What We Cannot Know: Explorations at the Edge of Knowledge

What We Cannot Know: Explorations at the Edge of Knowledge
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‘Brilliant and fascinating. No one is better at making the recondite accessible and exciting’ Bill BrysonBritain’s most famous mathematician takes us to the edge of knowledge to show us what we cannot know.Is the universe infinite?Do we know what happened before the Big Bang?Where is human consciousness located in the brain?And are there more undiscovered particles out there, beyond the Higgs boson?In the modern world, science is king: weekly headlines proclaim the latest scientific breakthroughs and numerous mathematical problems, once indecipherable, have now been solved. But are there limits to what we can discover about our physical universe?In this very personal journey to the edges of knowledge, Marcus du Sautoy investigates how leading experts in fields from quantum physics and cosmology, to sensory perception and neuroscience, have articulated the current lie of the land. In doing so, he travels to the very boundaries of understanding, questioning contradictory stories and consulting cutting edge data.Is it possible that we will one day know everything? Or are there fields of research that will always lie beyond the bounds of human comprehension? And if so, how do we cope with living in a universe where there are things that will forever transcend our understanding?In What We Cannot Know, Marcus du Sautoy leads us on a thought-provoking expedition to the furthest reaches of modern science. Prepare to be taken to the edge of knowledge to find out if there’s anything we truly cannot know.

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Marcus Sautoy du. What We Cannot Know: Explorations at the Edge of Knowledge

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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

About the Publisher

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To my parents, who started me on my journey to the edges of knowledge

Cover

.....

This is the quest at the heart of this book. Can we identify questions or physical phenomena that will always remain beyond knowledge? If we can identify things that will remain in the gaps of knowledge, then what sort of God is this? What potency would such a concept have? Could the things we cannot know act in the world and affect our futures? Are they worthy of worship?

But first we need to know if in fact there is anything that will remain unanswered about the universe. Is there really anything we cannot know?

.....

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