[JadeNB]

> Mathematically the minimum number of elements necessary for a pattern is three.

An assertion about mathematics requires a definition, and I don't believe this one for the usual definition of 'pattern'. For example, if I wanted to exhibit a linear pattern, two data points would be sufficient.

(But we're not talking about mathematical constructs anyway, so it's not clear what the relevance of mathematics is.)

[guhidalg]

2 points establishes local linearity, not global linearity. f(x) = x^2 looks linear if you take any 2 arbitrary xs, add a third and you can no longer draw one line that intersects all 3 points.

[JadeNB]

> 2 points establishes local linearity, not global linearity. f(x) = x^2 looks linear if you take any 2 arbitrary xs, add a third and you can no longer draw one line that intersects all 3 points.

Yes, certainly. And 3 points can show you a pattern that looks quadratic but isn't, and so on. More to the point, 3 points can rule out a claim of linearity, but they also cannot demonstrate a claim of linearity (e.g., you can usually find 3 collinear points on the graph of a cubic). My point was not to make a mathematical claim myself, but rather to argue that the claim "the minimum number of elements necessary for a pattern is three" is so vague to, I think, be nearly meaningless—and, in particular, unfalsifiable; in my mind, it doesn't deserve the adverb "mathematically".

[whoooooo123]

Only on HN could a comment thread devolve from "light observation on the nature of comedy" to "arguing about the nature of linearity in mathematical equations" in 6 comments.

[guhidalg]

In that I agree. Maybe a better word is “normally” as in “normally don’t assume a pattern until you see 3 of them”