Is Mathematics the Best Language for Understanding the Universe?

[micromass]

Micromass, a computer can verify and aply the substitution law.

Show me. Or give a reference if it has been done before.

 

[bcbwilla]

By the way, what will solving the schrodinger equation do to us? I'm asking it, yes, I have no idea.

...chemistry? Density functional theory, molecular dynamics, etc.

Please respond to this:
You said "These equations are not quantum mechanics. These equations are an algebraic model of quantum mechanics. It can be modeled by matters of objects and functions aswell."

I replied: "Objects and functions representing what? The equations!"

 

[DivisionByZro]

I don't understand why you get so offended when people ask what your level of knowledge/education is; it's a valid question. It seems to me (and I'm probably not alone in this) that you have no idea what physics and math are, yet you persist to argue. I tried to be helpful and tried to understand what it was you were asking, but I give up.

 

[WindScars]

Bcbwilla, objects and functions represent quantum mechanics. Using QM is not fair as I don't know anything about it, though. You can use something I am, the analogy will still be valid.

Micromass, I answered it does because I'm sure it does. The substituton law? I have seen a news about computers predicting and modeling a biologic "setup" (forgot the word). But there are probably many mathematical problems it can't solve, so I basically said, yes, your point is right! But it is just irrelevant because this topic is not about a computer solving things for you, is about using the computer as a replacement to ink and paper as your main tool. This said, changing your question to be valid to the topic:

Show me how you can use the computer to verify the substitution law for integrals:

1. Solve it programatically? (not really necessary for this one)
2. Use mathematica or anything else?
3. Just do your algebra on notepad or using a touchscreen?

Note: I also point why worrying too much with algebraic tricks is so important? For instance, is not it better to use your time to learn mathematica than to memorize integral tables?

Division I don't get offended, just upset, because it just simply no point? Having a background on physics have nothing to do with this topic? Would be it fair if I asked for your programming background? This is just elitism and it is very unecessary.

 

[micromass]

I don't understand why you get so offended when people ask what your level of knowledge/education is; it's a valid question. It seems to me (and I'm probably not alone in this) that you have no idea what physics and math are, yet you persist to argue. I tried to be helpful and tried to understand what it was you were asking, but I give up. I wash my hands of you, sir.

It's not his arguiring that is worrisome, I like a good argument. It's the fact that he tries to learn physics without actually doing the calculations. This will end in a disaster, and I'm trying to get the OP to not learn physics this way.

 

[bcbwilla]

Bcbwilla, objects and functions represent quantum mechanics. Using QM is not fair as I don't know anything about it, though. You can use something I am, the analogy will still be valid.

Pick any physics topic you'd like. Show me a simple function describing a problem within this topic without using a physics equation that has been derived in part through algebra.

 

[WindScars]

Micromass, you should't worry about me, you should answer the topic. If this is why you are asking for my background, allright: I just finished the first semester on calculus and physics 1. Scored a standard deviance above average and was the best on high school times. But this is off topic here. I have topics for this already. And again, you are misunderstanding completely my point.

 

[DivisionByZro]

Division I don't get offended, just upset, because it just simply no point? Having a background on physics have nothing to do with this topic? Would be it fair if I asked for your programming background? This is just elitism and it is very unecessary.

It's ok. I'm doing a minor in computer science too. I'm not pulling stuff out of my a**, or I try not to. It's not elitism, it's a prerequisite for any serious talk about science. You can't just walk around throwing your ideas and expect people to take you seriously. You have to give them a reason to take you seriously; that's making a reputation for yourself and working hard. I'm sorry to break it to you.

 

[WindScars]

Where was this a serious talk about science? I'm just asking for changing the paper to a computer, and replacing algebra tricks (not algebra, algebra tricks - things like memorizing integrals tables) to the understandment of programs like mathematica. When I made myself look like I'm trying to have a 'serious talk about science'?

bcbwilla, again, "algebra tricks" is not the same as algebra. You guys are not getting my point, at all. I know I need english classes, but I'm pretty sure it IS understandable if you read what I say. but anyway, I can model a vector class programatically without any algebra at all. I can further use it to model a mechanical system. I can easily aply advanced mathematical concepts just exporting functions and understanding why they work. And I can find out those functions using artifitial inteligence, there are some interesting articles on that. But again, this is not the point, I'm answering because you asked. The topic is JUST about replacing the pen and ink and the algebraic tricks like memorizing formulas into programming and learning to use software, respectively. Nothing beyound that.

 

[DivisionByZro]

I can easily aply advanced mathematical concepts just exporting functions and understanding why they work. And I can find out the simplest formulas using artifitial inteligence,

?

 

[WindScars]

Its hard if you don't say what did you not understand, but I'll rephrase:

I can aply hardest concepts (say, solving differential equations) by using the proper software instead of learning tricks. If I need to push knowledge beyound, there are many ways to do that using a computer. One example is that paper where a computer just found out all the rules of a simple biological system by itself. But this is NOT the point of the topic. The topic is just about using a computer instead of the paper, and understanding software like mathematica instead of memorizing integrals or methods of solving differential equations.

This is not being good, anyway. I should stop creating topics in english until I understand you better. Not just the fact my english is poor, it's a very different culture and I always tend to be misunderstood on those topics... and I already got my answer. This is so painly pointless...

 

[bcbwilla]

The topic is just about using a computer instead of the paper, and understanding software like mathematica instead of memorizing integrals or methods of solving differential equations.

If everyone only knew how to use Mathematica and not analytical solutions to integrals or different methods of solving differential equations, then there would be no one to write Mathematica in the first place.

 

[WindScars]

Someone has to understand it, but do everyone that wants to understand the fundaments of our universe has too? Can't someone just use software to do what was already discovered, and spend it's time on the topic he is interested in making an advancement (if he is, at all?)

I'll use my example. I would like to work on nanotech. It's a field on development and it's entire dynamics is dictated by quantum mechanics. But do I need to go through years and years of math and physics, to understand quantum mechanics in a mathematically advanced level, if I want to push nanotechnology? What if instead I just learn the concepts, the soul of quantum mechanics, and use that years to come making, for instance, making simulations, trying to model nanochemical machinery?

 

[micromass]

OK, Windscars, you claim that we don't understand what you mean. Fair enough. I probably don't understand what you mean.

Could you perhaps give an example of how your method would work?? What would be your method of studying something?? How would you do research?? Just give a very specific and concrete example.

 

[bp_psy]

The hardest math course I ever took was a numerical linear algebra course. It was kind of based around Trefethen and Bau textbook.This was the course I learned what you can do with a computer and how you can determine if what you do with it actually makes any sense.The proofs were hard and the programing usually required that you really understand the proofs.I think it is impossible to make computer do something useful without having a really good theoretical understanding of what you are doing.For me programing takes an hour on paper ,10 mins coding and 3 hours debugging.

 

[bcbwilla]

Can't someone just use software to do stuff and spend it's time on the topic he is interested?

Of course. But in your original question it seemed liked you were asking "Are math skill necessary?" in a more general sense.

Take more physics courses. You will then see that much of a person's understanding of the "fundamentals of our universe" comes from the mathematical relationships. Plugging some inputs into a computer and getting an output provides very little understanding.

 

[Ans426]

Someone has to understand it, but do everyone that wants to understand the fundaments of our universe has too? Can't someone just use software to do what was already discovered, and spend it's time on the topic he is interested in making an advancement (if he is, at all?)

I'm not sure about you, but if somebody gave me a ODE/PDE and just told me "This is the answer" I probably wouldn't be very happy about it, without even knowing how to derive the result...
And I doubt that would train anyone as a proper scientist...

Of course at some point I guess everyone uses Mathematica or Wolfram Alpha when you've pretty much mastered the skills and you're just doing it for convenience...

 

[WindScars]

Well guys, I don't know. This discussion is pointless, but this topic is being very enlightening, actually. I have not much to add to it, I guess. But as you guys are coming here and seems to be interested in helping, I'll be precise in why I made this.

As I said, I would like to work on nanotech. It's a field on development and it's entire dynamics is dictated by quantum mechanics.

So, what do I do? Something is obvious: I have to understand quantum mechanics if I want to actually push the field. But what do "understanding quantum mechanics" means?

I, for instance, could simulate mechanical systems years before I could do precise calculations. I could easily program and model systems of planets orbiting, charges interacting, springs oscilatting, etc, years before I could solve a mere quadratic equation. So I can say I did understand the classical mechanics, even though I couldn't do any serious math on it. After all, it's how our world seems to act.

So, I wonder: do I actually have to go though those years and years of "mathematical maduration" if I want to understand quantum mechanics? And I'm not sure what I'll be able to do when I have the math skills for it, but will it be useful for my purposes? For instance, do getting into QM means I'll be able to calculate precisely the motion of an isoled quantized particle, the same way I am able, today, to calculate the motion of a spring in function of time? Because if this is what "learning QM" is, I guess this is not what I need.

Will not it be more useful if I just get into quantum mechanics intuitivelly and spend those years I would be spending on the math doing simulations instead? As I said, I have no idea of how the physics of nanoscale works, but if I understood it, I could play with it here. I could do simulations and use my time actually trying to figure out how I could build machines from atoms. Wouldn't this be more useful?

Well I don't know. If you guys have any idea of where I can "see quantum mechanics" - that is, actually visualizing what happens there, before those years of 'maturation', this would be very insightful.

 

[Ans426]

Well guys, I don't know. This discussion is pointless, but this topic is being very enlightening, actually. I have not much to add to it, I guess. But as you guys are coming here and seems to be interested in helping, I'll be precise in why I made this.

As I said, I would like to work on nanotech. It's a field on development and it's entire dynamics is dictated by quantum mechanics.

So, what do I do? Something is obvious: I have to understand quantum mechanics if I want to actually push the field. But what do "understanding quantum mechanics" means?

I, for instance, could simulate mechanical systems years before I could do precise calculations. I could easily program and model systems of planets orbiting, charges interacting, springs oscilatting, etc, years before I could solve a mere quadratic equation. So I can say I did understand the classical mechanics, even though I couldn't do any serious math on it. After all, it's how our world seems to act.

So, I wonder: do I actually have to go though those years and years of "mathematical maduration" if I want to understand quantum mechanics? And I'm not sure what I'll be able to do when I have the math skills for it, but will it be useful for my purposes? For instance, do getting into QM means I'll be able to calculate precisely the motion of an isoled quantized particle, the same way I am able, today, to calculate the motion of a spring in function of time? Because if this is what "learning QM" is, I guess this is not what I need.

Will not it be more useful if I just get into quantum mechanics intuitivelly and spend those years I would be spending on the math doing simulations instead? As I said, I have no idea of how the physics of nanoscale works, but if I understood it, I could play with it here. I could do simulations and use my time actually trying to figure out how I could build machines from atoms. Wouldn't this be more useful?

Well I don't know. If you guys have any idea of where I can "see quantum mechanics" - that is, actually visualizing what happens there, before those years of 'maturation', this would be very insightful.

I doubt anyone can "intuitively" understand Quantum Mechanics...
" I think I can safely say that nobody understands quantum mechanics. " - Richard Feynman

 

[bp_psy]

I, for instance, could simulate mechanical systems years before I could do precise calculations. I could easily program and model systems of planets orbiting, charges interacting, springs oscilatting, etc, years before I could solve a mere quadratic equation.

How exactly did you do that? I am sorry but I don't see how someone could do that.Except for copy - paste programing.

 

[WindScars]

I can't visualizate the motion of atoms? How can it be so weird? It can be weird, but it must follow a rule.

bp_psy, why? This is easy I guess? Planets orbiting: 3d spheres as planets, position vectors atracting themselves every tick following the laws of gravitation, initial conditions to match the centripetal equilibrium. Charges iterating: basically the same. I even did a color mapping stuff when I was trying to understand eletrodynamics. This also made me understand a little better how electrons could oscilatte though a nuclei without falling on it or needing circular motion (I still don't understand many things, though). Springs oscillating: once I made several small balls glued together by a force. Then I noticed it acted as a string. Then I suddenly understood how springs works. It was beautiful. I had no idea of what I was doing. As I said, it was nothing serious or precise, yet I'm sure it followed the intuitive principles. And was fun.

 

[Jorriss]

I can't visualizate the motion of atoms? How can it be so weird? It can be weird, but it must follow a rule.

It does follow rules. Mathematical rules. Quantum is extremely difficult to understand physically. It requires an understanding of the math that goes along with it.

Special relativity is counter intuitive, but if one accepts that the speed of light is the same in all reference frames than the arguments of what occurs physically are crystal clear and it is easy to think about special relativity physically. Quantum is not this way at all. The postulates are mathematical, the thought experiments are very hard to grasp, it is very difficult to get a grasp of what quantum says physically.

 

[WindScars]

The classical world is not easy too, we are just used to it. Well I'm already advancing every day on the math, but I'll be very sad if when I finally get into QM I realize I could have understood it just with what I know today.

What are the pre-requisites of QM by the way? I'm stuck into that horribly bulky stewart calculus 2 book, still trying to understand why I have to waste my time on all those tricks that are not challanging and not teaching me anything I couldn't do with mathematica.

 

[Ans426]

Well guys, I don't know. This discussion is pointless, but this topic is being very enlightening, actually. I have not much to add to it, I guess. But as you guys are coming here and seems to be interested in helping, I'll be precise in why I made this.

As I said, I would like to work on nanotech. It's a field on development and it's entire dynamics is dictated by quantum mechanics.

So, what do I do? Something is obvious: I have to understand quantum mechanics if I want to actually push the field. But what do "understanding quantum mechanics" means?

I, for instance, could simulate mechanical systems years before I could do precise calculations. I could easily program and model systems of planets orbiting, charges interacting, springs oscilatting, etc, years before I could solve a mere quadratic equation. So I can say I did understand the classical mechanics, even though I couldn't do any serious math on it. After all, it's how our world seems to act.

So, I wonder: do I actually have to go though those years and years of "mathematical maduration" if I want to understand quantum mechanics? And I'm not sure what I'll be able to do when I have the math skills for it, but will it be useful for my purposes? For instance, do getting into QM means I'll be able to calculate precisely the motion of an isoled quantized particle, the same way I am able, today, to calculate the motion of a spring in function of time? Because if this is what "learning QM" is, I guess this is not what I need.

Will not it be more useful if I just get into quantum mechanics intuitivelly and spend those years I would be spending on the math doing simulations instead? As I said, I have no idea of how the physics of nanoscale works, but if I understood it, I could play with it here. I could do simulations and use my time actually trying to figure out how I could build machines from atoms. Wouldn't this be more useful?

Well I don't know. If you guys have any idea of where I can "see quantum mechanics" - that is, actually visualizing what happens there, before those years of 'maturation', this would be very insightful.

Apparently others asked for your background for a reason...
Even "Pop" QM tells you that nothing at the atomic scale is precise..

But I guess the key point here is that you won't be able to make any sense out of the system if you can't understand the mathematics behind...

If you're simulating extremely simple stuff like two charges interacting with each other, sure you'll be fine and the results will still make sense.

But just consider a slightly more complex system, and you'll understand why computational techniques alone don't do you any good.
For instance, consider a damped pendulum (Damping Force = -bv) and further driven by an external sinusoidal force with a certain frequency. (I'm sure you're aware the code is extremely simple)
Tune the magnitude of the external force a bit and you'll start seeing crazy results that will make no sense to you unless you've learned about differential equations and some chaos theory. And this is sophomore stuff.
Merely looking at the results generated by a computer in specific cases won't give you much insight in the generalized cases.

And I can assure you that the smartest physicists in the world have not spent decades working on something that a random undergraduate could do with his computer programs.

The classical world is not easy too, we are just used to it. Well I'm already advancing every day on the math, but I'll be very sad if when I finally get into QM I realize I could have understood it just with what I know today.

What are the pre-requisites of QM by the way? I'm stuck into that horribly bulky stewart calculus 2 book, still trying to understand why I have to waste my time on all those tricks that are not challanging and not teaching me anything I couldn't do with mathematica.

Differential Equations, Multivariable Calculus, Complex Analysis and of course linear algebra
Again, of course you can do everything on a computer because someone HAS ALREADY done the maths...

This in fact reminds me of the Hardy–Weinberg principle
http://en.wikipedia.org/wiki/Hardy–Weinberg_principle
Hardy's name is now in every genetic textbooks simply because Weinberg couldn't do high school probability and algebra

 

[bp_psy]

I can't visualizate the motion of atoms? How can it be so weird? It can be weird, but it must follow a rule..

.
The notion of "motion of atoms" at a quantum level is very different them motion of simple particles. This makes visualization of quantum phenomena impossible. There are some useful ways to visualize some aspects of Qm but they are all in some way or another incomplete or incorrect. An example would be this: http://www.falstad.com/qm1drad/

bp_psy, why? This is easy I guess. Planets orbiting: 3d spheres as planets, position vectors atracting themselves every tick following the laws of gravitation, initial conditions to match the centripetal equilibrium. Charges iterating: basically the same.
I even did a color mapping stuff when I was trying to understand eletrodynamics. This also made me understand a little better how electrons could oscilatte though a nuclei without falling on it or needing circular motion (I still don't understand many things, though). Springs oscillating: once I made several small balls glued together by a force. Then I noticed it acted as a string. Then I suddenly understood how springs works. It was beautiful. I had no idea of what I was doing. Nothing serious or precise, it was just fun.

One of the most basic reason for learning some actual physics and maths is that you might actually be understood by someone when you want to say something about them. I am sorry but I do not understand anything in that paragraph. Nothing actually makes sense.

 

[Jorriss]

The classical world is not easy too, we are just used to it. Well I'm already advancing every day on the math, but I'll be very sad if when I finally get into QM I realize I could have understood it just with what I know today.

The classical world is not easy, you are right but the fact we are used to it is an immense distinction over quantum.

What are the pre-requisites of QM by the way? I'm stuck into that horribly large stewart calculus 2 book, still trying to understand why do I have to waste my time on all those tricks that are not challanging and not teaching me anything I couldn't do with mathematica.

The baseline prerequisites are calculus, differential equations and if want to get a better grasp, baby linear algebra. If you grab a modern physics book, if you can learn some things about quantum but it's an immensely tiny fraction of what the theory actually says and is about. Everything you are learning now in your math classes is important.

You just can't understand quantum without math. It, more so than most, is a mathematical theory. All the axioms of quantum are mathematical in nature (except maybe about the existence of a wavefunction which contains the information of the system).

Even in the simplest cases of quantum, such as a free particle, have subtle physical issues due to mathematical issues such as nonnormalizable solutions.

 

[WindScars]

Ans426, if I can watch QM happening on my eyes, will not it give me an insight? For instance I always tried to find a program that would allow me to create a few atoms on void and watch them interacting. This would be awesome. Of course I never found one, but I was not sure if it was not possible or nobody did it because it is theorically useless. Words on this?

And allright, if this is the only way, at least what are the pre-reqs to QM? How fast can I get them starting from where I am (calculus 1)? Can you estimate in hours?

The baseline prerequisites are calculus, differential equations and if want to get a better grasp, baby linear algebra. If you grab a modern physics book, if you can learn some things about quantum but it's an immensely tiny fraction of what the theory actually says and is about. Everything you are learning now in your math classes is important.

This is all...? They said I'd need years?

What are your background, by the way? You all know QM? You think this is accurate to say understanding QM is important to nanotech?

 

[Jorriss]

Ans426, if I can watch QM happening on my eyes, will not it give me an insight? For instance I always tried to find a program that would allow me to create a few atoms on void and watch them interacting. This would be awesome. Of course I never found one, but I was not sure if it was not possible or nobody did it because it is theorically useless. Words on this?

What does a few atoms on a void even mean?

And allright, if this is the only way, at least what are the pre-reqs to QM? How fast can I get them starting from where I am (calculus 1)? Can you estimate in hours?

If you want to learn a little tiny bit of quantum, get a modern physics book.
y''+ky=0

Can you solve that differential equation? If so, you can probably follow it a bit. I suppose a modern physics book wouldn't be bad as those are mostly qualitative anyhow.

This is all...? They said I'd need years?

To really do quantum, yes it takes time.

To get to quantum you need Calc I-III, differential equations and linear algebra, then you can somewhat comfortably handle an upper division course on quantum mechanics that is not too theoretical nature.

That's at least 1.5 years of prerequisites.

What are your background, by the way? You all know QM? You think this is accurate to say understanding QM is important to nanotech?

Formally, I have one quarter of quantum chemistry and I do undergraduate research in quantum. I suppose it's some nanotech. Electron transport through molecular junctions, but it is theory.

 

[bcbwilla]

And allright, if this is the only way, at least what are the pre-reqs to QM? How fast can I get them starting from where I am (calculus 1)? Can you estimate in hours?

Okay, I lol'd.

 

[bp_psy]

And allright, if this is the only way, at least what are the pre-reqs to QM? How fast can I get them starting from where I am (calculus 1)? Can you estimate in hours?

Hours 3456H 54mins 15 secs.
But for me from end of calc 1 to quantum 1 it was 4 semesters in a physics program.It can probably be done faster.

 

[WindScars]

Actually I can't, but I just started studying differential equations so it's good news.

A few atoms on void means, for instance, creating two hydrogen atoms in an empty space and watching them react (that is, visualizing the nuclei, the electronic clouds)? Even if aproximately. Is this absurd? Why? This would be awesome.

bcbwilla don't ;s I didn't say estimate precisely... just because in "semesters" is very relative. Well I can estimate something in hours. Use this formula: your_answer_in_semesters * hour_you_expect_me_to_study_a_day * 180

bp_psy, can you remember your colleges pre-requisites to QM?

 

[Jorriss]

A few atoms on void means, for instance, creating two hydrogen atoms in an empty space and watching they react? Is this absurd? Why?

No, it's not absurd. But how are you modeling them? In reality to model something like that in fullest, surprisingly enough, requires group theory.

Are you simply modeling them as two point particles interacting via a potential?

 

[Ans426]

Ans426, if I can watch QM happening on my eyes, will not it give me an insight? For instance I always tried to find a program that would allow me to create a few atoms on void and watch them interacting. This would be awesome. Of course I never found one, but I was not sure if it was not possible or nobody did it because it is theorically useless. Words on this?

And allright, if this is the only way, at least what are the pre-reqs to QM? How fast can I get them starting from where I am (calculus 1)? Can you estimate in hours?


This is all...? They said I'd need years?

What are your background, by the way? You all know QM? You think this is accurate to say understanding QM is important to nanotech?

Just do me a favor, Google "Driven Damped Pendulum", write a program, play around with a bit and tell me what you've been generalize out of it just by "looking" at it.(This is a VERY TYPICAL classical system)

It seems to me that learning too much programming has actually did you more harm than good in terms of learning Physics, despite it usefulness nowadays

 

[WindScars]

Hmm this is pretty actually, but why this? Ans426 just asking. As you understand QM, do you consider yourself to understand an atom? Can a QM expert predict if a chemical reaction will occour (without using chemistry/testing on lab)? What would you tell me if I asked you what is the path of the motion of an electron around a hydrogen nuclei?

Jorriss, I can't answer you because I don't understand the motions of an atom. That is the point. If I could create isoled atoms, put them together, and their resulting motions leads to precise reactions in relation to what would be chemically expected, this would be awesome. I'm not sure if this is possible, but why not? And group theory? What is it? (=

 

[Jorriss]

Jorriss, I can't answer you because I don't understand the motions of an atom. That is the point. If I could create isoled atoms, put them together, and their resulting motions leads to precise reactions in relation to what would be chemically expected, this would be awesome. I'm not sure if this is possible, but why not?

Are you talking about experimentally or you modeling this with your computer?