Biomedical Engineering Reference
In-Depth Information
logic and explicit rules, that is, verbal reasoning. In brief, visual thinkers invoke visual rea-
soning during the solution-generating phase, while invoking verbal reasoning during the
solution-verifying phase.
The above scheme was based on Poincaré's hint, as cited above. However, he gave only
half of the story, presumably because he had no direct knowledge of the thinking process
of people who were severely handicapped in creativity. It is possible to invoke verbal, log-
ical reasoning during the solution-generating phase so as to discover solutions to certain
types of problems. High-school students, who learn Euclidean geometry, know that some
theorems can be found as logical consequences of other more fundamental theorems or the
combination thereof. These less fundamental theorems are often referred to as corollaries
or lemmas. But important discoveries as such have long been exhausted. Modern investi-
gators must rely on intuition to make major discoveries. As Poincaré once said, “Pure logic
could never lead us to anything but tautologies; it could create nothing new; not from it
alone can any science issue” [141].
It is apparent that the practice of visual reasoning in the solution-generating phase ensures
highly
inclusive
gathering of
potential
solutions, whereas the practice of verbal reasoning in
the solution-verifying phase ensures highly
exclusive
gathering of
accepted
solutions. In other
words, visual reasoning during the first phase avoids exclusion of false-negative solutions,
whereas verbal reasoning during the second phase avoids inclusion of false-positive solu-
tions. It is therefore obvious that this combined approach offers a better chance of solving
difficult and novel problems; failure in either or both phases diminishes the chance of suc-
cess, except by dumb luck. Obviously, those who stick to verbal thinking during the entire
problem-solving session are at a significant disadvantage. It is particularly precarious, if the
problem-solver combines the solution-generating phase and the solution-verifying phase
into a singe step of verbal thinking. It is even faster than the two-phase routine, but it lacks
the benefit of double-checking. Needless to say, the chance of solving a given problem by
luck alone diminishes exponentially with increasing complexity of the problem—a well-
known consequence of combinatorial explosion. Visual reasoning is a top-down constraint
to limit the search for solutions to a most likely range (i.e., free associations by pictures rather
than by keywords), while allowing sufficient exploration by means of loose matching. It is
an approach known as heuristic searching in the literature of artificial intelligence and
operations research [133,142].
This general principle of heuristic searching is demonstrated by the agent technology in
problem-solving computer programs [143]. Software agents, of which “cookies” are better
known examples, are empowered with limited freedom. Here, the computer programmer
provides a general strategy in the main program but does not micromanage the detailed
task. The general strategy prevents the computational resource from spreading out too
thin, whereas limited freedom allows the software agent to explore a wider range of
options than the programmer could have conceived ahead of time.
Our interpretation of human creativity also has the merit of explaining difficult concepts
such as intuition, the “aha” phenomenon, and the unpredictability of creativity. The key
concepts to be invoked are parallel and sequential processing. In brief, visual reasoning is
a parallel process, whereas verbal reasoning is a sequential process. This division of work
is reflected in the well-known cerebral lateralization: the dominant (usually left) hemi-
sphere is specialized for verbal reasoning, whereas the nondominant hemisphere is
equipped to perform visual reasoning. Mainstream psychologists usually dismissed any
correlation between creativity and the use of the right brain. But I believe it was a prema-
ture—i.e., false-negative—conclusion based on misinterpretation of experimental data
(see Section 4.15 of [132]).
The implication of creativity research to biosensor technology is obvious. Future smart
sensors ought to be empowered with the capability of analog pattern recognition and,
