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Why can we use mathematics to describe physical phenomena?

Cherry Cola

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i'd like Fukyo to ask redbaron why he's so irritable and reactive.

Indeed. I also wonder why Redbaron is incapable of seeing the parallels.

But I also really wonder why computerthx couldn't just admit what he did though. It's not like he murdered someone. He just happened to write something that was stupid and uninformed. It's not like everyone hasn't done that at some point.

It drives me crazy when people do that too. I guess we shouldn't care so much about each others stupidity, but at the same time the world would be a lot nicer if everyone could just be upfront with each other.
 

scorpiomover

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Why is it that physical phenomena can be expressed so simply with beautiful mathematics?
Let's take an example. If I buy 1 orange, and you buy 3 oranges, and we decide to share our food, how many oranges do we each have to eat? What about if we were talking about apples? What about if we were talking about beers? Doesn't really matter what the things that we're talking about, in that type of question. All that matters is that if I have 1 of it, and you have 3 of it, and we decide to share, then we'll each have 2.

Maths utilises a selective form of abstraction. In maths, we try to remove the details that are irrelevant to solving the problem. In this case, it's whether we are dealing with oranges, apples or beers that is irrelevant, because the results will be the same, no matter what. That way, we're only down to those elements that are absolutely necessary to solve the problem. Like having a chess game, where you remove any pieces that won't really affect whether you win or lose the game. The things that the irrelevant pieces do, are rather boring, because whatever they do, doesn't really affect the outcome. So you're only left with the few pieces that really determine the outcome of the game, the few pieces that really matter. When you are left with only the things that really matter, and that where they change, the overall picture changes, then you have a constantly changing kaleidoscope of the things that really matter. No extraneous garbage. Just pure harmony of the voice of the universe.

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?
They tried other models, and they didn't fit at all. In the case of quantum mechanics, they were lucky. Boltzmann decided to devise a thought experiment of how physics would work, if it was based on randomness like that found in Brownian motion (when you put lots of pollen grains in air in a big glass jar and watch them fly about). Boltzmann worked on the basic mechanics of his theory, called statistical mechanics or Boltzmann mechanics. The physicists investigating subatomic particles found that what they consistently observed, worked like nothing in Classical Physics, but was eerily similar to Boltzmann's equations. So they tried Boltzmann's equations, and discovered that their new physics was far more accurate than the most accurate of physics up to that point.
 

scorpiomover

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At 2 minutes in, he starts saying that he's OK with people blaming religion for atrocities, as long as you also blame nationalism for atrocities of fascism (the Nazis) and socialism for the atrocities of Marxism (the former U.S.S.R.). Basically, it's a Ti/Fe argument.

A Te/Fi user would have absolutely refused to admit such horrific atrocities are the result of something that he'd defend. He doesn't mind if you criticise Islam, so long as you accept when the criticism will also apply to you, which is something that Te/Fi users do NOT argue, but something that Ti/Fe users argue often.

He definitely uses Fe. I'd lean towards TP.

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.
It's supposed to be like that. If you're reasonably smart, and reasonably imaginative, you can normally invent arguments for and against anything. The only way to know whether it's right or wrong, is to calculate which one fits better with the details. But doing the calculations on all the details, to know which one fits, is difficult. Maths is how Westerners do those calculations, to know which argument only seems to be right, and which argument actually IS right.

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?
Einstein considered an argument against gravity. He thought about freefall. When you are falling, you feel weightless. Is it that gravity is used up by your increase in speed as you fall, and that's why you don't feel anything while falling? Or is it that you naturally fall, because that's the way that space directs you, and when you are not falling, you feel a push, because you are pushing against the natural trajectory of space itself? Both arguments are theoretically possible. So Einstein couldn't know which was which. He used maths to work out the different formulae for each possibility, so as to work out situations in which the results could tell us which was which.

The maths of relativity could then also be used to calculate how to use it to one's benefit. Again, one can make arguments for and against a satellite providing accurate GPS. But how would you know whether it would work for sure, and if so, how would you have to make the satellite work to get GPS to work? All those questions couldn't really be addressed by an "idea". You would need exact answers, which is where we used maths again.

In reality, maths gives us the formulae by which we can prove the validity of an idea, and the formulae by which we can work out exactly how to make them work.

Put another way, if we had Einstein's idea, but not the maths, could we have proved relativity? Nope. We'd need some way to understand the data of an experiment accurately. Could we have used relativity to make GPS? Nope. We'd have a basic idea, but not the measurements that would determine if it works or not.

Conversely, if we had the mathematical formulae of relativity, but not the idea, could we have proved the theory? Yes, because the formulae would have validated the experimental data. Could we have used relativity to make GPS? Yup. We'd have the formulae to calculate how the GPS satellite's measurements.

But if we had the maths but not the idea, would we have been able to understand the theory? Would it have been palatable to us, to accept a theory that clearly is incredibly accurate, but which we don't understand? Nope. Understanding is how we come to accept ideas.

The mathematical formulae of scientific theories describe what really happens in an accurate fashion. But the ideas of scientific theories are how we make them palatable and acceptable to us.
 

Black Rose

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math is the reference for the shape of reality
references form relationships tell you how to unfold those shapes is abstraction
 

marv

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The fundamental layer behind the physical world surrounding us consists of systems interacting with each other when viewed from a purely informational aspect. What we call math is a very developed formal language aimed at describing similar things to just that, hence the parallelism.
-> System theory, Information theory; S. Wolfram: A New Kind of Science
 

computerhxr

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Conversely, if we had the mathematical formulae of relativity, but not the idea, could we have proved the theory? Yes, because the formulae would have validated the experimental data. Could we have used relativity to make GPS? Yup. We'd have the formulae to calculate how the GPS satellite's measurements.

How would you have math for relativity without having an idea for it first?

See the scientific method:

http://en.wikipedia.org/wiki/Scientific_method#Process
 

computerhxr

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The fundamental layer behind the physical world surround us consists of systems interacting with each other, when viewed from a purely informational aspect. What we call math is a very developed formal language aimed at describing similar things to just that, hence the parallelism.
-> System theory, Information theory; S. Wolfram: A New Kind of Science

Awesome! I need to read that. It has the Golden Ratio all over the cover! Thanks!

I have been trying to explain how I use the Golden Ratio (natural math) to explain psychology. I use it in Poker, the Stock Market, and in Art but I'm always bashed by "the smart people" who tell me I'm full of shit and don't listen to ideas without "proof".
 

ENTP lurker

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It gets kind of humorous if we extrapolate it to Paul Dirac's level but I kind of think he has something right. If it all began from somewhere which started to expand, then narrowing it down with abstract logic sounds reasonable.

It is increasingly difficult to get your mind into hard natural sciences. Back in the days systems were simpler.
These days it takes lot of work to get basic understanding to a level when it allows innovative thinking.

I think this describes it well:

"Standing on the shoulders of giants"
 
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