Random Rants, Raves and Ramblings

The Final Copernican Revolution

Cosmologists have their quirks too. To me at least, they look like golfers who first drive the ball to within inches of the hole in one majestic stroke and then fail to putt.

What's the one-trillionth digit of pi? I've no idea, but it's an integer between 0 and 9 (inclusive). There's exactly one correct answer and nine wrong ones. So what do we do? We run the calculation to find out. That's an important bit of truth here: find out. By calculating the one trillionth digit, we don't create it. We find out what it is, but it's been this value all along.

When you're a mathematician that doesn't really surprise you. Any system of internally consistent and independent axioms describes a "world", in which certain things are true others are not (and yet others are unprovable). Properties are discovered, never created. Axiomatic systems have their properties whether or not someone bothers to find out.

Mathematics is involved with finding the properties of a given set of postulates. Physics is involved with finding a set of postulates that have a given collection of observed properties. In the former case, these postulates are called axioms, in the latter case they're called physical laws. Physical laws are reverse-engineered axioms so to speak.
Science itself is one grand scientific experiment to show that reality is internally consistent (thus proving its own validity!) and most scientists have their eyes firmly on the prize, a Theory of Everything, the system of equations that fully describes everything inside our universe.

Yet the same scientists who are positing that such a system of equation exists (if only in principle), still seem to be baffled into extreme speculation when trying to answer why the laws of physics (and more specifically the six physical constants) just happen to be suitable as they are for life to evolve in its present form. More precisely, they're asking why a universe with a set of physical laws conducive to life exists at all.

The fine-tuning problem is generally addressed using the so-called anthropic principle. The weak variant posits that the physical constants are not constant throughout the entire universe, but only in our neck of the woods (called the observable universe by virtue of having us as observers in it). The strong variant posits a large number, or even an infinity of universes, each with its particular combination. According to one, big bangs happen all the time in a multidimensional space, according to others, new universes are spawned in black holes from existing universes.

But why so fanciful? We accept that our universe is indeed governed by a limited (or even unlimited!) set of laws/axioms, and we realise that any set of postulates, whether already formulated or not, has all of its properties waiting to be discovered.

One age-old philosopers' games is to ask "suppose we were all living in one giant computer simulation?" The generally accepted answer is that there would be no way for us to find out. But hang on a second, what's this computer doing apart from just calculating i.e. finding out what is the outcome if this bunch of formulae is evaluated? Just like the one-trillionth digit of pi is just sitting there with an unknown but already predetermined value, the computer simulation is just chugging away, discovering what's already there. We can drop the computer and not change the outcome.

The aforementioned scientists are falling into the same trap they're trying to point out to their religious fellows: namely attaching intrinsic value to our perception. We perceive reality, therefore reality is, in some metaphysical sense? In the same way that we wouldn't be able to find out whether we exist physically or only in the RAM of a cosmic computer, there's no way to tell the difference between a physical universe that happens to behave according to certain physical laws and the properties of the same physical laws taken as axioms.

The only truly amazing thing is to realise that if science is true (i.e. if reality is internally consistent) there are apparently sets of equations that describe a world inhabited by creatures capable of figuring these equations out. Amazing, but no less true. I think this might be called The Extreme Anthropic Principle.

(I'm aware that this reading, as it stands, requires either a hidden-variables or a “many worlds” kind of quantum physics. I can live with the latter.)

Thursday 06 October 2011