x-rayed my spine and thought he had detected a spinal stenosis in my lumbar vertebrae, which was confirmed by an MRI. In fact, I have a double stenosis. A stenosis is when a vertebra touches or puts pressure on the spinal column, causing problems with the nerves affected and the parts of the body those nerves serve. He referred me to the specialist spinal unit of a local hospital for conservative treatment, which consists of epidural injections and physiotherapy. 

MRI of a lumbar spinal stenosis L4-L5. L4-L5 antherolisthesis of grade I Source: Wikimedia Commons My double stenosis is between L3 and L5

The clinic’s spinal specialist after examining and questioning me decided that my double stenosis didn’t explain my symptoms, and sent me for more tests and MRIs of different parts of my spine. The end result was that they still don’t know what is causing my symptoms, so they have decided to take me into hospital for more tests and for the conservative treatment initially suggested by my orthopaedist. 

I go into hospital at eight o’clock tomorrow morning, initially for three to five days for a series of epidural injections and further examination by orthopaedists, neurologists, internal medicine specialists, Old Uncle Thom Cobley and all. I have scheduled my normal weekly blog post for 10:00 am CEST on Wednesday; I have never done this before, so I hope it works. Theoretically I should be out of the clinic in time to write next weeks blog, but if I’m not I shall announce that here. 


Filed under Autobiographical


It’s that day of the year again. It seems to come around faster every time. On this day twelve years ago The Renaissance Mathematics first entered cyberspace. What does the word, twelve, actually mean? In the Germanic languages twelve and its equivalents means two left that is after counting to ten:

Old English twelf “twelve,” literally “two left” (over ten), from Proto-Germanic *twa-lif-, a compound of *twa- (from PIE root *dwo- “two”) + *lif- (from PIE root *leikw- “to leave”). Cognate with Old Saxon twelif, Old Norse tolf, Old Frisian twelef, Middle Dutch twalef, Dutch twaalf, Old High German zwelif, German zwölf, Gothic twalif

Online Etymological Dictionary

Twelve features widely in culture, religion, science, and society in general. There were twelve apostles, twelve days of Christmas, the twelve Olympians (the major ancient Greek deities), The Twelve Tribes of Israel, jury of twelve good men and true, somehow twelve has always been a favoured number for humans. But this is a history of science blog and here we meet many instances of the number twelve.

The Romans used a base twelve or duodecimal number system, the only fraction that they used were twelfths. The remnants of this system are present in many countries that were once parts of the Roman Empire.

Table of units from a base of 12
French unit
of length
English unit
of length
(Troy) unit
of weight
Roman unit
of weight
English unit
of mass
12−2ligneline2 scruples2 scrupulaslug

Table taken from Wikipedia

Also, in English we still have the term dozen for twelve and gross for twelve squared, which reflect a twelve based number system.

There are modern societies in both the UK and the US that wish to replace our decimal system with a duodecimal one or as they prefer to call it Dozenal to avoid the decimal in duodecimal. They argue that because twelve has more factors than ten, a Dozenal system would be arithmetically preferable to a decimal one.

Our twelve-hour day has a different source. To tell the time at night Egyptian astronomers used the so-called decans, a set of thirty stars or groups of stars, which rise consecutively on the horizon throughout each earth rotation. In any given night twelve decans rose successively over the horizon dividing the night into twelve.

Astronomical Ceiling of Senemut tomb showing various decans, as well as the personified representations of stars and constellations Source: Wikimedia Commons

Gradually they developed the habit of also dividing the day into twelve units, our twelve-hour day. Originally, twelve seasonal hours, the length of which, varied throughout the year. In the early modern period these became our equinoctial hours of equal length. Hours are divided into sixty minutes and minutes into sixty seconds, sixty is a multiple of twelve.  

Astronomy and astrology deliver up a two-significant-twelves. Twelve months in the year and twelve signs of the zodiac that are in fact related. The word month has the same etymological root and the word moon and originally referred to the lunar moon, which is about twenty-nine and a half days long. Early calendars were lunar calendars, but the solar year is about eleven days longer that twelve lunar months, so if you want to keep your calendar aligned with the solar year you have to add an extra lunar month about once every three years.  The Greeks adopted the Metonic cycle, named after a Greek, but conceived by the Babylonians, in which seven extra months are added in nineteen solar years.

The Romans used a more random method in which an extra month was added by a political official when it was thought necessary. Because the dates for elections were determined by the calendar, this led to political corruptions with manipulation of the calendar. Julius Caesar solved the problem by introduction a solar calendar borrowed from the Egyptians with three hundred and sixty-five days divided up into twelve months. Nothing says there should be twelve months in a solar year, the French Revolutionary Calendar only had ten months, but by analogy to the lunar calendar twelve was chosen. Now, the solar year is closer to three hundred and sixty-five and a quarter days, which was known to the Egyptians and Caesar’s astronomical advisors, so you have to add an extra day approximately every four years. Caesar’s astronomical advisors got this slightly wrong leading to the whole Julian Calendar/Gregorian Calendar reform, which we won’t go into here. 

That the ecliptic is divided into twelve thirty-degree signs of the zodiac, also goes back to the Egyptian solar calendar. The Egyptians divided the year into twelve thirty-day months, with five non-days between the beginning and the end of the year, making a total of three hundred and sixty-five days. These twelve thirty-day months became the twelve thirty-degree signs of the zodiac.

A 6th century mosaic zodiac wheel in a synagogue, incorporating Greek-Byzantine elements, Beit Alpha, Israel Source: Wikimedia Commons

And so, the Renaissance Mathematicus enters its thirteenth year expectantly looking forward to what its Gemini horoscope will deliver. We wish all of our readers, commentators and supporters, both active and passive, all the best for our next circuit of the Sun and hope you enjoy the future blog posts. 


Filed under Autobiographical

One Thousand and One Blog Posts

Because evolution has given human beings ten fingers, most of the time, we use a ten based positional value number system, in which the positions are powers of ten. This also means that we have a strong tendency to note, to acknowledge and even to celebrate the points when lists or collections reach multiples or powers of ten. For example, we tend to think that somebody’s fortieth birthday is more significant than their thirty-ninth or forty-first. We also make a big deal with major celebrations when something reaches a ten to the power of two, that is a hundredth, anniversary and even more of a big deal by a ten to the power of three, that is a thousandth, anniversary. The only real exception to this, are legal anniversaries, coming of age for example, or multiples of twenty-five because these are viewed as the significant fractions of one hundred, one quarter, one half, etc.

Because I call myself a history of science storyteller, I have decided instead to borrow the title of what is perhaps the most famous collection of stories or tales, One Thousand and One Nights, and celebrate instead of the thousandth, the one thousand and first Renaissance Mathematicus blog post.


Having actually written the last sentence, I have to take a deep breath, have I really written one thousand blog posts? Is this really the one thousand and first? The answer to both questions is, according to the WordPress statistics for this blog, a definitive yes, although I don’t quite really believe it. As I have pointed out previously, although I have posted one thousand posts here, I didn’t actually write all of them, as several of them were guest posts. However, I have written more guest posts for other peoples’ blogs than there are guest posts here, so yes, I have actually written more than one thousand blog posts.

As I have also pointed out in the past, because I suffer from both adult AD(H)D and dysgraphia, I was functionally analphabet for most of my life, literally too scared to put pen to paper or fingers to keyboard. I started this blog as personal therapy to help myself to overcome that fear and teach myself to write; in this I think I have succeeded.

There was, however, a second reason or, better said, motivation for beginning this journey into the written word. I had spent the best part of half a century absorbing, contemplating and trying to apprehend the histories of mathematics and the mathematical sciences. I even spent ten years at university studying them. During that time, I had formulated my own ideas about numerous aspects of those histories and blogging would supply me with a medium to express those ideas in public if only to a very limited public. You might say, it was opening a safety valve to reduce the accumulated pressure. A sort of intellectual Primal Scream therapy.

Now, I didn’t just sit down, turn on the metaphorical tap in my brain and pour out finished history of science copy. When I conceive a potential theme for a blog post, I set out to refresh and to extend my knowledge of the topic in question, so writing this blog also became a learning process for me. Conceiving, researching and writing approximately fifteen hundred words on a history of science topic once a week is as good as any university education.

What I’m now going to say is one of the biggest clichés in the history of human thought, but clichés are very often clichés simply because they are true. The more that I have learnt over the years, writing this blog, the more I become aware of how little I actually know. Knowledge is a vast ocean and at best I have dabbled my toes in the ripples on one of its shores. The compulsion to maybe one day be able to swim in that ocean is what keeps me going. I don’t know where that compulsion comes from, it has simply always been there.


A desire to plunge right in

To close, I would just like to thank all of those who have been along for the ride. As I have stated in the past, I don’t write for you or anybody else, for that matter, I write for myself but I am truly grateful for the fact that you find my scribblings worth reading.


Filed under Autobiographical

A book is a book is a book is a book


I assume that most of the people reading this would agree that a book is for reading. The writer of the book puts their words down on the page and the reader reads them; it is a form of interpersonal communication. However, if one stops to think about it books also fulfil many other functions and book historian Tom Mole has not only thought long and deeply about it but has put those thoughts down, as a series of essays, in the pages of a book to read, his delightful The Secret Life of Books: why they mean more than words[1], which has recently appeared in paperback.


I will say a bit more about Mole’s book about books not just being books to read in a bit, but first I want to sketch what books have meant in my life, thoughts provoked by his opening essay. Mole describes a university professor, he had as a student, whose office slowly disappeared under steadily increasing number of books. Ever more books meant ever more bookcases until the weight threatened the structural integrity of the building. This is a scenario that speaks volumes to me, and I suspect to many other lifelong book consumers.

I grew up in a house full of books. My father was a university teacher, and my mother was a voracious book reader. Reading books was an integral part of our family life, as long as I can remember. We, the four kids in the family, had a playroom, when we were small. In this playroom there was a book cupboard containing a collection of several hundred children’s books, a collection that grew steadily every year. I had taught myself to read by the time I was about three years old and at around the same age I acquired my first library card. Once a week the family would walk the short stretch to the village library, housed in the primary school, and each one of us would choose new reading matter for the following seven days. My mother always returned from these trips with four new novels, which would be consumed before the next outing. That library was a treasure trove; I can still remember the joy I experienced the first time I discovered Crockett Johnson’s Harold and the Purple Crayon. Later I was always excited to take home a new volume of Mary Norton’s The Borrowers or Richmal Crompton’s William Brown series.

Moving forward in time, when my mother died I, as the only child still living at home, was pushed off to boarding school, there was an excellent school library, and my father and I left our Essex village and moved to London, where my father worked. At the beginning we didn’t have a house, so we lived in the Royal Anthropological Institute on Bedford Square, which my father ran in those days. He had a small bedsitting room with an attached kitchen, that was his office and during the school holidays or weekends home I slept, on an inflatable mattress, on the floor of the Sir Richard Burton Library, that’s the nineteenth century explorer infamous for his translation of The Perfumed Garden. I can assure you that the bookshelves only contained boring tomes on geography, anthropology etc., and no porn, I checked.

When we did finally acquire a house in Colville Place, one of the most beautiful streets in London. My father and I spent several weeks lining the walls of the house with self-constructed bookshelves to house not only his books from our family home but from his office at the RAI and his office at SOAS, where he taught. That house didn’t need any wall paper. During the time that I lived there, now a maturing teenager, I perused many of the fascinating volumes on those shelves covering a bewildering range of topics.

Over the years, books continued to play a very central role in my life and I still own quite a few of the volumes that I acquired over the next decade that very much shaped the historian I am today. For example, Hofstader’s Gödel, Escher, Bach: an Eternal Golden Braid, Bronowski’s The Ascent of Man, Lakatos’ Proofs and Refutations, Criticism and the Growthof Knowledge edited by Lakatos & Musgrave, Polya’s How to Solve It, and Boyer’s A History of Mathematics. They are old friends and have shared my living spaces for more than forty years.

As regular readers of this blog will know, I moved to Germany forty years ago and one year later I started to study at the University of Erlangen. The professor, who most influenced and shaped me, Christian Thiel, is also a serious book consumer. The walls of his university office were completely covered with books and over the years his desk, the windowsills and the floor all acquired steadily growing piles of books. Thiel is the owner of a fairly large house and he is also a serious collector of logic books, he is said to own the second largest such private collection in the world. The walls of most of the rooms in his house are lined with this collection. It reached a point where his wife dictated that he could only acquire new volumes if he sold the same width in centimetres of the old ones.

The walls of my small appartement, where I am sitting typing this, are also lined with bookshelves, except for the 2,60 metres covered by my CD shelves. Those bookshelves are filled, to overflowing and the piles of not shelved books continue to grow. I keep telling myself that I must stop acquiring books or at least dispose of some of them but the thought of parting with one of them is on a par with the thought of having teeth extracted without anaesthetic and as I write, four new books are winging there way to my humble abode from various corners of the world.

My name is Thony and I am a bookaholic.

Returning to the volume that inspired this autobiographical outburst, as already mentioned above, Tom Mole’s book is really a collection of eight essays each of which deals with a different aspect of the book as not reading matter. There are also three interludes that take a look at books depicted in paintings, surely a topic for a whole book. I’m not going to go into detail because that would spoil the pleasure that the reader will get out of these carefully crafted gems, but I will list the topics as given in the essay titles: 1) Book/Book, 2) Book/Thing, 3) Book/Bookshelf[2] 4) Book/Relationship 5) Book/Life 6) Book/World 7) Book/Technology 8) Book/Future

 The book is completed with a relatively small number of endnotes for each chapter, which include bibliographical references for deeper reading on the given theme and an adequate index.

If you are a book lover then this is definitively a book you will want to own and read. Both the original hardback and the paperback are at almost throwaway prices and this small volume would make a perfect stocking filler for the bookaholic in your life. However, be warned if you do give them this book for Christmas, they probably won’t speak anymore after unpacking it, as their nose will be buried in The Secret Life of Books.


[1] Tom Mole, The Secret Life of Books: why they mean more than words, ppb., Elliot & Thompson, London 2020

[2] Mole is going to push me to buy Henry Petroski’s classic study (Mole’s term) The Book on the Bookshelf, London: Vintage, 2000. I already own Petroski’s The Pencil, Alfred A. Knopf, New York, 2004 and it’s brilliant.


Filed under Autobiographical, Book Reviews