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21 " Let us weigh the gain and the loss in wagering that God is [exists]. Let us estimate these two chances. If you gain, you gain all; if you lose, you lose nothing. Wager, then, without hesitation that He is. . . There is here an infinity of an infinitely happy life to gain, a chance of gain against a finite number of chances of loss, and what you stake is finite. And so our proposition is of infinite force, when there is the finite to stake in a game where there are equal risks of gain and of loss, and the infinite to gain. "
― Ian Stewart , In Pursuit of the Unknown: 17 Equations That Changed the World
22 " En realidad, una de las grandes fortalezas de la ciencia es la habilidad para inferir cosas que no podemos observar directamente a partir de las que sí podemos. "
― Ian Stewart , Calculating the Cosmos: How Mathematics Unveils the Universe
23 " Why resort to welfare cuts when you could aim more accurately at what you claim to be the real problem: intelligence itself? Why not improve education? Indeed, why aim your policy at increasing intelligence at all? There are many other desirable human traits. Why not reduce gullibility, aggressiveness, or greed? "
24 " This is rather an awe-inspiring statement to get out of a straightforward uniqueness theorem in mathematics. "
― Ian Stewart , Does God Play Dice?: The New Mathematics of Chaos
25 " Even today, women are generally under-represented in mathematics and science, but it’s no longer socially acceptable to attribute this to differences in ability or mentality, as several prominent men have discovered to their dismay. Nor is there a shred of evidence to support those views. "
― Ian Stewart , Significant Figures: The Lives and Work of Great Mathematicians
26 " Hilbert started talking about past lectures at the Club, saying that the quality had generally declined over the years. In his day, he said, people really thought about content and presentation, but nowadays young people usually gave poor talks. "
27 " This is Lorenz’s famous (and widely misunderstood) butterfly effect: a flap of a butterfly’s wing can cause a hurricane a month later, halfway round the world.If you think that sounds implausible, I don’t blame you. It’s true, but only in a very special sense. The main potential source of misunderstanding is the word ‘cause’. It’s hard to see how the tiny amount of energy in the flap of a wing can create the huge energy in a hurricane. The answer is, it doesn’t. The energy in the hurricane doesn’t come from the flap: it’s redistributed from elsewhere, when the flap interacts with the rest of the otherwise unchanged weather system.After the flap, we don’t get exactly the same weather as before except for an extra hurricane. Instead, the entire pattern of weather changes, worldwide. At first the change is small, but it grows – not in energy, but in difference from what it would otherwise have been. And that difference rapidly becomes large and unpredictable. If the butterfly had flapped its wings two seconds later, it might have ‘caused’ a tornado in the Philippines instead, compensated for by snowstorms over Siberia. Or a month of settled weather in the Sahara, for that matter. "
28 " The American mathematician Jeffrey Weeks analysed the statistics of these fluctuations for manifolds with a variety of topologies. One possibility fitted the data very closely, leading the media to announce that the universe is shaped like a football (US: soccer ball). This was an inevitable metaphor for a shape that goes back to Poincaré: the dodecahedral space. In the early twenty-first century footballs were made by sewing or gluing together 12 pentagons and 20 hexagons to make what mathematicians call a truncated icosahedron – an icosahedron with the corners cut off. An icosahedron is a regular solid with 20 triangular faces, arranged five to a corner. The dodecahedron, which has 12 pentagonal faces, gets into the act because the centres of the faces of an icosahedron form a dodecahedron, so both solids have the same symmetries. ‘Football’ is more media-friendly, albeit technically imprecise. "
29 " On the other hand, these events show real science in action, warts and all. If no one is allowed to get things wrong, no progress will ever be made. It also illustrates scientists’ willingness to change their minds when new evidence comes along or old evidence is shown to be misleading. "
