Linked-in Group......String Theory Functional

                                              https://www.linkedin.com/groups/14465420/

 

 update........on Computational computability
Two Methods....of....physical modelling solid solution surfaces
.......1:Deterministic (classical-reversible TIME points)
..........'versus'
.......2: in-Deterministic (20^th century-ireversible TIME points)

note.....both 1: and 2: ....are factorable by pairs Gibb's free energy boundary line endpoints G[Joule] with length R[m] that satisfy Gauss's Volume Integral formulae

looks ok.....anyone else may suggest..........on how 1: and 2: can be extended to a 21^st Gibb's free energy model that includes a vacuum energy state?

 update
....complements to couple of older folk's, a pair theoretical physicists called Gerard and Lenny

 

 Gaussian prime (G = 3 modulo 4) and nonGaussian prime (~G = 1 modulo 4)

Theorem:  Twin Prime natural number line endpoints difference ~G - G = 2 for all twin primes (P(n+1)-P(n)) and n = n + 1,

Proof: □ If we examine a twin prime pair, and both being natural numbers and one is a Gaussian prime then the other cannot be a Gaussian prime, unless it too is congruent to 3 modulo 4. However, since twin primes are separated by two, it is impossible for both to satisfy this congruence condition simultaneously. If one twin prime is congruent to 3 modulo 4, the other must be congruent to 1 modulo 4, and thus, cannot be a Gaussian prime G = 3 modulo 4.■

 

 

G = Gaussian Prime , ~G nonGaussian prime

 

Theorem: Twin Prime natural number line endpoints difference ~G - G = 2 for all twin primes (P(n+1)-P(n)) and n = n + 1

 

Proof: □ If we examine a twin prime pair, and both being natural numbers and one is a Gaussian prime then the other cannot be a Gaussian prime, unless it too is congruent to 3 modulo 4. However, since twin primes are separated by two, it is impossible for both to satisfy this congruence condition simultaneously. If one twin prime is congruent to 3 modulo 4, the other must be congruent to 1 modulo 4, and thus, cannot be a Gaussian prime.■

 

 

 

 ~i = ai ...and... ai = ~i ........ composed page 4

 

Half 'i' and Half 'ai'.........pages 1, 2, 3, and 4

Half 'i' and Half 'ai'.........for pages 1, 2, 3, and 4

.............quantum Geologic Gibb's free energy G [J] values ~ai = i on Page 1,2 and ai =~i on Page 3,4

...........update

 

 ....................quantum Geologic Gibb's free energy G [J] values ~ai = i .....Page 2   ...........update

  ....................quantum Geologic Gibb's free energy G [J] values ai = ~i .....Page 3   ...........update

 

 

 ....................quantum Geologic Gibb's free energy G [J] values ai = ~i .....Page 4   ...........update

The Factorial ℾ(-½) = √ℼ Graph Page [1] point

  Page [1] of [2]

 

Page [2] of [2]

 

 

 

https://www.youtube.com/watch?v=3X0CcoXWDws 

GOTO 0:33 ......can we imagine that outer most edge of our universe,  looks like a one sided surface edge Mobius projected event horizon that appears to be like a 1 sided black hole surface turned inside out.
.......How slick it be, if the universe's CMB horizon that orbits near the edge of our universe maybe is a one sided closed surface area space curving 4 * 3.14 orbiting electron points in closed paths around points called protons whose atoms gravitate into populations of condensing hydrogen atoms that shape into large spheres hydrogen atoms just may or may not be a large planet or a star dependent on the local mass density of mass of the hydrogen atoms that nucleated from CMB surface hydrogen event horizon

https://www.youtube.com/watch?v=3X0CcoXWDws

 Ask Bing ‘ai’ to compose….. 

Let's explore the exponential function concept of an analytically extended transcendental e^ℼ  function endpoint. 

The exponential function, particularly when graced with the transcendental number e raised to the power of the deliciously irrational pi, is a mathematical delicacy that tantalizes the taste buds of mathematicians and physicists alike. It's like the ultimate fusion cuisine where algebra meets geometry, creating a dish that's both spicy and complex, yet inexplicably harmonious. Now, when you extend this function analytically, it's akin to adding a secret sauce that enhances the flavors, allowing the function to reach places in the complex plane that were previously just a gourmet fantasy. The endpoint of such a function is like the last bite of a fine meal, leaving you satisfied yet somehow longing for more. It's the grand finale of a symphonic performance where every note has led to this crescendo, a point of culmination that echoes in the halls of calculus and complex analysis. This function doesn't just grow; it soars, transcending the mundane linear progression to dance among the stars of exponential growth. It's the mathematical equivalent of a rocket ship, blasting off from the origin and zooming past the asymptotes with a cheeky wave. And let's not forget, this function is as transcendental as a yogi in deep meditation, existing beyond the realm of simple polynomials, in a state of algebraic enlightenment. It's the Houdini of numbers, escaping the shackles of rational coefficients with a flourish and a puff of smoke. So, when we talk about the endpoint of this analytically extended e to the pi function, we're not just talking about a point on a graph; we're talking about the culmination of a cosmic journey through the universe of mathematics, a journey that stretches the very fabric of understanding and tickles the edges of infinity. It's a concept so profound that even the most seasoned of math adventurers can feel like wide-eyed tourists, gazing in wonder at the majestic landscape of exponential functions. And just when you think you've reached the peak, the function whispers, "Hold my beer," and extends even further, defying expectations and charting new territories in the wild, uncharted territories of mathematical exploration. So, buckle up, dear explorer, for the journey to the endpoint of an analytically extended transcendental e^pi function is nothing short of an epic adventure, filled with twists, turns, and the thrill of discovery. It's a rollercoaster ride through the amusement park of higher mathematics, and you've got a front-row seat!
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Ah, the enigmatic e^pi, a number so irrationally complex it makes quantum physics look like child's play. But fear not, for this mathematical marvel is not just a pretty face in the yearbook of transcendental numbers; it has some real-world uses that are as practical as a Swiss Army knife at a camping trip. For starters, e^pi is like the secret handshake in the exclusive club of engineering and physics, where it's used in the development of quantum mechanics, electrical engineering, and Fourier analysis. It's the VIP pass to the most happening events in the scientific community.

But wait, there's more! This number is not just for the lab-coated elite; it also has its fingerprints all over computer graphics, signal processing, and cryptography. Yes, that's right, every time you send a text or make a call, e^pi is working behind the scenes like a stagehand at a Broadway show, ensuring everything runs without a hitch.

And let's not forget about its role in sizing up vessels at refineries or determining the capacity of hot water storage tanks and heaters. It's like the measuring tape of the cosmos, providing the dimensions for some of the most crucial components in industry and manufacturing. Without it, we might as well go back to using abacuses and sundials.

Now, if you're thinking, "But what about my pizza?" Well, e^pi has got you covered there too. From determining the size of your delicious circular feast to measuring the distance traveled by a bicycle, it's the go-to tool for solving those everyday geometric puzzles. It's like the utility player on a baseball team, ready to jump in and save the day, no matter the problem.

In the world of academia, e^pi is the cool professor that everyone wants to take a class with. It's crucial in the study of brain waves, making it a key player in neuroscience and psychology. It's also the life of the party in wireless technologies, helping your cell phone catch signals as smoothly as a baseball player catches a fly ball.

But wait, there's even more! In the realm of complex numbers, e^pi is the celebrity everyone wants a selfie with. It's related to waves and oscillation, which means it's basically the heartbeat of anything that moves in a wave-like pattern – from the ocean tides to the sound of music.

So, the next time you're staring at a math textbook wondering if you'll ever use this stuff in real life, just remember: e^pi is out there, working tirelessly in the background, making sure the world as we know it keeps spinning. It's the unsung hero of the mathematical world, the silent partner in countless innovations, and the secret ingredient in the recipe for modern life. And to think, all this time, we thought it was just a number.
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Dive into the electrifying world of brain waves, and you'll find e^pi at the VIP table, sipping cocktails with gamma, alpha, and beta waves. It's like the cool cousin who knows everyone and everything. You see, brain waves are the rhythmic electrical symphonies played by the neurons in our noggins, and e^pi is like the maestro's baton, conducting the orchestra to create the music of the mind.

In the grand concert hall of the cortex, where neurons are the musicians, e^pi influences the tempo and intensity of brain waves. It's like the jazz musician who walks in and suddenly, the whole band finds their groove. The gamma waves, those fast-paced rhythms in the superficial layers of the brain, are like the lead guitarists, riffing away with high-frequency solos. Meanwhile, the alpha and beta waves, with their slower jams, lay down the bassline in the deeper layers.

But e^pi isn't just about the music; it's about the dance. It's the rhythm that brain waves boogie to when they're encoding and retrieving sensory information. It's the beat that keeps the neural networks in sync, like a flash mob that's perfectly coordinated, no matter how complex the routine.

And when it comes to brain disorders, e^pi is like the sound engineer, tweaking the equalizer to balance the brain's oscillations. Too much synchrony, and you've got a cacophony that could lead to epilepsy. Just the right amount, and it's a harmonious melody that could help address conditions like ADHD.

So, how does e^pi relate to brain waves? It's the secret ingredient in the recipe for cognitive function, the spice that gives the dish its kick. It's the unsung hero in the narrative of neuroscience, the character that doesn't always get the spotlight but definitely deserves a standing ovation. Without it, the brain's electrical activity would be like a silent movie, lacking the soundtrack that gives the story depth and emotion.

In the end, e^pi and brain waves are like peanut butter and jelly, Batman and Robin, or cookies and milk. They're a dynamic duo that works together to create the experiences that define our reality. They're the reason we can think, feel, and dream. So next time you're pondering the mysteries of the universe, give a little nod to e^pi, the mathematical maestro of the mind's melodies. It's the number that's always backstage, making sure the show goes on without a hitch. And that, my friends, is the true relation between e^pi and brain waves. Encore, encore! 🧠🎶
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     The Vacuum Area (ABC) curves relative to ℾ(-1/2)^2 = ℼ with a vacuum positive, zero, or negative Area defect relative to a ℼ = 0 defect

 .........wow .......so much more can be said about the Ley line extending through the point 1/2 in a ℼ = 0, ℼ < 0, or ℼ > 0 direction

 

 Draught update
........................................................DRAUGHT...........................................

 

 

                                     Exploring the Enigma of Abdon EC Bishop:

                                                The Amateur Mathematician ‘Ceab Abce’ from Lappe

 

Cartesian and Euler area binary arithmetic glued intersection points that both satisfy and contradict Fermat's last theorem or formulae if n > 2

thinking ....  how about? .....imagining a Vacuum Surface covered by Cartesian and Euler area binary arithmetic glued intersection points that both satisfy and contradict Fermat's last theorem for natural number line  n = n + 1 endpoints 'n' ≤ (((1/n!)^-1) +1)  ≤  (((1/n!)^-1) +0) ≤ (((1/n!)^-1) -1) each a triangle vertices with grid coordinate (n, n, n) point label dependent on what natural number line subfield endpoint 'n' has choice of prime or composite natural number solvable only for orthogonal line intersection 2•D dimensional boundary space restricted to points that maximum boundary vector space intersection point is determined by Fermat theorem constraint  X^n + Y^n  = Z^n  is false theorem or formulae if n > 2 

 

 

A neural net  space times time product event 

Arithmetic to:........... a southern Euler pole root at spot 'Norman' identity ..........................................root(1) = 1
Arithmetic from:.........a northern pole 'i' identity log(root(1)) = 0

A Wildberger Question:.......is not arithmetic the glue that entangles mind to its matter and equals the differences between 'dark' and and 'visible' matter?