Relationship between the abstract world of mathematics and the material universe?

[Megan]

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


Thoughts?

[Peter]

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


Thoughts?

A bit beyond me!!

[Chris]

The behavior of the material universe can often be described using laws that are expressed by mathematics. Sometimes in unexpected ways. For example, one might think that imaginary numbers are just a thing people invented to expand the abstract world of math, but it turns out they are very useful in electrical engineering to describe how a circuit is working.

[Preston]

A bit beyond me!!

Lol!

Megan, you might want to talk about your question with omnipotence, etc.?

Though, a relative point, I think, is that Pythagoras felt math could explain everything. And, a point I have long believed in too, that Pythagoras believed in, is that this universe is made* of sound - or feeling. To my mind, all things are made of feeling because without feeling there is nothing.

So basically math can explain feeling - while feeling being the roots of all things.

*the word made is probably not the best word but it can do

[Euan Mackinnon]

Megan

This is a very deep question indeed, one that (in my opinion) can truly be described as fundamental.

I have been considering and working on this question for several years and would like to make brief comments here.

However, first, I would like, subject to your approval, either to remove the word ‘abstract’ from your question or, alternatively, to ask you to define the word (in this context) and explain why you feel it is necessary.

Chris has given you a neat and succinct response, one that I believe few people would argue with. His response makes a very good starting point although, as with your question, I would want to discuss what is meant by ‘described using laws’.

Euan

[Preston]

sorry, if my previous post sounded a little pompous on my part - it is just that i figured the part about feeling out on my own (and consider it sacred -very) and am just, well somewhat proud of myself on that one.

now, i think this sounds even more pompous, lol. it is just that i believe in it very much so and pretty much worship that beautiful and terrifying thought.

[Chris]

[FONT="Verdana"]Megan
His response makes a very good starting point although, as with your question, I would want to discuss what is meant by ‘described using laws’.

Well, that kind of omits the essential words. "...described using laws that are expressed by mathematics", I said, by which I simply meant that our description of how something works in the universe is sometimes expressed mathematically. For example, the universal gas law pV = nRT. Yes, you could describe it in words instead of expressing it via mathematical symbols, but you would essentially just be describing mathematical concepts (equality, multiplication) in words, then.

[Preston]

[FONT="Verdana"]
However, first, I would like, subject to your approval, either to remove the word ‘abstract’ from your question or, alternatively, to ask you to define the word (in this context) and explain why you feel it is necessary.

I think Megan was referring to math as abstract - in the sense of not being complete, so to say? Such as, it is there but for a large part it is not correct. Seems to be but is not.
Math, as humanity knows it as probably as abstract as abstract can be. I don't know math, but I do know that it is anything but complete, really that's all, .
Also, most math is relative to our earth and our understandings - which both are highly limited. Other worlds, other galaxies, other realms, etc. = other math.

[Megan]

Ok, I may not grasp all of this , but it is interesting.


Here is how Anthony Rizi, a student of Jacques Maritain, himself a student of Aquinas, explains the relation:


Quote:
"mathematics: second level of abstraction that leaves behind all accidents of material things, save their extension. It consists of geometry, which leaves behind universal quantity, and arithmetic, which leaves behind all qualitative aspects of figure. By making analogies, the mind comes to understand the field of analysis, which builds the bridge between the two realms

Since they are abstracted from the mathematical real world, mathematical entities are real, even though they are conceived in an idealized condition not found in the world (they are, after all, abstractions from the particular). Following Jacques Maritain's excellent terminology, we call the world of mathematics the world of the mathematical preter-real. However, mathematical beings can be conceived in ways in which they cannot exist in the real world. Asking "where are those -2 cows?" manifests such a case. Again, all mathematical entities are reductively real; that is, they can be decomposed into real pieces, but as entities they can be beings of reason. "-2" is an operation of taking away followed by a number.

- Rizi, the science before science, page 374.

[Enrique]

The behavior of the material universe can often be described using laws that are expressed by mathematics. Sometimes in unexpected ways. For example, one might think that imaginary numbers are just a thing people invented to expand the abstract world of math, but it turns out they are very useful in electrical engineering to describe how a circuit is working.

As another example, Bernhard Riemann about the middle of the XIX century, developed a geometry that opposed our (geometric) intuition. It's very interesting, or it should be, to know how and why the so called non-Euclidean geometries were born. Did this theory serve any purpose. None, but the fruition of commerce with pure abstractions. Then came Einstein and chose Riemann's geometry as the cornerstone of General Relativity. Therefor, if you think General Relativity is a good approximation to the (macroscopic) physical reality, you have that we live in a Riemannian universe.

Changing the subject, if I may, there are three main schools of mathematics: logicism, formalism and Intuitionism, and these have been debating the topic proposed by Megan for over a century. Of course, this does not take away from us the right to have our own thoughts on the subject. Thinking is fun. A pity Euan did not posted again. He seemed to know a lot.