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Ask yourself dumb questions and answer them (2020)
- vegetablepotpie 3y agoOne of the things that separates ordinary people from smarter people is the topic of this article, the ability to imagine new concepts, questions, ideas. Colloquially we call this creativity, and it stems from a large degree of playfulness and enjoyment of the subject at hand. What separates geniuses from the crazies is the ability to test those ideas and the humility to dismiss the ones that do not work. It’s that combination that makes a great thinker.
- gerdesj 3y agoOoh, please define "ordinary" as opposed to "smarter". The article is about not artificially constraining your thoughts when considering a problem. Mathematics and by extension - mathematicians - are famous for looking kindly on a line of enquiry that subsequently turned out to be wrong. To be fair to mathematicians: Anyone can trot out any sort of bollocks and call it maths, rather cheaply, by jotting down some vaguely plausible looking ramblings on paper. If you try to fiddle up, say: cold fusion, you have to at least persuade your readers on archive that you have found the open end of a test tube and work on from there! There is a damn good reason why scientists, mathematicians and everyone else who works via publishing papers (for want of a better inclusive term) are rather dismissive of "dumb questions". Rather often the question ... is dumb. I hate that term and being British, I prefer: "stupid". This is all about "thinking outside of the box", which is nice until you note how people get treated for doing exactly that. I suggest you keep your thoughts inside your head when you are thinking outside of it! Once you have your thoughts all lined up and you are not wearing your underwear on your head and have stopped dribbling, you might be in a good place to deliver your pontifications. Your mother may well have given you the advice: "think before you speak" - she was a wise woman. She probably doesn't blog about it.
- justanotherjoe 3y agoI once thought like this. Still do. But I had known one guy who didn't seem to exercise any limit in thinking stupid questions. He was like the antichrist to me, everything i hate. But he said some things that i still remember today cause it's just pure genius, that perfectly encapsulates the reality in so little words. And there's some sick natural barriers that prevent 'normal' people from knowing them, cause the language, while precise, also sounds dumb. But it's really not.
- cookie_monsta 3y agoHmm, I would like to hear an example of one of the Antichrist's thoughts
- whatshisface 3y agoThe Eurasian region must (bleh)* be engaged in protracted war to ensure that the populace is distracted from the Omicron program. * Frog emerges from mouth
- justanotherjoe 3y agoi'm kinda hesitant to say most of them. Like I said, they sound silly and reductive at first. And none of them is exactly what people here will find interesting. One thing he said that a game becomes engaging when 'things that were once hard, is now easy'. I like the formulation cause it works on just right abstraction level. It lends to many interpretation and it works as long as the 'rule' is satisfied. And I've obsessed over it and just how true it is. Another thing he said that fantasy is about 'sky upon sky'. Which is one of the more abstract things he said. I swear I was fuming when he said it with such elation as if he's discovering electricity. The refusal to elaborate was also infuriating, as if I was supposed to understand what he meant. And I did, eventually. The abstraction works perfectly, at least for me...
- zmgsabst 3y agoI think a lot of the (over)reaction to “dumb” questions is that people of average capability can’t explain the conventional wisdom, and therefore feel an ego threat when it’s questioned. To quote the point: > So one should be unafraid to ask “stupid” questions, challenging conventional wisdom on a subject; the answers to these questions will occasionally lead to a surprising conclusion, but more often will simply tell you why the conventional wisdom is there in the first place, which is well worth knowing. I’m always amazed at how many people insist the world is round, but can’t explain how we know that. Or explain the experiments you can see yourself, eg pendulums or round pools.
- soundarana 3y agoCrazies say they validate and test their idea, but they actually suffer from severe confirmation bias where they summarily dismiss any counterexample or problem.
- gerdesj 3y ago"Crazies" Would you be able to spot a Ramanujan from the dross? You say that "they" ... something ... but ... they ... something ... disagree with the world. Care to flesh this out with an anonymised example?
- swagmoney1606 3y ago> Would you be able to spot a Ramanujan from the dross? Yes. We would do this by analyzing their arguments for logical errors, then testing their new theory, then hopefully proving their new theory. The difference between a crazy and genius is the results their new ideas produce.
- mulmen 3y agoIdeas are cheap and proof is expensive. It’s impossible to give all ideas equal consideration. You have to apply a filter, it’s inevitable. The question is just what filter you apply.
- l33t7332273 3y agoIn math, proof is not generally so expensive, so perhaps Ramanujan was not the best example.
- penteract 3y agoRamanujan was missed by at least one maths professor. Also, there are mathematical proofs such as that of Fermat's last theorem, or the claimed proof of the abc conjecture by Shinichi Mochizuki for which verification is very difficult. I'll agree that the costs don't come close to replicating work by LIGO or CERN.
- FPGAhacker 3y ago> One of the things that separates ordinary people from smarter people is the topic of this article, the ability to imagine new concepts, questions, ideas. Colloquially we call this creativity, and it stems from a large degree of playfulness and enjoyment of the subject at hand. Pretty sure we call that imagination. Creativity, shockingly enough, involves creation, not just imagination.
- phito 3y agoWhat's the difference? OP could have said "create new concepts, questions and ideas" and it would be exactly the same
- mym1990 3y agoYou can creatively destroy things as well. It’s kind of pedantic to say that creating in the mind does not count as “creating”, just imagining. What about solving abstract problems?
- p1necone 3y agoOne bit of advice for problem solving that I've taken to heart and find very effective is to not shy away from trying solutions you'd be embarrassed to tell other people because they'd probably think you were crazy/an idiot. Sometimes that direction is where the truly effective stuff is. Of course you should also try the obvious, simple, "normal" solutions - but don't be afraid to experiment. A bit like "write drunk, edit sober" but instead of drunk, you're a raving lunatic.
- broscillator 3y agoMan, I think feeling crazy for trying stuff even when completely alone, is something not enough people talk about. It's clear when you do it that most artists and creatively successful people have done it and gotten over it, but it's like something that you actually don't hear about or maybe don't register until you start doing it, and do it enough to get used to the feeling and carry on with whatever you were thinking of.
- mock-possum 3y agoThe way I frame this for myself is - just get the stupid solutions out of the way first. Do them so you can see how dumb they are, and move on to the better ones. And that comes with the proviso that sometimes, the stupid solution is actually just fine, and you didn’t even need to make it so complicated.
- hackerlight 3y agoGeneral research advice: I would also go in with the mindset "I am trying to disprove this approach as quickly as possible". This allows you to iterate quickly across hypotheses and not get dogmatically fixated on one approach. Cast the net wide in the initial search, including both normal and crazy solutions, then measure what approach is working, and then narrow the search based on that, learning lessons along the way. Don't start with a narrow search. Also, be sure that the different approaches you're trying are uncorrelated and ideally thematically/qualitatively different. Many researchers get tripped up trying "different" things that are really just superficial iterations of the same core concept.
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- jmbwell 3y agoRelated tangentially perhaps, but I find this to be a particularly helpful application of things like ChatGPT. Instead of asking it to give me the answer, I tell it what I’m trying to do and ask it to ask me questions about it. It’s great for gathering thoughts for writing, and I’ve been using it a little to try to help me think through software problems more quickly. It’s very good at asking “dumb” (ew) or at least simple, building-block questions, and it almost always ends up asking me about something I hadn’t considered that ends up contributing to what I’d have done without the machine. It’s also kind of fun.
- gerdesj 3y agoGood skills! Never thought of that, nor seen anyone else espousing it.
- sebg 3y agoDo you have a simple example prompt set? I am having trouble figuring out how to try it on my own? Thanks!
- jmbwell 3y agoJust something like, “I need to write an abstract for a presentation about XYZ. It need to this that and the other thing. Ask me questions about it.” Or “I have this data in this format and I need to write a program to transmit it using this system to an another system that accepts this format. I’m using Python. Ask me questions to help me figure out an approach.”
- AndyNemmity 3y agoI just tried this, and it was amazing. Great tip.
- lisper 3y agoEven more productive: ask yourself, is this really the best way to accomplish this? Why are we doing it this way? Is the standard solution bound by some constraint that was valid in its time but can now be discharged? My canonical example for this is standard mathematical notation, which was invented before computers and optimized for quill pens and chalk boards. How much leverage could you get by discarding it and starting over with something a computer can more easily process, like, say, s-expressions? Or... most programming languages use ascii for their standard syntax but nowadays we have unicode. How much leverage can you get by using more non-ascii characters, like, say, «balanced quotation marks»?
- constantly 3y agoThis is awesome. Glad we can improve on the “thought leadership” of theoretical people like Terrance Tao with some real titans’ advice like yours (I see you were a software engineer at Google!!!). Thanks for sharing.
- electrondood 3y agoDropped the /s
- constantly 3y agoYeah, true. I was being subtle. This narcissist is framing things as "even better" in comparison to someone who is likely, literally, the most intelligent person currently alive.
- Tainnor 3y agoThere is at least one person commenting that mathematical notation is stupid in every maths submission on HN, and the author usually never gives any indication as to having made any contributions towards mathematical research. It's an inevitability at this point.
- xanderlewis 3y ago
- tkgally 3y ago> It’s also acceptable, when listening to a seminar, to ask “dumb” but constructive questions to help clarify some basic issue in the talk. I think this is one of the reasons I hit a wall in my study of mathematics forty-five years ago. In the master's program I was enrolled in, the students never asked questions during class. The teachers would probably have welcomed questions, but the culture among the graduate students was never to show ignorance by asking. The result was that I often got lost in the lectures, was unable to catch up by studying the material on my own outside of class, and never became a mathematician.
- hasoleju 3y agoSomewhere between college and university I also lost my courage to ask "dump questions". Maybe it was for the same reason you mentioned. I don't want to look ignorant. I'm trying to get that ability back in my work life. I have the attitude asking dump questions and getting the answer helps yourself and most likely everyone else in the room. So don't feel ashamed of asking in the first place.
- ipsin 3y agoIs this different from Rubber Duck Debugging?
- 082349872349872 3y ago> if a simple result is usually proven by method X, you can ask whether it can be proven by method Y instead in particular, see https://en.wikipedia.org/wiki/Mathematics_Made_Difficult https://en.wikipedia.org/wiki/Mathematics_Made_Difficult (one of the distinguishing features of a good hack is that it leaves the Sherpas behind and takes a different —usually more direct— route to the solution than the siege approach that Conway's-Law-compliant enterprise team(s) would take)
- j7ake 3y agoAnother useful technique in understanding a topic is to find is to simple (but nontrivial) examples and make sure one can solve them fully and easily. Then slowly add complexity from that example to gain insight to more challenging cases.
- balaji1 3y agoAnswering popular questions like the "contrarian question" Thiel poses is a good exercise. Flesh out the answers to a degree you would feel good presenting it in an interview.
- ironmagma 3y agoTo me the existence of this post is particularly relevant given the contemporary context: https://twitter.com/StefanFSchubert/status/1738327056239169618 https://twitter.com/StefanFSchubert/status/17383270562391696...
- hervature 3y agoI think most people commenting in this thread are reading the headline and/or reading the article as outside the context of mathematics. This is Terry Tao's blog and not a VC's microblog. The very first block of text is a quote from "I want to be a mathematician". He is purely talking about how to approach mathematics at a level sufficiently close to the frontier. What he is saying is that when you are taught something like optimization theory, the definition of convexity is presented to you in the first lecture. A "stupid" question to ask is what makes convex functions special. After thinking a lot about this question, I've come to the conclusion that convex functions are functions that are trivial to optimize but the converse is not true. Not all function that are trivial to optimize are convex functions. There are then plenty of questions like which other classes are easy to optimize. In Terry's words, "the answers to these questions will occasionally lead to a surprising conclusion, but more often will simply tell you why the conventional wisdom is there in the first place, which is well worth knowing.". Another example I ran into was the notion of metric spaces and completeness. It is "stupid" to ask what happens if you get rid of completeness. Stupid because you were just taught completeness for a reason. Trying to understand gives you a whole new appreciation than being presented the formal definition refined over many years.
- alberth 3y agoSounds like “First Principles” thinking for mathematics.
- kragen 3y agoall of mathematics is first principles thinking, and that's not a brand name now get your damn car off my lawn
- kdwikzncba 3y agoAll maths is first principles, without the pretentiousness of using the phrase "first principles".
- fivestones 3y agoI asked gpt4 about this first and it didn’t really know. What is it about “First Principles“ that’s cringeworthy or pretentious? I think I’m out of the loop on this one.
- beltsazar 3y agoI'd go further to say that if you don't ask to yourself a single question while you're reading a substantial part of a book (a section, a chapter), then you don't really internalize what you think you're learning. The questions don't need to be answered perfectly, nor they need to be "good" questions. The questions can be general and simple, like: - Does it have to be this way? Why? - How is it related/connected to what I've learned previously (last chapter, last year, last decade)? Do I need to unlearn something or adjust my previous mental model?
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- zubairq 3y agoVery good thought process here… I always try to steel man oppositional arguments of things that I may think are true
- bmitc 3y agoI have found that many people don't respond well to one asking dumb questions. It can quickly marginalize you in a room of people trying to be the smartest in the room.
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- _trampeltier 3y agoOnce we had a very smart young guy on work. But he always asked things, even if he knew the answer. It was like a sickness, people refused to work with him, because of his many also stupid questions. So I told him he can ask me anything, but he allways has to present at least two ideas to solve the problem. He always came with a possible solution and if I asked him witch solution then the better would be, he always picked the right one. After a very short time he asked much less and it was much more calm to work with him.
- InCityDreams 3y agoI worked with a similar-type person. I gave them 15 minutes at the end of every day to ask whatever they wanted. Usually by the end of the day they had worked out the answers and had very few, if any, questions. I like your solution just as much, but we weren't in a 'many people could benefit' environment.
- oersted 3y agoCould someone recommend a good maths research book that covers the whole messy discovery process, rather than just the end result? I don't mind in which field, and it's fine if it's quite formal (not looking for pop science). But it would be good if it is relatively self-contained (doesn't require too much prior knowledge, it establishes some foundations and builds from them). I'm a fan of On Numbers and Games by Conway for instance, and the more literary Surreal Numbers by Knuth (written earlier but inspired by Conway's research before publication).
- ghufran_syed 3y agoI don't know if you would classify this as a "maths research book", but it's a wonderful personal and emotional description of the process of math discovery: Birth of a Theorem - A mathematical adventure by Cedric Villani https://us.macmillan.com/books/9780374536671/birthofatheorem https://us.macmillan.com/books/9780374536671/birthofatheorem
- spacecadet 3y agoGreat read. As a past adjunct, you can learn this through your students. No question is a dumb question. I eventually got to a point where I couldn't wait for the "dumbest" question of the session so that we could explore it as a class.
- Azan123 3y agoI need to involve students in carbon footprint activity, suggest an activity involving mathematical formula, simple for students