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An Obscure Field of Math Might Help Unlock Mysteries of Human Perception | Discover Magazine
▻https://www.discovermagazine.com/the-sciences/an-obscure-field-of-math-might-help-unlock-mysteries-of-human-perc
▻https://images.ctfassets.net/cnu0m8re1exe/qRT8mLm2TDqhzSePqF5gS/7dcbc0cc1116822294bc9c089615aa89/hyperbolicmind1.jpeg
Hungarian mathematician János Bolyai challenged the rules Euclid had outlined more than 2,000 years earlier.
Credit: Science History Images/AlamyThe human brain is both a marvel and a mystery of evolution: Packed into a volume about one-quarter that of an inflated soccer ball, somewhere around 86 billion neurons form networks that enable us to do everything from mindlessly scrolling through Instagram to safely sending people into space. But a deeper understanding of the structure of those networks is still an open question.
Perception remains particularly vexing: How does the human brain turn the deluge of incoming signals — photons, odor molecules, sound waves, sensations on our skin — into an accurate mental simulation? What neural network could represent, say, the smell of chocolate?
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The idea of breaking Euclid’s Fifth attracted big thinkers of the time, including Carl Friedrich Gauss and Nikolai Lobachevsky. One of the most remarkable figures was János Bolyai, a young, aspiring mathematician from Hungary who was one of the first to forge the rules of this new geometry. In 1820, he undertook a radical plan to thwart Euclid. János realized that relaxing Euclid’s Fifth Postulate opened new windows to stranger, non-Euclidean geometries.His father, Farkas, was not pleased, using language we don’t often hear from mathematicians. Or fathers, for that matter.
“For God’s sake, please give it up,” Farkas wrote to János.
“Detest it as lewd intercourse,” his letter continued. “It can deprive you of all your leisure, your health, your rest, and the whole happiness of your life.” Farkas, himself a mathematician and a lifelong friend of Gauss, noted that he, too, had once challenged Euclid. “I have measured that bottomless night, and all the light and all the joy of my life went out there.”
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