Reinvention of businesses. Natural Intelligence technology. Alexander Blinkov

also to suggest innovative solutions – such that something new happens, and in the right way and when we need it.

      Arising not subject to calculation

      Cheers cheers! Will physics help us now? Explain how fundamentally new businesses arise, how their products capture markets? Will he give the laws by which we will build formulas for success? Give us wisdom?

      Not so simple.

      If we carefully look at the very edge of both one and the other rays of Physics, we will see strange things.

      In the microcosm, as one penetrates into more and more subtle parts of matter, many basic concepts familiar to man become unsteady. Einstein’s space turns out to be a field that can move, bend, oscillate. Time can flow at different speeds. A particle to be at the same time a wave. Quantum mechanics has declared that in the world of very, very small objects, everything is «grainy», discrete. And in all movements there is an element of chance. Events at this end of the axis are ambiguous, probabilistic – the state of the particle at the moment cannot accurately determine what will happen to it in the next instant. At the microscopic level, you can calculate the probability of an event that will happen, but you cannot predict the future with complete certainty.

      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