The Ptolemaic system has some apparent coincidences in that some of the cycles and epicycles take exactly one earth year.
Copernicus’s model, by contrast, doesn’t just replace five circles (the cycles for Mercury and Venus, and the epicycles for Mars, Jupiter and Saturn) with one (for the Earth going around the Sun). It also automatically explains why the five superfluous cycles show an otherwise unexplained synchronic parallelism.
Some things are really just not worth worrying about.
A few other tidbits in the linked post. Solomonoff induction
Bayes’ Rule - which is the basis for the Kalman Filter:
Bayes’ Rule is an application of probability theory that tells you how you should revise probability estimates in the face of new evidence. Eliezer Yudkowsky gives one of the best introductions around to a counter-intuitive approach that has become enormously influential in recent years. (It’s fun to read too).
Also Occam’s Razor
And Kolmogorov
Solomonoff offers a different answer. He argues that we can use the theory of algorithmic complexity, as developed by Kolmogorov, to assign prior probabilities. Roughly, if your theory were turned into a computer program, how long would the program be? The longer the program, the lower the prior probability,
Andrey Nikolaevich Kolmogorov , 25 April 1903 – 20 October 1987)[4][5] was a Soviet mathematician who made significant contributions to the mathematics of probability theory, topology, intuitionistic logic, turbulence, classical mechanics, algorithmic information theory and computational complexity.[
A neural network was able to rediscover one of the most important paradigm shifts in scientific history: Earth and other planets revolve around the Sun.
The neural network — a machine-learning algorithm called SciNet — was shown measurements of how the Sun and Mars appear from Earth against the fixed-star background of the night sky.
The team “encouraged” SciNet to come up with ways to predict the movements of the Sun and Mars in the simplest way possible.
How do you quote like that?
If you select the desired text from a previous post, a “Quote” button will appear which will open a quoted reply as I just did here.
For other text, select it after pasting it in and then press the " button at the top of the editing box.
That’s what I needed, thanks.
You don’t see the quote in my previous reply because I quoted your entire post (one line) and the system removed it.
Yes, I know that, it’s how to quote stuff from outside sources that KC likes to do all the time that I never figured out.
I used Solomonoff induction.
The Ptolemy/Copernicus problem is simple and easy to understand. And the answer is known, so it makes a good example to solve problems in other cases where the answer is not known.
Ptolemy’s system makes intuitive sense, the earth does not appear to be hurdling through space. But the Copernicus system, while seeming contrary to common sense, is a simpler, shorter explanation.
Bottom line is if two answers both fit the data than the simpler explanation, even if it seems counter-intuitive, is more likely.
An example is convoluted conspiracy theories.
Eh… The solar system is a complex system. Man has tried to understand this system by constructing simple models. A fire god riding his chariot across the sky, spheres of rotating crystal with stars imbedded within them, or masses in motion maintaining the same energy state. They are models.
If a model, given a set of data, results in an observed condition then that model is useful or ‘correct’. If two contradictory models, both using the same set of data, result in the same condition then both are useful. The simpler one is preferred because it’s simple and therefore ‘correct.’
People confuse a useful model (the Earth goes around the Sun) with true (1=1). One plus one equals two is not a model. It is.
The question isn’t which model is correct, but which gives the most useful answer in a given situation using a set of data.
Say you’re a backyard skywatcher. To say the Earth goes around the Sun is good enough. If you’re a navigator making his own nautical almanac it would be wise to include the Moon (as the Earth goes around the Earth-Moon-Sun barycenter.) If you were an astronomer you may want to include Venus, Mars, Jupiter, Saturn and Neptune for the same reasons. If you’re a cosmologist… well, you get the picture.
If, as you say, the simpler answer is most likely then the Sun is a god riding a chariot.
Where did I say that?
Oh, this I guess.
EDIT: I should have said Ptolemy vs Copernicus not Ptolemy/Copernicus
Here is the problem. Two models:
Here is one
Here is the other:
It’s easy to see how these two models differ. Ptolemy uses the epicycles, Copernicus does away with them. Simple.
In Copernicus time both gave similar results but later, with more data Ptolemy’s model broke:
From the post:
Eventually other scientists would gather data in support of Copernicus. Galileo’s observation of the phases of Venus was the real clincher; you can see that under the Ptolemaic scheme you’ll never see a “full” Venus.
But the point of the post is that the smart money as to which model would break first the money should be on Copernicus.
The reason why it’s a better bet is because it’s the simpler of the two.
But the explanatory economy of Copernicus’ theory was a very strong reason for believing in it even before that.
Eh… the Chariot doesn’t fit the data.
Maybe I misunderstood your reason for starting this thread. To me what you were discussing was the classic philosophical branch of metaphysics, or how complex reality is perceived by our limited human minds.
Reality is complicated. Reality, in the case of the solar system, is an untold number of interactions. Because reality is far too complicated for our feeble human minds to grasp we construct simple models. One simple model is that the Earth goes around the Sun. Another (probably simplified) model is the universe is a bunch of one dimensional strings vibrating in eleven dimensions of which the Earth and Sun is a small part.
Between those two models which would you say is correct? Well, that would depend on which you find useful. Some people might object and say the two models are a discussion of two different things. They would be wrong. Both models can be used to describe the movements of the solar system.
Now many people will say that the vibrating strings might be true but the ‘Earth goes around the Sun’ is also true. Those people aren’t wrong. One model may be useful in some situations while the other is useful in other situations. Neither is actually True as both are simplified models of reality.
If you had some other point to discuss, like coincident patterns in celestial movements, I guess I missed it.
Not in my wheelhouse so to speak.
I was commenting specifically about this post, Copernicus versus the scientific method which was linked to in a Brad Delong post
I would say this was the key point: This is a formalization of Occam’s Razor, that simple explanations with fewer working parts are better.
I saw this some time ago, and found it very interesting. . . never really thought about it in this way. . … https://www.youtube.com/watch?v=0jHsq36_NTU
In that case I won’t continue down this rabbit hole except to say
This is a formalization of Occam’s Razor, that simple explanations with fewer working parts are better.
Simple explanations with fewer working parts [when given the same data and result in the same observation] are better [to use but may or may not be the most accurate explanations].
