Complexity Theory as it stands is a bit of a mishmash of concepts and doesn’t really have an agreed upon definition, so rather than analyse all the pros and cons of all the various definitions, here simply is my definition…

Natural Complexity is the result of the *“adaptive integration of co-emergent diversity”*, which ultimately results in *“emergent complex systems”* that have effectively *“organised themselves into existence”*. So, in the simplest possible terms, we could say that

“Natural Complexity is Self-Integrated Diversity”

To study complexity is basically to study evolution. Physicists/Scientists have long been perplexed by the creative power of evolution; not least because it seems to be in direct conflict with the *Second Law of Thermodynamics (SLOT)*. The SLOT is the law of physics that deals with the spontaneous behaviour of fluid systems. In everyday terms the SLOT is simply the fact that cold milk and hot coffee, if left unstirred, will spontaneously mix themselves (in both composition and temperature). The SLOT states that left undisturbed all systems gravitate towards a state of maximum disorder; a state that would seem to be the exact opposite of complexity.

So how to resolve this conundrum? How can complexity emerge in a universe dominated by the SLOT and the inevitable pull to disorder? What is the source of all the universe’s spontaneous order and complexity?

Well, there is a theory (called the *“Theory of Dissipative Structures”*) about how complexity can occur without negating the SLOT, but frankly it is over-engineered, over-complicated, and doesn’t actually explain the source of spontaneous order and complexity. We suggest that the answer to the conundrum of spontaneous complexity is actually something much more simple; something we call the *“Reverse Law of Large Numbers (RLLN)”*.

__The Law of Large Numbers (LLN)__

Most people are familiar with the concept that if you toss a coin four times, you won’t necessarily get a 50-50 split between heads and tails: indeed, you could get 4 tails, which could suggest (wrongly) that the coin will *always* land on tails. But if you toss a coin a million times, you will most definitely get the expected result. It is the *“Law of Large Numbers” (LLN)* that ensures that the one million coin tosses will produce an average of 50% heads and 50% tails.

So now let’s think about how this mathematical law applies to the Second Law of Thermodynamics (SLOT).

__The Damping Effect of the LLN__

The SLOT states that left undisturbed all systems gravitate towards a state of maximum disorder, a state that is referred to as *“Thermal Equilibrium”*. In reality however, the achievement of thermal equilibrium relies heavily on the mathematics of the Law of Large Numbers (LLN).

Because of the absurdly large numbers of particles in a thermal system, the chances of any *“statistical deviations”* in behaviour are extremely small, and consequently the system as a whole tends to exhibit uniformity.

So although on the microscopic level (of particle interaction) there is a lot of wild incompressible dynamics, these volatile dynamics are normally invisible on the macro system level thanks to *“The Damping Effect of the LLN”*.

__The Reverse Law of Large Numbers (RLLN)__

So thermal equilibrium relies on the LLN; but more specifically it actually relies on the number of independent elements (of the system) being significantly larger than the number of options available to each element.

This means that although fluid-like systems may spontaneously gravitate to thermal equilibrium, they can often *be held away* from this equilibrium by either, the inability to dampen excessive activity, or by the emergence of positive feedback – each of which are different forms of a *“Reverse Law of Large Numbers (RLLN)”*…

Now what is most interesting about this is that while weak negative feedback in isolation can cause incompressible diversity, and strong positive feedback in isolation can cause the emergence of asymmetric uniformity, the most interesting stuff occurs from the *interplay* of both.

Positive reinforcement in a system of great diversity, can spontaneously produce surprisingly complex *“Integrated Diversity”*. In other words, the secret to the creativity of natural evolution is that;

With the Co-Emergence of Diversity, Complex Integration comes for free!…

**— Now on a slightly different tact, let’s examine how this emergence of complexity relates to the concept of ***“Thermodynamic Entropy” —*

*“Thermodynamic Entropy” —*

__The Interplay of Entropy__

The RLLN has the effect of pulling all fluid-like systems away from thermal equilibrium. In systems of adaptive agents, positive feedback can ultimately reinforce a symmetry break which pulls the system far away from maximum entropy and thermal equilibrium. However we do not always need to be away from maximum entropy to be away from thermal equilibrium. Chaos theory has shown us that even at maximum entropy we can still be away from thermal equilibrium, because systems with incompressible dynamics produce turbulent-like behaviour and *“Information Entropy”*.

*“Information Entropy”* is a different type of entropy to *“Thermodynamic Entropy”*. Information entropy is a measure of uncertainty or unpredictability; whereas thermodynamic entropy is a measure of disorder.

Complexity is, in fact, a combination of these two types of entropy. *“**Complex Adaptive Systems”* are characterized by the fact that they have *“low thermodynamic entropy, but high information entropy”*; consequently such systems can be considered to be highly organized but unpredictable nonetheless.

**Below is the System Matrix reconstituted in entropic terms**

__The Source of Everything__

When Chaos Theory and Complexity Theory first emerged back in the 1970’s there was much excitement for Chaos + Complexity appeared to be on the verge of answering the biggest of big questions *“What is the source of nature’s spontaneous order and complexity?”*

This website is dedicated to answering that question. We suggest that since the SLOT effectively operates like a negative feedback system in that it pulls (or dampens) a system to equilibrium, it should be no surprise that complexity results from resistance to this pull, and as it turns out it is the interplay of two different types of resistance that drives natural evolution away from a featureless thermodynamic equilibrium.

All spontaneously Self-Designing Complexity is simple the interplay of Weak Negative Feedback and Strong Positive Feedback; simply the interplay of creative *“Incompressible Dynamics”* and reinforcing *“Emergent Dynamics”*…

Incompressible Diversity and Positive Reinforcement, combined in just the right measure, is the source of all natural *“Adaptive Integration”* and *“Self-Designing Complexity” * — and this self-designing complexity” is the universal process by which every complex thing in the universe *“self-organizes itself ** into existence”*; the process by which** “the emergent complex whole is always becoming greater than the sum of its less-complex parts”…**