Looking into the history of science, I've been struck by how continuous scientific progress seems. Although there are many examples of great intellectual breakthroughs, most of them build heavily on existing ideas which were floating around immediately beforehand - and quite a few were discovered independently at roughly the same time (see https://en.m.wikipedia.org/wiki/List_of_multiple_discoveries).

So the question is: which scientific advances were most ahead of their time, in the sense that if they hadn't been made by their particular discoverer, they wouldn't have been found for a long time afterwards? (Ideally taking into account the overall rate of scientific progress: speeding things up by a decade in the 20th century seems about as impressive a feat as speeding things up by half a century in ancient Greece).

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Cases where scientific knowledge was in fact lost and then rediscovered provide especially strong evidence about the discovery counterfactauls, e.g. Hero's eolipile and al-Kindi's development of relative frequency analysis for decoding messages. Probably we underestimate how common such cases are, because the knowledge of the lost discovery is itself lost — e.g. we might easily have simply not rediscovered the Antikythera mechanism.

Hero's eolipile was an invention that had no practical use. The stream engine that did have practical use relied on high quality brass that wasn't available at Hero's time and only available in the late 1600s.

Darwinian natural selection is sometimes pointed to as a late development, given that it could have been inferred by anyone who understood that certain traits are heritable. However, the fact that two people figured it out more or less independently at approximately the same time makes me think that it came at about the right time.

What about Mendelian Inheritance? It was initially discovered by Gregor Mendel in 1865, but it was seen as being a very narrow special case of genetics until about 1900, when de Vries, Correns and von Tschermak "rediscovered" his work. So that's about 35 years during which the statistical laws of inheritance were published, but weren't being used or built upon.

General relativity is an obvious candidate. While special relativity was hanging in the air, and so was quantum mechanics, there was no urgency to improve on the Newtonian gravity at the time. There were a few small discrepancies, like the perihelion of Mercury, but not until the discovery of expanding universe a decade later it was obvious that a new theory was needed.

Actually, general relativity seems to have been discovered by Hilbert at almost exactly the same time that Einstein did.


Yes, Hilbert formulated the equations (or at least the Hilbert action from which the Einstein field equations follow) at about the same time, a brilliant mathematician that he was, he only needed a few hints and he was familiar with Riemann's differential geometry. The idea that differential geometry could be useful for the description of gravity as a field had been known since at least 1913, after Grossmann, Einstein's classmate with whom Einstein had been collaborating on and off for a few years prior, since maybe 1907, published his paper on the topic. I don't know the full history, but I was under the impression that Einstein was the main driving force behind trying to come up with incorporating Lorentz invariance into a new theory of gravity.

Possibly Antonie van Leeuwenhoek's study of microorganisms; he made microscopes that were much better than anyone else's at the time, and he kept his methods secret and they weren't properly reverse engineered until the 1950s. (Conventional lens making techniques did catch up, and people like Robert Hooke had been investigating biology on micro scales, but he was probably a generation or so ahead of everyone else.)

Scientific progress is not at all continuous and not systematically forward. There have been many periods of scientific regress. The most famous is the Dark Ages between Antiquity and Modernity, hence Luke's example of Hero.

But regress is all over the place, even in well-known examples of progress, like the Italian Renaissance. People often say that Renaissance art began with Giotto or maybe even so specifically with his invention of perspective. But, actually, most accounts of Renaissance art skip ahead a century from Giotto's death in 1337. In particular, perspective regressed and was reinvented in 1413 by Brunelleschi. And this wasn't even an independent discovery: Brunelleschi could see Giotto's work and knew that better was possible. *

Going back to Hero, "ancient Greece" is a bad category. Hero isn't the pinnacle of ancient Greek science, but a figure of a Roman era of rebirth after a dark age 150 BC – 50 AD during which we know the names of no scientists. In fact, almost everything Hero writes about he attributes to Ctesibius (d. 222 BC). If he is truthful about his sources, then there was a either a 250 year pause in pneumatics or there was more progress that was lost in the interim. In general, a controversial question is whether the rebirth in Roman Alexandria reconstructed and surpassed Hellenistic Alexandria or whether it was only able to understand a few books.

* Lorenzetti (d. 1348) seems to have been pretty good at single buildings, but bad at putting them together. Compare the only city I can find by Giotto.

There are plenty of accidental discoveries that we might imagine happening much later - but I don't feel like this should be enough, because it's not that they were surprisingly early, they were just drawn out of a very broad probability distribution.

I'm more satisfied with disoveries that not only could have happened later, but happened when they did for sensible local reasons. Example: Onnes' discovery of superconductivity. Not just because superconductivity was discovered very rapidly (3 years) after the necessary liquefaction of helium, when it conceivably could have taken a lot longer to properly measure the resistance of mercury or lead at low temperatures. But because Onnes' lab in Leiden was the first place to ever make liquid helium to cool superconductors with, and it took 15 years for anyone else in the world (in this case, Toronto) to start liquefying helium!

In short, to my mind being ahead of your time is the opposite of multiple discovery - we push back the luck one step by asking not for a lucky break, but for a sensible and straightforward discovery that could only have happened in a very unusual place.

1 Related Questions

7Answer by ryan_b5y
Multiple angles of attack Richard Hamming had this to say about important problems, in his talk "You and Your Research": One reasonable attack makes the problem approachable. If there are multiple reasonable attacks, at least one succeeding becomes more likely and further they can exchange information about the problem making each attempt more likely on its own. If we switch to considering thoroughly understood problems, we usually have multiple good solutions for them (like multiple proofs in mathematics, or detection from different kinds of experimental apparatus in science). So if I am going to rank open problems by the likelihood they will be solved, my prior is a list ordered by the number of ways we know of to attack each problem. Without any other information, a problem with two reasonable attacks is twice as likely to be solved as a problem with only one. Then we could consider updating the weights of different kinds of attack. For example, if one requires very expensive equipment, or very rare expertise, I might adjust it down. On the other hand, if there are two different attacks but the relationship between those two approaches is otherwise very well understood, then we might not treat them as independent anymore and factor in the ease of sharing information between them but also that they will probably succeed or fail together. We can also consider the problem itself, but I feel like looking at the reference classes for a problem largely boils down to a way to search for reasonable attacks, where any attack which worked for a problem in the reference class is considered a candidate for the problem at hand. But as I think of it, I'm not sure it is common to do a systematic evaluation in this way, so highlighting it as a specific method for finding attacks seems worthwhile.
3Answer by Pee Doom5y
Initial Braindump (hopefully will edit) Knowledge dependencies (algebra before calculus) Necessary tools? (Did people who made simultaneous discoveries use the same tools?) The research community for that domain? (How much communication is there? How dense are the connections between people?) How new the field is. Whether there was a sudden jump in the number of researchers. How frequently discoveries happen in the field. Whether a major disaster or other event is obstructing scientific progress from being made at the time. Whether the existence of simultaneous discoveries is just an artifact of cherrypicking biases
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For clarification, when you say "ahead of its time" do you mean the biggest jump forward from what was known at that time, or the furthest behind when we expect to have benefited from it?

I ask because if you shift from theories and equations to things like inventions or processes, it is totally routine to encounter things that were actually invented 50-100 years ago but that never saw the light of day because the materials were impossibly expensive or the market wasn't around yet.

Biggest jump forward.

In assessing the question don't we also need to look at other, probably failed and perhaps even "quackish discoveries" to get much meaning from the identification? What I'm wondering about here is, are we fully identifying what was really a good scientific insight or merely the winner of a bunch if creative theories/ideas from the time?

I think it would also be interesting to consider cases where ideas were initially too at odds with the existing state of knowledge and largely ignored but later rediscovered and found to have been insights that did lead to advances in knowledge -- theoretical and applied.

That would be the companion volume to the one about "wrong theories and scientific facts we used to accept as true."

Anyone know of such a book?