I'm so proud to be giving my first lecture on the MRB constant at IUPUI on Tuesday, Jan 24, 2023.
Any advice?
I've attached a rough draft of my presentation and added images of it in a notebook below.
Just the printed text follows the images (text embedded).
Just the printed text:
original thoughts, being passionate
precious thoughts, humble
I’m known for discovering, or rather, inventing, an attractive quantity that has been read in Wikipedia two
million times.
Does that, then, a mathematician make?
Not entirely, merely insane.
It’s 1994, and as you wouldn’t treat a dog, 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 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 in life, one miserable
TV show after another, bed, work, one miserable TV show? Of what good, to the world, is this mind?
The deceased care not, have no abated hope grieve not and need no destiny… I DO!!”
“No more!” Frantically wails my dying heart.
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:
From 1*1=1 I got 1^(1/1)= 1^(2/1^2)
From (one squared equals one) I got the (first root of one) equals the (one squared) root of (one
squared).
From 2*2=4 I got 4^(1/4)= 2^(2/2^2)
From (two squared equals four) I got the (fourth root of four) equals the (two squared) root of (two
squared).
From 3*3=9 I got 9^(1/9)=3^(2/3^2)
From (three squared equals nine) I got the (nineth root of nine) equals the (three squared) root of
(three squared).
So, in general,
From n*n=n^2 I got (n^2)^(1/n^2)=n^(2/(2^2)^2)
From (n times n equals n^2) I got the (n^2 root of n^2) equals the (n squared) root of (n squared)
which is just an echo. Thus, I went from squares to roots.
Trying to form an original statement, I asked what If I would add them and all other principal nth roots of n
together in an alternating series and call it the root constant?
What was 1-sqrt(2)?,1-sqrt(2)+3^(1/3)?, 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 if I go until the 10th
root of 10?” Got 0.3…. “Until the hundredth root of a hundred?” Got 0.2…. “Until the thousandth root
of a thousand?” Got 0.1... “Until the previous odd number?” I got exactly one less.
I did it: I invented a new mathematical constant, so I told everybody. I didn’t care how much they
knew. They must know it!
My peers all said I was crazy. But without missing a beat, I went on and started writing mathematicians.
Without asking for my permission, they simply began publishing the Marvin Ray Burns constant (MRB
constant). (WOW!) I haven’t come back to earth since!
I found MRB constant (CMRB) by adding Grandi’s series to the following divergent sum,
can be proven to be convergent through simple calculus.
Proof of B
The following image is from Abel–Plana formula - Wikipedia, where there is also a proof
In the yellow highlighted areas, the Abel-Plana formula works for CMRB and other Abel-Plan formula
integrable series.
https://www.wolframcloud.com/obj/bmmmburns/Published/Abel-Plana.nb?
n digits prototype of MRB constant sum converges after about 10^(n+1)
iterations. However:
[Read slowly] Integrating over every 75i yields 100 addition digits of M2=
Attachments: