Zero
The Babylonians invented it, the Greeks banned it, the Hindus worshiped it, and the Church used it to fend off heretics. Now it threatens the foundations of modern physics. For centuries the power of zero savored of the demonic; once harnessed, it became the most important tool in mathematics. For zero, infinity’s twin, is not like other numbers. It is both nothing and everything. In Zero, Science Journalist Charles Seife follows this innocent-looking number from its birth as an Eastern philosophical concept to its struggle for acceptance in Europe, its rise and transcendence in the West, and its ever-present threat to modern physics. Here are the legendary thinkers—from Pythagoras to Newton to Heisenberg, from the Kabalists to today’s astrophysicists—who have tried to understand it and whose clashes shook the foundations of philosophy, science, mathematics, and religion. Zero has pitted East against West and faith against reason, and its intransigence persists in the dark core of a black hole and the brilliant flash of the Big Bang. Today, zero lies at the heart of one of the biggest scientific controversies of all time: the quest for a theory of everything.
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11recommend
15mentions
15people
2012–2024years
73% recommend27% neutral
Mentions per year
What Hacker News says
- I’m in the process of reading this article, but I recently read Zero: The Biography of a Dangerous Idea by Charles Seife (which is a great book) so I feel like I can explain:
The Greeks were ideologically opposed to the number zero. Aristotle outright refuses to acknowledge the existence of zero and of infinity. The Greeks were aware of the idea of zero, and they even used zero when they calculated using the Babylonian number system (which used zero as a placeholder number,) but they always converted the numbers back into their own system, and stubbornly refused to acknowledge its existence.
The fact that the Greeks saw geometry and math as interchangeable was their weakness here. There’s no way to represent the number 0 geometrically, but the Greeks weren’t gonna give up their belief in Geometry because it provided them with social and political power.
Pythagoras and Aristotle believed in a religious philosophy with logos at the center. Logos can be translated as “thought” or “word” (as it is in the Bible) or it can be translated as “ratio.” This is because they saw all these things as one (the Latin translation of the Greek word “logos” is “ratio.”) The ratio of numbers was thought the be the underlying mechanism that proved the order of the universe (which naturally saw the nobility as orderly and the peasantry as chaotic). This was a profoundly powerful sociopolitical tool that ended up spreading all across the world because Aristotles student just happened to be the greatest conqueror of the era: Alexander The Great.
Anything that threatened the philosophy of logos was suppressed, violently. Hippassus and Zeno were both murdered for the crime of talking about irrational numbers and infinity. Zero was one of these threats. 1:0 = infinity, 10:0 = infinity, anything:0 = infinity. This was not logos and therefore it was suppressed.
This philosophy extended beyond mathematics into the realm of astronomy and, weirdly enough, music (at the time, Pythagoras was actually most famous for his discovery of the golden ratio using an instrument called the monochord, which is a legend that seems to be false but nonetheless made him very famous.) This astronomical belief system was then later attributed to Ptolemy. This philosophy then was transplanted into Christian theology, and it took centuries for the monks to accept the existence of zero and infinity as a result. We even have cases of religious figures persecuting mathematicians about zero and infinity as late as the 1800s.
- "Zero: Biography of a Dangerous Idea" by Charles Seife is a great read you can finish in a few sittings.
- > For a long time the idea of 0 wasn't natural.
Yes! A long time ago I read a wonderful little book on just this bit of history:
https://www.amazon.com/Zero-Biography-Dangerous-Charles-Seif...
- Likely listed elsewhere, from the article for convenience:
Zero: The Biography of a Dangerous Idea - Charles Seife
Measurement - Paul Lockhart
Prelude to Mathematics - W. W. Sawyer
Proofs from The Book - Aigner and Ziegler
The Joy of x - Steven Strogatz
Things to Make and Do in the Fourth Dimension - Matt Parker
What is Mathematics? - Courant and Robbins
A History of PI - Petr Beckmann
An Imaginary Tale - Paul Nahin
e: The Story of a Number - Eli Maor
Imagining Numbers - Barry Mazur
Journey Through Genius - William Dunham
Prime Obsession - John Derbyshire
- Highly recommend "Zero: The Biography of a Dangerous Idea" [1] if you're interested in learning more about the number zero.
[1] https://www.amazon.com/Zero-Biography-Dangerous-Charles-Seif...
- I broke up my list into cultural (that is, about the people, history, etc), popular (that is, not aimed at a student or an expert), and texts.
CULTURAL
Einstein - Essays in Humanism
Frayn - Copenhagen
Feynman - Surely You're Joking, Mr. Feynman!
Feynman - What Do You Care What Other People Think?
de Grasse Tyson - Death by Black Hole
Hoffman - The Man Who Loved Only Numbers
Kaiser - Drawing Theories Apart
Kaiser - How the Hippied Saved Physics
Macaulay - The Way Things Work
Paulos - Innumeracy
Sagan - Cosmos
Sagan - Broca's Brain
Sagan - The Demon-Haunted World
Salam - Science in the Third World
Seife - Zero
Weisskopf - The Joy of Insight
POPULAR
Deutsch - The Beginning of Infinity (especially his explanation about fungibility in quantum mechanics)
Feynman - The Meaning of It All
Feynman - Lectures on Physics
Feynman and Weinberg - Elementary Particles and the Laws of Physics
Galison - Einstein's Clocks, Poincaré's Maps
Gamow - One, Two, Three... Infinity
Hadamard - Psychology of Invention in the Mathematical Field
Hawking - A Brief History of Time
Hofstadter - Gödel Escher Bach
Heisenberg - Physics and Philosophy: The Revolution in Modern Science
Polya - How to Solve It
Schrödinger - What is Life?
Susskind - The Theoretical Minimum
Susskind - Quantum Mechanics
Wallace - Everything And More
Weinberg - The First Three Minutes
Wiener - God & Golem, Inc.
TEXTS
Aaronson - Quantum Computing with Democritus (but I don't have a version with me in the acknowledgements https://books.google.com/books?id=jRGfhSoFx0oC&lpg=PR31&ots=... )
Abelson and Sussman - SICP
Abrikosov, Gorkov, and Dzyaloshinski - Methods of Quantum Field Theory in Statistical Physics
Cohen-Tannoudji - Quantum Mechanics (1+2)
Dirac - Lectures on Quantum Mechanics
Eddington - Space, Time, and Gravitation
Feynman - Feynman's Thesis
Feynman and Hibbs - Quantum Mechanics and Path Integrals
Fermi - Thermodynamics
Gattringer & Lang - Quantum Chromodynamics on the Lattice
Goldstein - Classical Mechanics (the old version, NOT with Poole and Safko)
Griffiths - Introduction to Electrodynamics
Griffiths - Introduction to Quantum Mechanics
Jackson - Classical Electrodynamics (2nd edition---the last one entirely in CGS---is preferable)
Kleppner and Kolenkow - An Introduction to Mechanics
Landau and Lifshitz - any book in this series
Nielsen and Chuang - Quantum Computation and Quantum Information
Pauli - Selected Topics in Field Quantization
Peskin & Schroeder - An Introduction to Quantum Field Theory
Purcell - Electricity and Magnetism
Ryden - Introduction to Cosmology
Sakurai - Modern Quantum Mechanics (up to chapter 5, after which Sakurai dies and the editors put his notes together)
Sussman and Wisdom - Structure and Interpretation of Classical Mechanics
Sipser - Introduction to the Theory of Computation
Thorne - Black Holes & Time Warps
Thouless - The Quantum Mechanics of Many-Body Systems
Weinberg - The Quantum Theory of Fields I, II, and III
Zee - Quantum Field Theory in a Nutshell
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