Dr. Juan Carlos Olabe (Electrical & Computer Engineering) presented a paper entitled “Solving Complex Problems with a Computational Mind: An Alternative to Heuristic Search” at the 2015 Hong Kong International Conference on Education in late November. In addition, Dr. Olabe and members of his research team met with leaders of the Lasallian family of schools in Hong Kong (there are eight Lasallian K-12 schools in the city). Two areas of collaboration were defined: the integration of the Computational Thinking curriculum developed by Dr. Olabe’s team in the local Lasallian schools, and the creation of a Computational Thinking Institute at La Salle College in Hong Kong to provide academic resources and teaching training support to the Lasallian schools in Asia and the Pacific Region as well as other school systems in the region. Hong Kong tops the list of countries in the international PISA tests in Sciences and Mathematics, and two of the Lasallian schools are members of the elite group Hong Kong Grant Schools.
It was Thanksgiving Day back home. I was on a morning walk
on the streets of Hong Kong, where it was another normal weekday. One of the
many things that surprised me, including the beautiful and somewhat unsettling
scaffolding structures constructed out of simple bamboo tied with plastic
strings and covering gigantic high rise buildings, was the large number of
young students, many walking alone, many with their friends, many with their
parents, most wearing elegant school uniforms purposefully walking to school.
School in Hong Kong’s culture is an enterprise, an endeavor
that requires boldness and boundless energy. This commitment to excellence is
rewarded with an outstanding education (Hong Kong is at the top of the
international PISA tests in Science and Mathematics.) At the same time it levies
the lives of families with insatiable demands of time and effort, not only for
the children, but the parents as well.
I was visiting with some of my research team colleagues at the
Lasallian family of Schools in Hong Kong. There are eight Lasallian schools in
Hong Kong. Two of them, La Salle College and St. Joseph’s College, are among
the elite schools in the city. The Lasallian family has been in that part of
the world since the beginning of the 20th century. Its history is marked, like
the rest of the city, by long periods of prosperity and short but intense
periods of crises and war. The classrooms where much learning has been
engendered for generations were also the temporary barracks for invading and invaded
armies, and generous makeshift hospitals.
My research team and I collaborate with these schools in the
area of Computational Thinking. Our work is done with public schools systems
(mostly in the developing world), and with private school systems (mostly in
the developed world). The governments of the developing world see Computational
Thinking as their best chance to close the gap in their education systems, and
the developed world sees Computational Thinking as the cornerstone of a
England is the first major developed country to formally
integrate into its public school system the subject of computation—the concept that
supports the development of Computational Thinking. Beginning in Kindergarten
and going through high school, children and young adults in England live the
world of Computational Thinking every day.
So, what is Computational Thinking? Why does it seem to
attract such diverse attention, and what can it bring us that we don’t already
The answers to these two questions are simple, and will be
the subjects of the next paragraphs. But first a warning to the reader: The
mind contains some cognitive traps that make some ideas difficult to see as
they are, like an optical illusion. I will alert the alert reader when the mind
may be tempted to throw a red herring.
First an introduction to the workhorse of our so-called rational
mind: the heuristic search. We think we are rational, but for the most part we
are not. There are good evolutionary reasons why we could not survive with a
reasoning mind—reasoning is slow, costly, and unreliable. The human species
survived and prospered because it developed a decision-making process that was
fast, inexpensive, and if not completely reliable, always favoring the safe
S1: All professors are vain; some non-vain people don’t
drink coffee; therefore some professors drink coffee.
Sentence S1 is a simple argument with two premises and one
conclusion. Computationally it is extremely simple, but many of us find it
convoluted and taxing to our energy and patience. We certainly don’t yearn
spending an afternoon playing that game.
S2: The old banker and his wife bumped into his young
Sentence S2 is computationally much more complex than S1, however
our mind has computed effortlessly, automatically, immediately (and unavoidably)
large sets of data, feelings, desires, reactions, and moods.
In 2002, psychologist Daniel Kahneman was awarded the Nobel
Prize in Economics for a simple, profound, and consequential idea: a) When we
make decisions we think we reason, but we don’t, we instead use heuristics; and
b) these heuristics are often biased and lead us to error.
The reasons why we use heuristics were listed before. Why,
however, we think we reason instead is perhaps a cognitive trap. To have an
accurate model of the mind, our computational machine, is the first step in
designing a productive educational system.
Type-A problems are such an important set of problems that
they deserve a name (perhaps a more descriptive name) and also a monument. A
monument not because we admire them, rather a monument in the spirit of the
Vietnam Wall Monument—something that reminds us of the past and makes us
reflect about the future.
During the K-12 years, Type-A problems are all that is done
in Math and Sciences classes. We may have the impression that those long years
cover a vast set of topics, but the reality is that it is only a variation on a
single theme: how to solve Type-A problems.
A Type-A problem consists of three phases:
are given a set of known data and unknown data, and we have to identify them.
There are rules that relate these data, and it is up to us to know them or to
we need to untangle the data attached to these rules and obtain the final
result (this often requires algebra and almost always arithmetic).
Type-A problems require for their resolution the activation
of a set of cognitive processes known as System-2, which involves attention.
System-2 tires soon, and it interferes, which means that no other task can be
implemented at the same time. A surgeon would have to pause her open heart
surgery, close her eyes, and deeply concentrate to correctly multiply 27 x 34
in her mind, if the life of her patient would depend on a correct answer (take
a minute to experience multiplying these two numbers in your mind). That is a
precarious system; a waste of the human capacities and training time.
Each day we know more about how the mind works. What it can
do and what it should not waste time trying to solve. Computational Thinking is
the set of fundamental ideas, derived from cognitive sciences and computation,
as well as epistemology, with two main goals: 1) Discover the uncharted world
of cognitive processes that the human mind can sustain, provided the required
tools; and 2) Develop a set of experiences that will allow students acquire
these tools, engage in these cognitive processes, and produce rich and
Ideas are supported in language, and complex ideas require
languages that support complex ideas. Natural language—English, Spanish, etc.—is
a miracle of evolution, and indeed allows for complex ideas, but as we saw
earlier with sentences S1 and S2, they seem to work unevenly in different
environments and soon find a limiting ceiling. Complex ideas require languages
that support complex ideas.
A language for representing complex ideas is based on a
simple set of three mechanisms: 1) a set of primitives that we start with; 2) a
means of combining these primitives; and 3) [this is the breakthrough that
natural languages did not evolve to implement well] a means of abstraction by
which we name the complex idea, and from now on it becomes a new primitive from
which higher level ideas will be created. This the root of Emergence.
The Chinese Room thought experiment deals with the concept
of whether a computer can think and have cognitive states, as humans do. For
the untrained mind this is a very difficult problem because we don’t know what
the mind is, and we don’t know what a computer is. Some cognitive traps may
supply some persuasive opinions, nonetheless unsupported.
Philosophy and Psychology classes studying this problem
start by first teaching students a language that supports the ideas of a Turing
machine or a Von Neumann machine and how they operate (Engineering freshmen
also learn this language, although with less philosophical objectives). This language
provides the primitives to entertain in their minds models about their minds,
and models about computers.
It also allows students to entertain in their minds the
fundamental idea of Emergence, how intelligence can emerge from non-intelligent
devices (this is where the fundamental difficulty of the Chinese Room problem
resides.) A NAND gate is an electronic device with two inputs. One output is always
one, except when both inputs are one; at that time, the output turns to zero.
Out of this simple, mindless, unintelligent device all the data and all computation
in the world is born.
Equipped with an appropriate language, the mystery that
plagued philosophy classes for decades (and still does in some universities) has
been downgraded to a simple problem that every student confidently solves. This
is Computational Thinking.
Thinking provides the path to higher cognitive
lives for our students and ourselves, but the path needs to be created.
Students need to be immersed in the world where this language is spoken and where
they can work with others and explore new ideas. It is similar to going to
China for one year, getting integrated in Chinese society, learning their
language and customs and culture and food and music by being with them and
interacting with them.
The world Computational Thinking is now being created by
many research groups. It begins with the creation of curriculum—the activities
that our children and young students will experience in their school life
during their formative years.
This work includes innumerable fields. My research team has
been working for the last decade in areas such as Vector Differential Geometry
(also known as the art of beautiful geometric), Cybernetics (the art and
science of self-controlled organisms, such as butterflies and self-driving
cars), Story Telling (the art of narrative self-expression), Discrete Calculus
(the art of the moving universe), and others.
A word on Discrete Calculus and the art of the moving
universe: Long ago, Galileo concluded that a ball rolls down a ramp with a
velocity that he described as the Law of the Odd Numbers (such as 1, 3, 5, 7,
9, …). That is probably one of the most beautiful laws in the universe. In
fact, it rules the motion of all planets, stars, and galaxies in the universe.
Later, Newton noticed that when subtracting the odd numbers the difference
between them was constant (3-1=2, 5-3=2, 7-5=2) and that is the constant
acceleration of the gravitational field. He also noticed that the cumulative
sum was (1+3=4..+5=9,..7=16.. +9=25…) a set of
square numbers: a parabola.
This insight is not lost in a ten-year-old child, who soon
creates a bouncing ball ruled by the Law of the Odd Numbers, which bounces like
her basketball when she plays with her friends at recess. The formal name of the
system that the child has created is a second order discrete differential
equation system. This creation moves the ball as if it were in the presence of
a real gravitational field. As the child plays with her creation, one day she
notices that in the presence of an unexpected obstacle—a table, for example—the
ball knows how high to bounce. Then she asks herself, “What is inside the Law
of the Odd Numbers, which is the only thing the ball knows, that allows it know
how high to bounce, regardless of the location of the obstacle?” The answer
comes to her in less than one hour. This is Computational Thinking.
These students live their school day in a cognitive world
that is far from the unnecessarily fruitless and unnecessarily unpleasant world
As I watch the children of Hong Kong briskly
walking to their schools on a windy and bright morning, I wonder what places
and experiences they will encounter today.
Dr. Olabe-Basogain is a professor of Electrical and Computer Engineering at Christian Brothers University
The Galleon is curated and managed by Christian Brothers University, a Memphis-based university founded in the Lasallian tradition (a sect within the Catholic faith). Part of our founding mission is to uphold respect for all persons-regardless of political, religious, or social beliefs. As an institution, we take no stand on political matters; to do so would undermine our commitment to intellectual inquiry and thoughtful response to events taking place in our World by members of the CBU community.