Understanding science: what we cannot know
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Contents

  • Introduction and guidance
  • What is a badged course?
    • How to get a badge
  • Introduction
  • 1 Chance
    • 1.1 Dice rolls and probability
    • 1.2 Adding more dice to the rolls
    • 1.3 Problem of points
    • 1.4 Pascal’s triangle
    • 1.5 Close to certainty
  • 2 Chaos
    • 2.1 Predicting the dice roll
    • 2.2 Laplace’s demon
    • 2.3 Is the solar system stable?
    • 2.4 Poincaré’s error
    • 2.5 Chaos theory
    • 2.6 Weather forecasting
    • 2.7 Double pendula
    • 2.8 One more roll of the dice
  • 3 This week’s quiz
  • 4 Summary of Week 1
  • Introduction
  • 1 What is matter?
  • 2 Symmetry
    • 2.1 Rotations of a triangle
    • 2.2 Reflections of a triangle
    • 2.3 Combining rotations and reflections
    • 2.4 When order matters…
  • 3 Symmetries in particle physics
    • 3.1 Elementary particles
    • 3.2 Quarks
    • 3.3 Forces and interactions
    • 3.4 The strong force
  • 4 This week’s quiz
  • 5 Summary of Week 2
  • Introduction
  • 1 The gaps in classical physics
  • 2 Waves or particles?
    • 2.1 Water waves
    • 2.2 Sound waves
    • 2.3 Electromagnetic waves
    • 2.4 Wave motion
  • 3 Quantum theory
    • 3.1 Quantum waves
    • 3.2 Radioactive decay
    • 3.3 Schrödinger’s cat
    • 3.4 Heisenberg’s uncertainty principle
    • 3.5 Quantum fluctuations
    • 3.6 Planck time and length
  • 4 This week’s quiz
  • 5 Summary of Week 3
  • Introduction
  • 1 Our place in space
  • 2 How far can we see?
  • 3 The observable universe
  • 4 The most distant objects
  • 5 Light from the edge
  • 6 Beyond the edge
  • 7 The wider universe
  • 8 The future of the observable universe
  • 9 Is the universe finite or infinite?
    • 9.1 Curved space
    • 9.2 What if the universe were finite?
  • 10 This week’s quiz
  • 11 Summary of Week 4
  • Introduction
  • 1 What is time?
  • 2 How time is measured
  • 3 Speed of light revisited
  • 4 Your time is not my time
  • 5 Curved space and gravity
  • 6 Time and gravity
  • 7 Black holes
    • 7.1 A picture of a black hole
    • 7.2 Falling into a black hole
  • 8 The end of time?
  • 9 This week’s quiz
  • 10 Summary of Week 5
  • Introduction
  • 1 What is consciousness?
    • 1.1 What are we actually talking about?
    • 1.2 The ‘hard problem of consciousness’
  • 2 Inside the brain
    • 2.1 Anatomy of the brain
    • 2.2 Neurons and neurotransmitters
  • 3 Studying the brain
    • 3.1 Microscopy and silver nitrate staining
    • 3.2 Technological advances
      • EEG
      • Imaging
      • Artificially stimulating the brain
    • 3.3 Into the future
    • 3.4 Brain study summary
  • 4 The brain at work
  • 5 Who is conscious?
    • 5.1 How conscious are we?
    • 5.2 Animals and babies
    • 5.3 Machines
    • 5.4 Neural networks
    • 5.5 Artificial neurons and neuromorphic computing
  • 6 Theories of consciousness
    • 6.1 An intrinsic property (Integrated Information Theory)
    • 6.2 The spotlight of consciousness (Global Workspace Theory)
    • 6.3 Studying consciousness in the laboratory
    • 6.4 Why might we never have an explanation for consciousness?
  • 7 This week’s quiz
  • 8 Summary of Week 6
  • Introduction
  • 1 Picturing infinity
  • 2 Hilbert’s Infinite Hotel
  • 3 Measuring infinity
  • 4 Proofs
    • 4.1 Primes
    • 4.2 Fractions
  • 5 The infinitely small
    • 5.1 Achilles and the Tortoise
    • 5.2 Dividing into infinitely many pieces
    • 5.3 Decreasing sequences
  • 6 The paradox of fractals
  • 7 This week’s quiz
  • 8 Summary of Week 7
  • Introduction
  • 1 Mathematics
  • 2 A brief excursion into philosophy
  • 3 What is a theory?
  • 4 Lost in maths?
  • 5 The limitations of mathematics
  • 6 Gödel’s incompleteness theorems
  • 7 This week’s quiz
  • 8 Summary of Week 8
  • 9 Conclusion: what we cannot know
  • Where next?
  • Tell us what you think
  • References
  • Further Reading
  • Acknowledgements

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