“Your life will be a story. It will be your story, with its highs and lows, its heroes and villains, its forks in the road that mean everything.” – Steve Jobs

It was a hot summer afternoon. The sun was starting to make its journey to the horizon. I was riding home on my bicycle after school. It was muggy but I was enjoying the cool breeze as I coasted down the neighborhood street. As I passed under a canopy of trees, I noticed how the branches were casting interesting patterns of light on the pavement below. It seemed to dance back and forth across the narrow road as if it were swaying to the music. My tires hummed along, wading through the light and dark patches. In the distance, I could hear cicadas. Their loud evening ballad of electrical buzzing sounds seemed to reach a crescendo as I drove deeper into the woods.

Click, click, click. My pedaling and the chain of my bicycle added a soothing rhythm section to the ambient song. I saw birds swooping from tree to tree and gently landing on neighboring power lines. They chirped and chattered, comparing notes from the day’s adventures. It was refreshing. I let my mind soak in everything around me. It was so peaceful. I was almost home.

I often think of moments like that and love to relive those times. My mind is full of stories, recollections, and feelings. Each passing year, I add more to my collection. They are like magical golden blessings that grow more valuable the more you remember them, tell them, and use them. Few things in life are like that! Stories are powerful.

We are storytellers. We craft and crave narratives that inspire, inform, and entertain us. Since the beginning of our human family we have passed down our experiences and knowledge through stories. They connect us. They bridge our human experience. They transcend time and space. They are deeply part of what it means to be human.

As we approach World Storyteller Day this Wednesday, think about your story. How is your story going? What can you tell or teach us? Don’t be afraid. Tap into your memory and find one of those gems. Relive that moment and maybe even consider telling it to someone else. That’s what it means to be human, after all. We are storytellers.

Excuse me for a few minutes… I need to get back on my bicycle…

A Slice of Pi

Archimedes poised to measure a circle behind him in the distance.

Circles. Those fascinating geometric shapes have perplexed us for millennia. The Babylonians began poking at these mysterious objects 4,000 years ago and discovered that the distance around a circle was slightly greater than 3 times its width, specifically 3 1/8 or 3.125, which they recorded on a stone tablet. About the same time, Egyptians, seeking the area of a circle, estimated the ratio to be 3.1605 and recorded their estimation in the Rhind Papyrus (1650 BC).

Fast forward to ancient Greece, Antiphon and Bryson of Heraclea developed the innovative idea of inscribing a polygon inside a circle, finding its area, and doubling the sides over and over. Unfortunately, their approach meant finding the areas of hundreds of tiny triangles, which was complicated and yielded very little results. Then came Archimedes. Instead of computing area, he focused on estimating the circumference based on the sum of the perimeter edges of the polygons. Imagine iteratively doubling the sides of these polygons, slicing them into many tiny triangles, each subdividing the former and pushing closer to the circle’s edge. Using a theorem from Pythagoras, Archimedes was able to compute the length of the sides of these right triangles. As he progressed, dividing the former triangles into smaller ones, an ever more accurate estimation of the circumference emerged. He started with a hexagon, then doubled the sides four times to finish with a 96-sided polygon. Through this method, he narrowed down the value to between 3 10/71 and 3 1/7 (3.141 and 3.143).

Using right triangle geometry and Pythagorean theorem, a2 + b2 = c2, you can compute the length of the edges to approximate the circumference of the circle.

Over the centuries, mathematicians across cultures and continents refined these approximations, each contributing a piece to the puzzle of this magical number. However, it wasn’t until the 17th century when mathematicians like Ludolph van Ceulen calculated this golden number to an unprecedented 35 decimal places. Humanity’s relentless pursuit of mathematical precision didn’t stop there. Our fascination with this mysterious golden ratio continued to motivate mathematicians, engineers, and enthusiasts alike. In 2022, researchers at Google announced computing it to 100 trillion decimal digits.  We still haven’t found the end. Its digits extend infinitely, never repeating in a discernible pattern, yet holding the key to understanding the fundamental property of circles. 

Of course, this fascinating ratio is the number we call Pi, represented by the Greek letter π. As we approach Archimedes estimate of 3.14 on our calendars as March 14, Pi Day, let’s celebrate the enduring curiosity and perseverance of our human family that led to the discovery of this remarkable number. It reminds us that even the most complex mysteries can be unraveled with dedication and ingenuity.

Here is a slice of Pi you can take with you this week. This simple python script will compute Pi to 100 places using Archimedes’ approach:

from decimal import Decimal, getcontext

def pi_archimedes(n):
    Calculate Pi using Archimedes method with n iterations to estimate Pi.
    This method approximates Pi by calculating the perimeter of a polygon 
    inscribed within a unit circle.

    Polygon edge lengths are computed using the Pythagorean theorem and 
    the geometry of the polygons. The number of sides of the polygon is
    also doubled in each iteration, as each side of the polygon is 
    bisected to form a new polygon with twice as many sides.

    The formula is:
        sides = 2 * 2^n
        length^2 = 2 - 2 * sqrt(1 - length^2 / 4))

    After n iterations, the function returns the approximate value of 
    Pi using the formula:
        perimeter = sides * sqrt(length^2)
    polygon_edge_length_sq = Decimal(2)
    polygon_sides = 2
    # Start with a line, then a square, then a octagon, etc.
    for _ in range(n):
        polygon_edge_length_sq = 2 - 2 * (1 - polygon_edge_length_sq / 4).sqrt()
        polygon_sides = polygon_sides * 2
    return polygon_sides * polygon_edge_length_sq.sqrt()

# Set the number of decimal places to calculate
PLACES = 100

# Calculate Pi with increasing iterations until the result converges at
# the desired number of decimal places
old_result = None
for n in range(10*PLACES):
    getcontext().prec = 2 * PLACES  # Do calculations with double precision
    result = pi_archimedes(n)
    getcontext().prec = PLACES      # Print the result with single precision
    result = +result                # Rounding
    print("%3d: %s" % (n, result))
    if result == old_result:        # Did it converge?
    old_result = result



Office with clutter and bookshelves full of books.

“Perfection is achieved, not when there is nothing more to add, but when there is nothing left to take away.” – Antoine de Saint-Exupéry

I confess, I’m a hoarder. I have boxes full of junk that haven’t been visited in over 10 years. There are ancient RCA, S-Video, Coaxial, and even Apple 30-pin iPhone 4 cables, just in case I ever need them again. I have broken electronics and computer parts for the same reason. My nostalgic tendency means I also collect piles of mementos from trips, photos, and even birthday cards. I love physical books and have shelves packed full of them. My digital life is just as bad. In fact, I don’t think I have ever really deleted an app. I collect them like souvenirs. Are any of you like that too?

Clutter. I’m sitting at my desk today in awe of the piles of things around me. Books, magazines, post-it notes, half-completed forms, empty boxes, and some left-over décor from the holidays. I was about to comment on the several coffee mugs sitting on the desk, but that isn’t clutter, that is essential equipment for survival. But still, so much clutter.

My mind is full too. I have to-do lists, incomplete thoughts, spurious worries about implausible events, un-actionable regrets, doubts, and a collection of unhelpful grudges in the corner. My mind is full. Time to relive that embarrassing moment? Worry about something? Think about something you can’t take any action on right now? You might have forgotten it or left something behind, time to worry about it. My mind keeps sorting the useless junk, going back and forth, wondering if it can collect more. It’s like trains of thoughts going in circles. Stop! 

The mental clutter is a bit noisy at times, isn’t it? It can be overwhelming. Do you ever have that? If so, it’s time to clean house. Yes, it’s time for some Marie Kondo magic of tidying up. Go through the clutter… Start with what is around you. What can be tossed. What needs to be kept? Start with what is in reach in front of you. As the haze clears, expand to the office area or room you are in. Be careful, it may get away from you! Don’t try to do it all. After all, we still need to visit the most important place of all. The mind palace. Those trains in your mind that are doing circles around each other, tell them to stop. Look around. Can you do anything about that thought? If not, cast it aside. Wrap up those worries, regrets, and grudges. Pack them in tight, thank them for their better days and ship them off to the garbage. Sweep out the useless fears and self-doubt. Is it getting better? 

Distill, reduce, minimize, and simplify. Clutter happens. In fact, it seems to collect around us like dust with little or no effort. It takes energy to remove it, but happiness awaits! I encourage you to join me in spending a few minutes this week purging the clutter, taming the thoughts, and sweeping out the mess that saps our energy. Find that clarity. Enjoy it and appreciate it! Oh, and set a reminder to do this again next week.

Have a great week!