Determinism

It has been far too long since my last blog post. And far too long since I've had a rant. I probably won't start with one, but I do hope to have one in the next few whatevers.

So, this first entry that have written in quite a long time, will be focused on determinism. Why? Why such a boring topic when I could rant about religious fundamentalists, cheese parties or the cutest dog in the world? Because that is what I will do. It is my fate, my destiny. Also, I've been thinking about this issue for a while and it seems best to put down my words and concepts before I move on to other things.

First, what is determinism and why do we care? To explain determinism, and much of what is to follow, I will use examples. To begin, let's consider an introductory-physics problem: two objects are moving along a plane, collide and bounce off, moving in new directions at new speeds. Determinism is this: a person not of the system, an outside observer, can look at this experiment at a point in time before the objects collide and can predict exactly what will happen in the future. Namely, the observer knows at what time the collision will occur and the resulting velocities of the two objects. That is determinism: objects of a system following a set of rules. Since there exist rules and things don't just happen at random, the future state of the system can be predicted if the current state is known.

Now, let's introduce another concept. I call it 'reverse determinism'. I'm not sure if there's a different name that older and wiser thinkers before me have come up with, but this is what I will call it. Reverse determinism is just that: ability by an outside observer to observe a system and accurately describe a previous state. Extending our above example, an observer can look at the system at a time after the objects have collided and be able to exactly calculate where the object originated and where the collision took place.

What's the point? Stop asking me that, if I knew the answer to that particular question, I imagine life would be much easier.

Now, let's look at our world, which is a hugely complicated system about which we know very little, and other comparable, but infinitely simpler, systems. First, let's consider a basic physics environment: a few objects moving on a frictionless plane. This is a very simple example, one that can be determined both forwards and backwards by a half-way competent physics student. The second example is Conway' Game of Life. This system is even simpler than the previous one: cells, or colonies, or whatever, exist on a grid. If a cell has 2 or 3 neighbors, it lives; any more or less, and the cell dies. If a space on the grid has exactly 3 cells as its neighbors, a new cell is born. You'd be surprised just how complex a system can be made from these simple rules: stable configurations of 'organisms' can be built from groups of cells. Some organisms are gliders, groups that fly diagonally across the playing field, replicators, groups that create exact copies of themselves, and glider factories, groups that go one producing gliders infinitely (or, at least, until interrupted). Some scientists have even devised computers that take input and perform calculation entirely within the Life playing field: they use gliders to communicate. I'm not sure how information is stored, or even if Computer Engineering concepts can be, or need to be, translated. But that's a deviation.

So, we have our three systems (our world, basic physics experiment, Game of Life), let's do some constructive thinkering.

First and foremost, the physics system is both deterministic and reverse deterministic, while the Game of Life is only deterministic. Why? The rules of the Game of Life are such that it is impossible in non-trivial cases to determine the previous state of a given system. Consider a very simple example: a blank board. Who is to say what the previous state was? Was the board empty, or was it just sparsely filled with single- or double-celled groups? All of this information is gone, so there are a large number of possible solutions for any particular state of the system. (The only exception to this is a state of the system termed Garden of Eden: these are configurations that are unattainable through the rules of the system, states that have to be set-up by an external source.)

What does it mean that the physics model is reverse deterministic? Who cares if the Game of Life is not reverse deterministic? I do. I care why one system can be 'wound back', while another can't be. I wonder what a non-deterministic system would look like. Imagine if that system was reverse deterministic. That means that you could reliably 'go back' through events that have already occurred, but going forward, 'Back to the Future', so to speak, is impossible, or perhaps simply inconclusive.

My theory on why the Game of Life is non-reverse deterministic is because of the lack of the conservation of energy (and of course matter): cells disappear into nothingness and are spontaneously born out of it. In the physical model, the two objects collide and change paths, but throughout it all they still remain, both mass and energy of the system staying constant. Even if we were to add friction to our physical model, a seemingly daunting problem to consider, the system still remains reverse-deterministic: friction results in heat, and by knowing exactly the amount of heat an object (in this case the plane and the moving objects) has it is possible to model the spread of heat back to source, giving us an accurate model of just what the state of the system was at some point in the past. The Game of Life lacks this ability to record events. There is no way to know that a cell existed in a particular location, or for how long.

Is our world deterministic? Is it reverse-deterministic? Perhaps.

First, is our world deterministic? If you were asked this question at the beginning of the 20th century, the answer would be a very loud 'yes'. That is, until quantum mechanics came along and spoiled the party. Quantum mechanics opened a dangerous flood-gate: there was no set path for an electron, no specific outcome for a simple interference experiment, the new fashion was chance, the new tool of the scientist was a probability graph. There are higher odds of electrons bouncing off a barrier, but a non-zero chance exists of that same electron passing right through. Poof! goes determinism, burned up like so much tinder in the fire. Granted, the probabilities are such that everyday objects, gargantuan in comparison to electrons, still behave in pre-quantum mechanics ways, but we are now faced with the reality about the most basic building blocks of our universe: no conclusion can be drawn about a future state. (Perhaps, if our world supports reverse-determinism, this is the world I tried to imagine a few paragraphs above.)

However, I do not agree that the universe plays with dice. Consider events in everyday life that can be assigned probabilities: the flip of a coin, tomorrow's rain, the chance of asking for 'a tall mocha, no whip, no lid' and the baristas actually getting an order right. All of these probabilities arise out of one fact: our lack of knowledge about the system in question. If you knew the state of every air molecule in the room and the velocity, both linear and rotational, of the coin, you could accurately predict the outcome of the toss. If you could instantly see the entire atmosphere of the Earth, knowing when and where it will rain will be a trivial task. Probabilities arise out of our lack of information. It is therefore possible that our current understanding of quantum mechanics as being a probability-driven field is based only on our sparse and inaccurate description of the universe. If that is indeed the case, quantum mechanics may very well be a deterministic part in the bigger deterministic system. If every part is deterministic, the system as a whole is deterministic.

What's it matter, though? Well, it doesn't. To accurately predict the future, or to look into the past, we must possess all the information about the current state of our world, have a working knowledge of all the underlying rules and a computational device powerful enough to calculate the next state of this monstrous machine. You'd better step outside for that, as well, since your actions will invariably change the outcome.