Category Archives: Autobiographical

Twelve

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
Relative
value
French unit
of length
English unit
of length
English
(Troy) unit
of weight
Roman unit
of weight
English unit
of mass
120piedfootpoundlibra
12−1pouceinchounceunciaslinch
12−2ligneline2 scruples2 scrupulaslug
12−3pointpointseedsiliqua

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. 

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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.

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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.

Iss007e10807

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.

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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.

falk04

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.

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It was forty years ago today…

As I don’t keep a diary, I don’t know the actual date in 1980 when I stuck my thumb out, at the beginning of the M4 motorway, on the Newport roundabout starting a holiday trip that would take me away from the UK forever. It was, however, sometime in the middle of a mild September. I had intended a trip of a few weeks maybe a couple of months but I have now lived outside of the land of my birth for forty years.

As I look back I wonder where the time went. What follows is a brief survey of some of the things that have filled out those forty years. The astute reader will note that they add up to more than forty years because many of them took place concurrently. 

I started out by going down the Orwell route and worked for six months as a dishwasher in a luxury hotel. If you don’t speak the language! That ended when I walked out after calling the manager a racist, because he was. I could never keep my mouth shut. This was followed by a period of working as a freelance gardener; growing up in the country, in a house with half a hectare of garden had to pay off sometime. Gardening brings meagre pickings in winter, so I got a job as an industrial cleaner, the man for special jobs, for the next four years. I got around quite a bit and got to see the inside of quite a lot of leading German companies. If you keep your ears and eyes open you can learn an awful lot, nobody takes any notice of cleaners, so you get to see and hear things that are supposed to be kept secret! 

The language thing was the most important problem and right from the beginning I started going to evening classes to learn German. This was too slow so I looked around for something better and started a German as a foreign language course at the local university. German lessons in the morning, cleaning factories and office blocks in the afternoon, the high life. This was the start of twelve years spent at university as a mature student. The first three years studying mathematics and philosophy, with an emphasis on history and philosophy of science. Then I shifted to philosophy, same emphasis, with English philology and history. For nearly all of those years at the university I worked as a research assistant in a major research project into the social history, read external history, of formal logic, my real apprenticeship as a historian of science.

Before I quit the cleaning firm I had already started working in a local cultural and youth centre that would become my home from home for fourteen years. Here I managed a jazz club for ten years and worked for a couple of years, as a fly poster. I spent two afternoons a week, for many years, working in a self help bicycle workshop, where people could maintain and repair their own bicycles, with assistance from people like me if required. For ten years I was one of the centres evening shift managers responsible for the running of the whole building. With up to three thousand guests on a Friday or Saturday night and a shift from six in the evening until four in the morning a more than somewhat strenuous task. In the same building when I wasn’t being evening manager I also worked as a live concert lighting and sound technician. I had been lighting and sound technician for theatre groups earlier in the UK.

In the middle of the 1990s I was studying full time working a paid thirty to forty-hour week and an average thirty-hour unpaid week, whilst basically living on drugs and alcohol. What inevitably had to happen, happened. As I have documented elsewhere the wheels fell off and I discovered the joys of German heath care for the mentally ill. I spent several months in the loony bin followed by several years as a very active member of the AA and even more years in outpatient therapy. These days I’m reasonably healthy, mentally that is, fairly stable but I am very much aware that I will never be cured; there is no cure for my afflictions.

In Germany I also became a dog owner for the first time in my life. I have owned loved, cared for and lost four wonderful dogs over the last thirty years. They have been my constant, loving and true companions through thick and thin. My dogs helped me to cope with and overcome my mental illnesses and I owe them big time.

When I was reasonably sober and stable, being aware that I was never going to become a professional academic, I quit my studies shortly before my master’s exams and left the research project. I was the most sensible way of reducing the stress in my life. A few years later the cultural centre dispensed with my services. After a period of unemployment, during which I was official classified as unfit for work, a judgement that is still formally valid, I spent a year working for a mail order company selling Apple computers and accessories. As a result, I acquired my first iMac a cute, Bondi Blue G3. There is a certain irony here, during my research project I had become an expert on the history of the computer but unlike many of my contemporaries I had never previously owned a computer. 

The computer company was bought up by a larger rival and moved to Stuttgart about 240 km from where I live and I became unemployed again. I then ran into the problem of agism, a concept which up till then I had found mildly amusing. I was only around fifty but apparently too old to be employable. A typical telephone conversation from this period:

Me: Good Morning, my name is Christie and I ringing about your job advert

Them: How old are you?

Me: fifty something

Them: Thank you for your call.

Some didn’t even bother to say thank you before ringing off, so I became self-employed.

Since then I have tutored school kids in maths and English, taught, mostly business, English to adults, copyedited a very wide range of English texts written by non-native English speakers and translated an equally wide range of German texts into English. It has never made me rich, but I have over the years mostly managed to pay my bills. Four years ago, I officially retired.

Somewhere down the line I got back into the history of science and seventeen years ago began holding public lectures on a diverse range of topics. Eleven years ago, I started this blog, having previously discovered the world of #histSTM blogging and having been encouraged by other #histSTM bloggers to do so. It still feels kind of weird but somehow late in life I seem to have carved out a rather strange career as a historian of science. 

I suppose the final consequence of my forty years of living, working, studying, loving, and suffering in Germany is that last year I became a German citizen. As should be obvious from this very brief sketch, my life has followed anything but the normal life and career path, or at least what is considered normal for a white, male Northern European, but has meandered over a wide terrain, taking quite a few detours along the way. I wonder what the future will bring, knowing me and looking back over the last forty years it probably won’t be anything normal or conventional.

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T’would appear so!

When you have very little income and no reserves and you run out of money, it is not easy asking other people for help, things like pride, shame and self-esteem tend to get in the way. Because of this I battled with myself for several weeks about setting up a Gofundme after it became clear that at some point I was going to have to buy a new computer. Even after I had grudgingly accepted that it was probably my best bet and wrote the text that I posted here on Saturday, I didn’t post it straight away but vacillated for more than a week, editing, rewriting and generally procrastinating, shall I, shan’t I? In the end I metaphorically closed my eyes, gritted my teeth and pushed out my text on Saturday afternoon, in my opinion probably the worst time of the week to launch an appeal, as lots of people take a sort of break from the Internet at the weekend. Because of this I was totally dumbstruck when I realised less that eighteen hours later, on the Sunday, that I had already almost doubled my original target in donations.

My immediate reaction was the following text that I posted on Twitter:

To say that I’m totally and utterly mind blown at the unbelievably kind and generous response to my appeal for help in buying a new computer would be an understatement. Will write a full response on the blog soon but till then thank you one and all!

Because so many people on Twitter had not only donated themselves but also boosted my signal on Twitter often added their own recommendation and praise for my humble scribblings, I added the following:

People moan and complain about Twitter but the #histSTM community is an incredibly rich and vibrant source of advice, information and help. Which is all offered openly, freely and with much good will. A true republic of letters.

Internet friend, seventeenth century historian and author of the excellent Killing Beauties, Pete Langman (@elegantfowl) tweeted the following:

Guess we all want you to keep on doing what you do!

To which I replied:

T’would appear so!

I currently have more than double the sum I asked for, donated by 119 wonderfully generous people and the donations haven’t stopped, yet!

I am totally overwhelmed by this unbelievable affirmation of the value of my work here on this blog and nothing I could say would adequately express my deep and heartfelt thanks that you all want me to keep on doing what I do to quote the good Dr Langman.

So I’ll just simply say:

 

thank-you-so-much-lettering_1262-7413

 

P.S. this week’s post is somewhat behind schedule but I’m working on getting it finished, so hang in there!

 

 

 

 

 

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Keep the Renaissance Mathematicus Online!

Difference_engine_plate_1853

My ancient iMac[1] is displaying increasing signs of giving up the ghost and moving on to the great electro-junk yard in the sky. My daily confrontations with the spinning beach-ball of death are increasing in frequency and the number of time where it doesn’t cease to spin and I am forced to shut down and reboot are also increasing. I assume it is only a matter of time before I will attempt to turn on my loyal workhorse and the screen will simply remain blank; this actually happened with its predecessor. This of course means that I will have to invest in a new computer, preferably before the current one decides to depart forever.

I am a pensioner with a very basic state pension, for which I am very grateful, but which doesn’t even totally cover the basics in life. I supplement this with private tutoring and some other bits and pieces. I have little or no reserves and can, quite simply, not afford a new computer at the moment. I have some potential work lined up for the autumn, but in order to do that I will need a fully functioning computer and I also don’t think that I will earn enough through that to cover the full costs of a new computer.

All of this being the case I turn to you, the readers of the Renaissance Mathematicus. I have never charged for the constant stream of history of science writing that I have delivered up over the last eleven years and I hope that the Renaissance Mathematicus will remain free for its readers in the future. I am asking you to make a onetime contribution now if you wish to go on reading the episodes of my Emergence of Modern Astronomy series, (or are waiting for the dead tree version, for which I will also need a computer), my scintillating book reviews, my accounts of obscure Renaissance scientists, mathematicians, cartographers et al and my occasional HISTSCI_HULK stomps all over bad #histSTM, then you are going to have make a small donation towards a shiny new Renaissance Mathematicus computer.

If all the readers of the Renaissance Mathematicus would each donate just €1 then I would have enough to buy two computers with enough left over for a celebratory meal. I appeal to my readers to help me in this endeavour and each to contribute, as they are able and as they are willed. Unlike book authors asking for funds to publish, I can offer no incentives or prizes for particularly generous contribution other than to promise that as long as I am able I shall continue to entertain, stimulate and educate you to the best of my ability as the Renaissance Mathematicus and of course you will have my eternal thanks.

A small special appeal to all the authors, whose books, book chapters and papers I have fact checked for their history of science content in recent years. I couldn’t have done so without a computer and will not be able to do so in the future without one.

For those who wish to donate to keep the Renaissance Mathematicus online. I have set up a Gofundme, which you can access here.

[1] Actually, in real world terms it’s not that old but in terms of computer generations it is positively stone age

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Chilli 19.02.2006–27.07.2020

The sweetest little lady in the world has left us. Somewhat more than a year ago I explained how Chilli came into my life. Yesterday she left it taking my heart with her as she went. In recent months she had begun to display the symptoms of dementia. They were unmistakable but still fairly mild, so I thought we would still have some time together.

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On Friday morning, on the way home from our early walk in the woods she had some sort of brain malfunction that seems to have blown some fuses in her head. She took off like a rocket and I had no idea where she had gone. She ran wild through the area for nearly one and a half hours, till I could finally catch her with the help of a very generous lady dog owner. She was in total panic and didn’t recognise me and attacked and bit me. She is normally the most passive and friendliest dog in the world. I managed to get her on a lead and she immediately calmed down and we walked home. Once there she fell into her bed and didn’t leave it again the whole day except when I took her briefly outside to pee.

Things did not really improve on Saturday; she was confused, disorientated and apathetic. By Sunday it was clear that the little lady, who had brought me so much joy over the last fifteen or so months was suffering without hope of recovery and that I would have to release here from her distress. On Monday afternoon the vet helped her on her way out the vale of suffering and now she is no more. My flat seems suddenly very empty.

Chilli as puppy005

Chilli as a puppy taken from her vaccination pass Added 29/08/2020

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Keith Tippett (25 August 1947 – 14 June 2020)

I was deeply saddened to learn yesterday of the death of the jazz pianist, composer and bandleader Keith Tippett (25 August 1947 – 14 June 2020).

Keith_Tippett

Source: Wikimedia Commons

I ran a jazz club for ten years in the 1980s, which is not as romantic as it sounds, consisting mostly of tedious bureaucratic bullshit, but if you manage the concerts themselves, as I did, you get to meet a lot of famous and not so famous musician. Some of them just remain names, hello-goodbye and little more. Some, however, become friends Keith was one of those.

I first met him as an artist performing at a small jazz festival I organised, “9 Performers on 3 Stages”, to celebrate the opening of the new large concert hall in the cultural centre in which I worked. Keith played a solo set in the smallest of the three venues. He came out, sat down at the piano, was still for a couple of minutes, then he began to improvise. He played forty continuous minutes of some of the most intense, beautiful, moving, technically challenging, live music I have ever heard and I have heard an awful lot of live music. The room was absolutely packed and during the entire forty minutes you could have heard the proverbial pin drop. When he finished the room erupted in a storm of applause and jubilation. After about five minutes of ear shattering exultation, he returned to the stage, sat down once more at the piano and played a very short Chopin etude. When he had finished he turned to the audience, smiled and said very softly, “that’s all I know” then he left the stage to stunned silence.

In those days I mostly booked my musicians into a small family hotel, Hotelchen am Theater, which was then run by a lovely lady called Tini, who was very artist friendly. In a normal commercial hotel, when you book in for one night, they tell you that breakfast is from 7 to 9 am and you have to vacate your room by 11 am at the latest. When you booked into Hotelchen, Tini would ask, “when do you want breakfast?” Musician, “2 pm!” Tini, “that’s cool, what would you like for breakfast?” Musicians loved her and her guest book is an awesome piece of artistic history. I had, of course, booked Keith into the Hotelchen. When Tini got up at about 7 am, she found Keith sitting on the floor with her then 3 or 4 year old daughter, Nora, polishing shoes! They were playing hotels. Tini died some years ago and Nora now runs the hotel and from time to time I remind her of this very magic moment.

Keith was a very intense family man and whenever he played you always had to arrange for him to call his family back in England. This was before mobile telephones and instant worldwide communications. International telephone calls were in those days expensive and not always easy to set up but I always made sure that we did it for Keith whenever he came to entertain us. Some years later I was working at a big jazz festival in Nürnberg, selling records for a small record company, when I got the chance to hear Keith in duo with the moderately insane but totally brilliant Dutch jazz drummer and percussionist Han Bennink, a mindwarpingly superb performance. Later in the evening I ran into Keith and got introduced to his wife Jules aka Julie Tippetts, a superb jazz singer. For many non-jazz fans she is better known, or should we say remembered, as the pop/rock singer Julie Driscoll, who had a massive hit with Brian Auger and the Trinity performing Bob Dylan’ This Wheel’s on Fire in 1968. Jules was very much one of the 60s ‘It Girls’ and the secret heartthrob of legions of pubescent, male teens. She was even more beautiful, as a mature lady and totally sweet and friendly.

I had quite a lot of Keith’s music before I even met him and have acquired more over the years but it is the real life person, whom I shall miss. Keith was a warm, generous, kind human being and a brilliant musician and the world just got a little bit darker with his demise.

 

 

 

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Eleven

Eleven is a number word in English that derives from the Old English ęndleofon, which is first attested in Bede’s Ecclesiastical History of the English People. There are cognates in all the Germanic languages, all of which have the same meaning of ‘one is left’. Left that is having counted up to ten. This is of course, a clear linguistic indication that we use, and have long used, a ten based, or decimal, number system contingent on the fact that through evolutionary chance we possess ten fingers or digits. Just to round up the picture twelve and its equivalents in other Germanic languages originally meant ‘two are left’ before we move onto thirteen, fourteen etc., which are simply three plus ten, four plus ten and so on and so fourth.

number-11-clipart

Coming back to eleven, on this day one year ago we celebrated, in our own inimitable way, the glorious tenth anniversary of the Renaissance Mathematicus that we are still here 366 days later, don’t forget that 2020 is a leap year, means that your favourite malcontent, #histSTM blogger has managed to fill yet another year with his incoherent scribblings. Counting up to ten we have one left. Ignoring such trivial matters, as the current world pandemic not much has changed in the world of the Renaissance Mathematicus. I have somehow managed, against my usually tendency to wander off and start something else, to complete another twenty-five slices of my, in the meantime, monumental series on the emergence of modern astronomy, bringing the word count up to a guesstimated fifty to sixty thousand. An end is actually in sight even if we haven’t quite reached it yet. This will be when the real work starts if I really want to turn it into a book. I need to go back to the beginning and basically rewrite the entire thing!

Turning to other matters, today is purely by chance the religious festival Corpus Christi or to give it it’s official title Dies Sanctissimi Corporis et Sanguinis Domini Iesu Christi (Day of the Most Holy Body and Blood of Jesus Christ the Lord), a Christian liturgical solemnity celebrating the Real Presence of the Body and Blood, Soul and Divinity of Jesus Christ in the elements of the Eucharist, to quote Wikipedia.

Carl_Emil_Doepler_Fronleichnamsprozession

Corpus Christi procession. Oil on canvas by Carl Emil Doepler Source: Wikimedia Commons

Now you might think that this particular piece of Catholic mumbo-jumbo (you might remember that one of the things that divided Catholics and Protestants during the Reformation, is that Protestants stopped believing that the bread and wine actually changed into the body and blood of Christ) has little or nothing to do with the history of science, you would be wrong.

To start with we need to address the chance bit. Corpus Christi, which is anchored to Easter, is one of those movable feasts in the Church calendar the irregular occurrences of which are determined by the Gregorian calendar, the introduction of which involved some very intricate astronomy and mathematics, which have the been the subject of a couple of blog posts here.

The actually Church feast was suggested by and campaigned for, thirty years long by Juliana of Liège (c. 1192–1258) prioress of the double canonry of Liège and her wish was granted by Pope Urban IV, who commissioned his chief theologian Thomas Aquinas (1225–1274) to compose an office for the Feast of Corpus Christi to be celebrated on the Thursday after Pentecost, which is itself celebrated fifty days after Easter Sunday. Thomas Aquinas plays a very central role in the history of European science, as it was he together with his teacher Albertus Magnus (before 1200–1280), who made Aristotelian natural philosophy acceptable for the Catholic Church, thus establishing it as the predominant scientific corpus in the European High Middle Ages.

The next #histSTM connection with the feast of Corpus Christi actually occurred in the life of Galileo. In his Il Saggiatore Galileo speculated a little bit with the ancient Greek theory of atomism. Because of this he was denounced anonymously to the Inquisition. The denunciation claimed that atomism contradicted the Church’s teaching on transubstantiation, which was based on the medieval Aristotelian theory of matter.  This distinguished between substantial and accidental properties of matter. In this theory the appearance of a piece of matter is accidental but its true nature is substantial. According to the transubstantiation theory the bread and the wine change in their substance into the body and blood of Christ whilst retaining the accidental appearance of bread and wine. If, however, the Aristotelian theory of matter were to be replaced with atomism this theory would no longer function. The Inquisition never proceeded against Galileo in this matter but it is of note that in England Thomas Harriot and Sir Walter Raleigh were held and questioned on a similar charge somewhat earlier.

Returning to personal matters, as is usually my wont in my birthday posts, I recently had an acrimonious exchange with one of my readers, whose comments were from the beginning aggressive, insulting and historically false. I tried to reason with him and he just got more abusive in his tone. In the end I blocked him and erased his comments but I found his parting shot insult, and it was clearly meant as an insult, fascinating; he stated that I was not a historian but a storyteller.

This is interesting because, as is very clear to see history and story share the same etymological root, the Latin historia, “narrative of past events, account, tale, story,” from Greek historia “a learning or knowing by inquiry; an account of one’s inquiries; knowledge, account, historical account, record, narrative.” It is not until the late 15thcentury that the two differentiated meanings for history and story began to slowly appear. In German the same word, Die Geschichte means both story and history, the different meanings depending on context.

Book of ideas

If I get asked in a formal or semi-formal context how I describe what I do, my answer is that I’m a narrative historian of the contextual history of science. That quite a mouthful and might sound, to some, rather pretentious. If I get asked what that means, my answer is I’m a storyteller. I don’t regard being called a storyteller as an insult; I regard it as a compliment.

 

 

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Time

Who is the old man shuffling into the kitchen? I don’t recognise him

Where has the youth gone, who on warm summer evenings

Ran barefoot through the streets of the small Welsh town

After a long day uncovering the remains of a Roman fort

His long hair and his thoughts flowing free on the gentle breeze

Now I sit, with naked skull, in doctors’ waiting rooms wondering

Where does the time go?

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