In Praise of Folly – Erasmus

20200602 In Praise of Folly

Erasmus of Rotterdam wrote this, probably now his most famous work, in 1509 in Latin and the Folio Society edition that I have uses the Latin title as its cover design Moriae Encomium. By intention this title can also be read as In Praise of More because he dedicated it to his friend Sir Thomas More whom he was staying with in London at the time.

The book is split into sixty seven sections in this edition, although looking at other translations it is not always the case that these are numbered. The text I have was originally produced  for the Penguin Books edition translated by Betty Radice, used by permission by Folio. For a while this use of Penguin texts was relatively common at Folio so presumably they had a formal arrangement to do this. I liked the numbered sections in this text as it gives an easy way of referring to parts but as this is apparently not a standard I will use the opening line of a section if I need to specifically mention it along with the number. This translation also has short footnotes, when Erasmus wrote the book anyone likely to read it would have known the classical examples he refers to but nowadays this is far less likely so a quick guide as to where the quotation has come from and the relevance to the text is extremely useful.

Erasmus decided to make Folly the equivalent of a Greco-Roman goddess addressing the reader as though in a forum or theatre. She introduces herself and her faithful companions

And as for such my companions and followers as you perceive about me, if you have a mind to know who they are, you are not like to be the wiser for me, unless it be in Greek: this here, which you observe with that proud cast of her eye, is Philautia, Self-love; she with the smiling countenance, that is ever and anon clapping her hands, is Kolakia, Flattery; she that looks as if she were half asleep is Lethe, Oblivion; she that sits leaning on both elbows with her hands clutched together is Misoponia, Laziness; she with the garland on her head, and that smells so strong of perfumes, is Hedone, Pleasure; she with those staring eyes, moving here and there, is Anoia, Madness; she with the smooth skin and full pampered body is Tryphe, Wantonness; and, as to the two gods that you see with them, the one is Komos, Intemperance, the other Negretos hypnos, Dead Sleep. These, I say, are my household servants, and by their faithful counsels I have subjected all things to my dominion and erected an empire over emperors themselves.

What follows is, at least at the start, a gentle satire of the foolishness of mankind pointing out how Folly and her companions lead people astray but at the same time saying that the only truly happy people are babes, aged citizens in their dotage and others not fully in control of their mind because only they are not worn down by the cares and realities of life. There are many examples of how her or her companions have affected people for good or ill depending on how you interpret the results, and if the book remained in this vein it would still be well worth reading for the way it pokes fun at pomposity and self-indulgence, greed and wilful ignorance is as relevant today as it was back then. However by section 53, which in this translation begins ‘Then there are the theologians’ you can sense the tone changes. Erasmus is on tricky ground especially in 1509, Martin Luther was still eight years away from writing his Ninety-Five Theses and setting in train the Reformation with his attack on the Pope and other members of the Catholic hierarchy  for the selling of indulgences amongst other things that he regarding as debasing the Christian faith for profit, but Erasmus got in ahead of him.

This was in a time when the office of Pope could certainly be bought, and it cost a lot of money and contacts to work your way up the greasy pole, however the rewards were huge for those that got there. The selling of indulgences was a massive money spinner for the church and ultimately for the Pope himself and this was spreading discontent. What was surprising was that Erasmus felt safe to attack this at the time and not only turned out to be safe in the clever way that he presented his arguments but that his work was the equivalent of a best seller. Erasmus was not an early protestant but he recognised the excesses of the Catholic church and through this book was highlighting the problems that it faced. That he built up to this slowly is of no surprise bearing in mind the recriminations that he could have faced and the power of the church in enforcing discipline in the early sixteenth century.

What starts out as a harmless satire of mankind’s foibles turns into a denunciation of the money grabbing nature of the church at the time, but it is worth noting that Erasmus, and his friend Sir Thomas More, did not support the Protestant breakaway from the Catholic church, and in a roundabout way this would cost More his life as he did not attend King Henry VIII’s wedding to Anne Boleyn which marked the break of England from the Papacy. Erasmus however would be safe back in The Netherlands and would die of natural causes in 1536 having lived though the schism in the church the reasons for which he highlighted in this book but which he couldn’t have foretold.

 

The Perilous Descent – Bruce Carter

20200526 Perilous Descent 1

I probably first read this book about forty years ago when I was the age it is most likely aimed at, what would now be classed as Young Adult by the publishing world, and I doubt I have read it since although the copy I have is still the one I had back then. I had no real interest in books as objects back then so never noticed that it is the first edition printed by The Bodley Head in 1952. The dust wrapper is missing, assuming I ever had one, which I doubt as I would have been careful with it even then and I would have bought the book from a second hand bookseller sometime in the mid to late 1970’s. I do know however that the picture on the wrapper was the same as the frontispiece reproduced above, with the title on the larger parachute and Bruce Carter on the smaller one.

Bruce Carter is the pseudonym of Richard Hough, which he used for the half dozen children’s books he wrote, with more than a hundred more titles in his own name which were mainly regarding ships or wartime escapades although he also wrote a few biographies. In 1952 he was working for The Bodley Head, hence his choice of publisher, and in the 1960’s he moved to Hamish Hamilton where he ultimately rose to the position of Managing Director of the children’s book division, Hamish Hamilton also published this book amongst others by him whilst he worked for them.

The Perilous Descent is a rollicking Boy’s Own adventure story apparently written in alternate chapters by the two Typhoon pilots Danny Black and Johnny Wild who were shot down at the start of the book on their way back to England ultimately ending up on a sand bar about a mile off the Dutch coast sometime in 1944. Hough was himself a Typhoon pilot in the war and had to make a forced landing after being hit during which he badly broke his leg which never properly healed although he lived until 1999. This first hand knowledge as to what the two protagonists would have with them regarding survival aids and how they could use the equipment they had certainly adds to the tale as they try to eke out their meagre rations after falling down a hole on the sand bar and into some mysterious tunnels. Ultimately the only way forward is down a huge cavern but fortunately they still have their parachutes so that is what is depicted in the frontispiece as they drop over 25,000 feet to the unknown world below.

20200526 Perilous Descent 2

The land and people they encounter far below the Earth are a strange mix of sixteenth century language, clothes and armaments along with futuristic cities and transport as can be seen in the image above, it is also not a friendly welcome. It turns out that a rebellion had recently occurred and they had been mistaken for some of the rebels, they soon manage to convince the Governor that they are nothing to do with the insurrection and are enlisted to take part in a surprise attack on the rebel stronghold. The story races along and I found myself reading longer sections in one go than I intended to and the denouement, which is foreshadowed in the introduction, has a nice twist right at the end.

The book appears to be no longer in print and I suspect that the Puffin Books edition that came out initially in 1958 and was still being reprinted up until at least 1977 was the last available publication. Children’s books related to the war fell out of fashion around then and although I have greatly enjoyed this nostalgic read I doubt the book would be a commercially viable publication nowadays.

The Age of Scandal – T H White

20200519 The Age of Scandal

First published in 1950, this is my Folio Society edition from 1993, The Age of Scandal is one of White’s lesser known works as nowadays he is most famous for ‘The Once and Future King’ his series based on the tales of King Arthur by Mallory which in turn were adapted by Disney as ‘The Sword in the Stone’ and by Lerner and Loewe as their musical ‘Camelot’. This however is White as a historian although as Raey Tannahill says in her introduction.

It seems wise, therefore, to warn the reader that T.H. White is not – was not, even in his own day – an orthodox historian.

an excursion into eighteenth century history which is outrageously partisan, appallingly opinionated, one hundred percent Politically Incorrect and highly entertaining from first to last.

This is certainly the case, if you like your history of the latter half of the eighteenth century to be apparently written by the gossip pages of the tabloids then this is the book for you and whilst it isn’t a option I had previously considered there is no denying that if any part of, mainly British, history is ripe for such an approach then this is the period. White does stray abroad a little but mainly whilst describing events that include somebody from these isles, the main exception to this is the final chapter but I will come to that in due course. Scandal, gossip and tittle-tattle were the driving force amongst the upper and middle classes for this was the age of the opinionated talkers and the  great letter writers and they had much to talk and write about. The main source for White’s book is Horace Walpole, the youngest son of the Prime Minister Sir Robert Walpole (or probably not as one of the scandals covered by White goes on to explain in considerable detail). To describe him as a prolific gossip would be an understatement, his collection of letters was eventually published by Yale University Press in forty-eight volumes and is available to browse online and White quotes him extensively.

The main talker of the time, I hesitate to call him a conversationalist because he preferred to dominate all conversations, was Dr Johnson and he duly gets a chapter all of his own. I hadn’t realised before reading this how sickly a child he was and how much he was still disabled into adulthood. This makes his rise in society at the time all the more remarkable. Another chapter is entitled ‘Men, Women and Herveys’ and this definitely falls in the one hundred percent Politically Incorrect category as it deals with the Hervey family whose males were all famously effeminate and/or eccentric during the time the book covers, Lord Hervey being ridiculed by Alexander Pope as his character Sporus in his poem Epistle to Dr Arbuthnot. The title of the chapter is however a contemporary quote from Lady Mary Wortley Montague who regarded mankind as split into those three categories as surely the Hervey family were not as everyone else, and it is one of these Herveys who is almost certainly the true father of Horace Walpole.

Other chapters are less specific such as ‘Royal Gossip’ which deals with the convoluted lives of George I, George II, George III and William IV, their actions, their courts, various wives and mistresses and anything else juicy that White feels like including. The following chapter though is probably the most enlightening regarding the reasons why the various characters exposed in this book behaved as they did and that is simply entitled ‘Bottom’.  It is probably best to quote White directly in his explanation of this term.

In the eighteenth century, but particularly under the Regency, a Gentleman was expected to have ‘Bottom’. It was a word of composite meaning, which implied stability, but also what the twentieth century calls ‘guts’. It meant being able to keep one’s head in emergencies, and, in a financial sense, that one was backed by capital, instead of being an adventurer. Bottom, in fact, was synonymous with courage, coolness and solidity.

This was an age of potentially sudden death either from accident or design, armed robbery was common and even Royalty were not immune from being held up by highwaymen but equally criminals were very much subject to capital punishment for crimes as little as burglary and these were quite a spectator entertainment. There were no anaesthetics, you would bear an operation with fortitude to be truly seen as one of the members of society and being to take your drink even in what now would be regarded as unbelievable excess was also to be expected. Dr Johnson is quoted as saying that he ‘had drunk three bottles of port without being the worse for it’ and two gentlemen are described in the book as having drunk ten bottles of champagne and burgundy between them at one sitting without it being regarded as exceptional. Needless to say a lot of people died young, if the alcohol didn’t get them than any of the various diseases prevalent at the time almost certainly would and the upper classes were trained to maintain the ‘stiff upper lip’ from childhood where violent and often sadistic masters would whip their pupils mercilessly.

I said earlier that I would get to the last chapter and this is one that sort of fits the rest of the book whilst feeling somewhat disjointed from it for it deals with the Marquis de Sade. I suspect that White felt that he couldn’t really write a book about his self described Age of Scandal without including such a notorious character but the way he does is surprisingly sympathetic which is out of sorts with everything that has gone before. However as Raey Tannahill puts it at the end of her introduction.

Whatever he may have lacked in scholarly discipline, Terence Hanbury White still deserves to be enjoyed as one of the last, unrepentant upholders of the rumbustious old tradition of Gibbon and Macaulay.

Thrown to the Woolfs – John Lehmann

20200512 Thrown to the Woolfs

This book arrived in a box of mixed titles bought on Ebay for about £10 a couple of years ago, all of which were something to do with books or publishing. I must admit that I barely looked at it at the time as I had purchased the collection of fifteen or so books for a couple of autobiographies that I thought sounded interesting so this just sat on the shelf until last week.  I wish now I had picked it up earlier as, for the most part, it was a thoroughly entertaining read. The book concerns Lehmann’s time either working for or later being a partner in The Hogarth Press, a small publishing house set up by Leonard and Virginia Woolf primarily to publish her books exactly as her and her husband wanted them. Now of course even an author of Woolf’s stature couldn’t keep a press going by her own work alone so they also published books by other writers as well and the company was quite successful from its foundation onwards.

John Lehmann knew Virginia’s nephew Julian Bell from their time at university and when he was deciding about working at the press as the manager Julian warned him that managers didn’t last long as Leonard was far too controlling over the tiniest detail, especially money, and he would have a difficult time. The first part of the book, it’s split into four sections, concerns this fairly disastrous first attempt at working at the press in 1931 and 1932.  The descriptions not only of the cramped offices and working conditions in this section but also of Leonard and Virginia set up the tone of the whole book. Lehmann is clearly a great admirer of Virginia, not only of her work but as a person and when he isn’t actually arguing with Leonard he also gets on well with him but Julian was right, Leonard was impossible as a boss and ultimately the only way forward was for him to leave the business immediately at the end of his initial contract. This caused further ructions between him and Leonard and they barely contacted one another for several years.

The second section has Lehmann in Europe in the lead up to WWII, which is where he made a lot of contacts with up and coming writers across the continent which would serve him well in the coming years. He also started, in 1935, a bi-annual book called New Writing, initially published by The Bodley Head this was looking for a new publisher in 1938 and as things had calmed down by then he approached the Woolfs and this time would end up paying £3,000 (£205,000 in today’s money) for Virginia’s share of the business making him joint partner with Leonard in the Hogarth Press.

The third and fourth parts deal with the eight years from 1938 to 1946 whilst this partnership lasted and make up the significant part of the book not only in pages but also in detail regarding the running of the press and the interactions of the three of them. The sections are split at the suicide of Virginia in March 1941 with by far the happier times being whilst she was alive. Not only does Lehmann tell more about the Press but was also get details of Virginia’s working method and home life. Once Virginia was no longer there to provide arbitration between the two men however things started to go downhill and the one part of the book I found more difficult was a long section where Lehmann quotes verbatim letters between them arguing about which books should be printed or not. Apart from that the book was a very quick read I really wanted to know more so just kept going although you know that the final cataclysm cannot be far off.

In the end Lehmann felt he couldn’t continue as the animosity between the two men over the direction the press should take was just too much and he instigated a clause in the original agreement that either partner could ask the other to buy them out at three weeks notice. This was duly done far faster than Lehmann expected and yet another long period of bad blood between them opened up until oddly in the 1960’s they had yet another rapprochement and as this time they didn’t end up working together this seemed to go well until Leonard’s death at the end of that decade.

The book was published by Widenfield and Nicolson in 1978 in the UK and Holt, Rinehart, and Winston in 1979 in America. Neither edition appears to have been reprinted but both are easily available via abebooks and is definitely worth adding to the shelves of anyone interested in books.

On Britain and Germany – Tacitus

20200505 On Britain and Germany

Back in January 1946 Penguin Books started a new series which is still going way beyond the dreams of the originators, that was Penguin Classics featuring all new translations of classic literature from around the world especially created for the series. They started in Greece with Homer’s Odyssey and the first Latin title was this one featuring two of the books by Tacitus, which was the fifth book in the series coming out in September 1948. On Britain and Germany is actually his two works Agricola and Germania and they were translated by Harold Mattingly who also wrote an extensive introduction along with the notes and glossary. His additional information in fact takes up almost half of the book at seventy six pages with Agricola being forty eight pages and Germania just forty.

Agricola

Representing Britain in this volume is Tacitus’s biography of his father in law Gnaeus Julius Agricola and whilst it does indeed include commentary on his seven years in charge of the conquest of most of Britain it does spends a significant amount of time back in Rome. Tacitus starts this work by stating that biographies are disapproved of in the current Roman society but that he will write this one anyway but unfortunately whatever his abilities as a historian way be revealed in his other works this is not a good example. He rarely states where any of the military actions he describes take place and his grasp of dates is also somewhat tenuous which makes working out what is going on quite tricky. He also has a rather odd idea as to the geography of Britain, stating that it is diamond shaped and not far from Spain with the island of Ireland being between the two countries.

This is where the text by Mattingly really comes into its own not only in the introduction, which prepares you for the lack of details but the notes which accompany almost every chapter clarify quite a lot of the text. One thing I really liked about this edition is that the notes are at the back of the book rather than at the bottom of the relevant pages, this allows the reader to more comfortably concentrate on the text and then pick up on the notes either as they go on or, as I did, complete Agricola and then read the notes. As stated above it is a fairly short biography so this is entirely practical.

Germania

Tacitus has barely started his description of Germania when he comes up with a sentence that I can safely assume is not one quoted by the German tourism authorities.

who would leave Asia, Africa or Italy to visit Germany, with its unlovely scenery, its bitter climate, its general dreariness to sense and eye, unless it were his home.

and a little later

The country in general, while varying somewhat in character, either bristles with woods or festers with swamps. It is wetter where it faces Gaul, windier where it faces Noricum and Pannonia.

He was remarkably polite about Britain in comparison, Noricum is modern Austria whilst Pannonia roughly equates to Hungary. After spending time being rude about the land he turns his attentions to the peoples and tribes of Germania, this is a place that includes not only present Germany but parts of France, Switzerland, the northern Netherlands and Poland. Beyond them is believed to be a great ocean rather than the Baltic Sea and the Romans seem to have almost no knowledge of Scandinavia. Rome appears to have only recently become aware of most of these peoples at the time of Tacitus and then only from contact through war so his descriptions of their lives are short of details and sometimes confused but he does discern a significant number of different tribes and kingdoms but does not ascribe what he would regard as civilisation to any of them other than the ones that have regular dealings with the Romans. His most damning assessment is applied right at the end of the short book with the little he has gathered regarding the Suiones (southern Swedes) and a neighbouring tribe that is only mentioned in Germania so is probably a misunderstanding by Tacitus of the same people or another part of Sweden.

Continuous with the Suiones are the nations of the Sitones. they resemble them in all respects but one – woman is the ruling sex. That is the measure of their decline, I will not say below freedom, but even below decent slavery.

Revisions

The book appears to have gained its original title in Penguin simply because it was translated soon after WWII finished and certainly in the notes Mattingly can be quite jingoistic at times for example in his opening line regarding Germania.

a detailed account of a great people that had already begun to be a European problem in the first century of our era, should still have a message for us in the twentieth.

It is clear that the choice of title was made to entice potential readers after the war whilst maybe calling it Agricola and Germania might not have done as much. Amazingly seventy four years after its first publication Mattingsly’s translation is still the one in the Penguin Classics catalogue, which now runs to well over a thousand titles, and most of the early titles have been completely replaced with updated translations. However it has been revised twice, initially presumably to replace the dated style of the introduction and notes but also to rename the book to the more useful ‘Agricola and Germania’ so that it is clearer what is actually included. The first revision was done by S.A. Handford and was published in October 1970, this book was renumbered from L5 to become L241 and the original version dropped. In 2009 it was revised again, this time by J.B. Rives and now has the ISBN 9780140455403 which makes it the equivalent of L540 when you breakdown the code and the Handford version is no longer available.

Conclusion

The book was very enjoyable and a good introduction to the works of Tacitus via two of his minor writings, what I now need to do is tackle his major works ‘The Annals’ and ‘The Histories’. Tacitus was a Roman senator so well placed to view the intrigues of the emperors and their rivals and this he covers in those more important works. Having the viewpoint from an insider of how the Roman empire was actually governed should be really interesting, I knew nothing about Tacitus before I read this book so I definitely need to find out more.

The Good Life – Dorian Amos

20200428 The Good Life

I have written about The Yukon sixteen months ago whilst reviewing some of the poetry of Robert Service and that also included some of my photographs of my time there in June 1995 with a friend paddling along the Yukon river from Whitehorse the same as Dorian and his wife Bridget would do four years later almost to the day. The difference is that Dave and I were doing it for fun and would leave Yukon by the end of the month, Dorian and Bridget were aiming to live there and had no idea how they were actually going to do this. It truly is wilderness, The Yukon Territory is 186,272 miles² (482,443 km²) which makes it big enough to fit in continental European countries Germany, The Netherlands, Belgium and Denmark together with room to slot in Cyprus. In all that space only 35,874 people live there (2016 census) of which 25,085 live in the capital, Whitehorse. The next biggest place is Dawson (pop. 1.375) and that is where Dave and Bridget were heading.

The book starts in 1998 in Polperro, a pretty coastal town in Cornwall, England, which is heavily dependent on tourism and fishing for its local economy. Dorian had a shop selling his pictures called Amosart and Bridget was a newly qualified psychiatric nurse, life was finally becoming easier after years of study and hard work building up a viable business, but Dorian was becoming bored and longed for some adventure in his life. Then a few months later, over an evening meal of fish and chips.

I heard her sigh “I’m sick of this shit” and I sat up with heart pounding. “Are you?” I said. “We can make a change you know.” Bridge looked at me in away she had only started to do after qualifying as a psychiatric nurse. I took the plunge and told her about my now overwhelming urge for adventure.

When I’d finished and slumped back into my chair, she said “if you think about something too much, you just talk yourself out of it and never do it. We are only here once. Let’s go get some action! Can you pass the salt please?”

Six months later Dorian was on his way to Canada, chosen mainly as they had relatives there so could get help with choosing where they wanted to be. Bridget was to follow four months after when her contract finished. The one practical thing they had done in the meantime was take a week long course on woodlore and bushcraft with survival expert Ray Mears but as he says in his introduction to the book

If I’d known then what Dorian and Bridget had in mind. I would certainly have advised further tuition in bushcraft, pointed them at expert canoe coaches and a host of other instructors.

However ignorance is bliss.

Soon after arrival in Canada Dorian purchased a truck which he nicknamed Pricey, not because it cost a lot of money but the repair bills certainly did, and started to accumulate items needed to exist in the wilderness but on a very tight budget. This meant that as tents were expensive he bought canvas to make his own and soon discovered why tents were so expensive. He also bought a dog called Boris partly as a companion and partly to protect Bridget and himself from wild animals, something that Boris proved many times over the coming months and years that he was incapable of, being more likely to hide behind them if any animals approached, assuming that he woke up anyway. Dorian writes with self deprecating humour regarding their travails in the wild open Canadian countryside and their total lack of preparedness. The trip up the Yukon after Bridget had joined him showed just how wild the country was and how much they had to learn, for example to avoid having to live on soup they were carrying with them they really needed to go fishing but neither of them had ever fished and despite buying the equipment didn’t know how to go about catching anything. The passages describing their fishing attempts are really funny and you feel their elation when weeks later they finally catch something much to their own surprise.

After getting to Dawson they turned back and explored the possibilities of living by one of the thousands of lakes closer to civilisation but found that these were already inhabited or were the play areas of people from the nearby towns so eventually decided that Dawson was the place for them. This time Bridget would go on ahead and get settled and a job whilst Dorian would stay at Bridget’s relatives and get a job there to pay for much needed repairs to Pricey and get some more equipment.  Eventually the two are together in Dawson, or at least on either side of the river as they eventually found a plot to build a cabin on opposite the town so whilst Bridget stayed in Dawson working as a waitress then as a support person for pregnant women, Dorian tried to build a cabin.

I won’t say any more about how this goes except that as you can imagine building a home from scratch when you have never attempted anything like this before, in a freezing Yukon winter (minus 20 degrees is a warm day) , on your own, largely in the dark as days are short that time of year was not a simple task. The book is full of details as to how they get along and amazingly they not only survive but thrive and Dorian is good at describing a scene so that it is easy to visualise.

The book was published by Eye Books who seem to specialise in first time authors, especially with stories to tell like this one and whilst looking to see if this book was still available found that Dorian has written a follow up where he gets ‘gold fever’ and I’ve no doubt that it is a funny as his first.

Mathematics in the Time of the Pharaohs – Richard J Gillings

20200421 Egyptian mathematics 1

There are four extant sources for this book, the Egyptian Mathematical Leather Roll (EMLR), the Reisner Papyri (RP), the Moscow Mathematical Papyrus (MMP) and the most important The Rhind Mathematical Papyrus (RMP) which was actually a training manual for scribes. Because it is there to teach this final papyrus document is crucial to our understanding of how the ancient Egyptians performed their calculations. This document along with the EMLR are in the British Museum in London, the RP is in the Boston Museum of Fine Arts whilst the MMP is in the Pushkin Museum of Fine Arts in Moscow, as you would expect from its name. Gillings wrote his book in 1971 and one or two errors have since been noted in the mathematical press as further studies have been made of the four sources and almost fifty years have passed since he wrote it, but these are largely technical and the book is mainly correct especially in its overview as to how ancient Egyptians calculated and is pretty comprehensive. Having said that it is definitely not a book for the layman, it is pretty solid mathematics and I would suggest that there is still a gap in the market for a simpler presentation which would introduce those with a curiosity in the subject to more easily come to some understanding as to how this worked.

Ancient Egyptian mathematics was largely overlooked and dismissed by scholars as simplistic especially when compared to that of ancient Greece but that overlooked the fact that it was more than capable of calculating the dimensions of the pyramids. For instance if you want a pyramid 139m high (the size of the Great Pyramid at Giza) just how big a base do you need to start with? It has also ensured that they still haven’t fallen down thousands of years after construction. Also the Egyptians had a large empire, so built irrigation canals, large granaries and temples, and of course had a comprehensive tax system to pay for all this so they must have been highly capable at least in the field of applied mathematics and engineering.

But let’s start at the beginning with the hieroglyphic representation of numbers, one is simply a vertical line, two is two of these and so on until you have nine lines drawn together to represent nine. Now this is easy and like all tally marks rapidly becomes unwieldy so you need symbols to indicate larger numbers and the earlier forms of these are shown below. I love the symbol for a million which appears to be the scribe throwing his hands in the air as if to say wow what a big number, what do I do with this?

20200421 Egyptian mathematics 2

In fact the papyrus scrolls were written in hieratic script which is sort of cursive hieroglyphic and is much more difficult to read and it is also important to note that they wrote right to left just as in modern Arabic so to our way of looking at it you would see the units first, then the tens, hundreds etc. There is a quick way of remembering this as animals or birds used in hieroglyphic writing always look towards the direction the writer. In the scrolls we have available to modern study addition and subtraction are regarded as so simple as to not need to show any working out which is unfortunate as this means we don’t actually know how they did it, you just get the required sum and then the answer. However everything beyond that is included and it should be understood that the ancient Egyptians managed their entire means of calculation by merely being able to multiply and divide by two and for reasons that are too complex to go into in this blog they also had the 2/3 times table (usually written down rather than memorised) and used this so extensively that when they needed to find a third of a number they would first get two thirds of it and then halve the answer.

So how did they multiply? Well the example given in the book is for multiplying 7 by 13 and this was done as follows. Start by writing two columns, the first of which has a 1 in it and the second has one of the numbers to be multiplied (this is the second example in the book as I think it is better to understand than the first). Under each number double the figure above until doing so in the column starting with one you would have a number larger than the number you are trying to multiply.

20200421 Egyptian mathematics 3

Simply adding up the values opposite the checked values in the first column gives the answer to 7 x 13 which is 91. If the number in the first column isn’t needed to sum to 13 in this case then you simply ignore the corresponding number in the second column. It’s simple really. Division is done the same way but a scribe asked to divide 184 by 8 would instead ask himself how many times do I need to multiply 8 to get to 184 so would create a similar chart to the one above.

20200421 Egyptian mathematics 4

Now at this point you hit the issue of fractions which we know that they understood as they had the 2/3 table but the way the ancient Egyptians handled them is definitely beyond me being able to explain here, I will simply say that with the sole exception of 2/3 they did not have any fractions with numerator other than 1, so to express ¾ for example they would write the equivalent of ½ + ¼. As you can imagine this becomes extremely messy very quickly. But the way they expressed a fraction, especially in hieratic is interesting as they drew a line over the number to indicate that it was a fraction and as the numerator was always 1 they didn’t need to show this, two thirds had it’s own specific character so that didn’t cause confusion. Later mathematical systems simply added a numerator above the line to indicate multiples of the denominator so this is where our way of writing fractions almost certainly originates from.

I only want to include one further example from the book and this one I chose as I particularly liked the calculation. I do recommend seeking out this book or the various online papers now available on the subject if you want to take this interesting branch of mathematics further. The calculation is how did they work out the area of a circle? Now courtesy of the ancient Greeks and their discovery of geometry (Euclid in particular) we know that the area of a circle is the square of the radius multiplied by the irrational number π which is 3.14 to two decimal places and that will do for most calculations. Archimedes worked it out to about that in 250BC but that is over 1300 years later than our poor scribe in ancient Egypt so how did he do it?

Well their calculation as given in problem 50 of the RMP is to take the diameter, work out a ninth of that figure, subtract that from the original number and then square the result. The sample problem takes a circle with a diameter of 9 khet (which makes the maths a lot easier), so if the diameter is 9 then a ninth of that is 1, subtracting that from the diameter gives 8. Multiply 8 by 8 as we know how to do above and that gives 64 setat as the area of the circle. It’s a hell of a big circle though as a khet is about 57 yards (roughly 52 metres) so a single setat, or square khet, is roughly 3250 yd² or 2720 m². But how accurate is the result of 64? Well (4½)² x π, which is our way of doing the calculation, gives 63.62 so it’s pretty good. If I ever needed to work out the area of a circle in my head (oddly something I don’t do often) then the ancient Egyptian way is definitely the way to do it, no messing around with π needed.

I was intrigued, so some basic algebra (also not something I do every day anymore) shows that the way the calculation works means that their equivalent of π is 256 / 81 which is 3.16 to two decimal places which explains the accuracy. It is also by far the simplest calculation that is remotely accurate as simply subtracting a ninth from the diameter is very easy. I spent a little more time with a calculator and found that the next easiest fraction that gives a better result is to subtract 4/35ths  which is lot more difficult than dividing by 9.

There is considerably more in the book for a keen mathematician to have fun with such as calculations of volumes and of course the all so important dimensions of a pyramid and truncated pyramid (i.e. one still under construction). So once you can get past the slightly confusing way it is written it’s fun to work through, preferably with some paper and a pencil nearby to do some quick calculations of your own.