Only 4 steps stand between you and the secrets hidden behind RSA cryptography. Find out how to crack the world’s most commonly used form of encryption.
Supertasks allow you to accomplish an infinite number of tasks in a finite amount of time. Find out how these paradoxical feats get even stranger once randomness is introduced. What happens when you try to empty an urn full of infinite balls? It turns out that whether the vase is empty or full at the end of an infinite amount of time depends on what order you try to empty it in.
Throughout much of human history, people consciously and intentionally produced randomness. They frequently used dice – or dice-shaped animal bones and other random objects – to gamble, for entertainment, predict the future and communicate with deities. Despite all this engagement with controlled random processes, people didn’t really think of probability in mathematical terms prior to 1600.
Last episode we saw that your neural network can be modeled as a graph, which — we’ll show in this episode — can be viewed as a higher-dimensional simplicial complex. So… what is a simplicial complex??
Random Walks are used in finance, computer science, psychology, biology and dozens of other scientific fields. They’re one of the most frequently used mathematical processes. So exactly what are Random Walks and how do they work?
If you needed to tell someone what numbers are and how they work, without using the notion of number in your answer, could you do it?
When you think about math, what do you think of? Numbers? Equations? Patterns maybe? How about… knots? As in, actual tangles and knots?