Reinvention of businesses. Natural Intelligence technology

But what about at the other end of complexity, at the tip of the ray of Thermodynamics? In a completely different way, but clarity and unambiguity also disappear. The foundation of physics – the measurability of the properties of objects, disappears with increasing complexity. The trouble is that if more and more complex systems are included in the consideration, the concepts of temperature, entropy, and energy for them lose their rigor. It is impossible to measure or mathematically describe such parameters for society or for an organization. The basic concepts of thermodynamics – energy, entropy, temperature – turn out to be only metaphors in the world of people. Physics, as you move up the scale of complexity, disappears as an exact science. It seems that the tips of both divergent beams blur in a haze of fundamental uncertainty.

And in this haze, our hopes for help from physics in the world of business problems dissolve?

And that’s not all – washes his hands and the instrument of physical knowledge – Her Majesty Mathematics!

Even where equations for the behavior of complex systems are still being written, they turn out to be nonlinear. In such complex systems and their models, everything depends on everything! Dependencies are sometimes contradictory: it is good for predators in the forest if there are many small animals around – their food supply. Predators multiply, and… and destroy their food supply. The population of predators begins to decline sharply.

Solutions of non-linear equations lose their stability at certain points, which means that they become ambiguous. Such points on the mathematical trajectories of mathematics are called bifurcations.

«The bifurcation point is a critical state of the system, at which the system becomes unstable and uncertainty arises: whether the state of the system will become chaotic or whether it will move to a new, more differentiated and high level of order. A term from the theory of self-organization.»

The number of both predators and their prey can fluctuate, and under certain conditions one or both populations can end their existence catastrophically.

How to «feel» this very bifurcation? Play with it, look at this strange self-organization. This, it turns out, is not difficult – there are a lot of bifurcations with us and around us!

Fig. 3. Expected behavior of an elastic object

It is unlikely that in today’s computer world someone uses an eraser – an elastic band to erase what is written with a pencil or pen. Maybe you remember this subject from school? Such a small brick of gum, which was fun to play with, squeezing it with your fingers. And now, let’s extract science from such an» anti-stress» of our childhood.

Squeezing the elastic between the fingers, we make it shorter. We compress even more – we deform the elastic bar even more.

But at some point, the elastic band suddenly refuses to compress further and bends to the side. Squeezing and unclenching our fingers, we repeatedly reach this point, when the behavior of a simple elastic object changes qualitatively. And each time in a different way: once the deflection will be in one direction, and once in the other.

Fig. 4. Buckling – the real behavior of an elastic object

We will not write the equation, as we promised, but we will only say that it has a unique solution only up to a certain compression. And at this critical point, the solution loses stability. If we imagine that we have an absolutely perfect bar of gum inside and out, and we press our fingers strictly along its longitudinal axis, the gum will continue to shrink without bulging. But this will already be an unstable segment of solutions. Just as a ball can, in principle, stick to the top of a convex surface, but only in an absolutely ideal case.

If you «move» your finger at least a little bit – physically, or the homogeneity parameter of our rubber band – mathematically, the solution of the equilibrium equation will immediately rush to another, stable state. But! Now there are two possible stable states in the solution – the deflection is either «to the right» or «to the left», and which one our object will fall into depends on those very random, literally microscopic «movements».

That is, the point is not that we do not know how to count, but that mathematics fundamentally cannot give an unambiguous solution. On the contrary, mathematics proves that now there can be no uniqueness! Moreover, if we took not a rubber block, but a rubber cylinder, we would get not two possible positions after the deflection, but an infinite number – any direction in a circle.

Fig. 5. The condition of the gum under pressure. Pitchfork bifurcation

To sum up, in what state the system will pass, hitting the critical point, mathematicians cannot unambiguously calculate – the solutions become unstable with respect to fluctuations. This means that there are solutions to the equations, but there can be many of them. And even infinitely many. What solution is implemented in practice depends on infinitesimal deviations in parameters that occur only in the real world, more precisely, in the microcosm, and which a person and, therefore, mathematics can never know. These are such small movements, such small inhomogeneities of the gum material, that it is impossible to measure, plan, or take into account in advance. Such small deviations are fluctuations. To calculate the exact state of a complex system in the future, it is necessary to know a huge number of initial conditions onshore, which will never be known to anyone. And someone who, and business is definitely a system with an infinite amount of uncertainty.

Qualitative Considerations

So it looks like we’re left with nothing?

However, let’s listen to the greats. It seems that not everything is so hopeless!

The mathematics of describing nonlinear effects is highly non-trivial. But, as Academician V. I. Arnold (1937—2010), one of the greatest mathematicians of the 20th century, said:

«These objective laws of the functioning of nonlinear systems cannot be ignored. Only the simplest qualitative conclusions have been formulated above. The theory also provides quantitative models, but qualitative conclusions seem to be more important and at the same time more reliable: they depend little on the details of the functioning of the system, the structure of which and the numerical parameters may not be well known.»

Henri Poincaré (1854—1912), «the last of the great universal mathematicians,» also said that only a limited amount of qualitative information is needed to understand qualitative changes in the behavior of systems.

So there are no formulas. They are useless. But there is good news! It turns out that it is important not to calculate the exact trajectory of changes, but to be ready for the phenomenon – for the critical point and for the qualitative transition that will follow. Actually, this is what we do in the morning when we boil water for tea. We do not calculate or measure anything, we just wait for the moment of a qualitative transition – we wait for the water to boil. And this is enough for us to understand that the moment has come, you can make tea.

Let’s return to our elastic band, to our manual bifurcation. When we squeezed it and got a deflection, we can play with it further, for example, try to put pressure on the bulge.

Fig. 6. Longitudinal and transverse action on an elastic object

Our «antistress» with a certain effort will begin to flip in the opposite direction. If we draw a set of solutions to the equation in the parameter space: Deflection / Longitudinal pressure / Transverse pressure, then we will find a funny surface in it, similar to the assembly of a fabric. This surface is in a section of mathematics called Catastrophe Theory and is called Cusp catastrophe.

On this decision surface, we will see the buckling path under longitudinal pressure, which we have already seen in Fig. 5. To do this, it is enough to cut our Assembly with a vertical plane, for which the transverse pressure is equal to zero.

Fig. 7. Surface of the state of an elastic object. Buckling under longitudinal compression

The area of instability is represented by a triangular «tongue», indicated by a dotted line in the middle of the Cusp, where the system can get and stay in this state for some time, until any infinitely small impact throws it into one of the stability zones – a deflection in one direction or another.

We can also trace the trajectory of the state of the object under the influence of transverse pressure.

Fig. 8. Transverse route on the state surface. Memory effect

By itself, the understanding of a mathematical catastrophe, as a kind of map, a qualitative picture of the space of possible states, already allows us to understand a lot about the behavior of an object, to be prepared for surprises, and moreover, to use these properties. Despite the fact that our pictures of catastrophic behavior do not promise any quantitative accuracy, the operating point of the system, having fallen into the zone of instability, for example, does not know when and where it will leave it.

The transverse route – the transfer of such systems from one state to the opposite (the so-called hysteresis phenomenon) is used in many places, for example, in binary memory cells. And in order to use this memory, it turns out that it is necessary to control only one control parameter, which switches the cell.

Is a high-quality picture enough to expect and manage high-quality transitions in our systems, including business ones? We will see this below.

Beyond the boundaries

Beyond the boundaries of physics as an exact science, there are attempts to generalize the formation and self-organization of structures in open systems that are far from thermodynamic equilibrium. As conceived by its creator, Professor Hermann Haken, synergetics is an interdisciplinary direction that is called upon to play the role of a kind of metascience, noticing and studying the general nature of those patterns and dependencies that private sciences considered «their own».

«Synergetics (from other Greek prefixes «syn» with the meaning of compatibility and «ergon» – activity) – «together action».

«It should be emphasized that synergetics is by no means one of the frontier sciences such as physical chemistry or mathematical biology, emerging at the intersection of the two sciences.»

This is a fairly new area of science – there are still no clear boundaries, or even clear definitions of areas. The area of research in synergetics is not clearly defined and can hardly be limited, since its interests extend to all branches of natural science. A common feature is the consideration of the dynamics of any irreversible processes and the emergence of fundamental innovations.

Since there are no clear boundaries and definitions, there is an inevitable dispute in scientific and pseudo-scientific circles. Anyone is ready to declare himself a zealot of true metaknowledge, and to call everyone else pseudo-scientists, scholastics and charlatans.

I must say that this is a completely normal phenomenon for science. True Science differs from faith or ideology in that it itself calls into question all its achievements. Especially on the frontier of knowledge, that is, exactly where new knowledge about the self-organization of matter is being formed today.

Maybe our approach will be accused of being pseudo-scientific. Real academics are simply obliged to do this.

Truth, scientists say, is just the most appropriate concept to explain facts. I think this principle is good for business as well. Let’s test our theory with practice.

So, what do we get from the sciences at the start of the path? No strict laws, no numerical mathematical apparatus. The more complex and larger the system, the less numerical accuracy, the more qualitative considerations. Is this enough to put such knowledge into practice and apply it successfully?

Here we’ll see. What difference does it make whether it is physics or something else, as long as the conclusions work! That is, they would help us in business.

Chaos that creates

Progress

The evolution of matter today is already widely considered as part of a global synergetic process. And the emergence of life on the planet, and the origin of the mind, the evolution of conscious life – as part of the epic self-organization of matter.