tag:blogger.com,1999:blog-69266990119120573952024-02-02T03:50:09.119-05:00Hogg's Teachingphysics, astronomy, statistics, and (now) writingHogghttp://www.blogger.com/profile/18398397408280534592noreply@blogger.comBlogger66125tag:blogger.com,1999:blog-6926699011912057395.post-62325539778177015912019-02-10T10:47:00.001-05:002019-02-10T15:23:49.557-05:00girls aren't the problem; the World is the problem!<p><i>My whole educational world is sharing <a href="https://www.nytimes.com/2019/02/07/opinion/sunday/girls-school-confidence.html">this </i>New York Times<i> article</a>, which argues that we need to modify education to make girls less responsible and more confident, to help them succeed. Here is an email I sent to my faculty (NYU Physics) about this article. I'm putting it here to make it an open letter to universities; what I say about NYU at the end is true of many universities, especially urban ones!</i></p><p>This piece (<a href="https://www.nytimes.com/2019/02/07/opinion/sunday/girls-school-confidence.html">Why Girls Beat Boys at School and Lose to Them at the Office</a>, <i>New York Times</i>, 2019 February 7) captures the point that girls are more responsible workers and better students and more stressed out. All these things are important and show that we should give tons of support to girls here at NYU.</p><p>But then the author’s interpretation is that the problem is with girls. That we should change how girls feel and act. That’s a classic statistical mistake of putting unjustifiable causal structure onto data. Isn’t an equally or even far more plausible explanation that the world is strongly biased against girls and women? See, eg, everything about hiring, promotion, and pay differentials? Then the psychological and behavioral reactions of girls reported in this article actually all make perfect sense as a reaction to this structure. And it’s sensible!</p><p>So I think the piece way over-steps in arguing that girls should change their reactions to things. I think it’s better and more likely correct to argue that girls are reacting rationally to a strongly biased world and we should support and promote them as much as we can. Similar things could be said (and I will say them!) about other disadvantaged groups, obviously.</p><p>But I agree strongly with my colleagues that this is relevant to our work! As I have said many times, NYU is biasing its undergraduate admissions against hard-working female potential science majors in favor of having a hard-to-justify gender ratio. That is making these structural problems even worse for girls!</p>Hogghttp://www.blogger.com/profile/18398397408280534592noreply@blogger.com0tag:blogger.com,1999:blog-6926699011912057395.post-48065994345031060252018-11-18T15:28:00.002-05:002018-11-18T16:02:22.516-05:00your weight is just your normal force!<p>Intro physics textbooks often jump over backwards to deal with the problem that astronauts (say) <i>feel</i> weightless, but in fact they are subject to a gravitational force that is only a few percent less than the gravitational force here on Earth. And then there is all the discussion of why they feel weightless when in fact they have nearly the same weights as we do.</p><p>I <i>simply don't agree</i> with this: In my view, <b>your weight <i>is</i> your normal force against the floor when you are in static equilibrium in your local rest frame</b>. Here are some arguments for my position:</p><dl><dt>the gravitational force is unobservable:</dt>
<dd>It is literally a constituent principle of modern physics that you can't tell a gravitational force from a non-gravitational force in an accelerated reference frame. So if we decide that “weight” is gravitational force, we have decided that weight is completely <i>unobservable</i>. So, presumably, everyone is wrong about their weight, and their weight is actually not a covariant property of anything.</dd>
<dt>everyone becomes right:</dt>
<dd>In the standard textbook view, astronauts are misguided about their weightlessness, as are passengers on the vomit comet. We have to say they “feel” weightless but aren't. Also, we have to say that people on a roller coaster who go over hills and valleys feel lighter and heavier, but when in fact (we have to say) actually nothing has changed. In my new view, the astronauts, passengers, and ride-goers are all correct: They really are weightless (in the space station and the comet), and they really are changing their weight (on the roller coaster) as they ride.</dd>
<dt>museum exhibits don't have to change:</dt>
<dd>It is still the case that you are heavier on Jupiter (if it had a surface) and lighter on Mars! Because the normal force you would feel would be higher and lower. Totally observable, totally true.</dd>
<dt>buoyancy gets taken care of naturally:</dt>
<dd>What does a helium balloon weigh? In the standard gravitational-force sense, something positive. But in the normal-force sense something negative! It has to be <i>tied down</i> to the floor. That seems sensible. Also, even humans have a buoyant force acting on them, it decreases their weight (in my view, but not in the standard view). Like should a doctor's office multiply everyone's weight measurement by (1+1/800) to account for buoyant force? They should if weight is weight is gravitational force, but not if weight is normal force. Again, this also connects to observability, and also the correctness of visceral feelings (like your feeling of weightlessness in a swimming pool). [Modification made later: Will Kinney (SUNY Buffalo) makes a great point: Your inner ear feels the normal force you would have with no abnormal buoyant force, whereas your feet on the floor feel a normal force that is modified if you are in a denser medium, so the buoyancy point here is complex to say the least.]</dd>
<dt>it disambiguates weight from mass better:</dt>
<dd>Mass is a gravitational charge, or an inertial constant. Weight is a force. If weight is going to be a force, it should be an observable, measurable force. Preferably the force you actually feel when you say “I feel heavy”. So make weight the observable force, and mass something to be inferred by inertial and gravitational arguments.</dd> </dl><p>The funny thing about all these changes is that they change nothing in natural language or natural discussion of weight, and they greatly simplify physical discussions of weight. They also make it less true that physics is in <i>Physics Land (tm)</i> where all your intuitions are wrong! I hate <i>Physics Land (tm)</i> and this redefinition of the word <i>weight</i> tears down one of its (many, many) walls.</p>Hogghttp://www.blogger.com/profile/18398397408280534592noreply@blogger.com0tag:blogger.com,1999:blog-6926699011912057395.post-28588110048521854132018-06-30T07:01:00.001-04:002018-06-30T07:56:30.642-04:00manipulating betting odds into probabilities and other odds<p>A colleague and I wanted to enter into a bet on a group-stage game of the World Cup of Football. We wanted our bet to have the following structure: He pays me something if Team A wins, I pay him something if Team B wins, and we push (that is, neither of us pays) if it is a draw between Team A and Team B. We are friends, so we wanted to give reasonable odds on this bet. How to calculate them?</p><p>Online, we saw the following odds posted on a reputable sportsbook (yes, such things exist) in European style:</p><p><table><tr><td>Team A wins</td><td>1.625</td></tr>
<tr><td>Team B wins</td><td>6.710</td></tr>
<tr><td>tie </td><td>3.910</td></tr>
</table></p><p>Is it possible to convert these data into what we want to know? Of course the answer is yes, but we need to make assumptions. Before we continue, I should note that these odds would be written in American style as follows:</p><p><table><tr><td>Team A wins</td><td>-160</td></tr>
<tr><td>Team B wins</td><td>+571</td></tr>
<tr><td>tie </td><td>+291</td></tr>
</table></p><p>Because that may be confusing, let's just check in on what these odds mean. Looking at the European odds, what they mean is that if I bet $100 that Team A wins, I will be paid $162.50 if they do indeed win. That is, I will be paid back my $100 plus $62.50 in winnings. If I bet $100 that there will be a draw, then I will be paid $391.00 (my $100 plus $291 in winnings) if they do indeed draw. Looking at the American odds, what they mean is that if I bet $160 that Team A will win, I will be paid $100 in winnings plus my original bet back, or a total of $260, if they do indeed win. And they mean that if I bet $100 that Team B wins, I will be paid $571 plus my original bet back, or a total of $671, if they do indeed win. The +/- sign at the beginning of those odds makes a big difference! So in this sense, to a scientist, usually the European-style odds writing makes more sense.</p><p>Strictly, what's written in European-style odds is not the odds, but the odds-plus-one. If the book was not out to make money—If the book was just trying to break even—then these odds would be the book's approximation to the inverse of the probabilities of the outcomes. If you want to see why, you can think about placing a Dutch bet: Putting money on each outcome in proportion to the probability. If you do that, and the odds are just right, then you will get the same payout no matter what the outcome. That's an exercise to the reader! But if we interpret these European odds as inverse probabilities, then the implied probabilities of the various outcomes would be:</p><p><table><tr><td>Team A wins</td><td>0.615</td></tr>
<tr><td>Team B wins</td><td>0.149</td></tr>
<tr><td>draw </td><td>0.256</td></tr>
</table></p><p>Which you can get just by inverting the numbers in the first chart. The observant reader will notice that these three numbers don't add up to one! They add up to a bit more than one. Why? Because the book is making money, and so they pay out odds slightly lower than what's fair, which means that they have an edge over the bettors, on average.</p><p>Now if we make the assumption that the book is relatively capable (or that the betting public is pushing the book's odds to something sensible), then we can assume that these are close to the correct probabilities for the three outcomes. That's a great start! But remember that we want odds for a win bet, with the draw as a push. The idea is, we want to know: What's the probability that Team A wins <i>given that there isn't a draw</i>. For that we condition on there not being a draw and re-normalize that probabilities. Probabilities for these outcomes are:</p><p><table><tr><td>Team A wins (conditioned on no draw)</td><td>0.805</td></tr>
<tr><td>Team B wins (conditioned on no draw)</td><td>0.195</td></tr>
</table></p><p>I got these by re-normalizing the two outcomes my colleague and I care about to get unity. Now we can convert to European-style odds by inverting again, and the odds we get are:</p><p><table><tr><td>Team A wins (conditioned on no draw)</td><td>1.242</td></tr>
<tr><td>Team B wins (conditioned on no draw)</td><td>5.128</td></tr>
</table></p><p>That is I should bet $100, and my colleague $24.20, and whoever wins gets it all. If there is a draw, we take our money back. Or at larger stakes, I should bet $412.80, my colleague $100, and so on.</p>Hogghttp://www.blogger.com/profile/18398397408280534592noreply@blogger.com0tag:blogger.com,1999:blog-6926699011912057395.post-34302216568865197412018-05-05T10:13:00.001-04:002018-05-05T10:19:26.067-04:00freshwater consumption<p>I'd like it to be a theme of my writing about teaching that I learn as much as any student in my class when I teach! It certainly is a fact. This semester has been huge for me because I'm teaching a subject I don't know much about (sustainability), and because I am teaching <i>writing</i>, which is a first (yes, in 25 years of teaching, I have never taught writing).</p><p>A few weeks ago I gave a (writing) assignment to estimate global freshwater needs by computing your own freshwater needs and extrapolating to the world. Then compare with estimates of global usage. My expectation: That a typical American college kid uses <i>way</i> more water than a typical person on Earth, and this would be a lesson about disparity. I wasn't wrong, but I also wasn't right either:</p><p>It turns out that global freshwater use is way larger than any estimate of your own personal water use, extrapolated to the globe! Isn't that odd? It's because global freshwater use is not dominated by household uses like laundry and toilets (which, by the way, don't need freshwater). It is dominated by <i>agriculture</i>. If you add in your own share of agricultural water use, a typical American uses way more than the average human! But it is hard to know or estimate this without significant engineering research.</p><p>There was one clue, however, in the essays I got: One student included the amount of water used to water a lemon tree in their dorm room. It was a trivial amount of water, so it was almost a joke. But then if you think about how much food we eat relative to the miniscule annual production of that tiny lemon tree, there is a little window into just how much water we must use for agriculture.</p>Hogghttp://www.blogger.com/profile/18398397408280534592noreply@blogger.com0tag:blogger.com,1999:blog-6926699011912057395.post-5959388404684068182018-04-03T17:31:00.000-04:002018-04-03T17:33:32.459-04:00Is the greenhouse effect like a greenhouse?<p>I am teaching a class at NYU this Spring that I am loving: It is called (with grandiosity) <i>The Art and Science of Approximate Reasoning: Physics, Sustainable Energy, and the Future of Humanity</i>. We are computing what we can about sustainability, from a physics perspective and with order-of-magnitude reasoning. The strangest thing about the class (for me) is that it is a <i>writing</i> class. So I am grading writing assignments, something I am certainly not qualified to do.</p><p>I have learned <i>a huge amount</i> in this class. Here's one tiny, tiny example:</p><p>How does a greenhouse work, and is it anything like how the greenhouse effect on Earth works? The answer is extremely cool. In both cases (greenhouse and greenhouse effect) the system permits visible radiation to enter, but deters infrared radiation from escaping. In this sense, the two effects are very similar.</p><p>However, there are critical differences: In the case of the greenhouse, much of the effect is that the glass walls cut off convective cooling to the upper atmosphere. That is, they trap the heat near the heated ground, not letting it mix with the rest of the atmosphere. This effect probably dominates over the infrared-reflectance effect of normal glasses and plastics. The fundamental point is that (to first order) the Sun heats the Earth, which then heats the atmosphere. If part of the Earth is put inside a glass box, that part gets to hold its heat without sharing it entirely with the surrounding atmosphere. And indeed, greenhouses control their temperatures through ventilation management (management of convection to the outside).</p><p>In the case of the greenhouse effect, increasing the CO2 (and water and methane and so on) in the atmosphere increases the opacity at infrared wavelengths, so the Earth can't cool radiatively as efficiently as when the atmosphere is more infrared-transparent. That certainly is an effect in greenhouses, but not the only effect, and probably not the dominant effect.</p><p>The Earth's atmosphere can only cool (to space) radiatively, so the greenhouse effect is purely an adjustment of that radiative cooling. The human-built greenhouse can cool radiatively or convectively, and it uses both of those mechanisms for heat management.</p>Hogghttp://www.blogger.com/profile/18398397408280534592noreply@blogger.com0tag:blogger.com,1999:blog-6926699011912057395.post-29662937685125135702017-09-07T09:59:00.002-04:002017-09-07T10:01:29.289-04:00the total eclipse<p><i>[This is an excerpt from a longer description I wrote for friends. The eclipse took place (for us) at 10:21 local time on 2017-08-21.]</i></p><p>We viewed the eclipse from high ground in central Oregon near Walton Lake in the Ochoco National Forest. We chose a viewing location with clear views to the WNW, and set up tripods, camera equipment, and a small refracting telescope with a solar filter. As the eclipse began, forest service and fire crews showed up at our location to watch. We gave them some of our excess eclipse glasses. Late in the partial phase, our shadows became really strange, with corners and pinpricks in our shadows turning into thin crescents. The light became strange—dark and direct, like the world was under tinted glass—and it started to get cold.</p><p>The eclipse glasses were magical; the full disk of the Sun could be viewed comfortably and inspected, and the cut from the Moon was dramatic. Through our small telescope, sunspots were visible. Another crew at our site had a larger reflecting telescope set up, also with a Solar filter. They had an astounding view of the sunspots.</p><p>But the transition from even a tiny sliver of visible Sun to totality is astonishingly stark! At totality, the sky became dark enough that we could see a few stars and planets. The corona of the Sun could be viewed directly without the glasses, and it was visible by eye out to a full Solar Diameter away from the eclipse limb. There was lighter sky at the horizon, and it was pink like a sunset in every direction! That, along with the enormity of the corona, was the most surprising thing about the eclipse for me. It was dark everywhere like late dusk, with late sunset on every horizon. It got cold enough that those of us fortunate enough to have brought sweaters to the viewing point put them on. The corona of the Sun was almost triangular in shape, with a dark black hole where the Moon lay.</p><p>Towards the end of totality (that is, about 2 minutes after the beginning of totality), we could see the light racing towards us from the WNW: The more distant hills lit up first. At the very last moment of totality a tiny pinprick of sunlight appeared on the limb of the sun making, with the ring-like corona a "diamond ring". Instantly it was too light to look at directly and we put our glasses back on.</p>Hogghttp://www.blogger.com/profile/18398397408280534592noreply@blogger.com0tag:blogger.com,1999:blog-6926699011912057395.post-47028345211026291322017-01-29T09:43:00.000-05:002017-01-29T09:43:10.384-05:00does the Earth really go around the Sun?<p><i>tl;dr:</i> Executive summary: It is not fundamentally true that the Earth goes around the Sun; it is just easier to calculate things that way.</p><p>We like to say that the critical event that started the scientific revolution is the discovery that the Earth goes around the Sun, and not the other way around. This was incredibly important; the hypothesis by Copernicus led to the immensely important data-taking by Tycho Brahe and the quantitative, theoretical explanation of it by Kepler. Galileo's discovery of moons of Jupiter bolstered the case in important ways, and Newton's quantitative description of it all in terms of the inverse-square law solidified it all into an edifice of great importance, that is just as important and valuable today as it was then. It is also a great example of how a scientific discovery requires both observational and theoretical backing to become confidently adopted by the community.</p><p>In the 20th Century, Einstein brought us General Relativity, with the eponymous generality granting us immense coordinate freedom. That is, there are (infinitely) many ways we can make decisions about what is stationary and what is moving, and what we choose as reference points. In some choices, calculations are harder. In other choices, calculations are easier. In yet others, certain symmetries become more obvious or more valuable for making predictions. That is, GR delivers to us lots of choices about how to think about what's moving and how.</p><p>So the crazy insane thing is this: <i>In GR, there is no answer to the question</i> of whether the Earth goes around the Sun or whether the Sun goes around the Earth. There is literally no observational answer to the question, and no theoretical answer. All observations can be incorporated to an analysis from either perspective. The question of which goes around which is <i>not a question you can ask in the theory</i>.</p><p>That said, it really is far, far easier to do calculations in the Copernican frame. Indeed, absolutely all calculations of Solar System dynamics are done in this frame with post-Newtonian code. The way I see it (with modern eyes) is that Copernicus's hypothesis was based on <i>parsimony</i> or <i>simplicity</i> and was adopted for that reason. Brahe and Kepler confirmed that the data are consistent with Copernicus's simple model (though with the eccentricities added). After Brahe and Kepler it was still <i>possible</i> to understand the observations in an Earth-centered (or even stranger) coordinate system, but was <i>far, far easier</i> to do calculations in the heliocentric frame.</p><p>Even today, now that GR is our model of gravity, we still calculate the Solar System with Newtonian codes (with adjustments to approximate GR corrections). And even today, now that we have this amazingly accurate model of the Solar System, we still often calculate the positions of celestial bodies by looking at paths on the celestial sphere, as did Ptolemy. How we calculate something is incredibly context-dependent, and doesn't always respect our most fundamental ideas. And the <i>truth</i> of Copernicus's hypothesis really just represents the <i>pragmatism</i> of the present-day mathematical tools. All these thoughts bolster my rejection of <i>scientific realism</i> and play into questions of social construction and so on. It also bolsters my view that Ockham's Razor should be thought of as a statement about calculation, not <i>truth</i>.</p><p>Sure the Earth goes around the Sun! But let's remember that this is a statement about calculation and pragmatism, not <i>the fact of the matter</i>.</p>Hogghttp://www.blogger.com/profile/18398397408280534592noreply@blogger.com7tag:blogger.com,1999:blog-6926699011912057395.post-27668481132519330762016-08-28T17:47:00.000-04:002016-08-28T17:56:27.397-04:00where's the information?<p>It came up frequently in discussions this summer (and last): Where is the information (in, say, a spectrum of a star) about some parameter of interest (say, the potassium abundance of the star, or the radial velocity), and how much information is there? The answer is very simple! But the issues can be subtle, because there is only calculable information <i>within the context of some kind of model</i>. And by “model” here, I mean a probability density function for the data, parameterized by the parameters of interest. That is, a likelihood function.</p><p>The fast answer is this: The information about parameter θ is related to the (inverse squared) amount you can move parameter θ and still get reasonable probability for the data. The nice thing is that you can compute this, often, without doing a full inference. It is easiest in linear (or linearized) models with Gaussian noise! That's the question we will answer here.</p><p>When you have a linear or linearized model with Gaussian noise, there are derivatives of the expectation Y for the data with respect to the parameter of interest, dY/dθ. Here (for now) Y is an N-vector the size N of your data, and θ is a scalar parameter (let's call it the velocity!). So the derivative dY/dθ is an N-vector. The information about θ in the data is related to the dot product of this vector with respect to itself: The accuracy with which you can measure θ given data with Gaussian noise with N×N covariance matrix C (possibly diagonal if the N data points are independent) is:</p><p>σ<sub>θ</sub><sup>-2</sup> = [dY/dθ]<sup>T</sup> C<sup>-1</sup> [dY/dθ]</p><p>where σ<sub>θ</sub> is the uncertainty on θ. That is, the inverse variance on the θ parameter is the inner product of the derivative vectors, where that inner product uses the inverse variance tensor of the noise in the data as its metric! Here we have implicitly assumed that the vectors are column vectors. When the N data points are independent, the C matrix is diagonal, as is its inverse. Note the units too: The inverse variance tensor has inverse Y-squared units, the inner product uses the derivatives to change this to inverse θ-squared units.</p><p>(When there are multiple parameters in θ—say K parameters—the inner product generalizes to making a K×K inverse covariance matrix for the parameter vector, and the expected variance on each parameter is obtained by inverting that inverse variance matrix and looking at the diagonals.)</p><p>But we started with the question: Where is the information in the data? In this case, it means: Where in the spectrum is the information about the velocity? The answer is simple: It is where the data—or really the inverse variance tensor for the noise the data—makes large contributions to the inverse variance computed above for θ. You can think of splitting the data into fine chunks, and asking this question about every chunk; the chunks or pixels or data subsets that contribute most to the scalar inverse variance are the subsets that contain the most information about θ.</p>Hogghttp://www.blogger.com/profile/18398397408280534592noreply@blogger.com0tag:blogger.com,1999:blog-6926699011912057395.post-36810928787017721042016-08-14T08:25:00.000-04:002016-08-21T10:14:26.121-04:00walk or take the elevator?<p><i>I'm just generally excited about getting back into the classroom after a long sabbatical. I'm thinking about problem-set problems for the Physics Majors. Here's what's in my head right now:</i></p><p>NYC has had a hot summer, with most buildings running air conditioning on a thermostat continuously. To save energy, NYU (and other large entities in NYC) asked their employees to conserve energy in various ways, some of which we might take issue with. Here's an uncontroversial one: You should take the stairs, not the elevator.</p><p><i>But is that uncontroversial?</i> What considerations are required to figure out whether this policy would reduce or increase energy consumption? Obviously—if you take the stairs—you use less elevator energy, but then you drop a metabolic load on the building air-conditioning. Which uses more power in the end? Use a combination of web research and simple physical arguments to make cases, and identify weaknesses in your argument as you change assumptions. Things that matter include: Neither humans nor elevators are 100-percent efficient delivery vehicles for potential energy (in fact, can you see a fundamental argument that elevators <i>must</i> spend more than 50 percent of their energy generating heat?). Elevators are heavy but counter-weighted. Some buildings have very busy elevators, so your contribution to the elevator load is only the <i>marginal contribution</i>; in other buildings you are typically the only person in the elevator. Air conditioning systems have efficiencies limited by fundamental ideas in thermodynamics, but are probably much less efficient than the limits. And so on!</p><p><i>Thanks to Andrei Gruzinov (NYU) for starting me thinking about this one.</i></p>Hogghttp://www.blogger.com/profile/18398397408280534592noreply@blogger.com0tag:blogger.com,1999:blog-6926699011912057395.post-1371493605839858392016-02-07T09:48:00.001-05:002016-02-07T10:03:08.030-05:00Syllabus (the book)<p>I just read <a href="http://www.amazon.com/Syllabus-Accidental-Professor-Lynda-Barry/dp/1770461612/"><i>Syllabus</i> by Lynda Barry</a>. It is a set of syllabi and daily in-class instructions, along with some reflections, from a few years of teaching cartooning and writing at Wisconsin. It is a combination of hilarious and insightful, both about learning to draw and cartoon, but also about the practice of teaching.</p><p><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgaeNwEsFMISJ-6DTNbGddzT_8jI1qe6PhrFJIpkCKAslVHAPRisCeS8mpl7g-71u5Q2VIrYamAv327pZVsP5XurEMtP0O9xKb5i9nXmCJvZLFjwU1AUwVTpkFJGQA6gsBB6kkgKq0vvUQ/s1600/IMG_2429.jpg" imageanchor="1" ><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgaeNwEsFMISJ-6DTNbGddzT_8jI1qe6PhrFJIpkCKAslVHAPRisCeS8mpl7g-71u5Q2VIrYamAv327pZVsP5XurEMtP0O9xKb5i9nXmCJvZLFjwU1AUwVTpkFJGQA6gsBB6kkgKq0vvUQ/s1600/IMG_2429.jpg" /></a><br />
<i>A page from Lynda Barry's </i>Syllabus.</p><p>The syllabi and daily exercises include many great practices. For example, when students are listening to something (being read or previously recorded), she has them either draw tight spirals in their notebooks or else color in a line drawing. She has the students sketch in <a href="http://www.dickblick.com/products/staedtler-non-photo-pencil/">non-photo blue pencil</a> and ink in later; it reduces inhibitions. She has simple forms for students to write daily diary or journal entries so that they make close observations of the world, in words and pictures. She loves most the students who have never drawn (since childhood), and she makes exercises that capitalize on their newness (and defeat those who are more experienced at rendering), like forcing them to do drawings in increasingly short time intervals.</p><p>The book is hilarious in part because she shows lots of great student work (it is not clear she has proper permissions here, because she does not individually credit each student drawing), and because the whole book is a collage of drawings, writings, and found objects, in the Lynda Barry style. I doubt there is another book out there on teaching that makes you laugh out loud all the way through.</p><p>A great question for me is what of Barry's practices could carry over to a class in Physics?</p>Hogghttp://www.blogger.com/profile/18398397408280534592noreply@blogger.com0tag:blogger.com,1999:blog-6926699011912057395.post-4295886823986492922015-09-14T14:36:00.000-04:002015-09-14T14:37:56.837-04:00Make it Stick<p>I just read <a href="http://www.amazon.com/Make-It-Stick-Successful-Learning/dp/0674729013"><i>Make it Stick</i></a>, about research-based results in how people learn and the implications for education. I loved it; it is filled with simple, straightforward ideas that will be useful in the classroom. For example, it is better to do many low-stakes quizzes than a few high-stakes exams. For another, it isn't useful for students to re-read the textbook, and it <i>is</i> useful for the lectures and the textbook to be misaligned. For another, students' perception of their learning is often wrong and misguided. For another, it is useful to interleave topics and not just do “massed practice”. It points out that it is very adaptive for learners to believe that their brains are plastic and their abilities are not innately limited. Luckily this also appears to be true. All of these things will come into my next pre-health (or other big) class. And I will explicitly explain to the students <i>why</i>.</p><p>My quibbles with the book are few. One is that they slag off unschooling, and then immediately follow with a long profile of a Bruce Hendry, who is a perfect example of the power of unschooling (he is entirely self-taught through self-directed projects of great importance to himself!). I also found the writing repetitive and a bit slow. But the book is filled with good ideas. Also, it is not just informative, it is <i>responsible:</i> The authors clearly differentiate between research findings and speculations or over-generalizations of them. This is a great contribution to the literature on teaching and learning.</p>Hogghttp://www.blogger.com/profile/18398397408280534592noreply@blogger.com1tag:blogger.com,1999:blog-6926699011912057395.post-44418305742099867202015-01-27T08:09:00.000-05:002015-01-27T08:09:45.076-05:00emission lines from stars<p>At the end of Mike Blanton's brown-bag talk at NYU yesterday, Matt Kleban asked: Why don't stars produce emission lines; why only absorption lines? Maryam Modjaz said "because they are hotter on the inside and cooler on the outside". That's true! But it is slightly non-trivial to see why the consequence is <i>always</i> absorption-lines only. And does it mean that if the stars were cold, condensed objects bathed in a hotter radiation field, they <i>would</i> produce emission lines? (I think the answer here might be "yes"; think of a gas cloud bombarded with ionizing radiation.) Also Kleban pointed out that actually the <i>very</i> outside of the Sun is in fact hotter than the surface, which is true, but it must be that this is just so optically thin it barely matters.</p><p>In some ways, the biggest paradox about stars is that they aren't all the <i>same temperature</i>: After all, the "surface temperature" of a star is the temperature around the place where the photosphere becomes optically thin; shouldn't this be around 10,000 K for all stars? After all, that's the temperature around which hydrogen atoms recombine (see, for example, the CMB). I don't know any simple answer to this paradoxical question; to my (outsider) perspective it seems like the answer is always all about detailed atomic physics.</p>Hogghttp://www.blogger.com/profile/18398397408280534592noreply@blogger.com1tag:blogger.com,1999:blog-6926699011912057395.post-30693860143706269932014-11-14T09:48:00.000-05:002014-11-14T09:48:41.593-05:00oscillations and the metric<p>In class, I was solving the normal-mode problem for a solid object near equilibrium, using generalized coordinates, in the usual manner. This starts by orthogonalizing the coordinates to make (what I call) the "mass tensor" (the tensor that comes in to the quadratic kinetic-energy term) proportional to (or identical to) the identity. This operation was annoying me: Why do we have to get explicit about the coordinates? The whole point is that the coordinates are general and we don't have to get specific about their form!</p><p>In my anger, I solved the problem without this orthogonalization. It turns out that this solution is easier! Of course it is: I can do everything with pure matrix operations.</p><p>I had two other in-class epiphanies about the problem. The first is that the solution you get when you <i>don't</i> do the orthogonalization is more analogous to the simple one-dimensional problem in every way. The second is that, in a <i>D</i>-dimensional problem with <i>D</i> generalized coordinates, the tensor that goes in to the kinetic energy term is some kind of spatial metric for a <i>D</i>-dimensional dynamical problem. (Or proportional to it, anyway.) That is simultaneously obvious and deep.</p>Hogghttp://www.blogger.com/profile/18398397408280534592noreply@blogger.com0tag:blogger.com,1999:blog-6926699011912057395.post-69580322786251248552014-10-22T20:44:00.000-04:002014-10-22T20:44:41.309-04:00many-body systems; composite objects<p>Every time I teach mechanics (and this is something like the 21st year I have taught it at the undergraduate level) I learn something new. This week we are talking about many-body systems; I had two epiphanies (both trivial, but still): The first is that the description of the object in terms of a center-of-mass vector and then many difference vectors away from the center of mass (one per "atom") is purely a coordinate transform. Indeed, it is just generalized coordinate system that is related to the Newtonian coordinates by a holonomic transformation. Awesome! So when the Lagrangian separates into external and internal terms, this is just a result of the appropriateness of that transformation.</p><p>The second is that the definition of the many-body system is completely arbitrary. It should be chosen not on the grounds of being bound or solid or connected but rather on the grounds of whether choosing it that way simplifies the problem solution. Both of these realizations are simple and obvious, but it took a lot of teaching for me to get them fully. I am reminded as I realize these things that the physics concepts we expect first-year undergraduates to manipulate and be comfortable with are in fact pretty damned hard.</p>Hogghttp://www.blogger.com/profile/18398397408280534592noreply@blogger.com0tag:blogger.com,1999:blog-6926699011912057395.post-38546369478916149362014-09-14T09:45:00.001-04:002014-09-14T09:45:40.667-04:00air resistance, again<p>I should stop complaining about air resistance, but I can't help myself! I am teaching this semester from <a href="http://www.amazon.com/Classical-Mechanics-5th-Edition-Kibble/dp/1860944353/">Kibble & Berkshire</a>, and in Chapter 3 there are problems about air resistance that use speeds of around 100 meters per second and an atmospheric drag law that is proportional to velocity to the first power. I don't think there is <i>any</i> physical system that could have these properties: If you are small enough to have viscosity matter, you can never go 100 meters per second. Well, I guess <i>molecules</i> can go that fast, but <i>(a)</i> that isn't what the authors have in mind, and <i>(b)</i> molecules aren't really well described by continuum mechanics!</p>Hogghttp://www.blogger.com/profile/18398397408280534592noreply@blogger.com0tag:blogger.com,1999:blog-6926699011912057395.post-69893086420911188362013-01-22T04:21:00.001-05:002013-01-22T04:27:48.226-05:00the answer "that question is ridiculous" must be accepted<p>My friends who work in education of the young (the 'fuzz included) like to quote studies that show students answering without comment or concern questions like "Farmer Jake has 13 sheep and walks them 21 miles. How old is Farmer Jake?" There are many mixed-up reasons for this problem; some relate to rote learning; some relate to the artificial dichotomy set up between reading and math; some relate to the decontextualized ways we teach math; some relate to the testing environment that saturates schools; and so on. I feel all these things!</p><p>Imagine we want to see students using their common sense and their judgement with every question they consider and answer. I think <a href="http://howdy.physics.nyu.edu/index.php/Undergraduate_physics_education">that would be good</a>. How do we foster this kind of thinking and exercise of common sense? I think we have to let the students call "bullshit".</p><p>Here's an example: "Johnny has twelve toy cars. He gives eight to Frances. How many does he have left?" Obviously we should accept the answer "four". But we should <i>also</i> accept the answer "<i>No way!</i> Who would give <i>more than half</i> of his toy cars to someone else?" If we don't accept that answer, we are saying to the students "calculate without thinking". That might be okay for quantum physicists (though I disagree), but it isn't okay for the rest of us.</p>Hogghttp://www.blogger.com/profile/18398397408280534592noreply@blogger.com2tag:blogger.com,1999:blog-6926699011912057395.post-67304310893592893172012-12-02T10:39:00.000-05:002012-12-02T13:29:15.213-05:00bad physics of Total Recall<p>On the airplane home from <i>Spitzer Science Center</i> and <i>LIGO</i> I made the mistake of watching the new <a href="http://www.imdb.com/title/tt1386703/"><i>Total Recall</i> (2012 <q>remake</q>)</a>. (I also made the <i>good</i> decision to watch <a href="http://www.imdb.com/title/tt1409024/"><i>Men in Black 3</i></a> but that is not relevant to this post.) Central to the story is a tunnel through the Earth through which a train called <q><i>The Fall</i></q> goes from Britain to Australia in 17 minutes. Important to the plot is a <q>gravity reversal</q> on the journey in the core of the Earth, where the riders on <i>The Fall</i> are briefly weightless, and their chairs rotate from one orientation to the opposite so they are reoriented for arrival.</p><p>As everyone in first-year physics (well, for Physics Majors anyway) ought to calculate, the no-air-resistance, free-fall time for this journey (indeed on any straight chord through the Earth) is about 45 minutes (yes, identical to the time to go half-way around the Earth ballistically). That means that if riders were <i>weightless</i> for the <i>entire journey</i> the crossing would take 45 minutes.</p><p>The fact that <i>The Fall</i> does the journey <i>faster</i> than that would mean not one gravity reversal but <i>three gravity reversals</i>, because you would have to start the journey accelerating <i>faster</i> than gravity, and end the same. So the whole thing, which was obviously so highly thought out and worked out for the story, was just straight-up wrong.</p><p>I think if we ever <i>do</i> dig a chord-like tunnel through the Earth (the <i>Chunnel</i> is getting close to the relevant scale), we probably <i>should</i> run the trips at 45 minutes, because I think for pretty deep reasons this will be very close to minimum-effort travel times. In thinking about this, I have also thought about the relevant engineering gains and safety losses incurred if the <i>Chunnel</i> were operated evacuated of air or at low pressure. There were also idiotic things in the movie related to the implied air pressure, temperature, and air flow in the tunnel outside <i>The Fall</i> but these are more subtle. I digress.</p><p>Actually, the excellent <i>MIB3</i> was even more physically unrealistic than <i>Total Recall</i> (bad time travel and so on), but the tone of the movie made it absolutely clear that you were expected to <i>cut them physics slack</i>.</p>Hogghttp://www.blogger.com/profile/18398397408280534592noreply@blogger.com0tag:blogger.com,1999:blog-6926699011912057395.post-50810860711444649312012-11-28T02:04:00.001-05:002012-11-28T02:04:53.883-05:00LHC energy and momentum<p><i>Problem: The LHC delivers 8 TeV per particle in bunches of 10<sup>11</sup> particles. What is the kinetic energy and momentum of a bunch, in SI units and then as compared to (a) a small-caliber bullet and (b) a Major-League baseball pitch?</i></p><p>I get that the bunch has far more kinetic energy than either a bullet or a baseball pitch, but far <i>less</i> momentum. A LHC particle bunch would burn you badly, but it wouldn't knock you down! Of course there are some 10<sup>9</sup> bunches per second, so you don't want to be hanging out in the beam line when it's running.</p>Hogghttp://www.blogger.com/profile/18398397408280534592noreply@blogger.com0tag:blogger.com,1999:blog-6926699011912057395.post-51158576817992212752012-04-26T16:12:00.000-04:002012-04-26T16:12:48.188-04:00scientific teaching?<div dir="ltr" style="text-align: left;" trbidi="on"><p>I am on a committee at NYU (related to NYU's Morse Academic Program) in which we were given copies of <a href="http://handelsmanlab.sites.yale.edu/sites/default/files/Scientific%20Teaching.pdf">this article on scientific teaching (PDF)</a> by Handelsman <i>et al.</i> The article has many sentences that include the word <q>should</q>, which is a little annoying, but the worst thing about it is that it advocates, repeatedly, basing our teaching methods on scientifically demonstrable successes, measured with metrics. I don't object to being scientifically accountable, and I, for one, use the research-supported techniques of active learning, participatory classroom activities, and peer instruction. However, the article goes on about metrics <i>without giving a single clear example</i>. Why? Because they don't want to undermine their point by bringing up controversial testing strategies. However, we can't be metric-driven if we don't have metrics! So let's all just stop talking about the philosophy of being <q>scientific</q> and find some metrics that we can agree on. I, for one, haven't found anything I like. After all, the goal of physics education is <i>not</i> to create students who perform better on isolated, decontextualized exams like the Force Concept Inventory!</p></div>Hogghttp://www.blogger.com/profile/18398397408280534592noreply@blogger.com0tag:blogger.com,1999:blog-6926699011912057395.post-77264532707385409682012-02-26T17:46:00.000-05:002012-02-26T17:46:24.102-05:00aha moments<p>I have been pleased to get a few <q>aha</q> moments out of my undergrads this semester in the small, advanced <a href="http://cosmo.nyu.edu/hogg/em2/">NYU E&M II</a> class I am teaching. The best was when we looked at the Poynting vector in a highly symmetrical ribbon-like circuit with a perfectly cylindrical resistor and we could see the power flowing from the battery to the resistor in the pure field geometry. That's nice! The point of the class is radiation, primarily, so we are about to start really doing that to death.</p>Hogghttp://www.blogger.com/profile/18398397408280534592noreply@blogger.com0tag:blogger.com,1999:blog-6926699011912057395.post-28395586663584676532011-11-12T18:17:00.001-05:002011-11-12T18:24:51.390-05:00what's the right answer?<p>In her K/1 class (ages five to seven), the 'fuzz was doing "the weather" when an argument broke out between those who thought the clouds "move the Sun around" and those who thought the clouds "block out the Sun". She let the discussion proceed, encouraging contributions. In the end, the "move the Sun around" group got the consensus. What to do? You can correct them all, and then they learn that scientific truths are handed down by more knowledgeable authorities ("How do you know the Universe is expanding?" "I read it in a book."). Or you can let it lie, in which case they go home thinking they know something that in fact is wrong. Or (best, but extremely time-consuming), you can go through the process of having them turn their pseudo-scientific explanations into <i>predictions</i> about other phenomena, or have them extrapolate their model into other domains, and then see why or where it breaks. That's (to my mind) the only solution you could possibly call <i>science</i>, but it would require an absolutely radical replacement of the current curriculum and structure of school. The 'fuzz didn't have the right (it was someone else's classroom) to blow the schedule, and she didn't want to be a priestess, so she let it lie and moved on to the next activity.</p>Hogghttp://www.blogger.com/profile/18398397408280534592noreply@blogger.com1tag:blogger.com,1999:blog-6926699011912057395.post-33211569390991270682011-09-14T23:27:00.000-04:002011-09-14T23:27:12.700-04:00vectors and their derivatives<p>The time derivative of velocity is acceleration, both vectors of course. But I was reminded in office hours today of just how hard it is to get across the idea that the velocity vector and the acceleration vector can point in totally different directions. And some students have trouble seeing this when a ballistic stone is going upwards along some (parabolic) arc, some have trouble seeing it when it is going down, and some have trouble seeing it at the top. That is, different students have very different problems visualizing the differences of the vectors over time.</p><p>I said in lecture that this issue was <q>deep</q> but I didn't emphasize it enough. I feel like it is so big it almost needs its own week!</p>Hogghttp://www.blogger.com/profile/18398397408280534592noreply@blogger.com0tag:blogger.com,1999:blog-6926699011912057395.post-1706563038871769642011-09-05T06:30:00.002-04:002011-09-05T06:33:27.994-04:00Stokes vs ram pressure<p>Macroscopically, air resistance is ram pressure (proportional to cross-sectional area times velocity squared). Microscopically, drag is Stokes-like (proportional to radius times velocity). Where does the cross-over happen? I didn't have the guts to put that on <q>problem set one</q> of my course for pre-health students, but it will be in around problem set eight. It <i>could</i> be on problem set one, because the transition can be obtained purely by dimensional analysis.</p><p>In transport processes, there are often qualitatively different effects working at small scales than at large. Another good example is diffusion vs convection.</p>Hogghttp://www.blogger.com/profile/18398397408280534592noreply@blogger.com0tag:blogger.com,1999:blog-6926699011912057395.post-21652196613249547702011-09-03T06:18:00.000-04:002011-09-05T06:31:09.530-04:00what does a future doctor not need to know?<p>My big challenge in preparing my <a href="http://cosmo.nyu.edu/hogg/gp1/">General Physics I</a> syllabus is to figure out what to <i>cut</i>, when the majority of the students are pre-health. I cut thermodynamics, because we have learned that it is taught also in chemistry (and other places). I then wanted to add more material about fluids and elastic solids (pretty relevant to medicine, it seems), so what to cut? I ended up cutting most of rotation, spinning, and angular momentum. Why? To understand the body, you <i>do</i> need to know about torques (how does your arm work, static structures, and so on) but you don't really need to conserve angular momentum. Or do you? The centrifuge spins, but it doesn't have angular <i>dynamics</i>.</p><p>(I <i>will</i> be doing the centrifuge.)</p>Hogghttp://www.blogger.com/profile/18398397408280534592noreply@blogger.com1tag:blogger.com,1999:blog-6926699011912057395.post-65530941985377313162011-07-15T03:08:00.002-04:002011-07-15T03:11:14.976-04:00parallax distance<p>The parallax distance to an object is the distance you get by moving your (single) eye's position by a transverse distance <i>x</i>, measuring the angular displacement θ of the object given that move, and dividing the transverse distance by the angle.</p>
<p>Problem-set problem: You are outside after the rain late in the day and you see a rainbow. What is the parallax distance to the rainbow?</p>
<p>(Thanks to Andrei Gruzinov at NYU.)</p>Hogghttp://www.blogger.com/profile/18398397408280534592noreply@blogger.com12