Acknowledgements
This free course was written by June Barrow-Green, Katie Chicot, Uwe Grimm, Tony Jones and Amanda Smith. It is adapted from the book What We Cannot Know by Marcus du Sautoy.
Except for third party materials and otherwise stated (see terms and conditions), this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 Licence.
The material acknowledged below (and within the course) is Proprietary and used under licence (not subject to Creative Commons Licence). Grateful acknowledgement is made to the following sources for permission to reproduce material in this free course:
Images
Introduction and guidance
Course image: adapted from https://www.pexels.com/@marek-piwnicki-3907296
Week 1
Figure 1:
(a) Blaise Pascal (1623–1662): https://commons.wikimedia.org/wiki/File:Pascal-old.png
(b) Pierre de Fermat (1607–1665): https://commons.wikimedia.org/wiki/File:Pierre_de_Fermat.jpg
Figure 2: VitalyEdush/Getty Images
Figure 5:
(a) Isaac Newton (1643–1727): https://commons.wikimedia.org/wiki/File:Portrait_of_Sir_Isaac_Newton,_1689.jpg
(b) Gottfried Leibniz (1646–1716): https://commons.wikimedia.org/wiki/File:Christoph_Bernhard_Francke_-_Bildnis_des_Philosophen_Leibniz_(ca._1695).jpg
Figure 6: brgfx/Freepik
Figure 7: Mary Somerville (1780–1872): https://commons.wikimedia.org/wiki/File:Thomas_Phillips_-_Mary_Fairfax,_Mrs_William_Somerville,_1780_-_1872._Writer_on_science_-_Google_Art_Project.jpg
Figure 8: Henri Poincaré (1854–1912) Photograph: Smithsonian Institution from United States: https://commons.wikimedia.org/wiki/File:Portrait_of_Henri_Poincar%C3%A9_(1854-1912),_Mathematician_(2551042945).jpg
Figure 9: The trajectory of a third body interacting with a large mass (Earth, left) and a small mass (Moon, right) from July 19, 2019 by DAVID D. NOLTE: Figure 1 from Getting Armstrong, Aldrin and Collins Home from the Moon: Apollo 11 and the Three-Body Problem: https://galileo-unbound.blog/2019/07/19/getting-armstrong-aldrin-and-collins-home-from-the-moon-apollo-11-and-the-three-body-problem
Week 2
Figure 1: Periodic table of elements. Humdan/Shutterstock Images
Figure 2: Particle accelerator (c) Jason Schwartz: https://commons.wikimedia.org/wiki/File:HERA_Tunnel.JPG https://creativecommons.org/licenses/by-sa/3.0/deed.en
Figure 3: Patterns in nature:
(a) apis florea nest, Sean Hoyland: https://commons.wikimedia.org/wiki/File:Apis_florea_nest_closeup2.jpg;
(b) chrysanthemum flower, monika1607/pixabay;
(c) nautilus spiral, Rpsycho/Getty Images;
(d) snowflake, Alexey Kljatov in Flickr https://creativecommons.org/licenses/by/2.0
Figures 7 and 8: Proton/neutron quark structure: Jacek rybak/Category:CC-BY-SA-4.0 - Wikimedia Commons
Week 3
Figure 1:
(a) Albert Einstein (1879–1955): https://en.wikipedia.org/wiki/File:Albert_Einstein_(Nobel).png;
(b) Robert Millikan (1868–1953),: https://commons.wikimedia.org/wiki/File:Robert_Andrews_Millikan_1920s.jpg
Figures 2 and 3: Diagram of a wave (not labelled and labelled): NOAA U.S. National Oceanic and Atmospheric Administration
Figure 4: Animation of a sonic boom: Jacopo Bertolotti/Creative Commons CC0 1.0 https://commons.wikimedia.org/wiki/File:Sonicboom_animation.gif
Figure 5: The electromagnetic spectrum: Penubag/ Creative Commons — Attribution-ShareAlike 3.0 Unported — CC BY-SA 3.0.5 https://commons.wikimedia.org/wiki/File:Electromagnetic-Spectrum.png
Figure 9: A half-life simulation: Sbyrnes321: https://commons.wikimedia.org/wiki/File:Halflife-sim.gif
Figure 10: Casimir effect: Emok: https://commons.wikimedia.org/wiki/File:Casimir_plates.svg
Week 4
Figure 1: The Milky Way: Xing-Wu Zheng & Mark Reid BeSSeL/NJU/CFA Copyright © 2019 by Xing-Wu Zheng and Mark Reid
Figure 2: Superclusters: Richard Powell: https://commons.wikimedia.org/wiki/File:Superclusters_atlasoftheuniverse.gif Creative Commons — Attribution-ShareAlike 2.5 Generic — CC BY-SA 2.5
Figure 3: M31 Andromeda: Luca Argalia: https://www.flickr.com/photos/skiwalker79/5309249905/ //creativecommons.org/licenses/by-nc-sa/2.0/
Figure 4: Screenshot of the Stellarium Web interface: Fabien Chéreau (creator of Stellarium) / Stellarium developer group https://stellarium-web.org/
Figure 6: The Extreme Deep Field: NASA, ESA, G. Illingworth, D. Magee, and P. Oesch (University of California, Santa Cruz), R. Bouwens (Leiden University), and the HUDF09 Team
Figure 7: A map of the CMBR: European Space Agency (ESA) and the Planck Collaboration
Figure 10: Positive curvature: Naypong/Getty Images
Figure 11: Negative curvature: Marat Musabirov/Getty Images Plus
Week 5
Figure 1: National Physical Laboratory (NPL): https://www.npl.co.uk/famous-faces/louis-essen
Figure 5: A photographic negative of the eclipse of 1919: https://commons.wikimedia.org/wiki/File:1919_eclipse_positive.jpg
Figure 6: Space flowing into a black hole: Courtesy Professor Andrew Hamilton https://jila.colorado.edu/~ajsh/insidebh/waterfall.html
Figure 7: Cygnus A: National Radio Astronomy Observatory (NRAO) / Associated Universities, Inc. (AU): https://astronomynow.com/2016/10/25/hotspots-in-cygnus-a-an-active-galactic-nucleus
Figure 8: The black hole in the centre of the galaxy M87; Event Horizon Telescope Collaboration: https://eventhorizontelescope.org https://creativecommons.org/licenses/by/4.0/
Figure 9: The process of ‘spaghettification’ NASA / Laura A. Whitlock, Kara C. Granger, Jane D. Mahon: https://en.wikipedia.org/wiki/File:Spaghettification_(from_NASA%27s_Imagine_the_Universe!)
Week 6
Figure 1:
(a) the human brain viewed from the side © The Open University;
(b) in a photograph from above © Unidentified;
(c) Left: a cut-away view through the middle of the brain © The Open University; Right: A post-mortem human brain sample with top layer removed: Dr. Terence Williams, University of Iowa.
Figure 5: Broca’s area (shown in red): Polygon data were generated by Database Center for Life Science (DBCLS) https://creativecommons.org/licenses/by-sa/2.1/jp/deed.en
Figure 7: ‘Golgi stained’ brain tissue viewed under a microscope:
(a) The OU;
(b) Anna Kamitakahara and Richard Simerly, PhD, from The Saban Research Institute of Children’s Hospital Los Angeles
Figure 8: Neurons in ‘Golgi stained’ brain tissue (drawings by Santiago Ramón y Cajal):
(a) Santiago Ramón y Cajal / public domain: https://commons.wikimedia.org/wiki/File:Purkinje_cell_by_Cajal.png;
(b) Santiago Ramon y Cajal / public domain: https://en.wikipedia.org/wiki/File:Cajal_cortex_drawings.png
Figure 10: An electron micrograph showing synapses. In Lodish et al., 4th edition
Figure 11:
(a): EEG headcap, used to apply electrodes to the surface of the head; Min Jing/Shutterstock;
(b): different types of brain wave activity measured using EEG: ScienceDirect Technological Basics of EEG Recording and Operation of Apparatus: Priyanka A. Abhang, Suresh C. Mehrotra, in Introduction to EEG- and Speech-Based Emotion Recognition, 2016 Figure 2.1. Brain wave samples with dominant frequencies belonging to beta, alpha, theta, and delta bands and gamma waves.
Figure 12:
(a) fMRI scanner, courtesy: Neuroimaging Core, Center for Integrative Neuroscience, University of Nevada, Reno;
(b) fMRI scan Dr Krish Singh
Figure 13: fMRI scans showing brain activity while tasks are imagined: Courtesy: Adrian M. Owen, OBE, PhD
Figure 14: TMS: Mayo Foundation for Medical Education and Research
Figure 15: The roundworm C. elegans: https://commons.wikimedia.org/wiki/File:CrawlingCelegans.gif https://creativecommons.org/licenses/by-sa/3.0/deed.en
Figure 16: The roundworm connectome: from: Controlling the C. elegans neural network (1c) from authors of Nature article: Gang Yan, Petra E. Vértes, Emma K. Towlson, Yee Lian Chew, Denise S. Walker, William R. Schafer & Albert-László Barabási
Figure 17: Tracing neurons: courtesy: Dr. Juan Burrone and Prof. Venkatesh Murthy
Figure 18: Artificial neurons: https://www.bath.ac.uk/announcements/world-first-as-artificial-neurons-developed-to-cure-chronic-diseases / University of Bath
Figure 19: A ‘signature of consciousness’ – patterns of brain activity recorded as a response to conscious (left) and non-conscious (right) visual stimuli (Dehaene and Changeux, 2011) Dehaene, S. and Changeux, J.P. (2011) ‘Experimental and theoretical approaches to conscious processing’, Neuron, 70(2), pp. 200–227.
Week 7
Figure 1: The Milky Way: AstroAnthony https://creativecommons.org/licenses/by/4.0/deed.en https://commons.wikimedia.org/wiki/File:Milky_way_nebula.jpg
Figure 2:
(a) Reinhard Genzel: https://commons.wikimedia.org/wiki/File:Reinhard_Genzel.jpg https://creativecommons.org/licenses/by-sa/3.0/deed.en;
(b) Andrea Ghez: Sipa US/Alamy Stock Photo;
(c) Sir Roger Penrose: Biswarup Ganguly https://commons.wikimedia.org/wiki/File:Roger_Penrose_9552.JPG https://creativecommons.org/licenses/by/3.0/deed.en
Figure 3: David Hilbert (1862–1943) Image: University of Göttingen
Figure 6: Fractions between fractions: adapted from https://www.basic-mathematics.com/density-property.html Basic-mathematics.com
Figure 7: Fraction grid: Cronholm144 https://commons.wikimedia.org/wiki/File:Diagonal_argument.svg https://creativecommons.org/licenses/by-sa/3.0/deed.en
Figure 9: Dividing a chocolate bar: Hyacinth https://commons.wikimedia.org/wiki/File:Eye_of_Horus_square.png https://creativecommons.org/licenses/by-sa/3.0/deed.en
Figure 10: Fractals:
(a) Romanesco broccoli: Ivar Leidus https://en.wikipedia.org/wiki/File:Romanesco_broccoli_(Brassica_oleracea).jpg https://creativecommons.org/licenses/by-sa/4.0/deed.en;
(b) lightning strike: José Eugenio Gómez Rodríguez https://www.flickr.com/photos/jegomezr/2926143475 https://creativecommons.org/licenses/by-nc-sa/2.0/;
(c) partial view of the Mandelbrot set: Wolfgang Beye https://en.wikipedia.org/wiki/File:Mandel_zoom_08_satellite_antenna.jpg https://creativecommons.org/licenses/by-sa/2.5/deed.en;
(d) an abstract computer generated fractal: Diep Hoang Hai/Shutterstock.com
Figure 11: Russian dolls: demidoffaleks/Getty Images
Figure 12: Koch snowflake: António Miguel de Campos https://commons.wikimedia.org/wiki/File:Von_Koch_curve.gif
Figure 13: Sierpinski triangle: Beojan Stanislaus https://commons.wikimedia.org/wiki/File:Sierpinski_triangle.svg
Week 8
Figure 1: Eugene Wigner (1902–1995) © unknown
Figure 2: Neptune – a mathematical discovery: NASA/JPL/Voyager-ISS/Justin Cowart
Figure 3: Immanuel Kant (1724–1804): https://commons.wikimedia.org/wiki/File:Kant_gemaelde_3.jpg
Figure 4: Sabine Hossfelder: File:Sabine Hossenfelder.jpg – Wikimedia Commons – Creative Commons — Attribution-ShareAlike 4.0 International — CC BY-SA 4.0
Figure 5: Kurt Gödel (1906–1978): https://www.flickr.com/photos/levanrami/24246848265 – public domain
Figure 6: What can we know? LEOcrafts/Getty Images
Audio/Video
Week 1
Video 4: The restricted three-body problem by Jim Belk: https://www.youtube.com/watch?v=jarcgP1rRWs Creative Commons — Attribution 3.0 Unported — CC BY 3.0
Week 2
Video 2: Voyage into the world: Daniel Dominguez/CERN
Week 4
Video 2: Timeline of our understanding © The Open University (2022) with thanks to the following: NASA/MSFC/Meteoroid Environment Office/Bill Cooke; NASA https://commons.wikimedia.org/wiki/File:COBE_cmb_fluctuations.png; G. Hüdepohl (atacamaphoto.com)/ESO https://www.eso.org/public/outreach/copyright/; Credit: NASA, ESA, A. Zitrin (California Institute of Technology), and J. Lotz, M. Mountain, A. Koekemoer, and the HFF Team (STScI) https://creativecommons.org/licenses/by/2.0/deed.en; Alfredo Garcia Saz/ Alamy Stock Photo; NASA https://commons.wikimedia.org/wiki/File:Horn_Antenna-in_Holmdel,_New_Jersey.jpeg; Credit: ESA/Hubble & NASA; https://commons.wikimedia.org/wiki/File:Milky_Way_galaxy1.jpg; ESO/S. Brunier https://creativecommons.org/licenses/by/4.0/; NASA Goddard Space Flight Center from Greenbelt, MD, USA https://creativecommons.org/licenses/by/2.0/
Video 3: The size of the universe © The Open University
Week 5
Video 7: Wonders of the Universe – Black Holes; BBC series: Wonders of the Universe. Episode title: Falling. BBC2 © BBC
Week 6
Video 5: Neuron networks viktorov.pro/Shutterstock
Video 6: How neurons communicate: Creative Commons — Attribution-NonCommercial 4.0 International — CC BY-NC 4.0. https://www.brainfacts.org/core-concepts/how-neurons-communicate BrainFacts.org
Video 8: Brain wiring: courtesy: National Institute of Mental Health (NIMH): https://www.nimh.nih.gov/
Video 9: The Rubber Hand Illusion, Horizon, BBC 2 © BBC
Video 11: Neural network simulation: Courtesy Denis Dmitriev: https://www.cybercontrols.org
Week 7
Video 4: Fractals in animation. Clip from BBC Two series from 2011. Marcus du Sautoy interviews Loren Carpenter. Collaboration with The Open University © BBC (2011)
Every effort has been made to contact copyright owners. If any have been inadvertently overlooked, the publishers will be pleased to make the necessary arrangements at the first opportunity.
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