While I was running today (yes, I'm insane enough to run in this weather), I was thinking about how I might explain dialectics to someone who knows nothing about it. It's actually not that difficult. Most of what follows is from Scott Meikle's Essentialism in the Thought of Karl Marx, though a lot of it comes from things I've read here and there.
Dialectics is a theory about (a) what exists and (b) how it exists. According to dialectics, entities are the sorts of things which exist. They have essences, and those essences are concepts which necessitate the life cycles of those entities.
A lot of words. Let's dig into it a little.
From a dialectical point of view, the basic units of being are entities. This contrasts with atomism, according to which the basic units of being are "atoms" (or quarks or whatever subatomic particles or forces you like). Briefly, atomism is the idea that an entity's being is defined by whatever it is composed of. Let's assume for a moment that there is one, unified theory of all of physics which we have yet to discover. From the point of view of that theory, there is no difference between interstellar dust and a human being. It's all described ultimately by the same laws. Those laws constitute "beingness". There is nothing else to say about being other than what is contained in those mathematical laws.
This contrasts with dialectics. Dialectics starts from an everyday point of view in which things like tables, chairs, supernovae, and days of the week are distinct, real things. To say that a chair can prevent me from falling into the middle of the earth because of quantum chromodynamics is a real, deep insight from the dialectical point of view. It's more than a mere social convention to say that; it's a profound insight into being. However, the macro-reality itself—the medium-sized dry goods like tables, chairs, and stars—exerts its own kind of cause.
To get what dialectics is about, it helps to start with living things. Dialectics isn't a new theory. It's not some weird off-shoot of 19th century thought. It's actually the oldest philosophical theory, going back to Plato, Heraclitus, Parmenides, Buddha, and the Upanishads. The first scientific thoughts about the world all arise in Eurasia along roughly the same line of latitude at roughly the same time. All these thinkers are trying to understand beingness itself, or, what is the same thing for them, living nature. The starting and ending points for them are the same: life.
In keeping with this orientation—and as a means of making dialectics concrete—we could ask: What is a human being?
From an atomistic point of view, there might ultimately be no answer to this question. A human being is a species of living thing, though all biological laws ultimately reduce to physical laws. And the same physical laws govern biological systems as govern non-biological ones. It's all atoms in the void interacting in accordance with very complex mathematical laws. Those laws are abstract, and they're indifferent to their content. It matters little whether we're talking about stellar fusion or getting a suntan. It's all pretty much the same thing.
But dialectics takes a different approach, one more oriented toward common sense. From a dialectical point of view, a human being is not just a species; it is a member of a family, hominidae, which is in turn part of an order, primate, which is in turn part of a kingdom, animalia, which is one of the main branches of life itself.
So whatever it means to be a "human being", to that concept also belongs what it means to (a) be alive, (b) be an animal, (c) be a primate, and (d) be a hominid. The essence of the human is defined, in part, the conceptual hierarchy into which "human" is placed.
Of course, to be a human is more than to be a great ape. According to Aristotle, man is a "reasoning animal", meaning (on one interpretation) he is an animal, but in addition to that he reasons. In a more modern spirit we might add that humans are animals that can know their own thoughts.
What makes up the essence of something is open-ended. One cannot rightfully claim from a dialectical point of view that we have to know, without doubt, the essence of everything. (Quite the opposite.) The point is that macro-entities—the sorts of things we see and deal with every day—are real things, and there is something it really means to be those things. They don't just reduce to their component parts and blend into one another. What something is is its essence, and we can articulate that essence using concepts which are organized into things like genus and species or wholes and parts. Dialectics, therefore, is an essentialist holism.
Now wait a second, you might say. All this sounds very modern—except that we know that living things do not have immutable essences. Human beings did not always exist. They evolved from other life-forms. In fact, they're still evolving—just like every other living thing—in accordance with mechanical laws. So one thing really does bleed into another. Inorganic matter evolved into living matter. Living matter evolved into multicellular organisms. Those evolved into vertebrates and eventually primates. We are primates, and we're evolving into something else. There are no "essences" here, just different states of "matter", whatever that is, transforming into other states of matter.
This is absolutely true, and this is the other insight of dialectics. To be is to be becoming something else.
Think for a moment about what it means to be a human being or really any living thing. Every living thing—or most of them we know about—has a life cycle. It's born, it lives, and it dies. The ancients saw this clearly, and they dealt with it in a number of ways. The essence of any living thing—say, a human being—is just the characteristic way in which it is born, lives, and dies. The Greek word for this was ergon, which we translate as "work". It makes up part of Aristotle's word for being, which was energeia. In other words, to be is to be born, to live, and to die. To be any particular thing is to be born, to live, and to die in the way characteristic of that particular thing. Obviously people are born, live, and die in ways different from how cats or amoeba do it. That's why we say they're different sorts of things.
The ancients did not know about evolution. Neither did Hegel. I'm not going to claim that dialectics somehow entails evolution. It doesn't. But it's not incompatible with it, so far as I can see. In fact, I think that as an ontology, dialectics is more compatible with evolution than atomism. From the dialectical point of view it makes sense to speak about species are real, existing things; and from the dialectical point of view, it makes sense to conceptually specify those beings in terms from their origins (what they evolved from) and their destinations (what they're evolving into).
So there are two directions I could go from here. One would be to talk about society from a dialectical point of view (that is, to talk about society as an organism or something organism-like with an essence); the other is to talk more about humanity itself and its destiny regarding technology. The first path is the typical Aristotlean-Marxist one. The second one hasn't been traversed too much. There are hints of it in Kurzweil's writings. He doesn't deal with things from an explicitly dialectical point of view, but his emphasis on patterns suggests it. I don't think patterns are anything other than essences, that is, concept which are real and which really determine the course some entity follows in its typical life-path. Kurzweil implicitly regards concepts as real. He doesn't seem to be an atomist, in other words, which is part of what drew me into his writings in the first place.
But unfortunately it's late, and this is already very long. Hopefully this gives some idea of what dialectics about. In short, it is essentialist holism. Organic wholes are the things which truly exist. These entities are ultimately their essences. An essence is what a thing truly is. But when we speak of an essence, we really mean the ergon, or the typical life and death of a thing. To be is to have a characteristic way of being born, of living, and of dying. All is in flux, as Heraclitus said; but everything is in flux in its own particular way, as defined by its essence.