Mathematicians taken up with finding the square roots of algebraic equations have had the niggling problem that such solutions involve illogical square roots of negative numbers.
Mathematicians taken up with finding the square roots of algebraic equations have had the niggling problem that such solutions often involve square roots of negative numbers, something which is seen as nonsensical and illogical to the mathematical mind. In fact until the 1700s it was believed that the square roots of negative numbers simply couldn’t exist because they be positive numbers. This is because conversely a negative multiplied by a negative is always a positive. Whereas a squared negative must achieve a negative solution. "There seemed to be no hope of finding numbers which, when multiplied by themselves, would give negative answers. We’ve seen crises like this before. They occur whenever an existing operation is pushed too far, into a domain where it no longer seems sensible. Just as subtracting bigger numbers from smaller ones gave rise to negative numbers and division spawned fractions and decimals, the free-wheeling use of square roots eventually forced the universe of numbers to expand…again. Historically, this step was the most painful of all. The square root of –1 still goes by the demeaning name of i, this scarlet letter serving as a constant reminder of its ‘imaginary’ status."
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China's Chang'e 4 biosphere experiment marks a first for humankind.
- China's Chang'e 4 lunar lander touched down on the far side of the moon on January 3.
- In addition to a lunar rover, the lander carried a biosphere experiment that contains five sets of plants and some insects.
- The experiment is designed to test how astronauts might someday grow plants in space to sustain long-term settlements.
Groundbreaking neuroscience confirms what Sigmund Freud first theorized.
Arranged marriages and Western romantic practices have more in common than we might think.
In his book In Praise of Love (2009), the French communist philosopher Alain Badiou attacks the notion of 'risk-free love', which he sees written in the commercial language of dating services that promise their customers 'love, without falling in love'.
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