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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 tan

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.

mindcrime 10y ago
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.
- lasfter 10y ago
  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 https://www.youtube.com/watch?v=SrU9YDoXE88
  - mindcrime 10y ago
    That was a very interesting video, thanks for sharing. Now I'm going to be addicted to VSauce...
  - 77pt77 10y ago
    That video is surprisingly decent given the abstract nature of the subject.
  - iammyIP 10y ago
    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.
- lmkg 10y ago
  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.
  - mindcrime 10y ago
    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.
  - vanderZwan 10y ago
    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 https://www.youtube.com/watch?v=0Oazb7IWzbA
    - gohrt 10y ago
      The Numerphile video has been debunked by everyone else in the math-popularization community: http://blogs.scientificamerican.com/roots-of-unity/does-123-really-equal-112/ 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.
- yk 10y ago
  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.
  - mattmanser 10y ago
    I'm guessing mindcrime's talking about Cantor and Godel and the continuum hypothesis https://en.wikipedia.org/wiki/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.
    - yk 10y ago
      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.
      - mattmanser 10y ago
        I honestly can't tell if this is utter gibberish or a real comment...
        yk 10y ago
        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...)
rch 10y ago
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.
- Xcelerate 10y ago
  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.
  - unexistance 10y ago
    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
GregBuchholz 10y ago
>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 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 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."
- eli_gottlieb 10y ago
  >"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-AMS.pdf http://www.stat.uchicago.edu/~lekheng/courses/191f09/mumford...
icelancer 10y ago
This is a form of bike-shedding, is it not?
- TillE 10y ago
  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.
  - kaybe 10y ago
    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>
mathattack 10y ago
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.
- Analemma_ 10y ago
  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.
  - Analog24 10y ago
    "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.
    - gohrt 10y ago
      eh, raise the terms as an exponent and subtraction becomes division. :)
    - dylukes 10y ago
      In log scale yes.
    - noobermin 10y ago
      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.
devishard 10y ago
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.
- semi-extrinsic 10y ago
  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.
  - wnoise 10y ago
    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 ...
    - devishard 10y ago
      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.
mildbow 10y ago
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.
Proof 10y ago
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.
- gohrt 10y ago
  What is your favorite number? Take comfort, I believe you exist.
  - hyperion2010 10y ago
    "n" That usually messes with them a little bit.
  - pbhjpbhj 10y ago
    Not the OP -- Pi.i -- sounds like a cockney insult.
noobermin 10y ago
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.
- Confusion 10y ago
  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-really-equal-112/ http://blogs.scientificamerican.com/roots-of-unity/does-123-...
- selimthegrim 10y ago
  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...)
chestervonwinch 10y ago
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>.
paganel 10y ago
> "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.
- SomeStupidPoint 10y ago
  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.
  - paganel 10y ago
    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).
tigershark 10y ago
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.

mindcrime 10y ago

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.

lasfter 10y ago
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 https://www.youtube.com/watch?v=SrU9YDoXE88
- mindcrime 10y ago
  That was a very interesting video, thanks for sharing. Now I'm going to be addicted to VSauce...
- 77pt77 10y ago
  That video is surprisingly decent given the abstract nature of the subject.
- iammyIP 10y ago
  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.
lmkg 10y ago
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.
- mindcrime 10y ago
  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.
- vanderZwan 10y ago
  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 https://www.youtube.com/watch?v=0Oazb7IWzbA
  - gohrt 10y ago
    The Numerphile video has been debunked by everyone else in the math-popularization community: http://blogs.scientificamerican.com/roots-of-unity/does-123-really-equal-112/ 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.
yk 10y ago
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.
- mattmanser 10y ago
  I'm guessing mindcrime's talking about Cantor and Godel and the continuum hypothesis https://en.wikipedia.org/wiki/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.
  - yk 10y ago
    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.
    - mattmanser 10y ago
      I honestly can't tell if this is utter gibberish or a real comment...
      - yk 10y ago
        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...)

rch 10y ago

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.

Xcelerate 10y ago
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.
- unexistance 10y ago
  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

GregBuchholz 10y ago

>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 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 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."

eli_gottlieb 10y ago
>"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-AMS.pdf http://www.stat.uchicago.edu/~lekheng/courses/191f09/mumford...

icelancer 10y ago

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

TillE 10y ago
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.
- kaybe 10y ago
  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>

mathattack 10y ago

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.

Analemma_ 10y ago
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.
- Analog24 10y ago
  "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.
  - gohrt 10y ago
    eh, raise the terms as an exponent and subtraction becomes division. :)
  - dylukes 10y ago
    In log scale yes.
  - noobermin 10y ago
    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.

devishard 10y ago

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.

semi-extrinsic 10y ago
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.
- wnoise 10y ago
  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 ...
  - devishard 10y ago
    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.

mildbow 10y ago

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.

Proof 10y ago

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.

gohrt 10y ago
What is your favorite number? Take comfort, I believe you exist.
- hyperion2010 10y ago
  "n" That usually messes with them a little bit.
- pbhjpbhj 10y ago
  Not the OP -- Pi.i -- sounds like a cockney insult.

noobermin 10y ago

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.

Confusion 10y ago
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-really-equal-112/ http://blogs.scientificamerican.com/roots-of-unity/does-123-...
selimthegrim 10y ago
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...)

chestervonwinch 10y ago

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>.

paganel 10y ago

> "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.

SomeStupidPoint 10y ago
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.
- paganel 10y ago
  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).

tigershark 10y ago

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.