This NPR article got me thinking: why wouldn't it be true that parallel universes must exist. Of course the term universe is being used rather loosely, if the universe IS infinite, there couldn't be a parallel universe, only a parallel containment unit within the universe (such as a parallel galaxy).
After a bit of thinking I realized that the hypothesis is false if you accept the idea from my previous post that the universe is not only infinitely big, but infinitely precise. The infinite precision would allow for an infinitely sized universe with no requirement that there ever be a 'parallel' containment unit.
There is probably some proof of this idea in set theory somewhere, but as a philosopher, I have immunity from having to come up with proofs. Maybe if there's a mathematician out there they can supply that. A good place to start might be this wikipedia article
Monday, January 24, 2011
Sunday, January 23, 2011
Rationalizing Free Will and Determinism
On the face of it, free will and determinism seem as irreconcilable as science and religion. With determinism, everything is pre-ordained, everything happens according to some master plan. If that is true, how can we have free will, we could just blame all our actions on this master plan, and we are just helpless bits of silt being washed down a stream. And yet, I can't help but believe in free will of some sort, I seem to be in control of many of my actions. When it comes time to assign blame for my actions, the buck stops here.
I think the key is predictability. With determinism, we tend to infer predictability. In the scientific model, once we can determine the master plan, or some piece of it, we can predict the future. We figure out the master plan for planetary orbits, and now we can predict when certain celestial events will occur. There still is an inference, as when we describe the master plan, we describe it with a mathematical model, so our inference moves away from prediction based on previous occurrences, to the inferences that our description matches reality. Basically, the scientific model relies on determinism, and the ability to isolate a certain piece of the master plan that is uninfluenced by other pieces.
On the nature of reality, I think we can ascribe two attributes to the universe. One, that it is infinitely large, and the other that it is infinitely precise. By infinitely large, that is to say it has no bounds, no matter what level you look at the universe, you can always go one level out in containment. Planets are part of star systems. star systems are part of galaxies, galaxies are part of something else. We use the term universe to describe not some final containment category, but to define a system of all containment categories, which I tend to believe is infinite. The other attribute of the universe is that it is infinitely precise. By that I mean that we can go in the reverse direction, and assign containment categories to an infinitely smaller and smaller set. Each level in minuteness we discover leads us to believe there is one level smaller, and this probably also goes on forever as well.
Now to problems with predictability. Let us think of a pole with a magnet near the base of it. Tethered to the top of the pole by a string almost as long as the pole is a magnet of the same polarity, so that it would naturally be repelled by the magnet at the base of the pole, which it would otherwise come into contact with. Lift up the tethered magnet and let it free fall. It will avoid the pole and be diverted to one side or the other. If the apparatus is built correctly, we cannot predict to which side the tethered magnet will divert, and yet it is a very simple mechanism easily described in this paragraph, and easily constructed.
So why can't we predict the above experiment? Why doesn't it fit into our system of using mathematical models to calculate outcomes? I believe that it does, as it is fundamentally no different than any other aspect of reality. It is in-calculable because of the infinitely precise nature of reality. To model a reality of infinite precision, you need a mathematical model of infinite size.
If it's that case that all of reality is infinite in precision, how can we model any of it with finitely sized mathematical models? We can because the aspects of reality that we model conform to describable patterns, so that we can describe not the actual model, but can describe the basic shape of the model. We can use advanced mathematics to calculate the outcome of certain describable patterns, even though we cannot express the actual model due to it's infinite size. The problem with the above experiment, is that it defies this reduction, and so must be described by a model of infinite size, which would be impossible to express, much less calculate.
So that is how we have a system that is both deterministic, and impossible to predict. One might be tempted to state that determinism is simply the ability to determine, or predict, and so say that this denies determinism. But I believe that determinism should be defined, not by our ability to predict, but on whether, given infinite capacity, something would be predictable, and to that I would answer yes. For the universe to not be deterministic, it would have to be influenced by some external force, and yet you could easily wrap that external force into the definition of the universe and it becomes deterministic again. For the universe to not be deterministic, it would have to make choices, and I don't believe it is capable of that.
To help differentiate that determinism does not mean OUR ability to predict, but simply predictability given infinite resources, I will use the term 'virtual determinism' By that I mean that something is deterministic and yet impossible to predict given finite resources. I believe that I have described above why the infinite nature of reality can cause things to be unpredictable, but there is another related aspect of reality that has the same effect, that is the infinite inter-connection of reality. In my second paragraph I added the qualification of using the scientific method as that an aspect of reality must be able to be isolated from all other aspects, and yet that is also impossible based on my assertion that reality has infinite inter-connections. However, some aspects can be isolated relatively well, such that the error caused by outside influence is negligible. That leads to a further impediment for prediction in a deterministic world.
I also believe this unpredictability is unrelated to Heisenberg's Uncertainty Principle, which I might generalize as 'measurement or understanding at one level of reality, requires elements from the level of reality contained in (at least one level lower than) the level being measured'. So to precisely measure elements at the atomic level, we need first to understand and master elements at the subatomic level or lower, which we have not done yet. Once we have a better understanding and control of subatomic matter, we will fill in many of the blanks and paradoxes that haunt quantum mechanics. But we will still have some 'Uncertainty Principle' in regards to subatomic matter until we go down yet another level in our understanding and mastery. I believe this can be seen historically, as our mastery of the atomic level filled in many blanks and paradoxes in our understanding of our reality.
So given a belief in determinism (or virtual determinism), how can I believe also in free will? Basically, I don't. What I do believe in I will term 'virtual free will'. It's an illusion of free will based on our inability to predict a deterministic reality. If someone says "I will raise my right arm", we cannot predict that they actually will, without the leap of faith of taking them at their word. We cannot build a mathematical model that connects the path from the statement to the action. We can make a judgement based on past experience that they will follow through on their word, but that is all. As conscience beings we have inside information that can better predict our actions than the outside world can using a scientific model and the more information about our future actions we divulge, the better the outside world can predict. But no one (including ourselves) can make a scientific statement about our future actions. We do not yet have the understanding to connect our motivations to our actions, other than to infer that one tends to cause the other. This, of course, includes our motivation to demonstrate our 'free will' whenever the need arises. We make a decision about which action to take, but that decision is at once deterministic, AND unpredictable with a mathematical model. We don't 'cause' the decision to be made, but we have enough inside information about it in the moments leading up to it to believe we are the cause because we have thought about consequences which feed into the deterministic decision making process. The thought of the consequences of our actions along with our character and willingness to face consequences (or ignore them in the decision making process) are all parts of some vast and possibly unknowable deterministic equation.
Because one's character (or tendencies, innate and learned) are part of the equation, in a social context we can make a judgement and take action based on someone's actions even if we don't fully understand the processes involved in the decision making. The actions can be to help alter a person's learned tendencies, by punishing unwanted behavior, or rewarding desired behavior, adding the punishment and reward to future consideration of consequences. They can be to isolate or reduce the power of someone with unwanted innate tendencies, or give greater power to someone with desired innate or learned tendencies. We have to try to make a distinction between innate and learned tendencies, even though we don't understand fully the distinction, and don't even understand the process that turns tendencies into actions. So when I say 'virtual free will' I don't mean to confirm free will or deny it. I simply mean that for all intents and purposes we can consider free will to be real, and part of the reality that we live in.
For many millennium man has drawn the conclusion that the sun will rise in the east, and yet only when we understood planetary orbits did we have scientific confirmation that this conclusion was true. That did not mean that the process was not in place until we understood it. Prior to our understanding, we ascribed a will to the sun to rise in the east, until we could see how it fit into a coherent description of reality. Such is the will that we ascribe to ourselves.
I think the key is predictability. With determinism, we tend to infer predictability. In the scientific model, once we can determine the master plan, or some piece of it, we can predict the future. We figure out the master plan for planetary orbits, and now we can predict when certain celestial events will occur. There still is an inference, as when we describe the master plan, we describe it with a mathematical model, so our inference moves away from prediction based on previous occurrences, to the inferences that our description matches reality. Basically, the scientific model relies on determinism, and the ability to isolate a certain piece of the master plan that is uninfluenced by other pieces.
On the nature of reality, I think we can ascribe two attributes to the universe. One, that it is infinitely large, and the other that it is infinitely precise. By infinitely large, that is to say it has no bounds, no matter what level you look at the universe, you can always go one level out in containment. Planets are part of star systems. star systems are part of galaxies, galaxies are part of something else. We use the term universe to describe not some final containment category, but to define a system of all containment categories, which I tend to believe is infinite. The other attribute of the universe is that it is infinitely precise. By that I mean that we can go in the reverse direction, and assign containment categories to an infinitely smaller and smaller set. Each level in minuteness we discover leads us to believe there is one level smaller, and this probably also goes on forever as well.
Now to problems with predictability. Let us think of a pole with a magnet near the base of it. Tethered to the top of the pole by a string almost as long as the pole is a magnet of the same polarity, so that it would naturally be repelled by the magnet at the base of the pole, which it would otherwise come into contact with. Lift up the tethered magnet and let it free fall. It will avoid the pole and be diverted to one side or the other. If the apparatus is built correctly, we cannot predict to which side the tethered magnet will divert, and yet it is a very simple mechanism easily described in this paragraph, and easily constructed.
So why can't we predict the above experiment? Why doesn't it fit into our system of using mathematical models to calculate outcomes? I believe that it does, as it is fundamentally no different than any other aspect of reality. It is in-calculable because of the infinitely precise nature of reality. To model a reality of infinite precision, you need a mathematical model of infinite size.
If it's that case that all of reality is infinite in precision, how can we model any of it with finitely sized mathematical models? We can because the aspects of reality that we model conform to describable patterns, so that we can describe not the actual model, but can describe the basic shape of the model. We can use advanced mathematics to calculate the outcome of certain describable patterns, even though we cannot express the actual model due to it's infinite size. The problem with the above experiment, is that it defies this reduction, and so must be described by a model of infinite size, which would be impossible to express, much less calculate.
So that is how we have a system that is both deterministic, and impossible to predict. One might be tempted to state that determinism is simply the ability to determine, or predict, and so say that this denies determinism. But I believe that determinism should be defined, not by our ability to predict, but on whether, given infinite capacity, something would be predictable, and to that I would answer yes. For the universe to not be deterministic, it would have to be influenced by some external force, and yet you could easily wrap that external force into the definition of the universe and it becomes deterministic again. For the universe to not be deterministic, it would have to make choices, and I don't believe it is capable of that.
To help differentiate that determinism does not mean OUR ability to predict, but simply predictability given infinite resources, I will use the term 'virtual determinism' By that I mean that something is deterministic and yet impossible to predict given finite resources. I believe that I have described above why the infinite nature of reality can cause things to be unpredictable, but there is another related aspect of reality that has the same effect, that is the infinite inter-connection of reality. In my second paragraph I added the qualification of using the scientific method as that an aspect of reality must be able to be isolated from all other aspects, and yet that is also impossible based on my assertion that reality has infinite inter-connections. However, some aspects can be isolated relatively well, such that the error caused by outside influence is negligible. That leads to a further impediment for prediction in a deterministic world.
I also believe this unpredictability is unrelated to Heisenberg's Uncertainty Principle, which I might generalize as 'measurement or understanding at one level of reality, requires elements from the level of reality contained in (at least one level lower than) the level being measured'. So to precisely measure elements at the atomic level, we need first to understand and master elements at the subatomic level or lower, which we have not done yet. Once we have a better understanding and control of subatomic matter, we will fill in many of the blanks and paradoxes that haunt quantum mechanics. But we will still have some 'Uncertainty Principle' in regards to subatomic matter until we go down yet another level in our understanding and mastery. I believe this can be seen historically, as our mastery of the atomic level filled in many blanks and paradoxes in our understanding of our reality.
So given a belief in determinism (or virtual determinism), how can I believe also in free will? Basically, I don't. What I do believe in I will term 'virtual free will'. It's an illusion of free will based on our inability to predict a deterministic reality. If someone says "I will raise my right arm", we cannot predict that they actually will, without the leap of faith of taking them at their word. We cannot build a mathematical model that connects the path from the statement to the action. We can make a judgement based on past experience that they will follow through on their word, but that is all. As conscience beings we have inside information that can better predict our actions than the outside world can using a scientific model and the more information about our future actions we divulge, the better the outside world can predict. But no one (including ourselves) can make a scientific statement about our future actions. We do not yet have the understanding to connect our motivations to our actions, other than to infer that one tends to cause the other. This, of course, includes our motivation to demonstrate our 'free will' whenever the need arises. We make a decision about which action to take, but that decision is at once deterministic, AND unpredictable with a mathematical model. We don't 'cause' the decision to be made, but we have enough inside information about it in the moments leading up to it to believe we are the cause because we have thought about consequences which feed into the deterministic decision making process. The thought of the consequences of our actions along with our character and willingness to face consequences (or ignore them in the decision making process) are all parts of some vast and possibly unknowable deterministic equation.
Because one's character (or tendencies, innate and learned) are part of the equation, in a social context we can make a judgement and take action based on someone's actions even if we don't fully understand the processes involved in the decision making. The actions can be to help alter a person's learned tendencies, by punishing unwanted behavior, or rewarding desired behavior, adding the punishment and reward to future consideration of consequences. They can be to isolate or reduce the power of someone with unwanted innate tendencies, or give greater power to someone with desired innate or learned tendencies. We have to try to make a distinction between innate and learned tendencies, even though we don't understand fully the distinction, and don't even understand the process that turns tendencies into actions. So when I say 'virtual free will' I don't mean to confirm free will or deny it. I simply mean that for all intents and purposes we can consider free will to be real, and part of the reality that we live in.
For many millennium man has drawn the conclusion that the sun will rise in the east, and yet only when we understood planetary orbits did we have scientific confirmation that this conclusion was true. That did not mean that the process was not in place until we understood it. Prior to our understanding, we ascribed a will to the sun to rise in the east, until we could see how it fit into a coherent description of reality. Such is the will that we ascribe to ourselves.
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