25
Jul

√42

Well, QuSheet was finally released yesterday, so it's time to break my silence here, and how better than with that little thorny question called "The Meaning of Life".

It seems to come down to me to a simple conflict between two incompatible principles: "Causality" and "Free Will".

Causality adherents claim that Free Will is an illusion. In The Science of Diskworld II, the authors actually devote a chapter to this called "Free Wont". I'm not sure why they, and the scientific community in general as far as I can see, throw their hats in so whole-heartedly with Causality. I, personally, favour Free Will.

And I do think it's a matter of favouritism, because neither can be proved. Free Will cannot be proved because it is impossible to re-run time and see whether someone would do something different. Causality cannot be proved because we cannot work backwards from what we see the universe is doing to whatever formula it is (if there is one) that is making it happen.

Consider this little thought experiment. Imagine two computers. One is infinitely powerful (really) the second one is finitely powerful. Call the first one Omega and the second one Squeak. Although Omega is a lot more powerful than Squeak, it doesn't actually know how powerful Squeak is. All that Squeak does is put out digit after digit of some irrational number, say the square root of some non-perfect square. Omega catches those numbers and is tasked with figuring out what Squeak is actually up to.

Assuming that Omega assumes that it is getting a square root, its problem is that at any point in time there are always an infinite number of possibilities as to what this irrational number is a square root of. The square root of 42 begins 6.4807406984, but then so does the square root of 42.0000000001, 42.00000000011, and an infinite number more. And where with the square root of 42 the next number is 0, with 42.0000000001 the next number is 1.

So Omega can never predict what the next digit will be, since it can never know exactly at what Squeak is taking the square root of. Even with Squeak being finite and Omega infinite, Omega doesn't know just how many 0s occur between the 42 and the 1 (and then the next 1, or 2 or whatever).

And given that, Omega can't even be sure that the numbers coming out of Squeak follow any formula at all. They might be random (as in truly random). Maybe Squeak has free will and is choosing what numbers to put out (and if you re-ran time it would choose different ones).

And if Squeak is our universe, where irrational numbers abound, then Omega will never be able to figure out how the universe works. Or even whether it actually works at all in accordance with logic and formulae.

Unless the day comes, of course, when someone figures out the one and only formula which could possibly work. It would have to be a formula which explained *everything*. Until then, there will always be more than one way to explain our observations, indeed an infinite number of ways, and while that is the case we can never be sure that the universe isn't choosing what it's up to.

Which in my opinion puts Causality and Free Will on an even footing.

And I choose to believe in the latter because, although I can see Causality at work when I throw a stone into a lake and watch it cause those nice little ripples, I know my senses can be fooled, whereas Free Will is a lot closer to home, if you see what I mean.

Richard

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