Your pi, my pi
How many digits of pi can you remember? 3.14? 3.1415? Well, it turns out that you may already be as right as you need to be.
There’s a fascinating piece on how ‘right’ you need to be when using pi, even when you’re trying to hit something accurately from a very long way away - 30 billion miles away:
“For JPL's highest accuracy calculations, which are for interplanetary navigation, we use 15 decimal places: 3.141592653589793. …Say we have a circle with a radius of exactly 30 billion miles in diameter, and we want to calculate the circumference, which is pi times the radius times 2. …by cutting pi off at the 15th decimal point, we would calculate a circumference for that circle that is very slightly off. It turns out that our calculated circumference of the 30-billion-mile diameter circle would be wrong by less than half an inch (about one centimeter). Think about that. We have a circle more than 94 billion miles around, and our calculation of that distance would be off by no more than the width of your little finger.”
As one commentator on X says, “15 digits is precise to one part per quadrillion. Jupiter is a billion miles away, so when you get there you might be off by a millionth of a mile, or about a tenth of an inch (2.5 mm).”
I covered the role of ‘directionally correct’ vs accurate in this piece on ‘pseudo positioning’ (and I was delighted to be reminded that I’d written
[An aside here: there has been a terrible idea spread across the industry that positioning can be ‘premise, promise, proof’, or some version of that. It is not just a wrongheaded idea, but a dangerous one. Positioning does not make a promise. It does not assert. Suggesting that you have ‘proof’ for your ‘promise’ turns positioning into a statement of fact today, instead of a way to help your customer see your value, over time. It diminishes the value of positioning to a repackaging of data that have already been collected: a passive positioning at best, a facile narrative at worst.])
But there’s an interesting dimension of ‘directionally correct’, which is really well covered in this piece. “Correlation and causality have consistent definitions. “Directionally correct” doesn’t. It is a lazy phrase with no real definition and it means different things to different people.”
However, despite its literal failures, there is a role for ‘directionally correct’ in positioning, vs ‘directionally unclear’ or ‘incorrect’. People may quibble on some of the stats in market research, but the biggest issue of research is that it often leads to directionally incorrect conclusions, because of problems in sampling, or methodology, etc. So this isn’t a lexicon challenge: we’re looking for the ‘gist’ of the opportunity - ask people, even people with marketed drugs, what the ‘gist’ of their drug is - the idea of the drug, and see how often they’ll give you un-gist-like answers, laden with stats and science, but very little in the way of product-market fit answers.