The Great Man paradox

Over the years a fair number of the blog posts here have been fairly speculative, basically me thinking out loud about something that has recently crossed my mind or my path. What follows is one of those posts and as I begin writing I have a germ of an idea what I think I want to say but I can’t guarantee that what will come out is what I initial intended or that it will be particularly illuminating or informative. At the end of last week I had the following very brief exchange with zoologist and historian, Matthew the Mancunian Maggot Man (@matthewcobb)

MC: What would have happened if Einstein fell under a tram in 1900? What difference would it have made, for how long?

Me: Not a lot, Poincaré was almost there and others were working on the various problems. I’d guess at most a ten-year delay

MC: So are there any true examples of ‘great men’ or is science all over-determined?

My instantaneous response to Mathew’s last comment was yes there are great men in the history of science and Einstein was certainly one of them but not in the sense that people usually mean when they use the term. It is this response that I will try to unpack and elucidate here.

When people describe Einstein as a great man of science what they usually mean is that if he hadn’t lived, see Matthew’s original question, we ‘wouldn’t have the theories of relativity’ or ‘physics would have been held back for decades or even longer’. Both of the expression in scare quote are ones that occur regularly following statements along the lines of if X hadn’t existed we wouldn’t have Y and both are expressions that I think should be banned from #histSTM. They should be banned because they are simply not true.

Let’s take a brief look at the three papers Einstein published in 1905 that made his initial reputation. The paper on quantum theory, for which he would eventually get his Nobel Prize, was, of course, in response to Planck’s work in this field and was a topic on which many would work in the first half of the twentieth century. The so-called black body problem, which sparked off the whole thing, was regarded as one of the most important unsolved problems in physics at the turn of the century. Brownian motion, the subject of the second paper, was another hot topic with various people producing mathematically formulations of it in the nineteenth century. In fact Marian Smoluchowski produced a solution very similar to Einstein’s independently, which was published in 1906. This just leaves Special Relativity. The problem solved here had been debated ever since it had been known that the Clerk Maxwell equations did not agree with Newtonian physics. We have both Lorentz and FitzGerald producing the alternative to the Newtonian Galilean transformations that lie at the heart of Einstein’s Special Relativity theory. The Michelson-Morley experiment also demanded a solution. Poincaré had almost reached that solution when Einstein pipped him at the post. The four dimensional space-time continuum now considered so central to the whole concept was delivered, not by Einstein, but by his one time teacher Minkowski. Minkowski’s formulation was, of course, also central for the General Theory of Relativity; the solution for the field equations of which were found independently by Einstein and Hilbert, although Hilbert clearly acknowledged Einstein’s priority.

Albert Einstein in 1904 (age 25)
Lucien Chavan [1] (1868 – 1942), a friend of Einstein’s when he was living in Berne. – Cropped from original at the Historical Museum of Berne.
Source: Wikimedia Commons

Without going into a lot of detail it should be clear that Einstein is solving problems on which a number of other people are working and making important contributions. He is not pulling new physics out of a hat but solving problems over-determined by the field of physics itself.

What about other ‘great men’? The two most obvious examples are also physicists, Galileo and Newton. I’ve already done a major demolition job on Galileo several years ago, in which I show that everything he worked on was being worked on parallel by other highly competent scholars that you can read here. And a more recent version here.

Galileo Galilei. Portrait by Leoni
Source: Wikimedia Commons

So what about Newton?As should be well known Leibnitz and Newton both developed calculus roughly contemporaneously, even more important, as I explained here, they were both building on foundations laid down by other leading seventeenth-century mathematicians. Newton was anticipated in his colour theory of white light by the Bohemian scholar Jan Marek Marci. As I’ve explained here and here Newton was only one of three people who developed a reflecting telescope in the 1660s. Robert Hooke anticipated and probably motivated Newton on the theory of universal gravity and Newton’s work on dynamics built on the work of many others beginning with Tartaglia and Benedetti in the sixteenth century. His first law of motion was from Isaac Beeckman via Descartes and the second from Christiaan Huygens from whose work he also derived the law of gravity. Once again we have a physicist working on problem of his time that were being worked actively on by other competent scholars.

Copy of a portrait of Newton at 46 in 1689 by Godfrey Kneller
Source: Wikimedia Commons

I think this brief analysis that the work of these ‘great men’, Einstein, Galileo and Newton, was to a large extent over-determined that is dictated by the scientific evolution of their respective times and their finding solutions to those problems, solutions that others also found contemporaneously, does not qualify them as special, as ‘great men’.

Having said all of that I would be insane to deny that all three of these physicists are, with right, regarded as special, as great men, so what is the solution to this seeming paradox?

I think the answer lies not in the fact that they solved the problems that they solved but in the breadth and quality of their work. Each of them did not just solve one major problem but a whole series of them and their solutions were of a quality and depth unequalled by others also offering solutions. This can be illustrated by looking at Hooke and Newton on gravity. Hooke got there first and there are good grounds for believing that his work laid the foundations for Newton’s. However whereas Hooke’s contribution consist of a brief series of well founded speculations, Newton built with his Principia a vast mathematical edifice that went on to dominate physics for two hundred years. Put simply it is not the originality or uniqueness of their work but the quality and depth of it that makes these researchers great men.

 

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40 responses to “The Great Man paradox

  1. Huenemann

    Very provocative reflections! I remember that at the beginning of one of the old “Mechanical Universe” lectures, the professor argues that if he had to choose between saving Newton’s writing of the Principia and saving Michelangelo’s painting of the Sistine Chapel, he would save the painting, since surely someone would have come along with Newton’s insights, and there’s no guarantee that anyone else would or could have come up with that painting.

    • On the whole I agree with him

      • I loved this post and loved Charlie’s response -to which I agree with his professor. As far as I can see it, it is indeed that they solved the problems. Someone else surely would have come along to do it as you suggest so in that sense it is the esteem bordering on veneration of them that is misguided in some sense –but our culture loves heroes and heroes are the guys who solve the problem. It’s the same with the Wright Brothers or anything else…. the problem was on the cusp of being solved by many but as a culture we tend to hold up the paradigm game-changers as opposed to a life of good work. Visionaries.

      • For me, Leanne Ogasawara (below, above?) really gets to the heart of this when she says, “our culture loves heroes.” For anyone who knows something about the history of math/science (or the history of anything else for that matter,) the label of “great” is always in the context of other contributors. The problem arises when the context is missing, or not understood, and “great” gets used to support a variety of pop cultural agendas. The solution is to explicitly include some context and not present ones subject in a vacuum, or at least call attention to the fact that there are other contributors.

    • @Paul Engle Your comment has inspired my next post, coming soon to this venue ;))

    • The Mechanical Universe series was by Caltech’s David Goodstein, FYI. (I used to live in Pasadena, and it was a regular on one of the local stations).

  2. I always thought it was kind of interesting that Einstein is both a “victim” and a beneficiary of the tendency to look at Science as the product of a few “Great Men”. As the “Great Man” of Relativity, his reputation has been enhanced at the expense of Poincare and Lorentz.

    On the other hand, his contributions to early Quantum Mechanics tends to get relegated to the photo-electric effect, with Planck, deBroglie and Schrodinger taking center stage.

  3. Matt Ridley has very similar ideas of the “big man” concept.

  4. In Virtue Epistemology and Virtue Ethics, we work with the concept of exemplars. (It’s different from Kuhn’s use of the term.) As both Socrates/Plato and Aristotle pointed out, the way to learn virtue is to associate with (be mentored by) people who embody the virtues to the greatest extent. I would argue that the Greats are our virtual epistemic mentors, whose courses of inquiry come to us from historians (so don’t screw it up, mate!) and provide us with the guidance we need to approach epistemic virtue in ourselves. Others could have done the individual pieces of work, but whose example should we follow?

    • What you are espousing is in fact the Renaissance theory of historiography. For Renaissance historians history was not about factual accounts of the past but the telling of stories, note history and story are etymologically related, about prominent historical figures to illustrate virtuous behaviour.

      As a historian I seriously doubt that we should return to this form of historiography and certainly not when applied to figures from the history of science.

  5. In my perversity, your essay reminded me of the Captain America movies. In the first of these flicks, a rather wimpy but patriotic kid is turned into a super soldier by scientific hocus pocus. He wants to fight—World War II is in progress—but the powers that be would rather use him as a glamorous mascot to pep up public morale. Of course he eventually rebels and goes to war, but the powers that be have a point. Super soldiers really don’t make much sense from a cost/benefit point of view. Artillery shells, which do most of the killing on real battlefields, don’t care whether you’re tremendously (and expensively!) well trained or just another grunt, so with the possible exception of a few highly specialized missions, it doesn’t pay to invest too much in any given recruit and the greatest practical value of the Green Berets, Seals, Howling Commandos, and other elite forces is probably in the contribution they make to public relations. Mutatis mutandis, the same is true of the Great Men of Science. A couple of dozen bearded profs might have figured out everything Einstein figured out, but they wouldn’t have made so admirable a recruiting tool for new scientists or lent sufficient glamor to arcane physics to get politicians to fund research on a massive scale. Real science is utterly mysterious to most people and deadly dull to them to boot. So I tend to be more tolerant of the smoke and mirrors involved in the erection of idols. Smoke and mirrors are necessary things.

    • B'Rat

      I’m rather sceptic about this argument. In my experience the “Great Men of Science” narrative is a fundamental part of the common man perception of Science as an arcane discipline impenetrable to the uninitiated: as soon as a kid shows some interest in it, it is immediately assumed that he’s blessed with some of that spark that made Great Men Great, a spark that makes penetrating the recondite mysteries of numerical knowledge possible and whose absence in the common folk advise them to not even attempt a similar venture.
      As such, I fear that the Great Men narrative is a factor in the abysmal scientific education of the masses. If schools were to somehow start teaching that Great Scientists are but the tip of a vast iceberg of contributions from a myriad of less known figures, maybe Science would seem less exclusive.

  6. David K Love

    What about Kepler? Surely if the “great men (and women!)” label can be applied to anyone, it is Kepler. He was surely unique, not merely in coming up with his laws of planetary motion but also (and as one of the inspirations for discovering these laws) beginning the necessary move of astronomy from a branch of geometry towards physics. He achieved this in spite of a frequently tragic personal life. His interests and writings also spanned a whole range of other subjects. In my view, definitely a “great man”. (You have yet to comment on my book “Kepler and the Universe”, other than to criticise the subtitle chosen by my publisher, but I shall be interested to know what you make of it if ever you read it.)

    • Galileo and Einstein are considered by the general public as being the game-changers. Just between me and you, though, I agree Kepler is the true visionary. Your book looks wonderful. I just ordered it and am already looking forward to reading it!

      • David K Love

        Thank you! Do let me know what you think of it.

      • Thony, David, Leanne – enjoying reading the post and the discussion! As I read some about Kepler, his life, his time, and trying to understand his approaches listed in his Astronovia Nova and his “war with Mars” I too would separate Kepler a bit from the others: In several steps he jumped over his own previous ideas (which some seem crude now a days) just by mathematical/physical surgery. After five years in trouble he broke the >2000 years massively settled axiom of circular orbits (philosophical background). I see this special point at Kepler for a single thinker with respect to ideas “lying in the air” – therefore he is more of an outstanding pioneering single scientist. Not missing the huge achievements of the others!
        Kurt

    • Kepler is in fact a first class scientific scholar, who, in my opinion, contributed far more to the evolution of modern science than Galileo but interestingly he is seldom regarded as one of the ‘great men’ of science. This is perhaps another reason to move away from the ‘great man’ concept completely as it can be shown, not just in the case of Kepler, to be rather arbitrary.

      On Kepler’s uniqueness or originality, a closer look at his work shows, like all other, that his work was well within the mainstream scientific endeavours of his times. Just looking at his greatest achievement, his three laws of planetary motion. Since the middle of the fifteenth century astronomers had been well aware that the planetary models and data of Ptolemaeus were not adequate for the tasks demanded of them and had been working on improving them. Peuerbach’s New Planetary Theory, used by Copernicus, Galileo and Kepler as a textbook, actually contains an elliptical orbit for Mercury (I think, I might be wrong and it’s Mars). Tycho’s work was devoted to improving the data and models for planetary orbits and without Tycho’s observations Kepler could not have done what he did. Yes, Kepler made the breakthrough but had ne not I’m fairly certain somebody else would have done not not too far in the future.

      • Mercury. However, Aiton’s translation uses the term ‘oval’:

        Sixth, from what has been said it appears clearly that the center of the epicycle of Mercury, on account of the motions stated above, does not, as in the cases of the other planets, describe the circular circumference of the deferent but rather the periphery of a figure that resembles a plane oval.

        In a footnote, he adds “Peurbach was the first European to describe the curve as similar to an ellipse, though it had been so described by al-Zarqali in the eleventh century”.

        But the important point is that Peuerbach is not talking about the orbit in our sense. For the inner planet Mercury, the epicycle itself corresponds to the orbit around the sun (under the geocentric-to-heliocentric transformation), not the path of center of the epicycle. This is not a real anticipation of Kepler’s elliptical orbits. Is there any evidence at all that this influenced Kepler?

        Was Kepler’s work “well within the mainstream scientific endeavours of his times”? Well, yes and no. Bringing physics into the discussion—that was a break from tradition, and met with disapproval even by Kepler’s Copernican mentor Maestlin, as I recall.

        OTOH, the technical tools Kepler’s wielded were well in the mainstream tradition of mathematical astronomy of the time.

        Finally, if Kepler had fallen under a carriage, most likely the elliptical orbits would eventually have been derived from Newtonian mechanics. (Or Huygenian-Leibnizian mechanics, if you throw Newton under a carriage too.)

      • I had another look at the essay “Mercury Theory from Antiquity to Kepler” in Gingerich’s The Eye of Heaven. Gingerich points out that a good deal of the classical difficulties with Mercury’s orbit stemmed from bad observations, not just the ellipticity.

        As for the oval orbit: Ptolemy threw in an additional epicycle (or “epicyclet”, as Gingerich calls it); “this small crank simply pushes the epicycle in and out during the course of a year. Various commentators [here Gingerich cites Puerbach, plus modern historians] have graphed the oval-shaped effective deferent produced in this manner, and Hartner [1955] has shown that it is almost indistinguishable from an ellipse.” In a footnote, Gingerich adds, “A sixteenth-century Castilian manuscript …shows the effective deferent as a rounded lozenge.”

        I have not yet been able to determine if Puerbach’s original Latin text used a word equivalent to “oval”, or to “ellipse”. In any case, the effective deferent is really a representation of the sun’s orbit around the earth, or the earth’s orbit once you make the switch to a heliocentric perspective.

        This is an instance of the perennial historical problem of anticipations—spurious or real? To cite a far more famous instance: does Newton’s corpuscular theory of light count as a valid anticipation of the quantum theory of photons?

  7. First off, I agree completely with the main message of this post.

    That said, the one case traditionally cited is the discovery of general relativity. Einstein himself once said that while special relativity was in the air, general relativity would have been delayed a long time (decades?) without his work. (Unfortunately I haven’t been able to locate the exact quote just now.) It’s fun to speculate. Good arguments can be made both ways.

    OT1H: If we look at what other people were doing at the time, trying to create a theory of gravity compatible with SR (Mie, Abraham, Nordström), no one was following anything like Einstein’s path. (See Pais Chapter 13 for a brief account.) To quote Jürgen Renn (“Classical Physics in Disarray:
    The Emergence of the Riddle of Gravitation”, in The Genesis of General Relativity):

    How could gravitation be made to fit into the framework of the relativity theory of 1905? A modification of Newton’s law of gravitational attraction was clearly necessary since it implies an instantaneous action at a distance … It quickly turned out that it was not at all difficult to adapt Newton’s law to this spatio-temporal framework; as the work of Poincaré, Minkowski and others between 1905 and 1910 showed, there were even several possibilities…

    Hilbert’s independent discovery of the field equation is really a red-herring, since (a) he was solving a fairly well-defined problem using mostly standard tools; the hard work of framing the problem had been done by Einstein during the preceding 7 years, mostly by himself; (b) Hilbert only really started working on the problem after Einstein’s Göttingen visit, where he had given 6 two hour lectures and stayed at Hilbert’s house. The lectures would have included Einstein’s “near miss” version of the field equation. In short, Hilbert got started when the problem had been mostly reduced to solving mathematical difficulties. (Even there, Hilbert had some crucial help from Emmy Noether.)

    OTOH: There’s more than one way to discover GR. In Gravitation (the “phone book”, by Misner, Thorne, and Wheeler), Chapter 7 discusses the so-called field-theory route, one seen only with 20/20 hindsight:

    Each of these theories [outlined in exercises] has significant shortcomings, and all fail to agree with observations. The best of them is the tensor theory… which, however, is internally inconsistent and admits no exact solutions. This difficulty has been attacked in recent times by [here they list 6 different authors, papers from the 50s and 60s] They show how the flat-space tensor theory may be modified within the spirit of present-day relativistic field theory to overcome these inconsistencies. By this field-theory route…they arrive uniquely at standard 1915 general relativity. Only at this end point does one finally recognize, from the mathematical form of the equations, that what ostensibly started out as a flat-space theory of gravity is really Einstein’s theory, with gravitation being a manifestation of the curvature of spacetime.

    While it’s impossible to say if this work would have been done without the model of Einstein’s theory, it seems that his remarkable insights are not a necessary condition for the discovery of the final theory.

  8. The case of special relativity also presents some interesting questions. Here there is no real doubt that lots of people got close, one way or another. The most nuanced and thoughtful treatment I’ve seen of the issues is Olivier Darrigol, “The Mystery of the Einstein–Poincaré Connection”, Isis, Vol. 95, No. 4 (December 2004), pp. 614-626.

    I happen to think that Poincaré deserves more credit than many physicists (e.g., Pais) are willing to give. There’s a strong case to be made that Poincaré understood the issues just as well as Einstein. The Poincaré group is well named. But if you spend enough time looking at the history, it becomes clear that Einstein’s 1905 paper was far more influential within the community of physicists of the time.

    Why was that? A big reason, I believe, is that Einstein explained the issues in just the right way. Poincaré’s treatment was perhaps a little to mathematical and philosophical to resonate with most physicists. Nowadays every physicists has “pay attention to the symmetry groups” practically tatooed on the brain, but it was a totally different story in 1905. (Also see the preface to Sternberg’s Group Theory and Physics.)

    Not just what you know, but how you communicate it.

  9. Actually without the work of Gauss and Riemann, who get no mention here, Einstein’s or Poincare’s physics were not possible.

    • I thought the question was, without Einstein (“what if he fell under a tram in 1900”), would general relativity have been discovered anyway, and if so, when?

      Not, would Einstein have been able to do what he did without the work of his predecessors? That’s a completely different question.

      For the second question, there’s nothing special about science. Take away all the predecessors of Shakespeare, and you don’t get Hamlet.

  10. And sometimes you really do get a lone genius who changes everything. Consider what you’re doing right now: reading something on a computer screen. What underlies it is a design methodology for digital circuits. That was invented in Claude Shannon’s 1937 master’s thesis at MIT, which depended only on George Boole’s invention of symbolic logic applied to relay control systems, both of which were in existence by 1860.

    Shannon himself said that there was no great leap of insight – he simply happened to be the first person who knew both fields and had a reason to solve the problem of ad-hoc relay control system design. It was a suggestion of his thesis advisor.

    • But the point is, surely someone else would have come along at some point who knew both fields and would therefore have reached the same solution.
      Lone genius usually means one who is not in touch with others, working by themselves. If Shannon was following the suggestion of his thesis advisor, that hardly makes him a lone genius, rather a well networked and encouraged one.

    • technicshistory

      Others had basically the same insight, independently, e.g. Zuse in Germany and Nakashima in Japan. Moreover, Shannon’s work was not really a critical path in the history of computing. People built working computers without modeling them in terms of Boolean algebra.

  11. Now, who is next? All three have contributed lot. But science is still facingvlot of problems especially in astro physics. The cause of gravity is still a mystery.

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  13. I wonder whether we are looking in the wrong place when we limit ‘great men’ to scientific discovery itself, rather than including creating the conditions for scientific discoveries to be made.
    Suppose Tycho, instead of just losing part of his nose in a duel, had developed sepsis and died. Without his observational data, Kepler could never have proved that the orbit of Mars was an ellipse. Precise measurement of positions of stars and planets might have waited until the development of the transit circle by Ole Rømer in 1690, over 100 years later.
    Similarly in the last decade of the 19th Century and the early decades of the 20th Century, George Ellery Hale persuaded a series of philanthropists to fund ever-larger telescopes at Yerkes, Mount Wilson, and Mount Palomar. If we consider the discoveries made at just the last two telescopes, there is a case for seeing Hale as a “great man”, even though the discoveries were actually made by others such as Shapley, Hubble, Baade and Sandage.

  14. This article made me think of the Antikythera mechanism, and its (unknown) designer. If it was as advanced as it seems, this person’s absence from the historical record makes me think they went to the sea floor along with the device. Wikipedia says that devices of similar complexity weren’t seen until the 1300s so that is quite a gap.

  15. zshrdlu

    What about Claude E. Shannon?

  16. The comments seems to have drifted into a general discussion of: “Is science a social enterprise, with many contributors besides the iconic ‘Great Men’?”

    And the answer is, obviously yes! And so is art, politics, literature, …..

    But the post raised a different question: to what degree is science ‘overdetermined’? Would we still end up with Newtonian physics without Newton, general relativity without Einstein, elliptical orbits without Kepler…. And with how much of a delay?

    Or to take a different slant: if Archimedes had turned his attention to falling bodies, would we have had Newtonian mechanics a thousand years earlier? (I think not, but YMMV.)

    Obviously art and literature are not overdetermined to the same degree. Partly that’s because the exact manner of expression is 90% of what we value in those fields. Hamlet isn’t just a play about the prince of Denmark.
    (Shakespeare wasn’t the first to do that). On the other side of the ledger, without Newton I’m quite sure we would never have had a book titled “Philosophiae Naturalis Principia Mathematica” with the same sequence of propositions proved in the same manner. But that’s not what matters for Newtonian mechanics.

    • A very astute comment by Michael Weiss

    • This is very true. Regarding Kepler, for example, we know from Jim Voelkel that the form, content and rhetorical strategy of the Astronomia Nova as a book was entirely contingent on Kepler’s unique personal situation. No one else would or could have written that book, and Kepler himself didn’t plan to write the book!

      It’s a really intriguing question about when, where and how the three laws of planetary motion would appear if Kepler was run over by a carriage on the way to Prague. Someone would have needed access to Tycho’s data (which was unlikely to have any equivalents for some time, if at all), and had the willingness to discard circular motion and incorporate physical causes into astronomy. Would Newtonian gravity had yielded the laws if Kepler’s laws (and the resulting very accurate Rudolphine Tables) didn’t yet exist? I don’t know.

      • I love this sort of counterfactual, much as most historians disparage it.

        I have no doubt that Kepler’s three laws would have been discovered eventually. The question is, how long. (My guess: 30 to 100 years.)

        First off, Tycho wasn’t making astronomical observations all by his lonesome. True enough, he stood head and shoulders above his contemporaries, but in very respectable second place you find the Landgrave of Hesse-Kassel. (For others, see “The contemporaries of Tycho Brahe” by Richard Jarrell in the Cambridge General History of Astronomy vol. 2A.)

        Second, this is before the invention of the telescope! Guaranteed you get lots of high quality observations after that.

        Third, what we call Newtonian mechanics was the work of many hands, as Thony already outlined in his post.

        Kepler’s second law is almost a trivial consequence of the conservation of angular momentum. The third law follows easily from the law of gravity for the special case of circular orbits, once you have the formula for centrifugal force (published by Huygens). The inverse square law itself was “in the air”.

        Deriving elliptical orbits from the inverse square law is not a walk in the park. Still, I’ve seen several different derivations. Once you have calculus, it’s not that hard—you’ll find equally hairy stuff in the first few decades after calculus arrived at the party. And calculus was coming with or without dear old Isaac.

        Finally, we have what you might call the ecological niche effect. Plenty of smart folk might have claimed some of the bounty, if Mr. Newton hadn’t gotten there first.

      • “Kepler’s second law is almost a trivial consequence of the conservation of angular momentum.”

        As Thony quotes:
        If your philosophy of [scientific] history claims that the sequence should have been A→B→C, and it is C→A→B, then your philosophy of history is wrong. You have to take the data of history seriously.

        Kepler’s second law came first; the concept of angular momentum conservation came much later. See:
        http://weatherglass.de/PDFs/Angular_momentum.pdf
        (particularly section 4)
        If your German is up to it, there is also a letter in the Euler archive:
        http://eulerarchive.maa.org/correspondence/letters/OO0153.pdf

        As I have previously commented:
        “Precise measurement of positions of stars and planets might have waited until the development of the transit circle by Ole Rømer in 1690, over 100 years later.”
        Certainly, they would have needed the invention of the filar micrometer (William Gascoigne, in the late 1630s, which later reached Robert Hooke through Richard Towneley). Hooke was trying to measure the parallax of Gamma Draconis in 1669, so we may assume that he knew of it before then.

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  18. The weekly reports from my summers in college selling books door-to-door included a field for nicknames. I chose “Kepler.”

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