And die with it — Hippyhead

Probably, but there are other scenarios too. Previously I tried to show the set of scenarios without death.

Crafting a new species. I agree there is likely nothing at all realistic about such an idea. — Hippyhead

I'm talking about a bit different thing. Crafting a new species isn't a big deal, but even in such case you will still have the same issue. Personal experience will still be there. The only way to avoid the trap of wisdom absence is to remove personal experience at least partially. Partial case will look like a programmable personalities, complete case will look like a collective mind. Both are too far from human nature and ability to choose own behavior.

So the only way for humans is to find a way to live with it. There is no way to evolve and forget this problem.

by genetic engineering we could redesign ourselves in to a more intelligent species — Hippyhead

wisdom is based on experience, not only on genetics. It means that in any given time in human society will be a significant number of people without wisdom and there is not way to avoid that (at least, without losing human nature). That was the first hint...

Sooner or later it hits the wall and crashes. — Hippyhead

I tried to say that there are more possible scenarios and actually it isn't a big deal to cover all of them. More importantly, some of them contains quite bold hints for your question.

The only hope is that wisdom will keep pace with scientific knowledge — EnPassant

It is a pity that wisdom is not inherited

4) An ever accelerating rate of knowledge development results in an ever accelerating development of new powers.

5) Thus, science gives human beings new powers at an ever accelerating pace. — Hippyhead

These assumptions are wrong actually. First of all, the endless exponential grows doesn't exist in nature, but it's quite widespread delusion. People have a limited mental capacity to grow and to acquire knowledge and we are reached the limit in many areas already.

Secondly, science doesn't exists separate from people. If people can't fully understand science then powers will decay. So here we have quite different picture but I can't say that it less dangerous than technological singularity. Best regards to Asimov

Guessing is random, right? — TheMadFool

It depends on your definitions and expectations. Randomness is slippery concept, that's why we have a concept of pseudo randomness and bunch of distribution parameters. Everything in this universe can be treated as random to some extent.

When you are guessing it may look random, even evenly distributed, but such assumption would be completely wrong. First of all, space of tries for guesses is very limited and it can be predicted very precisely. Secondly every try has a weight, so guesses are ordered. Thirdly, at some point tries space can be extend, but again it can be predicted quite precisely. So what is random here then? I would rather say that such method has some random elements but process itself is totally deterministic.

I suppose it all boils down to the cognitive ability of the problem solver — TheMadFool

I personally don't think so, and here I tried to show some fundamental things that much more important than personal abilities.

every problem consists of a core issue - it's heart as it were and once its sighted, the solution method immediately comes into view — TheMadFool

Almost all first page of posts I tried to show the whole process behind this simplification. Insight is just a finish point, at least if it's correct. I even showed that there are several classes of problems and some of that just can't be solved that way....

It looks like there is no sense to add more complex concepts here. In short, we have quite interesting solving algorithm wired into our brain. It can be very efficient for some classes of problems but it completely inappropriate for complex problems. If someone want to be able to solve such problems it have to learn to do so. Sad point here is that knowledge alone can't help us in any way. Problem solving abilities are limited by different factors that much harder to achieve (at least in terms of time)

{1} having a REAL interest in doing it.
{2) understanding very well the question/problem; not its words but the important idea(s) behind them. — KerimF

Thanks, interesting approach, but I would argue a bit

• In my world a necessity is equal to an interest. You can try to avoid some responsibilities but only if you can mitigate consequences.
• In soviet time there was an interesting mathematician specialization (unofficial). They were called "solvers". Main idea was to have a wide knowledge foundation and focus, first of all, on tools instead of specific domain area. Such people were able to solve problems in any domain area and quite efficiently. More importantly, there is no way to solve huge cross disciplinary problems without such people.

Nowadays we tend to think that problems should be solved by specialists from the specific area. It's sad since the problem solving is a dedicated art. We want to become solvers by learning a domain area, but we will become an encyclopedia, not solvers.

I think it might be reasonable to interpose something like a model and treat data only as state — Srap Tasmaner

At that point we can try to talk about models. Models is a quite difficult topic, most of all because of "duality principle". Every model has two layers. The first one was covered above and it's very important to understand that it's always under the hood and affect our understanding and decisions. The second one is in under consciousness control. It looks like you are talking exclusively about the second one. We can use our short term memory to create some models (states) in it. This process may looks very dynamic but it is very influenced by the first layer.

we only partially know what happened — Srap Tasmaner

It's true for most problems, and actually in general you don't need to know everything. There is always some kind of "basis" in the problem. We just need to find a minimum necessary information to describe the system with necessary accuracy. And there is entire field called "experiment planning" to help with that goal.

what seems to have happened doesn't make sense according to our model of the system — Srap Tasmaner

That point just means the lack of skills. The problem solver should create the model from the observed information, not the opposite. It's a common issue and I tried to touch it with "assessment of facts" in the previous post. This part should be trained intensively.

gathering more information is extraordinarily difficult — Srap Tasmaner

This is a little subjective. I don't believe in miracles so I don't care about restriction that impossible to overcome. But in general there are tons of ways to get additional information, and someone can find it, but others can't. And again, from such perspective it's feasible and trainable.

we do not know what will happen next or what we can do about it. — Srap Tasmaner

It's wrong in general. In most cases we can estimate all possible outcomes and our reactions for every cases (if we have enough time or skills). Actually security restrictions usually introduced in that way. Someone should evaluate all possible situations and to introduce a set of restrictions to prevent disasters from happening. It isn't always as precise as I described but still.

we do not know what will happen next or what we can do about it. — Srap Tasmaner

This part, actually, isn't related to Chernobyl case. Security requirements were neglected several times and everyone was aware of possible consequences... but such consequences were felt like highly improbable. I hope someone read carefully everything above, because I already mentioned that case. It's a part of our fundamental solving algorithm and we need to change it, if we want to be able to achieve precise results.

There are two main skills at the foundation:

• logic - we need to stop confusing the obviousness with logic, and it's really hard actually. The hardest part is to understand and to stop relying on own sense of obviousness. If you are on the process of solving, every fact should rechecked with pure logic.
• assessment of facts - it's very similar to previous case, but on a bit different plain. Our ability to estimate probability is completely broken and I don't thing that it's a big secret to anybody who aware of statistics. Never the less, during the solving we are heavily rely on our feeling of hypothesis importance and outcome probabilities. So, if you want to get precise results instead of fast one, you need to stop rely on own feelings and estimate importance and probability explicitly.

Most interesting part here is that after several years of practice sense of obviousness will be completely changed. It means that even such fundamental skills still can be trained.

I think it might be reasonable to interpose something like a model and treat data only as state — Srap Tasmaner

Reasonable, but it looks like we have some misunderstanding here. I just started and mentioned most fundamental things. The "data" here is the knowledge that is stored in the long term memory. It's necessary part of problem solving since the part of it happens unconsciously with direct access to that knowledge, without you control. Issues inevitable if you have errors on that layer.

Your comment is mostly related to the second layer that controlled by conscious. I roughly covered it with "skills", but it can be extended further in case of interest.

to reach even a tolerable resolution, they had to overcome several different types of problems — Srap Tasmaner

Yes, problem solving isn't an easy thing and skills part isn't the simplest part of it, but Chernobyl example is too sided. Reasons are too heavily depend on psychological effects. This point of view was deeply explained in "The Logic of Failure" Dietrich Dörner. As far as I remember there is entire chapter about Chernobyl.

If you have more specific details I would happy to discuss them here.

Let's talk about practice now. If we want to make something work better and without too much efforts we need to find the main source of troubles first off all. From all ideas that were written above we may estimate at least several such points:

• unreliable data - we have a lot of knowledge but for most of them we can't really say are they true or false and for which conditions. First thing that we need to do is to define precisely every term we use. This practice was intensively used even by Socrate. Such practice should be applied for every knowledge we gain. For some additional motivation and reasoning it worth to read "Gestalt Therapy: Excitement and Growth in the Human Personality" Perls, Hefferline, Goodman.
• incomplete data - our knowledge about system is usually incomplete and it's perfectly fine, but we need to clear understand where exactly it is incomplete. More knowledge we have, more important it become to understand that there is something that we don't know yet and where exactly it lies. And here I'm talking about very specific knowledge for very specific situation, not about abstract endlessly knowledge. If we want to fix a toaster, we need to understand what we know about it and what we don't.
• poorly structured data - it's less known part, unfortunately. Our ability to understand the system relies on our ability to see it entirely in our mind, so we have natural limitation with our attention volume. One good way to overcome the issue with attention volume is to structure our knowledge about the specific system with hierarchical layers, where every layer have only 3-5 components. Every component should be spited in 3-5 parts in the new layer and so on. The process works as an indexing in a database in some sense. Most beautiful part of such approach is that unconscious processes can use such structure very efficiently.
• lack of conscious efforts - or relying on guessing too much. The guessing is the way of solving problems and it can be very efficient in some cases but it will never become precise. You can practice in guessing if you want, but if you want to be a problem solver you need practice with precise solving approaches.
• lack of skills - arguably, most known case. Never the less, not so many people want to talk precisely about it. Probably it happens because of strange dichotomy, this question in general either obvious or completely unknown. It's usually obvious for people with strong math background, because that's were most skills were built, but outside of the math it may looks like a miracle sometime. The most important part of the math in that sense is the way of structuring knowledge and approaches to find the evidence of certain statements.

murder scenes in kid friendly movies like the Lion King — TheHedoMinimalist

Quite strange comparison I wold say. Can you estimate probability of your own death by watching the Lion King? You are falling into a single person view again, but I'm talking about society perspective. Is it possible to make a higher psychological impact without lethal consequences? Yes, for sure, but average people in our society are completely different. If you are going to create lows for society, you need to understand the typical behavior in that society and reasons behind it.

I have personally felt sick to my stomach — TheHedoMinimalist

It means only that you didn't get use to such a view, and it's almost impossible for an adult without psychological consequences, but picture is different for kids. Did you try to imagine what is going to happen to the mind in a place where violent death is all way around? And we have a lot of historical evidence on this topic. So society is pretty confident about things it want to avoid

At some point I think it will become possible to change weights and to understand that in some cases consequences may be much worse than just death. But there is no way to change historical process in a blink of the eye

interesting article, thanks. I’m aware of Ohlsson and GPS but history overview was very informative. Sometimes I really want to ask some researchers “do you remember that people can learn?”. Hopefully TRIZ will make job done before theoretical science will be ready to apply their knowledge to teach someone.

I would probably would go on disabilities and avoid working — TheHedoMinimalist

There are still some benefits for society but they are mostly psychological. There is always a tradeoff between aggression and compassion. In a long run such support may be much cheaper.

Do you mean to say that protests would become more lethal if we had a more lax attitude towards murder? — TheHedoMinimalist

I meant that lethal aggression has much higher psychological impact on people around, and I don't mean direct relatives here. In general such atmosphere will push people to be more aggressive. Even without direct immediate lethal context it may cause political disaster.

he would probably get charged with both rape and murder. — TheHedoMinimalist

Good point, the only thing is left is the way of punishment. Don't want see 1984 in reality :fear:
I like your points but according to the reaction on your posts Seneca isn't popular any more

I just tried to show that there are many different cases and not all of them have the potential to resolve themselves into something better. And it looks like your arguments missed such cases completely.

all of these griefs have the potential to resolve themselves into something better — Philosophim

I have only one question after reading your arguments, why does euthanasia exist in this world? Maybe your missed something?

Would you say that this is one of the biggest global concerns around there being more lax attitudes towards murder? — TheHedoMinimalist

With you OP in mind it's difficult to say what is worse, complete extinction or agony of endless surviving

In a bit more real world scenario I would rather said that a live person can be useful for society even in case of serious injury. The similar difference can be found in the religion... The next level of reasoning is the political instability. Protests may look very different in case of different mentality... and so on, with the serious degradation or even extinction at the end.

Actually it worth mention that we are on the middle of the humanization process. It means that things will change seriously later on. For example, right now, nonlethal harm is gaining more and more criminal weight.

I just think it’s not as bad as significant forms of torture — TheHedoMinimalist

There is no way to support such approach logically. Death is the termination state so you can't have something with more weight. The only logical way is to make them equal. Otherwise you will left possibility for rapist to kill his victim in a court to mitigate the punishment...

As usually, there are contradictions on different layers. It's understandable in case of specific individual but impossible in case of society.

By what standard have they succeeded — TheHedoMinimalist

By succeeded I meant that they were finally become able to significantly change humans psychology and attitude to the fact of murdering. Religions tried to achieve this goal many hundreds of years without luck but last couple of centuries were very different in that sense. It's difficult to say what was the main reason of such change, I personally tend to think about medicine actually.

Regarding standards, there are many approaches to measure impact. You can measure crime rate, attitude to death or even just death rate. More interesting measurement is the fraction of society that can murder without been psychologically injured.

My understanding is that your primary concern is that a more lax attitude towards murder will be instrumental in promoting the prevalence of vigilante justice and revenge — TheHedoMinimalist

Not exactly. There are many factors and I just mentioned the simplest one. Society is the system and it has many system effects. Most dangerous are psychological changes and attitude to death. That's why many topics are just forbidden for public discussions (at least our country has some). I don't think that it's too hard to see possible consequences of such changes. At least fast growth is incompatible with instability that can be caused by ability of people to kill easily.

a father should be more willing to engage in vigilante justice if the rapist of his daughter receives a light punishment then if the murderer of his daughter receives a light punishment — TheHedoMinimalist

In some sense I agree with you, I just wanted to show the possible reasoning behind the difference that we can see around.

It is usually regarded as being as bad or worse than acts such as rape, mutilation, putting a hot poker on someone’s chest, and long term imprisonment. — TheHedoMinimalist

And again, from point of view of society and religion it should be clearer why nonlethal harm is preferable even if it has devastating consequences for the specific individual or his entire life

You may notice that all arguments that you mentioned are single person centered. I don't think that it's a good way to find the objective answer.

I think that main murder dilemma arise a bit higher when you consider society interests. In some sense it was started by humanism or even religions and they succeeded. Main assumption was that people's ability to kill depend on their experience during growing up. So if someone grows in peaceful environment he will have strong psychological barrier to harm anyone. In hurst environment situation will be the opposite.

In that sense every murder is a destabilizing factor and it is very harmful for society in the long run. Several decade ago such stories were very popular in the literature. Even today there are some nations where revenge may wipe out entire families or even more.

Ok, it looks like attention limit exhausted. The last point that worth mention anyway is practical usage. All these words may sound useless but it isn't true. I'm aware of many heuristic approaches that pretend on problem solving efficiency, but all of them have one huge flaw, you can't generalize them. Some of them may help you with a specific issue but there is no heuristic that can help you to get "smarter".

That's why I decided to dig deeper and was able to find an ocean of answers. The model described above is rather rough and simplified but even in such condition it can bring the light to many our struggles. Even mathematics appears in a completely different light. We tend to see the math as the bunch of boring equations but it isn't the math actually, it's the result of the math.

But unfortunately, most people do not want to solve problems, they just want a solution.

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.

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

Buddhism seems to stick out like a sore thumb on that score. — TheMadFool

You may be interested in Leo Tolstoy's work then. He was able to find quite solid philosophical foundation behind the Christianity. He even wrote his own translation of the Bible to show possible original philosophical context of the text.

Do you consider other alternatives? It's still possible that religion was based on a philosophy for example. Secular Buddhism is a good argument in favor of this idea. All books were written long after Buddha's death after all.

Any community of human beings who have collectively agreed that such-and-such an act or course of actions is moral, have done so in the final analysis because they believed these actions to be in the service of human flourishing. — Thomas Quine

I would say it's too strong assumption for people in general. Equally likely (or even more likely) it can be result of an evolutionary like process. We are trying to evaluate moral value afterwards, that's a major source of distortion. In case of long term process, reasons and outcomes could be vary in different points in time.

For example at the beginning you can find something like an Abilene paradox and it could be spread widely afterwards. The main reason could be a reverse in some cases, I mean moral principles could be preserved because of absence of disagreement. The only example that come to my mind right now is fashion.

I personally think that main benefit from the moral rules are rules themselves. Almost any moral rule can be helpful if it isn't destructive for community, helps to understand easier people around you or stabilize people behavior.

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.

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...

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

what is the best one word alternative from your point of view then?

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.

The foundation of problem solving is not the sort of thing that has goals — creativesoul

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.

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.

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 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...

lack of dialectical capacity — JerseyFlight

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.

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.

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.

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.

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 us — Gregory

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.