Monday, September 27

Romance numbers | The game of science


Jesús López, one of the watchmakers in charge of maintaining the Puerta del Sol clock. This view from the inner side of the dial shows that IV is represented as IIII.
Jesús López, one of the watchmakers in charge of maintaining the Puerta del Sol clock. This view from the inner side of the dial shows that IV is represented as IIII.Emilio naranjo

In principle, knowing that two bodies falling at the same time from different heights reach the ground two seconds apart, as we saw last week, is not enough to determine those heights; But if the bodies in question are human bodies that fall from the windows of a building and come out unscathed, things change.

Suppose that the first person falls from the minimum height, that is, from a first floor about 4 or 5 meters from the ground. As is well known (or should be), the formula that relates the time of fall with the height from which an object falls is h = ½gt², from where t² = 2h / g, so the time of fall from a height 4-5 meters is approximately 1 second. As the other person has taken 2 more seconds to reach the ground, his time to fall is 3 seconds, and in that time a body in free fall travels, applying the formula, about 44 m.

If the first person falls from a second floor, about 8-10 meters high, their fall time is approximately 1.4 seconds and that of the other person, 3.4, which means a height of about 60 meters, in the limit of the viability of rescue mattresses for firefighters, so we can rule out higher heights. And the fact that both people not only survive, but are unharmed, suggests that, in all probability, the first person jumped from a first floor.

Fermi used to pose problems for his students in which the lack of exact data or precise formulas did not prevent them from reaching reasonable results. A classic in that line:

From a boat located on the Mariana Trench we throw an iron ball into the sea, how long does it take to reach the bottom?

And since Fermi was Roman …

Everyone knows Roman numerals, as they are still used to number centuries, kings, and popes, and they continue to appear on many watch faces. But romances are not so well known.

Let’s consider the following sequences:

1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4…

1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2…

2, 3, 5, 7, 2, 4, 8, 10, 5, 29, 4, 10, 5, 7…

All three are directly related to romance numbers, and with this information and a bit of Fermian spirit, my astute readers will undoubtedly be able to deduce the nature and characteristics of these numbers. And answer the following questions:

Returning to the dials of the clocks with Roman numerals, in many of them, as in the one at Puerta del Sol in Madrid without going any further, the 4 does not appear in the orthodox form, IV, but as IIII, in the Etruscan way. . What can be the explanation for such an anomaly?

As is well known, there is no 0 in Roman numerals. Needless to say, the famous Roman mathematician and astrologer Tarucio could answer from his grave. Why?

Carlo Frabetti is a writer and mathematician, member of the New York Academy of Sciences. He has published more than 50 popular science works for adults, children and young people, including ‘Damn physics’, ‘Damn maths’ or ‘The great game’. He was a screenwriter for ‘La bola de cristal’.

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