Vectors, vectors, vectors.

Had my third calculus class today. Still learning about vectors. Even though they don't excite me as much as calc does, they're really cool, useful, and powerful. I'm amazed at how much simpler they make expressing fuctions in two or more dimensions, or how they can make geometric proofs that took a page in ninth grade simple. 

What I wonder most, though, is why I've had so little exposure to them. In precalc we did a unit on them, but it was really no different than what you might do with lines in analytical geometry. there were no dot products or cross products. Then in physics, we learn a little more about vectors, but when it comes to dot products and cross products we are just told to plug values into some equation that magically works, with no explanation as to why. 

Yet, they are so simple. You can begin learning them in middle school, and all it takes to really fully grasp them is a deeper understanding of trigonometry, something students get their sophomore year. It's like not teaching concepts like radians or limits until 10th or 11th grade, when kids would internalize them and understand them much better having been taught them from childhood.

On Playing With Data

Recently at work I was put in the position of having some data, not much but enough to try to make some graphs, and needing to use it to understand what was going on.

More specifically, I had some dates and the mass of a thing from which we were trying to etch graphite. I wanted to find a way to express the rate of this etch both visually and comparably.

In the end, I didn't exactly reach these goals, but I did learn plenty about Playing With Data, and playing is really what it is!

In all my labs in highschool, you'd do some experiment, take some data, and then they'd have some lab questions or analysis where you'd be gently guided into seeing empirically the equations that you learned the day before. This is nice and all if you tend not to believe the teacher or textbook and you need concrete proof, or if you had a hard time internalizing and understanding the applicability of what you learned, or if you were just really interested (an interest that often went away after doing these labs."

This was quite different. I hadn't been taught the day before what was supposed to be going on (no one really knows), I hadn't learned the equations that the data should fit, and I didn't have some nice numbered questions that brought me gently to the main conclusion or point of the lab.

So I played. I fiddled around with and manipulated the data. I made tons of different graphs, and tons of different best fit lines or functions. 

The most important thing I learned, is that data without visual representation is largely meaningless and is not understandable. When you have just a list of x and y coordinates, it is very very rare that you can glance at them and go, "oh yeah, that clearly indicates this!" However, in a graphical representation of a data, one that's well done and clear, this can be done easily.

The creation of these graphs and the manipulation of this data also let me know another good lesson: more data is better. I was working with a very small amount of data, almost the minimum I could draw any reasonable conclusion from, and while I did have enough to draw such conclusions for my own purposes, it made it much harder and much less reliable. The more data you have, the easier it is to see trends and patterns, and the more exact your mathematical understanding of these will be.

Speaking of mathematics, I learned that it's very helpful to approach data from an analytical and mathematical way so as to gain and understanding of what you should do with the data. In this case we thought that the masses should change exponentially, that is Mass  = Ae^(kt), which would make sense since we assume that the longer it goes, the less graphite there is to etch, and so the rate slows.  This would indicate that if you took the natural log of the masses and graphed it against time, the relation should be linear. This we saw seemed to be true. With further data and investigation into this, we may be able to figure out a way to compare or standardize the etching rate, however I suspect that to do this we would need to look into the role of surface area on the rate.

And finally, documentation is key! in our digital world, no information need be delete (thanks, google) and everything is easily recorded and saved. So record and save it! I kept most of the graphs I made, even if they didn't make any sense, and I keep many of the pictures, even though they don't give any information towards figuring out the rate. All of it could be useful later on.

Work - Graphite etches and diamond-like hydrocarbons

Work today was good.

First off, things are working. I'm currently doing an electrochemical etch of a big thing covered in graphite, and I'm using weighing and pictures to attempt to determine the rate of the etch. So far, it has been pretty successful. Once I get more data points, I'll figure out some way to make the data useful so that it can be compared to further tests, with some variables. My boss suggested normalizing the data by getting percents of weight lost, which is probably what I'll end up doing. This is the first time I've really gotten to work interestingly with data, and to try to figure out on my own what to do with it and how to interpret it. In all the labs in high school, they make you take data and then tell you exactly what to do with it, and you've probably already learned what it means anyways. In this case, I don't really know what it means or how it relates to the variables. Very exciting. I think it would make a great science fair project, if that was what I was going to use it for.

Next interesting event was that I spent a bunch of time talking with my boss about the mechanism for the etch. This is something that no one knows, and that has mystified us from the beginning. If we knew the mechanism, we would know better how to improve the rate of the etch! Our current theories are as follows:

1: Some sort of reactive element or ion (OH-? H+?) is being created in the water and reacts with the graphite in some way, possibly to create CO or carbon dioxide. The problem with this is that most of the etched graphite seems to end up floating as macro-sized particles in the water, indicating that they've fallen off for some reason, which seems against the reaction to form gas unless this reaction likes to occur in crevasses underneath the graphite, taking away a layer and knocking everything above it off. 

2: The conductive graphite in the water creates a short that leads to a potential buildup on either end of the graphite, which causes the breakdown of water and possibly some sort of reaction to occur? This on is fuzzy, but it makes sense that this sort of potential buildup would occur.

3: This idea is weird, and seemed to be suggested in one of the papers I read. They seemed to think that the passage of current through the graphite may through random interactions (kind of like london dispersion, I guess) cause carbon atoms to momentarily become polar enough to be dissolved into the water. Again, if this were to happen, no visible graphite would be floating around in the water, unless it either ate below them or the graphite, after dissolving off the main structure, would fall out of solution and create visible particles.

With each of these potential mechanisms come potential ways to increase the rate:

1: Figure out how to create more of this ion, possibly with more current. Also, try to allow more of this to reach the surface of the graphite and avoid buildup of a layer around the graphite, either through ultrasonic agitation of the water or mixing. 

2: Use the purest least conductive water possible to make the potential difference across the graphite greater. Again possibly agitate the water to prevent the buildup of a layer.

3: More current. Possibly adding a surfactant (which the paper says they did, and that is slightly improved some of their performance)

Apart from this, my boss now wants me to find information about Diamond-like hydrocarbons, and the atomic hydrogen density of various types. So far, I've had little success in this, but I've not spent enough time.

As always, more to do!

Multivariable Calc

Had my second lecture of multivariable calc last night. It was more interesting than the first, though it was still all vector stuff. Dot product and cross product mostly.

The first homework wasn't particularly hard. The last question though had to you do a proof with vectors. It made me realize just how powerful they are. I'm still looking forward to getting to the real calculus, though. 

Physics

I ended up watching two physics lectures today, starting one between school and work, and then finishing it and another after getting home from practice.

The first was on 3d Kinetics, and free fall reference frames. It was pretty much all stuff I had encountered in honors physics last year, but Prof. Lewin never fails to make it interesting and fun to watch and learn about.

The second lecture was on circular motion. Again, it was mostly stuff I'd encountered before, though taught slightly differently. Also, as always, very entertaining.

I'm pretty happy so far with the rate I've been going through these. I've gone through 5 lectures in one week. If that rate keeps up, I could finish by November or December. However, I expect that once it gets harder and into newer material, I will go more slowly. We'll see!

Work - Ion implantation, Graphite Etching, and Ultrasonic Cleaning

Work was good today. Didn't do anything with the machines, rather some stuff with the graphite etch and a lot of talking with my boss about my various projects, where we are, what the ultimate goals are, and what the plan is. Very exciting, as it looks as if the work I've been doing, which has been working, could be really important and useful.

First off, we talked to a man named Jim Butler, whom Roy says is probably the most knowledgeable guy in the field. He told us a lot of info about ion implantation, in which basically ions are smashed into diamond at really high energies, and they end up going through a certain amount of diamond without doing any harm, but after they lose enough energy they start to bounce around and cause the diamond to amorphize. This creates and amorphous layer. I'm going to have to look into costs, and method, and companies, so more on that later.

Secondly, the graphite etch has been working really well. It's been going a lot faster than we though. We're going to start seeing if there's a detectable weight change, and figure out a rate, and see if that rate can be improved.

At work, we have a machine that uses ultrasonic waves to clean things. Basically, you put a liquid in a beaker and then the metal thing into the liquid and it shakes at such a high frequency that it shakes loose particles in the liquid. Problem is, ultrasonic as it is, it actually makes a terrible noise.

Interestingly enough, however, the noise changes drastically with different liquids. With ethanol, it's relatively quiet. With water, however, it makes a huge screeching noise, and you fear that the beaker may shatter (it doesn't, though. It just sounds like it). I wonder what causes this difference? 

So, as always, lots to do!

Humanities - History and Literature

Today was the first real class of humanities. We had history and literature. Mostly the classes were a review of the summer reading for the tests on Friday.

In History, we discussed some of the themes of King Leopold's Ghost, instances of them in the novels, and their relation to some quotes from Machiavelli and a couple other sources. I may write more specific things when I actually review for the test.

In Literature, we discussed themes and metaphors in the book. I didn't agree with much of what the teacher said about the book being entirely a metaphor. Since Conrad did actually travel up the Congo, and it was a huge issue at the time, I don't think the book was intended to be entirely disassociated from its setting. However, I do believe a lot of the things about the discovery of the emptiness at the core of societal morality. This, though, I think is deeply entwined with what was actually going on in the Congo, and Conrad's actual experiences, and the actual events of the book.

Tomorrow is the Art and Music review.