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I really like the idea of introducing difficult problems like these to outsiders (I'm an outsider in this instance) for the sole reason that it greatly increase
by JangoSteve 16y ago
I really like the idea of introducing difficult problems like these to outsiders (I'm an outsider in this instance) for the sole reason that it greatly increases the odds that someone may come out of left-field and either solve it or at least provide an insight that helps solve it.
Speaking of breaking down complex ideas with analogies, I'm reminded of this Wired article [1] which examines the inhibition of breakthroughs caused by experts' cognitive biases:
Modern science is populated by expert insiders, schooled in narrow disciplines. Researchers have all studied the same thick textbooks, which make the world of fact seem settled. This led Kuhn, the philosopher of science, to argue that the only scientists capable of acknowledging the anomalies — and thus shifting paradigms and starting revolutions — are “either very young or very new to the field.” In other words, they are classic outsiders, naive and untenured. They aren’t inhibited from noticing the failures that point toward new possibilities.
Or a more specific observation from one of the cited studies in the article:
[A diverse lab] mulled the problem [of unexpected protein synthesis results] at a group meeting. None of the scientists were protein experts, so they began a wide-ranging discussion of possible solutions. At first, the conversation seemed rather useless. But then, as the chemists traded ideas with the biologists and the biologists bounced ideas off the med students, potential answers began to emerge. “After another 10 minutes of talking, the protein problem was solved,” Dunbar says. “They made it look easy.”
[1] http://www.wired.com/magazine/2009/12/fail_accept_defeat/all/1 http://www.wired.com/magazine/2009/12/fail_accept_defeat/all...
- edanm 16y ago"I really like the idea of introducing difficult problems like these to outsiders (I'm an outsider in this instance) for the sole reason that it greatly increases the odds that someone may come out of left-field and either solve it or at least provide an insight that helps solve it." Really? I kinda doubt this happens often (or even at all) with hard Mathematical problems like P vs NP. We're talking about problems that tend to have so much history and theorizing about them that it would take enormous effort just to understand what is known about what's hard. Does anyone know of any statistics on Mathematical problems being solved by "outsiders"?
- JangoSteve 16y agoI guess I could have emphasized the "problems like this" and the "at least provide insight that helps solve" parts, as I wasn't suggesting that some amatuer will necessarily come along and completely solve this problem. And sure, I agree that in specific instances in which the problem is purely mathematical, outsiders probably rarely have much impact. That being said, it was my understanding that even the most recent paper posted here causing all this stir over the P/NP problem, was using statistical physics, which does indeed make it a somewhat "out of left-field" approach not used by the domain experts that have been traditionally studying this problem.
- eru 16y agoThe better justification is just: It's nice to tell people about hard problems. We do not have to expect them to solve them for us.
- joshfinnie 16y agoI think it is unfair to look at this in the context of the P=NP problem. I think there is a lot of good that can come from "outsiders" looking at problems from their view. If you leave P=NP for what it is (a REALLY hard mathematical proof) and take a look at some of the other unsolved mysteries, this outside-the-box thinking could be a huge asset.