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Marvin Ray Burns
original investigator of the MRB constant
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(You asked for it!) in part.

I just started accumulating all of my writings on the “how, what, when, where, and why” of my math hobby. It is long, but you can let a browser or Word read it aloud to you if you’re not much of a reader:

How did I discover the MRB constant?

What did I discover?

Why did I discover the MRB constant?

When did I discover the MRB constant?

How did I discover the MRB constant?

I discovered the MRB constant back in 1999 while playing with the Inverse Symbolic Calculator. I was looking for an idea for a new constant, by asking it questions: What was 1-sqrt(2)? What's 1-sqrt(2)+3^(1/3)? What's 1-sqrt(2)+3^(1/3)-4^(1/4)? Still curious, I tried to summarize what I was doing and considered the sum's additive inverse and asked what's sum((-1)^nn^(1/n),n=1..10) and got .3132317592546559751298942294317. Then I tried sum((-1)^nn^(1/n),n=1..100) and got .2113295433469410694850358682163. I wondered what was happening to the sum. Later, Steven Finch noted that if the upper limit was odd the sum converged to a different number which differs by 1 since limit(n^(1/n),n=infinity)=1. Neither sum was known to the ISC. Later, however, Simon Plouffe added the MRB constant to his inverter.

Why did I discover the MRB constant?

Drawing from an autobiographical essay about a significant educational experience that needed to have a connection to the book Geeks, by Jon Katz: Dear Reader, journey through the most exciting educational experience of my life. Please be patient and understanding as you accompany me, because you may not understand why I had my priorities or why I made some decisions. My story begins back in 1994, and it is from that time-perspective that you will accompany me.

Welcome to my cave. It is a damp, dark, and dreary fourth-floor apartment where the dim light of an old television set continuously petitions my undivided interest. Yes, it, my dearest confidant is always there to greet me after work. The only thing as steadfastly present as the TV 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 a 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 the creative spirit, have I made thee.

Dear Reader, let me break-in at this time and briefly take you back to my early childhood. My cravings for a sense of destiny began, in a dream that used to haunt me growing up. One long-since-forgotten night, in what must have been a divine calling, I saw a big writing board and on it was some writing and a number. In unimaginable trepidation wondering, what does this mean? I woke up with the impression that the aberration meant that my life had some meaning. Consequently, as a developing child, I always felt unmistakably set apart for some unknown purpose.

Now, Dear Reader, we shall move forward. We pass over to when I was in the seventh grade and first recognized my zeal for math in the open classroom of Forest Manor Junior High. My favorite teacher, Miss. Global, realizing that students bussed in from different grade schools would have an assortment of skill levels, taught math by using an individually paced program. With very little effort, by the end of that year, I was doing algebra. Math remained my strong suit throughout high school.

Now, Dear Reader, out of school and a stranger to “very little effort,” having endeavored to be successful in the military, in business, in ministry, and in general employment, I have lost all hope of mastering any one pursuit. Without single-minded direction, the ache for a sense of destiny only climaxes. Like boiling water in a sealed pressure cooker – soon something is going to change!

Today’s date is March 7, 1994; on this birthday of change, I celebrate another year of slothfulness. Here in this lackluster apartment the dim light of that old television once again summons my mind. Finding that something has changed, this bitter, old sloth finds his thumb, transports it all the way to the upper left-hand corner of the remote and buries the off button into the plastic. Then as strange as it might seem, I begin to write out the powers of two. “22=4… 22*2=8… et cetera.” As if I totally lost my wandering mind and found a working one, I spend the next two whole years buying blank paper, squeezing the lead out of pencils, and wearing out my vision making math tables. In my imagination, the whole world waits for me to put all its problems and solutions together. As for the present, I help no one but I see that in some numinous sense I alter my future and that of many others for the better.

Dear Reader, to help in this strange and yet glorious mission, I purchase my first computer (only a small pre-Palm, hand-held device) but sufficient for me to go onto the Internet. Not long after the purchase of my little computer, I start to post everything I know and then some on math message boards. Soon competent enough to answer many math questions, I develop a reputation for being a good math tutor. Through E-mail, I come across several mentors, who are professional mathematicians. However, my greatest mentor is not from the Internet. My inner self, the “Middle Me” impels me ever deeper into math. As the set of real numbers never ends, my curiosity becomes infinite. In like manner, as Jon Katz did set up the two geeks in the scrawling suburb, Richton Park, my hidden instructor sends me to a vast new world of numbers outside my cave (Katz 55).

Blindingly, after spelunking from my cave, I experience enlightenment surpassing all but my most spiritual experiences – exploring and searching out the secrets of mathematics. When curiosity possesses my imagination, I work besides myself with visions of discovery! One apex of this intoxication is the discovery of a mathematical constant. Dear Reader, you may retrieve links about my constant by entering “Marvin Ray Burns” into any one of the major search engines. Having said, “An enlightenment, which surpassed all but my most spiritual experiences,” perhaps my predicament of lacking in accomplishments would not be so expressively overwhelming if it was not for a time when I truly had felt perfect fullness of achievement.

Dear Reader, please allow me to take you back just a few years. One day, in October of 1979, while in the United States Marine Corps, I was born again and in place of all my vice, vulgarity, and violence, I began to experience joy, peace, and love. Thus, I became zealous in a personal faith in Jesus Christ. I spent several hours every day studying the Bible and communing with God. Furthermore, the sharing of my faith became my favorite pastime. In search of great fulfillment, when the military clock struck 14:2513 June ‘83, signifying that I had completed my enlistment in the Marines, I began preaching full-time. Yes, I lived a high life, full of a sense of achievement. However, my sky-scraping days were short-lived, unfortunately, and in June of 1992, in deep poverty and overcoming debt, I departed from the ministry and gave up on what I felt was all chance of feeling useful. See “My TWO Awakenings” for more on why I gave up.

Having spent two miserable years of exile in this cave of uselessness, I have finally waked up to not having to live as a stranger to value for the remainder of my life. (It is time to wake up and smell the success!) I no longer have to be just a bitter old sloth. From this very day forward, I can devise new ways to let my mind work for me, others, and God. With a completely new world of professions available to me, I ought to initiate a process of preparing my mind for a new service. The aspiration to re-embody myself with destiny is such an excellent obsession! As the two young men from “the poor unrelenting plains of southwestern Idaho”, I begin a journey of providence (Katz 4). As Eric and Jesse’s encounters were with the metropolis of Chicago, so from the poor unrelenting plains of my mind I shall move to a metropolis of ideas.

Dear Reader, it is high time for me to make a serious choice about school. Providence has blessed me with a second chance to further my education. Consequently, I can indeed relate to Katz’s story of helping Jesse enter the University of Chicago (Katz 117). Like Jesse, I am not proud of my high school grades simply because I did not demonstrate any effort to acquire good grades. Instead, I habitually made an effort to learn about only what interested me even though I knew that I was intelligent enough to get excellent grades. If I may brag, I was a successful member of the state champion Chess team and wrote a chess program for computers. I was a Junior Assistant Scout Master, earned the rank of Eagle Scout the day before my eighteenth birthday, and was First Trumpet in Scout Band. I even, in my junior year, graduated two-hundred-twenty-seven out of six-hundred-twenty-one. That graduation trick was quite a feat, considering I only attended classes three hours per day that last year of high school.

I guess a significant amount of talent and the desire for education was in me back then; I just did not care to take advantage of it. I knew more about computers than most college students did, so I could have gotten a job working on them – without college – if I had wanted to do so. However, more enticing was the possibility of enlisting in the Marine Corps and retiring in a short twenty years. Then there was the fact that no member of my family had ever gone to college. Neither of my parents had gone to high school, and they sure were not going to pay me to stay at home four to eight more years. Nonetheless, to be honest with myself, I guess the true reason I did not go to college was that I plain hated school.

Now, Dear Reader, having successfully climbed out of my cave of self-imposed ineffectiveness and ignorance and having accepted as my own, the highest standards of achievement, I push myself beyond educational limits that I have for over twenty years accepted.

In solemn introspect, Will I accomplish great things? Else, will the dim light of the television again master my mind and the lack of purpose shackle my hand to the remote control? Let no such thought protrude! I just submerge myself in the study, not in inanity. I must press on because there is a place that I must get to, moreover a person I am obligated to become. In failing to become that person, I would be cursing each of the years in which I have lived. Now, Dear Reader, not only is it my destiny to be a legend in my own mind but more so, a legend of the mind. Consequently, as I progress through my middle age, I trust that my wit will only sharpen. Therefore, when old I will release reserves of wisdom to the young from a storehouse of knowledge.

More generally, Dear Reader, I do not know why my life takes this turn. Is it just a mid-life-crisis inspiring me to begin a new career? On the other hand, is my crisis a part of a divine calling for my life? Still, am I just possessed with impulse and madness, or worse is it just a random chance that I take this turn in life’s road? Whatever it is, it metamorphoses my listless existence. More specifically, the exchanging of my purposefully bankrupt mind, for one that can actually see into and improve the future, begets within me craving for education. With the desire for knowledge, so comes promotion psychologically, socially, and spiritually. Most remarkably, an impractical little hobby like writing math tables indeed expands to become a symbolic token that I might never again feel so useless and unproductive. I now possess, more than ever before, a creative spirit and mind. Additionally, my overwhelming craving for a sense of destiny gloriously empowers me to create a legacy.

To follow-up, I bring you, Dear Reader, to December of 2001. Reading Katz’s Geeks, I feel as though I am reading a metaphor of the very experience that caused me to break out of my hapless cave and go back to school. I have never lived my life in such a way to make it look normal, and I have always tried to be me no matter how strange that may seem. Therefore, it was with mixed feelings – the fear that you might consider me to be strange – and the anticipation of sharing my vision that I considered hosting this journey from acrid, aging artisan to a portent prodigy of providence. Having understood most people have given up trying to find happiness or purpose in their existence, I considered it my responsibility to guide this journey. I put “hand upon keyboard” so you too may sing my chorus of change and gain a greater hope of having a productive future. Finally, in the hope that you will follow my example of leaving the dreary cave of mental darkness, I commend to you, Dear Reader, the spirit of destiny.

My TWO Awakenings as published in the mid-2010s:

I attended public schools and in 7th grade found that I could excel beyond my grade level in math. After high school graduation, I joined the military as an electronics technician, after which, I did mostly construction work, but perceived a “calling” to do something that had more effect on the world. After a failed spiritual attempt to find that calling, in a moment of crisis in 1994, I suddenly became obsessed with experimenting with mathematics. I first described the MRB constant (A03077) in 1999, and I find that I become very depressed when I am not actively pursuing my math hobby, so I spend all of my free time doing, writing or at least thinking about it.

I was a Boy Scout and I remember the pursuit of one merit badge really excited me; it was the Computers Merit Badge. Ever since then I've been fascinated by computers and calculators. In my Junior year in high school, I bought a TI-58 and matching printer from the money I earned from my Laundromat job. I was heavily involved in chess at that time and soon found a way to make my calculator emulate playing chess by making random legal moves. I later wrote a better program, which had a few openings memorized, for computers. I also found that I could actually make a little money by selling biorhythms computed by my calculator.

Marine Corps Boot camp was rather stressful, and I remember that one distraction that helped me cope was writing small "Basic" computer programs in my head. It did occasionally interfere with my mental performance, but I made it through OK anyway. The stress wasn't all bad; sometimes it motivated me and helped be to be proud to be a Marine. I would like to think that the stress had nothing to do with it; but, then there was that first pivotal point in my life: when I was stationed at 29 Palms that I had a spiritual awakening, and like I do with everything else, I took it to the extreme! I became quite a Christian fanatic and spent all my free time reading books on theology and at the same time endeavoring to see God at work in my life. I must admit that I did see evidence of God “working,” but how much of that was just my perception? I spent all of my expendable income, including selling my favorite calculator, to buy books and tapes; it sounds kind of silly, but something was building up inside me. It was something that I had to some degree for as long as I can remember. It was a sense that I would accomplish something in my life that would truly make me feel satisfied.

My Christian experience as a Marine was mixed with a measure of mysticism. The typical religious surroundings in 1979 were not as charismatic as they are today. Nonetheless, I was exposed to some early version of today’s mainstream “faith” theology. With only a feeling that something was true about it and absolutely no formal training, I soon diverted into a little bit of a mystical experience. I began really searching for evidence of God influencing reality; it became quite an obsession! I found that the mind, a part of the soul, could “receive revelation” about God, his will, and the nature of the universe. As with any such half-baked pursuit, my experience had a great deal of failure. However, there was a small amount of perceived success, which I guess, kept me going.

The euphoria of spirituality was all-consuming. So, consuming was it that my perception of reality changed from one that said that the universe was simply observed by people to one that said people through faith change the universe. Living in the desert, I would try out my faith powers and do really silly things. On one particularly hot day, I commanded the weather to consist of rain; I said it out loud! There was a friend whose spiritual interest I was trying to stir up present when I did so. The initial response was of course the impression that I made a fool out of myself. That evening we went to Palm Springs, almost a weekly experience, and staying at another friend’s house that night it started to rain so much that many of the streets were flooded. I then subtly reminded the bystander of my previous proclamation. Then there was the Friday that I felt lead to visit a certain location in Los Angeles. I had the money for a bus ride there, so I went. I left 29 Palms around 4:30 PM. The bus route transferred at Palm Springs and left for LA sometime around 7:00. Needless to say, it was night when I got there. The first thing that happened when I left the bus station was a gang of juveniles accosted me. Being in my “spiritual” frame of mind, I shined them on with a few religious phrases, and they went on to bug someone else. Throughout that night I simply followed a map in my head and went on a guided tour hosted by my thoughts. It was like I was dreaming; it did last all night. I saw what people did in the past, what they used various buildings for, and considered the spiritual state of them and the people who presently lived there. After my walking dream, I was presented with a small problem; I didn’t have the money to get home. Following my inner guide, I found the perfect solution. I bought a ticket to Palm Springs, spent the day with friends, and on Sunday I hitchhiked back to base.

My four years at 29 was filled with such experiences. I did mellow somewhat, however, in my spiritual taste; and by the time I left the Corps, I had at least an artificial aura of maturity about me, and followed the impressions I got from my inner guide to occupy myself with communicating with others all of the spiritual things that I had learned.

[In this space I would like to talk about my life from 1983 to 1994.]

After my Marine Corps experience, I was quick to call myself a “minister” and looking for people willing to listen to all I had learned. I was never a good communicator of my faith, however. I was always too conscious of the fact that many people thought what I had to say was “crazy,” and a few others thought what I had to say was spiritual. I was quick to decide which type of person any individual was, and I usually only spent time teaching the ones who I thought would accept what I had to say.

I did travel to Pennsylvania and New York, as well as a few churches here in Indianapolis “ministering.”

I believed that God would often speak through me and deliver supernatural power to those I was speaking to. I would usually end up telling people what all was bothering them and would attempt to heal their afflictions. Remarkably, a few of them would seem to get better after I was through doing my thing! I now assume the good effects was simply the power of my suggesting that they would get better; that focused their mind on getting better and even if they didn’t really get better, with their mind so focused, they only believed that they were better.

I found a great mentor, a pastor of a growing church who helped me mature in my spirituality. By mature, I mean that I began to communicate a more accepted form of the faith message than what I learned on my own. After learning that “improved” spiritual etiquette, I talked him into sending me back to California to share what I now learned and start churches. I called that an apostleship. It only lasted a little over a year, however, because my mentor was gravely ill and my wife at the time insisted on going back to Indianapolis. I thought it would be hypocritical to divorce my wife to stay in California. After a full night of crying, I relented.

My wife at the time was diagnosed with a mental illness that more than a few times left her in the hospital. I often felt guilty about her illness and thought that if I was really seeing God at work in my life that I could heal her! We soon had our first divorce. During that divorce, I began taking care of my mom who was suffering from Alzheimer's. I spent about five years taking care of her full-time. Finally, after I could no longer take care of her, I found a nursing home for her. I remarried my wife at the time during those five years, but we lived separately until my mom passed away. While I was taking care of my mom I began going to school (one or two classes a semester and tutoring and mentoring). Having no one else to take care of mom, I often brought her to school with me, where she sat quietly in calculus class.

That predicament changed my main pursuit in life from spirituality to find all I can about numbers, which involved the death of a major goal in life and the death of a mentor. But the point is that it was only a transition, an abrupt one, but it wasn’t a change in my level of passion and not necessarily a change in my level of faith. It was only a change in how I used it.

There seems to be a use for faith in exploring numbers, and of course, it has nothing to do with trusting what other people have said about them. It is a faith that says my imagination is the only limit to what I can find out and I can even discover things that haven’t been noticed before!

Although I am listed in Wikipedia as an amateur mathematician, I only study what interests me which is amazingly narrow. More specifically, I only study what I think can empower me to find original ideas and thus give me some long-term fulfillment. Since the time when I first described the MRB constant, most of my studying has had something to do with it. It has become quite an obsession!

In a since, what I feared has come upon me: I remember back in 1994 when I started my math hobby, I went to a library and read a book on mathematicians. I noticed that many of them had miserable lives outside of math. And it seemed that they were “possessed” by a spirit of math. I still called myself a Christian at that time and was horrified at the prospect of being possessed by anything but God! Perhaps I shouldn’t compare myself with those great mathematicians, but my life has indeed become centered solely on my math hobby to the point where often nothing else matters. I spend all my free time and disposable income on my hobby. I often pay google AdWords to get people to visit my website and see my work. I don’t know if it does any good to the furtherance of my legacy, but I just feel miserable when no one visits. As sad as it might sound, I even went as far as divorcing my wife again to help ensure success in my hobby. And when I feel my math hobby is being threatened, I become suicidal! They put me in the hospital for that one time!

My life would indeed seem silly if it wasn’t for the fact that real scholars have benefited from my little hobby. I’m not one to mention names, but you can find them and what they did with my MRB constant on Google Scholar.

What did I discover?

And was it a discovery or an invention?

I usually look at the coming about of my MRB constant as an invention of my faith in mentioning something that has been overlooked. Due to a great psychological crisis, I wanted to “come up with something new or die!” (That was my thinking.) I used what I already knew about, High School level integer roots of themselves, and tried to put them together in some way that made any mathematical sense, and which was not already discussed. (I did not really think of its usefulness, but fortunately, others [and myself to a small degree] did in time.) Thus, I usually call myself its “author.” You could say that I discovered something new to many people by inventing a formula.

According to MathWorld:

MRB Constant