If you understand a problem well enough, you've already solved it. So, if you understand why X is bad, you've understood what the better alternative is
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I want to solve the problem of how to escape from my jail cell. I've thought about the nature of the problem; ultimately it is that I am inside the jail cell, and wish to be outside it. Thus the obvious solution is to travel from inside to outside, say by walking through the wall. Now that I have solved the problem of how to escape from the jail cell, I can focus on the problem of how to walk through walls...
Understanding a problem will yield the subproblems that it is composed of; that may be 'solving' it in the sense that you now know what you need to do to fix the problem ("solve this list of subproblems"), but I'm not sure how useful that sense is. Applying the idea recursively will yield only an infinite sequence of smaller subproblems; it does not make the step from 'problem' to 'solution.'
What role does creativity play in this model of problem-solving?
Re: On UnderstandingubermammalJuly 7 2009, 03:41:00 UTC
> If it was just a wall, you could escape by it easily by shouting for help. But it isn't just a wall, it's a jail. It's much more complicated and contains stucture that you don't know about.
There's an idea this has reminded me of that I've been kicking around for a while. There are two directions in which we can understand things: inwards and outwards.
Inward understanding is understanding the structure of the problem as stated, its factors and facets. It is this understanding that yields subproblems.
Outward understanding is understanding how the problem fits into a larger context, why it is a problem at all, what it is a subproblem of, the extent to which it is correct as stated, and so on. It is this understanding that contextualizes problems, and allows us to recognise when we can discard a problem in favour of another one.
> Let's suppose that there is a thing that you could say to the jail warden that would cause he to be released early. You don't understand the jail well enough.
I agree with ubermammal in that this doesn't help with practical, "I am stuck inside a jail cell" problems.
And, after thinking for a little while, it doesn't apply to some mental problems either. If understanding a problem was equal to understanding the solution, I would already have my physics degree.
I would say that understanding a problem is necessary, but not sufficient, in understanding a solution.
This is only true when understanding the problem leads to you realizing there is no problem... Example: You think you believe in both X and Y, but have realized they contradict each other. Then once you've understood the problem properly you realize you don't actually believe in Y. So there is no problem.
Or if you already have all the knowledge for how to solve it and there are no sub-problems... Example: I want to be outside. I know where my door is, how to open it and walk outside.
In all other cases, there will be subproblems.
"So, if you understand why X is bad, you've understood what the better alternative is." "You can understand why something is bad very well, without having a clue what would be better."
Not contradicting: 'very well' does not mean 'entirely'. I was saying that you could understand something well, without understanding *all* of it (which would include what would be better).
If you're defining "total understanding" of something as including an understanding of what would be better, then yes, this is all tautological, all true by definition.
However, to totally understand what would be better, must you not also totally understand what must be better than that, and so on, recursively ad infinitum? Thus, by your definition, in order to fully understand anything, you have to fully understand everything.
It does not seem useful to work with the concept of "total understanding" when it is defined in this way.
* There is no such thing as a 'solved' problem in that it is always possible that there are better solutions than the one you have found. * Full understanding is unattainable. * Thus the problem is a practical one, similar to the principle of sufficient criticism: When should we focus on looking for better solutions, and when should we stop looking and focus on developing the best solution we have found so far?
Re: TL;DR versionubermammalJuly 7 2009, 22:41:03 UTC
Some solutions (theories) are inherently bad and we can rule them out before even seeking criticism. We do this internally all the time. Better solutions should always be desired and we look for new ones to explain a problem better only when the old one is proven false. Because of our fallibility we are never able to discern when the perfect solution to a problem presents itself. We can continue to use a falsified solution as it hasn't changed by being proven wrong (we assumed it wasn't absolute truth when we made it) and it hasn't changed since yesterday
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Re: TL;DR versionubermammalJuly 7 2009, 23:49:49 UTC
> Better solutions should always be desired and we look for new ones to explain a problem better only when the old one is proven false.
"Only" when the old one is proven false? Even when we have already got a working solution to a problem, we may be 'inspired' with a new solution that is more efficient. "The old solution is false" is sufficient but not necessary to come up with a new solution.
> 'focus on developing the best solution' -- in what way do you mean?
Sorry, that wasn't as clear as it could have been. I meant 'to take the best solution, and focus on developing it,' i.e. to being criticising it or acting on it.
> In the problem of how to escape a jail cell, a possible solution is to ask the guard for the keys. If you meant to escape through the physical wall directly then that is a different problem-situation than escaping your jail cell.
If a possible solution is to ask the guard for the keys, then it is indeed a different problem-situation than the one in which it is not a possible solution to ask the guard for the
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Comments 15
Understanding a problem will yield the subproblems that it is composed of; that may be 'solving' it in the sense that you now know what you need to do to fix the problem ("solve this list of subproblems"), but I'm not sure how useful that sense is. Applying the idea recursively will yield only an infinite sequence of smaller subproblems; it does not make the step from 'problem' to 'solution.'
What role does creativity play in this model of problem-solving?
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There's an idea this has reminded me of that I've been kicking around for a while. There are two directions in which we can understand things: inwards and outwards.
Inward understanding is understanding the structure of the problem as stated, its factors and facets. It is this understanding that yields subproblems.
Outward understanding is understanding how the problem fits into a larger context, why it is a problem at all, what it is a subproblem of, the extent to which it is correct as stated, and so on. It is this understanding that contextualizes problems, and allows us to recognise when we can discard a problem in favour of another one.
> Let's suppose that there is a thing that you could say to the jail warden that would cause he to be released early. You don't understand the jail well enough.
You can suppose anything at all on top of ( ... )
Reply
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And, after thinking for a little while, it doesn't apply to some mental problems either. If understanding a problem was equal to understanding the solution, I would already have my physics degree.
I would say that understanding a problem is necessary, but not sufficient, in understanding a solution.
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Example: You think you believe in both X and Y, but have realized they contradict each other. Then once you've understood the problem properly you realize you don't actually believe in Y. So there is no problem.
Or if you already have all the knowledge for how to solve it and there are no sub-problems...
Example: I want to be outside. I know where my door is, how to open it and walk outside.
In all other cases, there will be subproblems.
"So, if you understand why X is bad, you've understood what the better alternative is."
"You can understand why something is bad very well, without having a clue what would be better."
Aren't these contradicting?
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However, to totally understand what would be better, must you not also totally understand what must be better than that, and so on, recursively ad infinitum? Thus, by your definition, in order to fully understand anything, you have to fully understand everything.
It does not seem useful to work with the concept of "total understanding" when it is defined in this way.
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* Full understanding is unattainable.
* Thus the problem is a practical one, similar to the principle of sufficient criticism: When should we focus on looking for better solutions, and when should we stop looking and focus on developing the best solution we have found so far?
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"Only" when the old one is proven false? Even when we have already got a working solution to a problem, we may be 'inspired' with a new solution that is more efficient. "The old solution is false" is sufficient but not necessary to come up with a new solution.
> 'focus on developing the best solution' -- in what way do you mean?
Sorry, that wasn't as clear as it could have been. I meant 'to take the best solution, and focus on developing it,' i.e. to being criticising it or acting on it.
> In the problem of how to escape a jail cell, a possible solution is to ask the guard for the keys. If you meant to escape through the physical wall directly then that is a different problem-situation than escaping your jail cell.
If a possible solution is to ask the guard for the keys, then it is indeed a different problem-situation than the one in which it is not a possible solution to ask the guard for the ( ... )
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