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

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jimrob:
Mathematics is mainly not about numbers - that’s just the bit we learn at grade school.
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This is true.
Mathematics is not abstract: it applies itself to every aspect of the universe. Mathematics is about the laws to which the universe complies.
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This is false. Mathematics is necessarily abstract: it is about structure. Science, not mathematics, attempts to discover certain laws (viz., physical laws) about the universe. Since physical laws are evidently structural, mathematics is a useful tool to describe them.
It didn’t start with a bunch of school teachers writing down a load of numbers and making stuff up - it all comes from observation, experiment, theory and proof.
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Yes, yes, I think that the mathematical laity believes that we sit around and add up really large lists of numbers. Engineers, on the other hand, think we solve really difficult equations.
From my own experience, I can tell you that mathematicians tend to be a down to earth and fairly religious bunch.
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I wish that were my experience. I know only a few that are “down to earth” and none that are obviously religious.
 
jimrob said:
I don’t normally barge into this section, but I feel a few words from a mathematician might be in order.

Mathematics is mainly not about numbers - that’s just the bit we learn at grade school. Mathematics is not abstract: it applies itself to every aspect of the universe. Mathematics is about the laws to which the universe complies. It didn’t start with a bunch of school teachers writing down a load of numbers and making stuff up - it all comes from observation, experiment, theory and proof.

To a mathematician, God didn’t need to create our world and to fling stars into space (that doesn’t necessarily mean he didn’t). All God needed to do was invent the rules of mathematics, provide the initial source of energy and let the universe do the rest. (But why did he have to make quantum mechanics so mind-blowingly difficult?)

From my own experience, I can tell you that mathematicians tend to be a down to earth and fairly religious bunch. Atheists tend to study quasi-sciences like zoology (not much maths there). Mathematics and theology are the only two sciences that encompass the infinite and I’m privileged to be qualified in both.
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As a physicist, I disagree on the bold line on two counts:
(a) You make it seem like the universe has an option about complying with laws
(b) Mathematics doesn’t discover universal laws, physics does.
 
tdgesq said:
I wouldn’t go so far as to say mathematics has no meaning in itself. It is ultimately based upon quantity and extension, accidents that do exist outside of the mind. The human intellect can and does abstract from material reality only the aspect of quantity, which is why we can speak about such things as natural numbers. I suppose the the major limitation of mathematics is that it can only describe extension, which is only a part of what we experience of the reality of the material universe. It does so with great success in that regard though.
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What is 2+2=4 mean without expressing a physical option (like I have 2 apples, she has 2, together we have 4). Mathematics is abstract because it is non physical, so in and of itself, it has no meaning; it gains meaning by being related to something physical.

~Alberti Devoveo
 
Alberti_Devoveo said:
What is 2+2=4 mean without expressing a physical option (like I have 2 apples, she has 2, together we have 4). Mathematics is abstract because it is non physical, so in and of itself, it has no meaning; it gains meaning by being related to something physical.
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This is quite close to the truth: you only need “something” not “something physical”.
 
Mathematics has also hinted at the unseen as a reality , such as unseen dimensions as in the string theory - dark energy and dark matter and more.
 
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.
 
tonyrey said:
The success of science is largely due to mathematical precision - which implies that mathematics and the material universe are inextricably related.
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Please state clearly what you mean and demonstrate the implication.
 
cho_pilo said:
Thoughts?
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Mathematics is like an accounting language, but no formal mathematical system or representation represents reality. We always need to form new geometrical concepts to represent the discoveries we make in the physical universe. Mathematical language is like metaphor. Just as a piece of sheet music is more a mnenomic device to visually represent a piece of music than it is a literal transposition of the ideas in the composer’s mind.

Mathematical physics is like a digital science, which is limited to jagged edges. Physical chemistry is more analog, and in tune with the contour of the mind and ideas.

I don’t really know much about what I am talking about though. I know a few scientists though who deal with this specific question of the difference between mathematics and physics. I recommend studying Bernhard Riemann’s 1854 habilitation dissertation, On the Hypothesis that underly the foundations of geometry, as well as Carl Gauss’s 1799 fundamental theorem of algebra. These papers develop the idea of anti Euclidean or Riemannian geometry, which is important to understand the distinction between math and real world physics.
 
jimrob said:
I don’t normally barge into this section, but I feel a few words from a mathematician might be in order.

Mathematics is mainly not about numbers - that’s just the bit we learn at grade school. Mathematics is not abstract: it applies itself to every aspect of the universe. Mathematics is about the laws to which the universe complies. It didn’t start with a bunch of school teachers writing down a load of numbers and making stuff up - it all comes from observation, experiment, theory and proof.

To a mathematician, God didn’t need to create our world and to fling stars into space (that doesn’t necessarily mean he didn’t). All God needed to do was invent the rules of mathematics, provide the initial source of energy and let the universe do the rest. (But why did he have to make quantum mechanics so mind-blowingly difficult?)

From my own experience, I can tell you that mathematicians tend to be a down to earth and fairly religious bunch. Atheists tend to study quasi-sciences like zoology (not much maths there). Mathematics and theology are the only two sciences that encompass the infinite and I’m privileged to be qualified in both.
Click to expand...
Physics has to guide mathematics. One cannot make the universe conform to one’s own conception of what mathematics is. Mathematics if it is truthful has to conform to what the universe that has been made by God shows us to be true about mathematics.

The trend today is to try to force the universe to comply to one’s own arbitrarily constructed set of mathematical logical axioms. All that mathematics can tell us is whether an axiomatic theorem lattice (i think it is called ) is consistent with itself.

The subject at matter here really is creativity. Words like mathematics and science and physics, etc. mean nothing without human creativity. The ability to create new ideas cannot be left out of the discussion, which is what is almost always done in classrooms throughout the world today. Someone has to cause a new idea or discovery to be created, and without this creativity, there is no practice of mathematics or physics or whatnot.
 
joshrp said:
Mathematics is like an accounting language, but no formal mathematical system or representation represents reality. We always need to form new geometrical concepts to represent the discoveries we make in the physical universe. Mathematical language is like metaphor. Just as a piece of sheet music is more a mnenomic device to visually represent a piece of music than it is a literal transposition of the ideas in the composer’s mind.

Mathematical physics is like a digital science, which is limited to jagged edges. Physical chemistry is more analog, and in tune with the contour of the mind and ideas.

I don’t really know much about what I am talking about though. I know a few scientists though who deal with this specific question of the difference between mathematics and physics. I recommend studying Bernhard Riemann’s 1854 habilitation dissertation, On the Hypothesis that underly the foundations of geometry, as well as Carl Gauss’s 1799 fundamental theorem of algebra. These papers develop the idea of anti Euclidean or Riemannian geometry, which is important to understand the distinction between math and real world physics.
Click to expand...
English language does not represent reality. But it is used to do so.
Math language does not represent reality. But it is used to do so.
 
joshrp said:
Physics has to guide mathematics. One cannot make the universe conform to one’s own conception of what mathematics is. Mathematics if it is truthful has to conform to what the universe that has been made by God shows us to be true about mathematics.

The trend today is to try to force the universe to comply to one’s own arbitrarily constructed set of mathematical logical axioms. All that mathematics can tell us is whether an axiomatic theorem lattice (i think it is called ) is consistent with itself.

The subject at matter here really is creativity. Words like mathematics and science and physics, etc. mean nothing without human creativity. The ability to create new ideas cannot be left out of the discussion, which is what is almost always done in classrooms throughout the world today. Someone has to cause a new idea or discovery to be created, and without this creativity, there is no practice of mathematics or physics or whatnot.
Click to expand...
👍
 
Frankenfurter said:
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.
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Sorry, your answer interested me. What do you do when you exhaust the tools of maths? What do you do next?
In my idea, you would have to invent new math tools but your answer seems to imply not.
 
Alberti_Devoveo said:
Mathematics in and of itself has no meaning, but it can be extrapolated to the physical world by representing things, such as relating acceleration to velocity through the time-derivative or using vectors to derive conservation of momenta & energy. If I’m not mistaken, this is much like the position that Anthony Rizzi (cf. Alan Wostenberg’s posts) holds.
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Mathematics in and of itself DOES HAVE a meaning !!!
 
tdgesq said:
I wouldn’t go so far as to say mathematics has no meaning in itself. It is ultimately based upon quantity and extension, accidents that do exist outside of the mind. The human intellect can and does abstract from material reality only the aspect of quantity, which is why we can speak about such things as natural numbers. I suppose the the major limitation of mathematics is that it can only describe extension, which is only a part of what we experience of the reality of the material universe. It does so with great success in that regard though.
Click to expand...
Mathematics in and of itself DOES HAVE a meaning !!!
 
karbear said:
Letters and syllables have no meaning in and of themselves but sentences paragraphs and books sure can. Meaning is a tricky word when talking about math anyway. Why not ask, instead, what is the significance? Or better yet, just as the OP did, what is the relationship,? Someone above mentioned Vectors, others mentioned integers. These things arent really that interesting by themselves. They are like letters of an alphabet. We give arbitrary symbols to sounds which form words, just like we give arbitrary symbols to numbers and to abstract mathematical concepts and operations. Disclaimer I’m no mathematitian, I made it through calc 3 and some 400 level abstract geometry - matrix class that was taught by a guy who used to crack codes for the cia (really interesting stuff). Sill, when you get beyond basic building blocks and get a glimpse ( I just got far enough to get a glimpse) into the world of putting basic things like vectors and derivatives and matrices and the like together, its hard not to be awed by it all. When you sart combining abstract concepts (words) the sentence becomes meaningful and numbers do start having shapes and colors. Someone asked above, what shape is 2? I would ask back; what is the literary meaning in a book containing only the letter L?
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Letters and syllables DO HAVE A meaning in and of themselves…
 
jimrob said:
I don’t normally barge into this section, but I feel a few words from a mathematician might be in order.

Mathematics is mainly not about numbers - that’s just the bit we learn at grade school. Mathematics is not abstract: it applies itself to every aspect of the universe. Mathematics is about the laws to which the universe complies. It didn’t start with a bunch of school teachers writing down a load of numbers and making stuff up - it all comes from observation, experiment, theory and proof.

To a mathematician, God didn’t need to create our world and to fling stars into space (that doesn’t necessarily mean he didn’t). All God needed to do was invent the rules of mathematics, provide the initial source of energy and let the universe do the rest. (But why did he have to make quantum mechanics so mind-blowingly difficult?)

From my own experience, I can tell you that mathematicians tend to be a down to earth and fairly religious bunch. Atheists tend to study quasi-sciences like zoology (not much maths there). Mathematics and theology are the only two sciences that encompass the infinite and I’m privileged to be qualified in both.
Click to expand...
Great Post! 👍 Maths is a game. A University Professor I know plays on the longest number of digits of PI. I read a 700 page book on the fundamentals of Maths and what amazed me were the 2 theories about the origins of maths: 1) the reality (that is obvious); 2) the human spirit that puts problems that have nothing to do with reality like the problem of PI.
Now the funny thing of it is some pure and abstract maths theorems find sometimes a practical use. And those maths theorems did not come from reality but from a pure abstract and useless problem posed by a mathematician. And unknowingly, this guy was solving a mechanical, electronics engineering problem.
How come?
 
Alberti_Devoveo said:
As a physicist, I disagree on the bold line on two counts:
(a) You make it seem like the universe has an option about complying with laws
(b) Mathematics doesn’t discover universal laws, physics does.
Click to expand...
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.
 
Alberti_Devoveo said:
What is 2+2=4 mean without expressing a physical option (like I have 2 apples, she has 2, together we have 4). Mathematics is abstract because it is non physical, so in and of itself, it has no meaning; it gains meaning by being related to something physical.

~Alberti Devoveo
Click to expand...
“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 :D)
 
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