Hans Freudenthal (1905–1990)

Indeholder "Introduction", "1. Measuring the world", " Surveying", " Triangulation", " The size of the earth", " Astronomical distances", " Life on a curved surface", " The curvature of space", "2. Ad infinitum", " Counting", " Natural numbers", " Prime numbers", " Rational and irrational numbers", "3. What computers can do", " Dyadic system", " Nim", " As quickly as you can", " Wait a moment", " Automation", " Controls and memory", " The language of holes", " Processing", " Truth tables", " Machines which play games", " Matching pennies", " Monte Carlo methods", " Causal machines", " What can causal machines do?", " A survey of the class of Turing machines", " A sequence which cannot be produced by any machine", " Universal machine", " Chess automata", " Are thinking machines possible?", "4. The ABC of life", " The genetic code", " Space-free codes", " Solution of a problem", " Conclusions", "5. The art of drawing badly", " Distorting letters", " Geometry and topology", " Maps", " Examples of surfaces", " Surfaces in general", " Manifolds", " Mappings of a circle", " Degree of a mapping", " A second definition of degree", " Mappings of spheres", " A remarkable curve", "6. Give me a place to stand and I will move the earth", " The lever", " The plane", " Barycentric coordinates", " Linear programming", "7. The world in a mirror", " Reflections in the world", " Reflections in the plane", " Composition of reflections in parallel straight lines", " Translations", " Composition of reflections in intersecting straight lines", " Composition of rotations", " Composition of a rotation and a translation", " Arbitrary products of reflections", " Mappings", " Groups", " Congruences", " Displacements", " In three dimensions", " Orientation", "Acknowledgments", "Index".

Ideen er at vise matematik frem som et demonstrationsforsøg i fysik. Uden ønske om at skulle gøre tilskueren til matematiker. Hvert kapitel kan læses for sig selv uden reference til de andre kapitler.

Her er noget om opmåling, topologi, Turing-maskiner, at der er uendeligt mange primtal, også af formen 4n-1 og hvordan man checker ind på Hilberts hotel.
Og der er fine overvejelser om skak og om at de tommelfingerregler, man lærer for tiden, måske faktisk er forkerte. Jeg kommer til at tænke på Alpha Zero og dens måde at spille skak på! Nogle gange fem bønder nede i materiel, men til gengæld kan modstanderen ikke flytte nogle af sine og de spærrer alle officererne inde.… (mehr)