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Marcus Sautoy du. What We Cannot Know: Explorations at the Edge of Knowledge
Copyright
Dedication
EDGE ZERO:The Known Unknowns
WHAT WE KNOW
THE KNOW-IT-ALL PROFESSORSHIP
WHAT WE DON’T KNOW
WHAT WE’LL NEVER KNOW
TRANSCENDENCE
1
KNOWING THE WILL OF THE GODS
FINDING THE NUMBERS IN THE DICE
AN INTERRUPTED GAME
PASCAL’S WAGER
THE MATHEMATICS OF NATURE
MATHEMATICAL SNAPSHOTS
Calculus: making sense of zero divided by zero
THE RULES OF THE GAME
NEWTON’S THEORY OF EVERYTHING
THE FATE OF THE SOLAR SYSTEM
A SMALL MISTAKE WITH BIG IMPLICATIONS
2
THE DEVIL IN THE DECIMALS
THE REVENGE OF THE GRASSHOPPER
KNOWING WHEN YOU CAN’T KNOW
Feedback equation for population dynamics
THE POLITICS OF CHAOS
THE HUMAN EQUATION
LIFE: A CHANCE THROW OF THE DICE?
WHERE DID WE COME FROM?
THE FRACTAL TREE OF LIFE
A BUTTERFLY CALLED MERCURY
INFINITE COMPLEXITY
KNOWING MY DICE
DOES GOD PLAY DICE?
ON THE EDGE OF CHAOS
3
ZOOMING IN
THE MUSIC OF THE SPHERES
NUMBERS AT THE EDGE
IRRATIONAL EXUBERANCE
THE HARMONY OF TINY SPHERES
ATOMIC ALGEBRA
RECIPE FOR MAKING A DICE
POLLEN PING-PONG
PULLING APART THE ATOM
THE NEXT LAYER
TISSUE PAPER BALLISTICS
4
THE PARTICLE MENAGERIE
MAPPING THE PARTICLE ZOO
THERE IS NO EXQUISITE BEAUTY WITHOUT STRANGENESS
SYMMETRICAL ENLIGHTENMENT
SYMMETRY WITH MANY FACES
QUARKS: THE MISSING LAST LAYER?
FROM FANTASY TO REALITY
COWBOYS AND QUARKS
THE CELLO OR THE TRUMPET?
5
RANDOM RADIATION
WAVE OR PARTICLE?
COOKING UP A CACOPHONY OF WAVES
KICKING OUT ELECTRONS: THE PHOTOELECTRIC EFFECT
PHOTON BILLIARDS
EXPERIMENTING WITH ELECTRONS
THE SCHIZOPHRENIC ELECTRON
QUANTUM ANTHROPOLOGY
MULTIPLE HISTORIES
SPLIT PERSONALITY
ONE INPUT, MULTIPLE OUTPUTS
6
QUANTUM CARPETS
QUANTIFYING UNCERTAINTY
LIMITS TO KNOWLEDGE AT THE SMALL SCALE
OBSERVATION IS CREATION
A HIDDEN MACHINE
THE VEGETARIAN BUTCHER
SOMETHING OUT OF NOTHING
ZERO EQUALS ONE MINUS ONE
7
TRIANGULAR TELESCOPES
WRESTLING WITH INFINITY
HOW FAR CAN YOU SEE?
DISCOVERING A PLANET WITH THE POINT OF YOUR PEN
COSMIC SPEED LIMIT
THE STARS IN OUR NEIGHBOURHOOD
TWINKLE, TWINKLE LITTLE STAR
A HUGE GAME OF ASTEROIDS
COSMIC MAGELLANS
8
THE UNIVERSE THROUGH RED-TINTED SPECTACLES
ANT AND THE BAND
REWINDING THE UNIVERSE
THE STARS ARE GOING OUT
COSMIC FINGERPRINTS
MULTIVERSE
DIALLING UP DIFFERENT UNIVERSES
GUESS THE NEXT NUMBER
Why 31 is the next number …
IS THERE ANYONE OUT THERE?
BLACK SWANS, BIASES AND THE BACK OF THE BOOK
MAKING CHOICES
Why there could be infinitely many copies of you reading this book
CAN WE REALLY EVER KNOW WE WON’T KNOW?
9
WHAT IS TIME?
TORCHES ON TRAINS
Relativistic formula for combining speeds
SLOWING DOWN TIME
SPEED UP AND LIVE LONGER
RELATIVITY DOGS
SHAPE OF TIME
WHY SKYSCRAPERS AREN’T GOOD FOR YOU
ASYMMETRICAL TWINS
10
HORIZONS BEYOND WHICH WE CANNOT KNOW
SINGULARITIES
THE UNKNOWN HIDING INSIDE A BLACK HOLE
THE ULTIMATE PAPER SHREDDER
NOT-SO-BLACK BLACK HOLES
FUZZY EDGES
JOINING UP THE PAST AND THE FUTURE
A MODERN-DAY GALILEO
OUTSIDE OF TIME
TIME: AN EXPRESSION OF INCOMPLETENESS OF KNOWLEDGE
11
ARE YOU THINKING WHAT I’M THINKING?
WHERE IS CONSCIOUSNESS?
CUTTING CONSCIOUSNESS IN TWO
SWITCHING ME ON AND OFF
NEURAL TELESCOPES
IS MY CAT CONSCIOUS?
TRICKS OF THE MIND
THE JENNIFER ANISTON NEURON
OUT-OF-BODY EXPERIENCES
MIND/BODY
12
AM I IN CONTROL?
THE TIDE COMES IN
MAKING ‘ME’ MATHEMATICS
IS THE INTERNET CONSCIOUS?
SKYPING CONSCIOUSNESS
MAKING MINDS
DOWNLOADING MY CONSCIOUSNESS
ZOMBIELAND
13
SCIENCE V. MATHS
PROOF: THE PATH TO TRUTH
NUMBERS AT THE EDGE
Proof of the irrationality of the square root of 2
PROVABLY IMPOSSIBLE
RUNNING OUT OF NEURONS
PARALLEL UNIVERSES
WHAT IS THE NAME OF THIS SECTION?
THE NEXT SENTENCE IS FALSE
A JOKE
14
STARING OFF INTO INFINITY
INFINITY TAMED
UNCOUNTABLY INFINITE
NOW YOU SEE IT, NOW YOU DON’T
YES AND NO
WHAT WE CANNOT KNOW
IS GOD AN IMAGINARY NUMBER?
DO I OWN AN ODD OR EVEN NUMBER OF DICE?
CAN WE KNOW ANYTHING?
HERE BE DRAGONS
FURTHER READING
INDEX
ACKNOWLEDGEMENTS
ILLUSTRATION CREDITS
EDGE 1
EDGE 2
EDGE 3
EDGE 5
EDGE 6
Also by Marcus du Sautoy
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