Square Cut or Pear Shaped, These Rocks Won’t Lose Their Shape

The end is drawing near for Tipler and Mosca! Today I read two chapters: Solids and Relativity. There was an optional relativity chapter in the first volume, so that was mostly a repeat but always a good one refresher to get! More fun brain benders like the twin paradox and non-synchronous simultaneity. And a bit of general relativity too, which wasn’t in the first relativity section.

As far as the material about solids, that was interesting but also a bit difficult to follow because most of the math is hand-waved (too advanced for this text), so it becomes a bit abstract. There are a lot of interesting practical effects that are very important to the world today condensed into this chapter, such as semiconductors, transistors, etc. I had to laugh because one section talks about current technology and lists laptops and appliance processors as cutting edge. No mention of smartphones because, back when I got this book, smartphones didn’t exist yet! Yes, that’s right kids, the very first iPhone was released when I was in college. I got a BlackBerry Curve my senior year and thought I was fancy.

Over on the math side of things, I started the chapter on vector algebra. This was pretty easy, since I haven’t forgotten how to do vectors and they’ve been all over my physics textbook. Of course, Mathematical Methods manages to make topics that I already understand sound confusing, but I figured out what they were trying to say eventually. I can’t say I really understand the order that this book is going in, but that’s okay. I think it’s intended to be more of a reference than a book to work through, so I’m not using it in the most optimal way.

Today’s fun “new” fact: Superconductivity (a truly bizarre situation in which a material has zero resistivity and can sustain a current indefinitely without an emf source) is due to electrons forming Cooper pairs. Because the pairs act as a unit, they become bosons (integer spin) and are no longer bound by the Pauli exclusion principle. Although, as with most things in quantum physics, I believe this is more of a way of explaining it rather than a precise description what is actually happening.

(And as a bonus fun fact, Cooper pairs are named after physicist Leon Cooper, who is also the namesake of fictional physicist Sheldon Cooper on the TV show The Big Bang Theory.)

I Ain’t Trying to Do What Everybody Else Doing

Another day another dollar! Except not, because I have no dollars coming to me at all right now. Which is fine. This is fine. (Actually, it is fine, because I planned for it, but it is a little…unnerving?)

Today I got some more modern physics refreshed into my brain. I read two chapters, Atoms and Molecules. As advertised, I got to learn about both atoms and molecules! It was a very interesting perspective on things that are familiar from high school science classes. Ionic bonds! Covalent bonds! Except now with added quantum physics! Which I think is pretty damn cool. Suddenly the why of rather arbitrary things, like having 6 electrons in each p-orbital, makes sense. Or at least, makes as much sense as quantum physics ever does. =) Reading about the spectra for molecules made me think about taking spectra of exoplanet atmospheres and I got all excited all over again about what I get to do.

And then I got scared.

Forgive me for waxing a little personal/philosophical here, but reading about all these amazing physicists like Schrödinger and Dirac and Pauli is intimidating. These people were brilliant and able to come up with these new ideas that changed the way we understand the universe. I certainly can’t hope to do that. Don’t get me wrong, I’m a pretty smart cookie. And I’m really good at learning physics. But am I good at doing it? I honestly don’t know. And this is part of the reason why it took me so long to pursue this path. Anyway, it’s scary, but I just have to button up and carry on. I’ll do my best and not get ahead of myself.

In other news, I finished up my Python course today! That was pretty exciting. Do I feel like a coding genius? No, not even close. But I have a better understanding of the language now, and I feel more confident about my ability to tackle it and make it work for me. Overall, I think the Codecademy course was very helpful, and I recommend it to anyone trying to get the basics of Python down. Plus free is always a good price! But it’s definitely only a stepping stone and not a full education in a language.

I think I earned myself some ice cream!

Today’s fun “new” fact: The letters used to identify the l quantum number (s, p, d, f for l=0,1,2,3) were not just arbitrarily chosen to frustrate young chemistry students. According to a footnote in my textbook, they are “remnants of spectroscopists descriptions of various spectral lines as sharp, principal, diffuse, and fundamental.”

A Whole New World

Today I got to start on the part of the physics textbook that deals with the somewhat-misleadingly-named modern physics (dating back about a hundred years now!). Excitingly enough this is also the last section of the textbook. The end is drawing near for Tipler and Mosca! So today I read two chapters, Wave-Particle Duality and Quantum Physics and Applications of the Schrödinger Equation, and these were an introduction to quantum physics. They’re actually a pretty well-written introduction, explaining Schrödinger’s equation and wave-particle duality and probability densities in a matter-of-fact way that makes it sound like, okay that makes sense, and not like that is Totally Fucking Weird, which probably should be the default reaction to quantum physics. It covered some of the stuff that had previously been mentioned in the light chapters, and it was a good recap plus adding Schrödinger and some of the quantum things that arise that are classically forbidden like tunneling and partial reflection.

Math-wise, I worked on integrals today. It was actually a pretty easy chapter—I did the whole thing in one go—on multiple integrals. Basically integrating over areas and volumes. The trickiest part here is defining the limits of your integrals, and there was a fun section on change of variables which didn’t make a whole lot of sense because it was said to just use the determinant of the matrix, and if you don’t know what that is we’ll cover that in two chapters. I don’t really remember anything about matrices so that was not quite so helpful for me, but other than that I do feel like I have a good handle on the material in this chapter. I was pretty comfortable working through the problems, although I got a little bogged down in some of the actual calculations. But that’s just me being out of practice and doing stupid things like dropping random x’s when I was doing multi-line integrals.

Really, it was a good day. I feel happy with where I’m at, and I am looking forward to the rest of this week. It’s a little bit of a short week because I’m going to Chicago on Friday, both to go to my cousin’s wedding and to look at houses for when I move to Chicago in just a couple months now! I’m looking forward to that, and I’m a little nervous and hoping that all the places I see don’t suck and that I can find something I can afford. I’m also excited to show my boyfriend Hyde Park so he can get a feel for where I’m going to be living—and for me to get a better feel it because I’ve only been there once!

Today’s fun “new” fact: While I remembered the Pauli exclusion principle, I forgot that it can be seen in the construction of anti-symmetric wave functions, where if both quantum numbers are the same, the wave function will go to zero and so therefore, while it is still a valid solution mathematically, it is rejected as a wave function because it cannot be normalized. It’s a simple way of thinking about a complicated assertion.

Mysterious as the Dark Side of the Moon

Good morning and happy Monday! I had another nightmare about grad school last night. That was fun. My brain needs to just get over being anxious! I’m a grown-ass woman, I shouldn’t be this nervous about making a huge, upending life change. Oh wait. That’s totally normal.

Before I dive into my books this sunny Monday, I wanted to finish my Friday/Saturday update so I don’t fall so far behind again. Because I basically forgot to do a section on Thursday, I planned to do three on Friday. That didn’t quite work out, but I only pushed one and I got it done Saturday. So I did meet my goals last week! Just a teeny bit off-schedule.

Friday morning I finished off the chapter on partial differentiation. This got into some pretty interesting stuff, including deriving some of Maxwell’s thermodynamic equations, the Boltzmann distribution, and a series of problems where I got to solve systems of equations with some fun middle school algebra tricks. It took a bit of doing, but I enjoyed the problems.

In the afternoon, I turned back to trusty Tipler and Mosca. I had set a rather lofty 3-chapter goal that included the entire Part V on Light with the chapters Properties of Light, Optical Images, and Interference and Diffraction. This pretty much covered the entire (non-quantum) spectrum from wave-particle duality to color to rainbows to interference rings and ray diagrams. There was even a neat section about a rough physical model of how the eye works. Plus lasers, measuring the speed of light, and more! Light is a pretty cool topic, and one quite relevant for astrophysics, so this was a good refresher. They even included a few examples from astro, which is always nice to see.

After my lengthy physics read, I didn’t get to my Python course, so I tackled that on Saturday, finishing a lesson on classes. I wanted to do two lessons, but I also have a life and a boyfriend so that didn’t happen. Only one lesson to go before the final project! That’s on the schedule for this week, and I’ll do the final when I get back. I’m pleased with what I’ve learned so far and think it will help me out a lot going forward.

Today’s fun “new” fact: Mirages are due to the differing densities, and therefore differing indices of refraction, of air of different temperatures. Hotter air closer to the ground (near asphalt, for example) creates a boundary with the cooler air above. Some of the incoming light is reflected.

Here a Field, There a Field, Everywhere a Field Field

Only one day into the past, which doesn’t even call for the time machine, really. Just a time jump. Oh, you don’t know how to do that? Pity. *wahoo!*

This morning started out great with the first half of the chapter on Partial Differentiation. I’ve always liked partial derivatives. They almost feel like cheating, right? Like you have this whole mess of an equation with a million variables but…we’ll just ignore them all and only deal with one! Mwahaha. So it was a genuine pleasure to work through these sections. Even the one on changing variables that took me three pages of looseleaf and numerous cross-outs to work through.

The afternoon was not quite so great. For one, I didn’t get started until pretty late. You wouldn’t think I’d be so busy, being unemployed and all, but the days really do get away from me. By the time I went for a run and made lunch and washed dishes and so on and so on, it was already late afternoon. And my boyfriend and I were planning to go to a baseball game (free tickets since it was Military Appreciation Night, and we got vouchers for free hot dogs), so I had to knuckle down and get to work. And of course I had given myself three chapters that totaled over 90 pages: Magnetic Induction, Alternating-Current Circuits, and Maxwell’s Equations and Electromagnetic Waves. The magnetic induction material was especially long and took me a lot of effort to power through. I get frustrated sometimes trying to think through these problems. One moving charge creates a magnetic field which changes and induces an electric field which causes charges to move and create magnetic fields…okay, I know it’s really not that hard, but it just takes a lot of focus. By the time I got to poor Maxwell I couldn’t even be properly excited about him putting everything together!

But luckily I finished just in time to head out for the baseball game. (The Riverdogs won!)

Today’s fun “new” fact: Flux is quantized, and the small unit of flux is called a fluxon. That just sounds like some mad-scientist shit right there.

I Just Want to Feel Attractive Today

And now we have only a short hop back to Tuesday, June 13. That’s practically today. Tuesday, Thursday, who can keep track of all the T days? *doo-doot doo-doot*

Today I took a break from the mind-bending math but continued with good ol’ Tipler and Mosca. After the lengthy chapters on Monday, I ended up with a short pair of chapters today on The Magnetic Field and Sources of the Magnetic Field. I probably could have balanced this out better when I was making my schedule for the week, but I was just going based off a chapter list. In any case, these were interesting chapters. I especially liked that there was a good section about some practical applications of very basic magnetism concepts—velocity selectors, mass spectrometers, etc. Also I got a chance to look like an idiot at my desk by constantly doing the right-hand rule as I followed along with examples in the text. Good thing I study at home alone!

After the magnetic chapters on magnetism, I picked up with my Codecademy course on Python. Progress has been slower here than I like, but as the lessons are getting a little more complex, they take more time and brainpower, hence slower progress. Still, the end is in sight. I got to play around with creating mathematical functions, which actually felt useful (even though these are actually built in to Python), and got to start on “advanced” topics. Nothing too crazy, but it’s starting to feel a little more natural to get the code down. I also spent five minutes debugging something that turned out to be a single misplaced indent. Oops!

Today’s fun “new” fact: Two straight wires carrying parallel currents will attract each other due to their generated magnetic fields. And in fact, this attractive force is how the SI unit ampere is (currently) defined! The coulomb is then reverse-defined from the ampere.

Photo by Guy vandegrift / CC BY-SA 3.0

Everybody to the Limit

Okay, now we’re only jumping back in time to Monday, June 12. So long ago that was! The main news story was Trump’s bizarre Cabinet meeting. Ah, the good old days. Anyway… *bleep bloop blorp*

After a nice, relaxing weekend, I was ready for Monday morning, even though it brought the remaining sections of the Series and Limits chapter. I was a little worried, but it ended up being not nearly as strenuous as the first part of the chapter. What a relief! I got to practice convergence/divergence tests and practice taking limits. I finished pretty early in the morning and had plenty of time for my lunch break. Which ended up being most of the day, as I decided to make a layer cake for my boyfriend. It was delicious and time consuming! And I didn’t return to my studying until late in the evening. But that’s the joy of setting my own hours!

Of course, if I had known how long my physics section would take, perhaps I would have not been so determined to finish. I had assigned myself three more chapters on E&M: Electric Potential, Electrostatic Energy and Capacitance, and Electric Current and Direct-Current Circuits. They weren’t overly difficult, but by 10 PM I was having trouble concentrating. But even if I had to read some of the paragraphs a few times before I really read them, I did get through it!

I got a lot of flashbacks to the first time I went through this material, back in my Electricity and Magnetism I class my sophomore year of college. Our instructor was the most cliched version of a physics professor, with the big gray/white afro and same 2 ties in rotation and so many bad jokes about the subject matter. He always called one the “loneliest number” (a reference I didn’t get until years later) and referred to hippopotami that carried charges between the plates of a capacitor (an analogy that never made sense, but I guess it worked since I still remember it over ten years later!). Ah, Professor Korman. Hope he’s still puzzling the kids and telling bad physics jokes over at USNA.

Today’s fun “new” fact: Another math one today, but I couldn’t resist. I actually exclaimed out loud when I saw “L’Hôpital’s rule!” Because it’s so fun to say, of course, and because I had totally forgotten about it. It’s a simple and wonderful trick that allows you to take a limit of functions that tend to 0/0 or ∞/∞. You just take their derivatives and voila! It’s like magic. Except it’s math.

Photo by Papa November / CC BY-SA 3.0

She is Electric, Can I be Electric Too?

Oh, crap! I realized yesterday that I was getting woefully behind on my blogging. The good news is that it is not because I’m behind on my studying. I thought about just skipping ahead to today, but I’m really trying to document this journey. So let’s play catch-up, shall we? We’ll just hop into my time machine (patent pending) and travel back to last Friday, June 9. *insert appropriate science fiction bleeps and bloops*

Today I got to start on Volume II of Tipler & Mosca! That’s a pretty big milestone. It’s also a much less-used book, as I believe that we didn’t use this as our primary text for some of the topics it includes. In any case, today I got started on E&M with The Electric Field I: Discrete Charge Distributions and The Electric Field II: Continuous Charge Distributions. This is pretty interesting info, getting into some trickier math and less-pretty equations, and setting up the basic concepts that will (spoiler!) later lead to culmination in Maxwell’s equations. Field points have always tripped me up, but this time around I think I have a pretty good feel for it.

I started on the Series and Limits chapter in Mathematical Methods, and it was not a fun journey. I had assigned myself four sections and they took forever to get through. I’ve never been the best with series (I think my pattern recognition is subpar) and working through these examples was frustrating. It didn’t help that I was acutely aware that it was Friday afternoon and my brain was ready for a break after a long week of studies. But I kept with it and did get through every problem, teasing out the correct reasoning and applying it properly. That was good! As frustrating as it was, I feel like I actually made some concrete progress with my mathematics skills.

Another week of books in the books! I’m speeding through basic physics and the calendar is speeding by at an alarming rate, but I’m ready to think about something else for a day or two before diving back in on Monday.

Today’s fun “new” fact: It’s a fun party trick to be able to add a huge amount of numbers together, and I had forgotten the simple formula to do so. But it’s easy! The sum of the first N positive integers is N/2*(N+1). You can check out this site (or Google) for more details on the derivation.

We’ve Got a Big Big Mess on Our Hands Tonight

Good morning! I should have written this post yesterday, but my laptop battery ran out and I was too lazy to go charge it (the charging cord is upstairs, very very far from my couch!). But here we are now, time for a quick recap of yesterday’s work. It was a good day of studying. I actually finished quite early and had enough time on my hands to start consuming A Series of Unfortunate Events, which has been sitting in my to-watch list forever.

I got through another two chapters in Tipler and Mosca: The Second Law of Thermodynamics and Thermal Properties and Processes. This was a pretty big milestone, because not only did it complete Part III (Thermodynamics), but it also completed Volume I! That’s right, tomorrow I am on to Volume II where more of the fun resides. That made me feel pretty good, especially because after Tipler and Mosca I am going to dive into BoB and I am super excited for that!

One of the things I really enjoyed about this section was the various statements of the second law of thermodynamics. This text included five—the Kelvin statement, the heat-engine statement, the Clausius statement, the refrigerator statement, and the entropy statement. Here we have this fundamental law of nature, and we have all these different ways of trying to express and get at the underlying truth. To me, this kind of goes back to the debate of whether mathematics (and physics) are created or discovered. Not something I propose to answer (I’m not the philosopher in the family!), but something I find interesting to think about.

After the physics, I got to dive into some math. As I’m getting a little farther in the Mathematical Methods text, I’ve broken down my studying into sections (not trying to do a whole chapter at once) and I’ve started actually working through the in-line examples. It was fun to break out pencil and paper and get to work! I even got to bang my head against the wall of trigonometric identities and simplifying functions. I’m on the third chapter, focused on complex numbers, and did the sections on introducing complex numbers, manipulation of complex numbers, polar representation, and de Moivre’s theorem. Complex numbers are amazing. I remember being blown away the first time I learned that we could just assign an imaginary component to deal with a thorny issue (in this case, the square root of -1), and that it opened up a whole new world of math. It’s still pretty amazing to me today.

Today’s fun “new” fact: The entropy of the universe is constantly increasing ahhhh! Okay, so I didn’t actually forget this one, but for some reason reading about it always sounds vaguely ominous. Energy becomes unavailable to do work! It’s irreversible! Disorder is inevitable! Panic!

Just kidding! As the late great Douglas Adams would say, don’t panic. 🙂

It’s Getting Hot in Here

I had a busy day today! I spent the morning working on my Python course over at Codecademy. I finished going through the “review” material from when I previously completed the first few lessons and got into new stuff–which meant actually writing code! That was exciting. I made a (very rudimentary) Battleship game, and it worked with only a few issues to be debugged, so good for me. I’m at 61% through the course now, so a couple more sessions should finish it up.

After a busy interlude of running errands and finally getting to the gym for the first time in weeks, I dove back into Tipler and Mosca. I’m on to Part III now, and I covered the first two chapters: Temperature and the Kinetic Theory of Gases and Heat and the First Law of Thermodynamics. This is pretty familiar territory for me, since thermodynamics composed a large part of my Navy nuclear studies, but it’s also a somewhat tricky topic. Will I ever understand the equipartition theorem on a deep level? Ah, well, I shall have to be content with being semi-able to apply it for now.

Had a talk with my boyfriend this afternoon about whether I’m overdoing it or worrying too much about being prepared for school. I know he is a bit surprised I’m not relaxing more during my time off, but I think this is important. My fellow incoming students are all bright people (will admit I initially typed “kids” there), coming right out of undergrad, from prestigious universities. I was pretty good at physics back in my day, but the rust from the intervening years is very, very real. I want to be able to do quality research as soon as possible, and that means having the basics down, not struggling to remember the zeroth law of thermodynamics. I don’t think I will regret any of my self-study. Besides, I enjoy it!

Today’s fun “new” fact: The rms speed of hydrogen molecules is about 17% of the earth’s escape speed (11.2 km/s), which is (simplistically) why the atmosphere doesn’t retain hydrogen. The molecules eventually all just rocket off into space! This is a sort of duh fact, but one I hadn’t thought about in a while, and I think it is very cool. It’s also hugely relevant for me, as planetary atmospheres is a big component of the exoplanet field right now!

Photo by Cmglee / CC BY-SA 3.0