these approaches lead to the counterintuitive conclusion
Counter-intuitiveness is not a property of the conclusion alone. Surprise does have an important role in learning, because otherwise one may rationalize and modify a theory being tested to fit the facts discovered, so a good way to test a theory’s informativeness is to set predictions beforehand and notice one’s surprise whenever they don’t pan out.
However, experiments are never tests of a single hypothesis but of complexes of hypotheses. A problem with testing a theory’s predictions to evaluate the theory is that one may make terrible predictions; the strength of the predictions is not a test of the theory alone but of the tester’s ability at extrapolating from a theory.
E.g.: I have several times encountered the argument, “If evolution is true, then why do scientists wear clothes?!” The idea is that by wearing clothes scientists admit to weaknesses of the bare skin design, and evolutionary theory would never predict less furry creatures, creatures who would sometimes be well served by clothing, to evolve from furry creatures. That’s a really stupid thing to think, and the conclusion one may draw from noticing surprise that scientists believe in evolution and wear clothes is not that there is a problem with the theory, but with the predictor’s extrapolation from the theory.
Evolution is not disproved by scientists wearing clothes. That scientists wear clothes is not even the most infinitesimally small theoretical evidence against evolution.
Obviously, I post in hindsight. But “Participants who indicated greater endorsement of utilitarian solutions had higher scores on measures of Psychopathy, machiavellianism, and life meaninglessness...a set of psychological characteristics that many would consider prototypically immoral,” i.e. “Participants who were abnormally likely to endorse unpopular moral calculations were aneurotypical in ways society labels as bad, and they were more willing to defy societal conventions and trust their own moral judgement rather than society’s, and/or ignore society’s mores for personal gain.” Surprise?
I vaguely recall reading about a study showing that most people were better at estimating their grocery bill when they abstractly estimated as they went along than when they tried to keep track of dollars and cents in their heads. Suppose this is true, pretend that it was well know and that the workings of cash registers were a total mystery.
One might find that those more adept at calculating would be less likely to take approximations as representing objective truths, and less likely to respect seeing $2.95 or $2.99 and $3.00 as being qualitatively the same, even though all three numbers are of the same type—amounts that are “threeish dollars”.
Would the usually superior results of the approximaters’ models show that the true operation of the registers most resembles converting prices into approximations and arriving at a larger number in a formula no one understood but was approximately addition, and then adding a bit for tax and translating the result into a dollar amount? Would the counters who laboriously try to add the prices and carry the numbers and then calculate the tax by multiplying (rather than “adding a bit” as the good approximating models do—they never accidentally forget to move a decimal point) be obviously wrong, by having the only models that fail catastrophically, in addition to their doing worse on average?
The counters might claim that counting best represents the type of thing cash registers do, and present contrived thought experiments like a person buying two items, one for $1.60 and the other for $2.80, with a 7.5% tax rate. Obviously, no experiment can be run with a cash register as such prices are never found in practice; counters say ($1.60+$2.80)*1.075=$4.73, while approximaters say $1.60 is the type of thing that is one-and-a-halfish-dollars (a fringe position, still noteworthy, is that it is the type of thing that is twoish dollars), $2.80 is the type of thing that is threeish dollars, add them together to get four-and-a-halfish dollars, and a little bit more than four-and-a-halfish dollars is the price of that basket of goods: “$4.75”.
The consonance of “$4.75” and not “$4.73″ to apes counting in base ten is not relevant to unraveling the secrets of the cash register, or much else, as interesting as it is in its own right. Likewise a strong emotional aversion to pushing the fat man tells us about the psychology of someone, not the rightness of pushing the fat man (which is dependent on all facts, including of course the psychology of each person).
Counter-intuitiveness is not a property of the conclusion alone. Surprise does have an important role in learning, because otherwise one may rationalize and modify a theory being tested to fit the facts discovered, so a good way to test a theory’s informativeness is to set predictions beforehand and notice one’s surprise whenever they don’t pan out.
However, experiments are never tests of a single hypothesis but of complexes of hypotheses. A problem with testing a theory’s predictions to evaluate the theory is that one may make terrible predictions; the strength of the predictions is not a test of the theory alone but of the tester’s ability at extrapolating from a theory.
E.g.: I have several times encountered the argument, “If evolution is true, then why do scientists wear clothes?!” The idea is that by wearing clothes scientists admit to weaknesses of the bare skin design, and evolutionary theory would never predict less furry creatures, creatures who would sometimes be well served by clothing, to evolve from furry creatures. That’s a really stupid thing to think, and the conclusion one may draw from noticing surprise that scientists believe in evolution and wear clothes is not that there is a problem with the theory, but with the predictor’s extrapolation from the theory.
Evolution is not disproved by scientists wearing clothes. That scientists wear clothes is not even the most infinitesimally small theoretical evidence against evolution.
Obviously, I post in hindsight. But “Participants who indicated greater endorsement of utilitarian solutions had higher scores on measures of Psychopathy, machiavellianism, and life meaninglessness...a set of psychological characteristics that many would consider prototypically immoral,” i.e. “Participants who were abnormally likely to endorse unpopular moral calculations were aneurotypical in ways society labels as bad, and they were more willing to defy societal conventions and trust their own moral judgement rather than society’s, and/or ignore society’s mores for personal gain.” Surprise?
I vaguely recall reading about a study showing that most people were better at estimating their grocery bill when they abstractly estimated as they went along than when they tried to keep track of dollars and cents in their heads. Suppose this is true, pretend that it was well know and that the workings of cash registers were a total mystery.
One might find that those more adept at calculating would be less likely to take approximations as representing objective truths, and less likely to respect seeing $2.95 or $2.99 and $3.00 as being qualitatively the same, even though all three numbers are of the same type—amounts that are “threeish dollars”.
Would the usually superior results of the approximaters’ models show that the true operation of the registers most resembles converting prices into approximations and arriving at a larger number in a formula no one understood but was approximately addition, and then adding a bit for tax and translating the result into a dollar amount? Would the counters who laboriously try to add the prices and carry the numbers and then calculate the tax by multiplying (rather than “adding a bit” as the good approximating models do—they never accidentally forget to move a decimal point) be obviously wrong, by having the only models that fail catastrophically, in addition to their doing worse on average?
The counters might claim that counting best represents the type of thing cash registers do, and present contrived thought experiments like a person buying two items, one for $1.60 and the other for $2.80, with a 7.5% tax rate. Obviously, no experiment can be run with a cash register as such prices are never found in practice; counters say ($1.60+$2.80)*1.075=$4.73, while approximaters say $1.60 is the type of thing that is one-and-a-halfish-dollars (a fringe position, still noteworthy, is that it is the type of thing that is twoish dollars), $2.80 is the type of thing that is threeish dollars, add them together to get four-and-a-halfish dollars, and a little bit more than four-and-a-halfish dollars is the price of that basket of goods: “$4.75”.
The consonance of “$4.75” and not “$4.73″ to apes counting in base ten is not relevant to unraveling the secrets of the cash register, or much else, as interesting as it is in its own right. Likewise a strong emotional aversion to pushing the fat man tells us about the psychology of someone, not the rightness of pushing the fat man (which is dependent on all facts, including of course the psychology of each person).