I admit, the first time I saw this phrase in print, I was a little put off. Lie-to-children? That sounds like the kind of thing that gets you a lot of extra time in purgatory.
Then I learned more about it and decided that perhaps it wasn't so bad after all. Well, maybe. It still could be bad.
I should explain all that. The first thing I thought when I saw the phrase "Lie-to-children" was that people were talking about the kind of thing that you tell kids because it's convenient, even if in the long run it doesn't help them at all. That's not what it actually is.
What lie-to-children refers to is the type of simplification that happens when you are teaching someone (anyone, it turns out: doesn't have to be a child) about physics, or math, or chess, or any field of human endeavour with a deep and complicated body of knowledge. The idea is that throwing the full force of, say, quantum electrodynamics at a beginner will only turn them off the field all together, so you teach them simplified forms (in this case, simplified electricity and magnetism) that you know aren't entirely correct. Since it wouldn't really be good teaching practice to emphasis their incorrectness at each turn, you're sort of lying. Hence, lie-to-children.
In this sense the concept has some merit. I've come to realize, though, that there's two different types of simplification. One is a type that, while simplified, gives students the right intuition about how the more complicated process works. The other type does the opposite: it is a subject simplified in such a way that students either don't make any progress towards understanding the fuller ideas.
Here's an example of the good type. In high school and early undergraduate physics, we teach students a theory of friction. In this theory, friction forces depend on the materials rubbing past each other (eg rubber on concrete or skin on carpet) and the force pushing them together (gravity in most cases)--and the dependence of friction on the force pushing the two objects together is linear (double the one force, double the other). There's no dependence on the size or shape of the contact area, or any other factors.
Clearly this can't be the complete theory of friction. If it was, then all cars with the same material in their tires would have the same stopping distance, and sports cars wouldn't need fat tires or good suspension for good handling--skinny tires would work just as well. But it works as a lie-to-children because it lets students figure out things like force, energy, and work in ways that serve them well as they move on to more complete forces. (As an aside, the wikipedia article about friction is terrible. Please don't read it unless you want to be seriously confused and misled).
An example of the bad type of lie-to-children is how we teach uncertainty estimates. The most common way of introducing students to measurement uncertainty in high-school and first year labs is to tell them to look at the four or five data points we've told them to collect, and subtract the largest from the smallest to get a range of uncertainty.
Why is this so terrible? For starters, it gives students the idea that a range of uncertainty on a reported value means that the true value cannot possibly be outside of that range. That's an unfortunate idea, though one that even professional scientists sometimes seem to have. It's not the worst of it, though. The worst part of calculating uncertainty this way is that the uncertainty goes up the more measurements you take. Taking more measurements gives you a higher chance of having a particularly large or particularly small one, which makes an uncertainty based on max minus min get larger. This is bad; we want students to get an intuitive feel for uncertainty as a measure of the confidence in a set of data, then we give them a way of calculating it that implies that the more data you have, the less confident you are in it.
I'm not going to go into how I think uncertainty should be introduced in high school. All I want to do here is point out that we need to shift the question from "how can we simplify this body of knowledge?" to "does this simplified version build students' (or readers', depending on context) intuition in the right direction?" If we can do that, the lie-to-children will be a little less of a lie.
Showing posts with label science education. Show all posts
Showing posts with label science education. Show all posts
Wednesday, 28 August 2013
Monday, 15 July 2013
Why E=mc^2 is actually cool
E=mc^2 may be the most famous physics equation in history. Why this is, though, is misunderstood, both by the public at large and even by many physics students (at least ones I've talked to about this).
So, the Public Understanding: Einstein was a super-genius, and he invented E=mc^2. This has something to do with energy. Einstein used this to invent the atomic bomb and win World War II.
Why this is Wrong: Well, Einstein was actually a super-genius. I kind of have a crush on him, to be honest. And he did derive (an important point we'll come to later) E=mc^2. He did not, though, have much to do with inventing the atomic bomb. What's more, E=mc^2 didn't lead straight to the bomb in the sense that most people think it did.
So let's take a step back. The equation we're talking about says that Energy (E) is equal to (=) mass (m) times the speed of light (c) squared (^2). This tells us that (a) mass can be converted to energy, and energy can be converted to mass, and (b) a little bit of mass converts to an enormous amount of energy, since c^2 is a very big number. Now, it's certainly true that the mass of the final nuclei involved in a nuclear bomb is less than the mass of the initial nuclei, and that this change in mass is proportional to the energy released. But that's true of all processes. When I burn gas in my car, the final products are ever so slightly lighter than the initial ones. But I don't credit E=mc^2 with making my car run. So what's up?
The reason we associate E=mc^2 with nuclear (ie, a-bomb) processes and not chemical (ie, gas-burning) ones is basically a matter of technical convenience. When I burn gas, it's easy to measure the energy that came out, but hard to measure the change in mass, because it's incredibly tiny. When I split or collide nuclei, it's hard to measure the energy that comes out, partly because there's so much of it and partly because a bunch of the energy gets carried off by neutrinos, which we can't capture very well. But it's (relatively) easy to measure the mass of the initial and final nuclei, so that's what we do. E=mc^2 is always true, it's just sometimes convenient to use, and other times not.
In any case, most of the effort that went into building the atomic bomb was on rather practical questions like, "How do we separate out the uranium we want from the uranium we don't want?" and "How can we use precision explosives to bring that uranium together in just the right way?" These questions had really nothing to do with E=mc^2.
Now the Common Physics Student Understanding: Einstein was a super-genius, and he derived E=mc^2. This tells us that mass and energy are equivalent, two aspects of the same thing. This changed our view of reality.
Why this is Wrong: Well, it's really not. What it is, though, is incomplete. So to complete it, we have,
Why E=mc^2 is Cool and Important: To understand this, we need to take a look at where the equation came from. Where it came from was two papers Einstein published in 1905 on electricity and magnetism. Einstein starts off this little duology by noting that, at the time, the laws of electricity and magnetism were inconsistent with the laws of motion in a peculiar way. The example he used requires a bit of background, so I'm going to pick a simpler, but equivalent one.
You probably learned at some point that electric current can make magnetic fields--this is how we get electromagnets. In fact, any current, and any electric charge that's moving, creates magnetic fields. This, though, creates a problem. Say I rub a balloon on my head to put some charge on it, then put my charged balloon out in space, a long way away from anything. Now, if the charged balloon is moving, it creates a magnetic field; if it's not, it doesn't. But, how do we know in space what is moving and what is standing still? If one person (normally called Alice) is floating next to the balloon, and another person (normally called Quvenzhané) shoots past, they would disagree on who is moving and who is standing still, and hence they would disagree on whether or not the balloon was producing a magnetic field. But the magnetic field can't both be there and not be there, so we have a problem.
Einstein noted this inconsistency, and found a way to write physics laws in a way that didn't create these disagreements. It was a bit of a weird way, with time slowing down as you sped up, and lengths changing and whatnot, but it worked. And, almost as an aside, it produced the expression E=mc^2.
The details of how that all works aren't really important here. What is important is this: the laws of Electricity and Magnetism (EM), which you can work out with some styrofoam balls and plastic in a high school classroom, imply that every object in the universe has an intrinsic energy that only depends on its mass. Not its internal structure, of what it's made of, just its mass. So E=mc^2, which isn't really about EM, and applies to things that aren't charged or magnetic, and plays a large role in gravity, is embedded in the structure of electricity and magnetism. This should blow your mind. The laws of how electricity works also tell you that everything has an intrinsic energy proportional only to its mass. This is one of the best pieces of evidence so far that there is, in fact, a consistent mathematical structure underlying the universe. That Einstein figured out this implication pretty much cemented his genius status, even if he didn't single-handedly win World War II.
And THAT is why E=mc^2 is cool.
So, the Public Understanding: Einstein was a super-genius, and he invented E=mc^2. This has something to do with energy. Einstein used this to invent the atomic bomb and win World War II.
Why this is Wrong: Well, Einstein was actually a super-genius. I kind of have a crush on him, to be honest. And he did derive (an important point we'll come to later) E=mc^2. He did not, though, have much to do with inventing the atomic bomb. What's more, E=mc^2 didn't lead straight to the bomb in the sense that most people think it did.
So let's take a step back. The equation we're talking about says that Energy (E) is equal to (=) mass (m) times the speed of light (c) squared (^2). This tells us that (a) mass can be converted to energy, and energy can be converted to mass, and (b) a little bit of mass converts to an enormous amount of energy, since c^2 is a very big number. Now, it's certainly true that the mass of the final nuclei involved in a nuclear bomb is less than the mass of the initial nuclei, and that this change in mass is proportional to the energy released. But that's true of all processes. When I burn gas in my car, the final products are ever so slightly lighter than the initial ones. But I don't credit E=mc^2 with making my car run. So what's up?
The reason we associate E=mc^2 with nuclear (ie, a-bomb) processes and not chemical (ie, gas-burning) ones is basically a matter of technical convenience. When I burn gas, it's easy to measure the energy that came out, but hard to measure the change in mass, because it's incredibly tiny. When I split or collide nuclei, it's hard to measure the energy that comes out, partly because there's so much of it and partly because a bunch of the energy gets carried off by neutrinos, which we can't capture very well. But it's (relatively) easy to measure the mass of the initial and final nuclei, so that's what we do. E=mc^2 is always true, it's just sometimes convenient to use, and other times not.
In any case, most of the effort that went into building the atomic bomb was on rather practical questions like, "How do we separate out the uranium we want from the uranium we don't want?" and "How can we use precision explosives to bring that uranium together in just the right way?" These questions had really nothing to do with E=mc^2.
Now the Common Physics Student Understanding: Einstein was a super-genius, and he derived E=mc^2. This tells us that mass and energy are equivalent, two aspects of the same thing. This changed our view of reality.
Why this is Wrong: Well, it's really not. What it is, though, is incomplete. So to complete it, we have,
Why E=mc^2 is Cool and Important: To understand this, we need to take a look at where the equation came from. Where it came from was two papers Einstein published in 1905 on electricity and magnetism. Einstein starts off this little duology by noting that, at the time, the laws of electricity and magnetism were inconsistent with the laws of motion in a peculiar way. The example he used requires a bit of background, so I'm going to pick a simpler, but equivalent one.
You probably learned at some point that electric current can make magnetic fields--this is how we get electromagnets. In fact, any current, and any electric charge that's moving, creates magnetic fields. This, though, creates a problem. Say I rub a balloon on my head to put some charge on it, then put my charged balloon out in space, a long way away from anything. Now, if the charged balloon is moving, it creates a magnetic field; if it's not, it doesn't. But, how do we know in space what is moving and what is standing still? If one person (normally called Alice) is floating next to the balloon, and another person (normally called Quvenzhané) shoots past, they would disagree on who is moving and who is standing still, and hence they would disagree on whether or not the balloon was producing a magnetic field. But the magnetic field can't both be there and not be there, so we have a problem.
Einstein noted this inconsistency, and found a way to write physics laws in a way that didn't create these disagreements. It was a bit of a weird way, with time slowing down as you sped up, and lengths changing and whatnot, but it worked. And, almost as an aside, it produced the expression E=mc^2.
The details of how that all works aren't really important here. What is important is this: the laws of Electricity and Magnetism (EM), which you can work out with some styrofoam balls and plastic in a high school classroom, imply that every object in the universe has an intrinsic energy that only depends on its mass. Not its internal structure, of what it's made of, just its mass. So E=mc^2, which isn't really about EM, and applies to things that aren't charged or magnetic, and plays a large role in gravity, is embedded in the structure of electricity and magnetism. This should blow your mind. The laws of how electricity works also tell you that everything has an intrinsic energy proportional only to its mass. This is one of the best pieces of evidence so far that there is, in fact, a consistent mathematical structure underlying the universe. That Einstein figured out this implication pretty much cemented his genius status, even if he didn't single-handedly win World War II.
And THAT is why E=mc^2 is cool.
Saturday, 13 July 2013
Newton, Gravity, and How People Weren't Total Idiots
There's an unfortunate reality about getting a university degree in science: you end up knowing essentially nothing about the history of science. I was reminded of this recently because there was a relatively large history of science conference happening in the city I live in, sponsored by the school I attend. You would think it might be of some interest to some people in the physics department. You would be wrong. It wasn't mentioned once in the numerous emails I get describing the events of interest going on each day, wasn't discussed by any of the graduate students I ran into that week, and when I did bring it up, I got strange looks, as if, why would someone in physics care about the history of physics.
I'm not saying the state of affairs is all physics' fault; looking over the talks scheduled at this conference made me realize that the academics in the field, like all other fields, are mainly concerned with impressing their colleagues in their subfield, rather than building bridges across related disciplines. Still, it's sad, and these types of divisions mean, among other things, that you can get multiple degrees in science while maintaining a complete lack of understanding or appreciation of how your field came to be.
So hopefully I can do a small part, occasionally, to remedy the situation. Starting with Newton and gravity.
Isaac Newton, as everyone knows, invented gravity. Or discovered gravity. Something to do with gravity. There's two versions of the story. The first one, the one that is vaguely in the heads of non-scientists when they are asked about Newton, goes something like this: Newton was sitting on the ground one day when an apple fell on his head. This made him realize that gravity was a thing, so he told other people about it. They then realized that gravity was a thing and so declared Newton to be a genius.
This version of the story seems to imply that people back then were complete and utter idiots; that no one had ever noticed that things fall down, or commented on it, or thought about why this might be. Clearly, a little bit of though shows that this cannot be a true story.
The version that you get in first year physics is more like this: Ha ha, normal people are dumb, there was no apple. Newton realized that gravity is a force that is proportional to the inverse of the square of the distance between two objects, and also to the objects' masses. That is why he is famous for gravity.
This, while being closer to the truth, in that Newton did propose an inverse square law, doesn't fully explain Newton's fame and lasting influence. Hooke also proposed an inverse square law independently, and neither was the first person to make mathematical statements about gravity and the planets.
Newton's lasting influence arises from a bold claim he made with this theory (and others): that there is a single law of gravity, which applies to apples, and the Earth, and Mars, and Jupiter, and the Sun, and every single body that we can see, regardless of whether it lives in the heavens or the earth. It is this universal nature that sets Newton apart from the people who came before him, and it is that attitude that is perhaps his most influential contribution. Even if you don't remember a single law of motion, or how gravity works in a mathematical way, you know that things on Mars obey the same laws of physics as things on earth, and you believe, without needing it to be proven, that if we ever sent a probe to a planet in another star system, that the same laws of physics would apply there as well. That you believe that is Newton's most lasting contribution to science.
Why does that matter? Well, for one thing, it's always worth remembering that people in the past didn't necessarily think the same way we do now, and there's a lot we take for granted that would have been foreign to them. Prior to Newton (and yes, I know I'm simplifying things by implying it was all due to him), the idea that the universe operated under a set of consistent rules that applied everywhere was wouldn't have occurred to most people. In fact, if you go back far enough, you lose the distinction between the supernatural and the natural completely.
Secondly, in general I think that the more we educate ourselves about how science has worked, and how it works now, the better able we will be to make decisions about the many, many issues that science touches on today.
So there's the history lesson. For more on Newton, I. Bernard Cohen is a place to start. For more on pre-scientific world-views, the opening chapters of The Evolution of God offer a fantastic description.
I'm not saying the state of affairs is all physics' fault; looking over the talks scheduled at this conference made me realize that the academics in the field, like all other fields, are mainly concerned with impressing their colleagues in their subfield, rather than building bridges across related disciplines. Still, it's sad, and these types of divisions mean, among other things, that you can get multiple degrees in science while maintaining a complete lack of understanding or appreciation of how your field came to be.
So hopefully I can do a small part, occasionally, to remedy the situation. Starting with Newton and gravity.
Isaac Newton, as everyone knows, invented gravity. Or discovered gravity. Something to do with gravity. There's two versions of the story. The first one, the one that is vaguely in the heads of non-scientists when they are asked about Newton, goes something like this: Newton was sitting on the ground one day when an apple fell on his head. This made him realize that gravity was a thing, so he told other people about it. They then realized that gravity was a thing and so declared Newton to be a genius.
This version of the story seems to imply that people back then were complete and utter idiots; that no one had ever noticed that things fall down, or commented on it, or thought about why this might be. Clearly, a little bit of though shows that this cannot be a true story.
The version that you get in first year physics is more like this: Ha ha, normal people are dumb, there was no apple. Newton realized that gravity is a force that is proportional to the inverse of the square of the distance between two objects, and also to the objects' masses. That is why he is famous for gravity.
This, while being closer to the truth, in that Newton did propose an inverse square law, doesn't fully explain Newton's fame and lasting influence. Hooke also proposed an inverse square law independently, and neither was the first person to make mathematical statements about gravity and the planets.
Newton's lasting influence arises from a bold claim he made with this theory (and others): that there is a single law of gravity, which applies to apples, and the Earth, and Mars, and Jupiter, and the Sun, and every single body that we can see, regardless of whether it lives in the heavens or the earth. It is this universal nature that sets Newton apart from the people who came before him, and it is that attitude that is perhaps his most influential contribution. Even if you don't remember a single law of motion, or how gravity works in a mathematical way, you know that things on Mars obey the same laws of physics as things on earth, and you believe, without needing it to be proven, that if we ever sent a probe to a planet in another star system, that the same laws of physics would apply there as well. That you believe that is Newton's most lasting contribution to science.
Why does that matter? Well, for one thing, it's always worth remembering that people in the past didn't necessarily think the same way we do now, and there's a lot we take for granted that would have been foreign to them. Prior to Newton (and yes, I know I'm simplifying things by implying it was all due to him), the idea that the universe operated under a set of consistent rules that applied everywhere was wouldn't have occurred to most people. In fact, if you go back far enough, you lose the distinction between the supernatural and the natural completely.
Secondly, in general I think that the more we educate ourselves about how science has worked, and how it works now, the better able we will be to make decisions about the many, many issues that science touches on today.
So there's the history lesson. For more on Newton, I. Bernard Cohen is a place to start. For more on pre-scientific world-views, the opening chapters of The Evolution of God offer a fantastic description.
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