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.

You might find this article interesting.

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.

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.

I think it might be reasonable to interpose something like a model and treat data only as state, something like that. Then you can imagine having incomplete or untrustworthy knowledge of the current state of a system, but you could also have an erroneous model of how the system behaves, and those are quite different, which will become clear when you intervene.

I'm thinking as I write of the HBO series Chernobyl, where you can see almost every sort of problem: we only partially know what happened and what seems to have happened doesn't make sense according to our model of the system; we only partially know the current state of the system and gathering more information is extraordinarily difficult; we do not know what will happen next or what we can do about it. To reach even a tolerable resolution, they had to overcome several different types of problems, and some of those were not with data but with their model for the behavior of the system.

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.

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

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.

An interesting thread. Thank you.

I am not a philosopher but I guess that the first and second crucial steps in answering a question or solving a problem are:

{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.

Which one comes first depends on the situation.

This applies in my reality in the least :)
I mean; I have to ignore answering a question or solving a problem if the above two steps cannot be fulfilled first.

{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.

Last I read up on problem solving techniques, trial and error method is also known as guess and test. Guessing is random, right?

I suppose it all boils down to the cognitive ability of the problem solver. (By the way, I've lost the plot at this point). A problem is, in essence, a test of intelligence; the point being every problem consists of a core issue - it's heart as it were and once its sighted, the solution method immediately comes into view. Not all problems are such though, no?

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)