Calculating the Peace

Anyone who has experienced the Peace before the actual eucharist part of the eucharist service knows that unless few are present and are sat close together that congregants cannot shake hands with everyone.

Dave Walker produced one of his subtle cartoons to this effect in a recent Church Times. He came up with a formula, that I'll present slightly differently here:


H is the number of handshakes and C is the number of congregants. What he does not explain is how to understand the formula. Thanks to my very numerate wife, Elena, I can explain (thanks to the software, I can write the equation).

The common denominator of 2 below the line is because at each transaction, two and only two people are involved in shaking hands - thus halving the number of handshakes. The minus 1 above the line is because each handshaker is one and the transaction is with as many others to be met - so there must be one less than the total present in each case (think about it).

Incidentally, the priest is counted as one of the congregation. There is no point counting the priest separately as there is no special characteristic for the priest (in this case). He or she does what any other congregant does.

A congregation of 2 has one handshake - the priest and one other (you count just the one other involved, and a handshake always involves two thus halving everything: so it one other in each case that is multiplied by a half (halved) multiplied by the two who are doing it in the church). A congregation of 3 has 3 handshakes. A congregation of 4 has 6 handshakes. It rises very rapidly. A congregation of 10 has 45 handshakes but multiply those congregants by 10 and the handshakes rise to 4950.

I said to Elena that the one other must be like fence posts and gaps in the fence between the posts, but she didn't see my point. I don't think it is this either; after all, the others that the (minus) one does it to - once divided by the fact handshakes are done by two at a time - are multiplied by the number present. So this is like fence posts, gaps within, and then fences. I know - it is late at night.

Elena next day tells me that the reason for minus one is that no one can shake hands with oneself, so each source individual must be excluded in each case - minus 1. However, she further adds that Dave Walker's cartoon is wrong to put arrows on each line. The lines should be arrowless - the interactions go both ways.

Clearly there is an increasing time and space problem for large congregations, which could extend service times to a ridiculous level, but this is not straightforward. Everyone can shake hands at the same time for a fixed time period, but people are different distances from each other and these distances take time to traverse. I'll leave that to Elena to work out, based on D for distance. She won't do it - she is doing some statistics preparation before she goes to Reading to read Statistics properly.

Of course all this is rubbish because some people prefer to hug, and this alters the time taken, and this brings in probability, as indeed probability should be brought in for the expectation of excessive and restrained handshakers in the first place, as well as huggers, for which probabilities must be factored in the churchship [non-sexist word] of the people involved. People who hug in threes are a nuisance.

Anyone who reads this drivel (if anyone does read this drivel) and is competent in this area might like to send in a formula that covers all the probabilities using number sets.