What is the Difference between Maths and Classical Mechanics?

[Fiery Graviton]

TL;DR

Our mechanics lecturer keeps repeating that we shouldn't think mathematically, I am trying to understand the "physicist intuition".

I am guessing this has been posted before if that's the case please inform me.

I was wondering the difference between mathematics and physics. What makes them so different yet so similar? Why does the mathematical intuition does not work on physics, or vise-versa. I know physics is less "deterministic" than mathematics. I am just curious as I want to become better in physics.

Thank you for taking your time to read.

 

[brainpushups]

There is a series of lectures that Feyman gave at Cornell which you may be interested in. The second lecture in the series is specifically about the relationship between math and physics. They are all worth a watch.

https://www.feynmanlectures.caltech.edu/messenger.html

 

[Herman Trivilino]

You need a conceptual understanding of both math and physics. Your professor is asking you develop the latter without using only the former.

Here's why and here's the difference. Physics is the study of phenomena. The focus is on trying to understand how Nature behaves. It's not just a set of exercises in applied math, although it can tend to be thought of that way by students.

Your professor wants you focused on the phenomena. Physics is phenomenology.

It is not a set of math "word problems" where you search the wording of a problem for the algorithm you'll need to memorize your way to making answers.

Your professor wants you to be sense-making, not answer-making.

Here's an example. A ball is thrown upward at a speed of 4 m/s. How high will it go before it starts to descend?

Many students go equation hunting, looking for one that gives the answer. Your professor wants you thinking about how gravity affects the ball and consequently how that will affect the ball's motion. You'll end up solving for an answer the same way, but your thought processes will differ in a fundamental way.

This is a big problem for physics educators. How to get students away from thinking of physics as an exercise in applied math.

As the physics gets harder students who think of it only as an exercise in applied math get left in the dust. Your professor doesn't want that happening to you.

 

[QuarkyMeson]

I was wondering the difference between mathematics and physics.

Handwaving, basically.

I know physics is less "deterministic" than mathematics.

Anyway, what do you mean math is more deterministic than physics?

Why does the mathematical intuition does not work on physics, or vise-versa.

I'm struggling to envision what you mean here.

Your professor is probably asking you to look behind the mathematics and build physical intuition about what the problem is asking you to do. In your classical mechanics for example you can certainly learn say Lagrangian mechanics and learn what to do perfectly well mathematically without understanding what's going on physically or how you've managed to get there or what the big picture the problem is even asking is. You can even bypass understanding if you're looking at the problem locally using a d’Alembert approach or globally with least action. You're missing the physics. You're missing the interesting part of wondering, "why the **** does this work?" You're missing what would happen to your problem if I take your massless pulley and gave it mass. You're missing the physics.

Basically, he's likely saying "math good understanding better".

 

[Matterwave]

I was wondering the difference between mathematics and physics. What makes them so different yet so similar?

Physics heavily uses mathematics, but, at the end of the day, physics is about the real physical world and it's anchored by experiment. Physics, unlike math, is not an exercise in pure logic built from the ground up, in theorems and lemmas, on top of a set of axioms. At some point you need to make contact with the physical world.

To a physicist, mathematics is essential but not total. There is still a lot of physical intuition one builds that is not necessarily mathematical in nature.

For example, the statements "when I hit the breaks on this car, my body is going to lunge forward" or "when I'm free falling I feel weightless" are both physical facts building physical intuition without math. Of course you can (and should) use math to model those statements and make them precise, but the underlying physical intuition is very important.

At least this is how I view things.

 

[PeroK]

TL;DR: Our mechanics lecturer keeps repeating that we shouldn't think mathematically, I am trying to understand the "physicist intuition".

I am guessing this has been posted before if that's the case please inform me.

I was wondering the difference between mathematics and physics. What makes them so different yet so similar? Why does the mathematical intuition does not work on physics, or vise-versa. I know physics is less "deterministic" than mathematics. I am just curious as I want to become better in physics.

Thank you for taking your time to read.

I don't understand this type of thinking. It's a bit like asking what's the difference between chemistry and biology? Or, what's the difference between chili con carne and a cheeseburger? I can personally find no insight in comparing mathematics and physics. Instead, understand physics for what it is; and, understand mathematics for what it is.

Anyone who tells you not to think mathematically is a fool! You don't want to think ONLY mathematically. You may, if you wish, refer your mechanics lecturer to Roger Bacon:

Whoever then has the effrontery to study physics while neglecting mathematics should know from the start that he will never make his entry through the portals of wisdom.

Roger Bacon (1220-1292)

 

[javisot]

I was wondering the difference between mathematics and physics.

Physics=mathematics + natural philosophy

(Mathematical Principles of Natural Philosophy, Newton)

If you remove mathematics from physics, what remains is natural philosophy. If you remove natural philosophy from physics, what remains is abstract mathematics.

Using mathematical language to optimize natural philosophy and thereby explain certain aspects of reality opens up the possibility of conducting experiments, which are a fundamental pillar of physics.

 

[javisot]

TL;DR: Our mechanics lecturer keeps repeating that we shouldn't think mathematically, I am trying to understand the "physicist intuition".

I am guessing this has been posted before if that's the case please inform me.

I was wondering the difference between mathematics and physics. What makes them so different yet so similar? Why does the mathematical intuition does not work on physics, or vise-versa. I know physics is less "deterministic" than mathematics. I am just curious as I want to become better in physics.

Thank you for taking your time to read.

Agent?

 

[PhDeezNutz]

I gotta be honest.........Grad Classical Mechanics felt like a math class. Canonical Transformations, Hamilton-Jacobi Theory, Action-Angle Variables, etc. It felt completely divorced from physical intuition/reality (even though it is not, but I haven't reached that level yet to reconcile the two).