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The Free Will Function

by Sabine Hossenfelder (Feb. 3, 2012)

"In my paper I just pointed out that there exist time evolutions that are neither deterministic nor probabilistic, certainly not in practice but also not in principle. Functions that do that for you are just functions physicists don't normally deal with. The functions that we normally use are solutions to differential equations. They can be forward-evolved or they can't and that is exactly the problem. Yet, there are lots of functions which don't fall in this category. These are functions can can be forward evolved, yet you have no way to ever find out how. They are deterministic, yet you cannot determine them.

Take for example a function that spits out one digit of the number π every second, but you don't know when it started or when it will end. You can record as much output from that function as you want, you'll never be able to tell what number you get in the next second: π is a transcendental number; every string that you record, no matter how long, will keep reappearing. If you don't know that the number is π you won't even be able to find out what number the algorithm is producing.

The algorithm is well-defined and it spits out numbers in a non-random fashion that, if you'd know the algorithm, is perfectly determined. But even if somebody monitors all output for an arbitrarily long amount of time to an arbitrarily good precision, it remains impossible to predict what the next output will be. This has nothing to do with chaos, where it's the practical impossibility of measuring to arbitrary precision that spoils predictability: Chaos is still deterministic. The same initial conditions will always give the same result, you just won't be able to know them well enough to tell. Chaos too doesn't allow you to make a choice, it just prevents you from knowing.

But what if you'd make your decisions after a function like the one I described? Then your decisions would not be random, but they wouldn't be determined by the state of the universe at any earlier time either (nor at any later time for that matter). You need to have your function to complete the time evolution, which is why I call it the 'Free Will Function.' "
Reposted fromArchimedes Archimedes

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