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Our application of single quote marks below, e.g., 'composite,' most often shows our uses of
some problematic legacy classical terms — out of context — in a more general quantum comtext.

IBM, Sony, and Toshiba have juhst annoumced their n¤vel cæll chip quant¤l¤gy. Iht issi pr¤f¤umd!

That sihmple phasæmænt issi why wæ aræ ch¤¤sing t¤ debut iht hæræ ¤n this spæcial pagæ ihn Quantonics.

Why issi iht pr¤f¤umd?

Bæl¤w, wæ ask "H¤w can wæ quantum~m¤dæl vari¤uhs quantum mæmætihcs?"

Umtil cæll chip quant¤l¤gy wæ had n¤ mæans t¤ d¤ this ihn ræhl tihmæ ¤n circuiht~lævæl scalæs.

Cæll chip quant¤l¤gy isn't quantum computing (its basal 'technology' is classical and formal);
h¤wævær, iht issi an ihnterim prægmadigmatihc quant¤l¤gy shæar!
Cæll chip quant¤l¤gy exhibihts h¤w cæll chips can bæ ihn pr¤cæssings ¤f exhibihtings æmærscings,
REIMARings, quanton(¤thær_diræctings,sælf_diræctings) quantumæsquæ æv¤luti¤n.


Iht issi Earth's fihrst quant¤l¤gy which can mahssihvely m¤dæl fuzz¤ns.
Æssæntiahlly, ihf wæ can m¤dæl fuzz¤ns, wæ sh¤uld bæ capablæ ¤f m¤dæling ~any quantum~ræhlihty.

F¤r æværy m¤dæling pr¤blæm wæ dæsnouer bæl¤w, wæ sh¤uld n¤w bæ
capablæ ¤f quasi~quantum (i.e., beyond formal-classical) m¤dælings.

Als¤, ihn ræcænt TQS News wæ claimæd that NSF's fumding ¤f a classihcal m¤dæl
¤f that rat's brain ~comtr¤lling a flight simulat¤r issi a boguhs appr¤ach.

N¤w, wihth cæll chip quant¤l¤gy, wæ can bæings ræc¤mmændings that NSF ræquiræ that cæll chips
bæ uhsæd t¤ ihmplæmænt that s¤luti¤n. Ihf they d¤, they have ch3ings ¤f succæss.

Why? H¤w? Cæll chips can, apparæntly aræ capablæ ¤f, m¤dæl(ing) quantum~næurons!
That, folks, issi pr¤f¤umd!
Iht issi a FIRST ihn mankind's epistæmol¤gy!
Iht has birthed!
Læt's ænj¤y ihts æv¤luti¤n.

Fr¤m n¤wings ¤nings, ihn Quantonics, wæ shahll ræfer Cæll Chip Quant¤l¤gy mnæmonihcahlly as CCQ.

Watch f¤r m¤re ¤n CCQ ihn Quantonics TQS 2005 March News due 1Mar2005.

Doug - 9Feb2005.

In our other Möbius artwork discussions we have been telling you how we can use Möbius strips to model quantons, especially fermions.

Here is an example. This Möbius 'model' can represent any elemental triple fermion molecule of a form A2B and AB2. For example H2O, N2O, CO2, etc. In two of our example cases, as 'modeled' above, Oxygen is our large 'single' fermionic element. In our third example, Carbon is our large fermion.

Now ask yourself, "What is a Möbius 1-Primæ? A Möbius 2-Primæ? A Möbius 3-Primæ?"

Crucial aside:

It is important for you to view this model(ing) as an animate quantum included-middle quanton. Why? Recall in our review of Bergson's Creative Evolution how he showed us that classicists' two greatest delusions about reality are:

  1. Reality is stable, and
  2. Objects in reality are independent.

It is absolutely crucial for students of Quantonics to understand that these two — Aristotelian syllogistic borne — delusions are the underpinnings of all Western classical culture, thought, reason, mathematics, science, and philosophy. And, by-the-way, for your edification, Aquinas gave this same 'intellectual' disease to nearly all Western cultural religion.

These classical delusions deny quantum reality! As such, to students of Quantonics, they and their spawn are problematic in Quantonics.

End crucial aside.

Notice how those three c¤mpenetrating Möbius strips, though they may be 'modeled' individually, become 'one' Möbius strip which emerges a quantum animate (i.e., n¤t classically stable) included-middle (i.e., n¤t classically independent) 'one' surface and 'one' edge. Our 'two' smaller 'elements' are animate quantum included-middle coinside-nt their larger 'element.' Indeed, it is quantum_¤ne fermionic molecule, a fermion of fermions. A quanton of quantons.

Also note that each fermion's chiralty (handedness) is 'right.' Our Möbius example link above shows a left-handed 'model.' But can any fermion be a right-handed 'model?' (Comsider sugar-sucrose (natural, left-handed-) chiralty vis-à-vis Nutra Sweet (reversed, by human design, right-handed-) chiralty.)

Classical chemistry teaches us to view our quantons above as 'objects' connected by affine valency, (Pauli 'exclusionary' 'principle,') 'bonds,' like bricks conjoined with mortar.

Quantonics' version of quantum chemistry teaches us to use our quantum stages to view each fermion-quanton comstituent in our 'model' above as an animate included-middle quantum wave function whose own probability wave function spreads arbitrarily in ~Hilbert space according to its own unique animate included-middle probability distribution function.

Crucial aside:

Depending upon whether we choose to classically integrate or square our fermion's wave function vis-à-vis we quantumly integratæ or squaræ our fermion's wave function — we achieve unharmonious outcomes. This is an issue which needs significant attention, and soon!

Classical add-subtract, square-square_root, multiply-divide, integrate-differentiate, et al., results are always excluded-middle (independent) and single valued (stable). They can be so due classical delusions stated above. Classicists assume stable, state-ic, independent classical wave functions "collapse" or classically 'eigenvalue' 'stop' upon, e.g, add-, square-, multiply-, and integrate-measurements, et al.

Quantum additi¤n-subtracti¤n, squaræ-squaræ_r¤¤t, multiplicati¤n-divisi¤n, and integratæ-differentiatæ outcomings are animate (n¤n-stable), c¤mplementary, included-middle (n¤n-independent) and quantumly interrelated. They neither "collapse" n¤r 'stop.' They cann¤t "collapse," n¤r can they 'stop.'

Due their revered delusions, classical mathematics, science, et al., have n¤ current means to physially 'model' animate, c¤mplementary quantum reality.

End crucial aside.

Then as an aggregate quantum_3_primæ fermion, its own wave function may be described as we just did for a 'single' 'elemental' fermion. (Each 'element' may be further, subatomically described as a quantum primæ 'composite' of proton-neutron nuclei fermions-quantons and electron fermions-quantons.)

Further note that our quantum_3_primæ 'model' quanton's spin is a 'composition' of three ½-spin fermions, and its aggregate spin is ½! It is a fermion!

In Quantonics, we assert that all elemental fermions are both mathematically prime and quantum primæ. Their animate quantum primænessquantum_1. Their apparent (i.e., 'one' atom) mathematical primeness = classical_1. See examples of our quantum integers. See our Quantonics English Language Remediation of 'number,' and pay special attention to last few paragraphs there. Those paragraphs prepare your quantum stages for these remarks:

We also comjecture that all fermions are quantum primæ! Let's see why...

Our review of several chemical compounds in our copy of a CRC 82nd Handbook of Chemistry and Physics shows that many complex compounds are mathematically n¤n-prime based upon a classical integer count of atoms in a compound. They are still quantum primæ, though! How? They emerq a unique, ¤ne-¤f-a-kind, animate, n¤mæric, comtextual Möbius surface and edge, as described above. So classical mathematical primeness and quantum primæness are different perceptual species. Former we refer as stable and independent "concepts." Latter we refer as animate and quantum c¤mplementary "memes." As we have shown above in our graphical 'model,' many-most simple compounds are both mathematically prime and quantumly primæ. But H2O2 — hydrogen peroxide — is an example of a compound which is mathematically n¤n-prime while being quantumly primæ. Try making a simple paper model of this to see its quantum primæness. It will look like our 'model' above except two Möbius oxygen atoms replace our 'single' 'one' and each of those has a 'single' Möbius hydrogen atom, like this: H-O-O-H.

(As Al Pacino hollered in Scent of a Woman, "HOOH HA!" )

Essence: quantum primæness is perceptually and memetically omnifferent from classical mathematical concept primeness.

So, when we attempt to understand extraordinarily complex quantum memes, e.g., Riemann's Hypothesis, we find it almost impossible to describe them classically, and relatively easy to describe them quantumly using QTMs. And, any classical description, due its classical delusional fundamentals, is at best incomplete (As an example of classical descriptive incompleteness see Feynman's model of sliced collodion and black thread.). That is just what we observe, now, at Millennium III's beginning, in current classical efforts to both understand and describe Riemann's Hypothesis!

Fix those delusions...commence understanding! Doug - 7Jun2002.

Here are two templates:

one for a paper model you can make of a Möbius 4-Primæ hydrogen peroxide molecule,
and another model you can make of a Möbius 4-Primæ ammonia molecule:

For that H2O2 model, use an 8.5 x 11 sheet of paper (slightly narrower, e.g. primæs , 7 x 11, will work better since it will increase aspect ratios of strips and make them easier to manipulate) and cut out black areas. Cut along black lines. Start with oxygen Möbius strips first. Select which chiralty you want: right, left, mixed. Mark each strip with your selected chiralty. Make each strip into its chiral Möbius shape and tape, staple or glue ends together. You will end up with a model similar to our graphic above, except it will have 'two' oxygen atoms. Run a finger or pencil over all surfaces without lifting your finger-pencil. Ditto edges. It's ¤ne (i.e., quantum primæ ¤ne; quantum_primæ_1) Möbius quanton with quantum_1 surface, and quantum_1 edge!

For that NH3 model, use an 8.5 x 11 sheet of paper. Make your white strips 1" wide. Top and bottom black cutouts should be 1.33" wide and wider, middle black strips should be 2.67" wide. We used ammonia as another example here because of its tetrahedral static shape. However in physial reality its nitrogen atom's locus is quantum uncertain and quantum-superpositions itself bi-tetrahedrally both above and below an equilateral triangle formed by H3. Our Möbius model allows us to see how that can be so. Jeffrey Satinover describes this quite well in his The Quantum Brain as an analogy of our brain's memory cell EIMA quantum coherent superpositionings. See pages 132-135 there. Mentally fathom other ways you might 'design' this model. Is that 'N' strip variable in potential loci? Cannot we move it arbitrarily in x? Does it matter where N is in x? Chemically? Physially? Does Nature 'fix' its locus? Why? How can-could we 'model' Nature? Can we? Or perhaps better to ask Victorian-grammatically-incorrectly, "Howings cannings we beings modelings Naturings?" Quantum reality is not a linguistically classical active--passive-voice 'state' reality! Quantum reality is an animate(ings), ensemble(ings)-heterogeneous(ings), EIMA(ings), present(ings)-participle(ings) reality!!!

What do we mean by "quantum superp¤siti¤n" vis-à-vis "classical 'superposition?'" In our example here, of nitrogen's locus-loci in an ammonia molecule, "quantum superposition" literally means animacy AKA flux of locus which is another way of saying quantum animate uncertainty of location. Our ammonia molecule's nitrogen atom's location is bi-tetrahedrally ambiguous! But if we applied a classical notion of superposition, we would have to 'add' our nitrogen atom's loci. Classically 'superposition' means addition. Quantumly superposition means animate and classically undecidable loci. Quantum superposition applies to all atoms, molecules and their aggregations (cats, humans, and galaxies too ) in reality. Ammonia just makes it observationally obvious. Quantum superposition (superp¤siti¤nings) of fermions explains why their probability distributions are arbitrary in ~Hilbert 'space.'

Another interesting phenomenon appears above: it shows us that if we want to look thinner we should wear prisoner stripes. If we want to look heavier we should wear zebra stripes.

Now we did n¤t say that "all classical primes are fermions!" Indeed, as we shall show below, they are n¤t. However, we do say "all fermions are primæs!" Some primes and primæs may be quantum comdensed, and thus act like bosons.

What our comjecture offers is a novel way of interpreting the Riemann Hypothesis: i.e., all fermions reside on RH's ½ critical line!

As you k-now, assuming you have some k-now-ings of RH, Riemann himself used his own Möbius operator in his 'exact' prime counting function. (We place 'exact' in single quotes for a reason: all classical mathematics are, for now, and thus of necessity, classically state-ic. They have n¤ current means of representing, directly, animate quantum reality and quantum included-middles. All classical mathematical symbols represent classical 'objects,' which are by mathematics' Axiom of Independence, inanimate, classically excluded-middle objects.) So as you can see our Möbius modelings offer a direct connection to Riemann.

For more on Quantonics' Riemann hermeneutics and heuristics see:

A Beautiful Mind - Riemann
Quantonics Riemann Quanton Symbol
Fermionic Primæ N¤mbær
Flash 2001

For much more on others' views of Riemann see Dr. Matthew R. Watkin's superb:

RH Zeta site.

As students of Quantonics k-now, our map of reality is much different from classicists' map.

For classicists, especially classical mathematicians, objective reality is a tiny subset of quantum reality.

So what can we expect from any classicist's view of Riemann's Hypothesis?

Well, they only see RH as an 'objective' part of reality, i.e., they only see (some of them do n¤t even see this:) fermions. Well, they see real and imaginary parts of objective reality. They call these parts conjugate real and conjugate imaginary. In classical reality, real and imaginary are dichons: classical_reality=dichon(imaginary, real), and real's middle is excluded from imaginary's middle (comma-space textually annotates this excluded-middle). To a classicist — to be more formal — neither conjugate has any middle to be included. Latter is same as saying that real and imaginary conjugates have 'no' probability distributions: i.e., reality is ideally objective (which incorrectly denies existence of quantum reality). For a classicist that is all of known reality! And its only way of changing is via classically 'temporal' motion.

In Quantonics, our reality map calls classical reality a tiny conjugal subset of quantum actuality. We also add quantum n¤nactuality as quantum actuality's comjugate. We show this as quantum_realityquanton(n¤nactuality,actuality). Our comvention of comma-n¤space represents quantum reality's included-middle. Our Quantonics animate equals semiotic represents quantum reality's abs¤lute animacy. In Quantonics' heuristic of quantum reality temp¤rality is quantum flux — a n¤n spatially-measurable quantum flux. In Quantonics' version of quantum reality, time is n¤t a space identity. For example, we cann¤t represent time homogeneously, analytically, independently, continuous space-space as classicists do.

For more on classicists' delusional philosophical and theoretical underpinnings of time as a space identity see Henri Louis Bergson's:

Numerical Multiplicity and Space;
Space and Homogeneity;
Homogeneous Time and Space; and
Duration, Succession and Space.

So, as you may well comclude, all classical approaches have huge problematics in any attempts to describe quantum reality. RH is n¤ exception. In our view RH will eventually be shown to describe classically only a state-ic, fermionic actuality. It will be shown to need a more general expansion to include quantum n¤nactuality and actuality, and their included-middle animate mixings of quantum coherence (zeroentropy), decoherence (posentropy), and isocoherence (negentropy).

We offer a (to be extended) table of Relevant Quantum Quantonic Memes vis-à-vis Classical Concepts:

Quantonic Memes vis-à-vis Classical Concepts



All quantum interrelationships in this column are EIMA

All classical 'interactions' in this column are EEMD
Animate heterogeneous quantons(fluxings,timings) interrelationships Inanimate homogeneous dichon(space, time) identity
(quantum n¤nfactorability) Meme: quantum primæ

Concept: classical prime (objective prime factors)
(probability '1' everywhere associative quanton) Meme: quantum n¤mbær

Concept: classical number (Aristotle's syllogisms)

Conjugates(imaginary, real)
(a quantumly animate, c¤mplementary quanton) Quantum ¤ne

Classical one (a classically stable, independent monad)
(omniadic c¤mplementary c¤mmingling of quantons) Quantum additi¤n

Classical addition (dyadic copulum of paired monads)
(iterative quantum additi¤n emerscenture) Quantum multiplicati¤n

Classical multiplication (dyadic copulum of paired monads)
(omniadic c¤mplementary omnifferencings of quantons) Quantum subtracti¤n

Classical subtraction (dyadic copulum of paired monads)
(iterative quantum subtracti¤n emerscenture) Quantum divisi¤n

Classical division (dyadic Sheffer stroke copulum of paired monads)
(a BAWAM recursi¤n over actuality into nonactuality) Quantum squaræ r¤¤t Classical square root (EOOO special case of division)
Quantum squaræ Classical square (special case of multiplication)
(iterative quantum additi¤n emerscenture) Quantum integrati¤n Classical integration
(iterative quantum subtracti¤n emerscenture) Quantum ¤mnifferentiati¤n Classical differentiation
(self reference of quantons) Quantum recursi¤n Classical recursion (self reference of classical objects)
etc. etc.
(quantum n¤n-mathematics) Quantum Riemann Hyp¤theses Classical Riemann Hypothesis (classical mathematics)

Now, two simple (for students of Quantonics) questions: In general, how can we quantum dividæ a Möbius n-primæ model? What do our QTMs tell us to expect our answer-outcomes should be? Hint: What did Bergson tell us classicism's two most fundamental delusions are?

Thanks for reading,


To contact Quantonics write to or call:

Doug Renselle
Quantonics, Inc.
Suite 18, #368 1950 East Greyhound Pass
Carmel, INdiana 46033-7730

©Quantonics, Inc., 2002-2022 — Rev. 10Jan2013  PDR — Created  6Jun2002  PDR
(8Jun2002 rev - Minor text corrections and clarifications.)
(9Jun2002 rev - Add some red text extensions. Add links to n¤vel
QELRemediated terms.)
(21Jun2002 rev - Correct spelling of 'Matthew.' Add a missing 'of.')
(25Jun2002 rev - Correct some very minor formatting issues.)
(19Jul2002 rev - Add specific sugar-Nutrasweet chiralties.)
(21Jul2002 rev - Change QELR links to A-Z pages.)
(4Sep2002 rev - Correct some text formatting for quotation. Add "Pauli exclusionary principle" parenthetical.)
(26Sep2002 rev - Add third 'red' row to table above.)
(20Nov2002 rev - Extend 'division' row of table above. Delete prize offer which ended 8Oct2002.)
(7Feb2003 rev - For browser compatibility, substitute GIFs for some Wingdings and Symbol fonts.)
(23Apr2003 rev - Add ammonia model. Replace wingdings smileys with GIFs.)
(31Dec2004 rev - Reset red text. Repair some links.)
(9Feb2005 rev - Alter page bottom table constraints. Add cell chip comments.)
(20Aug2006 rev - Slight color reformating. Adjust P word links.)
(9Nov2006 rev - Add 'ammonia' anchor.)
(12Dec2007 rev - Reformat slightly. Add bitetrahedral graphic of ammonia molecule.)
(11Apr2008 rev - Add 'Quantum Primeness' anchor.)
(16May2011 rev - Make page current. Adjust colors.)
(7Apr2012 rev - Repair redudant 'of.')
(10Jan2013 rev - Add 'A Required Quantum Math' link near-below description of ammonia's nitrogen superposition.)

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