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Comment by Xcelerate | Hacker News Reader

Whenever I talk about physics (to non-scientists), I notice that people have a tendency to start veering away from the math and onto irrelevant metaphysical tangents. For instance, I'll be trying to explain the history of renormalization in quantum field theory, and someone will suggest, "Well maybe we don't really understand infinity". No, we understand "infinity" just fine. It's a concept that's clearly defined using a set of axioms that have been around for thousands of years. "Well maybe the mathematicians are wrong." I start losing my patience pretty quickly at this point. The other big one that annoys me is "Well it's just a theory". Sure, and gravity is just a theory too. If you doubt it, you're free to go skydiving without a parachute, but personally, I'm not taking any chances.

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I'll be trying to explain the history of renormalization in quantum field theory

I'm hard pressed to think of a situation where this would come up in a conversation with non-scientists.

I can see it happening. As a non-physicist programmer who knows a little bit about a little bit through popular science (like the people being discussed in the article), I know "just enough to be dangerous" about renormalization. i.e., that it was for a while a controversial practice derided by opponents as "handwaving problems away with division by infinity".

I also know that much smarter people than me don't consider it a problem anymore, but it's exactly the kind of gap in the door that self-taught "experts" would use to say that the whole edifice of science needs to be torn down as incorrect and replaced with their personal theory.

"handwaving problems away with division by infinity"

I'm being very pedantic here but it's a bit better to think of it as subtracting infinity from another infinity.

eh, raise the terms as an exponent and subtraction becomes division. :)

In log scale yes.

Renormalization is not the same thing as regularization. Regularization is a mathematical trick while renormalization has a very physical interpretation, for example, its use in statistical mechanics. In QFT, they are related and I think sometimes conflated, which is unfortunate.

You can easily describe renormalization without math because it's a physical concept. Regularization is more difficult. If the OP decided divergent integral regularization was an interesting conversation topic then I am on your side.

Please do then. Explain it without math, I mean.

The entire content of renormalization is summarized as this, given a calculation, you make it match the interaction at some energy. Assuming that the fix is essentially choosing the "scale" of quantities (say, voltage of the electric field, or how strongly electrons tug on other electrons) you are calculating, you fix that scale by making sure that after including it in your theory now, that your result matches the measured interaction at your chosen energy scale exactly. That is renormalization.

If you do this, you find that you need to choose a scale that "absorbs" the infinities of your calculations (yes, an "infinite" scale). But, the stuff that is not absorbed is a function of energy, and this actually agrees very well with experiment beyond the scale you normalized to.

Pretty sure he means people like you when he talks about his non-physicist friends.

If it's a part of Xcelerate's work, and he knows people who are not physicists, but are genuinely interested in what he does all day, I can see it coming up.

You'd be surprised, a mutual friend brings up your occupation (I'm a computational astrophysics grad), and then they inevitably ask you about black holes, and then you have to start delving into pretty complex topics.

As a PhD candidate in high energy nuclear theory, I've observed a lot of 'math wacking', i.e. reading theory papers which include pages and pages of detailed equations without a single experimental data point. Just take a look at arXiv/nucl-th if you want to see what I'm talking about. These same guys go to conferences, poo-poo less first-principle calculations which at least attempt to describe experiment, and espouse their untested pet theories as if it were gospel.

To be honest, I've been extremely disappointed by the scientific process in high-energy particle physics. People are so tethered to their theory convictions, that they accept derivations as physical realities and dismiss the importance of experimental validation. The old farts in the field are also completely averse to computational/numerical methods and dismiss the importance of production quality code development.

So while I embrace the sentiment that 'math is the essential language of physics', if you can't embed the mathematics into a simulation which describes reality, then what are you doing as a scientist?

The space of possible experiments is enormous. If someone takes time to find a conclusion that the theory predicts from the first principles but for which experimental data are lacking, may it be somehow valuable? Especially if the theoretically predicted effect is somehow interesting.

The goal is to disprove theory's not to validate them. Remember any valid counter example can disprove a trillion pieces of supporting evidence.

http://www.nytimes.com/interactive/2015/07/03/upshot/a-quick...

You can always over fit for existing data. Useful theory's should suggest a novel experiments to test them.

The experimental data may prove or disprove a theory. But when it's lacking, there's no way to tell. So finding areas where experiments were not made, but can be made, and where the theory predicts some clear results, can serve as a means of falsification.

I agree that they hate production quality code and numerical methods, but in some of these DFT codes for example (HF is only somewhat better), you fix some numerical bug and a bunch of theoretical results agreeing with experiment go straight out the window and with it your confidence in the computational model. These 'old farts' have probably seen this happen way too many times and on top of it from people who lack the basic theory knowledge, let along experimental, to point out a crap result from the code.

>and onto irrelevant metaphysical tangents.

For those with some time to spare, you might enjoy:

Clearing Up Mysteries -- The Original Goal

http://bayes.wustl.edu/etj/articles/cmystery.pdf

"Put most briefly, Einstein held that the QM formalism is incomplete and that it is the job of theoretical physics to supply the missing parts; Bohr claimed that there are no missing parts. To most, their positions seemed diametrically opposed; however, if we can understand better what Bohr was trying to say, it is possible to reconcile their positions and believe them both. Each had an important truth to tell us. But Bohr and Einstein could never understand each other because they were thinking on different levels. When Einstein says QM is incomplete, he means it in the ontological sense; when Bohr says QM is complete, he means it in the epistemological sense. Recognizing this, their statements are no longer contradictory. Indeed, Bohr's vague, puzzling sentences -- always groping for the right word, never finding it -- emerge from the fog and we see their underlying sense, if we keep in mind that Bohr's thinking is never on the ontological level traditional in physics. Always he is discussing not Nature, but our information about Nature. But physics did not have the vocabulary for expressing ideas on that level, hence the groping."

>we understand "infinity" just fine.

I enjoyed "Meta Math" by Gregory Chaitin:

http://arxiv.org/abs/math/0404335

"So the set of real numbers, while natural—indeed, immediately given— geometrically, nevertheless remains quite elusive: Why should I believe in a real number if I can’t calculate it, if I can’t prove what its bits are, and if I can’t even refer to it? And each of these things happens with probability one! The real line from 0 to 1 looks more and more like a Swiss cheese, more and more like a stunningly black high-mountain sky studded with pin-pricks of light."

>"So the set of real numbers, while natural—indeed, immediately given— geometrically, nevertheless remains quite elusive: Why should I believe in a real number if I can’t calculate it, if I can’t prove what its bits are, and if I can’t even refer to it? And each of these things happens with probability one! The real line from 0 to 1 looks more and more like a Swiss cheese, more and more like a stunningly black high-mountain sky studded with pin-pricks of light."

Bah! Chaitin makes so much of his discovery that there is randomness in mathematics, but doesn't ever seem to have made the shift to thinking of structures as parametric over randomness.

To wit, generating random real numbers by simply flipping a countable number of coins and writing down the bits is trivial, and from that point of view:

1) An open set is just a set about which we can have finite information.

2) A closed set is just a set about which we can have complete information.

3) A compact set is just one we can quantify over and prove theorems about given only finite information.

4) A continuous function is one that has finite character: producing finite information about an element of the image only ever requires finite information about the argument.

These statements are a bit rough, but hey, if I ever have a gajillion dollars I can spend my newfound spare time merging the computational view on synthetic topology, Chaitin's algorithmic information theory, and the old "Age of Stochasticity" talk to get a view of mathematics that properly accounts for its finities and infinities.

http://www.stat.uchicago.edu/~lekheng/courses/191f09/mumford...

See also "abstract stone duality". https://ncatlab.org/nlab/show/abstract+Stone+duality

It doesn't appear that the set of rel numbers exists. If it did, someone should be able to point to it and say, "this is the set". No one can do that because the available space to present the set appears finite, but producing the set would require an infinite amount of space (assuming you need some exclusive space to represent each number).

It is no surprise that the set remains elusive, it doesn't exist.

Sets of numbers aren't physical things. Physical things can't be infinite, but I don't see why you think a set can't. By this thinking, not even the natural numbers can exist, since you can't point to them either.

Natural numbers are easy to write: 1, 2, 3

You can even write a set of them: {1, 2, 3, 4}

You cannot write the set of real numbers.

{1, 2, 3, 4} is also a set of real numbers. Why is it a valid existence proof of the naturals, but not the reals?

Possible linguistic pedantry; he used "a" set of natural numbers, but "the" set of real numbers. It's equally difficult to represent the set of natural numbers.

It's not pedantry, it's just what the words mean.

To the question: I'm only saying that the "set of real numbers" and the "set of natural numbers" don't seem to exist.

Despite numerous downvotes, no one has yet produced them here (or even a link to them).

here is a representation of the real numbers: ℝ

and here is one of the natural numbers: ℕ

How can I select an arbitrary, or even random, element from either?

Who said that you could?

Zermelo?

Axiom of choice says I should be able to select an element from the set of real numbers (assuming it exists; but, I believe the assumption to be counterfactual).

I agree. Even though the axiom of choice is independent of ZF, I don't think it is self-evident axiom. It actually seems pretty counter-intuitive if you believe in infinite-precision real numbers that have an infinite amount of information and can't be compressed. I have more to say on this in "Digital Physics" (the movie). -Khatchig

According to Wikipedia, Zermelo formulated the axiom of choice.

I think it makes sense though; if I (claim to) have a thing, I should be able to choose/pick/select/point-to it (seems to be almost[?] tautological).

"Say you are playing a game that needs you to pick a real number. If you choose a computable real number, you lose the game. If you choose a real number that is not computable, which the majority real numbers are, then you win. You can imagine yourself choosing a non-computable real number, and winning the game, if you build in the axiom of choice. But in the real world version of the game you will never have enough time or space to non-ambiguously specify this infinitely precise real number which has an infinite amount of non-compressible information (see Kolmogorov complexity)."-Khatchig, from "Digital Physics" (the movie)

I can't produce the set of all humans on Earth either, but that doesn't mean they don't exist.

Both real and natural numbers can be reasoned about despite their infinite size (and we even know that e.g. there must be "more" real numbers than natural numbers, even though both sets are infinite)

The set of all humans is produceable, you simply bound by the planet, or solar system.

There are no bounds in the universe that can contain all the real or natural numbers.

If real numbers exist or not is irrelevant. The question is if we can solve some problems by assuming one way or another.

You may enjoy:

https://en.wikipedia.org/wiki/Ultrafinitism

...and "Set Theory, Should You Believe?"

https://web.archive.org/web/20110616020815/http://web.maths....

The universe may be infinite.

The set of real numbers is as big as the set of functions from the naturals to themselves. In fact, that's a pretty convenient way of modeling the real numbers sometimes: as systematic names for functions on natural numbers.

The set of real numbers most certainly exists, it is defined as the unique such set (up to an isomorphism) that satisfies the following properties:

It is at the same time a commutative additive group and a commutative multiplicative group such that the two group neutrals aren't the same. Furthermore the multiplication distributes over addition.

There exists a total order relation such that the addition distributes over the order relation and multiplication agrees with the order relation (if (0 leq x) and (0 leq y) then (0 leq x*y)).

Another axiom is required, which comes in many forms (all of which are equivallent) so take your pick, for example the supremum axiom https://en.wikipedia.org/wiki/Least-upper-bound_property

You can read about any of this in any texbook of real analysis (for example Spivak or baby Rudin).

If the axiomatic formulation of real numbers doesn't appeal to you, there is another way to define real numbers, namely to contruct them from natural numbers (and you seem convinced that natural numbers indeed exist). You can read about that in the appendix to chapter 1 of baby Rudin (Principles of Mathematical Analysis by Walter Rudin).

By no means am I an expert in this stuff, but don't you need the axiom of choice (or maybe something just a little bit weaker) to construct the reals?

I don't think it's fair to say the reals 'most certainly exist' without being misleading to a layman. They exist given some axioms that are used overwhelmingly often in mathematics, but you can still do some interesting stuff without those axioms, or with their negation.

You're correct. There is one object in all of mathematics that isn't defined (you've got to start from somewhere), it is just assumed that humans implicitly understand this concept, and it's the concept of a set (denoting a collection of objects).

Along with it, certain properties of this object are assumed (among them the ability to choose an element of a non empty set - this is typically called the axiom of choice). For a full list you can take a look at http://mathworld.wolfram.com/Zermelo-FraenkelAxioms.html

But the axiom of choice is logically independent of the other zermelo frankel axioms. You can assume zermelo franked plus choice, and get the standard framework (ZFC) that let's you build the reals.

But you can also assume ZF plus the negation of the axiom of choice, and get a system that is consistent if and only if ZF is consistent. It's not clear (to me, at least) that this other system will let you build the real numbers.

Clearly real numbers exist. I just don't believe you can have the set of every single real (they are unlimited).

> if I can’t calculate it, if I can’t prove what its bits are, and if I can’t even refer to it?

That guy is just a constructivist. Nothing new here.

The free will conversations drive me insane. People can't shut up about how Heisenberg's uncertainty principle proves random phenomena (which isn't exactly true) but worse, they insist it indicates that we have free will.

But a) what it really indicates is that it would be unmeasurable whether we have free will, and b) it also doesn't really prove that, because while electron positions are unpredictable, molecular reactions, the sort that happen in the human brain are pretty predictable.

Basically, my response to this is "That would be relevant if we had black holes or large hadron colliders in our heads, but we don't, so...". But people really really want to believe in free will and will use any sliver of half-truth to believe they've proved it.

EDIT: To be clear, I do not believe free will has been proven OR disproven.

EDIT 2: More sophisticated wrong people argue from Bell's Inequalities rather than the Heisenberg Uncertainty Principle, but that also results from a misunderstanding of the theory and also neither proves nor disproves determinism.

On the flip side of this, superdeterminism (that we have absolutely no free will at all) is a third way of explaining Bell inequality violations (apart from Copenhagen and hidden variables), but essentially everyone in the physics community refuses to consider superdeterminism seriously.

It's not that they don't take it seriously -- it's that it's boring and says nothing useful. Yes, everything could be a giant conspiracy that makes it appear as if the standard ways of approaching quantum mechanics are simple, nice, and right, but ...

That's not what superdeterminism would indicate at all.

"Conspiracy" indicates free will on a large number of actors.

And a superdeterministic system could exist which differs from standard ways of approaching quantum mechanics. One obvious way in which it could exist is if our means of gathering data remain as limited as they are currently--i.e. we don't ever find a way around Heisenberg's Uncertainty Principle and therefore can't ever model quanta deterministically. Superdeterminism doesn't mean that we'd always be able to measure the deterministic phenomena.

> [W]hile electron positions are unpredictable, molecular reactions, the sort that happen in the human brain are pretty predictable. Basically, my response to this is "That would be relevant if we had black holes or large hadron colliders in our heads, but we don't, so...".

What about those quantum effects that have recently been shown to potentially be part of brain activity:

https://www.sciencedaily.com/releases/2014/01/140116085105.h...

You could make the same argument to say that your PC adding 2+2 is indeterminate because it has the same underlay of supposed random quantum behavior. But at our material level, the world is pretty deterministic just as your PC or phone adding 2+2 is. And as far as neuroscience has gathered, quantum randomness hasn't affected it enough for those scientists to think it's non-deterministic, or else they wouldn't have a job.

Quantum effects are part of brain activity because they underly all electrochemistry--that's never been in question. The question is whether those quantum effects impart any non-determinism to the brain system, and the link you posted doesn't make any claims that they do or don't.

Given what we know about brains so far, doesn't it need to be proven, rather than disproven? Surely the burden of proof here is on people claiming a non-biological and non-predictable basis for brain function?

I don't see how subjective experience, i.e. consciousness, can come about from purely material interactions as currently understood. That means that a Turing Machine would be able to produce them, which means that a bunch of monks working with paper and pencil for thousands of years would be able to produce them. There's something fundamental that we don't understand and the scientific community is very opposed to talking about it, dismissing any and all speculation as quackery. This taboo is holding back serious inquiry into the matter.

    > I don't see how

Isn't that just The God of The Gaps? I suspect that many intelligent people 500 years ago wouldn't have been able to "see how" a 500 ton metal object could take controlled flight.

    > That means that a Turing Machine would be able to
    > produce them

Is there any specific reason to think it wouldn't?

    > the scientific community is very opposed to talking
    > about it

It sounds like you're suggesting there's a super-natural force at play, in which case, the scientific community is entirely justified in being opposed to talking about it.

I'm not suggesting anything supernatural. I'm suggesting that there's possibly physical phenomenon that do not fit our current materialist model.

Further, my big problem is with people trying to ignore the problem completely by claiming that there is no Hard Problem or even suggesting that consciousness is not real. It's a total head-in-the-sand position to take but it's the dominant stance.

Who is saying consciousness is not real? It just not non-physical and has no single set of hard properties from which to form a definitive boundary for discussion.

I'm curious at what point you think agency becomes consciousness. Is it self-awareness? Is a dog conscious? A mouse? A snail? An ant? A bacteria? A tree?

It has nothing to do with agency. I'm talking about the phenomenon of subjective experience. The difference between a computer that analyzes camera input and a being that actually sees the world. It would be the difference between you and a philosophical zombie.

If you aren't that "artificial" intelligence and can't put yourself in that subjective experience, how would you know that the AI's subjective experience differs from yours? Because you're relying on material observance? You realize your conundrum now? You have to rely on the material to gauge the material yet you try to invalidate the material experience using material observations.

> The difference between a computer that analyzes camera input and a being that actually sees the world.

How do you know there is a qualitative difference?

> That means that a Turing Machine would be able to produce them, which means that a bunch of monks working with paper and pencil for thousands of years would be able to produce them.

Yes. What's not to see? I think appealing to something other than Turing machines shows a lack of imagination; it takes a lot of thought to even scratch the surface of how profound Turing machines are.

Are you really arguing that a scribbling numbers on a piece of paper could give rise to a conscious being?

In another comment, you said:

> I'm not suggesting anything supernatural. I'm suggesting that there's possibly physical phenomenon that do not fit our current materialist model.

Absolutely. Sure, there are of course physical phenomenon that do not fit our current materialist model.

Let's say we discover those additional phenomenon. Ultimately, we'd want to build a machine to model that phenomenon. Perhaps encode a model of that phenomenon in software. Once that happens, scribbling numbers on a piece of paper indeed could give rise to a conscious being.

If it's some system that can't be covered by scientific understanding, isn't that what supernatural means? It's either some internally consistent (but possibly very complicated) set of rules, or it's supernatural.

No, it could be that the universe actually cannot be modeled computationally, that it exceeds the constraints of a Turing machine. This is an open question.

I think you're giving a good example of how poorly people visualize and understand infinity. A Turing Machine's capabilities are based on its infinite memory and infinite computation time, yet you imagine it as "a bunch of monks scribbling" and immediately dismiss its capabilities.

I would actually restrict things further, since introducing infinity can lead to unintuitive results orthogonal to computability ;)

Rather than 'possessing' an infinite tape and infinite time, I prefer to think of turing machines as always being allowed to perform one more step, and always being allowed to use one more tape cell. I find this characterisation of time quite intuitive as-is, whilst the tape can be made intuitive by imagining tape factories on each end, which produce more cells whenever the read/write head gets close.

In fact, such "tape factories" have been used to build universal turing machines in the game of life http://rendell-attic.org/gol/fullutm/index.htm

An order of non-celibate monks can also work for infinite amount of time and hold infinite data. Anyhow, it's not really relevant to my point. An infinite number of scribbles doesn't seem any more likely to give rise to consciousness than any finite number.

> Are you really arguing that a scribbling numbers on a piece of paper could give rise to a conscious being?

Yes. I find that no less plausible than a warm sack of meat giving rise to a conscious being.

I agree, which is why I suspect that consciousness is the result of some fundamental non-computable phenomenon that our minds tap into to perform some useful function.

No. The topic has simply been ceded to a subset of philosophers who fill large volumes that still don't manage to say more about this topic than you do. One big problem is that your thought experiments are designed specifically to make the null hypothesis sound silly. That's the same strategy you guys have been uding for thousands of years. Not so long ago people claimed that life couldn't be explained without some special substance.

You're aware of John Searle's Chinese Room gag?

> I don't see how subjective experience, i.e. consciousness, can come about from purely material interactions as currently understood. That means that a Turing Machine would be able to produce them, which means that a bunch of monks working with paper and pencil for thousands of years would be able to produce them.

Not without input data, they couldn't. You can produce a model, but unless you collect data to validate your model against, you're just speculating in a void.

> There's something fundamental that we don't understand and the scientific community is very opposed to talking about it, dismissing any and all speculation as quackery.

We're talking about it right now, and I haven't heard anyone opposed to talking about it.

However, I'll fully dismiss opinions as quackery if they clearly misrepresent the facts, i.e. claims that Heisenberg's Uncertainty Principle or Bell's Inequalities prove free will are quackery. This isn't because the ideas are taboo or because I'm opposed to talking about them, it's because they're misrepresentations or misunderstandings of facts which are clearly established.

In my experience, when people claim that scientists are opposed to talking about their hypothesis, it's because their hypothesis has been thoroughly and concretely disproven.

Even if we don't have free will, it's better to pretend we do. There is a difference between a driver that falls asleep at the wheel and causes an accident and a driver that flies into a rage and crashes their car into another driver. It's hard to justify the distinction if neither driver has a choice. I'd argue it's better for society to maintain that distinction.

Perhaps someone can reframe that in terms of types of error, and people prone to more serious types of error (road rage) face different consequences. But that gets real complicated real quick.

I dunno. I suspect the majority of the time i'm on autopilot. Alarm goes off, get up, brush teeth, shower. I pretend i'm capable of not doing that. i just don't choose the other way.

There are a lot of people who will not commit crime only because they fear the consequences. So it would be rational to punish criminals regardless of your thoughts on free-will. And if you don't believe in free-will then you have to accept that you have no "free" choice about punishing criminals.

Myself, I do not even know what the will is, or what it could possibly be free from. The influence of the universe?

> There are a lot of people who will not commit crime only because they fear the consequences.

Fear sounds like an implicit assertion of choice, but i think you mean something more subtle.

Let my try to put it another way. People are complex systems that can be influenced. Water tends to flow downhill, we can set up troughs to control the flow of water. The flow is complex, and some water will splash out, but generally the water does follows the system. Likewise, we can set up legal troughs to guide people to the behavior we want. (I know argument by analogy is crappy, i'm just hoping we can agree on this point, and i think we do.) There's a whole other argument about why we would set up those legal rules, but i'd like to set that aside for a moment (if it's a big deal, or fundamental in some way, i'd like to hear your side. I'm not sure i can meaningfully engage that point)

It seems like, punishment would need to be interpreted purely as societal cost. So you tally up the wreckage from the car accident example above, say $25,000 and 2 lives.

I don't really see how we can have both manslaughter and murder, without free will. What extra thing did the angry guy do? He didn't make a choice, because (for the sake of argument) he has no free will. What is the characteristic that makes what he did worse? The cost to society is the same.

> Myself, I do not even know what the will is, or what it could possibly be free from. The influence of the universe?

My personal interpretation (which is probably wrong, but something i'm willing to go back and forth on to come to consensus) Free will the mind having a choice in taking action, rather than the body just doing whatever, and the mind rationalizing it after the fact. Perhaps every action we take is just like a heartbeat. I have no control over that. Perhaps when i hold my breath, i'm not actually choosing to hold my breath, but the complex system that is my body holds it's breath and my mind is claims that it was responsible for that holding of breath. Or typing this comment, or whatever. I don't think there's any way i can know. It feels like my mind is in control, but my mind gets all of its information from (and the software runs on!) my body. my mind seems to control the hardware, but maybe i'm just rationalizing after the fact.

> I don't really see how we can have both manslaughter and murder, without free will. What extra thing did the angry guy do? He didn't make a choice, because (for the sake of argument) he has no free will. What is the characteristic that makes what he did worse? The cost to society is the same.

That doesn't require the concept of free will. Because for manslaughter and murder the reasons are different for the death. One is deliberate, one isn't.

> It seems like, punishment would need to be interpreted purely as societal cost. So you tally up the wreckage from the car accident example above, say $25,000 and 2 lives.

You would also want to calculate predicted future costs from that person, mainly from the point of view of harm to other people. If someone like them is likely to kill on average one or more people in the rest of their life then they aren't going to be allowed to interact with general society again. This doesn't need the concept of free will to implement. It only needs a sufficiently sophisticated way of determining of what harm a person like them will likely cause. This is in addition to the harm they have already caused, so there is no reason for someone to become a one time killer. And yes, getting the predictions right may be really tricky, and the way the courts currently sentence people may be a good as or better than trying to predict what people do on average. But the way courts sentence at the moment doesn't require the concept of free will anyway, because people do what they do because of reasons, human reasons, and they can differentiate there.

> It seems like, punishment would need to be interpreted purely as societal cost. So you tally up the wreckage from the car accident example above, say $25,000 and 2 lives.

I don't think so. I think determinism makes "punishment" as a concept, completely nonsensical--you can't punish someone for something they didn't choose to do. I think determinism pushes the focus to rehabilitation rather than punishment, which for many types of crimes (i.e. drug use, computer hacking, nonviolent robbery) is clearly more effective in preventing recidivism (and I'd argue that for crimes where it's not effective, that we haven't really explored rehabilititation because of the widespread belief in free will).

Agreed. But does this highlight a problem with a deterministic world view, or does it highlight a problem with the distinction between manslaughter and murder?

> But does this highlight a problem with a deterministic world view, or does it highlight a problem with the distinction between manslaughter and murder?

That is a really interesting point. I'm not convinced, but you've given me a ton to think about.

    > There are a lot of people
    > who will not commit crime
    > only because they fear the
    > consequences

Really? I'd say both crime rate and severity of consequences have taken a plunge over the last few centuries.

I used to feel this way too - I remember writing up drunken notes when I was at college saying exactly the same thing.

Punishments from crime have decreased substantially - nobody gets transported or hung for sheep theft anymore. The world has never been a safer place. States with the death penalty are no safer than those without. Fewer people genuinely believe in a Christian (or whatever) hell than in years past. At the same time, religion has faltered as a source in many people's lives.

I would argue this means that circumstances that lead people in to crime have decreased rather than a suggestion that people are making choices to commit crime but don't based on deterrence. I appreciate there exist counter arguments to this too, but also feel that if we treated crime as a function of situation rather than morality, we'd find ways to decrease it more cheaply.

I guess i'd ask the same question i asked of jeremyjh.

With no notion of free will, how do we distinguish between manslaughter and murder? When someone dies, the cost to society is the same either way. A consequence of no free will seems to be it's a distinction without difference. I disagree, but it might just be deeply embedded beliefs that are wrong.

> With no notion of free will, how do we distinguish between manslaughter and murder?

I'd argue that the distinction is not indicative of a phenomenon that exists.

I think a much better model would be predictive and preventive rather than punitive--the level assignment to rehabilitation should be based on the probability and severity of recidivism, rather than the level of punishment being based on the severity of the crime.

> Even if we don't have free will, it's better to pretend we do. There is a difference between a driver that falls asleep at the wheel and causes an accident and a driver that flies into a rage and crashes their car into another driver. It's hard to justify the distinction if neither driver has a choice. I'd argue it's better for society to maintain that distinction.

The distinction still matters without free will, because it's still a predictor of future behavior. A driver who crashes because of a preventable cause shouldn't be allowed to drive until the problem is resolved. If the problem is falling asleep, the solution may be simple (get more sleep?) or hard (narcolepsy), while anger issues are probably pretty difficult to provably solve.

Belief in free will has some seriously harmful effects on the way we deal with these situations. Most notably, it's the basis for a focus on punishment rather than rehabilitation. Deterrents don't work, largely because they don't fix the causes for bad behavior. Rehabilitation is the only sensible approach if you don't believe in free will, whereas punishment makes a bit more sense if you believe that people have free will.

> Perhaps someone can reframe that in terms of types of error, and people prone to more serious types of error (road rage) face different consequences. But that gets real complicated real quick.

This is fundamentally a free-will-based way of seeing the problem. "Consequences" are completely irrelevant in a deterministic worldview unless you can prove that they act as a deterrent (that is, that they are part of the cause). Since consequences are provably not significant deterrents for many crimes, I don't think that works.

Your argument basically that "this idea of punishment/consequences (which only makes sense in a free-will-based ideology) doesn't work in a deterministic ideology, and punishment/consequences are good in my free-will-based ideology, therefore deterministic ideologies are wrong". But you have to hold a free-will-based ideology for the preconditions of your argument to make sense.

Yes, i see that now. The distinction depends on free will, so isn't a good test.

Very insightful. Thank you.

Your talk of punishment vs rehabilitation is spot on, and very relevant to the "Doesn't the whole justice system collapse if there is no free will?" question. Have you ever heard of how some South American prisons are treating inmates with Ayahuasca, in order to rehabilitate their mind? Very interesting stuff considering the success rate.

You cannot derive is from ought.

That's the argument I use for not believing in assertions of existence ("God exists", "Pink unicorns exist"), because people basically don't think things exist that can't be proven to exist, but make a special pleading for Gods.

I guess you could argue that we generally assume a deterministic model exists and try to find it, but I hadn't considered that before.

Free will is the sensation of being in a brain that models counterfactuals. It is also a token concept that people like to use to do their "worship the mystery" so they can secretly believe that scientists are stupid and thus not have to be held responsible for their failure to understand them or their work.

Free will is akin to an emotion. Just because physicists haven't explained it in excruciating detail doesn't mean it doesn't exist, or we'd all be running around debating the existence of fear and love and curiosity.

> Free will is the sensation of being in a brain that models counterfactuals

No. Free will is the ability to make a choice not completely dependent on history.

I don't consider that free will then, that would just be "not completely" free will. If it's not dependent on a history, what would be the directive that effects the choice? To me, the notion of free will just defeats the ubiquitous cause-effect nature in everyday life and observance. What would be the nature of the effector that makes the "free" choice then?

That depends on the person defining it. Why can't it be the outcome my brain has determined for me to take which I subjectively understand as a self-chosen action? That may well depend on my history--my emotions, memories and all the things that shape me--but those are more reasons than constraints.

Isn't that like saying I want to fly, so I don't have free will if I can't?

Would flipping a coin count?

If you respond, "No, because the particles that make up the coin and the muscles that drive my thumbnail have a history that determines the outcome," then how about a slight variation? "I can't decide what to do. I have no idea what time it is, so if the minute digit on my clock is odd, I'll do X, otherwise I'll do Y."

Here I've explicitly refrained from using either a source of randomness or anything else with its own history to determine my fate. The decision to consult the clock might have been an act of free will on my part, but the outcome certainly wasn't.

I don't see why anyone should accept a useless definition as a correct one.

Nobody would argue that they had free will if they didn't feel like they had free will. Nobody is positing baseless metaphysical nonsense without some reverence in their actual experiences. If you want to usefully discuss free will, you have to account for the sensation of free will, not just some abstract model that you've merely assembled grammatical statements from.

We all understand fear and love and curiosity well enough that we can make rudimentary predictions about them. If I point a gun at someone they will experience fear and respond with fight or flight. If I spend a lot of time with someone and certain compatibility conditions are met, we will experience love and respond with caring behaviors. If I show someone something that they don't understand fully but that has properties that interest them, they'll likely experience curiosity and respond with questions and exploration.

Someone who studies these things (a psychologist or neurologist) could make even more sophisticated predictions.

We may not have a complete low-level electrochemical model of these phenomenon, but we have a good enough model to make some predictions. But if anything, one of the most salient criticisms of free will is that it doesn't allow us to model and make predictions--in fact, it eschews predictions altogether.

Right, I would clarify though, "single electron positions are unpredictable exactly[0]" but, I know that there are more electrons on this side of the cap than the other side, and it's physics at that scale (S >> \hbar) that matters.

[0] To be more pedantic than enlightening, add before wavefunction collapse.

Exactly.

Can tou explain why qm and bell's inequality do not categorically undermine determinism and prove deep randomness ?

Is it because on a macro scale amd normal energy levels effects are negligible? Because there are well followed probability distributions?

Bell's inequality refutes theories with local hidden variables (e.g. some unknown property of particles or spacetime). That leaves two possibilities: no hidden variables (the results truly are non-deterministic) or non-local hidden variables (e.g. some property which exists outside the spacetime which we're constrained to)

There's a third possibility, superdeterminism, in which literally everything is determined by previous conditions, so that no communication is needed, even via a property outside of our spacetime, because everything was determined by preconditions.

Think of it this way: you set two clocks to the same time. The next day, they both have the same time on them. This isn't because the clocks are communicating via nonlocal hidden variables, it's because their precondition was the same and the sequence of events which followed was deterministic.

Many people believe that free will and determinism are not incompatible (compatibilists).

Personally, I'm not even sure introducing non-determinism matters much. What would it even mean? That beyond determinsitic actions defined by our precise history, we get a bit of randomness permuting the whole thing? Does that really make it any freer?

> Many people believe that free will and determinism are not incompatible (compatibilists).

Could you explain how that works? I'm unfamiliar with that, but I suspect that they may be using a different definition of "free will" than I am familiar with.

> Personally, I'm not even sure introducing non-determinism matters much. What would it even mean? That beyond determinsitic actions defined by our precise history, we get a bit of randomness permuting the whole thing? Does that really make it any freer?

I think free will and randomness are both forms of non-determinism. Non-determinism doesn't prove free will, but it allows for the possibility that it might exist (and post people intuit that randomness could be indistinguishable from non-determinism).

To me, free will is the lack of external forces controlling my decisions and actions. That is, I can decide things for myself, even if those decisions are a deterministic product of my current state.

How are you defining it such that it must be non-deterministic and distinct from randomness? I don't really understand what that means. Assuming there's a single shared reality, what's the source of the non-determinism? Even if you say that's the free will itself, you'd be asserting that our "wills" are somehow capable of randomness.

> To me, free will is the lack of external forces controlling my decisions and actions. That is, I can decide things for myself, even if those decisions are a deterministic product of my current state.

Without some place in the sequence of events that isn't deterministic, I don't see how you can separate your current state from external forces. That is, if your decisions are a deterministic product of your current state and your current state is a deterministic product of other states before it (including states that existed before you did, such as your parents) then I don't see that as "the lack of external forces controlling my decisions and actions".

> How are you defining it such that it must be non-deterministic and distinct from randomness? I don't really understand what that means. Assuming there's a single shared reality, what's the source of the non-determinism? Even if you say that's the free will itself, you'd be asserting that our "wills" are somehow capable of randomness.

Part of the difficulty with talking about free will is that there isn't a clear definition of what it is. However, I do think I can say what it isn't--I think most people don't consider randomness or determinism to be free will. But I also think that it would be nigh impossible to distinguish randomness from free will without a clearer definition of free will.

The fallout of this belief is that I think we could disprove free will if we could prove determinism (but, I don't think we can prove determinism currently). But I don't think we can prove free will, even if we could disprove determinism (I don't think we can do that either). In order to prove free will we would have to disprove both determinism and randomness.

I think in the end we will find out that both interpretations of whether free will exists might be correct, but with determinism being more fundamental. Think about a deterministic machine learning algorithm with a fixed input of training data. The agent/algorithm learns by reacting to it's data input/environment, has goals in the form of a cost function it is actively trying to minimize, has options to adjust its neural weights depending on what it experiences, yet we know the system including the environment is predetermined from the moment we kick off the program. -Khatchig, from "Digital Physics" (the movie).

How would you test free will?

someone will suggest, "Well maybe we don't really understand infinity". No, we understand "infinity" just fine. It's a concept that's clearly defined using a set of axioms that have been around for thousands of years.

I am not a mathematician, but my understanding is that a considerable amount of research into how to properly address /use infinity in math was ongoing as recently as the early 20th century. Not that I disagree with your overall point though.

The issue is that there are different infinities. The infinity the parent is talking about, the one that you generally run into in calculus class and the like, is straightforward. The research in the past century was about what happens _past_ infinity, e.g. ordinal numbers.

I'm no mathematician either, so I'll stop there before I embarrass myself. The most accessible resource I found was this VSauce video [1].

[1] https://www.youtube.com/watch?v=SrU9YDoXE88

That was a very interesting video, thanks for sharing. Now I'm going to be addicted to VSauce...

That video is surprisingly decent given the abstract nature of the subject.

Regarding the video: The contraproductive and unnecessary use of pretty loud 'background-music' is pretty distracting and ruining this for me. It's a disregard for music and i view it also as a disregard me as a viewer, like it's assumed i wouldn't be able to listen to someone speak without the elevator soundsystem blaring around. They also do this on the radio when they tell you the weather forecast: of course only with loud music playing. And i then have to separate and throw away most of that audio info to get the information i want. Like everything wants to be a horrible rap song. I don't get it. This needs to stop.

The word 'infinity' refers to a few different concepts in different branches of mathematics. Some of them have been well-defined and well-understood for a long time. The point named "Infinity" as a limit in analysis/topology (which I think is what renormalization is related to) is very un-mysterious.

Cantor's work in the early 20th century was on infinite objects in the context of set theory. That work is also fairly well-understood but starts to get a bit esoteric. More recent research goes further in the same direction, and then you start getting the point where you can't prove whether a certain type of infinity exists or not, because the existence of an infinity that large would prove that set theory is consistent.

So yes, research is still ongoing into the nature of infinity, but it's the nature of a different infinity.

Fair enough. Like I said, IANAM. I just enjoy reading books like Everything and More: A Compact History of Infinity and Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World. It's certainly a wildly fascinating topic.

Is this related to that whole -1/12 business, which they talk about in this Numberphile video[0]? Because the video suggests it's ongoing work in mathematics and that it shows up in unexpected places in theoretical physics.

[0] https://www.youtube.com/watch?v=0Oazb7IWzbA

The Numerphile video has been debunked by everyone else in the math-popularization community: http://blogs.scientificamerican.com/roots-of-unity/does-123-... (and also see discussion of that article on HN

The "-1/12" "mystery" is well settled math (but mathematicians are always looking for more elegant or general perspectives on things), and (standard-issue) sloppy notation in physics.

The only "mystery" is why people who should know better intentionally use incorrect terminology to dazzle lay-people, creating a mystery where there is none.

Thanks for that follow-up!

As a theorist, theories in physics describe experiments and mathematics is the study of formal axiom systems. So if you want to reject the axiom of infinity, that is fine. If you want to have stronger axioms, like large cardinal axioms, equally fine.^1 However from experience, babbling on about truth in mathematics does almost never lead anywhere interesting.

^1 Basically large cardinal axioms give you additional types of infinity.

I'm guessing mindcrime's talking about Cantor and Godel and the continuum hypothesis

https://en.wikipedia.org/wiki/Continuum_hypothesis

I remember learning about them in the philosophy of maths, but have no idea if they have any consequences in Physics. And like /u/lasfter I'll stop there before I embarrass myself.

Probably, but in my view Godel's theorem basically states that there are limits to axiom systems. (In much the same way that you can not write a web server without touching sockets.) My point is, if it would be necessary to switch to a stronger axiom system than ZFC in physics, then one would do that, without claiming that that stronger system is real.

I honestly can't tell if this is utter gibberish or a real comment...

Yeah, I should stop commenting publicly on an ongoing thought process, before I figured out how to communicate that thought :/ Basically I am drifting towards hard mathematical anti-realism and towards a rather minimal scientific realism. (And when I saw the discussion I jumped the gun...)

My experience has been that experts in most fields tend to shy away from using precise, professional language when speaking to a layperson. I think this tendency indirectly results in the sort of dialogs you're describing.

That's true, and being able to describe complex concepts in a simple (yet still accurate) way is a skill in itself — one that requires a lot of practice. Feynman was notoriously good at this.

Given the rarity of such expert in any/all field, I'd dare say it's more like nature instead of nurture.

The best we can nurture is 'good' analogy, that still somewhat valid even if the analogy is expanded further

p/s: If only we have a list of Feynman-like experts in most of the fields :D

I'm glad I'm not the only one. Just today, I was in a conversation when trying explain broadly what Number Theory is and a little bit why I find it fascinating and pursuing Masters then Docterate. What annoyed me the most was being told that Mathematicians cannot simply understand not comprehend infinity. Shortly after explaining the number systems and infinity. I was asked about my favourite number. What was truly cringe worthy was the topic of Proofs, apparently i was told that they don't really exist! xD What a waste of 5 year ax in maths.

What is your favorite number?

Take comfort, I believe you exist.

"n" That usually messes with them a little bit.

Not the OP -- Pi.i -- sounds like a cockney insult.

When they say "it's a theory" they're probably hinting towards the fact that it's a model, and not that they think they are floating around.

It's interesting the top-comment displays such a supercilious attitude while the takeaway from article, at least for me, was the exact opposite.

Maybe you could have helped at least some of the people by using it as an opportunity to teach rather than deride?

Of course gravity exists, but to suggest we understand it 100% through what models we have seems silly. But, I'm not a physicist, and I don't play one at dinner parties.

Honestly, just because many particle physicists feel okay at this point what Feynman called 'hocus-pocus' doesn't mean it really is okay. Mathematically, it's just as unsound as saying the sum of all integers is -1/12.

There have been attempts at avoiding the regularization magic altogether but from what I gather, they are developments from mathematicians, and physicists don't really care about it.

EDIT: I knew it was a magic related term, not black magic.

  Mathematically, it's just as unsound as saying the   
  sum of all integers is -1/12.

But that is not unsound at all: http://blogs.scientificamerican.com/roots-of-unity/does-123-...

Care to enlighten some of us unwashed? I'm a physics grad student and I certainly learned things like Borel resummation in school (er, it was in textbooks they assigned us on QFT at least...)

This is a form of bike-shedding, is it not?

Yes, exactly. If you can't understand the details, you can only talk about irrelevancies. People (like me!) who have only the slightest grasp on the math involved probably shouldn't form strong opinions just because they saw a pop sci documentary that used some terrible analogies.

Most physicists are happy to talk to you about things if you're not veering off like the top comment described. If explained properly, you might just understand the details, and if not now, maybe next time (happens to the best of us during studies, sometimes understanding takes repeated exposure).

Actually, that is something I noticed: Many people are scared off for good if they don't understand something at once. Most of my physicist peers don't understand things at once, it's normal. The question is how to deal with that - do you run away or do you try again, and what are your tools for that?

I'm not sure what triggers the need to argue in people. It's just so far removed from the ideal most of us strive towards in discussions, which is trying to understand things by all means possible, and not defend a preconceived notion. This sounds obvious and easy, but for many people, I found it's not. They identify so much with their state of knowledge and arguments (not to say opinions, which I can kind of get) that one has to tread very carefully. One wrong expression and they turn into fighting mode, and the discussion turns from a search for understanding and rightness into a match for which derailing is a valid technique.

Lack of focus is also an issue, and can be a derailing method. (Ask questions faster than they can be answered and don't listen to the person trying to explain. In the end console yourself that we can't really know anything and thus all questions are unanswerable. End monologue, walk away. God, these people.)

As far as physics topics go, it is the worst in GRT (general relativity) lectures followed by quantum things. Biologists told me they get strange argumentative older people in evolution lectures too.

</rant>

> "Well maybe we don't really understand infinity".

Not a specialist, but "infinity" is indeed a tricky thing to make sense of.

First, if you decide to use and define it only in a "theoretical" sense (constructed through the set of axioms you mentioned) things are fine, there are lots of things we have constructed in an abstract way in the past which have proved to be intellectually solid (think of the idea of God constructed by the scholastics).

The problem appears when you want to apply your idea constructed on a "set of axioms" back to the real life. The scholastics' idea of God had a very short life when that happened (more or less during the early Renaissance), and I wouldn't say that the mathematical idea of "infinity" would have a better life were people to view it in a more critical way.

Because were you to apply the idea of infinity to the real life (the life made up of stars, planets and Hacker News) that would mean that there are an infinity of planets and stars out there (some of us have started to be ok with that) but that would else mean that there are an infinity of Hacker News instances out there and there are an infinity of "me", the user paganel, making this comment on HN. This is hard for a lot of people to grasp, including me.

There's a good general (mathematical) sense to what something "infinite" is: a thing able to contain something the same size as itself.

As an example, the natural numbers are infinite because they contain the even numbers and the even numbers are the same "size" (or cardinality) as the natural numbers themselves.

As a second example, the real numbers are infinite because they contain the interval (-1, 1), which has the same "size" as all of the real numbers.

Yeah, I'm aware of this (especially the second example, ever since my Calculus teacher in high-school used a very similar definition to it in order to make us understand what real numbers are), what I was trying to say is that, at the end of it all, the science of Physics should be about making sense of the real world (using mathematical concepts, if the need arises, but not to see those concepts as reality itself).

More exactly, I say that translating the concept/idea of infinity from mathematics to physics is not idempotent (not sure if this it's the correct term, but you get the idea), saying that infinity "exists" in the physical world the same as it does in mathematics is kind of tricky when you think of the consequences through and through. To take your second example, applied to Physics that would mean that no matter what two small particles we choose as being "fundamental" there will always be an infinity of (presumably even more small) particles separating the two, and so on and so forth (it's "turtles all the way down", so to speak).

Like I said, I'm not a specialist, just a programmer, but I think we should be aware of the presumptions we implicitly make when discussing about different topics but using the same language (in this case the of concept of "infinity" in maths vs physics). Hume explained it better than me (maybe in an "An Essay Concerning Human Understanding" ?!) when he said that the mathematical idea of a straight line (I'm talking about the geometrical line) is just that, an human-constructed idea, there's no absolute straight line in the real world (not sure what he thought about the idea of infinity, probably not much, judging by his being critical against mathematical induction).

My situation is similar as a math grad student, but worse in a way. When people hear I'm in mathematics, they often assume I know physics. Worse, they often seem to have the expectation that I can provide some insightful feedback into how <Insert Latest Physics Discovery> fits into <Insert Pet Theory About the Universe>.

No, we don't really understand infinity. We don't even know what is an infinite in our reality, unless I missed some really important news. You can understand perfectly infinity in the mathematical abstraction of reality. You can use it for renormalization or whatever theoretical instrument you want, but please don't tell me that you know everything about infinites when all the empirical observations at the moment go against an infinite universe and an infinitely divisible space-time that is probably discrete rather than continuous.

Stepping back in topic, from my point of view of a completely amateur physicist, I really appreciate her work. Whoever contributes to spreading knowledge is making the world a bit better than it was before (B.P.) I wish there were more people in the world keen to explain things rather than ridiculing others just because they don't understand something that for us is very obvious.

Just my two pence.

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