Identity
A.R. Ammons
Read the poem HERE.
What is entropy?
The center of a web is the signature of the spider’s species, and web after web, the spider recreates its characteristic pattern. The central part of the web is an element of the spider’s identity. But the narrator in Ammons’s poem notes that the spider must connect the web’s boundaries to the surroundings. For this reason, the setting of the web, not the species of the spider, determines its nature near and beyond its periphery. The narrator describes this trend by use of the thermodynamic term entropy, a measure of disorder.
The scientist speaks of the entropy of systems. A system is simply a part of the world that we choose to isolate and study—say, a cornfield, a ball in an inclined track, or a flask containing proteins dissolved in water. We say that the entropy of a system is high if the system is disordered, that is, if we find no pattern in the arrangement of its parts. If the parts are neatly arranged in a simple pattern, the entropy is low. To return to the example in the poem, the entropy of the web is lowest—the web is most ordered—at the center, where it makes a simple spiral, but entropy rises away from the center. At the points of suspension, the spider maps the web onto its surroundings, and the web’s entropy is equal to the entropy of the leaf tips, house eaves, twigs, or utility wires to which the web is attached, in what appear to be “… numerous occasions of accident.”
Entropy and protein design
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Structural unit of spider silk. Helices are colored by their order in the continuous chain, first helix blue, last one red. Some spider silks contain many such units, linked by disordered regions, like beads on a string. See Proteins, Membranes, and Entropy |
In the core of such a protein, even the substitution (as a result of mutation) of one building block for another similar one might disrupt the protein’s function; as a result, mutations of key residues result in death of the developing offspring. On the other hand, for many residues on the outer surface of water-soluble proteins, which simply interact with randomly moving water molecules that make up the surroundings, almost any building block that can interact with water is acceptable. A listing of conserved amino acids in a family of homologous proteins shows us which parts are critical, where the organism can accept no occasions of accident. Think of a 10-mm crescent wrench; its active center is its pair of faces, which must be just over 10 mm apart. There are, however, practically no design constraints on its handle, which can even be decorative if the designer prefers.
In this view, the center of a spider web is not so much a mark of identity as an evolutionarily conserved functional site, in which most variations damage the web’s effectiveness, thus reducing the spider’s food supply, and resulting in less successful reproduction. Spiders with less effective webs will produce fewer offspring, and spiders with less effective webs will become more and more rare.
Entropy and information
There is a subtle and interesting connection between entropy and description. An ordered, low-entropy system is easy to describe: “The corn is planted at intervals of 2 feet in rows three feet apart.” This description might tell us precisely the locations of thousands of cornstalks. But corn planted at random is a high-entropy system, and for the same precise description of the whereabouts of every stalk, we must describe each and every location, requiring far more words. In like manner, it takes many words to describe the web’s points of contact: “One suspending line is connected to the left end of the fluorescent light above the sink. Another runs to the right window frame 2.4 feet above the sill. The third drops from the left center of the web to the top of a small pestle that sits in a mortar on the sill. The three main supporting strands meet to from a triangle with the following sides and angles: … .” But we can describe the heart of the web succinctly: “It’s a garden cross spider web, 5.5 inches in diameter.” Or a brief mathematical equation can describe the dimensions of the spiral portion. A short description suffices where there is order, or low entropy.
For another example, consider the shape of a protein chain. At each residue, there are two bonds that can rotate freely, determining the direction that the chain turns at that building block. The turn can be described by specifying two rotation angles. Regular features, like helices, have the same two angles at each successive residue, so two angles plus the number of building blocks are all that you need to describe the shape of a helix containing 20 residues. But for 20 residues in a high-entropy, randomly shaped protein chain, you need to specify 40 different rotation angles to describe the conformation. More information is required to describe a higher-entropy system.
Mystery: entropy, self, and other
Returning to the poem, notice that when the narrator describes the web and its entropy, the language is almost technical. But when the narrator generalizes beyond the specific example of the web, the tone and language of the poem become more mysterious. What does the narrator mean by “the underlying that takes no image to itself” and that is “created fully in no particular form”? How is it made manifest in spider webs and moons and bladderweeds— or in those oxygen-binding sites of hemoglobins, for that matter? Is this “underlying” anything like the “spring” in Jacob Bronowski’s poem, The Abacus and the Rose? At the least, both authors use similarly elusive language to evoke elusive ideas.
The narrator places high value, enough to share it with a loved one, on something being interesting*, and finds it interesting that order (low entropy) prevails at the center, in the midst of the air where the spider operates with the fewest restrictions. In the heart of the web, she (among garden cross spiders, web builders are females) is not constrained by having to make connections to the surroundings. Yet she slavishly, precisely stamps her identity in the web’s active site, its crucial functional center. On the other hand, she must make the entropy of her web rise smoothly toward its boundaries, until the contacts match the disorder of the surroundings.
entropy equal to entropy.
Can we apply this view of the spider’s identity, and protein identity, to human identity, and more specifically, to the love expressed by the narrator? We might feel that we have a core self, an interior that is our true nature. Some might call it an identity or a soul. In contrast to the strictly inherited mark of identity in the spider’s web, it is arguable whether human identity is given, or whether we are free to mold it. Either way, when we establish a relationship with another, we make paths between their identity and our own. An unselfish relationship involves giving, adjusting, and shaping those paths if we are too meet another as fully as possible.
if the web were perfectly pre-set,
the spider could
never find
a perfect place to set it in: and
if the web were
perfectly adaptable
if freedom and possibility were without limit,
the web would
lose its special identity:
A loving relationship changes us. Does it alter our identity at its core? Or do we still have that core identity, with either its genetically determined constraints or its freedom? Does loving entail a compromise?
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| Some webs are not so simple. |
* In two online postings of the poem, the word "interesting" is mystifyingly replaced by "intersecting", rendering an important part of the poem completely nonsensical and mystifying.
