Musings on my faith going into Holy Week 1/n

As I stand on the precipice of entering Holy Week, the holiest, most important time of the year for Christians that the rest of the world kind of (mercifully) ignores because it has only managed to co-opt the Easter Egg and candy part of things, which is literally the least important part, I have been reflecting, as I ought, on what my faith means. A kind of all compassing musing on what it is I believe, why I bother to believe it, and going all the way to "What do I call myself, since 'Christian Scientist' is something other than what I am?" I'm going to try to write as much of it as I can on this blog, because I feel it is important, but being musings I can't promise they will be thesis like. They may ramble a bit. Some may be long and some may be short. If you come here for physics posts, sorry not sorry for the theological interlude.

Holy Week, particularly in the liturgical tradition, throws sharp relief on a lot of doctrinal points that Christians tend to go 'yeah, yeah I know' at and non-Christians think we are crazy for believing. It can also bring up, if you run in the right circles, friendly debates about atonement vs. redemption theology, the sufficiency of Christ's sacrifice, and even the purpose of baptism, getting into the paedobaptism vs. believer baptism debate. The practice of Holy Week is designed to remind us, in case Lent did not, that we are broken, and that Christ died to heal that brokenness, and rose again to usher in the coming of wholeness.

That we are broken is something of which I have no doubt. I don't see how anyone can disagree with it. As my father observed, "The doctrine of total depravity has never lacked for outside proof"[ETA: This is apparently a quotation from G.K. Chesterton]. That Christ died to heal that brokenness I also have no doubt, though this is where a lot of the people I know think I've jumped the shark, so to speak. A fair number of my peers (and superiors and inferiors, I have no doubt) think that my faith is odd, nutty, a bit of a relic or even 'something [I'll] outgrow'. I have no problem with the ones who think the first two, I can understand, though not agree with the third and the  fourth I find unbearably patronizing, but that is neither here nor there. Christianity *is* weird. And a lot of humans have horribly twisted it and corrupted it and I desperately wish we could make those corruptions a thing of the past, though there is something to be said for the devil you know.

So let's get something out of the way before I get any father into recording my theological thoughts. Just make this the first post.

My faith is not just a comfort in bad time (though it is that), or a I'll-go-someplace-nice-when-I-die wishful thinking, or a philosophy, or a way to connect with a larger community. It is in a very real sense *everything* to me. It defines the universe, my place in the universe, the purpose of the universe and myself; it defines my relationship to God, between myself and my family, between myself and my husband, between myself and every human I will ever encounter; it determines my responsibilities to this world, and everyone and everything in it; it is the entire framework on which my life is built. If you striped everything else away, my faith remains.

"How can you be a scientist and a Christian?" is a question I have heard a (frankly) irritating number of times. From both directions, actually. Scientists who are atheists look askew at my ability to trust science if I also believe in a man-god, and Christians with whom I have strong doctrinal disagreements don't trust my soul to be saved if I think we came from monkeys. The question makes as much sense to me as "how can you be a scientist if you are a woman?". If I really believe that God created the universe, and he created us, how can I *not* believe that this universe would be designed in such a way that we, striving to understand it as we follow our natural, God-given curiosity and using the minds He gave us, could understand? How could I not jump at the opportunity to study a master-craftsman's work? If you think I'm crazy for believing in a Creator, or for believing in a Triune God, or a Savior or whatever particulars of my doctrine baffle you  to the extent you doubt my science, you are welcome to check my math. If you think I'm going to Hell because  when the math and science say the universe is 14 billion give-or-take years old, I trust that it's right,  please point me to the passage in the New Testament where this is named as a salvific issue. I'll wait.

That I am a scientist is not a stumbling block to my faith, and  my faith is not a stumbling block to my science. Though I wont go quite so far as Kepler to say that math is the language of God, or even as far as the Belgic confession in favor of natural theology, I will say with the psalmist that the "heavens declare the glory of the LORD" and with Maltbie D. Babcock that "This is my Father's world".

Accepting that I'm qualified to do things

An interesting thing happened last week. Through a very long email forwarding chain, it came to my attention that one of the small, religiously affiliated schools in the area (actually half way between the university and my new city) was looking for an adjunct physics professor to teach an algebra-based physics 2 course during the spring semester. I jumped on the chance, after getting my adviser's blessing, because it's a chance to hone my teaching skills, it would look good on a resume, it's a foot in the door, a little more money coming in, etc. 

But I considered it to be a long shot. It required a master's degree, preferably a PhD, and while I could have my masters by now, I've never bothered with the paperwork and paying for it, so officially I have a bachelor of science and 3 years of grad school. I emailed the contact on the listing indicating my intention of applying. After writing up my CV (I had resumes but no CVs on tap), filling out the application and a phone interview, I have the job, pending the ok from HR. Turns out, I'm the only applicant and they need someone NOW because the person they hired for the entire year bailed after the fall semester. 

So as I'm talking about it with people, I've been say that I got the job because I was the only applicant. That, essentially, I got lucky.

Which is interesting because my husband and I were just reading an article in the Wall Street Journal on Sunday about how women communicate differently in the workplace, and will frequently say that they "got lucky" instead of taking credit for something. Females are socially trained to be self-deprecating, men are trained to brag, was what that part of the article boiled down to. 

As I was walking back from submitting my transcript request, and thinking to myself how I only got the job because they were desperate and I was the only choice, it suddenly hit me that I was doing the self-deprecating thing.

 I am perfectly qualified to do the job as advertised. I love teaching. I prepare before classes, I know what I'm teaching and I'm not afraid to say "I don't know, I'll get back to you" when a question comes up that I hadn't prepared for. I've taught college classes for 3 years, I done lab work and prep work and grading. There's nothing I'm going to learn in my last year or two of research that will help me teach basic physics to non-physics/engineering majors. The only thing my students and my supervisors agree on is that I'm a good teacher.  

When I texted a friend who had helped me with my CV that I had got the job and thanking him for his help, he texted back "Congrats! I doubt I had anything to do with it! You totally deserve the job."

So I'm going to stop saying that I only got the job because I was the only candidate. There is every chance I would have gotten the job if I had had competition. I am a dedicated, knowledgeable, and tested teacher. And I'm going to prove it. 

Basic Physics: Part 0, Section 4: Derivatives

Previously in this series, we covered algebra, trigonometry, vectors and vector multiplication. Now (after more delay than I would have liked) it's time to tackle the elephant in the room--calculus.

No, please don't close this tab! I swear, it's not as scary as you've been told. If you made it through trig and vectors (which, if you are reading this I assume you have) you've really made it through more mind bending stuff than we will need to cover here.

Why cover calculus at all? Aren't there algebra-based physics courses at every university? Yes, yes there are. And anyone who has taught physics with only algebra, trig and vectors will tell you it's actually harder to teach physics without reference to derivatives and integrals. Newton invented/discovered calculus so he could describe his theory of gravity and motion (his notation was abysmal, though). Calculus is the mathematics of change. Algebra is the mathematics of stability. And physics is really boring if nothing ever moves.

Now, depending on when you went to school, learning calculus may have been reserved for the students who were good at math, or who hadn't been told that "math wasn't for them". I am here to tell you this is like telling students who are going to live in another country that they don't need to learn the past or future tense, they can get along just fine with the present tense. Technically, this is true in a lot of cases, but it limits their ability to get everything out of their trip. Try to think of calculus in this way--not as some strange new kind of math, but just a different tense in this language.

We'll begin where most calculus textbooks begin with derivatives. Calculus has a very intuitive explanation of derivatives: they are the slopes of lines. That's it. What makes derivatives interesting is that they give you the slope at any point along a line*. You will generally hear the included caveat that the line must be smooth and continuous, but this isn't a calc class and I'm not going to show you any equations which are not differentiable (capable of having their derivative taken), so we aren't going to worry about that here.

Let's start with the simplest case, a straight line going through the origin of our coordinate system:

In this case, the slope of the line is going to be the same everywhere, and we can find the slope using the tried and true "rise over run" method. In moving 4 units to the right, the line has moved 3 units up, so our slope \(a\) is $$ a = 3/4 = .75 $$ So far so good. Nothing scary or uncomfortable  to date. A little algebra, that's all, and a little reading off a plot. Now, what if we were just given the equation for this line, in the slope-intercept form encountered in algebra class: $$ y = ax$$ $$y = .75 x$$
Still not too bad. And if I had presented this to your first, you probably could have told me the slope of this line just from this--the coefficient of \(x\) gives the slope, so \(.75\). Congratulations, you just took your first derivative without knowing it!

So, if derivatives are that easy, you ask your computer suspiciously, why is there an entire semester of calculus dedicated to it, hmm? Well, two reasons. First of all, because there are way more complicated kinds of lines than straight lines, and second of all, no one dedicates an entire semester to derivatives. They usually also teach limits (proto-derivatives) and numerical integration (proto-integrals) in the same semester. Derivatives are usually 4-5 weeks of the semester, a lot of that learning special cases.

What if I gave you the line with the equation $$ y = x^2 + 3, $$ would you know what it's slope is? It looks similar to the linear equation in slope-intercept form, but you probably have a feeling that the \(x\) being squared complicates things. And it does, since \(x^2\) is a parabola.

Parabola!

Now, you could draw tangent lines at a sampling of points along the parabola, and find the slope of those tangent lines, plot those slope values and approximate the slope of \(y = x^2 + 3\) and you would find that it came close to \(2x\). I can't speak for everyone here, but I find doing that unbelievably boring. Some algebra teacher once made me do that once and  it was tiresome to say the least.

But calculus and the tool of differentiation gives us a much better way.  Remember, mathematicians do not "invent" new kinds of math to torture students and non-mathematicians. They develop new techniques because the old way was inefficient or tedious or just didn't work all that well. Calculus is  a great example of this. Rather than calculating a bunch of individual slope points and extrapolating what we think the slope is, we can find the exact slope with a few simple rules, and a little new notation.

Let's look at our parabola again. So we have the equation $$y = x^2 +3$$ which describes the line itself. If we want to say that we are looking at the equation for the slope of that line we can write it in Leibniz notation as $$ \frac{dy}{dx}$$ which is nice and concise (there is also Lagrange notation and Newton notation). But Leibniz is nice for beginning with because it has a nice math to english translation: the change in \(y\) over the change in \(x\). This is the more formal way to say "rise over run" and is more generally applicable. Also, now that we are finding the slope of the parabola everywhere we call it a "derivative", and we find it by the process of "differentiation".

To find this, we need two rules. The first rule is formally known as the "elementary power rule" but I just learned it as "this is how you do it". For a function \(f(x)\) that has the form (i.e., it looks like or follows the pattern of) $$ f(x) = c x^n $$ where \(c\) is a constant, \(x\) is the variable and \(n\) is a real number (usually integer, but not necessarily) the derivative can always be found in the following manner: $$\frac{df}{dx} = c*n*x^{n-1} $$ If you are wondering what that \(f(x)\) is doing here, since I kinda just started using it, think of it as a way to label a generic equation. You could keep saying \(y=\) such and such, but then it's not always clear which \(y\) you're talking about. If you instead use the notation of Letter(variable) it lets you label both the equation uniquely (function f, function g, function h) and specify which letter is acting as your variable (x, y, z). Neat, huh?

That's it. That is the most basic rule and definition of the derivative. For the special case where there is no variable, just a constant, the derivative of a constant is \(0\). So, to summarize,

1. Given a function \( f(x) = c x^n\), the derivative is \(\frac{df}{dx} = c*n*x^{n-1}\).
2. Given a constant function \(f(x) = c\), the derivative is \( \frac{df}{dx} = 0 \)

So, let's apply these rules to the equation for our parabola.
$$y = x^2 + 3$$
$$\frac{dy}{dx} = (2) x^{(2-1)} + 0$$
$$\frac{dy}{dx} = 2x^1 = 2x$$

And so we find in three lines of calculus the  same answer that a bunch of line drawing and measuring and plotting got you. Let's try another one, that's a little longer.

And really funky looking on a graph.

$$f(x) = 3 x^{5} - 2 x^{2} + x^{-3} $$
$$\frac{df}{dx} = 3*5 x^{(5-1)} - 2*2 x^{(2-1)} + -3 x^{(-3-1)} $$
$$\frac{df}{dx} = 15 x^{4} -4 x - 3 x^{-4} $$

Longer, but still not too bad, right? See, I told you calculus wasn't the terror it was made out to be. One more rule and we've knocked out all the differential calculus we'll need for both physics 1 and physics 2. This rule is called the "chain rule" and it covers almost every other situation we could face outside of a calculus book or more advanced physics. What it is, really, is a short cut when your variable of interest is buried inside a parenthetical expression, instead of having to bother to separate it out by algebra (if it can be separated by algebra at all).

Let's start with something that we could mess around with algebra and get it into a form that our first two rules apply. Let's begin with the equation $$g(x) = (x+2)^2$$ By using the FOIL method, we  find that this could also be stated as $$g(x) = x^2 + 4 x + 4$$ Using the two rules laid out above, we find that it's derivative is $$\frac{dg}{dx}= 2x + 4$$ Now we have something to check the chain rule against.

Displaced parabola!

The chain rule is a way to approach these things methodically, working from the outside in. You start by treating everything inside the parentheses as a block. It does not matter how complicated it is inside the parentheses, or how simple. Treat it all as though it were just the variable. So step one of the chain rule gives us $$\text{ Step 1: } \frac{dg}{dx} = 2 (x+2)^{2-1}$$
Now you take the derivative of what's inside the parentheses, and multiply that result by the result of Step 1. $$\text{Step 2: } \frac{dg}{dx} = 2(x+2)^{1} (1+0) = 2x+4$$
Lo and behold, it's the same result. Now for something this simple is using the chain rule worth it? Maybe, maybe not. But what about something that I don't know how to FOIL, like $$h(x)= (x+2)^{-1/2} =\frac{1}{\sqrt{x+2}} $$

How do you FOIL a square root?! Tell me!

Let's try the chain rule on this and see if it doesn't save us having to look that one up in an obscure algebra text.
Step 1: Ignore what's inside parentheses, take the derivative as if (blah blah) = variable.
$$\frac{dh}{dx} = (-.5)(x+2)^{(-.5 - 1)} $$
Step 2: Take the derivative of what's inside the parentheses, multiply it by Step 1.
$$ \frac{dh}{dx} = -.5(x+2)^{-1.5} (1)$$
Step 3: Simplify if necessary
$$\frac{dh}{dx} = -.5 (x+2) ^(\frac{-3}{2}) = \frac{-1}{2 (x+2)^{\frac{3}{2}}}$$

I can guarantee that that was easier than trying to FOIL a square root. But what about something really nasty, like THIS

Honestly had no idea what this would look like before I graphed it

Behold, the rollercoaster that is $$ k(x) = (x^3 + 2)^{-.5}$$ Surely my nasty, terrifying calculuses gets horrifying and complicated now, heh? Stupid physicistses.

Um, nope. Not really. Let's take a look, shall we?
Step 1: Ignore what's inside parentheses, take the derivative as if (blah blah) = variable.
$$\frac{dk}{dx} = (-\frac{1}{2})(x^3+2)^{(-.5 - 1)} $$
Step 2: Take the derivative of what's inside the parentheses, multiply it by Step 1.
$$ \frac{dk}{dx} = (-\frac{1}{2})(x^3+2)^{-1.5} (3x^2)$$
Step 3: Simplify if necessary
$$\frac{dh}{dx} = (\frac{-3x^2}{2})(x^3+2)^{-1.5}  = \frac{-3x^2}{2 (x^3+2)^{\frac{3}{2}}}$$

Still just 3 bite sized steps.

Ah ha, you say, but what if there are parentheses inside the parentheses? What if I have a russian nesting doll of a problem?

You just repeat step 2 until you run out of parentheses inside parentheses. But I honestly can't say that I've ever seen that happen.

And that's nearly all you really need to know about differential calculus to conquer introductory physics! Hopefully you can see, at least a little bit, why physicists and mathematicians love it. It's like upgrading from a hand drill to a power drill. Or a sheet of sandpaper to a power sander. It might take a little getting used to, but it is a very powerful tool in our toolbox and one that will open up the rules of the physical universe to us in a way that algebra just can't. Because as I said in the beginning, the physical world is dynamic and changing, and algebra is the math of the static and stable.

There are two "special cases" that aren't really special cases that we will need, and they are very easy to use, but a bit lengthy to explain, so I'll cover them in a separate section, partly because they are both really cool, and partly because this post is already pretty long.

If anything is still unclear, or even a little foggy, let me know in the comments and I'll do my best to explain! And I hope to see you next time for integration!

* there are a few significant exceptions to this, which we don't have to be concerned with here. If you are interested in knowing more about these exceptions, brownian motion is a particularly interesting case being continuous everywhere and differentiable nowhere.

Kill the myth of "stupid"

For about a month now, I've been plugging away at a series called "Basic Physics", trying to go through a first year physics curriculum in a way that is understandable to people who aren't in STEM, and may not have even looked at 'math' in years. My mother has kindly been acting as one of the guinea pig for this experiment, reading through posts and giving me feedback on what is or isn't clear, is or isn't helpful. The last post on vector multiplication was particularly difficult for the both of us. It's hard to explain simply, and she really wanted to understand them in the same way she understood the trig section (after some rewrites at her suggestions). Every time we spoke and she said she still didn't get it, she would apologize "for being so stupid".

Now, stupid isn't a word I would use to describe my mother, and I sincerely doubt she has ever honestly been accused of that in her life. I reassured her that these were not easy topics, and pointed out that I had complained to her for at least 2.5 years now that my students, who nominally should walk into my classroom knowing this stuff, don't get it. I added a paragraph of encouragement at the top of the post, which seemed to help because I got this as a response:

ok I realized that I was trying too hard.

I get it now because I accept your math without trying to do it in my head every step.

Bring on the next chapter.

I called her up later in the day to thank her, because I realize that she probably hadn't been looking to learn this stuff before I asked for her help. She is a very gracious woman, and said she was always open to learning, but again apologized for being "stupid".

After we hung up, I realized that this is a refrain I have heard over and over when teaching: "I'm sorry I'm being so stupid". I've heard it from students in class, in office hours, in tutoring sessions back in college, and now from my mother. The general sentiment always seems to be that if they can't get it on the first go round, they are stupid and incapable rather than the reality that the topic is difficult. My students have gone so far as to tell me that I must be far more intelligent than them to understand this stuff.

There is an article in the New York Times today who headline was "Why do Americans Suck at Math?" and I can't help but think that the refrain of "I'm sorry I'm so stupid" and headlines like this are connected. Connected because they reinforce this idea that people "suck" at math in bulk. There is this weird perception that math is something only special people are good at, that you have to have some innate ability to do it and understand it. That people who are good at math look always use the Feynman method of problem solving: write the problem down, think about it, write down the solution. The idea that math people look at a new math topic and go "Oh, of course! Obviously this is true" and run off and use it seems to be weirdly pervasive, both consciously and unconsciously.

Of course, it would be lovely if this were true. I could have whole years of my life back if this were true. And of course it feels nice to be on the math people side of this, because it makes one feel smart and talented when in your work you frequently feel frustrated. It's like payback for the mockery, real or perceived, for being STEM types with all the cultural baggage that goes with it.

But I think it is also incredibly toxic. If math is something only special people can do, then why should ordinary people try? If we ignore or hide away our own struggles with understanding, we encourage this myth and scare people away who, even if they aren't in STEM, might enjoy seeing the beauty of it all. And it is beautiful. Being able to see the world with math and science at your back is awe inspiring, adding a whole new dimension to everything you can look at and experience.

I know very, very few people who haven't struggled to grasp every math and physics concept when they were first introduced. I think I've known two in my entire life. I was on the 'elevated' math track in school, which means I got all the way through AP Calc B in high school. And I still struggled and struggle with math. What my students (and my mother) never saw was me with wikipedia on my laptop and my calc book open as I desperately tried to understand different kinds of integrals, or tests for convergence. They never saw the early mornings, between classes and late nights in the physics lounge with scratch paper everywhere, chalk covered hands, asking anyone who entered the room, "Can you explain this? What is a [cross product, wave equation, probability density, etc]?" The extended arguments that eventually ended up with the stuffed monkey Harold on one of the professor's door in a plea for help. They will never know how much help I got from professors, from other students, from older students as I struggled to learn this stuff that I now seem so natural at. I'm not smarter than them. I was just persistent. When my students see me reduce a fraction on the board, or quickly do a cross product they assume it's just natural to me, like music is natural to my dad. What it really is is 7 years more experience and work.

Now, is there some natural inclination involved? Sure. But not nearly as much as people seem to think. Being good at anything, regardless of natural inclination, requires work above all else. My sister is more naturally inclined than I towards languages; she also studied more and is therefore far more fluent than I am (as in, actually fluent). No matter what your natural talent and inclination, if you never work at it, it will wither and dry up. And while you may never be a prodigy, hard work can get a person far in pretty much anything that's not sports.

People don't seem to believe me when it comes to math and science, so here's an analogy. I enjoy cooking. At this point in my life I am pretty good at it. I can make recipes up on the fly and nine times out of ten they work. I can tell if a cake is done by appearance and a light poke; I know if my steak is done to my liking by touch. Now, is there some natural inclination at work? Maybe. My mother is an excellent cook, and let me mess around in the kitchen at an early age. But mostly it's because I've been cooking for over half my life. Because I read cookbooks and watched masters and purposefully worked on my techniques, my understanding of the underlying food chemistry, the physics of different methods of cooking. Anything I am good at is maybe 5% natural talent, 95% work. Five percent alone gets you absolutely no where. Ninety five percent alone can get you pretty far.

This is something that we need to work on emphasizing more. We need to emphasize fewer Sheldon Coopers and Charlie Epps, boy geniuses grown up and solving MATH. We need to make it clear that what we do is not magic, not the result of some fluke of genetics that gave us special math powers. Something sparked an interest and we pursued it to the best of our abilities. We weren't destined to become mathematicians/physicists/chemists/what-have-you any more than non-STEM people were destined to be librarians/writers/bankers/secretaries/what-have-you. We chose to be what we are, and we worked hard to get here. Of course, this means admitting that we aren't special beings with math vision. But if we want to encourage people to engage with STEM, we need to kill this myth of "stupid".

Basic Physics: Editorial Consortium

The next promised post on trigonometry is in the final polishing stages, but in the meantime I would like a post to mention several people who have graciously agreed to help me in this endeavor to bring the first year of a physics majors schooling in physics to a non-math, non-science types audience.

 I know full well that as a grad student in physics I am a very bad judge of what is and isn't understood or common knowledge. Teaching has helped rein me in enormously, but my students are assumed to have at least basic calculus knowledge. So I anticipated myself having a problem recognizing what needed more explanation, what was over-explained or even patronizing. I don't want to be the detective novel criminal who spells all the easy words wrong and all the hard words right (in reverse, kinda). Dear Husband, my usual editor, is too well versed in math to much use in this particular arena, so I reached out to some other family members, specifically my mother, my sister, and my brother, to help make sure I do this right. I asked them to do this because each of them brings something that I felt I really needed on what I am dubbing my Editorial Consortium.

My mother is in the demographic group, you might say, that always gives me deer-in-the-headlights or horrified looks when I say I do physics and protest it was too hard for them. Though very talented, she has not directed her talents in a STEM field direction. She is, however, the only reason that I can do long multiplication or division and light years ahead of me in mental arithmetic (also cooking, social skills, language, and checkbook balancing). She is also a natural copyeditor of high standards who is not shy of letting me know when I have fallen short of the mark.

My sister, hereafter to be referred to as Sylvia, Historian Extraordinaire, just graduated college with an absurd amount of honors with a major in History and a minor in French, her thesis work (yes, thesis for undergrad) being on Dorothy L. Sayers. She has a good math background, but hasn't used it much, having no call to do calculus as a literary historian. Her one and only basic physics class was the same one in high school that inspired me to physics. She is also representing a group that I want to reach--younger adults--and she would know if a reference is too obscure. She is also incredible at calling me out for being obtuse and/or patronising.

Last, but not least, is my brother, who will start high school in the fall. I included him for three reasons. First of all, he has had all of the math that I claim is required to understand the blog, but has never taken a physics class in his life. He's interested in the sciences, but he is yet untainted by misconception and bad teaching (other than my own). Second of all, it turns out he inherited Mother's copy editing skills and is very good at noting my inconsistent use of single and double quotation marks. Thirdly, I'm curious if the explanations are clear enough for younger persons who might be interested, but don't have much of a background. The flip side of my mother, so to speak.

They have all agreed to read, edit and comment every post that I write in this series. Between them all I think there is a fair shot that I will do what I set out to do. But I won't know if I am actually succeeding unless you, the reader, let's me know. You are the other part of this Editorial Consortium. If something is not clear, if I mess something up or forget something or just plain gloss over with the hated "the reader can obviously see", let me know! There is a comments link below each post. I'd love your feedback.

Basic Physics Part 0, Section 0: Algebra

[This post is the first in a series intending to teach basic physics concepts in a blog format.]

As I mentioned in my introductory post, math is the language of physics. Physics cannot realistically be understood or done without math. While advanced physics requires some advanced math, basic first-year type physics requires some relatively basic math and math concepts. The first math topic that I want to cover is one that everyone who graduated high school should have covered at some point: algebra. 

Algebra has a kind of strange reputation. Among STEM people, it's the boring math that you needed to do to do the REAL math, or at least the non-boring stuff. It carries the same emotional connotations as diagramming sentences. Among non-STEM people, it's the boring math that they forced you to do and you never ever used again.

Until I really got into teaching and my research, I was mostly of the opinion that algebra was best left to machines. It was tedious and beneath my dignity to spend hours and pages rearranging symbols. When I started teaching, I began to understand the subtle power of algebra to make or break a solution. When I finally started to understand my research, I saw not only its power, but its beauty. Algebra is a tool that allows order to arise out of chaos.

To do the kind of physics this series is going to look at, you really only need 2 major algebra skills: the FOIL method, and some equation manipulation skills. The quadratic equation can come in handy, but that is one time that I am ok using a math program for because it doesn't pop up as frequently.

But before we get to that, I think some terminology definition is in order. When I speak of a "variable" I am referring to a symbol that can take on any value on the real number line (i.e., any where between negative infinity and infinity) within the confines of the equation and/or is the quantity we are solving for. A coefficient is a symbol that has a fixed value for that particular problem. Most physics texts I've seen and used have the convention that any letter from p-z can be used as a variable, while letters a-m are used as coefficients. The letter 'n' is a special case because it is typically used for integer numbers only. The letter 'd' is sometimes used as a variable because it's just so convenient to use it to stand for 'distance'. The letter 'o' is never used, because in handwritten notes it can all too easily look like a zero. A constant, for our purposes, is a symbol that has a fixed value that does not change from problem to problem. For example, \( \pi = 3.14159...\) no matter what problem we are doing. A 'term' is a catchall, just denoting that a symbol stands for something, without specifying type.

Now, on to algebra!

FOIL Method

The FOIL method (First Outside Inside Last) is one of the first things I was taught in algebra class, way back in 7th grade. It's basically a method for multiplying mathematical expressions together in a way that doesn't let you double multiply or leave something out.  If you are multiplying just two terms together, say \(a\) and \(b\), its easy to know when you got it all.
$$ (a)(b)  = ab$$
But what if you don't have just two items, but two expressions, \( (a+b) \) and \( (c+d) \) ? FOILing the two expressions makes sure you do all available multiplications without double counting.  You multiply the first terms from each expression, here \( a \) and \( c \), then the outside ones, here \( a\) and \( d\). Then you do the inner ones, \( b\) and \( c\), and the last ones from each expression, \( b\) and \( d\). Thus
$$ (a+b)(c+d) = ac + ad + bc + bd $$
This method can be logically extended to cover expressions with more than two terms, with the corresponding result being proportionately longer.

When I first learned this, it seemed incredibly useless. Why on earth would I need such a simple method? The answer is 'everywhere in physics'. From the simplest two-body problems to the most complex problems I've worked on for research, FOILing turns up again and again and again. Becoming not just  proficient, but a master at this technique has been crucial to my work. It is something that my students consistently underestimate, to their detriment, every semester.

Manipulating Equations

This isn't so much a single method as the Rules of Engagement for math. Equations are pretty flexible, but there are some rules. The underlying principle to these rules is that you have to do the same thing to each side of the equation, and you have to do it to everything on each side. For example, lets say we have this equation $$ 5 x + 2 y = 6, $$ and we want to solve for \( y\). We can start by subtracting \( 5x\) from each side like this $$ 5x + 2y - 5x = 6 - 5x$$ where you can see we have explicitly taken \( 5x\) from each side and thus have not changed the equation. By adding the same thing to both sides, we have effectively added zero, just like if you add a one pound weight to either side of a balance scale, it won't change position.  So now we have the equation $$ 2y = 6 - 5x,$$ but we still have not completely isolated \( y \). So now we have to divide both sides by 2, which is the coefficient of the variable \( y\). $$ \frac{2y}{2} = \frac{6 - 5x}{2}$$ Again, it is important to note that we have done exactly the same thing to both sides of the equation and in the case of division or multiplication we have applied that change to every term. $$y = \frac{6}{2} - \frac{5 x}{2}$$ $$ y = 3- \frac{5}{2}x$$ is the correct solution in this case. Do not, I repeat, DO NOT make the mistake I see so often, which is to only apply the division to one (usually convenient) term. The following 'solution' is wrong for this problem: \( y = 3- 5x\)

In certain cases, this also involves remembering the Order of Operations: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. The Multiplication/Division and Addition/Subtraction orders are less critical, since they are just two sides of the same coin. Division is the same as multiplying by a fraction, subtraction is the same as adding a negative number. But the parentheses-> exponents->multiplication/division->addition/subtraction ordering is inviolate. It is impossible, outside of sheer fluke, to get a correct answer if you do not abide by this rule.

And that's the basics of algebra that you may have forgotten  (accidentally or on purpose) that you need for physics, other than the kind that you, honestly, do intuitively. Next week, we'll cover some basic trig[onometry] that everyone should know.

Basic Physics: Introduction

I have done a few introductory physics posts in the past, but I have never been happy enough with them to continue them as a series. After writing my post yesterday on the problems with science communication, I have thought more deeply about why I wasn't happy with them. I've decided that I didn't like them because they weren't able to adequately explain what I wanted to convey. This is mostly my limitations, but also because I hadn't set in my mind who my audience was, and because I had never done posts that explained what I understood to be background material to the topics.

So, I am going to try again in a more cohesive manner. By which I mean that I am going to do a year-long series of blog posts that roughly coincide with what physics majors (and engineers, and other interested parties) learn in their first year, covering basic classical mechanics, electrostatics, magnetostatics and circuitry.

Why? Why would I do this? First of all, I think it will be good practice for when I (fingers crossed) become a professor. I have mostly been working off of the curricula and methods of other professors--I would like to find my own. Secondly, I want to show that physics isn't "hard". Nearly every time I mention that I do physics for a living, I hear the same story--the person I'm talking to either took it in high school and did miserably, thus putting them off the whole thing, or they never took it because they were never any good at that brainy stuff. I want to write a series that, even if it doesn't make physics converts, gives people the confidence that they understand key physics concepts, and maybe understand why physics geeks geek out over physics.

To that end, I am going to be writing for people who have never taken a physics class, but who have some basic math background. I am going to assume a high school level of education, though even that seems to be a somewhat variable standard anymore. I am not going to hold back on "vocabulary words" as my students put it, because it's a blog and you have instant access to a dictionary, but I will explain any technical terms or words that are used in a manner different from their colloquial usage.

To start out with, I am going to do a series of crash-course algebra, trig, vectors, and calculus, so that we have a common math starting point, and a kind of reference guide. Math is the language of physics and it is very hard to really understand what physics is without being able to speak about it using math. Otherwise you kind of end up with something more like Aristotle's physics than Newton's, simply because it is very difficult to describe it using just words.

Then there will be a longish series on basic classical mechanics, which is the one physics topic most people can grasp with at least a bit of intuition. We have all thrown balls, used a seesaw, and spun in an office chair. It will cover more or less the same material you would see in first semester physics class.

The last part will be on what I have taught for 5 semesters now--introductory electromagnetism, or Intro E&M. This will cover basic electrostatic forces/fields, currents, simple circuitry and basic magnetism.

I'm going to try to stick to a schedule of posting one a week, again, roughly like it would be in a classroom setting. This will also give me enough time (hopefully) to properly proof read them and weed out errors.

So, without further ado, on to Part 0, Section 0: Algebra!

The problem with science communication

As a break from everything else that's been going on lately, I've been reading/watching a variety of what could be largely lumped as "science communication" blogs/videos. While I've been doing so, I of course have run across the odd "why do science communication?" post. The answers usually boil down to geekery ("because science is so cool and people should know it"), political ("If everyone were more science literate, they would vote X"), or humanitarian ("if people understood [this], they wouldn't be hurt by [that] or taken in by charlatans"). These are  by no means bad motives for doing these things. And I utterly agree that science communication is a critical activity in our day and age.

But, why? Why is science so hard to communicate that we need not only institutionalized communication (e.g. science class), but grassroots efforts, from blogs to podcasts to videos to local science festivals? Humans have been communicating stuff to each other for centuries. We have developed a wide variety of methods and tools for convincing people of things. Heck, we have a whole industry dedicated to it (advertising). Why does science communication seem so hard to do sometimes?

First, there is the sheer logistical reality of it. The better you understand a topic, let's say optics since I know that one, the deeper you've gone into it and the more that subject and it's prerequisites have become second nature to you. You now now Maxwell's equations almost instinctually. You have a gut reaction when you see velocities faster than \( 3*10^8 \ . You either stopped asking what was waving or have dug really deep into it, but either way you probably can't explain it in 100 words or less to the average person on the street.  On the other hand, the less you know the topic, the easier it is to explain at your level of understanding to someone who doesn't know much or anything, because you remember being in that state.

I have slowly started to realize this as I've been teaching problem solving sessions for the past five semesters. When I started out, I was not remotely confident in the topic. I had taken a few courses beyond the level I was teaching, but I knew I didn't really *know*, in the sense of understanding and internalizing, even basic electromagnetism. My algebra/calculus was shaky because I didn't do it all day, everyday, and hadn't really touched it in 8 months (I took some time off between undergrad and grad school).

So everytime I taught, I had very very detailed notes explaining the calculation to myself, because I knew I couldn't do it unprepared. My students were able to follow my solutions (handwriting permitting) because I wrote everything out, every single step, no "and it can easily be shown that", no "clearly, this equals". It was there. But my analogies to explain the weirdness of electromagnetism were terrible. I mean, really really terrible. Confused, convoluted, mixed. And I didn't have a sense of the background of my students, what they would or would not be familiar with.

Now, I do algebra and calculus for my PhD research. My dining room table, my chalkboard, my whiteboard, my desk, random napkins are full of equations. I sit and do page after page (and redo page after page) of math. I've gotten better at recognizing common algebraic patterns. I no longer have to FOIL simpler multiplications. I do not question the utility of sines and cosines. It's obvious! So my worked out solutions in class have started to skips steps. Bit by bit, I assume a higher level of math literacy from my students. My analogies and metaphors have, generally, become better. I no longer mix metaphors, I stick with one main metaphor throughout a topic, and I don't use analogies to things that my students have no idea what that is. So while my students feel less baffled by my words, I get a dozen of them before and after class asking how we got from point A to point B in an equation.

And this is I think a hurdle science communicators have to face.  The best ones are good in their field. They breathe physics, chemistry, biology, what have you. It's a core component of their being and they are excited to share it with you. But it also means that they are far away from the confusion and doubts of their audience. They need to practice that skill of empathy which, at least in pop culture, we famously lack. It's not an easy skill, to put yourself back at that point of confusion and try to talk to that person. It's like trying to teach a small child something that is to you so easy you don't think about it, like tying your shoes. The best thing is to have a non-STEM friend to test out your explanations on, but even they can be a biased sample depending on how frequently you try to explain your work to them.

The second problem, as the many youtube comment sections to these videos attest, is that science bumps up uncomfortably against areas of worldview and identity for people. The world is a big, nasty, confusing place and people build their worldviews and identities in a way that, fundamentally, tries to make them feel safe, even if it is a very weird and convoluted safety. For example, conspiracy theorists, whatever their theory of choice, want to believe that someone is in control. The idea that violence or disease or natural disaster  just happen, is intolerable. Far preferable that a malevolent and powerful group somewhere is in charge than we being hostages to fortune.

And this is even harder than empathy for confusion, because it does not require a  shoveling on of better explained facts, or more facts. It requires the mindset of a missionary instead of a teacher and it is a very different mindset. Its also a mindset that makes many scientists uncomfortable. Science isn't a religion, it isn't faith, it's fact. Facts exist whether you want them to exist or not. But science is increasingly touching areas of our lives that are not experienced as fully rational, where strong beliefs are preexistent and the science communicators job is no longer to make clear something that was not thought of or not understood, but to modify or replace beliefs. And it is a much longer process.

I feel it is important to note here that science communicators should also be aware of where to stop. There is a fine line between  teaching scientific truth and teaching your world view.  Most of the time I have seen science communication blow up is where that line is crossed. For example, please, by all means explain the correct mechanisms for evolution and the strength of evidence we have for it. The minute you say "See? You don't need a god to make this work after all" you have lost any ground or good will you may have gained.

I think we could borrow a bit from missionaries, modified to our needs. One of the classic techniques for missionaries is to talk to people, and begin from their starting point. The missionary can then more easily lead in small steps to the point where the next step is faith or not faith. I don't see why would couldn't develop a similar method for science communication where the problem is not information but belief. Again, using evolution as an example. Starting with something close to home (antibiotic resistant infections), moving further afield to elephants losing their tusks as a defense against ivory poaching, to dogs from wolves, making the gradual transition from 'microevolution' to 'macroevolution' to a final understanding that it is all just 'evolution'. But again, changing beliefs is not fast. It requires investment.

So, what is it that I am trying to say? Are we doing science communication badly? Should we stop doing it unless we can be just great? NO. By no means. What I am saying is that we already have a community of science communicators who are really good at what they do. Dr Skyskull has a great blog for weird physics, occasionally cats and horror. Myles Power has a bunch of great videos largely debunking bad science/logic in a fairly respectful manner even if his language is a little coarse to american ears. JimTheEvo has a really cool series on infection, evolution and human history*. My point is that we can be even better. Maybe by focusing our audience, maybe just by being more thoughtful. I think it might be time to move to the next level.


*I know they are all males. The women scientist blogs I read are less explaining and more linking to it things people would know. Powered by Osteons does a great job pointing out where bioanthropology intersects popular culture, for example.

School Related Miscellany

Today,  I learned two interesting facts about the progress on my PhD, from an administrative standpoint. The first interesting thing is that, credit wise, I could graduate in a year.  The second interesting thing is that I have six months to select and recruit a thesis committee, create and defend my prospectus.

The first news is good, if a little irrelevant. It means that publications, not credits, are going to be what stands between me and the piece of paper that gives me three extra letters after my name as well as the authority to teach at the college level. Publications are slightly more in my control, since if it came down to credits, I can only take so many at once.

The second new is not bad news, its just a little frustrating. I should have learned this last January. In theory I could have learned it from reading the course catalogue, but the program description is  written in a maddeningly opaque manner. I *think*, so long as I can corale the necessary professors in a reasonably quick manner, that it can be done by early fall. At least that is what I am aiming for, which means it will be done by the December deadline. So maybe I can graduate in like a year and a half? Fingers crossed? I'm still going to say "something like 3 years" to any relatives who ask. Last time I tried to give something more concrete they started sending me "congrats on graduating" cards severely prematurely.

In other news, my little brother graduated middle school today, on the high honor roll to boot! I know it's cliche, but I can remember when he was born, so it's weird to have him graduate middle school, be something like a half foot taller than me and sound exactly like my dad on the phone*. I'm so proud of him, and I can't wait to see what he does. Last I heard he was planning on doing chemistry for college, but no matter what he does, I'll be proud, and he will almost certainly be very, very good at it. He's already way better at music, math, drawing and writing that I ever was, and I haven't exactly turned out to be a slouch. It's exciting to see him at what could be said to be a midway point of his academic career, and for him to have reached it with such success. I can totally see him turning out to be some kind of renaissance man/scientist.

Anyway, that's the end of the week news from around here. I really need to get back to some good science blogging, but that may have to wait for next weekend.

*I now only have a 50/50 shot of correctly guessing who is on the other end of the phone when I call their household now. My sister and my mom have sounded alike for years, but now with my father and brother sounding alike, its just too much.

Women and Science Part 1

There has been a lot of very good discussion lately on how women are treated in our society. It's a discussion that needs to happen, though it's a terrible shame people had to die for it to happen. The discussion has been going on long enough now that it has started to group off into subgroups a bit. One of the discussions on my twitterfeed for the a few days  was about how women still face discouragement when they try to enter STEM fields, with women sharing stories of subtle and not so subtle prejudice.

It's a discussion that I could probably be expected to enter. On paper, I look like the right kind of girl to have experienced this kind of thing. I came from a strongly religious background, I went to a small high school and a Christian college, entering a field with some of the worst male/female ratios. Someone somewhere along the line should have told me I shouldn't go into physics, right?

Fact of the matter is, no. No one in my life ever told me I couldn't do science. I had a handful of people tell me I couldn't be a pastor because I was a woman when I thought that was what I was going to do with my life (oddly enough, one of them was a chemistry teacher). But no one ever said or implied that I couldn't do science because I was a girl. Through my entire growing up, I was given the opportunities and encouragement to explore whatever interested me. The fact that I landed in science feels less like "I beat the odds! I am woman, hear me roar!" and more like "I followed my natural inclinations and talents and this is where I landed".

Though I am nearly 100% certain this was not their intention, my parents gave me what, in retrospect, was a fairly gender-neutral choice of toys growing up. I had baby dolls, a toy kitchen, dress up clothes and play make up. I also had a big bucket of blocks, a wooden train set, an erector set, an a tool belt with kid-sized real tools. I got a microscope and an EZ Bake. If I expressed an interest in something, they got me books on the subject or took me to the library and helped me find what I wanted using the card catalogue or the computer*.

So I read mystery stories, fantasy stories, books on bugs, plate tectonics, and anatomy. At my grandma's house I read the encyclopedia, I experimented on one of her many spider plants, I cooked weird things and found out what was inside bath beads. For a science fair my dad helped me build a contraption exhibiting different types of levers ending in connecting a circuit with a ball bearing and lighting a small bulb. He explained the physics of musical instruments and other things. No one ever told me that I shouldn't explore any topic I found interesting.

In school, I will admit science education was a little haphazard. On the bad side of things, my seventh-grade science teacher was actually qualified in english, not science, and we learned more about his college hockey career and the three types of rocks he could pronounce than we were supposed to. He thought the preserved frogs we were supposed to dissect smelled too bad and left them to soak in buckets of water over spring break. That wing of the school was unusable for a week after spring break since it turns out that when you wash the preservatives out of dead frogs and leave them in a 90 degree classroom, they rot pretty quickly.

But my high school physics teacher was a legend in my school. Physics had a reputation for being an easy class compared to the other sciences taught at my high school because he didn't believe in busy work (which the biology teacher was famous for). He had two classroom spaces that had been joined together into one mega-classroom, one half having a traditional lecture set up and the other half having lab tables. Everyone knew he kept a tea kettle and a hot plate in his backroom, because you could hear the kettle whistle 15 minutes into class time.

He was a brilliant teacher. He had a very simple philosophy--if you wanted to learn, he would spend hours with you, working on a single topic until you were solid on it. If you didn't, he wouldn't heap worksheets on you--you just had to take your D and not complain. He would lecture for the first 15 minutes of class, pause to get his tea, come back and answer questions we had articulated in the meantime, then set us free to the back tables to work on problem sets. We could ask him questions, and he would guide you to the answer while never giving you the answer. When you were done, you could do anything that wasn't disruptive (a small group of us worked on the NY Times crossword with him). He worked on a budget of pretty much nothing. The books were 20 years old and falling apart, and he had only one working set of equipment for each topic, if that. He improvised, he used youtube videos, anything to get his point across. He convinced me that no matter what else I wanted to do with my life, I wanted to study physics.

Sidenote: As a testament to how great a teacher he was, even among the students he failed, the legend/myth grew around him that when he retired, that science wing of the school would fall. We turned out to be half right--the year after he left they discovered they needed to retrofit that wing for asbestos before they could finish an expansion of the school, and that part was indeed destroyed.

In college, the physics professors were indeed mostly male, but we had almost 50% female physics majors during my years there (we had a minor celebration when we realized at one physics department tea time that there were more females than males there that day).  My professors were never anything but supportive of the young women in their classrooms, all without making us feel like a special class of citizen. The only questioning of my abilities that I ever got was with regard to my ability to lift heavy things. But since I'm 5' 1", I can't say I really blame them, even if I did prove them wrong.

I did research with a great professor who guided me from the student-who-takes-orders stage to being in charge of his labs and coordinating between members of the project. I learned valuable skills in macgyvering lab equipment, finding what you needed in odd places and managing people. I never felt like a second class citizen. I was a physics major. The fact that I was a woman meant that I could go to the Undergraduate Women in Physics conference, but had nothing to do with my intelligence or my prospects. They were excellent role models, as physicists and as citizens.

Strangely enough, the first time I encountered anything that I could have construed as sexism with regards to my being a physicist was after I had already been in grad school for a semester. I just laughed in the commenter's face. It seemed so anachronistic. It was ridiculous, a weird joke. But no, they were serious, and far from alone in their opinion.

So, that's my story. A non-exciting story of how a young woman faced no opposition when she set her sights towards science. A story that I wish were commonplace, and I hope I can help make unremarkable.

*Yes, I know how to use a card catalogue. I don't know if that shows my age or the slowness with which my town adopted computers in the libraries.

Update--Still here!

I know it's been quite a while (2 weeks? almost a month? something like that) since I posted anything here. It's not for a lack of ideas, I assure you, more due to a lack of time.

May seems to always be a bit of a crazy month for us. There's my insanity with end of the semester grading. Someone always seems to graduate, some  unforeseen event occurs and the transition to summer seems to take up a lot of time.

In mid May we took a long weekend and went up North to see my sister graduate college, summa cum laude and with more honors than I can remember. She had enough colorful ropes around her neck to tie back a house full of drapes or hogtie someone. We are, needless to say, incredibly proud of and happy for her. Not surprised, because she's just that kind of person, but still proud and happy.

Then she came and visited us, and for the first time since we came to NC she didn't have to help us move! For the 3 years previous, she had come down to help us move 1) to NC 2) from our first apartment to our second much nicer apartment or 3) paint our new house.  It was lovely to just be able to do sister-y things, like trying new restaurants, go shopping and hang out.

Big things are happening around our house. We finally got a new dishwasher to replace the one that had finally given up the ghost after 25 years back in March, and the new windows to replace the ones that are rotting out upstairs will be installed next week. We're hopefully going to finish all the repair work from last fall's adventure in faulty plumbing in the next few months. We might, fingers crossed, have the house ship-shape by fall.

Research is going fantastically. I even discovered that at some point last fall, I had done most of the work for project, which is like a time traveling gift to myself.

I have a lot of blog posts lined up for the rest of summer, so hopefully things are settling down now and I'll find time to write in the evenings more.

Final Exam Grading Marathons

The past five days have been consumed in end of the semester final exam madness. I am kinda past the stage of having final exams of my own to take (thank heaven), and I'm not yet to the stage where I am writing the exam and interesting posts like this on the thoughts of the exam writer/proctor. No, I'm stuck in the stage where I get to help proctor, and grade, and keep the other TAs on track.

Every semester, we grade a couple thousand exams. There are 4 common finals for 4 physics classes (intro to mechanics with and without calculus, intro to electromagnetism with and without calculus) and  enrollment ranges from a couple hundred to a thousand plus. The latter number is usually full of people in online sections, which poses a special problem in that there are no TAs assigned to those sections.

In the past, since the exams are all taken on a Saturday, we graded them all on Sunday (the next day). When I first started grad school two and a half years ago, this schedule was brutal, but doable. There were closer to 2000 exams, and 10 TAs could grade properly and enter the grades in 12-14 hours.

Problem is, the further the professors get from grading their finals themselves, the longer they make them. We once had to grade an exam with 18 problems, the lowest six of which got dropped, but that still meant they all had to be graded. Combine this with the (kinda understandable) push to include more online sections and you have a perfect storm of grading problems. The number of exams have doubled in number for some of the class but the number of TAs has remained the same or reduced. Grading them in one day was  no longer an option. When you have about 5 seconds to grade each problem, you cannot do more than a pass/fail analysis, which isn't fair to anyone, so that had to go.

So this year we spread it out over 4 days, and gave ourselves over 24 hours to get it done (it took 30 hours all told).

For consistency and an ability to give partial credit appropriately, the multi-day method wins hands down. But it also takes more time away from the TAs own exams (I'm an oddity. Most TAs are newer grad students and so still have exams), and it drags out the stress of grading from one intense day to 4 intense days.

Most of us have a love/hate relationship to final exam grading. It's a time suck, it's exhausting and it can be kinda depressing.  On the other hand, it generates a kinda of camaraderie among the TAs, that we have done this mountain of work together, that we have passed through all the emotional stages of grading together and when its done we celebrate.

 You start out vaguely hopeful--yes, there are a lot of exams, but come on guys, we can do this!

Then you hit a grinding stage where you start expostulating over mistakes--this person can't multiply 2 numbers, they can't do a basic line integral, they said it equals zero and then say it equal pi with no explanation--and celebrating correct answers--this person got everything right! They got everything but the unit! Our lives were not a total waste this semester.

Then you hit the pessimist stage--this will never be done, no one is getting this problem right, why can't you add two numbers together, did I teach you nothing this semester RARRR!

 Eventually, somewhere are around the 10 hour mark you hit the giddy stage. You start giggling at everything. Someone starts making random noises. You start laughing at the absurd mistakes people made, not maliciously but as a way to keep from crying. You hold up the particularly egregious ones and ask someone, anyone, to provide an explanation for what this person was thinking so you can award some partial points. The ones that are just full of 'brain barf' provide at least 3 minutes of laughter and commentary and searching for some relevance. The problem asks them to solve for the time to discharge a resistor-capacitor circuit half way, but they have labeled capacitors as resistors and the resistors as inductors, they seem to have thrown every equation they ever learned ever on the page, and ended up trying to solve it using some mismash of Gauss's law and rotational motion and give you an answer of 7 million Newton Joules per Amp radians. It makes no sense at all, not a single thing on the page is right, but there is just so much effort given.  A quarter point out of 10 because somewhere among the mess there is a vaguely-relevant-if-you-squint-hard-enough equation or unit.

Somewhere around hour 15 or the 1000th exam, whatever comes first, you move into exhausted stage. This needs to be done. There is still another box of exams, but they have to be graded by midnight. People who have completed their grading pitch in to tally and sort the exams as they are finished, while someone else enters the grades into the spreadsheet  just so everyone can leave sooner. Your eyes start having trouble focusing at any distance other than 2 feet, and you aren't sure if you stand up your legs will work anymore, because you haven't moved significantly since you grabbed some food some vague number of hours ago.   You are chugging energy drinks, coffee, spicy candy, anything to kick your brain into gear for another hour.

And then its done. They are all graded, even the ones that got stuck in the bottom of the box. They have been sorted according to the professor's wishes, alphabetized and entered. They are back in their appropriate boxes and safely stored for dispersal at an hour when normal human beings conduct their business. High, low and average scores are announced and congratulated and fretted over. You walk outside to breath fresh air for the first time in more hours than you would like to admit, and then you go home and sleep, and wait for the flood of student emails in 2 days.

Ah, the life of a TA.

Windows, definitions 1 and 2

Last week has somehow ended up focused on two kinds of windows--the kind that let me see the outside world from inside my house and the kind that provides the operating system to my computers at school.

It was discovered a couple of months ago that one of our windows, one in my home office to be specific, was rotting out. Shortly after that I discovered one of our bedroom windows was rotting out. It looked like someone had just painted over existing wood rot instead of replacing the sills, leading the the entire thing rotting. Because both culprits are in bays, we were looking at least 6 windows needing replacement.

So we called the local Anderson windows dealer, who discovered two more heavily rotting windows. These are windows that we never look out of since they just look into our neighbors windows and we can't easily see from the ground, but even we could see (when the blinds were drawn) that they looked like they belonged in a haunted mansion.

Hello custom, rot-proof windows. Goodbye nice vacation.

At school/work, IT is going crazy about replacing XP computers with Windows 7 computers. Yes, they are replacing the incredibly out of date operating system with a slightly less out of date operating system.

For most people, this is good news. Faster computers. New monitors, etc.

This is horrible for any sort of researcher. Custom software. Very expensive proprietary software that only allows one installation and is necessary to run a very expensive piece of equipment. Data that you don't want to run even the slightest chance of losing because that there's 4 years worth of work. For a theoretician, everything applies except the equipment.

Needless to say, most of us were trying hard to hide our computers and ignoring emails and personal inspections by the department IT guy.

I finally had to give in because the XP computers were going to be cut off from internet, and the program I depend on to produce graphs requires an internet connection, the stupid thing. But I'm keeping my old one, off network, lest I lose anything.

I was really excited to have two monitors at last. If only the new one actually worked.

Oh well, maybe I can get graphs in less than 2 hours computation time now.

Comfort Food: Pierogies, Sausage and Peppers

Here's something you'll rarely see anywhere: I've been trying to recreate a dish from the college cafeteria for years.

And yes, I mean a dining hall, not a fancified food court like some schools have. Over cooked vegetables, lots of things deep fried or baked within  an inch of their lives. Most days the only truly edible thing in the dining hall was the pizza, unless you arrived in time for the special, which was usually pretty good, but limited in quantity.

But there was one thing that the ladies in the dining hall kitchen did really really well--pierogies, sausage and peppers. I have a few theories why, but this is one of the few dishes I really looked forward to when it popped up in the menu rotation. Puffy, golden potato and onion filled dumplings, thin strips of red bell peppers sauteed until they were soft and sweet and just barely carmelized at the ends and perfectly fried sausage. It was an island of semi-home-cooked-ness in a sea of industrial, mass-prepared food.

I have been trying to replicated this ever since I left college. The timing of it all has always eluded me. Last night, I think I got it down method-wise, and next time I think I can even make it a one-sheet-pan meal to boot!

Start with some thinly sliced bell peppers

Toss with some olive oil and spread in a (roughly) single layer on a baking sheet.

Now, if you want to do everything in the oven, take a lovely pack of sausages

Cut them in halves or quarters and put them on the tray as well. Bake at 350 until the sausages are brown, the peppers are soft and starting to caramelize at the edges.

Now, if I had thought a little more, I would have taken the sausage and peppers off the tray and just tossed on some lightly oiled frozen pierogies. As it was, I did those mostly in a skillet, which was silly. But it did lead to this amusing series of pictures by Dear Husband. 

 He didn't quite hold it still, or activate the digital compensation.

I learned that I apparently stand with my legs crossed, for no obvious reason...

 Why is this picture at a 60 degree tilt? no idea

This could be really adorable if it weren't quite so blurry.

In any event, it was delicious, and very close to what I remember. 

Over all, a great sucess!

Final stretch of the semester, running on fumes

It happens pretty much every semester, as Dear Husband pointed out to me this morning when I said I just wanted the semester to be over already. I start out the semester with plenty of energy to form new minds, until we reach the last few weeks when I start to feel depressed about their lack of commitment to learning, their lack of understanding, and how utterly horrible it is to grade 3000 final exams written by undergrads who may or may not understand that physics requires math, and therefore can't be fluffed out of.

Basically, I feel like this:

Can we be done now?

It's not a place I like to be. And usually, this feeling occurs between teaching. Once I'm actually in the classroom, the students  remind me why I love teaching, I get in the zone and I will happily teach for the hour+ that I'm given. 

But this semester, three out of four of my classes are duds.  The students are disengaged with learning. They don't ask questions. Lower admissions requirements on the part of the university mean that the level of mathematical literacy is astoundingly lower than I'm used to. Because we reinstated weekly in-class paper quizzes instead of online weekly quizzes we did last semester, I have to deal with a whole crop of students who never learned the importance of drawing diagrams for every problem, even if they can solve it without, and who fight me constantly for the 2-3 points I dock if they don't draw one. In the past, students have looked at it as "woohoo, 2-3 free points, yeah!"; this semester, I was told I was "teaching my philosophy, not physics". Nevermind that this is standard and still required of problems well into grad school. 

One class is not like this. One class is wonderful and a joy to teach.

But it's hard to make up for the three classes where I walk in and get less energized because the students just aren't there, mentally. 

In short, I can't wait for the semester to be over. 

A Hectic Week

This week has been a rather hectic week for me, though not in crazy-running-around kind of way.

Teaching has been more time consuming and emotionally difficult because we had a series of schedule mishaps (including a snow day), combined with a class that seems to need a little more hand holding through the topics than usual. The result is I have to spend more time prepping, and a lot more time grading.

If a quiz is done correctly, it is usually obviously correct.

When it is wrong, it can be obviously wrong (blank page, doodles, completely unrelated equations, etc) or very very creatively wrong, or completely wrong in execution, but correct in the theory, or the execution is done completely correctly, but with the wrong theory. It can be very difficult to grade the creatively wrong quizzes.

In addition to teaching, on Wednesday, I volunteered to host a prospective grad student for the afternoon and evening. It was a lovely time, and I enjoyed it very much, but it did throw my usual schedule a little out of whack.

And now we are awaiting the arrival of the flight bearing my mother-in-law, who will be visiting a week. Her flight is unfortunately delayed, and we aren't sure if we should try to catch some sleep, or stay awake in case things change. We seem to have defaulted to the later.

A fitting end to a hectic, but good, week.

Everyday Optics: Cosmetic Mirror

Last week, while helping a friend study for the qualifying exam, I posed him this question--explain how a cosmetic mirror works.

For those of you who have never used one, a cosmetic mirror is a mirror that creates a magnified image. Usually they are small and hand held so you can use them to apply things like eye liner and see what you are doing.

I am embarrassed to say, while we had the right instincts in this matter, it took us a day to figure out how to do the ray tracing to prove we were right, so I figured I'd make a blog post out of it.

To start with, let's examine the three types of basic mirrors. There is the flat mirror, which is the kind that hangs over your bathroom sink and is the kind of mirror pretty much everyone is familiar with. It can not magnify, either positively (make it bigger) or negatively (make it smaller). So that one's out.

Don't you love my white board illustrations?

There is the convex mirror, which is bowed outward and is the kind you see in gas stations as a security measure. They create smaller, distorted images of whatever is in front of it. So that's out.

No? Too bad.

Lastly, there is the concave mirror, which bows inward. This is the  most complicated mirror, because what it does depends on what region you are in, as shown below.

I do need new markers though....

So this is the kind of mirror we need, and we know we need to be inside the focal point for this to work. That's fine, because you are usually holding this close to your face anyway. However, the image that it creates is imaginary, and that's the part that was tripping us up while we were drawing the ray diagram.

As you can see, to demonstrate the effect we know occurs, we need to trace partially real rays, and partially imaginary rays. The imaginary rays are what we perceive happens, the virtual image that is created 'in' the mirror.

Diagram a la Hecht

So there you have it. How a cosmetic mirror works. Incidentally, this also applies to the image created  in bowl of spoon. See if you can find the focal point!

~AMPH

Great is the mystery of the fridge

Life was weird today. But perhaps nothing quite so weird as my lunch missing from the break room fridge.

Now, I know that this sort of thing is not uncommon is some places, but you have to understand something about this particular fridge.

Nothing leaves this fridge.

When I came to the program, there was a three year old carton of eggnog in the fridge. It lived there for another year after I got there.

Chinese leftovers, hot pockets, soy sauce, this and much more have lived in that fridge for months without molestation.

I leave my yogurt in there overnight, one night, as I frequently do so I don't have to make a time-costly detour on teaching mornings, and it vanishes.

What gives?

5th Semester TA Enthusiasm Running Low

I love teaching. I love interacting with students. I love sharing knowledge in a setting where no one looks at me weird for explaining how old-style CRT TVs or MRIs work and why your microwave can't give you cancer (but could cook you if you got into one of the industrial ones) but the tanning bed can't cook you, but can give you cancer. I love encouraging students towards those ah-ha moments and deeper insights into the world. 

I'm also feeling a little burned out right now when it comes to teaching. This semester has been particularly bad in the getting-off-schedule department, because trying to coordinate between 4 teachers is hard enough without adding snow days to the mix. One of my classes is in a squashed, overcrowded classroom in the boondocks of campus (from my perspective, centered on the far reaches of the grad campus); the chalkboard there is 8 inches higher than standard, which means I have about half a chalkboard to work with, which because of angles is only visible to half the class at any given time, and there is a creepy diorama in the corner. I have an unusual concentration of mechanical engineers, who really do not care a bit about electric fields. I also have a crop of students who came untrained in the art of taking in-class weekly tests, so grading is more frustrating than usual.

Does any of this diminish my desire to be a teacher after graduation? 

No, not really. But it does make me long for smaller class sizes, and being in control of things like textbook choice, and schedule. Working with 1 other person would be fine. Trying to work with 3 in an insanely complicated schedule is exhausting (no one seems to actually know when the students are supposed to do what assignments, for example). 

Mostly it makes me long for days when I tutored, and could concentrate on teaching to a specific understanding and not the near-lowest common denominator. If I could start a from-home tutoring business I would almost be happiest, I think. But I am not charismatic enough to go build a customer base. 

I think this will get better as we move towards midterms and some of the students make the final decision to drop the class, and we get into we-must-stay-on-schedule mode. 

In the mean time, I'll just have to keep calm and teach on. 

~AMPH