Good explanations Science is usually presented as a set of *results*, facts and formulas to be memorized and applied on final exams. F=ma. E=mc^2. Atoms are made of protons, neutrons and electrons, yada yada yadum. That is *not* what this is about. There will be some of that, but the point here is not to talk about the results so much as the *process* that *led* to those results and how you can apply that *process* to your own life. Understanding general relativity and quantum field theory can be intellectually satisfying, but it's not the main attraction unless you aspire to be a physicist. The goal here is to teach you how to use the scientific method to give you leverage in everyday life. The scientific method (I'm going to just start calling it "science" even though that's a little misleading because the totality of science encompasses a lot more than just the scientific method, but writing out "the scientific method" all the time is going to get tedious) is all about seeking *good explanations*, which immediately raises the question: what *is* a good explanation? How do we distinguish good explanations from bad ones? It it just an aesthetic choice, or is there some objective criterion? (Spoiler alert: it's the latter.) A crucial point that I want to mention up front is that a *good* explanation is not necessarily the same as a *correct* explanation. We actually saw an example of that in the last installment when I told the story of how I assumed that I was being bullied because of some aspect of who I *was* (and which I therefore could not change) rather than something about my *behavior* (which I could change). The first explanation turned out to be *wrong* but it wasn't really a *bad* explanation. People *do* get bullied because of who they are, particularly if they are geeky Jewish immigrants in South. So the idea that this might be happening to me wasn't absurd on its face. In fact, even after an explanation is shown to be wrong that doesn't necessarily make it a bad one. The poster child for this is gravity, which, it is proclaimed to school children the world over, is an attractive force between massive objects that causes, among other effects, apples to fall off trees. That explanation of falling apples turns out to be *wrong* (the *correct* explanation is that space-time is curved -- just take my word for it for now), but it is not *bad*. Remember, the scientific method works by finding *good* explanations, not necessarily *correct* ones. If you act as if gravity were an attractive force you will not go very far astray. Even NASA uses this when designing spacecraft trajectories, and if it's good enough for NASA it's probably good enough for you. Now, don't get me wrong. All else being equal, a *correct* explanation is much more likely to be a *good* explanation than an incorrect one, so your odds of finding a good explanation gets much better if you eliminate incorrect explanations from consideration. But it's not strictly necessary. So what makes an explanation *good* if not correctness? There are four criteria: 1. It has to account for all known observations, or at least all of the observations in the domain that you care about. If you care about what happens near the event horizon of a black hole then explaining gravity as an attractive force won't work. But if you don't care about that, if you limit your attention to what happens here on earth, or even just in our solar system, then the attractive-force explanation works just fine. 2. Nothing in the explanation can be changed without causing it to fail to explain some of the known observations (again, in the domain that you care about). 3. The explanation includes the absolute minimum number of things that you have to include in order to allow it to explain all of the observations (in the domain that ... ah, you know the drill). 4. The domain can't be empty or facetious, i.e. the explanation has to explain something that someone actually cares about in good faith. That last criterion is pretty vague, so let me illustrate it with a famous example of an explanation that fails this test: "There is a teapot in orbit around the sun half way between the orbits of earth and Mars." This example is called "Russell's teapot" because it was invented by the renowned philosopher Bertrand Russell. It is a bad explanation not because it is false (though it almost certainly is) or even because it isn't falsifiable (it is) It's a bad explanation simply because it doesn't explain any observations, or at least not ones that anyone cares about. The situation could very well have been different. For example, suppose someone reported actually seeing something in orbit between earth and Mars. Russell's teapot teapot *would* explain that observation. So would Russell's coffee pot or Russell's bowling ball or an alien spacecraft or (by far the most likely) an asteroid. *Any* of these things would explain the observation equally well, so the teapot explanation fails by the second criterion: it contains an unnecessary detail (the teapot) which can be removed without reducing its ability to explain the observation of *something* in orbit between earth and Mars. The situation changes yet again if someone reports seeing a *teapot* in orbit between earth and Mars. Now we can no longer reject Russell's teapot as an explanation of this observation on the basis of containing an unnecessary detail. However, this *still* does not make Russell's teapot the best explanation possible. Much more likely is that the observer made some kind of mistake or was hallucinating or was telling a tall tale. Let's take it one step further: suppose *many* people report seeing the teapot. The Hubble space telescope takes photographs of it. A space probe is dispatched to retrieve it and bring it back to earth. The teapot is put on display at the Smithsonian Air and Space Museum. Does *that* make Russell's teapot a good explanation? Well, yes and no. It's probably the best explanation for the observations themselves. The reason that the Hubble telescope was able to take photos of it, the reason that you can go to the Smithsonian and see it, the reason it has an explanatory plaque describing its provenance, is very likely to be that there is in point of actual physical fact a teapot that was retrieved from orbit (as opposed to mass hallucinations or an elaborate conspiracy). But that immediately raises another obvious question: how in the world did a teapot end up in orbit in the first place? And so *for the question that we are now naturally led to care about* the mere proclamation that there is a teapot is not an explanation at all, it is the thing that cries out to be explained. The important point here is that the quality of an explanation *depends on context*. It depends on what you care about, and it depends on what you have actually observed. Russell's teapot was deliberately designed to be a plainly ridiculous example, but note the similarity to a less ridiculous case from the real world: there are people who report having experienced the presence of supernatural beings. One possible explanation of these reports is that there are supernatural beings in point of actual fact, and that the people who report experiencing their presence do so because they are, again in point of actual fact, in the presence of actual supernatural beings. It is possible that the people who report being abducted by aliens have in point of actual fact been abducted by aliens. It is possible that people who claim to have seen Bigfoot have in point of actual fact seen Bigfoot. If we want to reject any of these explanations we cannot do so on the basis of criterion #4. (Homework: on what basis *can* we reject these?) The reason for belaboring this is that too many people emphasize *truth* or *falsifiability* or the *ability to make testable predictions* as the gold standard of a scientific explanation. They aren't. Russell's teapot is falsifiable. It makes a testable prediction. But no one in their right mind would take it seriously enough to want to test it, and *that* is what makes it non-scientific. But it is important to note that this is context-dependent. If people suddenly start to care about celestial teapots for some reason, or if someone actually sees a teapot out there, that could change. Being falsifiable and making testable predictions is neither necessary nor sufficient for being a good explanation. Let's put these criteria to the test with a more realistic example. There are people who believe that the earth is flat. Can we debunk them -- can we reject flat-eartherism as a bad explanation -- based on the four criteria above? You might be tempted to reject on the bases of criterion #4 because flat-eartherism isn't an *explanation* at all, it's just a *proclamation*, a naked claim: the earth is flat. But this isn't true. Flat-eartherism is advanced as an explanation for all manner of observations, not least of which is that the earth *looks* flat when you are standing on its surface. Nowadays we know (or at least we think we know) that the earth is round because, among other reasons, we have maps that show it's round. We have photos taken from space that show it's round. There is an overwhelming consensus that it is round. But how do we know those are actually photos of earth taken from space and not the product of some elaborate conspiracy? Or, if we cast ourselves back to a day before space travel was possible, how could we know that the earth is round back then? For that matter, even if we manage to convince ourselves that the earth is round *now*, how can we be sure that it was always so? Maybe it was flat once and became round? These turn out to be a surprisingly challenging questions to answer, but it is a challenge well worth undertaking because it illustrates how even a very convincing-sounding argument can actually be *wrong*: the story of how humans first (as far as we know) figured out that the earth is round involves an ancient Greek named Eratosthenes who lived between 276 and 194 BC. Carl Sagan tells us about him in his book Cosmos: "The discovery that the Earth is [round] was made [by] a man named Eratosthenes. ... He was an astronomer, historian, geographer, philosopher, poet, theater critic and mathematician. He was also the director of the great library of Alexandria, where one day he read in a papyrus book that in the southern frontier outpost of Syene, at noon on June 21 vertical sticks cast no shadows. On this the summer solstice, the longest day of the year, shadows of temple columns grew shorter. At noon, they were gone. The sun was directly overhead. It was an observation that someone else might easily have ignored. Sticks, shadows, reflections in well, the of the Sun - of what possible importance could simple everyday matters be? But Eratosthenes was a scientist, and his musings on these commonplaces changed the world; in a way, they made the world. Eratosthenes had the presence of mind to do an experiment, actually to observe whether in Alexandria vertical sticks cast shadows near noon on June 21. And, he discovered, sticks do. Eratosthenes asked himself how, at the same moment, a stick in Syene could cast no shadow and a stick in Alexandria, far to the north, could cast a pronounced shadow. Consider a map of ancient Egypt with two vertical sticks of equal length one stuck in Alexandria, the other in Syene. Suppose that, at a certain moment, each stick casts no shadow at all. This is perfectly easy to understand - provided the Earth is flat. The Sun would then be directly overhead. If the two sticks cast shadows of equal length, that also would make sense of a flat Earth: the Sun's rays would then be inclined at the same angle to the two sticks. But how could it be that at the same instant there was no shadow at Syene and a substantial shadow at Alexandria? The only possible answer, he saw was, that the surface of the Earth is curved..." But Sagan is wrong! This happens to be the *correct* answer, but it is *not* the only *possible* answer. There is at least one other possibility given the information that we have been given in the story. Take a moment before you continue to see if you can figure it out on your own. It's not hard. (Hint: imagine putting two vertical sticks on the floor about a foot apart and shining a flashlight on them.) There's a clue in the next sentences: "Not only that: the greater the curvature, the greater the difference in the shadow lengths. The Sun is so far away that its rays are parallel when they reach the Earth." In order to show that the earth is round from the shadows cast in different places, the fact that the sun is very far away is *crucial*. If the distance to the sun is comparable to the size of the earth then the sun can cast different shadows in different places at the same time even on a flat earth. Of course, we modern humans "know" that the sun is very far away. But how could Eratosthenes have known? The answer is: he didn't. The earliest recorded estimate of the distance from earth to the sun was made by Aristarchus of Samos, who lived between 310-230 BC. So Eratosthenes probably knew of Aristarchus results, but there are two problems. First, Aristarchus got the answer wrong by a factor of 20. This is not quite the slam-dunk it appears to be because Aristarchus's answer was *too small* by a factor of 20, but the actual distance to the sun is so huge that even this colossal mistake doesn't materially change the conclusion. The bigger problem is that Aristarchus's method for estimating the distance to the sun *assumed* that the sun and the moon were spheres. Again, it turns out that this assumption is correct, the sun and the moon really are spheres (more or less), and this obscures the fact that the reasoning is actually wrong. Because if you're willing to assume that the sun and the moon are spheres, then there is a much more direct way to reach the conclusion that the earth is a sphere; simply add that to your list of assumptions! After all, what reason do you have to believe that the earth is *not* a sphere? The *only* evidence you have is that it looks flat when you're standing on its surface, but that is just was it feels like to stand on the surface of a sphere that is a lot bigger than you are. In fact the entire debate about whether or not the earth is flat is a red herring because "flat" is just a special case of "round". As the earth gets bigger and bigger, it appears flatter and flatter to someone standing on its surface. "Flat" is just the extreme where the radius of the earth actually becomes infinite! The entire flat-earth debate completely evaporates when cast in its proper light as candidate *explanations* for *observations*. The only observation for which a flat earth is a good explanation is that it appears flat to a human-sized observer standing on its surface. But that can also be accounted for by an earth that is not flat, just really big (compared to a human). But let us seriously consider for a moment the possibility that the flat-earthers are right and there really is a conspiracy. So we can't trust NASA nor the cartographers nor the GPS manufacturers. The only thing we can trust is observations that we personally make ourselves without the use of any fancy technology. With those constraints, is it possible to show that the earth is round? This turns out to be quite challenging, and there is a *reason* that it is challenging. I've already alluded to it: from the perspective of a human on the surface, the earth actually *is* very nearly flat! It is only on scales much larger than we are that the roundness of the earth really comes into play, and those large distances are not readily accessible to use without the aid of modern technology. But there is one observation that we can make that definitively debunks a flat earth: time zones. Now, flat-earthers have an explanation for time zones. They claim that the sun doesn't shine uniformly, but that it is focused on particular places like a cosmic spotlight, and so different places get lit up at different times. Fair enough except for one problem. There is one observation that anyone (or at least any non-blind person) can make with no technological assistance that definitively eliminates this possibility. See if you can figure out what it is. I'll give the answer next time.