These were mathematical challenges, in which two or more experts struggled to find the solution to a problem . The duel was carried out in public squares and was followed by thousands of inhabitants.
It was at this time that some Italian mathematicians began to realize that some equations were impossible to solve.
In particular, those whose resolution required calculating the square root of negative numbers.
As you may remember from school, negative numbers do not have square roots: there is no number which, when multiplied by itself, gives a negative number.
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This is because negative numbers, when multiplied, always produce a positive result. For example:-2 ×-2 = 4 (no-4).
But the mathematicians Niccolo Fontana (aka Tartaglia) and Gerolamo Cardano realized that if they allowed the existence of negative square roots, they could solve true equations-or with «real numbers», as it is known to the numbers that have a Decimal expression-.
That’s how they created a new unit, imagining the square root of-1 (or √-1 in mathematical terms).
Gerolamo Cardano was the first to disseminate the idea of the imaginary unit, which had thought Niccolo Fontana (aka Tartaglia) in 1573 another Renaissance mathematician, Rafael Bombelli, explained how arithmetic worked with this new concept, in a work called » Algebra. »
There he pointed out that the new unit was not positive or negative and therefore did not obey the usual rules of arithmetic.
For nearly a century many thinkers rejected this new idea, calling this invented unit «fictitious, impossible, or meaningless.»
One of the detractors was the French philosopher René Descartes, who in his work «La Géométrie» (1637) would baptize the invention with the derogatory term of «imaginary numbers».
It would take many more decades for mathematicians to start accepting these imaginary numbers, which defied logic, as something valid and genuine.
In 1707, another Frenchman, Abraham de Moivre, related the imaginary numbers with geometry, thus achieving using this discipline to solve complex algebraic problems.
Seventy years later, imaginary numbers would finally have its own symbol: I (thanks to the Swiss mathematician Leonhard Euler).
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And its use would allow to extend the system of real numbers (R) to the system of complex numbers (C), where real numbers are combined with imaginary numbers.
It may sound like a lot of meaningless numbers and formulas, but in reality they have many uses prácticosQuizás all this sounds like something completely abstract and without real utility, that could only interest to intellectuals who live in the world of ideas, but That’s far from reality.
In the TWENTIETH century, imaginary numbers began to have many practical uses, allowing engineers and physicists, among others, to solve problems that otherwise would not have had a solution.
Today these imaginary and complex numbers are behind some of the most essential technologies we use.
They were especially valuable when electricity was invented, as they are very useful for analyzing anything that is expressed in waves (such as electric waves).
Electrical engineering uses complex numbers, in which «I» is used to indicate the amplitude and phase of an electric oscillation.
The imaginary and complex numbers are especially useful for analyzing waves: from electricity and sound to mechanics cuánticaSin these numbers, telecommunications could not have been developed. There would be no radio, television and internet and today you would not be reading this note on your computer, tablet or cell.
Imaginary numbers also allowed all kinds of technological and scientific developments, from radar and GPS to magnetic resonance imaging and neuroscience.
Quantum physics reduces all particles to waveforms, which means that complex numbers are fundamental to understanding that strange world.
Not only could they be key to the future, but some believe that they could eventually serve to answer one of the great unknowns that remain perplexing to scientists: what happened before the Big Bang and when did the time really start?
The classic general Theory of relativity by Albert Einstein linked time with the three spatial dimensions with which we are all familiar (up-down, left-right and inside-out), creating a «space-time» dimensional in the That time can only move forward.
A brilliant theory, but when applied to the creation of the universe arise problems.
But if you invoke quantum theory and add some imaginary time and everything begins to make sense… At least for the cosmologists.
Imaginary time is measured in imaginary numbers and, unlike real time, it can move forward and backward as an additional spatial dimension.
And that gives the Big Bang a moment to start.