My neighbor’s lawn is luscious and green. It makes me jealous. So I devise a devious plan. One day I visit him and ask him if I may pluck a single blade of grass from his lawn, for the alleged purpose of analyzing it. He is an intelligent fellow, so I reason with him: Surely, the removal of just one blade of grass will not strip his lawn of its luscious and green character. He agrees.
I return to my neighbor sometime later, explaining to him that I do not yet have enough grass for my analysis. I reason with him as before: taking a single blade of grass from his lawn will not take away its luscious and green properties. He agrees, and I rip out another single blade of grass.
I come back a third time. My neighbor is getting irritated that I keep asking for permission for the simple purpose of taking a single blade of grass. We agree sensibly that there is no single blade of grass such that pulling it from his lawn will no longer make it lush and green. Henceforth I needn’t ask him permission to take single blades of grass. I return home, taking a single blade of grass on the way.
That night, I intend to fulfill my dishonorable desires. I return to my neighbor’s lawn with the intent to uproot it and make it as ugly as mine. However, even in my jealousy, I am a man that plays by the rules. I did not get permission to upheave lumps of grass, so I leave my shovel at home.
Instead, I reason as follows. Both my neighbor and I agreed that no single blade of grass could make the difference between a lawn that is luscious and green, and one that is not. So I kneel down and pluck out a blade of grass. I then grab hold of another blade of grass and repeat to myself the maxim that since no single blade of grass makes the difference, this blade of grass will not make the difference. I do this all night, until I’ve stripped his lucious green lawn bare. In the morning, my neighbor is upset. But jealousy has vanished.
How and why did my neighbor succumb to my underhanded trick? It turns out that when we consider objects made up of large numbers of small quantities, such as lawns made up of blades of grass, or a barrel full of many drops of whiskey, or a head full of hair, we are tempted to think that changes in the small quantities do not amount to differences in the larger object or property. This has been recognized as far back as antiquity under the title of sorites paradox (‘sorites’ means ‘heap’ or ‘heaped’ and the paradox stems from our inability to say which removal of a grain of sand turns a heap into a non-heap).
Why are we tempted by such reasoning? What is it about our minds that makes us ignore or insensitive to small changes? In some cases it is because our perceptual systems simply do not provide us with the required discriminatory powers. For example, two red patches, although different from one another, may appear to be the exact same to me. The way my visual system works simply doesn’t allow me to see beyond a fine-grained level of detail.
In most cases however, it is our conceptual systems that are the source of indiscrimination. Even if you were told how many drops of whiskey are in a barrel, or how many hairs there are on someone’s head, this information does not help you decide where the boundaries are for when a barrel becomes empty or a head becomes bald.
The point can be made clearer when we think about it in terms of artificial intelligence. Imagine we built a robot with predefined concepts, like RED = 635-700 nm wavelength intervals. This robot would not experience a sorites paradox about the color red (let’s assume that robots can have experiences). Why? Because it can tell you exactly where the boundary of red is. If we lined up a series of color patches that go from red to orange, our robot could tell you which patch is the last red one and which is the first orange one. All it has to do is consult its concept RED and make sure that its sensory input values are in that range. Since we can’t do this, our concepts can’t be predefined and static like this kind of robot.
Instead, our concepts are much more likely to be dynamic and adaptable. This means that their boundaries can move around when activated in the right way, so that sometimes the concepts says ‘Yes’ to a case and sometimes ‘No’. This is a good thing, because it allows us to track changes and trends over time. And in fact, robots built with these kinds of concepts do much better at certain tasks, like tracking colors in environments where lighting changes.
What is particularly interesting about concepts that can update is that the price of their adaptability is the temptation to succumb to the kinds of reasoning we have been talking about–to think that small changes do not make a difference. If the boundary of a concept, when considered at a fine-grained level of detail, is moving around quickly and inconspicuously, then we may not be able to give a direct answer about where a boundary is. Our mind would think, so to speak, that the concept is being indecisive.
This is the source of our temptation to say that there is no boundary. If the concept appears to be indecisive, we are naturally inclined to think that this is because there is no such boundary. But as we already saw, we should avoid such temptation. Just because my neighbor cannot say which blade(s) of grass would turn his luscious green lawn into one that isn’t, doesn’t mean that there is no such blade (or blades).
Appropriately then, my neighbor should have choosen to say that he doesn’t know which blade(s) of grass makes the difference. But his ignorance of where the boundary is does not warrant the claim that there isn’t one. There may be such a blade. Moreover, since he’d rather be safe than sorry, he should only allow me to take a minimal number of them. Even if the number he picks seems arbitrary, he and his lawn are better off placing the boundary somewhere. In fact, he should have stopped me at the first blade of grass.
- Birth of a Titan
- Island: special feature on autism
- What Is Thinking in Pictures?
- Of Cats and Frogs
- Memories, Dreams and Refractions
- Emergence Is Bitchin’
- Looking Up, Down and Back
- Mythos: Genesis
- Dynamic Concepts
- Vanyez’ Dream
- Journey to the Known
- Santa Fe Voices
- Men Who Work with their Hands
- Moon Dreams
- Georgia L. May
- Elusive Artists of the Mid-Cape
- Fevered Visions
- On the Horizon