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RE: What is the difference between physics and mathematics?

in #science4 years ago

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.

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! :)

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