Days of Pi and Wonder

by Shane L. Larson

My watch on Pi-day, 2012. The time makes the 4th through 8th digits of Pi: 3.14 15926!

My watch on Pi-day, 2012. The time makes the 4th through 8th digits of Pi: 3.14 15926!

Each year when Pi Day (March 14, or 3-14) rolls around, geeks around the world rejoice. Everyone seems to get their geek on, and that makes me walk around with a grin on my face.  People do all kinds of things, like make pies shaped like the Greek letter Pi, or making square pies because they are punny (“pie are square,” which is a pun for Pi*r2, the area of a circle). Or they take pictures of their watches at exactly a moment to write out the digits of Pi.

What is all this Pi business? Fundamentally, it is the number you get by dividing the distance around the outside of a circle by its diameter.  Not just any circle — every circle. It is one of the great wonders of the fabric of the Cosmos that it works for every circle. It’s the kind of thing that keeps me up late at night!

Pi is a natural number that appears from Nature. It is the ratio of the circumference around a circle to the diameter.  It is the same for EVERY circle!

Pi is a number that appears from Nature. It is the ratio of the circumference around a circle to the diameter. It is the same for EVERY circle!

Pi is an irrational number, meaning it cannot be written as a fraction. It has an infinite number of digits that go on and on and on and on.  The first 200 digits are: 

3.14159265358979323846264338327950288419716939937
5105820974944592307816406286208998628034825342117
0679821480865132823066470938446095505822317253594
0812848111745028410270193852110555964462294895493
038196...

You can see a million digits here, and here. There are even more digits (in case you want to memorize them in an effort to attract a date 🙂 ).

Wikipedia lists a LOT of things that happened on Pi Day in history, but I want to focus on a warm spring day in 1879, in the city of Ulm on the banks of the River Danube. On that day Hermann and Pauline Einstein welcomed their son, Albert, into the world.

Albert Einstein is one of the most easily recognized figures in our culture, so much so that he is recognized in imaginary fantasies, like this one of Albert being a master of the electric guitar in my band ("MC Squared and the Relatives"). In reality, his colleague Robert Oppenheimer noted that Einstein was "almost wholly without sophistication and wholly without worldliness ... There was always with him a wonderful purity at once childlike and profoundly stubborn."

Albert Einstein is one of the most easily recognized figures in our culture, so much so that he is recognized in imaginary fantasies, like this one of Albert being a master of the electric guitar in my band (“MC Squared and the Relatives”). In reality, his colleague Robert Oppenheimer noted that Einstein was “almost wholly without sophistication and wholly without worldliness … There was always with him a wonderful purity at once childlike and profoundly stubborn.”

There is perhaps no figure in the world, historical or otherwise, more recognizable than Albert Einstein. His Facebook page has 8.7 million likes (!), even though he died in 1955 (Einstein passed from this Cosmos on April 18, 1955, almost exactly 34 years before the birth of Facebook’s founder, Mark Zuckerberg).  He is widely regarded as one of the towering geniuses of the human race, and was named the Person of the Century in the 20th Century for the impact his scientific findings had on our modern lives. While most of us know about Big Al, do you know how his work filters into your every day life?  Let me tell you a few stories of how it does.

Einstein in 1905 in his famous "patent clerk" jacket. I always imagined it to be green!

Einstein in 1905 in his famous “patent clerk” jacket. I always imagined it to be green!

Let’s go back to 1905. Einstein had finished his doctorate at the University of Zurich, but unable to find an academic position had taken up work as a patent clerk in Bern. Now in those days, there was no evening reality television, no new episodes of Cosmos, so Einstein continued to work on physics “in his spare time.” This is the sort of thing scientists do when we’re between jobs, with the hope that by still being productive we will become attractive candidates for an academic position in the future. As it turns out, Einstein was very productive in 1905. The Latin phrase “annus mirabilis” (“year of wonders”) has in modern science become synonymous with Einstein’s published works in 1905. There were four seminal papers: (1) a paper explaining the molecular origin of Brownian motion; (2) a paper explaining the photoelectric effect by revitalizing the photon theory of light; (3) a paper describing special relativity, and proposing the ultimate speed limit in the Universe; (4) a paper describing the equivalence of mass and energy, captured by the famous formula E = mc2.  These four papers laid the foundations for our understanding of much of what we call “modern physics,” fundamentally altering the way we think about energy, space, and time.  What are these concepts, and what do they have to do with your life?

Brownian motion was named after botanist Robert Brown, who in the early 1800s was using a microscope to observe pollen grains suspended in water. Inexplicably, the grains appeared to move around at random, with no discernible cause. Brown tried in vain to discover the cause of the motion, but could not explain it. He then dutifully did what scientists do, he reported his observations to his peers and the phenomena passed into the scientific memory. Nearly a hundred years later, Einstein showed that the observed motion could be explained by the constant buffeting of the large grains by the motion of the much smaller particles of water that it was suspended in, what we today call molecules. There are many applications for the use of Brownian motion once you understand it. For instance, in modern pharmaceutical manufacturing, medicines delivered through pills are created from a suspension of the active drugs with inactive ingredients that comprise the entire pill; this controls the delivery of the drug on ingestion. Brownian motion is used to control the suspension in the mixing stages, to insure the proper distribution of the active drug throughout the pill.

Mixing pharmaceutical molecules is like mixing marbles. The active ingredients (white marbles) need to be mixed evenly with the inactive ingredients (green marbles). Brownian motion can be exploited for this mixing.

Mixing pharmaceutical molecules is like mixing marbles. The active ingredients (white marbles) need to be mixed evenly with the inactive ingredients (green marbles). Brownian motion can be exploited for this mixing.

The nature of light has always been a matter of intense scrutiny for physicists. In the early 1700’s, Newton famously championed the “particle theory” of light, but these ideas fell into disfavor when a particle approach could not explain effects like diffraction and interference; this gave way to the “wave theory” of light. In 1900, Max Planck proposed his “quantum hypothesis” to explain how objects like red-hot pokers and lightbulb filaments emit energy — in discrete packets called “quanta.” Einstein adopted the quantum hypothesis, and revitalized the particle  idea to explain how some materials eject electrons when you shine light on them: electric particles (electrons) are ejected when illuminated with light (photons) — the “photoelectric effect.”  The number of applications of this effect in modern technology are numerous, including solar cells, the imaging sensors in the digital camera in your smartphone, and remote controls.

Your TV remote emits infrared light (which you eye cannot see). When the sensor on your TV is hit by the light, the photoelectric effect generates an electrical signal that activates the control circuit in the TV.  The image on the right was taken by pulling the infrared filter off of an ordinary digital camera (most digital cameras can see infrared, but that light is blocked so your pictures don't look weird).

Your TV remote emits infrared light (which your eye cannot see). When the sensor on your TV is hit by the light, the photoelectric effect generates an electrical signal that activates the control circuit in the TV. The image on the right was taken by pulling the infrared filter off of an ordinary digital camera (most digital cameras can see infrared, but that light is blocked so your pictures don’t look weird).

Special relativity is one of the most profound and important discoveries about Nature that humans have ever made, and its veracity has been borne out, literally, by billions of experiments since its inception in 1905. Einstein’s insight that there is an Ultimate Speed Limit in the Universe (the speed of light) has profound consequences for how we think about motion and dynamics at high speeds, and challenges our old-fashioned notions about the distinguishability of space from time. Most of us have heard all kinds of special relativity stories about how it changes the nature of measurements of distances and times, and the resulting perception of paradoxes — length contraction, time dilation, old and young twins. It blows your mind and is vaguely unsettling because it seems far from our everyday lives, and as a result our everyday intuition built around watching baseballs, Volkswagens and chipmunks doesn’t seem to apply.

Calvin's father doesn't quite understand relativity. [From Calivn & Hobbes, by Bill Watterson]

Calvin’s father doesn’t quite understand relativity. [From Calivn & Hobbes, by Bill Watterson]

But special relativity explains why we see cosmic ray muons from space when they should have decayed before they hit ground; it is demonstrated by every one of the 115 billion protons the LHC bashed together at a time; and we have discovered that if our engineering is up to it, we can use special relativity to travel to the stars.  Mass-energy equivalence (E = mc2) is usually mixed into our thinking about relativity, and most prominently impacts the world through its application ot nuclear weapons and nuclear energy.  Deep in the heart of the Sun, the nuclear fusion of hydrogen into helium converts some of the mass of hydrogen into energy, which you and I eventually feel as the warm dapple of sunlight during a lazy afternoon picnic.

The Disintegration of the Persistence of Memory, by Salvador Dali. We have a vague and unsettled feeling, especially when confronted by relativity, that we do not understand the fabric of space and time.

The Disintegration of the Persistence of Memory, by Salvador Dali. We have a vague and unsettled feeling, especially when confronted by relativity, that we do not understand the fabric of space and time.

Perhaps the most important way that special relativity changed our lives is that it made us realize that all the laws of physics had to obey special relativity, which led Einstein to think about gravity. It took about 10 years, but he was the first person to understand how gravity and special relativity worked together, and the result was called “general relativity.” Today, general relativity has transformed the world because the Global Positioning System (GPS) would be impossible without it. General relativity (and special relativity) tells us that if you have two clocks that are moving differently, and experiencing gravity differently, then you will think they are ticking at different speeds when you compare them.  What does that have to do with GPS?  

Fundamentally, GPS works by broadcasting a clock signal from satellites. On the ground, your smartphone receives those signals and triangulates your position from the clock signals.  Suppose there are two GPS satellites, one is 100 km away from you, and the other is 200 km away from you. At the same moment, they broadcast their current time, say 2:00pm.  The 2pm clock signal from the satellite closest to you arrives first; the 2pm signal from the distant satellite arrives later. By comparing the arrival times of those two signals, you know exactly where you stand between the two satellites.  Where does relativity fit into this picture?  If you don’t include relativity, the clock signals from the satellites, compared to clocks on the ground (in your smartphone) are different by 38 microseconds — 38 millionths of a second!  That is so tiny!  Does it matter?  Sure it does, because the radio signal from the satellite is a kind of light, which travels 11.4 kilometers (7 miles!) in 38 microseconds!  If you didn’t have a little bit of relativity working inside your phone, your GPS would not be useful for navigation!  11.4 km is a HUGE distance when you’re trying to find a Dairy Queen, the Lego store, a hospital, or your kids’ baseball game.

GPS triangulates your location by comparing the received time from multiple satellites.

GPS triangulates your location by comparing the received time from multiple satellites.

Of course, Einstein’s work did not end with the annus mirabilis. In fact, he had a long and influential career after that, as most scientists do.  Let’s end with a story about a little paper he wrote in 1917. That year, Einstein explained the idea of stimulated emission –– light can cause an atom to emit an identical particle of light, and the two photons can travel along together exactly in synch. Okay, that sounds cool, but so what? You may shrug your shoulders, but what this leads to is the LASER. In fact, “laser” is an acronym built from Einstein’s idea — “Light Amplification by Stimulated Emission of Radiation.”  Einstein was the person who predicted the possibility of building a LASER, though it took until the 1950s for us to develop enough technology that one could actually be built. Today our world is literally filled with lasers — CD and Blu-Ray players, laser pointers, lasers for cutting industrial materials, lasers used to resculpt the lens of your eyes, and a whole host of medical applications.

Einstein is just one example of one scientist who changed our lives with his passion for uncovering Nature’s secrets. There are many examples of other scientists who have had similar influence on us, in ways that you and I don’t often think about nor quite possibly even know. But it is all there in our every day lives, from our trucks and carburetors, to our antibiotics and heart stents, to our smartphones and MP3 players, to our aerobees and yoga tights. It all comes from clever insights, accidental observations, random musings, and delight in something as simple as a round shape called a circle. Enjoy your Pi Day, and enjoy your pie!

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One response to “Days of Pi and Wonder

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