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

[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.