When I was sixteen and seventeen I did my 5th Year of secondary school twice. Amidst grinds, tears and two to three hours of Honours Maths homework each night, I just could not make it past Christmas and still understand what was going on. (The obvious and practical response; take Ordinary Level Maths instead and accept that a career in Medicine was out, just didn’t seem to present itself.) For two years I hungrily repeated the exercises in the small part of the curriculum I understood, and threw myself with increasing desperation and diminishing returns at the rest. The last chapter I remember mastering was called something like ‘Sequences, Series and the Binomial Theorem’.

Happily, understanding – at least a little – the concept of geometric progressions has turned out to be one of the most useful and widely applicable bits of Maths I could have picked up. It crops up everywhere; understanding the spread and gravity of DDOS attacks, why mouse infestations need to be hit early, why skimming stones on water is so hard, and how a young woman settling for less money than a man at the beginning of her career may still be paying for it when she’s middle-aged.

The definition of a geometric series or progression is ‘whenever a term of a sequence is a constant multiple of the preceding term’. When that multiple is greater than one, the numbers will get very big, very fast. If, for example, the multiple is two, you’ve got ‘exponential growth’, a mathematical term of art that’s often used inaccurately elsewhere to describe rapid but not geometric increases. Real exponential growth tends to sound pretty grim when the term is correctly applied in epidemiology.

At dinner the other night, I learnt that the rate of increase of cases of Ebola in certain African countries has been modeled as a geometric progression for weeks, if not months.* Since at least August, the number of new Ebola infections has started to double every month. Common sense dictates that the more people infected, the more people who will be infected. Mathematics predicts chillingly just how bad it will be. The battle to stop the spread of this disease reaching the threshold where it is now running like wildfire has already been lost. [click to continue…]

Of the three Jews described by George Steiner as, in Corey’s summary, having formulated a great and demanding ethics/politics, Jesus is to me the most interesting.[^1] That thought struck me while reading Jerry Cohen’s Self-ownership, freedom and equality, a Marxist response to Nozick. As Cohen observes early on, Marxists seem to have a lot more difficulty responding to Nozick than do (US) liberals or social democrats. That’s because the notion of self-ownership central to Nozick’s argument is closely allied to the Marxian idea that capitalism inherently involves exploitation (that is, extraction of surplus value from labor). Nozick’s claim was that the same is true of taxation, or any kind of claim on private property imposed by the state.

I’ll come back to self-ownership in a little while. The more interesting point, to me, is that Nozick’s argument was refuted in advance by Jesus when he was asked by Pharisees (arbiters of the law laid down by Moses) whether it was lawful for Jews to pay taxes to the Romans. This was, of course, a trap, since he could be arrested for saying No and discredited for saying Yes. Jesus showed them a coin with the emperor’s head on the obverse and said “Render unto Caesar the things that are Caesar’s; and unto God the things that are God’s”. And “when they had heard these words, they marvelled, and left him, and went their way.”

Jesus’ point is just as valid if the coin is replaced by paper currency bearing the picture of a president, or rent from a land title issued by a state, or a dividend coupon from a corporation established under state law. All of these things were initially obtained from states under conditions that (in most cases, explicitly) involved the obligation to pay taxes as determined by the legal processes of those states. Someone who takes Caesar’s coin and then repudiates the associated obligation to pay taxes is, quite simply, a thief (of course, theft implies property, and vice versa).

[click to continue…]