I’ve heard rumours of a course of five or six lectures Conway did many years ago (before he went to Princeton). The goal is to prove Gödel’s incompleteness theorem but somehow using geometry in some way. I think you need to allow comparing two lines and knowing which is longer (and this foundational thing is hard or maybe impossible) in some sense. I don’t know what is left of eg Gödel numbering or the formal languages stuff because I’ve only heard vague descriptions of this.
I believe the contents of this course were lost to time but I’d like to be surprised.
I saw Conway talk on Gödel’s incompleteness theorems shortly before he went to Princeton, and the proof he gave was the standard one (although very entertainingly and efficiently presented).
Exactly what I was thinking.
This kind of attitude can make people that are less connected to the topics John Conway is talking about, feels much more into it.
My understanding is that it says if anyone anywhere has free will, then so do some elementary particles. It doesn't say anything about if anyone or if any elementary particles actually have free will right? Does it lend support either way to if free will exists?
It shows that to whatever extent an experimenter can behave nondeterministically, so can an elementary particle. So it's useful as a simple way to convince people that quantum mechanical randomness is a true fundamental phenomenon (in particular, that hidden variable theories are all inherently invalid).
I've never seen a coherent definition of "free will", but I don't see how someone whose decision is random has any more or less of it than someone whose decision is nonrandom, so IMO it doesn't really have anything to do with free will one way or another.
Conway distinguishes Free Will from randomness by showing that randomness is just a special case of determinism. The random numbers could have been written down before the big bang and looked up when needed, which is still predetermined.
What makes Free Will free is that it's the selection of some future state independently from the information in a particle's past light cone. Only the particle determines that part of its state. One implication is that our brains, being composed of particles, derive their free will from the sum of the particles' free will. This doesn't imply that particles are conscious or aware, it only means that certain degrees of freedom evolve according to computations performed by the particles independently.
In one of the lectures Conway goes in depth into the philosophy of free will, which he believed in at a time when it was (and still is) almost universally unfashionable.
> Conway distinguishes Free Will from randomness by showing that randomness is just a special case of determinism. The random numbers could have been written down before the big bang and looked up when needed, which is still predetermined. What makes Free Will free is that it's the selection of some future state independently from the information in a particle's past light cone. Only the particle determines that part of its state.
That's a distinction without a difference - how would you tell whether the particle is magically looking up its results in the universe's big book of random numbers or deciding for itself? It's true that quantum-mechanical randomness is localised, in a provable sense, but there's no contradiction between that and what "randomness" is usually understood to mean.
> One implication is that our brains, being composed of particles, derive their free will from the sum of the particles' free will.
> That's a distinction without a difference - how would you tell whether the particle is magically looking up its results in the universe's big book of random numbers or deciding for itself? It's true that quantum-mechanical randomness is localised, in a provable sense, but there's no contradiction between that and what "randomness" is usually understood to mean.
one of the points the theorem makes is that you can't get the behaviour of fundamental particles by injecting randomness into an otherwise determinstic system. Free Will is different from randomness.
> one of the points the theorem makes is that you can't get the behaviour of fundamental particles by injecting randomness into an otherwise determinstic system. Free Will is different from randomness.
What is the distinction you're drawing, concretely? There simply isn't one unless you're using some very non-standard definition of randomness.
> What is the distinction you're drawing, concretely? There simply isn't one unless you're using some very non-standard definition of randomness.
AFAIUI by noting that the dice could have been thrown ahead of time and then looked up, we can treat it as a function of time and then it becomes as though another part of the information in the past light cone which doesn't explain the behaviour of particles, as exemplified by FIN, MIN & TWIN
Right, so if you had a fixed dice roll in the past and translated that into the measurement results on each axis in a static way, that wouldn't work. You have to make a fresh random dice roll after the experimenter chooses which axis to measure - or you have to translate the past dice role into the result for the axis in a way that depends on which other axes the experimenter chose to measure.
I assert that this is not terribly surprising, and Conway is actually just doing a sleight of hand around the definition of "random". We would normally expect a truly random event to be (by definition) uncorrelated with anything else, in this case including counterfactual versions of itself - the random measurement you get from a given axis must not be correlated with the measurement you would have got if you'd measured a different combination of axes. That's maybe a little odd, but I don't think it contradicts people's normal notion of "randomness", particularly in a QM context. It's like how in early online poker games people would cheat by figuring out the "random seed" and know all the cards - because that's not real randomness.
and I reply that I just record the "fresh" random roll ahead of time and you look that up. Doesn't make any difference. I think you're confusing random with pseudorandom.
> and I reply that I just record the "fresh" random roll ahead of time and you look that up. Doesn't make any difference.
Well, per everything that Conway's said, it does make a difference - if the experimenter is somehow able to choose which axes to measure after all dice rolls have been fixed, and the mapping of dice roll to measurement result is fixed (and does not depend on which axes the experimenter measures), then that creates a contradiction.
To my mind that's normal quantum behaviour - we see the same thing in the double slit experiment or Bell's inequalities (which this is just a variation on). Quantum behaviour cannot be explained by rolling dice ahead of time, because random results in different possible universes/branches must be uncorrelated with each other, even though we tend to assume that only one of those branches "actually happens". And this result is a cool demonstration of that. But there's no contradiction between that and most people's normal notion of "randomness", IMO.
aren't you mixing models of reality here ? You're describing a universe in which there's free will and determinism, somehow combined with many-worlds. It's hard to follow such hypercounterfactual logic
Well, the theorem pretty fundamentally relies on some kind of counterfactual reasoning - many-worlds is my preferred model, but you can use whichever you like. Ignoring the twin/spatially separated part[1], the meat of the theorem is that there is no possible fixed combination of spin along different axes that has the property that we always observe experimentally (that if we simultaneously measure along three axes at right angles to each other, we'll see two of one type of result and one of the other). So if the results we were going to observe were somehow fixed ahead of time, then there must be a contradiction: for some particular counterfactual combination of axes that we could have picked to measure, we would not have seen the two-and-one pattern that we always see.
The most frustrating part is that this is a cool, exciting result; while it doesn't really prove anything that we didn't already know from the Bell inequalities, the fact that everything's discrete makes for a much clearer contradiction. It shows that quantum-mechanical randomness is very fundamental and genuine: it's not just reading dice rolls off some list that was decided ahead of time, unless we want to commit to the idea that the whole universe works that way. But talking about "free will" just obscures and confuses everything.
[1] IMO that part doesn't add anything new or relevant to the result; it's just stapling the existing EPR paradox onto this new paradox.
I hate to criticise him under these circumstances, and I'm going to leave out the more personal side of things, but: The impression I got was that he was playing up the "free will" angle to appeal to a popular audience, at the expense of the physics. Most academics with a book to sell do that to a certain extent, but I felt that he went past what's reasonable. I won't speculate as to whether that was insincerity as such or belief in his own hype.
He devoted a whole lecture to explaining his belief in free will, going in depth into the philosphical history of the concept and his personal reasons which come across as entirely genuine. He also speculates as to how he thinks the limited free will of particles could result in our free will. It's six lectures and a lot of hard work with highly respected physicists by a mathematician who's old, accomplished and distinguished.
Fair enough. I honestly find that a lot sadder than the idea that he knew what he was doing and was sexing it up a bit. Reminds me of Penrose going off the rails.
He notes in the first lecture that he thinks it is impossible to disprove determinism. A determined determinist can always resort to the argument: all of your senses are deceiving you and you are simply experiencing some predetermined script of qualia (he uses the analogy of watching a movie a second time).
I think the invulnerable argument for it is even simpler than that: whatever apparently non-determined behavior we observe may only appear that way because we don’t yet know the rules underlying it.
Any system will appear unsystematic until the precise rules governing it are known.
Since we can’t ever demonstrate that we’ve exhausted all possible theories of a system, the possibility always remains that tomorrow we would discover a perfectly effective one, and from that point the system would be as plainly deterministic as anything else.
In other words: we lack the capability to definitively distinguish between our own lacking knowledge and a system’s (potential) intrinsic non-determinism.
Right: if you are a brain-in-a-vat observing some powerful play, what can you say about the world in which the vat is embedded? (or for that matter, how is it that you can even be made aware of the vat’s existence?)
We can perform some measurements [0] which show that spin exists. So, the 101 lemma used in the Kochen-Specker Theorem is related to existing laboratory experiments, and not just thought experiments. But indeed this doesn't say whether people have free will.
We might instead interpret the Free Will Theorem as demolishing a position otherwise claimed: People have free will, but people are special; most other things don't have free will, and certainly particles don't! But the Free Will Theorem explicitly contradicts this position.
In terms of philosophy, there are several nuances to consider. There's Kochen-Specker itself [1], its untestability and its applications. There's free will itself [2], including whether free will is definable, is useful for ethics, and indeed whether free will exists. I think it's interesting that [2] has no mention whatsoever of [1] or the Free Will Theorem more generally.
The HN crowd from my impression wants to deeply think of themselves as being in control of how their life transpired. I'm an outlier and I think free will is an illusion. Not only do I think everything is fated beyond our control but I have the belief that society would function better if people were educated young about understanding the concept of determinism and why we don't have control over how life transpires. Fundamentally we're living in a judgement & punishment system of society because religion adopted the stance of people being in control instead of what we describe as evil being a product of God. I think a society that replaces judgement & punishment with rehabilitation would be fundamentally just. I'm curious if society will evolve or stay unchanging but I think it likely won't be in my lifetime.
> Not only do I think everything is fated beyond our control but I have the belief that society would function better if people were educated young about understanding the concept of determinism and why we don't have control over how life transpires
We can’t really decide to do that because we don’t have the free will for it. Preordained fate has decreed for there to be no such education.
I mean, you argument appears self-defeating to me. Is it not?
"decide" is not incompatible with determinism, it just means the decision will always be the same. We all make decisions every day, they just aren't free.
So in this case, it has all been determined that we do not have the education currently, but that says nothing of what the future is determined to be.
I am certainly not holding my breath for society to bite the bullet and accept this. The only way I could see any kind of transformation happening (in the US, at least) is if the sitting president were to physically say "Free will is not a thing, and because of that I'm implementing these reformations". I think that would be enough to get _a_ percentage of the populace at least talking/thinking about it (if not a large percentage).
If free will is an illusion, why not the rest of the world (a la Descartes' Evil demon thought experiment)? Why do you trust your senses at all?
I am compelled by the notion of free will described by Schopenhauer (expanding on Kant). Namely, that 'one can do as he wills but not will as he wills'. Lived experience leads us to infer an indeterminate/inseparable energy/force/Will that we perceive with our senses and organize through the concepts of time/space/causality. However, we, being on the 'inside' of one particular object, are in a peculiar state: we are free to accept or reject this Will.
If I ask you to think of a number between 0 and 10, a number may pop up in your head (seemingly out of nowhere, though clearly through some process affected by genetics/neurochemistry). Despite this, you (whatever 'you' is) are still free to accept or reject this proposition.
In this sense, people can still be punished for accepting propositions of murder in some coherent way. You are affected by, but not the sum total of, your genetics and neurochemistry. Nevertheless, the latter might play a large role that we shouldn't discount.
> Despite this, you (whatever 'you' is) are still free to accept or reject this proposition.
The outcome happens from all the previous moments you lived. Randomness doesn't make a person have free will and randomness may just be an illusion from our lack of understanding when it comes to what's resulting in the outcome we appear as random.
We're the sum total of genetics, environmental factors and all the external forces upon us since birth. That means if we're being punished it was outside the realm of it could have been different.
Probably no more dangerous than free will beliefs because as with some determinist beliefs, it's moderated by thinking life is dictated by a greater order, see Calvinism or the many determinsts who aren't "dangerous" as well as those of us who think deterministic belief leads us to more nuanced and moderate views on societal events, that something begets something begets something, ad infinitum which can lead to better prevention and help mechanisms. I'm certainly not a danger other than to cheesecake or endangered anymore than anyone else who believes the will is free of physical influence and that at its core it's random, or a god or something fueling the RNG or whatever.
A single example: the US justice system is based on retribution. People are condemned to prisons and sometimes death as a result of ultimately how they are wired and the circumstances they were in- there was no 'choice' made regarding whether or not to steal or kill, they were always going to do that, they never had any real 'control' over their actions. If anything criminality in any form should be considered a mental illness, but instead we gladly put people in tortuous conditions because we have wantonly decided that they are guilty, bad/evil, people.
This focuses on the "retribution/punishment" aspect of the penal system, but it's also important to remember that "deterrence" and "reform" are also important. Even if you feel people don't deserve to be punished for their crimes due to the crimes' inevitability, it's still important for repercussions to exist to create a society where it is less likely for people to commit those crimes (for fear of punishment), and where people who do commit crimes undergo a process that makes them less likely to do so in the future. (There are better ways than prison to reform people, of course, but not as many to deter people from committing crimes in the first place)
That just sounds like a one sided convenience for people fated to not be hurt by the system that doesn't harm them. Deterrence can be from not having to go through the rehabilitation system.
I agree with most of your reply but imposing a contentious philosophy upon others wouldn't go well nor would I want to condone it. I'm not very determined to believe in determinism but I do and it doesn't change my views on punishment very much as I'm still determined to have a sense of self and societal protection in that I'd prefer "bad" people kept from society until reformed although I am less judgemental as a result from thinking about it more over the years.
Just because we can't determine why something happens doesn't mean its not predetermined. Every RNG gets its seed somehow, I don't see how we can be so sure that there is absolutely _zero_ cause for a given effect.
Bell's Theorem implies that if there is some kind of hidden variable controlling the outcome of a random quantum event like a seed, then it must work non-locally, which maybe doesn't completely rule it out, but it's really suggestive given that locality is one of the common assumptions like conservation of energy that has lead to a lot of progress in physics.
Interestingly, there is a local deterministic interpretation of quantum mechanics: the Many-Worlds Interpretation. The interpretation is considered by many to be what the Schroedinger equation by itself with nothing extra added (like wave function collapse) implies about the world. There is no objective randomness. The 10,000-foot view of it is that any random quantum event with multiple possible outcomes causes the world to branch into a separate world for each outcome. (Generally random quantum events have a continuous outcome space instead of discrete outcomes, but it's harder to talk about a continuous spectrum of "worlds". The "worlds" of MWI aren't necessarily discrete atomic things; the word "world" is more of a fuzzy label for our convenience, like the word "pile". Also, per the Schroedinger equation, there's situations where multiple histories leading to equivalent worlds can cancel out, decreasing the measure and therefore observed probability of that world occurring; that's how we could possibly know this whole splitting business is going on.)
However, a system like this would still have subjective randomness, in the sense that there's no way for you to predict the value of a random quantum event. (Say you have a device that when you press the button, it will measure radiation from a radioactive object inside it for a period of time, and then output "heads" if it measured more than the average amount and "tails" if less.) Assuming it's set up as advertised, the idea of predicting the result doesn't even make sense, because after the measurement, there will be a cluster of worlds with a version of you that sees "heads", and a cluster of worlds with a version of you that sees "tails". Predicting which one you'll be makes as much sense as predicting who you will be before you were born. (I find it interesting that no matter how deterministic of a universe you imagine, there's always the subjective randomness resulting from the indexical uncertainty in who you find yourself being. MWI extends indexical uncertainty like that to more situations.)
True, but I think this isn't a good response to the idea that determinism means you don't have control over your life. Reality having randomness doesn't give us more control over our lives. (If anything, I'd think that fact alone would mean we have less, because it means there's probably entropy getting in the way of whatever our true decision processes are.)
I really love the way this article puts the issue: https://www.lesswrong.com/posts/NEeW7eSXThPz7o4Ne/thou-art-p.... The idea that determinism takes away free will from us is inherently based on the idea that we're something outside of physics, and that physics is exclusively deciding the future instead of us. However, if you make the common assumption that our brain is a material object running within physics and producing our decisions, then there is no contradiction between deterministic physics and whatever is meant by free will.
Another way I like to think about it: If you made an AI and ran it in some closed simulation, would you expect it to care whether the simulation was completely deterministic (with all probabilistic events operating from a pre-chosen seed and a strong RNG) or had some kind of randomness? The question won't directly affect the AI's life inside the simulation either way. Wouldn't you find it weird if it did actually care and had a preference about that detail of its world, or if it thought it wasn't a true free AI if there was no randomness in its simulation? If the AI thought the world had randomness or not, and then learned the opposite, you'd find it weird if the AI restructured everything it knew about itself and the world directly based on that. If you the operator happened to toggle whether the simulation had randomness several times over its run while working on its code, and at some later point the AI was let out of the simulation, you wouldn't expect the AI to take offense at this change. There's nothing about its quality of life, decision-making abilities, or life circumstances that would be affected by the answer. It's just an implementation detail of its world that's not directly relevant to an intelligence, except in matters of modeling how the world works.
Fate wins in the end. However, it doesn't change the fact we're all systems. When information is presented the systems take it in like a variable and it will have a far greater significance if the information wasn't shared. I don't believe in free will.
I believe the contents of this course were lost to time but I’d like to be surprised.