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Why can we use mathematics to describe physical phenomena?

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Why is it that physical phenomena can be expressed so simply with beautiful mathematics?

I don't know much mathematics or physics but I do know that math is incredibly useful in modelling physical phenomena.

Also, it'd be nice if someone here could explain how linear algebra is used in quantum mechanics. I just did a course in school on the subject (linear algebra) and am excited to know why it's applicable in physics.

I mean, it's incredible, isn't it? The fact that the physical phenomena we experience has a mathematical structure to it.

How do physical know that a particular mathematical model fits a certain phenomena? How did Heisenberg come up with the idea of matrix mechanics? How did the string theorists know that the euler beta function can be used to describe whatever phenomena that it describes?

It'd be nice if someone knows a book or two which could be helpful in this domain. I know up to linear algebra so it'd be nice if the book isn't aimed at the popular level but at people with some mathematical background. Or, if someone has thought about these questions and would like to offer their opinion that'd be good too.

Thank you.
 

Cognisant

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Dude give up.

Yeah there's a lot of neat little formulas used mainly by engineers that explain how this or that is going to behave under certain conditions but quantum mechanics is nothing like that, it's an attempt to explain that which is so obtuse that it's practically inexplicable.

You need to be a special kind of crazy (high functioning autistic INTJ maybe?) to make any sense of that stuff.
 

Coolydudey

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Cog: you're wrong. QM is a precise description of a probabilistic system. And it doesn't take any kind of crazy to get a fairly good grasp on it.

But wait, let's take a step back. I said precise. All of physics makes certain assumptions. Precise under those assumptions. In fact however, much of QM is approximations; the Schrodinger equation itself for example. But if you were infinitely intelligent and powerful you could derive precise descriptions without approximations from what we know (for many things anyway).

Anyway, at a simple level, QM is based on certain differential equations. Certain functions solve these equations. These functions form a vector space; http://mathworld.wolfram.com/VectorSpace.html

Have a vector space, and you have linear algebra. You can model differential operators as infinite matrices in this so-called Hilbert space (an infinite dimensional vector space with certain properties). And so on.

Am I losing you? How familiar are you with differential equations?
 

Kuu

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Math is incredible useful for physics because math is a language invented and developed specifically to describe abstract physical phenomena. However, like in any language one can create absolutely meaningless expressions too. I don't know about beauty, but simplicity I think could be interpreted in two ways: because the fundamental workings of the world are relatively simple (and the mathematical description merely reflects that), or because we have nested so many layers of abstraction in mathematics to make the description seem simple (math has become more complex so that physics can seem less so, kind of working with a higher level programming language instead of machine code).


Regarding quantum mechanics: I don't think this is the best place to seek this knowledge. Ask on some forum specialized in physics.
 

Coolydudey

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Oh come on Kuu, surely a forum of INTPites can pull off a basic popularization of some aspects of QM - especially if Archie chimes in ;)
 
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Cog: you're wrong. QM is a precise description of a probabilistic system. And it doesn't take any kind of crazy to get a fairly good grasp on it.

But wait, let's take a step back. I said precise. All of physics makes certain assumptions. Precise under those assumptions. In fact however, much of QM is approximations; the Schrodinger equation itself for example. But if you were infinitely intelligent and powerful you could derive precise descriptions without approximations from what we know (for many things anyway).

Anyway, at a simple level, QM is based on certain differential equations. Certain functions solve these equations. These functions form a vector space; http://mathworld.wolfram.com/VectorSpace.html

Have a vector space, and you have linear algebra. You can model differential operators as infinite matrices in this so-called Hilbert space (an infinite dimensional vector space with certain properties). And so on.

Am I losing you? How familiar are you with differential equations?

We covered vector spaces in class so I kind of get where you're coming from. We also looked at function spaces for some reason so the idea of having functions form a vector space isn't that foreign to me. We haven't done differential equations though...But I don't think that's hindering me right now.

Could you go into detail? Particularly, how did the physicists think to use linear algebra to model phenomena at that scale?
How did that come about?

Gaah. Wish I'd taken up math or physics instead of engineering. It seems a lot more fun. Engineering's kind of boring, so far at least.
 
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Math is incredible useful for physics because math is a language invented and developed specifically to describe abstract physical phenomena. However, like in any language one can create absolutely meaningless expressions too. I don't know about beauty, but simplicity I think could be interpreted in two ways: because the fundamental workings of the world are relatively simple (and the mathematical description merely reflects that), or because we have nested so many layers of abstraction in mathematics to make the description seem simple (math has become more complex so that physics can seem less so, kind of working with a higher level programming language instead of machine code).


Regarding quantum mechanics: I don't think this is the best place to seek this knowledge. Ask on some forum specialized in physics.

Math as a language...I heard that a few places. I don't know enough math to comment on that though.
 
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Dude give up.

Yeah there's a lot of neat little formulas used mainly by engineers that explain how this or that is going to behave under certain conditions but quantum mechanics is nothing like that, it's an attempt to explain that which is so obtuse that it's practically inexplicable.

You need to be a special kind of crazy (high functioning autistic INTJ maybe?) to make any sense of that stuff.

I sometimes wish I were a high functioning autistic INTJ. Life would have been a lot more fun and less like how it is now. I don't know what the view is of INTJs are around here but I personally think that the most useful function to have is Ni and then either Ti or Te.
 

computerhxr

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How do physical know that a particular mathematical model fits a certain phenomena? How did Heisenberg come up with the idea of matrix mechanics? How did the string theorists know that the euler beta function can be used to describe whatever phenomena that it describes?

It'd be nice if someone knows a book or two which could be helpful in this domain. I know up to linear algebra so it'd be nice if the book isn't aimed at the popular level but at people with some mathematical background. Or, if someone has thought about these questions and would like to offer their opinion that'd be good too.

Cognisant and Kuu have hit the nail on the head. It's just an abstract representation of a real phenomenon.

It's mechanical from a low level, and the larger the system, the less mechanical it becomes (more variables). So quantum mechanics works on small physical systems. It's abstract and inaccurate, but close enough to work practically. They are just ideas and there are many ways to explain the same phenomenon that are equally as valid.

I'm working on some stuff that explains natural phenomena without using much math, if at all. Math is the slow and difficult way of understanding ideas. It doesn't allow you to make connections easily. Einstein for example came up with the idea of relativity while riding a bike, so it's likely that there wasn't much actual math involved. Math is used to explain the idea only after the idea has been had. Does that make sense?
 

redbaron

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Einstein for example came up with the idea of relativity while riding a bike, so it's likely that there wasn't much actual math involved

Nevermind the years of study, underpinning mathematical knowledge and obsession with his work. Not to mention that it took another 11 years from the time of its proposal to convert it into a system with reliable predictive capability.

Plus without Einstein Field Equations (among other things), relativity has no exceptional predictive capability - and is therefore useless. The real beauty of relativity.

http://upload.wikimedia.org/math/0/8/c/08cdba3d0a1bb384e07a0ea5d14a34fb.png

Yeah, he was just some guy riding a bike - not much actual maths involved. Just like Newton wasn't really a great mathematician, he just hung around in an apple orchard a lot :cat:
 

computerhxr

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Nevermind the years of study, underpinning mathematical knowledge and obsession with his work. Not to mention that it took another 11 years from the time of its proposal to convert it into a system with reliable predictive capability.

Plus without Einstein Field Equations (among other things), relativity has no exceptional predictive capability - and is therefore useless. The real beauty of relativity.

http://upload.wikimedia.org/math/0/8/c/08cdba3d0a1bb384e07a0ea5d14a34fb.png

Yeah, he was just some guy riding a bike - not much actual maths involved. Just like Newton wasn't really a great mathematician, he just hung around in an apple orchard a lot :cat:

Yeah, they both are stupid and suck at math. That's totally what I was saying. Thanks for clearing that up for everyone. :rolleyes:
 

redbaron

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Yeah, they both are stupid and suck at math. That's totally what I was saying. Thanks for clearing that up for everyone. :rolleyes:

No you said there wasn't much actual math involved. I pointed out that there was. Nice straw man though.
 

computerhxr

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No you said there wasn't much actual math involved. I pointed out that there was. Nice straw man though.

Math is a representation of reality, not the reality itself. Someone can have an idea that represents the same idea without math. Math is just one abstraction of reality.

Calling my comment a straw man— is a straw man argument. If anything you created the straw man argument to begin with by misrepresenting my point.

:storks:
 

redbaron

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Required reading:

http://www.ncbi.nlm.nih.gov/pubmed/10626367

There's a difference between ridiculing and misrepresenting. The idiotic sentiments of "Einstein came up with relativity riding a bike!" and "Newton saw apples falling and discovered gravity!" are pervasive, misleading and simply wrong. They and anyone who perpetuates them deserve whatever ridicule they receive.
 

computerhxr

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Required reading:

http://www.ncbi.nlm.nih.gov/pubmed/10626367

There's a difference between ridiculing and misrepresenting. The idiotic sentiments of "Einstein came up with relativity riding a bike!" and "Newton saw apples falling and discovered gravity!" are pervasive, misleading and simply wrong. They and anyone who perpetuates them deserve whatever ridicule they receive.

First of all, I never said either of those things. You are really good at taking my words out of context and arguing some irrelevant point as if it were related.

You are creating another straw man argument by using similar quotes and calling it "idiotic sentiments" to invalidate my point. Basically calling me an idiot.

Alright, let's go back and look at what happened...

Math is the slow and difficult way of understanding ideas. It doesn't allow you to make connections easily. Einstein for example came up with the idea of relativity while riding a bike, so it's likely that there wasn't much actual math involved. Math is used to explain the idea only after the idea has been had. Does that make sense?

Then, you cherry pick part of a sentence out of context and misrepresent my point.

Einstein for example came up with the idea of relativity while riding a bike, so it's likely that there wasn't much actual math involved

Nevermind the years of study, underpinning mathematical knowledge and obsession with his work. Not to mention that it took another 11 years from the time of its proposal to convert it into a system with reliable predictive capability.

Plus without Einstein Field Equations (among other things), relativity has no exceptional predictive capability - and is therefore useless. The real beauty of relativity.

http://upload.wikimedia.org/math/0/8/c/08cdba3d0a1bb384e07a0ea5d14a34fb.png

Yeah, he was just some guy riding a bike - not much actual maths involved. Just like Newton wasn't really a great mathematician, he just hung around in an apple orchard a lot :cat:

You call ideas useless, even though they are not.

Then you compare my comment to Newton not being a great mathematician, and say that I'm saying the same thing. Straw man argument.

Then I make fun of your comment because it is a ridiculous misrepresentation of my point. Obviously a straw man argument...

Yeah, they both are stupid and suck at math. That's totally what I was saying. Thanks for clearing that up for everyone. :rolleyes:

You then point out that I said there wasn't much math involved. And call my comment a straw man. :confused:

No you said there wasn't much actual math involved. I pointed out that there was. Nice straw man though.

All because I said there wasn't much math involved when you come up with an idea while riding a bike. Have you tried doing long division while riding a bike? Yeah, I guess you're right; he must have been doing super complicated formulas in his head. That is idiotic sentiment.

Besides, none of what you said had anything to do with my point. I mention that there is a lot of math involved, and it comes after the idea. I never said it was impossible to do it the other way around.
 

computerhxr

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Required reading:

http://www.ncbi.nlm.nih.gov/pubmed/10626367

There's a difference between ridiculing and misrepresenting. The idiotic sentiments of "Einstein came up with relativity riding a bike!" and "Newton saw apples falling and discovered gravity!" are pervasive, misleading and simply wrong. They and anyone who perpetuates them deserve whatever ridicule they receive.

Hahaha, YOU should read that. Just trying to call me an idiot in another way. Passive aggressive BS. Call me an idiot to my face, I don't care and it doesn't bother me.
 

k9b4

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The universe operates by cause and effect. Mathematics is just a language we use to describe that cause and effect.

Why can we use english to describe physical phenomena?
 

redbaron

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All because I said there wasn't much math involved when you come up with an idea while riding a bike. Have you tried doing long division while riding a bike?

Oh look, another straw man. Now read very carefully.

The point is this: Einstein never came up with relativity while riding a bike, any more than Newton discovered gravity by looking at falling apples. Contrasting one popular misconception with another, is not misrepresenting an argument.

Relativity is actually the culmination of nearly 15 years (later adjustments not included) of borderline obsession with the mathematical inconsistencies of Newtonian classical mechanics, which affect its predictive capabilities in special circumstances - hence the need for a theory of relativity in the first place.

In other words, there's a huge amount of mathematical understanding, trial, error and experimentation. He also made several adjustments to various tenets of relativity, owing to evidence found in the experiments of other physicists.

Since all of this was not done while riding a bike and there's actually a lot of math involved - your comment was demonstrably wrong.

Relativity wasn't created by Einstein while he was riding a bike, and there was so much math involved it took the experiments of several physicists and astronomers, as well as refinements to Einstein Field Equations for us to get to relativity in all its predictive capability that we now see it with today.

You know for someone who quotes Einstein a lot, it sure is strange the way you so disrespectfully diminish the sheer amount of effort he and his colleagues put into their work.


computerhxr said:
Then you compare my comment to Newton not being a great mathematician, and say that I'm saying the same thing

Could you find the part where I said that?

computerhxr said:
You call ideas useless, even though they are not.

No. I called ideas without predictive capability useless for predicting things. It's pretty obvious and I wasn't sure I needed to point it out really, although you seem to have a hard time understanding it. So let's do a little experiment. Here's how it works.

Find an idea with zero predictive capability of the universe and then:

Try and accurately predict how things in the universe work based on that idea.

Let me know how it goes, I promise not to say "I told you so" :)
 

computerhxr

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Oh look, another straw man. Now read very carefully.

The point is this: Einstein never came up with relativity while riding a bike, any more than Newton discovered gravity by looking at falling apples. Contrasting one popular misconception with another, is not misrepresenting an argument.

You confused "ideas" for well thought out and highly elaborated, tested, and confirmed "ideas".

Relativity is actually the culmination of nearly 15 years (later adjustments not included) of borderline obsession with the mathematical inconsistencies of Newtonian classical mechanics, which affect its predictive capabilities in special circumstances - hence the need for a theory of relativity in the first place.

In other words, there's a huge amount of mathematical understanding, trial, error and experimentation. He also made several adjustments to various tenets of relativity, owing to evidence found in the experiments of other physicists.

Relativity existed before anyone discovered it. Scientists didn't invent it or create the phenomenon. Someone can imagine it without all the math.

Since all of this was not done while riding a bike and there's actually a lot of math involved - your comment was demonstrably wrong.

I never said that. You inferred that, and asserted that I did. I've pointed this out many times.

Relativity wasn't created by Einstein while he was riding a bike, and there was so much math involved it took the experiments of several physicists and astronomers, as well as refinements to Einstein Field Equations for us to get to relativity in all its predictive capability that we now see it with today.

Again, no one created relativity. You're throwing a bunch of other combined ideas and saying that they are included in the idea of relativity. Did I say the Theory of Relativity? Did I try to exclude the hard work that was involved? No, I said the idea of relativity and that there was work involved.

Math is the slow and difficult way of understanding ideas. It doesn't allow you to make connections easily. Einstein for example came up with the idea of relativity while riding a bike, so it's likely that there wasn't much actual math involved. Math is used to explain the idea only after the idea has been had.

You completely refused to see that because your whole argument is based on me saying otherwise.

Am I wrong? Is math not used to describe phenomena?

You know for someone who quotes Einstein a lot, it sure is strange the way you so disrespectfully diminish the sheer amount of effort he and his colleagues put into their work.

I post an Einstein quote and you say his words diminishes his efforts? Why do you think he is quoted for saying that? I didn't attach any other words to convince you of anything, and you interpreted it as diminishing Einsteins work?

The Einstein quote is directly related to the original post. They were asking how someone could come up with an "idea" of something so complicated. I thought the quote was pretty spot on. It also just so happens to support my idea and point out a personality flaw.

How do physical know that a particular mathematical model fits a certain phenomena? How did Heisenberg come up with the idea of matrix mechanics? How did the string theorists know that the euler beta function can be used to describe whatever phenomena that it describes?

Intuition is the answer... They were intuitive.

“The intuitive mind is a sacred gift and the rational mind is a faithful servant. We have created a society that honors the servant and has forgotten the gift.”

― Albert Einstein


It means, ideas first via intuition. Followed by lots and lots of hard work. I really don't think that I'm bashing his quote or diminishing anyone's hard work.

I was trying to be helpful and I never implied that there was no math involved. You keep saying that like I did. Doesn't make it more true and it's the basis of your argument. Other than calling out "straw man" as an argument. You're probably just doing that because I reference it in another thread, and not because it adds any value. Calling out "straw man" argument is "literally" a straw man argument, unless you justify it with reason.

Originally Posted by computerhxr
You call ideas useless, even though they are not.
Could you find the part where I said that?

Plus without Einstein Field Equations (among other things), relativity has no exceptional predictive capability - and is therefore useless. The real beauty of relativity.

Just because something isn't predicative doesn't mean that it is useless.

No. I called ideas without predictive capability useless for predicting things. It's pretty obvious and I wasn't sure I needed to point it out really, although you seem to have a hard time understanding it. So let's do a little experiment.

I'm not having a hard time. You never said "for predicting things" which means that you said it was just useless.

You're trying too hard to make me look like an idiot, when all you're doing is luring me down a path and forcing me to be an ass.

Don't bother responding because I'm just going to ignore it. :facepalm: Find another thread to try and bash me in.
 
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Dear lord, what has the thread turned into?
Btw, @redbaron, I can't access that link for some reason.
 

Mithrandir

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You guys just need to give it up. computerhxr is trying to say the "idea for relativity" and redbaron can only think "idea of relativity". Both parties seem too invested in their own ego to admit such a small discrepancy. You both made a mistake. Let it go.
 

computerhxr

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Yeah, don't be such a J.

My ego is perfectly in check.

Just remember, you all exist in MY world and are like ants to me. :icon_pferdehaufen:

I would be the first to know if I actually had a problem.

...

edit: I should note that I am being facetious.
 

redbaron

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You confused "ideas" for well thought out and highly elaborated, tested, and confirmed "ideas".

And exactly how much use was relativity to anyone before it was fleshed out mathematically? Zero.

computerhxr said:
Someone can imagine it without all the math.

Okay then prove it. Accurately apply relativity without using mathematics. Hint: you can't.

computerhxr said:
I never said that. You inferred that, and asserted that I did. I've pointed this out many times.

Not sure why you bother denying it when it's obvious to anyone not illiterate that you did say it.

computerhxr said:
Einstein for example came up with the idea of relativity while riding a bike, so it's likely that there wasn't much actual math involved.

Again, no one created relativity.

No they created the theory of it and with workable equations that actually allow us to predict anything with it. Which is the whole point of a theory, to predict things. Without the mathematics, it remains just another useless idea.

Just because something isn't predicative doesn't mean that it is useless.

For any practical purpose it's certainly useless. When I say useless I assume that my audience are somewhat practical beings, bright enough individuals to understand that a scientific idea without any predictive capability has no practical use.

All you have to do is go ahead and show me an idea with zero predictive capability that is uniquely and practically useful and I'll admit defeat. You'll also be the first person in history to do so and would probably become a Nobel Laureate for such a feat.

computerhxr said:
You're trying too hard to make me look like an idiot.

Don't even have to try.

~

Anyway moving on to the overall point of this.

Mathematics isn't the slow way of understanding, it's actually the fast way. Hence why all great feats of engineering, computing, science, chemistry (anything really) are rooted in mathematical understanding.

Why do you think knowledge takes such dramatic leaps with new mathematical discoveries - because it's the fastest way to understand things in a usable way.

@Rudolph Mondal which link? The first one I linked still works for me.

@others I think you'll find that my argument here is intended to highlight the importance of predictive capability (and by extension mathematics) and that it's bullshit that you can develop workable understandings of any complicated physical concept without mathematics.

The human mind can't intuitively comprehend a distance of 13.72 billion light years, but it can easily enough understand the mathematics.
 
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@Red Baron

Ah, thank you for the link. It wasn't working when I tried accessing it with my phone for some reason.

Seems like a good article and I'll read it but do you have anything that explains the math?

In my opinion, if you understand the math intuitively, then you've pretty much understood the whole subject. Or at least you'd be able to reason about it more effectively.
 

redbaron

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I'm not sure I could find anything that explains the math other than just learning the math in the first place. You're basically just asking for a textbook.

You could also read about Schrodinger's Cat. It's a facet of QM that doesn't really require mathematical understanding (although it does make it easier).
 

Teax

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I mean, it's incredible, isn't it? The fact that the physical phenomena we experience has a mathematical structure to it.
math is a language for stating relations, and is based on the same premises as human-scale-macro-level-physics. math wasn't "developed" to be simple to describe macro-level physics, but, nontheless, is so out of necessity.

the other phenomenae like quantum effects/micro physics are part of the same reality and have to result in the known macro-phenomenae in sum. in other words - micro-physics must have a certain relation towards macro-physics. any such relation, once theorized, can be expressed in the language of math.

so the fact that math is capable of describing micro-physics is not surprising :^^: the part that is truly amazing is that our reality is coherent enough to be consistently following what seem to be reproducable laws of sorts.. - everything about math is just a consequence of that.
 

Grayman

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Not sure why you bother denying it when it's obvious to anyone not illiterate that you did say it.

I didn't intrepret it the way you did.

His initial statement was basically like saying you can imagine how something might work like the fusion of atoms before you go and 'prove' it with math.

Similar to seeing and imagining gravity and its force on objects before writing an equation that defines the phenomena in math.


I didn't get the idea from his statement that imagination was to be used without any regard to math at all.
 

redbaron

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Grayman said:
I didn't intrepret it the way you did.

Do tell me how I interpreted it :rolleyes:

Grayman said:
His initial statement was basically like saying you can imagine how something might work like the fusion of atoms before you go and 'prove' it with math.

Yeah which is useless until you give it some sort of predictive capability.

Grayman said:
Similar to seeing and imagining gravity and its force on objects before writing an equation that defines the phenomena in math.

And again the act of seeing gravity had no real value until someone had the bright idea to take advantage of it with systems for plumbing, milling etc. by interpreting it in such a way that allowed them to predict its effects. Not written but still obviously mathematical in nature.
 

Grayman

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And again the act of seeing gravity had no real value until someone had the bright idea to take advantage of it with systems for plumbing, milling etc. by interpreting it in such a way that allowed them to predict its effects. Not written but still obviously mathematical in nature.

I'm not trying to demean your job or passion but a lot of predictions are made in everyday life without math by implementation of intuition. Math allows for more accuracy but there are a number of times you youself have had to make predictions without it.
 

redbaron

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I'm not trying to demean your job or passion but a lot of predictions are made in everyday life without math by implementation of intuition.

That's all very nice but if you read the OP you'll find that the entire point of this thread was talking about mathematics as a predictive language (modelling physical phenomena) and not about just every day life.

So since the thread is about mathematics and its ability to explain physical phenomena, I'm talking about it in that context. It doesn't need to be explained that mathematics isn't required for every little action a human conceivably takes.

Although I could make the argument that all basic human action is just an abstracted and simplified form of mathematics but I'll leave that for another thread.
 

Grayman

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That's all very nice but if you read the OP you'll find that the entire point of this thread was talking about mathematics as a predictive language (modelling physical phenomena) and not about just every day life.

So since the thread is about mathematics and its ability to explain physical phenomena, I'm talking about it in that context. It doesn't need to be explained that mathematics isn't required for every little action a human conceivably takes.

Although I could make the argument that all basic human action is just an abstracted and simplified form of mathematics but I'll leave that for another thread.

I wasn't the one who took the tangent. I was just pointing out what you were overlooking.
 

redbaron

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I wasn't the one who took the tangent. I was just pointing out what you were overlooking.

Yes, I went on a tangent by discussing the predictive capabilities of mathematics - the entire point of the thread in the first place. Keeping responses relevant to the thread isn't the same as overlooking things.
 

Grayman

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Yes, I went on a tangent by discussing the predictive capabilities of mathematics - the entire point of the thread in the first place. Keeping responses relevant to the thread isn't the same as overlooking things.

A small personal comment was made and you turned it into an argument thus causing a tangent.

Regardless, one cannot understand the quality of mathematical prediction if one does not compare those to other methods of prediction. Thus my tangent is not really a tangent but an attempt at pulling other concepts in for comparison of the topic at hand.

By comparison of intuition vs math you can see math provides accuracy, reliability and repeatably. Intuition is useful in its own way and is often needed to initialize a new concept but math is important for the above mentioned qualities. Those qualities are necessary in proving, but not always necessary in discovering, physical phenomena. In physical phenomena that cannot be observed it becomes essential but I guess it wouldn't be a phenomena then...
 

Teax

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Although I could make the argument that all basic human action is just an abstracted and simplified form of mathematics but I'll leave that for another thread.
woudn't go that far, some instinct driven behaviour is devoid of conscious thought... but any conscious idea is mathematical by nature. I don't claim to know how intuition comes up with the ideas, but once they pop up....... so hearing people say stuff like the following sounded a bit ridiculous at first:

computerhxr said:
They are just ideas and there are many ways to explain the same phenomenon that are equally as valid.

I'm working on some stuff that explains natural phenomena without using much math, if at all. Math is the slow and difficult way of understanding ideas. It doesn't allow you to make connections easily.
....which leads to one conclusion, you guys are talking about different definitions of "math". Grayman and computerhxr are talking about school math or formal notation, which explains why they think math is the slower alternative... while redbaron seems to be talking about the core of math as a general descriptive language, which actually also encompasses all insights you guys thought are not math related. there are varying degrees of complexity.

the latter definition is useful for OP. there's no reason to limit math to its formal notation.

And again the act of seeing gravity had no real value until someone had the bright idea to take advantage of it with systems for plumbing, milling etc. by interpreting it in such a way that allowed them to predict its effects. Not written but still obviously mathematical in nature.
good example of math at work without them knowing that it was math.
 

Grayman

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good example of math at work without them knowing that it was math.

How is math at work without them knowing? When I implement such things it is based on cause and effect. I see how a thing is affected in certain situations and I use that in other situations to produce a similar affect.


EDIT: I see what you are referring to now. I see that as logic which yes math uses logic but logic is not necessarily math or what I felt what the OP was referring to.
 

Teax

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I see what you are referring to now. I see that as logic which yes math uses logic but logic is not necessarily math or what I felt what the OP was referring to.
technically logic is a part of math, but relating to this particular thread, there's no need to make any distinction at all. the terms only differ in usage, not in underlying structure. a cat by any other name stays the same cat. :cat:
 

Brontosaurie

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i'd like Fukyo to ask redbaron why he's so irritable and reactive.
 
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math is a language for stating relations, and is based on the same premises as human-scale-macro-level-physics. math wasn't "developed" to be simple to describe macro-level physics, but, nontheless, is so out of necessity.

the other phenomenae like quantum effects/micro physics are part of the same reality and have to result in the known macro-phenomenae in sum. in other words - micro-physics must have a certain relation towards macro-physics. any such relation, once theorized, can be expressed in the language of math.

so the fact that math is capable of describing micro-physics is not surprising :^^: the part that is truly amazing is that our reality is coherent enough to be consistently following what seem to be reproducable laws of sorts.. - everything about math is just a consequence of that.

I see. What do you mean by math being based on the same premises as human-scale-macro-physics? Do you mean that they both describe or state relations?

Yes, I wanted to ask about that too. How is it that our reality is coherent enough such that we have laws that hold for all entities? That's quite peculiar, in my opinion. How did our reality get to be the way it is?
 

redbaron

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Rudolph Mondal said:
How is it that our reality is coherent enough such that we have laws that hold for all entities? That's quite peculiar, in my opinion.

Your wording is a bit odd, not sure if I'm interpreting correctly. Do you mean to ask how it is that we live in a reality that we can exist in and find coherent?

In that case it's not peculiar if you think about it. If our reality didn't have coherence enough for humans to evolve, we wouldn't exist. So really the only reality we ever could observe is one that was coherent in the first place.

What would really be peculiar is if we somehow observed a in a reality we couldn't observe (or live in). So the universe is one that's coherent and observable...because we live in and can observe it. Might not be easy to wrap your head around at first.

Rudolph Mondal said:
How did our reality get to be the way it is?

There's a paper published recently which tackles that question from a QM perspective.

http://arxiv.org/pdf/1404.1207v1.pdf

As a less dense version you'd probably find this book interesting.
 
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I know next to nothing about quantum mechanics but I don't think the equations of quantum mechanics can help explain why the laws are the way they are. That, to me sounds like a tautology. http:// http://edge.org/conversation/think-about-nature The link above is Lee smolin talking about how nature forms habits which I think makes more sense. The laws of physics couldn't have always been there. That to me doesn't make any sense.
 

redbaron

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Well, perhaps read the study and the book before you come to any ideas. It's plausible that there's actually multiple universes all with different laws, dictated by random chance.

The reality is that, "why?" questions extending beyond the scope of the observable universe are somewhat a scientific dead end. Still it's possible to speculate on the plausibility of certain events and our current universe is one that doesn't discount the possibility of multiple universes. Indeed if one can spring into existence from the point of a singularity - there's nothing preventing the existence of others either.

Rudolph Mondal said:
The laws of physics couldn't have always been there. That to me doesn't make any sense to me.

Things don't have to make sense to anyone to be plausible. Whether or not it makes sense to you or what you choose to believe, it's no violation of anything known that the laws of physics could have always existed. Rejecting possibilities for either the affirmative or negative because they don't make sense to your mind is bad science.

Also thanks for the video.
 
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Well, perhaps read the study and the book before you come to any ideas. It's plausible that there's actually multiple universes all with different laws, dictated by random chance.

The reality is that, "why?" questions extending beyond the scope of the observable universe are somewhat a scientific dead end. Still it's possible to speculate on the plausibility of certain events and our current universe is one that doesn't discount the possibility of multiple universes. Indeed if one can spring into existence from the point of a singularity - there's nothing preventing the existence of others either.



Things don't have to make sense to anyone to be plausible. Whether or not it makes sense to you or what you choose to believe, it's no violation of anything known that the laws of physics could have always existed. Rejecting possibilities for either the affirmative or negative because they don't make sense to your mind is bad science.

Also thanks for the video.

I think science should always try and explain phenomena as we perceive it because after all, science has to be testable and the only way to test something would be to perceive it either directly or indirectly. We do not perceive parallel universes and the idea that laws are eternal basically means time is an illusion. As far as any human would tell you, which should be the aim of science after all, to explain phenomena that we as a species experience, time exists. So erasing time out from the picture or having solutions which allow for results both backwards and forwards in time implies that there's something wrong with the picture of reality we have.

I'm not arguing science here, What I'm arguing for is that underlying science or physics as it is practised today has a lot of underlying assumptions and not all of those assumptions hold in all circumstances.
 

redbaron

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I think science should always try and explain phenomena as we perceive it because after all, science has to be testable.

Right. Yet as I said, asking "why" questions in science is essentially a dead end.

In science you can't test a why, only a how. Asking a why question is asking for a cause. Causality isn't something science has ever claimed to be able to explain. It doesn't matter why the universe exists, only how it exists. People are free to attach any metaphysical or philosophical "why" to anything they want - it has nothing to do with science.

Rudolph Mondal said:
Underlying science or physics as it is practised today has a lot of underlying assumptions and not all of those assumptions hold in all circumstances.

You'll have to give an example.
 

computerhxr

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I know next to nothing about quantum mechanics but I don't think the equations of quantum mechanics can help explain why the laws are the way they are. That, to me sounds like a tautology. http:// http://edge.org/conversation/think-about-nature The link above is Lee smolin talking about how nature forms habits which I think makes more sense. The laws of physics couldn't have always been there. That to me doesn't make any sense.

The term always is subjective and objective. We don't know if time is linear, if it loops, or something unimaginable. We also perceive time differently and relative to your physical position in space-time. So saying that it has "always" been there may not necessarily mean the same thing that you might imagine.

Also, consider that the term "always" requires "time", and therefore any duration of time that encapsulates all of time would be considered always to exist. It doesn't necessarily mean that it existed prior to time itself.

Just like the word infinity may not necessarily mean that it cannot be a fixed length. For example, there are infinite values between the numbers 1 and 2. Or a circle is infinite but can be drawn to completion. Or a möbius strip that only has one side but continues infinitely.
 

Teax

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I see. What do you mean by math being based on the same premises as human-scale-macro-physics? Do you mean that they both describe or state relations?
only math states relations. the premise for that is the distinguishability and identifiability of objects (cannot confuse variables A and B), which is what the mind can do well. physics is just another word for "observation" and on our macro-scale we can distinguish and identify observations (e.g. differentiate apples from oranges and keep track of which is which. distinguish different positions, sizes).

this trivial structural similarity stems from the fact that language itself is a macro-scale-physical-observation. take this as a common premise between math and physics, and the rest induces itself accordingly. *zipper sound*

762zip1.jpg


which means that macro-level physical laws can be mapped 1:1 to mathematical constructs (=other physical phenomenae) and named accordingly with a single observable symbol.

like calling an orange by the word "orange", we're not explainig anything, we're naming stuff. other oranges can then be related to the original orange by naming those objects "orange" aswell, this way establishing a similarity between observations, without ever stating what the essence of the similarity is.

8521.jpg


Yes, I wanted to ask about that too. How is it that our reality is coherent enough such that we have laws that hold for all entities? That's quite peculiar, in my opinion. How did our reality get to be the way it is?
do we have such laws? all our models are approximations.... maybe what we perceive as "coherent enough" is merely a locally stable bubble.... talking about what is outside of the observable universe is a topic best discussed drunk.... more so...
 
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