I love physics, I love the ideas behind it and this forum has been especially enlightening to me over the few short months I have been on it. As a very quick example a thread threads like http://boards.straightdope.com/sdmb/showthread.php?t=614040 is incredibly interesting to me but…
My maths is terrible, I can understand the concepts of physics quite well, as in the thread I linked, the idea of space expanding into nothing I can comprehend. But I feel I’m only seeing a small part of the picture because the maths side eludes me?
Am I right? Do you need to understand the mathmatical side of it to a certain level. If so is there anything you good people could recommend (Books, online things etc) that would be of use.
(Mods, sorry if this is deemed in the wrong forum. First time thread start and all that)
My favorite is Conceptual Physics by Paul G. Hewitt. It has a little math, but lots and lots of descriptions and fun questions that make you think about the physics without the math.
You can’t go far without math though. Anything beyond physics for non-science majors in college will be heavy on math.
The answer to the question in the title is “not very far”. The sad truth is that physics and math are inextricably entwined. At the most basic level of mechanics you will need, at the very minimum, algebra. Knowing calculus will make understanding simple Newtonian mechanics easier because suddenly the relationships between position, velocity, and acceleration–to use an example–become much more intuitive. Sooner than later you’ll be required to know differential equations and lots lots more. For someone trying to self-teach, however, learning all of this will take years and years and be beyond daunting.
You are in luck; however, because there are many excellent popular science physics books that are written for people whose backgrounds are not so mathy. From a quantum perspective, Nobel Laureate Leon Lederman has written several excellent books, which include Quantum Physics for Poets and The God Particle. For the astrophysics, Carl Sagan has written many excellent books as well as Stephen Hawking (including the classic A Brief History of Time).
If you enjoy reading about physics, but don’t have the time and resources to essentially get an undergraduate degree on your own time, I say don’t worry about it. It can be akin to a physicist going to an art museum. The physicist can see and appreciate the beauty of a Van Gogh painting even without understanding it on the way an art history PhD might appreciate it. There is lots of great popular science writing out there.
I also found that thread very interesting, what I found is that my back-and-forth with *iamnotbatman forced me to really think about a few concepts.
Maths is very important to understanding physics because it’s basically the language in which it is written. I would say though don;t be disheartened by maths, whenever I see a mathematical explanation I don’t understand I always know it’s for one of two reasons: 1) I need to find out more about the underpinning concepts 2) it’s poorly explained. Maths is just a shorthand way of expressing sometimes quite complex concepts that can’t easily be expressed in plain English, what people often forget is that it’s designed to be understood.
There’s plenty of good resources online, though a good bit of advice is never be afraid to ask a question. If you feel you haven’t understood something, just ask.
Hmm, thanks for the posts, certainly I shall look at suggestions all three (Now five!)of you have posted. Thing is, I don’t want to make a career out of it or anything, and UTejas I actually find the ideas behind physics as interesting enough to maybe worth me seeing if I can start out out again from O-level (American High School?) maths and trying to have a go at pushing it on from there. I can pootle along with that and maybe see if I can get to degree level in my own time.
I found that physics really helped cure me of my own middle through high school math-phobia. I was very shaky with algebra before I took an algebra-based intro physics course and though that made the class pretty difficult, at the end my algebra was definitely solid and I was finding I was actually enjoying it. When I took calculus, I took it at the same time as a calc-based physics class and that worked really well for me. I don’t know if there’s any self-teaching books out there that try to teach you math and physics at the same time, but for me anyways I think that was the way to do it.
This. A lot of math was invented specifically to solve physics problems. Without math, you are pretty much limited to reading “pop physics” books written by people who can do the math and then tell you about what it means.
You really need to be able to follow and understand math for many fields of physics. But there is an out of sorts. There is a difference between being able to follow math and being able to DO math if that distinction makes any sense. Depending on your particular mental abilities, the following can sometimes be much easier than doing. An analogy might be being able to read French poetry and getting something out of it versus being able to create decent French poetry yourself.
approach it philosophically, and imagine things geometrically instead of algebraically. hawking was able to explain much of quantum physics and relativity while mentioning only one mathematical equation: e = mc^2
I attended Purdue University as a physics major several years back, and they require a VERY heavy co-curricular study of math/calc for physics majors. Although I wouldn’t expect **every **university to have quite as rigorous a math curriculum (Purdue is frankly world-class when it comes to the sciences), there’s no higher physics study without it. In the program I studied, you ended up coming out of a physics major with enough math to have a minor in math automatically, and with 4 or 5 extra high-level math courses (in 2004 anyway) you could tack Math on as a double major–this was quite common.
You can attain a respectable layman’s understanding of physical concepts without the mathematical component–I spent a lot of my free time studying black holes and quantum mechanics, even though I never studied past Calc II (I ended up changing majors after 2 semesters in physics), and those topics still fascinate me. But you’re not going to “grok” high-level stuff without a proper backing in the calculus and math behind the concepts. As it is, there is a lot I have to take on faith when I read about quantum mechanics… you basically have to abandon everything you know about logic to even BEGIN to understand it (and I hardly have, and have studied it frankly way more than I should, all things considered).
Even in the first semester of study, you will do a LOT of advanced trigonometry, geometry, equation derivation, and calculus. Vector calculation, springs, and buoyancy all require good math skills to calculate and understand–and those topics comprise basic first-semester study.
Even without a physics education, though, you can still read and understand a good breadth of topics–check out Isaac Asimov’s nonfiction popular science books. He covers SO MUCH and it is SO accessible, even if you lack math skills. The books are outdated (published in the 70s), which shows, but they are still wonderful reads for laypersons.
If he was so committed to avoiding the language of mathematical equations, why didn’t he just phrase that one in familiar English words as well? What’s so different about that one, other than its pop culture status?
i don’t remember the exact reason now but hawking said the publishers of “a brief history of time” warned him that sales will be halved for every equation he includes in the text. i think it was just a historical mention, and yes because the equation enjoys street recognition.
Yeah, I’ve heard that story before (straight from the horse’s mouth at the beginning of the book), and was under the impression Hawking had said something like “In the end, I found there was one equation it was impossible to avoid, it was too fundamental, blah blah…”, which seemed silly to me, and whose silliness I wanted to call out. However, checking the actual quote now, it doesn’t seem he quite said anything like that, so I guess my memory was just fooling me.
Hate to say it, but my first thought was “Well, you could probably stumble through a high-school physics course.” Beyond that, doubtful. Fact is, mathematics is how a lot of science describes the world. And you need that in physics.
But I wouldn’t let struggles in math deter anyone. Blunder through the math however you can. Get the ideas and the basics, don’t sweat too hard if the exercises are difficult. Once you get into calculus and beyond, you find that a lot of the math is kinda like physics - there’s a pattern and order to it. A lot of it gets abstract.
I was surprised, by Calc III and beyond, to find that a lot of math takes an “intuitive” feel. I myself have only the dimmest sense of this, but one of my good friends had this in spades, and while he hated algebra and geometry like the rest of us, by the time he got to upper level math he could just coast through on his “math intuition” alone. Bastard ended up getting a degree in Mathematics with like zero effort.
No, that amount of prerequisite math in a physics B.S. program is typical. We had three semesters of calculus, one of ordinary differential equations, one of vector and tensor analysis, partial differential equations, linear algebra, and then a three set of electives–usually introductory statistics, functional analysis, and some kind of nonlinear theory or numerical methods, although the more enthusiastic students would go in for topology or advanced calculus–which exceeded the minimum requirements for a minor degree in mathematics by several credits, and this was at a land grant state system university. I didn’t know any physics majors who doubled in math; philosophically, mathematicians and physicists tend to be at opposite ends of the spectrum, and most physics majors that doubled went for something like electrical engineering or computer science. (I knew one that was doubling in philosophy, but he dropped out to wander the world like Kwai Chang Caine or something.)
As for the o.p., math is the language of physics, and learning physics in English is like reading about a symphony: you can read someone’s description of what it sounds like, but you ca 't truly comprehend it without being able to play with the math. However, for the really speculative parts of modern physics, such as interpretations of quantum mechanics and cosmology, even knowing math doesn’t help very much, and even most trained physicists don’t have much better of a conceptual grasp than a well-read layman.