Number of the Month

June  2011

NUTS

Puritanism: The haunting fear that some one, some where, may be happy.
H L Mencken

"When the lunatics took over the asylum, the authorities let them stay there and called them psychiatrists." The old jokes always have an element of truth in them, but THIS ONE really took the biscuit. It had one considerable achievement in uniting all the regular columnists in an outcry of scorn. Various jibes appeared, describing the authors as “nannies” or “bullies”. It was, however, only the ever-reliable James LeFanu who pointed out that the main basis of this claim was the obstinate ignoring of the scientific evidence. It is one of the characteristics of the zealot movements that they pluck recommended limits out of the air, not only without any evidence but despite such evidence as exists.

These extremists urge that GPs become a secret police to prevent such enjoyment of life in its latter stages, another characteristic of the marching zealots. As if the poor GPs did not have enough on their plates.

Your bending author discussed this with a neighbour who is a retired neurologist. He related that, when he was in training, he was required to spend a period, reluctantly, among the psychiatrists – “They just sit around a table and think up theories on the basis of no evidence at all.” This is in line with the practices of giants of the subject such as Sigmund Freud.

Anyway, your bending author and spouse celebrated the event by having a second large gin and tonic at our regular 6 o’clock ceremony.

The modern myth of longevity

In media coverage of the inconvenient increase of human lifespan it is often stated or assumed that the reason for it is adherence to a new politically correct life style. This has little or nothing to do with it. What has changed is the increasing use of medication to fend off the big killers: strokes, heart disease and cancers. Most oldies are now dosed with rat poison, foxglove poison, fancy “blockers” and “inhibitors” with ludicrous names and many other new drugs. This in the jargon of the media results in many lives being saved, but the reality is that many deaths are postponed. There are now three additional commandments that the elderly are required to observe:

  1. Thou shalt order thy affairs to live as long as possible
  2. Thou shalt not enjoy thyself
  3. Thou shalt accept with grace thy due onerous punishment for living too long.

Twits’ Day

Here is a collectors’ item for students of academic tomfoolery.  A group of activists want to get rid of “pi” and replace it with a constant of twice the value. Although the proposal is self-evidentially stupid, it is a useful, if banal, exercise for number watchers to go through some of the reasons why.

Utility

Mathematics was first developed as an aid to measurement. Although no documentation has survived, the engineers of Ancient Egypt carried out exercises of great skill and precision in areas from irrigation to the building of the Great Pyramid (with errors of less that an inch).

Consider a spherical ball or a solid cylinder (say a section of broomstick). There are two quantities you can measure: the circumference (with a tape measure) and the diameter (with various forms of gauge). That is why pi is defined as the ratio of these quantities. The centre, and hence the radius, are but theoretical concepts.

We are misled at school by the presence of a pinprick on the paper left by the point of our compass. If that clue is missing, we have to locate the centre by a geometric construction involving chords and perpendicular bisectors. When we have done that we can measure the radius.

Continuity

It is a recurring phenomenon that groups of people emerge who wish to change the conventions of centuries. A recent example is that members of the politically correct movement want to do away with BC and AD, substituting inventions of their own (an example is the self-styled Skeptical Environmentalist). If they had their way future generations of scholars and general readers would have to cope with this abrupt discontinuity in nomenclature at an arbitrary point of time dictated by the intellectual fashions.

There are many millions of publications in applied mathematics, all linked by a web of cross-references. A sudden change of symbols, again at an arbitrary point in time, would create havoc for future professional scientists and engineers, who would have to deal with sources on either side of the discontinuity.

Motivation

The alleged reason for the proposed change is simplification: removing the irritating factor of two in the calculation of the circumference of a circle; though we are not told why this is more irritating than introducing a factor of one half in the calculation of the area.

It is, however, worse than that. Euler’s identity has been described as the most beautiful theorem in mathematics. It unites the five most basic quantities of mathematics in an equation of such startling simplicity that, when you first meet it, takes your breath away. These silly people want to put factor of two in the middle of it.

Perversity

It is not just the proposed elimination of pi that strikes at the heart of mathematics as an important language of human communication. Of all the symbols in the Greek alphabet to choose as a substitute, tau is the most perverse. Chemists, physicists, engineers and related professionals, even if they do not share a common written and spoken language, are able to communicate by means of mathematical equations. To do this they adopt a common convention as to the meaning of various symbols.

Apart from a few oddities, tau is universally used as the symbol for a time-constant, which distinguishes it from real time, t, or a period of time T, though they all have the same dimension.  Accepting such a convention means that applied mathematicians can communicate with each other without having lengthy language-dependent protocols (Let x be the unknown etc.)

Finally

Haven’t they something better to do with their time?

Number of the Month 

3.1415926535897932384626433832795…….

And long may it reign.

Link to this piece

Completed in July from notes made at the time, due to ill health

 

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