Learn how to see. Realize that everything connects to everything else.

(Leonardo da Vinci)

This universal thought of a brilliant polymath has set the observational point of the curious minds since the Renaissance. Educating people to question what they have learned on a path to progress.

In this article, synchronicity, a connecting principle introduced by Carl Jung is presented. A popular book, *One Two Three... Infinity* by George Gamow discusses the sciences of mathematics and physics. In our work, an integral property of the scale-space decomposition of a partition function is described.

### Synchronicity

*An Acausal Connecting Principle* is a book written by Carl Jung describing his view on subjective relativity of the causality principle. This investigation on the quantum nature of a cause and effect relation was developed during his 25 years of mutual exchange of views and ideas with Wolfgang Pauli. The idea from quantum physics that things move for a reason brought the profound psychiatrist to the conclusion that coincidences are connected, provided one looks deeply into it. He used the term synchronicity for the phenomena in our daily life experience and functioning that lack a clear understanding of a cause and effect.

### One two three... infinity

In this book, theoretical physicist George Gamow discusses a wide range of topics. Starting from number theory and topology, covers interesting interpretations of his research and views, from atomic physics and chemistry to cosmology. He was one of the founders of the "Big Bang Theory" of the origin of the universe together with Georges Lemaitre. The book ends with a question: is the universe finite or infinite?

### The scale-space property of an atomic structure: the elements of the prime numbers

In our study, the partition function is singular in scale at both ends of conjoined spaces, at the infinitely large and at the smallest. We have introduced a theoretical formulation of the scale-space information tunneling, describing the synergistic dynamics of wave couplings, in scale. Stochastic resonance synergies bind the atomic structure that satisfies the mass conservation principle.

Multidimensional information is expressed in a cascade of binding information quanta dynamically, via coordinate transformations, in 5D. The integral property of the scale-space decomposition is derived by dividing the partition function in a hierarchical network of coupled oscillators^{1-3}. At the smallest scale, a polynomial distribution limits the asymptotic freedom of the information exchange that binds the clusters together.

Circular search patterns, encoding information in the internal states of an atomic structure have been investigated with data analysis^{4}. Quantifying the dynamical process of decision making with quantum information carriers, in memories, attention and behavior.

No matter how thin you slice it, there will always be two sides.

(Baruch Spinoza)

### Concluding remarks

The integral property of the scale-space decomposition is derived by dividing the partition function in a hierarchical network of coupled oscillators, in scale.

The theory of stochastic resonance synergistic introduces genotype information processing. A cascade of quadrupoles has been applied in computational physics and neuroscience in the analysis of their distributions. Reversely, the quantum code defines the evolving patterns of multidimensional information, in the scale-space.

Our approach to data analysis of attention, memory, and behavioral dynamics of decision making derives from the internal states of the atomic structure of binding synergies, as well.

#### References

^{1} Jovovic, M., H. Yahia, and I. Herlin, *Hierarchical scale decomposition of images – singular features analysis*, INRIA, 2003.

^{2} Jovovic, M., and G. Fox, *Multi-dimensional data scaling – dynamical cascade approach*, Indiana University, 2007.

^{3} Jovovic, M., *Stochastic Resonance Synergetics. Quantum Information Theory for Multidimensional Scaling*, Journal of Quantum Information Science, 5/2:47-57, 2015.

^{4} Jovovic M., *Attention, Memories and Behavioral Data-driven Study*, Advances in Neurology and Neuroscience, 2019.