Free Will, Determinism, Infinity

(Essay subject to addition as I run across more retarded arguments.)

Determinism
I'm actually of the Free Will persuasion. However, I've followed the debate for years, first in New Scientist and later online, and I tend to be able to argue determinism better than actual determinists...

For instance, a common 'rebuttal' from the Free Will crowd (I'm going to shorten the terms to Choice and Fate) is that Fate would gut the criminal justice system, which ostensibly relies on responsibility.

The truly foggy-brained determinist argues that Fate doesn't kill responsibility. Instead, they should argue that incentives determine behaviour. The justice system already uses the ideology of incentives. (I can cite several unenumerated articles.) In fact transitioning the system from a Choice ideology to a Fate ideology would make almost no change at all outside terminology.

This kind of argument is extremely multi-purpose. Anytime you see a Choice argument saying that Fate kills a whatever ("Fate kills the meaning of preferences!") just say, "No, preferences are an incentive and they change the probability of various decisions. Further, the preferences arose by Fate anyway and if you're going to have them, you're going to have them."

This is the first of many times I'll show that the consequences of the 'theories' of Choice and Fate are eerily similar. They're very Freudian, in the sense that they cannot be disproved. As a justification for actions, each is an infinite regress of previous 'choices' or 'determinations' that can only be broken by appealing to the other principle. (I'll get to this below.) This also means that there's no actual evidence for or against either, which means you can pick whichever one you like.

There's a similar line of thinking that goes "But if it's all Fated, then why are you trying to change my mind? It's already been decided!" This is...naive. I can prove this with a single counter-example:

"It's already been determined that my arguments will change your mind. Unfortunately, you simply don't realize it yet."

This is an understandable position, as the Fate argument, from a physicalist perspective, is very strong. There is no evidence that Choice is necessary to explain anything. It looks instead as if Choice has a lot in common with the God of the Gaps, in that it's been pushed back many times yet never actually quits, although now the ramparts are stable due to Bell's Inequality, which bars decoherence from being anything but stochastic.

Which brings me to another stupid argument Choice advocates make. Stochastic phenomena are not free. Randomness is not will. While yes, they both share the property of unpredictability, (which I'll analyze in more depth below) quantum probabilities have averages. You cannot escape the probability envelope. The average is precisely defined. (What about having an average of the average? I'll get to this in a bit as well.) While technically the electrons in a one-slit experiment could pile up on any spot, they never will pile up on any spot except the average - the line directly in front of the slit, with outliers defined by the Guassian.

While I do seem to have a gift for definition,* defining Choice is as yet impossible. The problem here is that Choice advocates are confused about what Choice actually is, and that's not going to get fixed in the forseeable future. Still, we can make a go at understanding it by analyzing various situations. The sensation of choice is very important to us. Again, it's immaterial whether it affects our Choices or determines our Fate, so such an analysis should prove useful to everyone.

*(Current trophies; life, intelligence, art, ownership, philosophy.)

Free Will
So, how can one have Choice? Well, it's as yet impossible to answer, actually. Which directly means it's unprovable. Yet, we have an intuition we can examine.

For instance, of your sensation of Choice is an illusion there to fool you into thinking you have Choice for some purpose...then all your decisions are made for you. Your decision to keep reading this post (or not) has already been made or will be made by jittering atoms. Yet, oddly, this does not actually extinguish the existence of Choice.

Taking the Newtonian Fate position, every event was irrevocably encoded by the initial conditions of the Big Bang. However, the Big Bang is a special boundary condition; talking about its causes is meaningless. This is an identity; the thing for which it is meaningless to talk about causes is the Big Bang. This is a direct consequence of the finity of time and Godel's incompleteness theorem. There must in fact have been some first event with no cause, that was not an effect.

As a result, outside influences are plausible, including putative Gods. In other words, perhaps God fiddled with the Big Bang so that the choices you make today were decided by Him at that moment. (This makes God the thing with no cause, instead of the Big Bang.) While the choices are pre-determined and we're just going through the motions, Choice still existed - at one point in time. (This idea is the reductio ad absurdum of making a choice before you know you've made it.) In this scenario your 'soul' is a manifestation of a part of God in a very literal sense. You would be a direct expression of God's decisions.

While I use God for clarity, we could see that without an actual conscious God, the Big Bang readily takes His place. The Big Bang's initial conditions determine the rest of the universe - including the consciousness present there. We are all simply manifestations of the Big Bang's will.

Of course our universe is subject to unavoidable randomness due to the No Infinities Principle. The present was not determined by the Big Bang, but merely suggested. It was a probability. (Now it's a certainty.) So the determinition of those illusory Choices is pushed up, but not so much that it brushes up against the actual sensation of choice, under these assumptions.

Alternatively, Choice may in fact be real. You are given alternatives, but it is always impossible to predict which alternative you will Choose until the Choice has been made. (Notably this is a nearly a negative definition of choice; this lack of predictability is vital. If your Choices are somehow determined there will always be predictors in theory, and therefore a true opposite to Fate must be unpredictable.)

However, even if you have Choice, it is your choice that determines your actions. Without this deterministic step, your choices would be impotent. In other words Choice is - must be - simply another type of event to add to the deterministic scaffold.

This fact is the basis of compatibilism.

(Even when the real basis is irrational, I like to pretend that there's a good reason behind opposing beliefs. It leads to a more interesting debate, and indeed the alternative is simply to call them ninny-heads. Note the meta in this statement; in general, it's preferable to be gracious, not mean, in your interpretation of opposing views, because it benefits both parties. Even a hardcore selfish person - a Darkworker in Pavlina's lingo - benefits by being gracious.

(I'm not going to properly analyze compatibilism because I can't work out what it's supposed to mean.)

Nevertheless for compatibilism, for Choice to be meaningful - to be unpredictable - it cannot be like Fate. Compatibilism attempts to reconcile souls with physicalism, but fails because Choice is a fundamentally dualist kind of concept. Again, stochastic behavior is not Choice. It is perfectly predictable in average, even if not in instance.

Predictability
And what about those averages? So, even though individual quantum events are totally unpredictable, their average is predictable to a Newtonian degree. But what if we spread the love? What if we make the average itself unpredictable?

There are two problems with this, first mathematical and second physical.

First, the stacked probabilities are indistinguishable from an intial probability that's just shorter and fatter. A Guassian times a Guassian is just another Gaussian.

Second, this physically requires that the 2nd order average moves relative to the first average. In other words it must be a process on a separate timescale to the first.

This is difficult, so don't be surprised if I'm not making sense. Let me try to illustrate. In the electron one-slit experiment, the electrons create a Guassian shaped probability envelope centred on the line in front of the slit. For this Guassian to move relative to a fixed Guassian the envelope must jitter just as the electron strike locations jitter. Unfortunately, there's only one process going on. And it's electrons flying from a slit to a plate. Lets say it happens every second. Time is relative and the electron cannot act differently at different times - they cannot tell what time it is and react accordingly - which means no process of two seconds or 1.5 seconds or anything other than one second can occur. If there are two stochastic determinations of the electrons position, they must happen simultaneously with the electron-photoplate interaction, and thus the 2nd order averge is physically meaningless; it must always fold into the 1st order average.

For further illustration, imagine that there's actually two processes, say electron temperature and electron spin, which somehow both influence the envelope. Unfortunately, if both are random, they cannot vary more often or less often than once per electron. Thus, the processes are simultaneous and always fold into one probability.

There is an interesting consequence of taking this farther, but first I'm going to talk about infinity.

Infinity
Is a very important topic to Free Will and Determinism. First, let's talk about infinite regressions - turtles goin all da way down.

First of all, Determinism nearly fails as a logical concept, because of the Big Bang boundary condition. There must be a first event, that first event cannot have a cause, and thus must violate Determinism. Since every event depends, under determinism, on an unbroken chain of causality, every event depends on the Big Bang and thus every event has no actual cause. It's a bit amazing we don't have pure chaos, actually. As before, the initial conditions of the Big Bang can be seen as a kind of Choice - it was, absolutely, unpredictable. (There was, as far as we know, nothing to exist with which to form a prediction. Anything that did exist would have to be time-independent and thus incapable of acting.)

Determinists may be able to get out of this by ensuring that the First Cause is indeed special in some sense and therefore doesn't count, but this still doesn't address the complete lack of predictive ability Determinism has.

Free Will is also vulnerable to this kind of attack. The choices you made today were shaped by the choices you made yesterday. You paid opportunity costs yesterday. As a result, you're not truly free. Indeed, yesterday's choices were also determined by earlier choices. Eventually, there's a first Choice that arose by Fate. In other words, the only way to consistently believe in Free Will at the moment is to believe it was Determined to arise.

Thus, we can see that, logically speaking, the consequences of Free Will are Determinism and the consequences of Determinism are Free Will. This is just a tad surprising to me. It strongly suggests that even a well-defined debate would go nowhere, because the concepts are inherently incoherent, on top of their complete inability to make predictions are thereby be falsified.

After all this, it's a bit startling that I am so staunch in my belief in Choice. There are two reasons for this. First, Axiom One: I trust my senses. I have no alternative; if my senses are deceiving me, they will also deceive me about deceiving me. Second, what possible purpose would a sensation of Choice have if you do not actually have Choice? It would seem outrageously expensive to me. The incentives are all wrong.

Later I also found that consciousness isn't physical and that mind nodes require a download action - Choice.

So, one average or 2nd order averages or 3rd order averages can exist in a Platonic sense, but they always fold into a 1st order average in a physical sense.

But what if you had infinite averages?

Well, the Guassian multiplied by itself infinite times equates to a flat line. It is a constant function of y= ε where ε is the infinitesimal. This no longer has a meaningful mean or median. This kind of probability describes a spontaneous or true random or nondeterministic event. Notice that the predictability of this is not only low, as required for Choice, but actually zero.

What's more, this kind of event kind of makes physical sense. Imagine a tachyon, which when run through the single-slit experiment has an infinite-order average instead of a 1st-order average. The location of the tachyon strike is truly random. Luckily tachyons don't really exist, because we have to run this experiment on an infinitely large photoplate. (Otherwise we have an 100% chance of the tachyon missing the plate.)

The Platonic probabilitiy of the tachyon landing at any particular point is ε. That is, basically zero. Yet, it must land somewhere. So, if we run across a spontaneous event, it does in fact occur. So, our physical measured probability for the tachyon will be 100% at the point it landed. (Subject to uncertainty, with is important for the math. Ask me if curious.) It seems practically Newtonian until we get a second tachyon.

Now, we've got a second measurement, and the probability is split between the two spots, at 50% each. The average location will be halfway between them. For the third measurment we've got a triangle, 33% 33% 33%, with the location in the centre of the triangle. Notice this is like a 2nd-order average; the average of the third tachyon with itself is averaged with the first average. The fourth strike will create a 3rd-order average.

The tachyon, physically speaking, is approximating the infinite series of averages. With an infinite series of measurements it would approximate it perfectly.

The next fact about this is that the average, as desired, moves. If there are 999 hits recorded with an average at (0,6), an electron experiment would be unable to significantly move the average. Single outliers won't do it, and far outliers or many (1000) outliers are too improbable to even conveniently write out. By definition, the tachyon can have a single outlier at, say, (0,994 006) instantly moving the average to 1 000 000/1000 or (0, 1000).

Please note that for small numbers electron will act just the same way. However, I use small numbers to illustrate that the electrons converge on a Guassian, while the tachyons will diverge. The electrons eventually start landing inside the probability envelope, they do usually land near the average, building it up and up. Even if the tachyons do form an apparent envelope, at any time the average can move an arbitrary amount. (This is partially why we need an infinite photoplate for tachyons. For it to move an arbitrary amount requires that the tachyons hit an arbitrary distance away. Even if we magically assume a finite photoplate has a nonzero chance of being hit, the average will converge on the centre simply because the tachyons need more and more concentrated hits to move it away from the centre.)

So, the tachyon analogy is just that - an analogy. We can't ever build something like that; it simply proves that all such location experiments must be stochastically deterministic. However, there is such an infinite canvas we can use.

Information. This is the basis of the mind node; with the infinite canvas of information, if a machine can duplicate the behavior of the tachyon, then it must be nondeterministic. Unfortunately for Choice, for mind nodes to work a version of dualism must be true, which pushes the question back past the Bell's Inequality bulwark. While mind nodes are physically nondeterministic, mind nodes in combination with consciousness may still rescue determinism.

[I've never said this explicitly, but as always, corrections both logical and stylistic are welcome. I positively hunger for them, actually. I'm not one of those writers who scoffs at editors. Instead if I thought my ideas were perfect I'd likely not write about them much.]