Arcing Through the Void
Math and language seem to possess a common origin point as their methods for communication move in opposite directions. Yet, they share analogous structures. There are clear patterns which could be attributed to the fingerprint of humanity’s collective approach to producing meaning of a complex and overwhelming world that does not make sense. So, why is there a divide that stands between math and language? The gap is a result of a liminal realm we have yet to mine to its depths and feel certain of any answers: humanity itself.
How do you explore what you cannot see? This question explains why it is difficult to understand exactly where math and language originate, or if they even have a common source. We cannot even fully explain what we feel or why someone reacts the way they do with enough certainty to do so consistently. We are still trying to learn the hows and whys of human consciousness. How do we think and what value do emotions play in intelligence are questions scientists are trying to answer. As sciences go, those that look inward are woefully young in the face of other, “harder” sciences despite our preoccupation with them over the course of our species’ history.
Consider the advances in physics with the tell-tale discoveries of the Higgs-Boson particle and the subsequent claim by physicists that we have found the entire observable physical universe. Short of dark matter and dark energy, it seems science has allowed us to learn all there is to the behavior of the observable physical universe, barring the chaotic nature of the quantum. Biologists are decoding the human genome and closing in on what triggers various ailments or makes them likely to occur. And, as a science, biology is younger than astronomy. It is only a matter of time before we master biology to the extent we have physics. Psychology arose at the end of the Victorian Age as a codified field, meaning we have a long way to go towards understanding how the mind works in light of how long it has taken us to progress in other fields.
Think about this for a moment. Science is based on observations. The way the scientific method works is by recording results that can be measured and verified. So, how does one go about observing the unobservable? We do not try to. Instead, we measure as many of the results as possible. Depending on the trait being examined, this could be a reactions test, using an MRI, word associations, isolating the eyes, etc. In short, we measure how the mind works by measuring what it causes in relation to what can be observed.
Astronomers do the same with black holes. There is nothing to see, but we know the black is a real object by what it does. One of the effects is gravitational lensing, meaning that the light from objects behind the black hole is bent and thus they appear in a location other than where they truly are, namely to one side (or both) of the black hole. Accretion discs with superluminous jets of particles thrown out of a feeding black hole are also signs of the black hole’s existence. These visible signs help confirm the predictions that come out of the math that explains how such phenomena occur. In fact, it is the same math of gravitics that predicts where objects are, even if the object cannot be viewed. We can track things to the point that, barring some unknown interactions, we will find them at our leisure in the places we expect.
Think of the above being applied to the human psyche. We know that we all have an instinctual component that governs some of our responses, but why is that the case? That is one of the areas psychologists study; and like earlier pioneers in other fields of science, they have quite a bit of trial-and-error to go through before their theories begin to pan out. Two things to mention here: psychologists have an extensive body of analogous structures to draw upon in the shape of well established bodies of knowledge and people generally do not like being the subject of experiments. Ethics serves as a roadblock as well in light of some truly sensitive areas of our psychological makeup, making the black hole analogy not too far removed from the challenge.
The gulf between math and language might as well be from the Earth to Mars although it looks like a bridgeable gap. We cannot just create a bridge across a river without knowing its depth. For the metaphoric river that represents human consciousness, it is river wide, ocean deep. Know of any bridges anchored in water that deep? Until we can find a bottom we have to arc our way across the void, like a ship sent to rendezvous with another world.
The problem with an arc to reach our destination is that, for all its use, an arc goes around the core issue while passing through its space. Look at how we have managed to explore our neighbors in the solar system. We did not fully understand how space worked but we knew enough to work out how to get from here to there. The same held true for navigation of the ocean. We knew very little about what was beneath the surface of the ocean, but we knew how to cross it. This is in many ways similar to what remains for psychology.
What we can say for certain is that math and language work the way they do because we need them to. On some level we know that they have a similar structure and an origin rooted in how we process the universe. On another, we cannot seem to come to terms with that. Yet, there are languages where the mathematical values of combinations of certain words are equal to a related word that can symbolize a relationship of those words together.
The catachrestic dichotomy arises when we separate the role of language and math. In part, this is a result of how we perceive the world and share that information with others. Language may help us exchange concepts but not the same images used to form or receive the concepts. The function of language is purely conceptual. This is why what I saw when I envisioned the boy hitting a ball is different than your image. Think of the weirdness of idioms. They do not make literal sense and sometimes violate grammatical structure, but the concepts are well understood by members of the culture. Note that most people never question what the concept looks like, however. Math has similar elements, but where things begin to break down is in visualizing the equations. Why though? Language expresses while math evaluates. Language does not determine value, it describes it. Yet, we expect people to understand this on more than an unconscious level. This means we are expecting them to know the divide is there without qualifying they are aware of this. Most of the time, we do not recognize it for our own needs for some of the same reasons.
Language is used to describe how the world works. Math measures why it does. This distinction is important because it speaks to many of the reasons why the catachrestic dichotomy divide exists. Language is the attempt to share events and experiences as an individual perceives them whereas math evaluates processes as they are and shows how those values come to be through formulae that measure such changes. In essence, subjective v. objective observations.
As explained earlier in this series, math and language work together because we make them, but only inasmuch as we make one trigger the other. This is a cyclic process. We experience reality and then ask why. Just spend time around a small child. They keep asking why various things work the way they do. They are sorting out what they see and experience as a way to lessen the overwhelming sensation that they have no control. As children, we see more than we can ever put into words. There is a certain aspect of description that language cannot capture, hence the need to stretch words beyond their original meanings. Math can assist the process of catachresis by providing the tools for understanding why the concept is possible. The more the process can be replicated, the easier it becomes to describe it, which solidifies the concept.
So how do we get from childhood to math? The process of understanding begins with the infancy of our species. Recall the section of this series on specialization and techniques passed from one skill to another. Our body of knowledge develops on an individual basis in a manner not unlike the knowledge base we operate from as a species. We apply the knowledge from one experience to another with the assumption that the events are mechanically the same. And for many items, the analogies are close enough with few modifications to the base idea. Thus, words acquire new meanings in relation to our greater understanding of a concept.
The senses we possess and our mastery over them helps to explain a part of this phenomenon. Of all the senses we posses, the only one we can claim to have any control over is touch. Everything else is a stimulus done to us whether we want to experience it or not. Out of the remaining four senses, the strongest is hearing. Babies may have a sense of what tastes good to them, but they do not have a storehouse of experiences to know what types of flavors interest them the most. The same goes for smell. Our eyes are so complex that it takes a long time for them to develop in comparison of the others senses. What, then, do babies rely upon to make sense of the cacophony of the world they must learn to adapt to? Sound. From the soothing sounds of our mothers’ voices to the wailing sirens that fill the modern world, the familial voices provide an anchor.
As a baby gains greater control of its bodily functions, sound begins to take a secondary role. The eyes begin to develop the acuity necessary for a predatory species. (Yes, we are predators, it is why our eyes face to the front and not to the sides; sorry if this upsets you.) Why does sound take an evolutionary step backwards? A likely reason is that we replace the need to rely upon pure sound with language. A baby’s cry indicates some sort of stress, but not necessarily why or from what. Yet when the child gets older, he can express what the matter is. Pure sound is not as nuanced as speech. So, we sacrifice sections of the hearing range to focus on what conveys an even greater density of information.
As apex predators, sight becomes our primary sense because we inhabit a spatial world. This is a realm governed by pure math. Everything is measured. The eye is designed to determine the size of objects; when paired, eyes provide depth perception that makes such observations of mass and color much more informative instantly and with less guesswork. Whether it is estimating where a ball will be after it is thrown to hitting a deer with a spear, we are in a world of math. In these cases, it is trigonometry. Think of it as geometry in motion if you are not familiar with the math. When playing tag, you do not run to where the person currently is, you go where you think they will be. This is how children begin to recognize analogous structures in action through experimentation and observation.
The brain loves patterns. While rote activities bother us to no end because of their repetitive nature, the ability to recognize patterns lets us navigate through unfamiliar territory with greater confidence. While not perfect, this mechanism makes the inundation of sensory input manageable. The nuanced elements of the territory’s permutations of the pattern means mistakes are inevitable. In adults, this is often expressed as frustration. Children, however, are more likely to show their lack of understanding without feeling a sense of shame. One area where this is seen is in language acquisition. Look at irregular verbs and their conjugation. A child might say “I swimmed in the pool” before learning that not all verbs end in “ed” when speaking of the past. Likewise is the false analogy in games where the child says “I win you” rather than “I beat you.” These are attempts to span the divide between what is known and what is perceived, just like when kids are trying to master the coordination needed to catch a ball or throw one at a moving target.
Now, to return to the earlier thought about the complementary relationship between language and math, let us look at the continued development of all acquired knowledge. Language allows ideas to be shared; math proves the validity of many of them (arts and humanities being such fields). Generally, this is the concept behind technological developments. Think of it like this: “If we know X, then Y;” “If we know that a cannonball travels a certain distance before gravity pulls it down, then one that travels fast enough will never hit the ground.” This is what Isaac Newton proposed. In turn, it became known as the gravitational constant. While it may not hold in light of the quantum realm, this basic truth about gravity’s influence on Earth is part and parcel of the foundation of aeronautics that led to escaping Earth’s pull.
How much of an impact did Newton’s observation have on the world of language? Jules Verne’s “From the Earth to the Moon” is based on the work Newton and his followers built upon. Verne had figured out the math and discerned the best location from where to launch his vehicle: Florida. He even conceived of an oceanic splashdown for the return vehicle. His math was not accurate, but he extrapolated details based on existing concepts and then used the math to prove the validity of his concepts.
Conceive and measure, measure and conceive. This is the process we use to formulate ideas and have them evaluated. Trial-and-error applied to our pattern recognition abilities; if X, then Y. X is the catachresis used to fill in a linguistic gap for a logical process. In some cases the logic is sound; in others it fails miserably. The dichotomy between math and language is no different than that between introverts and extroverts. It is difficult to understand a desire for deep thought if you are interested in light conversation with as many people as possible and vice versa. So it is with math and language.
How can I make you see or feel what I do? I can only express the concept. The metrics are up to you unless we are observing the event together. Even then, our perspective is shaped by our vantage points. So, how do we agree on what we have actually seen? Experimentation and collaboration. Trial-and-error leads to catachresis when new experiences are observed. Why that occurs is in part the expectations of the rules (or laws of nature) not meeting known patterns. When what I believe should occur in a game based upon my understanding and experiences differs from yours, argument ensues. That is how important nomenclature in rules matters. It is also why, after arcing through the void, NASA lost the Mars Climate Orbiter in 1999 when one team used metric measures and another used English. Their frames of reference expressed different concepts and led to disastrous results, like most forms of miscommunication do.
Previous:
Anatomy of Game Design: An Unbridgeable Divide, Part 6
Next:
Anatomy of Game Design: An Unbridgeable Divide, Part 8.1