• Skeptic
    35
    There are a lot of discussions about education and ability to solve complex problems. I always felt that there should be a theory behind that but failed to find anything solid. In some sense the entire field was started by philosophy and logic, but the sad point here is that it became too abstract.

    To make someone a better solver you need to show him a starting point too, not just a last one. The most promising field here is cognitive psychology, it even has a dedicated topic: CPS (complex problem solving). I found a lot of interesting details there but not a solid, holistic view.

    Is that really so difficult to connect available knowledge to create something solid and meaningful and more importantly, useful?

    For example, I would start with following three main principles for that:
    • principle of similarity - it's a starting point of the mind, we need to sort out somehow a chaos around us.
    • principle of regularity - we need to be able to see interconnections, sequences and patterns. Principle of similarity creates a static world model and principle of regularity gives us a set of constraints to create a dynamic one.
    • principle of obviousness - if our world model produces a stable result about some fact then it become obvious for us

    All three principles are about fundamental unconscious processes. Principles are extremely simplified and it's only a part of them (unconscious part), but even such a model can already be very useful. For example:
    • the structure of our knowledge is directly related to our ability to solve problems. Knowledge itself isn't enough, it should be structured properly for the specific problem
    • our sense of obviousness is faulty but can be adjusted via structure of our knowledge

    P.S. The theoretical part will be further explained below on the first page, the practical hopefully on the second one
  • JerseyFlight
    782
    we need to be able to see interconnectionsSkeptic

    In my opinion this is the axiom of comprehension. Remove this and all one has, which accounts for nearly all contemporary philosophical positions, are a bunch of disconnected, abstract categories, which inevitably lead to confusion and disharmony, the opposite of comprehension.
  • Gregory
    1.9k
    People structure their ideas differently. Smart people are those who have a complexity of thought or who are able to go down an avenue of thought that is difficult. Look at animals. We really don't have a comprehensive way of studying the complexity or subtlety of their thought. Humans are so varied we can hardly do this with us
  • batsushi7
    45
    Can you train a man to be better at IQ test? And score higer after multiple attempts? I wonder if there is any scientific research done on the subject. Far as I know, the IQ stays same, and goes lower after time passes. But how can you even train one cognitive skills?
  • Philosophim
    386


    This is a good topic. I was a high school math teacher for 5 years, so its something that I've had time to think on. There are a few things I tried over the years, and there are quite a few factors that can help learning.

    1. Removing the road blocks

    One of the biggest road blocks to learning is fear. And fear, is often the fear of failing, and having other people be aware of it. When you fail, you are in a vulnerable position. No one wants to be ragged on or attacked in a vulnerable position. The best students are the humble one's that are open to failure. The worst are those who are full of themselves and think they know it all. Dunning Kruger to the extreme, they are always the most difficult people to teach.

    A second roadblock is unclear teaching material. If you cannot communicate the lesson in a clear and easy to follow manner, it is not the student's fault. It is YOUR fault (mine in this case).

    2. Showing a person the value of learning what you are teaching

    I can teach a person how to weave a basket underwater, but why would they want to learn? Demonstrating the value of the skill is essential as well. This is done by demonstrating a positive feeling to the particular student. Some love a challenge, some don't. Some like it when you work with them, some don't. I'm a big fan of giving different options of learning. I used to give my homework and the lesson plan page every morning. You were not required to listen to my lecture, only have the homework finished, and not to disturb others during the lecture. If you were found not completing the homework or doing poorly, only then were you required to listen.

    3. As an educator, removing low expectations, but respecting the results of effort given.

    If you give your students expectations, most will try to rise to it to some level. If you have expectations of your students that they are dumb or foolish, they will happily sink to that as well. That being said, if a person genuinely tries and comes up short of your expectation, respect that 100%. While sadly school require a timeframe of learning, that really shouldn't be the emphasis. Some things take longer for people to learn than others, and we should not punish those who are genuinely trying because of some arbitrary time frame.
  • Skeptic
    35
    In my opinion this is the axiom of comprehension.JerseyFlight

    totally agree, but it looks like you are talking about a bit higher level

    Humans are so varied we can hardly do this with usGregory

    definitely, but we are still making the same issues regardless of the hemisphere. It means that we have many things that identical across population and three principles that I described is an example. They are identical not only across humans but also across many species of animals.
  • Skeptic
    35
    Can you train a man to be better at IQ test?batsushi7

    One of the downsides of IQ test is that it's extremely easy to train for. There is one ancient approach to train cognitive skills: use them on daly basis :). Quite rough method, so not every one have enough power of will to handle it. That's why I think we need something a bit more delicate.
  • Skeptic
    35
    There are a few things I tried over the years, and there are quite a few factors that can help learning.Philosophim

    Totally agree with your points. My personal biggest roadblock was that no one even tried to explain how to approach a problem in a completely unknown domain. I spent many years to find that on my own. Not so long ago I even wrote the complete and intuitive solution for nine dot puzzle to just show that it's possible, to show that you don't need to guess solution even for puzzles in the completely unknown domain.
  • JerseyFlight
    782


    One thing I would try to clarify about this topic is that we need to be able to impart critical thinking skills to people. This helps to narrow the objective. The thing about this is that there are literally masterful texts written on this topic, which is good because it means we don't have to invent the wheel, it has already been done, all we need to do it make use of the material. Too many times we approach a topic with the assumption that we must start from scratch, in our modern world this is almost never the case.
  • Skeptic
    35
    One thing I would try to clarify about this topic is that we need to be able to impart critical thinking skills to people.JerseyFlight

    Very good point, but I had some troubles here. First of all it's relation between critical thinking and problem solving skills. I was able to meet personally many people with very good fundamental education and strong critical thinking but quite weak problem solvers. That was disappointing because I was interested in problem solving first of all.

    Secondly, problem solving itself looks like a cursed topic. Sometimes I think that Poincaré was the most knowledgeable person in this question with his four-stage model. I very appreciate job that was done by Dörner but still, after more that a hundred years after Poincaré, we stay still on the same place in the sense of the integrity of our understanding. We found enormous amount of details about process itself but holistic model is still a dream.

    That's why I decided to dive into this question deeper, and I got quite interesting results. They are mostly related to, as @Philosophim said, roadblocks. You need much more than just a knowledge or critical thinking to be a problem solver.
  • JerseyFlight
    782


    I would just like to take a moment and thank you for being a responsible thinker. Most thinkers are playing abstract games with each other until the day they die. This is the same as being religious, but thinkers like the Frankfurt School, Marx, Arendt, Foucault, Vygotsky and many others tried to figure out how to use thought to make a positive impact on society. I can see you are doing this and I applaud you for it.

    First of all it's relation between critical thinking and problem solving skills. I was able to meet personally many people with very good fundamental education and strong critical thinking but quite weak problem solvers.Skeptic

    I think a few things might be going on here 1) poor quality in critical thinking skills, the materials I know of in this area are very comprehensive, and 2) lack of dialectical capacity, which is really where problem solving comes from within the context of thought. In terms of dialectic most people are lacking these skills because almost no one understands dialectic. This is why American philosophy (analytical philosophy) just keeps on inventing new categories, it tries to evade contradiction (believing that is the way to progress) as opposed to understand it.

    I think we should continue this conversation in private message.
  • creativesoul
    9k


    Greetings. Welcome.

    :smile:

    Very relevant topic. My favorite.


    I think we should continue this conversation in private message.JerseyFlight

    I'd rather see it discussed openly.

    OP???
  • creativesoul
    9k
    Some starting considerations, given where we are...

    The foundation of problem solving is a name that - if adequate - will somehow pick out what all problem solving cases have in common, in terms of basic elemental constituency. The scope of the minimum criterion must be as broad as possible, ranging from the most simple, rudimentary, and/or basic examples of problem solving through and perhaps 'beyond' the most complex cases known.

    We are actually problem solving here and now, in this very thread. We are looking to acquire knowledge of what all problem solving has in common, how it evolves and/or grows in it's complexity, etc. So, if there is a single foundation underlying all of the different complexity levels, then it must be amenable to each and every one. If what we propose as the foundation of problem solving cannot adequately account for all known cases, then it is not the foundation. To quite the contrary, it would be utterly inadequate; otherwise sorely lacking, in it's explanatory power. If there is a foundation for problem solving, then all examples thereof must somehow, and in some way or other, be commensurate with and/or otherwise amenable to their own foundation.

    In light of these considerations, there needs to be yet another; a standard to bear. All candidates worthy of subsequent time and consideration - whatever they may be - must be amenable to evolutionary terms. This is already supported by and in large by the simple things we already know. All human knowledge is accrued. It begins simply and grows in it's complexity.

    Any and all foundational accounts are and must be put in bare minimalist terms, for there is no other way to be able to 'connect' all the cases ranging from what you've called "unconscious" through extremely complex metacognitive endeavors, such as what we're actually doing here and now. In this thread, we are thinking about our own thought and belief, with a particular 'kind' of them in direct view.

    A foundation is never equivalent to what's built upon it. Sometimes, the foundation consists of entirely different elemental constituents(think of a building). Other times, however, the foundation consists of the very same things albeit in much simpler 'form' as compared to the more complex things emerging and/or growing in complexity from that simple basic elementary 'form'.

    The foundation of problem solving is one such thing.
  • Skeptic
    35
    lack of dialectical capacityJerseyFlight

    Good point but quite risky. It requires careful definition and there is quite a big chance to start measuring and categorize people. It's too close to physiological predispositions. There always will be people who will become extremely smart even without a proper education. I don't think that it worth to discuss them here, so I think it would be better to focus on properties that don't have significant correlation with physiological features.
  • Skeptic
    35
    All candidates worthy of subsequent time and consideration - whatever they may be - must be amenable to evolutionary termscreativesoul

    Amazing intro. Thank you for such a detailed highlighting. After such a great reading I really hope that everyone will stop and reread my first post again. I already put the seed there, in third principle to be precise. From my point of view, evolutionary first problem solving system was built around obviousness. Сonsciousness is a secondary thing and simplest problem solving process should work with minimal efforts...
  • creativesoul
    9k
    All candidates worthy of subsequent time and consideration - whatever they may be - must be amenable to evolutionary terms
    — creativesoul

    Amazing intro. Thank you for such detailed highlighting. After such great reading I really hope that everyone will stop and reread my first post again. I already put seed there, in third principle to be precise. From my point of view, evolutionary first problem solving system was built around obviousness. Сonsciousness is a secondary thing and simplest problem solving process should work with minimal efforts...
    Skeptic

    A very kind review. Kinder than my own upon rereading. I should have further simplified/edited it. However, it seemed to at least skirt around what I wanted to emphasize, and it came off the top of my head after returning home from an emotionally intense trip abroad combined with a lack of both proper nutrition and sleep.

    :wink:

    I'm glad that we agree on the need for evolutionary amenability. It seems we also agree upon the apparent inadequacy regarding the shortcomings of current convention regarding that, in addition to the need for putting any of our notions/models to practical use. However, although I do not want to derail the thread by mentioning the crucial importance that truth plays in our accounting practices, it certainly deserves being kept in mind. Inaccurate and/or entirely false accounts of our minds(and thus problem solving) can be put to use no less than true and accurate ones. With that in mind, it seems that meeting the standard of evolutionary amenability ought perform double duty for us in that regard.

    I find that talk of consciousness is riddled with problems. I agree with you that it comes later. There are problem solving skills put on display by creatures who are incapable of taking account of their own mental ongoings. Such creatures are more than capable of figuring out how to acquire resources(food for instance) using a multiple step method including tool manufacture and use, but have no ability to take account of themselves and/or what they are doing. So, I would also concur with the general sentiment regarding last statement in the quote above.

    I would like to add the following consideration:Since it is the case that some problem solving does not require language use, language is not part of the foundation of all problem solving. Again, it seems that you agree. Below is an excerpt from the OP that seems to be commensurate with this crucial consideration on the one hand, but perhaps difficult to incorporate on the other...


    Is that really so difficult to connect available knowledge to create something solid and meaningful and more importantly, useful?

    For example, I would start with following three main principles for that:
    principle of similarity - it's a starting point of the mind, we need to sort out somehow a chaos around us.
    principle of regularity - we need to be able to see interconnections, sequences and patterns. Principle of similarity creates a static world model and principle of regularity gives us a set of constraints to create a dynamic one.
    principle of obviousness - if our world model produces a stable result about some fact then it become obvious for us

    All three principles are about fundamental unconscious processes. Principles are extremely simplified and it's only a part of them (unconscious part), but even such a model can already be very useful. For example:
    the structure of our knowledge is directly related to our ability to solve problems. Knowledge itself isn't enough, it should be structured properly for the specific problem
    our sense of obviousness is faulty but can be adjusted via structure of our knowledge
    Skeptic

    I'm quite hesitant to talk in terms of "principles" when it comes to the problem solving capabilities clearly demonstrated by language-less creatures, even if these principles are claimed to be about fundamental unconscious processes of those creatures. It would behoove us all to strive for more than just an account about the unconscious autonomous workings of the mind. We need to actually set those out in terms of their basic elemental constituency, and I do not find that similarity, regularity, and obviousness are basic enough. Although, they are most certainly helpful in sharpening the focus. The move us in the right direction, so to speak.

    Do the three principles share a set of relevant common denominators(basic elemental constituents), such that that set is more foundational and/or basic than any and/or all of the principles themselves? It seems to me that they do.

    Is this pursuit something worth continuing by your lights?
  • Skeptic
    35
    I'm quite hesitant to talk in terms of "principles"creativesoul

    I think it's time to clarify several points. First of all, english isn't my native language, so don't try dig too deep into a single term meaning. I really like an idea of meaning shades inside a phrase but I 'm not good enough in english still. Now it's time to clarify the idea of principles.

    Let's imagine you are working on a huge system. It's enormous and every corner still requires years to study... how to show it to someone? There is countless ways to describe such a big system and most of them will be too weird and complex. And... I decided to remove from description everything beside main points of interests. At the end of the day there is no sense in the description if you can't explain it to a child :wink: . Word "principle" is just the first thing that came into my mind when I started to describe every important part with one word.

    Now about term "foundation". You made amazing job with clarification, but I want point one important aspect, it's a goal of the foundation. I personally want to create a solid frame for further researches. Problem solving is a too complex system with too many connected parts affecting each other. Such feature creates cascades of side effects though the whole system. I saw several studies that failed just because researchers weren't able to understand that they are studying two interfering systems instead of one. That's why I want to fix main points of interests first of all, and such points may be present on a very different levels. So the main goal of the foundation is to limit unknown variance of the system with minimal efforts, but other requirements are still applied.
  • creativesoul
    9k


    If you already have a goal in mind for positing the foundation of all problem solving, then it is not the goal of the foundation. It is your goal. The foundation of problem solving is not the sort of thing that has goals. Rather it is the sort of thing that consists of the most basic elemental constituents that all examples of problem solving have in common.
  • Skeptic
    35
    The foundation of problem solving is not the sort of thing that has goalscreativesoul

    It depend on your point of view. Foundation is a tool anyway. You can say that toolmaker had a goal to help me with my goal but I would rather say that a tool has a goal.
  • TheMadFool
    7.5k
    My favorite technique, not because it's the best but because it's the one I use most often, is trial and error. It doesn't require genius - children use it - but you have to be patient - it's time consuming.
  • Skeptic
    35
    Not sure how far I will be able to go through before everyone will lose any interests but I will try to cover at least the fourth principle: duality.

    Duality comes from consciousness. In a simplest form you can think about two very different types of problem solving:
    • intuitive approach based on obviousness. You can try to guess an obvious solution and in case of failure you are trying to do some other "obvious" things. In general such approach looks like a "trial and error" method with gradual movement to gathering information. After a while, with new information learned you will finally get an insight of solution (or not).
    • strict plan. Complete opposite to the first one. You already know what to do, you aware of some kind of "ritual" to find a solution. This approach is widely know as imitation.

    As you may guess, people can easily mix both approaches, that where duality come from.
  • creativesoul
    9k
    I personally want to create a solid frame for further researches.Skeptic

    I understand that, but I'm not sure if you understand what I've been getting at here. What you create is not the foundation of problem solving. Problem solving and it's origen(the foundation) existed long before you and I. You're not creating it. To quite the contrary, you're attempting to discover and/or acquire knowledge of that which existed in it's entirety long before whatever you create.

    That much must be kept in mind.

    I'm not necessarily disagreeing with what you've put forward here. I mean, you've offered a few basic things, however, I'm merely pointing out that those things are themselves not basic enough. If you're ok with that, then so too am I. But, it would be a misnomer to call them the foundation of problem solving.
  • Skeptic
    35
    what is the best one word alternative from your point of view then?
  • creativesoul
    9k


    I do not want you to change the name, or discourage you from talking about the principles. It's a great start. I just wanted to encourage you to dig a little deeper. That said, I've just reread this thread, your OP, and my replies several times over. I want to apologize, because I find myself wanting to listen more and critique less. Please continue. I'll take off my hat of critique(looking for problems) and don my hat of mutual interest(looking for agreement).

    :wink:
  • Skeptic
    35
    We have four principles so far, lets move to examples

    2 + 2 = ?
    Easy enough, but how exactly you have got a solution? Someone may say "it's obvious"...

    7 * 9 = ?
    Still easy, but with a twist. Someone may follow the previous path but others may use a bit different. There is a simple mnemonic rule for that task, so you can transform and simplify it.
    7 * 9 <=obvious=> 70 - 7 = ...
    we still have obvious step in the solution (if you aware of the mnemonic) but in addition we need a bit of efforts to get a final solution.

    VI = VII + I
    Here we have a matches puzzle and you need to make the expression true. The main difference here is that we finally have a choice what to do, so we finally have a search space. What exactly are you going to do to solve it? Most interesting part here is that most people will just follow obviousness. They will try one guess then another one and so on. All guesses are just come to the mind, there is no direct efforts, but... all guesses are structured
    There is an amazing article about that part:
    Constraint Relaxation and Chunk Decomposition in Insight Problem Solving. Knoblich, Ohlsson

    Main idea is that the search space is already structured by our representation of the task. Most simple elements go first. If you have no results then, at some point, you will switch to more complex structures. For example, most people start from breaking digits and will switch their attention on other parts only later on.

    It worth to stress, there is a search space and there is a search process but it lies completely in the unconscious area. People in general are just following the obvious guesses.

    9-dots puzzle
    One more puzzle, but it has significant difference. Quite a few people can solve it. There is still a search space, there is still a search process but task representation is incomplete. It's a quite fun fact but natural representation of the task produces search space that for most people doesn't contain a solution. As a result there is no way find a solution intuitively without efforts. People are trying different ways again and again, starting to cycle at some point and losing an interest.

    There is one more interesting fact. You can give to some test subjects a different task to extend their representation of the task. Solution will be found easily in that case.
    The Role of Motor Activity in Insight Problem Solving (the Case of the Nine-Dot Problem). Vladimir Spiridonov
  • Skeptic
    35
    Depend on your education and interests you may find here many familiar details about search algorithms and its modifications for different purpose. In some sense it looks very similar to the beam search algorithm. Main goal here is to quickly find a solution at the expense of accuracy, and it's a reasonable goal in evolutionary perspective. The problem here is that we can't afford such approach any more.

    With that ideas in mind it's quite easy to show many ways to improve our ability to solve problems (one amazing example is TRIZ). Troubles start because of our mortal nature. Default problem solving approach is wired into our brain. Without proper education people will alway fall back to the flawed algorithm with well known issues...
  • Skeptic
    35
    I just wanted to encourage you to dig a little deeper.creativesoul

    I tried actually and found that such a job was done several times during the previous century. The problem is that in almost every case it ended up moving too far away from humans.

    From one side we have amazing results in mathematics and algorithms there is a lot of knowledge about "pure" problem solving. From the other side we have amazing results in cognitive psychology that describes in a very detailed way how our mind works. The missed point is the intersection. That's what I tried to achieve. The sad point here is that no-one actually need it in academic sense.

    I touched almost nothing but it's already clear how exactly heuristics work and how to make them precise. Quite interesting result here is that knowledge it-self is just a third part of the system, more over more knowledge you have, less efficient problem solving will be in case of absence of two other parts. Two other parts are knowledge structure and skills.
  • Skeptic
    35
    My favorite technique, not because it's the best but because it's the one I use most often, is trial and error. It doesn't require genius - children use it - but you have to be patient - it's time consuming.TheMadFool

    TIme consumption is quite controversial metric. For example an exhaustive search may look like a waste of time but in many cases it could be much faster than guessing.

    It would be much more useful to talk about the probability to solve specific problem, especially when it goes to zero. The simplest example is degrees of freedom. It's quite easy to understand in case of comparison of fifteen puzzle and Rubik's cube.

    The fifteen puzzle has relatively limited number of moves in any given time. More over, it's quite easy to estimate of outcome of every move and play several moves back. I think it's quite good example of the problem that can be solved with trials and error approach.

    The Rubik's cube is a very different beast. At the beginning it looks very similar to fifteen puzzle but it goes out of control very quickly. You can find two very dangerous properties here:
    • number of possible moves is much higher and number of possible paths is blowing exponentially.
    • the penalty for error is horrible. In most of the cases, you will be thrown back to the beginning.

    As you may guess, pure trial and error method just doesn't work here at all. In some cases trial and error may work similar to gradient decent search but not here, our penalties won't allow it to work. We need a completely different approach here
  • TheMadFool
    7.5k
    I have a feeling you're conflating trial and error with brute search.

    Trial and error is when you randomly try out different possibilities. Brute search is when you explore each and every possibility.
  • Skeptic
    35
    I have a feeling you're conflating trial and error with brute search.TheMadFool

    Maybe it worth to clarify a bit. In short no, there is a clear separation but it may be not too obvious at the beginning. I used a term "exhaustive search" for brute search and it isn't natural for people unlike trial and error.

    When you are using trial and error method it may really looks like random attempts from the point of view of a solver, but it much more complex under the hood (I hope you took a look on articles that I mentioned previously). First of all, all our guesses aren't random, they are prioritized according our problem representation and prior knowledge. Secondly, every trial has two purpose: to guess a solution and to learn more about the system.

    So fifteen puzzle is edge case of trial and error method. You are trying "random" moves and at some point the next move become obvious to you. Until the last row... that's where direct intervention into the solving process is required, but still, I know several people who was able to solve it without thinking about it deeply.

    With several trials you can form an understanding of the system to estimate an appropriate guess for the next trial. In that sense trial and error method may look like a gradient descent method. You don't need to check each and every case, you just need to estimate the direction of the gradient. Most amazing part is that such an algorithm is wired into our brain so we don't even need to think about all this stuff, we are just trying to guess a solution...

    It's almost impossible to solve the Rubik's cube that way. Trial and error method works amazingly well in case of smooth and continuous search space, but Rubik's cube is a discrete system and it's far from smooth. Fifteen puzzle is relatively simple to solvable only because of limited degrees of freedom that limits search space.

    Exhaustive search is very painful for trial and error method too. Search process is optimized for speed. Every guess has a priority and we tend to completely ignore low priority guesses. There is well known phenomenon named a "blind spot", and for every professional it's a really hard work to eliminate all of them. So in case of chess you may completely ignore bishop for example, because you don't have a good prior knowledge of using it.
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