In contrast, attempting to jump far away from the current state, and finding a brand new global-maxima, is a much more risky endeavor. The first couple iterations may produce results that are even worse than the current state of the world. But in the long run, it avoids the problem of diminishing returns, and can lead to occasional breakthroughs that are vast improvements over the status quo.
It seems to me that creativity is basically about foregoing the easy and predictable local-maxima-search, in favor of a more adventurous global-maxima-search. The first few iterations of your bold new idea may sound kooky and klunky, but once it's been developed with sufficient rigor and polish, it has the chance to give a much bigger payoff. Someone who's too focused on the small details, and getting every detail ironed out before committing to something, may find such an endeavor far too uncertain to undertake, thus missing out on what could be the next big thing to change things up.
Edit: and another way: the local-maxima situation has to do with finding solutions within some particular framework, whereas you get a shot at global maxima in the search for/attempt to build new frameworks.
Can we find this conundrum in other domains, say, neural networks? Can a machine become creative when we teach it to adhere to common knowledge?
+ generalization / overfitting
+ cross-domain knowledge transfer
In a more embodied approach it is free energy minimization as advocated by Friston. Consider us divided by the world through a Markov blanket, or even better consider our actions and perceptions divided by one. How do we continuously surprise ourselves without getting mad?
A guy who would say it's the same thing is probably Polani with empowerment: https://arxiv.org/abs/1310.1863. The rational choice is to navigate to that location in state space where you have most decisions.
I think curiosity-based research is quite interesting from the perspective of rationality and creativity.
Another thought on the local/less local/global maxima problem: it seems possible that, taking a very abstract view of things, the whole reason we developed the sort of thought which distinguishes humans from other animals is to address the escaping local-maxima problems (summed up by the situation where you're in a maze, but have to go 'backward' in some sense in order to get out). While discursive thought may be worse than analogical thought at this sort of thing, our lower 'animal brain' functionality is even more geared to dealing with local maxima/minima.
This seems really close to the standard creativity advice, to write down ideas before discarding them: https://www.scotthyoung.com/blog/2008/03/05/how-to-speed-up-... https://www.theguardian.com/books/2010/feb/22/will-self-rule...
"Rationality" is at best a filter of rule constraints applied to small part of solutions that reach consciousness in any solution-seeking process. As we know eg. from Lakoff and Johnson ('metaphors we live by' etc.) most of reasoning is actually done using our sensory faculties, mostly spatial, which barely guarantee any kind of correctness.
If you try to be rational and cling to concepts while trying to figure out an answer to difficult problem, you obstruct the process rather than help it. Hence the popular advice to 'forget about the problem' so that the mind can figure it out by itself. How on earth is it rational? Rationality is only applied when checking a solution, like checking a proof, which - as we know - is orders of magnitude less computationally complex than finding a proof.
The mind is all about 'what works' not 'what's correct', rationality is pretty modern invention and to honestly think that we're primarily rational is a delusion. Tversky and Kahneman's work is another obvious counterexample.
I believe you would love the book "The Romantic Economist" by Richard Bronk which outlines romantic ideals of creativity, entrepreneurship, and other magic as a necessary ingredient of progress that is missing from modern philosophy and science.
I think what Nielsen is getting at here is the idea that a commitment to accuracy doesn't necessarily entail an unwillingness to be wrong. As in Weber's case, the wrongness of one's work doesn't necessarily imply it's unimportance.
The "tension between creativity and accuracy" came up in a slightly different context at a party this past weekend. I was discussing with some other recent grads the flawed method of peer review in research journals, especially as it relates to reproducing results of well known papers. The crux of the discussion was whether the progress of science has benefited from the lack of strict guidelines for reproducing results and whether some papers are still important because they described an interesting idea although were later found to be irreproducible or based on false data. I would say that definitely the field has progressed, although there is certainly an intrinsic (and expensive) cost in having papers that are irreproducible and scientists should certainly strive to make their results as easily reproducible as possible. In the absence of necessity, I'd go further to say that having easily reproducible research is so valuable that the contrary is simply not worth it.
Unrelated to "value of research", there is a notion of fairness that should be considered. If being flexible on accuracy is a "competitive advantage" of sorts in research, then it's important that this is made obvious. When the principle of accuracy is implied it becomes a hurdle to newcomers who would follow unnecessarily difficult path given they have no way of knowing a priori that being inaccurate (even slightly) is allowed, possible, or beneficial.
You need both, but people vary widely in how much they emphasize on or the other: too much on the filtering side, you may end up a critic, but not an artist; too little on the filtering side, you may end up a crackpot; too much on the generative side, you may never get anything done; too little on the generative side, you may never come up with something worth working on.
The first principle is that you must not fool yourself – and you are the easiest person to fool.
So I don't get why he's using Feynman as an example here. Feynman was a very inventive and precise thinker. I think the post starts with a false dichotomy so whatever conclusions are drawn are resting on pretty shaky grounds.
"Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost. Rigour should be a signal to the historian that the maps have been made, and the real explorers have gone elsewhere."
-- W. S. Anglin
I think the problem is the article is trying to put vaguely defined terms on some spectrum and the tension he is talking about is just an artefact of his own special mapping. Really there is no tension and this mapping is not canonical because the terms are not well-defined. So comparing accuracy, creativity, etc. on a single spectrum doesn't make sense. Mathematics being an existence proof that you can do both things at the same time.
The most powerful ideas in science are concise, unexpected, predictive, and mathematically rigorous.
Creativity generates the unexpected. It opens up new spaces for exploration.
But it's easy to confuse it with mimicry, which is formulaic repetition of existing practices in existing spaces that may or may not have useful outcomes.
Einstein's development of SR and GR was creative. Weber's gravity waves claims were exploring a space that Einstein created, not generating a new space.
There's nothing wrong with mimicry - it's an essential process in human culture. We think of the arts as creative, but in fact most art is made by somewhat modified mimicry of existing tropes, not by outstanding originality.
Original creativity is much rarer and very different phenomenon. It expands human experience into spaces that weren't previously accessible at all.
Powerful ideas are made precise, but they don't spring into being that way -- their inception is usually a fuzzy mess of analogy and hunch. Similarly, if we had an idea in mathematics that didn't fit in a formal system, we wouldn't just bin it, we'd change the formal system so we could implement it. (It's not like we have a formal system, or even a formal system we think implements all the things one should. Formalisms research is a major ongoing topic only ~200 years old.)
The precision and formality are the final product, but almost no ideas would be had if we required that they met our standards for formality when they were first conceived.
Creativity happens without being precise, and precision is usually a sign that the creative portion of the work has moved elsewhere.
Well, people could be incapable of going for one or the other as needed, even just "for a moment" -- which is the main issue.
Just it being "for a moment" doesn't preclude that moment to be very crucial to the resulting development.
This is true in principle. In practice, efforts towards accuracy are based on current beliefs, ideas and assumptions about the world. However creativity allows one to move beyond that, to explore if there exists some other local maximum higher that the current one. A better truth, so to speak. And without creativity you won't get there.
That is what I believe the author means when they say "somehow [the creative scientists'] early errors helped them find their way to the truth. They were...making many mistakes, mostly in the right direction."
Accuracy is not so much fun, but computers do it well.
The computer should be accurate and the people be creative with them. That's the proper way to use tools.
Here's an interview with Jordan Peterson that discusses this: https://youtu.be/01Tln_6Bxk0?t=9m40s
Sorry for pulling in the two-party system, I'm in it for the theory on openness vs. conscientiousness.