Category Archives: Complexity

What Drives Consciousness?

Did “Consciousness” just appear from nowhere, or is there something about the physical universe that means that “Consciousness” is almost guaranteed to emerge?…

 

PART 1 – CONSCIOUSNESS

 

Over the last 400 years or so Mathematical Physics has become the science that we rely on to explain the behavior of the universe.  Mathematical physics is the ultimate science of deterministic cause and effect.  But although physics is good at explaining the obvious dynamics of  cause and effect, it turns out that it fails quite miserably when it comes to explaining the not-so-obvious dynamics of “Natural Evolution and Emergent Complexity”

Compressible Linear Dynamics

In general the science of physics likes to believe that all natural behavior can be explained mathematically, and consequently physicists like to build “mathematical models” of (cause and effect in) the real world.  Sometimes these models are unbelievably concise, and can be compressed into a single neat equation, and when this happens we confidently call the model a “Deterministic” “Law of Physics”.  However in reality the universe has a range of behavior, from simple to complex, and so unsurprisingly many behaviors are not so easily compressed.

Incompressible Nonlinear Dynamics

The reality is that physics is, in a sense, primarily a science of “linear” dynamics, a science of dynamics “without feedback”.  Such dynamics are indeed easily compressible, but our real world is a world that abounds with feedback, a “nonlinear” world full of “incompressible dynamics”.

Nature is the ultimate example of a complex “adaptive” system full of incompressible dynamics.  And while there are many systems within Nature which exhibit obvious cause and effect; most of Nature’s behavior is however much more nuanced, and consequently much more difficult to predict.

Complex adaptive systems do not follow strict cause and effect “rules” but instead they have a lot of emergent “associations”.  So unlike simple linear dynamics we cannot learn about complex nonlinear dynamics by simply discerning the “mathematical rules”.  To truly understand complex nonlinear systems we need a different type of model.

[Note: In the simplest possible terms, linear dynamics are dynamics where the effect is proportional to the cause, and nonlinear dynamics are where the effect can be disproportional to the cause.]

A Different Type of Model

The “Brain” is a “Biological Tool” that has been designed by millions of years of evolution to navigate an external world full of complex nonlinear dynamics.  The brain effectively “self-organizes” it own “neural” network, in an effort to best fit this internal model to the available data from the external world.  This neural network is, in effect, an abstract model — effectively a map of what is connected to what

[Note: In the real world, we use such abstract models all the time.  A map of the London Underground is a perfect example.  

Model/Map of the London Underground Transport System

This nonlinear map is obviously not an exact representation of locations in physical space, but it is nonetheless a good enough model, to give us a working understanding of the fundamental structure of the underground network.]

So the “Brain” is basically a complex connectivity map, and the “Emergent Mind” simply a reflection of how the brain is wired up.

“Consciousness” bubbles up from this emergent mind.  And at its most fundamental, “Emergent Consciousness” is nothing more than the surface representationof a subconscious library of “Instincts” and “Intuitions”.       

  

PART 2 – DEEP INTUITION

 

So emergent consciousness is simply the “surfacing” of a biological process of “abstract modeling and pattern recognition”.  But over many millions of years however, “The Conscious Mind” has developed way beyond mere pattern recognition.  This development is most obvious in modern humans.  Over long periods of time Mankind slowly turned recognizable patterns of cause and effect into technology and engineering by a gradual process of trial and error.  And in the last 400 years or so, human consciousness took things a step further by actually teasing out the underlying mathematics that governs the linear dynamics of cause and effect.  But despite all this incredible evolution of conscious and rational linear thinking, we can still struggle badly when it comes to dealing with “the dynamics of feedback and nonlinear complexity”…

Fast Nonlinear Thinking

The Brain has been designed to deal with a nonlinear world, and complex nonlinear pattern recognition is actually it specialty.  The subconscious mind is a library of instincts, and a “laboratory of intuitions”.  Essentially we can think of instincts as simply hard-corded intuitions, but intuitions themselves are better thought of as a soft-coded work in process…

Some time ago Daniel Kahneman wrote a book called “Thinking, Fast and Slow” in which he basically suggested that we cannot rely on our fast thinking intuition; that generally speaking while our intuition works well when dealing with simplicity, it tend to lets us down when we are dealing with even the smallest amount of complexity.

This however need not always be the case.  The reality is that, in an ever more complex interconnected world, our fast “nonlinear” thinking can be a much more valuable, and “insightful”, tool than our slow “linear” thinking – but in order for this to be so, we do need to train it correctly…

Integration for Free

In his book “Bounce” Matthew Syed argues that “Talent” is not God-given, but must be worked at — the ultimate result of many long hours of practice.  Virtually anyone who is any good at anything will recognize the truth in these words.  But how exactly does practice make perfect?…

Think about what is involved in learning to play tennis to very high level.  Bad tennis players essentially play every shot more or less the same way, the forehand is almost the same shot as the backhand, even the serve is essentially just racket meets ball.   People who play tennis well however, have learned to separate, or differentiate, one stroke from another; they have fine-tuned the mechanics of each individual stroke from hours and hours of practice and attention to feedback (i.e. “evaluated feedback”).

Strangely enough though, despite this constant focus on training the mechanics of each unique stroke, nobody ever seems to train the transition from one stroke to another — that somehow just seems to come naturally over time.  It seems that the co-training of a diversity of different strokes means that the integration comes for free…

In truth however while “practice focused on feedback” may consolidate the technique of each individual stroke, it is only through “competitive practice” that these finely-tuned strokes are ultimately combined into a single integrated style of play.  It is this competitive practice, this necessary “integration” (of a repertoire of differently trained strokes) that ultimately makes “the whole greater than the sum of its parts”

Differentiate + Integrate

Learning to play tennis (or anything else for that matter) is simply a process of work and play, of training and application, of differentiation and integration, repeated over and over again.  In a similar vein, “Intuition” can be thought of as a nonlinear map, built from the bottom-up by the constant interplay of conscious differentiation and subconscious integration.

[Note:   In general, as humans, we learn to model the world by trial and error (although trial and evaluation of feedback is probably a more accurate, if clumsier, representation).  The brain makes sense of the world, the same way a child makes sense of a jigsaw puzzle.   A child will separate out all the edge pieces, separate out all the sky pieces, separate out all the castle pieces etc, etc, and then try to fit them all together.]

The brain carries out the conscious process of differentiation when awake and deeply focused and the subconscious process of integration when asleep and deeply relaxed.  During sleep the subconscious mind is effectively trying its best to integrate the diversity of information it has learnt into a single “Coherent Whole”.

[Note:  The information can only be compressed to its maximum compression but no more — this is the basic idea behind something called “information entropy”].

Language is probably the most obvious example of the nonlinear emergence of integrated feedback.  A child does not learn to speak by learning the linear rules; it is only with much practice, attention to feedback, and deep sleep, that nonlinear language ultimately bubbles up to the surface…

This nonlinear learning, this subconscious integration, bubbling up to the surface is the same process that drives our “Intuitive Pattern Recognition.  And so if the premise of Matthew Syed’s argument (that only “evaluated” practice makes perfect) can be extended to the nonlinear mind, then any lack of “deep pattern recognition” is simply a lack of subconscious integration which itself results from a lack of both conscious diversity and consciously evaluated feedback…

Integration + Inspiration

It is often said about great discoveries that, “chance favors the prepared mind”, and so it is with deep pattern recognition.

Through the subconscious integration of a diversity of information a fully formed coherent idea can suddenly emerge into consciousness as if by a random thought.  But this is not really a random thought.  This “information structure” has probably been forming in the subconscious mind for a very long time indeed — before ultimately surfacing into consciousness in what appears to be a moment of “eureka” inspiration.

So although such spontaneous insights (about “how things fit together” ) can seem as if it they come out of nowhere; they are in fact simply the result of the nonlinear integration of a diversity of information which ultimately surface in moments of “Deep Intuition”.

Matrix of Intellectual Dynamics - Copyright - Kieran D. Kelly

 

CONCLUSION

 

So what drives consciousness and deep intuition?  Well as with all types of evolution the key to the surfacing of all emergent complexity is “The Natural Compression and Integration of Diversity”…

And just as the integrated game is a free by-product of the co-training of a diversity of different tennis strokes, so too the co-training of our nonlinear thinking on a wide diversity of information means that Deep Intuition can come for Free!”…

What’s Driving Evolution?

Wrdcloud of what Drives Evolution


According to the Second Law of Thermodynamics we live in a universe that irreversibly decays over time.  But if this is indeed the case, then it begs the question:   “How does Evolution’s Spontaneous and Progressive Complexity occur without some form of External Organizing Force?”


Evolution vs. Entropy

The Second Law of Thermodynamics (SLOT) is a law of physics that deals with “Spontaneous Change” (i.e. change that occurs without any external direction, change that happens all by itself…)

The SLOT is, more precisely, the law of physics that deals with how energy distributes itself within a thermal system, always moving spontaneously and irreversibly to “Thermal Equilibrium”.

In everyday terms the SLOT is simply the fact that hot coffee and cold milk, if left unstirred, will spontaneously mix themselves (in both composition and temperature), and will never spontaneously un-mix.

Despite the fact that this seems rather obvious and trivial behavior, the SLOT is nonetheless considered to be one of the most fundamental and important laws of physics — and the reason for this exalted status is that the SLOT is both a “Probabilistic Law” and also the “Law of Maximum Entropy”!

“Entropy” is a concept that deals with amount of “disorder” in a system, and it is widely understood that the spontaneous gravitational pull to maximum entropy is not restricted to simple thermal systems; but that all systems, if left undisturbed, will spontaneously gravitate towards a state of maximum disorder — a state that would seem to be the exact opposite of Nature’s “spontaneously self-organized complexity”.

This apparent conflict between physics and natural evolution obviously begs the question:   “How does Evolution manage to spontaneously generate such incredible Complexity in the face of the SLOT?”

How can natural complexity spontaneously arise in a universe dominated by the SLOT and its spontaneous and irreversible pull to disorder?  What exactly is the “Source” of all of Nature’s spontaneous order and complexity?

The Export of Entropy

In 1977, the Belgian chemist Ilya Prigogine won the Nobel Prize for Chemistry, for his work on his “Theory of Dissipative Structures”.  Prigogine’s theory suggests that complex ordered systems can indeed come into existence if these systems are open and capable of “exporting”  their internal disorder, to the external environment.

But while this theory would seem to go some way towards solving the paradox of how order can occur without negating the SLOT, it still does not manage to identify what fundamental forces are actually driving evolution to evermore progressive complexity.   Physics has as yet offered no explanation for “evolution’s progressive arrow of time”

As it turns out however, the resolution of this paradox is actually quite easy.  To resolve this apparent conflict  between physics and natural evolution we need merely to focus on a very simple fact that has been consistently overlooked about the “probabilistic” SLOT; the fact that it relies heavily on the “Law of Large Numbers (LLN)”…

The LLN

Most people are familiar with the concept that if we toss a coin four times, we won’t necessarily get a 50/50 split of heads and tails: indeed, we could actually get 4 tails in a row.  But if we toss the same coin a million times, we will almost certainly get something close to a 50/50 split.  It is the LLN that ensures that one million coins tosses will produce an average of 50% heads and 50% tails.

[Note: In the simplest possible mathematical terms, the reason the LLN works so well is that the number of independent tosses (i.e. 1,000,000) is significantly larger than the number of options available to each toss (i.e. 2 – heads or tails).]

The SLOT states that left undisturbed all systems gravitate towards the “most probable state”, a state that is referred to as “thermal equilibrium”.  In reality however, the achievement (and sustainment) of thermal equilibrium relies heavily on the number of independent elements (of the system) being significantly larger than the number of energy options available to each element.  Which means that the chances of any “statistical deviations” from the “most probable state” are extremely small, and consequently the system as a whole will (virtually) always exhibit uniformity.

So although on the “microscopic level” (of particle interaction) there is a lot of energetic dynamics and non-equilibrium abnormalities, these dynamics and abnormalities are normally invisible on the macro “system level” thanks to both the “Damping” and “Balancing Effects” of the LLN…

The RLLN

Our universe is fundamentally a universe of “systems”, and the probabilistic pull of equilibrium is a concept that is applicable to all fluid and fluid-like systems.

Now, in a thermal system there are billions of tiny particles which interact through collisions, but other than that we can more or less say that they behave completely independently of each other.

Systems however, where the parts – be they particles, elements, components, entities, agents, organizations, etc – behave independently of each other are actually quite rare.  Many systems are populated by adaptive elements or agents, and the behavior of these agents has a tendency to weaken the gravitational pull of equilibrium by engineering the “Reverse Law of Large Numbers (RLLN)”…

[Note: Since the LLN relies on the number of independent elements being significantly larger than the number of options available to each element, there are therefore two things can engineer the RLLN and they are:  either the number of independent elements in the system comes down, or, the number of options available to each element goes up…]

RLLN 1:  Emergent Positive Feedback

In all fluid-like systems, the LLN ensures the spontaneous movement to a “global equilibrium”; however for very small regions within these systems, there are not enough particles to ensure a “local equilibrium”.  At the very lowest level within all systems, random fluctuations are undampable and occurring all the time which means that local imbalances are constantly, and randomly, flittering in and out of existence.

Occasionally these random temporary fluctuations can randomly be very persistent.  In a thermal system this is naught but a mere statistical curiosity, but in a complex adaptive systems it can easily happen that some parts within the system will begin to adapt to these persistent fluctuations; and often such adaptation can serve to amplify the imbalance even further, and in so doing, further extend the fluctuation’s duration.  Thus random local fluctuations can lead to the localized emergence of positive feedback which reduces the independence of the elements and ultimately has an unbalancing and reversing effect on the LLN.

RLLN 2:  Insufficient Negative Feedback

Positive Feedback however is not the only thing that can engineer the RLLN.  Since the LLN effectively operates like a negative feedback system (in that it dampens a system to a equilibrium) it should be no surprise that the movement away from equilibrium could also be the result of insufficient negative feedback.

So although complex fluid-like systems might gravitate towards equilibrium, many can hold themselves some distance away from equilibrium by exhibiting excessive undampable adaptation and innovation.  Adaptation and innovation effectively increases element “Optionality” and such increased optionality among the elements of the system can also engineer the RLLN…

Integration For Free

So the reality of probability driven dynamics in the natural world is that just as the LLN pulls a system to thermal equilibrium, so too the RLLN can hold, or drive, a system away from equilibrium.

But ultimately what is most interesting about all of this probabilistic behavior is that: while strong positive feedback in isolation can cause the emergence of self-reinforcing local segregation; and while insufficient negative feedback in isolation can cause the surfacing of incompressible innovative diversity; the most interesting stuff actually occurs at the interface between the two…

Positive reinforcement in a system of great diversity, can spontaneously produce surprisingly complex “Integrated Diversity”.  So in other words,

with the co-emergence of diversity

Complex-Integration comes for Free!..


Natural Complexity

Evolution’s progressive complexity is often portrayed as spontaneous “Self-Organization”, but this is not the exactly accurate.  The secret sauce of evolution’s spontaneous and progressive complexity is actually spontaneous “Self-Integration”.

In the simplest possible terms, Natural Complexity emerges from the finely-tuned integration of of co-emergent self-organized diversity; and as a consequence “the complex whole is forever becoming greater that its less complex parts”…

Matrix of System Dynamics - Copyright - Kieran D. Kelly

So there we go, Natural Complexity explained (by mathematical probability).  “Easy Peasy Lemon Squeezy”…

In a universe supposedly dominated by the SLOT what drives nature’s progressive evolution is simply the mathematical interplay of the two distinct forms of the Reverse Law of Large Numbers…

What drives evolution’s spontaneous and progressive complexity is the interplay of insufficient negative feedback and strong positive feedback; or in other words what drives evolution is The Interplay of Random Innovation and Natural Reinforcement…

Matrix of Evolution Dynamics - Copyright - Kieran D. Kelly

The Coming Age of Accelerated Evolution!

What’s Driving The Evolution Of Everything?…  Back in 1994 I read a book called “Complexity – The Emerging Science at the edge of Order and Chaos”.  In this book the author suggested that theoretically complexity should not really occur naturally because it seems to defy the Second Law of Thermodynamics (SLOT) and the concept of maximizing “Entropy”.

I had come across the SLOT as a student and knew that it was related to the concept of the spontaneous distribution of “Heat”, but could not remember much about the concept of “Entropy”.  A little research however revealed — much to my surprise — that seemingly “entropy” is generally associated with “disorder”; and that according to physicists because heat spontaneously distributes it means that everything in the universe spontaneously moves towards maximum disorder; and that means that the universe itself is in fact irreversibly decaying over time.  This I found surprising, because if this assertion is true then obviously it does indeed beg the question:   “How does Evolution manage to spontaneously generate such incredible Complexity in the face of the SLOT?”

This apparent conflict between physics and natural evolution sparked my curiosity.  I became curious to understand firstly why physicists would believe that the spontaneous distribution of heat must mean that we live in a universe of irreversible decay; and secondly, and more importantly, I began to wonder “what actually is the sourceof Evolution’s Self-Designing Complexity?”

Evolution Dynamics

“So?…” you might well ask.  Have I managed to formulate any sort of an answer to this tricky and paradoxical question?  Well yes, I think I have.  The answer to why physicists believe what they do is simply a matter of history; but the answer to what’s driving evolution is much more interesting…

In the simplest possible terms, the SLOT is about the spontaneous pull of thermal equilibrium, and so it effectively about how the SLOT operates like a natural “Negative Feedback System” (like a natural thermostat) in that it pulls (or dampens) a system to the equilibrium state.  However a fact that has been consistently overlooked about the physical behavior of the “Second Law of Thermodynamics” is that it relies heavily on the mathematical behavior of the “Law of Large Numbers (LLN)”.  The LLN essentially says that a very large number of independent things will most likely exhibit the “Most Probable Distribution” (which in thermodynamics is the equilibrium state).

Consequently a system can be held away from thermal equilibrium by two things.  Firstly, the negative feedback effect of the LLN can sometimes not be strong enough to dampen the system to equilibrium.  And secondly, the strength of the LLN can sometimes be weakened by a reduction in the independence of the elements within the system.

So these two things can in effect act as resistance to the pull of thermal equilibrium.  But moreover, and more interestingly, it is the interplay of these two types of resistance that can (without any external direction) naturally drive evolution away from a featureless state of thermal equilibrium, to some extraordinarily creative complexity.

In the simplest possible terms, Evolution is the result of the interplay of Insufficient Negative Feedback, and Strong Positive Feedback; simply the interplay of “Incompressible Dynamics”, and “Self-Reinforcing Dynamics”

  • Insufficient negative feedback allows the surfacing of creative diversity and “Incompressible Dynamics”…
  • Strong positive feedback drives local symmetry-breaking and emergent “Self-Reinforcing Dynamics”…
  • And the interplay of both drives the “self-integration of co-emergent diversity” and emergent “Complexity Dynamics”…

Matrix of Feedback Dynamics

The above matrix of feedback dynamics can be rewritten in terms of evolutionary dynamics, thereby clarifying Complexity Dynamics as simply the result of “The Nonlinear Interplay of Random Innovations and Natural Reinforcement”…

Matrix of Evolution Dynamics - Copyright - Kieran D. Kelly


Entropy Dynamics

Moreover, and this is what is really interesting, both of the above matrices can also be represented in terms of thermodynamic entropy and “Information Entropy”.

Matrix of Entropy Dynamics - Copyright - Kieran D. Kelly

Information entropy is not much known outside the domain of computer, but it is a different type of entropy to thermodynamic entropy.  Whereas thermodynamic entropy is a measure of disorder, information entropy is a measure of uncertainty and unpredictability.

[Note: The concept of information being a measure of uncertainty can sometimes confuse people.  But think of it this way.  By its very nature, to you “information” is unpredictable, otherwise it would not be “information” — it would just be stuff that you already knew…]


Information Creation

Essentially natural complexity is, in fact, “self-integrated information”.  All natural complex systems are characterized by the fact that they have “low thermodynamic entropy, but high information entropy”; consequently these systems can be considered to be highly organized but unpredictable nonetheless.

So while most people might think about evolution in terms of “an ecosystem of plants and animals”, the reality is that plants and animal (and the ecosystem itself) are really just “information structures”, and evolution simply keeps creating evermore complex information structures.

So despite what most people might think, evolution is not solely a theory about the emergence of life, but a more Generalized Meta-Theory about the Emergence of Everything (of which biological evolution is merely a special case).  Evolution is, in the broadest possible terms, “Information Creation”…

Accelerated Evolution

Information is created from information.  Evolution is simply the constant integration of information.  Evolution’s ever-increasing emergent complexity is simply Mother Nature creating evermore complex information by “integrating stuff” as she goes along.  This constant integration means that “Nature’s complex whole is forever becoming greater than its less complex parts”

Evolution created us, and we in turn have created and are continuing to create ever more complex information structures.  But in these early years of the 21st century it could reasonably be argued that in our ever-more rapidly interconnecting world (in 2017), we are likely fast approaching a phase transition in human development, a transition to a whole new “Age of Accelerated Evolution and Information Creation”.  And this coming age will not be dominated by the old linear paradigm of predictable cause and effect, but by a whole New Nonlinear Paradigm of unpredictable “Integration and Emergence”…


The Century of Complexity and Creativity

Physics tell us that to understand the world we need simply to understand “the dynamics of cause and effect”; but the simple dynamics of cause and effect fail quite miserably when it comes to explaining “Natural Evolution and Emergent Complexity”...

Understanding evolution however is going to turn out to be much more important than anyone might previously have thought.  Because although science may have spent the last 400 years honing its understanding of The Linear Dynamics of Cause and Effect, the reality of life in the 21st century is that the really interesting stuff will increasingly result from the “Universal Creative Dynamics” of “Adaptive Integration and Emergent Complexity”…