Art of the Problem on MSN
From Plato to Markov chains, how probability revealed hidden patterns in random events
From Plato’s search for hidden forms to Bernoulli’s law of large numbers and Markov’s breakthrough on dependent events, this story traces how mathematicians discovered the patterns hidden inside ...
Plato was a famous Greek philosopher from ancient Athens who shaped Western philosophy. He was a student of Socrates and later taught Aristotle. Plato wrote many works in the form of dialogues that ...
In Plato's Allegory of the Cave, Plato provides a timeless insight into how we are often "prisoners" of our mind, in that we are born into a world of "shadows", which we confuse with reality. Wisdom ...
Plato described tyranny as the most disordered constitution in both cities and psyches. His ancient diagnostic tools still ...
A person who continually seeks after pleasure is leading a life that is unsuited to human being - it would be better suited to a life of a grazing animal. In contrast, Eudaimonia, as Aristotle defined ...
The people must believe in the politician. If mutual belief and respect do not exist, then chaos becomes the end result. Some ...
Ancient philosopher Plato's words on war's persistence resonate today. His quote, 'Only the dead have seen the end of war,' ...
When we experience music or dance together, our nervous systems synchronize. The performing arts may be one of the last ...
In the era of A.I. agents, many Silicon Valley programmers are now barely programming. Instead, what they’re doing is deeply, ...
Lucian and his men on the Moon fighting strange creatures. Illustration by William Strang (1894). Public Domain The first science fiction novel about man on the Moon was written in Greek by Lucian of ...
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