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New Scientist

Mathematician Rob Eastaway and physicist Len Fisher reveal their scientific approach to making a party go with a bang.

A good party begins with congestion, evolves through chaos, continues with chat, and ends with cheers. Science can help to smooth the transition from one phase to the next, to the benefit of partygoer and host alike.

## Sorting the Congestion

The host’s first job is to relieve the congestion that occurs when a jam of guests forms inside the doorway. Traffic jams arise on motorways when cars arrive at the back of a queue at a faster rate than those leaving the front. Crushes of people occur in doorways for a similar reason. You can’t control the rate at which guests arrive, but you can speed up their exit from the front of the jam by placing the drinks at the far end of the room to provide a magnet that will draw guests through the space.

A favourite welcoming drink is champagne, but the welcome is quickly damped if the precious bubbly foams up as it is poured and runs down the outside of the glass to cover the hand and arm of the eager recipient. Even if the champagne is pre-poured, there is a fair chance that the outside of the glass will be wet and sticky from the same effect, which happens because the surface of even the most expensive glass is covered with tiny tubular particles. Air is trapped in the tubes when the champagne is poured, and acts to “nucleate” the formation of a rapid succession of bubbles from the dissolved carbon dioxide. Most of the tubes eventually fill with liquid, but this takes a few seconds, during which the champagne foams furiously before it settles down to a slow rate of bubble release from the few tubes that have not filled up.

Understanding this process provides a clue to solving the problem of wet hands and sticky trays. Just pour a tiny bit of champagne and let it foam up (but not over the top) for a few seconds before pouring the rest in. A tiny spot of white wine, or even – heaven forbid – water added previously to the glass will have the same effect, which is to deactivate most of the nucleation sites by filling the tubes with liquid, so that foaming will be minimal when the rest of the champagne is poured.

## Sorting the Chaos

The drinks table gets people into the room, but there is danger of another jam unless you get them moving away again. The answer is to separate the food and drinks tables, so that each serves as a node to which guests will be drawn. The addition of a third node – for example, by keeping the beer at a separate location from the wine – encourages even greater flow.

Our observation over many parties is that guests are drawn from one node to another as the event progresses, the nodes acting as attractors. The resulting movement of each guest resembles the “chaotic” behaviour of a magnetic pendulum suspended over three magnets. With each guest moving in this fashion, something approaching optimal mixing is probably achieved. Too much flow in a restricted area, of course, can lead to random jostling of guests, resulting in a sort of “Brownian motion” as an individual attempts to move from one node to another. The consequence can be the dread of every host – red wine spilled on the carpet.

## Wine Spills

Members of a group involved in this catastrophic event are likely to split into three camps. The first will call for salt to be poured on to the stain – its more active members may even reach for the salt cellar and start right in. Members of the second camp will object that salt doesn’t help, and that the correct procedure is to pour white wine on the stain, although they will be strangely reluctant to waste the wine in their own glasses for the experiment. The third camp, otherwise known as the cowards, will melt silently away from the scene, convinced that red wine stains can never be removed from carpets.

Salt certainly seems to help, and its proponents will proudly point to the fact that the pile of salt turns red as it sucks up the wine by capillary action. Only when the host later vacuums or brushes up the salt will he or she discover that the salt has removed some of the wine, but by no means all. The correct solvent is white wine, following the logic that red wine is just white wine with red pigments added. These pigments will stick to most carpets, but when white wine is poured on to the stain they will distribute themselves between the white wine and the carpet. All that is then necessary is to mop up the white wine with a dry cloth and then repeat the process, removing a fraction of the stain each time until it becomes invisible. This approach will even remove old, dried-up stains in time. If you are worried about wasting white wine, you could follow the thrifty approach suggested by one of our partners, which is to use the dregs of white wine collected after previous parties and kept in a bottle labelled “carpet wine”.

### Who do you pull your cracker with?

If your guests are seated at a dinner table, a whole new set of problems arises. At large tables, and with noise levels high, it is often only practical to converse either with the neighbour immediately to your left or the one to your right. Likewise, you will only pull a cracker with your immediate neighbour. If you turn to the person on your right (say), there is a 50-50 chance that they will also have turned to the right. Confronted with the back of your neighbour, you turn the other way, only to run up against the 50-50 chance that this neighbour has also turned their back. There is now a serious risk that you will become a gooseberry.

Instant cracker-pulling pairs

Two instant gooseberries

Undetermined – could result in gooseberries

The diagram shows the possible situations for a table of eight people. If guests turn randomly left or right, there is less than a 1% chance that all will instantly form conversational or cracker-pulling pairs, as in A. There is a higher probability (over 10%) that three pairs will form spontaneously, leaving two unfortunate gooseberries as in B. Most likely of all, the initial situation will be indeterminate such as shown in C, and depending on the random choices made thereafter, the stable outcome will be A or B. One mathematical model of pairing behaviour shows the proportion of gooseberries in a room set out with round tables can be as high as one in five at any moment.

An obvious ploy to keep the gooseberry factor as low as possible is to ensure that each table holds an even number of people (an odd number at a table is of course bound to produce at least one gooseberry). A more formal approach is to enforce a protocol such as requiring men to spend the first course talking to the women on their left, and then to switch to the right for the main course. Best of all, avoid round tables and go for narrow rectangular tables where cross-table conversation is easy.

## Fooling the Palate

With your guests seated and happily conversing, you have time to sit back and worry about how much this dinner is actually costing. One place to save money is on the wine, but what if your guests notice that you have stopped producing the good stuff in favour of the cheap special from the local supermarket?

The answer is cheese. Recent research has shown that cheese, or any other salty food, acts to reduce the perception of bitterness, such as that from the tannins in red wine. So produce the good red with the main meal, where it belongs, but if you are producing a cheaper red later, make sure that your serve your guests with something salty as well. They may even comment on the smoothness of the wine!

Cheap wine may be excusable. Cheap coffee never is, but if you are forced for reasons beyond your control to resort to inferior coffee, or even instant coffee, there are two tricks that you can use to convince your guests that they are drinking something better. One, which is fairly well-known, is to put a few coffee beans under the grill so as to fill the room with a coffee aroma. Don’t forget that the beans are there, though, as one of us once did, or the acrid smoke that accompanies the smell will give the game away. A less well-known trick is to put a fresh cardamom pod into the coffee for a few minutes before serving. Even if your guests spot that they are drinking instant coffee, they will still be puzzled by its unusual quality.

## Guilt and the Last Mince Pie

Finally, and just when you thought it was safe to relax, there’s the potential for an awkward social problem when it comes to handing round the after-dinner chocolates or mince pies. Unless the host has carefully ensured that there is an over-supply, the chances are that somebody will be offered the last one. Few people enjoy being the person who removes the last mince pie on the plate, particularly if they suspect there is somebody else in the room who also has their eye on it. Invariably this means the last mince pie will remain untouched.

But should you feel guilty for taking the last mince pie? Why should all the guilt be left with the person who takes the last one, as opposed to the person who removed the penultimate pie? It is in fact possible to allocate guilt based on probability. Suppose there are five guests and four mince pies. Suppose also that guests have an 80% chance of being in the mood for a mince pie and a 20% chance of declining. If the first guest takes a mince pie, they can do so in the knowledge that the chance at least one guest would opt out was (1 – 0.8^4), or 59%. The second guest also takes a mince pie, but this time the chance that all the other guests will be happy is 49%. The third guest’s clear conscience quotient drops to 36%, and the fourth, faced with a single mince pie, to 20%. In this case, the person who takes the last mince pie should feel guilty, but only three times as guilty as the person who, with an air of innocence, cannily took the first one.

The most canny of all, though, is the host, whose bedazzling explanation of the mathematics of guilt can be used to conceal the fact that he or she has, in fact, swiped the last mince pie.

Cheers!