Humble Pi – Matt Parker

Subtitled ‘A comedy of Maths Errors’ this book looks at mistakes not only with mathematics but also some dodgy computer programming and some problems that fall in between like the fact that an employee kept disappearing from the company database and it turns out that his name was Steve Null. I used to be a programmer and more importantly for this example a Database Analyst so immediately saw the problem here, empty fields which should be populated are counted as Null in a database so you would search for Null entries and delete the records as they are clearly not filled in correctly and could cause processing errors later down the line, this person was actually called Null so kept being deleted.

Matt Parker is the Public Engagement Mathematics Fellow at Queen Mary University of London, amongst many other things, and has made a career out of explaining mathematics to the general public both on youtube and in highly successful theatre based tours. He started out as a maths teacher in his native Australia but has lived in England for many years and built his online presence here. The book is not only informative regarding maths errors and possible pitfalls but includes several mathematical jokes in its layout such as starting at page 314 and counting down which is clearly not normal behaviour for a book. The choice of 314 is deliberate as Matt is well known for his annual calculations of pi in different ways on pi day (American format dates for the 14th of March gives 3.14) including one ideal for this which uses the actual book I’m reviewing to calculate pi.

Other ways he plays with the normal structure of a book include having a chapter 9.49 between chapters 9 and 10, which appropriately covers problems with rounding errors, and the index which is surprisingly accurate as not only do you get the page with the entry on but as it is to five decimal places you get the location of the word you searched for.

Some of the errors I had come across before but surprisingly not many, this is a really well researched piece of work. One I hadn’t heard of in the past is now rapidly becoming my favourite mistake because it was so close to being right and then fell over at the final hurdle. There was a bridge being built between Switzerland and Germany and to save time it was decided to start from both sides and meet in the middle. Clearly this is a good idea but you do need to actually line up perfectly so the maths is even more vital than normal for an engineering project. There is a problem with matching heights and that is that they are calculated ‘above sea level’ now that wouldn’t be an issue if sea level was constant (it isn’t, the curvature of the Earth amongst other factors sees to that) bit also Switzerland does not have a coast but via a fairly convoluted route uses the Mediterranean Sea as its base point. Germany does have a coast but a long way from Switzerland on the North Sea. The engineers thought of this however and correctly calculated the difference as 27cm, which is pretty impressive (a) to think of it and (b) to get it right but then added the 27cm to the wrong side so the bridge missed its joint by 54cm.

If this post intrigues you Matt has done a couple of lectures based around the book and this is the link to the one he gave at The Royal Institution in London last year. In it he goes through several examples in the book including a section near the end where his wife, space scientist Lucy Green, brings into the lecture hall what remains of a satellite blown to pieces and dumped in a swamp after a simple maths error. You can’t easily get a more dramatic, or indeed more expensive example of maths gone wrong than that. I bought the book from Matt on his website so it is signed by him and yes I have posted this a day late from my usual Tuesday and between 7pm and 8pm rather than 7am and 8am to show that getting a number wrong is all too common and Matt also left in three errors for exactly that reason.

Dialogue Concerning the Two Chief World Systems – Galileo Galilei

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The final, and longest, book in my August reading marathon of important scientific works is also definitely the oldest and arguably the most significant in the leap of understanding passed on to those members of the public able to read a copy. Published originally in 1632 in Italian so that it was more accessible to the general public than it would have been if written in Latin it was immediately seen as an attack on the Catholic church as it presented as valid the then heretical Copernican system of the Sun at the centre of the Solar System rather than everything rotating around the Earth as taught by Aristotle and Ptolemy and adopted as clearly correct by the church as Earth should be the centre of Gods handiwork. Galileo was duly tried by the Inquisition and sentenced to life imprisonment at home and the book remained on the Catholic church’s list of banned works for over 200 years until 1835.

It is styled as a conversation over four days between three characters, Salviati is the instigator of the meetings and is clearly a Copernican, Simplicio is an adherent to Aristotelian and Ptolemaic systems and Sagredo is there initially to play devils advocate putting questions to both of the others but towards the end is obviously swayed by Salviati. Both Salviati and Sagredo are based on real people with those names who had been friends of Galileo but had both died many years before publication so could not be implicated by their names being used, whilst Simplicio appears to have got his name from the Italian word semplice which means simple minded. The choice of this name for the character backing the Ptolemaic system was also not lost on the Inquisition. Galileo was well aware that he was pushing at boundaries and originally got permission from the church to write a book about tides which grew into the final work covering far more than his original proposal, but even the characters acknowledge that this is potentially dangerous territory.

We are arguing for our own amusement, and are not obligated to any such strictness as one would be who was methodically treating a subject for professional reasons, with the intention of publishing it … it should be almost as if we had met to tell stories, so that it is permitted for me to relate anything which hearing yours may call to mind.

This edition was published by The Folio Society in 2013 using a translation originally done by Stillman Drake in 1953. It includes a modern introduction by Dava Sobel along with a foreword by Albert Einstein, which presumably dates back to the first publication of this translation. I did struggle a little with the verbose nature of the translation which whilst it may reflect Galileo’s original did also mean that I several times had to reread a sentence to make sure I followed the text correctly. This is not helpful when I was also trying to appreciate the leaps being made by Galileo whilst reminding myself that this was written decades before Newton formulated the Theory of Gravity so Galileo was truly groundbreaking in his explanations. His theoretically neutral but definitively pro-Copernican text starts from first principles with balls rolling down a slope to end up with not only the Earth rotating each 24 hours but also orbiting the Sun each year with the angle of the Earth’s axis also included to explain the equinoxes.

That is not to say that everything is correct as we would understand the cosmos now, Galileo has astronomical distances far too small, although much exceeding that of his contemporaries. A good example of this is the section of detailed calculations surrounding the two supernova that had been observed in the last few decades before he wrote the book. He is rightly dismissive of a book which aimed to prove that that these occurred within the orbit of the Moon so as to not disturb the changeless firmament which does so by carefully choosing between astronomical measurements of the period so as to find ones with sufficient error to support the authors position. However Galileo makes the same error in his selection by dismissing not only these examples but also any that would imply the nova occurred at an infinite distance from Earth which using the methods explained would actually have been the correct solution. Instead Galileo had decided that the stars were roughly six to eight times as far away as Saturn (then the furthest known planet) although some “could be two or three times further than that” to explain relative brightness and apparent size. He duly provides many pages of calculations regarding the sample set he has chosen, which are clearly there just to demolish the book and author he dislikes. Other ‘scientific’ books and papers from his time are likewise introduced and their methodology and reasoning torn apart. Galileo clearly wanted to leave no stone un-turned in his defence of Copernicus.

In the final section Galileo covers the subject that he originally stated was to be the main topic of the work, that is the tides and what causes them. Fortunately this makes up a tiny proportion of the whole book as sadly this is another area where he is in error by effectively ascribing them to the rotation of the Earth and the consequential ‘sloshing’ of the waters in the seas. The examples of mistakes given above are entirely understandable given the groundbreaking nature of the book and although I feel the translation could have been better this is still a book I thoroughly enjoyed as the insights presented by Galileo are not only good examples for today but give an understanding of the reasoning of the time and the turmoil between science and the Catholic church that would hold back scientific advances within its sphere of influence for decades if not centuries to come.

Galileo finally received an apology for his treatment at the hands of the church on the 31st October 1991 from Pope John Paul II over three hundred and fifty years too late.

The Voyage of the HMS Beagle – Charles Darwin

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At over 206,000 words this is the second of the three large books for my August scientific reading marathon. I chose it in preference to The Origin of Species (first published 1859) for several reasons, including the fact that it is a lot more readable, but mainly because in this you can see Darwin slowly edging towards the theory that would make him famous. This is especially true of the second edition (1845, the first edition was in 1839, twenty years before his more famous work), the text of which is used for this book as Darwin altered sections in light of his research and developing thoughts. Another reason is that I love the work of Robert Gibbings who illustrated this Heritage Press volume. Although called a journal which implies a diary like approach, and yes most of the entries do have the date at their start, it is not chronological. We do bounce around a bit for a few years as The Beagle was on a nearly five year surveying mission so tends to revisit places several times and Darwin to make things clearer and avoid the obvious repetition has entries that may be months or years apart but which are put together because geographically they make more sense that way. It actually took me a while to realise what was going on and it was only when I stepped back a couple of pages to refresh my memory that I spotted that the entry there was two years after the one I was reading.

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Throughout the text you can see Darwin edging towards evolution and the concept of gradual change in species. He also references many species which have the dubious distinction of being ‘described by Darwin but now extinct’ including a type of cattle in South America and on the Falkland Islands a species of wolf which he describes as a fox when he sees it and noted it’s decline.

Their numbers have rapidly decreased; they are already banished from that half of the island which lies to the eastward of the neck of land between St Salvador Bay and Berkeley Sound. Within a very few years after these islands shall have become regularly settled, in all probability this fox will be classed with the dodo, as an animal which has perished from the face of the Earth.

This may well be the earliest documented use of the dodo as a reference point for extinction of a species.

When you think of Darwin’s voyage then most people automatically think about the Galapagos Islands but in truth he spent very little time there arriving on 15th September and on his way to Tahiti by 20th October 1835. Just over a month out of a almost five year voyage and they take up in this edition twenty seven pages out of almost five hundred despite having more illustrations than most other sections. What we do get is a basic description of what have become known as Darwin’s finches as he realises that the bill shapes on different islands vary dramatically in order to make best use of the food supplies found there. Despite the giant tortoises being the most famous residents and symbol of the archipelago it was the finches that really drove his realisation of what became known as evolution. He is also one of the first people to accurately describe the marine iguanas found exclusive on these islands and notice their diet of seaweed rather then the belief up until then that they were after fish.

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When reading the book one thing you notice is just how much time Darwin isn’t on board The Beagle, he goes off on long expeditions inland sometimes for weeks at a time whilst Captain Fitzroy is engaged on his duties creating charts for the admiralty. You therefore get long passages where he either makes circuits when the ship will be in one place for a period of time or he arranges to meet the vessel at a specified port further along the coast. The observations he makes away from the coastal areas add greatly to his geological studies and give fascinating diversions to life on board ship, but I suspect they are also inspired by his desire to be on solid ground due to the really bad seasickness he was prone to, which almost made him leave the expedition within a few weeks of the start. Science was greatly enhanced by his decision to keep going regardless but it was so close to being abandoned before he could make any of his discoveries.

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Towards the end of the book the Beagle goes to the Keeling Islands and it is here that Darwin comes up with a theory for how coral islands and reefs are formed and ultimately writes another book on the subject. This is one of the few passages where the text becomes difficult to follow as he references maps from the other book without the reader of this volume having access to them, but there is enough for you to understand the process proposed. Other than this section the book is extremely readable even in this full form. Most versions printed nowadays, including the Penguin Classics edition are heavily edited and have more than 25% removed coming out at less than 150,000 words, which is still a substantial work but I would rather read a complete edition.

The Elegant Universe – Brian Greene

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I bought this book in the July 2020 Folio Society sale specifically for this August science marathon which I have just realised I am reading in order of length. After the relatively short ‘The Double Helix’ last week I jump to the 432 pages of this volume, next weeks is a similar length and the final book to tackle is over 550 pages. If you are a regular reader of my blog you will know that I do a reading marathon each August, previously I have read multiple books each week but this year I have decided to tackle major scientific works at the rate of one a week when normally I would have interleaved them with shorter and easier works. So what is the importance of ‘The Elegant Universe? Well it was originally published in 1999 and is one of the first books to attempt to summarise the issues between Einstein’s relativity theories and quantum mechanics and then go on to explain a possible solution to their inconsistencies using String Theory to a readership that is not composed solely of physicists. The book was nominated for the Pulitzer Prize so definitely qualifies for my requirement to be a significant science work for this months readings and represents theoretical physics as I have previously read and reviewed the logical book for this subject namely Einstein’s own book on Relativity.

After a couple of brief introductions, one written in 2017 especially for this new edition, and a brief summary of the current understanding of elementary particles which makes up section one of the book Professor Greene dives straight in with two chapters on the General and Special Theories of Relativity, how these moved us on from the Newtonian Laws of Motion and the odd effects that are predicted by Einsteins equations. After this is a chapter giving a good introduction to Quantum Mechanics, which is a surprisingly easy read given the counter intuitive behaviours of forces and particles at this level of magnification. These are followed by a chapter entitled The Need for a New Theory where he looks specifically at the contradictions between Relativity and Quantum Mechanics and the problems that are faced by physicists trying to unite the two in the search for the Theory of Everything. These four chapters make up the second section of the book and cover ground I was already familiar with however I have not read up on String Theory so from here on the theoretical physics was all new.


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The chapters get ever more complicated  as they try to explain the various aspects of String Theory, which by its very nature as the search for The Theory of Everything has to stretch from atomic level to cosmology. Professor Greene is very good at using analogies to express complex thoughts in a way the reader can approach them. For those who are fans of the Star Trek spin-off Deep Space Nine you will be pleased to find that String Theory allows for wormholes to exist. Spoiler alert – they probably don’t but at least there is some physics behind the idea as shown on the page spread above.

One potentially good way that the entire book is written is the ability of the reader to take it at their own pace and also to decide how deep they want to go. This is done by use of an extensive notes section at the back of the book which moves more complex discussions of points raised along with most of the mathematics out of the main body of the text. Now for me this became increasingly annoying as I had to keep two bookmarks to track where I was up to and to make skipping to the notes section easier but it does make the main text simpler to follow for the more lay reader who after all is probably the target audience.

Am I convinced by String Theory after finishing the book? The answer is probably no, there are far too many places where the solution to problems within the theory appear to be solved by the ‘with one giant leap our hero escapes’ methodology favoured by Flash Gordon short films from the 1930’s. Be it the ‘convenient’ choice of three holes in the six dimensions curved around a string so that the known three families of particles are predicted by approximate mathematical formulas. Or the super-symmetrical particles which are a cornerstone of most string theories (of which there are five versions which also doesn’t seem like a solid foundation) not being found as expected by the Large Hadron Collider so the assumptions of which they are based being changed so they ‘couldn’t have been discovered with current technology’ there are too many holes being papered over. Even assuming that the mathematics is finally worked out, and there is almost forty years of people trying, the idea that a mathematical model is also the physical construct is dubious to say the least and there is no need for the actual physical basis of the universe to match the mathematical representation for a theory to be valid in predicting motion and inter-reaction but String Theorists insist that this is the case.

Twenty years on from the book being written even those heavily involved in the physics back then are starting to have doubts about some of what is suggested. The most obvious candidate is super-symmetry. This is seen as one of the most important signatures that String Theory is correct and is number one on the list of things that ‘will prove or disprove the theory’ included in the book but few physicists now believe it is true as can be judged by this extract of a Royal Institution lecture by Dan Hooper, Head of the Theoretical Astrophysics Group at the Fermi National Accelerator Laboratory in the USA. Maybe String Theory will unravel, maybe it will be adapted to match experimental reality, who knows, but it is an fascinating subject and needs to be tackled to understand the fundamental basis of reality.

Read the book, it’s difficult, even with the solid background in Relativity and Quantum Mechanics that I have, but worth it. It will challenge your understanding of these subjects and that can only be a good thing, physics and mathematics rely on constantly pushing the boundaries and at least at the moment String Theory is the only game in town that attempts to mesh the Quantum Mechanics and what is happening at the smallest boundaries with Relativity and the physics of huge distances. It might be right, it might be wrong, but it will certainly push the boundaries of scientific endeavour for many years to come.

The Double Helix – James D Watson

For this years August reading marathon I have decided to tackle four of the most significant science books that I have on my shelves. Unlike previous years where I have needed to read multiple books in a week this year I only have one at a time but because of their very nature these books are not something you can quickly get through and rush onto the next one, also two of them are over 500 pages in length. Three are published by the Folio Society and the other by Heritage Press in America who often produced books of a similar quality until they ceased publishing.

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I’m starting with what is arguably the most significant scientific discovery of the twentieth century, the structure of DNA and how it could pass on genetic material. It is written by one of the three Nobel Prize winners for the discovery and provides a fascinating account of the race to be the first to crack how this mechanism worked and indeed what it was that did it. Now I freely admit that biology is easily my weakest science having dropped the subject at sixteen so was a little wary of this book and whether it was just going to go over my head but I need not have worried as Watson’s style pulls the reader along so that even in the technical parts I could keep up.

I hadn’t realised how quickly the science behind genetics changed in the early 1950’s or how competitive the search for the solution as to how genetic material was passed on became. Watson provides a good overview of the state of the science after the war where the general consensus was that the information had to be in proteins because they were more complex than DNA appeared to be so that had to be where something so important was encoded. Watson himself became interested in bacteriophages (phages for short) which are viruses which can have within them either DNA or the simpler RNA molecules surrounded by proteins and in 1951 started work at the Cavendish laboratory in Cambridge where he first met Francis Crick and the story begins. The original foreword which is included in this volume is by their departmental head Sir Lawrence Bragg who had himself won the Nobel Prize in 1915 for his work on X-Ray diffraction which was ultimately the way used to confirm the helical nature of DNA. Bragg says in his foreword regarding Watson’s style and tone in the book

He writes with Pepys like frankness. Those who figure in the book must read it in a very forgiving spirit. One must remember that his book is not a history, but an autobiographical contribution to the history which will someday be written. As the author himself says, the book is a record of impressions rather than historical facts.

Watson does indeed explain that he compiled the book from letters and diaries, which explains the large number of personal details such as dinners and his accommodation problems being included which all provide a more rounded narrative than the straight science. As for the Pepys like frankness, Bragg himself is subject to a few scathing comments especially when he specifically requires Crick and Watson to stop working on DNA and get on with what they were supposed to be doing. But his main target as a person obstructing their progress is Rosalind Franklin, a brilliant chemist and exponent of X-Ray crystalline photography and who took the images which ultimately confirmed Watson and Crick’s model. Franklin did not work with either Watson or Crick she was based in Kings College, London working with Maurice Wilkins or more accurately working against him according to this book as the two did not get on either personally or professionally so Watson’s impressions of her are strongly coloured by Wilkins’ opinions. Wilkins would ultimately share the Nobel prize with Crick and Watson in 1962, sadly Franklin had died of cancer in 1958 and posthumous prizes have only been awarded twice and have been specifically prohibited since 1974. Watson however has said that he thought she should have been included in 1962.

The tension mounts as Watson describes the various groups working on the genetic solution which ultimately comes down to three teams racing for the prize. Crick and Watson in Cambridge, Wilkins and Franklin in London and Linus Pauling in America. Ironically Pauling would also be a Nobel laureate in 1962 but he won the Peace prize for this campaign against nuclear testing. Wilkins and Franklin were the closest technically but due to their failure to work together were starting to trail but what really prompted Watson to get on with model building was Pauling who produced a paper which was close but which had a serious error in the chemistry and so produced the wrong result but Crick and Watson knew that once he realised his mistake it might be weeks rather than months before he fixed it and found the correct answer.

There have now been many more historical and less anecdotal accounts of the search for the structure of DNA, as predicted by Bragg in his introduction including another book by James Watson, which I also have, entitled DNA and written in 2003 to accompany a British TV series on DNA marking the fiftieth anniversary of the discovery. Watson was very young, only twenty four, when he and Crick made their breakthrough and that possibly also affected the style of this book. At the time of writing he is still alive, the only person involved who is, and at ninety two lives in his native America.

A better view of the cover design by Alice Stevenson based on a design by Gavin Morris.

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Darwin in Malibu – Crispin Whittall

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This play by Crispin Whittell was premiered by The Birmingham Repertory theatre in Birmingham, England in May 2003, it opened on the 9th May and finished its scheduled run on the 31st, I attended the performance on the 21st. The copy of the book I possess was bought at the theatre and includes several pages relating to the performance including biographical details of the performers along with details regarding the theatre company and the theatre itself. Presumably these pages are not present in later versions of the book as it is replacing the need for a programme at this particular performance and is not relevant to any later production.

The entire play takes plays on the deck of a beach house in Malibu, California and is viewed as though the audience are sitting on the beach looking towards the house with the sea behind them. It is clearly the present day from the attire of the young woman who appears on the stage as the play opens. Already seated on the deck is an old man with a white beard wearing a Hawaiian shirt and reading a book, which turns out to be Malibu by Pat Booth. Already I was intrigued by the set-up, as presumably this was Charles Darwin, and nobody had said anything yet. Sarah and Darwin chat aimlessly for a while, she is clearly a little ditsy and missing her boyfriend whilst Darwin appears to have discovered a rather unlikely liking for horoscopes.

The two are joined by Thomas Huxley who was Darwin’s friend and public champion of his theory when it was published in 1859 whilst Darwin himself had stayed at his home in Kent most noticeably at an acrimonious  debate at the British Association’s Oxford meeting in 1860. It soon becomes clear that both men are well aware that over a century has passed and that they are both dead. They are also puzzled as to why in that case they are sitting in a beach house in Malibu and also why they are joined by Sarah who is clearly not a Victorian ghost. Nevertheless they chat about the Oxford debate and also technological discoveries since such as DNA which shows how Natural Selection (as Darwin called it) works.

Then suddenly from along the beach the bishop of Oxford from that same debate, Samuel Wilberforce, arrives. It was with the bishop that Huxley famously, and possibly apocryphally, disagreed most. Apparently back in 1860 Wilberforce facetiously asked Huxley whether his ape ancestors were on his grandfather or grandmother’s side. Huxley replied that he would rather have an ape for a grandfather than a man with an impressive brain and considerable influence who chose to employ those facilities in the ridicule of science. The three of them attempt to continue the debate on stage and although it is now 143 years later it is clear there will be no meeting of minds, just as we also slowly find out who Sarah is and why she is there.

Now if that all sounds a little dry and overly intellectual for an evenings entertainment I have to say that nothing could be further from the truth. Whilst not a laugh a minute it is very funny when it wants to be and poignant when appropriate. I still have the flyer for the show I saw which is tucked into the book as a bookmark and the quote from Darwin’s lines in the play printed on it sums up the effect of California on the great thinker. The play is seldom performed although it has had a few revivals not just in the UK but America as well, if it ever on near you I recommend it.

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Penguin Science Survey

I recently completed my collection of this interesting series, some of which are surprisingly difficult to find, so I thought it was time to review the fifteen books that make the set and the history of how they came to exist. Although they were all published in the 1960’s their genesis was back in the 1940’s with two ‘quarterly’ periodicals also published by Penguin; Science News which ran to fifty four volumes from June 1946 to March 1960 and New Biology which had thirty one volumes from July 1945 to January 1960. As you can see from the date ranges, although these were theoretically quarterly, in practice only Science News managed anything like a volume every three months, in fact there was a gap of nineteen months between New Biology 1 and volume 2. These books each contained various articles covering a wide range of scientific advances written by scientists at a level where the interested layman wouldn’t feel intimidated but detailed enough to be of interest to the scientific community. By 1960 though Penguin Books were getting out of the periodicals business, however there was still seen to be a need for something like Science News and New Biology so Penguin Science Survey was born the following year.

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1961 The Specials

Science News and New Biology had their own series codes within Penguin Books but as those had come to an end a new home was needed. The logical place was within the Pelican imprint which was well established as the main factual part of Penguin Books output and the 1961 volumes were therefore planned to go there. Both books have the Pelican logo internally and volume 1 even has a number in the Pelican range A526 (which was re-assigned to The Living Brain by W. Grey Walter published August 1961) but for some reason very late in the day it was decided they should be Penguin Specials and came out as S193 and S194 in June 1961 in what looks like a hasty rebinding with laminated thin card covers unlike anything else from Penguin at the time.

Volume 1 replaced Science News and covers such diverse subjects as elementary particles, The US space plan, geophysics, the development of nuclear weapons and several other topics. Each article is around twenty pages long and there are a dozen in total along with a preface by the editor Arthur Garrett and a section on units and constants. Volume 2 is the equivalent of New Biology and has fifteen articles ranging from smoking and cancer of the lung (an article well ahead of its time), world food production, the life of viruses, the cockroach, the brain of the octopus, etc. again these are normally around twenty pages long each and there is also a preface by the joint editors S.A. Barnett and Anne McLaren. Both volumes also have numerous line drawings within the text and a section of black and white photographic plates in the middle of the book. Having created this template in these volumes it was largely stuck to for the following years.

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1963 A new home

There were no editions in 1962 and when they re-appeared in February 1963 they were oddly assigned to be part of the ‘main series’ with catalogue numbers 1924 and 1925 where they shared space with novels, travelogues, biographies and plays, they had also become A and B rather than 1 and 2 although A continued to be the equivalent of Science News with B covering New Biology with the same editors as in 1961. Volume A has amongst its eleven main essays a good article on optical astronomy by Patrick Moore and a fascinating piece on computers subtitled a progress review where the author describes an amazing IBM machine that could store a massive 100 million characters; which is several orders of magnitude less than an average mobile phone today. Roughly half of volume B is taken up with a series of articles linked under the heading ‘Matters of Life and Death’ which cover chromosomes, contraception, malformations and family planning. Also included in the rest of the book is a piece on tissue transplantation which was still in its early days, along with eight other essays.

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1964 and 1965 A short period of stability

These two years continued the pattern of 1963 with the same editors and a wide spread of subjects covered. The books are still in the ‘main series’, which is where they would remain, and are assigned the following catalogue numbers 2043 and 2044 (April 1964) along with 2225 and 2226 (April 1965).

In 1964 subjects included elementary particles, Soviet space research, adhesion and a quirky short article entitled ‘How discoveries are made: a plea for intuition’ all in volume A, whilst volume B has life on other planets, the origin of man, learning a birds language, communication in bees amongst many other essays. In 1965 part A is split into three sections: Physical Research including superconductivity (still very relevant today), the physics of the brain, and automated spacecraft of the US. The second section is entitled Industrial Applications of Science and has diverse subjects such as Diamonds in industry, rubber, and supersonic aircraft. The final part is entitled Communications and has just two articles, the communication of information, and science on radio. Part B bounces all over the place from mental images, athletic physique, homosexuality, tranquillisers, and the yeasts of wine to other subjects equally intriguing.

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1966 A missing book and a new title

Any collector looking for Penguin Science Survey A from 1966 will search in vain because it was never published. B did come out in March as number 2467 and it was joined, the same month, by Penguin Technology Survey 1966 (number 2439) which covered some of the same ground as Survey A would have been expected to do, it is also edited by the regular Survey A editor Arthur Garrett. This book is probably the one that interests me most with essays on the impact of electrical engineering, new methods of printing, computer aided design (remember this is 1966 so really surprising to see what feels like a new technology in use over fifty years ago) and a look forward to nuclear fusion reactors (which is still the case) along with other subjects. Science Survey B has a new editor, Anthony Allison, but apart from that little has changed. Like Technology Survey the subjects feel up to date including the challenge of insecticide resistance, two articles on fighting virus infections by differing means, and several more on the effects of temperature in biology and medicine.

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1967 And then there was three

Any thoughts that the 1966 Penguin Technology Survey was a re-branding of Survey A which wasn’t done very well and left Survey B stranded was dispelled this year by the existence of three titles 2640 Penguin Technology Survey 1967 (April), 2687 Penguin Science Survey 1967 Biology (July) and 2688 Penguin Science Survey 1967 Physical Sciences (also July). The renaming of the surveys was presumably to make it more obvious what they covered rather than A or B and the same editors continued from the previous year along with Nicholas Valéry who took over what used to be Survey A and was now Physical Sciences.

Technology Survey has a good article on technological advances in Japan, something we would all become familiar with over the following decades and there are also a couple of excellent essays on technology in medicine but my favourite has to be the last one which deals with the problems of naming things as technology advances and is entitled “Let’s make up the words as we go along”. The Biology Survey is subtitled The Biology of Sex and all fifteen essays are concerned with some aspect of this subject including four on sex in the insect world, a couple on mammals in general and others including anthropology, and the x-chromosome. With technology now in its own volume what was Survey A is more restricted in its subject matter but this means it can look deeper into specific areas, instead of one article on space science which was the most you got up until now there are three, this better reflects the 1960’s Space Age fascination. There are also pieces on solar energy, detecting underground nuclear explosions (also a hot topic at the time) and high energy physics.

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1968 The last hurrah

Technology Survey only lasted for two volumes and was gone after 1967. 1968 would be the final year of the Penguin Science Survey. 2840 Penguin Science Survey 1968 Biology and 2841 Penguin Science Survey 1968 Physical Sciences finally hit the bookshelves in November and had the same editors as in 1967. As with the previous year the Biology volume took one overarching subject, in this case photobiology, and the twelve papers look at all aspects of the effect of light in biology. From photochemisty, through photosynthesis, to the impact of light in controlling flowers, and on to bioluminescence with plants and animals producing their own light there is lots to get into in this book. Finally comes Physical Sciences, there are ten articles in this volume and several of these are still major paths of investigation today such as the worlds weather, superconductors, controlled nuclear fusion, and life in the universe.

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The other Surveys

Somebody at Penguin obviously thought that the Science Surveys were a good idea and decided to expand the concept because in April 1965 there appeared 2336 Penguin Survey of Business and Industry 1965 alongside 2337 Penguin Survey of the Social Sciences 1965. For the purposes of this article we can ignore the business book, as it doesn’t include the word Science in the title, other than to note that three more volumes were produced. Number 2528 in June 1966 was for 1966, number 2746 in July 1967 was for 1967 and oddly number 2882 in October 1968 was apparently for 1967-8. With four volumes the business series was considerably more successful than its fellow which proudly proclaimed on its back cover that it is “The first in a new series of annual surveys” but the Social Science ‘series’ in the end only had two volumes with the next, and final, edition being 2823 Penguin Social Sciences Survey 1968 coming out in October 1968 just in time for the whole Survey concept to be killed off.

Now I would be the first to say that I know little about the social sciences but some of the articles do look to be potentially quite interesting. In 1965 the book starts with ‘In Defence of Sociology’ which I feel is John Gould’s (the editor of both books) attempt to get his response as to why the book was produced in before anyone asked the question. But Trends and problems in Soviet studies sounds like a paper that could be written now and How small-scale societies change turns out to be quite a good study in social anthropology. I must admit however that Prolegomena to the study of British kinship had me reaching for a dictionary, it apparently means a preface so why not say so? Reading the article, or at least starting it,  confirms my initial opinion that the author was simply trying to show off, as the word choices are often unreasonably complex and make it virtually unreadable. The 1968 book does also have several very good papers, on the power of politics, armed forces and the political process, and the study of organisations being three that particularly drew my attention.


All properly written articles on science should finish with a summary of what we have learned and in this case I just want to stress how good these books are. As you can see from the selection of article titles I have picked out they are to some extent still relevant today and provide an interesting background to the development of modern science and technology. Apart from the 1963 volumes and 1965’s Social Sciences (by Josef Albers) the covers were all designed by F.H.K. Henrion which gives a pleasing consistency to the series, no designer is credited for the 1963 effort or 1967’s Technology Survey but that one at least also looks like his work.

The price more than doubled over the eight years from six shillings (30p) in 1961 to twelve shillings and sixpence (62½p) in 1968 and they were always considerably more expensive than other Penguin books at the time which probably helped with their demise. In 1968 a novel the same length as one of the surveys would have cost five shillings (25p) so less than half the price, the reason is probably down to the lower print runs for specialised titles so fewer being sold but equally the price must have put off a significant number of potential readers therefore contributing to the downward spiral of purchasers.

Search them out, they are worth looking for and when you do find them still only cost a few pounds.

Flatland – Edwin A. Abbott

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I asked my friend, Catalan booktuber Anna, best known under her nom de plume of Mixa, to choose this weeks read from a random group of titles I provided and she selected Flatland because she had never heard of it and was intrigued by the idea of a mathematical classic combined with social parody. Written in 1884 by an English headmaster who specialised in ‘classics’ i.e. Greek and Latin; this is as an unlikely cornerstone of multi-dimensional non-Euclidean geometry as can really be imagined. I first read it in my teens and although the copy on my shelves is from my mid twenties I probably haven’t read it in over two decades so it is well worth revisiting.

The book is split into two sections, the first describes Flatland and it’s inhabitants whilst the second deals with one of it’s inhabitants A. Square and his perspective of several other lands. Initially Lineland, then what is called Spaceland which is our own set of dimensions and finally Pointland before he finally returns to his own two dimensional world and the prison that we find him in at the start of the narrative.

But let us begin with a description of Flatland because it is with an understanding of this two dimensional land that we will start to see the effects of an extra dimension which is not apparent to the inhabitants. Our narrator A. Square is as you might expect a square and as such is a lawyer, the number of sides that each character has denotes his status in society as follows:

Our Middle Class consists of Equilateral or Equal-Sided Triangles. Our Professional Men and Gentlemen are Squares (to which class I myself belong) and Five-Sided
Figures or Pentagons. Next above these come the Nobility, of whom there are several degrees, beginning at Six-Sided Figures, or Hexagons, and from thence rising in the number of their sides till they receive the honourable title of Polygonal, or many-sided. Finally when the number of the sides becomes so numerous, and the sides themselves so small, that the figure cannot be distinguished from a circle, he is included in the Circular or Priestly order; and this is the highest class of all.

It is a Law of Nature with us that a male child shall have one more side than his father, so that each generation shall rise (as a rule) one step in the scale of development and nobility. Thus the son of a Square is a Pentagon; the son of a Pentagon, a Hexagon; and so on.

Below the Equilateral triangles are the ranks of workers and soldiers who are Isosceles and as the size of the smallest angle contained within a figure is an indication of intelligence clearly the more ‘pointed’ such a triangle is the lower the intellect and (bearing in mind this is a Victorian book) the more violent and criminal the individual is assumed to be. Rather than increasing sides with each generation Isosceles triangles gain half a degree to their smallest angle each time until they are finally assessed to be Equilateral and the family can then start to rise through society.

Now it should be noted that as indicated in the quote above this only applies to sons, so what about the females, well they are all just straight lines and this is where Edwin Abbott Abbott (yes the A. in his name really was Abbott as well) hit accusations of misogyny even in the 1880’s. Something he attempted to address in a preface added to the second and revised edition but without much success, one of the more offending sections being below…

Not that it must be for a moment supposed that our Women are destitute of affection. But unfortunately the passion of the moment predominates, in the Frail Sex, over every other consideration. This is, of course, a necessity arising from their unfortunate conformation. For as they have no pretensions to an angle, being inferior in this respect to the very lowest of the Isosceles, they are consequently wholly devoid of brain-power, and have neither reflection, judgement nor forethought, and hardly any memory.

Still enough of the first half of the book, there are lots of details given as to how houses are constructed, how the people recognise each other and various social mores which whilst interesting in the way Abbott has tried to give life to his creation do not really impinge on the main object of the book which is contained in part two. The important section is in the remainder where A Square visits other lands and learns about dimensions other than the North/South, East/West directions he is currently familiar with. The first of these is described as a dream where he perceives Lineland a place of just one dimension with all the inhabitants travelling over a single line with him floating over it so that he can see along the line.


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As A. Square interacts with the King of Lineland at first he is simply a disembodied voice coming from nowhere along the line and therefore not perceptible as a figure to his majesty. He therefore lowers himself onto (and through the line) revealing himself as a line as that is all he can be in just one dimension, but a line that can appear and disappear at will. This understanding is vitally important for him to grasp the concept of Spaceland later on in the book when a sphere visits him in his home.

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As can be seen from the diagram to A. Square the sphere is merely a circle within Flatland and one that can change size and also appear and disappear just as he could in Lineland but even though he had his dream he still struggles to comprehend what it is that he is seeing until the sphere lifts him off the plane of Flatland and shows him his world from above. Suddenly he can see inside his house and not only that but everyone and everything in it simultaneously. He can even see inside his sons, grandsons and servants and also his wife panicking because he has suddenly vanished.


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This is revelatory to him and at this point he grasps a logical progression that had eluded the sphere himself

I. Nay, gracious Teacher, deny me not what I know it is in thy power to perform. Grant me but one glimpse of thine interior, and I am satisfied for ever, remaining henceforth thy docile pupil, thy unemancipable slave, ready to receive all thy teachings and to feed upon the words that fall from thy lips.

Sphere. Well, then, to content and silence you, let me say at once, I would shew you what you wish if I could; but I cannot. Would you have me turn my stomach inside out to oblige you?

I. But my Lord has shewn me the intestines of all my countrymen in the Land of Two Dimensions by taking me with him into the Land of Three. What therefore more easy than now to take his servant on a second journey into the blessed region of the Fourth Dimension, where I shall look down with him once more upon this land of Three Dimensions, and see the inside of every three-dimensioned house, the secrets of the solid earth, the treasures of the mines in Spaceland, and the intestines of every solid living creature, even of the noble and adorable Spheres.

Sphere. But where is this land of Four Dimensions?

I. I know not; but doubtless my Teacher knows.

Sphere. Not I. There is no such land. The very idea of it is utterly inconceivable.

I. Not inconceivable, my Lord, to me, and therefore still less inconceivable to my Master. Nay, I despair not that, even here, in this region of Three Dimensions, your Lordship’s art may make the Fourth Dimension visible to me; just as in the Land of Two Dimensions my Teacher’s skill would fain have opened the eyes of his blind servant to the invisible presence of a Third Dimension, though I saw it not. Let me recall the past. Was I not taught below that when I saw a Line and inferred a Plane, I in reality saw a Third unrecognised Dimension, not the same as brightness, called “height”? And does it not now follow that, in this region, when I see a Plane and infer a Solid, I really see a Fourth unrecognised Dimension, not the same as colour, but existent, though infinitesimal and incapable of measurement? And besides this, there is the Argument from Analogy of Figures.

Sphere. Analogy! Nonsense: what analogy?

I. Your Lordship tempts his servant to see whether he remembers the revelations imparted to him. Trifle not with me, my Lord; I crave, I thirst, for more knowledge. Doubtless we cannot see that other higher Spaceland now, because we have no eye in our stomachs. But, just as there was the realm of Flatland, though the poor puny Lineland Monarch could neither turn to left nor right to discern it, and just as there was close at hand, and touching my frame, the land of Three Dimensions, though I, blind senseless wretch, had no power to touch it, no eye in my interior to discern it, so of a surety there is a Fourth Dimension, which my Lord perceives with the inner eye of thought. And that it must exist my Lord himself has taught me. Or can he have forgotten what he himself imparted to his servant?
In One Dimension, did not a moving Point produce a Line with two terminal points?
In Two Dimensions, did not a moving Line produce a Square with four terminal points?
In Three Dimensions, did not a moving Square produce – did not this eye of mine behold it – that blessed Being, a Cube, with eight terminal points?
And in Four Dimensions shall not a moving Cube – alas, for Analogy, and alas for the Progress of Truth, if it be not so – shall not, I say, the motion of a divine Cube result in a still more divine Organization with sixteen terminal points?
Behold the infallible confirmation of the Series 2, 4, 8, 16; is not this a Geometrical Progression? Is not this – if I might quote my Lord’s own words – “strictly according to Analogy”?
Again, was I not taught by my Lord that as in a Line there are two bounding Points, and in a Square there are four bounding Lines, so in a Cube there must be six bounding Squares? Behold once more the confirming Series, 2, 4, 6; is not this an Arithmetical Progression? And consequently does it not of necessity follow that the more divine offspring of the divine Cube in the Land of Four Dimensions, must
have 8 bounding Cubes; and is not this also, as my Lord has taught me to believe, “strictly according to Analogy”?

Sorry for quoting such a large section but this really is the whole crux of the book as we see that logically there must be a fourth direction that is no more visible to us as up/down was to the square in Flatland and north/south was to the inhabitants of Lineland stuck as they are in their eternal east/west line.

We leave Flatland as we began with A Square in prison for having committed the heresy of declaring of what he calls ‘upward not northward’ and trying to spread these ‘lies’ in Flatland. He is being visited by a priest, as he has been for seven years to try to get him to recant from his madness but instead he determines to write this book.

Flatland has never been out of print since it’s original publication over 130 years ago and it remains one of the great primers in understanding multidimensional geometry so important after the work of Einstein, I heartily recommend it and have thoroughly enjoyed rereading it so thank you Anna.

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Relativity – Albert Einstein

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If you are going to read a book about relativity then why not go for the man who created the theories, after all as Einstein says himself in his preface…

The present book is intended, as far as possible, to give an exact insight into the theory of relativity for those readers who, from a general scientific and philosophical point of view, are interested in the theory, but are not conversant with the mathematical apparatus of theoretical physics. The work presumes a standard of education corresponding to that of a university matriculation and despite the shortness of the book, a fair amount of patience and force of will on the part of the reader.

Consider yourself warned.

The edition I have was published by The Folio Society in 2004 and has an introduction by Emeritus Rouse Ball Professor of Mathematics at Oxford University Roger Penrose.  Einstein originally wrote the book in 1916, just a year after he published his main paper on his General Theory of Relativity and eleven years after he had formulated his Special Theory of Relativity. Originally in German the translation is by Robert W. Lawson and he does an excellent job especially considering the complexities of the subject. Put simply the two theories deal with different things, the special theory is concerned with resolving issues between the laws of electromagnetism (specifically Maxwell’s equations) and those of motion as described in Newtonian mechanics, this becomes especially problematic as speeds approach the speed of light and time ceases to behave the way you would expect it to. The general theory on the other hand deals with gravitation and the forces between bodies caused by this. This is where the concept of warped space-time comes into place and the highly satisfying rubber sheet model which can easily demonstrate the basics of the idea and has become largely familiar to most students over the last century. It should be noted for anyone who watches the video is that the reason that the objects ultimately collide is due to friction between the balls and sheet, without that elliptical orbits would continue as we are familiar with planetary motion so this can only ever be a rough approximation of space-time curvature.

There are two ways of approaching an explanation of the theories of relativity, one book which I read several years ago does it very successfully and that is Why Does E=mc²? (And Why Should We Care?) by Professors Brian Cox and Jeff Forshaw which takes eight chapters and roughly 250 pages (depending on the edition) to cover the subject including the derivation of E=mc². Yes there is quite a lot of mathematics but there is also a large number of diagrams and descriptions in simpler terms in order to expand the readers understanding over a extended period and a short appendix in later editions to add more detail to a section that readers had queried. Einstein takes the other approach, with thirty two chapters over 132 pages (in this edition) so you approach quite complex theories and mathematics in small bite size chunks and you can reread the short chapters until you have grasped the concept being covered. There are also five appendices in a further fifty four pages which go into significantly more detail of the mathematical models and theories underpinning the two theories which are not needed by the casual reader but are there largely for completeness. In his introduction Penrose explains that part of the calculations done by Einstein in the book are no longer done that way as expressing time with a fourth dimensional axis based on imaginary numbers is seen as an unnecessary complexity when it can be done by clocks instead. This negates the need for one of the appendices which deals with Minkowski’s four dimensional space model using the square root of -1, other than as an example of Einstein’s thinking at the time.

There is no denying that some of the chapters can be difficult to get your head around the first time of reading, especially if like me you haven’t done theoretical physics at this level for over thirty five years, but it definitely worth the effort as Einstein gradually takes you through the maths. Starting with Euclidean Geometry (the first chapter which also looks at the concept of ‘truth’ for a mathematical axiom) and then pushing your understanding through relative movement of co-ordinate systems until you hit the Lorentz Transformation less than thirty pages later which gives you the basics needed to understand relativity by comparisons of motion within relative co-ordinates systems.

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With the introduction of Gaussian co-ordinates later on we can finally approach non-Euclidean geometry, which combined with Minkowski’s four dimensional space leads to the mathematics behind the general theory and warped space-time, which for now is how we understand gravity. The book is complex, but not unreasonably so, and the short sharp sections work as a way for the reader to grasp the overall concept in practical chunks. A century on this work still underpins our understanding of the cosmos and reading this book or the one by professors Cox and Forshaw, whichever you get on best with, is a good way to exercise the brain.

Of course there is still a lot of work to go before physics hits its ultimate goal of ‘the theory of everything’. Relativity is very good at explaining the very large but when you hit the realms of the very small quantum mechanics is just plain strange to the layman and even Einstein for a long time refused to believe most of the concepts behind that branch of physics. I do have a very good book on that subject as well which I will look at later this year.

Robert Hooke’s Micrographia

2nd January 1666

Thence to my bookseller’s and at his binders saw Hookes book of the Microscope which is so pretty that I presently bespoke it.

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so to my bookseller’s and there took home Hookes book of Microscopy, a most excellent piece, and of which I am very proud.

21st January 1666

Before I went to bed I sat up till 2 a-clock, in my chamber reading of Mr Hookes Microscopicall Observations, the most ingenious book that ever I read in my life.

I have to agree with Samuel Pepys, I have added this book to my library in the last week and like the celebrated diarist I have spent hours late into the night reading and looking at the wonderful illustrations. It is hard to imagine just how revolutionary a work it was in it’s time, nobody had seen anything like it before. Very few people had access to a microscope and very little had been printed with illustrations of what you could see with the use of one. Micrographia was the first book published by The Royal Society, just three years after the society had been granted it’s royal charter in 1662 making it the oldest scientific academy in the world. Pepys had become a fellow of the society on 16th February 1665 so knew Hooke and would have been well aware of the book before publication.

Now it may seem odd to write a review of a book that came out over 350 years ago but the edition published by The Folio Society is the first high quality version printed in the last 200 years and reproduces in full size the original plates including large fold out pages that are up to 2 feet (60cm) across. The book is consequently large at 13½” × 8¾” (34.3cm x 22.2cm) and quarter bound in leather. The cover is printed on cloth and based on the eye of a grey drone fly and was designed by Neil Gower.

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Inside the illustrations are the first thing to catch your eye but then the text pulls you in. Although this is primarily an important, and in its time ground breaking, scientific work Hooke wrote for the interested layman and even after all these centuries it is still an engaging story. Instead of just describing the illustrations he explains why and how he came to look at them in the first place, you get his first impressions and you can share in his sense of wonder at what is revealed.

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A study of a piece of cloth to reveal the weave, the end of a pencil, a needle, nothing is beyond his inquiring mind and everything he looked at and wrote about was new to the reader who would not have had access to anything like this before.

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The picture above is of the black spots on the leaves of the rose bushes in his garden. To his surprise these turned out to be ‘tiny plants’ growing on the leaves themselves. Nowadays we understand what he is looking at but the text explains his reasoning that this is some sort of mould and the next thing he then examines is a blue mould on a book bound in leather from a sheep to see if his premise is valid. You learn with Hooke and it’s no surprise that Pepys found the book so fascinating.

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The large fold out plates are possibly the most famous pictures in the book and The Folio Society have reproduced pages from original 1st and 2nd editions (whichever were the best examples) held in the Bodleian Library in Oxford. There is also a small section at the end where Hooke turns his attention away from the very small to the very large and includes some observations he made with a telescope including an early map of part of the moon.

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It really is a joy to own and read this book, which was published in 2017 in a limited edition of just 750 copies, mine is number 635. Whilst I love the normal production of The Folio Society and have over 400 books printed by them; it is their limited editions that are their crowning glory. Printed on the finest paper and treated as a work of art in their own right these books are rightly regarded as something special and Micrographia was the winner of the “Scholarly, Academic and Reference Book” category at The British Book Design & Production Awards 2017. A fantastic addition to any library.

There is a video of the book from The Folio Society on YouTube which  gives a better idea as to the size and beauty of this amazing work and this makes an interesting comparison to a video from The Bodleian Library about their first edition.