1. February 3, 2010Free Will and Chaos1 Theo Pavlidis www.theopavlidis/com t.pavlidis@ieee.org

2. February 3, 2010Free Will and Chaos2 Free Will has been a Challenge to Philosophers (A) For Believers: If there is an omnipotent and omniscient God, how can a human being “surprise” God by exhibiting free will?

3. February 3, 2010Free Will and Chaos3 Free Will has been a Challenge to Philosophers (B) For Materialists: If all human thoughts and actions are determined mechanically, then they must be determined by what happened in the past. How can a person avoid materialist determinism?

4. February 3, 2010Free Will and Chaos4 Moral Dilemma If there is no free will how can we hold people responsible for their actions?

5. February 3, 2010Free Will and Chaos5 The Topic of this Lecture An escape clause for the materialistic model. There exist deterministic systems that are unpredictable!

6. February 3, 2010Free Will and Chaos6 Deterministic Systems If we know the current state of the system and its dynamics, then we can predict its state in the future. –Example: Motions of the planets.

7. February 3, 2010Free Will and Chaos7 Random Systems Even if we know the current state of the system and its dynamics we can predict its future state only with a probability. –Example: Tossing a coin.

8. February 3, 2010Free Will and Chaos8 A Third Kind: Chaotic Systems Chaotic systems are deterministic and unpredictable, or more precisely, we need to know their state with infinite precision in order to predict. In contrast to random systems, if we have complete information about their state, then their response is repeatable.

9. February 3, 2010Free Will and Chaos9 Background Reading James Gleick, Chaos - Making a New Science, New York, Viking, 1987. –A paperback edition came out in August of 2008. It sells from Amazon for $13.60. –The hard cover edition had 113 reviews on Amazon with a four star average.

10. February 3, 2010Free Will and Chaos10 A hard prediction: where is a rain drop going to end if it falls on a ridge?

11. February 3, 2010Free Will and Chaos11 Chaotic System: All raindrops fall on ridges. It is always hard to tell which ocean a raindrop will end.

12. February 3, 2010Free Will and Chaos12 Chaotic systems are common The weather system was the first one to be identified as chaotic (in the 1960’s) but most complex systems (and some not so complex) exhibit chaotic behavior.

13. February 3, 2010Free Will and Chaos13 We do not need something as complicated as the equations for weather prediction to find chaotic behavior. Consider the simple equation x[n+1] = r*x[n]*(1-x[n]) It describes the population of a species as fraction of the maximum number its environment can sustain. If x is 1 (100%) we have extinction. For those who remember their college physics:

14. February 3, 2010Free Will and Chaos14 Start at x[0]=0.6 with r = 3.2 x[n] oscillates between two values Start at x[0]=0.6 with r = 2.9 x[n] settles at 0.655

15. February 3, 2010Free Will and Chaos15 For r = 4 we observe chaotic behavior

16. February 3, 2010Free Will and Chaos16 Starting with slightly different values of x[0] we have quite different results after a few iterations.

17. February 3, 2010Free Will and Chaos17 The Brain as a Machine Even if we view the brain as purely mechanical, it is extremely complex. A mathematical model of the brain involves, at least, millions of nonlinear differential equations. Certainly models of the brain are sufficiently complex to exhibit chaotic behavior.

18. February 3, 2010Free Will and Chaos18 IBM’s Simulation In November of 2009 IBM scientists claimed that had simulated a cat’s brain using The simulation involves 1 billion spiking neurons and 10 trillion individual learning synapses, and was performed on an IBM Blue Gene supercomputer with 147,456 processors and 144TB of main memory. The simulation was disputed by other scientists as a hoax!

19. February 3, 2010Free Will and Chaos19 Unpredictability and Free Will Can a deterministic system be unpredictable? Yes! Does unpredictable behavior provide the illusion of free will? It looks that way. Is unpredictable behavior the same as free will? A hard question.

20. February 3, 2010Free Will and Chaos20 E. O. Wilson’s View “Because the individual mind cannot be fully known and predicted, the self can go on passionately believing in its own free will.” “Thus in organismic time and space, in every operational sense that applies to the knowable self, the mind does have free will.”

21. February 3, 2010Free Will and Chaos21 Source of quotations Edward Wilson Consilience - The Unity of Knowledge, New York, Vintage, 1998, pp. 130-132. –It sells for $10.88 on Amazon and it has 154 reviews with four star average.