was born in Hastane Maternity Hospital, near Drumroos in Scotland, at 8.15 a.m. on April Fools’ Day 1976. Jim was born in the same place, just seven minutes later.
Their mum remembers the day not only because of the happy occasion of their births but because of the Jovian–Plutonian gravitational effect that astronomer Patrick Moore reported would happen that day.
Jupiter is the largest planet in the solar system, with a mass of about two and a half times that of all the other planets glued together. Pluto on the other hand is so small that in 2006 it was reclassified as a dwarf planet.
Moore told listeners to BBC radio that as Pluto passed behind Jupiter at 9.47 that morning, a powerful combination of the two planets’ gravitation would decrease the gravity on Earth. People were told that if they jumped in the air at exactly the right time they would stay up longer than normal and briefly feel as if they were floating.
Shortly after the appointed time hundreds of listeners telephoned the BBC to report that they had indeed felt the effect. One woman said that she and some friends had been ‘wafted’ from their chairs and ‘orbited gently around the room’. Not that you can orbit around a room when you’re inside it, but never mind. (These people actually vote.)
Of course, the whole thing was an April Fools’ hoax by the mischievous Patrick Moore. Although Jupiter is very massive, it is also a very long long way away. At its closest to Earth the planet has a gravitational pull only about the same as that of a Renault Twizy on an old man standing a couple of feet away. The gravitational attraction of Pluto is even less. It’s about the same as a marble 100 yards away from you. Which means that even the combined gravity of the two distant planets is far too small to cause a person to become lighter or float while jumping. It’s a good job that gravity is such a weak force, or the gravitational pull of Bob and Jim’s obstetrician would have caused the tide to go out in their mum’s cup of tea.
The problem
Jim and Bob were born at the same place in the same hour of the same day of the same month of the same year, and to the same mother. Yet they are not twins. How can this be?
The mystery
Jenny Brown and Margaret Green are lifelong friends. They grew up together, they went to the same school together, and they graduated from teacher-training college together. Both of them applied for a teaching post at their local village primary and they were appointed at the same time, in the same September of the same year.
Jenny and Margaret now teach in that school, in adjacent classrooms. The school is a charming Victorian building with a steep tiled roof, and roses round the door. It smells, as many schools do, of shepherd’s pie and pine disinfectant. It has about 120 children each year and at the end of their four years most of them feed into the large secondary school in the town.
Jenny and Margaret’s school is a happy place, with a good head, good staff, generous playgrounds, a large sports field and plenty of trees. Not so long ago a local supermarket offered a great deal of money to buy the bottom end of the cricket pitch, but the headmistress, Miss Jean Piaget, had other ideas. The parents carried her in triumph on the day the supermarket abandoned its scheme (they carried her metaphorically, that is).
One day the two young teachers were sipping tea in the staffroom and discussing mathematics. They decided to teach their pupils that maths is not just for passing exams but is a useful and fascinating subject in the real world. They devised a lesson plan in which the children in their classes would measure the length of every child’s arms and deal with the numbers in different ways, to arrive at the three different sorts of average: the mean (got by adding up all the different lengths of the children’s arms and dividing this figure by the number of children in the class), the median (arrived at by listing in order the different lengths of the children’s arms and finding which arm length falls in the middle of the list) and the mode (found by seeing which arm length occurs most often).
On Monday morning Jenny and Margaret called their respective registers. There were 28 children present in each class, with no absences.
They then explained the task to their classes and allowed them to decide who would be in charge of the tape measure, who would take down all the measurements and who would check the figures before handing in the final calculations. The children got to work, and by lunchtime the numbers were all written down.
In the staffroom Jenny and Margaret compared lists and checked the maths. Miss Tijdelijk, a temporary supply teacher, was passing through with a sandwich and asked Margaret and Jenny what they were doing. They showed her the numbers and to her utter astonishment she discovered that, although everything had been done in exactly the same way in both classrooms, and although all the measurements were correct and all the mathematics properly done, the average (mean) arm length of the children in Jenny’s class was three inches greater than the mean arm length of the children in Margaret’s class.
The problem
The children in both classes are all physically normal, and nobody in either class has extraordinarily short or long arms. The arithmetic is correct and, in fact, accurately reflects the actual arm lengths of the children.
How is it that the children in Jenny’s class appear to have significantly longer arms than the children in Margaret’s class?
The mystery
Tall buildings are nothing new. Blocks of high-rise flats were all the rage in Ancient Rome, where they rose to a height of ten or more storeys. Some Roman emperors took against them, though, getting their togas in a right tangle trying to set a height limit on the pesky things, but without much luck. If an emperor can’t get something like that done it makes you wonder about your own planning department down at the town hall.
It wasn’t just Rome, either. Twelfth-century Bologna had many high-rise apartment blocks too, something like 180 of them. It looked like an ancient New York. The tallest of these buildings – which hasn’t fallen down over the centuries – is the Asinelli Tower, one of the so-called Duo Torri (Two Towers) that together resemble the old World Trade Center. The Asinelli Tower is 319 feet high, and I can imagine the 12th-century Bolognese sitting down to eat their spaghetti at sunset, grumpily looking out over the red roofs of the city and writing endless letters to the council to complain about being overlooked.
But neither the Roman nor the Bolognese towers were really skyscrapers. This term was first used in the late 19th century to describe steel-frame buildings of ten storeys or more. Nowadays it can refer to any very tall multi-storey
