Folha: 'The size of the Universe, according to Archimedes'

Reproduction of Marcelo Viana's column in Folha de S. Paulo. How many grains of sand fit in the entire Universe? The question is asked by the Greek mathematician Archimedes (287-212 BC), in a letter he wrote to his king around 240 BC, which has reached our days under the title "The Sand Reckoner". To answer, he needs to be able to calculate the size of the Universe… Archimedes bases his answer on the heliocentric model of his compatriot and contemporary Aristarchus of Samos (310-230 BC): "His hypotheses are that the stars and the Sun are immobile, that the Earth revolves around the Sun along a circumference with the Sun at the center, and that the stars are located on a sphere that is also centered on the Sun." It's far from being a consensus: critics point out that if the Earth moved around the center, then the position of the stars in the sky would have to vary with the planet's movement along its orbit, due to the effect that astronomers call parallax. Aristarchus's answer, explains Archimedes, is to postulate that the stars are very far away, at a distance much greater than the diameter of the Earth's orbit, such that the parallax caused by our movement around the Sun is imperceptible. Unfortunately, Aristarchus doesn't say how far away the stars are, so Archimedes makes another assumption: the diameter of the sphere of stars is to the diameter of the Earth's orbit around the Sun as the diameter of that orbit is to the diameter of the planet itself. He doesn't justify this rule, but I suspect he adopted it because it's elegant, as well as useful: practically all scientists believe that the laws of nature need to be mathematically beautiful (although beauty alone doesn't guarantee truth). Read more: 'We managed to do cutting-edge science', says Arthur Bizzi From scalpel to mathematics, Daniela Paiva defends thesis on Tuesday (25) Thyago Souza: an itinerant mathematician at IMPA Be that as it may, given this assumption, to calculate the size of the Universe Archimedes only needs to know the diameters of the planet Earth and its orbit around the Sun which, in theory, are more accessible data. Around the same time, in Egypt, Eratosthenes (276-194 BC) is conducting his famous experiment to measure the circumference of the Earth's meridian, arriving at a value of 39,700 km, very close to the currently accepted value (40,008 km). Archimedes is less precise, saying only that the circumference of the Earth does not exceed 55,000 km. Dividing this value by π (pi), he obtains a somewhat exaggerated estimate of the planet's diameter. To estimate the diameter of Earth's orbit, Archimedes uses astronomical observations of the Sun and Moon and Aristarchus's assertion that the distance from Earth to the Sun is 20 times greater than the distance from Earth to the Moon (the correct factor is much greater: 389). In this way, he concludes that the diameter of the sphere of stars is less than 2 light-years, about 18.5 trillion kilometers. It remains to determine how much sand can fit in a sphere with this diameter. Performing curiously elaborate calculations (even involving poppy seeds!), Archimedes finally arrives at the desired answer: the Universe can hold fewer than 10 ^⁶³ grains of sand. A fun fact: he considers fine sand, with grains three times smaller than normal. To read the full article, visit the newspaper's website. Also read: 35th Brazilian Mathematics Colloquium: registrations open; Final result released for IT specialist position 3