cal engineering”b: it is focused on the
creation of new mathematical objects
under constraints, such as low time
and space complexity for discrete algorithms, good numerical convergence
for numerical algorithms, or good
precision and recall for classifiers; the
difference between mathematics and
“mathematical engineering” is precisely the emphasis on such constraints.
As technology progresses, new constraints need to be considered. For example, time complexity is increasingly
irrelevant when communication (to
memory, disk, and network) replaces
computation as the main performance
bottleneck, and when energy consumption becomes the critical constraint.
New technologies that will take us “
Beyond Moore’s Law” (quantum computing, molecular computing) will require
new mathematical abstractions.
Part of C&I, namely computer engineering, has always been concerned
with the interplay between the mathematical abstractions and their physical embodiment. In addition to mathematics, physics is foundational for
this specialty, and will continue to be
so. Physics is also important for cyber-physical systems that directly interact
with their physical environment.
b Mathematical engineering was apparently
used as a synonym for “computer science” in
Holland, in the early days of the discipline. It
is now used by some schools as a synonym for
“scientific computing.”
I believe, however, that physical
constraints are a small fraction of the
constraints relevant to the design of C&I
systems. For example, software engi-
neering research has strived for de-
cades to define code metrics that rep-
resent how complex a code is (hence,
what effort is required to program or
debug it)—with limited success. Such
a code metric would measure how dif-
ficult it is for a programmer to com-
prehend a code. But this is a cognitive
issue: It is highly unlikely that one can
develop successful theories on this
subject without using empirically vali-
dated cognitive models that are based
on our best understanding of human
cognition. Unfortunately, traditional
software engineering research has not
been rooted in cognitive sciences.
figure 3. c&i—an inclusive view.
use-inspired
basic research
Applied
research
Prototypes
Mathematics,
statistics,
social sciences,
physical
sciences…
Products
Foundations
Science,
engineering,
arts, humanities,
business,
medicine
Systems, applications,
data repositories
Application areas
and the technical: One may well argue
that the essential insight that enabled
efficient Web search and led to the creation of companies such as Google is
that the structure of the Web carries
information about the usefulness of
Web pages—a socio-technical insight.
Progress in graphics and animation
increasingly requires an understanding of human vision: otherwise, one
makes progress in quality metrics that
have low correlation to the subjective
quality of an image; examples can be
easily multiplied.
Another important aspect of the
evolution of our field is the increasing
importance of applications. Precisely
because software is so malleable and
universal, one can develop very specialized systems to handle the needs
of various disciplines: computer-aided
design, medical imaging, DNA matching, Web auctions—these are but a
few examples of application areas that
have motivated significant specialized
C&I research. Such research cannot be
successful without a good understanding of the application area.
This suggests a new view for the
organization of C&I that is described
in Figure 3: Mathematics is no longer
the only foundation. For those working
close to hardware or working on cyber-physical systems, a good foundation
in physics continues to be important.
An increasing number of C&I research
areas (such as human-computer interaction, social computing, graphics and
visualization, and information retrieval) require insights from the social sciences (cognitive psychology, sociology,
anthropology, economics, law, and so
forth); human subject experiments become increasingly important for such
research. At a more fundamental level,
the development of artificial cognitive
systems provides a better understanding of natural cognitive systems—of
the brain and its function; and paradigms borrowed from C&I become
foundational in biology. Insights from
neuroscience provide a better way of
building artificial intelligent systems
and biology may become the source of
future computing devices. Finally, research in C&I is strongly affected by the
multiple application areas where information technology is used (such as science, humanities, art, and business),
and profoundly affects these areas.