Is Psi the Result of Morphic-Resonance-Guided Quantum-Level Multi-Agent Prediction?

ABSTRACT: Suppose that physically uncorrelated, morphically-resonant systems can implicitly  make predictions of each other (I suggest some details), and that these predictions can impact the reality?   Such systems will then need to take each others' predictions into account (and there will also be a recursive aspect), which will result in a lot of noise in their influence, but collective emergent-agent-system dynamical patterns popping up now and then.   Qualitatively this seems to me like the kind of thing that might explain the various sorts of oddities we see in psi data...

The existence of psi phenomena is in my opinion relatively well demonstrated (see references here   and many others); but we lack any decent theoretical explanation for how and why these phenomena occur.   I have made some speculations in this direction (see this page and prior entries in this blog), but these prior ideas – as well as being quite loosely defined – don’t deliver any conceptually clear route to explaining the numerous peculiarities associated with psi data (such as the weakness of psi phenomena, the decline effect, psi-missing, and so forth).

In this post  I will climb even further out on the limb of my previous speculative psi-theory ideas, and present some new sketchy conjectures about how psi might emerge from quantum-type dynamics, if one modified quantum theory in appropriate ways.   These ideas are aimed at giving a route to explaining why psi has the peculiar statistical properties it does.    Psi’s various statistical oddities are taken as a hint as to what kind of mechanism might exist at the underlying level.

For sure I do not give a completely detailed theory here -- just a sketch, which could be filled out in many different ways.   But given the paucity of promising theoretical ideas regarding the underpinnings of psi, even interesting new sketches of theories should be considered of value, I think.

Commonalities Between Psi and Finance

Last week, while walking through the Beijing airport, I was reflecting on the nature of psi results over time and some of their peculiarities, e.g.:

• The data is almost random – but it’s persistently not-quite-random
• Extremely non-normally distributed, with a lot of mediocre results and then extreme results now and then
• A tendency for patterns to be very distinct for a while, and then largely disappear
• Dependency of patterns on multiple factors that are difficult to pin down, so that when a pattern disappears or diminishes or amplifies, it’s hard to tell what happened

 -- and it occurred to me that I had seen all these patterns before, though with slightly different technical fingerprints.  Where?  In financial time series data.

First there is the basic observation that, while the “efficient market hypothesis” would dictate that stock or futures prices should be purely random (so that nobody can make money via trading in the long run), in fact they are NOT QUITE random – they are just close to random, but with various inefficiencies that do make them predictable.  But specific predictive patterns tend to come and go, and to get subtler and more sophisticated over time.

On top of its generally peculiar barely-and-only-complexly-predictable nature, financial time series data also has various famously odd statistical properties, which are referred to as “stylized facts” in the finance literature.   (The charming term “stylized facts” was introduced by Nicholas Kaldor for the reason that “facts as recorded by statisticians, are always subject to numerous snags and qualifications, and for that reason are incapable of being summarized” … so he felt that theorists “should be free to start off with a stylised view of the facts – i.e. concentrate on broad tendencies, ignoring individual detail”).  Among these are the following ( see this page ; see also some other ones here ):

1. Absence of autocorrelations: (linear) autocorrelations of asset returns are often insignificant, except for very small intraday time scales ( 20 minutes) for which microstructure effects come into play.

2. Heavy tails: the (unconditional) distribution of returns seems to display a power-law or Pareto-like tail, with a tail index which is finite, higher than two and less than five for most data sets studied.

3. Gain/loss asymmetry: one observes large drawdowns in stock prices and stock index values but not equally large upward movements

4. Aggregational Gaussianity: as one increases the time scale over which returns are calculated, their distribution looks more and more like a normal distribution. In particular, the shape of the distribution is not the same at different time scales.

5. Intermittency: returns display, at any time scale, a high degree of variability. This is quantified by the presence of irregular bursts in time series of a wide variety of volatility estimators.

6. Volatility clustering: different measures of volatility display a positive autocorrelation over several days, which quantifies the fact that high-volatility events tend to cluster in time.

7. Conditional heavy tails: even after correcting returns for volatility clustering (e.g. via GARCH-type models), the residual time series still exhibit heavy tails. However, the tails are less heavy than in the unconditional distribution of returns.

8. Slow decay of autocorrelation in absolute returns: the autocorrelation function of absolute returns decays slowly as a function of the time lag, roughly as a power law with an exponent β ∈ [0.2, 0.4]. This is sometimes interpreted as a sign of long-range dependence.

9. Leverage effect: most measures of volatility of an asset are negatively correlated with the returns of that asset.

10. Volume/volatility correlation: trading volume is correlated with all measures of volatility.

11. Asymmetry in time scales: coarse-grained measures of volatility predict fine-scale volatility better than the other way round.

12. Contagion: transmission of crises from one market to another

13. Regimes: Existence of long periods (e.g. months in daily time series) that appear as “trending” or “volatile” regimes

How can we formally explain these various peculiarities of financial time series?  One quite promising approach seems to be “agents models” – models of financial markets as comprised of various predictive agents, each of which is making predictions using its own variant of bounded rationality, on its own time horizon, and using its own risk-return profile.  

Agents models formalize the idea that financial time series largely consist of: The result of a somewhat diverse bunch of agents trying to predict one another’s predictions of future prices.   This sort of agent system tends to produce price time series that display the kinds of “stylized properties” generally seen in real financial time series.   The routes by which the stylized properties emerge from agent systems have been understood partially via formal analysis, and partially by computer simulations.

Thinking laterally and analogically, this gives rise to the question: Could the time series produced by psi results somehow be the consequence of a population of agents trying to predict one another’s predictions?

Certainly, the quirks characteristic of psi results are not the same as the ones characteristic of financial time series – though there are some overlaps.     Actually I’m not aware of any detailed study of the statistical quirks characterizing psi time series broadly speaking – unsurprisingly a lot more attention has gone into the statistics of financial time series (as, to understate tremendously, financial data analysis is a bit better funded than psi data analysis)….  My impression is that in psi we also have fat-tailed distributions, and regimes, and volatility clustering, and asymmetry of time scales (for example) – but this would need to be validated via careful analysis.  

An Agents-Based Version of the Precedence Principle

The idea that PREDICTION might have a fundamental role in psi brings to mind two connections.

First of all, many folks have argued that precognition is the basic psi phenomena and all the others ensue from that.   Indeed, every common psi phenomenon except for macro-PK (mental movement of big objects) seems to be explicable in terms of precognition, if one does enough mental gymnastics.

And secondly,  there’s Smolin’s Precedence Principle, an idea in theoretical physics that bears significant relevance to Sheldrake’s notion of morphic resonance (as I’ve noted here and in previous entries in this blog).   While a somewhat imprecise notion, morphic resonance has a clear conceptual connection with psi phenomena. 

The key idea of morphic resonance is that, once a pattern has occurred somewhere in the universe, it is more likely to occur somewhere else in the universe.  In an earlier entry in this blog, I have noted a direction for making this a more precise concept – the basic observation being that, if morphic resonance is true, then the variance in the distribution of patterns across the universe should be lower than one would expect from independence assumptions.  That is, the distribution of pattern frequencies should be peaked (pointy in the center) relative to a normal distribution.   Unlike the original formulation of morphic resonance, this formulation does not imply a direction of causation.

Smolin’s Precedence Principle states that, when something has happened frequently in the past, it is more likely to occur again in the future – as a matter of foundational physical “law.”

Smolin shows that, when this principle is applied to things that have occurred very frequently in the past, then in the right mathematical setting it provides a novel derivation of Schrodinger’s Equation.  When the principle is applied to things that have occurred sometimes but not yet that often, then it becomes a bit subtler; and Smolin has suggested that perhaps future occurrences will chosen based on the predictions of compact computational models of past data.

(Let me pause for a terminology/math note.   I will refer to “probability” in the following, in some places where it might be clearer to refer to “amplitude”.   But I’ll keep using the word “probability” for simplicity, especially since I like the Youssef formulation ofquantum mechanics where one replaces amplitudes with complex-number-valued probabilities.  So when I mention probabilities below, just remember these probabilities may be real or complex numbers)

So now we come to the punchline of this post: It seems interesting to explore a version of the Precedence Principle in which the probability  of some type of event occurring in the future, is determined by various agents’ predictions of the event-type’s probability – where the various agents are operating based on bounded rationality (due to having bounded spatial, temporal and energetic resources), and making predictions on various time-scales, and perhaps even using different criteria for measuring prediction success.    

Baked into this idea is that the different predictive agents would need to take each other’s predictions into account, in making their predictions.    So we would have the complex chaotic recursiveness that characterizes financial markets (plus some additional complex recursiveness of a different kind, that I’ll get to below).

The rough analogy with financial markets would suggest that this sort of framework might give rise to time-series of event-probabilities, that are conceptually analogous to financial time-series – in terms of being almost but not quite random, and in terms of having certain persistent statistical peculiarities (“stylized facts”).

But who would the predictive agents be, in this framework?  The most obvious answer is that, given a system S, any other system S1 that is to any degree correlated(*) with S can be viewed as being in a position to predict S (and consequently to influence S).  

(*) I’ll explain how I want to interpret “correlated” here a little later (hint: morphic resonance)

Here is one place I’m going to get a little bit creative.   According to quantum theory, such a system S1 will have stochastic dynamics, i.e. it will evolve according to a series of “random” choices, operating within constraints implicit in S1’s constitution.   One idea I want to suggest here is: The apparently random choices within the dynamics of a system S1 may often be BIASED in a way that implicitly reflects an effort of S1 to predict states of another system S (with which S1 is correlated).

How might this bias manifest itself?  One possibility would be that S1’s dynamics implicitly maximize some quantity – but they maximize this quantity only if a certain prediction regarding S’s future state comes true.  

What quantity might fit into this slot?   Two ideas that I came up with are:

• Entropy production
• Pattern creation

There is a Maximum Entropy Production Principle (MEPP), which comes out of classical thermodynamics, but appears to also apply in some form in quantum thermodynamics.   This says, roughly, that a system faced with multiple possible routes to change, will often choose the route that produces entropy at the maximum rate.

I have also articulated a Maximum Pattern Creation Principle(MaxPat).  This says that an intelligent system in a natural environment, will often choose the route that creates pattern at the maximum rate.   MaxPat is a fairly new formulation and I suspect it may hold more broadly than the current argument suggests; but as with MEPP, the precise contours and extent of the principle is not entirely clear.

There is definitely a connection between MEPP and MaxPat, which remains to be fully understood.   We know that

• Creating pattern tends to involve creating entropy, in practice … making a sculpture generates heat and piles of waste, etc.
• The entropy of a system is (in a sense) the average algorithmic information of the trajectories it contains

One may want to view maximum pattern creation as the way intelligent systems in natural environments carry out maximum entropy production.   On the other hand, one may want to view maximum entropy production as a crude average view of what happens when a lot of little, slightly-intelligent agents do their best at maximum pattern creation.   There are deep issues here in need of sorting.

However, my main point in this post is somewhat independent of what quantity is being maximized.   The point is that if the random choices in S1’s dynamics are made so that some key quantity is maximized only if S’s evolution unfolds in a certain way – then we can say that S1 is “implicitly predicting” S.

Implicit prediction doesn’t require psi or anything spooky.   So long as S and S1 are correlated in the ordinary physics sense, it can happen as a result of “physics as usual.”

However, things get really interesting if one counts S1 and S as “correlated" even when they are:

• Uncorrelated or only very, very slightly correlated according to ordinary physics, BUT are --
• Connected via having common patterns in their structures or dynamics

THEN one has spooky implicit prediction … one has a potential underpinning of psi.   Note that item 2 is basically good old Morphic Resonance, rearing its unstoppable morphic head once again.   But it’s occurring in a very special place here.  The hypothesis is that when two systems S and S1 have common patterns, they “morphically resonate” in a specific sense – S1’s dynamics will tend to get stochastically biased so that they yield critical maxima if S’s dynamics unfold in particular ways.   

Systems unfold over time in ways that implicitly constitute predictions of other systems with which they are morphically resonating.  But many different systems S1, S2, S3… may morphically resonate with different aspects of a given system S, so we may get many different predictions, all of which may take each other into account, resulting in a complex and noisy perturbation of whatever state S would be in without all that morphic resonance influencing it.   This complex, noisy perturbation usually looks a lot like noise – except when it doesn’t.  The statistical properties are going to be messy and intriguing.

That is: When one has multiple systems S1, S2, … all doing spooky implicit prediction of the same S – then one has a complex situation where the various systems all need to second-guess one another’s predictions as they make their predictions … which is a situation vaguely reminiscent of what happens in the financial markets, where such inter-agent predictive interactions give rise to near-randomness marked by numerous weird statistical quirks.

A note on causality and temporality.

It’s worth noting that the above formulation does not make any reference to notions of causality, nor any assumptions about “flow of time.”

Intuitively, one can interpret this sort of situation to imply: That the actual probability of S having event E at time t, is influenced by the predictions of the various systems Si that are correlated with S (the predictions regarding whether S will have event E at time t).   But note that this intuitive interpretation is leaping from the asymmetry of “entropy or pattern increase” to the notion of “influence.”  

Back to the Precedence Principle!

Tying this back to Smolin, one way to look at the hypothesized dynamics is that the Precedence Principle works, not on a universe-wide level, but within each individual observing system!  

(i.e. Precedence Principle meets Relational Interpretation of QM)

I.e., we are saying that each system S1 that is correlated with S, implicitly adjusts the random fluctuations in its dynamics based on the expectation that the prior patterns it has observed in S will continue into the future.

This is just another way of slicing “morphic resonance”, because the patterns S1 has observed in S in the past are likely to be the patterns that S1 and S has in common, i.e. the source of the morphic resonance between S1 and S.

Amplifying Small Morphic Resonances

If the patterns in S being predicted are the ones that S shares in S1, then the result of S1’s prediction being correct might be that S and S1 would, in future, have the same patterns at the same time.   That is: One consequence of this sort of dynamic might be that the maximization-based adjustment of S1’s dynamics (based on implicit prediction of S) would increase the odds that S and S1 would continue to have common patterns in future, i.e. would continue to “morphically resonate” in future.

Thus, what we have here is, in a sense, a theory of how morphic resonance might work.  If we assume a bit of morphic resonance, and assume impactful implicit prediction dynamics based on morphic resonance, then as a result we obtain a bit more morphic resonance.  

What Is a System?

In trying to clarify these ideas, we also face the question of “what is a system”?   I.e. one can partition the mass-energy correlated with S in many different ways. 

Do we want to consider every possible subset of this mass-energy as a system S1, making its own predictions that are then incorporated in determining S’s dynamics?  Perhaps we do.  But intuitively, it seems to me that more coherent systems S1 should be counted more than essentially random, disconnected collections of mass-energy quanta.  

Perhaps we can measure the coherence of a system S1 using its “quantum integrated information” (see http://integratedinformationtheory.org for the general idea due to Tononi; and this paper for the quantum version specifically, worked out together with Tegmark )  – a measure of the amount of emergent information in a quantum system, which amusingly has been proposed by Tononi and Tegmark as a measure of the degree of consciousness in a system.   (I think there is a lot more toconsciousness than that; but I still think the measure is interesting.)

Summary So Far

To summarize, then, I hypothesize that perhaps:

• the state of S is influenced by the predictions of the state of S made by systems S1 correlated with S (including S1 that share common patterns with S, thus are correlated with S via a morphic resonance hypothesis), where S1 makes predictions via a local Precedence Principle guiding its pursuit of maximization of some appropriate quantity (e.g. entropy or pattern creation)
• the degree of influence of S1 on S is proportional to
• the degree of correlation between S1 and S; and also
• the degree of Integrated Information possessed by S1 (or perhaps, the degree of II possessed by S1 and S considered as a collective system?).

Note also that a single system S1 may be involved with predicting many other system S.   This is not necessarily contradictory, but of course S1 only has a certain amount of information to throw around, in terms of the internal “random or spooky” degrees of freedom in its dynamics.   So if the other systems S being predicted are highly uncorrelated with each other, S1 is not going to be able to predict a large number of them, unless they are much simpler than S1.

This is somewhat of a complex conglomeration of ideas, but there is an obvious theme underlying the components: It’s all information theory.   The information-theoretic nature of the hypothesis resonates nicely with various previous observations of connections between entropy and psi.

The Precedence Principle in its simple form provides a sort-of “mechanistic” underpinning for morphic resonance.    But the observing-system-relative Precedence Principle proposed here, feeding into an ensemble-based dynamic of event probability prediction, seems potentially capable of something more as well -- providing an underpinning for the peculiarly elusive and tricky and odd statistical properties of morphic resonance in our universe.

Let me recap some of the motivations that led to this set of hypotheses:

1. My goal in conceiving these ideas was to propose a model in which the probabilities (or amplitudes) of events in the world are determined via the combination of the predictions of these probabilities by a bunch of different agents, predicting based on different biases due to their different natures and histories, and often predicting on different time scales.  
2. For this to be a sensible physical theory the “agents” involve have to be physical systems correlated with the system experiencing the event being predicted; and the predictions have to be implicit in these systems’ dynamics.  
3. One way to define an implicit prediction by a system, is to say that the system would maximize some physically important quantity if the prediction came true. 
4. To get a suitable variety of psi-type phenomena out of this, we'd better let "correlated" include correlation via morphic resonance as well as correlation via ordinary physical coupling ... otherwise we'd only get a kind of local precognition out of the implicit predictions...

Recursive, Polyphonic Reality?

But, the above doesn’t quite convey the thickness of the plot I’m hinting at here…

The clever reader may already have limned the recursive aspect of what I’m proposing....   It’s funky, eh?  

While

• S1 is evolving in a manner implicitly oriented to predict S, and S’s state is influenced by the predictions of various other Si that are correlated with it – at the same time,
• S is potentially evolving in a manner implicitly oriented to predict S1, and S1’s state is influenced by the predictions of various Sj that are correlated with it. 

And so we have a system of simultaneous equations, involving a network of agents (systems) that are all trying to predict each other, and whose states are all influenced by each others’ predictions of said states.   The result of this crazy recursive maze of predictions may generally look a LOT like noise – but it isn’t exactly noise, it has certain biases and peculiarities.

Due to this recursive aspect, what I am proposing here is fundamentally more complex than the situation with financial markets.  In the financial markets case, the agents involved are typically trying to predict the same set of external time series, and are predicting each other’s predictions only in this common context.  

On the other hand, the dynamic I propose here is more like a weird kind of financial market, in which each trader’s bank balance is treated as a financial instrument, and the various traders are each concerned with trying to predict the future states of multiple other traders’ bank balances.   I would suppose, though, that, if one simulated this odd sort of financial market, one would find a set of stylized facts somewhat similar to (but probably extending) the ones observed in typical financial time series. 

One could argue that the treasuries of various countries, in their interactions with each other, display a vaguely similar dynamic to the one proposed here.  Each country is trying to predict the future values of each other country’s currency, and make trades on these predictions … and the value of each country’s currency is influenced heavily by the predictions made by the bankers associated with other countries’ treasuries….   But of course this is only a loose analogy.

Obviously, what I’ve proposed here is more an idea for a theory – or a pointer toward a category of potential theories -- than a particular, well-fleshed-out theory.  There would be a lot of concrete choices required, to make these ideas quantitative; and/or to apply them in a careful way to particular psi phenomena.   What I’m aiming to do in this blog post is merely to outline a TYPE of theory that seems to me likely to provide a scientific grounding for psi phenomena.  

In philosophical terms, one might call this a “polyphonic” model of reality (I got this term from Bakhtin’s analysis of Dostoevsky, btw).  One is viewing reality as neither objective nor subjective, but as a sort of blend of multiple agents’ subjective views.    The blending takes place on the level of predictions that are implicit in system dynamics; and one of the core motivating observations is that blending predictions made by multiple bounded-rationality agents on multiple time-scales can give rise to time series that are almost but not quite random and that have non-Gaussian distributions, patterns that come and go in sudden and surprising ways, and other odd statistical properties that are broadly reminiscent of what is observed with psi phenomena.

(Well OK then – this is either ultra hi-fi sci fi; or a penetrating intuitive leap guessing the outline of a scientific theory that will ultimately be validated N decades from now after I or someone else does a lot more work.   Or else it’s just a lot of complicated-sounding words in sequence; one more meandering tale told by one more evolutionarily degenerate ape-chimp-thing, full of sound and fury, signifying nothing….  But hey, in any case, thinking about this stuff has been a heck of a lot of fun!)

Regimes and Knots

But wait – there’s more! …

One of the peculiarities (er, stylized facts) of financial time series is the existence of distinct “regimes.”   A market will trend up for a while  -- then it will start to get volatile for a while – then it will trend up or maybe down for a while … etc.   These regimes are often fairly clear to identify in hindsight; but predicting regime shifts in foresight is one of the hardest problems in the financial prediction arena.

Financial market regimes occur, it seems, as a result of emergent patterns in collective behavior of multiple predictive agents.   In some cases the underlying agent dynamics are relatively well understood – for example, bubbles arising and bursting.   Sornette has parsed out the mathematics and individual and collective psychology of bubble phenomena quite nicely.

The run-up to a “market bubble” is caused by some agents becoming overoptimistic, then other agents predicting these agents ongoing overoptimism, etc.   Until enough agents decide they have recognized the pattern that the bubble is about to burst – and then things get chaotic, because some agents are predicting “up” based on the same old overoptimism predictions, but a lot of others are predicting “bubble is about to burst.”   Then finally a critical mass is reached and there are more predictions of “bubble is about to burst”, which causes the bubble to burst.   And then the agents start to predict doom, and start to predict one another predicting doom and this causing doom, and this causes doom for a while.    A root cause here seems to be the presence of a bunch of agents who are prone to make overconfident predictions based on too few data points (and we know that real-world financial markets are full of these).  

In the multi-agent model of morphic resonance I have proposed here, various similar phenomena would seem likely to occur.   Multiple systems coupled together and predicting the same set of systems, will likely get into “collective behavior patterns” manifesting themselves as “regimes” with characteristic time-series property signatures.

The nature of a regime is that it’s resistant to small perturbations – e.g. when a market is trending up, a bit of volatility here or there tends to get smoothed over quickly by the general overoptimism.   This suggests an analogy with “metaphorical knots” in minds and other complex systems, as I have described in a previous post on this blog.   It seems that metaphorical knots could potentially emerge from the dynamics of multiple inter-predictive agents as proposed here.

For instance, consider a knot of the form “I am afraid of love, so I’ll hide my loving feelings; my loving feelings being hidden causes them to be unknown, which causes me to be afraid of them, since unknown things are scary.”   This could emerge, for instance, from a combination of:

• Agents that predict that bad things may happen as a result of loving feelings, based partly on evidence that loving feelings are hidden and therefore unknown
• Agents that predict that loving feelings will be hidden in future, based on the fact that they’ve been hidden in the past

If the dynamic is that predictions affect reality, then

• Agents of Type 1 will cause bad things (at very least bad psychological things) to happen as a result of loving feelings
• Agents of Type 2 will cause loving feelings to remain hidden (thus providing more grist for the motivating belief systems of Agents of Type 1)

and the system including these agents will be “stuck in a rut.”    The rut may start because of hiding loving feelings in one particular situation… then it may continue because of the dynamics of the agent system, including the element of stochastically self-fulfilling predictions.

To the extent that there are nonlocal correlations between physically distant subsystems of the universe (e.g. via morphic resonance as I've considered above), some networks of such subsystems could then get locked into complex regimes and knots via mutual predictive activity.   In a eurycosmic model these knots could have portions in the physical universe and portions outside in the eurycosm.    Knots involving the predictive agents associated with an individual mind, could have mutual-reinforcement relationships with knots involving the predictive agents involved with broader aspects of physical reality with which this individual mind interacts.   We have no experience studying or modeling this sort of complex dynamics; but based on other complex systems we have studied, its not hard to project the sorts of complex hierarchical and heterarchical networks of strange attractors (or similar phenomena) that might occur.

Could knots like the above on the collective level be responsible for the decline effect?   It’s certainly feasible.   In financial markets, once too many agents expect something to happen, others often start to expect that others will expect the opposite to happen, and then will predict the opposite will happen – which causes the opposite to happen.   Something similar could happen regarding predictions associated with multiple unconscious minds correlated with psi experiments.

These ideas are weird and complicated, but in the end they all seem to be explorable using conventional scientific methods.   They do imply the possibility of “experimenter effects” in which the predictions that experimenters (implicitly or explicitly) make regarding experiments, affect those experiments.   However, understanding the dynamics of prediction and psi at a layer below the experimenter effect, may allow us to design experiments in which this sort of effect can be carefully controlled (much as the effect of observer on observed in quantum mechanics can be taken into account in experimental designs, because we understand how it works pretty well).

Indeed this stuff is complicated -- but humanity has pulled off a lot of other tremendously complicated and conceptually and technically difficult things, like making the laptop I’m typing this on, and the Internet via which I’m conveying it to you….