Shriram | Week 11 | This is How I Study
I’ve just now come to the realization that the reason it’s called “log” footage is because the camera records footage in a logarithmic curve.
Sunlight is strong. We expose our cameras to the sun for barely a hundredth of a second and are met with a blindingly powerful light and an overexposed image. To counter this, video cameras record with a logarithmic curve, where shadows are lifted and highlights are compressed, preserving the most detail for editing. Of course, the digital camera is a marvel of engineering and technology, but I never truly understood how deeply connected math was to the art of videography.
AP Calculus BC, for the most part, is an incredibly straightforward course. You learn about derivatives and integrals, what they mean, and how to manipulate them. One specific section, though, caught my attention. In unit 7 (which most of us have likely just completed), a simple set of rules are used to govern certain quantities and their rates of change; for example, Newton’s Law of Cooling: the rate at which something cools is directly proportional to the difference between its temperature and that of the surroundings.
We may know this intuitively: a hot pan under cold water will undergo a much more dramatic heat transfer than a cooler one. We may also know it from physics or chemistry: If energy is conserved between molecular collisions, these collisions must accelerate the slower molecules and therefore level the temperature.
I always hated when math was unnecessarily abstruse. Through learning more of it, however, along with other fundamental sciences, I’ve realized that it’s an incredibly elegant way of representing the world around us. T = (T[0] - T[surroundings])e^(–kt) + T[surroundings] will forever make zero sense to me, but dT/dt ∝ –(T - T[surroundings]) is a relatively straightforward statement.
Another intersection I didn’t expect to find is that between math and biology, through another equation. The premise is once again simple: a population will continue to grow, but slow down as it reaches the carrying capacity of the habitat. From this simple statement, we can construct an equation that represents entire ecosystems and accurately models their behavior.
All of math is, inherently, a tool. Many feel that they have to learn it simply for the sake of school, but its applications remind us that it was initially created to help solve problems we couldn’t before. It doesn’t have to be intimidating or difficult, sometimes it’s just useful.
I hope I do well on my test.
Hi Shriram! I just finished my Unit 7 test and I PRAY I did well. I have always considered math my favorite subject at school. Which is ironic because it tends to be the subject I struggle with the most. Numbers plainly arranged across a page never made much sense to me because what’s the point. Sure I can integrate huge functions but why should I? What is the end result beneficial for? It always makes sense to me when I understand the need for those methods and long functions with more letters than numbers. Maybe my brain just chooses not to pay attention until then, who knows.
ReplyDeleteI found the relationship between logarithms and cameras very interesting. I think associating your interests to subjects at school is a really effective way to ensure that information is actually retained and not just floating around. Also, I realized that everything has some process behind it. In my mind, the camera just captured what it saw, I didn’t really give it an explanation as to why it does that. But after I read your blog, I saw a group of friends taking photos in Sausalito yesterday and I couldn’t help but imagine the log functions directly behind the camera’s lens. After that, I bought socks with graphs of e and ln on them—goes to show how much “power” your blog had on me I suppose.
When I saw you wrote about Calculus I audibly gasped. If you ask my friends they’ll tell you that I’ve been raving over integrals like some fan girl for the past two weeks. However your blog was definitely something I have been thinking about for quite some time.
ReplyDeleteI always knew in the back of my mind everything was connected, or maybe it was because people told me everything was. However as I began to take more advanced classes I truly realized the connection all around us. You explain it very well through your example of Newton's Law of Cooling. At first it seems like some chemistry concept, but then it turns into math, then biology, then history, then english; it’s like you're falling down this never-ending rabbit hole.
It’s fascinating how all these things are connected, and as much as I despise complex integrals, I really enjoy the science behind them.
Shriram, as you posted your blog right as I was studying for my unit 7 test regarding the topic of differential equations, I knew I had to hop off my computer. I was pretty much sick of seeing its applications. Reading through this post, I do realize that this sort of math truly does describe our world all these little aspects from collisions on the molecular level to massive population growth. I honestly hated the formula for the cooling law, but after learning the logic behind it, it’s grown on me.
ReplyDeleteWhen studying, I chanced upon a video explaining what differential equations were. While I didn’t get much calculation help from it, I did learn that they can be used to represent pretty much every possible change in the universe. Wacky equations, yes, but that was the power behind these things simply relating quantities to each other. Reflecting on the practical use of math, we really can remember how it came to be: through applications and our will to problem solve. Anyway, I hope you did well on your test!
I’ve always been “good” at math throughout most of my life, but, just like you, AP Calculus BC was truly the first time I’ve understood its real-world implications. Not long after finishing the Common Core curriculum (or perhaps even within), math slowly starts to become more and more abstract. There are certainly real-life examples that can be applied to math problems, but much of it was quite shallow—there’s only so many times in a human life where one has to calculate simple interest or how fast a rock hits the bottom of a cliff or the amount of fencing needed for the 10,000 square foot isosceles trapezoidal enclosure of our horse field. As terrible and evil as the company Collegeboard is (hi Mrs. Smith!), I can appreciate that they dedicate a significant portion of AP Calculus curriculum to real world applications and explanations.
ReplyDeleteOne part of our current calculus learning that I appreciated the same way you did with logistic growth and cooling functions is calculating volumes of nonstandard shapes using cross sections. I immediately recognized the parallels between that lesson and 3D modeling or CAD (computer aided design) software, a crucial part of all types of modern engineering; rotating an area around a central axis (a part of the calculus topic) is one of the most fundamental actions one can do in CAD softwares.