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Tuesday, December 07, 2004

A Tribute to Solution Space

There's concept in science known as solution space, and it colors my entire perspective. Solution space refers to the sum total of all possible solutions to a problem or question. For example, if you're asked in which month Arbor Day falls, your solution space is a list of the twelve months of the year. The thing about solution space is that most problems have a massive number of possible solutions. One, or even a few, may be right, but most are absolutely wrong.

There's more. Solutions that are wrong but not very wrong are often located closer in space to the right solution than solutions that are very wrong. So, since Arbor Day is usually the last Friday in April (I had to look it up, believe me), March is closer, in solution space, than February, which is closer than December. The idea is to kind of visualize an expanse of space and to think of the solution as being located in some tiny locale therein. In this case, our solution space is two-dimensional. But in most cases, when you factor in thousands of variables at work at any given time, the space expands in all directions.

I have found the use of the solution space concept very valuable over the years. For one thing, it keeps me very far from ever proclaiming certainty. Regardless of what we're trying to explain, there's a solution space for it and, very importantly, our imaginations play a large role in what areas of solution space we explore. We generally start where we've been before and extrapolate from there. Herein lies the wisdom of solution space. The moment we think we've thought of everything, we need only remind ourselves that solution space is gigantic and that the odds are very good that we're missing A LOT. It's humbling and produces a tendency to keep digging, which bring me to the next benefit of solution space.

Solution space is a creativity enhancer. By understanding that our current way of explaining things is limited to the insights gained from our previous experiences, each located in its own area of solution space, eventually we know where not to look. We're forced to reject the familiar if our question remains unresolved. We have to find environments that stimulate our brains in new ways. As soon as we experience new things and new ideas, we begin to consider the permutations that surround them in solution space. It's as if we're instantly transported to a new area of space with all new possibilities. This is why people go to movies, and it's also why a lot of people do drugs. Isn't a big screen experience the ultimate cure for boredom with the familiar? And didn't John Lennon and pals frequently refer to the mind expanding powers of whatever it was they were on? What the moviegoer and Lennon had in common was the desire to access some previously unaccessed areas of solution space. In looking for explanations for everything from meaning of life to the perfect melody line, the solution space jockey finds the thrill in the chase.

At some point in the internalization of solution space, we come to know that finding what we want may take a while. We develop tenacity to continue searching for solutions. Eventually, when we've run down one too many rat holes, it dawns that the most important solution space is the one related to what makes for a worthwhile question. It becomes instantly apparent that the good ones are daunting, where many have tried and all have failed, where the space of possibilities is enormous. But you have to pay your dues and the big questions aren't big for nothing.

Getting a crack at the biggest expanses of solution space requires years of training. One must learn to tell the difference between a correct and incorrect solution - between truth and fiction, at the end of the day. The base of this skill is the commitment to the notion that possibilities may only be proven wrong, never right. The only thing to do is disprove as many as possible and then evaluate the field that remains. Based upon a certain set of rules, a solution may or may not be chosen as the preferred solution. And preferred solutions are only allowed if they are accompanied by an admission of uncertainty (solution space is big, even for simple things).

The rules that determine if we can even prefer a solution are the same rules that we use to determine if a solution is true or false. These are the rules of logic. Once they are mastered, we must use them to acquire as much knowledge as we can - about a wide array of subjects. The more we learn, the more difficult the questions we can pursue effectively. This is pretty much where I am these days.

I'm on a mission to learn as much as I can about this world. This blog, I hope, will help me do that. I am constantly pondering the role of our genes in our ability to understand our experiences. So I'll throw out what I've encountered in my jaunts through solution space in the hopes that readers might help in the search. And if I stray into politics too much, well I can't help it - the drama's irresistable.

7 Comments:

Blogger TallahasseeJoe said...

More preferred ("less wrong") solutions are not always closer in the solution space to optimal ("right") solutions.

For example, if the problem is what policy to adopt toward a natural monopoly industry (such as providing power to a locality) and the solution space is a spectrum from free market to government ownership, with varying degrees of regulation in between, some points on the spectrum may be less efficient than EITHER of the extremes.

I think this is a common situation in U.S. politics, including energy regulation and health care. Liberals and conservatives come to some compromise that is actually worse than either of the extreme positions (a "lose-lose" compromise).

I think it is often possible to come to a compromise that is better than either of the extremes, (a win-win) but unfortunately this often does not happen, largely because neither side understands incentive structures very well and both sides are working blindly from ideological assumptions.

For example, consider health care. The U.S. system is a compromise between free markets and goverment control - but in some ways it is worse than a total free market AND worse than a single-payer universal health care system. This is because we use left liberal command-and-control policies such as requiring hospitals to provide emergency care regardless of the ability to pay, without compensating the hospitals for this - an "unfunded mandate".

Hospitals respond by charging insane prices for the people who can pay (or who have insurance). The result is that market signals are completely distorted and the whole health industry becomes inefficient. A more appropriate compromise would be allowing hospitals to charge the price they want and having government provide basic minimum coverage (of "usual and customary" charges) for emergencies, catastrophic illness, and some preventative care.

For a progressive view on politics, please visit my blog, The Tallahassee Progressive, at www.TallahasseeProgressive.blogspot.com

12/08/2004 04:00:00 PM

 
Blogger Chris Wilson said...

Joe, glad you commented on this. It'll give me a chance to clarify things a bit. More preferred solutions are, by definition, closer to the optimal solutions than are less preferred solutions. This is one of the real benefits of this model of thinking. It works like this.

Using your example, let's explore the question as to which healthcare system is best for all people. The solution space is all possible systems, from the most extreme free market systems to the most extreme collectivist systems to everything in between. Determining which system is optimal requires, first and foremost, the establishment of criteria that make for a good solution.

This is where things get dicey. If our primary deciding factor is having healthcare accessible to all people, then we find that true free market systems are less preferred than more state-influenced systems. On the flip side, if our number one criteria is lowest aggregate cost, then free market systems become more preferred. The point is that solution space, particularly the arrangement of solutions with respect to one another, changes dramatically as you modify optimal solution criteria.

The cool thing is that once you get used to thinking like this, you can ponder questions from all kinds of angles, thus sending you into areas of solution space you may not have considered previously.

12/08/2004 05:17:00 PM

 
Blogger TallahasseeJoe said...

If more preferred solutions are by definition closer to optimal solutions in solution space then are less preferred solutions, that's fine (you can define things however you want) but you have to accept that your solution space may be discontinuous with respect to variables other then preferredness.

If this conception of solution space helps you think outside the box and imagine solutions you otherwise would have ignored, that's great.

For me personally I don't see much use in the conception of solution space that you are advancing. Representing solutions in the kind of space you are proposing requires knowing which solutions are most (or at least more) preferred. But if we knew that, we wouldn't have a problem - it would already be solved!

Ultimately though, you can represent things however is most convenient to you - it's arbitrary.

Please visit my blog the Tallahassee Progressive for a progressive view of politics www.tallahasseeprogressive.blogspot.com

12/09/2004 08:38:00 PM

 
Blogger Chris Wilson said...

OK, something was nagging at me after I responded to the first comment. It was, it turns out, exactly what Joe pointed out in his response. So, I have to take back what I said and concede the point that preferred solutions may lie farther, in terms of proximity, away from optimal solutions than some non-preferred solutions. Solution space stays the same; where we are with respect to it is the variable.

Thanks for keeping me honest, Joe.

12/11/2004 05:53:00 PM

 
Blogger Brian said...

On the topic of health care:

Solution space is not necessarily one-dimensional, as it is with months of the year. As it relates to health care Solution space is multidimensional; though only two dimensions are relevant here. Imagine a square. The four corners represent StateFunding/StateControl, StateFunding/FreeControl, FreeFunding/StateControl, and FreeFunding/FreeControl. If the right solution lies somewhere below the line that joins StateFunding/FreeControl and FreeFunding/FreeControl, then it is quite possible that FreeFunding/StateControl is worse than both StateFunding/StateControl and FreeFunding/FreeControl.

12/18/2004 01:45:00 AM

 
Anonymous Anonymous said...

After the flogging I've received over this, I guess I should restate my commitment to solutions space. For one thing, I only used the months of the year example to indicate that preferred solutions are often closer to optimal solutions in space than non-preferred solutions. I fully realize and appreciate that multi-dimensional solution space is the rule and that my example was somewhat simplistic. But what I have to concede is there are definitely situations in which preferred solutions may not reside as close to the optimal solution as non-preferred solutions. So, in this respect, I think I over-promised on the value of solution space. Nevertheless, the concept is still immensely valuable, if for no other reason than it gives us a visual representation of problems and the panoply of solutions that can be considered. It's a creativity-enhancing mind opener. I'll leave it at that.

12/18/2004 02:31:00 AM

 
Blogger Chris Wilson said...

After the flogging I've received over this, I guess I should restate my commitment to solutions space. For one thing, I only used the months of the year example to indicate that preferred solutions are often closer to optimal solutions in space than non-preferred solutions. I fully realize and appreciate that multi-dimensional solution space is the rule and that my example was somewhat simplistic. But what I have to concede is there are definitely situations in which preferred solutions may not reside as close to the optimal solution as non-preferred solutions. So, in this respect, I think I over-promised on the value of solution space. Nevertheless, the concept is still immensely valuable, if for no other reason than it gives us a visual representation of problems and the panoply of solutions that can be considered. It's a creativity-enhancing mind opener. I'll leave it at that.

12/18/2004 02:32:00 AM

 

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