Saturday, January 10, 2015

On Computational Models

Alright, I'm going off the cuff here, so this post may not be at Max-level quality, but I'm not entirely sure where I stand on this issue so I'd just like to share my thoughts as they come to me.

To start, I would like to comment on the seemingly fundamental order of the universe as we perceive it. Throughout history, we have found countless examples of this order: from the simple fact that particles and macroscopic objects are discrete (self-contained, distinct), to Newton's observations of gravity's consistency, to more current scientific breakthroughs that I won't pretend I know about. Our observations about the order and constancy of the universe led us to attribute a deterministic model to it. That is, from our perspective, it seems like the universe had some initial conditions and rules governing its operation, and all action within the universe since its beginning has been causally determined by these rules and conditions. To make a little more clear what I mean, initial conditions include how much energy is in the universe, initial velocities of particles, etc, and rules include gravity, magnetism, etc. So, simply put, it seems like the universe started with a certain amount of particles with rules about how they interact, and our universe today is the result of those causally determined interactions.

For the sake of this post, I'd like to assume that the universe is deterministic. The general human experience points toward this being the case -- but after reading Hume and Descartes I can't say that we actually know that the universe is deterministic. For all we know the rules have changed, and will continue to change -- or maybe an evil demon is making me imagine everything! This gets away from the point, though, so bear with me on this assumption of the order and determinism of the universe.

This sort of deterministic behavior is exactly what computers are good at modeling, and it's no coincidence that the advent of computational modeling has been crucial in modern day science (especially physics). Computers take inputs, follow rules with what to do with those inputs, and send a certain output to a certain place depending on what the input was and what the rules said to do. All that you do as a programmer is tell the computer what inputs to expect, and give it a set of rules for what to do with those inputs. The universe works in a very similar fashion -- particles and objects receive inputs from other particles and objects and react accordingly -- and so computational models go hand in hand with the physical world.

As a simple example of how this would work so that you can wrap your head around what I mean, consider a universe with nothing in it but two bodies of mass, and no rules but gravity. If these objects are close enough, and initially moving, then when you "hit play" on the universe, the objects should begin to orbit. This is deterministic behavior -- their behavior is entirely determined based on their masses and proximities, as well as the rule of gravity. This simple universe would lend itself to an equally simple model, but I'll need to explain a bit about Object-Oriented Programming (OOP) first.

There are 4 main components of OOP: classes, methods, and fields, and objects. For our purposes, an object is just what it sounds like -- a thing/object. Objects have methods that describe what the object can do, and fields that describe the object's properties. A class, finally, is how you describe the general form of an object, and you create objects by making a new instance of the class.

So how does this apply to our simple universe model? Well, first we need a class that can generally describe a body of mass -- a BodyOfMass class. It would have fields for mass, location, and velocity. It would have one method (called move, or gravitate, something like that) that describes how it should follow the rule of gravity when other BodyOfMass's are around. Now that we have made the general class, we create our 2 objects -- called body1 and body2 -- and set their fields (meaning we can give them masses, velocities, and locations). Finally, we call their methods (gravitate/move), and those methods look at the different masses and locations associated with the different bodies of mass, and then move the objects accordingly.

For fun, here's (roughly) how that would look in Java (code in bold, my comments in light):

BodyOfMass body1 = new BodyOfMass(mass=3000, location=(25,25), velocity=6);
(**body1 is a BodyOfMass with mass 3000, location (25,25), and velocity 6)**)
BodyOfMass body2 = new BodyOfMass(mass=2000, location=(35,70), velocity=0);
(**body2 is a BodyOfMass with mass 2000, location (35,70), and velocity 0**)
body1.gravitate();
body2.gravitate();
(**"start up" our universe and tell the bodies to start following the rule of gravity**)


I really hope I explained that well, because understanding this is very important if I'm going to go on to describe a model of our more complex universe, and eventually the brain. The key points to get here are that (1) the universe is deterministic, (2) computers are good at modeling deterministic behavior, (3) they are good at this because OOP is all about initial conditions and rules governing action, just like determinism is. It will probably help to understand what I mean by method/class/object/field, but at this point I've already spent way too long on the subject.

Okay so, briefly, let me relate this alllll the way back to our deterministic perception of the universe. Fundamentally, our universe is no different than the simple one I described above, we just started with a lot more mass and a lot more rules. But you can (I hope) see the pattern -- as long as the universe is nothing but initial conditions (objects/classes/fields) and rules (methods), we can model it computationally just as we modeled our simple universe with few conditions and one rule.

Our universe wouldn't be as simple, though, and for the sake of making the brain less of a leap I'd like to describe how we would have to model our universe. It would have to be a bottom-up approach in order to work properly, meaning the model would attempt to model the behavior of the smallest subatomic particles, and have the operations of more macroscopic objects be a result of the amalgamation of these particles. So we have a Proton, Neutron, and Electron class, each with their different conditions and rules, and next level up we have an Atom class that can be composed of different amounts and combinations of Protons, Neutrons, and Electrons, and after that we have Molecules as being made up of Atoms, etc etc. Theoretically, we should be able to model all of the action in our universe just by describing the rules governing the interaction of these subatomic particles because everything is made up, at its core, of these particles.

Finally, I'd like to end with an attempt to relate this all to the brain. I am a materialist, and believe that I am nothing but a body with a brain (no soul, no mind, no nothing that isn't explicitly made of matter). What seems to follow is that the actions of the brain are, therefore, deterministic just like the actions of the universe. After all, our brains are made of matter, and the action of all matter is causally determined. Certainly, the operation of an individual neuron is determined -- they have a set "action potential" needed in order to "fire," and once that potential is reached, they ions flood down into the next neuron (google the phrase "action potential" if you need more convincing here). Even a system of 2 neurons is completely determined. The first either has enough energy to fire, or it doesn't, and if it does it excites the next neuron enough to make it fire, or it doesn't. Based on how much energy was initially given to the first neuron, and how much energy it releases when it fires, we can determine the behavior of the second neuron. This works the same way for a system of 3 neurons, and I can keep adding them one at a time until I have a conscious brain. The point is that the brain is nothing but neurons, whose behavior is deterministic, and so the behavior of the brain is deterministic...

...which (remember) is exactly what computers are good at modeling. I make a Neuron class, make a bunch of Neuron objects from that class, and hit play. If I knew exactly the rules governing the operations of a neuron, and the exact configuration of neurons in a given brain at given time (including how excited they are, where they are, how they are connected), I could model that brain using my Neuron objects, hit play, and have a brain in my computer.

3 comments:

  1. Theoretically, we should be able to model all of the action in our universe just by describing the rules governing the interaction of these subatomic particles because everything is made up, at its core, of these particles.
    ——what about when we don’t have the atom class, or we’re not done modeling the universe and we just have electron, neutron, and proton, and they need to create something that we don’t exactly anticipate? Does this throw a wrench in the deterministic assumption or can computers also account for this? just asking, genuinely curious

    What seems to follow is that the actions of the brain are, therefore, deterministic just like the actions of the universe. After all, our brains are made of matter, and the action of all matter is causally determined.
    —yes, teh actions of the brain are indeed, but the manifestation of consciousness, or the emergence of consciousness is like life on Earth, something that cannot (?) be predictable and or mappable? yes?

    (google the phrase "action potential" if you need more convincing here).
    —stfu



    This works the same way for a system of 3 neurons, and I can keep adding them one at a time until I have a conscious brain.
    — are we mapping the consciousness or no?


    but nice, very nice

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  2. Wow this is a really impressive essay! It's extremely clear, and the theory is fascinating. Still, a few things should be cleared up.

    You say you are a materialist. I agree in a basic sense. There is no soul, etc and the world does not come into existence through a perception or idea of it. At the same time, I feel that the dualism between matierialism and idealism is outdated. In terms of your topic, suppose we have a perfect model of the universe as well as the human brain -- and every existing human brain. So in our model we start out with a universe that is identical to our own. It seems obvious to me that the second after the model begins, there will occur moments, events, and phenomena that differ from the real universe. This is because the universe, although entirely material, contains immaterial systems and relationships that are, by nature, subject to chance -- even though these immaterial systems can still be worked into the model!

    The best example is human reproduction. There is a statistical chance that each child of a certain set of parents receives the gene for blue eyes. Perhaps it is a 25% chance for blue eyes and 75% for brown. Although the chromosomes and genes are material objects, the relationships between them and the ways they interact are immaterial factors. Still, these immaterial factors can easily be worked into a model. We can imagine a code that basically states: "When chromosome-piece A1 crosses over with chromosome-piece B1, there is a 25% chance the replicated gene codes for blue eyes, 75% for brown." This would be an example of working into the model the immaterial factor of the phenomenon of crossover. So it follows that every baby born after the model begins will most likely not be the same baby born in the real world.

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  3. The first implication is that although an idealist approach to the world seems absurd, the materialist approach needs to take into account immaterial phenomena. Not only statistical relationships but even entire government forms, religions, etc seem to be immaterial phenomena. Nonetheless they are based on material items. This might lead someone to argue that if the material is laid out perfectly, then the immaterial phenomena would replicate exactly. However I have already shown that human reproduction deviates from that theory, as each child is a new statistical chance, even if the material remains identical.

    The second implication follows smoothly: the world is not entirely deterministic. I, as an exact biological organism, was never even fated to enter existence. Instead, it was just a chance phenomena.

    Further, the brain might prove to be another example of a material object that allows immaterial phenomena to occur -- such as the mind (no soul, unless, when you say "soul," you really mean "mind"). In the same way that the material combination of my parents' genes creates another organism based on chance -- that is, an organism that was not necessarily destined to enter existence -- the brain also creates chance phenomena, such as decisions or specific thoughts. In other words, although my brain is completely material, it creates immaterial systems between its different material components which allow for free will, which might even be based on statistical chance. One example: I choose a red shirt today if I land a heads and a blue shirt if tails. If the universe you create is truly identical, there is a 50% chance that the computer model would choose something different from the real me -- even though the material is exactly the same!

    Perhaps I am looking too much into this by calling it "immaterial." After all, the relationship between the electrons and nuclei of atoms are material, so why not relationships between humans or chromosomes. Perhaps statistical chance is not immaterial, and the whole theory of statistics is just the way we articulate the material interactions between, say, chromosomes. Nonetheless, my argument here still holds. These statistical phenomena make the world inherently non-deterministic!

    I feel like I must be making a mistake somewhere along my reasoning. Perhaps you can explain how statistical chance can be worked into the idea of cause and effect. The way I see it, nothing "causes" a coin to land on heads -- or, if the physical world actually does cause it, nothing "causes" a computer simulator to choose a 1 over a 2. It is just chance.

    Let me know if I can clear up my argument anywhere. I'm actually writing this on my phone so I know it's choppy and unclear. I'm excited to hear what you have to say!

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