“The paper doll hyperplane theorem can be applied to all n-dimensional time spheres in m-dimensional Euclidean space using a series of nine sequentially linked nonahedrons [1 Definition: Any of the 2,606 topologically distinct convex polyhedra that have nine faces.] This activity results in an alignment of time streams thereby breaching the reality of personal continuums and providing direct access to unfiltered infinity.
To test this theorem, I will dispatch nine randomly-chosen people into the n-dimension. Subsequently, this paper will discuss the outcome of my experiment upon the recently dead.” [2 Riemann, Zachary H. “The Effect of n-dimensional Hyperplane Alignment on the Recently Dead” Unpublished Working Papers, 2014]
QUINN UNIVERSITY LECTURE: MELANCHOLIA I
The students rustled books and papers and at least half a dozen napped. That’s the problem with early morning lectures. Brown bottle flu is a mathematical conundrum unsolvable by most university professors.
I darkened the room as the InFocus warmed up. The projector bulb clicked and an image lit the screen behind the lectern. I heard groans as bright light pierced their eyes. I almost pitied them; I do remember my undergrad years.
“Turn to page 93 of the course materials,” I said into the mic. “I’ll start today’s lecture with our friend Albrecht Durer. Behold Melancholia I.”
I motioned to the image on the screen behind me.
“Observe that a winged woman sits and ponders the world, a compass grasped in one hand, a ring of keys tied to her belt. Her cheek rests on a clutched fist as she observes. The original engraving contained at least twelve clues to its meaning—a meaning instantly understood by any educated medieval viewer but which is hidden to us—sort of like The Da Vinci Code.”
Now I had their attention. Anything that smelled of a Hollywood thriller always grabbed their interest. It’s a cheap professor trick but I use it on the first-year students every semester.
I continued.
“You need to understand that melancholia, the effect of Saturn on man and the subject of this engraving, was the least desirable of all humours to Western medieval society.”
By now, my eyes had adjusted to the darkened hall and I could see a couple of raised hands.
“If you missed last Tuesday’s lecture about humours, please review the lesson on my YouTube channel.”
The hands withdrew.
“At the beginning of the Renaissance, melancholia was associated with depression, apathy, lethargy, and insanity. On the upside, it was associated with intelligent and creative persons such as artists, musicians, carpenters, physicians, and mathematicians. And that’s why we’re looking at Durer in today’s lecture. The engraving offers a mathematical proposition and proposes a philosophical solution. Take a moment. Do you see it?”
I sipped water from a bottle and waited for anticipation to build. Soon, restless bodies straightened in their chairs, papers rustled, someone coughed.
Stumped, every one of them.
B. F. Skinner is dead but not gone. [3 Skinner, B. F. Science and Human Behavior. New York: Macmillan, 1953. Print. “The strengthening of behavior which results from reinforcement is appropriately called ‘conditioning’. In operant conditioning, we ‘strengthen’ an operant in the sense of making a response more probable or, in actual fact, more frequent.”]
“First, let’s consider the problem,” I offered. “It is despair which leads to melancholia which destroys power and wealth as represented by the symbolism of the keys and the purse. The hourglass represents the inevitability of time. See the bat? Boiled bats were believed to be a cure used by the rich. The wreath is likely made of hellebore or dodder-vines, plants believed to relieve depression. Unfortunately, as we know today, no remedy actually provided relief.”
I lectured on for thirty minutes, my usual polemic on problem-solving. Or maybe rhetoric is a better word. What I told them was to isolate a solution, one must properly define the problem. And that’s what Durer shows us in Melancholia I. When I sensed the students couldn’t take much more, I relented by showing them the mathematical clue.
A red dot appeared on the screen as I clicked on my laser pointer.
“In the upper right corner of the engraving is a series of numbers on the side of a building. This is a mathematical magic square where the numbers all add to the same total – vertically, horizontally, and diagonally. Cleverly, the numbers 15 and 14 appear in the bottom row. This is the year that Durer’s mother died and the presumed year of the engraving. The magic square adds to 34. This was a talisman thought to attract the ancient god Jupiter who was believed to offset the influences of Saturn. The real secret revealed by Durer is the bell above the magic square. The bell represented eternity, and this reflected an emerging Renaissance belief that mathematics held the key to explaining the universe and the fabric of reality itself.”
Ironically, the school bell chimed indicating the end of the lecture.
“To sum up,” I said. “Mathematics is the path to a singular definition of the universe. More on that next week.”
The students hurried out, in need of coffee. As I gathered my papers, a pretty blonde approached with an armful of textbooks.
“Professor Riemann …”
“Call me Zach,” I said. “All the students do.”
“Ok. I’m having problems with the concept of palindromic primes, especially in the context of a magic square.”
She hesitated then added my name: Zach.
“Sure,” I said. “Why don’t you drop by my residence at seven tonight? I have an office there. We can go over your questions then.”
She smiled that sweet undergraduate smile.
She looked a bit like the woman in Melancholia I.
“I’m Madeline Blake,” she said, reaching out her free hand for a shake. “Everyone calls me Maddie.”
Her palm was shiny damp.
I shook it.
QUINN UNIVERSITY
(BROCHURE)
“Located in the Mad River Valley of Vermont, Quinn University is a residential campus occupying 4,000 acres of rugged foothills and forests. Previously a logging community and sawmill belonging to Meryl and John Quinn in the early 1800s, the university is fondly known by students as Camp Quinn.
“Today, students enjoy the Gothic Revival village that serves as the bustling campus center or can take time for quiet reflection by hiking Vermont’s famous Long Trail, a section of which bisects the nearby forests, streams, and mountains.
“The university offers a think-tank philosophy to learning that encourages personal research, professional development, and innovative thought. Over the years, Quinn University has produced a Nobel Laureate in Chemistry, three Fields finalists in Mathematics, and one Wolf Prize in Physics. With high academic standards and a low student-to-professor ratio, Quinn University has been in the Top Ten Best Small Universities for the past eleven years.”
I still remember the first time I read that.
POLYBUFOHEXANE-12
[4 Investigational New Drug Application (INDA), FDA, Clinical Trials Approval, (Federal Register May 2016, pages 37-38), Washington D.C., see “Induced Coma in White Mice with PolyBufoHexane-12,” Journal of Biometrics Research, June 2013, Pages 77-93]
Maddie’s chin dropped to her chest but when she realized what was happening, she bolted to her feet from the easy chair. She tottered, her breath slowing, her sense of balance failing. Then she whimpered the last rally of resistance often heard the moment before a horse is broken and the saddle accepted.
Now a gentle sleep crept toward her mind and the glass of Chardonnay that contained the dose of polybufohexane-12 shattered on the tile floor as her grip relaxed.
No matter, I would mop it up later.
I glanced at my watch. The digestive system can be so unreliable. She should have been down thirty seconds ago. How much cheese had she eaten? I should be more ob
servant.
She staggered to face me, her eyes meeting mine with intensity and hate. For a moment, I worried she might be fully conscious. Then her head jerked; she turned to stare at the flames in the fireplace and I waited and pondered the limitations of such a slow-acting drug.
I am no Lothario, so the probabilities of convincing eight more women to share a glass of wine was highly unlikely. And this outcome was certainly not quick enough. In the future, I would have to rely on surprise; a needle, and a vein.
Unexpectedly, Maddie screamed. But it was a swallowed scream repressed by muscle contraction, so it sounded like the involuntary mew or bark of a sedated pet on the operating table when the first incision is made.
I caught Maddie as she collapsed into unconsciousness and placed her gently back into the chair.
Her breathing was shallow and rhythmic.
I went to find the killing pillow.
ADVAITA (SANSKRIT, N.)
The belief there is only one reality.
THE ALIGNMENT OF ALL MATHEMATICAL STRUCTURES
I dug precisely, the lantern casting a dim circle in the darkness, the unkempt grass rippling in a cold wind that presaged winter, the soil steaming as I turned it over to reveal wriggling earthworms cut in halves or thirds. Maddie’s glistering eyes faded as she seemingly watched me; her body losing warmth on the hillside while I sweat.
I stacked the near-perfect squares of sod and then bent my back to drive deeper into the earth, the sharpness of the shovel easily slicing the loam.
A palindromic prime is a prime number whose decimal expansion is a palindrome.
Simple.
Definitional.
Maddie should have known that.
She probably did.
I measured.
The hole was deep enough.
I laid the shovel aside.
It has been argued by quantum cosmologists that beyond our vision, there is a singular and true reality waiting to be discovered.
Using my boot, I carefully rolled Maddie into the cradle of her journey to the Great Beyond. She flopped loosely onto her back and I bent to place her arms into paper doll position.
My transmigration ambassador to the true reality.
I flipped the switch on the nonahedron and balanced the nine-sided object below her chin. The fabric of her blouse was momentarily a problem, but I smoothed it, and all was fine.
Even in the darkness, the specialized palindromic prime worked on a limited scale as the nonahedron discharged. The air shimmered like a heat wave making Maddie’s face waver in the dim lantern-light.
She was the first.
Return to me, Maddie.
Prove there is one timeless reality.
Of course, I would have to send eight more ambassadors before the paper doll hyperplane was complete. The process required nine travelers in total as postulated by my formula.
I filled in the hole with the loose soil, re-laid the sod carefully, and tamped the edges to prevent discovery. This was university backcountry on my allotted parcel. I doubted I was in much danger of discovery.
Hoisting the shovel, I clicked off the lantern, left the clearing, and chose to descend the wooded hillside in the darkness of a moonless night.
In the distance, my kitchen light glowed through a thin curtain as a beacon. I had much to think about. I could only take one student from the university.
Maddie.
The other eight had to be random.
I stumbled on a stone.
Perhaps tomorrow I’d take a drive to Montpelier and check out the mall-walkers.
IMPLEMENTING A PAPER DOLL HYPERPLANE WITH A POWERED NONAHEDRON
[5 Riemann, Zachary H. “Embedding a Paper Doll Hyperplane in a Powered 3-D Nonahedron to Unravel Reality” Unpublished Research, 2003]
Any first-year student knows that a number is a mathematical object used to count, measure, and label. Numbers, and the mathematics that manipulate them, are concepts and nothing more. In the real world, numbers have no power other than the idea they represent.
Until now.
My discovery is that the physical universe reacts to rare sequences of numbers if combined and dispersed in a specific manner and order.
Of course, the first test rat, a female named Heidi, fragmented into an infinite number of sub-atomic particles, dissolving into nothingness. One expects failure in science experiments. But a week later, a pile of skin and bone and raw meat returned unexpectedly to my workbench. Spraying blood from half-formed veins, a struggling heart, melded to a twitching claw, pulsed erratically.
It was the rat, poorly reassembled by the universe. It squeaked incessantly from its malformed head and I beat it to death with a Gerzog mallet.
Conclusion: My first palindromes had been too small and not prime. Not powerful enough. And my homemade nonahedron: too primitive.
But from this singular experiment, demonstrating more than a modicum of success, I concluded there was a relationship between the complexity of an organism and the length of the palindromic prime; a more complex life form could be shifted in and out of the time stream with a larger number, thus unifying known and unknown reality.
That was many years ago.
A series of experiments followed.
As part of my next summer sabbatical, two doctoral engineering students helped me construct Nonahedron 2.0 as a summer project. One of them wrote an app for my phone that enabled the input of long strings of numbers and formulae. They believed it was to resonate the B-flat tone from the Perseus Cluster that is 57 octaves lower than Middle C on the piano. [6 Roy, Steve; Watzke, Megan (October 2006). “Chandra Views Black Hole Musical: Epic but Off-Key”. Chandra X-Ray Observatory. Harvard-Smithsonian Center for Astrophysics. Retrieved 20 February 2014.] Unknown to them, with a few modifications after their departure, the nonahedron could broadcast palindromic primes at a frequency of 9.6 million years.
The two students moved on to careers in Silicon Valley, none the wiser and happy for my doctoral endorsement.
And I moved on to more complex experiments.
Six years later, I had a filing cabinet filled with records of failed experiments complete with photo evidence of dozens of returned rats, cats, and dogs. Included were two chimpanzees, which had been extremely difficult to obtain. None survived their journey. Their remains were consigned to the ancient well outside the laboratory. By now, fur, flesh, and bones were nothing more than chunks of mush feeding a bacterial cesspool.
Discouraged, I became melancholic and then deeply depressed. I abandoned the research.
As Nietzche wrote, “Hope, in reality, is the worst of all evils because it prolongs the torments of man.”
And tormented I was.
One of the perks of professorship at Quinn University was privacy. My small house, previously the logging foreman’s, sat on forty acres surrounded by sugar maples and beech trees. A rustic barn functioned as my laboratory and the aforementioned composting well readily accepted my failed experiments.
My work had been unencumbered by discovery, literally or figuratively. But the problem is: Research is expensive. Certainly, I had received the odd university funding tied to some other hypothetical project and was also able to obtain foundation grant money without disclosure of my real intent. But by the end of the sixth year, I had depleted my life savings.
Work ceased for several years.
But then the largest known palindromic prime was discovered. A massive 320,237 digits long, it was expressible as 10320236 + 10160118 + (137×10160119 + 731×10159275) × (10843 − 1)/999 + 1.
The number was a thing of beauty. By itself, it was weak, just another number, but when combined with my nonahedron, it became quite powerful.
With this new expanded palindromic prime, I was able to send a dozen mice, four rats, and a dachshund named Pam across the Great Divi
de.
After creating a digital record of the experiments and photographic evidence, I destroyed them all. I had to. The creatures were somehow different.
Aggressive.
Extremely healthy.
By this point, I had cemented my theorem: a sequence of interlocked relational palindromic primes can unravel the time knot and unify all hyperplane realities. By happy accident, I had discovered that a live creature returns dead, but a dead creature returns alive as time realigns.
The implications were profound.
Now, I was ready for human trials, and that required nine women. Nine laid in a row like paper dolls cut from the same sheet of paper, holding hands; each powered by a nonahedron containing one-ninth of the master palindromic prime.
That would break the time stream for human beings and thrust the dead back into a singular reality called life.
The last piece of the puzzle that I needed to know was if there was continuity of memory. Would the person who departed exhibit the same consciousness of the person who returned?
One couldn’t tell with a lab rat and I’d never learned to teach a trick to a dachshund.
I needed a blonde.
Nine blondes to be exact.
HOW TO CATCH A SERIAL KILLER
[7 White JH, Lester D, Gentile M, & Rosenbleeth J (2011). The utilization of forensic science
and criminal profiling for capturing serial killers. Forensic science international, 209 (1-3), 160-5 PMID: 21333+473]
Maddie had been the first.
Initially, I underestimated the complexities of finding nine ambassadors in total.
Avoiding the police, who certainly would not understand the significance of my theory, required elegant planning.
The problem with serial killers is that they are serial.
What appears random isn’t, and thus, sooner or later, they are caught. The probability of being discovered is directly related to the number of seemingly independent factors that remain consistent over time. The more victims, the more consistency, the higher the probability of capture.
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