I'm not the one you're replying to, but the claim seems very reasonable to me.

Fundamental breakthroughs in how to think about scientific subjects usually are created by fairly small groups of people. A lot more people are involved in popularizing it, and then filling out the details. But it is rare for it to start with a large number of people.

For example that list in the case of quantum mechanics was Max Planck, Albert Einstein, Niels Bohr, Louis de Broglie, Max Born, Paul Dirac, Werner Heisenberg, Wolfgang Pauli, and Erwin Schrödinger.

You can think of this as the scientific version of the 2 pizza rule.

Humans sure love this story. A dozen Founding Fathers created the United States. A dozen physicists invented quantum mechanics. A dozen innovators caused the Industrial Revolution. It's always wrong.

Ask any of those dozen people where they got their ideas and (if they're honest) they'll each have another dozen people to name, and so on. Ask them who made minor contributions and suggestions and they'll again have dozens of people to name. Science is an ever-expanding body of work that always builds on its past successes and it's the height of naivete to reduce humanity's effort in a subject down to its few most visible people. It makes for good stories and trivia questions, but it's extremely far from the actual truth.

And even if it were true: how could you possibly identify those dozen people beforehand? It'd be like walking into a publishing house and proclaiming that everyone there is stupid because they waste all this money on books that don't end up best-sellers. Why don't they just only invest in the future best-sellers? Are they stupid?

I partly agree. A conceptual breakthrough always rests on a foundation to which many contributed. All of whom, in some sense, contributed. But my reading of history says that the reconceptualization that leads to intellectual breakthroughs themselves usually only involve small numbers of people.

If you've read The Structure of Scientific Revolutions, what I'm saying is that new paradigms are usually created by very small numbers of people. But they have both a foundation and their further success from the contributions of many.

I'm very much not offering an opinion on a great man theory of history in fields outside of science. Your example of the American Revolution is entirely off topic.

I'm also very much not saying that who will contribute what is in any way predictable. At best, the necessary collision of circumstances to make the breakthrough possible is chaotic, and therefore cannot be predicted. Nor did anyone else. The original point a few posts up was that, even if though there might be a haystack of clearly wasted effort, there may still be a needle powerful enough to make up for the rest.

All good points, but remember the claim in question was:

> But if we pay enough of these people to sit in rooms and work on problems, maybe one of them will figure something out.

and the response that you called "very reasonable" was:

> There’s more than enough already. (And, historically, you only need less than a dozen.)

So you were agreeing with someone who said we are paying too many physicists. There are too many people studying this problem. Okay, let's get rid of some then. Which ones?

> I'm also very much not saying that who will contribute what is in any way predictable

Uh oh, then how do we know who to get rid of? Which physicists should we not be paying? The claim that we should fire a bunch of scientists because we "only need less than a dozen" is nonsense, and you called this claim "very reasonable", with more examples. But maybe I should have replied to that person instead. It's a little awkward trying to have an N-way conversation when you can only reply to one response at a time.

The statement that there's more than enough, is not the statement that we should be firing them. It's a statement that we don't want more.

But if we had to fire some, I'd recommend ones who are not willing to do research outside of oversubscribed ideas. That's because the lack of success of existing lines of research means that additional effort there is less likely to work out than looking at less overpopulated approaches.

>> For example that list in the case of quantum mechanics was Max Planck, Albert Einstein, Niels Bohr, Louis de Broglie, Max Born, Paul Dirac, Werner Heisenberg, Wolfgang Pauli, and Erwin Schrödinger.

Those were not the only people working in that field at the time. Not by a long shot. In order to have pioneers in a field, there has to BE a field with a bunch of people in it.

You're right that these were not the only people working on the set of problems that lead to QM. Lots of people were thinking about the same problems at the same period of time. And lots more added to it later.

But what key concept underlying how we now think about QM doesn't go back to this list of people? OK, add Richard Feynman if you want to include the second breakthrough to QED.

Ideas that look like conceptual breakthroughs can usually be traced back to small numbers of people. Ideas that look like progress usually trace back to much larger groups.

> What key concept underlying how we now think about QM doesn’t go back to this list of people?

Off the top of my head: quarks, and therefore the existence of the colour charge quantum number; and the Higgs field.

All of the people in the list were also building on prior research by the likes of James Clerk Maxwell and Ludwig Boltzmann. Einstein himself said “I stand on the shoulders of Maxwell.”

There are other obvious candidates for inclusion like Henri Poincaré, Hendrik Lorentz, Satyendra Nath Bose…

You are adding people by changing the discussion to one where the point no longer makes sense.

I'm focused on how many people were needed to make the conceptual breakthrough from classical thinking to quantum thinking. I'm very explicitly not considering how many people were needed to further develop the idea of QM from there. I'm also not considering various other conceptual breakthroughs. Just how did we go from, "here's a bunch of weird observations that don't make sense," to, "here's a way of thinking that lets us explain them."

The discovery of quarks, color charge quantum number, and Higgs field are part of the further research, and so aren't relevant.

Maxwell was firmly part of classical mechanics. He provided a key foundation, but was not part of the transition.

Boltzmann was key to the creation of statistical mechanics. While converting classical statistical mechanics to QM was a key part of the success of QM, this was not work that Boltzmann was engaged with.

Henri Poincaré did indeed spend a fruitful few months on QM in the last year of his life. Sure, add him to the list.

Hendrik Lorentz contributed to SR, not QM. Yes, he did lecture on SR in the 1920s, but he was lecturing on what Schrödinger has already discovered. He did not originate new ways of thinking to QM.

You have an extremely good point about Satyendra Nath Bose.

So most of the topics you added were not part of the key shift that I was talking about. Most of the researchers that you added did not directly contribute to that theoretical transition.

We need lots of people to create the foundation. Lots to build out the new framework. But very few are needed to develop the new way of thinking that scientists transition to.