One could also appeal to the story about Gauss as a child adding up 1..100 by a clever trick, and none of his classmates figuring it out despite clearly seeing that Gauss must’ve done something clever.
But notice how your example does not fit my points: “since you don’t know how they solved it or usually how long they took”; in this case, you have a very good estimate of how long it will take them to use the O(n) summation algorithm from all your past sums, and since you were all assigned the problem at the same time, you also know precisely how long it took them.
In the Shannon anecdote, you know nothing about how long it took the brother to answer it nor, given how heterogenous puzzles can be, how long it might take him to solve it, nor is there even any ‘brute force’ approach for most puzzles which you could compare against a ‘clever’ approach and so choose to look for a clever approach rather than spend more time executing the brute force approach.
Similarly for web searching, there’s typically no brute force approach at all: if Google spits out a list of 10 hits total for the paper title and you look at all 10 and they fail, then what? What’s the dumb brute force approach in searching? You simply have to try another ‘clever’ approach, because you’ve exhausted all your available data.
Sorry, you’re right, I didn’t read your previous post carefully enough.
I agree that if this phenomenon is real, in order to explain it in terms of a rational agent you do need to either know something about the person who solved it, or how long they took, or some other detail about them in order for this to be helpful in any way.
In the real world, however, a declaration of having solved the problem always leaves some sort of knowledge. In the web search case that just unfolded in this thread, by posting a solution you leaked the information that a solution existed and that it didn’t take an unreasonable amount of time to figure out, which provided Benja additional incentive to start looking for a clever approach.
I’ll agree that it does seem like there is more than simple information gain going on here though. Perhaps there are other factors, such as the insertion of an element of competition?
I’ll agree that it does seem like there is more than simple information gain going on here though. Perhaps there are other factors, such as the insertion of an element of competition?
Certainly seems possible. I admit I tend to announce the time it took to find something that someone failed to as part of showing off and elevating myself, so it would be no surprise if the recipient felt shamed and inflamed into looking better—the difference between peak and average performance might explain the differential.
One could also appeal to the story about Gauss as a child adding up 1..100 by a clever trick, and none of his classmates figuring it out despite clearly seeing that Gauss must’ve done something clever.
But notice how your example does not fit my points: “since you don’t know how they solved it or usually how long they took”; in this case, you have a very good estimate of how long it will take them to use the O(n) summation algorithm from all your past sums, and since you were all assigned the problem at the same time, you also know precisely how long it took them.
In the Shannon anecdote, you know nothing about how long it took the brother to answer it nor, given how heterogenous puzzles can be, how long it might take him to solve it, nor is there even any ‘brute force’ approach for most puzzles which you could compare against a ‘clever’ approach and so choose to look for a clever approach rather than spend more time executing the brute force approach.
Similarly for web searching, there’s typically no brute force approach at all: if Google spits out a list of 10 hits total for the paper title and you look at all 10 and they fail, then what? What’s the dumb brute force approach in searching? You simply have to try another ‘clever’ approach, because you’ve exhausted all your available data.
Sorry, you’re right, I didn’t read your previous post carefully enough.
I agree that if this phenomenon is real, in order to explain it in terms of a rational agent you do need to either know something about the person who solved it, or how long they took, or some other detail about them in order for this to be helpful in any way.
In the real world, however, a declaration of having solved the problem always leaves some sort of knowledge. In the web search case that just unfolded in this thread, by posting a solution you leaked the information that a solution existed and that it didn’t take an unreasonable amount of time to figure out, which provided Benja additional incentive to start looking for a clever approach.
I’ll agree that it does seem like there is more than simple information gain going on here though. Perhaps there are other factors, such as the insertion of an element of competition?
Certainly seems possible. I admit I tend to announce the time it took to find something that someone failed to as part of showing off and elevating myself, so it would be no surprise if the recipient felt shamed and inflamed into looking better—the difference between peak and average performance might explain the differential.