## Feb 20, 2010

### Cavendish Experiment and Modern Machine Learning

This is just a joke, so do not follow it seriously...

The very usual case in modern machine learning is as follows:
1. design a model to describe the data, for example, suppose some kind of 2D points are generated along a quadratic curve y = a*x^2 + b*x + c, and
2. design an algorithm that estimates the model parameters, in our case, a, b, and c, given a set of data (observations), x_1,y_1,x_2,y_2,...x_n,y_n.
3. The model parameters can be used in some way, say, given a new x and predict its corresponding y.
So, when I was reading Prof. Feynman's lecture notes, which mentions Cavendish experiment, I thought this experiment is some kind of "learning using machines" --- using the specially designed equipment (machine), Cavendish measured the gravitational constant G in Newton's law of universal gravitation:
`F = G * m1 * m2 / r^2`
And, using the estimated model parameter G, we can do somethings interesting. For example, measure the weight of the earth (by measuring the weight/gravity F of a known small ball m1, and put them back into the equation to get m2, the mass of earth).

However, this is a joke as I said so you cannot use it in your lecture notes on machine learning. The fact was that Cavendish did not measure G as stated in many textbooks. Instead, he measures the earth directly by comparing (1) the force that a big ball with known mass attracts a small ball with (2) the force that the earth attracts the small ball. If the ratio (2)/(1) is N, then the earth is N times weight of the big ball.

Michael A. Gottlieb said...

The experiment Cavendish
performed measured the Earth's density compared to that of water. See: Cavendish, H. "Experiments to determine the Density of the Earth", Philosophical Transactions of the Royal Society of London, (part II) 88 p.469-526 (1798); Clotfelter, B. E. (1987), The Cavendish Experiment as Cavendish Knew It, American Journal of Physics 55 (3), 210-213, http://www.alphysics.com/cavendishexperiment/Clotfelter.PDF; Falconer I. (1999), Henry Cavendish: the man and the measurement , Measurement, Science & Technology 10 (6):
470-477. Also useful are http://en.wikipedia.org/wiki/Henry_Cavendish#The_density_of_the_Earth and http://en.wikipedia.org/wiki/Cavendish_experiment.

Yi Wang said...

Hi, Michael, thanks for the references. I did visit http://en.wikipedia.org/wiki/Cavendish_experiment after reading Feynman's lecture notes, but the link does provide details as other references.

In fact, it is a pleasure to see your comments on my blog, since I know your are maintaining http://feynmanlectures.info, and it is a great pleasure to read Feynman's lectures. Many thanks for your great work!

Michael A. Gottlieb said...

You're welcome!