I continue to have difficulty comprehending the very large and the very small.
Yesterday, thinking about the word “small” itself, I got to wondering what I mean when I call something small. I wondered how I would phrase a definition of the word, if I were assigned the task of creating one for a dictionary. For example, I could say “small” means the same as “little.” But what would that add, say, to the understanding of someone who spoke only Chinese, or Martian? My dictionary in fact defines “little” as “small in size.” Could I define “small” other than by simply using an English synonym for it? If you’re a word nerd like me, you might try doing this yourself. If you do, I’d be interested in hearing what you come up with.
I think my big American Heritage Dictionary (Houghton-Mifflin) struggled with the same problem. In that dictionary, as noted, “little” is defined as “small in size,” while “small” is defined as “being below the average in size or magnitude.” Fair enough, I thought, until I considered some other definitions in that same book, where “size” is defined as “the physical dimension, magnitude or extent” of something, but “magnitude” is defined as “greatness in size or extent,” and “extent” is defined as “the range, magnitude or distance over which a thing extends.”
Considering all these definitions together, I imagined my Martian visitor persuaded that abstractions like “small” and “little” mean the same thing, but having no idea what that is. When the words are only defined in terms of each other, how can anyone tell what they really mean?
Though I felt I was going in circles, I kept trying.
“Great,” I learned, is “Very large in size,” while “large” is “of greater than average size or extent.” So great means large and large means great. Great! But if I didn’t already have an idea of big and small, where would that get me?
Of course, linguists have long recognized this circularity of language. The problem isn’t just defining “small” by using a synonym like “little.” It’s more general than that, and it ultimately comes from the absurdity of trying to define words using other words. If we want to define what a word means by saying that word A is equal to words B, C, and D, the problem is that no matter how many words we go through, every set of words becomes equivalent to nothing but other sets of words. B, C and D are defined by E, F, and G, and those by H,I and J, but H, I and J are defined by A, B and C. Even in a language of 50,000 words, that fixed set of things is limited – a closed loop, explainable only by itself. Every word, sooner or later, can only be defined by reference to itself or to words that it has helped to define. And in any such closed system, entropy sets in.
The definitions of “small” and “large” above both make use of the concept of “average,” which might seem helpful, because “average” is a concept which takes me from the world of words into the world of mathematics. If small is less than average and large is greater than average, then that should prove helpful – provided I know what “average” means. But what do I mean by “average”?
My mathematical concept of “average” requires a finite set of numbers to consider. I can say that the average of two 12’s, one 17 and one 19 is 15, but only because I know how many of each number I have for my calculation. I’m dealing with a known, fixed, quantifiable set. I might even be forgiven if I say that the average (in size) of one golf ball, one tennis ball, and one soccer ball is (more or less) a baseball, because, again, I’m dealing with a know set of data. But what data set — what objects, and how many of them — should I use to compute an average, on my way toward understanding that small is below average, and large is above average? The average size of all things? If I take the smallest things I know, like quarks, and the largest, like the whole universe, don’t I still need to know how many quarks there are, and how many stars of various sizes, before I can compute an average size of things, and therefore to know what it means to be above or below the average of all things, and therefore, inherently large or small?
Meanwhile, in order to take into consideration, say, my dictionary, in order to count it in considering the average size of all things, do I count it as a single thing, about 14 inches in length and weighing a few pounds, or as a thousand smaller things, called pages, or several billion even smaller things, called molecules? Is my car just a single car, or is it an engine, a body, a chassis, and four wheels? Obviously, if I count myself as one person of my size, I have a very different impact on the “average” of all things than if I count myself as a few billion cells of far smaller size. With such questions pervasive about every thing and every size, I submit, it is impossible to formulate a data set capable of yielding any meaningful concept of an “average” in the size of all things — yet Houghton Mifflin has no problem saying that small things are things smaller than “average,” and large things larger.
(By the way, I submit that it it makes no difference if we think in terms of medians. Using medians, I suspect our calculation would yield something only slightly larger than a quark, and virtually everything else would then be considered very, very big by comparison. And if we used the half way point between the size of a quark and the universe, we’d get get something half the size of the universe, and everything else would be very, very small. Can our feeling that we understand what’s big and what’s small be so dependent on different mathematical ways of thinking about averages?)
Pulling out that big dictionary again, I wonder, what makes it big? At first glance, it doesn’t seem nearly as big as my car, yet I call it big while I call my car small. Surely, I mean that my dictionary is big because it has greater magnitude – more pages, and more words — than other things to which I tend to compare it (roughly speaking, those other things I also call books). I call my Toyota small because it has less trunk space and passenger seating than my daughter’s SUV. Could size, then, be a concept that is relative? It seems so – but relative to what?
I find this last question intriguing. I think a book big when I compare it to other books, and a car large (or small) when I compare it to other cars. That concept of relative size seems easy. But if I think for a second that a star can only be thought large in comparison to other stars, I quickly retreat from my relativistic comfort zone. Surely stars are always, and absolutely, larger than books, and surely books are always, and absolutely, larger than quarks. If so, surely there is something about size that is not relative to its own group of similar objects – something absolute which enables me to feel quite strongly that one group of things is inherently larger than some other group of things. And so, once again, I’m back to square one, wondering what makes one thing large and another thing small.
In desperation, I consult the dictionary again. This time, instead of “large” or “small,” I look up the word “big.” (After all, what could a big dictionary be better at defining?)
“Big” is defined by the folks at Houghton Mifflin as, “Of considerable size, magnitude or extent; large.” Size, magnitude, extent, large – nothing new here. Big is large, and large is big./ For a moment, I’m disappointed. But wait. (There’s more!) I look up “Considerable.” The first definition of “considerable” is “large in amount, extent, or degree.” ( Arghhh! Large means considerable, and considerable means large. I feel like I’ve been here before.) For a moment, I consider looking up the new words “amount” or “degree,” but I decide that effort won’t likely be useful. Then my eyes fall on the second definition of “considerable.”
“Worthy of consideration.”
Ah! We’ve left the world of physical dimensions, some place outside the closed loop of size words. Am I finally on to something? I look up “worthy.” I find, “Useful. The quality that renders something desirable, useful, or valuable.”
I think I’ve found the answer I’ve been looking for. Something is “considerable” if it is worthy of consideration, and it is worthy of consideration if it is useful. Size is indeed relative, but relative, primarily, to what I find useful.
I recently watched Season Six of the survival series “Alone.” (Synopsis: Ten people competing to survive in Ice Age conditions.) In that world, a moose was important, both because, unlike a squirrel, it could kill you, and because, if you could kill it, it could feed you for a very long time. The series contestants considered thirty-pound Northern Pike or lake trout more valuable than ten-pound rabbits, which were in turn more valuable as food than even smaller things like mice. The closer in size something was to the contestants, the more nutrition it brought. The more “worthy of their consideration” it was.
The contestants on “Alone” embraced the value of living as our primitive ancestors did, and I find myself reflecting that it was this ancestral way of life that shaped our species’ understanding of words like “big” and “small.” Pigs and cows and grizzly bears were more important than, say, mosquitoes. As human beings evolved, those who paid most attention to things about their own size — things between, say, the size of spiders and mastodons — survived and reproduced better than those who paid attention to grains of sand or the vastness of the Universe. I conclude that, as we generally use the terms “small” and “large,” absent a context which suggests a different relative comparison (a car being small compared to other cars), the default meaning is not really relative to a some incalculable “average,” but relative to ourselves. That is, smaller or larger than we are. I myself create my sense of the “average” size of things. Things smaller than me are small, and things larger than me are large. Things are large or small relative to me. And from an evolutionary perspective, it is the things closest to my own size that are (subjectively) important to me.
But are pigs and grizzly bears really more important than mosquitoes, objectively? Exploding supernovae and super massive black holes are not only extremely large. Astronomers and cosmologists now tell us that if it weren’t for them, we wouldn’t exist, as they create the very elements from which we’re made. Those who study life’s origins tell me all complex forms of life began when bacteria became essential parts of our cells, so we wouldn’t exist were it not for bacteria. And the importance of bacteria is not just historical. If, today, things like plankton and bacteria stopped being available as food for larger things, moving up the food chain, we’d have nothing to feed on ourselves. And all the time, quantum physicists remind us that without things as small as quarks, we wouldn’t exist either.
So it isn’t really true that lions, tigers and bears are most important to my existence. Nor were they, in fact, most important to our ancestors’ existence. From an evolutionary perspective, we succeeded by paying attention to things our own size, not because such things were more important to us, but because we could actually do something about them if we paid attention to them. Evolution proved that paying attention to them was useful to our survival.
But if the issue is usefulness to me – whether I can put my understanding of something to use, to help me eat it or to keep me safe from it – which should I consider more worthy of consideration, more considerable in size, to my current life in the 21st century – a black hole, or a virus? If the answer is that I can do more with my understanding of viruses than I can with my understanding of black holes, why do I think a black hole more worthy of my consideration – more considerable in magnitude —bigger — than a virus?
Our notions of smallness and bigness come from a time in our past when we could not deal effectively with things far smaller or larger than ourselves, a time when things our own size – the moose, the cow and grizzly bear – were most worthy of our consideration. We could not concern ourselves in those days with virology or pandemics, with things as small as molecules of CO2 or as large as ozone layers or the acidity of the oceans. Thinking about viruses rather than grizzly bears would have been fatal in those days. But such things, both the very large and the very small, are beginning to enter our sphere of influence. As science continues to broaden our understanding of the world, our ability to prosper (or not) in the face of things we previously thought too large, or too small, to matter, changes. Is it time, now, to revise our thinking about the meaning of words like “large” and “small”?