5 ms·

Shut up and calculate (2007)

35 points by nikolaypavlov 11y ago

tmerr 11y ago
Regardless of what you call the universe, we already know 1. Everything we know about it comes from sensory input, and 2. That sensory input's production can be modeled mathematically. But it's hard for me to make sense of what author really means by the claim "the universe is math". He claims after pulling away notation math is "A set of abstract entities with relations between them". Great! But then again... any idea I can conceive of can be said to be abstract entities with relations between them. That's an awfully vague definition. Then it's as if he fills in the void with baggage from his subjective understanding of mathematical structures (object movement is like 4 dimensional spaghetti). It's an interesting read but it seems like he just wants his idea of the universe to be more literal than it is.
- animefan 11y ago
  I disagree with 1 and 2, in the sense that i believe that sensory input has no fundamental ontological role, and is merely how we biological humans bootstrap our knowledge of macroscopic objects. The real dilemma of quantum theory is how to reconcile this macroscopic world with the world described by quantum theory. Personally I don't think many worlds approaches make sense because they don't have an adequate description of probability.
n4r9 11y ago
I agree that most physicists believe that an external reality exists. I agree that physical theories aim to describe how it works. But I disagree that it follows that our physical reality has a mathematical structure. My objections are: - There is no compelling reason to think that "purely abstract" mathematics any less anthropocentric than human language; - Even if mathematics transcends humanity, there is no compelling reason to think that there is a single overarching mathematical structure of the universe, despite being able to predict the outcomes of our interactions to greater and greater accuracy as our physical theories develop. It may be that Tegmark addresses these points in his "full strength" version, but given the way he glosses over these hidden assumptions in this paper, I'm not inclined to dig in and find out.
- tlb 11y ago
  Tegmark is explicit about his assumptions elsewhere. For an overview, see https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis https://en.wikipedia.org/wiki/Mathematical_universe_hypothes.... Indeed, it's not the only productive line of thinking in physics.
- kazinator 11y ago
  Tegmark believes (pardon me if I have this wrong) that all conceivable realities exist that can be described by equations, not only this reality. The reality we have access to is the one in whose equations we are ourselves locked up, so to speak. I'm basically with Tegmark. For one thing, what has physics ever come up with but equations, and improved equations to replace those, and so on? Everything so far has been math. So, going forward, either everything in physics will always be rooted in math, or else some "non-math stuff" has to be discovered. (The very idea of "non math stuff" being at the root of reality seems absurd.) What kind of thing would that be? I think if we discover the ultimate equations then that's all there will be: those equations, and mysterious constants embedded in them that just are. The only explanation for those constants will be the anthropic principle: if those constants were different, we wouldn't be here to contemplate why they are, and in some other universe there are beings completely different from us also wondering why their constants and equations are they way they are.)
  - animefan 11y ago
    For reference, the poorly named "standard model" which is the quantum theory of all forces except gravity, cannot really be called equations in the usual sense. This is because the kind of mathematical model that would describe the standard model (nonperturbative QFT) can't currently be done rigorously. It can only be done for simpler models in lower dimensions. The standard model is a very complex sort of approximation to a theory that is assumed to exist. This might be a mere detail to some but to me it is a sign that physics is complex in all kinds of ways, and can't really be described as "choosing the right equations". Even if you think that this is what physics is fundamentally, I think you would have to admit that it wasn't possible to describe what the meaning of "equation" was before qft was developed, and the same may be true about future theories that unify the standard model and gravity.
PaulHoule 11y ago
In your gut you know he's a nut... http://arxiv.org/find/physics/1/au:+Tegmark_M/0/1/0/all/0/1 http://arxiv.org/find/physics/1/au:+Tegmark_M/0/1/0/all/0/1
- danbruc 11y ago
  https://en.wikipedia.org/wiki/Max_Tegmark https://en.wikipedia.org/wiki/Max_Tegmark
  - JadeNB 11y ago
    I think that there are respected scientists who know all the facts in that article and still consider him a nut. (I say I think because most respected scientists are too polite, or politic, to say so directly, but it's the impression that I've got in reading discussions of him.)
Analemma_ 11y ago
This is known as the instrumentalist approach to quantum mechanics, where we deliberately avoid thinking about the philosophical interpretations of things like the wavefunction, and only focus on the results of experiments. The thinking being, the observables don't change regardless of whether you pick MWI or pilot wave or the Copenhagen interpretation, so what does it matter? (The actual phrase "shut up and calculate" is older than this paper; I think David Mermin coined it.) This approach rubs some people the wrong way, either because it's seen as a failure of imagination on the part of physicists to look at the bigger questions, or because it drifts close to the discredited logical positivism of the mid-20th century. Those are valid complaints, but I think it can also be seen as humility on the part of physicists, and an understanding that this is outside their field of expertise. "Science" is a fundamentally empirical exercise; if you're doing thinking without empiricism, it might still be valuable thinking, but it isn't science. "Shut up and calculate" is shorthand for, "Because these questions are not empirical, our tools and methods we have as scientists are not capable of addressing them." It's acknowledging that their powers are limited. (I do think it would be nice if more physicists thought about it anyway, because in their abscence the void has been filled with woo by a bunch of New Age cranks, but that's not a moral obligation on their part)
- n4r9 11y ago
  It's worth noting that Tegmark is advocating a particular approach to the entirety of physics, not simply quantum mechanics. Taken to an extreme, a further criticism of instrumentalism (due to Alan Sokal) is that the concept of "dinosaur" becomes nothing more than a fanciful way for paleontologists to come up with predictions about which fossils they will discover next. I'm not sure I agree with you that "instrumentalism" is an adequate description of the position of Tegmark outlines. Instead of neglecting to assign an ontological status to anything, Tegmark appears to be assigning an ontological status to the mathematical structures themselves.
  - danbruc 11y ago
    [...] Tegmark appears to be assigning an ontological status to the mathematical structures themselves. Which appears to me similar to rejecting the idea of an universe that just somehow came into existence or existed forever and introducing a god as the source of the universe but still leaving you behind with the same questions as before but now attached to the god instead of the universe. And I personally don't really buy into the idea of mathematical structures existing independent of humans or the universe or whatnot anyway. Humans bring mathematical structures into existence, they postulate the axioms and explore the consequences. That pieces of the universe are isomorphic to this or that mathematical structure and therefore show similar properties and behaviors is either accidentally or because a mathematical structure was explicitly designed to mimic certain aspects of the universe, at least as far as I am concerned.
ambicapter 11y ago
How does this square with Gödel's Incompleteness Theorem (https://en.wikipedia.org/wiki/Gödel%27s_incompleteness_theorems https://en.wikipedia.org/wiki/Gödel%27s_incompleteness_theor...)?
j-dr 11y ago
I find it ironic that the title of this article is 'Shut up and Calculate', seeing as he proposes no way to calculate the things that he proposes would qualify his theory as falsifiable.
poelzi 11y ago
I'm into the BSM-SG model and this approach, is the same as we have now and it failed. Using mathematical logic in quantum mechanics was one of the larger mistakes we did... reality is exactly the opposite, everything has a form, mass, movement,...

35 points by nikolaypavlov 11y ago

tmerr 11y ago

Regardless of what you call the universe, we already know 1. Everything we know about it comes from sensory input, and 2. That sensory input's production can be modeled mathematically. But it's hard for me to make sense of what author really means by the claim "the universe is math". He claims after pulling away notation math is "A set of abstract entities with relations between them". Great! But then again... any idea I can conceive of can be said to be abstract entities with relations between them. That's an awfully vague definition. Then it's as if he fills in the void with baggage from his subjective understanding of mathematical structures (object movement is like 4 dimensional spaghetti). It's an interesting read but it seems like he just wants his idea of the universe to be more literal than it is.

animefan 11y ago
I disagree with 1 and 2, in the sense that i believe that sensory input has no fundamental ontological role, and is merely how we biological humans bootstrap our knowledge of macroscopic objects. The real dilemma of quantum theory is how to reconcile this macroscopic world with the world described by quantum theory. Personally I don't think many worlds approaches make sense because they don't have an adequate description of probability.

n4r9 11y ago

I agree that most physicists believe that an external reality exists. I agree that physical theories aim to describe how it works. But I disagree that it follows that our physical reality has a mathematical structure. My objections are: - There is no compelling reason to think that "purely abstract" mathematics any less anthropocentric than human language; - Even if mathematics transcends humanity, there is no compelling reason to think that there is a single overarching mathematical structure of the universe, despite being able to predict the outcomes of our interactions to greater and greater accuracy as our physical theories develop. It may be that Tegmark addresses these points in his "full strength" version, but given the way he glosses over these hidden assumptions in this paper, I'm not inclined to dig in and find out.

tlb 11y ago
Tegmark is explicit about his assumptions elsewhere. For an overview, see https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis https://en.wikipedia.org/wiki/Mathematical_universe_hypothes.... Indeed, it's not the only productive line of thinking in physics.
kazinator 11y ago
Tegmark believes (pardon me if I have this wrong) that all conceivable realities exist that can be described by equations, not only this reality. The reality we have access to is the one in whose equations we are ourselves locked up, so to speak. I'm basically with Tegmark. For one thing, what has physics ever come up with but equations, and improved equations to replace those, and so on? Everything so far has been math. So, going forward, either everything in physics will always be rooted in math, or else some "non-math stuff" has to be discovered. (The very idea of "non math stuff" being at the root of reality seems absurd.) What kind of thing would that be? I think if we discover the ultimate equations then that's all there will be: those equations, and mysterious constants embedded in them that just are. The only explanation for those constants will be the anthropic principle: if those constants were different, we wouldn't be here to contemplate why they are, and in some other universe there are beings completely different from us also wondering why their constants and equations are they way they are.)
- animefan 11y ago
  For reference, the poorly named "standard model" which is the quantum theory of all forces except gravity, cannot really be called equations in the usual sense. This is because the kind of mathematical model that would describe the standard model (nonperturbative QFT) can't currently be done rigorously. It can only be done for simpler models in lower dimensions. The standard model is a very complex sort of approximation to a theory that is assumed to exist. This might be a mere detail to some but to me it is a sign that physics is complex in all kinds of ways, and can't really be described as "choosing the right equations". Even if you think that this is what physics is fundamentally, I think you would have to admit that it wasn't possible to describe what the meaning of "equation" was before qft was developed, and the same may be true about future theories that unify the standard model and gravity.

PaulHoule 11y ago

In your gut you know he's a nut... http://arxiv.org/find/physics/1/au:+Tegmark_M/0/1/0/all/0/1 http://arxiv.org/find/physics/1/au:+Tegmark_M/0/1/0/all/0/1

danbruc 11y ago
https://en.wikipedia.org/wiki/Max_Tegmark https://en.wikipedia.org/wiki/Max_Tegmark
- JadeNB 11y ago
  I think that there are respected scientists who know all the facts in that article and still consider him a nut. (I say I think because most respected scientists are too polite, or politic, to say so directly, but it's the impression that I've got in reading discussions of him.)

Analemma_ 11y ago

This is known as the instrumentalist approach to quantum mechanics, where we deliberately avoid thinking about the philosophical interpretations of things like the wavefunction, and only focus on the results of experiments. The thinking being, the observables don't change regardless of whether you pick MWI or pilot wave or the Copenhagen interpretation, so what does it matter? (The actual phrase "shut up and calculate" is older than this paper; I think David Mermin coined it.) This approach rubs some people the wrong way, either because it's seen as a failure of imagination on the part of physicists to look at the bigger questions, or because it drifts close to the discredited logical positivism of the mid-20th century. Those are valid complaints, but I think it can also be seen as humility on the part of physicists, and an understanding that this is outside their field of expertise. "Science" is a fundamentally empirical exercise; if you're doing thinking without empiricism, it might still be valuable thinking, but it isn't science. "Shut up and calculate" is shorthand for, "Because these questions are not empirical, our tools and methods we have as scientists are not capable of addressing them." It's acknowledging that their powers are limited. (I do think it would be nice if more physicists thought about it anyway, because in their abscence the void has been filled with woo by a bunch of New Age cranks, but that's not a moral obligation on their part)

n4r9 11y ago
It's worth noting that Tegmark is advocating a particular approach to the entirety of physics, not simply quantum mechanics. Taken to an extreme, a further criticism of instrumentalism (due to Alan Sokal) is that the concept of "dinosaur" becomes nothing more than a fanciful way for paleontologists to come up with predictions about which fossils they will discover next. I'm not sure I agree with you that "instrumentalism" is an adequate description of the position of Tegmark outlines. Instead of neglecting to assign an ontological status to anything, Tegmark appears to be assigning an ontological status to the mathematical structures themselves.
- danbruc 11y ago
  [...] Tegmark appears to be assigning an ontological status to the mathematical structures themselves. Which appears to me similar to rejecting the idea of an universe that just somehow came into existence or existed forever and introducing a god as the source of the universe but still leaving you behind with the same questions as before but now attached to the god instead of the universe. And I personally don't really buy into the idea of mathematical structures existing independent of humans or the universe or whatnot anyway. Humans bring mathematical structures into existence, they postulate the axioms and explore the consequences. That pieces of the universe are isomorphic to this or that mathematical structure and therefore show similar properties and behaviors is either accidentally or because a mathematical structure was explicitly designed to mimic certain aspects of the universe, at least as far as I am concerned.

ambicapter 11y ago

How does this square with Gödel's Incompleteness Theorem (https://en.wikipedia.org/wiki/Gödel%27s_incompleteness_theorems https://en.wikipedia.org/wiki/Gödel%27s_incompleteness_theor...)?

j-dr 11y ago

I find it ironic that the title of this article is 'Shut up and Calculate', seeing as he proposes no way to calculate the things that he proposes would qualify his theory as falsifiable.

poelzi 11y ago

I'm into the BSM-SG model and this approach, is the same as we have now and it failed. Using mathematical logic in quantum mechanics was one of the larger mistakes we did... reality is exactly the opposite, everything has a form, mass, movement,...