How did Archimedes manage to count all the grains of sand that would fit into the Universe of science and health

How did Archimedes manage to count all the grains of sand that would fit into the Universe of science and health

Ambition is sometimes thrown on – and this is something that Archimedes, a third-century BCE Greek mathematician, no doubt had.

But his greed was for knowledge, most commendable.

Tired of hearing the difficult things to count, as the grains of sand were endless, he set himself the task of counting them.

That’s right what you read right now: He had set out to count all the grains of sand in the Universe we know.

287 BC Born in Syracuse, Sicily, in Magna Grecia, Archimedes was obsessed with mathematics.

Among many things, it was he who created a value for π, one of the basic elements of science, and its approximation is still used today.

And yes, it was he who, after resolving a question for King Hiren 2 (c. 306–215 BCE), went naked through the streets of Syracuse while shouting “Eureka”, which, during the bath, Was exploring the theory of buoyancy.

Its name refers to water instead of sand … – Photo: SCIENCE PHOTO LIBRARY by BBC

It was to this king’s successor, Galeon 2, that he directed the essay O Condor de Aria, a work that is considered a relic, not only because it was one of the first scientific publications in history, but Because …

  • This included the only extant reference to his own father, the astronomer Phidias;
  • He demonstrated that it is possible to express very large numbers in some kind of annotation;
  • He introduced a way to expand the Greek numbering system to name large numbers;
  • He estimated the size of the universe that was known at the time;
  • It contains an account of a simple procedure Archimedes used to determine the apparent diameter of the Sun through observation with an instrument;
  • Crucially, it provides the most detailed description of Aristarchus of the Helioscentric System of Samos (c 310–230 BCE), indicating that the Copernican systems were defending two millennia before the latter Copernicus.

Countless is not infinite

“There are those who think, King Gailon, that the number of sand grains is infinite,” Archimedes began to say.

Furthermore, he writes, “Some people, considering it infinite, think that no number has yet been named which is large enough to surpass its plurality.”

By this, they mean, explaining to Archimedes, who is convinced that whatever number can express this magnitude will be greater than the amount of sand present.

“But I will try to show you through geometric displays that you will be able to follow (…) out of the numbers I have named, and not just the number of mass of sand that is equal to the magnitude of the Earth.” (…), But also equal in magnitude to the universe ”.

And that’s what they did in about eight pages.

To be more specific: Archimedes did not count the number of sand grains in the Universe, but if the sand were filled with sand, there would have been a greater number of sand grains all over the Universe.

In a finite world, there can be infinite grains of sand. There was a limit … but what was it?

Your Universe Was Not Like Us – Photo: GETTY IMAGES via BBC

At the time, the highest number for the Greeks was a name: 10 10,000 = 10,000, which they called μυριο) (deadly) – meant countless and was also a word for ‘infinite’ in ancient Greece.

The Romans changed that word into innumerable, as we know it today.

To make this immense calculation, they had to invent what we now call exposures or powers.

He started with innumerable and introduced a new classification of numbers.

He stated that the “first order” numbers were those which reached the myriad of myriads.

That is, 10,000 x 10,000 = 100 million or 100,000,000 or 10 x.

The “second order” ones went up to 100 million x 100 million = 10⁸ x 10 that is, ie (10⁸) ones.

And “third order” 10⁸ x 10⁸ x 10 that, ie (10 third) “, and so on.

But what order of numbers was needed to calculate the number of grains of sand that would fit into the Universe?

According to Archimedes ‘calculation, “eighth order” numbers were needed, ie (10⁸) ⁶⁴ = 10’.

In the same way Archimedes was conceived by the Spanish painter José de Ribér (1591–1652) – Photo: GETTY IMAGES via BBC

That is, at 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000.

And who would dare argue with him!

The second indisputable thing is that he had created such a large number that it was very unlikely that a large number would be needed to calculate anything in the universe that he imagined.

Hmm … no. Archimedes did not like the border.

Contemporary historians say that when he discovered increasingly complex mathematical forms, Archimedean was known as solids, ranging from the tracheated tetrahedron (8 faces) to the snub dodecahedron (92 faces).

And in terms of numbers, it cannot be different. Ultimately, its field of action – unlike grains of sand – was infinite.

Therefore, he could not resist the temptation to continue exploring the vastness.

To do this, he went from an “order” of numbers to what he called a “period”.

The first (10⁸) of these periods was increased to Shakti (10 power). That means 800 million zeros after 1.

In this case, we cannot show you: it is anticipated that, if written on paper, the number would occupy 380 thousand pages of a book.

Not satisfied, Archimedes (10,) raised to Shakti (10 शक्ति) Shakti, (10⁸) Shakti, a number he called “numerous-innumerable order from innumerable times”.

Um Dodekadaro Snub – Photo: WatchDDCK via BBC

If their number – 10⁶⁴ – to express the maximum grain of sand present in the known universe at that time was already too large to count what was reported at that time, there is still nothing that we know of We can count in the universe today it reaches near the greatness of the number she left us.

But, to give you an idea of ​​its enormity, it may be obvious if I say that it is 1 followed by 80 quadrillion zeros … a measure of the genius of its creator’s mind.

Video: Science and Health

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Raven Weber

About the author: Raven Weber

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