Calculus and statistics: different paradigms of thinking

One day I got a question from an academic star with almost perfect GPA in our university, “I did everything my professor asked us to do, I did regression on PE, PB ratio and stuff for prediction, why my target price for Goldman Sachs is still around $300? That’s too much off from everybody else in the market, I don’t understand.” I stared at him for more than 10 seconds, speechless.

As Arthur Benjamin proposed in his speech (link below), calculus has been on the top of the math pyramid for too long, now it’s time for statistics to take over. This matters because in general our mind is skewed too much towards the calculus-style, deterministic way of thinking. For one thing, it is much more intuitive for human mind to understand things that are either right or wrong; for another, people who claim they know everything and can “prove” that by making predictions always have much more audiences than those who say “this might be true, I could be wrong but it’s the closest we can get”. Also from my own experience, our education systems are mostly designed to reward people who get desired certainties, not people who comprehend things sensibly. Consequentially, students started to pick up the habit of “sacrifice reality for elegance” (Paul Wilmott) and the line between doing scientific research and confirming collective bias is blurred. Einstein was proven wrong about “God doesn’t play dice”, but regretfully that doesn’t stop ordinary people believing it’s possible to eliminate uncertainty in their own life.

On the opposite, not saying statistics is better, but it does focus more on observation and self-evaluation. Its purpose is not about to find the only perfect answer, instead it’s about seeing things from as many dimensions as possible (which is a very unnatural process to human brain). One accurate prediction doesn’t make a statistical model work; a long enough series of predictions under relatively bias free conditions with acceptable level of error does (now I kind of understand why people don’t like it…). Again, I don’t think it’s better than calculus, but I think this is the key to problems such as “if I did it right, how come I’m still losing money?”

Recommended Reading: Fooled by Randomness (N.Taleb)

Recommended Video: Arthur Benjamin’s formula for changing math education


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