Category Archives: Newton

Why Newton’s Apple is not a good story.

Over on the Scientific American Guest Blog we have another non-historian trying his hand at the history of science under the title Newton’s Apple: Science and the Value of a Good Story. Our author, Ned Potter a Senior Vice President of an international communications firm and former science correspondent, tells us that Isaac Newton almost invariably tops any list of history’s greatest scientists and then poses the question, why? His answer is that Newton had a great story to tell:

It’s the one about the apple. You remember it – how the young Newton, sent home from school at Cambridge to avoid the plague of 1665, was sitting under a tree one day, saw an apple fall to the ground, and, in a flash of insight, came to understand the workings of gravity.

Right there in his retelling, Potter, reveals why Newton’s Apple is anything but a great story but before I explain why, I have other fish to fry. In a lackadaisical paragraph our intrepid author summarises Newton’s scientific career:

He published his Principia Mathematica in 1687. In his spare time he designed the first reflecting telescope, laid the foundations for calculus, brought us the understanding of light and color, and in his later years – it would be disingenuous to leave this out – tried his hand at alchemy and assigning dates to events in the Bible.

He did not design the first reflecting telescope in his spare time. Investigating the nature of light and colour was at the centre of his scientific endeavours twenty years before he composed the Principia Mathematicae and his design of the reflecting telescope was his answer to the problem of chromatic aberration in lenses that his new theories on colour had discovered and explained. It also wasn’t the first reflecting telescope but the first functioning one, as I’ve already explained elsewhere. Laying the foundations of calculus was also not a spare time activity. We now turn to something that I’m slowly getting tired of correcting. Newton did not try his hand at alchemy and assigning dates to events in the Bible in his later years but started both activities in his youth continuing them for many years. They also played a very central role in the heuristics of his scientific research, as I’ve said on more than one occasion.

My readers may ask themselves why the dating of Newton’s, by modern standards, non-scientific activities is such an important subject for me. It’s rather the other way around. By pretending that Newton only did these things in his dotage people like Potter came claim that Newton was a rational modern scientist in his youth who went off the rail in his old age, poor man. This is the creation of a myth in the history of science. Newton’s alchemy, theology and chronology are a central part of what made him the scientist that he was, to deny this is to deny the man himself and to put a mythological figure, who never existed, in his place. That is not doing history of science and should also have no place in the popular presentation of science.  But back to Newton’s Apple!

The offending phrase is of course saw an apple fall to the ground, and, in a flash of insight, came to understand the workings of gravity. This is not what happened and it also creates a completely false impression of the scientific process of discovery.  Nobody, not even Newton, understands a complex scientific theory such as the theory of universal gravity in a flash of inspiration and claims that they do misinform non-scientists about how science works.

Assuming the apple story to be basically true, and there are many historian of science who think that it is a myth, what Newton thought is very different to coming to understand the workings of gravity in a flash of insight. The sight of the falling apple led him to pose a question to himself, something along the lines of, ”what causes the apple to fall to the ground?” This led to another question, and herein lies Newton’s brilliance, is that which causes the apple to fall downwards the same as that, which prevents the moon from shooting off in a tangent to its orbit as the law of inertia say it should? Here we have the beginning of an idea that can only have taken place in a mind prepared by the requisite study to be able to form this particular idea. The idea alone is in itself useless unless one possesses the necessary knowledge to test it. Newton did possess this knowledge of dynamics, astronomy and mathematics, which he had acquired through intensive personal study over the previous years rather than from his university lecturers. He then applied this knowledge to testing his newly won hypothesis, a fairly complex and demanding mathematical calculation that required both time and effort. And see here the result!  The two aren’t the same! Newton’s initial attack on the problem failed because of inadequate data. He put the problem aside and devoted himself instead to the study of optics (see above). However he did not forget that insight and many years later he returned to the problem with fresh data and showed that his initial insight had in fact been correct. The way was now open to the development of the universal theory of gravity. Note after all of the steps that we have already gone through we have not arrived at the workings of the theory of gravity, we have merely started down the road towards it. In fact Newton would have to invest two years of very intense work, to the exclusion of everything else in his life, between 1684 and 1687 in order to finally develop the theory in all of its glory, as published in his Principia. The process can hardly be described as “a flash of insight”.

I hope that I have made clear that, in the sense of Ned Potter, Newton’s Apple is anything but a good story, as it creates a complete misconception of the scientific process, a process that even in the case of a monster intellect such as Newton’s involves an incredible amount of study and sheer hard work.

The story as presented by Potter could however have its uses in teaching an introductory course in the history of science and in illustrating the scientific process. One presents the students with the myth of Newton’s Apple à la Potter and then have them research the real historical situation. To look for, read and analyse the original sources of the apple story, William Stukeley, as well as John Conduit and Voltaire, who both had the story from Catherine Barton, Newton’s niece and housekeeper as well as Conduit’s wife. Then have them study the real process by which Newton developed his theory of universal gravity, as I have sketched it, demonstrating how misleading such tales can be. As such I think that the Newton’s Apple story can be put to good pedagogical use, however as Potter wishes it to be considered:

Over the years, inevitably, the details have been embellished. Ask around today, and people may tell you that the apple bonked Newton on the head. But the point remains: if you have an important point to make, especially in science but also in other fields, there’s nothing like a good story to make it memorable.

I think it’s anything but a good story particularly if the important point being made is completely false.

7 Comments

Filed under History of science, Myths of Science, Newton

Alchemical confusion redux.

Yesterday, in my frustration with Mr Campbell’s drivel I missed another reference to Newton towards the end of his post to which Laura has drawn my attention in the comments.  Our Google expert delivers the following gem:

If I have limited time I want to read about Principia, not a failed effort later in Newton’s career. The fact that John Maynard Keynes believed in alchemy does not validate it, it instead shows us what was wrong with Keynes-ian economic beliefs. He believed in eugenics too, that didn’t make it valid.

In theses few lines Mr Campbell truly displays his total ignorance of subject he is pontificating about.  We start off with the classic, ‘Newton’s alchemy was a product of his dotage after he had produced his scientific work, the Principia’. Campbell doesn’t express it quite like that but it’s obvious what he believes. Nothing could be further from the truth. As I stated in the previous post Newton began his intensive study of alchemy in 1666 and continued it till 1696. He wrote the Principia in somewhat of a frenzy between 1684 and 1687, that is in two thirds of the way through his alchemy studies. Worse than this from Campbell’s standpoint Newton’s alchemical studies actually played a significant role in the conception of the Principia!

Newton conceived and wrote the Principia during a period in the history of science when the mechanical philosophy was totally dominant. This stated quite clearly that if object A moved as a result of object B then there must exist a mechanical contact between the two objects. Newton’s theory of gravity functioning through action at a distance was completely inacceptable. Newton was originally a supporter of the mechanical philosophy and as such would have been incapable of accepting his own later theory of gravity. What gave him the ability to go against the trend and embrace action at a distance? You guessed it, his study of alchemy. It has been clearly shown, mostly by Betty Jo Dobbs, that Newton’s acceptance of action at a distance and thus of a mental position from which he could formulate his theory of gravity was his study of the spirit forces in alchemy. Beyond this, Newton’s third law of motion is known to have been based on an alchemical principle.

In fact Newton’s introduction of the force of gravity acting at a distance led to the strongest criticism of and opposition to the Principia by the Cartesian and Leibnizian supporters of the mechanical philosophy. They accused him of reintroducing the occult (meaning hidden) forces into natural philosophy that they had banished. On these grounds whilst admiring the mathematical ingenuity of the Principia they rejected its central thesis.

Just as worrying as Mr Campbell’s total misrepresentation of Newton and his alchemy is his presentation of John Maynard Keynes. Now I’m not in anyway an expert on Keynes, in fact I know more about his father John Neville Keynes who was one of my nineteenth century logicians when I was serving my apprenticeship as a historian of mathematical logic. However I don’t really think that Keynes believed in alchemy. Worse than this, in the comments to his post, in response to just such doubt expressed by a reader, Campbell basically admits that he has no justification for this claim beyond his own personal animosity to Keynes’ economic theories and his support of eugenics as well as the fact that the fact that Keynes donated his personal collection of Newton’s alchemical writings to Cambridge University.

I shall ignore both the economics and the eugenics as non sequitur in a discussion on the history of alchemy. Viewing Keynes’ donation of the Newton papers as somehow damning is to say the least bizarre. This and other remarks scattered around Campbell’s incoherent piece lead me to the conclusion that Campbell is the worst sort of historical presentist.  He seems to be of the opinion that only those aspects of a historical researchers work that are still relevant by today’s standard are worth conserving or investigating, all the rest can be assigned to the dustbin of history. By totally misrepresenting alchemy and labelling it just pseudo-science Campbell thinks we dispense with it once and for all. The whole point of the fascinating and stimulating work of Principe et al is that they have clearly demonstrated that the real historical alchemy, as opposed to Campbell’s mythological version, made very significant contributions to the shaping of modern science.

9 Comments

Filed under History of Alchemy, Newton

Alchemical confusion.

On the 11th February 1144 the Hellenistic science of alchemy entered medieval Europe by way of the Islamic empire. In his translation of Liber de compositione alchemiae (Book about the composition of alchemy) Robert of Chester wrote the following:

I have translated this Book because, what alchemy is, and what its composition is, almost no one in our Latin [that is: Western] world knows finished February 11th anno 1144.

This was the start of long and popular period for alchemy within Europe, which reached its peak during the Renaissance during which alchemy gave birth to its daughter, modern chemistry. Rejected during the Enlightenment, along with astrology and magic, as a worthless occult science, alchemy was largely ignored by historian as superstitious nonsense not worthy of serious attention. The last decades have seen a rebirth of interest in alchemy by historians of science led by such prominent historians as Lawrence Principe, William Newman, Bruce Moran and Pamela H. Smith as well as a host of less well known figures such as my Internet friends Anna Marie Roos (@roos_annamarie) and Sienna Latham (@clerestories).

In the last few weeks there has been a surge in interest from the general Internet media mostly generated by Lawrence Principe’s recently published semi-popular history of alchemy The Secrets of Alchemy. This has been mostly fairly harmless but one Internet piece that I read last week is so confused that it provoked my inner Hist-Sci Hulk, especially as it totally misrepresents Newton’s interest and involvement in alchemy. The piece Is Alchemy Back In Fashion? by science writer Hank Campbell is on the Science 2.0 website.

Campbell’s piece was not inspired by Principe’s book but by the essay, Alchemy Restored, that Principe wrote for Focus section of ISIS vol. 102, No. 2 Alchemy and the History of Science. This essay is a very much-shortened version of chapter four of his book, Redefinitions, Revivals, and Reinterpretations: Alchemy from the Eighteenth Century to the Present.

To point out and correct everything that is wrong in Campbell’s piece would turn this post into a minor novel so I shall just content myself with a bit of sniping and correcting his mistaken views on Newton’s relationship with alchemy. The first thing I would note is that before writing his piece Campbell appears to have done his research at the Google University, beloved source of wisdom of vaccine deniers, climate change deniers, anti-evolutionists and other members of the Internet Luniverse. His piece would have benefitted immensely if he had read some of the books written by Principe, Newman, Moran et al. However reading doesn’t seem to be his forte as he doesn’t seem to have actually read the essay by Principe that he heavily criticises in his piece, either that or he maliciously misrepresents Principe’s views.

The whole of the opening paragraphs displays strong Google University influence containing as it does half information that is mostly at least half wrong. There are various conflicting etymologies for the word alchemy or better said the word chemy as al is purely the Arabic definite article. Principe thinks the Greek root cheimeia is the most likely as alchemy in antiquity was Greco-Egyptian, that is it was developed in Egypt but written in Greek. This leading to the Arabic al-kīmiyā of al-Rāzī and the alchemia of the Renaissance adepts. Like those in the eighteenth century who, as Principe tells us, tried to distance chemistry from alchemy Campbell falsely identifies alchemy with the transmutation of metals, correctly called chrysopoeia, whereas seventeenth century alchemy encompassed a wide range of activities including all of that, which in the early eighteenth century became chemistry.

The central point of Principe’s essay is that the chemist of the eighteenth century deliberately misrepresented the scope of alchemy in order to deny that their own discipline was alchemy’s daughter. I find it fascinating that Campbell a science writer with a background in computing, who very obviously knows next to nothing about the history of alchemy and chemistry lectures Principe, who is without doubt one of the world’s leading experts on the subject, on why he is wrong in his analysis of the eighteenth century’s denigrating of alchemy’s reputation. Even more bizarre in the following paragraph:

You know which group was also ridiculed, even until the mid-1800s? Medical doctors. Many people thought Harvard was out of its mind creating a medical school in 1782, but they took it seriously and within a few generations medicine had put quacks on the fringes and adopted evidence-based practices. Before then, legitimate doctors were Ph.D.s and Medical Doctors were that other thing that didn’t count. Today, though, if you say doctor people assume you are an M.D.

The whole of this is so mind bogglingly wrong that it is not even worth criticising except to say that if it were written on paper I would flush it down the toilet. Let us now turn our attention to the good Isaac Newton and his activities as an alchemist. The all-knowing Campbell informs us:

Newton tried alchemy, after all, because he wanted to get to the bottom of it and maybe show chemists he was smarter than they were, just like he showed everyone else he was smarter than they were (I mean you, Hooke.)

[…]

The break between alchemy and chemistry had been happening before Newton, that is why he took a shot at it, but until the 18th century they were interchangeable to the public.

I’ve read many misrepresentations of Newton’s alchemical activities but this has got to be one of the worst that has ever crossed my path. Campbell gives the impression that Newton took a swing at alchemy in passing nothing could be further from the truth. For the record, Newton devoted the winter months of the year to an intensive study of alchemy, in a hut especially specially constructed for the purpose, from 1666 until he departed Cambridge for London in 1696, a total of thirty years in case Mr Campbell can’t count.  He also wrote substantially more on alchemy than he ever wrote on physics and mathematics combined. I would not call that “taking a shot at it”.  Although there is some truth that the break between alchemy and chemistry began in the seventeenth century this is in no way the reason that Newton took up the study of alchemy. He was also not out to show chemists that he was smarter than they were. Apart from anything else Newton knew that he was smarter than everybody else, he didn’t need to show anybody anything. Before dealing with the real reasons for Newton’s intense interest in alchemy I’ll just deal with the ill informed sideswipe at the Hooke Newton conflict.

We’ve been here before but it bears repeating that it was Hooke who attacked Newton, not once but twice, and not the other way round. In fact, if anybody suffered from an intense need to show that he was smarter than everyone else it was the unfortunate Robert Hooke. Intensely jealous of others he, time and again, accused his contemporary natural philosophers of stealing his ideas, discoveries and inventions. He dismissed Newton’s first optics paper claiming that anything novel that it contained he had discovered already and then later he claimed that he should be acknowledge as the true discoverer of the universal law of gravity. It’s not really surprising that Newton disliked him. However I deviate from my purpose.

Why did Newton devote so much of his life to an intense study of alchemy? To understand his motivation one has to examine both his religious beliefs and the governing metaphysics of his whole life’s work, which are in fact two aspects of a single complex. Newton was an adherent of the prisca sapientia. This is the belief that directly after the creation, and Newton was a devote if more than somewhat heterodox Christian, humanity had a complete and perfect knowledge of the laws of nature, a knowledge that had become lost over the millennia as humanity degenerated. Following this metaphysic Newton did not believe that he was discovering the laws or secrets of nature but rediscovering them. In fact based on his reading of the Bible he believed that he had been especially chosen by his God to do so.  In line with the hermeticism of his age he believed that alchemy was the oldest form of knowledge possessed by humanity coming either shortly after Moses, or even from him or before him, and if he could unravel its secrets this would bring him closer to that perfect knowledge of nature once possessed by humanity in its early days. This is not a ‘modern scientist’ investigating the chemical aspects of alchemy, as Campbell would have us believe, but a man, we would have immense difficulty identifying with in anyway what so ever, following a twisted theological, metaphysical path that relates in no way to the world we now inhabit.

[1] This date and the following quote are taken from Aksel Haaning, The Philosophical Nature of Early Western Alchemy: The Formative Period c- 1150-1350, in Jacob Wamberg ed. Art & Alchemy, Museum Tusculanum Press, University of Copenhagen 2006 pp. 23-40, quote p. 25. When quoting the same date, in his The Secrets of Alchemy, Principe points out correctly that although it might be the first translation of an Arabic alchemy text it’s probably not the Latin West’s first contact with the discipline.

[2] Robert of Chester is well known in the history of mathematics for his translation of Abū ʿAbdallāh Muḥammad ibn Mūsā al-Khwārizmī’s Al-kitāb al-mukhtaṣar fī ḥisāb al-ğabr wa’l-muqābala (The Compendious Book on Calculation by Completion and Balancing) the book that introduced algebra to the Latin West and which gave us both the words algebra and algorithm.

15 Comments

Filed under History of Alchemy, Newton

The Renaissance Mathematicus Christmas Trilogy: An Explanation.

 

I seem to have garnered a number of new readers in the last twelve months who might be confused by my Christmas Trilogy especially as I have offered no explanation within the posts themselves, so I have decided to present a brief explanation of this Renaissance Mathematicus tradition.

Isaac Newton was born on 25th December 1642 (OS), Charles Babbage was born on 26th December 1791 and Johannes Kepler was born on 27th December 1571 (OS). These three are amongst my favourite figures in the history of science so I developed the habit of writing a post dedicated to some aspect of their life and work on their respective birthdays, hence The Renaissance Mathematicus Christmas Trilogy.

For those interested you can find links to previous years’ posts here:

2009: On Clocks and Triangles: a post for Newtonmas Is the question “who invented the computer” legitimate? Shedding some light.

2010: A Christmas Trinity I: Isaac was one too. A Christmas Trinity II: Charlie, Ivor, Robert and me. A Christmas Trinity III: Johann’s geometrical music.

2011: Only 26 and already a professor! How Charles tried to oust Isaac from Cambridge. Kepler contra Fludd, science contra woo?

2012:  Christmas Trilogy 2012 Part I: Did Isaac really victimise Stephen? Christmas Trilogy 2012 Part II: Charles and Ada: A tale of genius or exploitation? Christmas Trilogy 2012 Part III:  What to do if your mother’s a witch.

2 Comments

Filed under History of science, Newton

Christmas Trilogy 2013 Part I: The Other Isaac [1].

In a recent post on John Wallis I commented on seventeenth century English mathematicians who have been largely lost to history, obscured by the vast shadow cast by Isaac Newton. One person, who has suffered this fate, possibly more than any other, was the first Lucasian Professor of Mathematics at Cambridge, and thus Newton’s predecessor on that chair, Isaac Barrow (1630 – 1677), who in popular history has been reduced to a mere footnote in the Newton mythology.

Statue of Isaac Barrow in the Chapel of Trinity College

Statue of Isaac Barrow in the Chapel of Trinity College

He was born in London in 1630 the son of John Barrow a draper. The Barrow’s were a Cambridge family notable for its many prominent scholars and theologians. Isaac father was the exception in that he had gone into trade but he was keen that his son should follow the family tradition and become a scholar.  With this aim in view the young Isaac was originally sent to Charterhouse School where he unfortunately more renowned as the school ruffian than for his learning. His father thus placed him in Felsted School in Essex, where John Wallis was also prepared for university, and where he soon turned his hand to more scholarly pursuits. Barrow’s success at school can be judged by the fact that when his father got into financial difficulties, and could no longer pay his school fees, the headmaster of the school took him out of the boarding house and lodged him in his own private dwelling free of charge and also arranged for him to earn money as tutor to William Fairfax.

In 1643 he was due to go up to Peterhouse Cambridge, where his uncle Isaac was a fellow. However his uncle was ejected from the college by the puritans and so the plan came to nought. Cut loose in society young Barrow ended up in Norfolk at the house of Edward Walpole a former schoolfellow who on going up to Cambridge decided to take Barrow with him and pay his keep. So it was that Barrow was admitted to Trinity College in 1646. Following further trials and tribulations he graduated BA in 1649 and was elected fellow shortly after. He went on to graduate MA in 1652 displaying thereby a mastery of the new philosophy. Barrow’s scholarly success was all the more remarkable, as throughout his studies he remained an outspoken Anglican High Church man and a devout royalist, things not likely to endear him to his puritan tutors.

In the 1650s Barrow devoted much of his time and efforts to the study of mathematics and the natural sciences together with a group of young scholars dedicated to these pursuits that included John Ray and Ray’s future patron Francis Willughby who had both shared the same Trinity tutor as Barrow, James Duport. Barrow embraced the mathematical and natural science of Descartes, whilst rejecting his metaphysics, as leading to atheism. He also believed students should continue to study Aristotle and the other ancients for the refinement of their language.  During this period Barrow began to study medicine, a common choice for those interested in the natural sciences, but remembering a promise made to himself whilst still at school to devote his life to the study of divinity he dropped his medical studies.

It was during this period that Barrow produced his first mathematical studies producing epitomes of both Euclid’s Elements and his Data, as well as of the known works of Archimedes, the first four books of Apollonius’ Conics and The Sphaerics of Theodosius. Barrow used the compact symbolism of William Oughtred to produce the abridged editions of these classical works of Greek mathematics. His Elements was published in 1656 and then again together with the Data in 1657. The other works were first published in the 1670s.

In 1654 a new wave of puritanism hit the English university and to avoid conflict Barrow applied for and obtained a travel scholarship leaving Cambridge in the direction of Paris in 1655. He spent eight months in Paris, which he described as, “devoid of its former renown and inferior to Cambridge!” From Paris he travelled to Florence where he was forced to extend his stay because an outbreak of the plague prevented him continuing on to Rome. In November 1656 he embarked on a ship to Smyrna, which on route was attacked by Barbary pirates, Barrow joining the crew in defending the ship acquitted himself honourably. He stayed in Smyrna for seven months before continuing to Constantinople. Although a skilled linguist fluent in eight languages Barrow made no attempt to learn Arabic, probably because of his religious prejudices against Islam, instead deepening his knowledge of Greek in order to study the church fathers.  Barrow left Constantinople in December 1658 arriving back in Cambridge, via Venice, Germany and the Netherlands, in September 1659.  It should be noted that the Interregnum was over and the Restoration of the monarchy would take place in the very near future. Unfortunately all of Barrow’s possessions including his paper from his travels were lost on the return journey, as his ship went up in flames shortly after docking in Venice

Barrow’s career, strongly supported by John Wilkins, now took off. In 1660 he was appointed Regius Professor of Greek at Cambridge followed in 1662 by his appointment as Gresham Professor of Geometry at Gresham College in London. His Gresham lectures were unfortunately lost without being published so we know little of what he taught there.  On the creation of the Lucasian Chair for Mathematics in 1663 Barrow was, at the suggestion of Wilkins, appointed as it first occupant. In 1664 he resigned both the Regius and the Gresham professorships. Meanwhile Barrow had started on the divinity trail being granted a BD in 1661 and beginning his career as a preacher.

Barrow only retained the Lucasian Chair for six years and in this time he lectured on mathematics, geometry and optics. His attitude to mathematics was strange and rather unique at the time. He was immensely knowledgeable of the new analytical mathematics possessing and having studied intently the works of Galileo, Cavalieri, Oughtred, Fermat, Descartes and many others however he did not follow them in reducing mathematics to algebra and analysis but went in the opposite directions reducing arithmetic to geometry and rejecting algebra completely. As a result his mathematical work was at one and the same time totally modern and up to date in its content whilst being totally old fashioned in its execution. Whereas his earlier Euclid remained a popular university textbook well into the eighteenth century his mathematical work as Lucasian professor fell by the wayside superseded by those who developed the new analysis. His optics lectures were a different matter. Although they were the last to be held they were the first to be published after he resigned the Lucasian chair. Pushed by that irrepressible mathematics communicator, John Collins, to publish his Lucasian Lectures Barrow prepared his optics lectures for publication assisted by his successor as Lucasian Professor, Isaac Newton, who was at the time delivering his own optics lectures, and who proof read and corrected the older Isaac’s manuscript. Building on the work of Kepler, Scheiner and Descartes Barrow’s Optics Lectures is the first work to deal mathematically with the position of the image in geometrical optics and as such remained highly influential well into the next century.

As he had once given up the study of medicine in his youth Barrow resigned the Lucasian Professorship in 1669 to devote his life to the study of divinity. His supporters, who now included an impressive list of influential bishops, were prepared to have him appointed to a bishopric but Barrow was a Cambridge man through and through and did not want to leave the college life. To solve the problem his friends had him appointed Master of Trinity instead, an appointment he retained until his tragically early death in 1677, just forty-seven years old. Following his death his collected sermons were published and it is they, rather than his mathematical work, that remain his intellectual legacy. Throughout his life all who came into contact with him acknowledge Barrow as a great scholar.

Near the beginning of this post I described Barrow as, having “been reduced to a mere footnote in the Newton mythology”. What did I mean by this statement and what exactly was the connection between the two Isaacs, apart from Barrow’s Optics Lectures? Older biographies of Newton and unfortunately much modern popular work state that Barrow was Newton’s teacher at Cambridge and that the older Isaac in realising the younger Isaac’s vast superiority as a mathematician resigned the Lucasian Chair in his favour. Both statements are myths. We don’t actually know who Newton’s tutor was but we can say with certainty that it was not Barrow. As far as can be ascertained the older Isaac first became aware of his younger colleague after Newton had graduated MA and been elected a fellow of Trinity. The two mathematicians enjoyed cordial relations with the older doing his best to support and further the career of the younger. As we have already seen above Barrow resigned the Lucasian Professorship in order to devote his live to the study and practice of divinity, however he did recommend his young colleague as his successor and Newton was duly elected to the post in 1669. Barrow also actively helped Newton in obtaining a special dispensation from King Charles, whose royal chaplain he had become, permitting him not to have to be ordained in order to hold the post of Lucasian Professor[2].


[1] On Monday I wrote that I might not be blogging for a while following Sascha untimely death. However I spent some time and effort preparing this years usual Christmas Trilogy of post and I find that writing helps to divert my attention from thoughts of him and to stop me staring at the wall. Also it’s what Sascha as general manager of this blog would have wanted.

[2] Should anyone feel a desire to learn more about Isaac Barrow I can highly recommend Before Newton: The Life and Times of Isaac Barrow, ed. Mordechai Feingold, CUP, Cambridge, 1990 from which most of the content of this post was distilled.

8 Comments

Filed under History of Mathematics, History of Optics, History of science, Newton

What Isaac actually asked the apple.

Yesterday on my twitter stream people were retweeting the following quote:

“Millions saw the apple fall, but Newton asked why.” —Bernard Baruch

For those who don’t know, Bernard Baruch was an American financier and presidential advisor. I can only assume that those who retweeted it did so because they believe that it is in some way significant. As a historian of science I find it is significant because it is fundamentally wrong in two different ways and because it perpetuates a false understanding of Newton’s apple story. For the purposes of this post I shall ignore the historical debate about the truth or falsity of the apple story, an interesting discussion of which you can read here in the comments, and just assume that it is true. I should however point out that in the story, as told by Newton to at least two different people, he was not hit on the head by the apple and he did not in a blinding flash of inspiration discover the inverse square law of gravity. Both of these commonly held beliefs are myths created in the centuries after Newton’s death.

Our quote above implies that of all the millions of people who saw apples, or any other objects for that matter, fall, Newton was the first or even perhaps the only one to ask why. This is of course complete and utter rubbish people have been asking why objects fall probably ever since the hominoid brain became capable of some sort of primitive thought. In the western world the answer to this question that was most widely accepted in the centuries before Newton was born was the one supplied by Aristotle. Aristotle thought that objects fall because it was in their nature to do so. They had a longing, desire, instinct or whatever you choose to call it to return to their natural resting place the earth. This is of course an animistic theory of matter attributing as it does some sort of spirit to matter to fulfil a desire.

Aristotle’s answer stems from his theory of the elements of matter that he inherited from Empedocles. According to this theory all matter on the earth consisted of varying mixtures of four elements: earth, water, fire and air. In an ideal world they would be totally separated, a sphere of earth enclosed in a sphere of water, enclosed in a sphere of air, which in turn was enclosed in a sphere of fire. Outside of the sphere of fire the heavens consisted of a fifth pure element, aether or as it became known in Latin the quintessence. In our world objects consist of mixtures of the four elements, which given the chance strive to return to their natural position in the scheme of things. Heavy objects, consisting as they do largely of earth and water, strive downwards towards the earth light objects such as smoke or fire strive upwards.

To understand what Isaac did ask the apple we have to take a brief look at the two thousand years between Aristotle and Newton.

Ignoring for a moment the Stoics, nobody really challenged the Aristotelian elemental theory, which is metaphysical in nature but over the centuries they did challenge his physical theory of movement. Before moving on we should point out that Aristotle said that vertical, upwards or downwards, movement on the earth was natural and all other movement was unnatural or violent, whereas in the heavens circular movement was natural.

Already in the sixth century CE John Philoponus began to question and criticise Aristotle’s physical laws of motion. An attitude that was taken up and extended by the Islamic scholars in the Middle Ages. Following the lead of their Islamic colleagues the so-called Paris physicists of the fourteenth century developed the impulse theory, which said that when an object was thrown the thrower imparted an impulse to the object which carried it through the air gradually being exhausted, until when spent the object fell to the ground. Slightly earlier their Oxford colleagues, the Calculatores of Merton College had in fact discovered Galileo’s mathematical law of fall: The two theories together providing a quasi-mathematical explanation of movement, at least here on the earth.

You might be wondering what all of this has to do with Isaac and his apple but you should have a little patience we will arrive in Grantham in due course.

In the sixteenth century various mathematicians such as Tartaglia and Benedetti extended the mathematical investigation of movement, the latter anticipating Galileo in almost all of his famous discoveries. At the beginning of the seventeenth century Simon Stevin and Galileo deepened these studies once more the latter developing very elegant experiments to demonstrate and confirm the laws of fall, which were later in the century confirmed by Riccioli. Meanwhile their contemporary Kepler was the first to replace the Aristotelian animistic concept of movement with one driven by a non-living force, even if it was not very clear what force is. During the seventeenth century others such as Beeckman, Descartes, Borelli and Huygens further developed Kepler’s concept of force, meanwhile banning Aristotle’s moving spirits out of their mechanistical philosophy. Galileo, Beeckman and Descartes replaced the medieval impulse theory with the theory of inertia, which says that objects in a vacuum will either remain at rest or continue to travel in a straight line unless acted upon by a force. Galileo, who still hung on the Greek concept of perfect circular motion, had problems with the straight-line bit but Beeckman and Descartes straightened him out. The theory of inertia was to become Newton’s first law of motion.

We have now finally arrived at that idyllic summer afternoon in Grantham in 1666, as the young Isaac Newton, home from university to avoid the plague, whilst lying in his mother’s garden contemplating the universe, as one does, chanced to see an apple falling from a tree. Newton didn’t ask why it fell, but set off on a much more interesting, complicated and fruitful line of speculation. Newton’s line of thought went something like this. If Descartes is right with his theory of inertia, in those days young Isaac was still a fan of the Gallic philosopher, then there must be some force pulling the moon down towards the earth and preventing it shooting off in a straight line at a tangent to its orbit. What if, he thought, the force that holds the moon in its orbit and the force that cause the apple to fall to the ground were one and the same? This frighteningly simple thought is the germ out of which Newton’s theory of universal gravity and his masterpiece the Principia grew. That growth taking several years and a lot of very hard work. No instant discoveries here.

Being somewhat of a mathematical genius, young Isaac did a quick back of an envelope calculation and see here his theory didn’t fit! They weren’t the same force at all! What had gone wrong? In fact there was nothing wrong with Newton’s theory at all but the figure that he had for the size of the earth was inaccurate enough to throw his calculations. As a side note, although the expression back of an envelope calculation is just a turn of phrase in Newton’s case it was often very near the truth. In Newton’s papers there are mathematical calculations scribbled on shopping lists, in the margins of letters, in fact on any and every available scrap of paper that happened to be in the moment at hand.

Newton didn’t forget his idea and later when he repeated those calculations with the brand new accurate figures for the size of the earth supplied by Picard he could indeed show that the chain of thought inspired by that tumbling apple had indeed been correct.

 

11 Comments

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

The corresponding accountant, the man who invented π and the Earls of Macclesfield.

I recently stumbled over an exciting piece of news for all historians of the mathematics of the seventeenth century, Jackie Stedall and Philip Beeley have received a grant from the AHRC to edit and publish the correspondence of the English mathematician John Collins (1625 – 1683). Now anybody who is not up on the obscure aspects of seventeenth century mathematics is probably thinking who is John Collins and why should the publication of his correspondence be a reason to celebrate?

In the Early Modern Period before the advent of academic journals European scholars did not live in splendid isolation but spread, discussed and criticised each others newest thoughts by post. There existed a vast interlocking web of correspondence networks linking up the scholars in much the same way as the Internet does today but at a somewhat more leisurely pace.

The letters that scholars exchanged were often long detailed texts on their current research, resembling more a scientific paper than a conventional letter. These were also not private letters but were often conceived to be copied by the recipient and sent on by him to other interested parties in his own network. An early modern form of re-blogging or re-tweeting. Some scholar’s networks were so extensive that they are now referred to as ‘post offices’.  The most well known example of an early modern ‘post office’ is the French Minim Friar Marin Mersenne who appeared to be the hub around which the European scientific community revolved. He is particularly renowned for having championed Galileo’s physics. When he died letters from 79 different scientific correspondents were found in his monk’s cell in Paris. Even Mersenne’s prolific letter writing activities were over shadowed by another acolyte of Galileo, Mersenne’s countryman, Nicolas-Claude Fabri de Peiresc. We still have 10 000 of Peiresc’s letters.

Another European ‘post office’ was the German Jesuit professor of mathematics at the Collegio Romano, Athanasius Kircher. Kircher collected astronomical observations and other scientific information from all over the world and redistributed it to all of the leading astronomers of Europe, both Jesuit and non-Jesuit.

In England the first secretary of the Royal Society, Henry Oldenburg, also maintained a continent wide network of correspondents. In fact the contents of the early editions of the Philosophical Transactions, which Oldenburg started as a private enterprise to supplement his salary, consisted largely of letters of , often dubious, scientific merit from Oldenburg’s correspondents. His extensive foreign correspondence led to him, a German, being arrested and incarcerated on suspicion of being a spy for a time during the second Anglo-Dutch War in 1667. As we shall see John Collins came to serve as an assistant to Oldenburg dealing with the mathematical correspondence.

Collins, the son of an impoverished nonconformist minister, was born in Wood Eaton near Oxford in 1626. Unable to afford an advanced education he was apprenticed to the bookseller Thomas Allam. After Allam went bankrupt he became junior clerk under John Marr, clerk to the kitchens of the Prince of Wales, the future Charles II. Marr was an excellent mathematician and sundial maker and it was from him that Collin’s almost certainly received his mathematical education. During the civil war (1642 – 1649) he went to sea serving on an English merchantman engaged as a man-of-war in Venetian service. During this time he learnt navigation and taught himself accounting, mathematics and Latin.

Upon his return to England he earned his living in various positions as an accountant and began to develop a network of correspondents to acquire books and mathematical news. In 1667 Collins was elected to the Royal Society and for the next ten years he served the society as an unofficial secretary for matters mathematical. In this role he corresponded with most of the eminent mathematicians of Europe including Isaac Barrow (who christened him Mersennus Anglus), James Gregory, Christiaan Huygens, Gottfried Leibniz, John Pell, René de Sluze, Ehrenfried Tschirnhaus and possibly most important of all Isaac Newton. In fact it was Collins who outted, the then unknown, young Newton and dragged him out of his Cambridge seclusion into the seventeenth century mathematical community.

In 1669 Collins sent a new publication on analysis by Mercator (that’s Nicolaus the seventeenth century German mathematician and engineer not to be confused with Gerard the sixteenth century Dutch cartographer) to Isaac Barrow, then still the Lucasian professor of mathematics in Cambridge. Barrow responded by saying that he had a young colleague whose own work on the subject was far superior to Mercator’s. Collins thus obtained from Barrow a manuscript of Newton’s De analysi per aequationes numero terminorum infinitas (On Analysis by Infinite Series), which he proceeded to copy and distribute to a large number of European mathematicians including Leibniz. Thus making the world aware of the fact that there was a world-class mathematician in Cambridge and inadvertently igniting a slow fuse to the most notorious priority and plagiarism dispute in the history of mathematics.

Collins was also involved in the publishing business seeing several important mathematical and scientific works through the press: Thomas Salusbury’s Mathematical Collection (1661 – 1665), (including his translations of Galileo into English, which were also used by Newton), Isaac Barrow’s Lectiones opticae (1669) (prepared for publication by Newton), Lectiones geometricae (1670) and Archimedes (1675); John Wallis’ Mechanica (1669 –1671) and Algebra (1685); Jeremiah Horrocks’ Opera posthuma (1672 – 8); and others.

Collins was not a particularly skilled mathematician being more of a mathematical practitioner than a mathematician in the modern sense. He wrote and published works on accounting, surveying, navigating and dialling (the design and construction of sundials). He also wrote on the subject of trade.

Collins, who can best be described as a maths groupie, collected an extensive library of mathematical books and papers alongside his widespread correspondence. In the seventeenth century there was not the interest in papers and libraries of the deceased that exists today and there was a risk that Collins’ collection might have been dispersed after his death in 1683, enter William Jones.

William Jones, who was born on Anglesey in about 1675; was like Collins the son of an impoverished family with no prospects of an advanced education. However a local landowner recognised his mathematical talents and arranged a position for him at a London merchant’s counting house. He was sent by his employers to the West Indies and thus acquired a liking for the sea. From 1695 to 1702 he served as mathematics master on a man-of-war. Settling in London he became a private mathematics tutor publishing a book on navigation in 1702. In 1706 he published a textbook on the new calculus Synopsis palmarioum matheseos, or, A New Introduction to the Mathematics, which was the first book to include π as the ratio between the circumference and diameter of a circle; an honour often falsely attributed to Euler. William Oughtred had earlier used π to designate just the circumference. This publication probably first brought Jones into Newton’s inner circle.

In 1708 Jones bought up Collins’ collection of mathematical books, papers and letters. In 1711 he was elected to the Royal Society and appointed to the committee set up at the request of Leibniz to investigate the charges of plagiarism that had been made against him with respect to the invention of the calculus by Newton’s acolyte John Keill. Together with Newton, who should not have been involved at all being one of the disputing parties, Jones put together the Commercium  epistolicum (1712), which largely consisted of letters and papers from Collins’ collection and which, not unsurprisingly, found for Newton and against Leibniz. It did in fact contain a genuine smoking gun, the proof that Leibniz had received a copy of De analysi per aequationes numero terminorum infinitas from Collins, whereas Leibniz had always claimed to have had no knowledge of Newton’s early work.

Jones continued to work closely with Newton, acting as go between when relations became strained between Newton and Roger Cotes, when they were working on the second edition of Principia, and editing and publishing various of Newton’s other works.

Jones continued to earn his living as a private tutor and served for a time as mathematics teacher to Philip Yorke who would go on to become Lord Chancellor and the Earl of Hardwick. Through Yorke he was introduced to Lord Chief Justice Parker, who would become the first Earl of Macclesfield, and become tutor to his son George.

Involved in a political scandal Thomas Parker, who incidentally was one of Newton’s pallbearers, withdrew from public life and retired to his countryseat Shirburn Castle where Jones effectively became a member of the household. Parker was a great collector of books and built up a very impressive library. Meanwhile Jones continued to increase the Collins collection of mathematical books and papers.

Jones’ pupil George Parker, the second Earl of Macclesfield, was an avid amateur natural philosopher and astronomer, who added an observatory and a chemical laboratory to Shirburn Castle. In his role as a member of parliament he was instrumental in dragging Britain out of the Middle Ages and into the modern world by introducing the Gregorian calendar in 1752, two centuries after its adoption by Catholic Europe.

When he died Jones bequeathed the Collins-Jones mathematical collection to George Parker and it resided in the Shirburn Castle library for more than two hundred years largely inaccessible to historians. The astronomer and historian of mathematics Stephen Rigaud was granted access to Collins’ collection of letters and published some of them in his Correspondence of scientific men of the seventeenth century: including letters of Barrow, Flamsteed, Wallis, and Newton, printed from the originals in the collection of the Right Honourable the Earl of Macclesfield in 1841. The Macclesfield’s dissolved their priceless library at the beginning of the last decade, selling the scientific papers and letters to Cambridge University and the books by public auction. The three substantial volumes of the sales catalogue dealing with the mathematics books are themselves an invaluable history of mathematics resource (I know because a friend of mine owns them and I’m allowed to use them). That Collins’ letters collection is now going to receive the scholarly treatment it deserves is good news indeed for all historians of the seventeenth century and not just those of science or mathematics.

 

2 Comments

Filed under Early Scientific Publishing, History of Mathematics, History of science, Newton

Here we go again…

I know that I shouldn’t but I just couldn’t resist. A website called Telly Chat has a preview of the latest TV vehicle for the Poster Boy of Pop ScienceTM, Science Britannica. In the few brief lines of description we get told, amongst other thing, the following:

Over the three episodes, Professor Brian will teach us what science really is and about the British pioneers like Sir Isaac Newton who have helped shape it over the centuries.

and:

Episode one of Science Britannica takes a look at the scientists themselves and how they were able to put personal desires and beliefs aside in their quests to discover the scientific truths.

[my emphasis]

Now anyone who has been regularly reading my blog over the years or who is up to date on the historical research on good old Isaac can stop reading and go away and drink a nice cup of tea or read a good book or maybe both at the same time if they’re feeling adventurous. For those few who bother to stick around I shall one again explain why the two statements quoted above are from the standpoint of the historian of science more than somewhat unfortunate.

For about the last sixty years an awful lot of excellent historians of science and Newton experts have very clearly and definitively shown that Isaac Newton’s scientific work was totally dependent on and driven by his very deep personal beliefs in religion, prisca theologia and alchemy and that he believed that he and he alone had been personally selected by (his) God to reveal the secrets of God’s universe that had been know to the ancients but had become lost through the degeneration of humanity. I don’t know but somehow I don’t think that quite equates with putting aside ones personal desires and beliefs.

 

 

4 Comments

Filed under History of science, Myths of Science, Newton

“If he had lived, we might have known something”

The title of this post is Newton’s rather surprising comment on hearing of the early death of the Cambridge mathematician Roger Cotes at the age of 33 in 1716. I say rather surprising, as Newton was not known for paying compliments to his mathematical colleagues, rather the opposite. Newton’s compliment is a good measure of the extraordinary mathematical talents of his deceased associate.

Cotes the son of rector from Burbage in Leicestershire born 10th July 1682 is a good subject for this blog for at least three different reasons. Firstly he is like many of the mathematicians portrayed here relatively obscure although he made a couple of significant contributions to the history of science. Secondly one of those contributions, which I’ll explain below, is a good demonstration that Newton was not a ‘lone’ genius, as he is all too often presented. Lastly he just scraped past the fate of Thomas Harriot, of being forgotten, having published almost nothing during his all too brief life, he had the luck that his mathematical papers were edited and published shortly after his death by his cousin Robert Smith thus ensuring that he wasn’t forgotten, at least by the mathematical community.

Cotes was recognised as a mathematical prodigy before he was twelve years old. He was taken under the wing of his uncle, Robert Smith’s father, and sent to St Paul’s School in London from whence he proceeded to Trinity College Cambridge, Newton’s college, in 1699. Newton whilst still nominally Lucasian Professor had already departed for London and the Royal Mint. Cotes graduated BA in 1702. Was elected minor fellow in 1705 and major fellow in 1706 the same year he graduated MA. His mathematical talent was recognised on all sides and in the same year he was nominated, as the first Plumian Professor of Astronomy and Natural Philosophy, still not 23 years old. However he was only elected to this position on 16th October 1707. It should be noted that the newly created Plumian Chair was only the second chair for the mathematical sciences in Cambridge following the creation of the Lucasian Chair in 1663. In comparison, for example, Krakow University in Poland, the first humanist university outside of Northern Italy, already had two dedicated chairs for the mathematical sciences in the middle of the sixteenth century. This illustrates how much England was lagging behind the continent in its promotion of the mathematical sciences in the Early Modern Period.

Cotes election to the Plumian chair was supported by Richard Bentley, Master of Trinity, and by William Whiston, in the meantime Newton’s successor as Lucasian professor, who claimed to be “a child to Mr Cotes” in mathematics but was opposed by John Flamsteed, the Astronomer Royal, who wanted his former assistant John Witty to be appointed. In the end Flamsteed would be proven right, as Cotes was shown to be a more than somewhat mediocre astronomer.

Cotes’ principle claim to fame is closely connected to Newton and his magnum opus the Principia. Newton gave the task of publishing a second edition of his masterpiece to Richard Bentley, who now took on the role filled by Edmond Halley with the first edition. Now Bentley who was a child prodigy, a brilliant linguist and a groundbreaking philologist was anything but a mathematician and he delegated the task of correcting the Principia to his protégé, Cotes in 1709. Newton by now an old man and no longer particularly interested in mathematical physics had intended that the second edition should basically be a reprint of the first with a few minor cosmetic corrections. Cotes was of a different opinion and succeeded in waking the older man’s pride and convincing him to undertake a complete and thorough revision of the complete work. This task would occupy Cotes for the next four years. As well as completely reworking important aspects of Books II and III this revision produced two highly significant documents in the history of science, Newton’s General Scholium at the end of Book III, a general conclusion missing from the first edition, and Cotes’ own preface to the book. Cotes’ preface starts with a comparison of the scientific methodologies of Aristotle, the supporters of the mechanical philosophy, where here Descartes and Leibniz are meant but not named, and Newton. He of course come down in favour of Newton’s approach and then proceeds to that which Newton has always avoided a discussion of the nature of gravity introducing into the debate, for the first time, the concept of action at a distance and gravity as a property of all bodies. The second edition of Principia can be regarded as the definitive edition and is very much a Newton Cotes co-production.

Cotes’ posthumously published mathematical papers contain a lot of very high class but also highly technical mathematics to which I’m not going to subject my readers. However there is one of his results that I think should be better known, as the credit for it goes to another. In fact a possible alternative title for this post would have been, “It’s not Euler’s Formula it’s Cotes’”.

It comes up fairly often that mathematicians and mathematical scientists are asked what their favourite theorem or formula is. Almost invariably the winner of such poles polls is what is known technically as Euler’s Identity

e + 1 = 0

 

Now this is just one result with x = π of Euler’s Formular:

cosx  + isinx = eix

Where i is the square root of -1, e is Euler’s Number the base of natural logarithms and x is an angle measured in radians. This formula can also be expressed as a natural logarithm thus:

ln[cosx + isinx] = ix

and it is in this form that it can be found in Cotes’ posthumous mathematical papers.

As one mathematics’ author expresses it:

This identity can be seen as an expression of the correspondence between circular and hyperbolic measures, between exponential and trigonometric measures, and between orthogonal and polar measures, not to mention between real and complex measures, all of which seemed to be within Cotes’ grasp.

Put simply, for the non-mathematical readers, this formula is one of the most important fundamental relationships in analysis.

Cotes died unexpectedly on 5th June 1716 of a, “Fever attended with a violent Diarrhoea and constant Delirium”. Despite his important contributions to Newton’s Principia Cotes is largely forgotten even by mathematicians and their ilk so the next time somebody waxes lyrical about Euler’s Formula you can gentle point out to them that it should actually be called Cotes’ Formula.

 

7 Comments

Filed under History of Astronomy, History of Mathematics, History of Physics, Newton

5 Brilliant Mathematicians – 4 Crappy Commentaries

I still tend to call myself a historian of mathematics although my historical interests have long since expanded to include a much wider field of science and technology, in fact I have recently been considering just calling myself a historian to avoid being pushed into a ghetto by those who don’t take the history of science seriously. Whatever, I have never lost my initial love for the history of mathematics and will automatically follow any link offering some of the same. So it was that I arrived on the Mother Nature Network and a blog post titled 5 brilliant mathematicians and their impact on the modern world. The author, Shea Gunther, had actually chosen 5 brilliant mathematicians with Isaac Newton, Carl Gauss, John von Neumann, Alan Turing and Benoit Mandelbrot and had even managed to avoid the temptation of calling them ‘the greatest’ or something similar. However a closer examination of his commentaries on his chosen subjects reveals some pretty dodgy not to say down right crappy claims, which I shall now correct in my usual restrained style.

He starts of fairly well on Newton with the following:

There aren’t many subjects that Newton didn’t have a huge impact in — he was one of the inventors of calculus, built the first reflecting telescope and helped establish the field of classical mechanics with his seminal work, “Philosophiæ Naturalis Principia Mathematica.” He was the first to decompose white light into its constituent colors and gave us, the three laws of motion, now known as Newton’s laws.

But then blows it completely with his closing paragraph:

We would live in a very different world had Sir Isaac Newton not been born. Other scientists would probably have worked out most of his ideas eventually, but there is no telling how long it would have taken and how far behind we might have fallen from our current technological trajectory.

This is the type of hagiographical claim that fans of great scientists tend to make who have no real idea of the context in which their hero worked. Let’s examine step by step each of the achievements of Newton listed here and see if the claim made in this final paragraph actually holds up.

Ignoring the problems inherent in the claim that Newton invented calculus, which I’ve discussed here, the author acknowledges that Newton was only co-inventor together with Leibniz and although Newton almost certainly developed his system first it was Leibniz who published first and it was his system that spread throughout Europe and eventually the world so no changes here if Isaac had not been born.

Newton did indeed construct the first functioning reflecting telescope but as I explained here it was by no means the first. It would also be fifty years before John Hadley succeeded in repeating Newton’s feat and finally making the commercial production of reflecting telescopes viable. However Hadley also succeeded in making working models of James Gregory’s reflecting telescope, which actually predated Newton’s and it was the Gregorian that, principally in the hands of James Short, became the dominant model in the eighteenth century. Although to be fair one should mention that William Herschel made his discoveries with Newtonians. Once again our author’s claim fails to hold water.

Sticking with optics for the moment it is a little know and even less acknowledge fact that the Bohemian physicus and mathematician Jan Marek Marci (1595 – 1667) actually decomposed white light into its constituent colours before Newton. Remaining for a time with optics, James Gregory, Francesco Maria Grimaldi, Christian Huygens and Robert Hooke were all on a level with Newton although none of them wrote such an influential book as Newton’s Optics on the subject. Now this was not all positive. Due to the influence won through the Principia, The Optics became all dominant preventing the introduction of the wave theory of light developed by Huygens and Hooke and even slowing down its acceptance in the nineteenth century when proposed by Fresnel and Young. If Newton hadn’t been born optics might even have developed and advance more quickly than it did.

This just leaves the field of classical mechanics Newton real scientific monument. Now, as I’ve pointed out several times before the three laws of motion were all borrowed by Newton from others and the inverse square law of gravity was general public property in the second half of the seventeenth century. Newton’s true genius lay in his mathematical combination of the various elements to create a whole. Now the question is how quickly might this synthesis come about had Newton never lived. Both Huygens and Leibniz had made substantial contribution to mechanics contemporaneously with Newton and the succeeding generation of French and Swiss-German mathematicians created a synthesis of Newton’s, Leibniz’s and Huygens’ work and it is this that is what we know as the field of classical mechanics. Without Newton’s undoubtedly massive contribution this synthesis might have taken a little longer to come into being but I don’t think the delay would have radically changed the world in which we live.

Like almost all great scientists Newton’s discoveries were of their time and he was only a fraction ahead of and sometimes even behind his rivals. His non-existence would probably not have had that much impact on the development of history.

Moving on to Gauss we will have other problems. Our author again makes a good start:

Isaac Newton is a hard act to follow, but if anyone can pull it off, it’s Carl Gauss. If Newton is considered the greatest scientist of all time, Gauss could easily be called the greatest mathematician ever.

Very hyperbolic and hagiographic but if anybody could be called the greatest mathematician ever then Gauss would be a serious candidate. However in the next paragraph we go off the rails. The paragraph starts OK:

Carl Friedrich Gauss was born to a poor family in Germany in 1777 and quickly showed himself to be a brilliant mathematician. He published “Arithmetical Investigations,” a foundational textbook that laid out the tenets of number theory (the study of whole numbers).

So far so good but then our author demonstrates his lack of knowledge of the subject on a grand scale:

Without number theory, you could kiss computers goodbye. Computers operate, on a the most basic level, using just two digits — 1 and 0

Here we have gone over to the binary number system, with which Gauss book on number theory has nothing to do, what so ever. In modern European mathematics the binary number system was first investigated in depth by Gottfried Leibniz in 1679 more than one hundred years before Gauss wrote his Disquisitiones Arithmeticae, which as already stated has nothing on the subject. The use of the binary number system in computing is an application of the two valued symbolic logic of George Boole the 1 and 0 standing for true and false in programing and on and off in circuit design. All of which has nothing to do with Gauss. Gauss made so many epochal contributions to mathematics, physics, cartography, surveying and god knows what else so why credit him with something he didn’t do?

Moving on to John von Neumann we again have a case of credit being given where credit is not due but to be fair to our author, this time he is probably not to blame for this misattribution.  Our author ends his von Neumann description as follows:

Before his death in 1957, von Neumann made important discoveries in set theory, geometry, quantum mechanics, game theory, statistics, computer science and was a vital member of the Manhattan Project.

This paragraph is fine and if Shea Gunther had chosen to feature von Neumann’s invention of game theory or three valued quantum logic I would have said fine, praised the writer for his knowledge and moved on without comment. However instead our author dishes up one of the biggest myths in the history of the computer.

he went on to design the architecture underlying nearly every single computer built on the planet today. Right now, whatever device or computer that you are reading this on, be it phone or computer, is cycling through a series of basic steps billions of times over each second; steps that allow it to do things like render Internet articles and play videos and music, steps that were first thought up by John von Neumann.

Now any standard computer is called a von Neumann machine in terms of its architecture because of a paper that von Neumann published in 1945, First Draft of a Report on the EDVAC. This paper described the architecture of the EDVAC one of the earliest stored memory computers but von Neumann was not responsible for the design, the team led by Eckert and Mauchly were. Von Neumann had merely described and analysed the architecture. His publication caused massive problems for the design team because the information now being in the public realm it meant that they were no longer able to patent their innovations. Also von Neumann’s name as author on the report meant that people, including our author, falsely believed that he had designed the EDVAC. Of historical interest is the fact that Charles Babbage’s Analytical Engine in the nineteenth century already possessed von Neumann architecture!

Unsurprisingly we walk straight into another couple of history of the computer myths when we turn to Alan Turing.  We start with the Enigma story:

During World War II, Turing bent his brain to the problem of breaking Nazi crypto-code and was the one to finally unravel messages protected by the infamous Enigma machine.

There were various versions of the Enigma machine and various codes used by different branches of the German armed forces. The Polish Cipher Bureau were the first to break an Enigma code in 1932. Various other forms of the Enigma codes were broken by various teams at Bletchley Park without Turing. Turing was responsible for cracking the German Naval Enigma. The statement above denies credit to the Polish Cipher Bureau and the other 9000 workers in Bletchley Park for their contributions to encoding Enigma.

Besides helping to stop Nazi Germany from achieving world domination, Alan Turing was instrumental in the development of the modern day computer. His design for a so-called “Turing machine” remains central to how computers operate today.

I’ve lost count of how many times that I’ve seen variations on the claim in the above paragraph in the last eighteen months or so, all equally incorrect. What such comments demonstrate is that their authors actually have no idea what a Turing machine is or how it relates to computer design.

In 1936 Alan Turing, a mathematician, published a paper entitled On Computable Numbers, with an Application to the Entscheidungsproblem. This was in fact one of four contemporaneous solutions offered to a problem in meta-mathematics first broached by David Hilbert, the Entscheidungsproblem. The other solutions, which needn’t concern us here, apart from the fact that Post’s solution is strongly similar to Turing’s, were from Kurt Gödel, Alonso Church and Emil Post. Entscheidung is the German for decision and the Entscheidungsproblem asks if for a given axiomatic system whether it is also possible with the help of an algorithm to decide if a given statement in that axiom system is true or false. The straightforward answer that all four men arrived at by different strategies is that it isn’t. There will always be undecidable statements within any sufficiently complex axiomatic system.

Turing’s solution to the Entscheidungsproblem is simple, elegant and ingenious. He hypothesised a very simple machine that was capable of reading a potentially infinite tape and following instruction encoded on that tape. Instruction that moved the tape either right or left or simply stopped the whole process. Through this analogy Turing was able to show that within an axiomatic system some problems would never be Entscheidbar or in English decidable. What Turing’s work does is, on a very abstract level, to delineate the maximum computability of any automated calculating system. Only much later, in the 1950s, after the invention of electronic computers a process in which Turing also played a role did it occur to people to describe the computational abilities of real computers with the expression ‘Turing machine’.  A Turing machine is not a design for a computer it is term used to described the capabilities of a computer.

To be quite open and honest I don’t know enough about Benoit Mandelbrot and fractals to be able to say whether our author at least got that one right, so I’m going to cut him some slack and assume that he did. If he didn’t I hope somebody who knows more about the subject that I will provide the necessary corrections in the comments.

All of the errors listed above are errors that could have been easily avoided if the author of the article had cared in anyway about historical accuracy and truth. However as is all to often the case in the history of science or in this case mathematics people are prepared to dish up a collection of half baked myths, misconceptions and not to put too fine a point on it crap and think they are performing some sort of public service in doing so. Sometimes I despair.

 

17 Comments

Filed under History of Computing, History of Logic, History of Mathematics, History of Optics, History of Physics, History of science, Myths of Science, Newton