Connections Between Magic and Mathematics
Table of Contents
1 What are your ideas about math?
Essential idea behind math is relationship or ratio between quantities. For Example, combinatorics descibe how abstract objects are combined under constraints.
2 What are your ideas about magic?
Good magic tricks have their entertainent value because they are mathematically interesting. I would say the best magic performance has strong math underpinning, whereas magic that is gimmicky has nothing in common with math (and is bad magic).
3 Describe a magic trick you have seen that impressed you.
I don't know any card tricks that use math (yet). In general, though,
"Any sufficiently advanced technology is indistinguishable from magic."
That is, technology has as its basis mathematics, and I am a tech geek! The reverse is: An idea can start out as a magic trick, such as Gilbreath Principle in cards: When two stacks are cards, one of which are in reversed sequential order, are then (riffle) shuffled together, the lower cards in one stack pushes out the complement out of the group at the top of the other stack. In math terms of permutations and sets, this intuitive idea is
Theorem. The Ultimate Gilbreath Principle. For a permutation \(\pi\) of \({1, 2, 3, . . . , N }\), the following four properties are equivalent:
- π is a Gilbreath permutation.
- For each j, the top j cards \({\pi(1), \pi(2), \pi(3), . . . , \pi(j)}\) are distinct modulo \(j\).
- For each j and k with \(kj < N\), the \(j\) cards \({\pi((k − 1)j + 1), \pi((k − 1)j + 2), \ldots,\pi(kj)}\) are distinct modulo \(j\).
- For each \(j\), the top \(j\) cards are consecutive in \(1, 2, 3, \ldots, N\).
Gilbreath shuffling has been used to describe
(1) Mandelbrot sets
(2) Knuth -> Sorting algorithm ("Improved superblock striping technique")
(3) de Bruijn -> Quasicrystal Theory, using penrose tiles.
I am impressed these connections between math and magic exist and indeed hope to explore some of the ideas listed here further in this blog!
Created: 2018-08-26 dom 22:40
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