User Portlet
It's March 7, 1978. I'm about to graduate from high school and the Marine Corps recruiter thumps on my door. He wants to talk about life after graduation. I begin to think: "my grades aren't very great, there's no way to afford college; furthermore, school is hell!" He tells me adventure and glory are just one signature away and that I would make an excellent Marine! He tells me it will be the hardest, yet most rewarding career I could possibly experience. In short, he walks away with my John Henry. I served my time and then began a long second career in the construction trades. But something kept gnawing my guts out! Ever since a childhood dream that spooked me after hearing a preacher talking about, everyone has a time appointed to die, "God has your number." In my dream, God literally, showed me a number written on a child's writing board and told me it was mine -- (Could that have been a premonition of the MRB constant?) -- I always had an undeniable craving in me to leave a legacy that would help people in the future know I was here. I swore that if I didn't, my whole life would have been a total waste!
Discovery of the MRB Constant
My journey to discovering the MRB constant began with a deep fascination for mathematical series and their properties. This fascination was first ignited in the seventh grade at Forest Manor Junior High, where my favorite teacher, Miss Global, used an individually paced program to teach math. With very little effort, I was doing algebra by the end of the year, and math remained my strong suit throughout high school.
It's March 7, 1994: Welcome to my cave, a damp, dark, and dreary apartment where the dim light of an old television set continuously petitions my undivided interest. Yes, it, my dearest confidant, is always present to greet me after work. My only more zealous companion is total exhaustion from another ten-hour day of siding houses. Consequently, incapable of resisting its hypnotic power, I collapse into my recliner. The age-softened, albeit somewhat torn leather sensuously swaths my aching shoulders, once-broken back, and bruised neck. Hence, I assume a nearly horizontal position, leveraging my feet to just the optimum height for both snoozing and watching.
My mind assures my heart; my job is through for this twenty-four-hour life rotation, further assuming at best it is time to reflect on how much money I have earned, or at worst to envision all those things that I should have achieved in life. As a Roman Slave Master would have chained a galley slave to his oar, the absence of invention and poverty of purpose shackles my hand to the remote control. Here I lie, spellbound. Sounds and images cycle before me. Faster and faster, my forefinger makes love to the channel selector. The stations run their course at an exponentially increasing rate. As a condemned prisoner awaits the throw of the death switch, my mind entreats, haste the time when sleep silences reason. Then, as sudden as a coronary, my aching heart replies, Is this all that there is to life, one miserable TV show after another, bed, work, one miserable TV show? Of what benefit is it even to be alive? Of what good, to the world, is this mind? The deceased care not. They have no abated hope. The dead grieve not. They need no destiny.
No more! Frantically wails my dying heart, Mind, no more will you be useless and unproductive flesh; but creative spirit, have I made thee.
After this pivotal moment, I decided to change my life. I turned off the television and began writing out the powers of two. This seemingly simple act sparked a two-year journey of buying blank paper, squeezing the led out of pencils, and wearing out my vision making math tables. My imagination ran wild, and I felt as though I was altering my future and that of many others for the better.
Through extensive experimentation and analysis, I was able to define the MRB constant as the upper limit point of the sequence of partial sums of the series: $$ S_n = \sum_{k=1}^{n} (-1)^k k^{1/k} $$ As ( n ) grows to infinity, the sums have upper and lower limit points of approximately 0.187859 and -0.812140, respectively, separated by an interval of length 1. This constant, which I initially called the "root constant" (rc), was later renamed the MRB constant at the suggestion of Simon Plouffe.
The MRB constant is significant not only because it represents a new mathematical constant but also because it highlights the beauty and complexity of alternating series. While the constant does not yet have a known closed-form expression, its discovery has opened new avenues for research in number theory and mathematical analysis.
The discovery of the MRB constant is a reminder of the importance of curiosity and persistence in mathematical research. By exploring the behavior of series and seeking out new patterns, we can uncover constants and properties that deepen our understanding of mathematics. My journey from a struggling individual to a discoverer of a mathematical constant is a testament to the transformative power of curiosity and dedication. It is a testament to the power of curiosity and experimentation in mathematics.
Now, March 7,2024, you now know me for the never-ending decimal that haunts your calculators – the MRB constant. ![If you see this text, the images are not showing. Refresh the page.][7] ![The first 100 partial sums of][8] {![the CMRB series.][9]}