Matter Thinks

No Boundaries September 22, 2009

Boundaries as we conceive them do not exist in the real world.

The evidence for this is abundant. In summary:

• Boundaries are fractal and fuzzy.
• Boundaries are unknowable.
• Boundaries are immaterial (because they are functional).
• Boundaries are unnecessary (there are boundary-free ways of organizing perceptions and understanding reality).

The first assertion has to do with the empirically observed properties of objects at their boundaries. Look at any natural object through a high-powered microscope; you will see something closer to a landscape than the straight lines or smooth surfaces you see at a casual glance. Not only that, but, just like a landscape, if you zoom in further you find yet more details. As Benoit Mandelbrot pointed out regarding the length of the coastline of Britain, the shape and length of the boundary of any object depends on the length of your yardstick. Geometrically precise boundaries above the molecular scale are virtually nonexistent. Real objects have fractal boundaries.

Not only that, but they are uncertain as well. In the real world, objects are constantly changing — wearing down, reacting chemically with the environment, even, if it’s a living object, ingesting and excreting. Catch any of these processes in the act, so to speak, and you will find ambiguity — bits of material in the process of falling off or attaching or chemically transforming. It doesn’t help to look more closely, either; the ambiguity goes all the way down — to the planck distance, beyond which it is impossible to know.

This leads to the second assertion — boundaries are unknowable. The uncertainty principle is one reason, but there is another reason which operates at any scale. Determining a boundary is a computation. Computations take time. So boundaries always refer to the past. If an object is capable of change during the computational lag, you can’t be certain the boundary you computed is still accurate.

The obvious objection to the above assertions is that they amount to nitpicking. They may be technically accurate, but are of no practical import. When you pick up a bowling ball and roll it down the lane, how it does it matter in the slightest if a few million molecules fall off in the process? It’s still a bowliing ball. It’s still the bowling ball.

All of which is true. But this argument merely states that the functional definition of an object is not subject to the problems faced by the physical definition, and that meeting the functional definition is enough to prove the existence of the object.

If you are a materialist, however, this amounts to sleight-of-hand. Consider this: what if all the bowling balls at your alley look pretty much the same, and you can’t tell for sure if the bowling ball now being delivered by the return mechanism is the same one you rolled a moment ago, or the one someone else rolled at the same time in the next lane. Applying the functional argument here, you could claim that it’s the same object because it’s functionally the same. But no materialist would accept this. The material comprising your original bowling ball didn’t disappear into a functional cloud; within perhaps a fraction of a milligram that same material is either rolling back into your hands or it isn’t. Its existence doesn’t depend on your knowledge of its existence.

A functional definition, in short, is immaterial, so cannot by itself justify the existence of something physical, such as a physical object or its boundary.

One final justification for the existence of boundaries is to argue from necessity. Logically, a physical object must have a boundary. So if we can show that an object exists, we know that its boundary exists; we don’t need to actually identify it. And, plainly, some objects do exist. It’s hard to argue against the existence of a bowling ball, for example — to resolve any doubts, hold it directly over your toes and let go.

But this is just a failure of imagination. It’s possible to conceive of other ways of organizing our knowledge of the world and categorizing its contents, including bowling balls, that don’t rely on objects. I will mention two.

The first one could be called atomic reductionism. An atomic reductionist accepts the existence of no object larger than an atom. To such a thinker, a bowling ball, like all physical objects, is a collection of atoms. All chemical and biological processes consist simply of the movement and rearrangement of atoms, as do all physical processes (apart from fission and fusion, which transform atoms from one kind to another but in a limited and predictable fashion).

In principle, there is nothing we can know about the things we call objects that an atomic reductionist can’t, even though in practical terms the atomic reductionist faces a probably insurmountable burden in managing the huge quantities of information required to understand objects at familiar scales.

A second non-object-oriented way to think about the world is inspired by wavelets, a very elegant and powerful mathematical technique for representing information. A wavelet-oriented thinker, or waveleteer as I will call her, conceives of the world as made of matter organized into fields, one for each conceptual category. The field for a category determines the amplitude of matter organized according to that category at any point in space and time. So, for example, there exists a bowling ball field, which registers high amplitudes in bowling alleys and very low amplitudes almost everywhere else.

To a waveleteer, every noun is a non-count noun, like air or water. “There is a lot of bowling ball here,” the waveleteer might say upon walking into a bowling alley. It may seem like an odd description, but it is just as valid as an object-oriented description. And unlike atomic reductionism, waveletism could be a quite practical and useful way to think about the world, undoubtedly more useful in some ways than the object-oriented approach.

Both of the above ways of thinking about things may seem strange to us, and one of them is indeed not only strange but highly impractical. But as far as I can see they have just as much ontological validity and explanatory power as our “objective” way of thinking. And they do not require the boundaries our objects do. So boundaries are not, after all, a necessity for thinking about the world.