Similarity

It’s like this. Let me make use of an analogy. Metaphor and simile allow for comparison without contrast.


Human communication depends upon the comprehension of meaning. And, the ability to understand is a combination of the senses, the brain, and experience. So much of reasoning relies on analogy. “What is she like?” “She’s a tower of ivory; or a day at the beach.” “Warm as a handshake; yet cold as a sunflower.”


The answers to the question have meaning only to the extent that there are connotations in the analogies that can be applied to the character of a woman. Is there any similarity at all, or anti-similarity, as with one of Shakespeare’s sonnets?


Communication occurs when the sender and receiver speak the same language – in which the message, even if novel, can be understood. There must be a pre-existent capacity for receiver to comprehend what was sent. And, this capacity must also include the ability to learn – to receive progressive more complicated and elaborate messages. In other words, for communication to occur there must be similarity (if not identity).


So, what is the meaning of similarity, when we find it in Nature? We certainly understand that organisms inherit their form from their parents. And, the idea that an ecologic niche can be occupied by organisms of different lineages, which, nevertheless, develop similar structures – for example, dorsal fins on sharks and dolphins, and wings on insects, birds, bats, and flying squirrels.


But, such similarities can also be found in the inorganic realm. Of course, crystals are a manifestation of the molecular structure of particular solid elements and compounds. Such similarities in crystals of different sizes generally involve distinct symmetries: cubic, orthogonal, tetrahedral, hexagonal… In recent years, another kind of self-similarity has been identified, of which crystals are a subset: fractals. In Mandelbrodt’s formulation, fractals are mathematical constructs which appear to have the same structure at any scale over a wide range. In addition to a number of mathematical algorithms that produce fractals, a number of naturally occurring examples can be enumerated: clouds, earthquake occurrences, shorelines, gas-water contacts in natural gas reservoirs. The latter examples differ from crystals in that they do not possess inherent symmetries. Rather, while structures a various scales show similar variations in magnitude, they are not congruent when rescaled.


Fractals have a kind of scaling dimension that quantifies the variation similarity..


(11/26/2003)


The next few posts represent a first attempt to elaborate the connections between simile and metaphor in the arts and their analog in mathematics and science. (Actually, this effort is on the order of thirty years in the making, with a hypothetical increase in understanding coming with time.)


Next: Fractality