Deep-Learning-with-PyTorch

104 CHAPTER 5 The mechanics of learning
5.1 A timeless lesson in modeling
Building models that allow us to explain input/output relationships dates back centuries
at least. When Johannes Kepler, a German mathematical astronomer (1571–1630),
figured out his three laws of planetary motion in the early 1600s, he based them on
data collected by his mentor Tycho Brahe during naked-eye observations (yep, seen
with the naked eye and written on a piece of paper). Not having Newton’s law of gravitation
at his disposal (actually, Newton used Kepler’s work to figure things out),
Kepler extrapolated the simplest possible geometric model that could fit the data.
And, by the way, it took him six years of staring at data that didn’t make sense to him,
together with incremental realizations, to finally formulate these laws. 1 We can see this
process in figure 5.1.
candidate
Models
kepler’s
(first + second) laws
johaNnes
focus of
eLlipse
observations
for multiple
planets
faster
equal areas
over time
slower
(eCcentricity
is a lot larger
than the earth’s)
Figure 5.1 Johannes Kepler considers multiple candidate models that might fit the data at hand, settling
on an ellipse.
Kepler’s first law reads: “The orbit of every planet is an ellipse with the Sun at one of
the two foci.” He didn’t know what caused orbits to be ellipses, but given a set of observations
for a planet (or a moon of a large planet, like Jupiter), he could estimate the
shape (the eccentricity) and size (the semi-latus rectum) of the ellipse. With those two
parameters computed from the data, he could tell where the planet might be during
1
As recounted by physicist Michael Fowler: http://mng.bz/K2Ej.