The Essentials of Problem Solving
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- Опубліковано 20 тра 2024
- An introduction to the psychology of problem solving. Featured problems: the towers of Hanoi, the Chinese ring puzzle, the Wason 4-card selection task, the candle problem, Roman matchstick problems, and toothpick shape problems.
00:00 A quick note
00:47 The problem state space and the towers of Hanoi
4:45 Problems of representation and the Chinese ring puzzle
6:42 Context and variations of the Wason 4-card selection task
9:42 Introduction to insight problems: the candle problem
11:05 Differences between insight and incremental problems
12:15 Barriers to insight: Roman matchstick problems
17:30 Insight problems: too big of a distinction?
19:08 Well-structured and ill-structured problems
21:11 Representation and argument
23:34 Becoming a better problem solver: toothpick problems
26:45 Domain-specific knowledge and strategy change
30:55 What transfers across problem-solving domains?
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ACKNOWLEDGEMENTS
The towers of Hanoi footage comes from Math Playground's version of the towers.
The Chinese ring puzzle footage comes from UA-camr @Jojikiba, here • Chinese Ring Puzzle (B...
The candle problem visuals: • The Candle Problem - L... . If you made it or you know who did, please let me know. The link above seems to be the oldest and most complete version.
Paul Zeitz photo: www.imo-official.org/advisory...
Math and STEP problems: www.imo-official.org/problems... and www.usmle.org/sites/default/f..., respectively.
Physics problems: Badeau, R., White, D. R., Ibrahim, B., Ding, L., & Heckler, A. F. (2017). What works with worked examples: Extending self-explanation and analogical comparison to synthesis problems. Physical Review Physics Education Research, 13(2), 020112. doi.org/10.1103/PhysRevPhysEd...
Visit www.eternagame.org for more info on Eterna.
The Chess explanation clip: @BetterChessTraining.
The Starcraft 2 clip: an @ESChamp video, here: • The Science To The Per...
The go examples come from Sensei’s library: senseis.xmp.net/?CornersThenS...
Starcraft 2 map: news.blizzard.com/en-us/starc...
Parity example: artofproblemsolving.com/wiki/...
The free body diagram is from a Math and Science video: • Master It! Free Body ...
The map of Easter Island: en.wikipedia.org/wiki/File:Ea...
The cashflow statement: en.wikipedia.org/wiki/Cash_fl..., but is originally from Epstein, Barry J.; Eva K. Jermakowicz (2007). Interpretation and Application of International Financial Reporting Standards. John Wiley & Sons. pp. 91-97. ISBN 978-0-471-79823-1.
REFERENCES
Simon, H. A., & Newell, A. (1971). Human problem solving: The state of the theory in 1970. American psychologist, 26(2), 145.
The tower of Hanoi state space was adapted from Zhang, J., & Norman, D. A. (1994). Representations in distributed cognitive tasks. Cognitive science, 18(1), 87-122.
The Chinese Ring puzzle state space (for 5 rings) is adapted from Kotovsky, K. & Simon, H. A. (1990). What Makes Some Problems Really hard: Explorations in the Problem Space of Difficulty. Cognitive Psychology, 22(2), 143-183.
The “underage drinking” example of the Wason 4-card task comes from this classic:
Griggs, R. A., & Cox, J. R. (1982). The elusive thematic‐materials effect in Wason's selection task. British journal of psychology, 73(3), 407-420.
A short meta-analysis on the Wason 4-card task: Ragni, M., Kola, I., & Johnson-Laird, P. (2017). The Wason Selection task: A Meta-Analysis. In CogSci. www.researchgate.net/profile/...
On the insight experience: Webb, M. E., Little, D. R., & Cropper, S. J. (2016). Insight Is Not in the Problem: Investigating Insight in Problem Solving across Task Types. Frontiers in Psychology, 7. www.frontiersin.org/articles/...
The Matchstick Roman numeral problems and the discussion of constraints and chunks come from: Öllinger, M., Jones, G., & Knoblich, G. (2008). Investigating the Effect of Mental Set on Insight Problem Solving. Experimental Psychology, 55(4), 269-282. doi.org/10.1027/1618-3169.55....
On strategic change, see: Siegler, R. S. (2002). Microgenetic studies of self-explanation. Microdevelopment: Transition processes in development and learning, 31, 58.
On the importance of representations in ill-structured domains, see: Chandrasekharan, S., & Nersessian, N. J. (2011). Building cognition: the construction of external representations for discovery. In Proceedings of the Annual Meeting of the Cognitive Science Society (Vol. 33, No. 33).
This was invaluable. I wish kids were taught about problem solving strategies in school and not just techniques. It seems like people think they are not very smart, when really it's just that they haven't learned how to approach problem solving correctly.
You mean that they could figure it out by themselves.😅
But if they were smart, they wont need to be taught this, they would figure it out themselves.
Poor kids thinking they are dumb when they haven't been given the answer. I ask you, how is this cruel treatment supposed to prepare them for the realities of life?
Oh right.
well not necessarily, you might have all the potential but got troubles with interpretation of the problem, @@Chaloonoupada, its just one of the assets i think
@@Chaloonoupada The kids who are "smart" were very likely taught the methods shown in the video by their parents/personal tutors.
This video is legendary. Timings, visuals and the structure of the text all bring this very impactful knowledge to light very effectively.
Tower of hanoi was one of the projects we have to solve during my first year in computer science. I always believed I'm pretty good at problem solving but this problem boggled me. Then I saw the solution, almost 5 line recursive approach. I was shocked but analyzing it in depth taught me a very fundamental lesson in problem solving and it's stripping down a solution to various small steps. I remember one of the quotes I said, "just like all towers, we should build our approach layer by layer". God I love that game
Can you share your 5 line solution here, please?
Yep, divide and conquer/rule in action.
There's a fascinating phenomenon of problems "solving themselves" when you "sleep on them", literally or figuratively. You make an honest effort to crack a problem for a while, you seemingly make no progress, you go do something else for a time and then the solution "comes to you", seemingly in an exogenous manner. Apparently it applies to complex, multi-step problems, so it's not just a single insight.
Many mathematicians swear that this phenomenon exists, and it's more consistent than just scattered anecdotes. I tried finding research on it a couple of years ago, but I found next to nothing. It's probably due to methodological difficulties and entrenched views: the underlying mechanism must involve some sort of "unconscious reasoning", which is oxymoronic.
A related phenomenon, lateral thinking, is also on the fringe of science. There's functional fixedness, which is much more limited in scope, but that's about it.
Also, many matchstick equations can be cheesed by crossing the equal sign to make a "not equal to" sign. It's debatable whether that's constraint removal or cheating. :D
there's a book called the macgyver method, a woman reviewed it and said the premise was 'define/ articulate the problem you want to solve, enter the diffuse state of mind by goign for a walk or whatever, you should have your answer within a day or so. If not; repeat the cycle'. the creator of macgyver swears by it.
@@pepperpeterpiperpickled9805 Yeah, I know the term "diffuse mode" from Barbara Oakley's "Learning how to learn" book/online course. That's probably where the macguyver method guy got it from. It had a foreword by Sejnowski, who also lent credence to the existence of this phenomenon, but to my knowledge there is very little research on it.
I've seen various arguments justifying the "sleep on it" phenomenon. IMO, it's probably some combination of the following:
- Breaking mental set. You were attacking the problem from one way and time loosened your allegiance to that way of solving problem. Obviously taking an extended break doing something else provides a similar benefit.
- Sleep is magic. There's a lot of memory consolidation and learning that occurs when we sleep. And, from my understanding, sleep is associated with the formation of gist memories (more than verbatim memories)
- The "diffuse thinking" that other people mention. As you mentioned, I'm not sure that there's a lot of research on this (although various activities - walking, sleeping, etc. are associated with more creative solutions to problems). You might want to read section 4 of this piece: Schooler, J. W., Mrazek, M. D., Franklin, M. S., Baird, B., Mooneyham, B. W., Zedelius, C., & Broadway, J. M. (2014). The middle way: Finding the balance between mindfulness and mind-wandering. Psychology of learning and motivation, 60, 1-33. Currently www.academia.edu/download/43148088/The_Middle_Way_Finding_the_Balance_betwe20160227-5073-17at1w3.pdf
It might have further resources to check out.
Something else to consider is what happens when you have some kind of "insight" that doesn't work out? I suspect this happens quite frequently, but no one counts it as an insight experience because it turns out not to work. Personally, I have had these kinds of experiences - I get excited by something that I think is going to work, but then try it in practice and realize I just didn't account for something. But both the insights that work and those that don't must be caused by the same cognitive processes.
I believe the human brain can put problem solving in an unconscious "back burner" mode, disconnecting the problem solving part from the conscious mind. Because being self conscious about it may be one of the main blocking agents. Think writer's block, or insomnia.
I believe this back burner mode requires a slow but steady state of continued but unconscious problem solving during an extended period of time, a night's sleep or a couple of days of working on other things while not consciously thinking about it. Say it would drain a 5% brain function, while simultaneously doing other things?
When I solve problems this way, it's like I can feel all the cogs and wheels in my brain moving when working with the problem on the slow, and feeling that tells me instinctively there is a solution to the problem just because I can feel my brain working on it, and that usually gets me a high because I know a solution will present itself and the only thing I have to do is to wait for the insight to turn up. And it usually does.
My point being, it doesn't turn up from nothing, it does turn up from not consciously but unconsciosly solving the problem.
@@benjaminkeep
The "insights that doesn't work" is just another form of trial and erroring? Even if a solution presents itself in the form of an insight, if it is not applicable to the problem at hand, it is just another trial that errored. But it is of use as another step on the learning curve? Just because it didn't work in this instance doesn't mean it can't be of use in another?
If the insight is strong enough, perhaps that idea is of greater use as an entity of its own than the original problem at hand? Perhaps it will lead to the entire task pivoting to another task? Perhaps the main problem was that you locked yourself in to solving one problem but found a solution to another more important problem? You never know ...
This ntirely changed my insights on problem solving, just like what Dr. Keep said it's not about the solutions, but the learning process from domain-general strategy of acquiring knowledge into domain- specific strategy, while knowing how to use transfer to facilitate problem solving. I greatly appreciate the 37 minute long video on problem solving, great work Dr. Keep!!!
This was nothing short of excellent. Especially the part of using some strategy successfully, which might actually impair problem solving performance
Whenever I'm gonna solve any problem in my life I'll always gonna thankful to you!
This was the most interesting video I've watched in quite a while. In real-world problems, there are also bad actors. People/companies/organisations who will show an impressive solution (their choice) before analysing the problem with the interested parties. Creating a bias up front is such a great sales strategy. Large consultancies like to do this with free onsite workshops for future customers. It is also true that what a group of people currently want is not what they need. But, who is the trusted arbiter of truth?
Yeah , it creates a bigger problem of "getting everyone on the same boat/ensuring everyone has the same objective"
Wich is an harder bit
@@davidegaruti2582 Agreed. This has moved the scope from personal problem-solving to group problem-solving where politics raises its ugly head. I'm so happy to be retired and away from corporate software development.
It's called S.P.I.N : Situation (pre-bias), Problem (set viewpoint), Implication (final set-up), Need-payoff (Why my solution is best).
Beloved by politicians, trade magazines (advertorials), business-people, mums (& dad's), and anybody trying to get their point over.
@@philipoakley5498 I love that
For the matchstick problem at 15:37, I took a matchstick from the plus (turning it to a negative) and used it to turn the equality into an non-equality (the matchstick being moved to cross the equal sign), didn't see the video solution until watched it, but I didn't stop to wonder if it followed the rules until after, just an interesting observation for me.
since the question is "solve the EQUATION" I would assume non-equations are not allowed
@lhol1z hey you're explicitly stating your assumption about the problem! :D
I took a matchstick from the plus and moved it to the left of the X, making IXI=III-II or 1*1 = 3 - 2 for the one at 13:40
I solved the toothpick box problem like this.
There are 17 total toothpicks, so removing 5 toothpicks to make 3 squares is the same as using 12 toothpicks to make 3 squares, provided they fit in the original shape.
I then found a solution by trying to make 3 boxes with 4 matches each. If that didn’t work, I planned to do trial and error.
This is actually really smart. You made a logical implication from the prompt, restating it in another way that made the solution more obvious.
@@lorenzgluck5144 Thanks
thanks, saul goodman for teaching me the essentials of problem solving
This really did a great job articulating some thoughts I have had on problem solving for yrs now while also introducing other nuance I wasn't aware of. GREAT video and incredibly insightful.
The part where you talk about "what transfers across problem solving domains" is probably the most important part of this video. I feel like media perpetuates this idea that if you're "smart" then you'll face no difficulty solving problems in completely novel situations. I like to call these characters "Wizard Smart"(Rick Sanchez probably being the best example of this trope). Of course, everyone who's finished this video know that this isn't true, but think of all the people who lived their lives never realizing this and believing that they're "dumb" because they struggle with math(despite doing perfectly fine in other domains).
The most sad thing for me is that by thinking "I am dumb" people accomplish nothing but a bad mood and poor self-esteem. This horrible mindset of "I am not [any personal trait]" simply makes life worse and doesn't give anything in exchange. Some people actulally get desired traits after those thoughts, but it is because they learnt how to get them in the first place and could be done without traumatic thoughts IMHO.
Really smart people have a similar downside. Maybe they can solve 95% of problems without difficulty. Than there is a problem that comes up they can't solve. All the sudden doubt comes in. Maybe i was never smart to begin with. How can i be the best at thing A if i can't even figure out thing B that is unrelated. It doesn't make sense, doubting yourself is just a naturally human thing to do
Wow this was absolutely fantastic, as someone who loves playing puzzle-based games of all kinds its great to know the mechanisms behind it all.
I especially loved when you brought up the remove five toothpicks to get 3 squares problem. I ran through it in my head pretty quick and got it and assumed I'd just trial-and-errored it really well. But when you brought up how you noticed how removing each type of toothpick had a different effect, I realized that was exactly what I'd done in my head -- just so fast I hardly remembered doing it in the first place.
Absolutely loved longer format, please do it more
This video is an absolute gem. We need more of this. Thank you.
I didn't realize this had the old background despite binging your older vids just yesterday. I was also surprised at how similar the themes of this video were to the ones I had just watched. It felt very relevant as I was watching it! Awesome vid.
Your videos are greatly appreciated, Dr. Benjamin. It was a splendid gift to find your channel! I wish more people knew about all of these insights...
My desired career in the future hinges extremely on my ability to problem-solve, so I am grateful that you put this out so that I can internalize the messages and make use of what you have presented.
Thank you for sharing your knowledge with us, and especially never sacrificing the nuances and caveats involved! And providing sources! Your commitment to disseminating information in a fair way is something I respect.
I have to stop here and express my gratitude, there are so many nuggets in here which are very well written and articulated. Thank you
This is a fantastic BEGINNING to a more indepth series. I learned a lot and hope that you will publish more on this topic.
Nice. I've always 'ignored' those matchstick puzzles as being rather random.
Your explanation, and the slow motion movement of the stick for demonstration, has helped highlight the set of solving strategies and how they also form a state hierarchy of approaches.
I expect I'll be able to have a go more often now I've seen them and eliminated much of the randomness of the apparently may special cases!
Fantastic conclusion regarding personality and its impact on an individuals problem solving ability. It is a reminder to me to stay humble and to create time for purposeful self reflection. Thank you.
This video really put problem solving and learning into perspective in a way that's really useful. No wonders solving problems helps with learning. I guess it's because learning is part of problem solving.
Wow this video is so good! You have such an easy to listen to voice and way of speaking, honestly could have used a few hours of this(I'm not kidding) it really felt like just a few minutes, but I did pause and think at those spots too, seriously loved the whole thing, bookmarked, and sharing with everyone! Encore! Encore!
Dr Benjamin's video are top tier fr
So many great points! I work on videogames and we often have to teach players 'how to learn' in order to get past puzzles without giving up. It will be cool to take these ideas and see how our game levels align with some of these problem solving terms. This will also be helpful in figuring out why a puzzle isn't working as well as we might hope.
We would often make Insight preoblems with the goal of having an "ah-ha moment", which is the same as a 'Crux Move'. I see now that I prefer Incremental problems that challenge the mental set that the player has gotten used to. Making an Insight problem that doesn't feel frustrating can be much tougher.
- Engage with problem-solving puzzles before uncovering their solutions to enhance the problem-solving experience. 0:20
- Deduce that challenging problems might involve navigating a complex state space, which includes understanding the start, intermediate, and goal states, and the actions that lead from one to another. 2:51
- Recognize when a problem space is linear and straightforward, focusing on understanding your current state and available moves can significantly simplify problem-solving. 5:20
- Understand that your representation and interpretation of a problem heavily influence your problem-solving effectiveness. 6:21
- Reevaluate assumptions and explore different representations if initially stuck on a problem, as this can often lead to sudden insights. 10:14
- Identify and challenge implicit assumptions to overcome barriers to insight when solving more abstract or complex problems. 14:25
- Develop awareness of the distinction between well-structured and ill-structured problems to apply problem-solving skills more effectively across different real-world scenarios. 19:06
- Emphasize the importance of understanding problem representation and engaging in argumentation to navigate ill-structured problems effectively. 21:02
- Use domain-general strategies such as trial and error to initiate problem-solving when specific solutions are not immediately evident. 24:34
- Acquire domain-specific knowledge through exploration and practise to solve problems within a particular area more efficiently. 26:52
- Combine various strategies, gradually transitioning from domain-general to domain-specific tactics for enhanced problem-solving ability. 28:00
- Apply transferrable concepts from one domain to another to generate new solutions or understandings, recognizing the limits of direct application due to domain specificity. 31:10
- Cultivate strategic behaviors and personality traits such as organizational skills, explicit assumption stating, perseverance, and solution verification across problem domains. 33:18
- Recognize that enhancing your problem-solving capabilities is inherently linked to improving your learning processes, implying a symbiotic relationship between learning and problem-solving. 35:27
This video is brilliant, probably the best one you have put out.
This is just the greatest content ever. Thank you Benjamin very much!
High quality and educational. Love it!
Amazing video!! It was really fun to solve all of the problems in real time and see how they relate to the ideas talked about :)
What an insanely valuable video! Thank you, Ben! These insights put a lot of things in perspective for me!
This is a great video, and very interesting! I'm sure a wider audience would love it, hence why I'm commenting to boost it for the algorithm.
20:10 "What about the problem of sending humans to Mars?"
The goal state for that problem seems precisely-enough defined to me.
This channel is a gem
This is the BEST piece on problem solving I've ever encountered. As a child, I always confused problem solving with solving math problems and made that the general basis for solving each kind of problem, but with time I became more curious about GENERAL problem solving, which shall be applicable for every domain. This video was an eye-opener in that sense, made me realise there's so much more to it that I didn't consider while solving problems
Even During my JEE I used to think that this is what develops Problem Solving! :)
This is exactly the content I am interested in. Glad I clicked
Your videos really are one of a kind. The way you break down the thought process is something I can relate to.
I think regarding the card flipping problem specifically, there's likely a linguistic element of how the problem is phrased, where different phrasing may more accurately convey the rule, and thus avoid the misinterpretation of thinking you need to verify the even card has a vowel on the back. This being an element that is subverted by prior experience with what the drinking age rules are, meaning that even with wording that though technically correct, does not mesh with common communication behaviour, people then use their prior understanding of the rule rather than the erroneous first interpretation.
That is an excellent observation. Several researchers have argued along the same lines. Actually, experiments varying the wording (and which cards to flip) revealed that a part of the cognitive process is simple matching to the named cards. There are many puzzles that rely on a linguistic element (for instance: "a man married 40 women in the town of Gloucester, but he did not commit bigamy, how can this be so?" Which relies on a conversational norm of the meaning of 'marry'.) There is often some play with the logical form of the puzzle and how it's conveyed. I'm sure there's research I haven't read that explores your question.
For those as confused as I was, the man was the priest.
@AlterMego1 Can't we assume that they weren't simultaneously married with the man?
@@avimir8805 From a purely logical standpoint I suppose so, but that wasn't the point he was trying to make.
Excellent video! One thing I might add to this is questioning definitions. As I did the toothpick square problem, I had a ton of questions. Can the squares overlap? Can there be extra bits left over that aren’t part of a square? What do you mean by “remove”? On the toothpick math problems, you can make most of them true by making the ≠ symbol. When you have a problem, be creative. When trying to enclose a large space with a limited fence, can you just switch “inside” and “outside” to suddenly “enclose” more space? Asking all those questions helps you learn you can use the box as a tool. Or maybe you can flip the table upside down so the wax doesn’t drip on the tabletop and instead drips on the table bottom. When trying to make something faster, does it actually have to be faster or do people just need to think it’s faster? Can we put free internet on our train so people don’t mind how long it takes? Break the boundaries of what you think the problem is to help learn what those boundaries actually are.
the order in which you presented the toothpick problems and showing solutions for each introduced a bias in which I was expecting a different solution from one to another to require playing with different constraints. The way problems are presented can greatly impact our capacity to solve it.
excellent explanation brother Benjamin,
finally .... i have waited for your video toooo long.. thank u for uploading
Thank you for posting
For the candle puzzle, I figured since it was a door you could hang the tack box on the doorknob. Also depending on the shape and size of the doorknob or even the door itself, you could probably just stand the candle up normally. Also you could light the candle, have the wax melt and stick it on the door. The door doesn't even have to be vertical. The problem with the candle puzzle is that there are too many vague variables and you have to form assumptions about the weight and material of the tack box, the material of the wall/door and the weight of the candle.
I thought use the match box as the holder, there missing important information like can the pins push through the box they are in. Push pin the match box to the door, then pin the candle into the box.
Melt bottom of candle and attach to handle
Fascinating video
Im only in half (16:27) but im losing my shit now!!!! THANK U, THANK U, THANK U!!!!! those informations are more than gold, they're food for a starving man. Ive been painstakingly cracking my head to figure the "creativity equation" and it feels out of reach to me!!! "I cant be creative!" I grieved, and now a light at the end started to appear, you have THE BEST learning videos on youtube hands down.
WoW! 😯 Chapeau bas.
That was really good. I gained many valuable connections and video can be easly used in many online discussions to map out where the problem is 😀 and fill some missing places 🧩.
I am interested in human agency and this is - I think - highly related to seeing or missing affordances as well as creating ones when there are non. This explains in some part how cognitive constraits contained in grasping a context shape situatuations and actions.
I am interested in big ideas and in possibility of transfer patterns between domains.
Good job, sir. 🙏
Thanks Dr. great video, very interesting
It’s fascinating to hear that there is a way of systematic discipline to practicing problem-solving, especially for the part of ‘transfer’ of domain-specific knowledge. For especially finding general principles, or ‘big ideas’, for the reason to transfer it to other problems, that is what I think I’m very weak at. Since my strength it to apply smth(I mean, from general principles to specific ways to deal with problems, not from specific cases to general big ideas), and it’s what I’m really interested at, so further cognitive growth will be biased.
So my answer was to find the most abstract and formal way to deal with problems, such as mathematical logic or system dynamics, formal sciences, I thought it’ll be general enough to gain cognitive strength that can be help my ability to deal with problems, but the problem happens : there is no way to express explicit reason of problem-solving process(especially for ‘institutional’thought). So later I can express my argument cogent and watertight, but I CAN’T express why I thought some kind of idea is pop up on my mind, what methodology of thought I used in the context of inference, and what decided the direction of reasoning. It’s something like black box, so I can’t reason why.
So your video let, and helped me lot to and think about this topic, again, it’s very fascinating to hear about systematic way of inference, about how to use intuition and reason. Have a good day!
Great video! Thank you very much!
For the roman numerals, 17:00 , it is not specified anywhere that we can't create an ≠ sign
Yes, my mistake - I should have specified this. Lots of others have pointed this out. As someone mentioned - it's an implicit constraint that is smart to let go of because you can solve a lot of these puzzles that way!
thank you so much for this kind of content, keep going please !
Very insightful❤️🔥🔥
Hi there, Dr. Keep!
I hope you are doing well!
I need to begin this comment with yet another expression of absolute appreciation for your work! Law school has been keeping me busy as usual, but I was finally able to sit down and enjoy this video in full... and gosh, it is a FANTASTIC one! I really appreciate how you highlighted the value of spending some time on developing strategies and thinking outside the box (excuse the pun!). I also thoroughly enjoyed the interactive element of trying the puzzles out myself. Thank you for the hard work and expertise you share in your videos and newsletters.
If possible, I'd appreciate if I may ask a question related to your work on memory and learning. I have been thinking about the forgetting curve and was wanting to know your thoughts on the best practice for dealing with wholly/largely forgotten material. For instance, using free recall (my preferred method having watched your videos!), would it be helpful to revisit the source material if one has zero/negligible ability to remember even some of the material, before trying to actually do the recall?
Thank you!
Ash
Brilliant - realy helpful. I'm surprised not to see, 'assume the problem is harder than it appears' as a personality trait. I find myself struggling with coding puzzels, and I'm looking for ways to improve. I've worked in Public Policy and change management, the big mental breakthrough for me was systems analysis => causal loop diagrams - problem solving is hard, but solving problems without creatating new problems is much harder.
amazing video, thank you!
Hi Ben, I have a question. If we want to be better at solving math problems or solving coding questions is there a specific approach we can take that is backed by evidence. For example, when to look at the solutions, should we use spaced repetition, redo problems etc. Additionally I was curious if neuro-plasticity is a part of problem solving. I am curious if I could benefit from micro-rest intervals and non sleep deep rest while working on problem solving.
Thank you. This will probably improve my attempts at solving a problem, or at least make it less excruciating.
- Filip from Italy :)
incredible video
best video of yours I've seen
For the candle problem i decided i should melt part of the candle until it is thin enough to stick a tack through because i know that tacks will fly off if you try to use them for a shelf
Your communication skills 👌
In the Roman numeral problems, most matchsticks can be used to make a strikethrough of the equals sign, making it read "not equal", thus making the statement true.
Easiest solution that works for all four of the problems.
Very nice video. Many thanks 🙏👍
Hey I love your videos, they are really helpful! Though out of topic, I want to ask some questions:
1. What are your thoughts on second brain and apps like obsidian and notion? I like the idea of keeping everything I learned in an organized place but also to keep them because they are not really good enough information for me to memorize but rather just have laying around that I may use in the future. I like having two categories for learning things, one I must remember in my brain, other that I can forget but if I need it I just pull it up somewhere.
2. Is there any benefit for keeping everything I learned in a notebook/compendium? Or is it better to keep the materials themselves better for this purpose?
3. I love your free recall technique, but is it good for memorizing raw meaningless information like Pi or an equation, or memorizing a paragraph? What if I want to memorize something exactly how it is, like it's perfect definition? Are they important?
Edit: I added third question because I was disrupted when writing this comment.
Great video!
what an incredible channel :) i have so many question but i will first watch your other videos
Video deserves more views
28:20 - As a test subject I say I use old strategies to verify new strategies on the cases both should be valid. That helps reafirm the knowledge of the new strategy, helps me learn the new strategy and also works as a tool to develop a new strategy if you try to invert the process, somehow.
Suggestion towards editing: replace the black screen cuts with something more gradual, every time you did that I thought my screen died. Although I guess the sudden stress might've made me more alert
Otherwise this video is very valuable source of information and it helped me realize/understand my shortcomings about problem solving so thank you very much
Interesting video. The reason I clicked on it is because it approaches something I've been thinking about on and off for a couple of years now, without reaching a satisfactory answer: instead of wondering how to solve a well-defined problem, I'm actually interested in how to _create_ one. What I mean by that is, you often encounter interesting riddles such as the Red-Eyed Monks puzzle, which is the same as the Cheating Husbands puzzle, so both represent the same problem, and if we were to express them in more abstract terms, it would be the same for both. Kind of like seemingly dissimilar knots all represent the same knot in knot theory.
The interesting part about these puzzles is that they give you a minimal set of necessary and sufficient rules required to work out the problem and arrive at the one and only solution to the puzzle. There is no overlap between the rules, there is no redundancy. Take one rule away, and the problem becomes unsolvable (r degenerates into a problem with multiple solutions. Add one rule, and you can still solve it, but the problem loses its elegance because now you have redundancy between your rules. I wonder if there's a field of study that formalises the principles behind the construction of such puzzles. That treats them on their abstract level, divorced from the details of the specifics of the formulation (e.g. Red-Eyed Monks or Cheating Husbands), like what knot theory does for actual physical tangled ropes.
Read:
- "General Intelligence: Adaptation to Evolutionarily Familiar Abstract Relational Invariants, Not to Environmental or Evolutionary Novelty"
- "What is Relational Frame Theory? A Psychologist Explains"
- "AN INTRODUCTION TO RELATIONAL FRAME THEORY: BASICS AND APPLICATIONS"
- "Fluid Intelligence Emerges from Representing Relations"
- "Convergence of multiple fields on a relational reasoning approach to cognition"
hi! :) thank you so much for the amazing video! i have something to share about the squares problem. i removed them a little differently and, since the problem didn't say "remove five toothpicks to create only three squares", i felt satisfied with the result and didn't keep going. there might be studies about that, so i felt like sharing it (i'll try to post the image here in the next comment).
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i realized i couldn't post pictures in here (only yt shorts), so i tried to represent what i did in my mind
It would be interesting to see you do a video on a framework tocimprove problem solving skills. This video was amazing and the interpretation insight was definitely something i have never thought of. But im really curious on your take on how to improve, is it just pattern recognition or is there some intuition after some time?
Fascinating stuff
this is exactly what i needed to know. i wondered if developing problem solving skills in other areas could translate to programming problems. i guess not.
Loved the video and I'm a big fan! Your content is really helpful, but I struggle to organize the info of your videos into a practical study guide. Any chance of a course on study techniques from a to z , would appreciate it a lot? Also, when's the video on encoding strategies coming out? Thanks!
I don´t always leave a comment, but this time I had to! This video is top-notch!
Great job!!
I am super grateful for this; I've been trying to figure out the esoteric thoughts behind why I can so easily tackle issues so I can teach others and this gave me a lot of necessary language to make that translate.
13:40 this one is actually very tricky, since you either have to:
* pull the bottom stick of the X out (which necessarily move the top stick of the X),
* or make a slanted V by moving the top stick of the X.
You can also solve this by:
* making an inequals sign
* doing this:
* * take the top stick off the X
* * eat it (no one said you have to keep it on the board, right?)
* or doing this:
* * take the top stick of the plus sign, and put it to the right of the equal sign
* * turn it and connect it with the other I, making a skewed V
* * the right side now reads `VIIIIII`
* * if you think about `XI` = 10 + 1 = 11, and `VIIIIII` = 5 + 1 + 1 + 1 + 1 + 1 + 1 = 11
* * so, both sides are the same, even though `VIIIIII` is almost breaking the roman numeral formatting rules
I hope you’re doing well Dr. Keep! I’ve been missing your content - all the best 😁
yes he hasn't posted anything for 3 months
14:22 - the equation could also be adjusted to read 9 = 11 - 3. By moving the one of the sticks that form a "V" closer to the other to form an "X." Basically the opposite of what we did in the previous equation.
but 11 - 3 actually equals 8...
@@avimir8805 shit, you're right lol. Idk what I was thinking.
Very cool!
for the candle problem i actually immediately got the answer... and i had never seen the problem until then. like i originally thought i could tack the candle to the wall but that would burn, but then i realised the box is a thingy the candle could balance on
My immediate thought on the candle problem was, use everything and nail everything. I've never encountered this quest before, but my train of thought went like this in five seconds flat:
Tack the tack box bottom end against the wall. Remove the matches and tack the match "drawer" to the bottom ledge of the tack box, creating a reinforced ledge sticking out from the box. Tack the candle through both the tack box and match "drawer" with a single tack from underneath to the standing candle, to secure the candle to the construction. This would create a sturdy construction that would actually hold in real life.
8:51 I think that it's the opposite for me. I don't know what it is, but when I was trying to understand the problem the rules allowed me to pick apart the problem immediately and figure out that the right answer was to flip the leftmost and rightmost card, but when I tried to reason my way through the same problem but instead with my justification involving the drinks and ages it felt much more complex despite being the exact same.
Regarding the matchstick problem, you can also move one stick and cross the = sign to make it ≠ which would also make it true.
For the problem at 23:50 where you had to remove 5 toothpicks to create 3 squares, would it have been wrong to go with this approach? (spoilers below!)
Removing the middle 3 toothpicks, which leaves you with 4 squares. Then choosing one "square" and removing any 2 toothpicks from it other than the middle one. This technically leaves you with 3 squares, although now you have an extra toothpick hanging off one of the squares. It didn't come up as a solution in the video, and I was wondering if this would still work or if it would provide any interesting thoughts as to why one would solve it that way?
On another note, this was a great video! Just for clarity, in your opinion you think good problem-solvers are ones that try to learn as they approach or solve a problem, instead of just solving it without the intent to "learn"?
Sold the last two stick problems so far and the candle one I don't see where I'd be wrong in that problem solving just based upon and idea of thinking compared to thinking it through I changed one stick and ready to May the proper equation in both stick cases. And I didn't use the box with the candle but instead I use the very top of the door.
My solution to the candle and matchstick problem was to put tacks on the wall, and lean the candle onto the tacks.
The issue with using the box is that candles usually have rounded bottoms, they don't sit flat unless in a holder. Even moreso they are top heavy.
The official "solution" only works if the box is made of a very specific material. If it's thin cardboard, it won't be strong enough to hold the candle. If it's plastic, the tacks will not be able to pierce it.
I always seem to fail these types of problems because there are implicit assumptions you are expected to make. I wonder if autism/neurodivergency is related.
Has this aspect been studied? Whether or not a problem's solution would work in real life?
I will also add that dumping the thumbtacks box is dangerous and wasteful; thumbtacks in real life have to be contained. I think that is a barrier to not seeing the solution, at least for me.
You can put tacks in a circular outline on the bottom to create a makeshift holder which would ameliorate the issue of the candle having a circular bottom. If you put the candle closer to the wall in the box, the stiffness of the box is less of an issue.
If you want to get more involved, the match box, as well as the wooden part of the matches (assuming you are safe), can also be used to add additional support. Take the tacks and pierce holes into the matchbox. Then remove the flammable part of the matchsticks and and stick them into these holes so that they are sitting diagonally upwards away from the box (with the part of the stick inside the box facing against the matchbox's corner). Finally, use the tacks to fix the matchbox into the wall so that the sticks are facing upwards and out. If your the corner of the matchbox with the sticks is facing the wall, then the sticks should be sticking outwards and touching the bottom of the tack box, providing some additional support to the tack box by using the normal force of the wall against the matchbox's corner.
All good points. I think it has less to do with neurodiversity and more to do with what assumptions people bring to the problem. I actually tried to film the problem with real objects, but opted to just grab someone else's animation instead because I couldn't find a matchbook anywhere. They're all sold in boxes now. And, as you say, a lot depends on the shape of the candle etc. I tend to be terrible at these insight problems as well, especially when presented in the abstract.
One of the references in the description ("Insight is not in the problem") might talk more about the diverse experiences that people have when solving these problems. A lot of these problems "work" (or "don't work", depending on your perspective) by highlighting, hiding, or misleading in some way. For instance, there's a good argument that the cognitive reflection test involves defying some conversational norms, even though it was designed to test people's ability to inhibit leaping to their first, intuitive response to a question.
I should note that the candle problem was not presented as a hypothetical in the lab studies. People actually did go into a room, where there was a real candle and a real box of tacks and booklet of matches and, given those tools, the best solution seemed to be using the box of tacks as a candle holder.
The finding of functional fixedness, which is something that came out of Duncker's research on the candle problem, is something that comes up in other contexts as well.
Very interesting response, thank you!
I want to add a consideration regarding the Wason 4 card problem. In the numbers and letters version i got some intuition that the 4th card would be correct but i wasn't 100% sure and it would have required more mental effort to figure it out. The thing that i noted is that to me, as a non native english speaker, the words "odd" and "even" are quite ambigous, i confuse then quite often for some reason. In order to remember it i think that "odd" is dimilar to "strange", so if a number is not divisible by 2 it's quite "strange". But the point is that to me it required more effort just to understand the question just from a linguistic prospective
I’m doing a little project where I use the transcript of all your YT videos to create my own method of learning. I’m currently on video 20 something.
My goals are to learn to speak Korean (and type it to a good level), do a Uni course in a small amount of time and learn from books I’m curious about.
I’m supplementing your videos with some books. Memory - 3rd Edition - Alan Baddeley - Michael W. Eysenck, some of Stephen Kosslyn’s work at Minerva.
I’d appreciate greatly if you could link me up with any more key texts . Maybe a reading list from your Stanford course.
Thank you for all you do.
good luck, mate.
I'd be interested in following your progress. How long are you giving yourself?
I have some recommended books here: www.benjaminkeep.com/recommended-reading/
@benjaminkeep This was insightful as ever, particularly with someone getting to grips with metacognition in general.
On something else entirely, are you still planning to make your video covering all the encoding techniques with which you’re familiar? I’ve been looking forward to it!
@14:31 I think is problematic because you are typically not allowed to use the trivial solution. take almost any match and use it to cross the equal into a not equal. Dodgy problem statements may be at fault. A lot of times when I solve those "bad design puzzles" It's more about finding the arbitrary solution the puzzle maker intended.
Dr. Keep, i hope you will have a video on how to prepare for the bar examinations for lawyers.. thank you so much sir for your content..
Thanks for this very useful video. Do you have a suggestion of a book or other resources where I can find more big ideas and problem solving strategies, to improve my problem solving skills?
I think you have to look at discipline-specific stuff. Off the top of my head, in mathematics, The Art and Craft of Problem Solving is excellent. If you can get a copy of Diane Halpern's "Thought and Knowledge: An Introduction to Critical Thinking," that might have some good material.I would also recommend Scott Page's stuff on model-based reasoning.
As I say in the video, getting good at problem solving is really about getting good at problem solving in a specific domain. You can build connections across domains over time, but you first have to figure out what kinds of problems you want to solve.
Really good video, it gave me so much to reflect, think and test, i really liked the domain analogy and the "transfer" things to create a new domain faster, so we got a super domain? Like a big domain about general ideas and inside that domain smallers domains about especific ideas? Is learning the super big domain? And problem solving a even bigger domain than learning? Because we learn to resolve problems most of the time... love your videos
Dr. Keep, is it true that our brains are bad at multi-tasking?
Yes and no, our brain multi-task all the time, we breath, walk, talk, look around at the same time and so on, but at the same time multi-tasking things that requires focus just doesn't work well at all, doing a lot of back and forth between things isn't doing you any favours.
It's bad in general
@DennisBolanos one can multitask, but one should not expect high results from multitasking. When multitasking, our cognitive load increases, which should be allow for highly effective learning. But if you are going to multitask on smaller things which needs low cognitive load….then there is no problem. You can search about Cognitive load to learn more about this.
I think it depends. If you do two+ disparate activities simultaneously and consistently, you can become good at that chunked task. e.g. talking on the phone while burping a baby and cooking dinner.
Depends on how you Chunk them. There is a guy who was seen doing 8 or 9 activities at the same time.