Submitted by Marianne on May 16, 2017

This article is based on one of Budd's Gresham College lectures. Watch the full lecture here, and see here to find out more about this free, public lecture series.

### Blowing bubbles

Let's start with the head. One of the key features of a pint ofGuinness is the wonderful creamy foam head. This is in contrast to the

much smaller head that we find on a pint of bitter beer. For the

manufacturers of beer to get both types of head involves a lot of

science and maths. The foam in the head of a pint of bitter is made of

networks of bubbles of carbon dioxide separated by thin films of the

beer itself, with surface tension giving the strength to the thin walls

surrounding each bubble. The walls of these bubbles move as a result of

surface tension, with smaller bubbles moving faster as they have a

higher curvature. This results in the smaller bubbles being "eaten" by

the larger ones in a process called

*Oswald ripening*.

Basically small bubbles shrink and large bubbles grow, leading to a

coarse foam made up of large bubbles only. Eventually the liquid drains

from the large bubbles and they pop, and the foam disappears.

The remarkable mathematician John von Neumann,

who was (amongst many other achievements) responsible for the

development of the modern electronic computer, devised an equation in

1952 which explained the patterns that we see in such cellular

structures in two dimensions. In 2007 this was extended to three

dimensions by a group of mathematicians in Princeton interested in the

applications of maths to beer. It's a hard life!

### Why the widget?

Another group of mathematicians, appropriately from Limerick inIreland, have made a study of the foam on a pint of Guinness. This is

much creamier than the foam on a pint of bitter. The reason is that

whilst the foam on bitter is made up of air bubbles, the foam on a pint

of Guinness is made up of nitrogen. This gas diffuses a hundred times

slower in air than carbon dioxide, meaning that the bubbles are smaller

and the foam is much more stable and creamier.

The nitrogen needs to be introduced into the Guinness when it is

poured. In a pub this is achieved by having a separate pipe, linked to a

nitrogen supply, which supplies the nitrogen at the same time as the

beer is served from the barrel.

For many years Guinness in cans did not have a head. However, this problem was solved by the introduction of a

*widget*,

which is a nitrogen container in the can, and which releases precisely

the right amount of nitrogen when the can is opened. This process must

be very carefully controlled, and a lot of careful design work is

required to make the widget work well. The whole process was analysed by

(it appears!) the whole of the applied mathematics department at

Limerick, and described in the charmingly titled paper

*The initiation of Guinness*. Notably the same group has now done a complete analysis of the mathematics of making coffee.

### Why statisticians couldn't organise a piss up in a brewery

In the year 2005 the British Science Festivalcame to Dublin. At that time I had the honour of being the president of

the maths section of the British Science Association, which was

organising the festival, and had the responsibility of devising a

mathematics programme for the event.

William Sealy Gosset (1876 - 1937).

Breweries in Dublin. Obviously there are many reasons why we might want

to visit a brewery, but why should mathematicians want to go there, and

why should they want to go to Guinness? The answer to both of these

questions lies in the person of William Gosset (pictured) who was the chief statistician at Guinness in the first part of the 20th Century.

Guinness

was in many ways ahead of its time in the production and quality

control that it applied to its product (as well as the way that it was

advertised). Gosset was employed in part to ensure that the Guinness

stout was of a consistent quality. This was done by making careful

measurements of a sample of the product and using these to assess both

its general quality and its variability. This was, at the time, a

difficult problem in statistics. To solve it Gosset devised a new

statistical test to compare the measurements. This worked extremely well and made a very real difference

to improving the quality of Guinness stout. Gosset felt it important to

publish this test, but was reluctant to disclose his identity and that

of his employer. Instead it was published in the journal

*Biometrika*, in 1908, under the anonymous name of "Student". Ever since this test has been known as

*Student's t-test*. It plays a central role in testing and maintaining the quality of food and drink all over the world.

So, let's get back to the British Science Festival. Having decided to

go to Guinness we set up a sub-committee to organise the trip to it

during the science festival, in part to celebrate the invention there of

the t-test and its contribution to modern statistics. Clearly such a

trip should include a reception and a drink of a pint of Guinness.

Unfortunately, through no one's fault, it wasn't possible in the end to

do this. It was only after the event that we realised we could be

accused of being unable to organise a piss up in a brewery.

### Three mathematicians walk into a pub...

I will finish this article with a bad story/joke about mathematiciansand drinking. You have to concentrate a bit to get the joke.

Three mathematicians go into a pub and the bar tender asks, "Does anyone want a lager"?

The first mathematician pauses for thought, and then says, "I don't know".

The second mathematician likewise says, "I don't know".

Finally the third mathematician says, "No!"

So the bar tender ask, "Does everyone want a bitter then?"

The first mathematician pauses for thought, and then again says, "I don't know".

The second mathematician likewise says, "I don't know".

Finally the third mathematician says, "Yes!"

So they all have a bitter.

### About this article

This article is adapted from one of Budd's Gresham College lectures. See here to find out more about this free, public lecture series.Chris Budd.

He has co-written the popular mathematics book

*Mathematics Galore!*, published by Oxford University Press, with C. Sangwin, and features in the book

*50 Visions of Mathematics*ed. Sam Parc.

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