Dixon's Forum Posts from Dixon

My eyes glazed over at the long eccentric professor thundering theories and mathematic reflections.  The bald head, the fluffy tufts, the shoes . . . he began to resemble Bozo the Clown.    It reminded me of my similarly-endowed junior-high music teacher, “Bozart”.

“Are you catching all this, Mason?”, the professor was saying.

“Excuse me, Sir, please repeat.”

“[slightly annoyed] As I was explaining, every phenomenon in the Physical World is reflected in the Mathematical World.    And, every mathematical reflection corresponds to some physical phenomenon.    And, mathematics has evolved in parallel with scientific knowledge throughout Hisss-tory [snifff].

“[re-warming to the subject] The earliest math was arithmetic, to meet the accounting needs of animal husbandry and commerce.”    On the dusty blackboard, he tapped a lopsided line with a sloppy circle on the left, aberrated arrowhead pointed right, and a pair of uneven marks labeled ‘1’ and ‘2’.    “[tapping the marks] One[tap], two[tap], three, [tap-tippity]infinity.”

Glancing at the class, his glasses slightly slipped.

“The development of the building trades paralleled the development of abstract geometry, while evolving arithmetic gave rise to algebra, the bridge that connects all branches of mathematics together.” 

Facing the chalkboard, his blue labcoat tails flapping with each motion, he produced an equally limp line pointing left, labeled ‘‑1’ and ‘‑2’.    His y-axis missed the oblong origin completely.

Turning to the class, adjusting his glasses, a chalk-smudge appeared on his forehead.

“[absorbed in the discourse] From algebra and abstract geometry sprung the disciplines of trigonometry and analytic geometry, with applications in celestial navigation, astronomy, optics, transformations, variants, and group theory.    Complex and imaginary numbers enable us to tap the nature of energy and electrons – waves, particles and wavicles [serenely smiling].”

 One bushy eyebrow was trapped behind the glasses.

“As further discoveries were made, and the tasks of civilization grew more and more complex, [wildly gesticulating] new areas of mathematics were developed to explain, exploit, extend, expand, extract, new knowledge.    In other cases, a mathematical innovation led to an advancement in science.    At times, as with calculus and theoretical physics arising so nearly simultaneously, [folding his arms] nobody really knows (though it is passionately debated) which came first, [shrugging] the breakthrough or the innovation.

“[striking a stately pose] With quantum theory and relativity, we can probe the very universe! [shaking the up-pointed finger], from its minutest [pinching thumbs to forefingers, squinting] to its grandest [spreading arms and fingers wide] dimensions.”

The fluffy tufts skewed about the mottled scalp.

“[brushing it all aside] You’ve covered all this in Math and Science History, I’m sure.    The central theme if it all is this:    Whatever the breakthrough in Science, the Mathematical World has always developed an innovation to reflect it and, conversely, whatever innovations have occurred in Mathematics, Science has always found an application in the Physical World.

“Today, math and science are so intricately linked, the one does not exist without the other.    Trigonometry, calculus, statistics, quantum mechanics, relativity . . . each area of the Mathematical World reflects some aspect of the Physical World, and advancement in one world never occurs without a corresponding breakthrough in the other.    Doesn’t it make sense, Mason?”

“Doesn’t what make sense?, Sir.”

“[explosively] That early sheep herders did not need quantum mechanics!”, said Bozart.

“Of course not, Sir.    They only needed arithmetic, to account sheep.”

His name really is Bozart, and he has an elongated nostril.

“But, did quantum mechanics exist in the Mathematical World before our technology developed to the point where we needed it.    Certainly, there existed protons and electrons, molecules and energy levels and so forth before Humaaaanity[snifff]?”

“So it would seem, Sir.”

This Bozart is not a junior-high music teacher, like the real “Bozart”.    This Bozart is a fictitious physics professor, with dark hair.

“Then it stands to Reason that quantum mechanics, their mathematical reflection, has also existed all along.    Every Phenomenon in the Physical World has a Reflection in the Mathematical World, and mathematical innovations are discoveries, not inventions.”

The real “Bozart”, the music teacher, had blue eyes and white, perfectly symmetrical fluffy tufts, like cotton balls on an eggshell.

“Therefore, there must be a Physical Phenomenon for every Mathematical Reflection, yes?    The great, mysterious beauty of Nature is that all physical phenomena can be reflected mathematically, and all mathematical reflections are of actual physical phenomena [snif].”

“Now suppose there were some Mathematical Reflection for which [dramatically] there is no known Physical Phenomenon.    Would that indicate something as yet undetected exists here in the Physical World?    And provide clews to its identity, perhaps?    Its properties?”

This Bozart, the physics professor, wears faded striped wool pants, plaid shirt, and wobbles.

“[fists on hips, wobbling] What do you think, Wizard?”

The real “Bozart”, the music teacher, was always perfectly coordinated.

“It sounds plausible to me, Sir,” answered Kidd Wizard.    “I suppose we’ll never know, even if we ever do detect a real Reflection with a theoretical Phenomenon.”

This Bozart’s ears wiggle when he gets befuddled.    He smoothes down his fluffy tufts, which pop right back up, just like the real “Bozart”‘s, except this Bozart’s tufts puff chalk dust.

When the real “Bozart” once tried to sing in music class, his voice was so thin and high everybody laughed, turning his alabaster scalp hot pink.

“Yes, well, [clearing throat] . . . I have discovered in Mathematical Space a Reflection for which there is No Known Physical Phenomenon!”    He paused, contemplating us, brown eyes flooding thick, dark-rimmed glasses.    The trapped eyebrow popped out.

“And what are your Reflections on that, Sir.”, said Class Bozo.

This Bozart has a twisted tie, and his sleeves are too short.

“The Reflections exist on the Hyperpoles.”

Hyper poles?    Incomprehending shruggling rippled around the room.

The real “Bozart” had white, neatly-trimmed eyebrows, light, wire-rimmed glasses, and exquisite tailoring.

“Hyperpoles:    [tapping appropriate points with the chalk] On number line, Positive One[tap] is certain distance from Zero[tap].    Negative One[tap] is same distance from Zero[tap], different direction, yeh?”

This Bozart’s articles disarticulate during enthusiasm.

“Positive Two[tap] is twice as far from Zero[tap] as Positive One[tap], same direction, twice as far as Negative One[tap], different direction.    Negative Two[tippity-tap]:    same distance, different direction.    Positive and negative numbers have different polarities.    [tapping Positive One] There can be no number same distance, same direction from Zero as Positive One but [tapping harder] not equal to Positive One, yeh?, because, that would imply that here, in the Physical World, [tap] two different objects [tap tappity tap-tap] could occupy the same physical space [tap, tapITY THUD!; the chalk breaks, bouncing off his nose and plop! into his icewater].”

The real “Bozart” always articulated articles.

“[looking cross-eyed at the broken chalk] Well, I have discovered numbers same distance and direction from Zero[tap] as One[thump], but [tap thumpity tap] not equal to One.    [pause for effect] These numbers exist on the Hyperpoles.”    He cast a formidable glare, folding his arms, wobbling.

The real “Bozart”‘s illustrations were always impeccably precise.    The real “Bozart”, the music teacher, scored the board with a straightedge.

“Because of infinite number of directions, each distance from Zero actually represents a hollow sphere, made of infinite number of points.”

With the chalkstump, he drew a quick, sloppy circle around his origin.    His labcoat tails flipped apart, revealing a small tattered rip in the back of one pantleg.

The real “Bozart” never broke his chalk, not once!, and never wore a lab coat.

“Solid space is infinite number of such spheres, like shells around each other, [slap larger circle around first; flip tail, flash rip] each radius a different distance from Zero.    [slip-slap; flip-flash] All these infinite points on infinite spheres reflect . . . the Universe!”

His name really is Bozart.    And, the back of his leg is adorned with peppery hairs.

“[leaning closely] Now, listen closely; this is crux of theory:    Positive Two is twice as far from Zero as Positive One, equally positive.    Negative Two, twice as far as Negative One, exactly as negative, yeh?    Polarity Strength does not vary.”

I really did have a music teacher nicknamed “Bozart”.    There really was such a man.    And . . . he never tried to sing again.

“Suppose polarity strength did vary!” mused this Bozart, imaginary physics professor.    “Imagine a number same distance and direction as Positive One, but [tap thud tappity] twice! as positive.    Two unique points, Positive One[tap] and Hyperpositive One[tap], same distance[tap] and direction[thump] from Zero[thud]:    Mathematic Reflections of two different objects in the same physical space.”

He gulped his water, chewing the ice, glaring around the room, the broken chalk swirling down in the glass.

“A number same distance and direction as Negative One[tap], but only half as negative.    Another two unique points, Negative One[tap] and Seminegative One[tap], again, same spot:    More reflections of two physical objects in the same physical space.    This is Hyperpolarity.”

This Bozart has lively whiskers, and a slightly seedy reputation.

“Б(x) is the Hyperpole Function, and Б can fall anywhere on the interval (–∞,+∞), meaning it can hold any value from negative to positive Infinity.    Positive One as we know it can be expressed as Б(+1) where Б = 0, and every number on the range (‑∞ < Б < +∞)(+1) occupies the exact same spot on the number line. 

“In other words, for all values of Б, Б(x) is exactly the same distance and direction from Zero.    Positive One, Negative One, every other point in Mathematical Space, are, in effect, Zero on their own Number Lines, which are the Hyperpoles, composed of hyperpoints.” 

One-by-one, he locked eyes with every student in the room.    “Upon each hyperpoint rests another complete, whole universe, occupying the exact same physical space as ours.”

 I think of all these Infinite Spheres on every hyperpoint in the Infinite Universe as “Bozart’s Balls”.

“Just a moment, please, Professor Bozart.    I understand a number being more or less positive, or, more or less negative.    It’s like “semi-positive” one, and “normally-positive” one, and “super-positive” one, are three different numbers on the same point.    But Positive and Negative are only two directions from Zero.    Are there Hyperpoles on every direction from Zero, or just the Positive and Negative poles?”

This Bozart’s buttons are in the wrong holes, and one hairy ear is bigger than the other.

“In Polar Coordinates, Positive is nothing more than Angle Zero, and Negative is Angle One-Eighty.    I restricted the examples to these two poles for simplification.    Varying the strength, or Hyperpole Factor, works just as well no matter what the angle.    Try to think of it as some sort of distant cousin to acceleration:    you travel the same Direction from Zero (the Angle), and the same Distance from Zero.    Acceleration would change how you get there; Hyperpolarity changes what you find there.”

When this Bozart smiles, his cheeks clack.

“We can express a point in Hyperpolar Space as Б(r,θ,Φ), or Б(x,y,z) in Cartesian coordinates, where Б is the Hyperpole Factor (the “field strength,” if you will).    We would express Positive One as 0(1,0,0).    Using this function, we can access any universe in the Universe.”

Any of Bozart’s Infinite Balls.

“What exists in the Physical World that Reflects multiple objects in the same space?”

He stood, wobbling, forearms folded, eyebrows beetling, forehead furrowing, seeking suggestions.

Said Class Bozo, “If the Hyperpoles resolve the Universe, are they the Universal Resolvent?”

When this Bozart scowls, his whiskers vibrate.

Said Kidd Wizard, “Hey, wow!   Like, those other universes could be like multiple dimensions!    We could reach the Fourth, Fifth, Sixth, all the other dimensions!”

Replied Bozart, “Except that between any two points there is always another point.    We couldn’t reach our neighboring dimension from here; there would be infinite dimensions between.”

And I’m like, “Who says we’re on the first three dimensions, anyway?    Maybe we’re on the twelphth, thirteenth, and fourteenth dimensions and just don’t realize because we assume our Universe is centered on Zero, not Thirteen.  Maybe we’re in the Thirteenth Universe.  (That would explain an awful lot of crap around here.)”

“[triumphantly] Exactly, Mason!    Each and every universe on the Hyperpoles is centered around its own Zero!    We have no idea where ours is, relative to the True Center of Everything (if there even is one), and who cares?    Our task is to investigate Hyperpolar Mathematics.    How do they relate to known phenomena?    What do they reflect in the Physical World?    Parallel Universes?    Teleportation?    Dark Matter?    Supernatural Powers?    . . .    ?”

Said Class Bozo, “[smirking] Maybe the Hyperpoles are the stairway to Heaven.”

At that very moment, he was engulfed, poof! in a blinding flash which left his hair and clothing singed and smoking, skin scorched, glasses slanted.

Everyone stirred uncomfortably.    Bozart glared at him, folding his arms.

Bookworm suggested Time Travel.    “The Hyperpoles are one-dimensioinal, right?    So what if each Hyperpole Factor reflects a moment in Time, like Б = 0 is like the same as like, this moment we occupy, and Б > 0 is like, some moment in the future and like, Б < 0 is like, some moment in the past, and the farther ±Б is from 0, the farther away in Time from our moment?”, said she.

Bookworm has long straight hair, intelligent face, precise movements, and large, round, glasses.    Her fingers combed nervously her hair as the group stared at her dumbfounded.    Bozart, wobbling, nodded, approvingly.

Her name really is Bookworm, and mine is really Mason.

“The focus of our research will be to find and measure the physical phenomena which are reflected on the Hyperpoles.    [scowling at Class Bozo] Probably they aren’t the stairway to Heaven.”

We all looked at Class Bozo, who lowered himself in his chair, straightening his glasses.    His hair was still smoking.

“What marvelous wonders will the Hyperpoles unleash?    Who knows?    The time travel idea seems most suitable, yeh?    We’ll pursue that first,” decided Bozart.

Bookworm proudly preened.

“Mason, you work the calculations.    Develop software which can handle and manipulate Hyperpolar notation.    Now, this moment has an Hyperpole Factor of Zero, and every point in the Universe is actually the Origin of an Hyperpole.    To access this moment relative to another, reverse its Б.    In other words, in the moment represented by Б = +1, this moment is Б = –1.    In Б = –1, this moment is Б = +1.    And, every moment has an Hyperpole Factor of Б = 0, relative to itself.

Kidd Wizard was to look into the nature of the Time Stream, and try to tap its forces.    The plan was then to later link his equipment to my computer.

Said Class Bozo, “What about me?”

His name really isn’t “Class Bozo”, and he had quit smoking.

“You explain why, in the world of scientists and mathematicians, the world most riddled with genius on the entire planet, it took us only ten thousand years to notice the Hyperpoles, sticking out like sore thumbs on every point in Space all along.”

Bozart minored in Philosophy.

Bookworm was appointed Project Coordinator.    She helped “Bozo” explain why all of History’s genius overlooked the Hyperpoles:    Human Nature.    Early farmers and accountants did not need Hyperpoles, just plain old arithmetic.    As Mathematics evolved along with the horizons of Science and Discovery, our attention was focused on progress, the leading edge, never looking back to the origin, never suspecting anything more basic than simple arithmetic integers even existed.    So the Hyperpoles, essence of the Universe, have been sitting, invisible, on every number, real and imaginary, from Zero to Infinity, in all directions, everywhere, undiscovered, forever.

Why weren’t they discovered?    Because in this Universe, in all the factors and functions, constants and calculations, systems and formulas, that have ever evolved in the entire World of Mathematics, the Hyperpole Factor is Zero, therefore, transparent.    Ain’t that something?

* * *

Bookworm and Kidd Wizard are spending a lot of time together, trying to tap the Time Stream.    Their preliminary data seem to show it to be similar to a waveform, with each trough being a separate moment.    The moments move along in fixed order, a little like leaves on a river.    We can’t leave our moment, our trough in the waveform, because we can’t get past the peaks.    They believe the peaks are occupied by “antimoments”, which move the opposite way in Time.

They have postulated particles which interact with Time in a similar way that Gravitons interact with Gravity, and have named them Temporons.    They believe we could accomplish time travel by swapping Temporons and Antitemporons, moments and antimoments.

The beauty of their hypothesis is that it does away with all the problems and paradoxes in other time travel theories.    There are an infinite number of moments, and therefore no matter how many we mess with, we cannot alter the course of History.    There are infinity other moments where nothing changes.    They say, since it accounts for Paradox, it must be true.

They are working day and, night, on their Temporon detector . . . they seem to be getting, closer.

* * *

And I have finished the calculations, but haven’t the heart to tell the truth:    the Hyperpoles do not reflect parallel Universes, nor account for Dark Matter.    They aren’t the stairway to Heaven, and there will be no time travel.

* * *

* * *

The Hyperpoles lead to the dream world.