Category Archives: Myths of Science

Well no, actually he didn’t.

Ethan Siegel has written a reply to my AEON Galileo opinion piece on his Forbes blog. Ethan makes his opinion very clear in the title of his post, Galileo Didn’t Invent Astronomy, But He DID Invent Mechanical Physics! My response is also contained in my title above and no, Galileo did not invent mechanical physics. For a change we’ll start with something positive about Galileo, his inclined plane experiments to determine the laws of fall, the description of which form the bulk of Ethan’s post, are in fact one of the truly great pieces of experimental physics and are what makes Galileo justifiably famous. However the rest of Ethan’s post leaves much to be desired.

Ethan starts off by describing the legendary Leaning Tower of Pisa experiment, in which Galileo supposedly dropped two ball of unequal weight of the tower and measured how long they took to fall. The major problem with this is that Galileo almost certainly never did carry out this experiment, however both John Philoponus in the sixth century CE and Simon Stevin in 1586 did so, well before Galileo considered the subject. The laws of fall were also investigated theoretically by the so-called Oxford Calculatores, who developed the mean speed theory, the foundation of the laws of fall, and the Paris Physicists, who represented the results graphically, both in the fourteenth century CE. Galileo knew of the work of John Philoponus, the Oxford Calculatores and the Paris Physicists, even using the same graph to represent the laws of fall in his Two New Sciences, as Oresme had used four hundred years earlier. In the sixteenth centuries the Italian mathematician Tartaglia investigated the path of projectiles, publishing the results in his Nova Scientia, his work was partially validated, partially refuted by Galileo. His landsman Benedetti anticipated most of Galileo’s results on the laws of fall. With the exception of Stevin’s work Galileo knew of all this work and built his own researches on it thus rather challenging Ethan’s claim that Galileo invented mechanical physics.

Galileo’s central achievement was to provide empirical proof of the laws of fall with his ingenious ramp experiments but even here there are problems. Galileo’s results are simply too good, not displaying the expected experimental deviations, leading Alexander Koyré, the first great historian of Galileo’s work, to conclude that Galileo never did the experiments at all. The modern consensus is that he did indeed do the experiments but probably massaged his results, a common practice. The second problem is that any set of empirical results requires confirmation by other independent researchers. Mersenne, a great supporter and propagator of Galileo’s physics, complains of the difficulties of reproducing Galileo’s experimental results and it was first Riccioli, who finally succeeded in doing so, publishing the results in 1651.

A small complaint is Ethan’s claim that Galileo’s work on the laws of fall “was the culmination of a lifetime of work”. In fact although Galileo first published his Two New Sciences in 1638 his work on mechanics was carried out early in his life and completed well before he made his telescopic discoveries.

The real problem with Ethan’s post is what follows the quote above, he writes:

…and the equations of motion derived from Newton’s laws are essentially a reformulation of the results of Galileo. Newton indeed stood on the shoulders of giants when he developed the laws of gravitation and mechanics, but the biggest titan of all in the field before him was Galileo, completely independent of what he contributed to astronomy.

This is quite simply wrong. After stating his first two laws of motion in the Principia Newton writes:

The principles I have set forth are accepted by mathematicians and confirmed by experiments of many kinds. By means of the first two laws and the first two corollaries Galileo found that the decent of heavy bodies is the squared ratio of the time that the motion of projectiles occurs in a parabola, as experiment confirms, except insofar as these motion are somewhat retarded by the resistance of the air.

As Bernard Cohen points out, in the introduction to his translation of the Principia from which I have taken the quote, this is wrong because, Galileo certainly did not know Newton’s first law. As to the second law, Galileo would not have known the part about change in momentum in the Newtonian sense, since this concept depends on the concept of mass which was invented by Newton and first made public in the Principia.

I hear Galileo’s fans protesting that Newton’s first law is the law of inertia, which was discovered by Galileo, so he did know it. However Galileo’s version of the law of inertia is flawed, as he believes natural unforced motion to be circular and not linear. In fact Newton takes his first law from Descartes who in turn took it from Isaac Beeckman. Newton’s Principia, or at least his investigation leading up to it, are in fact heavily indebted to the work of Descartes rather than that of Galileo and Descartes in turn owes his greatest debts in physics to the works of Beeckman and Stevin and not Galileo.

An interesting consequence of Newton’s false attribution to Galileo in the quote above is that it shows that Newton had almost certainly never read Galileo’s masterpiece and only knew of it through hearsay. Galileo’s laws of fall are only minimally present in the Principia and then only mentioned in passing as asides, whereas the parabola law occurs quite frequently whenever Newton is resolving forces in orbits but then only as Galileo has shown.

One small irony remains in Ethan’s post. He loves to plaster his efforts with lots of pictures and diagrams and videos. This post does the same and includes a standard physics textbook diagram showing the force vectors of a heavy body sliding down an inclined plane. You can search Galileo’s work in vain for a similar diagram but you will find an almost identical one in the work of Simon Stevin, who worked on physical mechanics independently of and earlier than Galileo. Galileo made some very important contributions to the development of mechanical physics but he certainly didn’t invent the discipline.

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Filed under History of Mathematics, History of Physics, Myths of Science, Newton

A bit on the side

Galileo by Justus Sustermans/Wikipedia

Galileo by Justus Sustermans/Wikipedia

For those of my readers who don’t follow me on Twitter or Facebook I have indulged in my favourite pastime, slagging of Galileo Galilei, but this time in an opinion piece in the online science journal AEON. If you’ve already read my old Galileo post Extracting the stopper, this is just a shorter punchier version of the same. If not or if you want to read the updated sexy version then mosey on over to AEON and read Galileo’s reputation is more hyperbole than truth.

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It’s the wrong telescope.

I know I announced a blogging hiatus yesterday, but I have some time evenings and I simply couldn’t ignore this.

Caroline Herschel Source: Wikimedia Commons

Caroline Herschel
Source: Wikimedia Commons

 

Today is Caroline Herschel’s birthday and Google have celebrated it with a doodle, which is cool and an overdue acknowledgement of a great lady astronomer. If you don’t already know who Caroline Herschel is then you should read the two Guardian articles by Stuart Clark and Becky Higgitt. Google’s doodle is all well and good but I have a complaint, it’s the wrong telescope.

The Google doodle for Caroline Herschel’s 266th birthday. Photograph: google

The Google doodle for Caroline Herschel’s 266th birthday. Photograph: google

If you look at the picture Caroline is standing behind a mounted telescope and in the animated version of the doodle she bends down to look through the telescope as a comet flies passed overhead. This is to acknowledge the fact that she is most well known for the eight comets that she discovered. So what’s my problem? The telescope displayed in the doodle is a refractor that is a telescope with lenses at the front, the objective, and at the back, the eyepiece or ocular. The problem is that the Herschels, that is Caroline and her brother William, used reflectors; that is telescopes that have a mirror and not a lens as objective and then a lens or lenses as the eyepiece to observe the image created by the mirror. To be precise they used Newtonian reflectors that they built themselves. That they used Newtonians was rather unusual at the time because most other professional, or serious amateur like the Herschels, astronomers used Gregorian reflector telescopes, which are of a different design. The Gregorian is actually superior but the Newton is simpler to construct and this is almost certainly the reason that William stuck with Newtonians.

Replica of a Herschel Newtonian Refractor. Herschel Museum Bath Source: Wikimedia Commons

Replica of a Herschel Newtonian Reflector. Herschel Museum Bath
Source: Wikimedia Commons

Added: 17 March 2016

If you go to the article Caroline Lucretia Herschel – comet huntress (h/t Tony Angel)on the second page you can see sketches of the comet-sweeper Newtonian reflectors that William built for Caroline, which are not quite as elegant or impressive as the telescope pictured above but which served their purpose admirably.

The fact that the doodle shows a refractor and not a reflector is, viewed historically, not a trivial matter. In the eighteenth century the reflectors were capable of resolving much weaker light sources than the contemporary refractors and were thus superior for the type of deep space celestial mapping that William Herschel pioneered and which he taught to his younger sister. To show Caroline using a refractor and not a Herschel Newtonian reflector is a complete historical misrepresentation and totally misleading.

Now Google might argue that your average Google doodle viewer would probably not recognise a Herschel Newtonian reflector as a telescope and therefore they put a simple refractor in the picture as a generic telescope that people would recognise as such. All well and good but I can best explain my aversion by a simple analogy.

Lewis Hamilton is the current world Formula One racing champion. I want you to imagine the following. Next season Hamilton wins his fourth world championship and Google celebrate the occasion with one of their doodles, unlikely but you never know. So we get a cartoon of the well know figure of Lewis Hamilton in a Formula One racing car but he is not driving a Mercedes, the team for which he drives and has won two of his three titles up till now, but a Ferrari because that is the generic racing car that most people see in their minds eye when they think of racing cars. The Lewis Hamilton fans would probably launch a crusade against the Google head quarters in Mountain View and hang the offending doodler from a lamppost.

As far as I’m concerned in the history of science details matter a lot and the fact that the Herschels used Newtonian reflectors is not a triviality but an important factor in the astronomical achievements for which they are justifiably renowned. It should also be pointed out that this renown led to William becoming one of the commercially most successful telescope constructors in the eighteenth century because other astronomers wanted to own one of those telescopes, which had made the discoveries of William and Caroline possible.

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We’re British not European – Really?

Yesterday evening my #histsci soul sister Becky Higgitt tweeted the following:

Scientists for Britain on #bbcnews – we had Newton therefore we don’t want to be in Europe

As #histsci bloggers both Becky and I have been here before, Becky here on her H-Word blog at the Guardian and myself here on the Renaissance Mathematicus but as it’s something that can’t be said too often, I thought I would point out once again that science is collaborative and international and all attempts to claim it for some sort of lone genius, as is often the case with Newton, or to make nationalist claims on its behalf are a massive distortion of the history of science.

Becky’s tweet specifically mentions Britain’s science icon ‘numero uno’ Isaac Newton, so let’s take a look at his scientific achievements and the foundations on which they were built. As Newton, paraphrasing Bernard of Chartres, famously wrote in a letter to Robert Hooke: If I have seen further, it is by standing on the shoulders of giants. So who were these giants on whose shoulders Newton was perched? What follows is a bit shopping list I’m afraid and is by no means exhaustive, listing only the better known names of the predecessors in each area of study where Newton made a contribution.

Newton’s mathematics built on the work in algebra of Cardano and Bombelli, both Italians, and Stifel, a German, from the sixteenth century. Their work was built on the efforts of quite a large number of Islamic mathematicians who in turn owed a debt to the Indians and Babylonians. Moving on into the seventeenth century we have Viète, Fermat, Pascal and Descartes, all of them Frenchmen, as well as Oughtred, Wallis and Barrow representing the English and James Gregory the Scots. Italy is represented by Cavalieri. The Dutch are represented by Huygens and Van Schooten, whose expanded Latin edition of Descartes Géométrie was Newton’s chief source on the continental mathematics.

We see a similar pattern in Newton’s optics where the earliest influence is the 10/11th century Islamic scholar Ibn al-Haytham, although largely filtered through the work of others. In the seventeenth century we have Kepler and Schiener, both Germans, Descartes, the Frenchman, and Huygens, the Dutchman, pop up again along with Grimaldi, an Italian, Gassendi, another Frenchman, and James Gregory a Scot and last but by no means least Robert Hooke.

In astronomy we kick off in the fifteenth century with Peuerbach and Regiomontanus, an Austrian and a German, followed in the sixteenth century by Copernicus, another German. All three of course owed a large debt to numerous earlier Islamic astronomers. Building on Copernicus we have Tycho, a Dane, Kepler, a German, and of course Galileo, a Tuscan. France is once again represented by Descartes along with Ismael Boulliau. Also very significant are Cassini, an Italian turned Frenchman, and once again the ubiquitous Huygens. At last we can throw in a gaggle of Englishmen with Horrocks, Wren, Flamsteed, Halley and Hooke.

In physics we have the usual suspects with Kepler and Galileo to which we can add the two Dutchmen Stevin and Beeckman. Descartes and Pascal are back for the French and Borelli joins Galileo in representing Italy. Huygens once again plays a central role and one should not forget Hooke’s contributions on gravity.

As I said at the beginning these lists are by no means exhaustive but I think that they demonstrate very clearly that Newton’s achievements were very much a pan-European affair and thus cannot in anyway be used as an argument for an English or British science existing without massive European cooperation.

If we look at Newton’s scientific inheritance then things look rather bad for the British in the eighteenth century with the developments being made by a whole battalion of French, Swiss, German, Dutch and Italian researchers with not a Brit in sight anywhere. Things improved somewhat in the nineteenth century but even here the progress is truly international. If we take just one small example the dethroning of Newton’s corpuscular theory of light by the wave theory. Originated by Huygens and Hooke in the seventeenth century it was championed by Ampère, Fresnel, Poisson and Arago all of whom were French and by Young and Airy for the British in the nineteenth century.

I hope that yet again, with this brief example, I have made clear that science is a collaborative and cooperative enterprise that doesn’t acknowledge or respect national boundaries but wanders through the cultures where and when it pleases, changing nationalities and languages at will. Science is a universal human activity to which many different and varied cultures have made contributions and will continue to do so in the future. Science should have absolutely nothing to do with nationalism and chauvinism and politicians who try and harness it to their nationalist causes by corrupting its history are despicable.

 

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Founders of science?

World-renowned wheelchair driver and astrophysicist, Stephen Hawking, recently held the first of this year’s BBC Reith Lectures. This prompted the following tweet from Roger Highfield, science writer and director of external affairs at the Science Museum Group:

If Hawking could time travel, he would like to meet Galileo – ‘founder of modern science’ and ‘a bit of a rebel’ #Reith

Philip Ball, science writer, responded:

Though certainly not, as Hawking claimed, “the first to challenge Aristotle”…

To which I added:

Also not the founder of modern science.

Tom Levenson, another science writer, contributed:

Probably kicked his dog and stiffed his waiter too.

Roger Highfield reacted to this exchange thus:

Ha!

This moderately amusing, or not depending on you point of view, exchange on Twitter prompted Ángel Lamuño, Philosophy & Theology Follower of Bernard J. F. Lonergan SJ (self description), to pose the following question to me:

Who is (are) the founder(s) of modern science?

This whole rather trivial exchange contains several worrying aspects for historians of science, starting with Hawking’s original utterance. This is by no means the first time that Hawking has made such statements in public and in fact I quote one such in my take down of the founder of modern science and similar claims about Galileo – Extracting the stopper – that I wrote more than five years ago and which I’m not going to repeat here. The real problem is here that whatever Hawking’s merits as an astro-physicist he is not a historian of science and this is reflected in the naivety of his history of science comments that are almost invariably false. The problem is that Hawking because of his physical disability has become the most famous scientist in the world instantly recognised and admired whenever he appears in public. Whenever he makes a comment about the history of science then the majority of his audience, who don’t know better, immediately believe him because it’s ‘Stephen Hawking’! People believe Hawking because of who he is and not because his facts are correct, they aren’t. The irony of this situation is that what we have here is knowledge by authority, exactly the non-scientific epistemology that the scholastics supposedly practiced and which Galileo is said to have swept away, making him in Hawking’s words ‘the founder of modern science’.

Equally worrying is Ángel Lamuño’s question, [if Galileo isn’t the founder of modern science] “who is (are) the founder(s) of modern science?” This question is, in my opinion, based on a widespread misconception as to how science has evolved (developed, if you don’t like the word evolved). The misconception is supported in a vast number of texts, many of them written by highly respected historians of science but I think, in the meantime, rejected by a substantial part of the history of science community.

This misconception, or rather set of misconceptions, is that somehow major changes in the history of science are caused by one driving force in mainstream scientific thought and/or brought about by one heroic individual.

The traditional story that I grew up with was that the scientific revolution came about because science became quantified or mathematized when Neo-Platonism replaced Aristotelian scholasticism as the dominant philosophy in Europe. This is, however, not the Neo-Platonism of Plotinus of the third century CE but a Pythagorean Neo-Platonism. This theory was mainly propagated by philosophers. Mathematic historians however challenged this theory accepting that the scientific revolution was a mathematization of science but that this was brought about by an Archimedean renaissance beginning in the fourteenth century. Others have noted that the period also saw both a Euclidean and a Ptolemaic renaissance leading to increases in mathematical activity.

A different popular version of the story is that the scientific revolution was driven by the astronomical revolution brought about singlehandedly by Copernicus publishing his De revolutionibus in 1543. This is somewhat undermined by two facts. Firstly Copernicus’ work is only part of a general reform of astronomy carried out by a fairly large number of astronomers beginning with the first Viennese School of Mathematics in the fifteenth century. Secondly the so-called scientific revolution consists of far more than just astronomy.

There are theories that the astronomical revolution was driven by the renaissance in mathematical cartography sparked by the rediscovery of Ptolemaeus’ Geographia in 1406, alternatively by an attempt to put astrology on a solid empirical footing. At least one Arabic author has argued, with more than a little justification, that the astronomical revolution owes much more to the preceding Islamic astronomy than is usual credited. Another group of historians see the roots of the astronomical revolution in a shift in basic philosophy but not in a Neo-Platonic renaissance but in a Stoic one in the fifteenth and sixteenth centuries.

Another theory sees the scientific revolution being the rise in empirical experimental science, which has its roots in alchemy. An alternative explanation for this rise lies in the development of modern gunpowder based warfare and empirical studies of gunnery. Some see the rise of modern warfare as the driving force behind mathematical cartography, itself the driving force behind astronomical reform.

The above are some, but by no means all, of the theories that have been put forward to explain the emergence of modern science in the early modern period. So which one is the correct one? The answer is, all of them! The emergence of modern science was not caused by one single thing but by a whole range of activities, discoveries, renaissances as well as economic and socio-political developments. As historians we have a strong tendency to oversimplify, to want to find the ‘one’ cause for a given historical development, whereas in fact that development is almost inevitably the result of the interaction of a complex web of causes and it is often very difficult to weight the respective contributions of the individual causes. The mono-causal explanation only occurs if the researcher views the development from one standpoint whilst actively or passively ignoring all other possible standpoints. The same is true of the attribution of the titles ‘father of’ or ‘founder of’ to individuals. If you follow the link above to my earlier post about Galileo you will see how I show that he was only one of several, and sometimes many, making positive contributions to the fields in which he was active in the early seventeenth century and to raise him up on a pedestal is to deny due credit to the others and thus to falsify history. One can do the same with any of the other so-called ‘heroes’ of science, as I did fairly recently with exaggerated claims, contained in a book’s subtitle, for Johannes Kepler.

To repeat my central mantra as a historian of science, the evolution of science is driven by multiple complexly intertwined causes and is realised by the collective efforts of, often large, groups of researches and not by exceptional individuals. One day I hope that people will stop making the sort of statements that Stephen Hawking made, and which sparked off this post, but if I’m honest I’m not holding my breath whilst I wait.

 

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Christmas Trilogy 2015 Part 2: Understanding the Analytical Engine.

The Acolytes of the Holy Church of Saint Ada still persist in calling her a brilliant mathematician and the ‘first computer programmer’ despite the fact that both are provably wrong. In fact they have now moved into the realm of denialists, similar to evolution or climate denialists, in that they accuse people like myself who point to the historical facts of being male chauvinists who are trying to deny women their rights in the history of science! However the acolytes have gone a step further in the adulation of Lady King in that they now claim that she understood the Analytical Engine better than Babbage! Confronted by this patently ridiculous claim I’m not sure whether to laugh or cry. Babbage conceived, designed and attempted to construct parts of the Analytical Engine whereas Ada Lovelace merely wrote an essay about it based on her exchanges with Babbage on the subject, to suggest that she understood the machine better than its sole creator borders on the insane. I cannot be certain who first set this bizarre claim in the world as nearly all of those who repeat it give neither justification or source for their utterances but the most often quoted in this context is James Essinger and his biography of Ada, which appears to enjoy several different titles[1].

Trial model of a part of the Analytical Engine, built by Babbage, as displayed at the Science Museum (London). Source: Wikimedia Commons

Trial model of a part of the Analytical Engine, built by Babbage, as displayed at the Science Museum (London).
Source: Wikimedia Commons

Before going into detail it should be pointed out the Essinger’s book, which is popular rather then academic and thus lacks sources for many of his claims, suffers from two fundamental flaws. Like much pro Ada writing it doesn’t delve deep enough into the live and work of Charles Babbage. This type of writing tends to treat Babbage as an extra in the film of Ada’s life, whereas in reality in relation to the Analytical Engine it is Ada who is a minor character in Babbage’s life. Also Essinger writes about the translation of the Menabrea essay on the Analytical engine as if the appended notes were exclusively the product of Ada’s brain, whereas it is an established fact from the correspondence that they were very much a co-production between Babbage and Lovelace based on many exchanges both in personal conversations and in that correspondence. This means that in basing any argument on any idea contained in those notes the writer has the job of determining, which of the two would be the more probable source of that idea and not simply blindly attribute it to Ada. As we shall see Essinger’s failure to do this leads to a major flaw in his central argument that Ada understood the Analytical Engine better than Babbage.

Essinger’s approach is two pronged. On the one side he claims that Babbage didn’t understand the future potential of the machine that he, and he alone, conceived and created (on paper at least) and on the other he proposes on the basis of his interpretation of Note A of the essay that Ada, whom he assumes to be the originator of the thoughts this not contains, had a vision of the Analytical engine equivalent to modern computer science. As we shall see Essinger is mistaken on both counts.

Whilst offering absolutely no source for his claim, Essinger states time and again throughout his book that Babbage only every conceived of the Analytical Engine as a device for doing mathematics, a super number cruncher so to speak. If Essinger had taken the trouble to elucidate the origins of Babbage’s inspiration for the Analytical Engine he would know that he is seriously mistaken in his view, although in one sense he was right in thinking that Babbage concentrated on the mathematical aspects of the Engine but for reasons that Essinger doesn’t consider anywhere in his book.

Babbage lived in the middle of the Industrial Revolution and was fascinated by mechanisation and automation throughout his entire life. During the 1820s Babbage travelled throughout the British Isles visiting all sorts of industrial plant to study and analyse their uses of mechanisation and automation. In 1827 his wife, Georgiana, died and Babbage who had married against the opposition of his father out of love was grief stricken. Leaving Britain to escape the scene of his sorrow Babbage, by now having inherited his fathers fortune a rich man, spent many months touring the continent carrying out the same survey of the industrial advances in mechanisation and automation wherever his wanderings took him. It was on this journey that he first learnt of the automated Jacquard loom that would supply him with the idea of programming the Analytical Engine with punch cards. Returning to Britain Babbage now turned all those years of research into a book, On the Economy of Machinery and Manufactures published in 1832, that is a year before he met Ada Lovelace for the first time and ten years before Menabrea essay was written. The book was a massive success going through six editions in quick succession and influencing the work of Karl Marx and John Stuart Mill amongst others. It would be safe to say that in 1832 Babbage knew more about mechanisation and automation that almost anybody else on the entire planet and what it was capable of doing and which activities could be mechanised and/or automated. It was in this situation that Babbage decided to transfer his main interest from the Difference Engine to developing the concept of the Analytical Engine conceived from the very beginning as a general-purpose computer capable of carrying out everything that could be accomplished by such a machine, far more than just a super number cruncher.

analytical_engine

What is true, however, is that Babbage did concentrate in his plans and drafts, and the Analytical Engine never got past the plans and drafts phase, on the mathematical aspects of the machine. This however does not mean that Babbage considered it purely as a mathematical machine. I am writing this post on a modern state of the art computer. I also use the same device to exchange views with my history of sciences peers on Twitter and Facebook, to post my outpourings, such as this one, on my Internet blog. I can telephone, with visual contact if I choose, with people all over the world using Skype. At the touch, or two, of a keyboard key I have access to dictionaries, encyclopaedias and all sorts of other reference tools and through various means I can exchange documents, photographs, sound files and videos with anybody who owns a similar device. I can listen to and watch all sorts of music recordings and videos and with easily accessible software even turn my computer into an unbelievably flexible musical instrument. Finally when I’m done for the day I can settle back and watch television on my large, high-resolution monitor screen. This is only a fraction of the tasks that my computer is capable of carrying out but they all have one thing in common, they can all only be accomplished if they are capable of being coded into an astoundingly banal logical language consisting only of ‘0s’ and ‘1s’. Of course between the activities I carry out on my monitor screen and the electrical circuits that are only capable of reading those ‘0s’ and ‘1s’ there are layer upon layer of so-called sub-routines and sub-sub-routines and sub-sub-sub…, you get the idea, translating an upper layer into a simpler logical form until we get all the way down to those ubiquitous ‘0s’ and ‘1s’. The language in which those ‘0s’ and ‘1s’ exist is a mathematical language, known as Boolean Algebra, and so in the final analysis my super smart ultra modern computer is nothing but a super number cruncher and only two numbers at that.

Babbage, a brilliant mathematician, was well aware that he could only programme his Engine to carry out tasks that could be reduced over a series of steps to a mathematical language and this is the reason he concentrated on the mathematical aspects of his machine but this by no means meant that he only conceived of it only carrying out mathematical tasks, as we will see when addressing Essinger’s second prong.

Essinger quotes the following passage from Note A of the Malebrea translation:

In studying the action of the Analytical Engine, we find that the peculiar and independent nature of the considerations which in all mathematical analysis belong to operations, as distinguished from the objects operated upon and from the results of the operations performed upon those objects, is very strikingly defined and separated.

It is well to draw attention to this point, not only because its full appreciation is essential to the attainment of any very just and adequate general comprehension of the powers and mode of action of the Analytical Engine, but also because it is one which is perhaps too little kept in view in the study of mathematical science in general. It is, however, impossible to confound it with other considerations, either when we trace the manner in which that engine attains its results, or when we prepare the data for its attainment of those results. It were much to be desired, that when mathematical processes pass through the human brain instead of through the medium of inanimate mechanism, it were equally a necessity of things that the reasonings connected with operations should hold the same just place as a clear and well-defined branch of the subject of analysis, a fundamental but yet independent ingredient in the science, which they must do in studying the engine. The confusion, the difficulties, the contradictions which, in consequence of a want of accurate distinctions in this particular, have up to even a recent period encumbered mathematics in all those branches involving the consideration of negative and impossible quantities, will at once occur to the reader who is at all versed in this science, and would alone suffice to justify dwelling somewhat on the point, in connexion with any subject so peculiarly fitted to give forcible illustration of it as the Analytical Engine.

Attributing its contents to Ada he makes the following comment, “What Ada is emphasising here is the clear distinction between data and data processing: a distinction we tend to take for granted today, but which – like so much of her thinking about computers –was in her own day not only revolutionary but truly visionary”. What is being described here is indeed new in Ada’s day but is a well known development in mathematics know at the time as the Calculus of Operations, a branch of mathematics developed in the first half of the nineteenth century, which differentiates between operators and operations, and in which Babbage worked and to which he made contributions. If the ideas contained in this passage are indeed visionary then the vision is Babbage’s being channelled by Ada and not originating with her. The words might be Ada’s but the thoughts they express are clearly Babbage’s.

Essinger now quotes the next part of the Note:

It may be desirable to explain, that by the word operation, we mean any process which alters the mutual relation of two or more things, be this relation of what kind it may. This is the most general definition, and would include all subjects in the universe. In abstract mathematics, of course operations alter those particular relations which are involved in the considerations of number and space, and the results of operations are those peculiar results which correspond to the nature of the subjects of operation. But the science of operations, as derived from mathematics more especially, is a science of itself, and has its own abstract truth and value; just as logic has its own peculiar truth and value, independently of the subjects to which we may apply its reasonings and processes.

Essinger now reaches maximum bullshit level, “Ada is seeking to do nothing less than invent the science of computing and separate it from the science of mathematics. What she calls ‘the science of operations’ is indeed in effect computing”. As I have already explained what she calls the ‘science of operations’ is in fact the calculus of operation a new but well developed branch of mathematics of which Babbage was fully cognisant. If anybody is inventing the science of computing it is once again Babbage and not Ada.

Essinger now takes up the case further along in Note A:

The distinctive characteristic of the Analytical Engine, […]is the introduction into it of the principle which Jacquard devised for regulating, by means of punched cards, the most complicated patterns in the fabrication of brocaded stuffs… […]The bounds of arithmetic [emphasis in original] were however outstepped the moment the idea of applying the cards had occurred; and the Analytical Engine does not occupy common ground with mere “calculating machines.” It holds a position wholly its own; and the considerations it suggests are most interesting in their nature. In enabling mechanism to combine together general [emphasis in original] symbols in successions of unlimited variety and extent, a uniting link is established between the operations of matter and the abstract mental processes of the most abstract [emphasis in original] branch of mathematical science. [Ellipsis in quote by Essinger]

Essinger introduces this quote with the following: “In a terse passage she explains (perhaps better than Babbage ever could, who as designer saw many trees but perhaps no longer the forest itself) the essential relationship between the Analytical Engine and the Jacquard loom and how it is different from the earlier invention”. After the quote he then writes: “In perhaps one of the most visionary sentences written during the nineteenth century [he sure doesn’t hold back on the hyperbole], she lays out what these cards shall be capable of doing by way of programming the machine”

First off, if you put back the bits Essinger removed from this passage it is anything but terse, in fact it’s rather verbose. Is Essinger really trying to tell us that Babbage was not aware of what he was doing when he conceived of programming his Engine with punch cards? Unfortunately for Essinger Babbage himself tells us that this is not the case, writing in his notebook on 10 July 1836, that is 8 years before the original French version of the Malebrea essay was published, he has the following to say:

This day I had for the first time a general but very indistinct conception of the possibility of making the engine work out algebraic developments – I mean without any reference to the value of the letters. My notion is that as the cards (Jacquards) of the calc. engine direct a series of operations and the recommence with the first…[2]

Here we have in Babbage’s own words the germ of the idea contained in the Ada quote, an idea that would naturally mature over the intervening nine years before Ada wrote her piece, so I have problems whatsoever in again attributing the thoughts contained here to Babbage.

I’m not going to go on analysing Essinger’s Ada hagiography for almost all of the things that he attributes to Ada it is not difficult to find its origins in Babbage’s work thus reinforcing the claim in an earlier post that Ada is being used here as Babbage’s mouth piece. Not so much the originator as the parrot. I will however close with one last quote from Note A and Essinger’s comment to demonstrate that his grasp of the history of science in the nineteenth century is apparently almost non-existent. Without really introducing it Essinger quotes the following sentence:

Those who view mathematical science, not merely as a vast body of abstract and immutable truths, whose intrinsic beauty, symmetry and logical completeness, when regarded in their connexion together as a whole, entitle them to a prominent place in the interest of all profound and logical minds, but as possessing a yet deeper interest for the human race, when it is remembered that this science constitutes the language through which alone we can adequately express the great facts of the natural world, and those unceasing changes of mutual relationship which, visibly or invisibly, consciously or unconsciously to our immediate physical perceptions, are interminably going on in the agencies of the creation we live amidst: those who thus think on mathematical truth as the instrument through which the weak mind of man can most effectually read his Creator’s works, will regard with especial interest all that can tend to facilitate the translation of its principles into explicit practical forms.

Essinger wonderingly comments on this sentence, “This 158-word sentence is very likely one of the longest sentences in the history of science, but it is also one of the most intriguing. Ada succeeds in this one sentence in linking mathematics, science, religion and philosophy.” Any competent historian of science would immediately recognise this as a rather flowery expression of the basic tenets of natural theology, a philosophy that flourished in the first half of the nineteenth century. This statement could have been made by a very large number of natural philosophers starting with Isaac Newton and going up to and beyond William Whewell and Charles Babbage, for example in the dispute that I outlined on this day last year. What this example clearly illustrates is that Essinger is in no way a real historian who researches and understands his sources but one who thinks he can read the text of Note A and interpret it on the basis of his lack of knowledge rather than on his procession of it.

[1] The copy I read was James Essinger, A Female Genius: how Ada Lovelace, Lord Byron’s daughter started the computer age, London 2015

[2] Babbage notebook quote taken from Dorothy Stein, Ada: A Life and a Legacy, MIT Press, Cambridge Massachusetts &London, 1985 p.102

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Filed under History of Computing, Myths of Science

Mensis or menstruation?

I recently stumbled upon this rather charming rant by Anglo-Danish comedian, writer, broadcaster and feminist Sandi Toksvig.

Women's Calendar

 

Now I’m a very big fan of Ms Toksvig and was very sad when she retired as presenter of BBC Radio 4’s excellent News Quiz, so I don’t want to give the impression that I’m trying to put her down, but if she had know a little bit more about the early history of the calendar then she might not have jumped to the conclusion that this supposed bone calendar must have been made by a woman.

Before I start to explain why Ms Toksvig might be mistaken in her assumption that this purported primitive calendar came from the hands of a woman I would like to waste a few words on all such artefacts. There are a number of bone and stone objects of great antiquity bearing some number of scratches, incisions, notches, indentations or other forms of apparent marking and someone almost always comes along and declares them to be purposely created mathematical artefacts with one or other function. I must say that being highly sceptical by nature I treat all such claims with more than a modicum of wariness. Even assuming that the markings were made by a human hand might they not have been made in an idle moment by a Neolithic teenager trying out his newly acquired flint knife or in the case of our incised bone by an early musician making himself scraper to accompany the evening camp fire sing-a-long? What I’m am saying is that there are often multiple possible explanations for the existence of such marked artefacts and regarding them as signs of some sort of mathematical activity is only one of those possibilities.

However, back to Ms Toksvig and her revelation. She is of course assuming that the twenty-eight incisions are the result of a women counting off the days between her periods, the menstrual cycle being roughly twenty-eight days for most women. Now if Ms Toksvig had taken her thoughts a little further she might have realised that the word menstruation derives from the Latin word for month, which is mensis: a month being originally a lunar month which, depending on how you measure it, has approximately twenty-eight days. In fact much human thought has been expended over the centuries over the fact that a lunar month and the menstrual circle have the same length.

What we have here with this incised bone could well be not a menstrual record, as Ms Toksvig seems to assume, but a mensis record or part of a lunar calendar. This supposition is lent credence by the fact that, with the very notable exception of the ancient Egyptian calendar, all early cultures and civilisations had lunar and not solar calendars including the ancient Romans before Gaius Julius Caesar borrowed the Egyptian solar calendar, the forerunner of our own Gregorian one.

Assuming that the archaeologist or anthropologist who decided that said bone was a primitive calendar was right and it is not the idle whittling of some bored stone-age teenager, we of course still have no idea whether it was the work of a man or a woman.

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