A tale of two problem solvers | Average cube shadow area

Comments · 4K

• SP

  @spicemasterii6775 · 4 years ago

  At last, Alice and Bob are doing something other than sending cryptic messages to each other.

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• SH

  @Shivumgrover · 4 years ago

  <a href="https://www.youtube.com/watch?v=ltLUadnCyi0&amp;t=1710">28:30</a> &quot;And we can simplify that 2π/4π to simply be 1/2&quot;<br>Me: Finally something that I could&apos;ve done myself.

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• SA

  @savantshuia · 4 years ago

  Now if only Alice and Bob had a way to share their proofs, maybe by sending messages that no one else is able to read?

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• ON

  @ontheballcity71 · 4 years ago

  I did a PhD in pure maths. The main result in my thesis had a very pretty Alice-like proof. The way it eventually dawned on me was spending a couple of years doing Bob style calculations of specific examples.

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• YO

  @YonatanZunger · 4 years ago

  Another note: Alice&apos;s <i>result</i> is more generalizable than Bob&apos;s, while Bob&apos;s <i>method</i> is more generalizable than Alice&apos;s. (You can see this by thinking about the harder problem of a nearby light, where Bob&apos;s method keeps working while Alice&apos;s doesn&apos;t!)<br><br>This is one reason why combining the two approaches is so valuable. You can start with something you know will work but may not unlock a great mystery, and then look for patterns that clue you in to a wider story.

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• MI

  @MistaSkilla692 · 4 years ago

  When he started turning the sphere into a band I was preparing myself emotionally for him to turn the sphere inside out without pinching any points

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• MR

  @Mrsparky492 · 4 years ago

  Another thing to note about the two philosophies is that Alice&apos;s way is beautiful but it requires you to be clever or lucky to connect disparate ideas and exploit the general connection. Bob explores the space with calculation and uses the connections that he identifies. I think there is not &nbsp;a separate Alice and Bob but instead a bob thinker picks away at a problem until he is able to build up to a generalization that equals Alice&apos;s. Bob&apos;s next question should be what about other shapes? Followed by what about all shapes? Eventually he would come to the same conclusion and probably prove the problem in the same way as Alice. <br><br>One of my frustrations with learning (highschool/undergrad level) &nbsp;math was that we only see Alice&apos;s brilliant proofs and sometimes it appears as a magnificent logical leap that I would have no hope making if I was in their position.

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• DR

  @DrTrefor · 4 years ago

  I really appreciate this video&apos;s focus on contrasting different problem solving styles. I think it is important that we all be a bit reflective of our own biases and what we enjoy and what we find natural, particularly because some problems lean themselves more one way than the other. I know for myself I always thought of myself more as an &quot;Alice&quot;, but over time I&apos;ve actually come to really enjoy more computation-centric approaches.

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• DE

  @DelusionalLogic · 4 years ago

  To me this seems like the difference between what we in software call &quot;Top down&quot; versus &quot;Bottom up&quot; problem solving. Bob takes the &quot;bottom up&quot; approach of looking at the specific problem he&apos;s attacking, going through the motions of solving it, and through that, he might stumble into some generality that he can later come back to. Alice on the other hand starts from the top. She notices that if she manipulates and connects the abstract pieces of information to finally arrive that the simplest form of the problem, which she then solves.<br><br>One of my teachers had a nice saying about it: &quot;Always solve the problem top down, except the first time&quot;, echoing the conclusion hit here. Top down problem solving is fast and awesome, but it&apos;s really difficult (if not impossible) to solve real problems like that. It often while working through the bottom up tedium that we realize what top down abstractions we can manipulate.

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• BL

  @BluecoreG · 4 years ago

  I would have just taken the area of the smallest shadow, the square, the largest shadow, the hexagon, taken the average and called it a day

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• DA

  @danbornside3670 · 4 years ago

  I think a nice upside to &quot;The Bob approach&quot; that I&apos;d like to emphaize, is that you can make forward progress on a problem without having any particular insight into the problem. &nbsp;Sometimes it&apos;s a lot easier to have insight into an answer once you already have a solution.

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• PA

  @patrickoberholzer4278 · 3 years ago

  Anyone else incredibly impressed just by the process of drawing Bob and Alice?

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