**The laws of nature are described by equations, but to find them you often have to think outside of mathematics, can an artificial intelligence also do that?**

Last April, a scientific article published in Nature This spawned some sensational headlines, such as “The new AI thinks like famous scientists” or “The AI makes the same discoveries as Kepler & Co”.

What do scientists do? They start from known principles and infer the laws of nature, that is, rules that can be applied in general, such as the equations of physics. Supposedly, Descartes’ artificial intelligence was able to “discover” Kepler’s third law, which is the one that governs the period of planets in their orbit around the sun. He did? The equation discovered by Kepler applied to the Earth and the Sun is this:

Where **P** is the period of the planet **for** the size of the planet’s orbit, that is, the semi-major axis of the ellipse, **m** the sum of the masses of the Sun and Earth, and k the Gaussian gravitational constant.

However, the value of P according to Kepler’s third law equation “discovered” by the AI was this:

Where d=a. This is nothing like what we might remember from school lessons. There, we usually learn about Kepler’s third law of planetary motion this way: “The squares of the orbital periods are in the same proportion as the cubes of the semi-major axes of the ellipse.”

The square of the orbital period (p) and the third power of the planet’s distance from the Sun (d) can certainly be seen in the formula. However, the AI equation has little to do with Kepler’s third law as we commonly know it. In its exact form, one must take into account the mass of the Sun and the planets that inhabit it, as well as the gravitational constant. The masses, gravitational constant and other numerical factors in Kepler’s formula can be considered summed up in the number 0.1319 (and also keep in mind that, for technical reasons, the AI did not calculate with the usual SI units of meters). , kilogram and second). But this equation is far from being a true “law of nature” or an intuition approaching that of Johannes Kepler.

### An AI cannot be equated with Kepler or Newton

This already starts with the prerequisites: the artificial intelligence received not only data on masses, distances and orbital periods, but also various formulas, including Newton’s law of gravity. Unlike Johannes Kepler, the AI already “knew” how celestial bodies attract each other. If Kepler had this knowledge, he could have saved himself the trouble with his three laws, as they are just another formulation of what Isaac Newton later discovered (and much more accurately). The formula he developed for the connection between orbital period and distance also lacks some of its physical content. Precisely because factors such as the gravitational constant or the masses involved are not explicitly listed, it is almost impossible to deduce any further conclusions from it.

Artificial intelligence has created other formulas, some of which also take crowds into account. However, this has little to do with what a human would do with the data. For that, just take a look at “Astronomia Nova”: in this 17th-century work, Kepler wrote down, almost in diary form, the creative process that eventually led to his discoveries. AI, on the other hand, found only one useful formula for describing observational data. This is also a significant achievement: the new work has shown that an AI can be made to formulate quite meaningful mathematical relationships. But this has nothing to do with “thinking like the most famous scientists”.

**REFERENCE**

Combining data and theory for derivable scientific discovery with AI-Descartes