For hosts and guests alike, parties can spell nothing but trouble. But apply the appropriate scientific principles and fun is practically guaranteed, as Rob Eastaway and Len Fisher explain
1 Getting going
The host鈥檚 first job is to get people into the party 鈥� and then into a party mood. In other words, shifting them in through the door and getting a drink into their hand.
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It鈥檚 easier said than done. First there is the jam of guests inside the doorway as everyone arrives at once. It forms for the same reason that traffic jams form on the road: people join the back of a queue faster than they leave the front. So, short of turning guests away, the only solution is to speed up their exit from the front of the jam. And the sure-fire way to do thisis to place the drinks at the far end of the room. Where drinks go, party guests will follow.
Champagne is sure to go down well as a welcoming tipple. But the welcome will be dampened if the bubbly foams up as it is poured, runs down the outside of the glass,and covers the eager recipient鈥檚 hand. 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 overflow.
So what鈥檚 the answer? Champagne fizzes up because the surface of even the most expensive glass is covered with tiny glass tubes. Air trapped in the tubes when the champagne is poured provides 鈥渟tarter鈥� bubbles of the right size to promote the formation and growth of a succession of bubbles from the dissolved carbon dioxide. The tubes eventually fill with liquid, but in the few seconds it takes for this to happen the champagne foams furiously.
This analysis of the problem points to the solution: pour a tiny bit of champagne and let it foam up before pouring the rest. This fills the tubes and deactivates them. A tiny spot of white wine 鈥� or, heaven forbid, water 鈥� swilled around the glass will have the same effect.
2 Circulation
The drinks table might lure guests away from the front door, but unless you can get them moving on again it will just be the focus of another jam. A separate table with nibbles will serve as a further node to which guests will be drawn.
Adding a third node 鈥� for example, by keeping beer and wine separate 鈥� encourages even greater flow (see Diagram, above). The nodes act as 鈥渁ttractors鈥�, and as the party progresses guests should start moving from one to another in a pattern that resembles the chaotic behaviour of a magnetic pendulum suspended over three magnets. With each guest moving independently, something approaching optimal mixing is achieved.
3 Spilt wine
Too much flow in a restricted area, though, can result in random jostling among the guests 鈥� a sort of Brownian motion 鈥� leading inevitably to jogged elbows and red wine spilt on the carpet. Members of a group involved in this event are likely to split into three camps. The first will call for salt to be poured onto the stain. The second will say that the correct procedure is to pour on white wine (though advocates of this strategy may be strangely reluctant to use the wine in their own glasses for the purpose). The third camp, otherwise known as the cowards, will melt silently away from the scene, convinced that red wine stains can never be removed.
Salt certainly appears to help, and its proponents will point proudly to the fact that the pile of white crystals turns red as it soaks up the wine. Only later, when the host vacuums or brushes up the salt, will he or she discover that while it may have removed some of the wine, a great deal of it remains on the carpet.
The correct solution is white wine, following the logic that red wine is just white wine with red pigments. These pigments will stick to most carpets, but when white wine is poured onto the stain they will redistribute themselves between the carpet and the white wine. So mop up the by now slightly pinkish wine with a dry cloth and repeat the process as many times as necessary, removing a fraction of the stain each time until it becomes invisible. This approach will even remove old, dried-up stains. Regular party-givers who don鈥檛 like wasting wine can follow the thrifty approach: collect the white wine dregs when the guests have left and keep it for next time in a bottle labelled 鈥渃arpet wine鈥�.
4 Making a date
Parties are the time when relationships form and dates are made. But those whom Bridget Jones describes as 鈥渃ommitment-phobes鈥漺ill be wondering, as they chat up a potential partner, whether to make that date or wait until later in the hope of landing someone better. Sadly, there is no way of guaranteeing that you will end the evening with the perfect partner. But mathematicians have at least figured outa scheme for maximising your chances of ending up with the best who will have you.
The favoured strategy, it turns out, is to test the field and establish a benchmark before committing yourself. Suppose you will have the opportunity to meet N possible dates tonight. To calculate the benchmark, divide N by the transcendental number e, the base for natural logarithms, whose value is roughly 2.72. If it鈥檚 your lucky night and N is 25, then your benchmark is roughly 9.
So don鈥檛 make a date with any of the first nine acquaintances that you make, merely note which of them would make the best date. Having established this person as the benchmark, make a date with the first new acquaintance you meet who rates higher. While not guaranteed to deliver the best available partner, it will do so about 37 per cent of the time 鈥� as long as you don鈥檛 disclose what tactic you鈥檝e been using.
5 Gooseberry factor
Dinner parties, with guests seated around a table, pose a whole new set of problems. At large, round tables, with noise levels high,it is often only possible to converse or pull a cracker with your immediate neighbours 鈥� and that can lead to trouble.
If you turn to the person on your right,there is a 50:50 chance they will also have turned to the right. Confronted with the back of their head, you turn the other way only to run up against the 50:50 chance that this person too has turned away. You have suffered the ultimate indignity, and become a gooseberry.
The diagram (right) shows the possible situations for a table of eight people. If guests turn randomly left or right there is a less than1 per cent chance of no one being left as a gooseberry (A), and a more than 10 per cent chance of two gooseberries (B). By far the most likely initial outcome is indeterminate (C),and depending on the random choices made thereafter this will stabilise to A or B. The final outcome is hard to calculate but accordingto one model B is slightly more likely than A and the proportion of people ending up as gooseberries will stabilise at about 1 in 7.
To keep the gooseberry count as low as possible, one obvious ploy is to ensure that each table holds an even number of people:an odd number at a table is certain to produce at least one gooseberry. Best of all, avoid round tables altogether and use a narrow,rectangular one instead.
6 Money matters
With your guests seated and conversing happily, you have time to sit back and worry about how much the dinner party is costing. Next time, you resolve, you will save moneyon the wine. But how can you make the most of your limited budget?
Choosing the best-value wine is a game between you and the store. Cheapest doesn鈥檛 always mean best value, because most of the cost is in the bottle, cork, transport and tax. Many people compromise by buying second-cheapest for parties. However, the stores know this, and as astute game players they have been known to make their worst wine second-cheapest in the knowledge that this will fool customers who don鈥檛 want to be seen as cheapskates.
If you are forced to buy cheap plonk, then you will have to disguise it. And the key here 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 bring out the good red with the main meal and save the cheap stuff for the cheese course. You may even find guests commenting on the smoothness of the wine.
Cheap wine may be excusable. Bad coffee never is. If you are forced to resort to inferior coffee, or even instant coffee, there鈥檚 a trick you can use to convince guests that they are drinking something better. Putting a few coffee beans under the grill will fill the room with a delectable coffee aroma. But don鈥檛 forget the beans are there, or the acrid smoke will give the game away.
7 The last chocolate
Finally, just when you thought it was safe to relax, there鈥檚 the potential for an awkward moment when it comes to handing round the after-dinner chocolates. Unless you have stocked up with a generous oversupply, eventually somebody will be offered the last one. If you take that last chocolate, how guilty should you feel about depriving those further down the table? What about the person who took the penultimate one: shouldn鈥檛 they bear some of the responsibility, too?
It is in fact possible to allocate guilt. Suppose there are five guests and four chocolates, and each guest has an 80 per cent chance of wanting a chocolate. If the first guest takes a chocolate, they can do so in the knowledge that the chance at least one guest will opt out, and so all the guests will be happy, is (1- 0.84), or 59 per cent. The second guest also takes a chocolate, but this time the chance that all the other guests will be happy is 49 per cent. The third guest鈥檚 clear conscience quotient drops to 36 per cent, and for the fourth it is a mere 20 per cent. So everyone around the table bears some guilt- except the fifth guest, who didn鈥檛 even have the option of making a choice.
So next time you are faced with this tricky moral dilemma, try explaining to your fellows diners how the maths implicates them all. With a bit of luck your dazzling explanationof the mathematics of guilt can be used to conceal the fact that it was, in fact, you who swiped the last chocolate. Cheers!
Rob Eastaway writes and lectures on everyday mathematics, and is a consultant to the University of Cambridge Millennium Mathematics Project. Len Fisher is an honorary research fellow in physics at the University of Bristol
