Gruel for the Soul

I asked for a day off next week, for quite an important function – indeed one where my presence is mandatory.
The establishment which pays my salary – some call it a school – first asked me to fill out a form. Quite right. Entirely reasonable. No details of why I require time out is evident for completion.
The Principal – beige and uninspiring – coughed sheepishly behind me today and told me that I would have to write a letter requesting that in his magnanimity, the Personnel Manager might be kind enough to give me the day off, but, of course, could not pay me.
I have rescheduled my groups to another occasion when I am present, thus not a ripple disturbs the chaos of the day.
I remember in the sixties when my father was a personnel director and the unions were more than usually hairy-chested, how he bemoaned the ‘work to rule’ policies and ‘working without enthusiasm’ that resulted. It seems that people here are so accustomed to working to rule that the alternative of an environment where a well-motivated, productive and happy workforce goes above and beyond, simply because they want to, simply does not occur to them. Thomas Gradgrind, above, whose little vessels were arranged in order, ready to have imperial gallons of facts poured into them until they were full to the brim, would have been proud.

I’m reminded of a method of working out the sum total of pleasure and pain produced by an act, and thus the total value of its consequences; aka hedonic calculus. When determining what action is right in a given situation, we should consider the pleasures and pains resulting from it, in respect of their intensity, duration, certainty, propinquity, fecundity (the chance that a pleasure is followed by other ones, a pain by further pains), purity (the chance that pleasure is followed by pains and vice versa), and extent (the number of persons affected). We should next consider the alternative courses of action: ideally, this method will determine which act has the best tendency, and therefore is right. In 1789, Bentham envisaged the calculus could be used for criminal law reform: given a crime of a certain kind it would be possible to work out the minimum penalty necessary for its prevention. Spectacularly misleading, uninformed, grandiose in its stupidity. In other words, horseshit. But, it’s the way this place operates. It’s no wonder that this country, so rich in the things of the world, is emotionally and psychologically impoverished to the point of destitution.

Bumps in the Darkness

The Indian physicist Sidharth (I liked the syllabic connotation) suggests that space and time are granular like free flowing sugar, not continuous like golden syrup, at their smallest scales. He discusses how the quantisation of time – the existence of the chronon as time’s smallest quantum – leads to an explanation of the arrow of time. Perhaps the chronon is only able to face one way in the ‘real’ world.

This quantised spacetime is fuzzy, underlain with the order of fractal geometry – a new way of ‘looking at the world’ were it possible.

Such bumpy fractal spacetime’s road maps is not familiar Euclidean geometry. Quantized fractal spacetime is non-Archimedean, or ultrametric: lengths and distances cannot be measured with a ruler. How far is it between 3 and 5? I live in Kuwait and feel close to Esther, who lives in England. What do we mean when we say “close” or “far”? In mathematics, we’re used to using “real” distances x-y, but there are others, which are called “p-adic” and measure the common ‘factors’ two numbers have. We don’t measure p-adic distances in kilometres, they are more like the distance between people on a family tree, where brothers and sisters are close to each other and cousins are further away. So, this quantized fractal spacetime is also noncommutative: its geometry, its spacetime, is not flat or ordered according to our usual formulas of geometry and algebra. The image is of a 3-adic tetrad, showing crystal planes and their ‘nearness’.

Funny old world, innit………….