Getting it wrong

December 17, 2012

Mayan Mystic Mathematics, no thanks

Ed Vulliamy has some reasonable things to say about the Mayan `prophecy’ of the end of the world but he gets it wrong here:

The Maya were no fools. Likely inventors of the figure zero, their mastery of astronomy – bequeathed to history through various codices and stoneworks – was breathtaking not only for its time, but for all time. Their systems for measuring time were more sophisticated than ours, with pivotal numbers of 13, 18 and 20, based upon lunar, Venusian, astronomical and mathematical measurements, and expressed in glyphs.

Vulliamy seems to confuse obscurity and sophistication. Our Arabic-numeral, place-system, method for arithmetic is much more sophisticated than one based on different `pivotal numbers’, because it makes things simpler for the person using it. By having one, and only one, set of rules, all calculations are the same, no matter what size of problem you deal with, a point which will be appreciated by those who had to learn the pounds, shillings, pence system of currency, or by those in benighted countries which continue to use imperial measures. Try doing mental arithmetic switching from base 13 to 18 to 20, without mechanical aids.

Vulliamy then talks of `lunar, Venusian, astronomical and mathematical measurements’, without saying what a `mathematical’ measurement is, and how it might differ from the other three he mentions.

Finally, he is impressed by the Mayans’ use of glyphs: `glyph’ is a fancy word for `character’ or `letter’.

We seem to have here a journalist falling for the idea that any ideas which survive long enough are `ancient wisdom’ and therefore better than our own. Actually, mathematics, and arithmetic, are areas where we can be fairly sure that the modern state of knowledge is definitely better than what people had X centuries ago.

August 5, 2012

Today’s Sunday Independent reports on a Boeing 757 flying from London to Boston which had to land at Dublin, due to “technical issues with the Boeing 757-200 plane’s nose-wheel steering”. You might ask why an aircraft with duff nose-wheel steering might not simply continue to Boston to be fixed there.

Somebody with a clue gives us some more information:

When the left hyd sys is u/s consequences are:
– 1 autopilot (out of 3) inop;
– No autoland;
– No Autobrakes;
– Some spoilers on each wings inop;
– Rudder ratio inop;
– Left thrust reverser inop;
– Electric slats and flaps extention required (takes longer time and less flaps must be used for landing, Flaps 20 iso Flaps 30);
– Alternate gear extension required (then it is not possible to raise the gear knowing it makes a lot of drag);
– Alternate brakes inop (reserve and narmal brakes are still working);
– Yaw dampres inop;
– Nose wheel steering inop (towing required after landing).

Of all the things that weren’t working, the Sunday Independent noticed the minor one.

May 5, 2012

Under pressure

A recent issue of the London Review of Books had this:

The unit of measurement of this pressure is the atmosphere, named after the weight of the air bearing down on us at sea level. We don’t normally think of the air as having weight, but it does. Hold your hand out flat, and imagine an invisible column of air above each of your fingernails stretching up from where you are to the top of the Earth’s atmosphere. That column weighs 1.03 kg per square centimetre—in other words, about one kilogramme’s weight of air bears down on each fingernail. That amount of pressure is one atmosphere.

What is wrong with this is that it misses the point of pressure. The misconception is not unusual. A GCSE physics site says that atmospheric pressure is “about the same force as having over a dozen cars piled on top of you!”

So why are these statements wrong? The error is in the idea that pressure “bears down”. As engineers learn in their first course on fluid mechanics, pressure acts equally in all directions. When John Lanchester says that one kilogramme’s weight of air bears down on a fingernail, he would have been just as right, or wrong, if he had said that one kilogramme’s weight of air bears up on a fingertip. The force on the end of your finger, or anything else, is about one kilogramme of air pushing down, balanced by one kilogramme pushing up: in sum, almost nothing.

But, you object, things get squashed by atmospheric pressure, or by pressure in the deep ocean. The reason is not the pressure, but the pressure difference. When pressure inside a submarine, or an aeroplane, or a soft drinks can, is not the same as the pressure outside, the force is out of balance and the structure has to carry a load to maintain its shape. If you inflate a balloon, you can see how the material stretches as the internal pressure is increased until it is greater than the pressure on the outside. The rubber of the balloon stretches so that the total force due to the difference in pressure, and the tension in the rubber, is zero. Likewise, though you cannot see it, the shell of a drinks can expands slightly to balance the difference in pressure between inside and outside. An aeroplane fuselage behaves the same way; a submarine hull likewise, though with the high pressure on the outside, rather than the inside.