Category Archives: History of Technology

The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time

The title of this post is the subtitle of Dava Sobel’s Longitude, her mega bestselling account of the life and work of the eighteenth-century clock maker John Harrison; probably the biggest selling popular #histSTM book of all time.

I’m quite happy to admit that when I first read it I was very impressed by her account of a man I didn’t know from a period of history with which I was not particularly well acquainted. However, because I was very impressed, I went looking for more information about the history of John Harrison and the marine chronometer. I found and read quite a lot of academic literature on both topics and came to the realisation that Sobel’s account was not really the true story and that she had twisted the facts to make for a more exciting story but quite far removed from the true narrative.

P.L. Tassaert’s half-tone print of Thomas King’s original 1767 portrait of John Harrison, located at the Science and Society Picture Library, London
Source: Wikimedia Commons

The next segment of the subtitle is also not true. Harrison was supported and encouraged in his endeavours by George Graham, possibly the greatest eighteenth-century English clockmaker, and James Short, almost certainly the greatest telescope maker in the world in the eighteenth century. Both men were important and highly influential figures in the scientific and technological communities of the period. Their support of Harrison rather gives the lie to the claim that Harrison was a lone genius.

George Graham
Source: Wikimedia Commons

The final segment of the subtitle is also highly inaccurate. The problem that Harrison and others were working on in the eighteenth century was a reliable method of determining longitude at sea. They were trying to solve a technological problem not a scientific one. The scientific problem had already been solved in antiquity. Scholars in ancient Greece already knew that to determine the difference in longitude between two locations, one ‘merely’ had to determine the local time difference between them; knowing this the problem was how to determine that time difference, as I said a technological problem.

In antiquity and up to the early modern period cartographers and astronomers (usually the same person) used astronomical phenomena such as solar or lunar eclipses. Observers determined the local time of the occurrence of a given astronomical phenomenon at two different locations and it was then possible to determine their longitudinal difference. Unfortunately eclipses are not very frequent occurrences and so this method has rather limited usefulness. Something else had to be developed.

In the early seventeenth century both Galileo Galilei and Simon Marius discovered the four largest moons of Jupiter and Galileo realised that the orbits of these moons and their appearances and disappearances as the circled Jupiter could, if tabulated accurately enough, be used as a clock to determine longitude. Towards the end of the seventeenth century Giovanni Domenico Cassini and Ole Rømer succeeded in producing the necessary tables and Galileo’s idea could be put into practice. Whilst this method was very successful for cartographers on land, on a rolling ship it was not possible to observe the Jupiter moons accurately enough with a telescope to be able to apply this method; something else had to be used.

The two solutions that came to be developed in the eighteenth century and form the backbone of Sobel’s book, the lunar distance method (lunars) and the marine chronometer, were both first suggested in the sixteenth century, the former by Johannes Werner and the latter by Gemma Frisius. Other methods were suggested but proved either impractical or downright impossible. For lunars you need accurate lunar orbit tables and an accurate instrument to determine the position of the moon. Tobias Mayer provided the necessary tables and John Hadley the instrument with his sextant. For the clock method you require a clock that has a high level of accuracy over a long period of time and which retains that accuracy under the often very adverse conditions of a sea voyage; this is the technological problem that Harrison solved. Sobel presents the two methods as in competition but for navigators they are in fact complimentary and they were both used. As my #histsci soul sister Rebekah ‘Becky’ Higgitt constantly repeats, with the marine chronometer you can carry longitude with you, but if you chronometer breaks down you can’t find it, whereas with lunars you can find longitude, as James Cook did in fact do on one of his voyages.

As I said above, I began to seriously doubt the veracity of Sobel’s account through my own study of the academic accounts of the story, these doubts were then confirmed as I began to follow the blog of the Longitude Board research project set up by Cambridge University and the Maritime Museum in Greenwich, of which Becky Higgitt was one of the lead researchers. For a more balanced and accurate account of the story I recommend Finding Longitude the book written by Becky and Richard Dunn to accompany the longitude exhibition at the Maritime Museum, one of the products of the research project.

Recently I have become fully aware of another aspect of the Harrison story that Sobel does not cover. I say fully aware because I already knew something of it before reading David S. Landes’ excellent Revolution in Time: Clocks and the making of the Modern World (Harvard University Press, 1983). Landes covers the whole history of the mechanical clock from the Middle Ages through to the quartz wristwatch. One of his central themes is the increasing accuracy of clocks down the ages in which the invention of the marine chronometer played a central role, so he devotes a whole chapter to Harrison’s endeavours.

Landes quite correctly points out that after a lifetime of experimentation and ingenious invention John Harrison did indeed produce a solution to the technological problem of determining longitude with a clock. An astute reader with a feel for language might have noticed that in the previous sentence I wrote ‘a solution’ and not ‘the solution’ and therein lies the rub. Over the years that he worked on the problem Harrison produced many ingenious innovations in clock making in order to achieve his aim, an accurate, reliable, highly durable timepiece, however the timepiece that he finally produced was too complex and too expensive to be practicable for widespread everyday service at sea. Harrison had, so to speak, priced himself out of the market.

Harrison’s “Sea Watch” No.1 (H4), with winding crank
Source: Wikimedia Commons

Harrison was by no means the only clock maker working on a viable marine chronometer in the eighteenth century and it is actually his competitors who in the end carried away the laurels and not Harrison. Two clockmakers who made important contributions to the eventual development of a mechanically and financially viable marine chronometer were the Frenchman Pierre Le Roy and Swiss Ferdinand Berthoud, who were bitter rivals.

Pierre Le Roy (1717–1785)
Source: Wikimedia Commons

Plans of Le Roy chronometer
Source: Wikimedia Commons

Ferdinand Berthoud (1727–1807)
Source: Wikimedia Commons

Berthoud marine clock no.2, with motor spring and double pendulum wheel, 1763
Source: Wikimedia Commons

Neither of them can be said to have solved the problem but the work of both of them in different ways led in the right direction. Another contributor was George Graham’s one time apprentice, Thomas Mudge, his highly praised marine chronometer suffered from the same problem as Harrison’s too complex and thus too expensive to manufacture.

The two English clock makers, who actually first solved the problem of a viable marine chronometer were John Arnold and Thomas Earnshaw, who also became bitter rivals. This rivalry involved accusations of theft of innovations and disputes over patents. In the end it was John Arnold and Thomas Earnshaw, who became the most successful of the early clock makers, who worked on the development of the marine chronometer.


Chronometer-maker John Arnold (1736–1799) (attributed to Mason Chamberlin, ca. 1767)
Source: Wikimedia Commons

Thomas Earnshaw (!749–1829)
Source: Wikimedia Commons

Earnshaw chronometer No. 506
Source: Wikimedia Commons

I don’t intend to go into the details of which innovations in clock manufacture each of the man listed above contributed to the development of the marine chronometer that would go on to become an essential navigation tool in the nineteenth century. What I wish to make clear is exactly the same point as my essay on the history of the reflecting telescope for AEON made. From its first conception by Gemma Frisius in the sixteenth century, through the failure of Christiaan Huygens to realise it with his pendulum clock in the late seventeenth century (not discussed here), over its first successful realisation by John Harrison and on to the creation of a viable model by a succession of eighteenth-century clock makers, the marine chronometer was not the product of a single man’s (John Harrison’s) genius but a tool that evolved through the endeavours of a succession of dedicated inventors and innovators. Scientific and technological progress is teamwork.

4 Comments

Filed under History of Navigation, History of Technology, Myths of Science

Recipes in the Wild By Paul Engle June 1, 2017

The Recipes Project blog is, starting today, running a Virtual Conversation on the theme, “What is a Recipe?” I featured this in the editorial of the latest edition of Whewells Gazette the Weekly #histSTM Links List. Inspired by a comparison that I made between algorithms and recipes and a question that I posed, Paul Engle, author of the very excellent Conciatore: The Life and Times of 17th Century Glassmaker Antonio Neri and writer of the Conciatore Blog, sent me the following essay stating, “Feel free to do with it what you will.” So what I will is to post it here as a very welcome guest blog post from an excellent historian of technology who really knows what a recipe is.  

It has been suggested at Whewell’s Gazette in a recent editorial that in considering recipes, particularly technical recipes and their relation to algorithms, that, “the two words are in their essence synonyms and there isn’t really a difference.” [1] With all due respect to the author of this passage, I do not think that is quite right.

A recipe is much more than an algorithm, in fact I propose that while algorithms are quite powerful tools, they occupy a rather distinct niche in the universe of recipes. We do agree on some things however,

“For me a recipe is quite simply a set of instructions, which describe how to complete successfully a given task. The task does not necessarily have to have anything to do with cooking, the first thought that pops up when we hear the word recipe.” [2]

I have thirty-odd years of empirical experience writing and following technical recipes in a laboratory setting; I have several shelves full of them that I am looking at right now. I have been programming computers and dealing with algorithms, dare I say it, since the days of punch cards and paper tape. This is a subject particularly dear to me and besides, I sense an irresistible opportunity to make a fool of myself, so here goes.

In the realms of mathematics and computer science, an algorithm is a set of instructions that enjoy several conditions favorable over recipes; a well-defined environment where it does not matter if it is raining or sunny outside and an output or result that is usually unambiguous. For recipes, not so much; even the lowly baker known that on humid days, a prized and tested bread recipes must be adjusted to produce an edible product. These adjustments do not always take a form that can easily be measured or quantified and this starts to get at the heart of the matter.

Any day of the week, rain or shine, a computer running a straightforward algorithm can generate the first million digits of pi, (yes, the millionth digit is 1). While there may be a certain amount of difficulty in verifying a result, it is something that is done quite routinely. While some simple recipes fall into this form, many others do not. Consider that some technical recipes seem to work even if we do not know how. Others require “experienced” practitioners, not because of anything magical going on, but simply because the most reliable results are obtained by one who has done it before. Even with seemingly simple, well-documented tasks like polishing a material, there can be an enormous number of variables involved, some unknown, others that are not practical or possible to control.

An algorithm generally lives in an artificially constructed, tightly controlled environment, recipes, on the other hand, operate in the wild. An aspect of technical recipes often missed by outsiders is the level of attention that must be paid to the interaction of your “product” with its environment. This may mean frequent observation and testing, or, in the kitchen, it may mean tasting the gumbo every few minutes and making appropriate adjustments. No matter if the result is a well-polished sample in a materials laboratory, or a well-seasoned bowl of soup in the French Quarter, what makes the result “good” is not necessarily easy to define. We can calibrate our equipment and take great care with our materials. We can scrutinize the results, and take measurements until the cows come home, but in many instances, this is only a starting point; learning to perform a recipe “well” can be like a mini-education. Writing that down stepwise can be like trying to capture everything you learned at cooking school.

It is in this setting, where there are many variables to keep track of, many unknowns, and even the results may be hard to characterize, that we step into the realm of “art.” A successful outcome depends as much on what you bring to the table as what is written on the page. A recipe becomes like a roadmap for threading your way through a complex maze of decision points. Here is where I get passionate about my subject. Practicing a recipe, in a sense, can be viewed as the purest form of empirical science. And this can take place in a laboratory or in a kitchen. If science is the study of the way the world actually behaves, then going through a series of steps and paying close attention to what is happening, is as good as it gets. It is not a matter of imposing ones will on the world, but of interacting with nature and moving toward a result given the constraints of reality; there is a give and take. A scientific experiment can be viewed as the act of developing a new recipe toward a specific result. Writing that recipe down is an exercise in determining the important variables to pay attention to and capturing a method in a way that is repeatable by others.

As computer algorithms move into the realms of artificial intelligence, driverless cars and the like, they will start to encounter the same difficulties as our baker does on a humid day. Perhaps a true test of machine intelligence will be how well an algorithm negotiates real-world recipes.

[1] Christie, Thony 2017. Whewell’s Ghost blog, “Editorial, Whewell’s Gazette: Year 03, Vol. #41” 31 May 2017.
[2] Op. Cit.

8 Comments

Filed under History of science, History of Technology

On an excursion

If you wish to read the latest words of wisdom, this time on the conception and invention of the reflecting telescope, then you will have to take an excursion to AEON magazine, where you can peruse:

How many great minds does it take to invent a telescope?

Isaac Newton’s reflecting telescope of 1671. Photo ©The Royal Society, London

2 Comments

Filed under History of Astronomy, History of Optics, History of Technology, Newton

The problem with Jonathan Jones and #histSTM

It cannot be said that I am a fan of Jonathan Jones The Guardian’s wanna be art critic but although I find most of his attempts at art criticism questionable at best, as a historian of science I am normal content to simply ignore him. However when he strays into the area of #histSTM I occasionally feel the desire to give him a good kicking if only a metaphorical one. In recent times he has twice committed the sin of publicly displaying his ignorance of #histSTM thereby provoking this post. In both cases Leonard da Vinci plays a central role in his transgressions, so I feel the need to make a general comment first. Many people are fascinated by Leonardo and some of them feel the need to express that fascination in public. These can be roughly divided into two categories, the first are experts who have seriously studied Leonardo and whose utterances are based on knowledge and informed analysis, examples of this first group are Matin Kemp the art historian and Monica Azzolini the Renaissance historian. The second category could be grouped together under the title Leonardo groupies and their utterances are mostly distinguished by lack of knowledge and often mind boggling stupidity. Jonathan Jones is definitely a Leonardo groupie.

Jones’ first foray into the world of #histSTM on 28 January with a piece entitled, The charisma droids: today’s robots and the artists who foresaw them, which is a review of the new major robot exhibition at the Science Museum. What he has to say about the exhibition doesn’t really interest me here but in the middle of his article we stumble across the following paragraph:

So it is oddly inevitable that one of the first recorded inventors of robots was Leonardo da Vinci, consummate artist and pioneering engineer [my emphasis]. Leonardo apparently made, or at least designed, a robot knight to amuse the court of Milan. It worked with pulleys and was capable of simple movements. Documents of this invention are frustratingly sparse, but there is a reliable eyewitness account of another of Leonardo’s automata. In 1515 he delighted Francois I, king of France, with a robot lion that walked forward towards the monarch, then released a bunch of lilies, the royal flower, from a panel that opened in its back.

Now I have no doubts that amongst his many other accomplishments Leonardo turned his amazingly fertile thoughts to the subject of automata, after all he, like his fellow Renaissance engineers, was a fan of Hero of Alexandria who wrote extensively about automata and also constructed them. Here we have the crux of the problem. Leonardo was not “one of the first recorded inventors of robots”. In fact by the time Leonardo came on the scene automata as a topic of discussion, speculation, legend and myth had already enjoyed a couple of thousand years of history. If Jones had taken the trouble to read Ellie Truitt’s (@MedievalRobots) excellent Medieval Robots: Mechanism, Magic, Nature and Art (University of Pennsylvania Press, 2015) he would have known just how wrong his claim was. However Jones is one of those who wish to perpetuate the myth that Leonardo is the source of everything. Actually one doesn’t even need to read Ms. Truitt’s wonderful tome, you can listen to her sketching the early history of automata on the first episode of Adam Rutherford’s documentary The Rise of the Robots on BBC Radio 4, also inspired by the Science Museums exhibition. The whole series is well worth a listen.

On 6 February Jones took his Leonardo fantasies to new heights in a piece, entitled Did the Mona Lisa have syphilis? Yes, seriously that is the title of his article. Retro-diagnosis in historical studies is a best a dodgy business and should, I think, be avoided. We have whole libraries of literature diagnosing Joan of Arc’s voices, Van Gough’s mental disorders and the causes of death of numerous historical figures. There are whole lists of figures from the history of science, including such notables as Newton and Einstein, who are considered by some, usually self declared, experts to have suffered from Asperger’s syndrome. All of these theories are at best half way founded speculations and all too oft wild ones. So why does Jonathan Jones think that the Mona Lisa had syphilis? He reveals his evidence already in the sub-title to his piece:

Lisa del Giocondo, the model for Leonardo’s painting, was recorded buying snail water – then considered a cur for the STD: It could be the secret to a painting haunted by the spectre of death.

That’s it folks don’t buy any snail water or Jonathan Jones will think that you have syphilis.

Let’s look at the detail of Jones’ amazingly revelatory discovery:

Yet, as it happens, a handful of documents have survived that give glimpses of Del Giocondo’s life. For instance, she is recorded in the ledger of a Florentine convent as buying snail water (acqua di chiocciole) from its apothecary.

Snail water? I remember finding it comical when I first read this. Beyond that, I accepted a bland suggestion that it was used as a cosmetic or for indigestion. In fact, this is nonsense. The main use of snail water in pre-modern medicine was, I have recently discovered, to combat sexually transmitted diseases, including syphilis.

So she bought some snail water from an apothecary, she was the female head of the household and there is absolutely no evidence that she acquired the snail water for herself. This is something that Jones admits but then casually brushes aside. Can’t let ugly doubts get in the way of such a wonderful theory. More importantly is the claim that “the main use of snail water snail water in pre-modern medicine was […] to combat sexually transmitted diseases, including syphilis” actually correct? Those in the know disagree. I reproduce for your entertainment the following exchange concerning the subject from Twitter.

Greg Jenner (@greg_jenner)

Hello, you may have read that the Mona Lisa had syphilis. This thread points out that is probably bollocks

 Dubious theory – the key evidence is her buying “snail water”, but this was used as a remedy for rashes, earaches, wounds, bad eyes, etc…

Greg Jenner added,

Seen this ‪@DrAlun ‪@DrJaninaRamirez ? What say you? I’ve seen snail water used in so many different Early Modern remedies

Alun Withey (@DrAlun)

I think it’s an ENORMOUS leap to that conclusion. Most commonly I’ve seen it for eye complaints.

Greg Jenner

‪@DrAlun @DrJaninaRamirez yeah, as I thought – and syphilis expert @monaob1 agrees

 Alun Withey

‪@greg_jenner @DrJaninaRamirez @monaob1 So, the burning question then, did the real Mona Lisa have sore eyes? It’s a game-changer!

Mona O’Brian (@monaob1)

‪@DrAlun @greg_jenner @DrJaninaRamirez interested to hear the art historical interpretation on the ‘unhealthy’ eyes comment!

Alun Withey

‪@monaob1 @greg_jenner @DrJaninaRamirez doesn’t JJ say in the article there’s a shadow around her eyes? Mystery solved. *mic drop*

Greg Jenner

‪@DrAlun @monaob1 @DrJaninaRamirez speaking as a man who recently had to buy eye moisturiser, eyes get tired with age? No disease needed

 Mona O’Brian

@greg_jenner Agreed! Also against the pinning of the disease on the New World, considering debates about the disease’s origin are ongoing

Jen Roberts (@jshermanroberts)

‪@greg_jenner I just wrote a blog post about snail water for @historecipes –common household cure for phlegmy complaints like consumption.

Tim Kimber (@Tim_Kimber)

‪@greg_jenner Doesn’t the definite article imply the painting, rather than the person? So they’re saying the painting had syphilis… right?

Minister for Moths (@GrahamMoonieD)

‪@greg_jenner but useless against enigmatic smiles

Interestingly around the same time an advert was doing the rounds on the Internet concerning the use of snail slime as a skin beauty treatment. You can read Jen Roberts highly informative blog post on the history of snail water on The Recipes Project, which includes a closing paragraph on modern snail facials!

 

 

7 Comments

Filed under History of medicine, History of Technology, Renaissance Science, Uncategorized

Why Mathematicus?

“The Renaissance Mathematiwot?”

“Mathematicus, it’s the Latin root of the word mathematician.”

“Then why can’t you just write The Renaissance Mathematician instead of showing off and confusing people?”

“Because a mathematicus is not the same as a mathematician.”

“But you just said…”

“Words evolve over time and change their meanings, what we now understand as the occupational profile of a mathematician has some things in common with the occupational profile of a Renaissance mathematicus but an awful lot more that isn’t. I will attempt to explain.”

The word mathematician actually has its origins in the Greek word mathema, which literally meant ‘that which is learnt’, and came to mean knowledge in general or more specifically scientific knowledge or mathematical knowledge. In the Hellenistic period, when Latin became the lingua franca, so to speak, the knowledge most associated with the word mathematica was astrological knowledge. In fact the terms for the professors[1] of such knowledge, mathematicus and astrologus, were synonymous. This led to the famous historical error that St. Augustine rejected mathematics, whereas his notorious attack on the mathematici[2] was launched not against mathematicians, as we understand the term, but against astrologers.

The earliest known portrait of Saint Augustine in a 6th-century fresco, Lateran, Rome Source: Wikimedia Commons

The earliest known portrait of Saint Augustine in a 6th-century fresco, Lateran, Rome
Source: Wikimedia Commons

However St. Augustine lived in North Africa in the fourth century CE and we are concerned with the European Renaissance, which, for the purposes of this post we will define as being from roughly 1400 to 1650 CE.

The Renaissance was a period of strong revival for Greek astrology and the two hundred and fifty years that I have bracketed have been called the golden age of astrology and the principle occupation of our mathematicus is still very much the casting and interpretation of horoscopes. Mathematics had played a very minor role at the medieval universities but the Renaissance humanist universities of Northern Italy and Krakow in Poland introduced dedicated chairs for mathematics in the early fifteenth century, which were in fact chairs for astrology, whose occupants were expected to teach astrology to the medical students for their astro-medicine or as it was known iatro-mathematics. All Renaissance professors of mathematics down to and including Galileo were expected to and did teach astrology.

A Renaissance Horoscope Kepler's Horoskop für Wallenstein Source: Wikimedia Commons

A Renaissance Horoscope
Kepler’s Horoskop für Wallenstein
Source: Wikimedia Commons

Of course, to teach astrology they also had to practice and teach astronomy, which in turn required the basics of mathematics – arithmetic, geometry and trigonometry – which is what our mathematicus has in common with the modern mathematician. Throughout this period the terms Astrologus, astronomus and mathematicus – astrologer, astronomer and mathematician ­– were synonymous.

A Renaissance mathematicus was not just required to be an astronomer but to quantify and describe the entire cosmos making him a cosmographer i.e. a geographer and cartographer as well as astronomer. A Renaissance geographer/cartographer also covered much that we would now consider to be history, rather than geography.

The Renaissance mathematicus was also in general expected to produce the tools of his trade meaning conceiving, designing and manufacturing or having manufactured the mathematical instruments needed for astronomer, surveying and cartography. Many were not just cartographers but also globe makers.

Many Renaissance mathematici earned their living outside of the universities. Most of these worked at courts both secular and clerical. Here once again their primary function was usually court astrologer but they were expected to fulfil any functions considered to fall within the scope of the mathematical science much of which we would see as assignments for architects and/or engineers rather than mathematicians. Like their university colleagues they were also instrument makers a principle function being horologist, i.e. clock maker, which mostly meant the design and construction of sundials.

If we pull all of this together our Renaissance mathematicus is an astrologer, astronomer, mathematician, geographer, cartographer, surveyor, architect, engineer, instrument designer and maker, and globe maker. This long list of functions with its strong emphasis on practical applications of knowledge means that it is common historical practice to refer to Renaissance mathematici as mathematical practitioners rather than mathematicians.

This very wide range of functions fulfilled by a Renaissance mathematicus leads to a common historiographical problem in the history of Renaissance mathematics, which I will explain with reference to one of my favourite Renaissance mathematici, Johannes Schöner.

Joan Schonerus Mathematicus Source: Wikimedia Commons

Joan Schonerus Mathematicus
Source: Wikimedia Commons

Schöner who was a school professor of mathematics for twenty years was an astrologer, astronomer, geographer, cartographer, instrument maker, globe maker, textbook author, and mathematical editor and like many other mathematici such as Peter Apian, Gemma Frisius, Oronce Fine and Gerard Mercator, he regarded all of his activities as different aspects or facets of one single discipline, mathematica. From the modern standpoint almost all of activities represent a separate discipline each of which has its own discipline historians, this means that our historical picture of Schöner is a very fragmented one.

Because he produced no original mathematics historians of mathematics tend to ignore him and although they should really be looking at how the discipline evolved in this period, many just spring over it. Historians of astronomy treat him as a minor figure, whilst ignoring his astrology although it was this that played the major role in his relationship to Rheticus and thus to the publication of Copernicus’ De revolutionibus. For historians of astrology, Schöner is a major figure in Renaissance astrology although a major study of his role and influence in the discipline still has to be written. Historians of geography tend to leave him to the historians of cartography, these whilst using the maps on his globes for their studies ignore his role in the history of globe making whilst doing so. For the historians of globe making, and yes it really is a separate discipline, Schöner is a central and highly significant figure as the founder of the long tradition of printed globe pairs but they don’t tend to look outside of their own discipline to see how his globe making fits together with his other activities. I’m still looking for a serious study of his activities as an instrument maker. There is also, as far as I know no real comprehensive study of his role as textbook author and editor, areas that tend to be the neglected stepchildren of the histories of science and technology. What is glaringly missing is a historiographical approach that treats the work of Schöner or of the Renaissance mathematici as an integrated coherent whole.

Western hemisphere of the Schöner globe from 1520. Source: Wikimedia Commons

Western hemisphere of the Schöner globe from 1520.
Source: Wikimedia Commons

The world of this blog is at its core the world of the Renaissance mathematici and thus we are the Renaissance Mathematicus and not the Renaissance Mathematician.

[1] That is professor in its original meaning donated somebody who claims to possessing a particular area of knowledge.

[2] Augustinus De Genesi ad Litteram,

Quapropter bono christiano, sive mathematici, sive quilibet impie divinantium, maxime dicentes vera, cavendi sunt, ne consortio daemoniorum animam deceptam, pacto quodam societatis irretiant. II, xvii, 37

5 Comments

Filed under History of Astrology, History of Astronomy, History of Cartography, History of Mathematics, History of science, History of Technology, Renaissance Science

Christmas Trilogy 2016 Part 2: What a difference an engine makes

Charles Babbage is credited with having devised the first ever special-purpose mechanical computer as well as the first ever general-purpose mechanical computer. The first claim seems rather dubious in an age where there is general agreement that the Antikythera mechanism is some sort of analogue computer. However, Babbage did indeed conceive and design the Difference Engine, a special purpose mechanical computer, in the first half of the nineteenth century. But what is a Difference Engine and why “Difference”?

Both Babbage and John Herschel were deeply interested in mathematical tables – trigonometrical tables, logarithmic tables – when they were still students and Babbage started collecting as many different editions of such tables as he could find. His main object was to check them for mistakes. Such mathematical tables were essential for navigation and errors in the figures could lead to serious navigation error for the users. Today if I want to know the natural logarithm of a number, let’s take 23.483 for example, I just tip it into my pocket calculator, which cost me all of €18, and I instantly get an answer to nine decimal places, 3.156276755. In Babbage’s day one would have to look the answer up in a table each value of which had been arduously calculated by hand. The risk that those calculations contained errors was very high indeed.

Babbage reasoned that it should be possible to devise a machine that could carryout those arduous calculations free of error and if it included a printer, to print out the calculated answer avoiding printing errors as well. The result of this stream of thought was his Difference Engine but why Difference?

The London Science Museum's reconstruction of Difference Engine No. 2 Source: Wikimedia Commons

The London Science Museum’s reconstruction of Difference Engine No. 2
Source: Wikimedia Commons

Babbage needed to keep his machine as simple as possible, which meant that the simplest solution would be a machine that could calculate all the necessary tables with variations on one algorithm, where an algorithm is just a step-by-step recipe to solve a mathematical problem. However, he needed to calculate logarithms, sines, cosines and tangents, did such an algorithm exist. Yes it did and it had been discovered by Isaac Newton and known as the method of finite differences.

The method of finite differences describes a property shared by all polynomials. If it has been a while since you did any mathematics, polynomials are mathematical expressions of the type x2+5x-3 or 7x5-3x3+2x2-3x+6 or x2-2 etc, etc. If you tabulate the values of a given polynomial for x=0, x=1, x=2, x=3 and so on then subtract the first value from the second, the second from the third and so on you get a new column of numbers. Repeating the process with this column produces yet another column and so on. At some point in the process you end up with a column that is filled with a numerical constant. Confused? OK look at the table below!

 

x x3-3x2+6 xn+1-xn diff(1)n+1 –diff(1)n diff(2)n+1 – diff(2)n
0 6 -2 0 6
1 4 -2 6 6
2 2 4 12 6
3 6 16 18
4 22 34
5 56
6

 

As you can see this particular polynomial bottoms out, so to speak, with as constant of 6. If we now go back into the right hand column and enter a new 6 in the first free line then add this to its immediate left hand neighbour repeating this process across the table we arrive at the polynomial column with the next value for the polynomial. See below:

 

x x3-3x2+6 xn+1-xn diff(1)n+1 –diff(1)n diff(2)n+1 – diff(2)n
0 6 -2 0 6
1 4 -2 6 6
2 2 4 12 6
3 6 16 18 6
4 22 34
5 56
6

 

x x3-3x2+6 xn+1-xn diff(1)n+1 –diff(1)n diff(2)n+1 – diff(2)n
0 6 -2 0 6
1 4 -2 6 6
2 2 4 12 6
3 6 16 18 6
4 22 34 24
5 56
6

 

x x3-3x2+6 xn+1-xn diff(1)n+1 –diff(1)n diff(2)n+1 – diff(2)n
0 6 -2 0 6
1 4 -2 6 6
2 2 4 12 6
3 6 16 18 6
4 22 34 24
5 56 58
6

 

x x3-3x2+6 xn+1-xn diff(1)n+1 –diff(1)n diff(2)n+1 – diff(2)n
0 6 -2 0 6
1 4 -2 6 6
2 2 4 12 6
3 6 16 18 6
4 22 34 24
5 56 58
6 114

This means that if we set up our table and calculate enough values to determine the difference constant then we can by a process of simple addition calculate all further values of the polynomial. This is exactly what Babbage designed his difference engine to do.

If you’ve been paying attention you might notice that the method of finite differences applies to polynomials and Babbage wished to calculate were logarithmic and trigonometrical functions. This is however not a serious problem, through the use of other bits of higher mathematics, which we don’t need to go into here, it is possible to represent both logarithmic and trigonometrical functions as polynomials. There are some problems involved with using the method of finite differences with these polynomials but these are surmountable and Babbage was a good enough mathematician to cope with these difficulties.

Babbage now had a concept and a plan to realise it, all he now needed was the finances to put his plan into action. This was not a problem. Great Britain was a world power with a large empire and the British Government was more than ready to cough up the readies for a scheme to provide reliable mathematical tables for navigation for the Royal Navy and Merchant Marine that serviced, controlled and defended that empire. In total over a period of about ten years the Government provided Babbage with about £17, 000, literally a fortune in the early nineteen hundreds. What did they get for their money, in the end nothing!

Why didn’t Babbage deliver the Difference Engine? There is a widespread myth that Babbage’s computer couldn’t be built with the technology available in the first half of the nineteenth century. This is simply not true, as I said a myth. Several modules of the Difference Engine were built and functioned perfectly. Babbage himself had one, which he would demonstrate at his scientific soirées, amongst other things to demonstrate his theory of miracles.

The Difference Engine model used by Babbage for his demonstrations of his miracle theory Source: Wikimedia Commons

The Difference Engine model used by Babbage for his demonstrations of his miracle theory
Source: Wikimedia Commons

Other Difference Engines modules were exhibited and demonstrated at the Great Exhibition in Crystal Palace. So why didn’t Babbage finish building the Difference Engine and deliver it up to the British Government? Babbage was not an easy man, argumentative and prone to bitter disputes. He became embroiled in one such dispute with Joseph Clement, the engineer who was actually building the Difference Engine, about ownership of and rights to the tools developed to construct the engine and various already constructed elements. Joseph Clement won the dispute and decamped together with said tools and elements. By now Babbage was consumed with a passion for his new computing vision, the general purpose Analytical Engine. He now abandoned the Difference Engine and tried to convince the government to instead finance the, in his opinion, far superior Analytical Engine. Having sunk a fortune into the Difference Engine and receiving nothing in return, the government, not surprisingly, demurred. The much hyped Ada Lovelace Memoire on the Analytical Engine was just one of Babbage’s attempts to advertise his scheme and attract financing.

However, the story of the Difference Engine didn’t end there. Using knowledge that he had won through his work on the Analytical Engine, Babbage produced plans for an improved, simplified Difference Engine 2 at the beginning of the 1850s.

Per Georg Schutz Source: Wikimedia Commons

Per Georg Schutz
Source: Wikimedia Commons

The Swedish engineer Per Georg Scheutz, who had already been designing and building mechanical calculators, began to manufacture difference engines based on Babbage’s plans for the Difference Engine 2 in 1855. He even sold one to the British Government.

Scheutz Difference Engine No. 2. (1859) Maschine im Science Museum, London Source: Wikimedia Commons

Scheutz Difference Engine No. 2. (1859) Maschine im Science Museum, London
Source: Wikimedia Commons

5 Comments

Filed under History of Computing, History of Mathematics, History of Technology, Myths of Science

Werner von Siemens and Erlangen

I (almost)[1] live in the town of Erlangen in Franconia, in Southern Germany. Erlangen is a university town with an official population of about 110 000. I say official because Erlangen has a fairly large number of inhabitants, mostly student, who are registered as living elsewhere with Erlangen as their second place of residence, who are not included in the official population numbers. I suspect that the population actually lies somewhere between 120 and 130 000. Erlangen is dominated by the university, which currently has 40 000 students, although several departments are in the neighbouring towns of Furth and Nürnberg, and is thus the second largest university in Bavaria, and the company Siemens. Siemens, one of Germany’s largest industrial firms, is a worldwide concern and Erlangen is after Berlin and Munich the third largest Siemens centre in Germany, home to large parts of the company’s research and development. It is the home of Siemens’ medical technology branch, Siemens being a world leader in this field. 13 December is the two hundredth anniversary of the birth of Werner von Siemens the founder of the company.

Werner von Siemens (Portrait by Giacomo Brogi) Source: Wikimedia Commons

Werner von Siemens (Portrait by Giacomo Brogi)
Source: Wikimedia Commons

Werner Siemens (the von came later in his life) was born in Lenthe near Hanover the fourth child of fourteenth children of the farmer Christian Ferdinand Siemens and his wife Eleonore Henriette Deichmann on13 December 1894. The family was not wealthy and Werner was forced to end his education early. In 1835 he joined the artillery corps of Prussian Army in order to get an education in science and engineering; he graduated as a lieutenant in 1838.

Werner Siemens as Second-Lieutenant in the Prussian Artillery, 1842 Source: Wikimedia Commons

Werner Siemens as Second-Lieutenant in the Prussian Artillery, 1842
Source: Wikimedia Commons

He was sentenced to five years in military prison for acting as a second in a duel but was pardoned in 1842 and took up his military service. Whilst still in the army he developed an improved version of Wheatstone’s and Cooke’s electrical telegraph in 1846 and persuaded the Prussian Army to give his system field trials in 1847. Having proved the effectiveness of his system Siemens patented it and in the same year founded together with the fine mechanic Johann Georg Halske the Telegraphen-Bauanstalt von Siemens & Halske. They received a commission to construct Prussia’s first electrical telegraph line from Berlin to Frankfurt, which was completed in 1849, when Werner left the army to become an electrical engineer and entrepreneur. The profession of electrical engineer didn’t exist yet and Werner Siemens is regarded as one of its founders.

Pointer telegraph, 1847 (replica) Source: Siemens

Pointer telegraph, 1847 (replica)
Source: Siemens

Already a successful electrical telegraph construction company the next major step came when Werner discovered the principle of dynamo self-excitation in 1867, which enabled the construction of the worlds first practical electric generators. Werner was not alone in making this discovery. The Hungarian Anyos Jedlik discovered it already in 1856 but didn’t patent it and his discovery remained unknown and unexploited. The Englishman Samuel Alfred Avery patented a self-exciting dynamo in 1866, one year ahead of both Siemens and Charles Wheatstone who also independently made the same discovery.

Structure (with cross section) of the dynamo machine 1866 Source: Siemens

Structure (with cross section) of the dynamo machine 1866
Source: Siemens

Throughout his life Werner Siemens combined the best attributes of a scientists, an engineer, an inventor and an entrepreneur constantly pushing the range of his companies products. He developed the use of gutta-percha as material for cable insolation, Siemens laying the first German transatlantic telegraph cable with their own specially constructed cable laying ship The Faraday in 1874. The world’s first electric railway followed in 1879, the world’s first electric tram in 1881 and the world’s first trolleybus in 1882.

The Faraday, cable laying ship of Siemens Brothers & Co. 1874 Source: Wikimedia Commons

The Faraday, cable laying ship of Siemens Brothers & Co. 1874
Source: Wikimedia Commons

Werner Siemens was a great believer in scientific research and donated 500,000 Marks (a fortune), in land and cash, in 1884 towards the establishment of the Physikalisch-Technische Reichsanstalt a state scientific research institute, which finally came into being in 1887 and lives on today under the name Physikalisch-Technische Bundesanstalt (PTB). From the very beginning Werner Siemens thought in international terms sending his brother Wilhelm off to London in 1852 to represent the company and another brother Carl to St Petersburg in 1853, where Siemens built Russia’s first telegraph network. In 1867 Halske left the company and Carl and Wilhelm became partners making Siemens a family company. In 1888, four years before his death, Werner was ennobled becoming Werner von Siemens.

The research and development department of Siemens moved to Erlangen after the Second World War, as their home in Berlin became an island surrounded by the Russian occupation zone. Erlangen was probably chosen because it was already the home of Siemens’ medical technology section. In order to understand how this came to be in Erlangen we need to go back to the nineteenth century and the live story of Erwin Moritz Reiniger.

Siemens-Administration in the 1950s „Himbeerpalast“ Designed by  Hans Hertlein  Note the Zodiac clock dial Source: Wikimedia Commons

Siemens-Administration in the 1950s „Himbeerpalast“ Designed by Hans Hertlein
Note the Zodiac clock dial
Source: Wikimedia Commons

Reiniger born 5 April 154 in Stuttgart was employed as an experiment demonstrator at the University of Erlangen in 1876. He was also responsible for the repair of technical equipment in the university institutes and clinics. Realising that this work could become highly profitable, Reiniger set up as a self-employed fine mechanic in Schlossplatz 3 next door to the university administration in the Schloss (palace) in 1877, producing fine mechanical, physical, optical and simple electro-medical instruments.

Schloss Erlangen (university Administration) Source: Wikimedia Commons

Schloss Erlangen
(University Administration)
Source: Wikimedia Commons

Schlossplatz 3. Site of Reindeer's original workshop Source: Wikimedia Commons

Schlossplatz 3. Site of Reiniger’s original workshop
Source: Wikimedia Commons

Plaque on Schlossplatz 3

Plaque on Schlossplatz 3

By 1885 Reiniger was employing fifteen workers. In 1886 he went into partnership with the mechanics Max Gebbert and Karl Friedrich Schall forming the Vereinigte physikalisch-mechanische Werkstätten von Reiniger, Gebbert & Schall– Erlangen, New York, Stuttgart (RGS). The workshops in New York and Stuttgart were soon abandoned and the company concentrated on Erlangen. Karl Schall left the company in 1888 and Reiniger was bought out by Gebbert in 1895.

Reiniger Gebiert & Schall Letterhead 1896 Source: Wikimedia Commons

Reiniger Gebiert & Schall Letterhead 1896
Source: Wikimedia Commons

Wilhelm Conrad Röntgen discovered X-rays on 8 November 1895 and published his discovery in three scientific papers between then and January 1896.

Wilhelm Conrad Röntgen Source: Wikimedia Commons

Wilhelm Conrad Röntgen
Source: Wikimedia Commons

Famously he didn’t patent his discovery and RGS were already, as the very first company in the world, producing X-ray tubes and X-ray machines in 1896 and this would become the mainstay of their business. There is a rather sweet letter in the Siemens archive from Röntgen, who was professor in Würzburg, not too far away from Erlangen, asking if he could possibly get a rebate if he purchased his X-ray tubes from RGS.

Reiniger, Gebbert & Schall AG Factory in Erlangen constructed in 1883. Now a protected building. Source: Wikimedia Commons

Reiniger, Gebbert & Schall AG Factory in Erlangen constructed in 1883. Now a protected building.
Source: Wikimedia Commons

Following the First World War, RGS got into financially difficulties due to bad management and in 1925 the company was bought by Siemens & Halske, who transferred their own medical technology production to Erlangen thus establishing the medical technology division of Siemens in Erlangen where it still is today. Originally called the Siemens-Reiniger-Werke AG it has gone through more name changes than I care to remember currently being called ‘Healthineers’ to the amusement of the local population, who on the whole find the name ridiculous.

siemens-med-museum-erlangen-germany-620x410

Siemens Medical Museum in the Reiniger, Gebbert & Schall AG Factory Building “Source:  ©Travel Addicts(link) – 2014.  Used with permission.”

What of the future? Last week saw the laying of the foundation stone of the new Siemens Campus in Erlangen a 500 million Euro building project to provide Siemens with a new R&D centre for the twenty-first century.

Siemens Campus Architects Model

Siemens Campus Architects Model

 

 

[1] I actually live in a small village on the outskirts of Erlangen but the town boundary is about 150 metres, as the crow flies, from where I am sitting typing this post.

7 Comments

Filed under History of Physics, History of science, History of Technology