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Based on Innovation by Dr. Barry Robson

The Grand DesignPROBABILSTIC SEMANTICSImplicate to Explicate Order

and back again, via healthcare to worms to the simple theory of everythingbyBarry Robson (Feb 4th 2014)First presented at the DISCO Interuniversity Project Report Workshop on Theoretical Semantics and the Web, University of York March 18th 2014

Bioingine.com

IntroductionBioingine.com

Explicate & Implicate OrderImplicate order and explicate order are concepts coined by David Bohm to describe two different frameworks for understanding the same phenomenon or aspect of reality. He uses these notions to describe how the same phenomenon might look different, or might be characterized by different principal factors, in different contexts such as at different scales. Macro vs Micro overcoming Cartesian Dilemma.The implicate order, also referred to as the "enfolded" order, is seen as a deeper and more fundamental order of reality. In contrast, the explicate or "unfolded" order include the abstractions that humans normally perceive. http://en.wikipedia.org/wiki/Implicate_and_explicate_order

The methods of theoretical physics should be applicable to all those branches of thought in which the essential features are expressible with numbers. Paul A. M. Dirac, Nobel Prize Banquet Speech, 1933

Dirac was also certainly modestly referring to his extensions to physics via his notation and algebra as further extensible to human language and thought, because he explicitly considered poetry as emotional and economics as subjective.Probabilistic SemanticsImplicate to Explicate From Quantum Mechanics to Language & Thought System Dynamics to Systems Thinking

ContentsPrincipal Sources (Published Basis).PART 1. Universal Exchange Language a call by the Presidents Council.PART 2. Quantification Beyond Symbolic Manipulation - Probabilistic Semantics.PART 3. Information and Neuroscience Aspects Clues for A.I.? PART 4. Is all of physics ultimately syllogistic logic?

Principal Sources (Up to 2013)B. Robson, T. P. Caruso, and U. G. C. Balis (2013), Suggestions for a Web-Based Universal Exchange and inference Language for Medicine,Computers in Biology and Medicine, 2013 (12) 2297-2310.B. Robson, U. G. C. Balis, UGC , and T. P. Caruso (2012), Considerations for a Universal Exchange Language for Healthcare,IEEE Healthcom 11 Conference Proceedings, June 13-15, 2011, Columbia, MO pp 173-176Robson, B, and TP Caruso. (2013) A Universal Exchange Language for Healthcare. MedInfo 13: Proceedings of the 14th World Congress on Medical and Health Informatics, Copenhagen, Denmark, Edited by CU Lehmann, E Ammenwerth, and C Nohr. IOS Press, Washington, DC, USA. B. Robson, B. (2007) The New Physician as Unwitting Quantum Mechanic: Is Adapting Diracs Inference System Best Practice for Personalized Medicine, Genomics and Proteomics?, J. Proteome Res. (Am. Chem. Soc.), Vol. 6, No. 8: 3114 3126B. Robson (2009), Towards Intelligent Internet-Roaming Agents for Mining and Inference from Medical Data, Studies in Health Technology and Informatics,Vol. 149 pp 157-177B. Robson, (2009), Links Between Quantum Physics and Thought (for Medical A.I. Decision Support Systems), Studies in Health Technology and Informatics, Vol. 149, pp 236-248B. Robson, B. (2012) Towards Automated Reasoning for Drug Discovery and Pharmaceutical Business Intelligence, Pharmaceutical Technology and Drug Research, 2012 1: 3 ( 27 March 2012 )B. Robson, (2013), Towards New Tools for Pharmacoepidemiology, Advances in Pharmacoepidemiology and Drug Safety, 1:6, http://dx.doi.org/10.4172/2167-1052.100012B. Robson (2013) Rethinking Global Interoperability in Healthcare. Reflections and Experiments of an e-Epidemiologist from Clinical Record to Smart Medical Semantic Web Johns Hopkins Grand Rounds Lectures, http://webcast.jhu.edu/Mediasite/Play/ 80245ac77f9d4fe0a2a2 bbf300caa8be1dhttp://quantalsemantics.com/papers/Three key preprints of submitted papers.

REPORT TO THE PRESIDENT REALIZING THE FULL POTENTIAL OF HEALTH INFORMATION TECHNOLOGYTO IMPROVE HEALTHCARE FOR AMERICANS: THE PATH FORWARDPresidents Council of Advisors on Science and Technology (December 2010)PART 1. UNIVERSAL EXCHANGE LANGUAGE

Origins of Q-UELIn other sectors, universal exchange standards have resulted in new products that knit together fragmented systems into a unified infrastructure.The resulting network effect then increases the value of the infrastructure for all, and spurs rapid adoption. By contrast, health IT has not made this transition. and so they call for an XML-likeUniversal Exchange LanguageUEL!

The market for new products and services based on health IT remains relatively small and undeveloped compared with corresponding markets in most other sectors of the economy, and there is little or no network effect to spur adoption.

The Tower of BabelThe PCAST Report

Our Goal Is Also the Thinking Web WW4Especially for Medicine.

Language is Q-UEL - Quantum Universal Exchange Language - a Semantic Web technology but based on Dirac notation and algebra.

Current Set-Up and Sources667,000 PATIENT RECORDSMullins, I. M., Siadaty, M. S., Lyman, J., Scully, K., Garrett, C. T., Miller, W. G., Robson, B., Apte, C., Weiss, S., Rigoutsos, Platt, D., Cohen, S., Knaus, W. A. (2006) Data mining and clinical data repositories: Insights from a 667,000 patient data set Computers in Biology and Medicine, 36(12):1351-77ALL US PATENTSRobson, B., Li, J., Dettinger, R., Peters, A., and Boyer, S.K. (2011), Drug discovery using very large numbers of patents. General strategy with extensive use of match and edit operations. Journal of Computer-Aided Molecular Design 25(5): 427-441AUTOMATIC WEB SURFING (XTRACTS)Robson, B. , Caruso, T.P, and Balis, (2013), Suggestions for a Web-Based Universal Exchange and inference Language for Medicine,Computers in Biology and Medicine, 2013 (12) 2297-2310.IN-HOUSESEMANTIC WEB AND AUTOMATED REASONINGSEMANTIC WEB

Link to the Medical Semantic Web - Bra-Operator-Ket as Linguisitic

< subject expression | relationship expression | object expression>

Dirac braket notation maps to S-V-O languages.

The relation expression is in our system (as typically in QM) is always a real or complex Hermitian operator/matrix expression (if real, it is trivially Hermitian).

The above is a bi-directed edge in a general graph of probabilistic knowledge representation.It is one element in a general graph or net of knowledge representation.

The above dual spinor can appear in nested form physicists' call the twistor - corresponding to a parsed sentence structure or knowledge graph representation.

Q-UEL: Both Raw Data and Data-Mined Summaries Can Be Probabilistic Example data from medical record.

Statistical summary statement from data-mining such.

Q-UEL: Medical Examples Can be Quite Complicated! Here Is a Record of a Prescription

Q-UEL: Definition Example. Implied Probabilities Here are 1 (the Default).

Q-UEL: Autosurf-and-Spawn XTRACTs Parse and Re-express Source Text< Q-UEL-XTRACT-BIOLOGY "`The human _brain |^is `the center of| `the human nervous _system [0http://en.wikipedia.org/wiki/Nervous_system]; `The human _brain |^has `the `same `general _structure as| `the _brains |of| `other mammals [0http://en.wikipedia.org/wiki/Mammal]; `The human _brain |^is larger than ^expected on `the basis of| _body _size |among| `other primates [0http://en.wikipedia.org/wiki/Primate] [1(0)http://www.ncbi.nlm.nih.gov/pubmed/17148188] [2file:input.txt#cite_note-Brain-num-1]" | from | source:='http://en.wikipedia.org/wiki/Human_brain' time:='Wed Oct 3 14:02:19 2012' extract:=0 Q-UEL-XTRACT-BIOLOGY >

Q-UEL: ReasoningOne issue relates to the IBM Watson computer, which beat human champions at Jeopardy but thought OHare airport was in Toronto [35]. A Q-UEL metastatement did already know that if A travels to B, then A is not B. A key rule in that process was that below reached by an automatically generated Google query:-

Q-UEL: Thesaurus, Dictionary and Encyclopedia Extracts Aid XTRACTs

Note the increasing appearance of probabilities, which brings us to

PART 2. QUANTIFICATIONBeyond Symbolic Manipulation

(Bliss Symbolics)I want to go to the cinemaAre you sure?!!

Quantification - Dual NotationQ-UEL statements have Pfwd and Pbwd attributes (default 1). They can be most simply be described as a value by a dual. E.g.

= = {P(A|B), P(B|A)}

You can treat it pretty much as a real two-element vector (but see later) , but then you have to define the algebraic operations, to come out classically, e.g. products as for the chain rule and syllogistic form

= {P(A|B), P(B|A)} {P(B|C), P(C|B)} = {P(A|B) P(B|C), (P(C|B)P(B|A)}

This above is also a simplest example of a probabilistic knowledge representation as an inference net, analogous to a Bayes Net, but bidirectional.

Quantification - Iota (i) Notation i = (1+h), i* = (1- h)

h is the hyperbolic imaginary number such that hh = +1.From the known properties of h, all algebra can be defined. * indicates throughout complex conjugation, i.e. change the sign of the imaginary partA dual is really a hyperbolic complex value, and the form is

= iP(A|B) + i*P(B|A) = (iP(A) + i*P(B) )eI(A; B)

I(A; B) is Fanos mutual information ln(P(A, B) / P(A)P(B)).

Advantages of Iota Algebra: SimplicityIdempotent rule: ii = i, i*i* = i*Annihilation rule: i*i = 0, ii* = 0Normalization rule: i + i* = 1Eigensolutions exist for {x, y} as x and y with eigenvalues h=+1, h=-1 respectively.It follows from the above that Selection rule: i{x, y} = ix, i*{x, y} = i*y Exponent rules: 1/i = i, ix = i, ei = i, log i = i

F.Y.I. It is the simplest algebra, except powerfully and less obviously, for example,ehx = cosh(x) + hsinh(x) = ie+x + i*ex (link to quantum mechanics: case of mother form as conjugate symmetry) z(x+hy, n) = i z(x-y, n) + i* z(x+y, n) (Riemann zeta function summed to n)and note that hi = -ih (where ii = 1) is anticommutative,so that ehix = cos(x) + hi sin(x) = ie+ix + i*eix Note pervasive nature of the spinor projector form i. i*! !!!

Hyperbolic Complex Algebra in Quantum Mechanics and Classical Inferencing - Previous WorkHere i = (1+h), i * = (1- h) are physicists spinor projectors, quantum field operators, where h is the hyperbolic imaginary number corresponding to physics g5 and relates to Diracs gtime such that hh = +1.The Lorenz transform of the standard imaginary number i h renders wave mechanics classical (B. Robson, B. (2007) The New Physician as Unwitting Quantum Mechanic: Is Adapting Diracs Inference System Best Practice for Personalized Medicine, Genomics and Proteomics?, J. Proteome Res. (A.m. Chem. Soc.), Vol. 6, No. 8: 3114 3126)This hyperbolic number h has been used since the 1990s in neural nets solves the XOR problem in one neuron (e.g. Y. Kuroe, T. Shinpei , and H. Iima, H. (2011), Models of Hopfield-Type Clifford Neural Networks and Their Energy Functions - Hyperbolic and Dual Valued Networks, Lecture Notes in Computer Science Vol 7062, 560-569).Hyperbolic wave functions (probability amplitudes) have also been proposed as a basis of natural neural nets and the mind (A. Khrennikov (2004), On Quantum-Like Probabilistic Structure of Mental Information, Open Systems & Information Dynamics, Vol. 11:3, 267-275).

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Origin of Spinor Form - We can Construct a Hermitian Commutator to Express Categorical Logic = = (Categorical interpretation of conditional)= [P(A|B) + P(B|A)] + h [P(A|B) - P(B|A)] (Hermitian Commutator)where h is the hyperbolic number such that hh = + 1 so that we have classical behavior of like a dual (P(A|B), P(B|A), and[P(A|B) + P(B|A)] = = is the existential or some part and [P(A|B) - P(B|A)]is the residual universal or all part on the interval -1/2 ..+1/2 for P(All A are B) to P(All B are A) (we can always change the sign basis as a matter of definition, but we will keep it this way, to match ).More Theory: Q-UEL comprises Diracs bras, kets, brakets, ketbras and bra-operator-ketsThe bra = [, , ,..]TThese are probability distributions.The vector product is expressible in a law of composition of probabilities in vector space: = SXA|X> meaning Si=1,2,3, It holds classically in everyday space if SX P(A|B,X) SXP(A|X) = 0, SXP(B|A,X) SXP(B|X) = 0, and we can express this as a covariance law about direct independence by indirect dependence of A and B. Operator = Matrix = ketbra product = |A> (x) or < subject expression | relationship expression | object expression> can be manipulated in their own right as a scalar real or scalar complex object.Linguistic Consequences of Inserting a Hermitian OperatorConverse relationship (bidirected edge of directed graph) * = Trivially Hermitian operator (real valued) = Active-passive inverse = = Orthogonal vectors (mutually exclusive arguments) = = = < cats | are | dogs> = 0;chase |cats> or 0. The extent of identity of mutual exclusivity is in the real part of the value of = .We can indeed express all these as matrices and vectors!Example Twistor ExpressionsBy Diracs rules A R B in can be algebraic expressions with manipulation laws. < Jack and Jill | went up and went down | the hill or the mountain>It remains scalar complex.Also by Diracs rules the arguments in those expressions can be real or complex scalars, vectors, or operators/matrices, including brakets and bra-reltor-kets etc., so subject to his reules we can construct e.g. | in |Spain> | mainly stays on | the plain>With h-complex algebra alone, these contract under the idempotent and annihilation rules, e.g. < the rain in Spain | mainly stays on | the plain>.To keep a parsed tree structure, however, we encode clauses with different flavors of h: h1, h2, h3, (see later)Deep Grammar: MetastatementsFollowing Semantic Web terminology, the basic forms are called statements, and rules which we call metastatements act on them as operators, using binding variables.They evolve the inference network, say converting one or more statements to one or more others, as in a syllogism, or vice versa.They can be probabilistic too.Statements and metastatements can be input, but corresponding to PROLOG data and program respectively.Metastaments are said to have extended twistor form from physics, e.g. the syllogism template < |= | >Language is defined that way as input . Notice reverse Ogden reduction of vocabulary: < |= | >The processes are reversible. The system can reason work forwards and/or backwards by the above processes.Statement ReconciliationIn the course of inference net evolution, statements can be generated that are detectable as semantically equivalent to one already existing (therefore redundant information has been generated - literally as logs of underlying probabilities).Similarly two identical statements can exist with different values.They are converted into a canonical form determined by a metastatment, and the value is also reconciled. + - Repeated, this process is a bionomial expansion and independent of the order in which the statements are processed.It represents an inclusive OR and the fact that statements are independent and can be counted as independent observations of events. except that we decide to reconcile them to one.However, we can count (data mine) and get our underlying probabilities that way.Some Features of Hyperbolic Dirac Nets for Automated Reasoning (1)HDNs are networks composed of brakets and bra-relator-kets.and sometimes more complex sentences or knowledge elements as twistors (nested brakets or bra-relator kets analgous to a parsed sentence structure).The product of all the probability duals is a dual representing their collective degree of truth in two directions (e.g. of conditionality).To have further meaning, their must be a categorical or causal relationships, or represent some kind of chain of effect.That implies logical AND between bra-relator-kets etc. throughout, but other logical operators are possible.Some Features of Hyperbolic Dirac Nets for Automated Reasoning (2)The value is purely real (the imaginary part vanishes) for networks, or parts of them, whichrepresent a joint probabilityrepresent a cyclic path in the network (cyclic paths are no problem as they are in other inference systems, e.g. Bayes Nets!)represent a purely existential rather than universal statement, or analogously represent a trivially Hermitian relationship, as in = They may evolve under the action of metastatements, representing deep grammar, syllogistic and higher order logic, and language definition.PART 3. Information and Neuroscience Aspects (Clues for A.I.?) Hyperbolic Complex Processing by Neurons A. Khrennikov (2004), On Quantum-Like Probabilistic Structure of Mental Information, Open Systems & Information Dynamics, Vol. 11:3, 267-275).H. Iima, H. (2011), Models of Hopfield-Type Clifford Neural Networks and Their Energy Functions - Hyperbolic and Dual Valued Networks, Lecture Notes in Computer Science Vol 7062, 560-569).N. Chattergee and S. Sinha (2008) Understanding the Mind of a Worm. Hierarchic Network Structure Underlying Nervous System Function in C. Elegans http://www.ppls.ed.ac.uk/ppig/documents/ChatterjeeSinha.pdfAn Information-Theoretic PerspectiveIt is often convenient to work with logs of probabilities and probability ratios such as association constants.By hyperbolic complex algebra, if = {0.9, 0.7) then log = {log 0.9, log 0.7}This directly gives insight into the information content and information processing.For example, a knowledge or inference network of N brakets or bra-relator-kets etc. can contain up to N bits of information in each direction.Proof: we can always re-express a statement with some kinds of markers to indicate that one or both probabilities P less than 0.5 are now to be seen as 1-P, and hence the information log2P is between log21 = 0 and log20.5 = 1 bits. , , and is one way example way of indicating the three negations, though two would depart from normal English interpretation.Neural Net Information-Theoretic Interpretation of Generation of Associations and Dual ProbabilitiesEvent AI(B)Event BI(A; B)I(A)I(B|A)I(A|B)AddInformationtoSubtractInformationfromInput layerDual selfInformationlayerMutualInformationlayerDualconditionalInformationlayerHDNs can render I(X)as the Riemann Partially Summated Zeta function z(X) = z(s=1, n[X]) that goes from 0 at n[X] = 1 to ~ ln(X) as n[X] increases.Very Weak or Unused Associations may be deleted (as in Sleep?)I(B)I(A)AddInformationtoSubtractInformationfromDual selfInformationlayerMutualInformationlayerDualconditionalInformationlayerOur A.I. systems using duals (and so hyperbolic complex by implication) can be re-expressed in terms of many K(A; B; C;) = exp(I(A; B; C;)) and self probabilities. They take up a lot of memory. But we do not need those I(A; B; C;) 0, i.e. K(A; B; C;) 1, that represent negligible associations. As apparently in the human brain, we can (with some caveats) remove them. Alternatively, Strong Associations Can Be Grown to Include More Elaborate Elements Event AI(B)Event BI(C)Event CI(A)I(A, B, C)This example is complexity 3 (A, B, C), enough for a semantic triple , 3 constituents as words or basic phrases. What degree of semantic complexity can be achieved in a nervous system? It does not automatically follow that the elements of these diagrams are single neurons, but they can be, and we can address the matter for a very simple animal with few neurons.Caenorhabditis elegans Nervous System MappedOnly 302 neurons, average of roughly 18 synapses per neuron (1-35)Behavior DefecationTouch sensitivityEgg layingThermotaxisOxygen level sensitivityChemosensitivityFeeding locomotionConditioning to tap/touchExplorationC. Elegans Nervous System MappedSENSORYMOTORINTERDiagrams below give a rough indication of number of synapses per neuronThis suggests majority have complexity equivalent to braket = , semantic triple , and a few with a sentence or knowledge graph structure of up to about 10-12 constituents, i.e. words or basic phrases, and a few higher (20?).4. WORK IN PROGESSIs all of physics ultimately syllogistic logic?The Octonion-related Lie Groups http://en.wikipedia.org/wiki/An_Exceptionally_Simple_Theory_of_EverythingDirac Grammar AssertionThe idea is that we shouldnt really need metastaments for purely logical and abstract semantic manipulation.Diracs manipulative grammar as algebra should do the job, along with defining semantic significance of mathematical classes of operator/matrix etc.However , to handle sentence structure and knowledge graphs as a single algebraic entity, especially syllogistic and higher order logic, may need to be extended beyond the Clifford-Dirac algebra to do so.Hence the octonion project described now.Can we get rid of metastaments, e.g. can we express syllogisms purely algebraically? Figure 1Figure 2Figure 3Figure 4BarbaraCesareDatisiCalemesCelarentCamestresDisamisDimatisDariiFestinoFerisonFresisonFerioBarocoBocardoCalemosBarbariCesaroFelaptonFesapoCelarontCamestrosDaraptiBamalipWe went half way by being hyperbolic complex, but the classical syllogisms come in packs of fours or eights.Categorical NotationSet / categoricalSpatial analogNotesAThe set of A.The inside of A.~AThe set of non-A.The outside of A.Negative, complement.All B are A.The inside of A is inside and outside the inside of B.The Dirac analogue of P(A|B), but P(B|A) is encoded too: = **All A are B.The inside of A is inside the inside of B.The Dirac analogue of P(B|A), but P(A|B) is encoded too: * = *All non-A are B.The outside of A is inside the inside of B.B is the universe except possibly for at least part of A.*All non-A are non-B.The outside of A is inside the outside of B.* = * holds under certainty: logical law of the contrapositive.We Can build Syllogisms as pairs of brakets, but it requires metastatements to turn the answers (products) into language.LinearRight fork Left forkAnticlockwise rotationof Feynman diagramClockwise rotationof Feynman diagramInference net pair components are like the propositions of syllogisms. Feynman- spacetime-like rotations of 8 chain-rule structures generates the other 16 possible configurations. Related by the complex conjugate change sign of imaginary partEncoding Basic Categorical Logic in a Hermitian Commutator Requires 8 Imaginary Numbers? x ( [ P(A|B) + P(B|A)] + h1 [P(A|B)-P(B|A)] + [ P(~A |B) + P(B| ~A]) + h2 [P(~A|B)-P(B|~A)] + [ P(A |~B) + P(~B| A)] + h3 [P(A|~B)-P(~B|A)] + [ P(~A| ~B) + P(~B|~A)] + h4 [P(~A|~B)-P(~B|~A)] + [ P(A|B) + P(~B|~A)] + h5 [P(A|B)-P(~B|~A)] + [ P(~A|B) + P(~B|A)] + h6 [P(~A|B) - P(~B|A)] + [ P(A| ~B) + P(B| ~A)] + h7 [P(A|~B)-P(B|~A)] + [ P(~A|~B) + P(B|A)] + h7 [P(~A|~B) -P(B|A)] ) These 4 pairs are reverse conditionalities adjoints. When joint probabilities are established by multiplying by priors, we can think of the extent that they satisfy Bayes rule or law P(A,B) = P(A|B)P(B)= P(B|A)P(A), which is the first aspect of coherence. They also relate to marginal summation and the joint probability distribution, which is the second aspect of coherence. These 4 pairs are the logical laws of the contrapositive, P(A|B) = P(~B|~A) etc. as in All mammals are cats All non-cats are non-mammals. They also relate to marginal summation and the joint probability distribution, which is the second aspect of coherence. They are not adjoints and the laws hold only under certainty. The imaginary part measures departure from these laws. But there are no degreesof freedom in the real part. The sum over these terms is 8, after the normalization.No! - Encoding Basic Categorical Logic in a Hermitian Commutator Requires 7 Imaginary Numbers! 1/7 x ( [ P(A|B) + P(B|A)] + h1 [P(A|B)-P(B|A)] + [ P(~A |B) + P(B|~A]) + h2 [P(~A|B)-P(B|~A)] + [ P(A |~B) + P(~B| A)] + h3 [P(A|~B)-P(~B|A)] + [ P(~A| ~B) + P(~B|~A)] + h4 [P(~A|~B)-P(~B|~A)] + [ P(A|B) + P(~B|~A)] + h5 [P(A|B)-P(~B|~A)] + [ P(~A|B) + P(~B|A)] + hx [P(~A|B) - P(~B|A)] + [ P(A| ~B) + P(B| ~A)] + h6 [P(A|~B)-P(B|~A)] + [ P(~A|~B) + P(B|A)] + h7 [P(~A|~B) -P(B|A)] ) We can express P(A|B) and P(B|A) as explicit variables if we take out P(~A|B) and P(~B|A), since adding them to the above gives 2 or 1/8 after normalization. The sum of the remaining 4 terms here is 2, or 1/8 after normalization.To balance this with the imaginary part, we take out the corresponding terms in the laws of the contrapositive. It deletes one manifestation of the law, shown in red. The sum of the real parts of the remaining 6 terms here is 2+P(A|B) +P(B|A) or (1 + (PA|B)+P(B|A))/7 after normalization. Such an octonion system is the most complete description of the physical world (E8 particle symmetry)Note that ei ei = -1 (flavors of the well known imaginary number i)1e1e2e3e4e5e6e711e1e2e3e4e5e6e7e1e11+e3e2+e5e4e7+e6e2e2e31+e1+e6+e7e4e5e3e3+e2e11+e7e6+e5e4e4e4e5e6e71+e1+e2+e3e5e5+e4e7+e6e11e3+e2e6e6+e7+e4e5e2+e31e1e7e7e6+e5+e4e3e2+e11Hyperbolic Octonion Multiplication1h1h2h3h4h5h6h711h1h2h3h4h5h6h7h1h1+1+h3h2+h5h4h7+h6h2h2h3+1+h1+h6+h7h4h5h3h3+h2h1+1+h7h6+h5h4h4h4h5h6h7+1+h1+h2+h3h5h5+h4h7+h6h1+1h3+h2h6h6+h7+h4h5h2+h3+1h1h7h7h6+h5+h4h3h2+h1+1It is an octonion except that hi hi =+1, i.e. we applied the Lorenz transform i h as before.Octonion Spinor Projector Multiplicationii = (1+hi), i=1,2,3,4,5,6,7ii ii = ii ii* ii = iiii* = 0i1i2 = (1+h1+h2+h3)i1i3 = (1+h1+h3- h2)i1i4 = (1+h1+h4+h5)i1i5 = (1+h1+h5-h4)i1i6 = (1+h1+h6-h7)i1i7 = (1+h1+h7+h6)i2i1 = (1+h1+h2- h3)i2i3= (1+h2+h3+ h1)i2i4 = (1+h2+h4+h6)i2i5 = (1+h2+h5+h7)i2i6 = (1+h2+h6-h4)i2i7 = (1+h2+h7-h1)i3i1 = (1+h3+h1+h2)i3i2 = (1+h3+h2- h1)i3i4 = (1+h3+h4+h7)i3i5 = (1+h3+h5-h6)i3i6 = (1+h3+h6+h5)i3i7 = (1+h3+h7-h4)i4i1 = (1+h4+h1-h5)i4i2= (1+h4+h2- h6)i4i3 = (1+h4+h3-h7)i4i5 = (1+h4+h5+h1)i4i6 = (1+h4+h6+h2)i1i7 = (1+h4+h7+h3)i5i1 = (1+h5+h1+h4)i5i2 = (1+h5+h2- h7)i5i3 = (1+h5+h3+h6)i5i4= (1+h5+h4-h1)i5i5 = (1+h5+h6-h3)i5i6 = (1+h5+h7+h2)i7i1 = (1+h7+h1-h6)i7i2 = (1+h7+h2+ h5)i7i3 = (1+h7+h3+h4)i7i4= (1+h7+h4-h3)i7i5 = (1+h7+h6-h2)i7i6 = (1+h7+h7+h1)i6i1 = (1+h6+h1+h7)i6i2 = (1+h6+h2+h4)i6i3 = (1+h6+h3-h5)i6i4= (1+h6+h4-h2)i6i5 = (1+h6+h6-h3)i6i7 = (1+h6+h7-h1)QUESTIONS?