Digital infinity is a technical term in
theoretical linguistics
Theoretical linguistics is a term in linguistics which, like the related term general linguistics, can be understood in different ways. Both can be taken as a reference to theory of language, or the branch of linguistics which inquires into the n ...
. Alternative formulations are "discrete infinity" and "the infinite use of finite means". The idea is that all human languages follow a simple logical principle, according to which a limited set of digits—irreducible atomic sound elements—are combined to produce an infinite range of potentially meaningful expressions.
Noam Chomsky
Avram Noam Chomsky (born December 7, 1928) is an American public intellectual: a linguist, philosopher, cognitive scientist, historian, social critic, and political activist. Sometimes called "the father of modern linguistics", Chomsky is ...
cites
Galileo
Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He was ...
as perhaps the first to recognise the significance of digital infinity. This principle, notes Chomsky, is "the core property of human language, and one of its most distinctive properties: the use of finite means to express an unlimited array of thoughts". In his ''
Dialogo'', Galileo describes with wonder the discovery of a means to communicate one's "most secret thoughts to any other person ... with no greater difficulty than the various collocations of twenty-four little characters upon a paper." "This is the greatest of all human inventions," Galileo continues, noting it to be "comparable to the creations of a Michelangelo".
The computational theory of mind
'Digital infinity' corresponds to Noam Chomsky's '
universal grammar
Universal grammar (UG), in modern linguistics, is the theory of the genetic component of the language faculty, usually credited to Noam Chomsky. The basic postulate of UG is that there are innate constraints on what the grammar of a possible hum ...
' mechanism, conceived as a computational
module
Module, modular and modularity may refer to the concept of modularity. They may also refer to:
Computing and engineering
* Modular design, the engineering discipline of designing complex devices using separately designed sub-components
* Mo ...
inserted somehow into ''Homo sapiens'' otherwise 'messy' (non-digital) brain. This conception of human cognition—central to the so-called '
cognitive revolution
The cognitive revolution was an intellectual movement that began in the 1950s as an interdisciplinary study of the mind and its processes. It later became known collectively as cognitive science. The relevant areas of interchange were between th ...
' of the 1950s and 1960s—is generally attributed to
Alan Turing
Alan Mathison Turing (; 23 June 1912 – 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher, and theoretical biologist. Turing was highly influential in the development of theoretical com ...
, who was the first scientist to argue that a man-made machine might truly be said to 'think'. But his often forgotten conclusion however was in line with previous observations that a "thinking" machine would be absurd, since we have no formal idea what "thinking" is — and indeed we still don't. Chomsky frequently pointed this out. Chomsky agreed that while a mind can be said to "compute"—as we have some idea of what computing is and some good evidence the brain is doing it on at least some level—we cannot however claim that a computer or any other machine is "thinking" because we have no coherent definition of what thinking is. Taking the example of what's called 'consciousness,' Chomsky said that, "We don't even have bad theories"—echoing the famous physics criticism that a theory is "not even wrong." From Turing's seminal 1950 article, "
Computing Machinery and Intelligence
"Computing Machinery and Intelligence" is a seminal paper written by Alan Turing on the topic of artificial intelligence. The paper, published in 1950 in ''Mind'', was the first to introduce his concept of what is now known as the Turing test to ...
", published in ''
Mind
The mind is the set of faculties responsible for all mental phenomena. Often the term is also identified with the phenomena themselves. These faculties include thought, imagination, memory, will, and sensation. They are responsible for various m ...
'', Chomsky provides the example of a submarine being said to "swim." Turing clearly derided the idea. "If you want to call that swimming, fine," Chomsky says, repeatedly explaining in print and video how Turing is consistently misunderstood on this, one of his most cited observations.
Previously the idea of a thinking machine was famously dismissed by
René Descartes
René Descartes ( or ; ; Latinized: Renatus Cartesius; 31 March 1596 – 11 February 1650) was a French philosopher, scientist, and mathematician, widely considered a seminal figure in the emergence of modern philosophy and science. Mathem ...
as ''theoretically'' impossible. Neither animals nor machines can think, insisted Descartes, since they lack a God-given soul. Turing was well aware of this traditional theological objection, and explicitly countered it.
Today's digital computers are instantiations of Turing's theoretical breakthrough in conceiving the possibility of a man-made ''universal thinking machine''—known nowadays as a '
Turing machine
A Turing machine is a mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, it is capable of implementing any computer algori ...
'. No physical mechanism can be intrinsically 'digital', Turing explained, since—examined closely enough—its possible states will vary without limit. But if most of these states can be profitably ignored, leaving only a limited set of relevant distinctions, then ''functionally'' the machine may be considered 'digital':
An implication is that 'digits' don't exist: they and their combinations are no more than convenient fictions, operating on a level quite independent of the material, physical world. In the case of a ''binary'' digital machine, the choice at each point is restricted to 'off' versus 'on'. Crucially, the intrinsic properties of the
medium
Medium may refer to:
Science and technology
Aviation
*Medium bomber, a class of war plane
*Tecma Medium, a French hang glider design
Communication
* Media (communication), tools used to store and deliver information or data
* Medium of ...
used to encode signals then have no effect on the message conveyed. 'Off' (or alternatively 'on') remains unchanged regardless of whether the signal consists of smoke, electricity, sound, light or anything else. In the case of analog (more-versus-less) gradations, this is not so because the range of possible settings is unlimited. Moreover, in the analog case it ''does'' matter which particular medium is being employed: equating a certain intensity of smoke with a corresponding intensity of light, sound or electricity is just not possible. In other words, only in the case of ''digital'' computation and communication can information be truly independent of the physical, chemical or other properties of the materials used to encode and transmit messages.
Digital computation and communication operates, then, independently of the physical properties of the computing machine. As scientists and philosophers during the 1950s digested the implications, they exploited the insight to explain why 'mind' apparently operates on so different a level from 'matter'. Descartes's celebrated distinction between immortal 'soul' and mortal 'body' was conceptualised, following Turing, as no more than the distinction between (digitally encoded) ''information'' on the one hand, and, on the other, the particular physical ''medium''—light, sound, electricity or whatever—chosen to transmit the corresponding signals. Note that the Cartesian assumption of mind's independence of matter implied—in the human case at least—the existence of some kind of digital computer operating inside the human brain.
A digital apparatus
Turing did not claim that the human mind really is a digital computer. More modestly, he proposed that digital computers might one day qualify in human eyes as machines endowed with "mind". However, it was not long before philosophers (most notably
Hilary Putnam
Hilary Whitehall Putnam (; July 31, 1926 – March 13, 2016) was an American philosopher, mathematician, and computer scientist, and a major figure in analytic philosophy in the second half of the 20th century. He made significant contributions ...
) took what seemed to be the next logical step—arguing that the human mind ''itself'' is a digital computer, or at least that certain mental "modules" are best understood that way.
Noam Chomsky
Avram Noam Chomsky (born December 7, 1928) is an American public intellectual: a linguist, philosopher, cognitive scientist, historian, social critic, and political activist. Sometimes called "the father of modern linguistics", Chomsky is ...
rose to prominence as one of the most audacious champions of this 'cognitive revolution'. Language, he proposed, is a computational 'module' or 'device' unique to the human brain. Previously, linguists had thought of language as learned cultural behaviour: chaotically variable, inseparable from social life and therefore beyond the remit of natural science. The Swiss linguist
Ferdinand de Saussure
Ferdinand de Saussure (; ; 26 November 1857 – 22 February 1913) was a Swiss linguist, semiotician and philosopher. His ideas laid a foundation for many significant developments in both linguistics and semiotics in the 20th century. He is widel ...
, for example, had defined linguistics as a branch of 'semiotics', this in turn being inseparable from anthropology, sociology and the study of man-made conventions and institutions. By picturing language instead as the ''natural'' mechanism of 'digital infinity', Chomsky promised to bring scientific rigour to linguistics as a branch of strictly ''natural'' science.
In the 1950s, phonology was generally considered the most rigorously scientific branch of linguistics. For phonologists, "digital infinity" was made possible by the human vocal apparatus conceptualised as a kind of machine consisting of a small number of binary switches. For example, "voicing" could be switched 'on' or 'off', as could palatisation, nasalisation and so forth. Take the consonant
for example, and switch voicing to the 'off' position—and you get
Every possible phoneme in any of the world's languages might in this way be generated by specifying a particular on/off configuration of the switches ('articulators') constituting the human vocal apparatus. This approach became celebrated as '
distinctive features
In linguistics, a distinctive feature is the most basic unit of phonological structure that distinguishes one sound from another within a language. For example, the feature oicedistinguishes the two bilabial plosives: and There are many diffe ...
' theory, in large part credited to the Russian linguist and polymath
Roman Jakobson
Roman Osipovich Jakobson (russian: Рома́н О́сипович Якобсо́н; October 11, 1896Kucera, Henry. 1983. "Roman Jakobson." ''Language: Journal of the Linguistic Society of America'' 59(4): 871–883. – July 18,[morphophonemics
Morphophonology (also morphophonemics or morphonology) is the branch of linguistics that studies the interaction between morphological and phonological or phonetic processes. Its chief focus is the sound changes that take place in morphemes (m ...]
. During the 1950s, he became inspired by the prospect of extending Roman Jakobson's 'distinctive features' approach—now hugely successful—far beyond its original field of application. Jakobson had already persuaded a young social anthropologist—
Claude Lévi-Strauss
Claude Lévi-Strauss (, ; 28 November 1908 – 30 October 2009) was a French anthropologist and ethnologist whose work was key in the development of the theories of structuralism and structural anthropology. He held the chair of Social Anthro ...
—to apply distinctive features theory to the study of kinship systems, in this way inaugurating 'structural anthropology'. Chomsky—who got his job at the Massachusetts Institute of Technology thanks to the intervention of Jakobson and his student, Morris Halle—hoped to explore the extent to which similar principles might be applied to the various sub-disciplines of linguistics, including syntax and semantics. If the phonological component of language was demonstrably rooted in a digital biological 'organ' or 'device', why not the syntactic and semantic components as well? Might not language as a whole prove to be a digital organ or device?
This led some of Chomsky's early students to the idea of '
generative semantics'—the proposal that the speaker generates word and sentence meanings by combining irreducible constituent elements of meaning, each of which can be switched 'on' or 'off'. To produce 'bachelor', using this logic, the relevant component of the brain must switch 'animate', 'human' and 'male' to the 'on' (+) position while keeping 'married' switched 'off' (-). The underlying assumption here is that the requisite conceptual primitives—irreducible notions such as 'animate', 'male', 'human', 'married' and so forth—are genetically determined internal components of the human language organ. While this idea would rapidly encounter intellectual difficulties—sparking controversies culminating in the so-called '
linguistics wars
The linguistics wars were a protracted academic dispute inside American theoretical linguistics which took place mostly in the 1960s and 1970s, stemming from an intellectual falling-out between Noam Chomsky and some of his early colleagues and doct ...
' as described in Randy Allen Harris's 1957 publication by that name.
[ OCLC summary: "When it was first published in 1957, Noam Chomsky's Syntactic Structure seemed to be just a logical expansion of the reigning approach to linguistics. Soon, however, there was talk from Chomsky and his associates about plumbing mental structure; then there was a new phonology; and then there was a new set of goals for the field, cutting it off completely from its anthropological roots and hitching it to a new brand of psychology. Rapidly, all of Chomsky's ideas swept the field. While the entrenched linguists were not looking for a messiah, apparently many of their students were."] The linguistic wars attracted young and ambitious scholars impressed by the recent emergence of computer science and its promise of scientific parsimony and unification. If the theory worked, the simple principle of digital infinity would apply to language as a whole. Linguistics in its entirety might then lay claim to the coveted status of ''natural'' science. No part of the discipline—not even semantics—need be "contaminated" any longer by association with such 'un-scientific' disciplines as cultural anthropology or social science.
[Just as Bloomfield's mentalism was one way of keeping meaning away from form, by consigning it to psychology and sociology, so Chomsky's performance is a way to keep meaning and other contaminants away from form, by consigning them to "memory limitations, distractions, shifts of attention and interest" as well as to "the physical and social conditions of language , use" (1965 9643; 1977:3)—to psychology and sociology]
See also
*
Decoding Chomsky
*
Generative linguistics
Generative grammar, or generativism , is a linguistic theory that regards linguistics as the study of a hypothesised innate grammatical structure. It is a biological or biologistic modification of earlier structuralist theories of linguistic ...
*
The Library of Babel
"The Library of Babel" ( es, La biblioteca de Babel) is a short story by Argentine author and librarian Jorge Luis Borges (1899–1986), conceiving of a universe in the form of a vast library containing all possible 410-page books of a certain ...
*
Origin of language
The origin of language (spoken and signed, as well as language-related technological systems such as writing), its relationship with human evolution, and its consequences have been subjects of study for centuries. Scholars wishing to study th ...
*
Origin of speech
The origin of speech refers to the general problem of the origin of language in the context of the physiological development of the human speech organs such as the tongue, lips, and vocal organs used to produce phonological units in all spok ...
*
Recursion
Recursion (adjective: ''recursive'') occurs when a thing is defined in terms of itself or of its type. Recursion is used in a variety of disciplines ranging from linguistics to logic. The most common application of recursion is in mathematics ...
References
{{Reflist
Further reading
*Knight, C. and C. Power 2008
'Unravelling digital infinity'.Paper presented to the ''7th International Conference on the Evolution of Language'' (EVOLANG), Barcelona, 2008.
*Knight, C. 2008
'Honest fakes' and language origins.''Journal of Consciousness Studies,'' 15, No. 10–11, 2008, pp. 236–48.
Linguistics
Cognitive science