Gee, I didn't think I'd be responding to comments with posts so quickly. This one is just too good to pass up, though, as it presents an excellent exercise in critical thinking and analysis.
Kt writes: I know this blog isn't a question answer thing, but I'm gonna ask you anyway. What's the point in searching for something you can never find? If you need me to elaborate I will, but I'm hoping not because I want the initial reaction.
Well... There are a couple ways to address that question. There is the philosophical way, and the scientific way. Let's take the philosophical first.
The question assumes that you are (a) already searching and (b) already know that you can't find it. This means that the search is the answer, rather than whatever it is you're searching for. The search is it's own result. Now, if we don't make any of those particular assumptions, then we assume that you have started searching, but are now in doubt of the result's existence. In this case, you have to make a determination as to whether or not you should continue your search. The most correct philosophical answer then, would probably be to respond with the question, "How do you know you can never find it, if you have never searched?"
But, this is a skeptical / science and critical thinking blog, so for the scientific answer, let's do it my way: With math.
Note to math gurus: This is a thought exercise and not meant to be a complete theory. Just roll with it, 'k?
First, I'm going to show you a matrix. (I love matrices.) This describes the best to worst result based on each assumption. Positive numbers are positive results, negative numbers are negative results.
| Does Exist | Does Not Exist | Best Option | |
| Search | 2 | -2 | 0 |
| Don't Search | -1 | 1 | 0 |
The results, of course, are potential multiples, based on the value of the result in question, so the first thing we do is we decide how valuable the result is. Finding a dollar you carelessly left somewhere around the house is maybe a factor of 1. So your result range is somewhere between 2 and 2 Not a big change in value. Make that a one hundred dollar bill, and the factor becomes 100. Now your result range is between 200 and -200. So we see that the risk to reward ratio increases with the value of the goal. Now think about what this means when we change the goal from a one hundred dollar bill, to a cure for cancer. The reward and risk increase exponentially. For the sake of argument, let's say that it's a 100 dollar bill, and multiply the overall results by the value.
| Does Exist | Does Not Exist | Best Option | |
| Search | 200 | -200 | 0 |
| Don't Search | -100 | 100 | 0 |
The next thing we do, or should do, is decide how probable It is that the result exists. I know I have my car keys somewhere in the house. The 20 carat diamond and stack of gold bars is a little less likely to be lying around here somewhere…
[EDIT 2008.01.21.0442 by D]
On a scale of 1 to 10, with 1 being 'not probable at all', and 10 being 'almost definite', we can say how certain we are that the thing we're searching for either does or does not exist, then multiply that particular column by that factor. Let's say that the probability that a 100 dollar bill does not exist in my house is about a 3 out of 10. So we multiply the 'Does Not Exist' column by that factor.
[EDIT COMPLETE]
| Does Exist | Does Not Exist | Best Option | |
| Search | 200 | -600 | -400 |
| Don't Search | -100 | 300 | 200 |
At this point, the answer is a bit clearer. The best possible action at this point is not to search, since the highest potential result is there. (Best Option = 200). There's one more factor to take into account in this case, and that is search cost. How much are we willing to dedicate to the search? This is often tempered by the existing results matrix, which is why these steps need to be taken in order. This one is actually a formula, which looks like this:
Search cost is a scale of 1 to 10, just like the probability cost. Let's say, for example that we're just willing to keep our eyes open as we go about our normal daily duties, just in case a 100 dollar bill should be around here somewhere. This could be considered a search cost of 1.
Does Exist: ((-400 / 200) + 1) * 200 = -200
vs.
Does Not Exist = ((-400 / 200) + 1) * -600 = 600
Now the decision matrix looks like this:
| Does Exist | Does Not Exist | Best Option | |
| Search | -200 | 600 | 400 |
| Don't Search | -100 | 300 | 200 |
Get that. Now the math tells us that it's a better idea to search for something that has a probability of NOT existing. How is that possible? Remember... the search cost is very low. Since the gain is high, and the search cost is low, it does actually make sense to expend the minimal energy and resources to make that kind of a search, even with a low probability of existence. Now, lets ratchet the investment up a bit, and see how it shakes out. If we make plans to go through drawers, move furniture, look in unlikely places, etc… the search cost goes up to 5.
Does Exist: ((-400 / 200) + 5) * 200 = 600
vs.
Does Not Exist = ((-400 / 200) + 5) * -600 = -1,800
Result:
| Does Exist | Does Not Exist | Best Option | |
| Search | 600 | -1,800 | -1,200 |
| Don't Search | -100 | 300 | 200 |
Now the result is obvious. Given the likelihood of the object or goal's existence, and the cost we plan to expend in searching for it, the results are dramatic. Our mathematically best option is now most certainly not to tear the house apart looking for the money.
However...
I'm going to throw one last calculation at you. I call this "The Second Guess". Philosophically, it works this way: You may want to do your search anyway, since the fully positive results of finding the goal (Search / Does Exist) may outweigh the cost of a pointless search. Mathematically, we determine whether the absolute value of the Search/Does Exist result is higher than the difference between the Best Options. In this case...
[Search / Does Exist] = 600
vs.
[Search Option + Don't Search Option] = 1,000
The fully positive result (Search / Does Exist) is still less than the difference between the options. So the point stands. I'm not tearing my house up for this 100 dollar bill that probably isn't there.
So the final answer to all of this is, it comes down to what you consider to be the value of what you're searching for, what is the probability of it's existence, and to what extent you're willing to go to find it.
Make sense?
-D.