## Sunday, 30 December 2007

## Sunday, 23 December 2007

### A operational definition of free will?

Some reasonable people I know, who believe in the non-existence of free will (or are at least inclined towards believing so) state first that our life is governed by the laws of physics, chemistry and biology. No known experiment has, till date, demonstrated the violation of the second law of thermodynamics or achieved speeds faster than that of light. In that regard, I fully agree with them that every known thing in this universe is constrained to obey these laws in its day to day dealings. But does that mean one doesn't have free will?

Let's narrow our speculation to the things on this earth that possess both life and consciousness. A person likes me decides what time to wake up, what cuisine to eat for dinner, what movie to watch and what books to read. I'd like to call the options in each case as degenerate cases under the laws of physics. A recent essay I read about the "finite nature of consciousness" said the following:

Now we know that thebrainis a finite physical object, containing roughly 100 million neurons and 100 billion synapses linking the neurons together. But byconsciousnessbeing finite, I mean something stronger: that there are only finitely many lives that could possibly be lived; and that therefore free will, if it exists, must at some level be simply the selection of an element from a finite set. The goals of this article are threefold: to show that this proposition is true; to discuss how it affects Penrose's theory of consciousness; and finally to explain why we needn't worry about the finiteness of our minds.

But then an idea from James Gleick's Chaos managed to temporarily placate my fears. I have already mentioned the Lorenz Attractor in one of my earlier posts. Lorenz investigated the following system of deterministic equations in 1963. I downloaded a copy of the original paper and plan to read it as soon as I find some time.

He found two things - the system never settles down to a steady state. In other words it has a trajectory which never repeats itself over time and it is impossible to predict its state unless one numerically follows the equations themselves. At the same time the states of the system are bound - they don't blow up or become infinite. The phase portrait of the system looks like the following (x, y and z plotted on three orthogonal axes with time):

This elucidates an important fact in case you haven't noticed it yet. Suppose I were a deistic God and I decided that a human X would be governed by the system of three deterministic equations above. The boundedness of the solution would be the equivalent laws of physics that govern terrestrial behaviour (indeed in the case of the equations this seems to be embedded and doesn't call for any extra intervention). But then this deterministic systems yields a solution that is chaotic in a bounded region. It is deterministic but you don't know what it's gonna do next. Another point in this case is that the solution is extremely sensitive to the initial conditions of the differential equations.

My argument is hardly complete and I do not intend to reach a denouement here. All I wanted to share was that it is possible to reconcile determinism with free will in a way. Whatever the system is going to do exists as hidden information in the three simple differential equations. But it is impossible for a person to deduce that unless the system itself is simulated. And then again, knowing the system at a point in time is not going to help one realize what it's gonna be doing ten milliseconds, hours or years from then.

## Saturday, 22 December 2007

### Misanthrope

## Friday, 21 December 2007

I saw Taare Zameen Par today and I'm happy to have seen it at a moment as appropriate as this. I cannot sit and articulate everything, but I did learn two or three things from the movie, even if you'd like to call them quotidian. It was a beautiful film (despite some overtly melodramatic moments where I heartlessly smirked as the lady next to me was reaching for her handkerchief). But all said and done, amidst discourses from the Heisenbergs, Goethes and the Dawkinses of the world, a couple of hours at the cinemas is a necessary respite to help you realise that your feet are stuck to the ground. And it is a happy feeling to know that there is still much ground to cover :)

**Einstein was a giant. His head was in the clouds, but his feet were on the ground. Those of us who are not so tall have to choose!**

- Richard Feynman

- Richard Feynman

## Tuesday, 18 December 2007

### Chaos

1. Non-linear dynamics is beautiful. I don't understand why the chemical engineering curriculum at IITB avoids it. Even in the most utilitarian sense, I think an advanced course in non-linear dynamics can be a reasonable inclusion. I've heard that much work has been done in investigating the nonlinear dynamics of reactors by Amundson and Aris so it's not really a field alien to chemical engineering.

2. The poster child of non-linear dynamics or chaos theory is the so called Lorenz attractor. A simple system of 3 deterministic ordinary non-linear differential equations yields a solution with time that neither shows periodicity nor converges to a limit. Interestingly it was published in a journal of meteorology and was hardly noticed for nearly ten years. Now that Chaos theory has developed thanks to people like Feigenbaum, Mandelbrot and Smale any standard exposition on chaos begins by describing the Lorenz attractor. But it's nonetheless interesting to see that the genesis of ideas that led to such a rich theory involving physics and mathematics could come from a non-specialist in either. So much for the chauvinists!

3. "Turbulence", Gleick says, "is a problem with pedigree". Apparently Heisenberg is known to have quoted that when the time comes he "would have two questions for God, why relativity and why turbulence?" He added, "I think He will have an answer to the first question."

## Sunday, 16 December 2007

### The emotion of scholarship

He can tell the world to fuck off!

## Friday, 14 December 2007

### The incomplete man

I haven't completed a book cover to cover for a long time. I seem to live in the past. The worse thing is that I seem to enjoy it. I quit reading 'India after Gandhi' just before the economic liberalizations set in. The second stage of my thesis is done with and I feel a sense of complacency has set in. I fear incompleteness but I'm wondering if I can help it.

I see incompleteness in my thoughts, my opinions, my expressions and also my ambitions. I reciprocate to people incompletely. Even my love is incomplete. So is my hate.