What is the relationship between the abstract world of mathematics and the material universe?

[Texas_Roofer]

Please state clearly what you mean and demonstrate the implication.

The way this thread is going limit theory may be replaced soon, and the great answer finite verses infinite may soon exist. I wonder if we will leave base 10 soon. In all seriousness I hope you understand limit theory proves math is an imperfect system. If you are not familiar with limit theory the classical example is a fellow walks toward a door, what is the last ½ way point between him and the door? Or if you want to understand the finite issues modify the above to answer: since each movement of the fellow takes time and the ½ points are endless the math proves his action is an endless progression in time and thus it is impossible to walk to and through the door!!

 

[jdwood983]

Mathematics in and of itself DOES HAVE a meaning !!!

No it doesn’t. Mathematics is defined as “the abstract science of number, quantity, and space.” Abstract is defined as “existing in thought or as an idea but not having a physical or concrete existence.” QED: mathematics in and of itself has no meaning, it is a tool used to explain in some manner physical objects & reactions.
Think of it this way: If I hold a rock in my hand & drop it, does it fall due to gravity or does it fall because of Delta y = -gt[sup]2[/sup] (the physics equation for freefall)?? Mathematics gives a physicist a useful tool, that’s all.

I ask you:

1. Wasn’t it Newton who said that math was the language of God? God had an option of putting the Universe speaking math! Do you agree?
2. I agree that E=mc2 was discovered not by a mathematician. But not all maths comes from physics like in the old Greek times when they had to measure the pyramids and the Parthenon. But some equations discovered by Mathematicians in abstract help you! No wonder that Maths is a major in the 1st and 2nd years of physics in University.

(1) No, it was Galileo. He actually said, “Mathematics is the language with which God has written the universe.” I agree that God had any option he so chose, but if he chose an alternative option, wouldn’t all of our math as we know it be completely different? I don’t know the answer to that question, and I don’t know that anyone could know the answer to that question.
Note, also, that Einstein said once that, “insofar mathematical theorems refer to reality, they are not sure, and insofar they are sure, they do not refer to reality.”
(2) Mathematics is required to know/learn physics, but it is not superior to physics when relating physical laws. Note also that most recent advancements in mathematics has been due to physics: the integral & derivative (all of calculus, really), the sum, the exponential function, set theories, etc.

“Roses rain from the clouds”- this sentence has no meaning related to reality. Yet, it has a meaning in itself and very beautiful (I hope, !!!, for I invented it now )

The sentence in and of itself has no meaning, it’s a nonsensical phrase. The words themselves can relate to reality (roses, rain, from, & clouds all have physical meaning), but this is exactly what I’m trying to get across: 2 has no meaning until you say 2 apples or 2 chairs. You need to relate the mathematics to the physical.

 

[cho_pilo]

The sentence is clear as water…

Yup, and as useful as “Chickens are one species of bird among many”.

 

[wcknight]

I love it when people who know nothing about what they are talking about try to explain it to other folks (I majored in Math, but even that is nothing to the folks who really get deep into the theoritical research side of it). Mathematics is the language of science and science tries to explain the physical world using mathematics to describe it.

Theoritical mathematics is way out ahead of the physical sciences. BUT theoritical mathematics helped predict the existence of black holes, the relationship bettween energy and matter and many other physical phenomena long before anyone could see or show that they existed.

Practical real world mathematics is only a very small part of math. By the time you get to second or third year calculus and maybe matrix analysis, and linear algebra, you would have covered just about most of the real world applications for math.

Nuclear scientist and astro physicists may get into using more complex math. But most enegineers can get by on the more mundane stuff. The research theoritical side goes far beyond that. Math in its purest form is nothing more that the search for absolute truth. Either it is true or it is not. The really fun stuff is trying to examine or prove mathematical paradoxes. Theoritical mathematics was not my bag, applications was and in the real world, matrix analysis was as complex as I ever got, and most third year math students can handle that easily.

 

[tonyrey]

Please state clearly what you mean and demonstrate the implication.

If you know nothing about numbers how far would get with scientific research?

 

[wcknight]

Math does not bend itself to fit the physical world. The equation for a parabola to describe the trajectory of a missile exists and is true regardless of how the physical world reactions matches it. Other real world forces (wind or friction etc) may make the predicted landing different but the original math is true regardless.

The beauty of mathematics is that theories can and must be proved. There are no hidden lies or deceptions (except for mathematical paradoxes). FOlks can make errors in calcualtions (because they plugged in the wrong numbers or their arithmatoc is wrong) but the mathematic process itself is sound.

 

[wcknight]

(2) Mathematics is required to know/learn physics, but it is not superior to physics when relating physical laws. Note also that most recent advancements in mathematics has been due to physics: the integral & derivative (all of calculus, really), the sum, the exponential function, set theories, etc.

I seriously doubt that the above statement is true… sums , expodential function and Calculus has been around for a very long time… when is it that physics supposedly brought it about. It sounds like you are having the egg lay the chicken here.

 

[tonyrey]

Math in its purest form is nothing more that the search for absolute truth.

In other words it doesn’t presuppose the existence of matter but first and foremost the existence of the mind!

 

[wcknight]

In other words it doesn’t presuppose the existence of matter but first and foremost the existence of the mind!

Math does not presuppose anything in the physical world. It sets up a system of rules (called axioms and collaries) and processes and goes about proving with logic whether other statements or assumptions are true (theories). Theoretical math does even care if what they are dealing with applies to the real world. The fact that it does is a boon to the other sciences. The thing that mathematicians are concerned with, is the math sound ? that there are no errors in the logic or calculations.

Like philosphy, the only absolute truth is whether it is true or it is not. Is the math correct or is it in error ? I like it in terms of religion, the main absolute truth is, does God exists or does He not. I find it interesting that God’s name in Hebrew is Yahweh, “I am”, or I exist… it answers the only real question any of us should be concerned with.

 

[Pfaffenhoffen]

No it doesn’t. Mathematics is defined as “the abstract science of number, quantity, and space.” Abstract is defined as “existing in thought or as an idea but not having a physical or concrete existence.” QED: mathematics in and of itself has no meaning, it is a tool used to explain in some manner physical objects & reactions.
Think of it this way: If I hold a rock in my hand & drop it, does it fall due to gravity or does it fall because of Delta y = -gt[sup]2[/sup] (the physics equation for freefall)?? Mathematics gives a physicist a useful tool, that’s all.

(1) No, it was Galileo. He actually said, “Mathematics is the language with which God has written the universe.” I agree that God had any option he so chose, but if he chose an alternative option, wouldn’t all of our math as we know it be completely different? I don’t know the answer to that question, and I don’t know that anyone could know the answer to that question.
Note, also, that Einstein said once that, “insofar mathematical theorems refer to reality, they are not sure, and insofar they are sure, they do not refer to reality.”
(2) Mathematics is required to know/learn physics, but it is not superior to physics when relating physical laws. Note also that most recent advancements in mathematics has been due to physics: the integral & derivative (all of calculus, really), the sum, the exponential function, set theories, etc.

The sentence in and of itself has no meaning, it’s a nonsensical phrase. The words themselves can relate to reality (roses, rain, from, & clouds all have physical meaning), but this is exactly what I’m trying to get across: 2 has no meaning until you say 2 apples or 2 chairs. You need to relate the mathematics to the physical.

What is reality for you?
If I put the right hand in cold water and the left hand in hot water and then take the hands out and put then in warm water, on hand tells me the water is hot, the other tells me tha water is cold. Then?

A building, a chair, a symphony, a street exists in the head of man before existing in the so called real world. Walt Disney and Mickey Mouse gives more jobs to people in the States than General Motors. Mickey Mouse is real or not?

Sorry, the roses fall from the clouds and that means even cloudy days can give good tidings.

You forget that maths has a real life in the imgagination and that imagination is as real as the so called real world. Maths is full of symbols, the negative numbers and the irrational (negative? positive? rational? irrational?) and before something happens it has to be in the human mind (or as Galileo, thanks, said, in the mind of God).

 

[Pfaffenhoffen]

Yup, and as useful as “Chickens are one species of bird among many”.

Sorry, explain to me as if I were stupid: what is the relationship of the sentences ?

 

[cho_pilo]

If you know nothing about numbers how far would get with scientific research?

What do you mean by “mathematics and the material universe are inextricably related” and how is this implied by the success of science? (Refer to your earlier post)

 

[tonyrey]

What do you mean by “mathematics and the material universe are inextricably related” and how is this implied by the success of science? (Refer to your earlier post)

If mathematics were no more than an intellectual game like chess with arbitrary rules there is no obvious reason why it should be such a powerful tool for science. Is it a sheer coincidence that the Poisson distribution reflects the probability of events occurring in a specific period of time?

 

[cho_pilo]

If mathematics were no more than an intellectual game like chess with arbitrary rules there is no obvious reason why it should be such a powerful tool for science.

Quite, the claimed implication isn’t obvious. That’s why I’ve asked you to spell it out.

Is it a sheer coincidence that the Poisson distribution reflects the probability of events occurring in a specific period of time?

Asking me a question is not demonstrating an implication.

 

[Texas_Roofer]

… The equation for a parabola to describe the trajectory of a missile exists and is true regardless of how the physical world reactions matches it. …

um, I think the question at hand would be better exposed if one thinks about 2 missile shots in which one occurs between two points, say on earth, and the other missile shot occurs between two points in open space. The question at issue is the concept of will the missile in space follow the math or follow nature(Natural Laws). So the prediction provided by the parabola only has value when it aids human needs.

 

[Alberti_Devoveo]

What is reality for you?

The state of things as they exist, found through perception.

If I put the right hand in cold water and the left hand in hot water and then take the hands out and put then in warm water, on hand tells me the water is hot, the other tells me tha water is cold. Then?

Both are logical conclusions in reality. I see little reason in trying this line, it is not contradictory in any fashion.

There’s a story I loved as a kid where a man eats dinner with a friend (at the first man’ house). The first course is brought out and it’s too hot for the friend, so he blows on it. The man questions the friend, and the friend says he’s blowing on it to cool it down. The second course is brought out and it’s too cold for the friend, so he blows on it. Furious, the man kicks the friend out of his house, saying (paraphrasing from the actual story): “I cannot dine with a friend who will blow on his food to both cool it down and heat it up!”

You are trying to get me to be the man, when really the friend is right.

A building, a chair, a symphony, a street exists in the head of man before existing in the so called real world. Walt Disney and Mickey Mouse gives more jobs to people in the States than General Motors. Mickey Mouse is real or not?

You are confusing reality and real here. Mickey Mouse is not real because he is a fictional character, but he exists in reality because he is plastered all over Disney World.

Sorry, the roses fall from the clouds and that means even cloudy days can give good tidings.

It’s still nonsensical: in reality, clouds don’t produce roses (and not all clouds produce rain). By itself, the sentence has no meaning; in explaining it, you give meaning to it–this is my point about math: until you say 2 apples, 2 means nothing.

You forget that maths has a real life in the imgagination and that imagination is as real as the so called real world. Maths is full of symbols, the negative numbers and the irrational (negative? positive? rational? irrational?) and before something happens it has to be in the human mind (or as Galileo, thanks, said, in the mind of God).

You are still confusing yourself here (not that it should have changed between your first paragraph and here since you hadn’t been corrected until now), about the difference between reality and real.

Also, show me -2 apples. Or show me i apples.

 

[karbear]

um, I think the question at hand would be better exposed if one thinks about 2 missile shots in which one occurs between two points, say on earth, and the other missile shot occurs between two points in open space. The question at issue is the concept of will the missile in space follow the math or follow nature(Natural Laws). So the prediction provided by the parabola only has value when it aids human needs.

And the pythagoeran theorem does not work over large distances either, but all that means is that it is some sort of small distance approximation for a different formula that we do not understand/know.

 

[karbear]

From my experience as a physicist and engineer, I find that mathematics is a tool that we use to approximate how the universe works. But I am sure that what is actually going on makes no use of mathematics. Whenever I make use of math, I find that I exhaust the tools quickly and are left with more questions than answers. In engineering, we purposefully have to design things so that our limited math can be used to fully describe them.

Pure math can be beautiful and exist completely on its own, with no direct link to reality.

I do not think that God thinks using our math. If he does, it is a higher math that we have not yet conceived.

Certainly it is a higher math. Undoubtedly our tools are quickly exhausted.

 

[tonyrey]

If mathematics were no more than an intellectual game like chess with arbitrary rules there is no obvious reason why it should be such a powerful tool for science.

Since science needs mathematical precision to be successful mathematical quantities and proportions must be essential features of physical reality - and not arbitrarily superimposed. Numbers are not fictions but facts.

Is it a sheer coincidence that the Poisson distribution reflects the probability of events occurring in a specific period of time?

Asking me a question is not demonstrating an implication.

The fact that the Poisson distribution reflects so effectively the probability of events occurring in a specific period of time is convincing evidence that it is not an arbitrarily superimposed mathematical game.

 

[Pfaffenhoffen]

The state of things as they exist, found through perception.

The reality is the same for daltonics and normal people?

Both are logical conclusions in reality. I see little reason in trying this line, it is not contradictory in any fashion.

There’s a story I loved as a kid where a man eats dinner with a friend (at the first man’ house). The first course is brought out and it’s too hot for the friend, so he blows on it. The man questions the friend, and the friend says he’s blowing on it to cool it down. The second course is brought out and it’s too cold for the friend, so he blows on it. Furious, the man kicks the friend out of his house, saying (paraphrasing from the actual story): “I cannot dine with a friend who will blow on his food to both cool it down and heat it up!”

You are trying to get me to be the man, when really the friend is right.

Your story is different. in My story, which hand to believe?

You are confusing reality and real here. Mickey Mouse is not real because he is a fictional character, but he exists in reality because he is plastered all over Disney World.

Sorry, Mickey Mouse exists. Imagination is real. So real that the Empire State Building is a fruit of Imagination.

It’s still nonsensical: in reality, clouds don’t produce roses (and not all clouds produce rain). By itself, the sentence has no meaning; in explaining it, you give meaning to it–this is my point about math: until you say 2 apples, 2 means nothing.

Never heard of a Metaphor and personification and Prosopopeic?

You are still confusing yourself here (not that it should have changed between your first paragraph and here since you hadn’t been corrected until now), about the difference between reality and real.

Also, show me -2 apples. Or show me i apples.

Show me an electron, a proton, the air, the last star of the Universe, the bosom of Higgins, energy, a neutron, show me how come ONE photon can pass TWO HOLES AT THE SAME TIME to reach the same point, shoe me a black hole, and the 97% of black matter that constitutes the Universe… - 2 apples is a basket where there are missing 2 apples !!! I cannot show i now but give me time and I will show.