I can’t cite it exactly, but The Bad Astronomer has said that, yes, a geocentric and geostationary model of the cosmos is perfectly valid, mathematically. The same is true for any point in the cosmos, and for any degree of rotation about that point. You could have a cosmology based on Mars as the center, with Mars counter-rotating at 100 revolutions per second.
Such models are absurd. They’re insanely complicated. But…they’re valid.
Good point. That occurred to me, too, though it requires a bit of sophistication in physics.
That is, if you showed that to people post-Newton, no-brainer. If you showed it to people between Newton and Galileo, they’d like it but might wonder if Galileo’s observations (without a theoretic explanation) were correct.
I wonder what someone like Aristotle would have made of it.
You could correct that with a short course in number theory, where you’d find out it’s pretty much true by definition. Yeah, I know that’s not what you meant!
But you have to put that “faith” in quotes, because it’s not really faith.
Is it faith that makes us believe in an objective reality, or is it experience that shows it’s a good working principle? That’s the main difference between religious faith and scientific “faith”. The latter is always provisional. Contradictory experiences cause us to challenge our assumptions. Great example: relativity. The idea that time isn’t the same everywhere for everyone – that there’s really no such thing as simultaneity – is a pretty astounding leap, yet nobody had to die for the world to embrace it as canon.
(Contrast that with Lavoisier’s valence theory. Priestly went to his grave believing in phlogiston theory. It’s understandable, since the two theories give the same results, mathematically. But one made further predictions, and young chemists were drawn to it by its success. Science isn’t always as neat as we’d like it to be.)
Grin! I loved my old number theory class! It was wonderful! (But the sheer level of abstraction of topology was even more aetherial!)
Well, yes and no… In practice, it’s more like not giving a damn. We can’t function on the basis of solipsistic doubt, so we discard it for all practical purposes. But ultimately, we can never dispel it, just work around it.
Descartes might have added, in addition to being aware of my own mind, I’m also very aware of pain and pleasure. Trying to ignore the real world leads to very painful experiences.
Kicking the rock and declaiming, “I refute it thus!” hurts!
That’s another problem Descartes didn’t deal with: the “reality” around us is incredibly complicated, and yet also incredibly consistent. It bears very little resemblance to the “other reality” that our minds create: our dreams. I’m pretty sure that if my mind were creating “reality,” it would look a lot more like a dreamscape than like reality as we know it.
I love to quote from Bertolt Brecht’s “Life of Galileo.” “The aim of science is not to open the door to everlasting wisdom, but to set a limit to everlasting error.” Science works the way Sherlock Holmes did: “Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth.” It’s a strangely negative process; for every time science has “proven” something, there are ten other cases when it has “disproven” something else.
Another wonderful example. Phlogiston is not a stupid idea. It’s very descriptive, and explains everyday phenomena very well. It’s only when you get to a stage of technology sufficiently advanced to be able to weigh gases that you can perform the falsifying experiments.
As for the earth going around the sun – we’ve put satellites up into interplanetary orbit that have seen it happen! It isn’t a question of inference any more, but of observation!