The concept of a garden for handling knowledge is a very powerful idea-virus. It had a strong impact on my thinking - especially since it connected remarkably well with several of my old 'favourite ideas', as for example the concept of post-intellectualism. I have often argued that the so called 'post-industrial society' is better described as being 'auto-industrial' but 'post-intellectual'. In the historic year of 1968, the Swedish State Bank instigated the so called 'Nobel prize' of economics - thereby elevating the practice of economics into the 'noble status' of science. To me, this act symbolizes our definitive transition into the present post-intellectual state.
The trend of mathematics education that I have witnessed - more and more of 'know-how' and less and less of 'know-why' - is a natural consequence of this paradigm shift. It now occurred to me that a Garden of Knowledge would be the natural step forward - into the compost-intellectual information society. Just as any garden, this one would contain an 'intellectual compost' - in order to break down outmoded thoughts and concepts and encourage their organic recombination in the form of new ideas.
Since it is one of the aims of the GOK-program to support the concept-formation process and render it more visible in various ways, it became natural for me to refer to this program as a compost-intellectual philosophy s(t)imulator . The attempts to model the theorizing process in itself are based on an epistemology of science that has been put forward by Nicholas Georgescu-Roegen, who is one of the deep thinkers of the twentieth century. In his book The Entropy Law and the Economic Process he gives the following description of theoretical science:
Theoretical science is a living organism precisely because it emerged from an amorphous structure - the taxonomic science - just as life emerged from inert matter. Further, as life did not appear everywhere there was matter, so theoretical science did not grow wherever taxonomic science existed: its genesis was a historical accident. The analogy extends still further. Recalling that "science is what scientists do", we can regard theoretical science as a purposive mechanism that reproduces, grows and preserves itself. It reproduces itself because any 'forgotten' proposition can be rediscovered by ratiocination from the logical foundation. It grows because from the same foundation new propositions are continously derived, many of which are found factually true. It also preserves its essence because when destructive contradiction invades its body a series of factors is automatically set in motion to get rid of the intruder.
To sum up: Anatomically, theoretical science is logically ordered knowledge. A mere catalog of facts, as we say nowadays, is no more science than the materials in a lumber yard are a house. Physiologically, it is a continous secretion of experimental suggestions which are tested and organically integrated into the science's anatomy. In other words, theoretical science continously creates new facts from old facts, but its growths is organic, not accretionary. Its anabolism is an extremely complex process which at times may even alter the anatomic structure. We call this process 'explanation' even when we cry out ""science does not explain anything". Teleologically, theoretical science is an organism in search of new knowledge.
Some claim that the purpose of science is prediction. This is the practical man's viewpoint even when it is endorsed by such scholars as Benetto Croce or Frank Knight. Neo-Machians go even further. Just as Mach focused his attention on economy of thought without regard for the special role of logical order, they claim that practical success is all that counts; understanding is irrelevant. No doubt, if science had no utility for the practical man, who acts on the basis of predictions, scientists would now be playing their little game only in private clubs, like the chess enthusiasts. However, even though prediction is the touchstone of scientific knowledge - "in practice man must prove the truth", as Marx said - the purpose of science in general is not prediction, but knowledge for its own sake. Beginning with Pythagoras' school, science ceased to serve exclusively the needs of business and has remained always ahead of these. The practical man may find it hard to imagine that what animates science is a delight of the analytical habit and idle curiosity; hence, he might never realize what is the source of his greatest fortune. The only thing that exites a true scholar is the delight in adding a few bars to an unfinished symphony or, if he happens to believe in the ontological order of nature, in uncovering another articulation of that order. His interest in a problem vanishes completely the very moment he has solved it.
Others say that science is experimenting. As far as theoretical science at least is concerned, this view confuses the whole organism with one of its physiological functions. Those who commit this error usually proclaim that "Bacon is science's John the Baptist". Naturally, they also blame Aristotle's philosophy of knowledge with its emphasis on Logic for the marasmus of science until Francis Bacon's time. Facts have never been more ignored. To begin with, Aristotle never denied the importance of experience; one eloquent quotation will suffice: "If at any future time new facts are ascertained, then credence must be given rather to observation than to theories and to theories only if what they affirm agrees with the observed facts". In relation to the time in which he lived he was one of the greatest experimenters and keenest observers. As Darwin judged, Linneaus and Cuvier are "mere schoolboys to old Aristotle". His teachings should not be blamed for what Scholasticism did with them. Finally, mechanics was already moving fast on Aristotelian theoretical tracks at the time Bacon's works appeared. Without the analytical habit which had been kept alive by Euclid's Elements and Aristotle's writings, Kepler, Galileo and Newton, as well as all the great men of science that came later, would have had to join the Sino-Indians in contemplative and casual observation of nature. To the extent to which we may turn history around in thought, we may reason that without the peculiar love the Greeks had for Understanding, our knowledge would not by far have reached its present level; nor would modern civilization be what it is today. For better or for worse, we have not yet discovered one single problem of Understanding that the Greek philosophers did not formulate.
About this time I happened to think of the book Tankar från Roten by Tage Danielsson - and combined with traditional UNIX jargon this led to the idea of the root-priviledges of the gardener. Another fertile analogy was the comparison to the biblical approach. Here we find a Tree of Knowledge growing in Paradise, which could be described as the Garden of Innocence (? ignorance). It now occurred to me that we were dealing with a 'dual' type of situation - a Garden of Knowledge, which by reasons of symmetry ought to contain a Tree of Ignorance.
In my mind, this tree became associated with a state of randomness, where thoughts would be generated 'at random' by making use of different types of 'verbal one-armed bandits', which I had wanted to construct for a long time. When you pull the lever - instead of a variety of fruits - you would get a well formed sentence with the individual words selected at random out of suitable word-class repositories of nouns, verbs, adjectives, pronouns, preposition, etc. etc.
Moreover, in the contrast between the stochastic and the deterministic state lies the tension between the 'irrational dice magic' on the one hand, and a world model based on cause and effect - which forms the basis for the entire rational (? deterministic) scientific project - on the other. Here lies the conceptual basis for a description of the statistical (? stochastical) way of thinking that has been applied with such enormous success in modern times - within such diverse fields as e.g. quantum mechanics and financial mathematics.
Yet another strength of the GOK metaphor was that it could naturally accomodate the allegory of knowledge that is being transmuted into understanding. If the brain succeeds in the process of constructing a cocoon out of its mental reflections, then each 'catepillar of knowledge' is given a chance to develop its own eventual 'wings of understanding'. The analogy between the 'seeker of understanding' and the catepillar that spins itself into its own cocoon - based on an inner conviction (? instinct) of a necessary qualitative change - emphasizes the role of the teacher in assisting the students to nurture, focus and reflect on their evolving patterns of information (? knowledge).
To sum up, in the metaphor of a garden of knowledge I felt there was a strong conceptual environment for future development work, since this metaphor naturally represents the two-step process of weeding and reflecting which is necessary in order to transform information via knowledge into understanding.