Thursday, December 1, 2011

Lego Bricks: Components, Quantization, and the Discrete, and Tea

When I was a child, I used to play a lot with Lego bricks. I love Legos; I think in many respects they are an ideal toy. Besides being really fun, I think they also encourage creativity and help develop spatial reasoning skills and manual dexterity. Pictured here is a box of Lego bricks:

One thing that is interesting about Legos is that they are inherently finite and limited, unlike other creative media, such as drawing or painting, or even playing with a musical instrument. When drawing, an artist can choose to draw anywhere on the paper, and a musician can choose exactly when to play each note, how loud to play it, and what tone or timbre to play with, whereas with Legos, the bricks can only connect in a predetermined number of ways.

But as anyone experienced with playing with Legos knows, the amount of possible combinations of even a modest number of lego bricks is so great that it is essentially endless for our limited human comprehension.

Components, The Discrete, and Quantization:

In the language of mathematics, Legos are discrete, whereas many other forms of art are continuous. This distinction parallels the distinction between calculus, which studies continuous changes, and discrete mathematics, which studies things broken into individual units. In the language of physics and quantum mechanics, Legos are quantized. Both of these mean that legos can be broken into smallest units or components, which can be placed or combined only in certain pre-determined configurations.

The Nature of the Universe:

When we look at the world around us, we see a world that looks for all practical purposes continuous. For example, we can raise our arm and move our arm or hand through various motions of distance or angle. We can cut a slice of cake, or a cucumber, exactly where we want to, rather than being constrained by only being able to divide it into a certain number of pieces.

But people who have studied science in more depth will know that the continuous nature of the world around us is actually an illusion. What looks like the unbroken surface of our skin, or the surface of the cucumber pictured above, is actually made of cells, and what looks like a smooth piece of metal is actually an array of individual atoms held together by electromagnetic forces. Furthermore, more modern advances in quantum physics have given us both theoretical grounds and empirical data to suggest that distance and time itself are quantized--that is, that there is a "smallest unit" of distance and smallest unit of time, and that particles cannot exist just anywhere in space and time. Like lego bricks, they can only be placed on the allowed grid.

Components, Quantization, and The Discrete, and Tea:

These concepts may seem very far removed from tea, but they are actually much more directly related than you might think. There are many macroscopic elements of our world that are broken into indivisible, discrete components. On a very basic level, we see these in terms of the individual leaves of a tea plant, which are well-defined units that we can see after brewing whole-leaf tea. But the same is actually true of more deeper things, things that are actually relevant to the important questions of how we experience tea. One particularly poignant example of something that is broken into a finite number of components is the olfactory receptors which we use to perceive aroma. The quantization or finite nature of the olfactory receptors is of paramount importance to how we experience tea because aroma is arguably one of the most important aspects of tea.

Humans, like any animals, have a finite number of receptors for aroma. These receptors are very numerous and very diverse, and they vary greatly from one individual to another. But for each person, the same basic fact or constraint is true: each chemical activates some finite number of receptors, in some combination, which are then processed by our brain. And the number of chemicals out there in the universe, even in our daily environment, far exceeds the number of aroma receptors we have. Our perception of smell is limited. This is why there are a variety of different chemical compounds which smell similar to us. When two teas seem to share the same aroma, it can sometimes mean that they share individual chemical components, but it can also mean that they have chemical components that are similar enough that they activate some of the same receptors.

When we try to communicate our experience of aroma to others, we run into another form of quantization: language. There are only a finite number of words with which we can describe aromas, and there are far fewer words available than there are possible combinations of olfactory receptors that can be activated by the chemical compounds in a cup of tea.

The Limitations of Being Human, and Being At Home in the Universe:

Smell, however limited it is, is still extremely complex, even when constrained by language. But I find it interesting to think about how, when it comes down to it, our experience of everything in life is finite, limited. It reminds me of our inherent limitations as human beings, but it also can make us feel more at home in the universe. Perhaps it is not so bad after all that we are finite human beings, as the very universe we live in seems to also be finite, discrete in some strange sense, like a set of lego bricks. But just like the lego bricks, it is so complex so as to effectively be boundless and infinite, offering far more depth and richness of experience than any one person could ever hope to experience in their lifetime.

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