A Picture of a Banana

You may have noticed that I did not get this post up yesterday like I desired. Oh well, if I had an extra dollar, I would give it to you. Anyway, I set myself up with the metaphor post because today I want to talk about models.

One of the important thing to keep in mind with any model is that the model is not the thing that is supposed to be modeled. Or, to put it another way, if you draw a portrait of a bowl of fruit, the image contains no fruit, it only contains the picture of fruit. On a more serious note, if you have equations worked out that seem to represent the way physical objects interact with each other, a la physics, the equations are not physical interactions, nor are physical interactions equations.

I remember seeing a Far Side comic with a monkey drawing a banana, a full wastebasket beside the drawing board filled with drawings rejected because they did not taste right. Sadly I couldn't find this comic in order to share it with you. When I did an image search for "monkey eating banana picture" I found a lot of images of monkeys with bananas, but none of images of monkeys with pictures of bananas. Remember, the picture of a banana is not a banana.

So, the question has been kicking around in my mind for a while, can something simulate itself? One reason this thought comes up is in philosophy of consciousness, as it becomes interesting to ask if a brain can be used to simulate a brain. John Searle believes that brains cannot be multiply realized, that is, there is something unique to the human brain that cannot be replicated by an artificial attempt to create a "brain," ie, artificial intelligence. But what if you didn't write a program to replicate the perceived functions of a brain, such as conversation, but rather a program to replicate the brain on a neuron by neuron level. Shouldn't something like that function exactly like a brain, by assumption? Now suppose you were to build your computer out of a human brain, does it still function exactly like a brain (simile), or is its functioning the functioning of a brain? Can it be both, can the model be the action.

When talking about this with a friend a couple of weeks back, the following example occurred to me. As noted above, a picture of a banana is not a banana. However, what if you were to paint a picture of a banana on a banana (ok, in the conversation we actually iced a doughnut so that it looked like a doughnut, but some principal applies). In this case the banana is also an image of a banana.

Certainly you can imagine a banana with a picture of a banana drawn on its side. In this case the (actual) banana and the (image) banana are easy to separate, because the image is contained in the actual. But suppose that instead of painting the (image) banana on the side of the (actual) banana, we instead painted the entire (actual) banana in such a way so it looked exactly like it did before we painted it. Now the entire (actual) banana is also the (image) banana, at least on the exterior. True, were you to open it up, you could quickly discard the entire (image) banana along with the (actual) banana peel, leaving yourself with only the pieces of the (actual) banana, no longer entwined with the (image) banana, but hopefully you see how (image) and (actual) are getting closer to each other.

The fact that it was something interior to the banana gives us a hint as to what we should next consider. Suppose Monet goes out and paints some lilies, creating an image of lilies. Now suppose a perfect forger paints an image of Monet's painting of lilies. While Monet's painting may be an attempt to model something about the actual lilies, the forger's painting is certainly an attempt to model Monet's image of lilies, as the forger will faithfully and intentionally duplicate even the errors Monet makes when depicting the lilies. If the forger's painting is identical to Monet's, is there a difference between the (actual) Monet and the (image) Monet?

So far we have had actual phenomena and subsequently made a separate model for them. The last thing I want you to consider is slightly different. Suppose you are a maker of candy and you need to make a window display to show prospective customers how delicious your candy is. What if you were to take some of your actual candy and treat it in such a way so that it would keep indefinitely, but was no longer edible. Because it no longer can fulfill the function of candy, namely tasting deliciously sweet, the display candy transitions from (actual) candy to (image) candy. But this time, instead of making the model as a separate thing reflecting the actual, we instead turn the actual into the model. Can we do this in such a way so that the (image) candy is also still (actual) candy?

I don't have any answers for these questions, but I hope you have as much fun thinking about them as I do. Just remember, the model you are thinking about is not the actual model, is not the thing that is being modeled. This post is about my ideas, it is not my ideas.

Metaphorically Speaking

I think that metaphors, and their cousins similes, are incredibly useful tools, both for the educator and the artist, so I thought I'd spend a post explaining why I admire them so much. If all goes well, this will set the stage, metaphorically, for my next post tomorrow.

As I see it, the purpose of every metaphor is to get someone, perhaps just yourself, to look at something differently by comparing it to a similar object/process. The reason for doing this falls into two broad categories. It may have a didactic purpose, as when someone uses a metaphor to explain a foreign concept by appealing to a familiar one. For example, I often attempt to explain why proofs are important in mathematics by noting that the ability to perform a calculation is like being able to drive a car, but a mathematician is like a mechanic in that she or he should understand what is going on underneath the hood. The other reason is exploratory, the metaphor brings to light a new way of understanding the process in question, this is the reason that interests me most.

Metaphors are used in this sense by the artists. The poet who calls a sunrise a bird taking flight, or life a path through the woods, does not do so in order to explain the phenomenon at hand. Rather, he or she intends that we discover something new about the phenomenon by viewing it in a new light. This same notion can be used in an academic setting. Upon establishing a baseline metaphor between object of interest A and object of explanation B based on a given list of similarities, one can ask what properties of B that are not on the list have, in some sense, a corresponding property in A, in doing so, one often has new ideas about the nature of A. This is why I habitually try to extend most every metaphor to the point that it breaks down, just to see if anything interesting happens.

The last thing that I want to mention is that models, be they physical or theoretical, or both, are an important example of a metaphor. Whether you are trying to simulate something in a smaller, controlled environment or with mathematical principles, you are replacing the actual thing with a representation of it, which is a form of metaphor.