Is it possible to be bad at math and understand the structure of the universe?

August 20, 2008 9:47 AM

Is it possible to be bad at math and understand the structure of the universe?

A recent question about the structure of the universe got me thinking about my own attempts to understand these ideas. I'm fascinated by cosmology, but I suck at math. It's a frustrating combination ;) I read cosmology books (like Carl Sagan) and listen to astronomy podcasts, and I feel like I'm gaining some understanding. Am I just fooling myself? Is it only the physicists and mathematicians who truly understand the structure of the universe?

To put it another way, most of my understanding is based on analogies provided by people who understand the math. Are these analogies so partial and flawed as to be useless?

posted by diogenes to Science & Nature (19 answers total)

I recently struggled with a similar question. I have always had an aversion to math and never been very good at it but was doing a good deal of research that involved high math. I decided that I woudl learn the math needed to "understand" the topic. Well after months of working my way up from a jr high proficiancy to a college math proficiancy I realized that while math deepened my understandings and in many cases simplified seemingly complex analogies my basic understandings without the math were still correct. In short, whiel learning the math behind astronomy would most likely give you an oppourtunity to understand it at a more intrinsic level, the analogies you hear form astronomers are going to still hold true.
posted by elationfoundation at 10:06 AM on August 20, 2008

Dude -- it's not even possible to be good at math and understand the structure of the universe.
posted by escabeche at 10:09 AM on August 20, 2008 [9 favorites]

Unless you intend to do anything with this information that would require some sort of math, a layman's understanding is just fine. Its kind of like the difference between knowing how to program and knowing how to use a computer. The former is very useful but not for everyone, the latter is usually all you need.

Yeah, if you get in a conversation with an astrophysicist, you'll be overwhelmed, but you'll still be doing better than most other people. As long as you can listen to someone talk about something like perpetual motion and have your BS detector go off enough to not be fooled, that should be all you need.
posted by cimbrog at 10:09 AM on August 20, 2008

Are these analogies so partial and flawed as to be useless?

Well, useless for what? If you're intent is to think originally about these ideas, then yes, I'm quite certain you can't do that without a very serious mathematical background.

If your goal is a more personal notion of wanting to understand (to whatever extent possible) the world you live in, which I can sympathize with, I think any amount of intellectual honesty will require learning some mathematics.

The folks at physicsforums are really helpful if you're serious about learning more.
posted by phrontist at 10:10 AM on August 20, 2008

As long as you can listen to someone talk about something like perpetual motion and have your BS detector go off enough to not be fooled, that should be all you need.

Eh, but then you're miming the high level "rules" of physical theories instead of understanding how they arise. Not everyone needs to understand astrophysics, but if you want to be one of those people, I don't think mathematics is available.

(I should point out I Am Not An Astrophysicist, just an engineering student, but all of my experience with physics has born this out. The people without mathematical backgrounds seem to quickly end up in gene ray territory like this guy.)
posted by phrontist at 10:15 AM on August 20, 2008 [2 favorites]

I don't think mathematics is available.

Sorry, that should read avoidable.
posted by phrontist at 10:16 AM on August 20, 2008

I sometimes get a kick out of telling people I took 300-level cosmology course in college, but there was practically no math involved in it, and what math there was I certainly didn't learn. The class basically fit the description of what it sounds like you're looking for -- a basic explanation of the structure of the universe and how things work at that scale. There was a lot of stuff on relativity (both general and special), which, while not really requiring math knowledge to understand can screw your head up nonetheless. That, plus doppler shifting and a few other concepts seem like a pretty good foundation for a general layman's understanding of the universe. We didn't get into string theory at that time, but I have a couple books I'm planning on reading to learn about it.

Anyway, I don't think math is critical to understand how cosmological concepts work, although it will come up every once in a while. Unfortunately, I'm in the same boat as you, so I can't really give a definitive answer on the subject.
posted by LionIndex at 10:28 AM on August 20, 2008 [1 favorite]

Eh, but then you're miming the high level "rules" of physical theories instead of understanding how they arise.

I was just trying to point out any potential usefulness of having a layman's understanding of science. Yes, you're just miming the "rules", but it is better than staying in complete ignorance because you can't do the math.
posted by cimbrog at 10:32 AM on August 20, 2008

I'd just like to point out that string theorists are notoriously bad at math, and yet that doesn't hinder them from doing physics. I know a well-accomplished string theorist who couldn't even give the definition of a module over a ring. It was embarrassing for him, but it is promising for you.
posted by metastability at 10:39 AM on August 20, 2008

I'd just like to point out that string theorists are notoriously bad at math, and yet that doesn't hinder them from doing physics.

String theory people barely do math, and certainly don't do physics.
posted by phrontist at 10:58 AM on August 20, 2008

I'd just like to point out that string theorists are notoriously bad at math, and yet that doesn't hinder them from doing physics.

Doing physics? I thought you just said they were in string theory?

diogenes: It depends on what you mean by "understand". In some senses you could understand calculus without being able to actually do calculus. I can explain to you what an integral is, about the area under a curve, etc. You can understand, in words, what a triple integral is. About differential equations. And so on. Do you understand calculus if you can explain, in words, what you use differential equations for and what they are but can't actually use them? Probably not. But it's a darn sight better than someone who just stares blankly when the idea comes up.

So you can get that sense of cosmology. It isn't the same, of course, but it's a lot better than nothing.
posted by Justinian at 11:00 AM on August 20, 2008

The balance between mathematics and intuition that you need to do physics is an interesting philosophical question. On one hand, it's sort of miraculous that mathematics works at all. Consider the computer: an object that knows nothing but math, and has no understanding of anything.

On the other hand, formal logic has only been part of the human experience for a few thousand years. Newton was famously good at math. Did he understand the structure of the universe? Did he still in his later years, when he devoted his efforts to astrology? Faraday figured out that changing magnetic fields make electric fields. He was a gifted experimenter but supposedly never got the hang of calculus. Did he understand the structure of the universe?

Mathematics serves a dual purpose in physics. You aren't doing physics if you can't compute things. If I drop this on my foot, will the bone break? If I drop water on this turbine, will it spin? Will it still spin if I put a load on it, so it gets hot? Will it get hot enough that I can cook my breakfast with it? But the logical part of mathematics lets you figure things out without computing them. This computation is just like that one, and I already know how to do that one, so I know what to expect from this one even though I have to deal with some details.

I think that's probably what you mean by "understand," is "have a good analogy for." Noticing analogous systems, and getting insight from them, doesn't necessarily require mathematical skill. But knowing details about mathematics helps you anticipate where the analogy will stop working, and how, which can (a) give you something to look for, and (b) keep you from saying something embarrassing.
posted by fantabulous timewaster at 12:23 PM on August 20, 2008 [4 favorites]

Of course it's possible.

Perhaps not on a nuts-n-bolts how-it-all-works level, but one can certainly grasp basic concepts without being very good at math. I do think you need to be good at visualizing internally, though, and being open to simply accepting things that don't make sense in your everyday world.
posted by Thorzdad at 1:04 PM on August 20, 2008

You think all Carl Sagan used was math?

I'm not specifically advocating drug use, nor attempting in any way to de-emphasize the important and pivotal role math plays in understanding structure of the cosmos (and some would say reality)..... but, simply trying to make the point that in your effort to understand or learn ANYTHING new, its best to keep your mind open to the possibility that alternative non-traditional approaches have just as much potential value as expected learning paths.

You never know how learning fractal patterns might unintentionally teach you a certain subset of math you might never discover if you focused to hard on standard cosmological math subjects. You might not expect taking a break from a chalkboard full of equations and watching the interaction of balls on a pool table might generate some fresh ideas. You might take a vacation to a empty desert (no light pollution) and spend a few nights hiking under a galaxy of stars and come up with some crazy theories that might one day pan out.
posted by jmnugent at 1:07 PM on August 20, 2008

I'm currently reading The Road to Reality: A Complete Guide to the Laws of the Universe by Roger Penrose. The goal of this book is to outline precisely the mathematical background necessary to achieve a full understanding of current models of the universe, both cosmological and particle.

Of course, this runs completely contrary to the poster's goal of understanding the universe without slogging through the math, but if the desire for understanding someday outweighs the desire to avoid math, then by all means get this book. Cuz it's completely awesome.
posted by rlk at 1:13 PM on August 20, 2008 [1 favorite]

diogenes: Is it only the physicists and mathematicians who truly understand the structure of the universe?

To put it another way, most of my understanding is based on analogies provided by people who understand the math. Are these analogies so partial and flawed as to be useless?

To give another perspective:

Many would say that our modern conception of mathematics (such as, say, Heidegger and Apollonius of Perga) actually constitutes a fairly fundamental misunderstanding of the universe. Specifically, modern mathematics seems to me to be (a) a fairly arbitrary set of often-irrational rules that have been encouraged and proliferated until everyone who uses them can't even see whether they make sense or not, but simply assume that they're intuitive; and (b) the origins of the modern conception are so murky that most of us can't even begin to imagine how our assumptions are coloring and changing our conclusions about the way the world works.

Algebra and the algebraic conception of calculus are shorthand for more original and intuitive spacial ideas. But they've generally turned into the heart of those conceptions. To see this clearly, find somebody who knows calculus and ask them to calculate D(3x + 1)^2. Easy, right? Now show them a curve and ask them to calculate the area under it, or ask them why a derivative constitutes the calculation of the area under a curve. Almost every person I've met who knows calculus can't tell me these things; I've know engineers and scientists who couldn't tell me why calculus does what it does. That's the very high cost we've had to pay for acting as though these symbols are the essence of mathematics. It's amazing - only the most intuitive and skillful mathematicians can pick up Newton's Principia Mathematica, one of the books that founded calculus, and make sense of its very simple diagrams and explanations.

Basically, modern mathematics is practical and workable, but it isn't very essential. It's good for building anything from lawn mowers to spaceships, but it isn't much good for understanding the universe. It's not built for understanding. That's why so many people don't really understand it, even after being forced to study it for a decade in their youth.

For a good development of this point of view, you should read a superlative book called The Great Dialogue of Nature and Space by Yves Simon. It's a very worthwhile and clear explanation of the incredible amount of change that happened in mathematics over the last five hundred years and the benefits and drawbacks of this change.
posted by koeselitz at 1:45 PM on August 20, 2008

koeselitz, nice example. Feynman gives a nice example of this in his "Surely You're Joking," when he was in Brazil:

We first took two strips of polaroid and rotated them until they let the most light through. From doing that we could tell that the two strips were now admitting light polarized in the same direction --- what passed through one piece of polaroid could also pass through the other. But then I asked them how one could tell the absolute direction of polarization, from a single piece of polaroid.

They hadn't any idea.

I knew this took a certain amount of ingenuity, so I gave them a hint: "Look at the light reflected from the bay outside."

Nobody said anything.

Then I said, "Have you ever heard of Brewster's Angle?"

"Yes, sir! Brewster's Angle is the angle at which light reflected from a medium with an index of refraction is completely polarized."

"And which way is the light polarized when it's reflected?"

"The light is polarized perpendicular to the plane of reflection, sir." Even now, I have to think about it; they knew it cold! They even knew the tangent of the angle equals the index!

I said, "Well?"

Still nothing. They had just told me that light reflected from a medium with an index, such as the bay outside, was polarized; they had even told me which way it was polarized.

I said, "Look at the bay outside, through the polaroid. Now turn the polaroid."

"Ooh, it's polarized!" they said.

After a lot of investigation, I finally figured out that the students had memorized everything, but they didn't know what anything meant. When they heard "light that is reflected from a medium with an index," they didn't know thatt it meant a material such as water. They didn't know that the "direction of the light" is the direction in which you see something when you're looking at it, and so on. Everything was entirely memorized, yet nothing had been translated into meaningful words. So if I asked, "What is Brewster's Angle?" I'm going into the computer with the right keywords. But if I say, "Look at the water," nothing happens --- they don't have anything under "Look at the water!"

You can have exactly this exchange with people who sell sunglasses in shopping malls. They know that the polarized sunglasses let you see the colors in their otherwise-transparent demonstration thingy, and they know that polarized sunglasses "reduce glare," but they don't (in my experience) know that the glare includes reflections off the floor, or that it comes back if you rotate the sunglasses. (Of course, Feynman was interviewing physics majors, not sales people.)
posted by fantabulous timewaster at 2:20 PM on August 20, 2008

Response by poster: Thanks for the thoughtful answers everybody. (I love this place).
posted by diogenes at 6:06 PM on August 20, 2008

I earned a B.S. in physics. But before I ever took calculus, I developed a deep understanding of physical processes. My advantage was that my father was a college librarian, so nosing through the stacks and finding the good stuff were habits and skills that I acquired very early. I started learning physics intensely in 9th grade, early enough that I'm hardwired for it.

To answer your question: yes, if you start early and read a LOT of good stuff.

While I'm here, I'll recommend Taking the Quantum Leap as a great intro to quantum theory for the layman.
posted by neuron at 9:49 PM on August 20, 2008