Understanding science: 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?This free course, Understanding science: what we cannot know, investigates the boundaries of our understanding across numerous scientific fields. It asks whether it’s possible that we will one day know everything, or if some knowledge will always lie beyond the bounds of human comprehension.This course has been created in collaboration with Marcus du Sautoy, Simonyi Professor for the Public Understanding of Science and author of What We Cannot Know. Here’s Marcus to introduce the course.Transcript This OpenLearn science course was produced with the kind support of Dangoor Education, the educational arm of The Exilarch's Foundation. Enrolling on the course will give you the opportunity to earn an Open University digital badge. Badges are not accredited by The Open University but they’re a great way to demonstrate your interest in the subject and commitment to your career, and to provide evidence of continuing professional development.Once you are signed in, you can manage your digital badges online from My OpenLearn. In addition, you can download and print your OpenLearn statement of participation – which also displays your Open University badge.The Open University would really appreciate a few minutes of your time to tell us about yourself and your expectations for the course before you begin, in our start-of-course survey. Once you complete the course we would also value your feedback and suggestions for future improvement, in our end-of-course survey. Participation will be completely confidential and we will not pass on your details to others. This course is accredited by the CPD Standards Office. It can be used to provide evidence of continuing professional development and on successful completion of the course you will be awarded 24 CPD points. Evidence of your CPD achievement is provided on the free Statement of Participation awarded on completion.Anyone wishing to provide evidence of their enrolment on this course is able to do so by sharing their Activity Record on their OpenLearn Profile, which is available before completion of the course and earning of the Statement of Participation.

• Introduction and guidance
• Introduction and guidance
• What is a badged course?
• How to get a badge
• Acknowledgements
• Week1Week 1: Chance and chaos
• 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
• References
• Acknowledgements
• Week2Week 2: Particle physics
• 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
• Acknowledgements
• Week3Week 3: Quantum physics
• 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
• Acknowledgements
• Week4Week 4: Space
• 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
• Acknowledgements
• Week5Week 5: Time
• 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
• References
• Acknowledgements
• Week6Week 6: Consciousness
• 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
• Further reading
• Acknowledgements
• Week7Week 7: Infinity
• 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
• Acknowledgements
• Week8Week 8: What can we know?
• 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
• Acknowledgements