• Cognitio nostra est adeo debilis quod nullus philosophus potuit unquam perfecte investigare naturam unius muscae: unde legitur quod unus philosophus fuit triginta annis in solitudine, ut cognosceret naturam apis. — Sancti Thomae de Aquino Expositio in Symbolum Apostolorum (1273).
• Our knowledge is so weak that no philosopher has ever perfectly discovered the nature of a single fly, whence we read that one philosopher was thirty years in the wilderness that he might know the nature of a bee. Thomas Aquinas, The Apostles’ Creed.
A good short popular guide to perhaps the most interesting, and certainly the most irrational, of all numbers: the golden ratio or phi (φ), which is approximately equal to 1·6180339887498948482… Prominent in mathematics since at least the ancient Greeks and Euclid, phi is found in many places in nature too, from pineapples and sunflowers to the flight of hawks. Livio catalogues its appearances in both maths and nature, looking closely at the Fibonacci sequence and rabbit-breeding, before going on to debunk mistaken claims that phi also appears a lot in art, music and poetry. Dalí certainly used it, but da Vinci, Debussy and Virgil almost certainly didn’t. Nor, almost certainly, did the builders of the Parthenon and pyramids. Finally, he examines what has famously been called (by the physicist Eugene Wiegner) the unreasonable effectiveness of mathematics: why is this human invention so good at describing the behaviour of the Universe? Livio quotes one of the best short answers I’ve seen:
Human logic was forced on us by the physical world and is therefore consistent with it. Mathematics derives from logic. That is why mathematics is consistent with the physical world. (ch. 9, “Is God a mathematician?”, pg. 252)
It’s not hard to recommend a book that quotes everyone from Johannes Kepler and William Blake to Lewis Carroll, Christopher Marlowe and Jef Raskin, “the creator of the Macintosh computer”, whose answer is given above. Recreational mathematicians should also find lots of ideas for further investigation, from fractal strings to the fascinating number patterns governed by Benford’s law. It isn’t just human beings who look after number one: as a leading figure, 1 turns up much more often in data from the real world, and in mathematical constructs like the Fibonacci sequence, than intuition would lead you to expect. If you’d like to learn more about that and about many other aspects of mathematics, hunt down a copy of this book.
• Roses Are Golden – φ and floral homicide
The most mysterious thing in the universe is also the most intimate: consciousness. It’s an inti-mystery, something we experience constantly at first hand and yet cannot describe or explain. We are each a double bubble: a bubble of flesh and a bubble of conscious experience. The second bubble bursts regularly, when we sleep. Sooner or later, the first bubble will burst too, when we die. And that will be it for the second bubble, the bubble of consciousness. Or will it? Can consciousness survive death? Can it exist without a material substrate? Or without a particular kind of material substrate: the soggy, sparky substance of the brain? Can the clean, dry metal of a computer be conscious? Who knows? The double bubble attracts lots of double-u’s: what, where, why, when, (w)how. What is consciousness? What is its relation to matter? Is it king or courtier? Where does it exist? Why does it exist? When? And how?
Continue reading Double Bubble…