Shut Up and Calculate: Exploring Feynman's Ideas on Physics

[humanino]

As far as i can tell, everyone that gets out of a quantum theory or relativity major is very confused.

To this I certainly agree. I quote Grothendieck sometimes :

Passer de la mecanique de Newton a celle d’Einstein doit etre pour le mathematicien comme passer du vieux dialecte provencal a l’argot parisien dernier cri, passer a la mecanique quantique j’imagine c’est passer du francais au chinois
Alexandre Grothendieck, Recoltes et Semailles

which loosely translate into
"To go from Newton's mechanics to Einstein's must be for a mathematician like going from provincial dialect to the latest parisian slang, to go to quantum mechanics I imagine must be like going from french to chinese language"

 

[yossell]

The meaning of equations are, at most, a fun intellectual aside.

Mach's relationist interpretation of Newtonian inertial frames, Einstein's (and Poincare's) interpretation of the t' in the Lorentz transformations as genuinely representing time in a frame (as against Lorentz' view that they were just mathematically useful adjuncts), Born's interpretation of the wave function as probability, Minkowski's geometric interpretation of Relativity, QFT's reinterpretation of creation and annhilation operators to avoid Dirac's infinite sea and negative energy.

I think there's still debate about the degree of significance of these interpretations, but conceptual changes about the interpretation of the mathematics has played an active role in inspiring or motivating at least some physicists and at least some physics at least some of the time, and so can be more than just a fun intellectual aside.

 

[Pythagorean]

Really? You are now mandated to speak on behalf of the scientific community?

Don't be so hostile. You can ask for sources without implying arrogance. Would you perhaps trust a poet?

"The aim of science is not to open the door to infinite wisdom, but to set a limit to infinite error."
— Bertolt Brecht (Life of Galileo)

If not, read on for scientific sources:

The interpretation of the controversial issues are called foundational problems, not religion. Witten is not working for the clergy.

of course, I didn't mean literally "working for the clergy" I meant this whole concept of whether "everything fits together" is fantastical. Please find me one non-celebrity (i.e. you can't find them on Wikipedia) physicist that really thinks like that and get them to post in this thread. If you're correct, it shouldn't be hard; there's a big pool to choose from here. If you're right, and I'm wrong, they'll put me in my place as the authority on the subject.

Also, if you ask a scientist how to detect a pseudo-science, that's one of the fundamental traits of a pseudoscience: it claims to explain everything:

Lack of boundary conditions: Most well-supported scientific theories possesses well-articulated limitations under which the predicted phenomena do and do not apply.

(citation)
Hines T (1988) Pseudoscience and the Paranormal: A Critical Examination of the Evidence Buffalo NY: Prometheus Books.

"How everything fits together" is the holy grail of science. How and why this may become (or is becoming) unattainable is another matter.

Ah, here we are... the "holy grail" of science... a contradictory notion in the first place...

 

[Reasonable1]

Math can be used as a tool of predictability but at times the unknowns may well prove to be it's undoing. As an example let's travel at the speed of light, then the traveler turns on a flashlight pointed in the direction of travel. Do we see the light, a ray, or the reflection on an opposing surface? Math says the light from the flashlight will never be seen by the traveler because we consider the speed of light as diffinitive. But is it or is that speed a point of perspective? Until we travel that fast we will never know if the math is correct and can only infer that it is.

 

[apeiron]

The initial construction of general twistor was due to Penrose in the 70s.

Yes, and I like twistor theory because of its conceptual appeal rather than because I can speak its mathematics. This soliton-style approach to particles as trapped broken symmetries is the kind of theory that seems most natural to me (as it is a systems view).

I accept your point that twistors were long ignored until some concrete mathematics came along to animate them - to do some actual calculating. But also it is amusing that Penrose is far from a "shut up and calculate" type of guy. He is very conceptual in his physics (as he admits himself with all his drawing in the Road to Reality). He is an ardent Platonist. And he is happy to throw himself into fields like mind science where really he has not mastered the basics at all. (But a lot of people did that in the 1990s I guess).

 

[apeiron]

I meant this whole concept of whether "everything fits together" is fantastical.

Why is it fantastical in principle? Is there an argument to support this? And why do people talk about arriving at a theory of everything (ToE)?

Personally I think it is possible that there is only one way reality can self-organise. The alternative is that there are infinitely many and we just happen to exist randomly and anthropically in one of those realities. If those are the choices, I think the simpler one at least deserves a shot.

 

[Pythagorean]

Interesting... You're one of the people I thought wouldn't mistake the ToE for an explanation of everything (the title is deceptive).

We wouldn't, for instance, be able to suddenly explain all mammilian behavior with a ToE. The ToE is a reduced model that explains all four fundamental forces at once.

 

[apeiron]

Interesting... You're one of the people I thought wouldn't mistake the ToE for an explanation of everything (the title is deceptive).

We wouldn't, for instance, be able to suddenly explain all mammilian behavior with a ToE. The ToE is a reduced model that explains all four fundamental forces at once.

Correct. But people in physics do talk about final theories. And when it comes to reality, it does seem reasonable to believe that everything does seem to fit together (that there are not a number of separate causalities or whatever). So a final theory seems conceivable rather than fantastical.

But you may have some no go theorem in mind. Or you might be arguing that we can know that it is all just too complex for puny human minds to grasp. Or that we cannot in principle extrapolate beyond the measureable.

Is there a strong reason to call it fantastical? I don't really think so.

(And on mammalian behaviour, already it seems quite possible to account for that in a physically general way by reference to the second law of thermodynamics - dissipative structure, MEPP, etc.)

 

[brainstorm]

Correct. But people in physics do talk about final theories. And when it comes to reality, it does seem reasonable to believe that everything does seem to fit together (that there are not a number of separate causalities or whatever). So a final theory seems conceivable rather than fantastical.

But you may have some no go theorem in mind. Or you might be arguing that we can know that it is all just too complex for puny human minds to grasp. Or that we cannot in principle extrapolate beyond the measureable.

Is there a strong reason to call it fantastical? I don't really think so.

(And on mammalian behaviour, already it seems quite possible to account for that in a physically general way by reference to the second law of thermodynamics - dissipative structure, MEPP, etc.)

I don't think it's silly to think that certain essential forces drive all physical processes at every scale, or that certain patterns of force interaction are the same for different forces at different scales, etc. What I think is ridiculous is when someone thinks there is an underlying logic to the universe that explains everything from biological development to psychology to physics to culture to political economy. The kinds of principles invented to account for such qualitatively distinct fields are so peculiar to one's philosophical perspective or political worldview that they could never be generalized to the subject material itself in a valid way, as far as I can imagine anyway.

 

[Pythagorean]

But you may have (a) some no go theorem in mind. Or you might be arguing that we can know that it is all just (b) too complex for puny human minds to grasp. Or that (c) we cannot in principle extrapolate beyond the measureable.

(reference letters added)

Little bit of b, little bit of c. But b doesn't quite say what I was thinking. It's a matter of information. You couldn't possibly hope to build a complete model of the universe with only the universe available as a resource, other than just moving every atom and interaction over to a new spot and saying "there, I did it". This is a common theme in modeling: there's no way to generalize and specialize at the same time. You always lose information (and this is just considering relatively simple systems, not the whole universe).

Is there a strong reason to call it fantastical? I don't really think so.

Well, you ask for argument and reason and that's a lot like asking for an argument or reason that god doesn't exist. Of course, I don't have one, I can't prove a negative, etc. It's a matter of the history: scripture and pseudoscience are the two types of information that have always claimed knowledge of everything. This pertains to my reply to George, as part of regime for detecting pseudoscience.

(And on mammalian behaviour, already it seems quite possible to account for that in a physically general way by reference to the second law of thermodynamics - dissipative structure, MEPP, etc.)

Of course, this is the kind of research I'm interested in so I won't argue with your statement here, but it's still not an implication at all that a theory of everything is possible. It's still subject to the same constraints logistically: you'd need all the computers in the world ever made (and more) to completely describe an system in all its complexity. The best we can do is ask a specific question and tweak our model towards that question, losing information about other questions.

My disclaimer remains, of course, that I can't prove a negative. But in the same vein, I think the idea of a supreme being is equally fantastical, though I can't prove it. The more recent emergent view is actually of a non-euclidean stochastic universe, which philosophers have used as evidence both for a lack of god and a lack of causality. Of course, I don't really have an opinion here, just presenting similar views.

Iovane, G. (2004) Stochastic self-similar and fractal universe.
Berera, A. (1994) Stochastic fluctuations and structure formation in the Universe.

 

[apeiron]

Little bit of b, little bit of c. But b doesn't quite say what I was thinking. It's a matter of information. You couldn't possibly hope to build a complete model of the universe with only the universe available as a resource, other than just moving every atom and interaction over to a new spot and saying "there, I did it". This is a common theme in modeling: there's no way to generalize and specialize at the same time. You always lose information (and this is just considering relatively simple systems, not the whole universe).

But that is a simulation. A model does indeed shed information about local particulars so as to arrive at a general truth.

A simulation hopes to recreate reality in all its detail (artificial intelligence, artificial life, artificial realities like the Matrix). A model instead is a general abstract statement that can predict particulars. You plug in some specific measurements and crank out some specific predictions.

Ideally, a model is so reduced that it becomes an equation you can write on a t-shirt. So a fundamental model of the universe would not be its simulation but its most compact prediction-generating algorithm.

Well, you ask for argument and reason and that's a lot like asking for an argument or reason that god doesn't exist. Of course, I don't have one, I can't prove a negative, etc. It's a matter of the history: scripture and pseudoscience are the two types of information that have always claimed knowledge of everything. This pertains to my reply to George, as part of regime for detecting pseudoscience.

But you described the idea as fantastical. I just thought that was rather too strong. And I certainly do not agree that believing “everything fits” is the hallmark of psuedoscience. Rather it is the presumption of science traditionally.

It's still subject to the same constraints logistically: you'd need all the computers in the world ever made (and more) to completely describe an system in all its complexity. The best we can do is ask a specific question and tweak our model towards that question, losing information about other questions.

Again, you are thinking of simulation rather than modelling.

Of course there is going to be a problem of levels of description. A model of everything might be too general to be useful when modelling higher level phenomena. But success would be defined by the way everything does still fit.

My disclaimer remains, of course, that I can't prove a negative. But in the same vein, I think the idea of a supreme being is equally fantastical, though I can't prove it.

Seem quite different cases to me. God explanations are illogical (infinite regress, etc). But for reality to be all one – to have some over-arching causality – seems only logical.

 

[Pythagorean]

@Shut up and Calculate discussion:

Ok, so while writing a reply to apeiron, I had a kind of ah-ha moment. It's consistent with the point I'm trying to make about mathematics being a language. Shut up and Calculate is quite simply an attitude towards learning the language of mathematics. I hope that's well and accepted. I think what people are having trouble accepting is that mathematics actually conveys qualitative concepts that DO have a common language title (i.e. "nullcline"), but DO NOT have a common language definition.

Now, you all KNOW this. You exchange money with services and you can count integers easily. You're taking for granted how mathematics has already ingrained itself into our common language because of it's necessity. You realize the importance of this language on an unconscious level. This is only because you were much more willing to shut up and calculate when you were taught basic mathematics by your parents before you even went to school where you learned even more mathematics, through calculating, and practicing the language, just like you did with the alphabet to practice common language.

(the bold sentence below represents what triggered this thought)

@ apeiron: Well we're getting off-topic. I would participate in a discussion in a new thread. To reply to your post shortly though, I think any time you make predictions with a model that you are simulating (even if you solve a Newtonian equation on paper to figure out the trajectory of a cannonball... it obviously has it's shortcomings. But those shortcomings come from the assumptions of the model, and apply where the assumptions fail.

More complex simulations are done on computers; sometimes people get crazy and add 10 or 12 models into a simulations (wtf, right?) to generalize more, the where the word "simulation" gets its bad name.

Is this consistent with your definitions of simulation and model? Anyway the point is that models are useless without simulation (which predictions are made from, but predictions add a layer of intuition to it).

Anyway, a theory of everything would mean: Find a model for which all of it's assumptions are always true, prove me that negative!

You can write maxwell's equations as one equation... but it's pretty useless without the full development of the four equations, and the full development of what each of those equations means. So really, it's a compression algorithm for humans: a sort of memory recall/filling system. Then you have to add the relativistic equations to it if you want to get to QM.

 

[SixNein]

Generally, physicists don't work on "mathematical problems". They use math in physical problems.

I disagree, respectfully. Physicists create mathematical models that mirror the world, and they work on those models. Those models are indeed matheamtics.

The most simple example I can think of is counting. People learn how to count at a very young age. At first, they start out counting apples or maybe oranges, but eventually, they progress to using mathematical models such as integers.

Do you think in apples or integers?

 

[SixNein]

@Shut up and Calculate discussion:

Ok, so while writing a reply to apeiron, I had a kind of ah-ha moment. It's consistent with the point I'm trying to make about mathematics being a language. Shut up and Calculate is quite simply an attitude towards learning the language of mathematics. I hope that's well and accepted. I think what people are having trouble accepting is that mathematics actually conveys qualitative concepts that DO have a common language title (i.e. "nullcline"), but DO NOT have a common language definition.

Now, you all KNOW this. You exchange money with services and you can count integers easily. You're taking for granted how mathematics has already ingrained itself into our common language because of it's necessity. You realize the importance of this language on an unconscious level. This is only because you were much more willing to shut up and calculate when you were taught basic mathematics by your parents before you even went to school where you learned even more mathematics, through calculating, and practicing the language, just like you did with the alphabet to practice common language.

(the bold sentence below represents what triggered this thought)

@ apeiron: Well we're getting off-topic. I would participate in a discussion in a new thread. To reply to your post shortly though, I think any time you make predictions with a model that you are simulating (even if you solve a Newtonian equation on paper to figure out the trajectory of a cannonball... it obviously has it's shortcomings. But those shortcomings come from the assumptions of the model, and apply where the assumptions fail.

More complex simulations are done on computers; sometimes people get crazy and add 10 or 12 models into a simulations (wtf, right?) to generalize more, the where the word "simulation" gets its bad name.

Is this consistent with your definitions of simulation and model? Anyway the point is that models are useless without simulation (which predictions are made from, but predictions add a layer of intuition to it).

Anyway, a theory of everything would mean: Find a model for which all of it's assumptions are always true, prove me that negative!

You can write maxwell's equations as one equation... but it's pretty useless without the full development of the four equations, and the full development of what each of those equations means. So really, it's a compression algorithm for humans: a sort of memory recall/filling system. Then you have to add the relativistic equations to it if you want to get to QM.

There must be something in the air causing people to think about integers today.

"You're taking for granted how mathematics has already ingrained itself into our common language because of it's necessity"

That was my fundamental point about translating math and physics. And I would go further and say it is ingrained in your mental process. I doubt you count in apples.

 

[Pythagorean]

I disagree, respectfully. Physicists create mathematical models that mirror the world, and they work on those models. Those models are indeed matheamtics.

The most simple example I can think of is counting. People learn how to count at a very young age. At first, they start out counting apples or maybe oranges, but eventually, they progress to using mathematical models such as integers.

Do you think in apples or integers?

In the advanced courses, you don't even USE numbers for most of the work. It's all variables. The variables represent real, physical, measureable things. So yes, I think in "apples" (or whatever physical observable I'm modeling), not integers.

Even in my advanced math classes, the best math teachers (in my opinion, of course) demonstrated the concepts in real systems to give people an intuitive grasp of the information.

Think about it... if I think in integers, I have to remember x (hehe) different symbols. If I think in variables, I remember one symbol. If I think in functions, I remember a shape of the function on a plot, not the numbers at all (the shape scales to many different sizes and shapes for different integers, but ANY behavior of interest has NOTHING to do with the numbers (until you start making predictions with a model to fit to reality, or start engineering a technology in reality to exploit the behavior).

Of course, we eventually HAVE to use numbers in physics, but they're definitely the annoying part of the whole job.

As for a translation... that's basically what math and physics courses are.

 

[yossell]

In the advanced courses, you don't even USE numbers for most of the work. It's all variables. The variables represent real, physical, measureable things.

But there are mathematical variables used in physics that don't represent real, physical, measurable things, the most famous being classical quantum mechanics' values of the complex wave function that are solutions of S's equation. Although \Phi is mathematically manipulated in the theory, it's |\Phi| which receives a physical, probabilistic interpretation. Indeed, it was probably the amount of brain power wasted arguing over what the wave represented that gave the shut up and calculate brigade a big boost.

It's not for nothing that the root of minus one is called imaginary!

Line elements, Riemannian metric fields, infinite dimensional Hilbert spaces, dirac delta functions...these mathematical objects appear in our physical theories, but it's not at all clear to me that they represent real, physical, measurable things - though of course, we can and do use them in mathematical operations to get results about things that are measurable - as we do with \Phi.

 

[Pythagorean]

But there are mathematical variables used in physics that don't represent real, physical, measurable things, the most famous being classical quantum mechanics' values of the complex wave function that are solutions of S's equation. Although \Phi is mathematically manipulated in the theory, it's |\Phi| which receives a physical, probabilistic interpretation. Indeed, it was probably the amount of brain power wasted arguing over what the wave represented that gave the shut up and calculate brigade a big boost.

It's not for nothing that the root of minus one is called imaginary!

Line elements, Riemannian metric fields, infinite dimensional Hilbert spaces, dirac delta functions...these mathematical objects appear in our physical theories, but it's not at all clear to me that they represent real, physical, measurable things - though of course, we can and do use them in mathematical operations to get results about things that are measurable - as we do with \Phi.

Agreed. (Though, imaginary truly is a terrible term for imaginary numbers).

I don't think this conflicts with my point though. We start with observables in physical modeling... and end with them.

 

[SixNein]

Agreed. (Though, imaginary truly is a terrible term for imaginary numbers).

I don't think this conflicts with my point though. We start with observables in physical modeling... and end with them.

I prefer complex instead of imaginary. Imaginary should have never been adopted as the name.

Like string theory? Anyway, I'll retract.