Notes for chapter 2: "Computation in science"
Terence Tao's lecture "The Cosmic Distance Ladder" (1h 37mn) provides much background information about the observation of celestial bodies and the mathematical interpretation of astronomical data.
Complex computational models
Climate research is an excellent illustration for the tendencies that I outline in chapter 2. Climate models are in fact non-trivial pieces of software. One of them, the Community Earth System Model, is Open Source software, allowing a detailed inspection by anyone.
Statistical models, machine learning, data science
The November 2015 issue (@ IEEE, @ AIP) of "Computing in Science and Engineering" magazine has "Computing & Climate" as its theme. Several articles explain how traditional physical models are being complemented by generic empirical models that are adapted to observed data using machine learning techniques.
In "The Rise of Computer-Aided Explanation", Michael Nielsen gives examples for data-driven approaches to science and engineering problems.
Algorithmic information theory
Christopher Ford's presented a nice illustration (video, 42 mn) of Kolmogorov complexity at the Strange Loop 2015 conference, using music as the data being described by algorithms. A companion site contains the programs and further references.