The Nature of Consciousness

Piero Scaruffi

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These are excerpts and elaborations from my book "The Nature of Consciousness"

Searching for the Universal Patterns

Another way to probe the ultimate nature of the universe is to look for patterns that arise in different kinds of phenomena, apparently unrelated phenomena.

In 1951 Wigner suggested that statistical physics should adopt mathematical tools called "random matrices" to model phenomena like the energy spectrum of the uranium nucleus ("On the statistical distribution of the widths and spacings of nuclear resonance levels", 1951). The phenomenon that he observed is now known as "universality" and consists in a fine balance of randomness and regularity, at the border between chaos and order. It seems to be widespread in nature, almost a hallmark of all complex correlated systems (systems with strong interactions and correlations between the constituent particles). A spectrum looks like a bar code: a sequence of lines separated by blank spaces. The distribution of lines in the spectrum of complex correlated systems follows a mathematical formula called the "correlation function". Wigner realized that this distribution mirrors the spacing between the eigenvalues, or solutions, of a vast matrix filled with random numbers, a random matrix. And viceversa: any system that exhibits this property of universality turns out to be a complex and correlated system that can be modeled as a random matrix. It turns out that universality is closely related to the most famous distribution in number theory: the distribution of prime numbers, numbers that cannot be divided by other numbers (2, 3, 5, 7, 11, 13, 17, 19, 23, etc).

Another ubiquitous pattern that can be modeled with random matrices is "hyperuniformity", discovered by the Italian physicist Salvatore Torquato ("Local density fluctuations, hyperuniformity, and order metrics", 2003). Physicists have found that hyperuniformity is widespread in nature, from bird eyes to the large-scale structure of the universe.

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