Multiple discoveries - a rule rather than an exception?

Part 2 - Merton's multiple pieces of evidence

"…There is even a stronger feeling inspired of the presence of that Truth to which we all profess to minister, when we find our own discoveries, such as they are, coincide independently with the discoveries of other men. The voice which is heard by two at once appears to be more real and external - one is more sure that it is no personal and private fancy, no idiosyncratic peculiarity, no ringing in sick ears, no flashes seen by rubbing our own eyes."

William Rowan Hamilton, in a letter to John Herschel, Nov 23, 1846

Merton’s hypothesis states that all scientific discoveries are in principle multiples, that it is the singletons that require special explanation and that, on a closer look, they often end up being multiples.

As first, the hypothesis may seem a bit far-out and immune to testing and verification. One can declare even the historically known singletons to be multiples-in-principle or would-have-been multiples, since we don’t have a perfect knowledge of history, and so absence of evidence (that they are multiples) is not evidence of absence. But there’s no need for such sophistry. Merton presents abundant evidence supporting the hypothesis which I will examine below. Moreover, the way scientists work is already built on an assumtpion that multiple discoveries (MDs) happen all the time and are a predominant pattern in the course of scientific progress, rather than a peculiar exception.

The first class of evidence has to do with rediscoveries:

  1. Rediscoveries of previously unpublished work, as in the cases of Cavendish and Gauss discussed in the previous post, is one mechanism by which discoveries thought to be singletons turn out to be multiples.

A special category of rediscovery deserves its own subsection:

Curious Cases of Cryptomnesia among Scientists

There are many records of scientists who found, to their own amusement and incredulity, that an idea that seemed to them new and original at the time had in fact been written down or even already published by them years ago, and then forgotten - cases of self-rediscovery.

From the correspondence of Joseph Priestley, the English chemist and discoverer of oxygen1:

I have so completely forgotten what I have myself published, that in reading my own writings, what I find in them often appears perfectly new to me, and I have more than once made experiments, the results of which had been published by me.

Augustus de Morgan, a 19th century British mathematician, had his own cheerful version of the experience2:

I have read a Paper (but not on mathematics) before now, have said to myself, I perfectly agree with this man, he is a very sensible fellow, and have found out at last that it was an old Paper of my own I was reading, and very much flattered I was with my own unbiased testimony to my own merits.

Cryptomnesia refers to the fact that sometimes an idea that seems fresh and original to its author may in reality be the trace of a forgotten exposure to an idea of another (or even themselves) - something that they’ve read or heard before but have no memory of having encountered. So self-rediscovery is also a case of cryptomnesia.

Awareness of the possibility of cryptomnesia can undermine the certainty that one has indeed come up with a new idea oneself, when encountering another version of the same idea developed by someone else (this is somewhat akin to the anxiety of influence in literature and music).

After William Rowan Hamilton, of quaternions fame, learned at 19 that his discovery in optics was “only” a rediscovery, he developed a lifelong morbid fear of being plagiarized and unwittingly plagiarizing others. In a letter to his friend de Morgan (same de Morgan who had a case of self-rediscovery), he wrote:

As to myself, I am sure that I must have often reproduced things which I had read long before, without being able to identify them as belonging to other persons.


Where is the priority business to end? I am sick of it as you can be; but still, in anything important as regards science, I should take it as a favour to be warned, if I were inadvertently exposing myself to the charge of plagiarising.

With the rise of collaborative research, the risk of cryptomnesia has likely fallen, since even if one member of the team forgets about an earlier exposure to an idea, others probably won’t. But it is remarkable how often it had happened in the past when research was largely conducted by individual scientists.

Let’s now turn to another class of evidence for Merton’s hypothesis, forestalled multiples - “discoveries that are historically identified as singletons only because the public report of the discovery forestalled others from making it independently."3

  1. There are reports in print stating that a scientist has discontinued research on a particular problem, well along the way, because a new publication has anticipated both their hypothesis and the experimental design to test the hypothesis. In other cases, despite having been anticipated, scientists still go ahead with the publication of their original work and often lament in the footnotes of their papers along the lines of “Since completing this experiment, I found that so-and-so had arrived at this conclusion last year and that so-and-so did it 50 years ago.”

This is from Lord Kelvin’s biography:

The experience of Lord Kelvin as an undergraduate of 18, when he was still the untitled William Thomson, who sent his first paper on mathematics to the Cambridge Journal only to find that he “had been anticipated by M. Chasles, the eminent French geometrician in two points . . . [and] when the paper appeared some months later, prefixed a reference to M. Chasles' memoirs, and to another similar memoir by M. Sturm. Still later, Thomson discovered that the same theorems had been also stated and proved by Gauss; and, after all this, he found that these theorems had been discovered and fully published more than ten years previously by Green, whose scarce work he never saw till 1845.”

(You may start noticing that prominent scientists are especially prone to being involved in numerous multiples throughout their research careers - I will return to this point later.)

  1. Many scientists cannot bring themselves to report in print that they were forestalled. These cases are usually known only to a close circle of friends and collaborators who are familiar with their work. As is evident from diaries, letters and memoirs of scientists, these people have dutifully or reluctantly notified them that their recent discovery that they were so elated about is a multiple. With the effect that those ideas never find their way into print.

W. R. Hamilton again, on a result in optics that he thought he was first to arrive at:

A fortnight ago I believed that no writer had ever treated of Optics on a similar plan. But within that period, my tutor, the Reverend Mr. Boyton, has shown me in the College Library a beautiful memoir of Malus on the subject. . . With respect to those results which are common to both, it is proper to state that I have arrived at them in my own researches before I was aware of his.

Third class of evidence is the behavior of scientists themselves. They act on an assumtion that singleton discoveries are imminent or potential multiples, that if one scientist does not soon make the discovery, another will.

  1. The social institution of science puts a premium not only on novelty but also on chronological priority in discovery.

As Merton poignantly put it:

…the values and reward system of science, with their sometimes pathogenic emphasis upon originality, help account for certain deviant behaviors of scientists: secretiveness during the early stages of inquiry, lest they be forestalled; violent conflicts over priority; an unending flow of premature publications designed to establish grounds for later claims to having been first.

Along with lab fires and explosions, multiple discoveries are an occupational hazard of science. Scientists are affectively involved with their discoveries: nuggets of knowledge are revealed to them as a result of long, hard work, so it is no wonder that finding out that theirs is “just” another instance of a discovery already made by another is a matter of acute stress.

It may seem that the quote by W. R. Hamilton4 at the beginning of this post may testify to the contrary. But the effects of that charitable insight of his did not last long. Later in the very same letter he announced that he had anticipated the work on ellipsoids by the mathematician Ferdinand Joachimsthal in “a long extinct periodical of whose existence he [Joachimsthal] probably never heard, with a date which happened to be a precise decennium earlier.”

Autobiographies, letters and diaries of scientists like Wiener, Huygens, Newton, the Bernoullis and many others contain numerous examples of expressions of a similar sentiment.

  1. Friends and family of scientists can be outspoken about matters of priority when the scientists themselves aren’t.

Elder Bolyai warned his son János about the necessity of publishing his [János’s] results in non-Euclidean geometry sooner than later:

first, because ideas pass easily from one to another, who can anticipate its publication, and secondly, there is some truth in this, that many things have an epoch, in which they are found at the same time in several places, just as the violets appear on every side in spring… Thus we ought to conquer when we are able, for the advantage is always to the first comer.

Friedrich Bessel, a faithful friend of Gauss, for years on end encouraged him to publish his discoveries to avoid being forestalled. Ironically, once Gauss published a manuscript on dioptrics and sent a copy to Bessel, it turned out that this work fully anticipated Bessel’s own unpublished results.

Adrien-Marie Legendre warned Karl Jacobi about the possibility of Niels Abel’s overtaking him in the race for coveted results in the theory of elliptic functions unless “you take possession of that which belongs to you by letting your book appear at the earliest possible date.”

Many such cases.

  1. Lastly, there are institutional devices designed to protect scientists' priority of discovery. It’s been an established practice, since the 17th century, for scientific academies and societies to have sealed and dated manuscripts deposited with them to protect the priority and the ideas themselves.

From Royal Society’s archives5:

When any fellow should have a philosophical notion or invention, not yet made out, and desire that the same sealed up in a box might be deposited with one of the secretaries, till it could be perfected, and so brought to light, this might be allowed for the better securing inventions to their authors.

The French Academy of Sciences also practiced this arrangement - among the many documents deposited under their seal was Antoine Lavoisier’s on combustion.

And of course, the patent system is a formalized way of securing priority of discoveries and inventions with a commercialization potential.

Merton’s multiple pieces of evidence all seem to testify that scientists, in practice, if not in theory, already assume that his hypothesis is true: all discoveries are potential multiples, and singletons are most often forestalled multiples.

I found these arguments pretty compelling, especially the last bit on the practical behavior of scientists - this I have witnessed first- (and second-)hand, having worked in several biology labs over the years.

In the next post, I will look into what MDs mean for the history of ideas and if and how the pervasive fact of multiples can be harnessed in economics of science. Thanks for reading!

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  1. Life of Priestley, Centenary Edition, p. 74 ↩︎

  2. From his letter to William Rowan Hamilton, in Graves, Life of Hamilton, 3: 494 ↩︎

  3. Robert K. Merton, Singletons and Multiples in Science (1961) ↩︎

  4. By this point he has inadvertently become something of a main character of this post. I blame that on Merton who has quoted Hamilton extensively in his essays (though for good reasons). ↩︎

  5. Thomas Birch, The History of the Royal Society of London (London: A. Millar, 1756), 2:30 ↩︎