Cheers!

Now we are going to talk about drink. About time.

Specifically the martini.

The original classic martini cocktail is two thirds gin, one third dry vermouth shaken with ice (if you are James Bond) or stirred (for Somerset Maugham). The ratio of vermouth to gin has decreased over the years, reaching a lower limit with Noel Coward, “A perfect martini should be made by filling a glass with gin, then waving it in the general direction of Italy.”

You can use vodka instead of gin in a vodka martini. Or both, as favoured by Bond, who also specified Lillet instead of vermouth. Lillet isn’t technically a vermouth. Although it is also a fortified wine only vermouth contains wormwood.

To confuse matters there is a brand of vermouth called Martini. This may or may not have been the source of the lower-initial-cap cocktail’s name.

I’m thirsty.

Before getting too carried away (from under the table?) let’s look at some of the mathematics of the martini.

It is the best of drinks and the worst of drinks.

The best is clear. But why the worst? It is because it is so depressing drinking one. Not because of the depressive effects of alcohol but because of the shape of the glass. I shall explain. But first a question.

The classic martini glass is cone shaped. Suppose you have a generous bartender who fills your glass to the brim. You sip. Before you know it the martini is half way down the glass. How much drink is then left?

This is where you get to think like a mathematician. Although that is rarely so depressing as here.

The martini glass is a cone. To mathematicians the cone is a three-dimensional (although this can be generalised) body having a horizontal cross section that is the same shape at any position and where the size, say diameter, of that shape increases linearly with the height of the cross section. We think of the cone having circular cross sections. But that need not be the case. The Egyptian pyramids are also cones.

The bottom half, or any fraction, of the martini glass is therefore the same shape, technically “similar,” to the whole martini glass. This wouldn’t be true of, say, a champagne flute. The bottom of the flute is flattish, but higher up the sides are steep. The sides of the martini glass are always the same angle from bottom to the rim. And it doesn’t matter what that angle is, as long as it’s the same all the way up.

This means that the relationship between the volume of the liquid and its depth is very simple. You just take the fraction of the height of the level of the liquid to the depth of the original and then raise that to the power of three. Why three? Because we are working in three dimensions.

This means that if we are already (so soon?) half way down then the remaining volume is one eighth of what we started with.

You see why that is depressing. Most people when asked about this will say something like, oh there’s about one third left. But, no, it’s far worse than that.

I hope I haven’t spoiled your drink. Don’t be like me. As I see the level falling I am continually in advance thinking about how little is left. No wonder I have to order a second.

Oh, and avoid olives, they make the mathematics even more depressing, large olives, less alcohol.

A short poem to end.

“I like to have a martini

Two at the very most

After three I’m under the table

After four, I’m under my host.”

Dorothy Parker