Category Archives: Autobiographical

An anniversary

My mother died fifty years ago at midnight on the 24th December 1966. I had just turned fifteen, five days before, and was in many senses still fairly immature. At nine o’clock in the evening I was having my first ever adult conversation with my mother, on the subject of religion, enquiring what religious views she and my father held. I had recently come to the conclusion that I was an atheist and was curious what views my parents held. We were not a religious family and didn’t discus such things, so I was genuinely curious. She told me that my father was an atheist but that she was an agnostic. She added however that she categorically rejected all organised religions and having grown up in India in a Christian family she had personally experienced Christianity, Hinduism, Buddhism and Islam, so her rejection was well informed. In the middle of this, for me, fascinating conversation my mother suffered a massive heart attack and three hours later she was dead.

I didn’t go through five stages of grief; within twenty-four hours I went from a state of extreme shock, to boiling anger, to total shut down. This was not denial; I was more than aware that my mother was dead but was incapable of grieving or mourning. I refused to attend the funeral; I have no idea why and that was the state I remained in for a very, very long time. Looking back I now know that I desperately needed help, therapy, counselling or whatever but nobody was offering and I didn’t ask.

For the next nine months my two elder sisters and I rather grimly tried to maintain a semblance of family life. We were all fairly capable on a practical level because that was how we had been brought up but there was very little joy in existence at that time. At the end of summer in 67 my sisters both moved out to start their careers and my father dumped me in a boarding school. It was the school where I had been a dayboy for the previous four years so the rupture wasn’t total. For the next two years I was fairly miserable, mildly obstreperous and didn’t really give a shit about anything. The result was that I got expelled. I spent my A-level year living in London attending, the then notorious, Holland Park Comprehensive and consuming vast quantities of drugs. It was after all 69-70. Having scraped together an abysmal set of A-level results I now trundled off to Cardiff to study archaeology. Still not really giving a shit about very much I dropped out after one year.

I was now completely adrift with a head full of mental health problems and would basically remain so until 1993 when my father finally died after having the life slowly sucked out of him by emphysema over a period of about twenty year. As my father died the dams broke and I wept as I have never wept before or since in my life and I cry easily, often and copiously. I wasn’t weeping for my father, I did that later when I took my departure in the hospice and at his funeral, but for my mother. Twenty-seven years of grief, hurt, confusion and god only knows what poured out of me in the hours following the phone call telling me of my father’s death.

This is not a Hollywood movie, so I was not instantly ‘cured’ but took many years to finally come to terms with the circumstances of my mother’s death and find balm for my ravaged soul. Once many years later because of a chance remark about Christmas made by somebody in my presence I became haunted by my father’s voice on the phone dictating the telegram to my grandparents in Australia informing them that my mother had died. It took several weeks of professional psychiatric care and some fairly strong anti-depressants to once again banish that voice out of my head.

However, that night marks an important step in my long and weary fight to regain my mental health, which I talked about in my earlier post about my mental health problems, and now, as then, I’m not writing this to elicit sympathy or to self aggrandise, hey look how I’ve suffered, but in the vague hope that I might help somebody else in a similar situation.

If you have lost somebody you love under tragic circumstances or know somebody who has, in particular children, then please, please make sure that you or they grieve if necessary fetch professional help. Bottling up your grief will seriously damage you, gnawing at your soul like a bad tooth. You might not even be aware of the damage on a conscious level but believe me it’s there.

I don’t celebrate Christmas and never will, my bother and my sisters did and do because they have had children and grandchildren of their own, but I have never had children, which is good because I would have been a lousy parent, I was not even capable of coping with myself let alone being responsible for another vulnerable human being. However this post is my Christmas present for those who might be in need of it. It is given freely and if you can take anything positive from it then you are very welcome to do so.




Filed under Autobiographical

I was robbed (twice)! – Vague ramblings on rites of passage, anniversaries, calendrics and the human desire to control time – on the occasion of the winter solstice.

Sunrise at Stonehenge on the Winter Solstice Photo: Mark Grant Source: Wikimedia Commons

Sunrise at Stonehenge on the Winter Solstice
Photo: Mark Grant
Source: Wikimedia Commons

As I was growing up in a remote corner of North-East Essex there were two birthdays that were considered to mark important moments in a person’s life, the twenty-first and the sixty-fifth. The first marked the entry into adulthood and the second the exit out of the world of work. Both were celebrated as special occasions, the former with a lavish party and, in well off families, with a spectacular coming of age present, the later with a somewhat more sombre ceremony and traditional the presentation of a timepiece (quite why it is/was traditional to give people a timepiece when they retire I have absolutely no idea!) The celebration of such points in ones life are known as rites of passage because they mark the transition from one socio-cultural group to another – coming of age from the community of the children to that of the adults, retirement from the working community to the community of the retired. Humans find it necessary/comforting/important to mark these transitions in some significant way.

I was going on nineteen when the British government decided to reduce the age of majority from twenty-one to eighteen meaning that my transition into adulthood took place on some arbitrary date by act of parliament without any form of acknowledgement/ceremony or whatever. As the title of this post says, I was robbed! Two days ago I celebrated my sixty-fifth birthday or rather didn’t celebrate but I still turned sixty-five. The German government is in the process of incrementally raising the retirement age to sixty-seven so I would have been due to retire at sixty-five and six months. However that same government persuaded me to retire at the beginning of September, actually carried out retrospectively meaning once more I was robbed of my rite of passage. As, however, I am self employed in that work that I do, and continue to do, there would have been nobody to hand around the cucumber sandwiches and the plastic glasses of cheap bubbly or to hold a boring and embarrassing speech whilst presenting me with my timepiece anyway.

Being from a non-religious, middle class, English household, and not for example Jewish, I did not undergo a biological coming of age at a nominal puberty such as the Jewish Bar Mitzvah. That is unless you count the eleven plus exam and the transition from primary school to secondary school. Which, at my very elite and very posh, grammar school included the tradition of being dragged through a hedge backwards or having ones head stuck in a toilet bowl and flushed by members of the fifth form during the mid morning break on the first day of school, delights that I managed somehow to avoid. By the time I reached the fifth form the tradition had thankfully died out.

Human seem to have some sort of innate desire to mark time and to celebrate certain events on some sort of regular basis. On the secular side birthdays, wedding anniversaries, first meetings, for some final school exams and whatever. On the religious side, for all religions, a whole cartload of religious festivals of various types. As political communities independence days, armistice days and an assortment of other national holidays. These celebrations and the rites of passage discussed above have one thing in common they are almost all arbitrary, the one exception being anniversaries to which we will return to in a minute.

The only natural timekeepers that we have are the diurnal rotation of the earth, the phases of the moon and the apparent passage of the sun around the ecliptic, which give us respectively the day, the (lunar) month and the year. All other divisions of time are of our own devising and as such arbitrary. Calendars were invented to help us keep track of those days that we have chosen to mark out for special attention of some sort – a public holiday, a religious observance or whatever. They are crib sheets for rites and rituals, which as already remarked almost all take place on arbitrary days. Good examples of arbitrary ritual days are the rapidly approaching Christmas and New Years festivals, as I have pointed out for the latter in an earlier post, different cultures having different New Years celebrations on differing dates.

The only rituals that are in a sense not arbitrary are, because the solar year is periodic, anniversaries. These occur, with a little bit of fudging, once every three hundred and sixty-five days. The fudging is necessary because the solar year is, as should be well-known, a little bit longer than three hundred and sixty-five days. With the Gregorian calendar we have a tolerably good system of fudging, although other calendars, the Jewish and Islamic ones for example, do things differently.

Because the ecliptic is tilted at approximately twenty-three degrees with relation to the equator, known technically as the obliquity of the ecliptic, we have as a result the seasons and also four days in the solar year that are not arbitrary. These are the equinoxes and the solstices. The equinoxes are the days in spring, the vernal equinox around the twentieth of March, and autumn, the autumnal equinox around the twenty-second of September, when the sun appears to be over the equator and the day and night are equally long. The summer solstice (Northern hemisphere, winter for Southern hemisphere) takes place when the sun appears to be over the Tropic of Cancer (approximately 23° of latitude north of the equator), that is its Northern most point on its journey around the ecliptic, around the twenty-first of June, and marks the longest day and shortest night in the Northern hemisphere and vice versa in the Southern hemisphere. The winter solstice (Northern hemisphere, summer for Southern hemisphere) takes place when the sun appears to be over the Tropic of Capricorn (approximately 23° of latitude south of the equator), that is its Southern most point on its journey around the ecliptic, around the twenty-first of December, and marks the shortest day and longest night in the Northern hemisphere and vice versa in the Southern hemisphere.

Many of the folk customs that occur around these days are celebrations of these astronomical events, their origins often forgotten, as they are co-opted into other, oft religious, celebrations. This is certainly true for many of the Christmas customs, which have their origins in various winter solstice celebrations, now lost in the mists of history.

I celebrate neither Christmas nor New Years but am prepared to acknowledge the winter solstice as a fulcrum or turning point of the year, so I wish all of my readers all the best for their next three hundred and sixty-five and a bit days journey around the sun, it is of course we who orbit the sun and not the sun us, and may you enjoy in your own ways those arbitrary calendrical dates that you choose to celebrate.


Filed under Autobiographical, History of Astronomy

Whilst I was away


As you may have noticed I have, after a comparatively long break, begun blogging again. When I stopped, I wrote a post saying that my inability to finish my review of David Wootton’s The Invention of Science was my reason for doing so and whilst this was true it doesn’t actually explain why the break has become so extended. Because over the years I have built up a collection of intelligent, loyal, benevolent and sympathetic readers I think that they have earned an explanation for my absence.

Two years ago on the fifth anniversary of the Renaissance Mathematicus I wrote a post explaining that I have suffered mental health problems nearly all of my life to a large extent, but not exclusively, caused by a combination of AD(non-H)D and dysgraphia and that writing this blog started as attempt to cure a forty year long writer’s block. One of the side effects of this double whammy of so-called learning difficulties is that I have always had massive problems with any form of bureaucratic bullshit that involves filling in forms. Please don’t make the mistake of saying, “oh nobody likes filling in forms” that is like telling somebody with clinical depression that everybody gets sad from time to time. I really have major psychological problems with all types of official forms. The content is in itself not really a problem; it is actually sitting down and confronting the offending object that is often nigh on impossible. The result is that I have always done such things at or mostly (well) past the final deadline and there have been periods when piles of official letters have accumulated unopened, often for months at a time, and often with disastrous results.

In September the German employment service forced me to take early retirement, I would have been due to retire in May next year so not that early. Due to my more than somewhat erratic work record, not unrelated to my mental health problems, and the fact that I have been officially unfit for work for almost the last twenty years, mental health problems combined with physical infirmities, my earned old age pension might just stretch to buying you a beer if we go to a very cheap bar. All of this meant that I had to apply for a German state social security pension (Grundsicherung im Alter).

Now this application consists of a very long complicated bureaucratic form to which one also has to collect a lot of official documents. Having completed this and sent it off, a couple of weeks later one gets another set of forms and another list of required documents. Having completed this a couple of weeks later you get… You get the picture? Unfortunately for me whilst I was going through the bureaucratic equivalent of Dante’s Inferno I also had to apply for a new British Passport, my old one being due to expire in the middle of October, as well as doing my tax returns for 2015, only one week past the final deadline. To make my life perfect I was also attempting to get a new extraordinary treatment for my back problems granted by my health insurance, whose bureaucratic hurdles equal those of the state social security pension application. The result of this bureaucratic tsunami over the last weeks has seen me scraping along and sometimes crossing the boundary to a major clinical depression, which sucked out all the will and energy I might have had for blogging or anything else for that matter. In the middle of this I actually held a public lecture on Babbage’s & Boole’s contributions to the history of computing, which I prepared literally the night before and held on autopilot. It went surprising well.

The current state of play is that I have a new passport, my tax affairs have been dealt with for another year and my state social security pension has been granted. My application for back treatment has been rejected, which is par for course and was expected and I now have to appeal the decision, more bureaucratic bullshit. I seem to have managed to avoid a full-blown depression and whilst I am feeling fairly battered, things are starting to look decidedly better. One positive aspect of the whole affair is that ten years ago such an episode in my life would almost certainly have had me back in a psychiatric hospital chewing the curtains, so I seem to be making progress, whatever that might be.

Of course for the readers of my blog the million dollar question is, have I finished my review of David Wootton’s The Invention of Science to which the answer in no but I am working on it. I think and I hope that you can expect regular history of science blog posts again here at the Renaissance Mathematicus and I look forward, as ever, to your comments.


Filed under Autobiographical

A public service announcement

For several months I have been writing a review essay of David Wootton’s fascinating and challenging book The Invention of Science, or better said not writing, as I have stalled, hit a roadblock, lost the thread or whatever. This being the case I have been doing what apparently writers are supposed to do in such situations writing other things. Now this is all very well but all that has happened is that I have found it increasingly more difficult to return to my review essay and complete it, so I have decided this has got to stop. Today I recommenced writing my review essay and have decided that I won’t write or post anything else until I do finish it, which might take some time. How long I can’t say at the moment. Until then nothing new will appear here at The Renaissance Mathematicus, I hope the break won’t be too long. When however blogging does resume here, normal service and frequency will be resumed, as I have several new posts already in the pipeline.



Filed under Autobiographical




Seven is the largest single digit prime number and a Mersenne prime. It is the number of planets in ancient Greek astronomy and the number of days in the astrological week, named after those planets. Isaac Newton decided to give the rainbow seven colours to match the seven notes of the major scale. Albrecht Dürer included a construction of a seven-sided polygon, the heptagon, in his maths book, which was criticised by Kepler as being only an approximation. Rome was built on seven hills. There are seven deadly sins, of which I have committed all seven more than once in my life, and seven heavenly virtues, of which I possess none. Two of my favourite films are Akira Kurosawa’s The Seven Samurai and John Sturges’ glorious Hollywood rendition of it, The Magnificent Seven. Snow White had seven dwarfs and there were seven brides for those seven brothers. David Fincher’s neo-noir psychological thriller was simply called Seven. Seven is a number that turns up in a multitude of historical, mythical, literary, musical, artistic, mathematical and scientific contexts and today is the seventh birthday of the Renaissance Mathematicus.

I came comparatively late to computers. There are no Ataris, Sinclairs or C64s collecting dust in my cellar and I didn’t spend my youth painfully learning to programme in Fortran, BASIC or Pascal. I also came comparatively late to the Internet. I was not one of those who cobbled together a dial up modem and spent a fortune on telephone fees to gain online contact to a fellow enthusiast on the other side of the world. However when I did take the plunge the world of blogging was still very young and when I first discovered them a blog that was seven years old definitely belonged to the pioneer founder generation and was venerated as a Methuselah amongst its peers. Given the short lived and oft fickle nature of blogs, over the years seven continued to remain a sort of bench mark for a successful, mature, established blog. This being the case I regard today as the day that The Renaissance Mathematicus has become part of the cyberspace establishment.

When I started this blog I never imagined, even in my wildest dreams, that I would be sitting here typing a post to mark or celebrate my seventh anniversary. Over the last seven years the content and the aims of this blog have remained constant but the style of the blog posts has developed (degenerated!) and matured (gone stale!). I very rarely look at blog statistics, as doing so makes me too aware of the fact that people are reading the rubbish that I write and I start to worry about pleasing/insulting them and that impedes my ability to write freely. I do however know that, for a moderately hard-core history of science blog, a surprisingly large number of people read my regular outpourings. A thought that both frightens and humbles me. I would like to mark this milestone by issuing some thanks.

Thanks to all the people who, for whatever reason, read what I present here on a regular basis. Thanks to those highly knowledgeable and critical souls, who brave my wrath and comment on my posts, particularly on the more provocative or contentious ones. Thanks to all those who tweet or retweet links to my posts on Twitter or share them on Facebook. And a very special thanks to all the members of the Internet history of science community for letting me, a bungling amateur, be part of your world. I hope that at least some of you will stick around for the next seven years.


Filed under Autobiographical

The Renaissance Mathematicus “Live & Uming”

Those of you with nothing better to do can listen to a podcast of the Renaissance Mathematicus (that’s me folks!) searching for words, desperately trying to remember names, uming & ahing, thinking on his feet (I was actually sitting down the whole time) and generally stumbling his way through an eighty minute spontaneous, unrehearsed, live interview with Scott Gosnell of Bottle Rocket Science on such scintillated topics, as why the Pope got his knickers in a twist over Galileo or that notorious seventeenth century religious fanatic Isaac Newton. In fact the same boring load of old codswallop that you can read at you leisure here on this blog. As I say if you have nothing more exciting to do, such as watching paint dry or listening to the grass grow, then go listen.

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Filed under Autobiographical, History of Astronomy, History of science, Myths of Science, Renaissance Science

The Internet and the history of science community

Yesterday evening I had a very pleasant evening meal in Nürnberg with Karl Galle. Now somebody reading this statement, who doesn’t know Karl, might wonder what this has to do with the title of this post. Things might become a little bit clearer if I explain that Karl is, like myself, a historian of science. Now this post is not actually about Karl but rather more how I came to be eating with him yesterday evening on the Market Square of the picturesque Renaissance city of Nürnberg. Before I give a direct answer to this implied question I first want to go back in time to those dim and distant days when the Internet didn’t exist.

When I first became seriously interested in the history of science in the 1970s, I was living in Cardiff, the capital of Wales, with no real contact to other historians of science other than through the books on the subject that I was eagerly consuming at the time and I never truly imagined that I could get to meet and converse with a real historian of science in the flesh. Occasionally I would meet up with somebody who shared my interest on some level and would then enthusiastically engage them on the subject, often whilst getting stoned or drunk or both.

In 1980 I moved to Germany more by accident than design. It was never planned, thought through or aimed for; it just happened. In 1982 I returned to university in Erlangen having dropped out of university in Cardiff in 1971. This time round I studied mathematics and philosophy with an emphasis on the history and philosophy of science. In the middle of the 1980s because the maths department were not interested in history I changed over to philosophy, English philology and history. For most of the 80s and into the 90s I also worked as an, albeit badly paid, researcher into the history of mathematical or formal logic. I was for a decade an integrated part of a history of science community. Professors, lecturers, students, doctoral students and postdocs lots of local possibility for informative exchanges. However to go beyond the local was not so simple.

In this age of cheap instant communications, I think we forget how new this all is. In the 1980s there was no Internet. Telephone calls were expensive even a long distant call within your own country would cost you an arm or a leg, so to speak, so they were outside of the possibilities of a poverty stricken student and not encouraged by employers etc. If you wanted to communicate with another historian of science in Canada for example you sat down and wrote a letter; the sending of which and any eventual reply could and often did take several weeks. Truly snail mail. If you wanted to meet non-local historians of science you either went to conferences, although travel was in those days also prohibitively expensive compared to now, or you hoped that they would come round on the lecture circuit. If your university department had the necessary funds they could invite the luminaries of the discipline to guest lectures when they were on tour. We had money and through this system I got to know and converse with such luminaries of the history of maths and logic as Martin, Davis, Joe Dauben and Ivor Grattan-Guinness amongst others.

In the early 1990s I dropped out of university because of serious mental illness, having completed about 95% of my masters degree but never passing the finishing post. Most of the next decade I had little or no contact with the history of science community although I kept up my reading on the discipline. In 2002 I returned to the fold about the same time as I acquired my first computer. The last is somewhat ironic, as compared to many of my contemporaries I came late to the computer although one of the things that I had studied intensely was the history of computing. In fact at the drop of a mega-byte I will launch into a whole lecture series on the history of computing starting with the Babylonian sexagesimal number system and going up to Alan Turing, Johnny von Neumann and beyond. On my return to being a historian of science my first public lecture was on George Boole and the contribution of Boolean algebra to the history of computing. During my absence the emergence of the Internet and the World Wide Web and completely changed the rules of the game. Being a member of the history of science community had taken on a wholly new meaning, although it took me some time to recognise and to experience this.

Initially my interest in the Internet was connected to my love of music, the first website I ever visited was The first maths or science web site was Mark Chu-Carroll’s Good Math Bad Math, which often has a history of maths content. In those days Mark was on Science Blogs and through visits to his blog I stumbled across John Wilkins, an Australian historian and philosopher of biology. John is actually responsible for the existence of this blog set up in 2009, as is here in various places well documented. Through my own blogging and my comments on other related blogs I slowly began to get to know other historians of the sciences scattered all over the world. Direct contact and instant communication that was unthinkable in the 1980s.

In 2010 John together with John Lynch, a lecturer for the history of science at Arizona State University set up the Whewell’s Ghost blog as a collective history of science blog, providing a one stop distribution point for people wishing to read posts by a diverse collection of history of science bloggers. Yours truly was invited to participate, an invitation, which I accepted with alacrity. Amongst those participants whom I didn’t already know was Rebekah “Becky” Higgitt, then a curator at the National Maritime Museum at Greenwich and now a lecturer at Kent University. Unlike myself and other participants Becky didn’t originally have her own blog but used Whewell’s Ghost as her blog. Later she would leave the nest to first found her own blog Teleskopos and then moving on to found with Vanessa Heggie the H-Word blog at the Guardian, a rare history of science blog embedded in a major science blog collective. Very early I realised that Becky and I shared similar attitudes and approaches to the history of science and I christened her, my “#histsci soul sister”. On visits to London I would come to know her personally along with her Greenwich colleague Richard Dunn.

Even before I met her in the flesh, Becky and I became good Internet friends and when I blogged something about Albrecht Dürer and Nürnberg she said that I would probably be interested in the doctoral thesis of her earlier doctoral studies colleague Karl Galle. I said I was and could she supply me with his email address. Having checked that he agreeable, she did so and I wrote an email to Karl asking if he could supply me with a pdf of his thesis. He could and did, and I read it with great interest and we continued to exchange emails. All of this took place over a couple of days. In the 1980s Becky, who I might never have got to know, would have supplied me with a postal address. I would have written a letter and posted it off hoping to maybe get a reply some weeks or even months later. If Karl had then agreed to my request he would have had to photocopy his rather substantial thesis, parcel it up and send it to me at not inconsiderable cost. It then hopefully arriving after a longer period than the letter took in the other direction. Times change!

Sometime later Karl, who lives in Cairo (the one in Egypt) came to Nürnberg to do some research connected to turning his thesis into a book and we met up for the first time, spending a happy summer’s day together rapping about things scientifically historical. This week Karl was back doing some more research, this time with his charming wife, and, as I said at the beginning of this post, we continued that conversation over things scientifically historical during a very pleasant meal sitting on a balcony overlooking the Market Place in Nürnberg.

The Frauenkirche Nürnberg our view during supper yesterday evening Source Wikimedia Commons

The Frauenkirche Nürnberg our view during supper yesterday evening
Source Wikimedia Commons

To recap, through the Internet I got to know a historian of biology living in Sydney, Australia who introduced me to a lady historian living and working in London, England, who in turn introduced me to a historian of Dürer the Nürnberger mathematician, who lives in Cairo, Egypt. I have also had the pleasure of meeting all three of these generous historians in the flesh.

This is just one set of connections that I have made through cyberspace since I decided to become a history of science blogger. I sit in a small flat, in a small village in Middle Franconia physically cut off from the rest of the world but through the medium of the Internet I am an integral part of a flourishing history of science community that is still growing and the members of which can communicate with each other instantly on a daily basis exchanging ideas or sending papers, theses or illustrations equally instantly as data files. Only physical books still have to be sent with the traditional post, although I will admit to having quite a few scans of books on my computer and iPad.

This is a situation that I would not have dreamt of when I started on my personal journey into the thickets of the history of science almost fifty years ago and one that I am very grateful to have experienced and hope to continue to enjoy for some time to come. If you know any historians of the sciences, who still haven’t discovered the Internet history of science community tell them to dive in, the waters lovely.




Filed under Autobiographical, History of science