I think she’s been correct more often, though an accurate estimate is made difficult by the fact that, after three hours of extensive debate, we tend to discover we actually never disagreed much in the first place and were simply expressing ourselves unclearly. Still, I have adjusted my confidence in my own intuition downwards in light of her possibly having been correct more often.
Incidentally, trying to estimate our respective competences in this leads to an interesting circularity. Much of my intuition is grounded in what I know of mathematics and computer science, while she appealed to examples from medicine and biology. I’m tempted to think that math and cs, which in principle study all the possible ways in which any phenomena could be modeled, would be more useful than the estimates of doctors and biologists whose conceptual toolkits are limited to what has traditionally worked in their more narrow domain… but that would require me to first assume that the very general models studied in math and cs can be easily adapted into specific complex domains, and that ease of adaptability was the very thing the disagreement was all about! So in order to judge whose expertise is more applicable for resolving the question, we’d first need to resolve the question. (This is what I was talking about when I said we ran into the conflict of intuitions on at least five separate times.) Of course, I still don’t know that much cs and math, so I might also be mistaken about how much credence those fields lend to my intuition.
a) In the cs domain, suppose that the phenomenon that you were trying to model was the output of a cryptographic-quality pseudo-random generator for which you did not know the seed. Would you expect to be able to model its output accurately?
b) My gut reaction to your original post was that I’d expect them to partition roughly between cases where there is lots of experimental data compared to the parameter space of the system in question vs. where the parameter space is much larger than the reasonably accessible volume of experimental data. Of course, one doesn’t really know the parameter space till one has a successful model :-( …
suppose that the phenomenon that you were trying to model was the output of a cryptographic-quality pseudo-random generator for which you did not know the seed. Would you expect to be able to model its output accurately?
Uhh, no, I wouldn’t. But that hardly describes most naturally occurring phenomena.
Ok. In a sense, all of the difference between your intution and your friend’s intuition can be viewed as how to construe “most”. There are lots of systems in both categories. There is also a bias in which ones we research: Unless a problem is extraordinarily important, if attempts to build models for a phenomenon keep failing, and we have any reason to suspect e.g. chaotic behavior, we fall back to e.g. settling for statistical information.
Also, there is a question of how much precision one is looking for: The orbits of the planets look like clockwork even on moderately long timescales—but there do turn out to be chaotic dynamics (I think the part with the fastest divergence turns out to be one of the orbital elements of Mars, iirc), and this injects chaotic dynamics into everything else, if you want to predict far enough into the future.
I think she’s been correct more often, though an accurate estimate is made difficult by the fact that, after three hours of extensive debate, we tend to discover we actually never disagreed much in the first place and were simply expressing ourselves unclearly. Still, I have adjusted my confidence in my own intuition downwards in light of her possibly having been correct more often.
Incidentally, trying to estimate our respective competences in this leads to an interesting circularity. Much of my intuition is grounded in what I know of mathematics and computer science, while she appealed to examples from medicine and biology. I’m tempted to think that math and cs, which in principle study all the possible ways in which any phenomena could be modeled, would be more useful than the estimates of doctors and biologists whose conceptual toolkits are limited to what has traditionally worked in their more narrow domain… but that would require me to first assume that the very general models studied in math and cs can be easily adapted into specific complex domains, and that ease of adaptability was the very thing the disagreement was all about! So in order to judge whose expertise is more applicable for resolving the question, we’d first need to resolve the question. (This is what I was talking about when I said we ran into the conflict of intuitions on at least five separate times.) Of course, I still don’t know that much cs and math, so I might also be mistaken about how much credence those fields lend to my intuition.
Two comments:
a) In the cs domain, suppose that the phenomenon that you were trying to model was the output of a cryptographic-quality pseudo-random generator for which you did not know the seed. Would you expect to be able to model its output accurately?
b) My gut reaction to your original post was that I’d expect them to partition roughly between cases where there is lots of experimental data compared to the parameter space of the system in question vs. where the parameter space is much larger than the reasonably accessible volume of experimental data. Of course, one doesn’t really know the parameter space till one has a successful model :-( …
Uhh, no, I wouldn’t. But that hardly describes most naturally occurring phenomena.
Ok. In a sense, all of the difference between your intution and your friend’s intuition can be viewed as how to construe “most”. There are lots of systems in both categories. There is also a bias in which ones we research: Unless a problem is extraordinarily important, if attempts to build models for a phenomenon keep failing, and we have any reason to suspect e.g. chaotic behavior, we fall back to e.g. settling for statistical information.
Also, there is a question of how much precision one is looking for: The orbits of the planets look like clockwork even on moderately long timescales—but there do turn out to be chaotic dynamics (I think the part with the fastest divergence turns out to be one of the orbital elements of Mars, iirc), and this injects chaotic dynamics into everything else, if you want to predict far enough into the future.