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Request for stories of when quantitative reasoning was practically useful for you.

by elityre1 min read13th Sep 20196 comments



I'm studying more math and CS these days than I have in the past, and I would like to seize any opportunities to generalize those mental skillsets to other domains. I think that generalization would be easier if I had concrete targets: I knew of the specific low level skills that have been useful for folks.

Therefore, I'm looking for anecdotes that express the value of quantitative thinking, and mathematical competency, in "real life". What does that skill set allow you to do? What concrete problems has it solved for you? etc.

Feel free to interpret "quantitative thinking" or "mathematical competency", as broadly as you want. If there's an attitude or mindset that you learned from studying biology, or or from building software, and that mindset has proved practically useful for you outside of that domain, please share.

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Back of the envelope statistical significance calculations: "Yes, sales per lead have gone up since the change went out, but we've only had 150 sales come through since then so we'd expect a difference of about 12 just based on random noise, and indeed the difference is about 10 sales."

Noticing unknown unknowns: "We'd expect hourly signups to vary by about 50 people based on independent random decisions, but we're actually seeing variation of about 250 people, without any clear time-of-day pattern. There must be some underlying factor which makes a bunch who come in around the same time all more/less likely to sign up." (In this case, the underlying factor was that our server wasn't able to handle the load, so when it got behind lots of people had lots of lag at the same time.)

Noticing corner cases: "If two people are sharing one account, what do we do when they both edit at the same time? What if someone updates X, but we've already done a bunch of logic using the original X value, and now we need them to go back and input some other information?"

Critical path reasoning: "We usually end up waiting around on the appraisal - that's what takes longest. And we're not ordering the appraisal until we have form X. But we don't actually need to wait that long - we can parallelize, and order the appraisal while we're still waiting on form X. We could also parallelize fetching the insurance forms, but that won't matter much - they're usually pretty fast anyway."

Sparsity: "This loop is running over every possible pair of words. That's something like 100M word pairs. But the data only contains 100k sentences with ~10 word pairs in each of them, so at most only about 1M word pairs actually occur. If we loop over sentences and only look at pairs which actually occur, that should be at least a 100X speedup."

Little-o reasoning: "These changes just aren't that big, so the relationship should be roughly linear."

Queueing theory: "If we're trying to keep all of our people busy all of the time, then our wait times are going to grow longer and longer. If we want short wait times, then we need to have idle capacity."

I'm excluding economic-style reasoning, because so much has already been written about applications of economics in everyday life. But if you want me to add some econ examples, let me know.

Financial literacy enormously reduced worries about things like retirement and buying a house which increased my risk tolerance which lead to me working on projects that I actually care about.

A practice I have found useful is estimating the time it takes to do things: length of a journey door to door, time to write a piece of code and get it reviewed, time from setting off shopping to everything being stored away. People are generally on the optimistic side, and time falls through the cracks between stages of a task.