Beyond Computability

Previously on C-Muses with William T, we examined the Church-Turing thesis. It says, “Anything that can be computed in principle can be computed by a Turing machine.” Furthermore, there is a Universal Turing machine, a Turing machine which simulates all others. Thus, the Universal Turing machine computes everything that can be computed, perhaps even, the entire history of the universe. We got a sense of what this sort of simulation would be like by taking a turn in the Chinese Room.

The Chinese Room is an isolated chamber, isolated except for a small slot through which you can pass messages. The only remarkable artifact in the room is a book full of detailed instructions. By following those instructions, you produce documents containing interesting and insightful commentaries on every subject. (For kicks and giggles, suppose that book contains all the instructions of the Universal Turing machine as well.) The only problem, for you at least, is that all the insights and comments are in Chinese. If you don’t know Chinese, then tough luck, no enlightenment for you. So even if you follow all the rules, you won’t be aware of what the messages say. You have to have the right kind of relationship to the messages to know what they say. (In particular, you need to know Chinese.) Searle articulates the idea of right relationship with the saying, “no one would expect to get wet jumping into a swimming pool full of ping-pong balls simulating water.” You can’t get wet because no matter how well the ping-pong pool simulates water, you won’t have the right relationship to the simulation to get wet.

Before leaving the Chinese room, note one final thing. Though the book in the room has all the instructions for composing sagely messages, it is useless to a Chinese speaker. Since the instructions are in English, there is no way to follow them except through the efforts of an English speaker. However, since the following the instructions produces messages in Chinese, there is no way to understand the messages except through the attention of a Chinese speaker. These three (book, English speaker, and Chinese speaker) each exemplify one fold of computation’s threefold nature. I call the first fold Essence. I call the second fold Substance. And the third fold, I call Experience.

Essence: The Nature of Abstraction

Usually, if you see a movie in the theater, on VHS, and on DVD, the movie will be the same. (There are a few exceptions.) The screen may be a different size, the quality of the image may differ, but you are essentially watching the same movie. Sameness, for movies at least, doesn’t depend on the film, tape, or disk that they’re recorded on. Movies are characterized by particular sequences of light and sound. This is the essence of what makes a movie a movie and what differentiates one movie from another.

Likewise, the essence of a story is its characters and plot. You can tell the same story in different ways. You can write the story in a book, make a movie, or recite it from memory. You can tell long and short versions, but what makes a story a story is removed from the details of a particular telling.

Likewise, the essence of a triangle is its sides and angles. You can draw a picture of a triangle, but what makes a triangle a triangle isn’t to be found in any particular drawing. No line you can draw will be perfectly straight, nor will it be “length without width”. Every drawn line will have some color or other, but Euclid never said anything about color. Any drawing of a triangle will be more than just a triangle. The drawing will have unnecessary details. Triangles are abstract entities. They have a form, shape, and structure; but they don’t need to have a color. Similarly, numbers are abstract. You can hold three things in you hand. But you can’t hold the number three. (Symbols representing the number three don’t count.)

Computer programs are very much like stories, triangles, and numbers. They have form, shape, and structure; but the structure doesn’t correspond uniquely to any physical object. You can store a computer program in many different mediums: on your hard drive, on the Internet, on a napkin. It doesn’t matter. The form of the program is removed from its physical embodiment. I call this abstract structure or form the “Essence of Computation.”

Physical embodiment does matter when it comes time to run the program. If the program is on your hard drive, your computer needs to have the drive mounted. If the program is on the internet, you need a connection. If the program is on a napkin, you probably need to type it in and run a compiler. To run a computation takes more than its Essence.

Substance: The Nature of Instantiation

When it comes to cooking, just having a recipe won’t get you any food. You need someone or something (like a breadmaker) to actually go through the steps one by one. The same holds for computer programs. The formal description of a program isn’t enough to actually run the program. You need something else to run the program. The program runner can be a laptop, a person, a tinker toy assemblage, or even DNA. All the runner needs to be able to do is follow steps. Whether the following process is electrical, intentional, mechanical, or chemical doesn’t matter. Performing a computation requires rules to follow and a performer who follows the rules. I call this rule following process the “Substance of Computation”.

The word “substance” has a long and sordid history in Philosophy. In Aristotle’s Metaphysics, the substance of something is it’s underlying reality including both formal and material aspects. Other philosophers define things a little bit differently as will I. I call the formal aspect of a computation (the instructions for performing it), Essence. I use “substance” to refer to the actual performing of a computation. Substance, in my sense, isn’t so much the material aspect of a computation as it is the motion or process through which a computation is accomplished. Thus, if you care to draw the distinction, the substance of a computation would be identified with Aristotle’s third cause (“efficient cause” or the source of motion and change in a thing) rather than its first cause (“material cause” or what something is made of). Aristotle talks about two other causes. His second cause is called “formal cause.” It refers to the structure or pattern of a thing, what I call Essence. His fourth cause is “final cause.” It refers to the reason or purpose of a thing, and I roughly associated it with the third nature of computation.

Experience: The Nature of Participation

Imagine you have a computer that’s been sealed behind a wall. Except in this case, the computer has no connection to the outside world. Such a machine could run for years doing calculations, but unless someone eventually finds the computer, the results won’t do anyone any good. Or to put it another way, “If a tree falls in the forest and there is nobody around, does it make a sound?” Even if someone is around to see the results, this doesn’t mean they’ll be in a position to interpret those results. The English speaker in the Chinese room cannot interpret the messages if he doesn’t know Chinese. Who you are, your relationship to a computation, how you experience it—these can make all the difference. Thus, the “Experience of Computation” is the third fold.

Summing Up

Quite a bit can and will be said of the three folds. For today, I just want you to remember them: Essence, Substance, and Experience. Essence is the abstract structure or form of a thing. It’s the idea for a story minus all the details. It’s content minus the container. As you add details, the Essence can become a very detailed specification. Perhaps the specification of a submarine, a better toaster, or a computer program. Until the specification is implemented in the world, until Essence puts on Substance, you’ll be able to think about the thing, but you won’t be able to use it.

Substance is the incarnation of Essence in the world. In the case of submarines and toasters, the incarnation is going to be material. Computations, on the other hand, are characterized by motion and change. Hence, the Substance of a computation is efficient (as in efficient cause).

In addition to Essence and Substance, there is Experience. Experience fills the gap between a person (subject) and a thing (object). Experience characterizes our perception of an object or our participation in an event. If you do not experience a thing, then you do not have any direct knowledge of it. You could, however, learn about it through the experience of someone else. Such Experience passes through a chain of intermediaries. The collective effect of all the intermediary filters in a chain is an interface. Any subject/object pair will have many interfaces, one for each chain of filters between them. Sometimes, the interface obscures properties of the object: we see through a glass darkly. Sometimes the interface is as clean as a freshly windexed window. Sometimes the interface works as a magnifying lens, a microscope, or a telescope. With each interface, Experience differs, perception differs, and understanding differs.