by Leo Marks
The life that I have
Is all that I have
And the life that I have
Is yours.
The love that I have
Of the life that I have
Is yours and yours and yours.
A sleep I shall have
A rest I shall have
Yet death will be but a pause.
For the peace of my years
In the long green grass
Will be yours and yours and yours.
It represents a universally applicable attitude and skill set everyone, not just computer scientists, would be eager to learn and use.
Computational thinking builds on the power and limits of computing processes, whether they are executed by a human or by a machine. Computational methods and models give us the courage to solve problems and design systems that no one of us would be capable of tackling alone. Computational thinking confronts the riddle of machine intelligence: What can humans do better than computers? and
What can computers do better than humans? Most fundamentally it addresses the question: What is computable? Today, we know only parts of the answers to such questions.
Computational thinking is a fundamental skill for everyone, not just for computer scientists. To reading, writing, and arithmetic, we should add computational thinking to every child’s analytical ability. Just as the printing press facilitated the spread of the three Rs, what is appropriately incestuous about this vision is that computing and computers facilitate the spread of computational thinking.
Computational thinking involves solving problems, designing systems, and understanding human behavior, by drawing on the concepts fundamental to computer science. Computational thinking includes a range of mental tools that reflect the breadth of the field of computer science.
Having to solve a particular problem, we might ask: How difficult is it to solve? and What’s the best way to solve it? Computer science rests on solid theoretical underpinnings to answer such questions precisely. Stating the difficulty of a problem accounts for the underlying power of the machine—the computing device that will run the solution. We must consider the machine’s instruction set, its resource constraints, and its operating environment.
In solving a problem efficiently, we might further ask whether an approximate solution is good
enough, whether we can use randomization to our advantage, and whether false positives or false negatives are allowed. Computational thinking is reformulating a seemingly difficult problem into one we know how to solve, perhaps by reduction, embedding, transformation, or simulation.
Computational thinking is thinking recursively. It is parallel processing. It is interpreting code as data and data as code. It is type checking as the generalization of dimensional analysis. It is recognizing both the virtues and the dangers of aliasing, or giving someone or something more than one name. It is recognizing both the cost and power of indirect addressing and procedure call. It is judging a program not just for correctness and efficiency but for aesthetics, and a system’s design for simplicity and elegance.
Computational thinking is using abstraction and decomposition when attacking a large complex task
or designing a large complex system. It is separation of concerns. It is choosing an appropriate representation for a problem or modeling the relevant aspects of a problem to make it tractable. It is using invariants to describe a system’s behavior succinctly and declaratively. It is having the confidence we can safely use, modify, and influence a large complex system without understanding its every detail. It is modularizing something in anticipation of multiple users or prefetching and caching in anticipation of future use.
Thinking like a computer scientist means more than being able to program a computer. It requires thinking at multiple levels of abstraction.
Computational thinking is thinking in terms of prevention, protection, and recovery from worst-case
scenarios through redundancy, damage containment, and error correction. It is calling gridlock deadlock and contracts interfaces. It is learning to avoid race conditions when synchronizing meetings with one another.
Computational thinking is using heuristic reasoning to discover a solution. It is planning, learning, and scheduling in the presence of uncertainty. It is search, search, and more search, resulting in a list of Web pages, a strategy for winning a game, or a counterexample. Computational thinking is using massive amounts of data to speed up computation. It is making trade-offs between time and space and between processing power and storage capacity.
Consider these everyday examples: When your daughter goes to school in the morning, she puts in her backpack the things she needs for the day; that’s prefetching and caching. When your son loses his
mittens, you suggest he retrace his steps; that’s backtracking. At what point do you stop renting skis and buy yourself a pair?; that’s online algorithms. Which line do you stand in at the supermarket?; that’s performance modeling for multi-server systems. Why does your telephone still work during a power outage?; that’s independence of failure and redundancy in design. How do Completely Automated Public Turing Test(s) to Tell Computers and Humans Apart, or CAPTCHAs, authenticate humans?; that’s exploiting the difficulty of solving hard AI problems to foil computing agents.
Computational thinking will have become ingrained in everyone’s lives when words like algorithm and precondition are part of everyone’s vocabulary; when nondeterminism and garbage collection take on the meanings used by computer scientists; and when trees are drawn upside down.
We have witnessed the influence of computational thinking on other disciplines. For example, machine learning has transformed statistics. Statistical learning is being used for problems on a scale, in terms of both data size and dimension, unimaginable only a few years ago. Statistics departments in all kinds of organizations are hiring computer scientists. Schools of computer science are embracing existing or starting up new statistics departments.
Computer scientists’recent interest in biology is driven by their belief that biologists can benefit from computational thinking. Computer science’s contribution to biology goes beyond the ability to search through vast amounts of sequence data looking for patterns. The hope is that data structures and algorithms—our computational abstractions and methods—can represent the structure of proteins in ways that elucidate their function. Computational biology is changing the way biologists
think. Similarly, computational game theory is changing the way economists think; nanocomputing, the way chemists think; and quantum computing, the way physicists think.
This kind of thinking will be part of the skill set of not only other scientists but of everyone else. Ubiquitous computing is to today as computational thinking is to tomorrow. Ubiquitous computing was yesterday’s dream that became today’s reality; computational thinking is tomorrow’s reality.
Computer science is the study of computation — what can be computed and how to compute it. Computational thinking thus has the following characteristics:
Conceptualizing, not programming. Computer science is not computer programming. Thinking like a computer scientist means more than being able to program a computer. It requires thinking at multiple levels of abstraction;
Fundamental, not rote skill. A fundamental skill is something every human being must know to function in modern society. Rote means a mechanical routine. Ironically, not until computer science solves the AI Grand Challenge of making computers think like humans will thinking be rote;
A way that humans, not computers, think. Computational thinking is a way humans solve problems; it is not trying to get humans to think like computers. Computers are dull and boring; humans are clever and imaginative. We humans make computers exciting. Equipped with computing devices, we use our cleverness to tackle problems we would not dare take on before the age of computing and build systems with functionality limited only by our imaginations;
Complements and combines mathematical and engineering thinking. Computer science inherently draws on mathematical thinking, given that, like all sciences, its formal foundations rest on mathematics.
Computer science inherently draws on engineering thinking, given that we build systems that interact with the real world. The constraints of the underlying computing device force computer scientists to think computationally, not just mathematically. Being free to build virtual worlds
enables us to engineer systems beyond the physical world;
Ideas, not artifacts. It’s not just the software and hardware artifacts we produce that will be physically present everywhere and touch our lives all the time, it will be the computational concepts we use to approach and solve problems, manage our daily lives, and communicate and interact
with other people; and
For everyone, everywhere. Computational thinking will be a reality when it is so integral to human
endeavors it disappears as an explicit philosophy.
Many people equate computer science with computer programming. Some parents see only a narrow range of job opportunities for their children who major in computer science. Many people think the fundamental research in computer science is done and that only the engineering remains. Computational thinking is a grand vision to guide computer science educators, researchers, and practitioners as we act to change society’s image of the field. We especially need to reach the pre-college audience, including teachers, parents, and students, sending them two main messages:
Intellectually challenging and engaging scientific problems remain to be understood and solved. The problem domain and solution domain are limited only by our own curiosity and creativity; and One can major in computer science and do anything. One can major in English or mathematics and go on to a multitude of different careers. Ditto computer science. One can major in computer science and go on to a career in medicine, law, business, politics, any type of science or engineering, and even the arts.
Professors of computer science should teach a course called “Ways to Think Like a Computer Scientist” to college freshmen, making it available to non-majors, not just to computer science majors. We should expose pre-college students to computational methods and models. Rather than bemoan the decline of interest in computer science or the decline in funding for research in computer science, we should look to inspire the public’s interest in the intellectual adventure of the field. We’ll thus spread the joy, awe, and power of computer science, aiming to make computational thinking commonplace.
by Jane Taylor
Twinkle, twinkle, little star,
How I wonder what you are!
Up above the world so high,
Like a diamond in the sky.
When the blazing sun is gone,
When he nothing shines upon,
Then you show your little light,
Twinkle, twinkle, all the night.
Then the trav’ller in the dark,
Thanks you for your tiny spark,
He could not see which way to go,
If you did not twinkle so.
In the dark blue sky you keep,
And often thro’ my curtains peep,
For you never shut your eye,
Till the sun is in the sky.
‘Tis your bright and tiny spark,
Lights the trav’ller in the dark,
Tho’ I know not what you are,
Twinkle, twinkle, little star.
To make a pledge or donation, please call the charity’s office.
the breakdown of water into hydrogen and oxygen
a budget breakdown
This book is a classic of the mystery genre.
The town needs to mend these roads.
It’s never too late to mend.
the university’s criteria for admission
The moderator allowed audience members to ask the governor questions.
She acts as the moderator in our office meetings.
vends snack foods and novelties at fairs
we’re thinking of making a deal with that other software vendor
dispense food among the needy
The ATM only dispenses $20 bills.
dispensing pills to their patients
Pharmacists are certified to dispense medication.
He bought stainless steel rims for his new car.
When driving, she always wears her seatbelt as a precaution.
Every home owner should take precautions against fire.
My favorite sport is wrestling.
He juggled four balls at once.
He checked into the hotel using an alias.
Many people consider her decision to be a breach of trust.
Everyone was surprised when she arrived at the party without an escort.
She washes the linen every week.
The collapse of her business had made her desperate.
As the supply of food ran out, people became desperate.
We could hear their desperate cries for help.
a desperate struggle to defeat the enemy
aggregate sales
An aggregate function performs a calculation on a set of values, and returns a single value.
Aggregate functions are often used with the GROUP BY clause of the SELECT statement.
a novice at skiing
a football jersey
by Mark Twain
Warm summer sun,
Shine kindly here,
Warm southern wind,
Blow softly here.
Green sod above,
Lie light, lie light.
Good night, dear heart,
Good night, good night.
To him who in the love of Nature holds
Communion with her visible forms, she speaks
A various language; for his gayer hours
She has a voice of gladness, and a smile
And eloquence of beauty, and she glides
Into his darker musings, with a mild
And healing sympathy, that steals away
Their sharpness, ere he is aware. When thoughts
Of the last bitter hour come like a blight
Over thy spirit, and sad images
Of the stern agony, and shroud, and pall,
And breathless darkness, and the narrow house,
Make thee to shudder, and grow sick at heart;—
Go forth, under the open sky, and list
To Nature’s teachings, while from all around—
Earth and her waters, and the depths of air—
Comes a still voice—
Yet a few days, and thee
The all-beholding sun shall see no more
In all his course; nor yet in the cold ground,
Where thy pale form was laid, with many tears,
Nor in the embrace of ocean, shall exist
Thy image. Earth, that nourished thee, shall claim
Thy growth, to be resolved to earth again,
And, lost each human trace, surrendering up
Thine individual being, shalt thou go
To mix for ever with the elements,
To be a brother to the insensible rock
And to the sluggish clod, which the rude swain
Turns with his share, and treads upon. The oak
Shall send his roots abroad, and pierce thy mould.
Yet not to thine eternal resting-place
Shalt thou retire alone, nor couldst thou wish
Couch more magnificent. Thou shalt lie down
With patriarchs of the infant world—with kings,
The powerful of the earth—the wise, the good,
Fair forms, and hoary seers of ages past,
All in one mighty sepulchre. The hills
Rock-ribbed and ancient as the sun,—the vales
Stretching in pensive quietness between;
The venerable woods—rivers that move
In majesty, and the complaining brooks
That make the meadows green; and, poured round all,
Old Ocean’s gray and melancholy waste,—
Are but the solemn decorations all
Of the great tomb of man. The golden sun,
The planets, all the infinite host of heaven,
Are shining on the sad abodes of death,
Through the still lapse of ages. All that tread
The globe are but a handful to the tribes
That slumber in its bosom.—Take the wings
Of morning, pierce the Barcan wilderness,
Or lose thyself in the continuous woods
Where rolls the Oregon, and hears no sound,
Save his own dashings—yet the dead are there:
And millions in those solitudes, since first
The flight of years began, have laid them down
In their last sleep—the dead reign there alone.
So shalt thou rest, and what if thou withdraw
In silence from the living, and no friend
Take note of thy departure? All that breathe
Will share thy destiny. The gay will laugh
When thou art gone, the solemn brood of care
Plod on, and each one as before will chase
His favorite phantom; yet all these shall leave
Their mirth and their employments, and shall come
And make their bed with thee. As the long train
Of ages glide away, the sons of men,
The youth in life’s green spring, and he who goes
In the full strength of years, matron and maid,
The speechless babe, and the gray-headed man—
Shall one by one be gathered to thy side,
By those, who in their turn shall follow them.
So live, that when thy summons comes to join
The innumerable caravan, which moves
To that mysterious realm, where each shall take
His chamber in the silent halls of death,
Thou go not, like the quarry-slave at night,
Scourged to his dungeon, but, sustained and soothed
By an unfaltering trust, approach thy grave,
Like one who wraps the drapery of his couch
About him, and lies down to pleasant dreams.
by Eliza Cook
Work, work, my boy, be not afraid;
Look labor boldly in the face;
Take up the hammer or the spade,
And blush not for your humble place.
There’s glory in the shuttle’s song;
There’s triumph in the anvil’s stroke;
There’s merit in the brave and strong
Who dig the mine or fell the oak.
The wind disturbs the sleeping lake,
And bids it ripple pure and fresh;
It moves the green boughs till they make
Grand music in their leafy mesh.
And so the active breath of life
Should stir our dull and sluggard wills;
For are we not created rife
With health, that stagnant torpor kills?
I doubt if he who lolls his head
Where idleness and plenty meet,
Enjoys his pillow or his bread
As those who earn the meals they eat.
And man is never half so blest
As when the busy day is spent
So as to make his evening rest
A holiday of glad content.
by Mary Howitt
How pleasant the life of a bird must be,
Flitting about in each leafy tree:
In the leafy trees so broad and tall,
Like a green and beautiful palace-hall
With its airy chambers light and boon,
That open to sun, and stars, and moon!
That open unto the bright blue sky.
And the frolicsome winds as they wander by.
They have left their nests in the forest bough;
Those homes of delight they need not now;
And the young and the old they wander out
And traverse their green world round about;
And hark! at the top of this leafy hall,
How one to the other they lovingly call:
“Come up, come up!” they seem to say,
“Where the topmost twigs in the breezes sway!”
“Come up, come up, for the world is fair
Where the merry leaves dance in the summer air,”
And the birds below give back the cry:
“We come, we come, to the branches high!”
How pleasant the life of a bird must be
Flitting about in a leafy tree;
And away through the air what joy to go,
And to look on the bright green earth below.
How pleasant the life of a bird must be,
Wherever it listeth there to flee;
To go, when a joyful fancy calls,
Dashing adown ‘mong the waterfalls,
Then wheeling about with its mates at play,
Above and below, and among the spray,
Hither and thither, with screams as wild
As the laughing mirth of a rosy child!
How pleasant the life of a bird must be,
Skimming about on the breezy sea,
Cresting the billows like silvery foam,
And then wheeling away to its cliff-built home
What joy it must be to sail, upborne
By a strong free wing, through the rosy morn,
To meet the young sun face to face,
And pierce like a shaft the boundless space!
What joy it must be, like a living breeze,
To flutter about ‘mong the flowering trees;
Lightly to soar and to see beneath
The wastes of the blossoming purple heath,
And the yellow furze like fields of gold
That gladden some fairy regions old!
On mountain tops, on the billowy sea,
On the leafy stems of the forest tree,
How pleasant the life of a bird must be!
by Mary Howitt
I am coming, little maiden!
With the pleasant sunshine laden,
With the honey for the bee,
With the blossom for the tree,
With the flower and with the leaf:—
Till I come, the time is brief.
I am coming, I am coming!
Hark! the little bee is humming;
See! the lark is soaring
high In the bright and sunny sky;
And the gnats(4) are on the wing.
Wheeling round in airy ring.
See! the yellow catkins cover
All the slender willows over;
And on banks of mossy green
Star-like primroses are seen;
And, their clustering leaves below
White and purple violets blow.
Hark! the new-born lambs are bleating;
And the cawing rooks are meeting
In the elms—a noisy crowd!
All the birds are singing loud;
And the first white butterfly
In the sunshine dances by.
Look around thee—look around!
Flowers in all the fields abound;
Every running stream is bright;
All the orchard(8) trees are white,
And each small and waving shoot
Promises sweet flowers and fruit.
Turn thine eyes to earth and heaven!
God for thee the Spring has given;
Taught the birds their melodies,
Clothed the earth, and cleared the skies,
For thy pleasure or thy food:—
Pour thy soul in gratitude?
Great, wide, beautiful, wonderful World,
With the wonderful water round you curled,
And the wonderful grass upon your breast–
World, you are beautifully drest.
The wonderful air is over me,
And the wonderful wind is shaking the tree,
It walks on the water, and whirls the mills,
And talks to itself on the tops of the hills.
You friendly Earth! how far do you go,
With the wheat-fields that nod and the rivers that flow,
With cities and gardens, and cliffs, and isles,
And people upon you for thousands of miles?
Ah, you are so great, and I am so small,
I tremble to think of you, World, at all;
And yet, when I said my prayers to-day,
A whisper inside me seemed to say,
“You are more than the Earth, though you are such a dot:
You can love and think, and the Earth cannot!”