Coil Shuffling — June, 2007
Hundreds of years before you took your first geometry course, a man named Pythagoras sat in the desert dreaming about circles, rhombuses, parallelograms, and triangles. Apparently it's hard to pick up women with a name like Pythagoras. With all his free time, however, old Pythagoras realized one day that the sum of the squares of the sides of any right triangle is exactly equal to the square of the hypotenuse of that triangle. As excited as he was about this realization, he had a difficult time explaining it to his friends. So in an act of desperation, he decided to express his profound thought mathematically, and it came out like this:
Expressed this way, his friends were better able to understand the idea. What's more, they could put the idea to use when designing stables for their camels and sheep. It immediately became easier to design solid trusses.
Several years after Pythagoras shuffled off this mortal coil, Sir Isaac Newton was sitting below a banana tree pondering various physical phenomena when it dawned on him that force can be expressed—and understood—as the product of a mass and the vector quantity of acceleration to which that mass is subjected. This didn't make any sense at all to Newton's friends, so he, too, resorted to math and scribbled down the following:
Knowing that force equals mass times acceleration, Newton's friends figured out that you could make a cannonball more destructive by making it heavier or faster—not simply one or the other. They could understand this without knowing anything about “vector quantities”.
Several years after Newton shuffled off this mortal coil, Einstein sat in a Swiss patent office contemplating some of the things Newton had said. It dawned on Einstein that Newton was probably wrong about a few things. I won't encumber you with my attempt at explaining Relativity; it would be confusing and largely incorrect anyway. But Einstein had to resort to mathematics, too. The world knows it as:
Expressed this way, it became a whole lot easier to build atomic bombs.
The point is that things are sometimes easier to express, understand, and put to practical use when they are expressed mathematically. It may seem odd that math could be easier to understand than natural language descriptions, but it frequently is. And lucky for us.
Several years after Einstein shuffled off this mortal coil, I stood in the shower simultaneously pondering the power of mathematics, singing Cake songs, and thinking about Shakespeare's Hamlet. If you're still with me, you're probably thinking that I need to think about different things while I'm in the shower. I know. I know. I'm a geek. And if we just accept that, I can move on.
I was thinking about how Shakespeare said, “brevity is the soul of wit.” He felt that for any given thought, its wittiness—and therefore value—increased as its expression became shorter. As I washed my left knee, I began wondering if there might be any value in expressing this idea mathematically. And that's when I came up with this:
WT represents the “wittiness”, or overall value, of the thought as it is expressed.
MT represents the magnitude of the thought, or how profound the idea is itself.
LT represents the length of the expression necessary to convey the thought.
Now you're asking yourself, “how is this going to help me build stronger trusses, better cannonballs, or an atomic weapon?” It won't. It may help you better evaluate the correspondence and conversation you share with others, though.
Any time someone has a thought, if she chooses to express it, she chooses not only what to say but also how to say it. Both of these are important to the wittiness and value of communication. Revisiting this 'wittiness' equation, we can see that wittiness is expressed as the quotient of a thought's magnitude and its length. We could also say that wittiness is directly proportional to the magnitude of the thought and indirectly proportional to the length of the thought. It doesn't matter how I describe this equation. What matters is that better thoughts are wittier and shorter thoughts are wittier still.
So with that, we can put our equation to some basic use. For MT, we must develop a quantitative means of evaluating the magnitude—or profoundness—of a thought. We can “rate” thoughts on a scale of 1 – 10 if we choose. Or we can use a scale of 1 – 100 if we need to be more granular. It doesn't matter, as long as we pick a scale and stick to it. For LT we must choose a means of quantifying the expression's length. But this is a little easier. We can, for instance, count the number of words, number of letters, or number of syllables. Again, it doesn't matter as long as we pick one scale and use it consistently to compare expressions. Once you've chosen your scales, simply assign values to MT and LT and do some simple division. You can now compare the relative wittiness of any two thoughts—as they are expressed.
Let's try it out.
Thought 1 — Exclusive dedication to necessitous chores without interludes of hedonistic diversion renders Johnny a hebetudinous fellow. *
Thought 2 — All work and no play makes Johnny a dull boy.
In both cases, the thought is equally profound. The exact same idea is conveyed in both sentences. So, we can safely assign MT a value of 30 for both of these expressions. Thought 1 uses 15 words. Thought 2 uses 10. Perform a little division and Thought 1 earns a WT score of 2 and Thought 2 earns a WT score of 3. See how this works?
Let's try another comparison using a different measurement of length. This is OK so long as we base our comparisons on the same scale.
Thought 1 — Pulchritude possesses solely cutaneous profundity. *
Thought 2 — Beauty is skin deep.
Again, both thoughts are of equal magnitude. I'll assign them MT values of 40. Thought 1 uses 16 syllables. Thought 2 uses only 5. Therefore, Thought 1 earns a WT score of 2.5 while Thought 2 earns a WT score of 8.
Now, armed with this equation and your own choice of measurement scales, you can go forth evaluating the wittiness and value of your daily communication. It's that easy.
Well, actually, it's not quite that easy. This equation has a couple of issues. For instance, my equation is based solely on two factors: profundity of thought and length of thought. There are circumstances when you may feel these variables are inadequate. For instance, take the following poem I wrote:
'Tween Hitherto and Henceforth
'Tween hitherto and henceforth
is a moment called “right now”.
But briefly do we know it
then it's hitherto somehow.
'Tween hitherto and henceforth
lasts for just a beat.
Then it's onward into henceforth
to see what we shall meet.
'Tween hitherto and henceforth
forever shall we fly.
But I'll never forget the “right now”
when you first caught my eye.
In this case we could rate MT on what is conveyed in the poem—in one of life's fleeting moments, I met a girl, she made me stir, and so stirred did she make me that I will never forget her. That should be easy enough to put a value on, right? But do I get credit for the word play? Do I get credit for rhyming? Is there anything in the poem that makes MT worth more than the simple expression of the thought? I hope so, because I used a lot of words to state the thought.
Try another example. We'll look at another Shakespeare quote:
“Able was I ere I saw Elba.”
Shakespeare's statement is pretty simple. Everything in his life was OK until he saw Elba. After that, it was never the same. But take a moment to point Shakespeare's quote at a mirror and you'll find it reads the same in both directions. Does Shakespeare get extra credit for writing a palindrome? I surely hope so. But it's really up to you.
So, my equation breaks down quickly due to the subjectivity of assigning a value to MT. There is no agreed-upon yard stick for measuring the profundity of thought. Sorry.
My equation breaks down in another circumstance as well—multiple languages. What if you find yourself evaluating the same thought expressed in two different languages? Not all languages are created equally—though some scholars would argue this point. So, how do you fairly evaluate these situations?
Well, this I've fixed, by introducing a coefficient into my equation.
The coefficient, CILC, is based on the Index of Language Complexity scale. You can read about it in the 200 pages of reference material listed to the right if you're deeply intrigued. A simple example will be enough to summarize why this coefficient was necessary for our purposes.
Consider the following two simple statements:
Thought 1 — The banana is yellow.
Thought 2 — La banana es amarilla.
In both cases the thought is exactly the same. MT is obviously equal. In both cases, 4 words are used. So we could say that LT is equal—and for this example I would probably agree. But Thought 1 is only 17 letters long while Thought 2 is 18 letters long? Does this matter? Some linguists may say that English has greater information density per letter than Spanish. Or consider this. Thought 1 is 7 syllables. Thought 2 is 9 syllables. Does this matter? Some linguists may say that English has greater information density per syllable than Spanish. This may not be all that concerning when describing the color of fruit, but it may become important when discussing love, politics, or the complexity of anxiety disorder. So it's worth considering.
Therefore, if you have to evaluate expressions in multiple languages, simply scour the 200 pages of documentation and evaluate each expression with a language-appropriate coefficient. You'll find that languages with greater information densities will have lower coefficients while those with lower information densities will have greater coefficients. Alas, it's not so easy to actually put my coefficient to use. But it's conceptually sound, and I wish you the best of luck with it.
So where does all this get us? We've got a somewhat silly equation for measuring the wittiness of expressions. We've got an equation with some subjectivity flaws. We've got an equation with some multilingual weaknesses. It's a pretty weak equation indeed. But I hope you won't give up on it too quickly. Though you may not use it on a daily basis, there are some important points to take away from all my rambling.
The first of these is when people speak or scribble words but nothing useful comes out; meaningless, irrational, or irrelevant thoughts earn MT scores of zero.
The second of these circumstances is when people say things that are patently false; lies, slurs, and hateful things earn MT scores of less than zero.
I've graphed what this looks like below:
You can see that as MT approaches, reaches, and passes below zero, the utility of the statement to the world quickly becomes negative.
A third circumstance occurs when people have thoughts but choose to say nothing. In these cases, no matter how profound MT could be, LT equals zero. Basic algebra will tell you that anything divided by zero is undefined. It has no value, not even zero. The thought doesn't exist. It is nothing. It makes no impact on the world even though it may be profound.
I've graphed what this looks like below:
You can see that when LT nears zero, the graph of wittiness approaches genius, but quickly ends. It is not defined if you say nothing.
So now where does all this get us? We've got a somewhat silly equation for measuring the wittiness of expressions. It has subjectivity flaws. It has multilingual weaknesses. It can actually equal less than zero in some circumstances. It can be completely undefined in others. If my shower-inspired equation has no other value in the world, I hope it stresses at least this:
Some day you too will shuffle off this mortal coil, and I hope that in the “right nows” of your life, you will never let my silly equation equal zero for you. I hope you will never let it become undefined. I hope you will say something when it's most necessary. And I hope you will say the right thing—and the true thing. If you manage to interject some wittiness, all the better. But it's unnecessary.
Now if you'll excuse me, I've just finished reading Much Ado About Nothing and Cake just came on the radio. I'm going to do some pondering in the shower.
~ topher
* I originally saw these statements in the Milwaukee Journal, years ago.