Overview for Week 2
Activity 1 | Week 2 | Overview
He who knows nothing, loves nothing. He who can do nothing understands nothing. He who understands nothing is worthless. But he who understands also loves, notices, sees… The more knowledge is inherent in a thing, the greater the love. Anyone who imagines that all fruits ripen at the same time as the strawberries knows nothing about grapes.
– Paracelsus
Words of wisdom, the meaning of life, perhaps even the answer sought by Borges’s librarians — all of these may wash over us every day, but they can do little for us unless we savor them,engage with them, question them, improve them, and connect them to our lives.
– Jonathan Haidt
The greatest enemy of knowledge is not ignorance, it is the illusion of knowledge
– Daniel J. Boorstin
The goal for Week 2
Motivation
Last week, you measured the period of a simple pendulum at two starting angles, \(T_{10^\circ}\) and \(T_{20^\circ}\), and used your measurements to decide whether the two periods were distinguishable within experimental uncertainty. In a sense, however, we were working “blind”: we did not have a theoretical prediction to guide our experiment or to assess the quality of our results.
So, this week, we will approach the same question from a modelling perspective:
An experimental result becomes more meaningful when it can be compared with an theoretical or computational prediction.
The three pillars of science
Scientific understanding rarely comes from a single source. Scientific investigations often connect three elements:
- physical theory and mathematical models, which describe how a system is expected to behave;
- computation, which helps us work out the consequences of a model; and
- experiment, which allows us to compare those consequences with the physical world.
In experimental science, modelling is not a one-way process. Evidence from an apparatus can lead to a model being retained, revised, or replaced. At the same time, a model can show that the measurement apparatus or procedure needs to be improved1. Modelling therefore involves constructing predictions, comparing them with measurements, identifying mismatches, and deciding what should happen next2.
What you will be learning
In these background notes, I will show you how to turn a physical description of the pendulum into a mathematical model which we then solve numerically. We will:
- describe the physics and identify our assumptions
- express the model mathematically
- solve it numerically
- check whether the solution is physically sensible
- compare its predictions with our measurements
Along the way, we will learn to distinguish between errors arising from the model, the numerical method, and the measurement.
Although our subject is a pendulum, this way of thinking applies across science, making it a highly transferable set of skills.