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August 20, 2019

CATEGORY: Blog [back]
TOPIC: Measuring Free Will: Ian Durham at the 6th FQXi Meeting [refresh]
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Blogger Ian Durham wrote on Aug. 14, 2019 @ 19:08 GMT
It feels a bit odd blogging about myself, but here goes...
The author at the 6th FQXi Meeting


For most of the history of modern science the debate over free will has been largely left to the realm of philosophy. Indeed, the debate is as old as philosophy itself. But, increasingly, free will has gained in importance in certain areas of science. For example in quantum mechanical tests of Bell’s inequalities, it is assumed that the “choices” made regarding the settings on the measurement devices are “freely” made by whatever is operating those devices (FQXi member Nathan Argaman argues that this is merely freedom in the variables themselves, but this is a debatable point). This led mathematicians John Conway and Simon Kochen to develop a free will theorem that posits that if we have free will, then, subject to certain assumptions, so do elementary particles. Specifically they take free will in this context to be the fact that our choices do not depend on the past. Their theorem is often interpreted as showing that science is incompatible with determinism.

Nobel laureate physicist and FQXi member Gerard ‘t Hooft disagrees with this sentiment. In his view, the “choices” in a Bell test are ultimately determined from the entire history of the universe up until the point at which the choice is ultimately made. This is sometimes referred to as superdeterminism. FQXi member Anton Zeilinger strongly opposes this view as antithetical to the entire scientific enterprise as he sees it as undermining falsifiability.

What is notable about both these views is that neither is particularly favorable toward free will as a concept. While Conway and Kochen certainly argue against determinism, by concluding that elementary particles must have free will if we do, it seems as if they are, through the apparent absurdity of that conclusion, arguing against free will.

This debate is far from purely academic. The modern legal system in many countries assumes that human beings have some level of free will while modern science seems to be pushing back on this assumption. Understanding the actions of our fellow humans entails a better understanding of consciousness and, by extension, free will. The fact is, whether or not we actually have free will, we behave as if we do. But what are the characteristics of this behavior? What does it mean to have (or behave as if we have) free will and can we quantify it?
What is free will?


This is a question that I addressed at the recent FQXi conference in Tuscany.

Free Podcast

Measuring Free Will. To what degree are our choices really free, rather than determined? And how much control do we have over them? Quantum physicist Ian Durham presents a new mathematical model for free will. From the 6th FQXi Meeting, in Tuscany.



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I began with a simple example. Suppose that I open my refrigerator in order to have a snack and am presented with the option of having either carrots or peppers. What would it mean from a behavioral standpoint for either choice to be seen as being “free”? In other words, what do we really mean when we say a choice is “free”?

For one thing, we need to have the confidence that whatever choice we make, that choice needs to have a high probability of actually occurring. That is, suppose that I choose to have a carrot. For that choice to really be free I need to have the confidence that at some point between making the choice and actually eating the carrot, it doesn’t spontaneously turn into a pepper or a potato or a chair.
What are we actually doing when we choose, say, between carrots and peppers from a refrigerator?
If the latter happened with any regularity, we would simply throw up our hands and stop making choices altogether because we could never be certain of the outcomes. Choices could just as easily be made by throwing darts at a wall. Outcomes would be completely random regardless of what we thought we chose. This is not free will. As philosopher Robert Nozik pointed out, “An action’s being non-determined is not sufficient for it to be free–it might just be a random act.”

This also suggests that we weigh our options against one another. Again, if we didn’t, we could accomplish the same thing by throwing darts at a wall. This, in turn, suggests that the options we didn’t choose generally don’t change once we’ve made our choice (and started to act on it) either. Again, if it routinely did, we would simply give up in frustration.

None of this necessarily means that our choices are about fitness. I may simply “be in the mood” for carrots rather than thinking that carrots are somehow a more optimal choice than peppers at the time. But the point is that I have the time and ability to think about them. That is, I have “read” them into my memory and then contemplated them. In order to do so, however, the number of all possible choices must be processed in a finite amount of time or we have to consciously eliminate some without really processing them.

In order to quantify all of this in some way, we nevertheless need to recognize the fact that, at the most fundamental level, the universe is random. Whether or not we actually have free will, it is clear that there is a deterministic element to our behavior concerning choices, namely that those choices have a high likelihood of occurrence once chosen. But that level of determination has to arise from something more fundamentally random. How is this possible? A simple example provides a hint.

One of the more popular games at casinos around the world—and one of the oldest games of chance known—is the game of craps. The game of craps is relatively simple. It simply involves rolling a pair of dice and betting on the outcome. But not every outcome of the roll of a pair of dice is equally probable. Anyone who has ever played a board game knows that a roll of 12 (“double boxcars”) or 2 (“snake eyes”) is much less common than other rolls. But why is that?

The roll of each individual die is assumed to be completely random. That is, each number from 1 to 6 is assumed to be equally likely to arise. In fact, to try to ensure this is the case in the long run, casinos paint the dots on their dice rather than use dice whose dots are little holes as is common in most dice. This is to ensure that the center of gravity is as close to the physical center of the die as possible which helps keep the die balanced.

So if each number on a single die is equally likely to occur over the long run, how is it that a roll of 12 or 2 is less common than, say, a roll of 7 (which happens to be the most common)? The answer is that there are more combinations that give a 7 than give a 2 or 12. In fact, there is only one way to roll a 2 or 12—both dice have to be 1 or both dice have to be 6 respectively. But there are six ways to get a 7. So the probability of getting a 7 is higher because there are more configurations that lead to a 7.

While a 7 is more likely than a 2 or a 12, it isn’t that much more likely in the grand scheme of things. Most people have rolled a 2 or a 12 while playing a board game at some point in their lives. We call the number rolled on the pair of dice (between 2 and 12) the macrostate and we call the number rolled on each die individually the microstate. But there are physical systems with macrostates that are overwhelmingly more likely than nearly every other macrostate such that the system almost always ends up in this state. Examples include two-state paramagnets and interacting Einstein solids (I discussed some of these in a recent FQXi essay). In other words, it would be like having a pair of dice that, despite the individual dice ending up on a random number each roll, the pair would always end up on the same overall roll. This isn’t a strange quantum behavior. It’s simply how combinations work when the number of combinations is very, very large.

The point of all this is to show that it is possible to get a nearly deterministic macrostate from a large collection of entirely random microstates. In fact, in statistical mechanics, this is known as the thermodynamic limit. There is nothing mysterious about it.

How does this help with modeling free will? Let’s go back to the refrigerator again. What am I actually choosing when I choose carrots over peppers? The fact is that the carrots and peppers are in different places in the refrigerator. As such, the act of getting a carrot out of the refrigerator is an entirely different process than the act of getting a pepper. So when we make a choice, we are choosing between two different processes. Each of these processes has a probability distribution such that one macrostate is overwhelmingly more likely than any other—the chance that the act of choosing a carrot leads to eating a pepper is vanishingly small. That is, the variances of the probability distribution for each process is very small. This seems in line with the what we might think of as a “free choice” since it ensures that our choice is very likely to occur.

If all of our choices have probability distributions, we can represent the ensemble of possible choices with what is called a mixed distribution. There are a number of interesting properties of such distributions including something known as the Mahalanobis distance which can be construed as measuring just how distinct a pair of choices is. The Mahalanobis distance between two different carrots is going to be smaller, for example, than the corresponding Mahalanobis distance between a carrot and a pepper since the carrots are more “alike”. One assumes that the freer the choice, the larger the Mahalanobis distances to all the other possible choices.

So one possible measure of “free choice” would be some function (which I call the zeta-function) of the minimum Mahalanobis distance between that choice and any other choice in the ensemble. Likewise it would be proportional to a time function that ensures that the full ensemble of choices can be read into our memory and processed in a finite amount of time. The zeta-function should also be inversely proportional to the variance of the choice (the smaller the variance, the greater the freedom as I just described).

The zeta-function is a measure of the freedom of an individual choice. It is safe to say that sometimes our choices are not free. Many actions in our life are instinctual. But it’s safe to say that if a certain number of our choices are free we might say we have free will. So a measure of free will itself, which I call the Z-function, would be some function of the collection of zeta-functions for all the choices we have.

There are a lot of details that can’t be captured by a blog post or a simple twenty minute talk (a paper is forthcoming). Certainly there are valid criticisms of such a model. But my aim was really to stimulate discussion and hopefully research into formal models of free will as it is becoming increasingly important in science, particularly in areas like quantum foundations and consciousness studies. So one can view this work as me throwing down the gauntlet and challenging the scientific community to start thinking about this in some depth. Hopefully I will have at least succeeded in that.

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FQXi Administrator Zeeya Merali wrote on Aug. 14, 2019 @ 21:56 GMT
This is probably not the most important thing to have taken away from this, but I did not know that little fact about casinos painting the dots on dice.

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Saibal Mitra wrote on Aug. 14, 2019 @ 23:07 GMT
Within the MWI one can also address this issue by invoking the fact that our subjective state (everything that we're aware at some instant), doesn't fully specify the exact physical state of our brain. The number of distinct physical brain states is so astronomically large that your mindset and how you are feeling about everything isn't going to be consistent with only one physical brain state. This means that given your subjective state, the physical state of your MWI sector should be described as a very complex superposition involving a large number of brain states that are entangled with the environment.

It's then possible for you to find yourself in a physical state where you really have different choice. While one can attribute that to a lack of knowledge, the "you" as an entity that has a subjective feeling of who you are and what you are experiencing, may only exist as an entangled superposition. A problem within the computational theory of mind is the relevance of counterfactuals. Suppose that a computer running an AI program is generating consciousness. Then the fact that this AI is conscious at any given time is due to the algorithm being run.

But at some moment in time, the physical state of the computer is just transitioning from one particular state to another state. If consciousness is related to the actual physical state of the computer, then replacing the computer by a dumb device that doesn't compute anything, which simply cycles through physical states that the computer would move through given some particular set of inputs, should also be conscious.

This absurd conclusion is hard to avoid, somehow getting counterfactual actions as a response to counterfactual inputs must be relevant, but there is no room to do that within classical physics. But a realistic MWI picture as described above does get around this problem.

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Lorraine Ford wrote on Aug. 15, 2019 @ 01:31 GMT
When oh when will physics stop the utter nonsense about free will: THE PHYSICISTS MODEL OF THE WORLD DOES NOT PERMIT GENUINE FREE WILL. Genuine free will is about a living thing having “the power of acting without the constraint of necessity or fate” [1].

Apparently, physicists think it is OK to massage the true nature of their model of the world, and redefine determinism as “free will”. Now they have added the laughable concept of “probability distributions”, as if a “probability distribution” ever caused a single actual outcome.

Either the physics model of the world is correct, in which case no free will exists OR free will exists, in which case the physics model of the world is incorrect. Clearly, the physics model of the world IS incorrect: the physicists view of the world is very badly mistaken.

1. https://www.lexico.com/en/definition/free_will (Oxford dictionary).

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Blogger Ian Durham replied on Aug. 15, 2019 @ 17:39 GMT
I do not redefine determinism as free will. Actually, my claim is that free will (at least as we seem to experience it) lies somewhere between full determinism and full randomness. But, as I point out in my response to your second comment below, I am actually not attempting to define free will here. I am simply mathematically modeling the behavior we most commonly view as attributable to free will. I am not saying that probability distributions themselves have any causal agency. They are simply a way to model data. That's all I'm doing.

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Lorraine Ford replied on Aug. 16, 2019 @ 15:08 GMT
I agree that you personally didn’t try to “redefine determinism as free will”, but a lot of physicists and philosophers do try to “redefine determinism as free will” (e.g. philosopher Daniel Dennett, who seems to be admired by a lot of physicists).

See my question below.

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Blogger Ian Durham replied on Aug. 16, 2019 @ 17:25 GMT
Yes, many do try to do this. Many also define its exact opposite---indeterminism---as free will. I think both are misguided.

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Lorraine Ford wrote on Aug. 15, 2019 @ 03:05 GMT
The world is burning; environmental catastrophe is looming. But all physics can say is that the laws of nature caused it, or “probability distributions” caused it. According to physics, matter itself (e.g. matter in the form of human beings and other living things) has no power over outcomes: only laws of nature and “probability distributions” have power over outcomes. Is it any wonder that many people have no respect for science?

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FQXi Administrator Zeeya Merali replied on Aug. 15, 2019 @ 17:14 GMT
Hi Lorraine,

I understand your frustration. Many scientists and philosophers would agree that it's tough to come up with a version of libertarian free will that fits with physics. But I think Ian would be the first to agree that environmental catastrophe is looming -- he highlighted the climate change crisis as the biggest issue of 2018 on a previous edition of the podcast.

I don't think his intention with his model is to explain away our moral responsibility for our actions, so we can all just give up and blame our powerlessness in the face of the laws of nature for climate change.

Whether we can come up with a physical account of free will that can deal with moral accountability, that I don't know. But I think it's reasonable for Ian and others to try and take steps towards framing the puzzles surrounding free will in a mathematical way.

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Blogger Ian Durham replied on Aug. 15, 2019 @ 17:36 GMT
Thank you for that comment Zeeya. Yes, I absolutely think the climate crisis is a looming disaster that we are entirely responsible for. In fact I do not actually attempt to explain free will with my model. I am simply mathematically modeling the behavior of free will. My model works regardless of whether or not free will actually exists (I, personally, think it does). Again, I am in no way attempting to absolve anyone of responsibility in this. We are all responsible through our actions (or lack thereof).

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Steve Dufourny replied on Aug. 16, 2019 @ 11:40 GMT
Hi dear FQXi friends,

Lorraine,what you tell is a reality. I Don't understand the high sphères of power.They must take their responsabilities because they exist these solutions.Here is a global solution in all humility. We must industrialise the solar system in liberating the funds of this world bank.That will catalyse the 197 governements and they shall be able to give water,food,energy,jobs,hopes to majority. On earth we adapt due to climate and others problems and we harmonise the ecosystems on earth on soils and océans with the vegetal multiplication and composting at big global scale.For space too we need these ecosystems.This solution is deterministic,we are obliged to adapt us.We opeouhumanity,this earth to our universe,it's a logic step of evolution,a new era.Economically speaking too it's important to tell that all wins without exception.We are obliged to change,if not we shall add chaotical exponentials.If they didn't exist these solutions,I could understand,but no they exist and are rational,we does not lack norbspace,nor Energy,nor potential.We lack of a real responsible ONU taking its responsabilities.We can do it,we must convice this ONU.Maybe FQXi can create a system,it will be the biggest revolution of all times.We can do it.The hour is serious after all,for us and the next générations.

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Eric Aspling wrote on Aug. 16, 2019 @ 00:44 GMT
Professor Durham,

Your talk and related blog were very fascinating. I enjoyed them very much. I have some "novice" cautions that I am curious to know your thoughts on:

Time certainly can't be treated like an independent variable. It's not so obvious with the carrot/pepper example (though valid). However, the decision to charge a burning car to save a life is directly tied to time as...

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Blogger Ian Durham replied on Aug. 16, 2019 @ 17:40 GMT
Hi Eric,

Those are some really awesome observations. You are right that the Mahalanobis distance is a temporally fixed quantity. I think I need to flesh out the locality issues in a bit more depth.

Regarding the thermodynamic limit, I think you are partly right about that. We certainly don't understand it enough. I'm not convinced it matters here, but I could be wrong.

I definitely think you have nailed some of the issues with the role that time plays in this and I have been thinking a lot about how to incorporate it into the theory. In the write-up I am working on I took out the inverse-dependence on the time function because some folks at the conference made some similar observations. I just have to figure out how to come up with a clearer model.

Speaking of which, if you have any further ideas or insights, feel free to drop me an e-mail. One of my goals in this work is the stimulate further work by people other than myself. Basically I'm trying to get the scientific community to think about free will in a different way.

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Steve Dufourny wrote on Aug. 16, 2019 @ 11:19 GMT
Hello Professor Durham,

Thanks for sharing,this article is a pleasure to read and your interprétations of free will too. I d like share a thought,general,here is the idea.

We have this general relativity considering this gravitation like a curvature of our spacetime due to mass.It's not really a force for this GR which has been recognised like correct.The newtonian mechanics correct...

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Steve Dufourny replied on Aug. 17, 2019 @ 11:02 GMT
Professor Durham,

sorry ,it's not about your mathematical free will,but I d like to have your point of vue about this quantum gravitation.

Here are still reasoning correlated.

This Dark matter probably has a mechanism at quantum and cosmological scales. We have in logic annihilation of this matter giving particles and antiparticles,but how at this cosmological scale?

This implies that so they are bosons if they are encoded in nuclei,of SPIN 2 so like this quantum gravitation.

Now let's imagine that this matter is correlated with the cold and permits to balance these two scales about heat.Like if gravitation balanced electromagnetism,like the cold balances the heat.

That implies that we have a kind of standard model encircled,balanced with this entropical cold gravitation.The same for our cosmological scale.

Now we arrive at a paradox about this gravitation.This force is the weakest quantum force,but too the strongest if we insert a serie of quantum BHs farer than our nuclear forces and its quarks,gluons.

Like Simply our cosmological scale and its DM and BHs supermassive. This can explain our quantum gravitation,bosonically speaking more this serie of quantum BHs.

Regards

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Steve Dufourny replied on Aug. 17, 2019 @ 13:48 GMT
hope my equation can be proved,experimented.It's intuitive about this dark matter encoded.So I have Simply added to E=mc².That gives E=mc²+X l² ,X is a parameter unknown that I consider correlated with the cold and l is the linear Velocity of particles of DM.

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Steve Dufourny replied on Aug. 19, 2019 @ 09:25 GMT
Lie groups, there are SU(N),SO(N),Sp(N), and the exceptional G_2, F_4, E_6, E_7, and E_8.

About Lie groups,it's Indeed a wonderful tool for the ranking and fractalisation. That said ,I have suggested to Klee Irwin to consider these finite serie of sphères with cold and heat instead of points and strings.The distribution between the zero absolute and the planck temperature due to codes Inside these finite series of this gravitational aether can give relevant resulsts it seems to me humbly.

Imagine the combinations,infinite if we insert the volumes,surfaces,densities,senses of rotations,oscillations,.....We have a concrete general road to rank and explain all our forces,mass,energy transformations,encodings…..synchroniztions,superimposings
, sortings appear with the good mathematical methods.

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Member Tim Maudlin wrote on Aug. 16, 2019 @ 16:13 GMT
Free will—as a characterization of some human actions—has indeed been discussed by philosophers for millennia. John Locke and David Hume correctly pointed out that there is no incompatibility at all between complete determinism and the existence of "acts of free will". One could have a discussion of their conceptual analysis, but that would really be counterproductive here. Because the main...

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Blogger Ian Durham replied on Aug. 16, 2019 @ 17:24 GMT
Hi Tim, if you listen to the podcast you will see that my work has nothing to do with Bell's theorem. And I fully agree with you that the concept of free will has done nothing but muddy the waters with regard to Bell's theorem (I have read all of Bell's works multiple times---my copy of "Speakable and Unspeakable..." is literally falling apart). My work here is nothing more than a mathematical model of the behavior that we associate with what we colloquially refer to as free will. I take no stance on whether free will actually exists or not. Neither do I make any claims about compatibilism or incompatibilism. It's simply a mathematical model of behavior. That's it.

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Steve Agnew wrote on Aug. 17, 2019 @ 04:16 GMT
So the title is about measuring free will, which would be very interesting, and then the talk denies any way to measure free will.

Is this helpful?

We all act as if we have free will and we therefore we all do have free will. We all act as if we are conscious and so we are therefore conscious as well. This is just how the universe is.

Then people argue that free will and consciousness are illusions and not therefore "real" as if there is any difference between reality and illusions. Most of what we think we sense is actually an illusion and so what? That is just how the universe is and the whole point is survival and so if we survive, reality is what is real.

Clearly evidence shows that free will is subconscious and some therefore argue that free will is not purposeful since it is not part of conscious reasoning. However, our subconscious feeling and emotions are what make us who we are and are hardly random. Morality is not random and has taken thousands of years and morality is decidedly not random or it would have been established thousands of years ago.

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Steve Agnew replied on Aug. 17, 2019 @ 15:52 GMT
Nevertheless, I do find this discussion of free will interesting since it is very revealing of how very smart people think. In fact, people make very reasoned arguments for free will as an axiom and free will as an illusion of consciousness. Of course, since nearly everything that we think we sense we make up anyway because of the complexity of sensation, it turns out that most of consciousness is really an illusion anyway.

We are subject to our subconscious archetypes for most of reality and that includes free will. Likewise, our morality derives from our archetypes and therefore are all subject to the same free will and responsibility for all of our choices. Regardless of the circumstances of our lives, we always have a choice between carrots and peppers from the fridge. Right now, I would choose peppers but then I don't happen to have carrots right now.

Durham argues that random choices are not free choices, but we did freely decide to throw the dart and we did freely decide to roll the dice. So some choices are just 50:50 propositions, but we do make decisions even for these.

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Steve Agnew replied on Aug. 17, 2019 @ 15:57 GMT
The technical reason that we have free will is that we actually cannot always know the reasons why we make the choices that we make even though those reasons do exist in a causal universe. What we do is first make a decision based on our subconscious feeling and then we tend to rationalize that choice with conscious reasoning that may or may not have had anything to do with our choice.

In very technical terms, we each live in our own quantum universe of matter, action, and quantum phase and while matter and action are how things change, quantum phase is also an important part of how things change and we also have quantum phase. In fact, the very nature of neural action potentials has to do with quantum phase so our quantum phase affects how we see matter action and then how we perceive reality.

It is because of quantum phase that some precursors are not knowable even though they do exist as superpositions of quantum phase. We can only know the outcomes of free choice, which, as Durham states, are very certain to happen whether or not you believe in free choice.

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Blogger Ian Durham replied on Aug. 17, 2019 @ 17:34 GMT
I'm confused. I give a very specific measure of free will that I call the Z-function which is a concatenation of what I call the zeta-function which measures a the freedom of an individual choice. So I certainly don't deny any way to measure free will. The entire point of the talk was the exact opposite.

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Robert H McEachern wrote on Aug. 17, 2019 @ 18:29 GMT
"In other words, what do we really mean when we say a choice is “free”?"

It means that the entity that made the choice is an essential "actor" in the causal chain: In other words, no other entity, could either produce or even reliably predict, the choice the entity would make, before the entity made it.

Free will exists precisely because even the universe, in its entirety, is not vast enough to predict some things, in any other manner, than by simply enabling them to happen in real-time; in that sense, the occurrence of the event and its prediction are one-and-the-same thing. It is the vast information content of the initial conditions, not the negligible content and properties of the physical laws, that is ultimately responsible for the existence of free-will.

"we nevertheless need to recognize the fact that, at the most fundamental level, the universe is random." No it is not. At the most fundamental level, the universe consists of entities that encode exactly one bit of information, as Shannon, not physicists, define the term. A single isolated bit cannot exist without noise being present. But the fact that each such bit is a combination of both signal, and noise, and not JUST random noise, is what ultimately makes all repeatable (hence predictable) behaviors possible.

Rob McEachern

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