What is the difference between physics and mathematics?

in #science4 years ago

There is one big difference between people who don't understand math and those who seem to have intuitive grasp on it. People in fist category usually think that math is about numbers, while people in the second one will confidently disagree. Math is about nature in it's most fundamental form. Numbers is just one particular example.

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Math is often described as purest form of science, and science for some mysterious reasons is often viewed as opposite of nature. Nothing can be further from truth. We haven't invented gravity, electromagnetism or thermodynamics. It's something that exists whether we care about it or not. It's the part of reality, and the fact that we can explain it's influence on the world around us does not change what it is.

Numbers are the easiest example: 2 + 1 = 3 not because scientists say so, but because it is what it is. Because whenever you have 2 things of something and you add another something to it - you get three somethings. It works the same way for apples, atoms and galaxies, because that's what math is about: the most basic rules of reality, those which don't depend on a context.

That's actually the main difference I see between physics and math. Physics does differentiate between objects. Atom of hydrogen is fundamentally different from atom of oxygen and is treated as such. Even two hydrogen atoms might be different, depending on their states and conditions. Light travels differently through air and through water. Numbers aren't like that. You will not see sentences like this in any math book:

it is recommended to calculate derivative of the functions in the second week of January outside of deep gravity wells to get the most precise results

Even physicists that work in most abstract theoretical fields need to establish "rules of engagements" before getting to work: describe the conditions and rules for the predicted phenomenon. Mathematicians are lucky, they can get directly to business with "there exists x such that... ".

Seems like mathematicians have unfair advantage then. But that's not exactly true. The same core difference, dependence from context, allows physicists to test their theories in the real world. Physics benefited immensely from all the practical experiments throughout the history, from simple ones like double slid experiment to ginormous projects like Large Hadron Collider. In math, the only tool available is human brains. Yes, you can calculate some things on a computer, but computer will only do what it was programmed to do, it can not verify consistency of the theory, for example.

Physicists dream of finding famous "Theory of Everything" - unified rule or set of rules that would explain everything we know about the universe. I would argue that if such thing were to exist it would be as much a mathematical theorem as it would be physical theory. Since such theory by definition works in all possible physical environments, it does not need a context. A rule applicable in any context can be only classified as math. So theory of everything not only unifies multitude of physical laws and principles, it also blurs the line between physics and math.

But physics being context-aware is not a means to an end, we might want to dig deeper and think why physics is like that. I think this stems from the fact that we are discovering physics from top to bottom: reverse-engineer nature's complex behaviour into its constituent parts. With mathematics we go in opposite direction: building complex structures from simple blocks already known to us.

Can it be that they will eventually meet in the middle? What if some advanced branch of mathematics will suddenly explain phenomena we observe in quantum world?..

Sort:

Hypothetically speaking; If we vibrate frequency different from aliens out there, therefore the way we perceive nature is also different from aliens the way they perceive nature. Since mathematics is the language of science or nature our way of communicating to them, hence aliens out there also had a different language communicating their own nature of reality, the faster inventions of a new language would mean a faster perception to our core reality. :)

This is a very interesting article. I agree that a lot of people see science as somehow running counter to nature, and I also think it's a little silly.

However, I think there is a philosophical question as to whether numbers exist without us to perceive them. Is 2 an inherent trait of the universe that exists apart from humans? If so, where is "2" located, exactly?

But strangely, even though I think that, I also think that physics is essentially math by another name. This is strange because I am much more confident that physics is an inherent trait of the universe.

When you show statements about physics people having to vary their measurements based on conditions, all you're saying is that in physics there is more of a need to reduce the amount of 'noise' variable that will affect results... however, these variables are still inherently interconnected dependent variables and are therefore a form of mathematics.

Thanks for the thoughtful comment, @jenkinrocket. It's very interesting to read your thoughts about this topic.

I'm aware about philosophical argument about math as invention vs math as discovery. For me personally, concept of 2 is as real as concept of information, for example. Information is not attached to any physical place and might be viewed as a purely abstract concept, yet it is clearly defined in physical phenomena like uncertainty principle.

Physical environment (noise) can be modelled through math, but when you're working with pure math you never (as far as I know) have to think about this kind of inherently uncontrollable variables, because environment is essentially defined by you (or arises from other precise mathematical definitions).

4 years ago (edited)

yes please always down for some #science/ #astronomy/ #physics
#sciencechannel 4Life
#cosmos #howtheunverseworks #spacenerd
thank you @laxam for the post

Such a fascinating/perplexing question... I'm so frustrated because I got an undergrad degree in philosophy but didn't get into these sorts of deeper metaphysical questions until after I graduated, almost 2 yrs ago now.

One of the best things I've read that I think gets to the heart of the relationship between mathematics and the physical world is Eugene Wigner's, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences" whose title sort of speaks for itself!

Here's two quotes from Wigner's paper linked above that you might find relevant,

It is difficult to avoid the impression that a miracle confronts us here, quite comparable in its striking nature to the miracle that the human mind can string a thousand arguments together without getting itself into contradictions, or to the two miracles of the existence of laws of nature and of the human mind's capacity to divine them. The observation which comes closest to an explanation for the mathematical concept's cropping up in physics which I know is Einstein's statement that the only physical theories which we are willing to accept are the beautiful ones. It stands to argue that the concepts of mathematics, which invite the exercise of so much wit, have the quality of beauty. However, Einstein's observation can at best explain properties of theories which we are willing to believe and has no reference to the intrinsic accuracy of the theory.

The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.

I'm not a mathematician but I love admiring from afar, and I've been seriously considering diving back into the subject. I would guess that if I have a genuine interest then cranking out "homework" will be a bit more bearable than in high school haha

Thanks for the post! It was an enjoyable read!

Thank you for wonderful feedback.

I'm not a mathematician as well, I enjoy it in the same way I enjoy philosophy - it's a great exercise for mind, and can be something to ponder about when you're bored. :) I can recommend 3Blue1Brown youtube channel for this kind of "conceptual" math. By the way, I also never liked math during my education, go figure...

Thanks for Wigner's quotes, very interesting.

4 years ago (edited)

That video was A++... I've been surfing around and taking occasional dips into Khan Academy, but I like the way this guy was explaining everything. And even the comments!!

This is the second comment on the video and I related immediately.

This video illustrates the big problem with how we teach math in the United States. Teachers and professors leap right into equations and numbers, completely skipping any conceptualization of them such as illustrations or high level explanations.

For example, I remember back to my algebra class in high school when we first learned about functions. The teacher started to explain how to graph functions, and how to write them using f(x) notation. We learned more advanced concepts such as factoring, completing the square, etc. Not once did the teacher say anything to the effect of "a function is a thing you put a number into and get a result out". They never explained how a graph is a visualization of how a specific function's result changes based on the input. They only described the mechanics of it, and "how to do it".

It's no wonder when many kids get to calculus that they have no idea what's going on, because they still don't actually understand in their head what a function or graph really is. The unfortunate consequence is that so many people now think they're just bad at math, when really it was just never properly explained to them on a conceptual level, and the ones who did well in high school math were simply the ones who could make the conceptual leaps on their own.

I unfortunately did not qualify as a 'leaper' and got left behind, aka taught myself the material through Khan Academy the night before the test. My teacher could not grasp the intuitions underlying the formalisms... there were entire sections she could only teach using some heuristic she learned in HER high school days and was incapable of explaining it to us!!

I digress...

I'm really hoping Steemit turns out to be a fruitful place to learn a subject like mathematics in a peer-to-peer/collective way. Or at least to find good resources. But looks like it's off to a good start! :)

Thank you for collaborating with me to promote this post as explained at https://steemit.com/steemit/@jerrybanfield/10-ways-to-fund-a-steem-growth-project.

very good explanation. Greetings to all lovers of mathematics and its derivatives. @laxam

Gracias.

Math is great, I wish I would have more time to study it. And physics too :)

I do not study as such, but I study engineering and the best thing that exists is mathematics is the explanation of everything. I hope you support me with a vote, greeting. I follow you @laxam

great explaination and I think to make the difference simple:

Math is the theory behind all things
physics are more the functional part in reality

or do I see it wrong here?

In a nutshell you are correct, plus one complication that on some level they might be the same thing.

This post has received gratitude of 1.46 % from @appreciator thanks to: @laxam.

4 years ago (edited)

this is a nice post, please follow and upvote me too

This post has received a 11.8 % upvote from @boomerang thanks to: @laxam

Can one do physics without mathematics? I'd like to hear your opinion on that.

You got a 32.22% upvote from @upmewhale courtesy of @laxam!

Just goes to show what a huge difference a persons perception can make within their own reality!

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