Philip Doty
INF 380E
Perspectives on Information
FA 2012
ABBREVIATED STUDY GUIDE
Hobart, Michael E., & Schiffman, Zachary S. (1998). Information ages: Literacy, numeracy,
and the computer revolution. Baltimore, MD: The Johns Hopkins University Press.
Chapters 5 and 6 (pp. 112-172) from Part II: The Modern Age of Numeracy
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Chapter 5: “Numeracy, Analysis, and the Reintegration of Knowledge”
113ff
perhaps the most fundamental aspect of Hobart & Schiffman’s argument in this middle
section of the book is their description of Descartes’ proposal for a new sort of abstract
thinking, based on mathematics and mathematical reasoning [you may wish to do a little
research about what is commonly called “Descartes’ dream.”]
115
the strongest tool of this mode of thought was the symbolic language of the emerging
mathematics we now recognize as modern
as elsewhere in the book, here Hobart & Schiffman put a misplaced emphasis on the
turning away from experience that literacy and computation supposedly support
116ff
the concepts of correspondence (cardinal principle or “nomination”) and recurrence
(ordinal principle or rank) are quite useful and are among the strengths of this section of
the book – in your studies you will encounter these principles again, if you have not
already, in the discussion of levels of measurement
121
Similarly, the concept of positional counting or place holding is important, although their
claim that it might be the “’most successful intellectual innovation ever made on our
planet’” (Barrow, Pi in the Sky, 1992, p. 92) is overblown. What about language, writing,
reading, music, and so on?
the concept of zero is similarly fundamental
122
pay special attention to the status of “algorithmic techniques” and “algorithm” in Hobart
& Schiffman’s argument generally as well as in this particular chapter and section of the
book
focus as well upon the discussion of the (often obscure) origins and diffusion of
mathematical symbols
123
their evocation of the differences between modern, abstract mathematics (“’relation
mathematics’”) and pre-modern, concrete mathematics (“’thing-mathematics’”) is
especially worth considering. It gives us some specific insight into how we think,
especially about dynamic, process-oriented ways, but it still falls prey to the book’s
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dismissive attitude about our cultural forebears and to Hobart & Schiffman’s rather naïve
empiricist epistemology
124ff
the remarkable role that François Viète played in the development of symbolized algebra
is worth a close look
125
chief among his contributions was the combination of geometric and algebraic methods
126
as elsewhere, Hobart & Schiffman use the inexplicable “container talk” to describe
mathematical symbols – why they do not say symbols are signs or representations is well
beyond me ;~)! But that is part of what we wrestle with in this class.
127
of course, Descartes went further still than Viète by uniting Euclidean geometry and
symbolic algebra through the development of coordinate geometry, what we colloquially
call graphs with x- and y-coordinates (and sometimes more). Also note their mention of
Pierre de Fermat.
read the material about ordered pairs closely – it is of importance in and of itself, of
course, but it also sets up the latter stages of their argument about the calculus, maps,
and sub-atomic physics
136f
make note of their mention of the Cartesian tree of knowledge, shared by the French
philosophes, and its subsequent utility for the encyclopedic project in the late 18th century
[see Denis Diderot and Encyclopédie, ou dictionnaire raisonné des sciences, des arts et des
métiers]
Bibliographical Essay (pp. 285-287)
285
Hobart & Schiffman say that “[t]o date there exists no major study that interprets
numeracy and mathematics as information technology in the manner we have adopted”
– why? What does that say about the strengths and weaknesses of their approach? Has
one or more appeared in the almost 15 years since their book was published?+
They identify many of the major works in the history of numeracy and mathematics –
although there is not as much controversy about this topic as there is about the meaning
of literacy, radically different schools of thought and factions, too, characterize it
286
the concept of a mechanical, numerically describable cosmos is central to the modern
perspective and the basis of the post-modernist reaction to it. Hobart & Schiffman are
especially useful in giving us insight into the constituent parts of the modernist point of
view – read them carefully and follow their citations as your interests and expertise allow
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Chapter 6: “The Analytical World Map”
147
unfortunately, they invoke the concept of the “discovery” of the calculus – there is a
fundamental and radical rift among intellectual and cultural historians about whether
mathematics is developed or discovered. Hobart & Schiffman cannot simply pass over
this rift without doing their reader a major disservice.
Further, here as elsewhere, they use a particularly impoverished idea of information:
“the content of our exchanges with the outer world.” As should be clear from the
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material we engage in the Perspectives on Information class (INF 380E), this supposed
definition of information is inadequate in a number of ways. Two fundamental ones are
these: (1) how can exchanges have “content”?, and (2) it presumes an absolute
dichotomy between the self and the “outside world.” Hobart & Schiffman’s
epistemological and methodological clumsiness is much too strong at times – this is one
of them.
148ff
the discussion of Denis Diderot and Jean Le Rond d’Alembert is crucial to their argument
and should be part of the ordinary knowledge of any information professional. While we
may quibble with elements of their discussion, it is quite valuable.
Recall the power and limitations of the metaphor of the tree of knowledge, for the
encyclopedists as well as for Descartes
149
spend some time considering the hierarchic nature of encyclopedic arrangement and the
other encyclopedic metaphor of the map of knowledge
151
Leonard Euler is a pivotal figure in the history of mathematics, especially his convention
for denoting a function, i.e., y = f(x)
151ff
one of the most important concepts that you can take away from this section of the book
is its emphasis on the calculus as a dynamic system able to compare variations in rates of
change – this is a remarkable and pivotal achievement.
154
here and elsewhere, be certain to take the time to read the argument and integrate the
text with the figures – it’s well worth your time.
155
Their mention of determining the rate of change at a given moment is, of course,
evocative of Heisenberg’s Uncertainty (or Indeterminacy) Principle. It also encapsulates
the dilemma of observation: how to describe a changing, dynamic phenomenon.
159
this and related concepts are brought together in the notion that symbols in the calculus
and modern mathematics “stand for procedures, not merely things or objects.” A superb
point, but also remember the warning about their dismissive attitude toward earlier
cultural expressions that, according to them, were too tied to things.
160
for Hobart & Schiffman (and many others), the two “critical components of the analytical
vision and of the modern information age” are formulas and algorithms.
162
as throughout this chapter, the reductive vision of the modern, analytical point of view is
emphasized
166
a good reminder that the bases of analysis also grounded the encyclopedic vision and
that the philosophes believed that “these principles issued from the faculties of the human
soul or mind” – especially important are reduction and analysis
171
reductionism was important because it “provided closure to the process of exhaustive
information gathering”
Bibliographical Essay (pp. 287-288)
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287
Hobart & Schiffman use the term “Whiggish.” They exhibit many of the symptoms of a
Whiggish approach to history -- that is, that history is teleological (has a goal), recites a
narrative of “progress’ however defined, and that history takes us ever upward. Their
use of the term “ages” to identify their main focus carries some of this assumption.
Another major weakness of the historical approach is that they seem less than sensitive to
the cultural politics and complexity of many of the concepts they discuss. One of the
strongest symptoms of their Whiggish, teleological approach to history (although they
clearly know better) is their constant and unexamined evocation of the rhetoric and
ideology of “advancement,” e.g., their unquestioned participation in the narrative of
Renaissance “advancement” and of “invention.” With all this said, however, the book is
an unusually good one, and Hobart & Schiffman are to be commended for the many and
manifold strengths of the book.
288
be certain to put all of this section’s discussion, especially that in Chapter 6, into the
overall context of the Enlightenment and its history. As many of you realize, the
Enlightenment has been one of the major intellectual battlegrounds of the past several
decades, especially in the development of post-modernist perspectives on knowing.
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