
Sunday March 18, 2007
[ Society ]
Axiomatization of Transactions -- A Fable for Relational Algebra
David Hilbert had a program for axiomatizing science, in particular, and all the rest of thought, in general:
David Hilbert, Axiomatisches Denken, Math. Ann., 78 (1918) pp. 405– 415. English translation in: William Ewald (ed.), From Kant to Hilbert: A Source Book in Mathematics, Oxford 1996
Hilbert's program of axiomatization faced challenges even in mathematics, as Jan Brouwer unfolded his approach to doing mathematics.
What were axioms? Axioms were simply a set of consistent statements written in a language composed of symbols representing variables, constants and relationships. "Models" were then constructed to give meaning to the symbols in a manner consistent with the Axioms. In this sense, "natural numbers" composed a model for some arithmetic axioms, say the Peano Arithmetic Axioms. However, models were rarely "minimal" to the axioms unless constructed from the axioms in particular ways, all of which produced isomorphic models of a certain kind. Not all models of the same axioms were equivalent or isomorphic. So, a theory of models had to be developed to explore the relationship among models.
In the world of business and economics, and in the social milieu of transactions, digitization of these transactions, i.e. the tendency towards demarcating sharp boundaries for transactions, led to the axiomatization of "rules" governing these transactions while at the same time managerial hierarchies built continuity into vertical integrations of such transactions within large organizations.
As the number of transactions vertically integrated within an organization increased in proportion to the volume of business activities, the managerial hierarchy faced growing coordination challenges. However, axiomatization of many "business processes" (read "out-of-market transactions") had already begun to work its magic to make the managerial hierarchies independent of particular men or women. What was needed was a mechanics to propagate the axioms through individual transactions.
The mechanics was relational algebra and the machine that operated according to its principles was the relational database. The rest is history -- of modern business enterprises' use of IT technologies.
2007-03-18 00:43:23.0 --
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Friday December 09, 2005
[ Philosophy ]
Communities of Practice, Learning, Meaning, and Identity
I've begun reading Etienne Wenger's Communities of Practice: Learning, Meaning, and Identity.
I ran into this book while reading John Seely Brown and Paul Duguid's Social Life of Information, about which I've written here earlier. I've always been interested in how social groupings and organizations learn, evolve, prosper and survive, how we learn and work, and how we come to be who we are as individuals.
Wenger's book would be a good start for whoever wants to explore these topics. Wenger is also deeply interested in building the conceptual framework that will help with the design of organizations, artifacts and processes.
Wenger's ambitious enterprise suits the practitioner as much as it stimulates the theoretician. As the book plate says, the material "is presented with all the breadth, depth, and rigor necessary to address such a complex and yet profoundly human topic."
2005-12-09 00:13:05.0 --
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education
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learning
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