Monday, June 25, 2018

Why quantum math is unclassical

For me, the important thing about quantum mechanics is the equations, the mathematics.  If you want to understand quantum mechanics, just do the math.  All the words that are spun around it don't mean very much.  It's like playing the violin.  If violinists were judged on how they spoke, it wouldn't make much sense.
Freeman Dyson, in an interview with Onnesha Roychoudhuri, Salon, 2007.

Put aside all metaphysical questions about what sort of universe could be described by quantum mechanics.  Given that quantum mechanics is a recipe for making predictions about the physical world, and that those predictions are rather peculiar by classical standards, what is it about the recipe that causes these peculiarities?

In this post, I'm going to try to vastly simplify the recipe while still producing those peculiarities:  I'm going to build a toy cosmos, a really tiny system with really simple rules that, on their face, have almost none of the specific structure of quantum mechanics; yet, if it works out right, the system will still exhibit certain particular effects whose origins —whose mathematical origins— I want to understand better.  Here's my list of effects I want:

  • Nondeterminism.
  • Quantum interference.
  • Disappearance of quantum interference under observation.
  • Quantum entanglement.

I've tried this before, more than a decade ago, but my perspective has recently changed from my explorations of co-hygiene.  A little after the turn of the millennium I was studying a 1988 MIT AI Lab memo by Gary Drescher, "Demystifying Quantum Mechanics:  A Simple Universe with Quantum Uncertainty", and wanted to use a similar technique to explore some specific peculiarities of quantum math.  I used an even simpler toy cosmos than the 1988 memo had, which I could because my goals were narrower than Drescher's.  I eventually put my results up on the web through my WPI CS Department account (2006), though I didn't feel right at the time about making it a WPI CS Department tech report (a decision I eventually came to regret, after I'd got my doctoral hood and left, and it was too late).  But, nifty though the 2006 paper was in some ways, I now feel it didn't go far enough in simplifying the simple universe.  At the time I wanted to keep the "quantum" math similar enough to actual quantum mechanics to retain its look-and-feel, so that the reader would still think, yes, that is like quantum mechanics.  Now, though, I really want to strip away almost all the structure of quantum mechanics; because I'm now very interested to know which consequences of quantum mechanics are caused by which parts of the mathematical model from which they flow.

The result, with most of the instrument missing, won't be recital-quality violin; not even musical, really.  But I hope to learn from it a bit of how the instrument works.

Contents
Classical toy cosmos
Quantum toy cosmos
Nondeterminism
Interference
Observation
Entanglement
Why
Classical toy cosmos

A quantum view of a cosmos can only be constructed relative to a classical view.  So we have to start with a classical toy cosmos.

The instantaneous state of this cosmos consists of just two boolean —true/false— variables, a and b; so there are only four possible states for the cosmos to be in, which we call TT, TF, FT, FF (listing a then b).  Time advances discretely from one moment  t  to the next  t+1, and we're allowed to apply some experimental apparatus across that interval that determines how the state at  t+1  depends on the state at  t.  There are just three kinds of experimental apparatus, each of which has two variants depending on whether it's focused on  a  or  b:

  • set v: causes the variable to be true in the next state.
  • clear v: causes the variable to be false in the next state.
  • copy v: causes the value of the variable in the old state to become the value of both variables in the next state.
Nothing changes unless explicitly changed by the apparatus.

For example, from state TF, here are the states produced by the six possible experiments:

TF set a TF
TF set b TT
TF clear a FF
TF clear b TF
TF copy a TT
TF copy b FF

Quantum toy cosmos

A quantum state of the cosmos consists of a vector indexed by classical states; that is,  q = ⟨ws⟩  where s varies over the four classical states of the cosmos (in order TT, TF, FT, FF).

We understand a quantum state to determine a probability distribution of classical states of the toy cosmos; for quantum state  q, we denote the probability of classical state  s  by  ps(q).

As always when reasoning about quantum mechanics — but this bears repeating, to keep the concepts straight — we, as physicists studying the mathematics of the situation, are not observers in the technical sense of quantum theory.  That is, we are not part of the toy cosmos at all.  We can reason about the evolution of the quantum state of the toy cosmos; how an experiment changes the probabilities from time  t  to time  t+1, from  ps(qt)  to  ps(qt+1); and our reasoning does not alter the system.  Observation is one of the possible processes within the toy cosmos, which we will eventually get around to reasoning about, below.

What sorts of values, though, are the weights  ws  within the quantum state?

In current mathematical physics, one would expect these weights to be what's called a gauge field — one of those terms that doesn't mean much to outsiders but, to those in the know, carries along a great deal of extra baggage.  We don't want that baggage here; and it's worth a moment just to consider why we don't want it.

In classical Lagrangian mechanics, one considers the evolution of a system as a path through the system's classical state-space (where points in the space are classical states of the system).  A function called a Lagrangian maps points in the state-space to energies.  The action of the system is the line integral along this path.  The principle of least action says that from a given state, the system will follow the path that minimizes the action.  One solves for this minimal path using a mathematical technology called the calculus of variations.  And Noether's theorem (yeah, yeah, Noether's first theorem) says that each differentiable invariant of the action — each symmetry of the action — gives rise to a conservation law.

In recent quantum physics, the system state — the range of points in the state-space — consists of a classical state together with what I've called here a "weight"; that's the wavy part of the wave function.  While part of that weight can be perceived more-or-less directly as probability (traditionally, probability proportional to the square of the amplitude of a complex number), the rest of it can't be perceived; but its symmetries give rise to conservation laws which in turn come out as classes of particles.  Photons, gluons, and whatnot.  The weights form a gauge field, the invariances that give rise to the conservation laws are gauge symmetries, etc.

Physicists tend to ground their thinking in an imagined "real world"; a century or so of quantum mechanics hasn't really dimmed this attitude, even if the "real world" now imagined is Platonic such as a gauge field.  The attitude has considerable merit imho (leading, e.g., to the profound change I've noted in my view of λ-calculus, which was after all originally an exercise in formalist meta-mathematics, essentially a manipulation of syntax deliberately disregarding any possible referent); but the attitude does seem to make physicists especially vulnerable to mistaking the map for the territory.  That is, in treating the gauge field as if it were "really there", the physicist may forget to distinguish between a mathematical theory that successfully describes observable features of reality, and mathematics that is "known" to underlie reality.  The Lagrangian (as I pointed out in an earlier post) isn't some magic deeper level of reality, it's just whatever works to cause the principle of least action to give the right answer; and Noether's theorem, profound as it is, points out the physical consequences of a mathematical structure that was devised in the first place from the physical world, with the mathematical structure thus serving as essentially a catalyst to reasoning.  Physicists, lacking a traditional classical-style model of reality, observe (say) a force and construct a gauge theory for it which they then think of as a theorized "real thing" (not necessary a bad attitude), reason through Noether's theorem to a class of particles, look for them using massive devices such as the Large Hadron Collider, and when they observe the phenomenon they predicted, then treat the particle as "known" and even take some properties of the gauge field as "known".  The chain of reasoning is so long that even the question of whether the observed particle "exists" is somewhat open to interpretation; and the gauge field is even more problematic.

More to the immediate point, the purpose of this post calls for avoiding the entire baggage train attached to the term "gauge", in pursuit of a minimal mathematical structure giving rise to the specifically named peculiar behaviors of quantum mechanics.

Taking a semi-educated stab at minimality, let's have just three possible weights:  a neutral weight, and two polar opposites.  Call the neutral weight 0 (zero).  One might call the other two 1 and −1, but really the orientation of those has to do with multiplication, and we're not going to have any sort of multiplication of weights by each other, so to avoid implying any particular orientation, let's unimaginatively call them left and right.  Two operations are provided on weights.  Unary negation, −w, transforms left to right, transforms right to left, and leaves 0 unchanged.

In the classical toy cosmos, each experiment determined, given the classical state  s  at time  t, the resulting classical state  s'  at time  t+1.  In the quantum version, each experiment determines, for each possible classical state  s  at time  t, and each possible classical state  s'  at time  t+1, what contribution does weight  wt,s  make to weight  wt+1,s'.  Each weight at time  t+1  is simply the sum of the contributions to that weight from each of the weights at time  t.  This requires, of course, that we sum a set of weights; let the sum of a set of weights be whichever of left or right there are more of amongst the arguments, or zero if there are the same number of left and right arguments.  This summation operation —for which we'll freely use the usual additive notation— is, btw, not at all mathematically well-behaved; commutative, but not associative since, for example,

left + left + (right + right)  =  left
left + (left + right) + right  =  0
(left + left) + right + right  =  right.
The ill-behavedness however is a bit moot, because in the six possible experiments of our toy cosmos, no sum will ever have more than two non-zero addends, and non-associativity only happens when there are at least three non-zero addends.

We understand a zero weight to mean that classical state is not possible at that time; and assign equal probabilities to all non-zero-weighted classical states in the quantum state.  Presumably, for all possible experiments, a zero weight at time  t  contributes zero to each weight at time  t+1. 

It remains to define, for each experiment, the contribution of each weight before the experiment to each weight after the experiment.  We'll write  s  for a classical state before,  s'  after; before weight  ws, after weight  w's', and contribution of the former to the latter  wss'.  We have  w's' = Σs wss'  (that is, each after-weight is the sum of the contributions to it from each of the before-weights).  We'll mainly represent these transformations by tables, rather that depending on all this elaborate notation.

Consider any  set/clear v  experiment.  Before-state s contributes nothing to any after-state that changes the non-v variable. If s already has v with the value called for, only the contribution to s'=s can be non-zero, w'ss = ws.  If s doesn't have the value of v called for, it contributes its weight to the state with v changed, and also contributes the negation of its weight to the unchanged state.  In all,

set a
TT  wTT wTT + wFT
TF wTF wTF + wFF
FT wFT wFT
FF wFF wFF

set b
TT  wTT wTT + wTF
TF wTF wTF
FT wFT wFT + wFF
FF wFF wFF

clear a
TT  wTT wTT
TF wTF wTF
FT wFT wTT + wFT
FF wFF wTF + wFF

clear b
TT  wTT wTT
TF wTF wTT + wTF
FT wFT wFT
FF wFF wFT + wFF
Follow the same pattern for a  copy v  experiment, adjusting which values are changed.
copy a
TT  wTT wTT + wTF
TF wTF wTF
FT wFT wFT
FF wFF wFT + wFF

copy b
TT  wTT wTT + wFT
TF wTF wTF
FT wFT wFT
FF wFF wTF + wFF
This has, btw, all been constructed to avoid awkward questions when interpreting quantum states probabilistically by guaranteeing that each experiment, operating on a predecessor quantum state with at least one non-zero weight, will always produce a successor quantum state with at least one non-zero weight.

Demonstrating the intended quantum effects is —if it can be done— then just a matter of assembling suitable compositions of experiments.

Nondeterminism

The fundamental difference between quantum state and classical state is, always, that any observed state of reality is classical.  Quantum state evolves deterministically — we've just specified precisely how it evolves through each experiment — and our difficulty is that we see no way to interpret the probability distributions of quantum mechanics as deterministic evolution of classical states.

Interference

The effect to be demonstrated is that a sequence of two experiments produces a probability distribution that doesn't compose the probability distributions of the two individual experiments.

Suppose we  set a  and then  clear a.  To be clear on what's going on, we start from a pure state, that is, a quantum state in which only one classical state is possible.  If that pure state has a=true, the quantum state after  set a  would be unchanged, so the final probability distribution would be just that of the second experiment,  clear a.  So choose instead a pure starting state with a=false.

  set a
clear a
TT wFT wFT
TF
FT wFT wFT
FF
Here, the second experiment produces a quantum state at time  t+2  where the weight on classical state FT is the sum of the weights on states TT and FT at time  t+1; and since the first experiment has left those two as polar opposites, they cancel,  wFT − wFT = 0, so the outcome of the sequence of two experiments is pure state TT.  Even though each of the experiments individually, when applied to a pure state where the value isn't what the experiment seeks to make it, would produce a probability distribution between two possible classical result states.

Observation

In the standard two-slit experiment, electron wave interference disappears when we observe which slit the electron goes through.  So, to disrupt the interference effect we've just demonstrated, put a  copy a  in between the other two operations, to observe, within the toy cosmos, the intermediate classical state of the system.

set a
copy a
clear a
TT  wFT wFT wFT
TF
FT wFT wFT wFT wFT
FF wFT wFT
Here, the final experiment gives a time  t+3  weight for FT that is the sum of the time  t+2 weights for TT and FT, but now they have the same sign so they don't cancel.

Interestingly, although this does spoil the interference pattern from the previous demonstration, it doesn't produce the crisp "classical" probability distribution that we expect observation to exhibit in a similar scenario in real-world quantum mechanics.  In my 2006 paper, I did get a crisply classical distribution; but there, the transformation of weights by the  copy v  operation was itself deterministic, assigning zero weight to those classical outcomes in which the value was not copied.  I defined the copy transformation differently this time because it had always bothered me that the 2006 paper did not guarantee that an experiment could not result in an all-zero quantum state.  My best guess, atm, as to why this zero-outcome problem doesn't ordinarily arise in full-blown quantum mechanics is that it has to do with the overall coherence provided by the wave equation, a structural component of quantum mechanics entirely omitted here.  At least, I've never heard of this particular anomaly arising in full-blown quantum mechanics; though full-blown quantum mechanics does have anomalies of its own that seem no less alarming if perhaps more sophisticated, such as infinities that may crop up causing renormalization problems in quantum gravity.

Conceivably, this may be a clue that the presence of a wave equation is profoundly fundamental to the overall structure of quantum mechanics.  Identifying the deep structural role of a wave equation, independent of the details of any particular wave equation, would seem to be another exercise for another day — though possibly not all that distant a day, given the sorts of questions I've been asking regarding co-hygiene.

At any rate, the intervening  copy a  experiment does alter the probability distribution of values of a despite the fact that the classical effect of the experiment on a pure classical state never alters the value of a.

Entanglement

The idea of entanglement, in its strongest sense, is that things done to one variable affect the other variable.  Loosely, we want to perform experiments on one variable that don't touch the other variable, yet alter the probability distribution of the other variable.  There is so little mathematical structure left in our toy cosmos, that there aren't a lot of options to consider for demonstrating this effect.  The only operations that don't touch one variable are set/clear of the other variable.  Asymmetric handling of states can be derived from the fact that the set-clear sequence we used to demonstrate interference only causes interference on a pure start state if a=false.  So, suppose we run our  set-clear  on an initial quantum state with a correlation between a and b.

set a
clear a
TT  wFT wFT
TF wTF wTF wTF
FT wFT wFT
FF wTF
The two starting weights never get added to each other, so it doesn't matter for this sequence whether they have the same polarity, as long as they're both non-zero.  In the start state, the probability of  b=true  is 1/2, as is the probability of  a=true; in the final state, the probability of  b=true  is 1/3, while the probability of  a=true  is 2/3.

Why

Our toy cosmos deliberately leaves out most complications of quantum mechanics.  We do require, in order that the theory be at all quantum-y, to be able to understand the mathematical model as describing a probability distribution of possible perceived classical states; to understand the quantum state as being partitioned into elements associated with particular classical states; and to understand each of these elements as contributing to various elements of the successor quantum state.  That leaves the question of what sort of information a quantum state associates with each classical state; that is, what is the range over which each weight varies; and then, of course, what are the rules by which a given experiment transforms predecessor quantum state to successor quantum state.  In order to exhibit interference, it seems there must be a way for weights to cancel each other out during the summation process, and in this post I've deliberately taken the simplest sort of weight I could imagine that would allow canceling.

The resulting toy cosmos does exhibit the quantum interference effect, and clearly the demonstration of this effect does rely on weights canceling during summation.

Nondeterminism —relative, that is, to classical states— arises, potentially, when a single predecessor classical-state contributes non-zero weight to more than one successor classical-state.  Interference arises (given the cancellation provided for), again potentially, when a single successor classical-state receives non-zero contributions from more than one predecessor classical-state.

The quantum interference effect depends crucially on the fact that weights are holistic.  That is, a weight is assigned to a classical state of the entire cosmos; it isn't a characteristic of any particular feature within the classical state of the cosmos.  This is why observation within the toy cosmos disrupts interference:  once the particular part of the cosmos we're manipulating (variable a in our demonstration) is "observed" by another part of the cosmos (variable b in our demonstration), the classical state of the cosmos as a whole may differ because of what the observer saw, so that interference does not occur.  (Tbh, this point was more clearly exhibited in the 2006 paper, where observation was absolute — as it is in the full-blown quantum mechanics of our physical world; but it is still there to be found in the toy cosmos of this blog post.)

Entanglement was something I really wanted to understand in 2006; curiously, in 2018 I'm finding it less interesting than observation.  An experiment can cause interference amongst the successors of one classical-state and not amongst the successors of another classical state, so that, in the quantum successor-state, successors of one classical-state are collectively more probable than successors of another classical-state.  If the experiment only manipulates one variable (a) without affecting the other (b), this difference in probabilities of successor states can mean a difference in probabilities of values of the unmanipulated variable (b).

These latter two points are somewhat murkier from the above demonstrations than they were from the 2006 paper; the murkiness is apparently due to my decision in this blog post to define the  copy v  operation as something that might or might not change the state, rather than something that always changes the state in the 2006 paper; and that decision was made here due to considerations of avoiding possible quantum zero-states.  As noted earlier, this seems to be something to do with the absence, from this immensely simplified mathematical structure, of a wave equation that would ward off such anomalies.

It seems, then, that I went into this blog post seeking to clarify minimal structure needed to produce certain quantum effects; and confirmed that those effects could still be produced by the chosen reduced structure; but the structure became so reduced that the demonstrations were less clear than in the 2006 paper, and questions arose about what other primal characteristics of quantum mechanics may have already been lost due to evisceration of internal structure of the transformation of quantum state, i.e., the "wave equation" which has been replaced above by ad hoc tables specifying the successor weights for each experiment.

Saturday, June 2, 2018

Sapience and the limits of formal reasoning

Anakin:      Is it possible to learn this power?
Palpatine:  Not from a Jedi.
Star Wars: Episode III – Revenge of the Sith, George Lucas, 2005.

In this post I mean to tie together several puzzles I've struggled with, on this blog and elsewhere, for years; especially, on one hand, the philosophical implications of Gödel's results on the limitations of formal reasoning (post), and on the other hand, the implications of evidence that sapient minds are doing something our technological artifacts do not (post).

From time to time, amongst my exploratory/speculative posts here, I do come to some relatively firm conclusion; so, in this post, with the philosophical implications of Gödel.  A central notion here will be that formal systems manipulate information from below, while sapiences manipulate it from above.

As a bonus I'll also consider how these ideas on formal logic might apply to my investigations on basic physics (post); though, that will be more in the exploratory/speculative vein.

As this post is mostly tying together ideas I've developed in earlier posts, it won't be nearly as long as the earlier posts that developed them.  Though I continue to document the paths my thoughts follow on the way to any conclusions, those paths won't be long enough to meander too very much this time; for proper meandering, see the earlier posts.

Contents
Truth
Physics
Truth

Through roughly the second half of the nineteenth century, mathematicians aggressively extended the range of formal reasoning, ultimately reaching for a single set of axioms that would found all of logic and mathematics.  That last goal was decisively nixed by Gödel's Theorem(s) in 1931.  Gödel proved, in essence, that any sufficiently nontrivial formal axiomatic system, if it doesn't prove anything false, cannot prove itself to be self-consistent.  It's still possible to construct a more powerful axiomatic system that can prove the first one self-consistent, but that more powerful system then cannot prove itself self-consistent.  In fact, you can construct an infinite series of not-wrong axiomatic systems, each of which can prove all of its predecessors self-consistent, but each system cannot prove its own self-consistency.

In other words, there is no well-defined maximum of truth obtainable by axiomatic means.  By those means, you can go too far (allowing proofs of some things that aren't so), or you can stop short (failing to prove some things that are so), but you can't hit the target.

For those of us who work with formal reasoning a lot, this is a perplexing result.  What should one make of it?  Is there some notion of truth that is beyond the power of all these formal systems?  And what would that even mean?

For the question of whether there is a notion of objective mathematical truth beyond the power of all these formal systems, the evident answer is, not formally.  There's more to that than just the trivial observation that something more powerful than any axiomatic system cannot itself be an axiomatic system; we can also reasonably expect that whatever it is, we likely won't be able to prove its power is greater axiomatically.

I don't buy into the notion that the human mind mystically transcends the physical; an open mind I have, but I'm a reductionist at heart.  Here, though, we have an out.  In acknowledging that a hypothetical more-powerful something might not be formally provable more powerful, we open the door to candidates that we can't formally justify.  Such as, a sapient mind that emerges by some combination of its constituent parts and so seemingly ought to be no more powerful than those parts, but... is.  In practice.  (There's a quip floating around, that "In theory, there is no difference between theory and practice. But, in practice, there is.")

A related issue here is the Curry-Howard correspondence, much touted in some circles as a fundamental connection between computation and logic.  Except, I submit it can't be as fundamental as all that.  Why?  Because of the Church-Turing thesis.  Which says, in essence, that there is a robust most-powerful sort of computation.  In keeping with our expectation of an informal cap on formal power, the Church-Turing thesis in this general sense is inherently unprovable; however, specific parts of it are formally provable, formal equivalence between particular formal models of computation.  The major proofs in that vein, establishing the credibility of the general principle, were done within the next several years after Gödel's Theorems proved that there isn't a most-powerful sort of formal logic.  Long story short:  most-powerful sort of computation, yes; most-powerful sort of formal logic, no; therefore, computation and formal logic are not the same thing.

Through my recent post exploring the difference between sapient minds and all our technological artifacts, I concluded, amongst other things, that  (1) sapience cannot be measured by any standardized test, because for any standardized test one can always construct a technological artifact that will outperform sapient minds; and  (2) sapient minds are capable of grasping the "big picture" within which all technology behaves, including what the purpose of a set of formal rules is, whether the purpose is achieved, when to step outside the rules, and how to improvise behavior once outside.

A complementary observation about formal systems is that each individual action taken —each axiomatic application— is driven by the elementary details of the system state.  That is, the individual steps of the formal system are selected on a view looking up from the bottom of the information structure, whereas sapience looks downward from somewhere higher in the information structure.  This can only be a qualitative description of the difference between the sapient and formal approaches, for the simple reason that we do not, in fact, know how to do sapience.  As discussed in the earlier post, our technology does not even attempt to achieve actual sapience because we don't know, from a technical perspective, what we would be trying to achieve — since we can't even measure it, though we have various informal ways to observe its presence.

Keep in mind that this quality of sapience is not uniform.  Though some cases are straightforward, in general clambering up into the higher levels of structure, from which to take a wide-angle view, may be extremely difficult even with sapience, and some people are better at it than others, apparently for reasons of both nature, nurture, and circumstance.  Indeed, the mix of reasons that lead a Newton or an Einstein to climb particularly high in the structure are just the sort of thing I'd expect to be quite beyond the practical grasp of formal analysis.

What we see in Gödel's results is, then, that even when we accept a reductionist premise that the whole structure is built up by axioms from an elementary foundation, for a sufficiently powerful system there are fundamental limits to the sorts of high-level insights that can be assembled by building strictly upward from the bottom of the structure.

Is that a big insight?  Formally it says nothing at all.  But I can honestly say that, having reached it, for the first time in <mumble-mumble> decades of contemplation I see Gödel's results as evidence of something that makes sense to me rather than evidence that something is failing to make sense to me.

Physics

In modern physics, too, we have a large-scale phenomenon (classical reality) that evidently cannot be straightforwardly built up by simple accretion of low-level elements of the system (quanta).  Is it possible to understand this as another instance of the same broad phenomenon as the failure, per Gödel, to build a robust notion of truth from elementary axioms?

Probably not, as I'll elaborate below.  However, in the process I'll turn up some ideas that may yet lead somewhere, though quite where remains to be seen; so, a bit of meandering after all.

Gödel's axiomatic scenario has two qualitative features not immediately apparent for modern physics:

  • Axiomatic truth appears to be part of, and therefore to evolve toward, absolute truth; the gap between the two appears to be a quantitative thing that shrinks as one continues to derive results axiomatically, even though it's unclear whether it shrinks toward zero, or toward some other-sized gap.  Whereas, the gap between quantum state and classical state is clearly qualitative and does not really diminish under any circumstances.
  • The axiomatic shortfall only kicks in for sufficiently powerful systems.  It's not immediately clear what property in physics would correspond to axiomatic power of this sort.
The sapience/formalism dichotomy doesn't manifest the same way for different sorts of structure; witness the aforementioned difference between computational power and axiomatic power, where apparently one has a robust maximum while the other does not.  There is no obvious precedent to expect the dichotomy to generate a Gödel-style scale-gap in arbitrary settings.  Nonetheless; might there still be a physics analog to these features of axiomatic systems?

Quantum state-evolution does not smooth out toward classical state-evolution at scale; this is the point of the Schrödinger's-cat thought experiment.  A Gödel-style effect in physics would seem to require some sort of shading from quantum state-evolution toward classical state-evolution.  I don't see what shading of that sort would mean.

There is another possibility, here:  turn the classical/quantum relationship on its head.  Could classical state-evolution shade toward quantum state-evolution?  Apparently, yes; I've already described a way for this to happen, when in my first post on co-hygiene I suggested that the network topology of spacetime, acting at a cosmological scale, could create a seeming of nondeterminism at comparatively small scales.  Interestingly, this would also be a reversal in scale, with the effect flowing from cosmological scale to small scale.  However, the very fact that this appears to flow from large to small does not fit the expected pattern of the Gödel analogy, which plays on the contrast between bottom-up formalism and top-down sapience.

On the other front, what of the sufficient-power threshold, clearly featured on the logic side of the analogy?  If the quantum/classical dichotomy is an instance of the same effect, it would seem there must be something in physics corresponding to this power threshold.  Physics considered in the abstract as a description of physical reality has no obvious place for power in a logical or computational sense.  Interestingly, however, the particular alternative vein of speculation I've been exploring here lately (co-hygiene and quantum gravity) recommends modeling physical reality as a discrete structure that evolves through a dimension orthogonal to spacetime, progressively toward a stable state approximating the probabilistic predictions of quantum mechanics — and it is reasonable to ask how much computational power the primitive operations of this orthogonal evolution of spacetime ought to have.

In such a scenario, the computational power is applied to state-evolution from some initial state of spacetime to a stable outcome, for some sense of stable to be determined.  As a practical matter, this amounts to a transformation from some probability distribution of initial states of spacetime, to a probability distribution of stable states of spacetime that presumably resembles the probability distributions predicted by quantum mechanics.  As it is unclear how one chooses the initial probability distribution, I've toyed with the idea that a quantum mechanics-like distribution might be some sort of fixpoint under this transformation, so that spacetime would tend to come out resembling quantum mechanics more-or-less-regardless of the initial distribution.

The spacetime-rewriting relation would also be the medium through which cosmological-scale determinism would induce small-scale apparent nondeterminism.

Between inducing nondeterminism and transforming probability distributions, there would seem to be, potentially, great scope for dependence on the relative computational power of the rewriting relation.  With such a complex interplay of factors at stake, it seems likely that even if there were a Gödel-like power threshold lurking, it would have to be deduced from a much better understanding of the rewriting relation, rather than contributing to a basic understanding of the rewriting relation.  Nevertheless, I'm inclined to keep a weather eye out for any such power threshold as I move forward.

Monday, March 5, 2018

Thoughts on Jaynes's Breakdown of the Bicameral Mind

It is one of those books that is either complete rubbish or a work of consummate genius, nothing in between!  Probably the former, but I'm hedging my bets.
— comment about Jaynes's The Origin of Consciousness in the Breakdown of the Bicameral Mind in Richard Dawkins's The God Delusion, 2006.

I've just read Julian Jaynes's 1976 book The Origin of Consciousness in the Breakdown of the Bicameral Mind, and here I'm posting my thoughts; built on roughly the structure of, though wider-ranging than, a book review.

This book engages three of my particular interests, deeply entangled in the instance so that they come as a package.  I'm interested in the evolution and nature of the human mind, which of course is Jaynes's subject matter.  I'm also interested in how to read a forceful presentation of a theory without missing its fault lines.  And I'm interested in how best to present an unorthodox theory.  (I've touched on all three of these in various past posts on this blog.)

To be clear:  I enjoyed reading Jaynes's book; I think he's glimpsing something real though it might not be quite what he thinks it is; and I think his book, and his ideas, are worth studying.  Keep those things in mind, moving forward through this post.  My interests will cause me to emphasize criticisms of Jaynes's theories, I'll be trying to assemble a coherent alternative to contrast with Jaynes's theories, and with all that going on in this post the positive aspects of my assessment might get a bit buried.  But I wouldn't be paying such close attention to Jaynes if I didn't see his work as fundamentally deserving of that attention.

When studying any forceful presentation of a theory, there is risk of joining the author in whatever traps of thinking they're caught in.  The best time to scout out where the traps/fault lines are (take your pick of metaphors) is on first reading.  That's true of both orthodox and unorthodox theories, btw, indeed it's a common challenge for orthodox theories, where the traps must be easily overlooked for the theory to have achieved orthodoxy.  Unorthodox theories are sometimes presented with markers that make them sound crazy, in which case the larger challenge may be to avoid underestimating them; but a strong unorthodox presentation, without craziness markers, — such as Jaynes's — can also contain hidden traps, and moreover the reader has to distinguish genuine traps from, so to speak, legitimate unorthodoxy.

Hence my reading Jaynes slowly and cautiously, jotting down whatever notes came to mind as I went along.

It wouldn't be difficult for Jaynes's basic theory to sound crazy; Dawkins has a point there.  At its baldest, Jaynes's big idea is that until about four thousand years ago, human beings didn't have a conscious mind, but instead had a self-unaware left brain that took orders from hallucinated gods generated by their right brain — the bicameral mind.  You don't want to dive right into the thick of a thing like that, and Jaynes doesn't do so.  He builds his case slowly, so that as he adds pieces to the puzzle it's clear how they fit.

I see no need to choose between completely accepting or completely rejecting Jaynes's ideas, though.  There seems room for Jaynes to be seeing some things others have missed, while missing some factors that lead him to a more-extreme-than-necessary explanation of what he sees.  This particularly works if one has a suggestion for what Jaynes might be missing; and I do.  I have in mind broadly memetics, and particularly the notion of verbal society which I suggested on this blog some time back and have revisited several times, notably [1], [2].

As for a work of consummate genius, well, that depends on one's view of genius.  If it's possible for a work to be a masterstroke regardless of how much of it is right or wrong, then, why not?  It's easy, when the Iliad says that someone did something because a god told them to, to say, oh, that's a poetic device; but in an academic climate where "poetic device" is the standard explanation, it takes something special to say — seriously, and with extensive scholarly research to back it up — that maybe, when the Iliad says a god told them to do something, the Iliad means just what it says.

Contents
Caveats
Background
The book that Jaynes wrote
Commentary
Storytelling
Caveats

When seeking to show an audience the plausibility of a paradigm scientific theory, it's common to point out things that are consistent with the theory.  However, if you're trying to show plausibility of a highly unorthodox scientific theory (the sort whose opponents might call "lunatic fringe"), imo that technique basically doesn't work.  My reasoning has to do with contrast between rival theories.

Imagine I've got a large whiteboard, with nothing written on it.  (When I was in high-school, it would have been a blackboard; and some years from now perhaps it'll be some sort of giant touchscreen technology.  At any rate, it's big; say at least a yard/meter high and wider than it is high, perhaps a lot wider.)  The points on this whiteboard are possible explanations for things; that is, explanations that we could, in principle, entertain.  I draw on it a small circle, perhaps the size of the palm of my hand.  The points inside the circle are tried and true sorts of scientific theories; we have repeatedly used experiments to test them against alternative explanations, and in that way they have earned good reputations as solid, viable explanations.  So if one of those well-reputed explanations works very well for some new thing you're looking at, it's a credible candidate to explain that thing.

What if none of the explanations in that small circle works for the new thing you're studying?  I'll draw a larger circle around that one, maybe four times the diameter.  Points inside this larger circle are explanations we have thought of, even if they seem quite loony.  There are flying saucers in there, and Sasquatches, and ancient aliens visiting Earth to build pyramids.  But they're all explanations that we've thought of, even if we didn't think highly of them.  Even the strangest among them, though, may have some people who favor them.  And when we've got a new thing that doesn't afford an explanation in the smaller circle, but it could be explained by, say, ancient pyramid-building aliens (to take a vivid example), some people will claim that's evidence for ancient pyramid-building aliens.

Except, it isn't evidence for ancient pyramid-building aliens.  It's consistent with ancient pyramid-building aliens, but ancient pyramid-building aliens don't have the earned reputation of things in the smaller circle.  Remember, those orthodox explanations earned their reputations through experiments that contrasted them against alternatives.  But when none of those orthodox explanations works for this new thing, and ancient pyramid-building aliens does work for the new thing, what alternative theories should we be considering?  Presumably, anything that has as much repute as ancient pyramid-building aliens.

Uhuh.

And this is why I've made these circles much smaller than the whole whiteboard.  The points in the larger circle are explanations we have thought of; but most of the whiteboard is outside that circle, and all that larger outside is explanations that we could consider, but we haven't thought of them.  And really, we don't know how much of that vast array of explanations we haven't thought of might be (if we thought of it) at least as well reputed as ancient pyramid-building aliens.

The moral of the story, it would seem, is that if you're studying a really unorthodox explanation, and you want to be able to say something stronger than just that it would suffice to explain the phenomenon, you should work at finding alternatives.

I don't mean to lambaste Jaynes for not coming up with alternatives; Jaynes was pulling off a profoundly impressive feat by coming up with one solid unorthodoxy, it's hardly fair to complain that he didn't come up with several.  But it does seem that however many facts he finds to be consistent with his unorthodoxy, one ought not to interpret that as support for the unorthodoxy, as such.  Throughout my reading of Jaynes, I kept this sort of skepticism in mind.

Another sort of trap for the unwary researcher in areas relating to the mind —orthodox or no— is highly abstract terms that really don't mean at all the same thing to everyone.  (The same sort of problem may arise in religion, another area with really extraordinarily abstract terms.)  I experienced this problem myself, some years ago, when reading Susan Blackmore's The Meme Machine.  Through most of the book I felt Blackmore seemed pretty much on-target, until I came to her chapter on the self; and when I hit that chapter it was quickly clear that something was going horribly wrong.  Suddenly, I found Blackmore saying things that on their face (the face presented to me, of course) were obviously, glaringly false.  And not just saying them, reveling in them.  She was quite excited, after having believed all her life that she had a self, to realize that the self did not exist.  This struck me as beyond silly.  If she was so sure she didn't have a self, who did she imagine had written her book?

I didn't take this to be, necessarily, a mistake by Blackmore; it didn't feel that way, though there wasn't any other explanation that felt compellingly right either.  But not chalking it up to a mistake by Blackmore did not in any way change the overt falsity of what she was saying.  Hence my initial phrasing, that something was going horribly wrong.

After considerable puzzling (about a week's worth), I worked out what was going wrong.  It wasn't a problem with the concepts, neither on Blackmore's part nor mine.  It was a problem with the word "self".  Susan Blackmore had believed all her life in... something... and was quite excited to realize that that something did not exist.  But she called that something "self".  And that thing, that she called "self", was something I had never believed in to begin with.  I had always used the word "self" to mean something else.  So when she said she had realized that the self does not exist, to me she was denying the existence of something quite different from what she intended to say did not exist.  I think she was denying the existence of what Daniel Dennett would call the audience of the Cartesian theater — which Dennett spent much of his classic book Consciousness Explained debunking.

The moral here would seem to be, don't assume that other people mean the same thing you do by these sorts of highly abstract words. 

Those two potential traps came to mind for me pretty quickly when I started reading Jaynes.  Another, more content-specific, trap occurred to me a few chapters into the book.  There is a well-known (in some circles) phenomenon that medical students, as they learn about various diseases, start worrying that they themselves may be suffering from those diseases.  I've inherited a story of someone remarking, about an instance of this phenomenon, "Just wait till they start studying psychiatry."  Well.  Jaynes was a psychologist.  There's this tendency to think in terms of pathologies.  And it seemed to me, as I got into the thick of the book, that Jaynes was placing undue weight on pathological states such as schizophrenia.  Without that emphasis, it seemed, one should be able to formulate a theory in the same general direction as Jaynes was exploring, without going to the extreme he went to (his bicameral man).

Background

Jaynes is concerned with the development of consciousness over time, and, peripheral to that, the development of language over time.

Some major milestones of human development, more-or-less agreed upon:

  • About two and a half million years ago, stone tools appear.  Start of the paleolithic (old stone age).
  • About forty or fifty thousand years ago, give or take, there is an explosion in the variety of artifacts.  Art, tools for making tools, tools with artistic flare, tools for making clothing, etc.  Start of the upper paleolithic (late stone age).
  • About ten thousand years ago (your millennium may vary), human agriculture begins.  Start of the neolithic (new stone age).
  • About four thousand years ago, the first writing appears.  This is a bit after the neolithic (perhaps a thousand years) and into the Bronze Age.
  • About 2500 years ago, around the time of Plato, science and philosophy blossom in ancient Greek civilization.  Eric Havelock proposed that this is when ancient Greek society passes from orality to literacy.
According to Havelock's theory, the shift from oral society, in which knowledge is founded on oral epics such as the Iliad, to literate society in which knowledge is founded on writing, profoundly changes the character of human thinking.  Modern Afghanistan has been suggested as an example of orality.

To Havelock's theory, I've proposed to add a still earlier phase of language and society, preceding orality, which I've tentatively called verbality.  My notion of what verbality might look like has been inspired by the Pirahã language lately studied by Daniel Everett as recounted in his 2008 book Don't Sleep, There Are Snakes: Life and Language in the Amazonian Jungle.  In particular, amongst many other peculiar features of the Pirahã, their culture has no art or storytelling, while their language has no tense and no numerical or temporal vocabulary.  It seems perfectly reasonable that the Pirahã would not be typical of verbality, since it's typical for a verbal culture to have vanished many thousands of years go; but I see it as a demonstration of possibility.  It may be significant for Jaynes's theory that Everett describes a Pirahã group hallucination.

I don't have a good handle on just what precipitated the ancient transition from verbality to orality — although, if one speculates that the story of the expulsion from Eden might be, in some part, a distant memory of the verbality/orality transition, it may have been pretty traumatic.  However, I do have a timeframe.  If verbality does not support art, one would expect the transition to be clearly marked by the appearance of art; besides which, I expect a dramatic acceleration of memetic development starting at the transition; so, I place the end of verbality and start of orality circa forty thousand years go, at the beginning of the upper paleolithic.

Once orality starts, about forty thousand years ago, it would then be necessary to work out increasingly effective ways to tell stories.  It seems likely to have been a very difficult and slow process; one would, on reflection, hardly expect ancient humans to immediately shift from not telling stories at all to great epics.  I'm guessing that writing, which didn't show up for about thirty six thousand years, was a natural development once the art of storytelling reached a certain level of maturity.  I really hadn't thought about oral society struggling to develop the art of storytelling, though, until I started reading Jaynes.

The book that Jaynes wrote

Jaynes begins with a chronological rundown of theories of consciousness.  This is good strategy, as it places his ideas solidly into context, allows the reader to see him doing so, and allows him to be seen considering alternatives, which helps not only the credibility of the theory, but also of Jaynes himself; not incidentally, as proponents of unorthodoxy need to be seen to be well-informed and attentive.  On the downside, his treatment of individual past theories tends to make light of them — although, I notice, on at least one occasion some chapters later, he acknowledges having just used such a tactic, suggestive that he perceives it as a perfectly valid stylistic mode and not something to be taken too much to heart.  I think he'd come across better by showing more respect for rival theories; at any rate, it's my preference.

His rundown of past theories seems likely to suffer from a problem, such as I described earlier, with the highly abstract term consciousness.  He's quite clear that these different theories are saying different things, but he appears to assume they are all trying to get at a single idea.  The difficulty might also be described in terms of Kuhnian paradigms (which I've discussed often on this blog, e.g. [3], [4]).  Amongst the functions of a paradigm, according to Kuhn, it determines what entities exist, what sorts of questions can be asked about them, and what sorts of answers can be given.  So, while the different paradigms Jaynes describes are all searching for truth in the same general neighborhood, one should expect that some of the variance between them is not merely about what answer to give to a single common question that all of them are pursuing, but about what question is most useful to ask.  As a reader, I struggled to deduce, from how Jaynes presented these past theories, just what question he wanted to answer; and I was still working on pinning that down after I'd finished the book.  His own notion of consciousness is, to my understanding, substantially about narratization, essentially telling a story about the self.  This notion of the self as a character in a story told by the mind seems fairly close to what I think of as self (as opposed to what Susan Blackmore apparently used to think of as self before studying memetics); and is clearly an application of storytelling (the thing that, by my hypothesis, is missing from verbality).

He is a good writer; reading his prose is — at least if you're interested in the subjects he's discussing — perhaps not a page-turner but nonetheless interesting rather than oppressive.

Following the introduction, he divides the work into three parts — Books I, II, and III — addressing the nature of the bicameral mind (Book I); the evidence he sees, burning across history, of the bicameral mind and its progressive breakdown (Book II); and the remnants of bicameralism he sees in our modern state (Book III).  He added a substantial Afterword in 1990, apparently when he stopped lecturing at Princeton, at the age of 70, and seven years before his death.

Jaynes's central idea is that for some time leading up to about 4000 years ago, human minds functioned along different lines than the narratization-based consciousness we experience today.  Instead, the human mind was, in Jaynes's terminology, bicameral.  The left brain (more properly the hemisphere opposite the dominant side of the body, but most people are right-handed) handled ordinary stuff, and when additional oversight was needed, the right brain provided a hallucination of someone telling the left brain what to do.  These hallucinations were perceived to be gods; or rather, in Jaynes's framework, by definition they were gods.  One illustration he mentions, from the Iliad, has an angry Achilles asking Agamemnon to account for his behavior, Agamemnon says a god told him to, and Achilles just accepts that.  The way Jaynes talks about these gods often makes them sound as if they were coherent beings, which struck me as an overestimation of how much coordination a civilization would likely be afforded simply by its population being bicameral.  Jaynes portrays a nation of bicameral humans as extraordinarily well-coordinated (in terms that sometimes seem to flirt with group selection, a particular pet peeve of Richard Dawkins that he spent most of his book The Selfish Gene debunking).

Jaynes's notion of bicamerality is extensively tied to his ideas about human language.  The area of the brain ordinarily responsible for language is on the left side of the brain but the corresponding right-side structure is largely unused; he figures that right-hand structure is where hallucinated voices came from.  His general view of the differing functions of the hemispheres is largely in line with, if distinctly more cautious than, the pop-psychology notion of analytic left brain and synthetic/artistic right brain (apparently the pop-psychology view had just gotten started a few years before Jaynes's book came out).  He has some specific notions about the stages by which human language developed, which I didn't fully absorb (too detailed, perhaps, to pick up while struggling with the big picture of the book on a first reading), though apparently he sees metaphor as key to the way full-blown human language works in general.  In a passage that stuck in my mind, he says that his linguist friends tell him human language is very old, stretching far back in the paleolithic (I've read estimates from a hundred thousand years all the way back to the start of the paleolithic at two and a half million years); he suggests this is implausible because things ought to have moved along much faster if language had been around during all that time, and instead he proposes language only started at the beginning of the upper stone age, forty thousand years ago.

He dates the start of bicamerality to the onset of agriculture, at the paleolithic/neolithic boundary, circa ten thousand years ago.  His reasoning (to the best of my understanding) is that to make agriculture work required coordination of large groups, and this coordination was achieved via bicameral gods.  For some thousands of years (nominally, about six thousand) this worked well, but then the world got more stressful, partly due to increasing population through agriculture enabled by bicamerality, and the gods couldn't keep up, forcing the development of the new regime of consciousness.

Commentary

Jaynes seems to me to be operating at a disadvantage.  Drawing inspiration from something he's familiar with, and viewing history through the lens of his individual perspective, he sees a pattern that he finds compellingly evident in history.  It seems — from my individual perspective — that a less extreme explanation for the historical evidence might well be formulated; but the less extreme explanation I see uses tools that weren't available yet when Jaynes was developing his theory.  Jaynes draws inspiration from his knowledge of the phenomenon of schizophrenics taking orders from hallucinations; which imho really is a delightfully bold move to shake up an orthodoxy that, like most orthodoxy, could do with a good shake-up.  But, Jaynes's book was published in the same year with Dawkins's The Selfish Gene, which coined the word meme.  It's easy to look back from four decades later and say that memetics can account for profound changes in population dynamics on a scale that Jaynes felt needed a radical hypothesis like bicamerality; but you can't stand on the shoulders of giants who haven't arrived yet.

Jaynes is concerned primarily, of course, with the breakdown of the bicameral mind, over time starting about four thousand years ago; he has little to say about the upper paleolithic, the thirty-thousand-or-so years from the start of language (by his reckoning, or the start of orality by mine) to the onset of bicamerality (by his reckoning, when the technological practice of agriculture was developed).  His later discussion of modern hallucinations describes them as vestiges of bicamerality, which rather begs the question of whether humans in the upper paleolithic had hallucinations.  The example of the Pirahã suggests to me that hallucinations —and language— were already part of the human condition even before the upper paleolithic.  (An interesting question for further consideration is whether the Pirahã's group hallucinations were non-linguistic.)

My own preference is for less radical transitions (consistent with Occam's razor).  Jaynes may be underestimating how much of qualitative consciousness can exist without narratization in the modern sense; how much of language can exist without support for art or storytelling; how far social structure may be determined by what is believed without involving any fundamental change in how belief is processed by the mind.  He also appears, in particular, to be underestimating how loosely organized the modern "conscious" mind is.  His view of consciousness is monolithic (something I particularly noted when he began to discuss schizophrenia in Book III).  Recall the atomic notion of self, which Susan Blackmore described rejecting after having previously believed in it.  If the self is a character in a story we tell ourselves, then the mind that's telling the story was never really atomic in the first place, and we needn't expect a mind that tells such a story to be fundamentally differently organized than one that doesn't tell such a story.  If hallucinations are somewhere within the penumbra of normal human mental functioning (and to my non-psychologist's eye it seems they may bear some kinship to narratization), it's possible for such phenomena to have had changing roles in society over the millennia without requiring a traumatic shift to/from a bicameral mind.

Another major pitfall he's at risk for concerns interpretation of evidence.  Our perception of the distant past is grounded in physical evidence, but we have to build up layers on layers of interpretation on it to produce a coherent picture, so that what we actually see in our coherent picture is almost all interpretation.  That leaves tremendous scope for self-fulfilling expectations in the sort of reasoning Jaynes is doing, where he reconsiders the evidence in light of his theory to see how well it fits.  Some of his remarks reveal he's aware of this, but still, there it is.  When he talks about how the meaning of a word changed over time, one should keep in mind that this is how he supposes it changed over time; the actual evidence is only written words themselves, while all the meanings involved are couched in a vast network of guesses.

The distinction between supportive evidence and consistent evidence is not absolute; it depends on how distinctive the evidence is — how much it calls for explanation.  This needs care when applied at scale.  Jaynes, in particular, examines a great pile of assorted evidence.  When the theory intersects with a sufficient mass of evidence, just being consistent with so much begins to seem impressive; but really one has to sum up over the whole mass, and the sum of very many data points can still be zero; it depends on the data points.

One doesn't want to give an unorthodox theory credit for explaining things that hadn't needed explaining.

Sometimes an explanation seems warranted.  Jaynes remarks of the Iliad that it never describes human bodies as a whole, but rather as collections of parts, and that the same trend is visible in visual art of the time; though that seems open to an explanation in terms of evolving technology for storytelling, it doesn't seem gratuitous to ask for some explanation of it.  Another point that gave me pause was his claim that the extraordinarily easy Spanish conquest of the Inca Empire was because the Inca Empire was bicameral, with the entire population following the dictates of their bicameral gods; though I didn't find it an altogether compelling case for his explanation, that chapter in history is odd enough that orthodox explanation isn't entirely at ease with it either.

Jaynes as a whole, though, gave me some general sense of unnecessary explanations.  He sees evidence of hallucinations where I see unremarkable phenomena (such as "Houses of God") that may be consistent with his theory but don't need it.  In Book III he is particularly keen on the idea that modern humans look for authority to take the place of the bicameral gods they have been deprived of; he sees a quest for bicameral authority in our attitude toward science (he's missing the difference between science and religion, btw, which may in part follow from predating memetics but I still found unsettling), and even sees the same quest for authority in our enjoyment of stage magic; but I have never felt that people looking for authorities to follow needed explanation.  I figure it's a basic behavioral impulse with some evolutionary value, rather like the impulse to be fair to others, or the impulse to hate people who don't belong to one's own social group (a very mixed bag, our basic behavioral impulses).  Yet more broadly, throughout the book he presents religion as a remnant of bicamerality.  Admittedly, this may come under the heading of things he missed by predating memetics; I now react to it by thinking, religion is neatly explained by evolution of memetic organisms — which ties in to the verbality/orality hypothesis — but I only made that evolutionary connection myself in the mid-1990s (earlier post).

Occasionally, in Jaynes's efforts to fit his theory to know facts, he encounters facts that don't fit easily.  Overall, this happens to him only sporadically.  He is aware that demonic possession doesn't fit his model, and tries to make it fit anyway.  He finds himself reaching to explain why poetry and music, which he maintains are remnants of bicameralism, still exist — which wouldn't be a problem if he hadn't started by hypothesizing they were remnants of a radically different type of mind rather than being phenomena within the normal range of the sort of mind we now have.

Storytelling

I look forward — after I fully digest my first reading of Jaynes — to a second reading.  My particular objective on a second reading would be to consider in detail how the evidence he claims for his bicamerality storyline fits with my verbality/orality storyline.  This objective wouldn't have been possible on the first reading, as I was too busy struggling to grok the overall shape of what he was saying; in fact, though I'd been accumulating thought fragments throughout his book, it wasn't until Jaynes's Afterword that I realized, in a definite Aha! moment (my notes pinpoint it at the top of page 458), that the key concept in relating Jaynes's theories with mine is storytelling, which underpins Jaynes's notion of consciousness and my notion of the verbality/orality transition.  So, as part of that full digestion, following is the more elaborated form that my theories have achieved from their first pass by Jaynes.

My narrative timeline, as it now stands (yes, theorizing is itself storytelling, which in this case feeds into the story being told since it implies that the advent of storytelling would produce a tremendous acceleration of human intellectual development), starts with the transition from verbality to orality at the beginning of the upper paleolithic.  Speculatively, this cultural transition may coincide in language development to the introduction of one or both of the two devices mentioned above as missing from Pirahã:  time, and numbers.  Jaynes's ideas about consciousness are rather close to those two factors, as well.  Once the orality-threshold device is introduced, whatever it is, there is a distinct expansion of human activity.

If the start of the upper paleolithic is when orality starts, it's a long time before the period Jaynes primarily discusses, as his breakdown of the bicameral mind starts only about four thousand years ago.  The intervening thirty six thousand years, be the same more or less, would have to be accounted for by the very slow process of inventing the art of advanced storytelling.  As mentioned above, Jaynes has little to say about this period.  He reckons language only began where I'm placing the verbality/orality transition, at the start of the upper paleolithic, and he (iirc) briefly describes a series of stages in the development of language that would have taken place during the upper paleolithic before the fully developed device of language catalyzed the emergence of the bicameral mind and the neolithic.  Some of Jaynes's language stages would likely precede storytelling, but certainly a second reading should carefully examine these stages in case some of them offer some inspiration on storytelling after all.  On the other hand, if he is indeed overestimating how much of consciousness must postdate his bicameral era, his timeline for the development of consciousness starting four thousand years ago might, on careful examination, be mapped more widely onto the entire oral period from (nominally) forty thousand to twenty five hundred years ago.

After the verbality/orality transition, the next specific event in my timeline is the emergence of writing, the point at which, by my conceptual framework, the art of storytelling exceeds a critical threshold enabling it to support the written form.  This coincides with Jaynes's start of the breakdown of the bicameral mind, four thousand years ago.  Jaynes's bicameral age is for me the late part of the larger oral period prior to emergent writing; his bicameral age might well be plausibly reinterpretable as a phase in the development of storytelling, perhaps something milder than but similar to bicamerality, though quite what that would be is unclear (and might stubbornly remain unresolved even after a second in-depth reading).

The period from the advent of writing onward is intensively covered in Jaynes's book, and wants close reconsideration from top to bottom.  Several complications apply.

Reinterpretations are likely to be steep in this period, with a wide conceptual gap.  In Jaynes's framework, bicamerality is an absolute state of mind with power to direct ancient empires, while religions are pale echoes of it; in mine, bicamerality is expected to fall within the normal operating range of the human mind (though perhaps not a part of the range commonly exercised in the modern era), while religions are memetic organisms with the power to direct ancient empires.

I remarked earlier on the treacherous nature of physical evidence with multiple layers of interpretation built on it.  A particular complication here is that Jaynes is judging what people think by how they describe their experiences, but I am hypothesizing that throughout the entire period people were trying to figure out how to describe their experiences, and in particular I'm guessing that explaining one's own thoughts was especially hard to figure out; so that the further back in time you go, the less people's descriptions reflect their inner life.

Judging by the above rough sketch of a timeline, the Iliad as we know it — even after compensating (or trying to) for mutation between being composed and being written down — should already represent an extremely advanced stage of storytelling, chronologically about seven eighths of the way from the onset of storytelling toward the present day.  Hopefully, a close second reading can use the depth of Jaynes's treatment to conjecture intermediate steps in the long evolution of advanced storytelling.

Tuesday, February 13, 2018

Sapience and non-sapience

DOCTOR:   I knew a Galactic Federation once, lots of different lifeforms so they appointed a justice machine to administer the law.
ROMANA:  What happened?
DOCTOR:   They found the Federation in contempt of court and blew up the entire galaxy.
The Stones of Blood, Doctor Who, 1978.

The biggest systemic threat atm to the future of civilization, I submit, is that we will design out of it the most important information-processing asset we have:  ourselves.  Sapient beings.  Granted, there is a lot of bad stuff going on in the world right now; I put this threat first because coping with other problems tends to depend on civilization's collective wisdom.

That is, we're much less likely to get into trouble by successfully endowing our creations with sapience, than by our non-sapient creations leaching the sapience out of us.  I'm not just talking about AIs, though that's a hot topic for discussion lately; our non-sapient creations include, for a few examples, corporations (remember Mitt Romney saying "corporations are people"?), bureaucracy (cf. Franz Kafka), AIs, big data analysis, restrictive user interfaces, and totalitarian governments.

I'm not saying AI isn't powerful, or useful.  I'm certainly not suggesting human beings are all brilliant and wise — although one might argue that stupidity is something only a sapient being can achieve.  Computers can't be stupid.  They can do stupid things, but they don't produce the stupidity, merely conduct and amplify it.  Including, of course, amplifying the consequences of assigning sapient tasks to non-sapient devices such as computers.  Stupidity, especially by people in positions of power, is indeed a major threat in the world; but as a practical matter, much stupidity comes down to not thinking rationally, thus failing to tap the potential of our own sapience.  Technological creations are by no means the only thing discouraging us from rational thought; but even in (for example) the case of religious "blind faith", technological creations can make things worse.

To be clear, when I say "collective wisdom", I don't just mean addressing externals like global climate change; I also mean addressing us.  One of our technological creations is a global economic infrastructure that shapes most collective decisions about how the world is to run ("money makes the world go 'round").  We have some degree of control over how that infrastructure works, but limited control and also limited understanding of it; at some point I hope to blog about how that infrastructure does and can work; but the salient point for the current post is, if we want to survive as a species, we would do well to understand what human beings contribute to the global infrastructure.  Solving the global economic conundrum is clearly beyond the scope of this post, but it seems that this post is a preliminary thereto.

I've mentioned before on this blog the contrast between sapience and non-sapience.  Here I mean to explore the contrast, and interplay, between them more closely.  Notably, populations of sapient beings have group dynamics fundamentally different from — and, seemingly, far more efficacious from an evolutionary standpoint than — the group dynamics of non-sapient constructs.

Not only am I unconvinced that modern science can create sapience, I don't think we can even measure it.

Contents
Chess
Memetics
The sorcerer's apprentice
Lies, damned lies, and statistics
Pro-sapient tech
Storytelling and social upheaval
Chess

We seem to have talked ourselves into an inferiority complex.  Broadly, I see three major trends contributing to this.

For one thing, advocates of science since Darwin, in attempting to articulate for a popular audience the profound implications of Darwinian theory, have emphasized the power of "blind" evolution, and in doing so they've tended to describe it in decision-making terms, rather as if it were thinking.  Evolution thinks about the ways it changes species over time in the same sense that weather thinks about eroding a mountain, which is to say, not at all.  Religious thinkers have tended to ascribe some divine specialness to human beings, and even scientific thinkers have shown a tendency, until relatively recently, to portray evolution as culminating in humanity; but in favoring objective observation over mysticism, science advocates have been pushed (even if despite themselves) into downplaying human specialness.  Moreover, science advocates in emphasizing evolution have also played into a strong and ancient religious tradition that views parts/aspects of nature, and Nature herself, as sapient (cf. my past remarks on oral society).

Meanwhile, in the capitalist structure of the world we've created, people are strongly motivated to devise ways to do things with technology, and strongly motivated to make strong claims about what they can do with it.  There is no obvious capitalist motive for them to suggest technology might be inferior to people for some purposes, let alone for them to actually go out and look for advantages of not using technology for some things.  Certainly our technology can do things with algorithms and vast quantities of data that clearly could not be done by an unaided human mind.  So we've accumulated both evidence and claims for the power of technology, and neither for the power of the human mind.

The third major trend I see is more insidious.  Following the scientific methods of objectivity highly recommended by their success in studying the natural world, we tried to objectively measure our intelligence; it seemed like a good idea at the time.  And how do you objectively measure it?  The means that comes to mind is to identify a standard, well-defined, structured task that requires intelligence (in some sense of the word), and test how well we do that task.  It's just a matter of finding the right task to test for... right?  No, it's not.  The reason is appallingly simple.  If a task really is well-defined and structured, we can in principle build technology to do it.  It's when the task isn't well-defined and structured that a sapient mind is wanted.  For quite a while this wasn't a problem.  Alan Turing proposed a test for whether a computer could "think" that it seemed no computer would be passing any time soon; computers were nowhere near image recognition; computers were hilariously bad at natural-language translation; computers couldn't play chess on the level of human masters.

To be brutally honest, automated natural-language translation is still awful.  That task is defined by the way the human mind works — which might sound dismissive if you infer mere eccentricities of human thinking, but becomes quite profound if you take "the way the human mind works" to mean "sapience".  The most obvious way computers can do automatic translation well is if we train people to constrain their thoughts to patterns that computers don't have a problem with; which seemingly amounts to training people to avoid sapient thought.  (Training people to avoid sapient thought is, historically, characteristic of demagogues.)  Image processing is still a tough nut to crack, though we're making progress.  But chess has certainly been technologized.  It figures that would be the first-technologized of those tasks I've mentioned because it's the most well-defined and structured of them.  When it happened, I didn't take it as a sign that computers were becoming sapient, but rather a demonstration that chess doesn't strictly require whatever-it-is that distinguishes sapience.  I wasn't impressed by Go, either.  I wondered about computer Jeopardy!; but on reflection, that too is a highly structured problem, with no more penalty for a completely nonsensical wrong answer than for a plausible wrong one.  I'm not suggesting these aren't all impressive technological achievements; I'm suggesting the very objectivity of these measures hides the missing element in them — understanding.

Recently in a discussion I read, someone described modern advances in AI by saying computers are getting 'better and better at understanding the world' (or nearly those words), and I thought, understanding is just what they aren't doing.  It seems to me the technology is doing what it's always done — getting better and better at solving classes of problems without understanding them.  The idea that the technology understands anything at all seems to me to be an extraordinary claim, therefore requiring extraordinary proof which I do not see forthcoming since, as remarked, we expect to be unable to test it by means of the most obvious sort of experiment (a structured aptitude test).  If someone wants to contend that the opposite claim I'm making is also extraordinary — the claim that we understand in a sense the technology does not — I'll tentatively allow that resolving the question in either direction may require extraordinary proof; but I maintain there are things we need to do in case I'm right.

Somebody, I maintain, has to bring a big-picture perspective to bear.  To understand, in order to choose the goals of what our technology is set to do, in order to choose the structural paradigm for the problem, in order to judge when the technology is actually solving the problem and when the situation falls outside the paradigm.  In order to improvise what to do when the situation does fall outside the paradigm.  That somebody has to be sapient.

For those skeptics who may wonder (keeping in mind I'm all for skepticism, myself) whether there is an unfalsifiable claim lurking here somewhere, note that we are not universally prohibited from observing the gap between sapience and non-sapience.  The difficulty is with one means of observation:  a very large and important class of experiments are predictably incapable of measuring, or even detecting, the gap.  The reason this does not imply unfalsifiability is that scientific inquiry isn't limited to that particular class of experiments, large and important though the class is; the range of scientific inquiry doesn't have specific formally-defined boundaries — because it's an activity of sapient minds.

The gap is at least suggested by the aforementioned difficulty of automatic translation.  What's missing in automatic translation is understanding:  by its nature automatic translation treats texts for translation as strings to be manipulated, rather than indications about the reality in which their author is embedded.  Whatever is missed by automatic translation because it is manipulating strings without thinking about their meaning, that is a manifestation of the sapience/non-sapience gap.  Presumably, with enough work one could continue to improve automatic translators; any particular failure of translation can always be fixed, just as any standardized test can be technologized.  How small the automatic-translation shortfall can be made in practice, remains to be seen; but the shape of the shortfall should always be that of an automated system doing a technical manipulation that reveals absence of comprehension.

Consider fly-by-wire airplanes, which I mentioned in a previous post.  What happens when a fly-by-wire airplane encounters a situation outside the parameters of the fly-by-wire system?  It turns control over to the human pilots.  Who often don't realize, for a few critical moments (if those moments weren't critical, we wouldn't be talking about them, and quite likely the fly-by-wire system would not have bailed) that the fly-by-wire system has stopped flying the plane for them; and they have to orient themselves to the situation; and they've mostly been getting practice at letting the fly-by-wire system do things for them.  And then when this stacked-deck of a situation leads to a horrible outcome, there are strong psychological, political, and economic incentives to conclude that it was human error; after all, the humans were in control at the denouement, right?  It seems pretty clear to me that, of the possible ways that one could try to divvy up tasks between technology and humans, the model currently used by fly-by-wire airplanes (and now, one suspects, drive-by-wire cars) is a poor model, dividing tasks for the convenience of whoever is providing the automation rather than for the synergism of the human/non-human ensemble.  It doesn't look as if we know how to design such systems for synergism of the ensemble; and it's not immediately clear that there's any economic incentive for us to figure it out.  Occasionally, of course, something that seems unprofitable has economic potential that's only waiting for somebody to figure out how to exploit it; if there is such potential here, we may need first to understand the information-processing characteristics of sapience better.  Meanwhile, I suggest, there is a massive penalty, on a civilization-wide scale (which is outside the province of ordinary economics), if we fail to figure out how to design our technology to nurture sapience.  It should be possible to nurture sapience without first knowing how it works, or even exactly what it does — though figuring out how to nurture it may bring us closer to those other things.

I'll remark other facets of the inferiority-complex effect, as they arise in discussion, below.

Memetics

By the time I'm writing this post, I've moved further along a path of thought I mentioned in my first contentful post on this blog.  I wrote then that in Dawkins's original description of memetics, he made an understandable mistake by saying that memetic life was "still in its infancy, still drifting clumsily about in its primeval soup".  That much I'm quite satisfied with:  it was a mistake — memetic evolution has apparently proceeded about three to five orders of magnitude faster than genetic evolution, and has been well beyond primeval soup for millennia, perhaps tens of millennia — and it was an understandable mistake, at that.  I have more to say now, though, about the origins of the mistake.  I wrote that memetic organisms are hard to recognize because you can't observe them directly, as their primary form is abstract rather than physical; and that's true as far as it goes; but there's also something deeper going on.  Dawkins is a geneticist, and in describing necessary conditions under which replication gives rise to evolution, he assumed it would always require the sort of conditions that genetic replication needs to produce evolution.  In particular, he appears to have assumed there must be a mechanism that copies a basic representation of information with fantastically high fidelity.

Now, this is a tricky point.  I'm okay with the idea that extreme-fidelity basic replication is necessary for genetic evolution.  It seems logically cogent that something would have to be replicated with extreme fidelity to support evolution-in-general (such as memetic evolution).  But I see no reason this extreme-fidelity replication would have to occur in the basic representation.  There's no apparent reason we must be able to pin down at all just what is being replicated with extreme fidelity, nor must we be able to identify a mechanism for extreme-fidelity copying.  If we stipulate that evolution implies something is being extreme-fidelity-copied, and we see that evolution is taking place, we can infer that some extreme-fidelity copying is taking place; but evolution works by exploiting what happens with indifference to why it happens.  We might find that underlying material is being copied wildly unfaithfully, yet somehow, beyond our ability to follow the connections, this copying preserves some inarticulable abstract property that leads to an observable evolutionary outcome.  Evolution would exploit the abstract property with complete indifference to our inability to isolate it.

It appears that in the case of genetic evolution, we have identified a basic extreme-fidelity copying mechanism.  In fact, apparently it even has an error-detection-and-correction mechanism built into it; which certainly seems solid confirmation that such extreme fidelity was direly needed for genetic evolution or such a sophisticated mechanism would never have developed.  Yet there appears to be nothing remotely like that for memetic replication.  If memetic evolution really had the same sort of dynamics as genetic evolution, we would indeed expect memetic life to be "still drifting clumsily about in its primeval soup"; it couldn't possibly do better than that until it had developed a super-high-fidelity low-level replicating mechanism.

Yet memetic evolution proceeds at, comparatively, break-neck pace, in spectacular defiance of the expectation.  Therefore we may suppose that the dynamics of memetic evolution are altered by some factor profoundly different from genetic evolution.

I suggest the key altering factor of memetic evolution, overturning the dynamics of genetic evolution, is that the basic elements of the host medium — people, rather than chemicals — are sapient.  What this implies is that, while memetic replication involves obviously-low-fidelity copying of explicitly represented information, the individual hosts are thinking about the content, processing it through the lens of their big-picture sapient perspective.  Apparently, this can result in an information flow with abstract fixpoints — things that get copied with extreme fidelity — that can't be readily mapped onto the explicit representation (e.g., what is said/written).  My sense of this situation is that if it is even useful to explicitly posit the existence of discrete "memes" in memetic evolution, it might yet be appropriate to treat them as unknown quantities rather than pouring effort into trying to identify them individually.  It seems possible the wholesale discreteness assumption may be unhelpful as well — though ideas don't seem like a continuous fluid in the usual simple sense, either.

This particular observation of the sapient/non-sapient gap is from an unusual angle.  When trying to build an AI, we're likely to think in terms of what makes an individual entity sapient; likewise when defining sapience.  The group dynamics of populations of sapients versus non-sapients probably won't (at a guess) help us in any direct way to build or measure sapience; but it does offer a striking view of the existence of a sapience/non-sapience gap.  I've remarked before that groups of people get less sapient at scale; a population of sapiences is not itself sapient; but it appears that, when building a system, mixing in sapient components can produce systemic properties that aren't attainable with uniformly non-sapient components, thus attesting that the two kinds of components do have different properties.

This evolutionary property of networks of sapiences affords yet another opportunity to underestimate sapience itself.  Seeing that populations of humans can accumulate tremendous knowledge over time — and recognizing that no individual can hope to achieve great feats of intellect without learning from, and interacting with, such a scholastic tradition — and given the various motives, discussed above, for downplaying human specialness — it may be tempting to suppose that sapience is not, after all, a property of individuals.  However, cogito, ergo that's taking the idea of collective intelligence to an absurdity.  The evolutionary property of memetics I've described is not merely a property of how the network is set up; if it were, genetic evolution ought to have struck on it at some point.

There are, broadly, three idealized models (at least three) of how a self-directing system can develop.  There's "blind evolution", which explores alternatives by maintaining a large population with different individuals blundering down different paths simultaneously, and if the population is big enough, the variety amongst individuals is broad enough, and the viable paths are close enough to blunder into, enough individuals will succeed well enough that the population evolves rather than going extinct.  This strategy isn't applicable to a single systemic decision, as with the now-topical issue of global climate change:  there's no opportunity for different individuals to live in different global climates, so there's no opportunity for individuals who make better choices to survive better than individuals who make poorer choices.  As a second model, there's a system directed by a sapience; the individual sapient mind who runs the show can plan, devising possible strategies and weighing their possible consequences before choosing.  It is also subject to all the weaknesses and fallibilities of individuals — including plain old corruption (which, we're reminded, power causes).  The third model is a large population of sapiences, evolving memetically — and that's different again.  I don't pretend to fully grok the dynamics of that third model, and I think it's safe to say no-one else does either; we're all learning about it in real time as history unfolds, struggling with different ways of arranging societies (governmentally, economically, what have you).

A key weakness of the third model is that it only applies under fragile conditions; in particular, the conditions may be deliberately disrupted, at least in the short term; keeping in mind we're dealing with a population of sapiences each potentially deliberate.  When systemic bias or small controlling population interferes with the homogeneity of the sapient population, the model breaks down and the system control loses — at least, partly loses — its memetic dynamics.  This is a vulnerability shared in common by the systems of democracy and capitalism.

The sorcerer's apprentice

There are, of course, more-than-adequate ways for us to get into trouble by succeeding in giving our technology sapience.  A particularly straightforward one is that we give it sapience and it decides it doesn't want to do what we want it to.  In science fiction this scenario may be accompanied by a premise that the created sapience is smarter than we are — although, looking around at history, there seems a dearth of evidence that smart people end up running the show.  Even if they're only about as smart, and stupid, as we are, an influx of artificial sapiences into the general pool of sapience in civilization is likely to throw off the balance of the pool as a whole — either deliberately or, more likely, inadvertently.  One has only to ask whether sapient AIs should have the right to vote to see a tangle of moral, ethical, and practical problems cascading forth (with vote rigging on one side, slavery on the other; not forgetting that, spreading opaque fog over the whole, we have no clue how to test for sapience).  However, I see no particular reason to think we're close to giving our technology sapience; I have doubts we're even trying to do so, since I doubt we know where that target actually is, making it impossible for us to aim for it (though mistaking something else for the target is another opportunity for trouble).  Even if we could eventually get ourselves into trouble by giving our technology sapience, we might not last long enough to do so because we get ourselves into trouble sooner by the non-sapient-technology route.  So, back to non-sapience.

A major theme in non-sapient information processing is algorithms:  rigidly specified instructions for how to proceed.  An archetypal cautionary tale about what goes wrong with algorithms is The Sorcerer's Apprentice, an illustration (amongst other possible interpretations) of what happens when a rigid formula is followed without sapient oversight of when the formula itself ceases to be appropriate due to big-picture perspective.  One might argue that this characteristic rigidity is an inherently non-sapient limitation of algorithms.

It's not an accident that error-handling is among the great unresolved mysteries of programming-language design — algorithms being neither well-suited to determine when things have gone wrong, nor well-suited to cope with the mess when they do.

Algorithmic rigidity is what makes bureaucracy something to complain about — blind adherence to rules even when they don't make sense in the context where they occur, evoking the metaphor of being tied up in red tape.  The evident dehumanizing effect of bureaucracy is that it eliminates discretion to take advantage of understanding arbitrary aspects of big picture; it seems that to afford full scope to sapience, maximizing its potential, one wants to provide arbitrary flexibility — freedom — avoiding limitation to discrete choices.

A bureaucratic system can give lip service to "giving people more choices" by adding on additional rules, but this is not a route to the sort of innate freedom that empowers the potential of sapience.  To the contrary:  sapient minds are ultimately less able to cope with vast networks of complicated rules than technological creations such as computers — or corporations, or governments — are, and consequently, institutions such as corporations and governments naturally evolve vast networks of complicated rules as a strategy for asserting control over sapiences.  There are a variety of ways to describe this.  One might say that an institution, because it is a non-sapient entity in a sea of sapient minds, is more likely to survive if it has some property that limits sapient minds so they're less likely to overwhelm it.  A more cynical way to say the same thing is that the institution survives better if it finds a way to prevent people from thinking.  A stereotypical liberal conspiracy theorist might say "they" strangle "us" with complicated rules to keep us down — which, if you think about it, is yet another way of saying the same thing (other than the usual incautious assumption of conspiracy theorists, that the behavior must be a deliberate plot by individual sapiences rather than an evolved survival strategy of memetic organisms).  Some people are far better at handling complexity than others, but even the greatest of our complexity tolerances are trivial compared to those of our non-sapient creations.  Part of my point here is that I don't think that's somehow a "flaw" in us, but rather part of the inherent operational characteristics of sapience that shape the way it ought to be most effectively applied.

Lies, damned lies, and statistics

A second major theme in non-sapient information processing is "big data".  Where algorithms contrast with sapience in logical strategy, big data contrasts in sheer volume of raw data.

These two dimensions — logical strategy and data scale — are evidently related.  Algorithms can be applied directly to arbitrarily-large-scale data; sapience cannot, which is why big data is the province of non-sapient technology.  I suggested in an earlier post that the device of sapience only works at a certain range of scales, and that the sizes of both our short- and our long-term memories may be, to some extent, essential consequences of sapience rather than accidental consequences of evolution.  Not everyone tops out at the same scale of raw data, of course; some people can take in a lot more, or a lot less, than others before they need to impose some structure on it.  Interestingly, this is pretty clearly not some sort of "magnitude" of sapience, as there have been acknowledged geniuses, of different styles, toward both ends of the spectrum; examples that come to mind, Leonard Euler (with a spectacular memory) and Albert Einstein (notoriously absent-minded).

That we sapiences can "make sense" of raw data, imposing structure on it and thereby coping with masses of data far beyond our ability to handle in raw form, would seem to be part of the essence of what it means to be sapient.  The attendant limitation on raw data processing would then be a technical property of the Platonic realm in broadly the same sense as fundamental constants like π, e, etc., and distant kin to such properties of the physical realm as the conditions necessary for nuclear fusion.

Sometimes, we can make sense of vast data sets, many orders of magnitude beyond our native capacity, by leveraging technological capacity to process more-or-less-arbitrarily large volumes of raw data and boil it down algorithmically, to a scale/form within our scope.  It should be clear that the success of the enterprise depends on how insightfully we direct the technology on how to boil down the data; essentially, we have to intuit what sorts of analysis will give us the right sorts of information to gain insight into the salient features of the data.  We're then at the short end of a data-mining lever; the bigger the data mine, the trickier it is to reason out how to direct the technological part of the operation.  It's also possible to deliberately choose an analysis that will give us the answer we want, rather than helping us learn about reality.  And thus are born the twin phenomena of misuse of statistics and abuse of statistics.

There may be a temptation to apply technology to the problem of deciding how to mine the data.  That —it should be clear on reflection— is an illusion.  The technology is just as devoid of sapient insight when we apply it to the meta-analysis as when we applied it to the analysis directly; and the potential for miscues is yet larger, since technology working at the meta-level is in a position to make more biasing errors through lack of judgement.

One might be tempted to think of conceptualization, the process by which we impose concepts on raw data to structure and thus make sense of it, as "both cause and cure" of our limited capacity to process raw data; but this would, imo, be a mistake of orientation.  Conceptualization — which seems to be the basic functional manifestation of sapience — may cause the limited-capacity problem, and it may also be the "cure", i.e., the means by which we cope with the problem, but neither of those is the point of conceptualization/sapience.  As discussed, sapience differs from non-sapient information processing in ways that don't obviously fit on any sort of spectrum.  Consider:  logically, our inability to directly grok big data can't be a "failure" unless one makes a value judgement that that particular ability is something we should be able to do — and making a value judgement is something that can only be meaningfully ascribed to a sapience.

It's also rather common to imagine the possibility of a sapience of a different order, capable of processing vast (perhaps even arbitrarily vast) quantities of data.  This can result from —as noted earlier— portraying evolution as if it were a sapient process.  It may result from an extrapolation based on the existence of some people with higher raw-data tolerances than others; but this treats "intelligence" as an ordering correlated with raw data processing capacity — which, as I've noted above, it is not.  Human sapiences toward the upper end of raw data processing capacity don't appear to be "more sapient", rather it's more like they're striking a different balance of parameters.  Different strengths and weaknesses occur at different mixtures of the parameters, and this seems to me characteristic of an effect (sapience) that can only occur under a limited range of conditions, with the effect breaking down in different ways depending on which boundary of the range is crossed.  Alternatively, it has sometimes been suggested there should be some sort of fundamentally different kind of mind, working on different principles than our own; but once one no longer expects this supposed effect to have anything to do with sapience as it occurs in humans, I see no basis on which to conjecture the supposed effect at all.

There's also yet another opportunity here for us to talk ourselves into an inferiority complex.  We tend to break down a holistic situation into components for understanding, and then when things fail we may be inclined to ascribe failure to a particular component, rather than to the way the components fit together or to the system as a whole.  So when a human/technology ensemble fails, we're that much more likely to blame the human component.

Pro-sapient tech

How can we design technology to nurture sapience rather than stifle it?  Though I don't claim to grasp the full scope of this formidable challenge, I have some suggestions that should help.

On the stifling side, the two big principles I've discussed are algorithms and scale; algorithms eliminate the arbitrary flexibility that gives sapience room to function, while vast masses of data overwhelm sapiences (technology handles arbitrarily large masses of data smoothly, not trying to grok big-picture implications that presumably grow at least quadratically with scale).  Evidently sapience needs full-spectrum access to the data (it can't react to what it doesn't know), needs to have hands-on experience from which to learn, needs to be unfettered in its flexibility to act on what it sees.

Tedium should be avoided.  Aspects of this are likely well-known in some circles, perhaps know-how related to (human) assembly-line work; from my own experience, tedium can trip up sapience in a couple of ways, that blur into each other.  Repeating actions over and over can lead to inattention, so that when a case comes along that ought to be treated differently, the sapient operator just does the same thing yet again, either failing to notice it at all, or "catching it too late" (i.e., becoming aware of the anomaly after having already committed to processing it in the usual way).  On the other hand, paying full attention to an endless series of simple cases, even if they offer variations maintaining novelty, can exhaust the sapient operator's decision-making capacity; I, for one, find that making lots of little decisions drains me for a time, as if I had a reservoir of choice that, when depleted, refills at a limited natural rate.  (I somewhat recall a theory ascribed to Barack Obama that a person can only make one or two big decisions per day; same principle.)

Another important principle to keep in mind is that sapient minds need experience.  Even "deep learning" AIs need training, but with sapiences the need is deeper and wider; the point is not merely to "train" them to do a particular task, important though that is, but to give them accumulated broad experience in the whole unbounded context surrounding whatever particular tasks are involved.  Teaching a student to think is an educator's highest aspiration.  An expert sapient practitioner of any trade uses "tricks of the trade" that may be entirely outside the box.  A typical metaphor for extreme forms of such applied sapient measures is 'chewing gum and baling wire'.  One of the subtle traps of over-reliance on technology is that if sapiences aren't getting plenty of broad, wide hands-on experience, when situations outside known parameters arise there will be no-one clueful to deal with it — even if the infrastructure has sufficiently broad human-accessible flexibility to provide scope for out-of-the-box sapient measures.  (An old joke describes an expert being called in to fix some sort of complex system involving pipes under pressure —recently perhaps a nuclear power plant, some older versions involve a steamboat— who looks around, taps a valve somewhere, and everything starts working again; the expert charges a huge amount of money —say a million dollars, though the figure has to ratchet up over time due to inflation— and explains, when challenged on the amount, that one dollar is for tapping the valve, and the rest is for knowing where to tap.)

This presents an economic/social challenge.  The need to provide humans with hands-on experience is a long-term investment in fundamental robustness.  For the same reason that standardized tests ultimately cannot measure sapience, short-term performance on any sufficiently well-structured task can be improved by applying technology to it, which can lead to a search for ways to make tasks more well-structured — with a completely predictable loss of ability to deal with... the unpredictable.  I touched on an instance of this phenomenon when describing, in an earlier post, the inherent robustness of a traffic system made up of human drivers.

Suppression of sapience also takes much more sweeping, long-term systemic forms.  A particular case that made a deep impression on me:  in studying the history of my home town I was fascinated that the earliest European landowners of the area received land grants from the king, several generations before Massachusetts residents rose up in rebellion against English rule (causing a considerable ruckus, which you may have heard about).  Those land grants were subject to proving the land, which is to say, demonstrating an ability to develop it.  Think about that.  We criticize various parties —developers, big corporations, whatever— for exploiting the environment, but those land grants, some four hundred years ago under a different system of government, required exploiting the land, otherwise the land would be taken away and given to someone else.  Just how profoundly is that exploitation woven into the fabric of Western civilization?  It appears to be quite beyond distinctions like monarchy versus democracy, capitalism versus socialism.  We've got hold of the tail of a vast beast that hasn't even turned 'round to where we can see the thing as a whole; it's far, far beyond anything I can tackle in this post, except to note pointedly that we must be aware of it, and be thinking about it.

A much simpler, but also pernicious, source of long-term systemic bias is planning to add support for creativity "later".  Criticism of this practice could be drawn to quite reasonable tactical concerns like whether anyone will really ever get around to attempting the addition, and whether a successful addition would fail to take hold because it would come too late to overcome previously established patterns of behavior; the key criticism I recommend, though, is that strategically, creativity is itself systemic and needs to be inherent in the design from the start.  Anything tacked on as an afterthought would be necessarily inferior.

To give proper scope for sapience, its input — the information presented to the sapient operator in a technological interface — should be high-bandwidth from an unbounded well of ordered complexity.  There has to be underlying rhyme-and-reason to what is presented, otherwise information overload is likely, but it mustn't be stoppered down to the sort of simple order that lends itself to formal, aka technological, treatment, which would defeat the purpose of bringing a sapience to bear on it.  Take English text as archetypical:  built up mostly from 26 letters and a few punctuation marks and whitespace, yet as one scales up, any formal/technological grasp on its complexity starts to fuzz until ultimately it gets entirely outside what a non-sapience can handle.  Technology sinks in the swamp of natural language, while to a sapience natural language comes... well, naturally.  This sort of emergent formal intractability seems a characteristic domain of sapience.  There is apparently some range of variation in the sorts of rhyme and reason involved; for my part, I favor a clean simple set of orthogonal primitives, while another sort of mind favors a less tidy primitive set (more-or-less the design difference between Scheme and Common Lisp).

When filtering input to avoid simply overwhelming the sapient user, whitelisting is inherently more dangerous than blacklisting.  That is, an automatic filter to admit information makes an algorithmic judgement about what may be important, which judgement is properly the purview of sapience, to assess unbounded context; whereas a filter to omit completely predictable information, though it certainly can go wrong, has a better chance of working since it isn't trying to make a call about which information is extraneous, only about which information is completely predictable (if properly designed; censorship being one of the ways for it to go horribly wrong).

On the output side —i.e., what the sapient operator is empowered to do— a key aspect is effective ability to step outside the framework.  Sets of discrete top-level choices are likely to stifle sapient creativity rather than enhance it (not to be confused with a set of building blocks, which would include the aforementioned letters-plus-punctuation).  While there is obvious advantage in facilities to support common types of actions, those facilities need to blend smoothly with robust handling of general cases, to produce graceful degradation when stepping off the beaten path.  Handling some approaches more easily than others might easily turn into systemic bias against the others — a highly context-dependent pitfall, on which the reason for less-supported behavior seems to be the pivotal factor.  (Consider the role of motive-for-deviation in the subjective balance between pestering the operator about an unconventional choice until they give it up, versus allowing one anomaly to needlessly propagate unchecked complications.)

Storytelling and social upheaval

A final thought, grounding this view of individual sapiences back into global systemic threats (where I started, at the top of the post).

Have you noticed it's really hard to adapt a really good book into a really good movie?  So it seems to me.  When top-flight literature translates successfully to a top-flight movie, the literature is more likely to have been a short story.  A whole book is more likely to translate into a miniseries, or a set of movies.  I was particularly interested by the Harry Potter movies, which I found suffered from their attempt to fit far too much into each single movie; the Harry Potter books were mostly quite long, and were notable for their rich detail, and that couldn't possibly be captured by one movie per book without reducing the richness to something telegraphic.  The books were classics, for the ages; the movies weren't actually bad, but they weren't in the same rarefied league as the books.  (I've wondered if one could turn the Harry Potter book set into a television series, with one season per book.)

The trouble in converting literature to cinematography is bandwidth.  From a technical standpoint this is counter-intuitive:  text takes vastly less digital storage than video; but how much of that data can be used as effective signal depends on what kind of signal is intended.  I maintain that as a storytelling medium, text is extremely high-bandwidth while video is a severe bottleneck, stunningly inefficient at getting the relevant ideas across if, indeed, they can be expressed at all.  In essence, I suggest, storytelling is what language has evolved for.  A picture may be worth a thousand words, but  (a) it depends on which words and which picture,  (b) it's apparently more like 84 words, and  (c) it doesn't follow that a thousand pictures are worth a thousand times as many words.

In a post here some time back, I theorized that human language has evolved in three major stages (post).  The current stage in the developed world is literacy, in which society embraces written language as a foundation for acquiring knowledge.  The preceding stage was orality, where oral sagas are the foundation for acquiring knowledge, according to the theory propounded by Eric Havelock in his magnum opus Preface to Plato, where he proposes that Plato lived on the cusp of the transition of ancient Greek society from orality to literacy.  My extrapolation from Havelock's theory says that before the orality stage of language was another stage I've called verbality, which I speculate may have more-or-less resembled the peculiar Amazonian language Pirahã (documented by Daniel Everett in Don't Sleep There are Snakes).  Pirahã has a variety of strange features, but what particularly attracted my attention was that, adding up these features, Pirahã apparently does not and cannot support an oral culture; Pirahã culture has no history, art, or storytelling (does not), and the language has no temporal vocabulary, tense, or number system (cannot).

'No storytelling' is where this relates back to books-versus-movies.  The nature of the transition from verbality to orality is unclear to me; but I (now) conjecture that once the transition to orality occurs, there would then necessarily be a long period of linguistic evolution during which society would slowly figure out how to tell stories.  At some point in this development, writing would arise and after a while precipitate the transition to literacy.  But the written form of language, in order to support the transition to literate society, would particularly have to be ideally suited to storytelling.

Soon after the inception of email as a communication medium came the development of emoticons:  symbols absent from traditional written storytelling but evidently needed to fill in for the contextual "body language" clues ordinarily available in face-to-face social interaction.  Demonstrating that social interaction itself is not storytelling as such, for which written language was already well suited without emoticons.  One might conjecture that video, while lower-storytelling-bandwidth than text, could have higher effective social-interaction-bandwidth than text.  And on the other side of the equation, emoticons also demonstrate that the new electronic medium was already being used for non-storytelling social interaction.

For another glimpse into the character of the electronic medium, contrast the experience of browsing Wikibooks — an online library of some thousands of open-access textbooks — against the pre-Internet experience of browsing in an academic library.

On Wikibooks, perhaps you enter through the main page, which offers you a search box and links to some top-level subject pages like Computing, Engineering, Humanities, and such.  Each of those top-level subject pages provides an array of subsections, and each subsection will list all its own books as well as listing its own sub-subsections, and so on.  The ubiquitous search box will do a string search, listing first pages that mention your chosen search terms in the page title, then pages that contain the terms somewhere in the content of the page.  Look at a particular page of a book, and you'll see the text, perhaps navigation links such as next/previous page, parent page, subpages; there might be a navigation box on the right side of the page that shows the top-level table of contents of the book.

At the pre-Internet library, typically, you enter past the circulation desk, where a librarian is seated.  Past that, you come to the card catalog; hundreds of alphabetically labeled deep drawers of three-by-five index cards, each card cumulatively customized by successive librarians over decades, perhaps over more than a century if this is a long-established library.  (Side insight, btw:  that card catalog is, in its essence, a collaborative hypertext document very like a wiki.)  You may spend some time browsing through the catalog, flipping through the cards in various drawers, jotting down notes and using them to move from one drawer to another — a slower process than if you could move instantly from one to another by clicking an electronic link, but also a qualitatively richer experience.  At every moment, surrounding context bears on your awareness; other index cards near the one you're looking at, other drawers; and beyond that, strange though it now seems that this is worth saying, you are in a room, literally immersed in context.  Furniture, lights, perhaps a cork bulletin board with some notices on it; posters, signs, or notices on the walls, sometimes even thematic displays; miscellany (is that a potted plant over there?); likely some other people, quietly going about their own business.  The librarian you passed at the desk probably had some of their own stuff there, may have been reading a book.  Context.  Having taking notes on what you found in the card catalog and formulated a plan, you move on to the stacks; long rows of closely spaced bookcases, carefully labeled according to some indexing system referenced by the cards and jotted down in your notes, with perhaps additional notices on some of the cases — you're in another room — you come to the shelves, and may well browse through other books near what your notes direct you to, which you can hardly help noticing (not like an electronic system where you generally have to go out of your way to conjure up whatever context the system may be able to provide).  You select the particular book you want, and perhaps take it to a reading desk (or just plunk down on the carpet right there, or a nearby footstool, to read); and as you're looking at a physical book, you may well flip through the pages as you go, yet another inherently context-intensive browsing technique made possible by the physicality of the situation.

What makes this whole pre-Internet experience profoundly different from Wikibooks — and I say this as a great enthusiast of Wikibooks — is the rich, deep, pervasive context.  And context is where this dovetails back into the main theme of this post, recognizing context as the special province of sapience.

When the thriving memetic ecosystem of oral culture was introduced to the medium of written language, it did profoundly change things, producing literate culture, and new taxonomic classes of memetic organisms that could not have thrived in oral society (I'm thinking especially of scientific organisms); but despite these profound changes, the medium still thoroughly supported language, and context-intensive social interactions mostly remained in the realm of face-to-face encounters.  So the memetic ecosystem continued to thrive.

Memetic ecosystem is where all of this links back to the earlier discussion of populations of sapiences.

That discussion noted system self-direction through a population of sapiences can break down if the system is thrown out of balance.  And while the memetic ecosystem handily survived the transition to literacy, it's an open question what will happen with the transition to the Internet medium.  This time, the new medium is highly context-resistant while it aggressively pulls in social interactions.  With sapience centering on context aspects that are by default eliminated or drastically transformed in the transition, it seems the transition must have, somehow, an extreme impact on the way sapient minds develop.  If there is indeed a healthy, stable form of society to be achieved on the far side of this transition, I don't think we should kid ourselves that we know what that will look like, but it's likely to be very different, in some way or other, from the sort of stable society that preceded.

The obvious forecast is social upheaval.  The new system doesn't know how to put itself together, or really even know for sure whether it can.  The old system is pretty sure to push back.  As I write this, I look at the political chaos in the United States —and elsewhere— and I see these forces at work.

And I think of the word singularity.