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Mathematics is the basis of so much of our modern world that it's hard to imagine life without them, but where do they come from? Have they been invented or is it something that we discover?
The ancient Greeks had no doubt about it.
his fascination was the result of his experiences with music.
With them, they discovered patterns that linked sounds and their relationships to digital proportions from which they deduced the beauty and pleasure of music.
It could not be a coincidence: was a window on the world of the gods .
Harmonious Mathematics
"Any sound you hear is produced by something moving, if you make the string vibrate, produces a sound," says mathematician and musician Ben Sparks at the BBC.
"What the Greeks have noticed is that you can make the rope vibrate twice as fast, halving its length." [19659002] So, if you touch the tense rope, you produce a note. If you touch it again by pinching the string in the middle, you will immobilize a part of it and vibrate only the other half, which will produce another similar but distinctly different note.
"This is what we call an octave ," points out Sparks.
"In the octave, the frequency ratio is 2: 1."
Will there be other fractions that sound good? Asked the Greeks. And indeed, they found that other divisions of the rope, in progressive proportions, produced sounds judged beautiful and well proportioned .
It looked like the fifth fair, in which the ratio is 3: 2, that is, the high note is two-thirds the length of the lowest note.
But what happens when you play something that is not one of those ordered fractions?
"When the notes are not in these simple proportions, we tend to notice that we are not aware of mathematics," says Sparks.
The Greeks discovered that squeezing other fragments of the string too close or much farther and in a difficult proportion compared to the fundamental note- produced unpleasant sounds. in his ears
Otherwise, why would there be such schemes if not to reveal the kingdom of the gods ?, thought the Pythagoreans.
The music of the cosmos
"For Pythagoras and their s It was important to discover the principle that commanded everything and found it in the figures," says Ricardo Rozental, music commentator, BBC Mundo.
"They explained the proportions in which pleasing sounds could be produced and with which it was possible to make a music that pleases the ear and, therefore, promotes the spirit and l '. intelligence . "
The patient observation of the sky gave similar conclusions regarding the movement of planets and stars, which did not work.
"The conclusion corroborated the idea that the movements of celestial bodies and pleasant sounds were related in the same way that is to say according to the same mathematical proportions", adds the expert.
"Where the notion of cosmos as an ordered whole according to the same numerically explainable scheme".
] Low pbadions
A beautiful melody that used the correct notes, for the ancient Greeks, looked like this, because the numerical proportions that were consistent with the stars had been correctly used.
Relationships between the largest and the smallest acted together and made it possible to understand the principle that everything was ordered in an orderly and harmonious way.
So how was the unpleasant sound explained?
"As it was also possible to produce them, the Pythagoreans understood that they should be avoided because they were capable of causing enormous consequences for those who listened to them, because they would modify the good balance of the body and the body. spirit and would be outside the laws of the cosmic order. ", says Rozental.
"They therefore deduced that weak pbadions, anger and violence could be excited by this means, as well as calmness and ranching could be induced by harmonious and gentle music."
Diabolus in the music
Several centuries later, when Christianity adopted many principles from Greek culture and to the extent that the practice of liturgy incorporated diversity. of music, some unpleasant aspects for the hearing habit – such as the use of second-grade notes – were considered to be malévol or and were therefore excluded canons musical of the church .
"His use would have been the intervention of the diabolical.It was necessary to exclude them, avoid the presence of the devil in the church and in the spirit and the l & # 39; spirit of his disciples, "says the expert.
Still in the nineteenth century, some of these ideas of the sixth century BC were still in the news.
"The violinist Nicoló Paganini is well known for having used what was called in Latin diabolus in music some agreements also called tritons, which were part of the practice excluded by the rules of the well ordered, "says Rozental.
"Nevertheless, Paganini was a public favorite and helped to alleviate some fears badociated with what was considered beautiful and ubiquitous, ugly and dissonant, cosmic and chaotic, divine and demonic." [19659002] Our ear and our musical tastes today admit greater numerical diversity than previously offered by the Greeks and we appreciate the amplitude of sound in the context of an expanding cosmos.
The Origin of Mathematics
Tastes have changed, but the Greeks did not find the same motives
The Pythagoreans were not the first to use mathematics.
There is some evidence that marks found in bones from the Late Paleolithic era 37,000 years ago were carved and used for counting.
However, they were the first to look for reasons.
And what they found seems to indicate that mathematics is all around us and is something that we have discovered a fundamental part of the world in which we live.
For them, mathematics was as real as music and was more brilliant and elegant than anything the human mind could conceive of .
But that is what one of the most important figures of ancient Greece said about the origin of mathematics that is still the basis of what many mathematicians believe.
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