Turning Coffee Into Theorems

[the tree]

Based on the paper Recursive Binary Sequences of Differences by R. M. Richman, an article on the Guardian website tells us how to pour the perfect [two] cup of coffee.

 

I think it was Alfréd Rényi who said "A mathematician is a device for turning coffee into theorems."

 

The result is fairly intuitive: if there is a flavour gradient in the coffee pot then the average of the top and bottom should match the strength of the middle, when you're dividing the pot into two cups - assuming a well behaved distribution of flavour (I don't think you could apply the same principle to fairly sharing a bottle of beer, since there are no virtually dregs in the top or middle).

 

The Guardian article implies that it's yet to be generalised to n cups, but I don't think that'd be too difficult - even if the method would be very computationally intensive.

[Cap'n Refsmmat]

Or... get a stirrer for your coffee machine?

[the tree]

Machine? If you're using a machine that has a tank of coffee ready made then it'd have dripped in, and all been equally close to the coffee as it did so, so the issue wouldn't come up. But who uses drip machines anyway?

 

Making coffee without a machine, stirring varies from making no difference at all (because you're not moving stuff vertically) or being quite dangerous (because you are).

[Cap'n Refsmmat]

Real scientists make their coffee on a hotplate with a magnetic stirrer, while wearing goggles and a plastic apron.

 

I do wonder if the strength gradient in a coffee pot is linear, though. As time passes, won't more and more content settle to the bottom, making the bottom portion significantly stronger than the top portions?

[the tree]

I wouldn't know exactly what sort of distribution you'd be looking at. The article presumes c(x)>0, c'(x)<0 and c''(x)>0 for c=1 being maximum strength, c=0 being minimum strength and 0<x<1 being the distance from the bottom, which allows for a whole host of functions.

 

Of course, some empirical science should be able to provide information on that. Blotting paper perhaps?