Someone is Wrong on the Internet.

Many of the readers of this blog will probably recognise the title of this post, as the punch line to one of the best ever xkcd cartoons. Regular readers will also know that the Renaissance Mathematicus cannot resist stamping on people who post inanely inaccurate or downright wrong history of science claims, comments etc. on the Internet. This last pre-Christmas post brings two examples of such foolishness that crossed our path in recent times.

The first concerns a problem that turns up time and again, not only on the Internet but also in many books. It is the inability of lots of people to comprehend that there cannot be a year nil, year zero or whatever they choose to call it. (Have patience dear reader the reason will be explained soon). Even worse are the reasons that such people, in their ignorance, dream up to explain the absence of the, in their opinion, missing numberless year. I stumbled across a particularly juicy example on the BBC’s History Extra website last Thursday, in a post entitled, 10 of the most surprising numbers in history. Actually the whole post really deserves a good kicking but for now I will content myself with the authors surprising number, AD 0…  the date that never was. The entry is very short so I’ve included the whole of it below:

The AD years of the Christian calendar are counted from the year of Jesus Christ’s birth, and, as the number zero was then unknown to the west, Dionysius began his new Christian era as AD 1, not AD 0. [my emphasis]

While it is now the consensus that Jesus was probably born between 7 and 3 BC, Dionysius’s new calendar is now the most widely used in the world, while AD 0 is one of the most interesting numbers never to have seen the light of day.

The first time I read this sparking pearl of historical wisdom I experienced one of those extremely painful ‘head-desk’ moments; recovering from my shock and managing at least a semblance of a laugh at this stunning piece of inanity I decided to give it the Histsci Hulk treatment.

Before I explain why there cannot be a year zero, let us look briefly at why Dionysius Exiguus, or Dennis the Short, started his count of the years with AD 1. Dennis, he of little stature, was not trying to create the calendar we use today in everyday lives but was making his contribution to the history of computos, the art of calculating the date of Easter. Due to the fact that the date of Easter is based on the Jewish Pesach (that’s Passover) feast, which in turn is based on a lunar calendar and also the fact that the lunar month and the solar year are incommensurable (you cannot measure the one with the other), these calculations are anything but easy. In fact they caused the Catholic Church much heartbreak and despair over the centuries from its beginnings right down to the Gregorian calendar reform in 1582. In the early centuries of Christianity the various solution usually involved producing a table of the dates of the occurrence of Easter over a predetermined cycle of years that then theoretically repeats from the beginning without too much inaccuracy. Dennis the vertically challenged produced just such a table.

In the time of our little Dennis there wasn’t a calendar with a continuous count of years. It was common practice to number the years according to the reign of the current monarch, emperor, despot or whatever. So for example the year that we know as 47 BCE would have been the third year of the reign of Gaius Julius Caesar. For formal purposes this dating system actually survived for a very long time. I recently came across a reference to a court case at the English Kings Bench Court in the eighteenth century as taking place on 12 July ‘4Geo.III’, that is the fourth year of the reign of George III. In Dennis the Small’s time the old Easter table, he hoped to replace, was dated according to the years of the reign of the Emperor Diocletian (245-311, reigned 284-305). Diocletian had distinguished himself by being particularly nasty to the Christians so our dwarf like hero decided to base his cycle on the 525 532 years “since the incarnation of our Lord Jesus Christ”; quite how he arrived at 525 532 years is not really known. AD short (being short, Dennis liked short things) for Anno Domini Nostri Iesu Christi (“In the Year of Our Lord Jesus Christ”). It was only later, starting with the Venerable Bede’s History of the Church (Historia Ecclesiastica) that Dennis’ innovation began to be used for general dating or calendrical purposes. The idea of BC years or dates only came into use in Early Modern period.

We now turn to the apparently thorny problem as to why there cannot be a year zero in a calendrical dating system. People’s wish or desire to find the missing year zero is based on a confusion in their minds between cardinal and ordinal numbers. (In what follows the terms cardinal and ordinal are used in their common linguistic sense and not the more formal sense of mathematical set theory). Cardinal numbers, one, two, three … and so on are used to count the number of objects in a collection. If, for example, your collection is the cookie jar there can be zero or nil cookies if the jar is, sadly, empty. Ordinal numbers list the positions of objects in an ordered collection, first, second, third … and so on. It requires only a modicum of thought to realise that there cannot be a zeroeth object, if it doesn’t exist it doesn’t have a position in the collection.

This distinction between cardinal and ordinal numbers becomes confused when we talk about historical years. We refer to the year five hundred CE when in fact we should be saying the five hundredth year CE, as it is an ordinal and not a cardinal. Remember our little friend Dennis’ AD, Anno Domini Nostri Iesu Christi (“In the Year of Our Lord Jesus Christ”)! We are enumerating the members of an ordered set not counting the number of objects in a collection. Because this is the case there cannot be a zeroeth year. End of discussion!

That this error, and particularly the harebrained explanation for the supposedly missing year zero, should occur on any history website is bad enough but that it occurs on a BBC website, an organisation that used to be world renowned for its informational reliability is unforgivable. I say used to be because I don’t think it’s true any longer. I would be interested in who is responsible for the history content of the BBC’s web presence as it varies between sloppy as here and totally crap as witnessed here and discussed here and here.

My second example is just as bad in terms of its source coming as it does from the Windows to the Universe website Brought to you by the National Earth Science Teachers Association. You would think that such an educational body would take the trouble to make sure that the historical information that they provide and disseminate is accurate and correct. If you thought that, you would be wrong, as is amply demonstrated by their post on Hellenistic astronomer, Ptolemy.

Ptolemy was a Greek astronomer who lived between 85-165 A.D. He put together his own ideas with those of Aristotle and Hipparchus and formed the geocentric theory. This theory states that the Earth was at the center of the universe and all other heavenly bodies circled it, a model which held for 1400 years until the time of Copernicus.

Ptolemy is also famous for his work in geography. He was the first person to use longitude and latitude lines to identify places on the face of the Earth.

We don’t actually know when Ptolemaeus (Ptolemy) lived, the usual way used to present his life is ‘fl. 150 CE’, where fl. means flourished. If you give dates for birth and death they should given as circa or c. To write them as above, 85–165 A.D. implies we know his exact dates of birth and death, we don’t! This is a trivial, but for historians, important point.

More important is the factual error in the second sentence: He … formed the geocentric theory. The geocentric theory had existed in Greek astronomy and cosmology for at least seven hundred years before Ptolemaeus wrote his Syntaxis Mathematiké (the Almagest). Ptolemaeus produced the most sophisticated mathematical model of the geocentric theory in antiquity but he didn’t form it. Those seven hundred years are not inconsequential (go back seven hundred years from now and you’ll be in 1314!) but represent seven hundred years of developments in cosmology and mathematical astronomy.

The last sentence contains an even worse error for teachers of the earth sciences. Ptolemaeus did indeed write a very important and highly influential geography book, his Geographike Hyphegesis. However he was not “the first person to use longitude and latitude lines”. We cannot be one hundred per cent who did in fact first use longitude and latitude lines but this innovation in cartography is usually attributed to a much earlier Alexandrian geographer, Eratosthenes, who lived about three hundred and fifty years before Ptolemaeus.

This is an example of truly terrible history of science brought to you by an organisation that says this about itself, “The National Earth Science Teachers Association is a nonprofit 501(c)(3) educational organization, founded in 1985, whose mission is to facilitate and advance excellence in Earth and Space Science education” [my emphasis]. I don’t know about you but my definition of excellence is somewhat other.

 

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Filed under History of Astronomy, History of Cartography, History of science, Myths of Science

A very similar luminous lustre appears when one observes a burning candle from a great distance through a translucent piece of horn.

On 15 December 1612 (os) Simon Marius, Court Mathematicus in Ansbach, became the first astronomer to record a telescopic observation of the Andromeda Nebula. The importance of this observation was that whereas other known nebulae such as the Orion Nebula, had resolved into individual stars when viewed with a telescope, the Andromeda Nebula as recorded by Marius appears as “…a weak and faint lustre at the centre with a diameter of about one quarter of a degree. A very similar luminous lustre appears when one observes a burning candle from a great distance through a translucent piece of horn” (Simon Marius, Mudus Iovialis, 1614 my translation).

In the history of astronomy the Andromeda Nebula would go on to play a central role in the deep space observations of Charles Messier (M31) and William Herschel in the eighteenth century. In the early twentieth century its nature and status then became the bone of contention in the legendary dispute between Shapley and Curtis.

2014 being the four hundredth anniversary of the publication of Marius’ major astronomical work the Mundus Iovialis we have been celebrating his live and work in Middle Franconia. First high point of the various activities were the launching of the Marius Portal, an Internet website giving researchers free access to all primary and secondary works by and about Simon Marius with navigation in almost thirty different languages.

On 20 September a one-day conference was held with contributions covering the various aspects of Marius’ life and academic work (mathematics, astrology and astronomy) in Nürnberg. The proceedings of this conference are due to appear in book, form hopefully in 2015.

This coming Wednesday, 17 December 2014, will see the founding of the Simon Marius Gesellschaft (Simon Marius Society) in Nürnberg to further research and promote his life and work. Anybody who is interested is herewith cordially invited to apply for full or corresponding membership. There are no membership fees!

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Filed under History of Astronomy, History of science, Local Heroes, Renaissance Science

Retelling a story – this time with all the facts

Before 1995 probably only a handful of people interested in the history of navigation had ever heard of the English clockmaker John Harrison and the role he played in the history of attempts to find a reliable method of determining longitude at sea. This situation changed radically when Dava Sobel published her book Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time[1] in that year. This volume caught the public imagination and very rapidly became one of the most successful popular history of science and technology books of all time. It was followed just three years later by a lavishly illustrated expanded edition. Just one year after that followed the equally lavish television documentary film based on the book. By the year 2000 at the latest John Harrison had become a household name and a British scientific hero on a level with Newton and Darwin.

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,

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,

All of this would have been well and good if Sobel had actually adhered to the first three words of her subtitle, The True Story…, but unfortunately she sacrificed historical accuracy to the expediency of telling a good story, basically reducing a complex historical narrative to the fairy tale of a poor honest hero, John Harrison, overcoming adversity to finally triumph against the evil machination of his dishonest scheming opponent the Astronomer Royal, Nevil Maskelyne. Sobel’s lurid narrative proved, as already stated, commercially very successful but left its readers with a highly distorted view of what actually took place in the long eighteenth century in the endeavours to find a method of determining longitude and the role that the various people involved played in those endeavours. In particular Nevil Maskelyne was left in the popular public imagination looking rather like the devil’s evil cousin.

 

Rev. Dr Nevil Maskelyne Source Wikimedia

Rev. Dr Nevil Maskelyne
Source Wikimedia

About five years ago a major historical research project, under the auspices of the Arts & Humanities Research Council, was set up by Cambridge University and the National Maritime Museum in Greenwich on the history of the British Board of Longitude, the official body set up to oversee and direct the search for a method to determine longitude at sea in the eighteenth century. Led by Simon Schaffer for the University of Cambridge and Richard Dunn and Rebekah Higgitt for the National Maritime Museum this project featured a cast of excellent doctoral and post doctoral researchers some of whose findings can be found on the excellent Longitude Project Blog. To date this research project has produced a remarkable list of achievements. Alongside a volume of papers on the much maligned Nevil Maskelyne, which has just appeared and which I am looking forward very much to reading,

4114.1.450.450.FFFFFF.0

the whole of the Board of Longitude archive has been digitized and made available online to researchers. Currently on at the Museum in Greenwich is a major exhibition Ships, Clocks and Stars: The Quest for Longitude, which you can still visit if you hurry, it closes on the 4th of January 2015. If you are uncertain whether or not it’s worth visiting, it has just been awarded the British Society for the History of Science Great Exhibitions Award for 2014! If like myself you are unable for some reason to make the journey to Greenwich do not despair you can bring the exhibition into your own living room by acquiring the accompanying book Finding Longitude: How Ships, clocks and stars helped solve the longitude problem[2] by Richard Dunn and Rebekah Higgitt, a review of which is the actually subject of this post.

Finding Longitude001

My review is actually very simple this book is magnificent. If you have any interest in the histories of navigation, sea voyages, astronomy, clocks, John Harrison, Nevil Maskelyne, Tobias Mayer, and a whole ship’s cargo of other related and interrelated topics then buy this book! I guarantee you that you won’t regret it for one second. It combines thorough research, first class scholarship, excellent writing, unbelievably lavish illustrations, fascinating narratives and historical accuracy in one superb and, for what it is, surprisingly low priced large format volume. Unlike Sobel’s, from a historians standpoint, ill-starred volume, this work really does tell the true story of the solution of the longitude problem with all its complex twists and turns giving all the participants their dues. Although written for the general reader this book should also find a home on the bookshelves of any working historian of navigation, astronomy, horology, sea voyages or just the science and technology of the long eighteenth century.

This book will take you on a voyage through the choppy waters of eighteenth century science, politics and technology and deliver you up on the shores of the nineteenth century much more knowledgeable then you were when you boarded ship and entertain and delight you along the way. It will also make for a first class Christmas present.

[1] Dava Sobel, Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time, Fourth Estate, London, 1995

[2] Richard Dunn & Rebekah Higgitt, Longitude: How Ships, clocks and stars helped solve the longitude problem, Collins and Royal Museums Greenwich, London 2014

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Filed under Book Reviews, History of Cartography, History of Navigation, History of science

The weather and the stars

My attention was recently drawn to the MacTutor history of maths website article on The History of Weather Forecasting. The article is largely concerned with the mathematics of weather forecasting from the nineteenth century onwards but has some short introductory paragraphs covering the prehistory of meteorology, which unfortunately displays a woeful ignorance of the subject. Under the heading Early Attempts we get served up the following:

It is not known when people first started to observe the skies, but at around 650 BC, the Babylonians produced the first short-range weather forecasts, based on their observations of the stars and clouds. The Chinese also recognised weather patterns, and by 300 BC astronomers had developed a calendar which divided the year into 24 festivals, each associated with a different weather phenomenon. Generally, weather was attributed to the vagaries of the gods, as the wide range of weather gods in various cultures, for example the Egyptian sun god Ra and Thor, the Norse god of thunder and lightning, proves. Many ancient civilisations developed rites such as rain dances and animal sacrifices in order to propitiate the weather gods.

The ancient Greeks were the first to develop a more scientific approach to explaining the weather. The work of the philosopher and scientist Aristotle (384-322 BC) is especially noteworthy, as it dominated people’s views on and their knowledge of the weather for the next 2000 years. In 340 BC, Aristotle wrote his book Meteorologica, where he tried to explain the formation of rain, clouds, wind and storms. In addition, he also described celestial phenomena such as comets and haloes. Many of his observations were — in retrospect — surprisingly accurate. For example, he believed that heat could cause water to evaporate. But he also jumped to quite a few wrong conclusions, such as that winds form “as the Earth exhales“, which were rectified from the Renaissance onwards.

Throughout the Middle Ages and beyond, the Church was the only official institution that was allowed to explain the causes of weather, and Aristotle’s Meteorologica was established as Christian dogma. Besides, weather observations were passed on in the form of rhymes, which are now known as weather lore. Many of these proverbs are based on very good observations and are accurate, as contemporary meteorologists have discovered.

This brief synopsis, which covers approximately one thousand years actually almost completely ignores the main form of weather forecasting practiced throughout the period covered astrometeorology. As any astute reader will have already deduce astrometeorology is a branch of astrology and is in fact astrological weather forecasting. This is one of the more rational forms of astrology; weather comes from the heavens, be it sunshine, fog, wind, or one of the many forms of precipitation (rain, snow, sleet, hail), so it would seem fairly logical to assume that the heaven cause or control the weather. This is exactly what people in antiquity did in many different cultures and actually what the article above is referring to in both of the first two quoted sentences although the author doesn’t seem to or doesn’t want to know it. It was not Aristotle’s views as expressed in the Meteorologica that “dominated people’s views on and knowledge of the weather for the next 2000 years” but astrometeorology. There is a slight irony here as a quote from Aristotle’s Meteorologica delivered one of main justifications for astrology in Western thought up to the Early Modern period. Astrometeorology is along with astro-medicine one of the branches of natural astrology and as such was even accepted throughout the Middle Ages and the Renaissance by people who rejected other forms of astrology, for example judicial or horoscope astrology.

This very widespread acceptance meant that it was astrometeorology that was the dominant form of weather forecasting in the Middle Ages accepted even by the Church at a time when judicial astrology was, at least official, heavily frowned upon. One might well say, so what? What does it matter what people believed before the emergence of scientific meteorology in the seventeenth century, when this superstitious twaddle got drop anyway? The answer is quit simple; astrometeorology played a significant role in the emergence of that scientific meteorology.

During the Renaissance astrology reached its highest level of popularity in the history of Western culture. Almost all mathematicians and astronomers (mostly one and the same) were also practicing astrologers and they were not just doing it for the money as is often falsely claimed by those who try to deny the significance of astrology in the Early Modern period; they really believed in it. However these were the people who also laid the foundations of the modern empirical approach to the sciences and they were often painfully aware of the lack of empirical justification for the science of astrology that they practiced. To counter this weakness they set about developing various projects to give astrology a solid empirical base, one of the principle projects involving astrometeorology. This project consisted of keeping accurate and continuous weather diaries. They thought that by recording the weather over long periods of time on a daily basis they could then distinguish the correlation, that they were sure existed, between the weather and the movement of the celestial bodies. The oldest known such weather diary was kept by Roger Bacon in the thirteenth century. Bacon was of course not only a fervent believer in astrology but also an early proponent of empirical methods in science. There are other scattered medieval weather diaries but the process first really kicked off at the end of the fifteenth century. The keeping of weather diaries was greatly furthered by the introduction of printed ephemerides, which provided the potential meteorologist with a convenient place to record his observations directly next to the astronomical/astrological information for the day.

A notable writer of weather diaries was Johannes Stöfler (1452-1531), who taught and influenced Philipp Melanchthon (a powerful advocate of Renaissance astrology), Sebastian Münster and others. Another was the Nürnberger mathematicus Johannes Werner (1462-1522), who first suggested the chronometer method of determining longitude. Probably most well-known as weather diary keeper was Tycho Brahe (1546-1601), without doubt the important observational astronomer in the pre-telescope era. Tycho is possibly also responsible for David Fabricius (1564-1617), discoverer, amongst other things, of the first variable star, Mira, keeping a weather diary. Fabricius help Johannes Kepler (1571-1630) to formulate his theory of elliptical planetary orbits in an extended correspondence; systematically criticising Kepler various formulations. Kepler a passionate astrologer also kept a weather diary. He famously established his reputation as an astrologer by correctly predicting an especially hard winter in his first prognostications as district mathematicus in Graz in 1594. Weather diaries were also kept by many other less well-known figures. It is significant that Pico della Mirandola (1463-1494) the most strident Renaissance critic of astrology also kept a weather diary and used the results as one of his arguments for rejecting astrology.

Pico della Mirandola was of course right the systematic keeping of weather diaries did not, as hoped, provide an empirical basis for the science of astrology but did exactly the opposite showing that astrometeorology, at least, was a refuted theory. However the results were not all negative. The systematic empirical weather observations contained in the diaries laid the foundations for scientific meteorology in the seventeenth century. The data collected by those Renaissance astrologers is still used by modern meteorologists to help establish long-term weather patterns.

 

 

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Filed under History of Astrology, History of science, Renaissance Science

Mega inanity

Since the lead up to the Turing centennial in 2012 celebrating the birth of one of the great meta-mathematicians of the twentieth century, Alan Mathison Turing, I have observed with increasing horror the escalating hagiographic accounts of Turing’s undoubted historical achievements and the resulting perversion of the histories of twentieth-century science, mathematics and technology and in particular the history of computing.

This abhorrence on my part is not based on a mere nodding acquaintance with Turing’s name but on a deep and long-time engagement with the man and his work. I served my apprenticeship as a historian of science over many years in a research project on the history of formal or mathematical logic. Formal logic is one of the so-called formal sciences the others being mathematics and informatics (or computer science). I have spent my whole life studying the history of mathematics with a special interest in the history of computing both in its abstract form and in its technological realisation in all sorts of calculating aids and machines. I also devoted a substantial part of my formal study of philosophy to the study of the philosophy of mathematics and the logical, meta-logical and meta-mathematical problems that this discipline, some would say unfortunately, generates. The history of all of these intellectual streams flow together in the first half of the twentieth century in the work of such people as Leopold Löwenheim, Thoralf Skolem, Emil Post, Alfred Tarski, Kurt Gödel, Alonso Church and Alan Turing amongst others. These people created a new discipline known as meta-mathematics whilst carrying out a programme delineated by David Hilbert.

Attempts to provide a solid foundation for mathematics using set theory and logic had run into serious problems with paradoxes. Hilbert thought the solution lay in developing each mathematical discipline as a strict axiomatic systems and then proving that each axiomatic system possessed a set of required characteristics thus ensuring the solidity and reliability of a given system. This concept of proving theories for complete axiomatic systems is the meta- of meta-mathematics. The properties that Hilbert required for his axiomatic systems were consistency, which means the systems should be shown to be free of contradictions, completeness, meaning that all of the theorems that belong to a particular discipline are deductible from its axiom system, and finally decidability, meaning that for any well-formed statement within the system it should be possible to produced an algorithmic process to decide if the statement is true within the axiomatic system or not. An algorithm is like a cookery recipe if you follow the steps correctly you will produce the right result.

The meta-mathematicians listed above showed by very ingenious methods that none of Hilbert’s aims could be fulfilled bringing the dream of a secure foundation for mathematics crashing to the ground. Turing’s solution to the problem of decidability is an ingenious thought experiment, for which he is justifiably regarded as one of the meta-mathematical gods of the twentieth century. It was this work that led to him being employed as a code breaker at Bletchley Park during WW II and eventually to the fame and disaster of the rest of his too short life.

Unfortunately the attempts to restore Turing’s reputation since the centenary of his birth in 2012 has led to some terrible misrepresentations of his work and its consequences. I thought we had reach a low point in the ebb and flow of the centenary celebrations but the release of “The Imitation Game”, the Alan Turing biopic, has produced a new series of false and inaccurate statements in the reviews. I was pleasantly pleased to see several reviews, which attempt to correct some of the worst historical errors in the film. You can read a collection of reviews of the film in the most recent edition of the weekly histories of science, technology and medicine links list Whewell’s Gazette. Not having seen the film yet I can’t comment but I was stunned when I read the following paragraph from the abc NEWS review of the film written by Alyssa Newcomb. It’s so bad you can only file it under; you can’t make this shit up.

The “Turing Machine” was the first modern computer to logically process information, running on interchangeable software and essentially laying the groundwork for every computing device we have today — from laptops to smartphones.

Before I analyse this train wreck of a historical statement I would just like to emphasise that this is not the Little Piddlington School Gazette, whose enthusiastic but slightly slapdash twelve-year-old film critic got his facts a little mixed up, but a review that appeared on the website of a major American media company and as such totally unacceptable however you view it.

The first compound statement contains a double whammy of mega-inane falsehood and I had real problems deciding where to begin and finally plumped for the “first modern computer to logically process information, running on interchangeable software”. Alan Turing had nothing to do with the first such machine, the honour going to Konrad Zuse’s Z3, which Zuse completed in 1941. The first such machine in whose design and construction Alan Turing was involved was the ACE produced at the National Physical Laboratory, in London, in 1949. In the intervening years Atanasoff and Berry, Tommy Flowers, Howard Aikin, as well as Eckert and Mauchly had all designed and constructed computers of various types and abilities. To credit Turing with the sole responsibility for our digital computer age is not only historically inaccurate but also highly insulting to all the others who made substantial and important contributions to the evolution of the computer. Many, many more than I’ve named here.

We now turn to the second error contained in this wonderfully inane opening statement and return to the subject of meta-mathematics. The “Turing Machine” is not a computer at all its Alan Turing’s truly genial thought experiment solution to Hilbert’s decidability problem. Turing imagined a very simple machine that consists of a scanning-reading head and an infinite tape that runs under the scanning head. The head can read instructions on the tape and execute them, moving the tape right or left or doing nothing. The question then reduces to the question, which set of instructions on the tape come eventually to a stop (decidable) and which lead to an infinite loop (undecidable). Turing developed this idea to a machine capable of computing any computable function (a universal Turing Machine) and thus created a theoretical model for all computers. This is of course a long way from a practical, real mechanical realisation i.e. a computer but it does provide a theoretical measure with which to describe the capabilities of a mechanical computing device. A computer that is the equivalent of a Universal Turing Machine is called Turing complete. For example, Zuse’s Z3 was Turing complete whereas Colossus, the computer designed and constructed by Tommy Flowers for decoding work at Bletchley Park, was not.

Turing’s work played and continues to play an important role in the theory of computation but historically had very little effect on the development of real computers. Attributing the digital computer age to Turing and his work is not just historically wrong but is as I already stated above highly insulting to all of those who really did bring about that age. Turing is a fascinating, brilliant, and because of what happened to him because of the persecution of homosexuals, tragic figure in the histories of mathematics, logic and computing in the twentieth century but attributing achievements to him that he didn’t make does not honour his memory, which certainly should be honoured, but ridicules it.

I should in fairness to the author of the film review, that I took as motivation from this post, say that she seems to be channelling misinformation from the film distributors as I’ve read very similar stupid claims in other previews and reviews of the film.

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

The Renaissance Road Show – November 2014

If you happen to be in Nürnberg tomorrow evening (Wed 12 Nov) I shall be babbling on about Christoph Clavius in the Nicolaus Copernicus Planetarium (in German) at 7:00pm MET. This is an updated version of the lecture I held five years ago in Bamberg, a summary of which forms the first substantive post on this blog. You are welcome to come along and throw peanuts or whatever and if you’re nice to me I’ll even let you buy me a coffee.

For those who miss the blogging activity around here, you can rest assured that normal posting will resume next week, the Norns willing. For those waiting patiently or maybe not so patiently for reviews of their books, and there are a couple, all review obligations will be fulfilled before the end of the year. (But which year? – Just kidding).

 

 

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Financing Tycho’s little piece of heaven

On Chris Graney’s recent guest post I linked to an earlier guest post that he had written about the Danish Renaissance astronomer Tycho Brahe and one of the new readers, that this link attracted, posted a question that I seem to have answered a lot of times in my life so I thought that this time, I would turn the answer in to a new post.

Source Wikicommons

Source Wikicommons

In his guest post Chris Graney wrote, “…Brahe ran a major observatory (“Uraniborg”) and research program on his island of Hven.  The cost of Brahe’s program to the Danish crown was proportionately comparable to the budget of NASA.” This is probably somewhat hyperbolic but it is certainly true that Tycho had financial resources for his observatory that would make any wannabe astronomer jealous. It is these financial resources that prompted the question that I’m going to answer here. Commentator Daniel N. asked:

Once again an excellent post… I have known most of this, however, I got surprised to learn that the Kingdom of Denmark was giving NASA-sized budget to Brahe. What was the reason? NASA started as a combined military/race-against-communist pursuit, in an age of science…

Given that Tycho’s scientific island paradise was indeed financed by the Danish Crown this is a very valid and historically interesting question.

Map of Hven by Blaeu

Map of Hven by Blaeu

 

Surprisingly, in the first place the simple answer is enthusiasm, Tycho’s all consuming desire to obtain an accurate set of astronomical data on which to base cosmological speculations. This might seem a little bizarre, as you are being expected to believe that the Danish Crown coughed up a small fortune in the last quarter of the sixteenth-century to fulfil the private offbeat desire of one of their aristocrats, but this is exactly what happened, but it was the fact that Tycho was one of their aristocrats that led to this situation. Before going on to explain this let us take a brief look at what exactly it was that Tycho got from his liege lord.

 

Uraniborg in garden

Uraniborg in garden

The Danish Crown granted Tycho the island of Hven, which lies between Denmark and Sweden, as his fief and supplied him with the money to build both a large manor house, Uraniborg, incorporating the most sophisticated astronomical observatory in the world at the time as well as a Paracelsian chemiatry laboratory, alongside extensive living quarters.

Uraniborg main building

Uraniborg main building

In the grounds he constructed a second sunken observatory, Stjerneborg, equipped with the most advanced observing instruments of his own design.

Stjerneborg

Stjerneborg

 

Stjerneborg subterranean observatory ground plan

Stjerneborg subterranean observatory ground plan

Tycho lived in and managed this, at the time unique, research institution with his family and a large staff of technical assistants and servants as well as a tame elk and a dwarf as court jester. The whole operation financed by a generous yearly appanage from the Danish Crown. Why should the Danish Crown finance all of this? The seemingly paradox answer is that if Tycho had not become the Danish court astronomer/astrologer he would have cost the Crown considerably more in lands and money than he did, how come?

In the sixteenth-century Denmark was basically a feudal warrior society ruled by an oligarchy of about twenty families that was still in the process of transitioning into a modern state. Tycho’s parents Otte Brahe and Beate Bille were both prominent and highly influential members of that oligarchy. When he was two years old Tycho was kidnapped by his uncle Jørgen Brahe (it’s a complicated story) and was brought up by him and his wife Inger Oxe. Jørgen Brahe was an admiral in the Danish navy and Inger Oxe was head of the Queen’s court. Inger’s brother Peder Oxe was finance minister and Lord Steward of Denmark and as such the most influential man in the realm. Tycho didn’t have to climb the greasy pole; he grew up at the top of it and was destined for great things from his birth.

It might have been considered odd for Tycho the scion of warriors to become a scholar, both his father and his uncle Jørgen would definitely not have approved, but both were dead before Tycho came of age. However Peder Oxe was a humanist scholar who had studied at the leading European universities and had helped the King Frederick III to set up a humanist university in Copenhagen. For various reasons (astrology, cartography, navigation etc.) astronomy was regarded as an important discipline and Peder Oxe brought his influence to bear, supporting Tycho in his desire to become an astronomer. Tycho was also supported by Wilhelm IV of Hessen-Kassel (who had already set up his own observatory in Kassel), a cousin of Frederick’s, who also recommended giving Tycho the wherewithal to set up an observatory in Denmark. Accepting the advice of Tycho’s prominent supporters Frederick did just that and Uraniborg came into being.

However had Tycho completed his university studies of law and become a Danish politician, as was originally planned by his family, then given his connections and his position in Danish society his fief and the incomes granted to him by the crown would have been considerably larger than those he received for his observatory on the island of Hven. By granting Tycho’s wishes and financing what was probably Europe’s first modern research institute, despite the elk and the dwarf, Frederick almost certainly saved crown income.

 

The map of Hven and the pictures of Tycho’s buildings are all taken from Wikicommons  and are all originally from Joan Blaeu’s Atlas Maior. Joan’s father Wilhelm Janson Blaeu had worked as an assistant for Tycho on Hven.

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