Butterfly in the Quantum World by Indu Satija, with contributions
by Douglas Hofstadter, is the first book ever to tell the story of
the "Hofstadter butterfly", a beautiful and fascinating graph lying
at the heart of the quantum theory of matter. The butterfly came
out of a simple-sounding question: What happens if you immerse a
crystal in a magnetic field? What energies can the electrons take
on? From 1930 onwards, physicists struggled to answer this
question, until 1974, when graduate student Douglas Hofstadter
discovered that the answer was a graph consisting of nothing but
copies of itself nested down infinitely many times. This wild
mathematical object caught the physics world totally by surprise,
and it continues to mesmerize physicists and mathematicians today.
The butterfly plot is intimately related to many other important
phenomena in number theory and physics, including Apollonian
gaskets, the Foucault pendulum, quasicrystals, the quantum Hall
effect, and many more. Its story reflects the magic, the mystery,
and the simplicity of the laws of nature, and Indu Satija, in a
wonderfully personal style, relates this story, enriching it with a
vast number of lively historical anecdotes, many photographs,
beautiful visual images, and even poems, making her book a great
feast, for the eyes, for the mind and for the soul.
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