Are math and physics fundamentally different?

[Cristiano]

…Consider the trick that older children play on younger siblings, getting them to exchange a dime for a nickel (US). YS sees size quantification easily, but confuses it with value, which is an unrelated artificial construct for which we are not innately prepared. And OC takes advantage. No doubt something comparable happens in real world economics.

ICXC NIKA

That confused me when I came to the US as an adult. I looked for the numerical value on the dime and it did not show anything thus I assumed that it had a smaller value than the nickel, just to show that physicist look for the simplest model and they can be wrong.

 

[meme1961]

Math is a specialized form of Philosophy. It is of the class of “constructed”, “independent” philsophies dealing with the concepts of what it means “to be” a thing separate from another thing of the same genus.

In english: math is a kind of philosophy constructed by human beings, and one that has no relationship to reality at all, in any way, period.

What physics does is, basically, study God’s creation, and then attempt to describe that creation using either newly constructed maths that express the physicist’s current understanding of said creation, or by re-using maths that already exist that can be applied without serious contradiction.

This introduces the risk of believing the math is the creation, and thus infering what is implied by the math, but not by the reality.

Examples of the gaps between human constructed maths and creation are many, but for the lay person, Einstein did some of the basic work to correct the model created by Newton, et al.

The most obvious examples of math having no relationship to reality are, however, much easier for the layperson to grasp. Look at any “third person shooter” real time video game where the characters are allowed to do things that violate the laws of physics. The mathematical model of the game allows for these actions, thus these actions are logical, correct and reasonable within the model of the game (they are “mathematically valid”), but try them in the real world, and you are toast.

A computer programmer spends inordinate amounts of time trying to get his mathematical models sufficiently coherent with reality as to avoid “crashes”.

A man bent over his checkbook, trying to get it to match the reality of the money in his wallet knows the difference between math and the real world, too.

 

[Marc_Anthony]

xkcd has a comic on this.

Also, if you put your mouse over the comic and hold it there, mouse-over text will come up and it will give, shall we say, a rather inappropriate comparison between math and physics.

Instead of posting the mouse-over text here I expect you take a look yourselves. Xkcd is always worth the time.

xkcd.com/435/

 

[levinas12]

If yes, they are different in what ways?

Mathematics and physics involve two different senses of “necessity”.

In physics, necessity is contingent (a posteriori). For example, the equation for gravity could be different. The laws of physics do not apply to all possible worlds. That’s why we have to experiment. For example, we cannot simply “deduce” the equation for gravity.

In mathematics, necessity is absolute (or “a priori”). Mathematics (after adjusting for certain differences) is true of all possible worlds. Because of its “a priori” character, we do not have to do experiments in mathematics - at least, in the sense of the experiments done in physics.

I’m sure that not everyone would agree with all of this - and certainly it can be elaborated upon and nuanced. But suffice to say that the distinction between physical necessity and mathematical necessity is one of the great philosophical distinctions. Note that I haven’t brought up the distinction between logical necessity and mathematical necessity (but I think there is a distinction here as well). In Kantian terminology, mathematical necessity is synthetic “a priori” while logical necessity is analytic “a priori”. This distinction has a controversial history. But I won’t pursue it - it would derail the thread.