Think of the long centuries in which attempts were made to change mercury into gold because that seemed like a very useful thing to do. These efforts failed and we found how to change mercury into gold by doing other things that had quite different intentions. And so I believe that the availability of instruments, the availability of ideas or concepts—not always but often mathematical—are more likely to determine where great changes occur in our picture of the world than are the requirements of man. Ripeness in science is really all, and ripeness is the ability to do new things and to think new thoughts. The whole field is pervaded by this freedom of choice. You don’t sit in front of an insoluble problem for ever. You may sit an awfully long time, and it may even be the right thing to do; but in the end you will be guided not by what it would be practically helpful to learn, but by what it is possible to learn.
On July 25, the science writer Ash Jogalekar shared this excerpt from Robert Oppenheimer’s 1964 book The Flying Trapeze, a compilation of the Whidden Lectures that he delivered in 1962.
Oppenheimer’s invocation of the notion of ‘ripeness’ is quite fascinating: it is reminiscent of the great mathematician Carl Friedrich Gauss’s personal philosophy, which is also inscribed on his seal: “pauca sed matura“, Latin for “few but ripe”. Gauss adhered to it to the extent that he would only publish his work on mathematics that was complete and with which he was wholly satisfied. As a result, he had a large body of unpublished work that anticipated discoveries that other mathematicians and physicists would only make much later.
‘Ripeness’ also beings to mind one of the French mathematician’s Alexander Grothendieck’s beliefs. In the words of Allyn Jackson:
One thing Grothendieck said was that one should never try to prove anything that is not almost obvious. This does not mean that one should not be ambitious in choosing things to work on. Rather, “if you don’t see that what you are working on is almost obvious, then you are not ready to work on that yet,” explained Arthur Ogus of the University of California at Berkeley. “Prepare the way. And that was his approach to mathematics, that everything should be so natural that it just seems completely straightforward.” Many mathematicians will choose a well-formulated problem and knock away at it, an approach that Grothendieck disliked. In a well-known passage of Récoltes et Semailles, he describes this approach as being comparable to cracking a nut with a hammer and chisel. What he prefers to do is to soften the shell slowly in water, or to leave it in the sun and the rain, and wait for the right moment when the nut opens naturally (pages 552–553). “So a lot of what Grothendieck did looks like the natural landscape of things, because it looks like it grew, as if on its own,” Ogus noted.
Ripeness, in Oppenheimer’s telling, is the ability to do new things, but I find the preceding line to be more meaningful, with stronger parallels to both Gauss’s and Grothendieck’s views, in the limited context of scientific progress: “the availability of instruments, the availability of ideas or concepts … are more likely to determine where great changes occur in our picture of the world than are the requirements of man.”
Oppenheimer says later in the same lecture that progress is inalienable to science; this, together with his other statements, provides extraordinary insight into where progress occurs and why. Imagine the realm of knowledge that science can reveal or validate to be a three-dimensional space. Here, the opportunities to find something new are located at, or even localised to, points where there is already a confluence of possibilities thanks to the availability of information, instruments, techniques, resources, and sensible people. It is in a manner of speaking, and as Oppenheimer also indicates (“than are the requirements of man”), the substitution of individual people’s needs and pursuits as the prime mover of discoveries with the social and cultural prerequisites of knowledge itself.
This also seems like a better way to think about what some have called “useless knowledge”, which supposedly is knowledge produced without regard for its applications. I’m referring not to Abraham Flexner’s excellent 1939 essay* here but to the term as wielded by some political leaders, policy-setters, and the social-media commentariat, and which often finds mention in the mainstream English press in India as the antithesis of “knowledge that solves society’s problems”. Rather than being useless, such knowledge may just be charting new points in this abstract space, and could in future become the nuclei of new worlds; and when we dismiss it as useless, we preclude some possibilities.
I won’t deny that a strategy of randomly nucleating this opportunity-space could be too expensive (for all countries, not just India: I don’t buy that our country has too little money for science for the reasons discussed here) and that it might be more gainful for governments to assume a more coordinated approach. But I will say two things. First, when we’re pursuing or being forced to pursue a more conservative path through scientific progress, let us not pretend – as many have become wont to do – that we’re taking a better path. Second, let us not wield short-sighted arguments that privilege our earthly needs over something we simply may not even known know we’re losing.
Finally, perhaps these ideas apply to other forms of progress as well. Happy Independence Day. 🙂
(* Flexner cofounded the Institute for Advanced Study, which Oppenheimer was the director of when The Flying Trapeze was published.)