The Harmonic Theory; A mathematical framework to build intelligent contextual and adaptive computing, cognition and sensory system

The Harmonic Theory A mathematical framew ork to build in telligen t con tex tual and adaptiv e computing, cognition and sensory system Nic k Mehrdad Loghmani Jan uary 17, 2011 Bac kground: Most contempor ary computing systems are based on V on Neumann ar chitec- ture 1 . While such systems are efficient in so lv ing certain mathematical prob- lems inv olving data sto r age, retriev al and rep etitive and predetermined tasks, they are less succes s ful in op erating outside of the well-defined env elop e they are designed for . F urthermore, interaction with such systems has to happ en in a very sp e cific and narrow spe c tr um of interfaces, with limited mar gin of flexibility and adaptability . BRIEF SUMMAR Y Harmonic theory provides a mathematical framew ork to describ e the structure, behavior, ev olution and emergence of har monic systems. A harmonic system is context a ware, contains elemen ts that manifest characteristics either co llab ora- tively or indep endently according to system’s expr ession a nd can interact with its environment . This theory provides a fresh w ay to analyze emer gence and collab ora tion of “ad-ho c” and complex systems. Harmonic system 2 comp onent, cha racteristics and relation mo del ex- plained 1. A har monic system is defined within an environmen t. Environment pro- vides the b oundary for the sys tem and resourc e s necessa ry for fo rming and k eeping comp ositions. The environmen t also acts as a medium for ex- change with other systems. Environment’s characteristic mo del influence s 1 (Blundell, 2008)(2008). Computer Hardware. Cengage Learning EMEA. p. 54. ISBN 97818448 07512. 2 “Harmonic System” is an inte lligent conte xtual computing, cognition and sensory system operating based on the principle of the Harmonic theory . 1 system’s expression and context as w ell arrangement and type of character- istics its co mpo sition’s manifests. Diversity in en vironment’s characteristic mo del ensures sustainability of ha rmonic state. T rade and exchange, along with tra nsformation, a re among the factor s that influence and transform the harmonic en vironment. 2. A Harmonic system has a context. Cont ext is the situational co nstraint set by the sys tem’s structure (environment, comp osition, expressio n) a s well as by its action (state, ev olution, transforma tion, exchange). Ha r - monic sta te dep e nds on the harmonic v alue o f comp ositions relative to harmonic e xpression. Role, gra nularity and ar rangement of characteris- tics a comp ositio n manifests dep end o n the con text it is in. By imp osing patterns, restrictio ns and control of the domain of har monic co mpo s itions context controls measura bilit y a nd co mpa rability of characteristic mo del. 3. A Har monic system has a Harmonic expr ession. Harmonic expr e s sion creates the criteria and characteristic mo del based on which (in a given context) harmo nic comp ositions can be a r ranged and ra ted. 4. A Harmonic system contains c omp ositions. Comp ositio n is a pattern of ent ities fr o m the harmonic environmen t formed to manifest a ra nge o f characteristics in accorda nce to express ion and context. There are three types of comp ositions: 1. (a) i. Activ e comp os ition is present in the harmo nic system environ- men t and cont ributes to harmonic state 3 ii. Passive comp ositio n is pre s ent in the harmonic sy stem environ- men t but do es not have a direct rela tion with harmonic (W eis- stein E . W.) (W eisstein E. W.) (W eisstein E . W.)expres sion. How ev er it has a characteristic mo del, which is in demand by other sys tems. Therefore it ca n be used as a r esource in an ex- change scenar io. iii. T arget comp osition is NOT present in the har monic system en- vironment. How ever, if o btained,(either through exchange with other sy s tems, through transformatio n, or through a combina- tion of b oth) it can b o ost the system’s harmonic sta tus. As a gener a l rule any harmonic system with a suitable characteristic mo del can b e used as a compos itio n in a lar ger system. There are tw o categor ies of characteristic mo del; referential or in trinsic; in trinsic characteris tic a re those which stem from compo sition’s structure a nd natural mak eup, for instance w ater molecular c haracter istic mo del is H2O, r eferential characteristics a re th ose which are obser ved o r infer by a third par t y system and as such a re sub jective and relative to co mpo sition r eal characteristic prop erties, for instance “W ater” is the referential characteris tic of H2O in the context of Englis h la ng uage. 3 Herein after referr ed to as having a harmonic relation with the harmonic expression 2 Character is tics role can b e clas sified a s: Inhibitor: reduces the harmonic v a lue of sp ecific characteristics by suppressing or comp e nsating their manifestation to r educe sy stem risk (if characteristics are risk factors ) or promotes a c ompe ting characteristics. Inhibitors play an impo rtant role, as they limit the sco p e o f av a ilable options a nd allow the s ystem to fo cus its r e sources Activ ator : incre a ses the harmonic state by dir ectly conforming to har mo nic e x - pression. A pattern of characteristics is activ ator of a certain harmonic pa tter n if its confor mance to the har monic expres s ion causes the expansio n of the latter. F acilitator: increases the harmonic state indirectly b y enhancing and amplifying contributing characteristics 1. System comp onents, including environment , context, expressio n a nd co m- po sition, all hav e Abstract Cha racteristic Mode ls . A Character istic Mo del is the deriv ative of the underly ing s ub ject (environmen t, context, co mpo - sition or expr ession). As men tioned earlier, depending on the context, a characteristic mo del represents either the stable or dyna mic asp ect of the underlying sub ject. The evolution and transfor mation of a sub ject influence its c hara cteristics. Harmonic v alue provides a method to co mpare a manifested characteristic 4 to the express e d or desir e d characteristic; Harmonic v alue is calculated by co m- paring the characteristics of H c and H e as re pr esented on the Har mo nic helix 5 by c 1 to c n and e 1 to e n resp ectively; wher e L obs =measure of compar ison, is the observed difference be t ween tw o characteris tics and L t = measure o f com- parison, is the true difference in a given context b etw een tw o characteristic as measured o n an intertwined do uble helix where: 1. θ is the ang le betw een obser ved and reference characteristic 2. µ is the mag nitude of observed characteristic measured by its deference from reference c harac ter istic divided by π : 3. Its radius is 1 (for simplicit y for single context can b e r epresented by a unit circle 6 ) 4. r is the dis ta nce o f obs e rv atio n (r a dius o f co mparison circle); for the unit circle r=1 4 Characteristic of the underlying sub ject 5 Harmonic characteristics for Hc & He are plotted as p oints on a double heli x structure circumference, its radius represen ts observ ation distance and arc length betw een observ ed and reference cha racteristic represent s m easure of comparison 6 W eisstein, E r icW., h ttp://math w orld.wolfram.com/UnitCircle.html 3 Figure 1 Harmoni c v alue i s calculated b y comparing the c haracteris- tics of H c and H e as represented on the Harmoni c he lix 7 b y c 1 to c n and e 1 to e n resp ectively; where L obs =measure of com parison Harmonic v alue is calcula ted using the following fo r mula: Figure 2 Harmonic v alue calculation 7 Harmonic characteristics for Hc & He are plotted as p oints on a double heli x structure circumference, its radius represen ts observ ation distance and arc length betw een observ ed and reference cha racteristic represent s m easure of comparison 4 Where θ is the angle b etw een characteris tic for H e and H c expressed in ra dian 8 , as plotted on har mo nic helix , with -1 and 1 r epresenting the min and ma xi- m um of the H v , and n is the qua ntit y o f characteristics for H c , if θ =0 then characteristic has harmonic v alue of 1. 1. The under lying sub ject significanc e is highlighted b y its Harmonic Signif- ic anc e. Ha rmonic Significance is a weight ed harmonic v alue: Where m r epresents the total num ber o f characteristics be longing to a ll comp o- sitions participating in the ex pr ession character istic mo del 9 . Harmonic Significance indicates the harmonic comp osition p otential for con- tributing to the har monic state. Significance is r epresented b y the granularity of comp osition characteris tics , with mo re sig nifica nt co mpo s itions repr esented by a higher num ber o f characteristics. In a given con text if multiple comp ositions hav e equal or close harmonic v alue, harmonic s ignificance b ecome a deciding factor for compos ition s election. Significance Expressio n Char - acteristics Comp osition Character is tics Increase Increase Increase Decrease Decrease Don’t care Significance increases when the granularity of ‘expressio n characteristics’ and conforming 10 ‘comp osition characteristics ’ incr e ases 11 ; Significance decr eases when the gr anularit y of ‘expressio n c hara cteristics’ decr eases 12 . 1. Harmonic state represents the quadra tic mean 13 (RMS) o f harmonic v al- ues of the selected 14 comp ositions (selected based on their significant) in a given cont ext. Har monic State (H s ) is calculated by the following form ula: where { X 1 ,X 2 ,.. X n } repres ent harmonic v a lue s of the selected comp ositions in the cont ext and n represents num b er o f selec ted compo sitions in the context. Comp ositions with higher significanc e hav e mor e p o sitive influence on harmonic state. 8 M ax θ f or tw ochar acter isticsinthe samecontext − π 4 < ϕ < π 4 is π 9 Depending on the cont ext, expression can hav e multiple c haracteristic model 10 Conforming ch aracteristic ha ve p ositive HV 11 Increasing granularit y of ch aracteristic for expression and comp osition is called enri chmen t 12 Decreasing granularit y of ch aracteristic for expressi on and comp osition is called simpl ifi- cation 13 Kenneth V (F all 2007), ”Determining the Effect ive or RMS V oltage of V arious W a veforms without Calculus”, T echno logy In terface 8 (1): 20 pages 14 Selected composition are those whi ch hav e the highest significance 5 Change in the comp osition characteris tics mo del can increa se o r decrease the harmonic significance, therefore changing the sys tem’s state. Change in the system’s environment ca n also for ce a state transition by changing context a nd comp ositions. The r esp onse of a Har monic system to state transition can be clas sified a s: 1. Reactive; system resp onds to change rea ctively , a fter state trans ition ha s bee n detected, either by enriching comp osition characteristics, to confor m to the enriched expre s sion mo del, or simplifying the expression mo de l, to conform to the simplified c o mpo sition model. 2. Activ e; system tries to maintain o r ac hieve a sustaina ble ha rmonic state by cr eating o ppo rtunities and avoiding risks preemptively , through en- richmen t, simplification, exchange or a combination of a ll three. Active systems retain transfor mation patterns, whic h ca n b e reused in similar contexts and subseq ue ntly ca n b e replicated in succe s sive ev olution, there- fore forming a gener ational memory . 1. Ha rmonic Status (HS): represents the av erage of harmonic v alues of a ll participating comp ositions ov er an interv al [a,b] where ‘a’ and ‘b’ r epresent evolution b oundaries. 1. Harmonic Exchange V alue (X v ); harmonic exc hange v alue is the total ”v a lue realized” by exchanges b etw een systems and de p ends on the har- monic v alue realiz e d by each system, divided by the n umber of exchanging parties. Dir e ct Ex change V alue 15 betw een tw o systems (S 1 and S 2 ) is calculated by the following for m ula: = Harmonic e xpression of system S 1 = Comp osition of sy stem S 1 = Harmonic e xpression of system S 2 = Comp osition of sy stem S 2 15 F or b oth parties, each party can calculate its r eturn by using ; for instance in a game of chess each participan t goal i s to maximize o wn return while minimizing her/his opponent’s 6 Exchange efficiency is : Where n is n umber of exc hanging parties in the exchange chain The e xchange motiv atio n factor is the difference b etw een harmonic state b efore and a fter the exchange. Longer exchange chains can provide p otential v a lue otherwise not attainable in direct exc hange. F or instance in the following ex change s c enario: Set A c o nt ain: { (10,12,1 4 ),(1,4,5) } Set B co ntain: { (2,3),(23 ,24,25) } Set C contain: { (6 ,7 ,8,9,10 ),(1 6 ,26,27 ) } Figure 3 Co mp osi tion transformation enhance excha nge opp ortunity System A transforms comp osition to c reate an exchange opportunity with B and C 16 ; the ab ove example is a multi part y exchange scenario which in volv e more than tw o exchange parties; the le ng th of the exchange chain depends on capa- bilit y of participating systems to tr ansform and cr eate desir able co mpo sitions for further tra de a nd exchange. Indir e ct exchange value is when pay out to one par ty in the exchange is done through a thir d party (indirectly) Figure 4 indirect exc hange scenarios An example o f the ab ov e scenario is the natura l recycling pro cess , where com- po sition used by plant s and animals is recy cled, thus creating a Self sufficient exchange e c osystem where exchange chain is self sustaining. 16 System A i s able to acquire composition from B b y differing its payme nt after trading with C 7 Figure 5 self-sustaini ng exc hange c hain 1. Harmonic T ransforma tion; is change in the character istics o f comp osition, environmen t, context o r expression to maintain or increase harmonic state, status and exchangeabilit y; there are tw o types of Harmonic tra nsforma- tion: (a) Simplification: i. Simplifying the under lying sub ject 17 OR ii. Reducing gra nularity of the c harac ter istics mo del 18 OR iii. A combination of both Decomp osing a comp osition to create tradable comp os itio ns is an example of simplification. 1. (a) Enrichmen t: i. Increasing granularit y of the ch ara cteristic mo del 19 ii. Enriching the underlying sub ject and creating po ten tial for in- creasing granularit y of the characteristic mo del Combining comp ositions to create a trada ble characteristic mo del is an example of E nrichmen t Positiv e tra nsformation pa tterns emerge when: F or Context C 1 and Expres sion E 1 transforming 20 the underlying sub ject or the c hara cteristic mo del always results in harmonic s ta te b eing maintained o r improv ed. In other words: If compo sition A is exchanged with, or transformed to compo sition B , OR If c hara c ter istic mo del X 1 is transformed to X 2 THEN AL W A YS Harmonic s tate S 1 is maintained or improv ed. 17 Characteristic mo del may be mai n tained or si mplified as we ll 18 Underlying sub ject may b e m ain tained or s implified as we ll 19 While maintaining the underlyi ng sub j ect 20 T ransformation can b e either enri c hment or simplification 8 1. Mathematical and Logical oper and in a harmonic system Basic Ma thematical op eration is conducted using the following technique: There are tw o in tertwined helix, blue p o sitive, red negative Figure 6 Math op e ration using harmoni c helix Addition implies com bining Multiplying implies scaling Adding implies incr easing Deduction implies decreasing Increase of increase= increa se Decrease of increase= dec r ease Decrease of decrease= decrea se Decrease fro m p ositive num be r is alwa ys turn CCW, decrease from nega tive nu mbers is alw ays CCW Increase from p ositive num ber is always turn CW, Increase from nega tiv e num- ber s is always CW Helix start at p ositive 0 , turn by 0 π is negative 0 When a num b er is decreased to zero, further decreas e from zero follows negative nu mber rule, start fr om -0 (decrease fro m 0 to -0 is 0 π ) X+Y= T urn CW b y magnitude of Y π fro m X X-Y= T urn CCW by magnitude of Y π fro m X X*Y= if b oth side increa se or decreas e: T urn CW from 0 mag nitude of Y π , X times Else T urn CC W from 0 magnitude of Y π , X times 1 Logical relation 2 A A ND B = C Expansion of C, the outcome, depe nds on pr esence of b oth Character istic A a nd B, in o ther word A and B a re activ ator for C, if any of them is miss ing inhibitor 9 preven t expa nsion of C; condition o f existence co uld be concurr ent or delay ed (within a defined interv al); expans io n of C in this case is ser ial, dep ending on o ccurrence and co nfo r mance of all characteristics . If Outco me of the ab ov e equation is equal or less than 0 then the arg umen t is false; otherwise it is true. Figure 7 Bo olean op eration on Harmonic helix (where p ositive and nega tiv e helix intersect at 0 , π ) log i- cal ev a lua tion is represented by tr ansforming predicates on an ev aluation helix with every predicate sym b ol centered on π /2, observed θ > =90 implies mov e to negative (Red) helix whic h is interpreted as fa lse F orced expansion By injecting enoug h activ ator sys tem can b e forced int o e x pansion even if one of the op era nd is no t present and inhibits the expa ns ion, effectively neutralizing the effect o f inhibitor . 3 A OR B = C Expansion of C (the outcome) dep ends on existence o f either Char acteristic of A o r B, unlike conjunction there is no inhibitor, therefor e lack of either A or B do e s not preven t expa nsion of C. Condition of existence could b e concur r ent or delay ed (within an int erv al) ; expansio n of C this case is parallel, as so on as co nfo r mance of a ny observed character is tic is confirmed expansion of C is triggere d. Evidently it is slow er to exa mine ar guments inv olving co njunction; therefore there is an opp ortunity for optimization by tr a nsforming cluster of characteristic mo dels into a unit of characteristic mo del, which ca n b e tested in its en tirety . Ho w recognitio n happ ens, H armonic sens ory system Based on harmonic theory pr inciples and in order to fo cus on desired c hara c- teristics and eliminate noise, sensory system is close ly b eing influence d b y the context; this pro cess is c alled sensory sy stem pr iming . 10 Figure 8 Harmonic system pri med b y memory system Above diagram illustra tes how s ensory system in primed by its relev a nt memor y system (visual, audito r y ,..); harmonic cont ext determines pattern stub which act as a primer for the sensory s ystem. Har monic expansio n of stub happ ens when a clos e eno ugh obser ved pattern is detected (conformity is ev aluated us ing har- monic v alue formula); harmonic expansio n triggers fur ther cycle of priming and observing. Optimum cy cle frequency is c alculated by dividing sub ject charac- teristics (re pr esented by observ able patterns) div ided by quadra tic mea n 21 of cognition sys tem av ailable capacity (represented by pr imed pattern stub) and sensory system capa bilit y (represented by observed pattern), rounded to next whole n umber. f = C sbj RM S ( C s , C C ) Optimum freq ue nc y is achiev ed when b oth cognition system c apacity a nd sen- sory system ca pability conv erge to quadra tic mean. Cycle’s frequency can b e further optimized b y reducing gra nularit y of sub ject characteristic mo del (simplification), or by increasing pr imed & obse rved pat- terns (capacity of c o gnitive and sensory system). Context has a g r eat influence on priming the se ns ory system with patterns to lo ok for a nd se le c tion o f patterns to expand. Thinking Thinking is the ability to use referential characteristics to cr eate scenario s to transform, rearr ange a nd co m bine v arious character is tic patterns in or der to fa- cilitates emergence of new expre s sion and comp osition; it also entails ev aluating harmonic v alue and co mpo sition a rrang e ment in v a rious c o nt ext scenario s. This pro cess creates the p os sibilit y to observe collab ora tive emerg ence of e x pression and dis cov er caus e a nd effect. Imagination Imagination is the ability to virtualize sensor y sy stem to simulate and inv oke referential characteristics (pa tterns) “as if they were observed” to trigger de- tection a nd expa nsion of stub patterns; in o ther w ord, arr anging patterns and priming them in virtualize d sensory system to cre a te r eal or virtual (imagina - tive) r esp onse 22 . 21 Chris C. Bi ssell and David A. Chapman (1992). Digi tal signal transmi ssion (2nd ed.). Camb ridge U niv ersity Pr ess. p. 64. ISBN 9780521425575. 22 Virtual resp onse triggers cognitive patte rn and li mited external motor functions 11 Creativit y Creativity is s ystemic use of refere n tial characteris tic, virtualiza tion and trans- formation to increase efficiency (b y reducing cycles) and num b e r o f desir able characteristics (through arra ngement of comp osition) as well as the ability to per mut e and combine comp os itions to facilitate emergence o f new expr e ssions and s ystems 23 and o bserve and memorize the pro cess. Instincts and “need” Instinct express ions ar e ma jor contributor to the harmonic system’s health and harmonic status, they are requir ed to main tain the integrit y , hea lth and contin u- it y of the system, har monic status that stem from instincts a cts as a mo tiv ator to maintain and increa se comp ositio ns whic h are required to satisfy instinctive expressions 24 (b y manifesting conforming characteristics). Sensory syste m and conscious ness Harmonic s e nsory system captures informatio n on its own term 25 , co g nitive system primes sensory sys tem for “familiar ” o r pattern of “interest”. Sensory system transmits information a s “ha rmonic patterns” (which are “ referential” characteristics); ability to observe a nd memor ize these patterns constitutes “ sen- sational familiarity ”. Sensa tional familiar it y is system’s abilit y to observe, mem- orize and prime (repro duce) referential c haracteristics exp e r ienced b y its sensor y apparatus. Sensa tional familiarity in co njunction with cognitive s y stem abilit y to pr o ject 26 referential characteristics of s ensory system in “virtualized s e ns ory” is the bas es fo r a wareness and self-image. Harmonic System Self a w areness and vision of se lf (P ersonality) “Self ” is a Cluster of vir tual comp os itio ns based o n referential and intrinsic characteristics 27 , which exhibits 28 characteristics pattern and traits acco r ding to virtual or r eal scenar io 29 . Aw are ness of “Self ” a s a co nstruct, stems fr o m the ability to o bserve and pre dict manifestatio n 30 of characteristics accor ding to stimu lus (either virtual or rea l). Developmen t of self is vital for simulation and imagination, through which s y stem can cr eate and rate permutation of v arious scenarios to incr ease e fficie ncy and r educe r isk. So cial b e ha vior So cial interactions arise from the need to enrich av a ilable comp ositions in the environmen t, enhance exchange o ppo rtunities a nd increase efficiency by s pe- 23 New comp osition arrangemen t and cha racteristic mo del leads to emergence of gov erning expression 24 “Need” ari se fr om the fact that to m ai n tain the harmonic status there must b e enough compositions to provide the required cha racteristic mo dels 25 Harmonic system Sensory system is alwa ys b eing primed by cognitiv e system 26 In order to create simulation scenarios 27 Referen tial and intrinsic characte ristics are the result of sensory and cognitive system operation and interact ions 28 Referen tial characteristic help forming a composition with intrinsic characteristics 29 Creating a Scenario is done by priming the virtual sensory w i th s tub pattern to trigger a resp onse from cognitiv e system 30 Manifested capabilities are those patterns which ha ve been observed, memorized and expanded 12 cialization. Collab ora tio n a nd so cial int era c tion aids emerge nce 31 of new op- po rtunities and reduce risk 32 ; harmonic exchange requir es a collab ora tive a nd co op erative environmen t where new comp osition ar r angements would lea d to increase oppo r tunit y for all of its participa n ts. Belief, v alue system and Morality Risk mitigation, increas ed so cial & environment al int era ction and exchange o p- po rtunities a r e amo ng the driving for ces to form Harmonic System b elief and v alue system, which is key and influential in its governance. Beliefs and v alue system compr ise of clus ter of vir tual comp ositions ; which are formed ba sed on observed (or inferred) intrinsic characteristics when manifested by externa l or int ernal 33 comp ositions. F o r exa mple so cialization incre a ses the o dd of surv iv al and inc r ease exchange opp or tunities; therefo r e intrinsic characteristic o f so cial- ization 34 contributes to for ming system’s v alue & b elief co mpo sition. Intrinsic characteristics bas e d on v a lue s a nd b eliefs ar e s trong contributors to harmonic status a s they influence the decision to pursuit a nd e x pand a pattern stub; if pursuit of pattern caus e s reduced harmonic v alue fo r “v a lues and beliefs” char- acteristics, harmonic status declines subs tant ially 35 . Emotions Emotions are intrinsic c haracter istic comprising of sensational and cognitive pat- terns expr essed by instinctive comp ositions. Demonstra tion of characteris tics by Ins tinctive comp ositions dep ends on co nt ext, environment, and observ ation or detection (a particular ) arr angement 36 of characteristics. When manifested, instinctive comp osition c hara cteristics ca n lead to expa nsion of harmo nic pat- terns, expr ession of refer ent ial characteristics (that can b e inferred as emotio nal resp onse) o r transformation o f co nt ext a nd environmen t characteristic pattern (whic h is more subtle). Change in harmonic state, (whic h itself is gov erned by intrinsic and r e ferential characteristic co nformity to a n express e d ha r monic expressio n) c an act a s a trigger for expression of emotional pattern. Ther e is a co rrelation betw een characteristic pattern, its context and t yp e o f emotion; for instance an act which is a t o dd with characteris tic pa ttern o f “mo r ality” creates a sig nificant delta in harmonic v a lue, therefor e ca uses expression of characteristics pa ttern which is asso ciated with “guilt” 37 . Context plays a ma jor role in 38 t yp e o f emotion tha t 31 Exc hange opp ortunities to i m prov e harmonic status and exploit oppor tunit y in arrange- men t of comp osition to cause system emergence 32 Reduce ri sk through collab oration to cause emergence of characte ris tics w hi c h are risk inhibitors 33 In ternal sensational or cognitiv e comp osition stemming f rom instincts pro vides imp ortan t input into b elief and v alue system. 34 Manifested as cognitiv e and sensational patterns, f or instance exc hange capability 35 Degree of decline dep ends on gran ularity of “V alues and Beliefs” system charact eristics and granu larity and significance of opp ortunity pattern 36 Arrangemen t of charact eristics is key in triggering emotional response, arrangement expression of particular characteristics can hav e direct relation to emotional expression 37 Emotional pa ttern emplo y inhibitor charact eristics to suppress other patte rns and become dominan t 38 Through transforming the gran ularity of expression pattern sensitiv e to emotional c har- acteristic pattern, or manipulating/cha nging the response pattern 13 are ex pressed 39 and exp erienced. Reason Logical re la tion mo del defines the arr angement, s e quence, relatio n and role 40 of characteristics according to a reference patterns 41 . Rea son is based o n the ability to observe the lo g ical rela tion of patterns and construct a r efer enti al logical relation model 42 according ly . Rationality Reason is the ability to infer causality based on obse rv atio n and construction of the r eferential logical rela tion mo de l; ra tionality is the ability to o ptimize the r e lation mo del and sy stem r e spo nse cycles 43 according to the c ontext . It inv olves using s im ulation, o bserv a tion and transformatio n to cre a te elab orate per mut ation of expansion s cenarios as well as to optimize granularit y of the resp onse pattern for the given co nt ext. Language Spo ken language is base d on series of auditor y patterns; consisting of so und char- acteristic 44 , expressed and o bserved by the auditor y s ystem to form a referen- tial characteristic mo del to r epresent familiar se ns ation or cog nitiv e patterns 45 . W ritten symbols (characters, words) a re referential characteristics based on fur- ther abstraction o f the auditory patterns. Conclusion Harmonic theory pr ovides a mathematical framework to describ e the s tructure, behavior, evolution and emerg ence of ha rmonic systems. Using the Harmo nic theory , the emerg ence of ad-ho c collab or ative systems can b e mo deled and ex- plained. It also provides a model to desc rib e m ulti context 46 complex systems. Harmonic theory can b e used to build new clas s es o f systems, which understand the problem context and find alternative and mo re efficient solutions 47 , by con- tin uously building and improving their vo cabulary o f trans formation patterns, such systems c a n increase their efficiency a nd accuracy within their op er ating environmen t. Such sy stems would b e more effective in unders ta nding, adapting and exchanging with their environment and partners as well as solving unantic- ipated pr oblems. Harmonic theory pr ovides a framework for building Intelligen t contextual and adaptive computing, cognition and senso ry system that comprise of but not limited to a uditory , visual and tactile prime-able a nd vir tualize-able memory 39 Emotion expressed as observ able referential c haracteristic 40 Characteristic role can b e as“ expansion activ ator”, “facilitator” or “inhibitor” 41 Reference patterns are constructe d from ch aracteristics manifested by intrinsic or vir tual compositions. 42 Based on the ability to Observ e, memorize and r eference relation of c haracteristic patterns to eac h other, expression conte xt and environmen t. 43 Rationalit y inv olve s examining relationship of different patterns (ch aracteristic models) from causalit y pers pective in different con text (simulating s cenarios) 44 Linguistic charact eristics are referential 45 Auditory patterns acts as the auditory ch aracteristic of the underlying s ub ject of the expression 46 Multi con text complex harmonic system can b e m odeled as harmonic cub e 47 Efficien t solution can b e found using Through transformation of either the characteristic model or the underlying sub ject 14 and sensory system, it also em b o dies cognitive appar atus comprising of cluster of harmonic systems that participate in exchange and trade to enhance ha rmonic status (by gaining access to comp osition capable of manifesting characteristics that better conform to its harmonic expressio n). This framework enables the system to: 1. F or m virtual co mpo sition that is able to ma nifest context sensitive char- acteristics according to s ensory and cognitive sys tem demand. 2. Detect, obse r ve, memorize and repr o duce referential characteristics man- ifested by compo sitions in its environmen t, understand and co nstruct re- lational logica l mo del of character istics and develop vir tual comp osition capable o f manifesting characteristics acco rding to context and sy stem state. 3. Develop a sense o f “self ” through co nstructing virtual co mpo sitions bas ed on r eferential characteristics deriving fr om its own intrinsic or external observed comp ositions. 4. Sim ulate vir tual scenarios based on imaginary referential c harac ter istics to reduce risk and cre a te new characteristic p ermutation a nd a r rangements. 5. Rearra ng e characteris tics of environment, co n text, comp osition or expr es- sion in o rder to incr ease s ystem benefit (har mo nic s ta te) 6. Communicate using abstrac t symbo lized referential c hara cteristics derived from intrinsic and observed comp ositio ns that are agr eed upo n thro ugh exchange with p eers. References [1] M. Abra mowitz and I.A. Stegun. Handb o ok of mathematic al functions with formulas, gr aphs, and mathematic al tables . Number v. 55, no. 1972 1 964. [2] John Ba ckus. Can pr o gr amming b e lib er ate d fr om the von Neumann style?: a functional style and its algebr a of pr o gr ams . ACM, 2 0 07. [3] C.C. Biss e ll and D.A. Digital signal t r ansm ission . Cambridge University Press, 1992 . [4] O. Macr o e c onomics . Pearso n P rentice Hall, 2 0 08. [5] P .M. Exchange and p ower in so cial life . T ra nsaction Bo oks, 196 4. [6] B. Computer Har dwar e . Thomson, 2008. [7] B. Time fr e quency signal analysis and pr o c essing: a c ompr ehensive r efer- enc e . Elsevier , 2 003. 15 [8] K.J. The joy of sets: fundamentals of c ontemp or ary set the ory . Springer- V erla g , 1 993. [9] D. F re edman and D. Mathematic al metho ds in st atistics: a workb o ok . Nor- ton, 1981. [10] A. Gray , E. Abb ena, and S. Mo dern differ ential ge ometry of curves and surfac es with Mathematic a . Chapman and Hall CR C, 2006. [11] P . Metamathematics of F uzzy L o gic . Kluw er, 2001. [12] G.W. Basic Statistics for t he Behavio r al Scienc es . Ce ng age Learning , 2010 . [13] J.R. Elements of algebr aic t op olo gy . Perseus Bo o ks, 1984. [14] J. Piag e t, N. C ho msky , a nd M. L angu age and le arning: the deb ate b etwe en Je an Piaget and No am Chomsky . Harv a rd Univ ersity Press, 1980. [15] D.P . Siewiorek , C.G. Bell, and A. Computer s t ructur es: princip les and examples . McGr aw-Hill, 1982 . [16] J.N. Intr o duction to p ost-tonal the ory . Prentice Hall, 200 5 . [17] Kenneth V. Determining the effective or rms v oltage o f v ar ious wa veforms without calculus. T e chnolo gy Interfac e , 8(1):20, 2007. [18] E. W W eisstein. Helico id, 2 010. [19] E. W. W eisstein. Unit circle., 201 0. 16