Words can be isomorphic to numbers but are not the same as numbers, even words such as five. Imagine, dear reader, a compound number, 155, or one hundred and fifty five. The three digits are made of individual characters which more or less map onto specific, particular words. This means that the word Five is isomorphic in terms of creating mathematical structures to the number 5.
Isomorphic is from the Greek words iso-equal and morphe-shape or form. The idea here is that, despite different systems being setup to handle different sorts of information and different states in different linguistic computational activities, we have nonetheless molded them to fit together in some ways - though, importantly, not *all* ways.
This essay will briefly touch on a few different examples of this fascinating phenomenon. In *Formal Dialectics* I was able to explore these ideas in detail, and any intrigued reader should not hesitate to track down a copy of that now-out-of-print primary source philosophy text I wrote and had peer reviewed, which was published in 2018. The logic is simple enough: imperfections in representation between languages is a feature, not a bug. The relationship between language and the world is similar—isomorphism. Value created by use is the source of power for these concepts, not objective structure or a one-dimensional KPI vector.
The upshot here is that language will always be imperfect when we observe it in the wild and if it were different, language would become the world and cease to have any value as a communicative instrument.
This idea fascinates me for the same reason that studying the consciousness of the human being fascinates me: it reveals certain characteristics of the world that, when modeled, can empower us to make accurate guesses about what comes next. This is the true power of philosophy and it explains divergent phenomena at a massive scale, such as the market success of George Soros and his apolitical attitudes which nonetheless somehow goad the global moneyed right wing into a defensive posture without him even needing to take any action at all.
The fact of the matter is that brains are prediction machines. Our consciousness represents our body’s ability to continue existence by modeling behavior to process the past, survive the present, and plan for contingencies and/or to thrive in the future. Success in markets can come from unpredicted sources, can be generated by appropriate action, or can be accidental. In all cases we say that the person who achieved success has earned it through (occasionally we lump a value judgement here) means.
In the concept of isomorphism, an interesting relationship between description and world becomes possible. A description could be an uttered speech act, a written word, or a thought that no one else ever becomes aware of that exists with or without language. Our brains generate a model which is, in the ideal scenario, an accurate description of our surroundings. This model is used to generate the behavior of the organism in response to the characteristics of the environment primarily, but in conscious human beings at the very least an entirely different phenomenon is able to take place.
The ability we have to think is a bastardization of the mental modeling activity we participate in as a means of survival. In this case, we take up the ability to make something wrong; i.e., to model something that isn’t directly represented in our environment. All sorts of rational superpowers emerge for us: the ability to think abstractly about solving problems, the ability to use words and pictures as symbols to represent particular situations even if the scenario imagined thusly has not yet occurred.
In physics, a lot of new mathematics has been discovered by scientists who invent them to describe theories and observations. This mathematical theory generator, the field of physics, is the branch of science in which the most fundamental aspects of nature are studied. Repeatedly, physicists have made new technologies possible by developing technical jargon and mathematical tools that can become widely used or discarded in accordance with their standing among leading attempts to solve the particular problems they solve.
In physics, the subject is the most real thing in the world: the fundamental nature of the stuff all of this is made of. Primarily, this consists of the electromagnetic force for humans, but there are other forces too.
The science of chemistry builds upon physics by taking the fundamental principles and proven mathematical models of how stuff works and weaving it into a more tangible vernacular. Now, rather than particles, we have particular sorts of conglomerates made from particles. And so on into biology, ecology, anthropology, political science, ethics, and philosophy.
The reason all of these vernaculars and mathematical models can apply across different domains of study is that the fields and their concepts, though in many ways very different from one another, share isomorphic symmetries based on the fact that they arise from the repeated act of publishing in a variety of languages.
Isomorphism is the ability to use an existing concept to create a slightly different concept. I think a lot of science is going to turn out to be explained by saying something like this: I take a concept I know well and observe a phenomenon that exhibits similarities. I'm able to apply the existing concept to a new subject and trim it to fit. This speeds up my learning process.