Note: I wrote most of this, and the sat on it for a couple days. I’m commenting here just to get it out there, because I think the approach is a good one, but I haven’t proofread it or tweaked the phrasing to make it clearer. Hopefully I’ll come back to it soon, though.
1. If you lived in the time of the Copernican revolution, would you have accepted heliocentrism?
No, absolutely not. I think this is roughly how we should have reasoned:
The best models of physics say that earthly objects are inherently center-seeking. It’s the nature of rocks and people and such to move toward the center. That’s the simplest explanation.
Now, celestial objects don’t have this property, which is why they are found so far from the center. What mechanisms govern their motion are a mystery, but the models which best fir the data are not heliocentric.
Sure, you could separate the ideas of “center” and “what attracts objects”. There’s no *a priori* reason they should coincide. And, Tycho Brahe’s combined geoheliocentric theory does just this. It places the sun at the center of the rotations of the planets, and the earth at the center of the rotation of the moon and the sun.
But, this only changes our interpretation of the celestial world, not the earthly world. And, our knowledge there is much less intimate than our practical, day-to-day knowledge of the physical laws that govern earthly objects. So, rocks are still drawn to their respective puller when thrown, and the sorts of objects that don’t fall and aren’t bound by this pull rotate around whatever it is they rotate around, sun or earth.
But, we know the moon orbits earth, so it is just a question of whether it’s simpler to have everything else also orbit us, but with complex epicycles, or to say that everything but the moon orbits the sun.
But, this second approach still requires the introduction of epicycles, and so is strictly more complex. So, in all likelihood, the earth is the center of all things.
I think this logic is correct and sound, at least until Newton. We should have notices we were confused after Galileo. He shattered the illusion that celestial objects were of a fundamentally different nature than earthly objects. Before that, earthly objects were rough and oddly shaped, while celestial objects were all perfectly round, or infinitely small points of light.
Celestial objects glowed, for god’s sake, and nonstop, in a way that we could only reproduce temporarily with fire. Conservation of energy clearly didn’t apply to them, especially because they moved constantly in mysterious unceasing patterns. Earthly objects are subject to friction, and even the fastest moving bullet eventually succumbs to gravity. The proper and natural thing to do is to classify them as fundamentally different.
2. How should you develop intellectually, in order to become the kind of person who would have accepted heliocentrism during the Copernican revolution?
I think the proper lesson here is NOT epistemic humility. We shouldn’t retain high degrees of model uncertainty forever, and agonize over whether we’re missing something that fuzzy, spiritual, mystical insight.
Mysticism happened to get the right answer in this case, but not because of anything intrinsic to mysticism. Instead, I think we can pull out the property that made it work, and leave the rest. (Pull out the baby, pitch the bathwater.)
But first, let’s look at our model for model uncertainty. Bayes’ Theorem would have us update from our priors to some ideal probability estimate, hopefully >99.9%, or <0.1%, if we can dig up enough data. Usually, we only pay attention to the p, but the amount of total evidence collected is also a decent measure of the progress from priors to truth.
Another measure I like even better is how large you expect future updates to be. Maybe I’m 20% sure of my best hypothesis, and I expect to update by +/- about 5% based on some experiment which I can’t do yet. The relative ratio of these 2 percentages is telling, because it tells you how much variability is left in your model. (Or, more precisely but using different units, maybe you give odds 10:1 in favor of something, but still expect to update by a factor of 100 after the next experiment, in one direction or another.)
By conservation of expected evidence, you can’t know in which *direction* that update will be. (Or if you can, than you should already have updated on *that* knowledge.) But, you can at least get a feel for the size of the update, and compare it to the probability of your current model.
So, you start out with uncountably many priors, all of which have only a tiny chance of being true. Then, as more and more evidence comes in, some hypotheses go past the 1% threshold, and you have a humanly manageable number, some of which are more probably than others. But, these shouldn’t add up to 100%. Most of your probability mass should still be on unknown unknowns. And really, most of your models should only be thought of as rough outlines, rather than formal definitions.
I think this is where Capernacus should have considered himself to be. He had bad reasons for trying to come up with variants of the current best models. But, that’s exactly what he should have been doing, regardless of the reasons. And, note that, despide getting quite close, he was still wrong. The sun is not the center of the universe, or even the galaxy. It’s just the center of the solar system. Ish. Really, there’s some point that’s the center of mass of everything in the solar system, and if I recall it’s actually technically outside the sun. The sun and everything else just orbit that point.
So, you can only really expect to put non-negligible probability on models in this state of understanding when you include a bunch of weasel words, and phrase things as broadly as possible. Instead of “The earth and all the celestial objects but the moon rotate around the sun”, append this with “or the majority of them do, or they approximately do but some second-order correction terms are needed.”
And even then, it’s probably still not quite right. In this sense, we’re probably wrong about just about everything science claims to know, with probability nearly 1. But, I think we’re homing in on the truth asymptotically. Even if we never quite get to anything that’s 100% right, we can get arbitrarily close. So, is everything we know a lie, then? Should we put near-zero probability on everything, since we probably haven’t added enough weasel words to capture every possible subtlety we may have missed?
John, when people thought the earth was flat, they were wrong. When people thought the earth was spherical, they were wrong. But if you think that thinking the earth is spherical is just as wrong as thinking the earth is flat, then your view is wronger than both of them put together.
It would be nice to have some absolute measure of this similarity in terms of Kolmogorov complexity or something. Like, a circle and an ellipse are quite similar mathematically, and there are probably plenty of ways to quantify how far a circle is from an ellipse. So, it seems like it should be possible to quantify how similar any 2 arbitrary mathematical models are. Maybe in terms of how different their predictions are, or how similar their mathematical structure is? I dono.
But, I’m not aware of any generalizations of circle/ellipse differences to all possible computations. How far is 1+1 from the Pythagorean theorem? I dono, but I think modeling something as a circle when it’s really closer to an ellipse (ignoring orbital perturbations from nearby planets) is a lot closer than 1+1 is to the Pythagorean theorem. And, I think that modeling everything as revolving around the sun is significantly closer to reality than modeling everything as orbiting the earth. It’d be interesting to be able to quantify exactly how much closer, though.
Note: I wrote most of this, and the sat on it for a couple days. I’m commenting here just to get it out there, because I think the approach is a good one, but I haven’t proofread it or tweaked the phrasing to make it clearer. Hopefully I’ll come back to it soon, though.
No, absolutely not. I think this is roughly how we should have reasoned:
I think this logic is correct and sound, at least until Newton. We should have notices we were confused after Galileo. He shattered the illusion that celestial objects were of a fundamentally different nature than earthly objects. Before that, earthly objects were rough and oddly shaped, while celestial objects were all perfectly round, or infinitely small points of light.
Celestial objects glowed, for god’s sake, and nonstop, in a way that we could only reproduce temporarily with fire. Conservation of energy clearly didn’t apply to them, especially because they moved constantly in mysterious unceasing patterns. Earthly objects are subject to friction, and even the fastest moving bullet eventually succumbs to gravity. The proper and natural thing to do is to classify them as fundamentally different.
I think the proper lesson here is NOT epistemic humility. We shouldn’t retain high degrees of model uncertainty forever, and agonize over whether we’re missing something that fuzzy, spiritual, mystical insight.
Mysticism happened to get the right answer in this case, but not because of anything intrinsic to mysticism. Instead, I think we can pull out the property that made it work, and leave the rest. (Pull out the baby, pitch the bathwater.)
But first, let’s look at our model for model uncertainty. Bayes’ Theorem would have us update from our priors to some ideal probability estimate, hopefully >99.9%, or <0.1%, if we can dig up enough data. Usually, we only pay attention to the p, but the amount of total evidence collected is also a decent measure of the progress from priors to truth.
Another measure I like even better is how large you expect future updates to be. Maybe I’m 20% sure of my best hypothesis, and I expect to update by +/- about 5% based on some experiment which I can’t do yet. The relative ratio of these 2 percentages is telling, because it tells you how much variability is left in your model. (Or, more precisely but using different units, maybe you give odds 10:1 in favor of something, but still expect to update by a factor of 100 after the next experiment, in one direction or another.)
By conservation of expected evidence, you can’t know in which *direction* that update will be. (Or if you can, than you should already have updated on *that* knowledge.) But, you can at least get a feel for the size of the update, and compare it to the probability of your current model.
So, you start out with uncountably many priors, all of which have only a tiny chance of being true. Then, as more and more evidence comes in, some hypotheses go past the 1% threshold, and you have a humanly manageable number, some of which are more probably than others. But, these shouldn’t add up to 100%. Most of your probability mass should still be on unknown unknowns. And really, most of your models should only be thought of as rough outlines, rather than formal definitions.
I think this is where Capernacus should have considered himself to be. He had bad reasons for trying to come up with variants of the current best models. But, that’s exactly what he should have been doing, regardless of the reasons. And, note that, despide getting quite close, he was still wrong. The sun is not the center of the universe, or even the galaxy. It’s just the center of the solar system. Ish. Really, there’s some point that’s the center of mass of everything in the solar system, and if I recall it’s actually technically outside the sun. The sun and everything else just orbit that point.
So, you can only really expect to put non-negligible probability on models in this state of understanding when you include a bunch of weasel words, and phrase things as broadly as possible. Instead of “The earth and all the celestial objects but the moon rotate around the sun”, append this with “or the majority of them do, or they approximately do but some second-order correction terms are needed.”
And even then, it’s probably still not quite right. In this sense, we’re probably wrong about just about everything science claims to know, with probability nearly 1. But, I think we’re homing in on the truth asymptotically. Even if we never quite get to anything that’s 100% right, we can get arbitrarily close. So, is everything we know a lie, then? Should we put near-zero probability on everything, since we probably haven’t added enough weasel words to capture every possible subtlety we may have missed?
Isaac Asimov wrote a fantastic description of this problem, which he summed up this way:
It would be nice to have some absolute measure of this similarity in terms of Kolmogorov complexity or something. Like, a circle and an ellipse are quite similar mathematically, and there are probably plenty of ways to quantify how far a circle is from an ellipse. So, it seems like it should be possible to quantify how similar any 2 arbitrary mathematical models are. Maybe in terms of how different their predictions are, or how similar their mathematical structure is? I dono.
But, I’m not aware of any generalizations of circle/ellipse differences to all possible computations. How far is 1+1 from the Pythagorean theorem? I dono, but I think modeling something as a circle when it’s really closer to an ellipse (ignoring orbital perturbations from nearby planets) is a lot closer than 1+1 is to the Pythagorean theorem. And, I think that modeling everything as revolving around the sun is significantly closer to reality than modeling everything as orbiting the earth. It’d be interesting to be able to quantify exactly how much closer, though.