MIT and The Butterfly Effect

Ed Lorenz discovered the “Butterfly Effect” by accident, and that was precisely what led him there.

Jeff Cunningham

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Published in

Once Upon A Terroir

28 min readAug 17, 2023

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Monday, December 11, 1961

Two things were annoying the ordinarily serene Professor Ed Lorenz. Standing at his desk, lost in contemplation — a common pose for the quiet meteorologist — now he had to void another computer simulation. It was growing wearisome. It began to grate. More importantly, he was yearning for a rich, hot cup of dark roast, and that was the first problem. The only espresso machine was Café Pamplona in downtown Cambridge. The acrid concoction served in the MIT canteen just wasn’t going to do it this morning.

Back in 1959 when Eliodora “Josefina” Yanguas Perez, a Spanish immigrant from, as you might have guessed, Pamplona, opened her café it was the first in Harvard Square to serve the invigorating brew. It didn’t take long before Lorenz became addicted. But to get there, he had to drive two miles from MIT to the corner of Bow and Arrow Streets.

As you approached, you knew you were near when you heard the soft melodies of Josefina’s Spanish folk songs coming from a quaint three-story townhouse she had purchased with her life’s savings for $23,000. Navigating down a brief flight of stairs past a terrace of tables led you to the café’s cozy underground interior. The effect was all mirth and merriment, and fragrance. The trek would cost Lorenz about thirty minutes, provided the weather was on his side. Ironically, that was the second problem. He was a meteorologist who could not tell you what the weather would do next. His problems seemed to be mounting.

While foremost experts like Lorenz could tell you why people get less wet by running through the rain (yes, but only by 10%) — he had no idea what the weather’s mood would be, and a cup of coffee was about to teach him why.

Lorenz trudged down the sunlit corridor and headed to the parking lot of MIT’s Department of Earth, Atmospheric, and Planetary Sciences. He sensed a rawness in the air, a telltale sign of snow. The frigid winds of Cambridge whispered, but it was a language he couldn’t decipher. If it starts to come down hard, he thought, he’d have to settle for the MIT faculty lounge. But there was no way to tell. That moment of hesitation not only changed his course that morning, but the trajectory of Ed Lorenz’s life, and the body of scientific theories we’ve come to know as Chaos.

In The Eye of The Storm

Ed Lorenz had been fixated on long range weather forecasting ever since his days as an Army meteorologist. In theory, it was a passionate romance. In practice, they were an old married couple, ranting about broken promises and vows they could never live up to, even on a sunny day. By this time, he had been running weather simulations nonstop since the early hours, again without result, and badly needed a change of scenery.

Following his graduation from Harvard, Lorenz got a masters and doctoral degree from MIT, and joined the meteorology department of MIT in 1948. His slow, methodical rise culminated in a professorship in 1962, and by 1977, he took on the leadership. But despite a profound grasp of meteorology — the art of weather forecasting remained hopeless. It wasn’t that it couldn’t be done. It just couldn’t be done right. The humble meteorologist’s mind crackled with the buzz of equations and he was a diviner of mysterious patterns, but his graphs and calculations were telling him to forget it. Weather was a tough nut to crack.

His opinion of the subject echoed Churchill’s description of Russia, barely twenty years earlier in 1939 as “a riddle wrapped in a mystery inside an enigma.” Now, on that fateful day of December 11, 1961, a computational error — he would prefer to call it an aberration — a twist of fate, a blip in a carefully constructed narrative, was about to alter his view of how the weather worked, and with that, the very foundation of life itself.

But first, Lorenz had an errand to run.

The Quest for Patterns

The prize at stake — the ability to predict long range weather precisely — was no ordinary treasure. An accurate forecast meant a delightful holiday for dedicated New England hikers and cross-country skiers like Lorenz. Yet, its significance captivated pilots, farmers, and national defense strategists.

The echoes of seventeen years past still resonated. The world was engulfed in the maw of history’s most sinister adversary, and weather forecasters played a covert role. The Allies orchestrated a brilliant blood-drenched maneuver on the Normandy beaches, exploiting rudimentary weather predictions to perfection. It was a lesson not lost on the Harvard-educated mathematician, who sensed that more extensive answers to survival and liberty lay within his dogged pursuits.

The weather could be a coy mistress, a metaphor coined by Andrew Marvell, hinting that our destiny is impatient and anxious for us to find the key. Even the most advanced weather simulations teased partial truths but withheld their assent. Neither flattery nor promises would stir them to reveal their secret. After years of grappling with this puzzle, Lorenz teetered on the edge of despair. Yet, little did the soft-spoken meteorologist know that his time had arrived. The heart of the matter lay in finding the delicate balance between the gods of disorder and order that governed the skies.

Nonetheless, the goal remained frustratingly elusive for Lorenz, at least within his lifetime. The tools at his disposal fell shy of the mark, their pace lumbering and their intricacy unprepared for the bold leaps of faith demanded by the art of weather forecasting. Churchill’s words rang true — this was an enigma.

As the dim lights of his LGP-30 computer danced with their muted glow, Lorenz embarked on a fresh simulation for what seemed like the millionth time. His fingers retraced the footprints of prior algorithms and models, looking for the elusive clue. But for the moment, it was time to take a break, a pause to gather thoughts and much-needed energy for the next battle.

The Coffee Break That Changed The World

Before he could permit himself a well-deserved respite, Lorenz ran one more simulation. Yet, for the time-conscious scientist, the computational work would take several hours, and he had a class at noon. There was a solution, and as always, a problem.

Blocking the forward path was a formidable Royal McBee LGP-30 computer, which stood for Librascope General Precision, a collaboration between Stan Frankel of the Manhattan Project, who initially developed it at CalTech in 1954, and a joint venture with the Royal McBee Corporation, the world’s largest typewriter manufacturer. The perfect harmony of brains and brawn. Except in the case of weather.

Developed in the 1950s, the LGP-30 computer was one of the earliest computers and was quite limited in programming capabilities. The LGP-30 was no bargain price-wise, however. It fetched the equivalent of $500,000 in today’s currency and combined the intricacy of three-dimensional chess with the demeanor of a grumpy teenager.

By today’s standards, it had severely limited capabilities. The instruction manual of the day suggested that before pressing the start button to run a simulation, one had to follow these steps: Understand the computer architecture, select a simulation type due to its memory and processing constraints, write a simulation program using its assembly language, allocate the LGP-30 limited memory (32 words of drum memory) efficiently, debug using limited tools, load the program manually, and run the simulation.

Despite reigning as the market leader through the early ’60s, the LGP-30 bragged in its literature that it was awkward to program “because the programmer has to work around the constraint of the sequential access to data and instructions on the drum, it is compact and affordable, using only about 100 tubes!”

In other words, slow.

It demanded a six-minute warm-up, produced answers on ticker tape, and spoke a high level language called ACT-III. Every instruction had to be delimited by an apostrophe, making it hard to read and even harder to prepare tapes:

s1'dim'a'500'm'500'q'500''index'j'j+1 'j-1''daprt'e'n't'e'r' 'd'a't'a''cr''rdxit's35''s2iread'm'1' 'iread'q'1''iread'd''iread'n''1';'j'' 0'flo'd';'d.''s3'sqrt'd.';'sqrd.''1'u nflo'sqrd.'i/'10';'sqrd''2010'print's qrd.''2000'iprt'sqrd''cr''cr''...

The engineers responsible for crafting such a convoluted complexity would have been dismissed by Steve Jobs. But as he the future California wunderkind was only six years old at the time and wouldn’t introduce the personal computer until 1976, the recourse for Lorenz was to give the cumbersome LGP-30 a gentle kick in the buttocks.

To save time — a phrase that rings throughout history with ominous intent — Lorenz repeated one of the simulations but tweaked it to range over a more extended period. Instead of repeating the whole program, which could take hours, he dipped his toe into the middle of the previous run, lifting those numbers as initial conditions. It was like measuring a race from the midpoint to the finish line. The result should be the same.

At least, that is what Lorenz reasoned.

The weather parameters of the second run were the same and should have logically had a similar outcome as the first. The same but different, right? Except that he did something so trivial it barely merits mention. Lorenz rounded off one of the twelve variables the model used to capture factors like temperature and wind speed fluctuations, so that the simulation would be ready when he returned. The small change was scientifically meaningless, even for an enigma like the weather. That’s what we tell ourselves when stuff happens.

The Emergence of Chaos

Upon his return, cradling a mug of steaming dark coffee, Lorenz settled comfortably into a wooden swivel chair, his gaze wandering over the computer screen. He did not like what he saw. Rather than the “ah-ha” moment he expected, it felt more like “uh-oh.” The once-familiar weather simulation had transformed into a most peculiar pattern, one that was unhinged from its predecessor. Twins separated at birth? It did not seem possible.

What was even less believable was that a trivial rounding error triggered a momentous revelation. Two identical trajectories of weather were now veering sharply in different directions, upending the established notions about weather patterns and more, much more.

For a fleeting moment, Lorenz questioned himself, the computer and then the program. Soon, he realized that the discrepancy was somehow tucked inside the conditions he had entered. The computer data was calculated to six decimal places, but the printout shortened the numbers to three to save space. When he keyed in the new conditions, Lorenz had unthinkingly picked up the rounded figures on the printout, a minor deviation of less than 0.1 percent, yet this resulted in a completely different outcome.

At that moment, Lorenz reckoned that if a slight change in an initial stage could warp the outcome, the pursuit of a perfect weather forecast was a fantasy. Such an achievement would demand a flawless understanding of global conditions instantly. The tiniest discrepancy could inspire dissimilar results. The room was tense as the baffled professor thought deeply about this turn of events.

A different researcher might have dismissed the findings as noise, opting for a swift reset to erase the disturbance from history. But Lorenz was not an ordinary scientist. He didn’t sweep mysteries under the rug. He looked underneath to find missing puzzle pieces.

Lorenz was an inveterate pattern-seeker and a detective of hidden codes. His diverse interests, spanning from chess to the challenges of cross-country skiing, had fashioned a unique mindset. Every riddle, every anomaly, was an invitation to question the unknown. The conundrum facing him now was a new one called interconnectedness. It meant that something ephemeral in intent could become monumental in impact.

As his fingers wrapped around the mug’s handle, Lorenz’s gaze lingered on the coffee. He stirred it absentmindedly, lost in thought as the brew performed a delicate ballet. A single droplet of milk would transform the rhythmic dance into improv, creating an entirely new swirling pattern before it reverted to form. It was a trivial change that triggered a transformative result.

Lorenz discerned in sudden weather shifts the same sleight of hand, and the way disturbances cause it to sway between order and randomness. It felt like the handiwork of nature, capricious — yes, secretive — yes, frustrating — yes, but unnatural — no.

In fact, it was the same force that governed the universe — cycles of harmonious chaos.

He endeavored to find words to capture this essence precisely, yet neither blandishments nor blarney could coax its hidden truths. Lorenz stood on the precipice of despair as only three citations acknowledged his research over the ensuing decade. But unbeknownst to the modest meteorologist, he was about to escalate to a much higher tier.

The Butterfly Takes Flight

The concept, now recognized as the “butterfly effect,” wouldn’t achieve scientific significance until Lorenz presented the findings in 1972. His commentary employed a fascinating metaphor: “Can the Flap of a Butterfly’s Wings in Brazil Trigger a Tornado in Texas?”

His neat turn of phrase would over time lead to a clamor, and a fresh look at the unpredictability of the weather, so much so that it caught the world by storm. The phenomenon spread its wings to an ever-growing circle of appreciative fans.

One astonishing outcome of Lorenz’s work was that it crumbled the foundations of Determinism, which asserts that all events, even human interactions, are determined by external causes. It implies that individuals do not bear full moral responsibility for misdeeds or take credit for achievements. Life is determined by other things; some ride by elevator while others get the shaft.

It took an MIT meteorologist to convince us that trivial interconnections could rally to trigger sweeping, often astonishing outcomes as the gentle flutter of a butterfly sets in motion an unpredictable chain of events.

For example, if you’ve driven a car on a bustling highway, think about a driver ahead of you suddenly switching lanes. This inconspicuous action has the potential to create traffic snarls that ripple across miles of road, leading to delays for numerous commuters. These delays cascade into missed job interviews, medical appointments, and reunions of friends — substantial effects from insignificant triggers.

Lorenz’s revelation demonstrated that certain phenomena in our linear, structured world, can only be understood by examining chaotic solutions. The ideal answer to those kinds of things is more often found in the unlikely realm of non-linear thinking that demonstrates the underlying order in all that surrounds us.

The novel concept prompted Lorenz to reconsider his approach to long-range weather forecasting. A pebble could cause a landslide. This revelation indicated the need for enhanced accuracy, objectivity, and precision in information gathering, paying attention to the minutest details, framed by meticulous documentation and a comprehensive retraining of meteorologists. And mainly, an open mind that doesn’t dismiss anomalies.

Indeed, of all the causes of systemic failure, it is the utter disregard for minor fact patterns throughout history that has consistently led to disasters. In the 20–21st centuries alone, the sinking of the Titanic, the Great Depression, two World Wars, two Financial Crises, two Pandemics have roots in the neglected details. But standing in the way of critical inquiry and independent thinking are legions of devotees either corrupted by the system or who cling to established norms as a protective barrier against personal admission of failure. They resist any alteration by subjecting questioners to harsh skepticism eventually transforming into animosity, now recognized as ‘cancel culture,’ as a fatal consequence of asking ‘why’.

For proof, one need only examine the numerous once-great empires and organizations that have succumbed to the passage of time. Inattention to seemingly inconsequential events emerges as a recurring factor in their downfall.

This is why Lorenz took on the job of persuading his colleagues that a rational and deterministic method for weather forecasting was fundamentally flawed.

Given the voluminous amount of data, it was incapable of encompassing all contributing factors. If one were to graph every conceivable “outcome” within a complex system — whether it be weather patterns, highway traffic, or the stock market — and plot each potential twist and turn, the outcome would manifest as a mathematical illustration of the Butterfly Effect, now recognized as the Lorenz attractor.

By accounting for all available data, the solution miraculously emerges. Naturally, it assumed a curiously familiar form in perfect harmony with nature.

Chaos in Real Life

In fact, ‘Sensitivity to Initial Conditions,’ the technical meaning of the Butterfly Effect, is even more true today than in Lorenz’s time. Now, all it takes is a viral social media post to sway public sentiment, instigate boycotts, steer political results, or get a genius high-tech chairman fired.

When Elon Musk tweeted “funding secured,” it set off an avalanche of excitement in most quarters but not those of the Securities and Exchange Commission, the federal agency charged with protecting investors, where instead the tweet prompted a civil suit. It reached a settlement with Musk in which he and Tesla each agreed to pay $20 million in fines, and Musk gave up his chairmanship of the company.

Musk is not the only perp or victim of a butterfly. As you can see, life’s orderliness can be easily disrupted whenever a minor initial disturbance has the potential to escalate into a significant anomaly. And it isn’t just about the weather but about subtleties that lead to far-reaching consequences that reverberate across the globe.

The choice of regulators to disregard bank balance sheets set off a chain reaction that leads to the ’08 Global Financial Crisis and Great Recession, costing homeowners and bondholders more than $2 trillion in global economic growth, according to Moody’s Analytics.

The dwindling bee population in the United States, where according to Ohio University, the buzzers are responsible for pollinating about one-third of the world’s food supply that requires pollination, triggered a cascade effect, resulting in diminished crop yields and food supply chain disruptions.

In healthcare, an infectious disease outbreak in China swiftly disseminated worldwide, impacting daily existence on a global scale and killing over three million people, according to the WHO.

Decoding Extraordinary

A change in the weather is sufficient to recreate the world and ourselves. — Marcel Proust

The realization gave birth to a new science called Chaos Theory, a framework that emerges amid disorder. It is why, throughout history, humans had to turn to mythologies, religions, and ideologies to grapple with the enigma of unpredictability. Now they can satisfy their curiosity with a butterfly.

Although Lorenz introduced the Butterfly Effect in 1961, for the next ten years prominent scholars disregarded his breakthrough, while the general public continued to find comfort in the old black magic of deterministic beliefs. When faced with complex problems, the stronger inclination is to assign blame to peripheral actors and stick by our story without fail.

Now we know that approach is not only short-sighted but leads to disasters because the original cause remains unknown. It is why the French journalist assured us that “Plus ça change, plus c’est la même chose” — or the more things change, the more they remain the same. The reason we continue to have pandemics to high rates of divorce is that things don’t change because we fail to diagnose them properly in the first place.

The turning point in Lorenz’s academic career was when the 1972 paper propelled him into one of history’s most profound scientists. It was his ‘butterfly effect’ moment, as MIT geophysics professor Daniel Rothman confirmed it as “a wonderful instance of a seemingly esoteric piece of mathematics that had verifiable applications in the real world.”

But what makes Lorenz such an astonishing case study in unconventional thinking is that he alone saw various patterns such as feedback loops, repetitions, and self-organization nestled within the realm of orderly phenomena. Lorenz’s idea has been profitably applied to realms as diverse as stock markets to children’s behavior and the result is that we look to science and not mysticism to explain complex behaviors. He revealed that a cascade effect exists and we have to reconsider even the most insignificant variables in order to unearth underlying causes.

Ed Lorenz may have been an academic with a Ph.D., but the dogged researcher embodied the tenaciousness of Sherlock Holmes equipped with a magnifying glass traversing rugged landscapes to uncover overlooked and novel clues. It formed the bedrock of a profound life of discovery and laid the cornerstone for chaos theory, which proved that intricate systems will display unpredictable behavior that appear to violate the underlying rules.

The second thing about Lorenz was that his endeavors were driven by a loftier purpose than fame. Recognizing that disruptive phenomena determine our success or failure — in his case of weather forecasting, he taught us that the same patterns were apparent in other complex domains. Then he structured his thoughts by using a colorful metaphor that could be appreciated by even the most uninformed public.

What more can you ask of a scientist?

While Lorenz passed away on April 16, 2008, his legacy lived on through his words written in 1962: “The weather forecaster is forced to willy-nilly predict the details of large scale turbulences — which are continually arranging themselves into new patterns.”

Aren’t we all?

Massachusetts Institute of Technology (MIT)

“Can the Flap of a Butterfly’s Wings in Brazil Trigger a Tornado in Texas?” — Ed Lorenz

Monday, December 11, 1961

Two things were bothering professor Ed Lorenz. As he stood at his desk, absorbed in thought, not an unusual condition for the meteorologist, a computer simulation came back empty — and he had to do yet another run. It was starting to feel tedious. It began to grate on his nerves. More importantly, he was craving a steaming cup of dark roast. That was the first problem. The only espresso machine was Café Pamplona in downtown Cambridge.

Two years earlier back in 1959, when Eliodora “Josefina” Yanguas Perez, an immigrant from, as you might have guessed, Pamplona, Spain, opened her shop it was the only coffeehouse in Harvard Square that served the invigorating brew. Lorenz was addicted to the stuff. But to get there, he had to drive two miles from MIT to the corner of Bow and Arrow Streets. You were nearby when you heard her humming Spanish folk tunes in a small three-story townhouse which she bought with her savings for $23,000. Then you climbed down a short flight of stairs past a patio with tables until you arrived at the café’s subterranean interior. Lorenz could make it in a good half hour if the weather cooperated. And that was the second problem. He was a meteorologist who could not tell you what the weather’s mood would do next.

His problems seemed to be mounting.

While the world’s foremost experts like Lorenz could tell you why people get less wet by running through the rain (yes, but only by 10%) — he had no idea what the weather’s mood would be next, and a cup of coffee was about to teach him why.

Lorenz trudged down the sunlit corridor and headed to the parking lot of MIT’s Department of Earth, Atmospheric, and Planetary Sciences. He sensed a rawness in the air, a telltale sign of snow. The frigid winds of Cambridge whispered, but it was a language he couldn’t decipher. If it starts to come down hard, he thought, he’d have to settle for the intensely acrid brew served in the MIT faculty lounge. But there was no way to tell, not with the weather. That moment of hesitation not only changed his course of that morning, but the trajectory of Ed Lorenz’s life.

In The Eye of The Storm

Ed Lorenz had been fixated on long range weather forecasting ever since his days as an Army meteorologist. In theory, it was a passionate romance. In practice, they were an old married couple, ranting about broken promises and vows they could never live up to, even on a sunny day. By this time, he had been running weather simulations nonstop since the early hours, again without result, and badly needed a change of scenery.

Following his graduation from Harvard, Lorenz got a masters and doctoral degree from MIT, and joined the meteorology department of MIT in 1948. His slow, methodical rise culminated in a professorship in 1962, and by 1977, he took on the leadership. But despite a profound grasp of meteorology— the art of weather forecasting remained hopeless. It wasn’t that it couldn’t be done. It just couldn’t be done right. The humble meteorologist’s mind crackled with the buzz of equations and he was a diviner of mysterious patterns, but his graphs and calculations were telling him to forget it. Weather was a tough nut to crack.

His opinion of the subject echoed Churchill’s description of Russia, barely twenty years earlier in 1939 as “a riddle wrapped in a mystery inside an enigma.” Now, on that fateful day of December 11, 1961, a computational error — he would prefer to call it an aberration — a twist of fate, a blip in a carefully constructed narrative, was about to alter his view of how the weather worked, and with that, the very foundation of life itself.

But first, Lorenz had an errand to run.

The Quest for Patterns

The prize at stake — the ability to predict long range weather precisely — was no ordinary treasure. An accurate forecast meant a delightful holiday for dedicated New England hikers and cross-country skiers like Lorenz. Yet, its significance captivated pilots, farmers, and national defense strategists.

The echoes of seventeen years past still resonated. The world was engulfed in the maw of history’s most sinister adversary, and weather forecasters played a covert role. The Allies orchestrated a brilliant blood-drenched maneuver on the Normandy beaches, exploiting rudimentary weather predictions to perfection. It was a lesson not lost on the Harvard-educated mathematician, who sensed that more extensive answers to survival and liberty lay within his dogged pursuits.

The weather could be a coy mistress, a metaphor coined by Andrew Marvell, hinting that our destiny is impatient and anxious for us to find the key. Even the most advanced weather simulations teased partial truths but withheld their assent. Neither flattery nor promises would stir them to reveal their secret. After years of grappling with this puzzle, Lorenz teetered on the edge of despair. Yet, little did the soft-spoken meteorologist know that his time had arrived. The heart of the matter lay in finding the delicate balance between the gods of disorder and order that governed the skies.

Nonetheless, the goal remained frustratingly elusive for Lorenz, at least within his lifetime. The tools at his disposal fell shy of the mark, their pace lumbering and their intricacy unprepared for the bold leaps of faith demanded by the art of weather forecasting. Churchill’s words rang true — this was an enigma.

As the dim lights of his LGP-30 computer danced with their muted glow, Lorenz embarked on a fresh simulation for what seemed like the millionth time. His fingers retraced the footprints of prior algorithms and models, looking for the elusive clue. But for the moment, it was time to take a break, a pause to gather thoughts and much-needed energy for the next battle.

The Coffee Break That Changed The World

Before he could permit himself a well-deserved respite, Lorenz ran one more simulation. Yet, for the time-conscious scientist, the computational work would take several hours, and he had a class at noon. There was a solution, and as always, a problem.

Blocking the forward path was a formidable Royal McBee LGP-30 computer, which stood for Librascope General Precision, a collaboration between Stan Frankel of the Manhattan Project, who initially developed it at CalTech in 1954, and a joint venture with the Royal McBee Corporation, the world’s largest typewriter manufacturer. The perfect harmony of brains and brawn. Except in the case of weather.

Developed in the 1950s, the LGP-30 computer was one of the earliest computers and was quite limited in programming capabilities. The LGP-30 was no bargain price-wise, however. It fetched the equivalent of $500,000 in today’s currency and combined the intricacy of three-dimensional chess with the demeanor of a grumpy teenager.

By today’s standards, it had severely limited capabilities. The instruction manual of the day suggested that before pressing the start button to run a simulation, one had to follow these steps: Understand the computer architecture, select a simulation type due to its memory and processing constraints, write a simulation program using its assembly language, allocate the LGP-30 limited memory (32 words of drum memory) efficiently, debug using limited tools, load the program manually, and run the simulation.

Despite reigning as the market leader through the early ’60s, the LGP-30 bragged in its literature that it was awkward to program “because the programmer has to work around the constraint of the sequential access to data and instructions on the drum, it is compact and affordable, using only about 100 tubes!”

In other words, slow.

It demanded a six-minute warm-up, produced answers on ticker tape, and spoke a high level language called ACT-III. Every instruction had to be delimited by an apostrophe, making it hard to read and even harder to prepare tapes:

s1'dim'a'500'm'500'q'500''index'j'j+1 'j-1''daprt'e'n't'e'r' 'd'a't'a''cr''rdxit's35''s2iread'm'1' 'iread'q'1''iread'd''iread'n''1';'j'' 0'flo'd';'d.''s3'sqrt'd.';'sqrd.''1'u nflo'sqrd.'i/'10';'sqrd''2010'print's qrd.''2000'iprt'sqrd''cr''cr''...