Laws of Logic

Physicists are translating commonsense principles into strict mathematical constraints on how our universe must have behaved at the beginning of time.  Patterns in the ever-expanding arrangement of galaxies might reveal secrets of the universe’s first moments.

M.C. Escher’s Circle Limit III (1959). M.C. Escher

For over 20 years, physicists have had reason to feel envious of certain fictional fish: specifically, the fish inhabiting the fantastic space of M.C. Escher’s Circle Limit III woodcut, which shrink to points as they approach the circular boundary of their ocean world. If only our universe had the same warped shape, theorists lament, they might have a much easier time understanding it.

Escher’s fish lucked out because their world comes with a cheat sheet — its edge. On the boundary of an Escher-esque ocean, anything complicated happening inside the sea casts a kind of shadow, which can be described in relatively simple terms. In particular, theories addressing the quantum nature of gravity can be reformulated on the edge in well-understood ways. The technique gives researchers a back door for studying otherwise impossibly complicated questions. Physicists have spent decades exploring this tantalizing link.

Inconveniently, the real universe looks more like the Escher world turned inside out. This “de Sitter” space has a positive curvature; it expands continuously everywhere. With no obvious boundary on which to study the straightforward shadow theories, theoretical physicists have been unable to transfer their breakthroughs from the Escher world. orld, the fewer tools we have and the less we understand the rules of the game,” said Daniel Baumann, a cosmologist at the University of Amsterdam.  READ MORE...

The Limits of Simplicity

Seven hundred years ago in a commentary on a religious tract, William of Ockham, a Franciscan friar, wrote that “plurality must never be posited without necessity.” Such is Occam’s razor.

A bit gnomic, you might think. A bit hard to see at first how it earned its status as one of the most prized intellectual tools in scientific endeavour. But in his new book Life is Simple, Johnjoe McFadden proclaims it world-changing, “cutting through the thickets of medieval metaphysics to clear a path for modern science.” In short, this is a book of hero-worship, and just possibly McFadden has a point.

For most of us, Occam’s razor is like a country we can’t quite place on the map; we know it’s something to do with simplicity, but we’re not sure exactly what. Cited widely in science, but often misunderstood, for some it’s invaluable, hinting at profound truths about the nature of knowledge. For others it’s worse than useless. The old line attributed to HL Mencken has it that for every complicated question there is an answer that is clear, simple and wrong.

At its heart is the idea that simplicity can in some way help us decide between competing theories, all else being equal. “It is futile to do with more what can be done with fewer,” as William put it elsewhere. Perhaps the most persistent of the confusions is that this means simpler wins every time, against any alternative. 

A more accurate paraphrasing might be “don’t add complications if you don’t have to.” That still leaves plenty of room for interpretation, not least about whether all else is ever really equal between two competing theories, giving us one of the most debated—and for my money intriguing—heuristics around. Mental shortcut or philosophical thicket? Questions about the razor’s true use and meaning abound.  READ MORE