Maybe you only think that way if you are me. Eternal optimism and such. But why tarry with rivulets of self-awareness? On to the boring reality at hand.
I'm working on my physics lab write-up, or at least I was until I started writing this. These write-ups occur, naturally, after the lab is completed. They are very useful. For instance, when I pick up my notes from lab, I find that I am in dire need of recalling, first, exactly what we were doing in the lab, second, why we were doing it, and, if I feel particularly important, third, why it worked. It's a good thing the third part is optional, because sometimes we break all the rules. Compile all the laws of nature that we've broken in Physics lab, and you'd probably vaporize due to a lack of intermolecular forces.
That said, the past few days of working on my write-up have been very productive. I've definitely made recollection one (singing Christmas carols). Step two is in progress (because we wanted to drown out the guys who were rapping). And step three is a no-brainer (because our prof. sang with us).
In fact, I've been so productive that I've actually made The Graph twice. The Graph is where I put all sorts of numbers into boxes in particular orders, then realize I put the wrong numbers in the wrong boxes, and try to fix it, only to make a different mistake. Finally, I get all the numbers in the right boxes, save the file to text and to j-peg, close it, realize I forgot to label my axis, and find that my simple graphing program, whose name is Linefit, cannot read the text file. Thus, I am working on the graph for the second time today. For various reasons which I prefer not to go into right now (Translation: I'm embarrassingly inefficient) I have computed nine different logarithms six times each. Any math major can tell you that's fifty-four computations. My calculator is groaning about the mundanity of life.
My calculator, however, has it easy. All it needs to run are four triple-As and a few of those natural laws that we break in lab every week. Its purpose is predetermined. It never had to go to school, and all I have to do is press the right buttons to teach it something new. It has cool circuitry, is a "silver edition," and was apparently born in Texas.
In contrast, I need things like internet and pizza just to exist; despite what some of my non-Reformed friends think, my purpose is predetermined, but I am not yet aware of the specifics; I most certainly do have to go to school; learning requires things like long study breaks to write blog entries; I have amazing circuitry but it's too small to see; there's no such thing as a silver edition of me; and I was born in Alabama.
All this about the superiority of life as a calculator and repetitious graphing aside, my real problem, until I started writing this blog, was how in the world I was supposed to propagate errors through a logarithm (now, it's how I'm ever going to stop writing and get back to work).
See, there's errors in everything. Ask a mathematician what he ate for breakfast, and he'll tell you 2-and-1-third strips of bacon, 1-and-3-eigths cups of grits, 1 cup of factory rejects cereal, and 1-thirds cup 2% milk. Ask a physicist (we do not respond well to 'physician'), and he'll tell you 2 plus-or-minus 1 cups of lucky charms (Factory rejects? Please!) and 1.67 plus-or-minus 0.05 cups of whole milk. As you can see, physicists have far too much on their plate to eat a lot for breakfast. In fact, I saw one eat his cereal standing up this morning because he had no time to sit down. I'm not kidding! In addition, physicists have much better taste in milk. But aside from this, the astute reader will notice, because I am about to point out to him or her, that the physicist included error bars. We use these all the time, plus or minus 5% of the time.
Getting measurement errors is easy. You simply turn to your lab partner and say "what error will be big enough to cover our mistakes, but small enough to make it look like we didn't really break all the laws of nature today?" I'm just kidding, of course. Really, what you do is estimate the largest possible error you could have made in carrying out the measurement, and then double it for good measure, because there's no way you can cover up that you just broke all the laws of nature, so you might as well not try.
Propagating error gets more difficult. First, the word "propagating" is easy to trip over, like a gate that's been propped open, or a propane tank you left out while tail-gating. Second, you forget how and, when you figure it out, you are so excited that you blog about it for an hour and get very sleepy.
Thankfully, I have written the rules in the beginning of my Physics notebook from last semester. As a faithful nerd, I have it with me in the computer lab, and so I can share with you the propagation rules.
When adding or subtracting values, simply add the errors. Subtracting errors may seem like a good idea at the time, but trust me, in the end you will regret it.
When multiplying or dividing, use a very large formula that you would have memorized by now if you were in Physics II, and which I do not know how to code in html, and so will not try! (If you are interested, I can whip it up on TeXnicCenter and send it to you in Adobe. And yes, TeXnicCenter is supposed to be spelled like that. To computer programmers and their strange typing ways I say, "w00t!").
These were the rules I remembered. Unfortunately, I couldn't recall what to do when taking a logarithmic function of something. But then I found it. Yes, dear readers, it's the moment you have all been waiting for:
In order to propagate the error through a log function, simply divide the error of the original value by the value itself.
Now, if I can just get gravity turned back on, I'll try to finish my graph so that Linefit can eat it again. Life as a computer program must be so easy...