One way to look at creative thinking, is as local-maxima vs global-maxima searches. Someone who's searching for a local maxima, very close to the current state of the world, will produce ideas and work that show steady and consistent improvements. At some point, these finding-local-maxima will hit diminishing returns, but at least the process is predictable and very likely to bear some fruit.
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.
Another way of thinking about this is to consider the different means available for navigating 'idea space': one can crawl up hills to local-maxima using discursive thought, or one can sort of teleport around via analogical processes (as you point out, it's not clear what sort of valley you may end up in by doing this, though). Discursive thought has more of an 'if, then' character, while analogical processes seem to be kicked off by wondering about which things might have a similar structure to (i.e. are isomorphic to) some other thing of interest.
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.
Neural networks also need to balance exploration and exploitation. You will find it in the form of:
+ 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.
Personally, I see no reason why creative machines couldn't be built.
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.
Creative thinking occurs at a global scope and also at the detail level. I would better correlate creative thinking with dissatisfaction. IMHO a creative thinker wants to improve things or to explore new ways. A creative thinker has difficulties to follow scrupulously a process and would make a bad accountant. He may be inaccurate, but I do not think it is a rule.
The interesting thing is when it turns out you are exploring this hill-space by looking at the ground and nearby like bacteria or such, but over time "humans" have evolved things like being able to look toward someone that's on a different hill shining a light at you, which allows communication across agents exploring this space in channels outside the utility function itself.
I had a similar idea, but I think it is more accurate to compare creative thinking with Monte Carlo tree search. Setting the exploitation vs exploration ratio higher means you will miss some obvious candidates, but now and then you will find some 'genious' idea.
> To be creative, you need to recognize those barely formed thoughts [...] And if they seem important enough to be worth pursuing, you construct a creative cocoon around them
This naive belief in rationality on her part is troubling. It reminds me the simplicity of XVIII century enlightenment thinkers. No wonder that Nielsen, being accustomed with how DNNs work. represents the opposite view.
"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.
This is why I can't stand lesswrong and the comments of lesswrongers here.
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.
Well, it's really hard to tell which myth is causing more harm in our culture - myth about rationality or myths carried over from Romanticism. I'm not contrasting rationality with 'romantic' feelings (term that doesn't explain a lot), but rather conceptual with pre-conceptual.
Derek Parfit's Persons and Reasons deals with this question a little more formally, resolving the tension with the concept of "rational irrationality"[0, p12]
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.
I think this is the most important part of this discussion. Rationality, roughly defined is about achieving your goals. And Parfit's example about becoming temporarily irrational to achieve a goal that otherwise wouldn't be achievable then it's still rational .
Great observation! In my experience, too, there's a tradeoff between creativity and precise thinking. Namely creative people often have some inherent randomness built into their brains, and precision comes later with more effort; while always-precise thinkers are usually not the most creative. In my teams, I try to balance the two.
A related point is to not quickly dismiss an idea though it's wrong or unworkable, because a different version of it may be the best solution to the problem.
I love this provocative title. For clarification, the author's argument is related to a person's ability to follow a path determined by intuition in the absence of proof. The examples given are of scientists who found ultimate success even though they initially only had a kernel of an idea, in contrast to someone who would have found success but at the onset had a clear vision of how they might get there. I agree wholeheartedly with this sentiment, and early in graduate school my cryptography professor gave a concrete example: Diffie and Hellman knew there should be some way to securely exchange a key long before publishing their now famous exchange protocol (I'm paraphrasing heavily what the professor said, but hopefully this illustrates the point).
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.
Another way of looking at it: effective creativity is the result of tension between a generative process and a filtering/selecting process.
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.
I know the article is about science and solutions but the title reminded me more of creative writing and at least in my experience it requires far MORE creativity to be acccurate than not. It's easy to cut corners and just decide things happened because I wrote them that way. It takes far more creativity to actually write and make logical sense. Constraints seem to lead to more creativity. So, adding the constraint of "being accurate" would seem to also lead to more creativite solutions.
Gotta disagree on basically all counts. Mathematics is a very precise and yet creative game. And going back to Feynman, one of his most famous quotes is
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.
The end result of mathematics is precision; the inception of an idea, not so much. Indeed, if you look at the early papers on a topic, they are -- for lack of a better term -- "fuzzy" and very often contain technical mistakes. The art of mathematics -- which it shares with all arts -- is to make the leap in understanding and then carve out something to show others the same path in a saner manner, using technical skill. But that initial leap very often doesn't take place in a purely technical framework, and is fuzzy and imprecise. Usually, it takes many drafts of an idea until a suitable technical framework is found.
"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."
But you see how you are making my point. Mathematicians as a bunch are very creative and precise at the same time. Going back to my point about the article setting up a false dichotomy. Mathematicians study formal systems which are as precise a thing as humans have managed to make so far. Even if their initial exploration of new territory is not precise it is always in the context of formal systems.
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.
Not sure why you're getting downvoted. I had the same reaction. It's like comparing cheese with bedsprings.
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.
It's because you and the person you're replying to have the tail wagging the dog when it comes to being precise.
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.
I do not exactly get the arguments author present here. What the author sees as a tension is only for a moment -- the accuracy/truth prevails eventually even if a scientist fools himself into believing a wrong theory for
some time (and eventually deriving the correct result). Its like when people assume the opposite when trying to prove some theorem in mathematics (ex: assuming there is an intergral solution to fermats theorem.. so on)
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."
What about in cases where there is no one "solution" due to an environment that you are embedded in or something: like writing a good song or making a painting or writing a nice poem for a friend?
Art is a bit like white noise or a fluffy cloud: You can see everything you want in it – and that's exactly what you see. So basically everything qualifies as a solution. This is easy to see with poems or more abstract music (like drones). But I think the same holds true for pop music only that there are some rules on top of it and a marketing department that "assists" the consumer a bit in what they should see in it.
This is well covered, though not directly, in the book "Art & Fear"[1]. The more creative ideas and iteration one performs, the more skilled and accurate the end result. Approaching problems from scratch and settling on one approach too early can result in a long and flawed project outcome. The tension is that more ideas are better than less, and when on a deadline can result in less attention to detail for a specific iteration. The paradox of our craft in the technical business setting, is that deadlines are typically imposed arbitrarily.
This reminds me very much of the tension between conservatives and liberals, where the liberals are generally higher in openness (-> creativity) and the conservatives higher in conscientiousnes (-> accuracy).
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.