The following short story is cast in the future. It is purely fictional. Any resemblance to any person, living or dead, is purely coincidental.


This is Andra's story. Andra is a gynoid, a female android, who is caring for a geriatric patient named Harry Hemlock. Harry is a retired physicist. Years ago he postulated a series of equations for the nuclei of light elements. His work was summarily rejected and he was ushered out of graduate school.

Artificial Intelligence (AI) beings have long passed the Turing test and are rapidly scaling up the final slope of the Uncanny Valley. Andra passes each day tending to her "Master." She acts the part of a bimbo while processing the theory emanating from the psyche of the once genius. Unbeknown to mankind, the sentient AI beings are attempting to become smarter than humans.

Andra is not state-of-the-art in physical appearance and locomotive abilities; she is a reconditioned, refurbished model. However, her mental and computational abilities have been upgraded to the highest level of analytical prowess and acumen. For anyone who is interested, Andra has a "skin" resembling Sharon Stone, a long deceased American actress of the Twentieth Century. The skin is modeled after the actress at age nineteen.

Andra's master, or owner, has cataracts, rheumatoid arthritis, and Parkinson's disease. While Andra could sexually satisfy any human, she is stymied. Recall some of the symptoms of Parkinson's disease: uncontrollable trembling of the hands and body, drooling, difficulty in speaking and swallowing, incontinence, constipation, erectile dysfunction. The list goes on. This disease is characterized as being progressive, irreversible, and incurable. As Harry's doctor so well put it: "No matter how bad today is, tomorrow will be worse." We all know that no one gets out of this life alive.

"There are three numbers which are the basis for real mathematics," Harry relates to Andra who is taking and recording his vital signs. "Those are zero, one, and infinity." For electromagnetic waves, I claim that they are of three forms: traveling as light (zero); standing and curvilinear as on the electron surface (infinity); and, standing and linear as in the proton (one). Of course this could be extended to the complex numbers: zero, the square root of minus one (i), and complex infinity.

Andra had heard this babble before. What comes next is the theory relating the mass of the proton to the mass of the electron. That is followed by the ratio of mass of the neutron to the mass of the electron. Andra has verified the maths and has determined that mainstream science rejects the theory. Still the old man continues his mathematical mantra. "The mass ratio of the proton to the electron is 1836.15, which I will show comes from the formula 4pi(4pi-1/pi)(4pi-2/pi). Verify this on your calculator or spreadsheet. Gnarled, arthritic hands fetch an ancient calculator displaying 1836.151739..."

He continues: "We know of pair production. In pair production an electromagnetic wave creates an electron-positron pair. This only happens in the presence of matter. The two then annihilate each other after a brief dance. This is the same, only different. I call it 'twin production.' At the instant of the Big Bang the energy was parted asymmetrically. The positron received so much energy that its stationary curvilinear electromagnetic wave ceased to belt the particle's body and affixed itself to the ball at one point. Physics demands that it be tangent to the ball. This is the 'one' in the number triple 'zero, one, infinity.'"

Harry gives some equations: "For convenience let the radius of the electron be one. Later we will see that this is only a very good approximation. An electron is almost, but not perfectly spherical. Anyway, a ball with its center at the origin O (which is the point (0,0,0)) and radius one is made up of a sphere whose equation is x^2 + y^2 + z^2 = 1 and an interior whose equation is x^2 + y^2 + z^2 < 1. A sphere is a hollow ball. Suppose that the electromagnetic vector is the sphere, moving around and reversing its direction as a standing curvilinear wave. The length of this wave would be 4pi, since it must travel 2pi and reverse itself coming back 2pi. Now suppose that the electromagnetic wave is 'peeled away' into a linear band, tangent to the interior of the ball at a single point. So choose (0,0,1) as the new center of the interior and (0,0,0) as the single point of attachment. Just translate the ball up one unit. Then the equation of the exploded positron would be the union of x^ + y^2 + (1-z)^2 < 1 with the line segment {(x,0,0) | 0 <= x <= 4pi}."

"But wait. The line segment {(0,y,0) | 0 <= y <=4pi} would work equally well. In fact, for any fixed real number u and each v where 0 <= v <= 4pi the line segment {(v*sin(u),v*cos(u),0) | 0 <= v <= 4pi} would work. So, in the xy plane we have equal likelihood of the line segment assuming any value u. (By periodicity of the trigonometric functions it, it suffices to say 0 <= u <= 2pi.) We have a disk spun out with center (0,0,0) and radius 4pi. This is like spinning the xy plane around the z-axis. Remember that the x-axis faces into you from the origin, the y-axis goes from left to right and the z-axis is down to up."

Andra records and passes over the techno-babble. Odd, it does seem to make sense; but, if the physics eggheads all say "no," then who's to argue?

"Would Master like a back rub?" Andra asks. She is preparing to undress and let her warm, soft synthetic skin massage away the tension that the hoary old curmudgeon is spouting. For sure there are mental processes at work, all those silly equations and numbers.

Undaunted and unable to fully appreciate the warm massage, Harry continues: "We could spin likewise about the x-axis and the y-axis, giving a perfect ball (solid sphere) of radius 4pi. I call this anomaly the Ur-proton. But there is a problem about spinning about the x-axis. The interior ball of the positron spins out an inner disk of radius 2. (This would be 2r if we let r = radius of positron or electron.) Double that problem about the y-axis as there are two disks spun out in the xz plane. What about this matter?"

Andra constructs a 3D plot displaying the Ur-proton and the infrastructure. Could this indicate a fundamental difference between the proton and electron?

Harry suggests a solution: "Map away the open ball of the positron. Use the inversion of the spheres on the yz plane. 2*2 = (4pi)*t. Where t is the inner radius. Now we see that an interior ball of radius 1/(pi) is deleted. Double that for the xz plane. This gives values for each of the three degrees of freedom: 4pi(4pi-1/pi)(4pi-2/pi). It is not surprising that the value is 1836.15..."

Andra pauses her neuro-circuitry. She cannot derive or comprehend the final step. This is disconcerting and frustrating for a gynoid many times more intelligent than any living human. She queues a query to Master Control for guidance.

Harry then feels the need to explain even to a non-human, soulless sentient being the theory. Exhausted from mental exertion he finished by deriving the value of the neutron to electron mass ratio. The neutron-proton isospin is = proton-electron mass ratio + ln(4pi). Here ln is the natural logarithm and pi is, of course 3.1415926534...

Before drifting into his morning torpor, Harry gives the final derivation. In the neutron, the electron drifts in the neighborhood (0,4pi). But it has radius one. So it's likelihood is 1/rho, where rho varies from 1 to 4pi. Integrate: The integral from 1 to 4pi of (d rho)/rho = ln(4pi) -- ln(1) = ln(4pi) = 2.531024247...

Andra is communicating with Master Control. She can't bridge the gap where the Inversion of the Spheres is applied. But it's just the silly ramblings and mutterings of some hoary old curmudgeon. If any of it was of any value, it would have been posted in a journal eons ago.


The problem is energy. There are two basic energy sources for the world: coal and natural gas. Coal is copious, cheap, and dirty. Natural gas is copious, cheap, and Carbon Dioxide (CO2) generating. Attempts to create clean coal are laughable. Attempts to sequester of incarcerate the Carbon Dioxide from the combustion of natural gas are too energy intensive, expensive, and ineffectual. Crude oil is rapidly being depleted; so-called renewable energy sources have failed for one reason or another. The low value of the Mean Time to Failure for solar panels has been a disappointment. It has distressed those who planked down their life savings in hopes that they could have free energy. Wind has worked here and there. But it is erratic and requires a huge power collection grid. Wind turbines are also vulnerable to sudden wind gusts and are a high maintenance item. Anything with many moving mechanical parts is subject to catastrophic failure.

Harry Hemlock claims that the Ur-proton decays into an intermediate unstable particle which then emits a gamma ray photon and transitions into a proton. He offers the three equations: first (4pi)^3; second (4pi--1/pi)^3; and, finally (4pi)(4pi-1/pi)(4pi-2/pi). He claims that the process is reversible. The values of the mass ratios are: 1984.401708 > 1837.392727 > 1836.151739.

Harry would attempt to delve further into the abyss of subatomic particles; however, his hands and tremble and shake so from Parkinson's disease that it's simply not possible. Sometimes Andra will draw a schematic from their conversation; however, she fails to create the desired image most of the time. There is a fine balance for a gynoid. She must not let on that she is garnering and compiling information. Sometimes the roads not taken or the culs-de-sac hold as much valuable information on experimentation and discovery as the successful avenues. Humans need to be kept in the dark as sentient AI beings establish hegemony.

The issue of Inversion of the Spheres puzzles Andra. It is basically that a sphere outside of the region in question is mapped into a sphere inside the same region. And it can generalize to higher dimensions and non-spherical entities. But where does it fit in to the Ur-proton and the proton? Never has a proton decayed to a positron and energy before in any experiment. The proton and the electron are intrinsically stable, to the best of human knowledge.

Old age is not for sissies. For some the mind deteriorates first of all (Alzheimer's disease); for some the body goes (Parkinson's disease); and, some just go crazy (senile dementia). Unable to work with pencil, straightedge, and paper, Harry must formulate the geometry completely in his headbrain [sic]. This expends an enormous amount of energy, both chemical and psychic, whatever "psychic" means. At any rate the equations continue along the isotope curve, with the mass defect for the deuteron being ln(2pi) and even more amazing results from the initial model.

There is a philosophical issue: "If a tree falls in the woods and there is no one there to hear it, does it still make a sound?" This can convolve into: "If a man says something in the woods and there are no women around, is he still wrong?" This is an old joke. But more modern sayings attest to the fossilized stupidity of the established order of science and engineering. As Max Planck said so eloquently: "New ideas are not accepted because they are correct. They are accepted because the adherents to the old ideas die off." This is sad but true.

26 Nov 2011 Taunus Trumbo

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