prev "Autoformalisation - Knowledge acquisition of professional skills" by Gregory Gromov,
   Microprocessor Devices & Systems, Moscow, 1986, N 3, p.80--91, Chapter 2


 Mathematics as the Basic Methodology of the Knowledge Industry

    As the industrial revolution progressed, the need for organized, actively-functioning scholarly apparatus in all fields of professional knowledge became more acute, so that the dissemination of knowledge could with time become a regular stage in a standard process, rather than have this knowledge remain an ‘in-shop sacrament’. It was at that time that most fundamental concepts and primary means of professional knowledge formalization appeared, today known more generally as the ‘knowledge industry’.

    This process appears to go back to ancient history, when priests—the first professional keepers of communal treasuries of knowledge—began to gradually assert their exclusive right to control this vast ‘magic’ and began to specialize in specific fields of primary interest. Thus emerged the first specialists: star-gazers became astronomers, ‘disease charmers’ became psychotherapists, and so on. As the socioeconomic need for specific, subject-oriented knowledge grew, different areas of knowledge that had been developing insularly under a lump-heading of ‘magic’ for thousands of years began developing into ‘pre-scientific’ disciplines, which then became the scientific and para-scientific disciplines that we are familiar with today.

    For instance, many nations had fairly highly-qualified priest-astrologers even thousands of years ago. However, the era of navigation made the shortage of such specialists only too evident. Facing this acute socioeconomic need, the greatest scientific minds of the Middle Ages were brought to bear on this problem. Shortly thereafter the first progress was made in divorcing the mysteries of the sky from their ‘divinely selected’ repositories.

    The successful formalization of astronomic knowledge made it possible to equip ocean vessels with navigational tools and books with astronomic tables, diagrams, and precise formulas, which all made it possible for practically any literate child (provided with the requisite diligence and education) to become a ship’s astronavigator (Celestial Navigatior) after a few years’ experience.

The success or failure of attempts to separate professional knowledge from its divinely-selected repositories has until recently been determined by the possibility or impossibility of formalizing this knowledge using mathematical methods. The fields of professional knowledge that lent themselves to such formalization were called ‘hard sciences’.

    In the three centuries after the printing-press’s invention in 1445, there was the accumulation of a critical mass of publicly-available knowledge, which brought on the avalanche of changes that was called the 'industrial revolution'.

    At the beginning of this process, the printing-press was an open valve on the wellsprings of information, drastically increasing the throughput capacity of the public exchange of knowledge.

The process of knowledge formalization became the process of sifting through a great variety of different pieces of information in a specific sphere of human activity to produce a relatively small but logically-significant nucleus that determined a great deal of other things and could be formalized using mathematics. If successful, this process made it possible to create a formal, standardized ‘local knowledge system’. As a result, the majority of relevant communications about gradually accumulating knowledge within a given area of expertise could be described linguistically while observing certain formal rules, thus eliminating ambiguity. Such a text would be intelligible to others and could thus be communicated, intact, to the entire professional community, or it could be proved false. Among other things, this meant that knowledge transfer from the author of a printed work to an interested reader within the local knowledge system became a practical, reliable, functional process instead of a rare, essentially happenstance event, the probability of which could only indirectly be improved by increasing the size of a print run.

The benefit reaped by formalizing any significant area of human knowledge had an effect that can only be compared to the biblical marvel of sight recovery. It is sufficient to mention a well-known poetic commentary on Newton’s scientific exploits:
    Nature and Nature's Laws lay hid in Night
    God said, Let Newton be! and all was Light

    ~Alexander Pope

    It was only natural that the level of mathematization was accepted as the main criterion for separating science from art, crafts, and other forms of pre-scientific activities. According to Immanuel Kant: “"in every special doctrine of nature only so much science proper can be found as there is [applied] mathematics in it".” Until quite recently, the study of nature seemed to include no facts significant enough to shake academic circles’ trust in this long-canonized mathematical criterion of truth. What is more, in recent decades and particularly in the early years of the computer era, the relative weight of the hard sciences in the general system of scientific knowledge began to increase ever more rapidly.

    The essence of the cybernetic boom of the early 1950s was the rapidly proliferating conviction among ‘hard science’ researchers that what they considered relatively slow development in certain fields of natural sciences—biology, for instance—was due to the fact that this field was worked by shallow-brained specialists devoid of mathematical knowledge, and that educated representatives of hard science had yet to get around to dealing with these problems: “We have no time to write a mathematical model of the cell (and maybe even the organism as a whole), otherwise we’d have an end to these centuries of fussing about with test-tubes and pipettes...“

    At the same time, economics, psychology and many others fields previously considered inaccessible to traditional mathematics also underwent similar ‘cavalry charges’ by hard science. Claude Shannon may have been the most accurate in describing the atmosphere of a 'mathematical Klondike' of the first decade of the computer era. In his article “The Bandwagon", published at that time, he openly warned his colleagues: “It will be all too easy for our somewhat artificial prosperity to collapse overnight ...


 "Autoformalisation - Knowledge acquisition of professional skills" by Gregory Gromov,
   Microprocessor Devices & Systems, Moscow, 1986, N 3, p.80--91, Chapter 2

  Copyright © 1986-2011 Gregory Gromov