Not at all clear to me. Examples?

There's a popular paradigm shift theory that posits that we tend to adopt frameworks that explain the world, then work incrementally within those frameworks until they cease to make as much sense/have as much explanatory power as they once did.

Then someone (Newton, Darwin, Einstein) comes along and assembles a new framework based on new observations/theories that do a better job of explaining things. Eg the switch from creationism to evolution, or from newtonian physics to relativity.

Here are some more examples:

https://en.wikipedia.org/wiki/Paradigm_shift#Examples_of_par...

There is an important truth here, but be aware that the popular history of science and technology over-emphasizes the 'lone genius' narrative (it is the 'lone' part that is exaggerated.)

Agreed, but that's the story we like to hear, so it's the one that gets repeated. That nobody lives and works in a vacuum is an implicit assumption.

The switch to relativity seemed pretty incremental to me. Einstein's special relativity work builds hugely on that of Lorentz published one year before.

Could Einstein have justified his course of research as an attempt to incrementally innovate on some existing work?

Sure. "I'm trying to figure out a more consistent way of applying the Lorentz contraction" or something on those lines.

What chances would a person claiming that have had for getting funding?

I guess what I'm trying to say is that the incentives are strongly biased to what can be easily seen as a increment on what has been done before, and that this is biased against work that may draw on what has been done before but is presenting a fairly different view to what is currently accepted.

Could Darwin have presented his view as an incremental extension of some existing view? (I am aware there were existing theories of evolution, but there weren't any like Darwin's or Wallace's to be built upon).

> What chances would a person claiming that have had for getting funding?

Einstein didn't get funding, i.e. an academic position. He did his initial groundbreaking work while having a day job in a patent office. He published his four groundbreaking papers in 1905 and was offered a lecturer position only on 1908.

I'm aware of that, the question was about the sorts of research that are likely to recieve funding.

I think this is a good case for showing that the dichotomy is not particularly useful as the last word. Darwin was influenced by Malthus and Adam Smith, and also by Paley's watchmaker argument insofar as he sought to refute it, but his work was nothing short of revolutionary.

Tenure with reduced teaching responsibilities is the way big thinking gets funded these days.

Incremental innovations of the sort you are talking about means extending some pre-existing framework. There are obvious examples of important developments that involved developing different frameworks, which took many years to fully justify with evidence. The heliocentric view of the solar system, Newtonian physics, natural selection, relativity...

EDIT: I would also argue that developments like the printing press and the world wide web would have been difficult to justify as incremental extensions of existing work.

I'm not saying these developments came from nowhere, nor that they didn't build on previous work. I'm specifically arguing against the idea that it's fruitful to just focus on work that would be seen as incremental improvements on existing work.

If the printing press or web were proposed as research topics by a new PhD student today, they'd probably be laughed out of the room. But if they were proposed by someone with credibility, who knows what research is like from top to bottom, in a EUR2M grant proposal with a good demonstration of how the new ideas relate to existing work, featuring an appropriate-sized team and a detailed risk management plan up-front -- they'd be funded.