When I read Ptolemy in college, one thing that struck me was how clear he was that he was advancing a probable hypothesis that needed to be supported with arguments and evidence. Some points he makes that stand up well in hindsight:
What’s simple from a god’s-eye view may seem complicated to us (i.e. our intuitive standpoint based on the objects we are used to interacting with may not carve reality at the joints).
At multiple points, he takes care to demonstrate the mathematical equivalence (from the observer’s point of view) of very different-seeming formalizations of the motions of the planets.
He is careful to point out that he isn’t positing a material mechanism, just providing a mathematical model that can produce the observations, consistent with the prevailing Platonic-Aristotelian belief that celestial objects naturally have uniform circular motion. (This compares favorably to Copernicus’s giant crystalline spheres.)
He uses concrete physical arguments as probable arguments for geocentrism. (Amusingly, “how would birds keep up if the Earth were moving so fast?” is a key consideration.)
The main argument for heliocentrism was that under geocentrism, there’s an unexplained coincidence in the way all the planets’ motions track the motion of the sun, and unexplained coincidences are mathematically unaesthetic. This unexplained coincidence is very clear in the Almagest, no effort was made to hide it.
As far as I can tell, the correct position at the time—and at Copernicus’s time—was that Ptolemy’s theory seemed more physically plausible, but that there were strong mathematical-elegance reasons to favor some sort of heliocentric theory if you could get the details worked out, so one should keep one’s mind open to both hypotheses until more evidence became available.
I think that the Copernican revolution looks less like people had some sort of mysterious epistemic insight, and more like just another plausible fad that happened to be especially epistemically lucky, when you take it in the context of the history of intellectual fashion. (Mesmerism does not hold up so well, for instance, and Cartesian physics got crucial questions badly wrong, even though it laid some of the conceptual groundwork for Newton.)
Thank you! I was quite nervous about posting but am very happy with the reception, and strongly update towards how remarkable a community LW2.0 might become (in terms of how welcoming it is of truth-seeking discussion and how constructively it forwards it).
Reading your comment, I’d update towards the relative importance of mathematical aesthetic compared to physical plausibility in finding true theories. I only want to believe in luck as a last resort. You seem to be making the “opposite” update. Is this correct? And, if it is, why do you update that way?
I think this is unambiguous evidence for the mathematical aesthetic heuristic, over the heuristic of support by existing physical theories. But in general we should expect that any good heuristic is occasionally going to outperform other good heuristics. Before you have an account of which heuristic to apply when, the best you can do is model this as a stochastic process with multiple imperfect predictors.
Along those lines, it’s worth noting that the germ theory of disease prior to epidemiology is not mathematically elegant at all, since it adds a new causal factor on top of ones that we already had extremely good arguments and evidence for (environmental and behavioral causes).
By contrast, it was not luck that Newton was persuasive, because he gave a mathematically elegant account that simultaneously provided an alternative model of physics to explain not only astronomical data, but much other empirical data.
When it comes to the germ theory of disease it’s worth noting that it isn’t that good at predicting when people will get a cold.
It doesn’t help you to predict that a person who’s outside in the cold is more likely to get a cold. It doesn’t help you to predict that people will more likely to get a cold in winter. It doesn’t help you to predict that a person who’s vitamin D3 deficient is more likely to get a cold.
You would expect bacteria to have a harder time when it’s cold outside.
If you on the other hand assume that there’s a life force that gets stronger or weaker that makes you more of less suspectible to disease you can find new ways to reason about those phenomena.
We could build a mathematical model that measures what kind of action correlate with changes in the life force and how changes in the life force correlate with events such as getting a cold.
As a result of the germ theory of disease children who are good at math enjoy their physics classes with nice mathematical models and the biology classes don’t include formula for calculating the life force.
Quite obviously germs are a causal factor, but I think the way the germ theory of disease tries to monopolise the discussion of disease it caused also a lot of harm. Maybe this post should let us become more skeptical of the strong version of the germ theory.
This post is great! Thanks for writing it.
When I read Ptolemy in college, one thing that struck me was how clear he was that he was advancing a probable hypothesis that needed to be supported with arguments and evidence. Some points he makes that stand up well in hindsight:
What’s simple from a god’s-eye view may seem complicated to us (i.e. our intuitive standpoint based on the objects we are used to interacting with may not carve reality at the joints).
At multiple points, he takes care to demonstrate the mathematical equivalence (from the observer’s point of view) of very different-seeming formalizations of the motions of the planets.
He is careful to point out that he isn’t positing a material mechanism, just providing a mathematical model that can produce the observations, consistent with the prevailing Platonic-Aristotelian belief that celestial objects naturally have uniform circular motion. (This compares favorably to Copernicus’s giant crystalline spheres.)
He uses concrete physical arguments as probable arguments for geocentrism. (Amusingly, “how would birds keep up if the Earth were moving so fast?” is a key consideration.)
The main argument for heliocentrism was that under geocentrism, there’s an unexplained coincidence in the way all the planets’ motions track the motion of the sun, and unexplained coincidences are mathematically unaesthetic. This unexplained coincidence is very clear in the Almagest, no effort was made to hide it.
As far as I can tell, the correct position at the time—and at Copernicus’s time—was that Ptolemy’s theory seemed more physically plausible, but that there were strong mathematical-elegance reasons to favor some sort of heliocentric theory if you could get the details worked out, so one should keep one’s mind open to both hypotheses until more evidence became available.
I think that the Copernican revolution looks less like people had some sort of mysterious epistemic insight, and more like just another plausible fad that happened to be especially epistemically lucky, when you take it in the context of the history of intellectual fashion. (Mesmerism does not hold up so well, for instance, and Cartesian physics got crucial questions badly wrong, even though it laid some of the conceptual groundwork for Newton.)
Thank you! I was quite nervous about posting but am very happy with the reception, and strongly update towards how remarkable a community LW2.0 might become (in terms of how welcoming it is of truth-seeking discussion and how constructively it forwards it).
Reading your comment, I’d update towards the relative importance of mathematical aesthetic compared to physical plausibility in finding true theories. I only want to believe in luck as a last resort. You seem to be making the “opposite” update. Is this correct? And, if it is, why do you update that way?
I think this is unambiguous evidence for the mathematical aesthetic heuristic, over the heuristic of support by existing physical theories. But in general we should expect that any good heuristic is occasionally going to outperform other good heuristics. Before you have an account of which heuristic to apply when, the best you can do is model this as a stochastic process with multiple imperfect predictors.
Along those lines, it’s worth noting that the germ theory of disease prior to epidemiology is not mathematically elegant at all, since it adds a new causal factor on top of ones that we already had extremely good arguments and evidence for (environmental and behavioral causes).
By contrast, it was not luck that Newton was persuasive, because he gave a mathematically elegant account that simultaneously provided an alternative model of physics to explain not only astronomical data, but much other empirical data.
When it comes to the germ theory of disease it’s worth noting that it isn’t that good at predicting when people will get a cold.
It doesn’t help you to predict that a person who’s outside in the cold is more likely to get a cold. It doesn’t help you to predict that people will more likely to get a cold in winter. It doesn’t help you to predict that a person who’s vitamin D3 deficient is more likely to get a cold.
You would expect bacteria to have a harder time when it’s cold outside.
If you on the other hand assume that there’s a life force that gets stronger or weaker that makes you more of less suspectible to disease you can find new ways to reason about those phenomena.
We could build a mathematical model that measures what kind of action correlate with changes in the life force and how changes in the life force correlate with events such as getting a cold.
As a result of the germ theory of disease children who are good at math enjoy their physics classes with nice mathematical models and the biology classes don’t include formula for calculating the life force.
Quite obviously germs are a causal factor, but I think the way the germ theory of disease tries to monopolise the discussion of disease it caused also a lot of harm. Maybe this post should let us become more skeptical of the strong version of the germ theory.