There is a companion video for this post: Computation of Being
Reading Laws of Thought chapter 2 today helped me to crystallize a few ideas I’ve been struggling to convey. This happened by bringing to mind simultaneously the work of Shannon, Turing, Boole, and others in a particular historical context.
The key realization was that I can decompose a Turing machine into two state machines that interact (one being the rules set and the other being the tape and rw head) then generalizing each as the same kind of system. Two state machines, each interacting with the other in ways that change their state. They communicate.
Let’s call the rules set and controls state machine the “controller” and the tape and rw head state machine the “memory.” In operation, each machine alters the state of the other in a series of transactions where information is encoded in each change of state. In the controller the change of state is the rule that applies next; and in the memory the change in state is the position of the rw head and the bit at that position.
Conventionally, the memory would have an infinite tape; and the rules in the controller would be fixed. However, we can generalize both of these concepts to define these machines as specific instances of the same type of “general state machines” by allowing for two conditions:
- If the rules in the controller could be changed but in practice are not changed then they are essentially a fixed memory.
- If the tape in the memory is finite but in practice large enough that it never affects the computation, it is as good as infinite.
So then a universal Turing machine can be described as two general state machines bolted together where one is configured to operate as a controller and the other is configured to operate as a memory.
If I were to build these machines out of raw parts: resistors, transistors, diodes, and such; then the resulting networks of parts would be able to do computation even though the individual components are not capable of that. They are, however, capable of altering each other’s state in ways that pass those changes in state through the network. This means that each of these components is a general state machine; and that any pair of them can propagate information through the network by interacting and encoding the information in their altered states.
Extending that thought I could see that in practice, each of these components can be decomposed into systems of interactions between quantum objects arranged in such a way that they are able to persist thereby gaining the ability to maintain “state.” Here, “state” is the essence of persistence—loosely defined as a capacity for reproducing a particular interaction or sequence of interactions. Each interaction at the quantum level causes the objects involved to change state by altering one or more of the properties of the objects. This by its nature transfers information that is encoded in those states. Therefore even the smallest of quantum systems are general state machines and so they can be arranged into computational networks that are Turing complete.
A hydrogen atom, having been a hydrogen atom a moment ago, generally continues to act like one in this moment, and again and again over time. In a way, it “remembers” this condition reliably—especially as far as any other interacting object is concerned. It maintains its “state” of being—such as a specific spin, energy level, mass, momentum, and position—enabling it to behave predictably.
In this way, all computation can be reduced to networks of communication whereby at its most fundamental level some object (abstractly defined) interacts with another in such a way that the “state” of that relationship is altered. These transactions (it feels like I should invent a new word for them) are the truly fundamental and universal components of both physical reality and of thought in that they share the same substrate which has a unified dual nature ( is that paradoxical? ):
That dual nature being the physical existence of the objects and the network of dynamic relationships between them. The mere existence of objects creates the possibility of relationships which in turn give rise to networks of interactions. Ultimately, these networks may crystallize into persistent structures. Conway’s game of life is a good way to visualize this.
Rising from there back up the stack of emergent complexity to Turing machines, you can see how each component of such a machine decomposes into networks of more fundamental objects which persist specific behaviors—those behaviors being the characteristics of the combined components.
In simplest terms: The fundamental element of reality, computation, and consciousness is any object altering the state of some other object. In a word: communication. (did you think I was going to say 42?) Each of these objects is a general state machine and each interaction is communication.
There are some important insights here. Some are:
Simple states bound to networks…
The “state” of an object can be as simple as its existence alone—perhaps just its position and momentum. Interestingly, even these are only meaningful in relation to other objects and, importantly, the ways in which these objects might interact. For example, can they occupy the same location? How, if at all, do they interact?
It is the relationships between objects that matters even if the individual objects have a complex state of their own. Consider two objects related to each other by some distance, charge, momentum, and mass. Now consider the possibility that one of the objects also has a “color” but nothing about that color has any impact on the behavior of the objects. This means, effectively, that the “color” is invisible. So, essentially, “color” does not exist.
If you change one of the other characteristics (those that do matter) on either of the objects then the network has changed because the behavior of the network will be impacted by the change. It has become, in effect, a different network.
This observation may seem obvious and a little pointless, but it does matter as we will see later. Objects may participate in multiple networks at once. It is possible that some state might change that is invisible to one network while having profound effects on another.
Hierarchical Computational Meaning…
Objects can “exist” at multiple levels of complexity and in multiple networks. Consider that even small networks of objects can give rise to emergent characteristics. If these emergent characteristics can also interact then it is possible to contemplate the interactions between these networks as if the component networks were objects themselves within these higher order networks.
This emergent hierarchy of computational “meaning” is universal and not necessarily exclusive or “strict.” Depending upon which emergent characteristics are more important at any given interaction, the more dominant properties will tend to have stronger effects on the outcome of any given interaction.
Consider pressure, for example. Individual molecules in a gas don’t possess a pressure; but a collection of them has both pressure and temperature. These emergent characteristics interact in specific ways distinct from the behavior of individual molecules. Similarly, a water molecule by itself is not wet; but a body of them all together have viscosity, and surface tension, and incompressibility, and so forth…
Another way to visualize this is by examining superorganisms such as ant colonies. An individual ant has a life and some relatively simple habits and reflexes. By interacting with all of its sisters the colony has its own behaviors and instincts that emerge from that network. The individuals contribute to the whole, and the whole influences the individuals.
More abstractly, this kind of hierarchical computational “meaning” can be seen in how evolutionary mechanisms exhibit competence without cognition whereby complex solutions are “invented” by means of exploring a configuration space and favoring the persistence of arrangements that are more suited to their environment. In such a case we say the system “evolves toward” fitness even though the individual actions that occur along the way have no apparent “awareness” of a goal nor guidance toward it.
This same hierarchy of computational meaning also helps when reasoning about what purpose consciousness may have from an evolutionary perspective as well as how consciousness emerges. As for how consciousness emerges, one can theorize that it is inevitable for some emergent properties of complex networks to exhibit characteristics analogous to “awareness” as well as other aspects of intelligence, thought and consciousness. To the extent that these emergent properties are advantageous from an evolutionary perspective, one can expect those traits to be selected and enhanced. This mirrors how social insects evolved the higher-order intelligence of a hive mind, augmenting the fitness of each individual.
Composition at all scales…
It takes more than one object to do any kind of meaningful computation; but not much more than one. As a thought experiment, even a pair of charged particles orbiting each other alone in their own universe have a kind of memory in that they persist in relation to each other. Each can “observe” the other verifying this relationship. If you add another particle then it might interact with the first two causing them to oscillate in various ways and thus that system would be able to exhibit complexity and evolve: Each new state dependent on the “memory” of the previous states and the continuing “communication” between the particles as they move through their tiny universe.
Opacity and uncertainty…
Any expected transaction has some limit on its reliability dependent on the larger network of relationships that exists unseen behind the discrete interface of the transaction in question. Put more metaphorically: every interaction is irreducibly the tip of an iceberg that extends to the limits of reality. Some of these quantum state machines will be subtle, unreliable, and short lived (like flames, or waves crashing on a beach) while others (such as life forms or laptops) may be more robust. All, have a “secret life” beyond what can be seen.
Universality and unity…
All of reality is fundamentally capable of participating in computation with varying degrees of efficacy and repeatability. This implies that thought and consciousness are also fundamental and universal and that this model informs how that universality can be explained and reasoned about.
Not all arrangements of quantum objects produce what we might recognize as useful or meaningful computation; and few give rise to the complexity and sophistication we might recognize as thought or subjective awareness.
Like a box of parts not yet assembled into a working radio, or molecules of water in a rain-drop not yet flowing through a living being, or a carbon atom floating on its lonesome through intergalactic space, many arrangements of quantum objects don’t appear to be doing very much most of the time. Perhaps they have done, or have yet to do… or perhaps they are even now but are doing so in ways we cannot recognize at the scale we are viewing the networks in which they are embedded.
A few more deep thoughts…
As we who believe that we think and are convinced we possess consciousness are made of the same “stuff” as the rest of the universe, it is likely we are part of a larger consciousness than we realize… even if we sometimes feel alone. So too are the smaller things all around us even if they are far too small to perceive; and the larger things around us even though they are also effectively as invisible as the forest we can’t see due to all of the trees that are in the way.
What part of what atom in what molecule in what particular neuron in your brain played a role in the thought you just had? As you zoom in on your existence, what fraction of yourself finally becomes so small that you no longer recognize it as part of your consciousness? How small a part of you is no longer “you?”
Going the other way, thinking about how you influence the world and how you are influenced by it, how far do you zoom out before you cease to recognize your presence? How much did a particular blood cell in your eye influence society?
As you consider these questions, take a moment to recognize that you are a part of the universe and so it is part of the universe that is asking these questions and a part of the universe that will acquire the answers. How will that change what you do next? How will that change the rest of the universe?
The universe is a question pondering itself and we are each a part of the answer.
I should write this down somewhere…
