4 ms·

So far my favorite expository example on this subject involves whether any kind of machine learning model trained on Tycho Brahe's astronomical observational da

So far my favorite expository example on this subject involves whether any kind of machine learning model trained on Tycho Brahe's astronomical observational data (late 16th century) would be able to extract the equations of Johannes Kepler (1609) from them. It would likely be able to make good predictions of where planets would be in the future, but that wouldn't be based on simple equations that were easy for humans to look at and understand. (Those are: elliptic orbits, equal areas are swept in equal time by a line joining the orbiting bodies, and orbital periods (time) are proportional to the geometry of the ellipse (distance) by a square:cube ratio, and they're all more or less approximations in the solar system (which has many complicating interactions due to all the bodies involved).) Someone commented that most humans wouldn't be capable of doing that either, which is true enough... Perhaps if the machine learning model was also trained on a large set of equations as well as on a large set of astronomical data?

mxwsn 4y ago
There's a subfield called symbolic regression that considers this problem. https://www.science.org/doi/10.1126/sciadv.aay2631 https://www.science.org/doi/10.1126/sciadv.aay2631 The Kepler equation is relatively simple compared to other equations re-discovered by ML.
- sampo 4y ago
  > The Kepler equation is relatively simple compared to other equations re-discovered by ML. But the ML was given, as input, the locations of the planets already in the solar system level Cartesian (x,y,z) coordinates. I am skeptical that any AI system would be able infer Kepler's model of elliptic orbitals around the Sun, if all they were given was Tycho Brahe's data as (altitude angle, azimuth angle, time) as seen from the point of view of an observer on the surface of Earth at the location of Denmark.
aj7 4y ago
Those “simple” equations underlie almost ALL scientific thought. They have implications far beyond the motions of the planets, which stimulated them. It’s hard to make a quantitative argument about how much more powerful they are than a statistical model, which I am sure is possible with today’s modeling, as you suggest. Ahh, but without Newton’s Laws, there would be no machines to run the models! It IS useful to have machines GUESS models in science, by the way. You might know that a consequence of the inverse square law of gravitation and electromagnetism implies that the surface integral of those fields over a closed surface enclosing mass or charge depends ONLY on mass and charge enclosed, and NOT on it’s detailed distribution therein. You have to have the model to actually prove this.
jackmott42 4y ago
You could probably do a proof of concept with a much simpler virtual world, and see what types of training can lead to an AI developing an understanding of that world's laws. this might give insight into how you could train an AI with data to derive some physics, and might give us insight into how we are misled into simplified models of reality maybe?

mxwsn 4y ago

There's a subfield called symbolic regression that considers this problem. https://www.science.org/doi/10.1126/sciadv.aay2631 https://www.science.org/doi/10.1126/sciadv.aay2631 The Kepler equation is relatively simple compared to other equations re-discovered by ML.

sampo 4y ago
> The Kepler equation is relatively simple compared to other equations re-discovered by ML. But the ML was given, as input, the locations of the planets already in the solar system level Cartesian (x,y,z) coordinates. I am skeptical that any AI system would be able infer Kepler's model of elliptic orbitals around the Sun, if all they were given was Tycho Brahe's data as (altitude angle, azimuth angle, time) as seen from the point of view of an observer on the surface of Earth at the location of Denmark.

aj7 4y ago

Those “simple” equations underlie almost ALL scientific thought. They have implications far beyond the motions of the planets, which stimulated them. It’s hard to make a quantitative argument about how much more powerful they are than a statistical model, which I am sure is possible with today’s modeling, as you suggest. Ahh, but without Newton’s Laws, there would be no machines to run the models! It IS useful to have machines GUESS models in science, by the way. You might know that a consequence of the inverse square law of gravitation and electromagnetism implies that the surface integral of those fields over a closed surface enclosing mass or charge depends ONLY on mass and charge enclosed, and NOT on it’s detailed distribution therein. You have to have the model to actually prove this.

jackmott42 4y ago

You could probably do a proof of concept with a much simpler virtual world, and see what types of training can lead to an AI developing an understanding of that world's laws. this might give insight into how you could train an AI with data to derive some physics, and might give us insight into how we are misled into simplified models of reality maybe?