# Computational Dynamics of Natural Information Morphology, Discretely Continuous

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## Abstract

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## 1. Introduction

## 2. Dichotomy—The Simplest Kind of Classification

## 3. Leibniz’s Binary Notation

“To his contemporaries, the picture must have seemed like a somewhat outrageous joke. To us it looks both prophetic and frightening, because it appears as a confirmation of the trend to think the world in terms of digital information. But Leibniz’s picture suggests that we must even go beyond thinking world in terms of digital information, for he presents the world as being the set of all digital information ([8], p. 160).”

## 4. Dualism in Physics: Discrete vs. Continuous

“There are therefore now two theories of light, both indispensable, and—as one must admit today in spite of twenty years of tremendous effort on the part of theoretical physicists—without any logical connections.”Albert Einstein [9]

## 5. The Finite (Discrete) Nature Hypothesis

“A fundamental question about time, space and the inhabitants thereof is "Are things smooth or grainy?" Some things are obviously grainy (matter, charge, angular momentum); for other things (space, time, momentum, energy) the answers are not clear. Finite Nature is the assumption that, at some scale, space and time are discrete and that the number of possible states of every finite volume of space-time is finite. In other words Finite Nature assumes that there is no thing that is smooth or continuous and that there are no infinitesimals.”(Fredkin, Finite Nature) [13] (Emphasis added)

## 6. The True Nature of the Universe: Discretely Continuous?

“(A)s we delve deeper and deeper into both natural and artificial processes, we find the nature of the process often alternates between analog and digital representations of information. As an illustration, I noted how the phenomenon of sound flips back and forth between digital and analog representations. In our brains, music is represented as the digital firing of neurons in the cochlear representing different frequency bands. In the air and in the wires leading to loudspeakers, it is an analog phenomenon. The representation of sound on a music compact disk is digital, which is interpreted by digital circuits. But the digital circuits consist of thresholded transistors, which are analog amplifiers. As amplifiers, the transistors manipulate individual electrons, which can be counted and are, therefore, digital, but at a deeper level are subject to analog quantum field equations. At a yet deeper level, Fredkin, and now Wolfram, are theorizing a digital (i.e., computational) basis to these continuous equations. It should be further noted that if someone actually does succeed in establishing such a digital theory of physics, we would then be tempted to examine what sorts of deeper mechanisms are actually implementing the computations and links of the cellular automata. Perhaps, underlying the cellular automata that run the Universe are yet more basic analog phenomena, which, like transistors, are subject to thresholds that enable them to perform digital transactions.”[21]

“In a quantum computer, there is no distinction between analog and digital computation. Quanta are by definition discrete, and their states can be mapped directly onto the states of qubits without approximation. But qubits are also continuous, because of their wave nature; their states can be continuous superpositions. Analog quantum computers and digital quantum computers are both made up of qubits, and analog quantum computations and digital quantum computations both proceed by arranging logic operations between those qubits. Our classical intuition tells us that analog computation is intrinsically continuous and digital computation is intrinsically discrete. As with many other classical intuitions, this one is incorrect when applied to quantum computation. Analog quantum computers and digital quantum computers are one and the same device.”[17]

“Digital vs. analogue is a Boolean dichotomy typical of our computational paradigm, but digital and analogue are only “modes of presentation” of being (to paraphrase Kant), that is, ways in which reality is experienced and/or conceptualized by an epistemic agent at a given level of abstraction. A preferable alternative is provided by an informational approach to structural realism, according to which knowledge of the world is knowledge of its structures.”[20]

## 7. Continuum as a Result of Interaction

## 8. Analog/Digital—Continuous/Discrete—Differentiation/Integration

“Information can be defined in terms of categorical opposition of one and many, leading to two manifestations of information, selective and structural. These manifestations of information are dual in the sense that one always is associated with the other. The dualism can be used to model and explain dynamics of information processes.”(Schroeder [30])

## 9. Conclusions

## Acknowledgments

## Conflicts of Interest

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Dodig-Crnkovic, G.
Computational Dynamics of Natural Information Morphology, Discretely Continuous. *Philosophies* **2017**, *2*, 23.
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**AMA Style**

Dodig-Crnkovic G.
Computational Dynamics of Natural Information Morphology, Discretely Continuous. *Philosophies*. 2017; 2(4):23.
https://doi.org/10.3390/philosophies2040023

**Chicago/Turabian Style**

Dodig-Crnkovic, Gordana.
2017. "Computational Dynamics of Natural Information Morphology, Discretely Continuous" *Philosophies* 2, no. 4: 23.
https://doi.org/10.3390/philosophies2040023