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# My science teacher once said.... watch

1. ...'this may be strange but most physics needs to be explained through maths.'

Yes, I know this. But why?
Who can simply explain to me the role of maths in physics. Why is it essential. Why can't words explain stuff... why maths? why numbers?
2. Your Science teacher is 100% correct, as Physics becomes more complex throughout A Levels and eventually degree in university, the ability of words to describe such things break down.

An example would be quantum mechanics, the physics of the small, I am sure that one could imagine quarks and electrons but in the case of wave-particle duality (where its wave function collapses under observation such that it behaves differently on the basis of being observed or not), our imagination and words could not describe the phenomenon in a comprehensible way. Therefore, mathematics is the only tool capable of providing an explanation that obeys the laws of physics.

I personally am fascinated by the fact that mathematics is the universal language and the means by which physics functions in our world.

Mathematics is after-all fundamental and physics is in essence the study of the fundamental.

Other examples would be, how could one describe special relativity without mathematics to calculate figures or mathematics to model planetary motion (the issues of eccentricity and chaos would render a description through words impossible).
...'this may be strange but most physics needs to be explained through maths.'

Yes, I know this. But why?
Who can simply explain to me the role of maths in physics. Why is it essential. Why can't words explain stuff... why maths? why numbers?
He/she is correct, Physics is based on Maths. The further you go when studying physcis, all sciences in fact, the more mathematical it becomes. If you want to have a way of understanding simply, basically Maths is pretty much our only system of logic and therefore can be used to prove things in the way that words can only really make assumptions.
4. Mathematics is a very powerful framework to deal in - if you can break a physical problem down into a mathematical one then you can find out much much much more than you would ever otherwise be able to infer. For example we have the motion of the planets under gravity. You can take as many measurements as you like, and i suppose as many experiments as you like but you'll only really have a deep understanding and be able to make precise statements about the situation when you apply some mathematics to it. Generalising the notion of a force using mathematics allows us to derive a wealth of more general results and much more interesting statements that not only fully explain planetary motion, but weather patterns, the behaviour of atoms etc etc, without having to do a experimements and take measurements for each individual case
5. My dad always said 'maths is the key to all sciences' when I was little, I resented maths then though after A level and now in my first year of my Economics degree I have developed an appreciation for it. put it like this.... If I want to 'be' a physicist or a chemist or a 'economist' or an 'engineer' then maths is going to get involved, remember a good deal of what we even know about space like the shape of the universe (i think) had to be discovered by special satellites which needed plenty of maths to a) programme and b) make sense of the picture (not visual) it had taken.

Basically if you want to gain a decent understanding of physics then the popular science books like a brief history of time, or the elegant universe will give you that, if you actually want to be a physicist then you will have to learn and understand the complex math behind the books....

there is no escape from maths... practice, work hard, and you begin to appreciate its elegance, essays seem quite boring now....
6. Hmm, there's an XKCD that deals with this, can't find it though.

Essentially, Maths is the only thing that can 'Prove'.

And so Physics is applied Maths. And then all other sciences are applied equivilents of other fields. Such as chemistry is basically applied Physics.
7. (Original post by Steevee)
Hmm, there's an XKCD that deals with this, can't find it though.

Essentially, Maths is the only thing that can 'Prove'.

And so Physics is applied Maths. And then all other sciences are applied equivilents of other fields. Such as chemistry is basically applied Physics.

I believe you mean this one. It might be in my bookmarks...

Anyway, to the OP -

For me, it boils down to:
• Mathematics is a really great way to get a very concise statement that would take a lot of words to explain clearly in English. Take Newton's second law for example - "A body of mass m subject to a net force F undergoes an acceleration a that has the same direction as the force and a magnitude that is directly proportional to the force and inversely proportional to the mass. Alternatively, the total force applied on a body is equal to the time derivative of linear momentum of the body." (stolen from Wiki)

Or, in maths: or
You get the same information from both statements, but the maths is so much more concise.

• Related to the above: being able to express the relationship between things as an equation allows one to more clearly see the relationship between physical quantities, taking Ohms Law as an example this time

Ok, so in English, current is proportional to voltage and inversely proportional to resistance. What does that even mean?
Increase the voltage, you increase the current. Reduce the resistance, you increase the current. How do we know from the equation? It's just basic knowledge about fractions, and how they behave as the numerator or denominator changes.

• Finally, we can use maths to not only express ideas, but realise connections between them. For example, continuing from Ohms Law above:

(Power = current x voltage)

But hold on, power is related to current. So surely we can rearrange to make current the subject of the above equation, set them equal to each other and get a relationship between resistance and power?

(I've used pretty basic relationships in the above - but the same principles run through every part of physics. If you follow a theory through, and the maths gives you a weird result, you need to rethink your theory. IIRC, this is actually how Relativity started - "Well, what if there is no such thing as absolute time?", following through the thought process and developing equations that were mathematically sound, but also agreed with the experimental data)
...'this may be strange but most physics needs to be explained through maths.'

Yes, I know this. But why?
Who can simply explain to me the role of maths in physics. Why is it essential. Why can't words explain stuff... why maths? why numbers?
It's not so much to do with numbers. The further you go into maths the less relevant numbers become; numbers are a useful tool for understanding more abstract concepts though. Maths is about studying structure, change, quantity and so on, and since it's in these terms that we study physics, our understanding of physics must be fundamentally mathematical. If we could study physics through a different paradigm then maths might not be necessary, but currently it is (and arguably if we had a different paradigm then it wouldn't be physics).

EDIT: Reading other replies, I'd dispute that mathematics is the 'universal language', as people so often call it. I don't even think maths is a language. I think mathematical notation is perhaps a form of language which enables us to describe mathematical phenomena, and mathematical phenomena can describe lots of things, but I certainly wouldn't say that maths is a language. I'd also dispute that it's universal; mathematical objects are 'universal' (if we must call it that), but there can be many equivalent descriptions of any one abstract object, and it's not immediately obvious that they're equivalent. For example, why should it be obvious that you can describe the surface of a doughnut as a square whose opposite edges are 'the same'? Why can we describe an equation in terms of a set of points in some abstract space (like a curve on a graph)? If anything the notation blurs the 'reality', rather than making it clearer, which kind of undermines the point of a language. The only thing is that the notation is all we have through which to understand it.
9. (Original post by nuodai)
It's not so much to do with numbers. The further you go into maths the less relevant numbers become; numbers are a useful tool for understanding more abstract concepts though. Maths is about studying structure, change, quantity and so on, and since it's in these terms that we study physics, our understanding of physics must be fundamentally mathematical. If we could study physics through a different paradigm then maths might not be necessary, but currently it is (and arguably if we had a different paradigm then it wouldn't be physics).

EDIT: Reading other replies, I'd dispute that mathematics is the 'universal language', as people so often call it. I don't even think maths is a language. I think mathematical notation is perhaps a form of language which enables us to describe mathematical phenomena, and mathematical phenomena can describe lots of things, but I certainly wouldn't say that maths is a language. I'd also dispute that it's universal; mathematical objects are 'universal' (if we must call it that), but there can be many equivalent descriptions of any one abstract object, and it's not immediately obvious that they're equivalent. For example, why should it be obvious that you can describe the surface of a doughnut as a square whose opposite edges are 'the same'? Why can we describe an equation in terms of a set of points in some abstract space (like a curve on a graph)? If anything the notation blurs the 'reality', rather than making it clearer, which kind of undermines the point of a language. The only thing is that the notation is all we have through which to understand it.
So true!

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