56.

Hospitable Formalism
R. A. Fairthorne

The formalism of a developing science has to grow with,indeed rather ahead of, that science, adapting to changes in
the phenomena studied and the way in which they are studied
and interpreted.
The assumption behind all formalized sciences is that this is possible, if only in retrospect, provided that changes in interpretation do not contradict experience as it stands at the time.
It is also assumed by many
that where the existing formalism is inadequate to novel situations, the inadequacy arises from the formalism being a special case of a wider or deeper unifying formalism.
Thislast assumption implies that even if drastic changes takeplace in the understanding of the phenomena, these affecttechniques and procedures only in the novel areas.
For instance, even after many years relativistic principles are still
irrelevant to most applications of physics to engineering, andwhere relevant do not invalidate the techniques of Newton,
d'Alembert and St. Venant, but extend them.
On the other
hand, understanding and interpretation of mechanical phenomena is profoundly affected.
This suggests that for a developing science the soundest
approach is to start formalism at the most concrete procedurallevel that just qualifies as a part of information science,and then develop outwards and upwards.
If the formalism ison the correct lines its elements, structures and principles
will need redefinition and refinement as its scope and store
of experience expands but, with good fortune and some prophetic
talent, these modifications will be ahead of existing techniques
for dealing with current situations.
They will, in fact, allow
early warning of changes in technique through scale factorsthat indicate the balance of influences on phenomena (cf theReynolds, Mach and Glauert Numbers in aeronautics).
To

57.

achieve such scaling factors we must to some extent know theanswers in advance; one of the less advertised requirements
for all science, technology and mathematics.
But even apartfrom this there are two obvious springboards, Information (ieSignalling) Theory, and Discourse in the timeless, non-spatial
sense of, say, library classification.
The first contains
the distinct, if not strictly defined, elements of Message,
Code and Channel.
A message here is an abstract entity, oneof a socially agreed set of distinct items.
The task of thesignaller is to indicate which message has been chosen bymeans of a set of patterns, the code, that have to be represented by patterns of events in a physical medium and environment, the channel.
Discourse, in the narrowest effective sense, is notdirectly concerned with the physical world, it deals directlywith whom, the Source, speaks to whom, the Destination, about
what, the Designation.
Neither Signalling nor Discourse can exist without theother, or without other activities.
But between them theycertainly contain the six elements that are enough to formalize basic procedures, provided that we look at the latter asof the form 'influence of A upon B as mediated by C .
Thetwenty such configurations cover all the procedures ofNotification,ie those parts of discourse that are delegable, andare not changed by the discourse.
That is, Notification is1
the frozen, 'snapshot , aspect of discourse at a given timeand place (the 'timelessness' and •unlocalized1 nature of discourse exists only at the place of the delegable activity andonly as long as the activity lasts).
If we study the successive notification structures asunits of a higher level we should arrive at a formalism of
discourse in which the structure of discourse is changed byreason of the discourse itself, the level of Conversation.
The procedures of Conversation, whatever they may turn out tobe (clues to this lie in Rhetoric), should in their turn be
the elements of the next higher level, in which not only theterms of discourse, but also the cognitive structure of thediscussants changes by reason of the discourse.

This is thelevel, or floor of the level, of CognitionSuch an approach, by elements and levels, is hospitableto various philosophical viewpoints.

For instance, on theNotification level, both the view that science fbreaks thecode1 of the physical universe, and that it constructs a code
to fit observation, can be accommodated though not, of course,
at the same time.

The first view is represented by conjoin-

ing the Observation and Readership triads, the second by conjoining Observation and Authorship.
A possibly greater advantage is that it not only clears
up confusions between various interpretations of 'information1and its measures, but also indicates where different interpretations and measures (where applicable) are likely to befound. The selective information of Shannon clearly applies
on the Notification level, in the sense that similar entropic
measures - not necessarily of any kind of information in any
sense - can be applied to any of the twenty triads, not onlyto Signalling.
Information about changes of the structureof discourse can be measured only at the second level,Conversation.
Its measure may have the same entropic form,
but the elements will no longer be the elements of Notification
but the procedures of Notification.
Similarly, for the various manifestations of 'Information1
at the Cognitive level.
The mathematical tools of information science should beequally hospitable in order to keep pace with the developmentof the formalism.
Statistical and combinatorial techniques,properly selected, do not need any boosting.
Algebraic techniques as usually employed are inadequate to deal with eventhe existing situations.
This could be corrected if Boolean
algebra applied to Notification procedures were regarded as adegenerate form of Brouwerian or its dual, Heyting algebra,
eg even if the difference between 'ail-but-not-only' and 'onlybut-not-all' parts of a collection were vanishingly small,there would still be a limit on the length of a hierarchical59.

chain and on the number of terms that can be effectively coordinated in retrieval operations.
Similar considerations
give limits to the precision of (selective) information measures corresponding to these situations.
The parallel here
is to the effect of even a vanishingly small viscosity in theformulation of fluid flow.
Introduction of a zone of imprecision, however narrow, between a subset and its complement,(which is, in terms of information retrieval, the distinction
between Brouwerian and Boolean algebras) formally extends thetechniques to cover the joint effects, but may have no numerically significant effect throughout a given operation at agiven place and time.