Mathematical Modeling: The Ultimate Tool for Understanding the World?

[mather]

Hello!

I wonder if math is the ultimate science, it is possible, and the at the same time, to represent/predict, eg. the behaviour of a material to the light, the metabolism of a drug after injections, the chemical structure of a molecule, the function of an electronic circuit, etc with just a bunch of math!

What is your opinion?

PS: Please note i am not native english speaker, so pardon me for the chanchea a term i use is not accurate or appropriate

 

[Number Nine]

Yes, we can do all of those things. Mathematical modelling is nothing new.

 

[arildno]

Maths can't predict what physical laws actually exist, because strictly consistent mathematics can be constructed that, if regarded as a model of the universe, is totally in violation of known physical laws.

But, there is no particular reason to suspect that the "ultimate laws" of the universe cannot be mathematisizable in some form or shape.

 

[Ken Natton]

Hmmm. Here is an idea that might provoke some interesting reactions, but I state in the clearest terms that, in this case, I am merely the messenger. In any case, a British acedemic I once spoke to told me that at his college, maths was classified as a humanity. When I scoffed at the very idea, he gave a very clear and lucid argument as to why it was unarguably the case that maths is a humanity. Sorry, I can't reproduce or even give the hint of his argument - it is all too long ago. But still, for him it was clear that, not only is maths not a science, it is a humanity.

 

[arildno]

Hmmm. Here is an idea that might provoke some interesting reactions, but I state in the clearest terms that, in this case, I am merely the messenger. In any case, a British acedemic I once spoke to told me that at his college, maths was classified as a humanity. When I scoffed at the very idea, he gave a very clear and lucid argument as to why it was unarguably the case that maths is a humanity. Sorry, I can't reproduce or even give the hint of his argument - it is all too long ago. But still, for him it was clear that, not only is maths not a science, it is a humanity.

Maths is a game of logic, a form of art, in my opinion.

 

[zoobyshoe]

I don't think math, itself, is a science, but it is the ultimate tool of science. All math is counting of one form or another; keeping track of quantities under various conditions. By focusing exclusively on what can be quantified about a given phenomenon science attempts to make objective statements about it that others can check.

 

[mather]

can Mathematical Modelling be a single science sector? or it is always part of the science it serves, eg mathematical modelling in chemistry, mathematical modelling in engineering, etc

because if Mathematical Modelling can stand as a unique science, with its study material, resources, etc, I am interested to follow it

thanks

 

[BobG]

I think zoobyshoe hit on the relationship between math and science.

Math is to science what a balance scale is to chemistry, what a balance scale is to physics, what a balance scale is to medicine, what a balance scale is to nutrition and dieting, what a balance scale is to postalry, what a balance scale is to illicit drug dealing. Damn! That started out as an analogy, but you can use those things for nearly anything!

Of course, come to think of it, you can use math for nearly anything, too!

 

[Pythagorean]

1+1 = 2 is meaningless without a qualitative assignment. For example, one of the following statements is wrong:

1orange + 1apple = 2fruits
1apple + 1orange = 2 apples
1apple + 1apple = 2 apples

Science qualifies quantities, which complicated the assessment of truth statements with definitions and convention. Science is mathematics+philosophy (generally empirically based philosophies)

 

[Jimmy Snyder]

Math isn't science. Science is an application of inductive logic. Math is an application of deductive logic.

 

[madness]

I don't think maths is a science at all.

1+1 = 2 is meaningless without a qualitative assignment. For example, one of the following statements is wrong:

1orange + 1apple = 2fruits
1apple + 1orange = 2 apples
1apple + 1apple = 2 apples

Science qualifies quantities, which complicated the assessment of truth statements with definitions and convention. Science is mathematics+philosophy (generally empirically based philosophies)

I think you need to distinguish pure maths and the use of maths to model some empirical data. For example, I think that 1+1=2 is perfectly meaningful in a purely abstract sense in an axiomatic system. The application of maths to the real world is philosophically a bit more confusing, but it seems to work very well.

I also disagree with previous posts that we can somehow discover some fundamental laws through mathematics. We can construct models of the world through mathematics, but we are not "discovering" some "law" in my opinion.

 

[BobG]

I also disagree with previous posts that we can somehow discover some fundamental laws through mathematics. We can construct models of the world through mathematics, but we are not "discovering" some "law" in my opinion.

This is true.

With enough epicycles and deferrents, people were able to make the Ptolemaic model of the solar system work (geocentric with circular orbits). With enough epicycles and deferrents, people were able to make the Copernican model of the solar system work (heliocentric with circular orbits).

Both models were wrong, but the math still worked well enough in both that you could predict the future locations of the planets.

 

[chiro]

We need language to make sense of the world. We first need a capacity to describe it, and we also need a way to break it down and divide it and bring things together.

Mathematics is the best way to do this for science because it provides something that all scientists can agree on as well as a lot of tools for actually analyzing and synthesizing data and concepts.

It's the best thing we've got, is universal, is something that people agree on, and is powerful in terms of an analytic and descriptive capacity and thus is the preferred choice amongst scientists, analysts, and people in general for this kind of thing.

 

[mather]

as for mathematical modelling, are there any principles, any textbooks, etc?