Happy Pi Day!

According to Schoolhouse Rock, three is a magic number – and it is. But just as pi is equal to a little more than three, pi itself is a little more than magical. It is downright metaphorical.

Mathematicians, scientists, and philosophers have been chasing down the elusive number for thousands of years. Pretty much since we gained awareness of numbers themselves, and round things. It didn’t take us long to figure out that the ratio between a circle’s circumference and its diameter was a constant number or that the number was just over three, but several hundred lifetimes would pass before we got more accurate than that.

*What do you get when you divide the circumference of a jack o’ lantern by its diameter? Pumpkin pi!*

The true quest for pi was borne out of our desire to “square the circle”. In a literal, mathematical sense this means finding a simple – or at least consistent – way to calculate a square with equal area to any given circle. Symbolically, squaring the circle is a much deeper human desire.

Circles have always been mysterious. They represent the infinite, even sometimes defined as “a polygon with infinite corners.” With no beginning or end point, they symbolize that which is eternal and immeasurable. According to Nietzsche and Matthew McConaughey, time itself is a flat one. Even this post is circular (it ends where it begins). Circles are unknowable, spiritual.

Squares, on the other hand, are a symbol of all that is solidly defined. They are firmly knowable, easily measured, comfortably comprehensible. There is a reason one of the earliest words in our culture for the nerdy and rule bound was “square.”

To search for an exact value of pi – to seek to square the circle – is to attempt to make the unknowable known. To define the undefined. Another term for pi is the “circular constant”, or in other words a mystery that is rock steady.

*What was Sir Isaac Newton’s favorite dessert? Apple pi!*

Historically, some have considered this quest to understand the mysterious a dangerous game. The poet John Donne wrote the verse, “Eternal God – for whom who ever dare / Seek new expressions, do the circle square, / And thrust into straight corners of poor wit / Thee, who art cornerless and infinite,“ explicitly condemning the search for an exact value for pi. Many more, like Archimedes, devoted their entire lives to the quest. All of them died without reaching it.

Because, of course, the quest is impossible. It took us several thousand years, but eventually (by the 18^{th} century) we humans finally proved that the number pi is irrational – its digits go on forever and never repeat. About a hundred years later, we also determined that pi is transcendent, which means it is not the solution to any algebraic equation. Irrational and transcendent – just like the human mind.

Those two vital discoveries – that the circular constant is both never ending or repeating and impossible to equate – combine to prove without doubt that we cannot find a square with equal area to a circle. The circle, quite literally, can never be squared.

*“Secant, tangent, cosine, sine, 3.14159!” – MIT cheerleaders
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So the number pi is simultaneously proof that some things can never be known *and* that there are rock-solid constants we can rely on. Constants such as our drive to always dig deeper and know more, even if we can never understand it all. No wonder pi is the most enduringly studied number in human history.

These days, pi continues to symbolically bridge the mysterious and the defined. It has become our computational bedrock, used to test computers for bugs or weakness, and at the same time our mathematicians are scouring its digits through billions of decimal places (and counting!) in search of any pattern or logic to its order. So far, we’ve found nothing. It is proving uniquely and stubbornly random.

*“Knowledge is limited. Imagination circles the world.” – Albert Einstein*

On March 14^{th}, we celebrate this metaphorical number by eating pie, something both circular and delicious. We also celebrate another wonder of the universe – Albert Einstein, who was born on 3/14/1879. Einstein himself is a perfect representation of pi’s duality, as his life continuously bridged math and creativity, science and spirituality, and social consciousness with humor. He understood better than nearly anyone the perfect paradox embodied by pi: that the more we learn, the less we know.

Or, to put it in terms of the constant itself, “the wider the circle of light, the larger the circumference of darkness.” (Not an Einstein quote, but one of *his* favorites.)

Happy Birthday, Albert. And…

Happy Pi Day!