Externalize your Thinking
In a physics problem, there is usually more information than you can comfortably keep in your head at once. You need a good diagram, a good list, a good way of keeping track of information. The diagram/list/table/picture should represent what you know up until this point.
If you’re having trouble solving a problem, ask yourself this question: “Is everything I know represented in my diagram?”
It’s important to put even seemingly self-evident stuff into your diagram, because sometimes what’s holding you back is that you haven’t seen all the implications of what you know is true. Put the obvious stuff in your diagrams because then you’ll see the less-obvious implications.
Problem solving is a process of taking one small step at a time. With a really good problem, you probably won’t be able to see the solution, or even how to get to the solution, until you are nearly there. Instead, you just keep asking yourself “what can I try now?”
You just keep adding things to your diagram, trying things out, getting more information, until patterns start to emerge.
Solve a Simpler Problem
A good example of this is what xkcd calls “The Hardest Logic Puzzle in the World.” I won’t summarize it here- you can go read it and come back.
Back? Ok. This problem is really really hard. First, do step one and figure out a good way to draw the problem, maybe just with L’s for blue-eyed people and R’s for Brown-eyed people.
Then, step two, simplify the problem. Thinking about what a hundred people know (about themselves, and about every other person) is a bit of a stretch. Instead, try this problem with just one islander. Seriously. Just one.
If the guru says I see at least one blue eyed person, then that one guy knows he has blue eyes, and he leaves. Yay! That was easier. At this point, we’ve basically solved the problem. All we have to do is figure out what happens when there are more people.
Try it with two islanders. Then three. Then four. Then extrapolate to 50 once you see the pattern. Easy! Jusy kidding, it’s not easy. But figuring out a simpler problem to solve makes it waaay easier. I won’t deprive you of the logical joy of this problem by telling you the answer.
You could probably simulate being tutored by me pretty well just by asking yourself “what is one thing I can figure out at this point?”
I love asking students this, because it shows them that they already have all the knowledge they need to solve a problem, and the capability to do so, they just need the willingness to try. (Some students of course need some explanations, but you’d be surprised how often students who come to me failing physics and feeling completely confused actually do just great after a couple of meetings and all I said the whole time was “what’s one thing you could figure out?” I exaggerate a little, but not all that much.)
Physics is hard not because there is a lot you have to learn, but because applying the small amount of learned information takes courage. It takes the courage to try something and see what happens and trust yourself that if you try enough things you’ll eventually find your way to the answer.
The problems are often so complex that it’s impossible, until you become an expert, to map out the path to the solution. Instead, you have to just figure out one thing, then another, then another, until a way to find what you’re looking for jumps out at you.
Can you solve for the time? Can you find the total force? Can you find the mass?
(Mass by the way, is often something that drops out. If you find yourself confused because “they don’t give you the mass” then just use m for mass and be happily surprised when it magically cancels out a few steps later.)
Just do whatever you can do, write it all down, be as organized as possible, and you will find the answer… eventually… most of the time.
Use Difference Reduction
One tried and true method for solving problems in any context, including physics, is called difference reduction. In this method, you simply look at what you have and look at what you want and ask yourself, what’s one small change that will make what I have look more like what I want?
I’m starting to feel a little bit like a life coach now, but hey, real life problems are problems too.
Sometimes to move forward you must go back
Have you heard the riddle about the farmer crossing the river with the fox, the goose, and the bag of beans? There are tons of versions of this riddle, but here’s one:
A farmer has a fox, a goose, and a bag of beans and he wants to cross a river. His boat will only hold one item at a time in addition to the farmer. If he leaves the fox with the goose the fox will eat the goose, and if he leaves the goose with the beans the goose will eat the beans. How can he do this?
I’m going to give you a partial spoiler here in about two lines, so if you want to try this on your own now is a good time.
The key to answering this problem is that you have to bring the goose back to the wrong side of the river at one point. The reason this riddle is hard is that it involves moving away from your goal state. You already have the goose on the right side, why would you bring it back?
But, in many contexts, taking a step back is the best way forward. Maybe you move home after college. This feels like the worst step back in the world, but you save money and buy a house and a car much sooner than you would have otherwise. Maybe you’ve been working on a physics problem for three hours and you feel like you’re almost there but you just can’t get the last little bit. This might mean that you’ve actually gone down the wrong path and if you keep on doing exactly what you’ve been doing you’ll never get there and what you really need to do is start over. Before you start over, though, you should:
Take a Break
There is this thing called neuronal activation. Certain neurons in your brain light up, and they have their own associations with them, which makes you more likely to think of things in one way rather than in another. Sometimes if you’re having trouble with a problem it’s because you’re thinking of it in one specific way that isn’t letting you see the route to the answer.
If you take a break you can come back fresh, with different neural pathways activated, which means you might just see the answer right away. (There is some disagreement about whether this is because of the “fresh perspective” or because your subconscious was working on the problem without you. Either way it works.)