Paths
1. Follow Me
Come, let’s take a walk. You see a cave over there? Let’s check that out.
So the other day I came across this term called “Scientific determinism” in the book “The Grand Design: by Stephen Hawking and Leonard Mlodinow”. What it basically states is, if we know the state of the universe at a given instant of time, using a wide range of set of laws, we can peek into its past as well as predict its future. This surely seemed true. Maybe because me and my colleagues work with this idea almost everyday. You know, taking the state of a spacecraft or planet, predicting its state in future, using this to plan maneuvers etc. But then I started to think, is everything in this entire universe captured by some law? Maybe not yet but will it be some time? What is a law anyways?
2. Darkness
It sure is getting dark inside this cave isn’t it? Let’s just keep walking
Law is something that we come up with to explain the things happening around us. We use these laws and formulate models that can explain things in an objective manner, i.e. both you and me will arrive at the same results irrespective of how your day had been, if it was raining when you were thinking and applying the model etc. But more often than not, these laws have a domain where they are valid and new laws are made to explain things beyond this domain or to bring a bigger domain under its umbrella. A good example is of Classical and quantum physics. (Not getting into the details). Usually there is an overlap region thus patching up things and giving us the entire picture.
3. Silence
Woah, my voice and our footsteps are the only thing I can hear!
Ok, so ascertaining that I was understanding what I was reading, I read further. The argument goes like this. We humans are also a part of universe. So it is only right to accept that everything human would also be deterministic provided we figure out the laws and obtain initial conditions. Now imagine this. If we were able to account for every thing that makes you human and formulate a model that represents well, “YOU”, I will be able to exactly predict what you are thinking right now if I knew your “precise state” before we started this walk. The only problem is, you are too complex of a system for me to model and get precise states. But theoretically, it should be possible. Because treating you or me like an ensemble of trillions and trillions of smaller things is practically impossible, I would choose not to model you and ask you “What are you thinking?” directly :P .
If I claim that given infinite resources, I will be able to model you and predict your future exactly, you will be like “No way. So you are claiming I have no free will? That whatever I will do or will happen to me is all written down in some model ?”. To that I will say, “YES!”. Let’s take an example. I know your favorite color is Blue. We go to a shop to buy a bag and there are two options for you. A blue one and a yellow one. I can predict with great deal of certainty that you will choose blue. That’s because my brain has a small model of you. But lets go a bit further. Why do you like blue in first place? Maybe you felt it suits you better when you wear blue. Why do you feel that way? Because you brain had generated the “like” signal when you had blue around you sometime. So if I could write down the equations modeling your brain and precisely know what electrical activity was happening at a particular instant of time, I would have been able to predict that it will generate “like” when it sees blue.
This raises an important question which is addressed in the same book. Does this mean there is nothing like “free will”? That everything about you is determined? YES. I am sorry but everything was determined when the universe itself began. Its analogous to what many call FATE. But because we cannot model and solve equations of the complex interactions between every single thing in universe, and cannot determine the precise initial states of all of these, we choose to model it using “Effective Theories”. Where we satisfy out attempts to model everything by grouping things rather than individually. Modeling your brain through psychology instead of countless number off equations relating everything that makes up your brain. Because we cannot model everything, we use the effective theory that is okay with stating that you/me have free will.
4. Light
I can see a ray of light over there. I guess we will reach the end in a while
Reading all this got me thinking. Do I have anything myself to justify all these claims? Stephen hawking says this but how do I experience the gravity of these claims myself? Then I remembered something I had studied in a course called Non-linear dynamics and Chaos. Something called a Lorenz system. Let me explain it in as simple words as possible. Basically, it is this set of equations:
Vx = S (y — x)
Vy = Rx — y -xz
Vz = xy — Bz
Where (x, y, z) is position of a particle and (Vx, Vy, Vz) its velocity and rest are parameters.. So the above equations depict a system showing how a particle would move given an initial position. The system is non linear, as you would expect a comprehensive system of equation of universe to be. I coded this simulation in python to give a visual representation. The beauty of it is, if you take two particles which are very very very close to each other but not at the exact same place, they evolve to move in very different directions as the time progresses (sensitivity to initial conditions, also known as chaos). I started thinking of myself as a particle in this system. The particle’s path never cuts itself, a good representation of our lives where time flows and we are never in the same state ever again.
If you take multiple particles, their paths never cut too for if they did, they would be one and the same (plotted projection on x-z plane for clarity. It only seems that paths are cutting because its 2D projection. You can imagine how it is in 3D from above video). Again nicely analogous to me and you. You are on your own journey, I am on mine. The blank canvas being the universe.
5. A Walk To Remember
So, I guess it’s like this. On a cosmic scale, me and you, we started out very very close to each other, both of us being humans. But we had our minuscule differences to begin with. Thus we set out on our own paths, determined by how we started. And on the cosmic scale, yes, our fates are fixed. The beauty though is, you are a world of your own and you actions and decisions (which we assume are you free will) will shape your tiny world within that particle but you are still following the path that you happened to be on, in the cosmic scale. The same goes for me. Because we don’t have resources to model and predict future, we accept it as it comes.
But I am thinking, what are the chances that our paths that we were destined to be on came so close that here I am, talking to you for this long and you are patiently listening to me. So close that I know you. It’s amazing right?
Indeed you are a special one for me aren’t ya! 😊
Oh, I guess we are out of the cave. Ok then, I’ve gotta go this way. Hope you have a safe walk down your lane and hope to meet you sometime soon again.
Bye !
