3.5.2 How Maths Powers Other Knowledge Notes

Mathematics Is A Toolbox of Methods and Languages

1. Medicine, climate science, economics, and even social sciences use mathematics to test ideas, spot patterns, and make predictions.
2. This makes maths both powerful and problematic: powerful because it adds precision, problematic because its reliability depends on the assumptions, data, and ethics of how it is used.

Statistics As Proof of Effectiveness

1. In medicine, statistical analysis is used to determine the effectiveness of treatments, identify risk factors for diseases, and make predictions about patient outcomes.
2. For example, clinical trials rely on statistical methods to compare the outcomes of different treatment groups and determine whether a new drug is more effective than a placebo.
3. Key Concepts:
   1. Randomized Controlled Trials (RCTs): These trials use randomization to eliminate bias and ensure that the results are statistically valid.
   2. P-values: A measure of the probability that the observed results occurred by chance. A low p-value (typically less than 0.05) indicates that the results are statistically significant.
   3. Confidence Intervals: These provide a range of values within which the true effect of a treatment is likely to lie.

Climate Science Models The Unobservable

1. Scientists use mathematics to create models, simulations of the climate system that let them test how the atmosphere, oceans, land, and ice interact over time.
2. These models rely on physics expressed in equations that can’t capture every single variable, so scientists make simplifications and approximations.
3. The strength of maths here is that even if we can’t experiment on the real Earth, we can experiment on a virtual one.

Ethical Considerations in Mathematical Modeling

1. As mathematics becomes more embedded in daily decision-making from medicine to policing to finance ethical concerns move to the forefront.
2. And while the equations themselves may seem neutral, the data they use and the way they’re applied reflect human choices and values.
3. This is where ethics intersects with mathematics as an Area of Knowledge.
   1. Bias: Models inherit the flaws of their data. Predictive policing trained on crime records often targets the same communities, reinforcing inequality.
   2. Transparency: Complex algorithms can act as “black boxes.” If a medical model denies treatment, neither patients nor doctors may know why, making accountability difficult.
   3. Consent: Patients must know when models guide their care. Without clear explanations of risks and uncertainties, consent is incomplete.