Why people find math/physics incomprehensible

[medwatt]

Hello,
It isn't uncommon to hear someone say, "I was horrible in Math". The problem with such utterances is that 'horrible' is a relative word and so I have really never understood what level of Maths was the speaker 'horrible' in. But I have come to some conclusion based on the profession of the people who were 'horrible' in maths that the implied maths level is secondary school maths.
What is really difficult for me to understand is how can people find school maths hard ? When I was in school preparing for my O-Levels, Maths/Physics were the only subjects I looked forward to because they took the least of my time, whereas other subjects like biology/literature too so much of my time. I preferred maths related subjects for the mere fact that once the relationship between what is discussed is discerned it will always stay in my head no matter how. For some reason my brain likes relationships and hence anything I see/do, I try to find patterns.
One of the subjects which was always cumbersome to me was literature because I was never connected to most of the stories I read. I remember in junior secondary school we had Romeo and Juliet as one of our prescribed books and was always nervous taking tests. I simply failed to understand the expression of human sentiment, passion behind the words and discern the sociological factors they present. Questions like, "Why did Romeo say such and such?" used to baffle me.
The general consensus is that most people tend to prefer literature over maths, the reason of which I am still ignorant to and baffled by.

You can weigh in your insights.

 

[Evo]

Why do you find other subjects so difficult?

 

[russ_watters]

Math is hard. It is unusual for someone to find it easier than other subjects, but if you do, consider yourself lucky.

 

[Choppy]

There are a lot of factors to consider.

A person's experience with a particular subject can have a lot to do with how it is introduced and taught. It also has a lot to do with the person's own background, experiences, circle of friends, as well as their innate abilities.

I never used to appreciate Shakespear either. But as I grew older and got more experience with life a lot of the stories in the plays that we studied began to make more sense. When I was fourteen I had never really been in love with anyone, or faced choices between competing desires, or been hurt by a close friend, or had to make a sacrifice to accomplish something I really wanted, and so when I encountered such things in literature I simply couldn't relate. But these things happened as I got older and there have been many times where things that I'd read and they suddenly made a lot more sense.

I had a passion for physics early on partially because in the circle of friends that, for whatever reason, we placed a lot of value on understanding how and why things in the natural world worked. We would have arguments about whether things we'd seen in movies were possible. We would build and modify remote controlled cars. I had a friend who thought he figured out how to build a perpetual motion machine. We weren't afraid to challenge concepts that we were taught in science class . And I think all of that really helped me as a student because what I learned in the classroom never stopped in the classroom in subjects like physics and mathematics and the other sciences.

I think comparatively many other students had things happen the other way around. They got into romantic relationships sooner that I did and they didn't have discussions after class about whether the "kinetic theory of heat" was valid.

 

[medwatt]

Choppy, that's well articulated and a very reasonable answer. Come to think of it, I, too, never related to the characters in the books I read. The only characters I related to were the star trek characters and in my mind I used to be captain Picard!

 

[leroyjenkens]

I'm by no means great at math, but I didn't have to start studying for math tests until I hit calculus. Just listening to lectures was enough to understand the material. But I'd much rather take a history or literature class than a class like abstract algebra or advanced calculus. As humans, we think about history and read literature all the time. Aside from addition and subtraction, how much math does a person do? That's why people are typically not that good at, and; therefore, don't find math enjoyable.
Also, in a lot of other subjects, you don't normally hit a wall where you can't proceed because you don't understand the material. In anatomy, for example, you learn about the different parts of the body, and there's nothing to not understand about that. The kneecap is called the patella, and that's that. There's nothing to figure out. There's nothing to get stuck on and get aggravated.

 

[adjacent]

The kneecap is called the patella, and that's that. There's nothing to figure out. There's nothing to get stuck on and get aggravated.

The problem is when you sit in the exam chair,that word "kneecap" returns a
404: Name not found error.

I find it really hard to memorise all those weird names.
On the other hand,there's nothing to "remember" in maths.Once you understand what's happening,that's it.There's nothing to worry about.

 

[D H]

The problem is when you sit in the exam chair,that word "kneecap" returns a
404: Name not found error.

I find it really hard to memorise all those weird names.
On the other hand,there's nothing to "remember" in maths.Once you understand what's happening,that's it.There's nothing to worry about.

I think you've touched on a key difference between those who understand math and physics versus those who find it incomprehensible.

You have to have a headful of memorized facts at the ready when asked to write an essay in an exam that asks you to compare and contrast two specific moments in history. There is no singular correct answer to that essay question. You'll get a good mark if you have made a persuasive case regarding the thesis of your answer. To do well in the humanities, a student needs a vast warehouses full of memorized facts and an ability to tie those memorized facts into a unified whole.

Except for "Physics for Poets" type classes, that's not how mathematics and physics work. Memorization is not the key to understanding mathematics or physics. Math and physics students have a tiny closet of first principle memorized concepts, and maybe another tiny closet or two of more specific memorized concepts pertaining to the class at hand. Vast warehouses of memorized concepts? Doing that hinders rather than helps understanding of math and physics. In math and physics, the ability to solve a problem from first principles is much more important than is memorized trivia.

 

[Evo]

I think you nailed it DH, biology, geology, chemistry, history, etc... all require a vast amount of memorization, while math, engineering and physics require more original thinking based on a smaller set of memorized facts.

I am always blown away when I find people that have a mastery of both, and we do have a lot of those people here.

I am a lowly "memorizer", but it makes me really good at things like Jeopardy and trivia games. So THERE.

 

[leroyjenkens]

The problem is when you sit in the exam chair,that word "kneecap" returns a
404: Name not found error.

During an exam, I can skip that question and maybe it'll come to me later. Anatomy isn't just random words, they actually have some structure and meaning.
During a math exam, however, if I don't remember the process of doing one of the problems, such as finding the eigenvalues and eigenvectors of a matrix, there's several steps that I have to remember. If I forget the second step, I could be screwed, even if I remember all the other steps.
I once had a test in linear algebra that was one question, with like 10 parts all linked together. I start with a matrix, find one thing, use that result to find something else, use that result to find something else, etc. I remember doing something wrong early on and quickly had an unusable matrix.

Everything comes from your memory. In order to do math problems, you have to remember how to do them, which is coming from your memory. In math, you can derive equations and formulas, but that's time consuming, and you'll have to use your memory to remember how to derive it.

 

[medwatt]

The concept of recalling from memory was something I dreaded when I was in primary school simply because in primary school you're not expected to think. As a result, although I was a good student I was always outside the top 5. Oh, God. How are used to hate those darn history/literature questions. I really enjoyed history particular the industrial revolution but somehow the questions were intertwined with politics, sociology etc that never interested me.
When I was 13, everything started to change as Mr Physics was no longer about pasting definitions on the answer sheet. Of all the Physics that we studied about 95% of the students hated optics. Rotating mirrors used to be the devil . . .

 

[Hepth]

Everything comes from your memory. In order to do math problems, you have to remember how to do them, which is coming from your memory. In math, you can derive equations and formulas, but that's time consuming, and you'll have to use your memory to remember how to derive it.

I agree more with this sentiment than DH's. I feel that in mathematics and physics its a LOT of memory.

Say I introduce some new pseudoscalar particle into the standard model. I don't "understand" or "think" out the UV divergent piece of its two-loop mass renormalization, I have to remember EVERY step to calculate it (and there are a lot). And you can't possibly hope to derive the process yourself from scratch if you somehow "forget". Maybe that's the difference. Mathematics and Physics seem to be heavily reliant upon memorization of not only the principles of the problem, but the decades of work that went into the processes of solving it. There is so much subtlety and unmentioned tricks that you only learn during practice that turn an impossible problem into something tangible.

There is also the necessary skill to RECOGNIZE things in your problem as related to things in your memory. This is a huge requirement. You can't rely on reasoning everything out all the time or you will be reinventing the wheel. If you can't recognize that the integral you have, upon 2 coordinate changes, takes the form of the definition of a polylogarithm then you're going to waste a lot of time trying to get an algebraic answer (probably about 5 days, give or take... :( )

 

[HomogenousCow]

I agree more with this sentiment than DH's. I feel that in mathematics and physics its a LOT of memory.

Say I introduce some new pseudoscalar particle into the standard model. I don't "understand" or "think" out the UV divergent piece of its two-loop mass renormalization, I have to remember EVERY step to calculate it (and there are a lot). And you can't possibly hope to derive the process yourself from scratch if you somehow "forget". Maybe that's the difference. Mathematics and Physics seem to be heavily reliant upon memorization of not only the principles of the problem, but the decades of work that went into the processes of solving it. There is so much subtlety and unmentioned tricks that you only learn during practice that turn an impossible problem into something tangible.

There is also the necessary skill to RECOGNIZE things in your problem as related to things in your memory. This is a huge requirement. You can't rely on reasoning everything out all the time or you will be reinventing the wheel. If you can't recognize that the integral you have, upon 2 coordinate changes, takes the form of the definition of a polylogarithm then you're going to waste a lot of time trying to get an algebraic answer (probably about 5 days, give or take... :( )

Well, at least the things you have to remember aren't arbitrary.
In biology and literature many of the facts are completely arbitrary.

 

[Hepth]

Well, at least the things you have to remember aren't arbitrary.
In biology and literature many of the facts are completely arbitrary.

If they were arbitrary for everyone you would never learn them. To someone in the field they may need to remember it someday. I don't remember off the top of my head what the density of a Hexagonal Close-Packed Sphere lattice is, but I know I learned it years back, and I know someone doing materials science at my level would know it off the top of their head, as its basic knowledge to them.

The same I believe would be true in biology or literature. Someone wanting to be a brain surgeon might not feel like they need to know the chemical structure of foot sweat. I think that anytime you're in a pre-Graduate school learning environment you have to appreciate that what is being offered to you is general knowledge so you can approach a variety of fields with at least cursory knowledge of the basics.

I guess I would characterize math,physics and engineering undergraduate and high school educations are some very broad concepts all with a strongly-related core principle, whereas literature, history, bio and other fields tend to teach you a broad-sampling of some very detailed, unrelated topics. I would argue that this makes these fields much MORE difficult, as you become specialized and will have a tougher time innovating and finding tools and experience from semi-related fields.

 

[HomogenousCow]

If they were arbitrary for everyone you would never learn them. To someone in the field they may need to remember it someday. I don't remember off the top of my head what the density of a Hexagonal Close-Packed Sphere lattice is, but I know I learned it years back, and I know someone doing materials science at my level would know it off the top of their head, as its basic knowledge to them.

The same I believe would be true in biology or literature. Someone wanting to be a brain surgeon might not feel like they need to know the chemical structure of foot sweat. I think that anytime you're in a pre-Graduate school learning environment you have to appreciate that what is being offered to you is general knowledge so you can approach a variety of fields with at least cursory knowledge of the basics.

I guess I would characterize math,physics and engineering undergraduate and high school educations are some very broad concepts all with a strongly-related core principle, whereas literature, history, bio and other fields tend to teach you a broad-sampling of some very detailed, unrelated topics. I would argue that this makes these fields much MORE difficult, as you become specialized and will have a tougher time innovating and finding tools and experience from semi-related fields.

I took an introductory course on psychology this year, and suffice to say by the end of it I had very little respect for the discipline.
The theories taught were horribly vague and poorly defined, often I felt like all they were doing was labelling things with fancy words.
We had to memorize hundreds of these experiments and terms, I did well in the course but felt no more knowledgeable about human behavior than I did before.

 

[WannabeNewton]

Psychology isn't a good example-it isn't even a science let alone a hard science, by which I mean biology, physics, and chemistry. I agree with Hepth: I find biology to be much harder than physics and math. Biology is certainly not rote memorization of facts. If that was the case then my AP biology class would have been infinitely easier for those who took it. On the other hand, my mother is a biological researcher and she finds physics and math to be harder. Trying to universally classify one or the other as harder is pointless.

 

[leroyjenkens]

Well, at least the things you have to remember aren't arbitrary.
In biology and literature many of the facts are completely arbitrary.

Actually, there's quite a bit of arbitrary things to remember in science. One of the biggest problems I have is remembering what all the variables mean. Those are arbitrarily assigned. Just last semester I had astrophysics homework I had to do, and I would look up a formula, then have to look up a few of the variables in that formula, and each variable had its own formula that had its own variables, and other "variables" ended up being "constants", with constants being quoted because they're not really constant.

But what kind of arbitrary facts in biology can you think of? I can't really think of any. The nomenclature?

Psychology isn't a good example-it isn't even a science

Why isn't psychology a science? You don't think the scientific method was used to discover, for example, classical conditioning?

 

[ModusPwnd]

I took an introductory course on psychology this year, and suffice to say by the end of it I had very little respect for the discipline.
The theories taught were horribly vague and poorly defined, often I felt like all they were doing was labelling things with fancy words.
We had to memorize hundreds of these experiments and terms, I did well in the course but felt no more knowledgeable about human behavior than I did before.

Judging a discipline based a lone introductory course seems like a ridiculous thing to do.

The theories in psychology are poorly defined. Psychology can be thought of as being in a pre-paradigm state. Its very hard, that's why its taking psychology much longer to develop a over arching paradigm than astronomy, for example (which is often taken to be the first science to develop a paradigm).