Aeoli’s Super-Great Coherence Axiom: If there are n symbols that can be fully described by an internally consistent model A, then as n approaches infinity the probability of A approaches 1.
Less esoterically, if we’re looking at a bunch of correlations that indicate a common factor, then as n approaches infinity it follows necessarily that the common factor must exist. I’m putting this forth as an axiom when it would be more properly described as a conjecture, but I’m confident that it follows from the weight of evidence phenomenon. I may someday undertake to prove this, but there is already a great deal of work ahead of me.
For a rather trivial example application, see Tuesday’s post which explains that common belief implies common experience for very large n. A belief about something is itself a symbolic entity, although the thing it is about is not. Therefore, like all symbols belief can be subjected to computation. Otherwise, it would be impossible for belief to produce action.
A less trivial example follows from this, which is that common action implies common belief for very large n. This probably explains a peripheral observation about Asian culture:
The Asian answer to all societal issues can be summarized as “harmony”. That is, individual people doing different activities in concert for a common purpose. When they individually come to this understanding it consistently fills them with spiritual euphoria.
In order to try out this axiom, think about this example. Let A = “thrown rocks fall to earth”, n = “number of trials”, S(i) = 1 for successful trial i and 0 for unsuccessful trial i, and understand that “belief” is a number between 0 and 1 expressing a person’s willingness to accept that trial i meets the requirements to be included in the dataset.
But my concern is primarily what this implies about cognitive function.
We know from EEG that there exist temporary cognitive states where the activation level is the same across the entire neocortex. This means that all regions we’re looking at have the same approximate rate of electrical activity. We often refer to this as a “creative” moment or a “flow” state, but in physical terms it’s just a common level of electricity. If we dig deeper and look at individual neurons, we will almost certainly find that they are not all firing simultaneously with the same voltage drop each time. But the emergent behavior at some level higher than this (but lower than simply looking at the entire brain as one region) is that of coherent behavior.
The activation level of a region may be expressed as a symbolic quantity, say 1 volt or 1 volt per second or something like that. Because this is possible, it follows necessarily from the axiom (or conjecture) that for many regions n it becomes necessarily true that this behavior has some common cause. (I often say that this is just hyperfocus on something in the environment or an idea in the mind, but this is an inference on my part. We can only strictly deduce that there exists some common factor.) If there is a common factor, then what we casually observe must follow by logic as well: there is some common purpose to the activity.
What this implies is that all neurons which exhibit this behavior are capable of acting in support of some general-purpose activity.
Say you’re looking at the voltages of many NAND gates on a processor in a computer. One of them in particular is in an addition circuit. Now say the entire circuit begins to show this coherent behavior, where local regions are activating at similar rates. This is unexpected! We would have to conclude that there are more wires than we can see, which are using the same transistors for some coherent general purpose. Why else would the addition circuit be active at the same rate as the other opcodes?
It is just as unusual for this to occur in the electrical activity of the brain (even if everything else about the brain seems miraculous). This means that a neuron which is used to convert sounds into comprehensible words can also be tagged to undertake some other, more general activity. Perhaps this is during a vision, during which time a person is experiences an auditory hallucination as part of the realization of some idea.
From this, I believe I can explain precisely what is involved in creativity and the problem-solving process.