Marcin J. SCHROEDER​

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Professor Emeritus, Akita International University (AIU), Japan

Editor-in-Chief of the journal Philosophies (MDPI)

Vice-President for Research (former President 2019-2021) of the International Society for the Study of Information (IS4SI)

Academic President of the International Society for Interdisciplinary Studies of Symmetry (SIS)

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 Reincarnations and Consequences of the Distinction Between Analog and Digital Information
 

ABSTRACT​

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The distinction between analog and digital information has entered the vernacular vocabulary and may seem as obvious as the meaning of the word data. Whatever is obvious, as a rule, hides an unpenetrable depth of the foundations of our thinking. The terms “analogy” (proportion) and “digit” (finger or toe) are very old and both very early acquired some association with numbers or measuring. However, their opposition is relatively new, and most likely it was introduced or at least popularized by John von Neumann in the late 1940s in the context of computing automata. [1]. He considered the opposition of the Analogy Principle and the Digital Principle where in the former numbers are represented by physical magnitudes and in the latter by “aggregates of digits”. In his explanation, he focused on the difference in the process of calculation (operations on numbers) which in analog machines involves physical interactions, and in digital machines manipulation of digits. Also, he observed that in analog machines we can never get exact outcomes of calculation due to unavoidable errors in the transition between the state of the machine and the reading of the result, but the results of digital calculations are exact. Both types of machines existed in those days, but the main direction of computing technology was in the type of digital machines mainly as a result of Alan Turing’s invention of universal computing machines whose operation can be programmed by providing appropriate information to the machine instead of restructuring its design.

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The development of electronic technology has brought later different manifestations of this distinction, for instance in the way sound or music was recorded, transmitted, and reproduced. Already in von Neumann’s original writings, the focus was on the distinction between the continuous characteristic of the operation of analog machines and the discrete of digital ones. This distinction has important consequences for the theoretical description of computation and following it development of information technology. With the extraordinary importance of this technology, in the popular view, the distinction of analog-digital is identified with the opposition of continuous-discrete. In reality, all digital computers are actually analog in the sense that at the level of machinery, they operate in a continuous way, and the process of discretization is conventional to implement the computation in terms of digits [2]. 

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Thus, what exactly is the analog-digital opposition in the context of information, not as usually assumed computing machines that all are analog in their operation? In my recent publications [3] I presented the view that the difference between analog and digital information is similar (i.e. analogous) to the difference between the concepts of physics characterizing physical systems by physical states (analog) and observables (digital). This distinction in physics acquired recognition and fundamental importance with the rise of quantum mechanics but was already present earlier, although only indirectly. We can trace it all the way to the invention of the earliest forms of writing and in particular its alphabetic form. This way of understanding analog-digital distinction was not explicitly formulated by von Neumann but can be identified in his explanation of the two types of machines. Analog information is encoded in an object or alternatively can be identified with its state, while digital information is the result of observation or measurement of this object. In the context of computation, the calculation by an analog machine operates on the states of the computing machine while in digital computing the operation involves measurement (e.g. reading of the tape of Turing machine).

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The distinction between analog and digital information has been obscured by confusing terminology, especially by the use of the deceiving term “data.” Its Latin meaning, the plural form of “given” suggests the direct accessibility of information ignoring the stage of the transition from the encoding of information within an object (understood usually as what information is about) to the encoding of information in the specific format (frequently, but not always of numerical type). The transition is the process of observation or measurement. Naturally, this stage of the transformation of information was outside of the interest of those who were searching for the abstract mathematical process of calculation and was left outside of the description of information processing. The transformed information was simply “given,” but actually it was “taken” from the object by an observer, as it is reflected in the English expression for photographing as “taking a picture of something.” What was “given” by the object was considered identical to what was “taken” by the observer which with the advent of quantum mechanics became unwarranted. Thus, what commonly is called “data” (given) should be called using the Latin “capta” (taken). Data are most frequently inaccessible.

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The distinction between a state and an observable has many precedents in philosophy. Probably the best-known analogy can be found in Immanuel Kant’s distinction of the thing as it is (state of the thing) and our human perception involving synthetic a priori apparatus of knowing (observable). In a much more practical context, von Neumann’s concern about the errors involved in analog computing is similar. However, the analog-digital distinction, upon careful reflection, rises from a marginal technical issue to the role of the one of most fundamental principles of the study of information and knowledge.

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References

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von Neumann, J. (1963). The General and Logical Theory of Automata. Ed. Taub, A. H.,  John von Neumann, Collected Works, Vol. V, Pergamon Press, Oxford, UK, 1963, pp. 288–326.

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Papayannopoulos, P., Nir Fresco, N., and Shagrir, O. On Two Different Kinds of Computational Indeterminacy. The Monist 105 (2022): 229-246. 

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Schroeder, M.J. Theoretical Unification of the Fractured Aspects of Information. In Schroeder, M.J. & Hofkirchner, W. Eds. Understanding Information and Its Role as a Tool: In Memory of Mark Burgin. World Scientific, Singapore, 2025, pp. 131-185.

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