Entropic Dynamics (10)

The general problem of the Scientific Method, in my mind, is behind several interesting features of the mathematical description of scientific observations.

Here I will present the minumum role that Information Theory plays in Science. More sophisticated situations may appear in future contributions.

I am reading right now one of the papers that represent the culmination of over twenty yers of work by Alexei V. Filippenko et al..

Besides the impressive amount of work this paper represents, it is a good example of my point here.

The Lick Observatory Supernova Search (LOSS) is an important contribution to our understanding of this amazing group of natural phenomena.

The paper I use here for my example, in its own right, is a good example of the general use of Information ideas in the description of reality.

From the D. Maoz et al. paper cited above we get.

"VESPA SFHs consists of 3505 galaxies that hosted 201 SNe, among them 82 SNe Ia, 93 SNe II, and 26 SNe Ibc (see Filippenko 1997 for a review of SN types; here we classify SNe Ib and Ic as “Ibc”)."


This is the sample.

Now what do they do with it?

Using the known Information, they maximize a probability function to get the best fit parameters.

This is the basic technique of statistical methods in science. Not only physicists, any scientist presents data using this method. The oldest application I know of, is Legendre's linear regresion method of 1805.

This Scientific Statistical Method is best when, like in Filippenko's case, all the data were obtained with the same procedure, this way one gets a uniform sample with less uncertainty. Of course one needs corroborating teams to validate results. In this case they get together with another group, SDSS. Not everything was measured by the LOSS collaboration, but for this paper they work closely with at least one other team. In cases where they cannot get together; then objectively they have to add systematic uncertainties to consider this lack of Information.

"With these techniques one can conclude things like: at the 99% confidence level, this test supports the existence of SNe Ia that explode within 420 Myr after star formation."

"Furthermore, examining the time integrals over the best-fit DTD in each of the bins, and attempting to correct for the leak from bin 1 to bin 2, suggests a relative contribution to the total SN Ia numbers of (prompt:medium:delayed) ≈2:2:1. However, this is subject to large statistical and systematic uncertainties."

Both quotes tell us the kinds of things we can learn from an statistical analysis of the data, together with some physical assumptions that the authors try to quantify.

The quantitative result "... suggests a relative contribution to the total SN Ia numbers of (prompt:medium:delayed) ≈2:2:1", seems to me an important take away point. Half very delayed, and most promptly produced SN Ia. Now I have numbers in my head, i.e., new Information, based on painstakingly work by these scientists, consistent with the given Information they started with.