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
( Read more... )
Walking through walls is a harder problem than getting out of a jail cell.
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.
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.
A problem is a conflict between theories. Your problem isn't exactly how to escape from your jail cell -- that's just one theory about how to solve your problem. Maybe you would would like to visit your family, but you can't because the jail guards won't let you. The problem is the conflict between those two theories. (A whole other way doesn't involve leaving the jail at all. It involves being happy within the jail. Maybe your family can come visit you. Or maybe you don't actually have to see them, but could phone them instead. Or whatever.)
So, yes, understanding a problem will yield subproblems (or better formulations of the original problem -- e.g. from 'I want to be outside my jail cell' to 'I want to see my family'). And, yes, understanding these subproblems is part of fully understanding the original problem.
People often think they understand a problem, but not its solution. The fact is, they don't understand the problem well enough. For example, lots of people see problems with conventional romantic relationships, and some decide to be poly or something instead, but then they end up reverting because they didn't fully understand the problem. (And they might still claim they fully understand the problem, but the ring on their finger suggests otherwise. Ahem.)
Anyway, the point is: a good understanding consists of looking at lots of different options and elements of the problem. People don't take the role of understanding seriously enough. In your example, you're assuming that the very first idea of what a solution must look like has to be the only possible answer. Instead of looking for understanding, you're saying "I already understand it, I just want to know how to get through the wall." But if you understood the problem better, you would realise that getting through the wall is not your problem.
As for what role creativity plays: you understand things through conjecture. Conjectures are formed by a creative process. I think you know the rest? Were you asking something different?
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.
You can suppose anything at all on top of my original problem scenario and then claim that therefore I don't fully understand the problem. Well, I did fully understand it before you started adding extra suppositions to it. :P
It's equally valid to say: Let's suppose there isn't a thing that I could say to the jail warden that would cause me to be released early. Therefore, I do understand the jail well enough, for having this extra information - that a given solution avenue is unavailable - does not solve the problem.
(This reminds me of DD's reasons for avoiding the use of examples. Either you can't see the point I'm trying to make, or you think that an example to support my argument cannot exist. Which is it? If neither, we'd save some time if you accepted the existence of a solid example, or at least helped to provide it. Assume Good Faith and all that).
> A problem is a conflict between theories. Your problem isn't exactly how to escape from your jail cell -- that's just one theory about how to solve your problem.
Sure, the problem can be contextualized - to ask why I want to escape from the jail cell. And maybe the answer is that I would like to see my family. But can I not then ask you to contextualize that problem again? In truth, I don't actually want to see my family; what I want is to be happy, and maybe there are other ways of doing that. But then we can contextualize again: I don't actually want to be happy; what I want is actually something else, and being happy may only be one way of achieving that. Etc.
To contextualize a problem is to question its justification, and so unbounded contextualization is justificationism, and produces an infinite regression as we well understand. The solution, as usual, is either to accept an irrational root - I want out of the jail cell because I just do, okay?! - or to set some condition on when contextualization is permitted.
How do we know when it's permitted? I'm not sure about this, but say for now that it's acceptable to contextualize when it's easier than the working set of subproblems. It's acceptable to answer, "why am I trying to escape from this jail cell, anyway?" when the alternative is to answer, "how do I walk through walls?"
Let's suppose that my reason for wanting to escape the jail cell is not to see my family, but because I theorise that it is morally wrong to exist in confinement like this, that to exist in a state of restricted freedom is not the best way to live. What will contextualization give us here?
Re: On UnderstandingubermammalJuly 7 2009, 03:41:21 UTC
(...cont...)
> So, yes, understanding a problem will yield subproblems (or better formulations of the original problem -- e.g. from 'I want to be outside my jail cell' to 'I want to see my family'). And, yes, understanding these subproblems is part of fully understanding the original problem.
Yep. As noted, I think it's worth distinguishing these two types of understanding - inwards (yielding subproblems) and outwards (better formulations of the original problem).
> People often think they understand a problem, but not its solution. The fact is, they don't understand the problem well enough. For example, lots of people see problems with conventional romantic relationships, and some decide to be poly or something instead, but then they end up reverting because they didn't fully understand the problem.
I'd suggest that they revert because their perception of the solution to their perception of the problem changes with time. Their perception of the problem is "how can I be sexually/emotionally fulfilled in my interactions with others," and contextualizing that is, for the vast majority of people, a harder problem to solve than the transient myriad of smaller problems that plague day-to-day relationships.
> (And they might still claim they fully understand the problem, but the ring on their finger suggests otherwise. Ahem.)
Hah! Or maybe they've contextualized it further than you have, maybe they understand it even better than you do ;-)
> Anyway, the point is: a good understanding consists of looking at lots of different options and elements of the problem.
> People don't take the role of understanding seriously enough. In your example, you're assuming that the very first idea of what a solution must look like has to be the only possible answer.
No, I never said that. I simply said it was a possible answer, and, rather than continuing to search for further possible answers, decided to focus my attention on applying that answer instead.
What does it mean, to solve a problem, if not to find some possible answer to that problem?
Maybe the reason that I want to escape the jail cell is because I want to see Sweden before I die. By some technique I am able to escape the jail cell, but I never go to Sweden before I die. Does that mean that I never successfully escaped the jail cell? It sounds like that's the conclusion you'd have to draw; because my technique didn't eventually solve the underlying problem, it didn't solve the sub-problem. And when put like that, hopefully it's obvious that it's fallacious.
> Instead of looking for understanding, you're saying "I already understand it, I just want to know how to get through the wall." But if you understood the problem better, you would realise that getting through the wall is not your problem.
No, escaping the jail cell is my problem. I've found a solution: walk through the wall. I can now solve this new problem of how to walk through walls, or I can revisit an already-solved problem and try to find another solution.
There is no such thing as a solved problem.
> As for what role creativity plays: you understand things through conjecture. Conjectures are formed by a creative process. I think you know the rest? Were you asking something different?
I conjecture that understanding a problem is a mechanical process, founded on analysis, potentially devoid of conjecture. Making the leap from the understanding of the problem to the understanding of the solution is the moment where creativity is required, as it is the point at which you are creating something new (an idea). Everything up to that point is simply chopping the problem into smaller and smaller pieces.
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.
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.
A problem is a conflict between theories. Your problem isn't exactly how to escape from your jail cell -- that's just one theory about how to solve your problem. Maybe you would would like to visit your family, but you can't because the jail guards won't let you. The problem is the conflict between those two theories. (A whole other way doesn't involve leaving the jail at all. It involves being happy within the jail. Maybe your family can come visit you. Or maybe you don't actually have to see them, but could phone them instead. Or whatever.)
So, yes, understanding a problem will yield subproblems (or better formulations of the original problem -- e.g. from 'I want to be outside my jail cell' to 'I want to see my family'). And, yes, understanding these subproblems is part of fully understanding the original problem.
People often think they understand a problem, but not its solution. The fact is, they don't understand the problem well enough. For example, lots of people see problems with conventional romantic relationships, and some decide to be poly or something instead, but then they end up reverting because they didn't fully understand the problem. (And they might still claim they fully understand the problem, but the ring on their finger suggests otherwise. Ahem.)
Anyway, the point is: a good understanding consists of looking at lots of different options and elements of the problem. People don't take the role of understanding seriously enough. In your example, you're assuming that the very first idea of what a solution must look like has to be the only possible answer. Instead of looking for understanding, you're saying "I already understand it, I just want to know how to get through the wall." But if you understood the problem better, you would realise that getting through the wall is not your problem.
As for what role creativity plays: you understand things through conjecture. Conjectures are formed by a creative process. I think you know the rest? Were you asking something different?
Reply
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 my original problem scenario and then claim that therefore I don't fully understand the problem. Well, I did fully understand it before you started adding extra suppositions to it. :P
It's equally valid to say: Let's suppose there isn't a thing that I could say to the jail warden that would cause me to be released early. Therefore, I do understand the jail well enough, for having this extra information - that a given solution avenue is unavailable - does not solve the problem.
(This reminds me of DD's reasons for avoiding the use of examples. Either you can't see the point I'm trying to make, or you think that an example to support my argument cannot exist. Which is it? If neither, we'd save some time if you accepted the existence of a solid example, or at least helped to provide it. Assume Good Faith and all that).
> A problem is a conflict between theories. Your problem isn't exactly how to escape from your jail cell -- that's just one theory about how to solve your problem.
Sure, the problem can be contextualized - to ask why I want to escape from the jail cell. And maybe the answer is that I would like to see my family. But can I not then ask you to contextualize that problem again? In truth, I don't actually want to see my family; what I want is to be happy, and maybe there are other ways of doing that. But then we can contextualize again: I don't actually want to be happy; what I want is actually something else, and being happy may only be one way of achieving that. Etc.
To contextualize a problem is to question its justification, and so unbounded contextualization is justificationism, and produces an infinite regression as we well understand. The solution, as usual, is either to accept an irrational root - I want out of the jail cell because I just do, okay?! - or to set some condition on when contextualization is permitted.
How do we know when it's permitted? I'm not sure about this, but say for now that it's acceptable to contextualize when it's easier than the working set of subproblems. It's acceptable to answer, "why am I trying to escape from this jail cell, anyway?" when the alternative is to answer, "how do I walk through walls?"
Let's suppose that my reason for wanting to escape the jail cell is not to see my family, but because I theorise that it is morally wrong to exist in confinement like this, that to exist in a state of restricted freedom is not the best way to live. What will contextualization give us here?
(...damn this LJ character limit...)
Reply
> So, yes, understanding a problem will yield subproblems (or better formulations of the original problem -- e.g. from 'I want to be outside my jail cell' to 'I want to see my family'). And, yes, understanding these subproblems is part of fully understanding the original problem.
Yep. As noted, I think it's worth distinguishing these two types of understanding - inwards (yielding subproblems) and outwards (better formulations of the original problem).
> People often think they understand a problem, but not its solution. The fact is, they don't understand the problem well enough. For example, lots of people see problems with conventional romantic relationships, and some decide to be poly or something instead, but then they end up reverting because they didn't fully understand the problem.
I'd suggest that they revert because their perception of the solution to their perception of the problem changes with time. Their perception of the problem is "how can I be sexually/emotionally fulfilled in my interactions with others," and contextualizing that is, for the vast majority of people, a harder problem to solve than the transient myriad of smaller problems that plague day-to-day relationships.
> (And they might still claim they fully understand the problem, but the ring on their finger suggests otherwise. Ahem.)
Hah! Or maybe they've contextualized it further than you have, maybe they understand it even better than you do ;-)
> Anyway, the point is: a good understanding consists of looking at lots of different options and elements of the problem.
Here's a blog post I've just written about logical implication and optimization; through abstraction and implication we often skip looking at lots of different options and elements of the problem because we can see that they're not relevant/useful/applicable.
> People don't take the role of understanding seriously enough. In your example, you're assuming that the very first idea of what a solution must look like has to be the only possible answer.
No, I never said that. I simply said it was a possible answer, and, rather than continuing to search for further possible answers, decided to focus my attention on applying that answer instead.
What does it mean, to solve a problem, if not to find some possible answer to that problem?
Maybe the reason that I want to escape the jail cell is because I want to see Sweden before I die. By some technique I am able to escape the jail cell, but I never go to Sweden before I die. Does that mean that I never successfully escaped the jail cell? It sounds like that's the conclusion you'd have to draw; because my technique didn't eventually solve the underlying problem, it didn't solve the sub-problem. And when put like that, hopefully it's obvious that it's fallacious.
> Instead of looking for understanding, you're saying "I already understand it, I just want to know how to get through the wall." But if you understood the problem better, you would realise that getting through the wall is not your problem.
No, escaping the jail cell is my problem. I've found a solution: walk through the wall. I can now solve this new problem of how to walk through walls, or I can revisit an already-solved problem and try to find another solution.
There is no such thing as a solved problem.
> As for what role creativity plays: you understand things through conjecture. Conjectures are formed by a creative process. I think you know the rest? Were you asking something different?
I conjecture that understanding a problem is a mechanical process, founded on analysis, potentially devoid of conjecture. Making the leap from the understanding of the problem to the understanding of the solution is the moment where creativity is required, as it is the point at which you are creating something new (an idea). Everything up to that point is simply chopping the problem into smaller and smaller pieces.
Reply
Leave a comment