Picture-Based vs. Rule-Based Learning
Felix
T. Hong,
Department of
Email:
fhong@med.wayne.edu
Like most educators, I have taken for granted the conventional view of two
modes of learning. The preferred mode is to understand the subject matter being
studied. Rote memorization should be kept at a minimum and reserved only for
those topics that are almost impossible to rationalize, such as one's own
social security number or telephone number. As a veteran teacher, I am fully
aware of the desirability to write examination questions that encourage
thinking. Questions of simple recall type are to be used at a bare minimum and
should be reserved only for those facts that we wish to ingrain firmly in the
students' mind. It therefore came as a surprise to myself that there is yet a
third mode of learning - something in between true understanding and rote
memorization. For lack of a better terminology, I shall call it
"rule-based learning."
Although I have long been
intrigued by the topic of creative problem solving, my active involvement in
this area was fairly recently and almost totally unplanned. In fact, it was
quite accidental and was the consequence of a "merger" of two
unrelated activities of mine.
Like most contemporary
scientific investigators, my research topic has almost always been separated
from my teaching activity. I taught classical electrophysiology of nerve
membranes for years. But my research was about electrophysiology of
light-sensitive membranes - a different kind of electrophysiology that requires
a different approach and different methodology. The latter topic is
traditionally omitted in the standard curriculum of biomedical sciences. Having
worked on bacteriorhodopsin membranes for almost two decades, I gradually
strayed into molecular electronics and biocomputing. Being a relatively young
discipline, biocomputing aims exclusively at machine intelligence rather than
at human intelligence presently. However, it appears natural to extend
biocomputing research to include creative problem solving and education. Thus,
with an additional stretch of argument and through a tortuous big circle, the
great divide between my research and my teaching is eventually bridged.
In 1995, I wrote an
electrophysiology essay question for physiology graduate students who took a
comprehensive examination at the end of their first year. I was astonished and
disappointed by the outcome of the examination because only one out of ten
students answered my question satisfactorily, in spite of my attempts to provide
some hints in a review session about a week prior to the examination. I decided
to try the same question again on a student after I provided additional hints.
The student failed again and confessed that he really did not know what I
wanted. However, I was convinced that my question was clearly written
because at least one student gave a nearly perfect answer. After I eventually
revealed the desired answer, the student said "Oh! I know the basic
knowledge, but I just never linked it to the question you asked."
That evening I did nothing else
but thinking about this incident. Why did the student who knew the materials
fail to recognize the connection? Events like this have certainly happened to
me before, but I usually dismissed the incident as a consequence of rote
memorization. However, it was different this time. First, the student was known
to be intellectually capable in other endeavors. Apparently, rote memorization
was not the right explanation. Second, the incident took place at the time when
I was working on an article about biocomputing for an encyclopedia. Confluence
of these two unrelated factors led me onto a different path of thinking.
Suddenly, my research on biocomputing and my teaching activity became
"short-circuited" like a flash of spark touching off the two live
wires inadvertently held too closely. I had abruptly come up with a working
hypothesis (plausible but unsubstantiated explanation).
I asked the same student the
next morning: "Did you learn electrophysiology by memorizing a set of
rules and by mastering how to manipulate the rules in taking
exams?" He said "Sure! That is the most efficient approach [in
answering multiple choice questions]." As the student explained to me,
what he did was simply match the question to a set of previously learned rules,
identify the relevant rule to be used, and quickly find the correct answers
from the provided choices. As I subsequently found out, some other students
even went a step further by using a one-step procedure - identify the correct
choice by simply matching the keywords. Apparently, saving time and effort was
the primary driving force in determining these students' mode of learning.
The event reinforced a
long-held suspicion of mine: the standardized multiple choice test was to
blame. The student failed my essay question because my question demanded the
ability to generate new rules from old knowledge. For rule-based
learning to work, the rule being called for in an examination question must
have already been included in the repertoire of previously acquired
rules. Since standardized questions seldom require generation of new rules,
rule-based learning works satisfactorily most of the time. Surely,
practitioners of rule-based learning can still "think," if they have
previously acquired the necessary rules and have learned the correct procedure
("cookbook recipe") for manipulating the rules. Thinking is thus
reduced to the practice of manipulating previously established rules according
to some "canned" procedures. In this way, learning is relatively
passive and requires minimal intellectual investment. Superficially, the
practice is still logical thinking. However, it is certainly not creative
or independent thinking because it was pre-programmed by the teacher or
authority.[1] Pundits
may argue that cleverly written multiple choice questions can still enforce
independent thinking. However, in my opinion, learning to think by practicing
on multiple choice questions is like learning to ride a bicycle with the
training wheels permanently attached. Why? Because multiple choice questions
often contain most of the clues or hints, whereas problem solving in real life
requires active gathering of clues or hints. Besides, a student can only choose
the answer from a limited number of possibilities, which are either false or
previously known to be correct. The incurred thinking process bares little
resemblance to creative problem solving.
If
rule-based learning is so inadequate, what should the alternative be? What does
true understanding mean if rule-based understanding is not? Literature
about creative problem solving abounds. Imagination, intuition and divergent
thinking are usually associated with creative problem solving. However,
imagination, intuition and divergent thinking carry a mystical notion that
these qualities seem to be part of innate ability rather than human traits that
can be taught or learned. As shown in the psychoanalysis literature, free
association is a powerful approach to dig up those deeply buried or repressed
unconscious feelings and is certainly useful in creative problem solving. But
does not a practitioner of rule-based learning also utilize free association to
achieve a match between rules and test questions? What is sorely needed is a
set of specific recommendations that can be followed by students. In other
words, how can training enhance imagination, intuition and divergent thinking,
if at all possible? Perhaps certain steps, if not all steps, in creative
problem solving can be enhanced by training, especially those steps where
habits are involved. Part of the answers is contained in the biographices of
eminent scientists (especially physicists).
Albert
Einstein was described to be highly visual in his scientific endeavors. His
celebrated gedanken experiments demand audience participation in the
form of "visualization" of fictional scenarios. Richard Feynman
solved difficult physics problems by utilizing "Feynman diagrams."
Stephen Hawking also described himself as being visual in his approach to profound
cosmology problems. The much-valued ability of abstract thinking in
science actually demands concrete visualization in terms of diagrams of
representation. The history of mathematics offers a display of the human
being's incessant desire to abstract (or rather, extract) rules from concrete
pictures exhibited by natural phenomena. Moreover, the same set of rules often represents
a wide variety of superficially unrelated phenomena. Thus, the preferred
antidote to the practice of rule-based learning is what I call
"picture-based learning" or "picture-based reasoning." What
is wrong about rule-based learning is not the use of rules in reasoning but
rather the practice of complete separation of rules from pictures.
Although
it is most convenient to use real life examples to illustrate picture-based
reasoning or learning, an explicit definition seems desirable, and a number of
individuals who have heard my view have demanded it. Of course, picture-based
reasoning relies on visualized pictures or diagrams in reasoning. The
visualized picture may be a real and concrete picture. Or, it may be a somewhat
"fictionalized" picture like atomic orbitals. Or, it may be a
conceptual diagram that extracts the essence of an event in abstract terms,
such as the reaction coordinate diagram of the transition state theory and the
"peak and valley" landscape in evolutionary processes. Or, it may be
a mental picture based on analogy or similarity of the mathematical equations.
In this way, one resorts to what is known in mathematics as homomorphism.
For
example, in explaining the electrical processes of nerve phenomena when I teach
electrophysiology, I routinely resort to the homomorphism between the behavior
of a resistor-capacitor (RC) electrical network under the action of a battery
and that of a water reservoir (capacitor) with a small drain pipe (resistor)
under the action of a water pump attached to the bottom of the reservoir. The
two superficially unrelated physical phenomena behave according to the same
mathematical equations. Originally, I was motivated to this practice of
teaching by means of analogy because of the ever-declining mathematical
proficiency of medical students. I used the hydraulic analogy merely to side
step the unpopular practice of solving a first order differential equation.
Thus, a less familiar and psychologically more intimidating phenomenon
(electricity) is transformed into a user-friendlier phenomenon (water flow)
encountered in our daily life.[2]
Picture-based reasoning may take the form of
a metaphor, like referring to the response of a dictator to criticism in terms
of a physiological (and engineering) concept of positive feedback (a dictator
quenches criticism by throwing dissidents in jail or executing them, thus becoming
even more oppressive), or referring to the
"customers-are-always-right" approach in business in terms of a
similar concept of negative feedback (answering a customer criticism by giving
them what they want).[3] The more general form of
picture-based reasoning is thus heavily tainted with rule-based reasoning
(homomorphism of different kinds or levels of rules). In fact, purely
picture-based reasoning is rare and almost impossible. Many of us biologists
accept rules from physics and chemistry without questioning the validity or
fully understanding them, but use them to construct picture-based reasoning in
biology any way.
From the
above definition, picture-based reasoning demands representation of events or
phenomena by concrete diagrams, and the ability to process these diagrams by
means of pattern recognition. In contrast, rule-based learning
represents events or phenomena in terms of rules that can be enunciated by
spoken or written languages in a sequential fashion. Thus, in a typical
lecture, the instructor uses spoken words to present the rules but uses
audiovisual aids to convey the entire pattern ("big picture"). Rules
and pictures are inseparable in a typical and traditional lecture. However,
that does not mean students will assimilate both rules and pictures equally. It
is conceivable that a student, when under great time pressure and/or great
pressure to achieve, is tempted to retain the rules and ignore the pictures. As
a consequence, the rules so learned become somewhat abstract and devoid of
concrete meaning. It is obvious that picture-based reasoning often takes the
form of "parallel processing," whereas rule-based reasoning primarily
takes the form of "sequential processing." Thus, rule-based reasoning
is similar to the operating principle of expert systems, which was developed in
the early stage of artificial intelligence (AI) research, whereas picture-based
reasoning is akin to neural network operation that was launched as a
counterculture to traditional AI. From cognitive science's point of view,
rule-based reasoning comes close to what the left cerebral hemisphere does,
whereas picture-based reasoning is what the right cerebral hemisphere does
best.
Unfortunately,
giving definitions without providing real examples is itself an attempt to
enforce rule-based learning because definitions are rules by themselves.
Therefore, I could not resist the temptation to explain my view with some real
life examples. Such pertinent examples allow for establishing representing or
representative "mental pictures" about picture-based reasoning
itself.
As a
teenager, I had plenty of free time to engage in personal endeavors and hobbies
because I was lucky to have narrowly escaped the assault of a subsequent wave
of immense pressure for high school students to succeed academically; success
became measured solely by being admitted to one of a small number of elite
colleges. Therefore, I even had time to read "trash" novels in my
spare time.
I once read a
mystery novel, the title of which I have since forgot. Nor do I remember the
plot. But one event sticks firmly to my mind. The detective in the story scored
an important breakthrough and he was able to nail the murderer. Initially, the
detective was searching for a piece of hard evidence (a strand of hair or
something like that), but got nowhere after combing the carpet at the crime
scene. One day, a stroke of inspiration hit the detective. He decided to check
the alleged murderer's trouser cuff, which was recovered at the crime scene. He
found what he had wanted right there. Apparently, while falling down, the piece
of evidence had been trapped by the cuff before it hit the floor. I was so
impressed with that discovery that it became the only part of the plot I
remember almost forever.
A couple of
decades later, I inadvertently dropped a tiny but hard-to-replace screw. I
began a frustrating search on the floor in vain. Then, I recalled the story
line of that mystery novel, and I checked my trouser cuff and found it right
there.
The incident
repeated itself again several years later. Only this time, I wore a pair of
trousers without a cuff. Here is how picture-based reasoning could make a
difference. I would not have been able find anything had I simply followed the
rule: check the trouser cuff when you drop something to the floor.
Picture-based reasoning helped me formulate the notion of a "trap" -
something that can trap an object while it is in the process of falling to the
ground.[4]
Although the example I present above is trivial,
conceptualization often is formulated by means of picture-based reasoning. The
simple conceptualization process, which is based on the shape and a
"latent" function of a trouser cuff, [5] leads to a generalization
that includes pockets of my lab coat, where I found the dropped object instead.
This simple conceptualization is certainly not an extraordinary intellectual
feat, but the habit of making such attempts every time opportunity
arises can make a big difference in solving more serious problems. Several
times in my own research I managed to see clues that eluded most of my fellow
investigators, who were better trained than I. I owed my advantage to the
practice of picture-based reasoning. This trait (actually a habit) is commonly
referred to as having a good physical intuition. I believe that picture-based
reasoning is a better description than intuition itself because the notion of
intuition mystifies the accompanying mental process, whereas picture-based
reasoning depicts the process explicitly and makes it possible and feasible to
acquire that trait by conscious practices. I do not think the only way to
acquire good intuition is to pick the right parents, although I cannot prove
it. [6]
As another example, let us consider the following
problem. A lotus growing in a pond doubles its surface coverage every 24 hours.
If it takes 60 days for the lotus leaves to cover the entire pond, how long
does it take for lotus leaves to cover 50% of the pond surface? Picture-based
reasoning allows one to answer this question in a fraction of a second. All one
need to do is visualize a growing coverage as in a movie. In order to get the
answer, one need only run the movie backward and consider the "half
life" instead of the "doubling" time by pushing the entire
period of 60 days back one full day to get 59 days.
Surely, one can solve the above problem by rule-based
reasoning. Get a piece of paper and a pencil ready, write down the first order
ordinary differential equation, and solve it. Solving this differential
equation probably takes 5 minutes if one still remembers the rule so many years
after schooling: the (first) derivative of an exponential function is the same
exponential function. Otherwise, it may take somewhat longer, depending whether
one has a book of mathematical tables handy. Or better still, if one is in the
business of solving differential equations on a daily basis, one may recognize
that it is exactly the same problem as population growth and the answer is well
known - an exponential growth curve [not decay curve] and the doubling time
[not half life] is 24 hours. The answer will come out in approximately 1-2
minutes. Please note that the second approach is half picture-based and
half-rule-based reasoning because one must first recognize the same pattern
shared by population growth and lotus growth - the recognition requires
picture-based reasoning.
The above examples highlight several important points
about reasoning. First, picture-based reasoning is intimately related to
conceptualization and generalization. In doing so, one relies heavily on
analogy.[7] Analogy is best
implemented through pictures, although not exclusively so. Therefore, there is
a heavy component of pattern recognition and parallel processing - recognition
of the underlying analogy. Picture-based reasoning thus constitutes what
Gestalt psychologists frequently preach - Gestalt synthesis (Gestalt
means "form" in German). On the other hand, rule-based reasoning is
more precise, and better defined and straightforward and easy to verbalize.
Rules usually are concise statements of lengthy reasoning or even
crystallization of somebody else's lifetime work. Strictly speaking, concepts
are rules. Recipes (including the real ones enunciated by reputed cooks such as
Julia Child) are condensed forms of reasoning and wisdom. Direct uses of rules
and concepts save time. This may be why modern medical and premed students are
forced or lured into the practice of purely rule-based reasoning long before
students of other disciplines become similarly infected. I believe this new
trend has a lot to do with the information explosion and increasingly fierce
competition (arguments in support of this conclusion are omitted here). At the
very least, these two factors explain why there is a high incidence of this
malady among our own medical or premed students. Thus, saving time is
apparently an important strategy for student survival when the pressure to
succeed is mounting and when time becomes a premium. The problem is: Is
rule-based learning really timesaving, especially in the long run?
No, rule-based reasoning
does not always save time. As the second example above has illustrated,
recognition of a similar pattern in an entirely different problem (lotus growth
vs. population growth) allows one to cut through the tedium of having to solve
the same differential equation over and over again, and quickly get right to
the answer. This is especially so if the recognition and transfer of rules
(imitation) are done across the boundary of disciplines. Recently, I refereed a
scientific paper that applied finite elemental analysis to a problem of
electrode design for drug delivery (by means of electroporation) in cancer
therapy. It appears quite innovative in biology, but finite elemental analysis
has been around in engineering practices even before cheap and fast computers
became available to individual investigators. Finite element analysis is such a
common place in engineering that I have even seen it featured in a TV
commercial from one of the "Big Three" automakers.[8] Thus, by drawing inspiration or hints from resources and
discoveries made in other disciplines, picture-based reasoning prevents
"reinvention of the wheel."
Ironically, the most extreme form of rule-based reasoning
in the classroom also relies on "pattern recognition": recognition of
key words. It is an efficient approach in handling a large number of
multiple choice questions. However, it is a very serious educational problem
because a real life problem seldom presents itself with a combination of
correct and commonly known key words.[9]
There are several
consequences that I have observed as a teacher and as a course director of a
team-taught course.
A direct consequence of
rule-based learning to the students is their having to learn the same materials
over and over again, including as many times as possible variations or
disguises the same question can assume. A mere rephrasing of the same question
and/or a change of test format may throw the students completely in the dark.
This is why students are so voracious in reading old examinations.[10] This is also why students have to work so hard (the
information explosion is not the only reason) because they must study the same
problem in different (all possible) formats of variations and disguises.
Interestingly, in a neural network designed for face
recognition, the systems performance improved dramatically by merely suggesting
to the artificial neural network program that there is a left-right symmetry of
a human face.[11] By way of crude
analogy, students who resort to purely rule-based learning must memorize not
only the left and the right sides of a face, but also more views from many
intermediate angles, and then must independently store all these views as
separate "templates" for future retrieval when the need to recognize
the face arises. Although this analogy is absurd, the absurdity of the implied
approach is quite apparent.
Because of the
unnecessary duplication of efforts, students naturally have no time left to
think because of the unnecessary duplication of effort. Without adequate
thinking, they are forced to dig deeper and deeper into the practice of
rule-based learning, leaving them even less time for thinking. And there you go
again with a vicious cycle (positive feedback process). The pity was: lack of
picture-based reasoning might have prevented some students from recognizing the
fact that they were being trapped in the misery of a vicious cycle.
Students who took my
advice and started the practice of picture-based reasoning reported back to me
that picture-based learning is not really more time consuming. It is true that
picture-based learning requires an initial capital outlay in the form of extra
time needed to assemble the pictures and to explore the subject from different
angles. But once done, the acquired knowledge is retained much longer
("almost impossible to forget!"). Thus, picture-based learning saves
time in the long run. In contrast, the short retention of knowledge acquired by
means of rule-based learning forces students to "cram" their study into
the last few days or even the last few hours prior to an exam. In view of
ever-accelerating information explosion, rule-based learning leads to a
dilemma. If one starts too early to prepare for the exam one may not remember
by the time of exam. If one starts too late one runs out of time, instead. [12] Rule-based learning thus defeats the primary purpose of
education - retention of knowledge for future uses.
Another problem of rule-based learning is that the
practice gives a student a false sense of understanding, as the following
example demonstrates. A freshman medical student came to me after attending a
session of my lectures on electrophysiology. She told me that she had
previously taken a physiology course elsewhere in a highly reputed medical
school and had successfully handled a mock Medical Board Examination. She felt
totally lost in my lecture but insisted that she understood electrophysiology.
I therefore gave her a simple test about a well-known topic in electrophysiology
(and electrochemistry): Nernst potential. The Nernst potential in an electrical
voltage in a nerve membrane that arises from unequal distributions of an ion
such as potassium across the two sides of the nerve membrane, through which
only that particular ion can go via tiny ion channels (literally holes through
the membrane). My question is: a 10 to 1 ratio of potassium ion distributions
across the membrane ("ionic gradient across the membrane") gives rise
to a potassium Nernst potential of -61 mV at body temperature whereas the same
ratio of calcium ion distribution leads to a calcium Nernst potential of -30.5
mV, instead. Why?
She answered "because the Nernst equation requires
the computed calcium Nernst potential to be divided by 2." I asked why again.
She said, "because a calcium ion carries 2 positive charges instead of one
as in a potassium ion." I asked why again a third time. Why? Why? Why? -
Like a string of endless questions from an innocent child. Why not multiply by
2, or divided by the square root of 2, etc.? Aren't there a zillion ways to
manipulate the number 2?
The student finally admitted, "I really don't know
why." Thus, understanding in rule-based learning is somewhat superficial
and relies on others' judgment for its validity ("because the textbook
said so!"). While rule-based reasoning usually satisfies the requirements
of logical reasoning, rule-based learning eventually undermines logical
reasoning; persistent reliance on others' judgment eventually eliminates one's
ability to judge. This is why our students often present ridiculous and absurd
arguments in their answers to essay questions without realizing their logic
flaws. They have no way of knowing for sure whether the arguments are valid
other than just giving it a try and let the teacher decide.[13]
I then spent the next
fifteen minutes explaining the picture behind the mathematical
derivation of the Nernst equation without writing a single mathematical
equation.[14] She had no difficulty following my reasoning, and
admitted that it wasn't hard, and wasn't time-consuming either. I further
convinced her that learning the Nernst equation via diagrams is a lot more
reliable than merely memorizing the equation. This is because the Nernst
potential carries either a plus or minus sign, which depends on the sign of the
charge carried by the ion (plus for potassium ion and minus for chloride ion)
as well as the "sense" of ratio of ion distribution across the nerve
membrane (a regime with a 1 to 10 ratio gives rise to a sign opposite to that
of a regime with a 10 to 1 ratio). Thus, a single mistake in memorization leads
to the wrong sign, and two mistakes compensate each other and gives rise to the
correct answer. Topics like that are potentially confusing if one relies solely
on memorization. With some practices, my fifteen-minute verbal rendition of
picture-based reasoning can be executed in less than five seconds quietly in
one's own mind. It is foolproof but not really time-consuming. The
understanding is also deeper.
Thus, picture-based
learning relieves the burden of having to memorize many rules that can be
derived de novo or "re-discovered" in a reasonably short time.
The time saved can then be diverted to study of other subjects for which rote
memorization is a demanded premium, such as anatomy.[15]
Rules are usually made
by others, especially by those who are good at picture-based reasoning. The
wisdom associated with the rules usually gets distorted or lost during the
information transfer (teaching of the rules). Therefore, another big draw back
of strictly rule-based learning is misuses of the rules for lack of fully
understanding the wisdom behind the rules, or abuses of the rules for lack of
fully recognizing the limitation of the rules.[16] This conclusion applies not only to science but also to
real life situations in terms of regulations or laws, as the two following
examples will illustrate.
I once took a newly arrived graduate student from a
foreign country by car around
As a second example, a freshman medical student
challenged one of my examination questions for its validity. The question was
about how a change of the sodium ion distribution across the nerve membrane can
affect the amplitude of an action potential (the size of a nerve impulse). The
objection of the student was based on a well-known and well-publicized rule
called "all or none principle," which states that if the stimulus to
a nerve is intense enough to excite the membrane a full-fledged nerve impulse
(with full size) appears; whereas if the stimulus is inadequate, no nerve
impulse emerges (a weaker stimulus does not lead to a smaller nerve impulse);
sort of like "winners take all" in a U.S. presidential election by
the electoral college voting. The student forgot the rule applies to a
situation where the only factor that is stipulated to change is the stimulus
intensity, while implicitly the ionic distribution across the nerve membrane
are held unchanged. It worried me a lot; not because the student did not learn
enough electrophysiology; but because the same mode of reasoning may cause a
patient to die prematurely and unnecessarily in the future.
While I was developing my "view" about
rule-based vs. picture-based thinking, I often brought up the topic at cocktail
time. Some colleagues questioned the validity of my view presumably because my
"success" cases are anecdotal (based on a small number of subjective
observations) and/or because I was not trained in education (few, if any,
college professors are graduates of a college of education). It is therefore my
obligation here to demonstrate the scientific basis of my view. I will
highlight the scientific basis in three disciplines: cognitive science,
artificial intelligence and biocomputing. A more detailed, more rigorous and
perhaps more scholarly exposition will be published elsewhere.
Here, I must point out that traditional research in
education relies on psychology and cognitive science whereas machine
intelligence research belongs to the realm of engineering and computer science.
Biocomputing is a relatively young discipline that can be described as a hybrid
of cognitive science and computer science and engineering, and may offer some
new insight into education. Curiously, biocomputing primarily aims at machine
intelligence, and the author's attempt to include education as part of the goal
has already elicited some protests from several colleagues in the name of
maintaining focus in a given discipline ("If you include everything in
biocomputing, you don't have a [research] field."; perhaps it means that
the membership in a research field should be made somewhat exclusive.). The
author's view remains relatively untested and therefore must be regarded as
unproved. However, by now it is obvious that repeated attempts for educational
reform, made since the 1983 appearance of the famed document "A Nation at
Risk,"[17] were not working
satisfactorily. In my opinion, it was getting worse over the last two decades
based on my "anecdotal" and somewhat subjective observations. My
approach to instigate picture-based learning apparently has worked for those
students who were willing to try. I am thus eager to share my views and to make
them available to those students who are willing to take a risk and try it out.
If one suspects a reason why a house has been repeatedly on fire, it seems to
me very foolish to ignore the suspicion until a large number of repetitions
eventually permits a valid statistical analysis.
From the point of view
of computer science, it is quite apparent that the two modes of reasoning,
rule-based vs. picture-based reasoning, are intimately related to a major issue
in artificial intelligence: pattern recognition and machine vision. A linear
sequential algorithm in digital computing is similar to rule-based reasoning.
It comes as no surprise that rule-based reasoning is most suitably developed in
an environment of digital computing because it is easy to program the rules by
means of a linear program in a step-by-step fashion. The decision making steps
are implemented as "conditional jumps" in a branching linear program,
e.g., "if then ... else". Rules are usually made in such a way that
the dichotomy of "yes" or "no" can be handled by the very
digital nature of not admitting any signals unless the signal is either a
"1" or "0" (typically, in hardware, a "5 volt" or
a "0 volt" signal). A number of early AI expert systems were so
successful in part because problems that are amenable to rule-based reasoning
were preferentially selected for implementation. But medical expert systems
failed to put physicians out of job because physical diagnosis is still partly
science and partly art (requiring an overall judgment based on conflicting
information).
The existence of
conflicting rules in digital programming is considered a program
"bug." Resolving mutually conflicting rules requires an ability
tantamount to political wisdom. Thus, digital computing or linear sequential
programming is utterly incompatible with a political or esthetic judgment
because the latter requires judgment as a whole and assigning appropriate
(desirable) weights to conflicting factors. By the same token, digital
computing is ill suited for implementing the capability of pattern recognition.
Almost by definition, pattern recognition requires judgment on the pattern as a
whole. This is in part because pattern recognition requires matching patterns
that are not exactly identical, in size, in shape, in spatial
orientation, and often in disguised appearance. Pattern recognition
demands only a crude match of "shape" and in fact requires a
crude match. In other words, pattern recognition requires the ability to
distort and stretch the "template" before making the match. Pattern
recognition relies on the ability to distinguish between essence and triviality,
or rather, between signals and noises. Digital computing cannot
tolerate "imperfections." Yet tolerance to "imperfections"
is the key to pattern recognition much like "compromise" is the key
to political wisdom. In short, digital processing has little natural affinity
for pattern recognition, much less value judgment.
Informed readers in
computer technology will certainly object to my rather "rigid" and
harsh indictment of digital computing. They will cite the emergence of
"fuzzy logic," and neural network processing as counter-examples to
my claim. The points are well taken, and I certainly should make a more
"flexible" interpretation instead. Both "fuzzy logic" and
neural network processing have been successfully implemented in the environment
of digital computing. But digital computing is not a natural environment either
for "fuzzy logic" or "pattern recognition." Computer
scientists and engineers have to create a virtual environment within the
digital environment, and to create a virtual machine within a real
digital machine. This implementation has often incurred an enormous software
overhead because of the need to emulate a virtual machine in a digital
machine.[18] However, increased memory size and the enhanced speed of
modern digital computers make such emulation possible. But it is neither as
efficient nor as flexible as computer experts haved wanted and/or real life
problems have demanded. This is one of the reasons why scientists and engineers
are trying to find an alternative approach by seeking inspiration in biology,
thereby leading to the birth of a new discipline - molecular electronics. But
this field is still in its infancy.
On the other hand, neural network processing is more
flexible in processing pattern recognition or in decision making under
ambiguous conditions. The kind of catastrophe usually associated with
programming "bugs" is minimized or eliminated in part because
information processing is distributed among many "synapses" in the
artificial neural network. A neural network program can be trained and can
learn with or without supervision. A training session sometimes involves
presentation of a large number of examples to serve as representative patterns
or pictures.
The above reference to artificial neural network
computing does by no means imply that real neural network computing (i.e.,
brain function) resorts only to picture-based programming. In fact, cerebral lateralization
led to the segregation of the two modes of information processing: for a
naturally right-handed person, the right cerebral hemisphere is critical for
the exploratory processing of novel cognitive situations whereas the
left hemisphere is critical for information processing based on pre-existing
representations and routinized cognitive strategies. Here, I use the
more modern interpretation proposed by Elkhonon Goldberg of
Thus, in cognitive
terms, our premed and medical students have increasingly levitated towards the
use of their left brain at the expense of their right brain. In artificial
intelligence terms, our premed and medical students have been trained like an
expert system (or "robot"), and education is reduced to the
fabrication of examination-taking machines. But, unlike the digital
computer-based expert systems, our students lack the vast data base, the high
speed, the unfailing accuracy and extraordinary stamina of a good expert system
-- not to mention that they are expensive to make. Furthermore, examination-taking
machines quickly become obsolete because of information explosion. While the
first round of expert system uprisings failed to put physicians out of jobs,
the outcome of repeated assaults from future generations of artificial
intelligence remains to be seen.
A lingering question
remains. Why does the human brain resort to both rule-based and picture-based
reasoning? Clearly, rule-based reasoning must have some survival values despite
my misgivings mentioned above. I have looked into the problem and, through
introspection, I propose the following explanation. In solving a problem, the
human brain needs to examine a large number of possible solutions before
arriving at a workable one (what cognitive scientists refer to as "search
space"). The accompanying information processing is handled in short-term
(working) memory. But short-term memory fades quickly. It is therefore
advantageous to utilize rules or concepts ("compressed" or
"zipped" information) in order to score a quick match between the problem
and one of the solutions. The ability to search available options at
high speed enables one to search for more options within a given time (larger search
space). Slow searching makes the process ineffective because the working
memory cannot hold the temporarily stored options forever for a delayed
comparison or delayed processing. Thus, one big advantage of rule-based
reasoning is speed and efficiency in solution searching. But is it also
effective?
Exclusive rule-based
reasoning is not effective because it lacks the exploratory nature of
picture-based reasoning. A big drawback of strictly rule-based reasoning is its
inability to cope with a novel situation or novel problem. An
important phase in creative problem solving is searching for possible matches
between a problem and available solutions. Picture-based reasoning allows for a
bigger search space by recognizing the analogy between superficially unrelated
phenomena, of which the subtle analogy may escape detection by purely
rule-based reasoning. Alternatively, given the same size of search space,
picture-based reasoning allows for detection of matches that eludes those who
practice rule-based reasoning exclusively.[20] Thus, picture-based reasoning is effectively increasing
the search space by looking into areas that would otherwise be neglected or
effectively enhances the ability to recognize solutions that are normally
ignored.
Rule-based reasoning serves yet another important
function. French mathematician Henri Poincare once said " ... it is by
logic that we prove. It is by intuition that we discover." Because false
matches by picture-based reasoning are not uncommon, subsequent verification is
necessary. Verification is usually performed in terms of logical reasoning
which applies well-established rules in a sequential and rigorous fashion; a
crude match cannot be tolerated. As pointed out above, misuses or abuses of
rules are likely because condensed knowledge gives scanty clues about its range
of validity. It is often necessary to "decompress" or
"unzip" the condensed rules or concepts in the step of verification. [21] Persons who practice
exclusively rule-based reasoning are less likely to remember or even pay
attention to the detail of "decompressed" or "unzipped"
knowledge or the reasons leading to formulation of rules. Thus, practitioners
of purely rule-based reasoning often suffer from misuse or abuses of rules (see
examples above).
While properly executed
rule-based reasoning constitutes a form of thinking - logical reasoning,
exclusive uses of rule-based reasoning or learning present a slippery slope.
When pressured by time, knowledge about the reasons behind the rules becomes a
luxury. Pretty soon, judgment by authority becomes the sole criterion of
validity. Habituation eventually "desensitizes" an individual to the
point that one really cannot care less about the validity of rules.[22] Thus, logical reasoning become quickly transformed into
a guessing game. Rule-based learning thus disintegrates into pure rote
memorization.[23]
Some concerned teachers
often point out the declining proficiency of mathematics among American
students as a major factor contributing to their inability to think logically.
Superficially, this is a plausible cause because mathematics (especially
geometry) provides an excellent training ground for logical thinking for many
of us. Although there may be some truth in this assertion, the problem goes
deeper than that. In fact, many individuals trained in humanity and social
sciences became superb thinkers, apparently without much help from training in
mathematics. On the other hand, training in mathematics does not guarantee the
ability to think creatively or logically.
I accidentally found
that some engineers, though amply trained in mathematical manipulation, knew
only the mathematical rules (procedures) without knowing the reasons underlying
the procedures. Mathematics is just a black box into which one plugs in the
parameters, and canned procedures bring out the solution automatically.[24] This was probably the consequence of American
pragmatism. American students often say that "hands-on practice is cool,
but theory is nerdy." It seems to me that a significant fraction of
mathematics-literate Americans know the mathematical rules but lack an
intuitive feeling about the subject matter. Again, this was a consequence of
rule-based learning. This is also analogous to the following situation. Those
who are accustomed to using a calculator but are not familiar with long hand
calculation eventually lose the intuitive feeling about numbers and become
insensitive to blatant arithmetic errors at a supermarket checkout lane.
On the other hand, because of the tendency for students
to disregard the reasoning behind mathematical rules, I usually view reports of
superior performance in mathematics and science by Asian students with some
reservation and skepticism because that type of reports were often based on
standardized tests. However, a total denial to the warning about the decline in
the performance of American students as compared to their Asian counterparts
will almost certainly postpone a timely solution until it becomes too late.
As a closing remark, I now routinely preface my teaching
with equal emphasis on rule-based and picture-based learning.[25] Since rule-based
learning needs no incentives from the teachers' encouragement, I usually take
pains to explain the shortcomings of exclusive rule-based learning. First,
picture-based learning ties superficially different but fundamentally similar
phenomena together, making information storage more organized and information
retrieval more feasible and efficient, and thus effectively averts premature
information overflow and overload. Second, picture-based learning facilitates
retention of information over a prolonged period. Third, picture-based learning
is less time-consuming in the long run because it eliminates the need to learn
similar and related phenomena or mechanisms over and over again separately as
individual and unrelated modules of knowledge. It also eliminates the need to
memorize certain subjects or formulas if one can reconstruct the knowledge or
derive the formula quickly at a moment's notice. Fourth, picture-based learning
fosters innovation because of its inherent exploratory nature and of its
inherent affinity for recognizing novel solutions. Picture-based reasoning
provides a natural environment to implement what psychologists and
psychiatrists refer to as "free association", and free
association is essentially a mental linkage of superficially dissimilar but
fundamentally related "pictures" or "patterns."
Picture-based reasoning makes one more creative by recognizing solutions that
eluded others by virtue of the enhanced ability to make an imperfect or subtle
match of patterns. Fifth, picture-based reasoning strengthens logical reasoning
because of an enhanced feeling about the reasoning behind the formulation of
rules, and thus averts misuses or abuses of rules and the uses of pseudo-logic.