**Ep. 27 - Awakening from the Meaning Crisis - Problem Formulation — Transcript & Summary | SozAI** Source: https://sozai.app/transcript/awakening-meaning-crisis-problem-formulation/ Vervaeke's episode 27 on problem formulation: how intelligence handles combinatorial explosion via relevance realization, contrasting Newell & Simon's problem-space model with ill-defined problems. ## Key Takeaways - Intelligence is best understood through the processes of problem solving and knowledge acquisition, not just outcomes. - Combinatorial explosion makes exhaustive search impossible, so cognition must rely on relevance realization. - Problem formulation, reframing a problem so that salient features guide the search, is central to intelligence. - Ill-defined problems require reformulation into more tractable representations before they can be solved. ## What the video covers - Recaps prior episode: cognitive science should pursue synoptic integration, avoiding equivocation about intelligence. - Argues for focusing on the process of acquiring knowledge rather than knowledge products. - Presents Newell and Simon's problem-space framework: initial state, goal state, operators, and path constraints. - Notes the problem-space diagram is misleading because it is drawn from a God's-eye view, while real problem solvers are in the middle of the space. - Explains combinatorial explosion using chess: roughly 30 moves per turn over 60 turns yields about 4.29 x 10^88 pathways, exceeding brain capacity. - Argues the brain cannot exhaustively search problem spaces, so it must use heuristics and selective attention. - Introduces relevance realization as the core cognitive capacity for making information salient and filtering the space. - Critiques the purely algorithmic, certainty-seeking approach as cognitively unworkable. - Distinguishes well-defined from ill-defined problems, using examples like defining 'game' (Wittgenstein's family resemblance). - Concludes that good problem formulation is needed to turn ill-defined problems into tractable ones, illustrated by the chessboard domino covering puzzle and a parity strategy. ## Chapters 1. 00:00 Recap and Synoptic Integration 2. 03:50 Intelligence as General Problem Solving 3. 06:54 Problem Spaces and Newell and Simon 4. 10:46 Combinatorial Explosion in Chess 5. 14:50 Relevance Realization and Heuristics 6. 17:53 Critiquing Algorithmic Certainty 7. 21:09 Ill-Defined Problems and Wittgenstein's Games 8. 28:37 Problem Formulation and the Domino Puzzle Answers ## Questions about this video What is combinatorial explosion, according to the video? It is the rapid growth in the number of pathways in a problem space as steps increase. The speaker calculates it for chess as about 4.29 x 10^88 possible pathways, far beyond what the brain could search exhaustively. What does the speaker mean by relevance realization? It is the cognitive capacity to determine what information is relevant to a problem, making some features salient and filtering out the rest. The speaker argues this is how intelligence avoids combinatorial explosion. Why does the speaker say the problem-space diagram is misleading? The diagram is drawn from a God's-eye view showing all pathways at once, but a real problem solver is inside the space and does not know which pathway leads to the goal. ## Full Transcript — Download SRT & Markdown 00:00 Speaker A [Music] you [Music] welcome back to awakening from the meeting crisis this is episode 27 so last time we took a look at the nature of cognitive science and argued for synoptic integration that addresses equivocation and fragmentation and the 00:36 Speaker A ignorance of the causal relation between these different levels which we talked about mind and study mind and it does that by trying to create plausible and potentially profound constructs and then I propose to you that we start doing 00:53 Speaker A cognitive science in in two ways first of all just trying to look at the cognitive machinery that is responsible for meaning cultivation but also try to exemplify that pattern of bringing about synoptic integration through the generation of plausible and potentially 01:19 Speaker A profound constructs so we took a look at the central capacity to be a cognitive agent and this is your capacity for intelligence and of course intelligence is something that neuro scientists are looking for in the brain and that 01:38 Speaker A artificial intelligence machine learning is trying to create they're trying to create intelligence psychology of course has famously been measuring intelligence since it's very inception the word intelligences has reading between the lines which seems we'll see has a lot to 01:56 Speaker A do with your use of language and etc culture of course seems to be deeply connected to the application and development of intelligence so intelligence is a great place to start and then I said we need to be very 02:12 Speaker A careful we don't want to equivocate about intelligence we want to make sure we we approach it very carefully because although it is very important to us we often are using the term in an equivocal and confused and therefore bullshitting ourselves an 02:30 Speaker A important way and then I propose to you that we don't focus on the results the product of our intelligence our knowledge and what our knowledge does for us our technologies for example we focus instead on the process that allows 02:47 Speaker A us to acquire knowledge because that way we have something we can use intelligence to explain how we have acquired the knowledge we have I then propose to you to follow the work that was seminal both in the psychometric 03:03 Speaker A measure of intelligence Binet and Simon and the attempt to artificially generate intelligence the work of New Orleans Simon and this is the idea of intelligence is your capacity to be a general problem solver to solve a wide variety of problems across a wide 03:22 Speaker A variety of domains and then in order to get clear about that we took a look at the work of New Orleans Simon trying to give us a very careful formal analysis of what is going on in intelligence and 03:40 Speaker A I'm going to come back to those you know those ideas in a minute or two this idea of an analysis of formal analysis a problem was analyzed into a representation of an initial state in the goal state and I have a problem when 03:54 Speaker A my initial state and my goal state are significantly different I can then apply operations or operators these are actions that will change one state into another State remember me moving towards the cup raising my hand for example and 04:07 Speaker A I can have a sequence of operations that will like take me from my initial state into my goal state but I have to follow the path constraints I want to remain a general problem solver I don't want to 04:17 Speaker A solve any one problem to the detriment of my capacity to be a general problem solver or then my solving this problem will undermine my intelligence in general so to solve a problem is to apply a sequence of operations that will 04:32 Speaker A transform the initial state and the goal state while following the path constraints and then you can analyze that by taking a look at the space and it was this explication making explicit of the problem space that was the radical and I will in fact argue 04:50 Speaker A profound power in what New Orleans Simon was doing that's what made that their work so impactful right in so many disciplines now there's two things we have to note about this that are potentially misleading right first of all one is I didn't draw the whole 05:11 Speaker A diagram out and that wasn't just happenstance okay we'll come back to that the second one is this diagram is misleading precisely because it is created from God's eye point of view if I were to fill the diagram out you could 05:24 Speaker A see all of the pathways at once and you could see at once which pathway leads from the initial state to the goal state but of course in life when you have a problem that you are not out here having a problem is 05:37 Speaker A precisely to be here and you do not know which of all these pathways will take your initial state to your goal state while obeying the path constraints you don't know that you're ignorant because remember we're not confusing intelligence with knowledge solving this 05:53 Speaker A is how you acquire knowledge a problem-solving method is any method for finding the sequence of transformations that will take you from the initial state into the goal state while obeying the cop constraints and you say ok I get 06:09 Speaker A it the diagram isn't complete and you're over here you can't see the whole thing you don't know which of all the pathways yeah so what well here's so what when I have analyzed this and formalized it when I've 06:20 Speaker A explicate Edyta in terms of problem space it reveals something I can calculate the number of pathways here by the formula F to the D where F is the number of operators on the plying at any stage and D is the number of stages I go 06:34 Speaker A through so Keith holyoke gave a very famous example of this right psychologist who was instrumental in doing important work on the psychology of problem solving let's do a concrete example of this and then it's a great example because it brings 06:55 Speaker A machines that we have today so let's say you're playing a game of chess right so on average the number of operations you can perform on any turn that's f is 30 now don't say to me well many of those 07:14 Speaker A are stupid that's not the point I'm trying to explain how your intelligence that's what I have to explain it's not what it can assume okay so there's 30 legal moves and on average there's 60 turns that's the number of 07:30 Speaker A pathways that are in the problem space this is known as combinatorial explosion it sounds like a science-fiction weapon but it's actually a central fact this is a vast number it's something like four point two nine times ten to the 88 in 08:01 Speaker A standard and sort of scientific notation now I want to I want you to understand how big this is how astronomically incomprehensibly large this is okay so one thing you might say is well you know that's easy I have many different 08:22 Speaker A neurons and they all work in parallel and they're all checking different alternative pathways and that's how I do this parallel distributed processing and there's an important element in that but that's not going to be enough because you know you probably have sort of 08:39 Speaker A around that many neurons now that's a lot but it's nowhere near this and you say ah but it's not the neurons it's the number of connections and that's something like five to the 10 to the 15th and that's a big number but you 08:53 Speaker A know what it's no it's astronomically far away from it's astronomically far away from this so even if it's each synaptic connection is exploring a pathway this is still overwhelming your brain in fact this is greater than the number of atomic particles that are 09:11 Speaker A estimated to exist in the universe does this is in a literal sense bigger than the universe it's big and what does that mean that means you cannot do the following you cannot search the whole space for very very 09:38 Speaker A many problems the problems are combinatorially explosive and therefore you cannot search the dust space you do not have the time the machinery the resources to search the whole space now here is what is deeply deeply interesting about you this is sort of my 10:01 Speaker A professional obsession you might put it if I could represent it this way right if this is the whole problem space this is somehow this is what you do somehow you can't search the whole space and in and I mean you can't sir 10:23 Speaker A you can't look here and then reject because if you look at this part of the space and reject it and then look at this part of it then you end up searching the whole space it's not a matter of checking and rejecting because 10:33 Speaker A that's to search the whole space what you do is somehow do this you somehow zero in on only a very small subsection of that whole space and you search in there and you often find a solution you somehow zero in on the relevant 10:50 Speaker A information and you make that information right effective in your cognition you do what I call relevance realization you realize what's relevant now this fascinates me right and and this and and that fascination is due to the work of new orleans simon because 11:16 Speaker A how do you do that like and you say oh the computers are really fast even the fastest chess-playing computers don't check the whole space they can't they're not powerful enough for fast enough that's not how they play this issue of avoiding combinatorial 11:36 Speaker A explosion is actually a central way of understanding your intelligence and you probably hadn't thought of that before that one of the things that makes you crucially intelligent is your ability to zero in on relevant information and of course you're experiencing that in two 11:52 Speaker A related but different ways one way is your and the way this is happening so automatically and seamlessly for you is the generation of obvious Ness like what's obvious well obviously I should pick up my marker obviously I should go 12:11 Speaker A to the board obvious 'no siz not a property of physics or chemistry or biology obvious Ness is not what explains your behave explains your behavior in a common-sense way but obviously this is what I scientifically have to explain how does your brain make 12:27 Speaker A things obvious to you and that's related to but not identical to this issue of how things are salient to you how they stand out to you how they grab your attention and what we already know right is that that process isn't static 12:47 Speaker A because sometimes what you how you how you zeroed in on things as relevant what was obvious to you what was salient to you how you join the nine dots is obvious and salient to you and yet you get it wrong and part of your ability is 13:03 Speaker A to restructure what you find relevant and salient you can dynamically self organize what you find relevant and salient now Newell and Simon wrestled with this and there's a sense in which this is the key problem that the project 13:26 Speaker A of artificial general intelligence is trying to address right now in fact that's what I argued I've argued in some work I did with Tim Leela crop and Blake Richardson work I've done with Leo Ferraro there's a related work by other 13:41 Speaker A people but New Orleans Simon realized that in some way you have to deal with combinatorial explosion to make a general problem solver you have to give the Machine the system the capacity to avoid combinatorial explosion we're gonna see that this is probably the best 14:05 Speaker A way of trying to understand what intelligence is people like Stan a argue that what we're measuring when we're measuring your intelligence and psychometric tests is precisely your ability to deal with computational limitations to avoid combinatorial explosion Christopher charity act argue 14:23 Speaker A something similar so what did New Orleans Simon propose well I want to talk about what they propose and show why I think it's important and then criticize them and in what in what they mistook or misunderstood and therefore 14:43 Speaker A why their solution and they I don't think they would have disputed that why their solution was insufficient so they proposed a distinction that's used a lot but the term has these terms have slipped I've watched them slip in in in 14:59 Speaker A the 25 years I've been teaching at U of T I've seen that the terms flip around but I want to use in the way Newell and Simon use them within the context of problem solving and this is the 15:10 Speaker A distinction between a heuristic and an algorithm they actually didn't come up with this distinction this actually came from an earlier book by polla on called how to solve it which was a book just on the psychology and it was a set of 15:24 Speaker A practical advice for how to improve problem-solving so remember we talked about what a problem-solving technique is a problem-solving technique is a method for finding a problem solution that's not trivial because a problem solution has been analyzed in terms of a 15:41 Speaker A sequence of operations that takes the initial state into the goal state while obeying the path constraints okay so what's an algorithm an algorithm is a problem-solving technique that is guaranteed to find a solution or prove and I'm using that term technically 15:55 Speaker A not give evidence for but or prove that a solution can't be found right and of course there there are algorithmic things you do you know the algorithm for doing like multiplication for example you know 33 times four right there is a 16:13 Speaker A way to do that in which you can reliably guaranteed get an answer so this is important and I remember I said I'd come back to you and explain why ttyl de cartes project was doomed for the failure because algorithmic processing 16:28 Speaker A is is processing that is held to the standard of certainty you use an algorithm when you are pursuing certainty now what's the problem with using an algorithm as a problem-solving technique well it's guaranteed to find an answer or prove that an answer is not 16:44 Speaker A fun not findable so algorithms work in terms of certainty ask yourself in order to be certain that you've found the answer or proved that an answer cannot be found how much of the problem space to have to search so there's some a 17:08 Speaker A priori things you can do to shade the problems face down a little bit and you know computer science talks about that but generally for all practical purposes and intents in order to guarantee certainty I have to search the space the 17:21 Speaker A whole space and the space is combinatorially explosive so if I pursue algorithmic certainty I will not solve any problems I will have committed cognitive suicide if I try and write B algorithmically certain in all of my processing if I'm pursuing 17:40 Speaker A certainty and right as I'm trying to get over to the cup Comet or explosive space opens up and I can't get there because my life time my resources my processing power is not sufficient to search the whole space that's why a cart was doomed 17:58 Speaker A from the beginning you can't turn yourself into mr. Spock you can't turn yourself into data you can't turn yourself into an algorithmic machine that is pursuing certainty that is cognitive suicide that tells us something right away by the way because 18:14 Speaker A logic deductive logic is certainty it is algorithmic it works in terms of certainty an argument is valid if it is impossible for the premises to be true at the conclusion false logic works in terms of the normativity of certainty it 18:32 Speaker A operates algorithmically so does math you cannot be comprehensively logical if I try to be mr. Spock and logic my way through anything I'm trying to do most of my problems are combinatorially explosive and I won't solve even one of 18:51 Speaker A them because I'd be overwhelmed by a combinatorial explosive search space this tells you something this is what I meant earlier when I said trying to equate rationality with being logical is absurd you can't do that the issue these 19:20 Speaker A terms are not and cannot be as much as Descartes wanted them to be they are not and cannot be synonymous now that doesn't mean that rational means being illogical or willy-nilly the ratio rationing pay attention to this ratio 19:41 Speaker A rationing being rational means knowing when where how much and what degree to be logical and that's a much more difficult thing to do and I would argue more that being rational is not just the psycho technology of logic but other 20:02 Speaker A psycho technologies knowing how knowing where when and how to use them in order to overcome self-deception and optimally achieve the goals that we want to achieve often when I talk about rationality people think I'm talking about logic or 20:23 Speaker A consistency and they misunderstand that is not what I've meant and that's what I said when Descartes was wrong in a deep sense from the beginning okay Nolan Simon realized this that's why precisely why they proposed the distinction a heuristic is a 20:45 Speaker A problem-solving method that is not guaranteed to find a solution it is only reliable for increasing your chances of achieving your goal so I've just shown you you cannot play chess algorithmically of course you can and even the best computer programs do this 20:59 Speaker A play chess heuristic alee you can play chess doing the following things right here are some heuristics you know get your Queen out early control the centreboard castle your king you can do all of these things and nevertheless not 21:14 Speaker A achieve your goal winning the game of chess right and that's precisely because of how heuristics work what heuristics do is they try to pre specify where you should search for the relevant information that's what a heuristic does it limits the space 21:40 Speaker A you're searching now what that actually means is it's getting you to prejudge what's going to be relevant and of course that's where we get our word prejudice from and a heuristic is therefore a bias it's a source of bias 21:56 Speaker A this is why the two are often paired together heuristic bias approach look what my chest your wrist extension I focus on the centreboard I focus on my queen if I'm playing against somebody who's very good they'll notice how I'm 22:12 Speaker A fixated on the centreboard in the queen and they'll keep me focused there well playing a peripheral game that defeats me I played a game of chess not that long ago and I was able to use that strategy against someone okay there is 22:27 Speaker A this is called the no free lunch theorem that it is unavoidable you have to use heuristics because you have to avoid combinatorial explosion you can't be comprehensively algorithmic logical mathematical the price you pay for avoiding combinatorial explosion is you fall prey to by us 22:47 Speaker A again and again and again the very things that make us adaptive are the things that make us prone to self-deception now there's going to be deep reasons later while why this is insufficient right but if you remember we talked about these heuristics and 23:10 Speaker A biases when we talked about the representative heuristic and the availability heuristic the representativeness heuristic and the availability heuristic that were at work when you take your friend to the airport because you can't calculate all the probabilities it's combinatorially 23:25 Speaker A explosive so you use the heuristic how easy can I remember plane crashes how much how prototypical to do this how representative are they of disasters and tragedies and because of that you judge it highly probable that the plane will 23:40 Speaker A crash and then you ignore how deeply dangerous your automobile is right so the very things that make you adaptive make you prone to self-deception now this account I think I I have tremendous respect for Nolan Simon right first of 24:10 Speaker A all let me tell you why I have respect and then what what criticisms I have so first of all this idea that part of what makes you intelligence is your ability to use heuristics I think that's a necessary part and the empirical 24:25 Speaker A evidence that we use these heuristics is quite quite powerful and convincing and well replicated this is also an instance of doing really really powerful work and this will add one more dimension to what it is to do good cognitive science 24:51 Speaker A yes it's about creating plausible constructs that afford synoptic integration but there there is another way in which New Orleans Simon exemplified they model to us what it is to do it well their proper properly and again this is going to relate to the 25:09 Speaker A meaning crisis notice what they've done notice how all all of the aspects all of the great changes that have made the scientific way of thinking possible are exemplified in what New Orleans Simon are doing notice that they're analyzing 25:22 Speaker A they're taking right a complex phenomena and they're trying to analyze it down into its basic components just like they Lee's did so long ago when he was trying to get at the underlying substances and forces they're trying to do that 25:37 Speaker A ontological depth perception and then like Descartes they're trying to formalize it they're trying to give us a graphical mathematical representation the problem space is a formalization that allows us to do calculations equations that's how I was able to 25:53 Speaker A explain to you combinatorial explosion and then what they were doing right is they were trying to mechanize I know that will make some people's hackles rise but the point of this is I I've got this right if I can make a machine that 26:11 Speaker A can carry out my formal analysis because that means I haven't snuck anything in and that really matters because it turns out that trying to explain the mind we often fall into a particular fallacy okay so you know how would you see well 26:40 Speaker A here's a triangle out here and the light comes off of it when it goes into your eye right so that's a really horrible eye goes into your eye and then the nerve impulse is and then I'll equivocate on the notion of information 26:54 Speaker A to hide all kinds of theoretical problems and then it goes into like it goes into this space inside of my mind wait but it's called maybe working memory or something and it gets projected onto some inner screen and 27:06 Speaker A there there it is it's projected there and then there's a little man in here the Latin for little man is homunculus and the little man maybe it's your central executive or something says triangle so that's how it works right and notice notice what's 27:25 Speaker A going on here it sounds like I'm giving a mechanical excellent and then I invoke something now what you should ask me right away is the is the following ah yes but John how does the little man the little homunculus see the inner 27:39 Speaker A triangle oh well inside his head is a smaller space with a smaller projection in the middle and there's a little man in there that okay and so on and so forth and you see what this gets this gives you an infinite regress it doesn't 27:57 Speaker A explain anything why this is the circular explanation remember we we talked about this right this is when I'm using vision to explain vision and you say well yeah that's stupid I get by that stupid that's non explanatory circular explanations are non 28:16 Speaker A explanatory yes or not they are they're not explanatory but here's what I ultimately have to do and this is what Newell and Simon are trying to do they're trying to take a mental term intelligence and they're trying to 28:35 Speaker A analyze it formalize it and mechanize it so they can explain it using non mental terms because if I always use mine to explain mine I'm actually never explaining the mine I'm just engaged in a circular explanation what Newell and Simon are 28:58 Speaker A trying to do is analyze formalize and mechanize an explanation of the money they're not doing this because they're fascists or they're worshipers of science or they're in enamored with technology maybe some of those things are true about them but independent from 29:13 Speaker A that I can argue is which is what I'm doing that the reason they're doing this is that it exemplifies the scientific method because it is precisely designed to avoid circular explanations and as long as I'm explaining the mental in 29:31 Speaker A terms of the mental I'm not actually explaining it I call this the naturalistic imperative in cognitive science try to explain things naturalistically again some of this might be because you have a prejudice in favor of the scientific worldview and 29:52 Speaker A there's all kinds of cultural constraints of course I'm not denying any of that critique but what I'm saying is that critique is insufficient because here's an independent argument the reason I'm doing this is precisely because I am trying to avoid circular 30:10 Speaker A explanations of intelligence why does that matter remember the Scientific Revolution produced this scientific worldview that seems to be explaining everything except how I generate scientific explanations my intelligence my ability to generate science is not one of the things that is 30:35 Speaker A encompassed by the scientific worldview there's this hole in the naturalistic worldview that's why many people who are critical of naturalism always zero in on our capacity to make meaning and have consciousness as the thing that's not being explained their right to do that I 30:52 Speaker A think they're wrong to conclude that that somehow legitimates other kinds of worldviews right we'll come back to that because I think what you need to show is you need to show that this project yeah because this is an inductive argument it's not a 31:13 Speaker A deductive you have to show that this project is failing that we're not making progress on it and that's a difficult thing to say you can't you can't defeat a scientific program by saying 22 things that hasn't yet explained because if 31:27 Speaker A that will always be the case you can't point to problems it faces right what you have to do and this is something I think that lack ratash made very clear you have to point to the fact that it's 31:36 Speaker A not making any progress in improving our explanation and it's really questionable and I mean that term seriously that we're not making any progress in explaining intelligence by trying to analyze formalizing mechanize it that's that's getting really hard to claim that 31:54 Speaker A we're not making any progress now why does this matter because if cognitive science can have give create a synoptic integration by creating plausible constructs theoretical ways of explanation like what Newell and Simon are do doing that allow us to analyze formalize and 32:16 Speaker A mechanized they have the possibility of making us part of the scientific worldview not as animals or machines but giving a scientific explanation of our capacity to generate scientific explanations we can fit back into the scientific worldview that science has 32:38 Speaker A actually excluded us from as the generators of science itself so New Orleans címon are creating this powerful way of analyzing formalizing and mechanizing intelligence there's lots of stuff converging on it there's stuff from how we measure intelligence talk about it I were trying to make 33:06 Speaker A machines right and and it holds a promise for revealing things about intelligence that we didn't know before like the fact that the one of the core aspects of intelligence is precisely your ability to avoid common tutorial explosion make things salient and 33:23 Speaker A obvious and do this in this really dynamically self-corrective fashion like when you have an insight so I'm done praising New Orleans Simon for now now I want to criticize them because New Orleans Simon's notion of heuristic also a valuable part of the multi Optus a 33:43 Speaker A valuable new explanatory way of dealing thinking about our intelligence while necessary is insufficient because New Orleans Simon were failing to pay attention to other ways in which we constrain the problems faced and zero in on relevant information and do that in a 33:59 Speaker A dynamically self-organizing fashion well what were they failing to to notice they were failing to notice right that they had an assumption in their attempt to come up with a theoretical construct for explaining general problem solving they assumed that all problems were 34:30 Speaker A essentially the same this is kind of ironic we have a heuristic a heuristic you remember charlie nostalgia we have a heuristic of essentialism this is also a term that has been taken up and I think often applied loosely within political 34:55 Speaker A controversy and discourse the idea of essentialism is that when I group a bunch of things together with a term remember Ockham's ideas about we group things together just by the words we use for them that's nominalism but when I group 35:11 Speaker A a bunch of things together they must all share some core properties they must share an essence remember that's the Aristotelian idea of a set of necessary and sufficient conditions for being something now it is of course the case 35:26 Speaker A that some things clearly fall in that category triangles have an essence all triangles no matter what their shape or size have three straight lines three angles and the angles add up to 180 degrees and if you have each and every 35:41 Speaker A one of those you are a triangle right and there are also natural kinds one of the things that science does and we'll see why this is important later is it discovers those groupings that have an essence so all gold things have a set of 35:54 Speaker A properties that are essential to be in gold right and we'll talk about why that's the case later not everything we group together and this was famously pointed up by Vic and Stein right has an essence oh let's use Vic in Stein's 36:12 Speaker A example first if you remember right we call many things games now what what set of necessary and sufficient conditions do all and only games possess right well all they involve competition well there are many things that involve competition 36:34 Speaker A that aren't games war and there are games that don't seem to involve competition like catch oh well you at least they involve other people solitaire oh they well they have to involve imagination it's all the terror but they have to involve pretense catch 36:54 Speaker A what do you pretending to do and this is Vic and Stein's point you won't find a definition that includes all and only games and this is the case for many things like chair table etc remember this was all part 37:12 Speaker A what Arkham was pointing to I think so the idea is we come with a heuristic we treat any category as if it has an essence but many categories don't have essences we're going to come back to that shortly in a few minutes when we 37:31 Speaker A talk about categorization why do we use this heuristic because it makes us look for essences why do we want to look for essences because this allows us to generalize and make very good predictions yes I can over generalize 37:53 Speaker A but I can also under generalize that's also a mistake so we use this heuristic because it's adaptive it's not algorithmic because there are many categories that don't have essences Newell and Simon thought this category had an essence that all problems are 38:20 Speaker A essentially the same that all problems are essentially the same and therefore they could come up with one base all I needed to call it if all problems are essentially the same then to make a general problem solver I basically need 38:36 Speaker A one right one problem solving strategy I just have to find the one essential I may have to make variations on it but I have to I have to find the one essential problem solving strategy and because of this how you formulate a 39:03 Speaker A problem how you set it up to try and apply your strategy how you represent the initial state the goal state the operators the path constraints that's that's trip that's trivial right that's not important because if all problems are essentially the same you're going to 39:20 Speaker A be applying basically the same problem solving strategy now both of those assumptions that are driven by they were in fact being driven by a psychological heuristic of essentialism essentialism isn't a bad thing at least talking about it as a cognitive heuristic alright it 39:46 Speaker A shouldn't be treated algorithmically but we shouldn't pretend that we can do without it okay now if Nolan's Simon were right about this then of course these aren't problematic assumptions but they're actually wrong about it because there there are and many people have converged 40:14 Speaker A on this at different times in using different different terms but there are fundamentally different kinds of problems and there there's different ways in which a different kind of roblems I'm just I just want to talk about a central one that's really 40:27 Speaker A important to you your day to day life this is the distinction between well-defined problems and ill-defined problems seeing a well-defined problem I have a good meaning and effective guiding representation of the initial state the goal state the operators so that I can 40:56 Speaker A solve my problem so I take it that for many of you that problem I gave earlier and as there is a relationship between something being well-defined an algorithmic they are not identical but there is a relationship right for many 41:09 Speaker A of you that should be a well-defined problem you can tell me your initial state this is a multiplication problem and that gives you useful guiding information you know a lot of things by knowing your initial state you know what 41:22 Speaker A the the goal state should look like this should be a number when I'm done and you know that this number excuse me should be bigger than this number these two numbers the most beautiful picture of all time of a platypus does not count as 41:36 Speaker A an answer you know what the operations are singing and dancing are irrelevant to this this is well demand you and a lot of your education was getting you to practice making whole sets of problems well-defined and part of what psycho 41:58 Speaker A technologies do is they make well-defined problems for us like literacy and numeracy mathematics now because of that power and because of their prevalence in our education we tend to get blinded and we tend to think that that's what most problems are like 42:17 Speaker A and that means we don't pay attention to how we formulate the problem because the problem is well formulated for us because I Slee precisely because it's a well-defined problem but most of your problems are ill-defined problems and most of your problems you don't know 42:34 Speaker A what the relevant information about the initial state is you don't know what the relevant information about the goal state is you don't know what the relevant operators are you don't know what the even the relevant path constraints are 42:53 Speaker A you're sitting in lecture perhaps at the University and you've got this problem take good notes okay what's the initial state well I don't have good notes and well yeah okay okay so what should I do and all you'll do is 43:11 Speaker A give me synonyms for relevance realized right I should pay attention to the relevant information the crucial information the important information and how do you do that oh well you know it's obvious to me or it stands out to 43:25 Speaker A me great but how how would I make a machine be able to do that what are the operations oh I write stuff down do you do I just write stuff down right like I draw I make arrows I do I write 43:41 Speaker A everything down well no I don't write everything down and I don't just what are the operations does that mean everybody's notes will look the same no when I do this in class everybody's notes look remarkably very different so 43:53 Speaker A what are the operations and what does what's the goal state look like well good notes great what are the properties of good notes well they're useful why are they useful well Beco oh right because they contain the relevant information connected in 44:07 Speaker A the relevant way that makes sense to me and so I can use it to Sofia right I get it what's actually missing in an ill-defined problem is how to formulate the problem how to zero in on the relevant information and thereby 44:23 Speaker A constrain all right the problem so you can solve it so what's missing and what's needed to turn to deal with your ill-defined problems and turn them something into something like well-defined problems for you is good problem formulation which involves 44:47 Speaker A again this process of zeroing in on relevant information relevant relevance realization and you see if they had noted this if they had noted that this bias made them trivialize formulation they would have realized that there are problems aren't all 45:08 Speaker A essentially the same and they would have realized the important work being done by problem formulation and that would have been important because that would have given them another way of dealing with the issue of combinatorial explosion let me show you so we already 45:28 Speaker A see that the relevance realization that that work and problem formulation is crucial for dealing with real-world problems taking good notes that's another fun problem following a conversation that's another fun part well I should say things what things well oh the relative when well you oh 45:46 Speaker A it's appropriate how often well sir tell a joke go on a successful first date all of these are ill-defined problems most of your real-world problems are ill-defined problems so you need the relevance realization within good problem formulation to help you deal 46:09 Speaker A with most real-world problems already problem formulation is crucial but here's something that New Orleans Simon could have used and in fact Simon comes back and realizes it later in an experiment he does with Kaplan in 1990 and I want to show you this 46:32 Speaker A experiment because I want to show you precisely the power of problem formulation with respect to dealing with constraining the problem space and avoiding combinatorial explosion I need to be able to deal with ill-defined problems to be genuinely intelligent I 46:48 Speaker A also as we've already seen have to be able to avoid combinatorial explosion that has something to do with relevance realization and that has a lot to do as we've already seen with problem formulation let me give you the problem 47:01 Speaker A that they used in the study of the experiment okay so this is called the mutilated chessboard example right there are eight columns and eight rows and so we know that there are 64 squares now because this is a square I didn't draw it 47:24 Speaker A perfectly square but pretend it is if I have a domino and it covers two squares it'll cover two squares equally if I put it horizontally vertically how many dominoes do I need to cover the chessboard well that's easy two goes 47:36 Speaker A into 64 right I need 32 32 dominoes will cover this without overhang or overlap now I'm gonna mutilate the chessboard I'm gonna remove this piece in this piece okay so how many squares are left here right 62 there's 62 squares left so I've now 48:00 Speaker A mutilated the chessboard here's the problem can I cover this with 31 dominoes without overhang or overlap and you have to be able to prove the duct of Lee demonstrate that your answer is correct now many people find this a hard problem 48:21 Speaker A they find it a hard problem perhaps you're doing this now because they formulated as a covering problem they're imagining they're trying to imagine a chessboard and they're trying to imagine possible configurations of dominoes on the board so they adopt a covering 48:40 Speaker A formulation of the problem a covering strategy and they try to imagine it that strategy is combinatorially explosive so famously there was somebody one of the people in one of the experiments one of the participants trained in mathematics and was doing this topographical 49:03 Speaker A calculation and they worked on it for like what is it 16 to 18 hours and filled 81 pages of a Hillary notebook and they didn't come up with a solution why because if you formulate this as a covering strategy you hit combinatorial 49:18 Speaker A explosion this the problem space explodes and you can't move through it and that's what happened to that participant not because they lacked the logic or mathematical abilities in fact it was precisely because of their logic and mathematical abilities that they came to grief now 49:44 Speaker A you should know by now that I am not advocating for Romanticism oh just give up logic and rationality that's ridiculous you've seen why I'm critical of that as well but what I'm trying to show you again is you cannot be 49:58 Speaker A comprehensively algorithmic okay so if you formulate this as a covering strategy you can't solve it let's reformulate it you can't quite see this on the diagram but you'll be able to see it clearly in the panel that comes up 50:14 Speaker A right these squares are always the same color on a chess board in fact that's not hidden in the diagram and and what's used in the actual experiment clearly that's clearly visible these squares are always in the same color you say so what 50:32 Speaker A right that's the point you can see them but they're not salient to you in a way that makes a solution obvious to you they're not salient to you they're there but they're not standing out to you in a 50:44 Speaker A way that makes a solution obvious to you but let's try this if I put this Domino on the board if I put it horizontally or vertically I will always cover a black and white square always there is no way 50:58 Speaker A of putting it on the board that will not cover a black and white square so in order to cover the board with dominoes I need an equal number of black and white squares I must have an equal number of 51:11 Speaker A black and white squares that must be the case but these squares are the same color is there now an equal number of black and white squares there no because these are the same color there is not a number an equal number of black and 51:27 Speaker A white squares I must have an equal number of black and white squares I know for sure because these are the same color I do not have an equal number of black and white squares therefore I can prove to you that is an impart it is 51:41 Speaker A impossible to cover the board with the Domino's if I go from replicas from formulating this problem as a covering strategy which is combinatorial explosive to using a parity strategy in which the fact that they are the same color is salient to me 52:03 Speaker A such that now a solution is obvious no it's obvious that it's impossible I go from not being able to solve the problem because it's combinatorially explosive to a search space that collapses and I solve the problem this is why the phenomena we've been talking 52:23 Speaker A about when we talked about flow and different aspects of higher states of consciousness is so relevant this capacity to come up with good problem formulation problem formulation that turns ill-defined problems into well-defined problems for you problem formulation that goes from a 52:39 Speaker A self-defeating strategy because of combinatorial explosion to a problem formulation that allows you to solve your problem that's insight that's insight that's why the title of this experiment is in search of insight that's exactly what insight is it is the 53:02 Speaker A process by which bad problem formulation is being converted into good problem formulation that's why insight in addition to logic is central to rationality and in addition to any logical techniques that improve my inference I have to have other kinds of 53:28 Speaker A psycho technologies that improve my capacity for insight and we've already seen that that might have to do with things like mindfulness because of mindfulness capacity to give you the ability to restructure your family its landscape so we're starting to see how problem 53:53 Speaker A formulation and relevance realization are actually central to what it is for you being a real-world problem solver avoiding combinatorial explosions avoiding ill-defined Ennis we're going to continue this next time as we continue to investigate the role of relevance realization in intelligence 54:15 Speaker A and related intelligent behaviour like categorization action communication thank you very much for your time and attention [Music] you [Music] you you Topics: relevance realization problem formulation combinatorial explosion Newell and Simon problem space intelligence cognitive science heuristics ill-defined problems John Vervaeke Study this video - [Flashcards from this video](https://sozai.app/tools/flashcard-maker/?from=transcript&id=91135) - [Quiz on this video](https://sozai.app/tools/quiz-generator/?from=transcript&id=91135) - [Crossword from this video](https://sozai.app/tools/crossword-maker/?from=transcript&id=91135) - [Word search from this 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