{"id":1460,"date":"2024-12-14T19:45:58","date_gmt":"2024-12-14T19:45:58","guid":{"rendered":"https:\/\/www.allendowney.com\/blog\/?p=1460"},"modified":"2024-12-14T19:45:58","modified_gmt":"2024-12-14T19:45:58","slug":"reject-math-supremacy","status":"publish","type":"post","link":"https:\/\/www.allendowney.com\/blog\/2024\/12\/14\/reject-math-supremacy\/","title":{"rendered":"Reject Math Supremacy"},"content":{"rendered":"\n

The premise of Think Stats<\/em>, and the other books in the Think<\/em> series, is that programming is a tool for teaching and learning<\/a> — and many ideas that are commonly presented in math notation can be more clearly presented in code.<\/p>\n\n\n\n

In the draft third edition<\/a> of Think Stats<\/em> there is almost no math — not because I made a special effort to avoid it, but because I found that I didn’t need it. For example, here’s how I present the binomial distribution in Chapter 5<\/a>:<\/p>\n\n\n\n

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Mathematically, the distribution of these outcomes follows a binomial distribution<\/strong>, which has a PMF that is easy to compute.<\/p>\n\n\n\n

from scipy.special import comb

def binomial_pmf(k, n, p):
    return comb(n, k) * (p**k) * ((1 - p) ** (n - k))
<\/pre>\n\n\n\n
SciPy provides the comb<\/code> function, which computes the number of combinations of n<\/code> things taken k<\/code> at a time, often pronounced \u201cn choose k\u201d.<\/p>\n\n\n\n
binomial_pmf<\/code> computes the probability of getting k<\/code> hits out of n<\/code> attempts, given p<\/code>.<\/p>\n<\/blockquote>\n\n\n\n
I could also present the PMF in math notation, but I’m not sure how it would help — the Python code represents the computation just as clearly. Some readers find math notation intimidating, and even for the ones who don’t, it takes some effort to decode. In my opinion, the payoff for this additional effort is too low.<\/p>\n\n\n\n
But one of the people who read the draft disagrees. They wrote:<\/p>\n\n\n\n
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Provide equations for the distributions. You assume that the reader knows them and then you suddenly show a programming code for them — the code is a challenge to the reader to interpret without knowing the actual equation.<\/p>\n<\/blockquote>\n\n\n\n
I acknowledge that my approach defies the expectation that we should present math first and then translate it into code. For readers who are used to this convention, presenting the code first is “sudden”.<\/p>\n\n\n\n
But why? I think there are two reasons, one practical and one philosophical:<\/p>\n\n\n\n