Mental Mental Mental Models

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Posh Hugs Inn was excitedly explaining his new experimental hypotheses regarding visual working memory. All his words and sentences were lucidly put, so it would be easy to parrot back what he said and answer basic questions about it, but it quickly became obvious to me that I had no mental model of what was actually, physically going on, and so I was unable to reason about the topic beyond what I’d been told or meaningfully connect his ideas he was sharing to my own. I pointed this out, and he offered me what he described as the current scientific “model”: working memory is like two people fighting over pizza slices. Maybe I’m just too socially clueless to deduce the consequences of that, but regardless of the reason, I can’t use that analogy. So, not one to be daunted by ideational challenges, I threw together my own slapdash (and probably crazy) mental model.

Just to be clear, this model is entirely speculative. I’ve done zero empirical testing of it. It was built on introspection and intuition out of straightforward modular concepts. It’s pretty obviously got heavyhanded analogies to electrical circuits. Real biology is built on millions of years of random mutations filtered for usefulness by natural selection. It’s unpredictably complex, interdependent on countless other systems, and intractably nonlinear. So this model is just flat wrong. But it’s truer than a pizza fight. More on that after the model.

(100% speculative) Stages in the function of working memory

  1. ACTIVATION – endogenous and exogenous sensory inputs activate associated neural pathways
  2. CENTRALIZATION – working memory is a set of neural tracts that receive input from many neural pathways and provide them a positive feedback loop
  3. PRIORITIZATION – the most active input pathways rapidly come to dominate the working memory signal due to resonance through the feedback loop
  4. DISTRIBUTION – working memory then allows all connected systems to focus on the same inputs
  5. LOCAL PROCESSING – the various specialized regions are primed by the signal in working memory to operate only or primarily on the matching signal from among their own inputs

(100% speculative) Model of divvying working memory

  • There’s a total quantity Q of available working memory.
  • Over all inputs there’s a dynamic mean level of activity A(t).
  • Each signal S develops in response to exogenous and endogenous sensory inputs I(S,t).
  • Each signal S has an activation level A(S,t) akin to firing rate or dendritic or somatic depolarization.
  • Each signal S has a complexity C(S) akin to the sum of the minimum number of synapses passed through along all neural pathways that compose the signal.
  • Each signal S passing through working memory captures a quantity Q(S,t) of working memory.

Then the relations between the factors are…

A(S,t)’ = I(S,t) + k1*Q(S,t) – k2*C(S)
Q(S,t)’ = A(S,t) – A(t) – k3*(Q(S,t) – Q/2)

…where k1 is the gain on the positive feedback provided to a signal by working memory, k2 is the decay rate of the signal, and k3 is selected to enforce sigmoid growth of Q(S,t).

OK, so given that this model is wrong, why do I say that it is nevertheless “truer”?  And why is it even worthwhile?  In an earlier post, I claimed that “science advances by replacing true statements about the world with truer statements”, where “a statement is truer the more it increases achievable utility”.  On Posh Hugs Inn‘s first explanation of the material to me, I had no model of the material by which to reason or make predictions.  Now I do.  And that by itself virtually guarantees that I can now make better predictions than before and reason about the material better than before.  Obviously that’s true if the model performs better than random predictions.  But it’s also true if the model does worse than random predictions, because then when I find that out I can simply say the opposite of what the model says.  And most importantly, it provides a foundation which can be compared to experimental results and observed facts and then refined, rebuilt, or replaced.

“The instant you hear about anything whatsoever that varies between a spy and a nonspy, you should immediately think of exploiting it to distinguish spies from nonspies. Similarly, to distinguish reality from lies, you need a process which behaves differently in the presence of truth and falsehood – that’s why ‘faith’ doesn’t work as a discriminant, while ‘make experimental predictions and test them’ does.”
— spoken by Harry in Eliezer Yudkowsky’s “Harry Potter and the Methods of Rationality”, Ch. 86

[Posh Hugs Inn has already informed me of a major flaw, which is that there is no biological feature corresponding to my description (#2 centralization) of working memory.  So my first revision, of many, is to replace that description by supposing the feedback loop is located internally to the active neural pathways and prioritization is forced by convergence of pathways.]

In short: Mental models are the beginning of wisdom.  Whenever you notice you’re confused, find one or put one together yourself.  Don’t be afraid to start out with one that you’re completely sure is wrong, so long as you’ll have the opportunity to gradually make it righter.

The sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work. — John Von Neumann

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