Recently, I've been watching a lot of science shows on Netflix. I have a certain proclivity to gravitate towards shows and documentaries about ancient history and cosmology. Most recently, I began wtaching National Geographic's The Universe, a 64 episode series, and I think it's begun to affect the body of things that I think about these days. that is, to say, I think about physics and the cosmos and interaction of those things with a distinct regularity. I've always been interested in those types of things, and have retained a fair amount of that knowledge from when I was studying chemistry and physics in high school and early college.
Last night, as I was trying to go to sleep, my mind was racing (attention deficit is a bitch, let me tell you). My mind began to apply logic and a rudimenary understanding of mathematics in one coalescing body of theory. The theory is a rather simple one, but takes a bit of conceptualization to grasp methinks. It begins as a the concept that one result, A, is the sum of its causes, B and C. In logic, the cause is almost always a result of the variable that are applied in some way to produce the result. For instance, when you add yellow paint to blue paint the result is green paint. Taking this model, we can see that the yellow paint, B, and Blue Paint, C, combine to form green paint, A. This can be described in a simple equation:
A=B+C
In describing the simple logic of combining values to yield a new value, we can infer a couple of things:
1. A is the sum of the properties of both B and C.
2. The properties of B are independent of the properties of C.
3. The properties of C are independent of the properties of B.
The forst statement is proved by the original eqation. The next two statements are proved by a simple mathematical reorganization where the original equation is rearranged thus:
A-B=C
and
A-C=B
Both B and C have an intrinsic, or inherent, values that are true regardless of whether or not those values are known. The mere existence of one paint doesn't determine the properties of another paint unless combined with that paint, therefore paints B and C are independent variables of A. At this point, we can apply the Law of Composition as derived by the logical premise that states while A is the result of both B and C, the properties of each of the three variables are, for the most part, separate from one another. In other words, while A may have properties similar to properties that exist in both B and C, the totality of said properties in each are not equal. As pointed out by Madeleine L'Engle in her famous book, A Wrinkle In Time, "Like and Equal are not the same thing."
Q1: Ok, so how can we use this in everyday life? After all, I'm not a painter.
A1: Let's pretend your boss comes to you and says "Finish your work. You're spending too much time fraternizing and playing on the internet." For now, we'll assume that there are only two apparent variables that yield a result. Your boss assumes that a lack of production, A, is due to fraternizing, B and Internet usage, C.
First we infer that your internet usage is intrinsically independent of your fraternizing, or B has a value that would exist whether or not C was present, and vice versa. If your boss observed a decline in your production, he or she could also infer that if you removed B or C from A, then the value of production, A, would increase. This is easily stated as A-B=C. But to this point, we've only proved that B and C are independent. Surely, if you cut out talking to your co-workers the time you spend unsing the internet will not equal the time that you spend working, right? Wrong.
Q2: But this contradicts what you just said. How can this be?
A2: When we start talking about things relative to a time frame, then we have to include another variable because time itself is only relative among the variable themselves. This is the dependent variable. Our equation has evolved at this point. Time was previously irrelevant to blue and yellow paint, but it is a key component, the crux of the argument by your boss, if you will. In order to instigate an change in A, it must be offset by a change in time, x. Let's take a look at our new equation:
Ax=(B+C)(-x)
As time is relevant to both cause and result, it exists on both sides of the equation. In order for A to increase with the reduction of the equation by B (or C, depending upon which value you use), then some varaible, x, (time in this case) has to become dependent upon one of the other variables. Here, we can say that when A is reduced by B, the value of x is decreased by a factor of C. But how can this be? Because the relationship between varaibles B and C to that of time, x, is inversely proportional.This also means that as x gets smaller on one side of the equation, it gets larger on the other side. Thus we get:
Ax=(B)(-x)+(C)(-x)
In conclusion, if we spend less time (-x) doing B and C, then we will spend more time (+x) doing A. This brings us to two equations:
The relationship of a sum to its elements:
1. A=B+C
The relationship of a sum to its elements when time is introduced:
2. Ax=[(B)(-x)] + [(C)(-x)]
See? This is what happens when I drink energy drinks and watch National Geographic. I told you this stuff was happening. I've got to get this sort of thing OUT OF MY HEAD. Math isn't my strong suit, and I freely admit that. In fact, if t wasn't for my buddy, TD, then I'd be stuck like a broken record at the very end of things. So, what I'm trying to say is don't beat me up if there's some mathematical problem there. I don't take too much responsibility for it i it exists.
Invino Veritas
7/1/11
EOF
No comments:
Post a Comment