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Feynman’s method to understand complex problems is so simple and elegant! Surely you’re joking, mr Feynman: ”I can’t understand anything in general unless I’m
by wimagguc 9y ago
Feynman’s method to understand complex problems is so simple and elegant! Surely you’re joking, mr Feynman:
”I can’t understand anything in general unless I’m carrying along in my mind a specific example and watching it go. Some people think in the beginning that I’m kind of slow and I don’t understand the problem, because I ask a lot of these “dumb” questions: “Is a cathode plus or minus? Is an an-ion this way, or that way?” But later, when the guy’s in the middle of a bunch of equations, he’ll say something and I’ll say, “Wait a minute! There’s an error! That can’t be right!” The guy looks at his equations, and sure enough, after a while, he finds the mistake and wonders, “How the hell did this guy, who hardly understood at the beginning, find that mistake in the mess of all these equations?” He thinks I’m following the steps mathematically, but that’s not what I’m doing. I have the specific, physical example of what he’s trying to analyze, and I know from instinct and experience the properties of the thing. So when the equation says it should behave so-and-so, and I know that’s the wrong way around, I jump up and say, “Wait! There’s a mistake!”
- therein 9y agoI read that in Feynman's voice in my mind. His tone is unmistakable with each word he utters you can hear him smile with astonishment at the complexity of things. https://www.youtube.com/watch?v=eqtuNXWT0mo https://www.youtube.com/watch?v=eqtuNXWT0mo
- malmsteen 9y agoSo. much. Using simple examples, low dimensions and physical analogies is really a key to advanced math.
- deleted 9y ago[deleted]
- sundarurfriend 9y agoAlso from the same book: "I had a scheme, which I still use today when somebody is explaining something that I’m trying to understand: I keep making up examples. For instance, the mathematicians would come in with a terrific theorem, and they’re all excited. As they’re telling me the conditions of the theorem, I construct something which fits all the conditions. You know, you have a set (one ball) – disjoint (two balls). Then the balls turn colors, grow hairs, or whatever, in my head as they put more conditions on. Finally they state the theorem, which is some dumb thing about the ball which isn’t true for my hairy green ball thing, so I say, ‘False!’"
- kqr 9y agoNot from the book but personal experience: This is also useful to understand preconditions by reduction. I.e. if you want to understand a theorem, it can sometimes be useful to start by figuring out the reason behind the preconditions. "Why does this apply only to balls that have hair?" Simply go, "What would the theorem imply if I start with a smooth ball instead?" This practise can also lead to generalisations. Oftentimes starting with a smooth ball will make you go "What? That't can't be possible." But sometimes, starting with a smooth ball leads you to, "Huh, that's really, really weird. But it's not a contradiction in and of itself. I could use that result in another context!"
- j2kun 9y agoWhat kind of second-rate mathematician tries to prove a theorem without writing down examples? That's Proving Theorems 101.
- ColinWright 9y agoI have no idea why you were being down-voted, and I wonder how many of the down-voters are actually mathematicians. If they were responding to your tone they need to know that it's incredibly mild compared with what one could say. I upvoted you, but clearly didn't undo all the downvotes.
- Koshkin 9y agoRight. The very first step in trying to prove a theorem is to try and disprove it (by looking for a counter-example).
- jwdunne 9y agoWhich are a form of example. You don't store those counter examples in your head - you write them down. If they don't turn out to be counter examples, what are they?
- obastani 9y agoI agree that having possible examples in mind is a great way to learn mathematics. There are whole books on useful counterexamples, e.g. https://www.amazon.com/Counterexamples-Analysis-Dover-Books-Mathematics/dp/0486428753 https://www.amazon.com/Counterexamples-Analysis-Dover-Books-... These counterexamples are sometimes a bit involved, but I find they are often useful for understanding the purpose of the technical assumptions that accompany many theorems.
- felideon 9y agoThere's a lesson somewhere in there that is applicable in software engineering.
- balabaster 9y agoThis is so exactly how I think... When you're talking about complex abstract systems, I have 2 or 3 real world models going on in my head and playing out chains of consequences at the same time. When your abstract system falls down I can tell you where and what caused it despite not understanding a word of your explanation as to why it should. All those mathematical equations and models may as well be Greek to me.