This seems to be a common response—Tyrrell_McAllister said something similar:
I think that your distinction is really just the distinction
between physics and mathematics.
I take that distinction as meaning that a precise maths statement isn’t necessarily reflecting reality like physics does. That is not really my point.
For one thing, my point is about any applied maths, regardless of domain. That maths could be used in physics, biology, economics, engineering, computer science, or even the humanities.
But more importantly, my point concerns what you think the equations are about, and how you can be mistaken about that, even in physics.
The following might help clarify.
A successful test of a mathematical theory against reality means that it accurately describes some aspect of reality. But a successful test doesn’t necessarily mean it accurately describes what you think it does.
People successfully tested the epicycles theory’s predictions about the movement of the planets and the stars. They tended to think that this showed that the planets and stars were carried around on the specified configuration of rotating circles, but all it actually showed was that the points of light in the sky followed the paths the theory predicted.
They were committing a mind projection ‘fallacy’ - their eyes were looking at points of light but they were ‘seeing’ planets and stars embedded in spheres.
The way people interpreted those successful predictions made it very hard to criticise the epicycles theory.
The issue people are having is, that you start out with “sort of” as your response to the statement that math is the study of precisely-defined terms. In doing so, you decide to throw away that insightful and useful perspective by confusing math with attempts to use math to describe phenomena.
The pitfalls of “mathematical modelling” are interesting and worth discussing, but it actually doesn’t help clarify the issue by jumbling it all together yourself, then trying to unjumble what was clear before you started.
They tended to think that this showed that the planets and stars were carried around on the specified configuration of rotating circles, but all it actually showed was that the points of light in the sky followed the paths the theory predicted.
I’ve never gotten that impression. Proponents of epicycles were working from the assumption that celestial motion must be perfect, and therefore circular, and so were making the math line up with that. Aside from trying to fit an elliptical peg into a circular hole, they seemed to merely believe that the points of light in the sky follow the paths the theory predicts.
But then, it’s been a few years since I’ve read any of the relevant sources.
This seems to be a common response—Tyrrell_McAllister said something similar:
I take that distinction as meaning that a precise maths statement isn’t necessarily reflecting reality like physics does. That is not really my point.
For one thing, my point is about any applied maths, regardless of domain. That maths could be used in physics, biology, economics, engineering, computer science, or even the humanities.
But more importantly, my point concerns what you think the equations are about, and how you can be mistaken about that, even in physics.
The following might help clarify.
A successful test of a mathematical theory against reality means that it accurately describes some aspect of reality. But a successful test doesn’t necessarily mean it accurately describes what you think it does.
People successfully tested the epicycles theory’s predictions about the movement of the planets and the stars. They tended to think that this showed that the planets and stars were carried around on the specified configuration of rotating circles, but all it actually showed was that the points of light in the sky followed the paths the theory predicted.
They were committing a mind projection ‘fallacy’ - their eyes were looking at points of light but they were ‘seeing’ planets and stars embedded in spheres.
The way people interpreted those successful predictions made it very hard to criticise the epicycles theory.
The issue people are having is, that you start out with “sort of” as your response to the statement that math is the study of precisely-defined terms. In doing so, you decide to throw away that insightful and useful perspective by confusing math with attempts to use math to describe phenomena.
The pitfalls of “mathematical modelling” are interesting and worth discussing, but it actually doesn’t help clarify the issue by jumbling it all together yourself, then trying to unjumble what was clear before you started.
I’ve never gotten that impression. Proponents of epicycles were working from the assumption that celestial motion must be perfect, and therefore circular, and so were making the math line up with that. Aside from trying to fit an elliptical peg into a circular hole, they seemed to merely believe that the points of light in the sky follow the paths the theory predicts.
But then, it’s been a few years since I’ve read any of the relevant sources.