All posts by Kieran D. Kelly

About Kieran D. Kelly

Experimental and Applied Mathematician, Specialist in Nonlinear Systems and Dynamics…

Website Reboot No.3

In September 2013 I started putting together this website because I wanted a place to “gather my thoughts” on Chaos Theory.

Back then I explained Chaos Theory as being about the “Coarse Damping to Equilibrium” meaning that chaos describes the type of behaviour that emerges when a system has difficulty fine-tuning its way to an orderly equilibrium (thanks to the aggressiveness of their internal dynamics)…

This explanation didn’t seem to gain much traction with the world at large, so in January 2016 I tried a different approach. 

This time I decided to explain chaotic behaviour as “Incompressible Dynamics”: meaning that chaotic behaviour is behaviour that is not easily mathematically compressed or verbally summarized…

To my mind this piece of phraseology captured chaos very neatly; because it relates chaotic behaviour to how difficult it is to explain that behaviour.  Chaotic behaviour is effectively difficult to explain behaviour.

The easiest behaviour to explain is a complete lack of behaviour – the thing or system, or person is doing nothing.  The next easiest is constant behaviour, like constant motion, or a constant oscillation, or constant periodic behaviour.  Such behaviour is easy to describe — night always follow day, day always follows night, etc.  However as things become a little more complicated they become a little harder to describe, both mathematically and verbally.

Physics is all about explaining behaviour, ideally in mathematical form.  The trouble is that the more complicated the behaviour, the harder it is to put some mathematics on it.  So much so that for complicated systems scientists usually resort to using averages.  Averages allow us to forget about the details and concentrate on the system as a whole…

Chaos Theory is really all about the behaviour of systems where averages don’t seem to work.  Chaos Theory deals with all types of system behaviour, both orderly and chaotic; but the term “chaos” within these systems refers to behaviour that doesn’t seem to exhibit any form of consistency (i.e. this behaviour doesn’t settle down to some form of average behaviour – and consequently we cannot compress these dynamics into some form of simple mathematics).  Chaos is effectively describing systems with constantly changing dynamics…

This approach seems to be better; got a little more traction, but still didn’t really catch fire…


Anyway over the last 3 years or so I have been distracted with other things, but during this time I have also come to the conclusion that what Chaos Theory is ultimately about can essentially be boiled down to 3 key ideas.

  1. Chaos theory is about the Mathematics of Dynamic Equilibrium – in other words, the concept of mathematical equilibrium is not limited to pure stability, but can come in many different forms ranging from stable to dynamic…
  2. Chaos Theory is about Emergent System Behaviour – and the type of system behaviour that ultimately emerges is determined by the strength of system’s internal dynamics
  3. Chaos Theory is about the Existence of Mathematical Attractors (both orderly and chaotic) – which give the impression that there is an invisible hand at work in pulling the system to a particular form of equilibrium…

This new perspective probably demands another reboot of this website, which will require that I review (/alter/correct) a number of the fixed pages on this website.  Unfortunately I am a bit short on time at the moment so I will have to get to that in due course.

In the meantime, I have some more pressing work to attend to…

The Coming Age of Augmented Creativity

We are entering a new age, and everything gonna change.  In recent years we have seen the rise of machine learning thanks to advances in computer processing power and the accumulation of large amounts of data from which the machines can learn.  These advancements have been significant, but they are nothing compared to what is to come.  Machine learning is growing exponentially; soon machines will know stuff that we don’t even know.  So does this mean that our digital servants are about to become our digital masters?  The question on the minds of many is “are we on the verge of machines taking over?”…


Rule Based Systems

Computers took their first baby steps towards “Artificial Intelligence (AI )” when we started using them to implement simple diagnostic systems.

The earliest such systems were effectively a top-down design; usually built by simply encoding or storing “expert” knowledge in a large database.

These so-called “expert systems” however were really nothing more than table-look systems (if the patient has X, Y and Z symptoms then the patient has “Disease #23975648”).  Such systems were, in reality, merely rule-based systems; they were not really expert systems…

Complex Systems

True expert systems are systems that are capable of deep analysis and deep pattern recognition.  Expert systems are fast becoming an evermore sought after resource because, in our evermore interconnected world, we are increasingly going to have to deal with ever more complex systems, which means we are increasingly going to need access to expert systems that can “see beyond the rules”…

Most real problems always require some form of “expertise beyond rules”; because most real problems are so complex that there usually is no way of generating a clearly defined solution.  In fact, in many cases, the problems are so complex that there probably doesn’t exist a clearly defined solution — which seems to conflict with some of our basic assumptions about how things work…

To a certain extent, it could be argued that for the last 400 years we have been living in a time dominated by the concept of “deterministic cause and effect”.  We believe in “rules of behavior”; we believe in the concept that clearly defined clauses will always have a clearly defined effect.  Mathematical Physics is the ultimate science of such deterministic cause and effect.  Physics prides itself on being the science that identifies “mathematical rules” of behavior that link cause to effect.  In reality, however, physics is really just the science of simple systems (systems without the friction of feedback), because, unlike simple systems, the behavior of complex systems (systems with feedback) do not obey clearly defined mathematical rules.

Beyond The Rules

So to tackle complex problems, and the behavior of complex systems, many  computer scientists are beginning to turn away from rule-based systems (build from the top down) and instead are focusing their efforts on “Artificial Expertise” (generated from the bottom up).

Artificial expertise is basically an algorithmic way of producing “educated guesses” (intuitive guesses you might say) — a way of producing “Artificial Intuition”…

The basic idea that drives this artificial intuition is that machine knowledge is built, not by encoding linear rules of cause and effect but, by evolving a deep neural network to accumulation, and generate, nonlinear “Emergent Expertise”.

Practice Makes Perfect

We all know that to become a true expert at anything requires a lot of practice — learning the rules just doesn’t cut it.  True expertise requires practice because expertise always emerges from the bottom up.

For practice to be useful however, it needs to contain “feedback”; because practice without the evaluation of feedback is effectively useless – condemning us to do the same thing over and over again.  Practice with feedback is what we really mean when we talk about “training”

Over the last number of years, we have witnessed the rise in the concept of so-called “Big Data”.  Big data is considered to be something of a game-changer; but, in truth, most of the time the people who are using the term are really just writing reports.  Big whoop!  Very cutting edge!..

Nevertheless, despite all of the over-hyped nonsense, there is actually some real value to be had from “big data” from an AI point of view…

In the past there were really just two things that were holding back true AI; and they were, the sheer computing power required for processing a bottom-up methodology, and, the diversity of data required to feed such a methodology.

However, the recent explosion of big data means that we now have lots of “training data” to feed our deep neural networks.  This means that we now have lots of diverse actions and feedback that we can use to generate the digital equivalent of Malcolm Gladwell’s 10,000 hours of practice.

But the thing about digital practice hours is that our digital friends are not operating in the same fixed time environment as us.  With the right amount of data AI systems should be able to build deep knowledge and expertise on just about anything (really really fast)….

Matrix of Cognitive Dynamics


So artificial expertise is fast becoming a very real possibility; but any machine/system that has the potential to learn from practice (to learn from the bottom up), also has the potential to become an expert at virtually anything…

And so as we move further and further away from rule-based systems to emergent-expert systems we are also moving closer and closer to a form of “Artificial Generalized Intelligence (AGI)”.

AGI has been the stuff of science fiction novels and Hollywood movies, and is often equated with a dystopian future of machine rule.  However now that AGI is actually beginning to graduate from science fiction to science fact, it is worth remembering that there is more to human intelligence than Logical Reasoning and Intuitive Deep Pattern Recognition.



To be human is to be creative and we humans are capable not only of seeing and recognizing complex patterns of information, but also being able to “Design and Create” them.

The brain is a biological tool designed, by millions of years of evolution, to compress “data” into “information”, and subsequently integrate this information into an intuitive map of the external world.

Intuition, therefore, is, in reality, a totally natural but subconscious process of compression and integration; a subconscious mental process that tries to figure out what is real and how these real things fit together.  But there is a side-effect to this mental integration.  The side effect of trying to figure out how things fit together is the potential awareness of “how things could  fit together”.

And so the subconscious process of information integration not only drives intuition, but it also drives “imagination”; and consequently, deep neural integration offers not only the potential to see hidden patterns of information but also to “imagine the unseen”….

Emotional Intelligence

Neural integration drives imagination.  It is in this compression and integration of information that “thoughts” begin to emerge; imagination is simply a conscious process of focusing on these subconsciously generated thoughts.

Our internal thoughts are like our own personal “internal data”, and when we focus on our thoughts we are effectively trying to extract information from our personal data.  But the question arises, “How do we go about evaluating what information can be extracted from internally generated thoughts without any form of external feedback?”….

Evolution once again comes to the rescue.  As a result of the emergence of thoughts and imagination, evolution obviously set to work on developing “Emotional Intelligence”

Over the last few million years, evolution has developed an internal feedback mechanism to evaluate internal thoughts.  Feelings are evolution’s feedback mechanism of choice.  Feelings and Emotional Intelligence are our internal mechanism for determining the “value” of thoughts and intuitions.

Diversity of Ideas

Traditionally our modern society has placed great store in the value of human reasoning, and has reserved merely a degree of curiosity in the value of human feelings and intuition.  However history has shown us that intuition has often been the seed of human insight, and many of our greatest leaps in understanding have been the result of such subconscious moments of inspiration.

And so it is with creativity; just as the integration of a diversity of information, can inspire “deep intuition”, so too the integration of a diversity of ideas can inspire “deep creativity”

Deep Creativity

To be human is to be creative; deep creativity is nearly always a combination of both emotional intelligence and a diversity of ideas.

Most types of experts (be they people or systems) are in fact domain-specific experts, but creativity finds it hard to breathe in domain-specific environments.  Creativity is almost always the result of the cross-pollination of ideas; creative innovation requires not only a diversity domain experience but also the ability to “sense” connectivity across seemingly unconnected domains.   Creativity in innovation requires being able to “feel” that maybe there is a certain value in the integration of a diversity of seemingly unrelated ideas…

And so it is that the natural and subconscious process of neural integration not only offers the potential for deep cognitive understanding of complexity, but also the potential for “Deep Creativity in Imagining the Complex Unseen”…

Matrix of Creative Dynamics


 Breaking the Rules

We have long known that anything repetitive or rule-based can essentially be carried out by a machine.   The arrival of “computing” machines prompted the concept of the computer database, which ultimately led to the concept of expert machine systems.

Early expert systems were really just glorified databases but recent developments in AI have shown us that if we really want to build true expert systems, we need to do so by evolving artificial intuition from the bottom up (because top-down intelligence design just doesn’t work)…

As the field of artificial intuition systems develops further we will increasingly find that machines will able to exhibit emergent expertise and resultant creativity when it comes to problem-solving.

But creativity is obviously not only limited to intuitive problem-solving.  True creativity drives the imagination, and deep imagination is (nearly always) the interplay of a diversity of ideas and some degree of emotional intelligence.

On this score, human evolution is way ahead of the game.  From birth, every person on this planet carries with him, or her, a legacy of emotional software that time has hard-coded into his, or her, very DNA; and it is probably safe to say that we could equate this complex information repository to many trillions of hours of equivalent digital practice…

Evolutionary Thinking

As humans we have the potential for great creativity; but to be truly creative requires not only an imagination to see beyond the rules, but also a willingness to break some of these rules.  To be truly creative requires a willingness to entertain the idea that some to the so-called “rules” (and accepted wisdom) which might actually be holding us back.  And this creative potentiality is the most likely future of work…

The future of work is likely to be less about reasoning and more about creativity.  And a future that involves artificial intelligence is less likely to be about machine rule and more likely to be about “machine assistance”; about machines capable of creative suggestion.

We already know that the future of work will likely see the rise of artificial intelligence and the demise of many boring factory and office jobs.  So what is going to be left for us to do?

Creativity!..  The future of human work is to be creative, in jobs that will require “Evolutionary Thinking and Design”.  The future of human work is likely to be all about “Creative Innovation augmented by Artificial Expertise”.  And in this new age of augmented creativity, it seems likely that it will not just be our current creative jobs that will thrive, but that all future jobs will be much less boring and far more creative…

From Creation to Creativity…

Everything in the Universe is fundamentally a system of some sort.  And all systems fundamentally have the same Universal Dynamics…

Matrix of Universal Dynamics - Copyright - Kieran D. Kelly

Our Universe is fundamentally the interplay of 2 things; Energy and Probability.  Excessive Energy can cause Incompressible Dynamics.  Probability can cause Random Energy Clustering which can ultimately lead to Natural Reinforcement.  And the interplay of both incompressible dynamics and probabilistic reinforcement can cause the emergence of Self-Integrated Matter.

Matrix of Energy Dynamics - Copyright - Kieran D. Kelly

Everything in the universe is ultimately some type of “System”.  These systems have a range of behavior from Simple Non-Adaptive Systems to Complex Adaptive Systems.  All systems are essentially the interplay of 2 things; Energy and Feedback.   Excessive Energy can cause Incompressible Dynamics.  Feedback can cause Natural Reinforcement.  And the interplay of Incompressible Energy and Natural Reinforcement can cause of the emergence of Self-Integrated Complexity.

Matrix of System Dynamics - Copyright - Kieran D. Kelly

The Brain is a Complex Adaptive System.  The Brain is capable of modeling Data from the External World.  The more data the brain is exposed to the more likely there will be diversity within the data.  The Brain is dominated by 2 things; External Data and Conscious Evaluation.  An excess of data can produce a great diversity of data.  Experimentation can extract information and knowledge from data.  And the interplay of both a Diversity of Data and Conscious Evaluation can generate Spontaneous Self-Integration and Deep Intuition…Matrix of Cognitive Dynamics

The Mind is a Complex Adaptive System.  The Mind is capable of modeling Thoughts and Intuitions from its own Internal World.  The more thoughts the mind is willing to entertain the more likely there is diversity within the thoughts.  The Mind is dominated by 2 things; Thoughts and Feelings.  A lot of thoughts can produce a great diversity of intuition.  Thinking can extract ideas from thoughts and intuitions.  And the interplay of both a Diversity of Intuition and Emotional Reinforcement can generate Spontaneous Self-Integration and Deep Creativity…Matrix of Creative Dynamics