Epistemic status: It is better to be wrong than to have no model at all. I recommend the footnotes.^[1]

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On my current models of theoretical^[2] insight-making, it looks something like this:

1. A gradual build-up and propagation of salience wrt some tiny discrepancy between highly confident specific beliefs
   1. This maybe corresponds to simultaneously-salient neural ensembles whose oscillations are inharmonic^[3]
   2. Or in the frame of predictive processing: unresolved prediction-error between successive layers
2. Immediately followed by a resolution of that discrepancy if the insight is successfwl
   1. This maybe corresponds to the brain having found a combination of salient ensembles—including the originally inharmonic ensembles—whose oscillations are adequately harmonic
   2. Super-speculative but: If the "question phase" in step 1 was salient enough, and the compression in step 2 great enough, this causes an insight-frisson^[4] and a wave of pleasant sensations across your scalp, spine, and associated sensory areas

This maps to a fragile/chaotic high-energy "question phase" during which the violation of expectation is maximized (in order to adequately propagate the implications of the original discrepancy), followed by a compressive low-energy "solution phase" where correctness of expectation is maximized again.

In order to make this work, there are several homeostatic mechanisms which make the brain-state hug the border between phase-transitions as tightly as possible.^[5] A corollary of this is that the brain maximizes dynamic correlation length between neurons,^[6] which is when they have the greatest ability to influence each other across long distances (aka "communicate"). This is called the "critical brain hypothesis", and it suggests that good thinking is necessarily chaotic in some sense.

Another point is that insight-making is anti-inductive.^[7] Theoretical reasoning is a frontier that's continuously being exploited based on the brain's native Value-of-Information-estimator, which means that the branches with the highest naively-calculated-VoI are also less likely to have any low-hanging fruit left. What this implies is that novel insights are likely to be very narrow targets—which means they could be really hard to hold on to for the brief moment between initial hunch and build-up of salience. Concisely: epistemic frontiers are anti-inductive.

1. ^{^}

   🦶

2. ^{^}

   I scope my arguments only to "theoretical processing" (i.e. purely introspective stuff like math), and I don't think they apply to "empirical processing".

3. ^{^}

   Harmonic (red) vs inharmonic (blue) waveforms. When a waveform is harmonic, efferent neural ensembles can quickly entrain to it and stay in sync with minimal metabolic cost. Alternatively, in the context of predictive processing, we can say that "top-down predictions" quickly "learn to predict" bottom-up stimuli.

   

4. ^{^}

   I basically think musical pleasure (and aesthetic pleasure more generally) maps to 1) the build-up of expectations, 2) the violation of those expectations, and 3) the resolution of those violated expectations. Good art has to constantly balance between breaking and affirming automatic expectations. I think the aesthetic chills associates with insights are caused by the same structure as appogiaturas—the one-period delay of an expected tone at the end of a highly predictable sequence.

5. ^{^}

   Or, in terms of bullshit math (ht. w̸͕͂͂a̷͔̗͐t̴̙͗e̵̬̔̕r̴̰̓̊m̵͙͖̓̽a̵̢̗̓͒r̸̲̽ķ̷͔́͝ ):

   

6. ^{^}

   I highly recommend this entire YT series!

7. ^{^}

   I think the term originates from Eliezer, but Q Home has more relevant discussion on it—also I'm just a big fan of their chaoticoptimal reasoning style in general. Can recommend! 🍵