Leave it to a philosopher to offer a counterintuitive idea cascading through history as a wise observation on humanity, echoed and adopted by people as famous as Benjamin Franklin, Woodrow Wilson, John Locke, and Henry David Thoreau.

In his "Lettres Provinciales" of 1657, the philosopher and mathematician Blaise Pascal penned a French phrase that roughly translates today to "I have made this longer than usual because I have not had time to make it shorter."

The idea that constraints can lead to breakthroughs in creativity with profound results has been proven true in ways beyond just the clarity of words on the printed page.

It is a theory whose validity has been tested in varied contexts and produced meaningful innovations that have changed the course of history. These constraints may be self-imposed, as with writers and artists challenging their creative spirits, or they may pre-exist and drive engineers and scientists in directions they would not have otherwise gone.

Letting constraints dictate the size and shape of a solution may be one of the more unheralded factors in developing new technologies and approaches that have allowed society to evolve quickly.

Self-Imposed Constraints and Creativity

Artists and writers have a lot to teach us about the creative process in the way they challenge themselves to reach new heights in their disciplines. Take the example of Phil Hansen, who developed a shake in his hand that prevented him from drawing straight lines as an art student. As he would later observe in his TED Talk, the shake "was doomsday for an artist."

Initially, Hansen reacted as many of us would. He left art school and stopped doing art altogether, especially after learning that he had developed a permanent neurological condition.

But then his neurologist said something that made all the difference: "why don't you embrace the shake?" the doctor said. This, Hansen says, "was the first time I'd encountered this idea that embracing a limitation could actually drive creativity."

It didn't happen immediately for him. Through many struggles, Hansen developed a unique style that has since earned him the nickname of "artist for the people," given his penchant for creating art out of everyday items such as Starbucks coffee cups and hamburger grease.

He has become a highly successful commercial artist who has done work for the Grammy Awards, Skype, Diesel, and Arby's. He's even written a book on the idea: "Tattoo A Banana: An Innovative Approach to Everyday Creativity."

"Limitations may be the most unlikely places to harness creativity, "but perhaps one of the best ways to get ourselves out of ruts, rethink categories, and challenge accepted norms."

A 2014 article Fast Company magazine article highlighted several other examples of creative types finding breakthroughs by imposing limitations on themselves to see how they could hone their skills and produce work that would not have been possible if the sky were the limit.

Constraints Shaping Innovation

Physical or cognitive constraints are not always controlled by choice. Sometimes they exist when an engineer or scientist takes up a problem, and their presence shapes the solution or the outcome.

Perhaps the most famous example: The invention of the telephone in 1876 by Scottish inventor Alexander Graham Bell. According to many biographies, the telephone emerged as part of Bell's search for ways to integrate the deaf and hard of hearing with the hearing world. Bell's mother was deaf and an accomplished pianist; Bell's wife was also deaf.

Bell also worked alongside his father as they explored ways of creating "visible speech," something that later became sign language.

Bell's initial focus was on the telegraph but later morphed into efforts to convert the human voice into electronic signals that could be transmitted over wires. Bell received the first patent for the telephone in 1876 and eventually started the company that would become AT&T.

A Solution Driven by Poor Eyesight

The development of eyeglasses has a much longer and older history than the telephone. Still, it represents another example of a physical limitation leading to a technological breakthrough - even if that breakthrough was primitive at the time.

Eyeglasses could date back 1,000 years or more, as the historical references are unclear. One of the first people associated with the development of spectacles was Roger Bacon, a Franciscan friar and scholar. The Guinness Book of World Records credits Bacon with creating the first magnifying glass and says he was motivated to help older Franciscans continue their work and service to themselves and others.

Ultimately many historical sources attribute the development of wearable eyeglasses to Italian Monks in the 13th Century. But the catalyst from the start was the knowledge that the older you get, the poorer your eyesight becomes.

Using Modern Printing Technology to Create Affordable Prosthesis Hands

Some physical challenges point to apparent solutions. But those solutions may be too difficult or costly to produce, leaving progress at a standstill. It took creativity, resourcefulness, and determined thinking to overcome obstacles on the way to breakthroughs.

That's the great lesson behind creating a robotic limb for Liam, a 5-year-old South African boy born without fingers on his right hand. The hand resulted from a unique collaboration between two entrepreneurial-minded tinkerers committed to making good come from bad.

Ivan Owen of Washington and Richard Van As of South Africa teamed up across the miles to figure out a way to create an open-source design for using 3D printers to produce robotic hands. At the time of their collaboration, 3D printers were an emerging technology searching for useful and practical applications.

Van As had a vested interest in the project that made him determined to find a way. He was a carpenter who lost four fingers in a workplace accident. When he investigated possible prosthetics, he discovered that the options were either too costly or not likely.

Hundreds of people have been fitted for these printed hands since the Van As/Owen collaboration began.

Innovation Creating Constraints

The state of the natural world in the late 1800s created a constraint that led directly to the development of another innovation that we probably take for granted today. Until the invention of the light bulb, days slowed and eventually came to an end when the sun went down. Without a consistent light source, there wasn't much else to do except go to bed.

As with many inventions, the development of the electric light bulb was not the result of one big "eureka" moment but rather a series of small steps along the way. Thomas Edison is widely credited as the inventor of the light bulb, even though he and his team built on and benefited from three or four decades of different lines of research.

The constraint of lack of light brought the light bulb into our lives. And in a way, it has led directly to other types of constraints. Now people can stay up later than they should because they have reliable power and sources of light. And as a result, we're getting less sleep.

Breaking Free So Small Businesses Can Blossom

Constraints often exist at the outer limits of technological capabilities and entrenched business models. The ongoing revolution in the payment industry, triggered by Square, illustrates how creative thinking can lead to solutions that help the economy grow.

The genesis of Square, a peer-to-peer payment system, traces back to a friend of Twitter founder Jack Dorsey. The friend was a small business owner who made and sold artisanal glass faucets. One day he got an inquiry from a customer in Panama who could only pay using an American Express card -- which the friend did not accept because of high fees.

Enter Square. Dorsey and his friend conceived of creating small dongle-like card readers that could be attached to mobile devices such as smartphones and iPads. In doing so, Square provides every merchant with an always-on point-of-sale system wherever they are in the world.

The innovation was not just in the hardware/software connection. Square offers a simpler upfront flat fee for processing credit card and debit card transactions. All types of cards are charged the same fee.

Management Thought on Constraints

The idea that constraints can trigger creative thought and breakthrough solutions increase traction as part of management science and theory. It has been explored in book form and in multiple business articles.

A recent Harvard Business Review article, for example, cites the example of a General Electric electrocardiograph machine. Engineers were given a challenging set of specifications they had to meet in the device's design -- for instance, management gave them 18 months and a $500,000 budget, which is modest at a research-driven organization such as GE.

"The next time you struggle with innovation, take a look at your constraints structure," the article's author, Professor Oguz A. Acar of the City University of London, writes. "Instead of blaming them, frame them as creative challenges. Tell your employees that constraints help by ensuring focus and direction, and ask them to take up the challenge." And don't forget the many successes throughout history, as forecast years ago by Blaise Pascal.