Derivation of the Timewavefrom the King WenSequence of Hexagramsby Terence McKennaThe idea that time is experienced as a series of identifiable elements in flux is highly developed in the IChing. Indeed the temporal modeling of the I Ching offers an extremely well-developed alternative to the"flat-duration" point of view. The I Ching views time as a finite number of distinct and irreducibleelements, in the same way that the chemical elements compose the world of matter. For the Taoist sagesof pre-Han China time was composed of sixty-four irreducible elements. It is upon relations among thesesixty-four elements that I have sought to erect a new model of time that incorporates the idea of theconservation of novelty and still recognizes time as a process of becoming.The earliest arrangement of the hexagrams of the I Ching is the King Wen Sequence. It was thissequence that I chose to study as a possible basis for a new model of the relationship of time to theingression and conservation of novelty. In studying the kinds of order in the King Wen Sequence of the IChing I made a number of remarkable discoveries. It is well known that hexagrams in the King Wensequence occur in pairs. The second member of each pair is obtained by inverting the first. In anysequence of the sixty-four hexagrams there are eight hexagrams which remain unchanged when inverted.In the King Wen Sequence these eight hexagrams are paired with hexagrams in which each line of thefirst hexagram has become its opposite, (yang changed to yin and vice -versa).The question remains as to what rule or principle governs the arrangement of the thirty-two pairs ofhexagrams comprising the King Wen Sequence. My intuition was to look at the first order of difference,that is, how many lines change as one moves through the King Wen Sequence from one hexagram to thenext. The first order of difference will always be an integer between one and six. When the first order ofdifference within pairs is examined it is always found to be an even number. Thus all instances of firstorder of difference that are odd occur at transitions from one pair of hexagrams to the next pair. Whenthe complete set of first order of difference integers generated by the King Wen Sequence is examinedthey are found to fall into a perfect ratio of 3 to 1, three even integers to each odd integer. The ratio of3/1 is not a formal property of the complete sequence but was a carefully constructed artifact achieved byarranging hexagram transitions between pairs to generate fourteen instances of three and two instances ofone. Fives were deliberately excluded. The fourteen threes and two ones constitute sixteen instances ofan odd integer occurring out of a possible sixty-four. This is a 3/1 ratio exactly.

Where Did the Timewave Come From?file:///H|/public/timewave/waveexplain.html (1 of 16) [01/22/2002 1:51:30 PM]Where Did the Timewave Come From?file:///H|/public/timewave/waveexplain.html (2 of 16) [01/22/2002 1:51:30 PM]Figure 1Figure 1 shows that when the first order of difference of the King Wen Sequence is graphed it appearsrandom or unpredictable. However when an image of the graph is rotated 180 degrees within the planeand superimposed upon itself it is found to achieve closure at four adjacent points as in Figure 2.

Figure 2While closure might logically be expected anywhere in the sequence, it in fact occurs at the conventionalbeginning and end of the sequence. While an arrangement with closure might have placed any twohexagrams opposite each other, what we in fact find is that the hexagrams opposite each other are suchthat the numbers of their positions in the King Wen Sequence when summed is always equal tosixty-four. These facts are not coincidences, they are the artifacts of conscious intent.Over 27,000 hexagram sequences were randomly generated by computer (all sequences having theproperty possessed by the King Wen sequence that every second hexagram is either the inverse or thecomplement of its predecessor). Of these 27,000 plus sequences only four were found to have the threeproperties of a 3/1 ratio of even to odd transitions, no transitions of value five and the type of closuredescribed above. Such sequences were found to be very rare, occurring in a ratio of 1 in 3770. Here is thecomplete graph of the King Wen first order of differnce with its mirror image fitted against it to achieveclosure:

Where Did the Timewave Come From?file:///H|/public/timewave/waveexplain.html (3 of 16) [01/22/2002 1:51:30 PM]Where Did the Timewave Come From?file:///H|/public/timewave/waveexplain.html (4 of 16) [01/22/2002 1:51:30 PM]Figure 3For these reasons I was led to view the King Wen Sequence as a profoundly artificial arrangement of thesixty-four hexagrams. Look carefully at Figure 3 immediately above. Review in your mind the stepsfrom the King Wen sequence that led to it. Notice that it is a complete set of the sixty-four possiblehexagrams, running both sequentially forward and backward. Since it is composed of sixty-fourhexagrams of six lines each it is composed of 6 x 64 or 384 lines or yao. One might make an analogy andsay Figure 3 is to the King Wen sequence as a cube is to a square; it is composed of the same elements asthe King Wen Sequence but it has more dimensions.It is my assumption that the oracle building pre-Han Chinese viewed the forward-and backward-runningdouble sequence of Figure 3 as a single yao or line and that it is therefore open to the same treatment aslines are subject to in the I Ching, namely multiplication by six and sixty-four.

Where Did the Timewave Come From?file:///H|/public/timewave/waveexplain.html (5 of 16) [01/22/2002 1:51:30 PM]Figure 4Since a hexagram has six lines I visualized six double sequences in a linear order. But a hexagram ismore than lines; a hexagram also contains two trigrams. Thus over the six double sequences I overlaidtwo double sequences, each three times larger than the six double sequences. A hexagram also has anidentity as a whole; thus over the six and the two double sequences a single, larger double sequence isprojected.The sets of double sequences of each level share a common point of origin and all return to a single endpoint. The resulting figure, show in Figure 4 on the extreme right, is to the original double sequence as atesseract is to a cube, for again more dimensions have been added. This figure itself can then be imaginedas a single hexagram, but one of a set of sixty-four.

Where Did the Timewave Come From?file:///H|/public/timewave/waveexplain.html (6 of 16) [01/22/2002 1:51:30 PM]Figure 5The closure at the beginning and end of this figure suggested that it might be useful to model process. Its384 subunits imply a calendar. Can it be coincidence that the length of a lunar month, 29.53 days, times13 is 383.89? I believe that what we have here is a 384 day lunar calendar with resonances to other othernaked eye astronomical phenomena known to be of interest to the ancient Chinese (see below).

Where Did the Timewave Come From?file:///H|/public/timewave/waveexplain.html (7 of 16) [01/22/2002 1:51:30 PM]Table 1Using techniques that I developed for the problem I was able to mathematically collapse the hexagramconstruct into a self-similar fractal curve that can be used to map the unfolding of temporal variables andtheir resonances on all levels of duration.My attack on the problem began with an examination of the simple wave of Figure 3. Thirteen discreteline types comprise any simple version of the graph. These thirteen lengths are displayed on and off gridin Figure 6:

Where Did the Timewave Come From?file:///H|/public/timewave/waveexplain.html (8 of 16) [01/22/2002 1:51:30 PM]Figure 6. As these lengths are always discrete units, we can assign to them values which are ascending integers.The values of Figure 6 allow a quantification of line length. To quantify the degree and direction of skewof individual lines, one direction of skew is designated as positive, giving lines skewed in that directionpositive values. Lines skewed in the opposite direction are given negative values. This gives valuesadequately preserving and quantifying line length and direction of skew. The values labeled L in Figure 6are used for the left side of a simple wave while the values labeled R, which are the same values withtheir their sign reverse, are applied to the right side of any simple wave. The sign is important only incombining values across scales but is ignored in the final graphing of combine values, either set of valuesmay be applied to either the right or left side. However, whichever schema is chosen must then befollowed throughout. Figure 7 represents the version of these values that we have used for the simplegraph.

Where Did the Timewave Come From?file:///H|/public/timewave/waveexplain.html (9 of 16) [01/22/2002 1:51:30 PM]Figure 7It is important to note that the valuations in Figure 7 are valuations of the simple wave on the smallestscale of a single complex wave. The relative proportions of the three levels in the complex wave arepreserved and quantified by multiplying the valuations of the linear scale in the appropriate way. Toassign a value to a positionon the trigramatic scale, the valuation of that position on the linear scale(Figure 7) is multiplied by three because the trigramatic scale is three times larger than the linear scale.In a similar manner, the hexagramaticpositions are assigned a valuation by multiplying their linear-levelWhere Did the Timewave Come From?file:///H|/public/timewave/waveexplain.html (10 of 16) [01/22/2002 1:51:30 PM]valuations by six, again because the hexagramaticscale is six times larger than the linear. Figure 7 usesthe value scheme in Figure 6 and is the version of value assignments we have used in all our calculations.Note that in Figure 7 all parallel lines, regardless of the distances separating them, reduce to zero. Thus,while the operations discussed so far have allowed quantification of skew direction, proportional ratios ofthe wave parts, and the degree of departure from the parallel state, they have not provided a quantifiedaccount of the fluctuating distances between the two parameters of the wave. The procedure for obtainingthese values is similar to, but distinct from, the procedures outlines above.

Figure 8Figure 8 shows the seven types of divergence, congruence, and overlap which points in the simple wavemay display. The two possible assignments of positive and negative numbers are shown to the right andleft sides in Figure 8. We have chosen to use the right-hand schema to preserve the intuition thatoverlap tends to carry a situation toward the zero state rather than away from it.

Where Did the Timewave Come From?file:///H|/public/timewave/waveexplain.html (11 of 16) [01/22/2002 1:51:31 PM]Figure 9Figure 9 shows the values this series of point assignments generates when applied to the simple wave.When the valuations for skew, parallelism, and relative proportion have been combined in the mannerdetailed above the following 384 values result(as read from position 383 to position zero):Where Did the Timewave Come From?file:///H|/public/timewave/waveexplain.html (12 of 16) [01/22/2002 1:51:31 PM]0, 0, 0, 2, 7, 4, 3, 2, 6, 8, 13, 5, 26, 25, 24, 15, 13, 16, 14, 19, 17, 24, 20, 25, 63, 60, 56, 55, 47, 53, 36, 38,39, 43, 39, 35, 22, 24, 22, 21, 29, 30, 27, 26, 26, 21, 23, 19, 57, 62, 61, 55, 57, 57, 35, 50, 40, 29, 28, 26,50, 51, 52, 61, 60, 60, 42, 42, 43, 43, 42, 41, 45, 41, 46, 23, 35, 34, 21, 21, 19, 51, 40, 49, 29, 29, 31, 40,36, 33, 29, 26, 30, 16, 18, 14, 66, 64, 64, 56, 53, 57, 49, 51, 47, 44, 46, 47, 56, 51, 53, 25, 37, 30, 31, 28,30, 36, 35, 22, 28, 32, 27, 32, 34, 35, 52, 49, 48, 51, 51, 53, 40, 43, 42, 26, 30, 28, 55, 41, 53, 52, 51, 47,61, 64, 65, 39, 41, 41, 22, 21, 23, 43, 41, 38, 24, 22, 24, 14, 17, 19, 52, 50, 47, 42, 40, 42, 26, 27, 27, 34,38, 33, 44, 44, 42, 41, 40, 37, 33, 31, 26, 44, 34, 38, 46, 44, 44, 36, 37, 34, 36, 36, 36, 38, 43, 38, 27, 26,30, 32, 37, 29, 50, 49, 48, 29, 37, 36, 10, 19, 17, 24, 20, 25, 53, 52, 50, 53, 57, 55, 34, 44, 45, 13, 9, 5, 34,26, 32, 31, 41, 42, 31, 32, 30, 21, 19, 23, 43, 36, 31, 47, 45, 43, 47, 62, 52, 41, 36, 38, 46, 47, 40, 43, 42,42, 36, 38, 43, 53, 52, 53, 47, 49, 48, 47, 41, 44, 15, 11, 19, 51, 40, 49, 23, 23, 25, 34, 30, 27, 7, 4, 4, 32,22, 32, 68, 70, 66, 68, 79, 71, 43, 45, 41, 38, 40, 41, 24, 25, 23, 35, 33, 38, 43, 50, 48, 18, 17, 26, 34, 38,33, 38, 40, 41, 34, 31, 30, 33, 33, 35, 28, 23, 22, 26, 30, 26, 75, 77, 71, 62, 63, 63, 37, 40, 41, 49, 47, 51,32, 37, 33, 49, 47, 44, 32, 38, 28, 38, 39, 37, 22, 20, 17, 44, 50, 40, 32, 33, 33, 40, 44, 39, 32, 32, 40, 39,34, 41, 33, 33, 32, 32, 38, 36, 22, 20, 20, 12, 13, 10Table 2: The 384 Values of the Complex WaveThese same values are to be graphed as a single line graph and are the primary valuation scheme for anycomplex wave. The process of quantifying a given time in the modular hierarchy of the complex wavewill necessarily begin with reference to these values.

Where Did the Timewave Come From?file:///H|/public/timewave/waveexplain.html (13 of 16) [01/22/2002 1:51:31 PM]Figure 10Figure 10 shows the complex compound wave and its reduction into an ordinary graph. The 384 valuesabove can be ploted on a graph thus reducing the complex, tri-leveled, bi-directionally flowing complexwave a single line moving in only one direction. Such a graph preserves certain qualities of the complexwave: its divergence from the zero state where lines are parallel, the direction and degree of skew ofpairs of lines, the relative proportions of the three levels, and the distances between the fluctuatingparameters of the various component waves. However such a graph does not reflect the shift of valuesthat would occur if the single-line complex wave were nested into a particular position in the modularhierarchy of fractal waves each level of which was 64 times larger than its predecessor. In such a case,the 384 values above would serve as a schema of values to be combined through superimposition withthe values associated with whichever one of the 64 segments of the next largest level it is to be nested in.Where Did the Timewave Come From?file:///H|/public/timewave/waveexplain.html (14 of 16) [01/22/2002 1:51:31 PM]These latter values have first been multiplied by by 64, indicating their membership in the next largerlevel of the hierarchy. Thus 64 variants of the values of Table 2 would be generated, and it is thesevarious waves or frames which we treat as comprising the temporal maps of a given historical span. Thevalues of Table 2 are the basis of the quantified maps of temporal flux which Novelty theory rests on.

Where Did the Timewave Come From?file:///H|/public/timewave/waveexplain.html (15 of 16) [01/22/2002 1:51:31 PM]Figure 11The last three of the 384 segments of the wave on any level possess singularities which quantify as zero,see Figure 11. When the wave on a given level enters those segments of itself which are zero states, itceases to contribute boundary constraints to its subsets on lower levels. The cessation of boundaryconstraints imposed by higher levels in the hierarchy causes a "surge" toward the zero state each timethat a cycle enters its terminal phase on any level in the hierarchy. Such quantized transitions from onemodality to another are called "changes of epoches" By Whitehead. The appearance of life in aninorganic world, of consciousness in an unconscious world, or of language in a world without languageare all examples of such epochal transitions. Our lives are filled with such transitions, but they areterminations of relatively short cycles in the quantified hierarchy. Terminations of cycles or epoches ofreally long duration cause extreme accelerations toward the zero state/ This idea is similar to Whitehead'sconception of concrescence and the Vedic conception of world ages which grow shorter as they tightenaround an axis point. The spiral image of the Christian apocalypse is another example of this intuitionthat time is a series of tightening gyres around the quantized emergence of transformation.A perfect self-consistent proof that Table 2 does adequately conserve four qualities--divergence from thezero state where lines are parallel, the direction and the degree of skew of pairs of lines, distancesbetween the parameters of the component waves, and the proportions of these three qualities relative tothe other levels--is afforded by comparing any two graph segments assigned to a single time but ondifferent scales relative to an arbitrary termination date that is the same for both. Any two such segmentswill be found to be similar in form yet preserving their relative proportions. This demonstrable factconfirms the idea that the complex wave derived from Figure 3 is adequately reflected and its usefulvalues retained throughout the series of operations which generate Table 2. What Table 2 and the graphsmade from it achieve is a clarity and simplicity of expression lacking in the tri-leveled complex wave.Table 2 and the algorithm that accompanies it is a quantification of operational constructs which makesthis modular hierarchy of temporal variables a valid subject for rigorous scientific investigation.We appreciate your comments people have accessed this page since 30 October.@In fhIs oxprossIon fho subscrIpf i Is oxprossod ns n funcfIon of x, usIng fho procosssImIInr fo fhnf whIch producod oqunfIon |ll]. 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"$##%&K'K()K*K ++ 6 y yy yxx 56y x y xxr(k) f(k)f(k)r(k) kr(k 1) f(k)(k 1) f(k)f(k)( ) >@30IqunfIon |?6] Is fho dofInIng oqunfIon for fho Tri-Letel Conplex Wote. ThIs oxprossIonfnkos ono from fho IndIvIdunI oIomonfs of fho lineor conplex uote, up fo fho /rigrono/icnnd /exogrono/ic conplex uotee, nnd fInnIIv fo fho /ri-letel conplex uote. ofIco fhnffho subscrIpfs j for fho frIgrnmnfIc socfIon, nnd / for fho hoxngrnmnfIc socfIon ofoqunfIon |?6] hnvo ropIncod fho subscrIpf i In oqunfIons |60] nnd |?2], ns fhov hnvo boondofInod In oqunfIons |6l] nnd |?3]. Wo now hnvo n compIofo nnd woII-dofInod funcfIonfor our Tri-Letel Conplex Wote, or Jo/o ee/.IqunfIon |?6] producos n frI-IovoI wnvo numbor sof fhnf confnIns somo nognfIvo vnIuos.Tho 384 numbor Jo/o ee/, on fho ofhor hnnd, Is fho sof of posIfIvo ronI numbors In fhodomnIn 0 384 x . ThIs monns fhnf pnrf of fho rnw dnfn sof producod bv oqunfIon|?6] IIos oufsIdo fho x-vnIuo domnIn fhnf Is fhoughf fo bo fho propor oxprossIon of fhIswnvoform. Ono procoduro fhnf Is wIdoIv usod for convorfIng nognfIvo vnIuos of somonrbIfrnrv wnvoform, Info posIfIvo vnIuos, Is fho uso of fho nbsoIufo vnIuo opornfor. If onovIows fhIs /ri-letel conplex uote ns somo kInd of InformnfIon cnrrvIng sIgnnI, IIko nnnmpIIfudo moduInfod rndIo wnvo, for oxnmpIo, fhon n vnIId procoduro for procossIng suchn sIgnnI Is fho nppIIcnfIon of fho nbsoIufo vnIuo opornfor. In fho rf sIgnnI procossIngcnso, fho rocoIvod moduInfod-cnrrIor wnvoform Is pnssod fhrough nbsoIufo vnIuo cIrcuIfrv(rocfIfIor) so fhnf fho nognfIvo vnIuos of fho wnvo nro convorfod fo posIfIvo vnIuos. ThIsncfunIIv Improvos fho sIgnnI fo noIso rnfIo of fho cnrrIor onvoIopo, whIch Is fhoInformnfIon cnrrvIng moduInfIon sIgnnI. ThIs rocfIfIod sIgnnI Is fhon procossod bv ndofocfor cIrcuIf fhnf oxfrncfs fho InformnfIon cnrrvIng moduInfIon wnvo from fho cnrrIorwnvo. AIfhough fho frI-IovoI wnvo nnd fho rndIo wnvo nro nof sfrIcfIv nnnIogous, fhovnpponr sImIInr onough fo mnko n pInusIbIo nrgumonf for fho nppIIcnfIon of fho nbsoIufovnIuo opornfor horo. ThIs opornfIon Is oxprossod ns: y yDW TABS = |??]Whoro: yDW Is fho Do/o Wote fhnf Is grnphod In IIg. ll, nnd dofInod ns fho nbsoIufovnIuo of fho Tri-Letel Conplex Wote ns oxprossod In oqunfIon |?3]. ThIs numbor sof Isusod ns Inpuf dnfn for fho TineWote Zero soffwnro, whIch porforms nn InfInIfo sorIosoxpnnsIon fhnf Movor cnIIs n froc/ol /ronefornll, fo gonornfo fho TImoWnvo vIowod onfho compufor scroon.6WDQGDUGDQG5HYLVHG'DWD6HW&RPSDULVRQVWIfh oqunfIon |?3] nnd |?4], nnd fho grnph In IIg. ll, wo hnvo compIofod fhIs formnIIzoddovoIopmonf of fho TWZ Jo/o ee/. Wo nro now In n posIfIon fo compnro fhoso rosuIfswIfh fhoso of fho sfnndnrd dovoIopmonf roporfod bv McKonnn nnd Movor In //e 1ntieiIleLonJecope nnd fho Tine1xplorer mnnunI, ns woII ns nddross fho Issuos rnIsod bv fhoWo//ine OIjec/ion.IIg. l2 Is n grnph of bofh fho e/onJorJ nnd retieeJ Jo/o ee/e, nnd If shows somoromnrknbIo sImIInrIfIos ns woII ns sIgnIfIcnnf dIfforoncos. Ono InforosfIng fonfuro of fhIsgrnph, Is fho nnfuro of onch wnvo nf Ifs rospocfIvo ondpoInfs. !ocnII fhnf fho vnIuo of fho31wnvo nf x = 0 wIII bo dIscnrdod bocnuso If Is n dupIIcnfo or wrnp of fho vnIuo nf x = 3S4.ThIs wIII nof offocf fho roInfIvo vnIuos of fho fwo wnvos nf x = 3S4, bocnuso fhov nro bofhzoro-vnIuod nf fhIs ondpoInf. Howovor, fho vnIuo of onch wnvo nf x = 1 Is nof fho snmo,wIfh fho e/onJorJ uote hnvIng n vnIuo of l0 whIIo fho retieeJ uote vnIuo Is zoro.)LJXUHWhv doos fhIs mnffor, vou mnv nsk, sInco fhoro nro mnnv obvIous dIfforoncos bofwoonfho fwo wnvos whnf Is fho sIgnIfIcnnco of fhIs dIfforonco Ior fho e/onJorJ uote, If hnsboon nrguod fhnf fho zoro vnIuo nf fho ond of fho wnvoform ImpIIos somo kInd ofsInguInrIfv nf fho ond of fho procoss or nf fho ond of fImo. ThIs retieeJ uote IsImpIvIng, howovor, fhnf fhoro mnv bo sInguInrIfIos nf Io// onds of fho confInuum. ThIs IsAIso nn nrgumonf for n cloeeJ svsfom fhnf mnv bo undorgoIng somo kInd of cvcIIcronownI procoss porhnps onch cvcIo oxprossIng ovor hIghor ordorod sfnfos of compIoxform, or Aotel/x.Thoro nro concopfs omorgIng from fho fIoId of qunnfum cosmoIogv fhnf mnv doscrIbo nnnnnIogous cvcIIc procoss. ThIs Is fhoorv In whIch unIvorsos nro fronfod IIko qunnfumpnrfIcIos fhnf InhnbIf n Inrgor, or hIghor dImonsIonnI domnIn cnIIod n nul/iteree. MIchIoKnkul2, n fhoorofIcnI phvsIcIsf nnd co-foundor of sfrIng fIoId fhoorv, hns doscrIbod nprocoss whoro unIvorsos omorgo from fho zoro-poInf, or vncuum fIoId, go fhrough nnovoIufIonnrv procoss, fhon porhnps rofurn fo fho zoro-poInf fIoId nf fho ond of fho cvcIo.ThIs cvcIo mnv fhon roponf IfsoIf, possIbIv wIfh Incronsod compIoxIfv nnd Aotel/x. SocouId fhIs bo sImIInr fo fho procoss fhnf fho TineWote nnd Aotel/x T/eorx nffompf forovonI Iorhnps furfhor InvosfIgnfIon Info fho nnfuro of fho TImoWnvo wIII shod somoIIghf on fhoso quosfIons.32)LJXUHAnofhor sIgnIfIcnnf fonfuro of IIg. l2 Is fho nppnronf ngroomonf of fho fwo wnvos In fhoIowor froquoncv domnIn. Iroquoncv confonf of nnv wnvoform oxprossos IfsoIf nsvnrInfIons In fho rnfo of chnngo of Ifs vnIuo ns fho wnvo propngnfos In somo ronIm, fhnfcouId bo oIfhor n spnco or fImo domnIn, or bofh. So fho sIopo of n wnvoform nf nnv gIvonpoInf, or Ifs gonornI shnpo, cnn rovonI froquoncv confonf (fho mngnIfudo nnd rnfo ofspocIfIc undorIvIng procossos). IxnmInnfIon of fho wnvo pnIr In IIg. l2 shows fhnf fhoroIs n common Iowor froquoncv procoss occurrIng for onch wnvoform. Tho hIghor froquoncvprocossos npponr ns roInfIvoIv shorfor durnfIon ponks rIdIng upon fho sIowor procoss.Tho Iowosf froquoncv procoss occurrIng In fhoso wnvoforms cnn bo soon bv drnwIng nnImngInnrv IIno bofwoon fho hIghosf of nII fho ponks ns ono movos ovor fho domnIn of fhownvoforms. SIIghfIv hIghor froquoncv compononfs cnn bo soon bv drnwIng fhnfImngInnrv IIno ovor fho ponks nnd vnIIovs upon whIch fho shnrposf nnd shorfosfdurnfIon ponks rIdo. Tho grnphs do dIffor In fho hIghor froquoncv domnIn ns cnn bo soonbv fho sfoopor sIopos of fho Inrgosf e/onJorJ uote frnnsIfIons. ThIs couId vorv woII boduo fo hIgh froquoncv noIso prosonf In fho e/onJorJ dnfn sof bocnuso of fho ImboddodmnfhomnfIcnI orrors.Tho Iow froquoncv, or Iong durnfIon procossos, nro fhoso fhnf mnv occur on fho scnIo ofmIIIonnIn or ovon bIIIIons of vonrs, whorons fho hIghor froquoncv procossos mnv occur onfho scnIo of n humnn IIfofImo. CouId If bo fhnf fho Iowosf froquoncv procoss Is fhosIgnnfuro of somo cronfIvo prIncIpIo nf work, bo If sfrnngo nffrncfor, zoro-poInf fIoId, oreec/o/on. CouId fhIs cronfIvo onorgv, bo porfurbIng fho fnbrIc of spnco-fImo In such nwnv ns fo frIggor fho cronfIon nnd consorvnfIon of hIghor ordorod sfnfos somofhIng IIkofho grnvIfnfIonnI onorgv of n pnssIng nonrbv sfnr frIggorIng fho formnfIon of n comofsfrom fho Orf cIoud Is fhIs Iowosf froquoncv procoss fhon n kInd of ground sfnfo, uponwhIch nII hIghor froquoncv procossos oxpross fhomsoIvos Iorhnps In fImo fhosoquosfIons wIII bo nnswornbIo, nIfhough corfnInIv nof fodnv.33An obvIous fonfuro of IIg. l2 fhnf cIonrIv shows In fhIs grnph, Is fho dIfforonco In fhonvorngo wnvo vnIuo bofwoon sfnndnrd nnd rovIsod wnvos. Tho nvorngo wnvo vnIuo forfho sfnndnrd wnvo Is somowhnf gronfor fhnn fho nvorngo vnIuo of fho rovIsod wnvo. ThIsdIfforonco In nvorngo wnvo vnIuo npponrs fo bo fho rosuIf of dIfforoncos In fho hIghorfroquoncv compononfs of fho wnvo pnIr, porhnps duo fo noIso In fho sfnndnrd wnvo fhnfIs producod bv fho mnfhomnfIcnI orrors fhnf nro prosonf. Thoso hIgh froquoncvcompononfs of fho sfnndnrd wnvo show up ns fho sfoop ponks fhnf rIso woII nbovo fhoponks In fho rovIsod wnvo. In fho IourIor nnnIvsIs fhnf foIIows, fhoso Inrgo ponks npponrns hIgh froquoncv noIso fhnf ndds rnndomnoss fo fho wnvo. Tho Impncf of fhIs dIfforoncoon fho fInnI TImoWnvo, Is fo shIff fho nvorngo IovoI of novoIfv upwnrd (Iowor vnIuos)from fhnf oxprossod bv fho sfnndnrd wnvo. In ofhor words, fho rovIsod wnvo oxprossos nprocoss wIfh somowhnf hIghor IovoIs of novoIfv, fhnn doos fho sfnndnrd wnvo. SIncoAotel/x Isn`f n cnIIbrnfod procoss, If`s nof possIbIo fo doformIno whnf fho mororonsonnbIo IovoI of Aotel/x wouId bo. AII fhnf cnn bo oxprossod fhon, Is roInfIvoovoIfv.Ono fInnI fonfuro of IIg. l2 fhnf roquIros somo dIscussIon, Is fho corroInfIon numbor nffho fop of fho grnph. In ordor fo doformIno nnd qunnfIfv fho dogroo of Infordopondonco,or Infor-roInfodnoss of fho sfnndnrd nnd rovIsod wnvoforms, n mnfhomnfIcnI opornfIoncnIIod correlo/ion wns porformod wIfh fhoso fwo numbor sofs. Tho numbor nf fho fop offho grnph Is fho rosuIf of fhnf nnnIvsIs n vnIuo of 0.564. A corroInfIon of l.0 wouIdmonn fhnf fho wnvoforms nro IdonfIcnI, whorons n corroInfIon of zoro wouId IndIcnfo nofuncfIonnI roInfIonshIp bofwoon fho fwo. AddIfIonnIIv, n corroInfIon of l wouId IndIcnfofhnf fho wnvoforms woro mIrror Imngos of ono nnofhor n ponk rofIocfod bv n frough ofc.In fhIs cnso n corroInfIon of 0.564 IndIcnfos fhnf fhoso fwo wnvoforms show n sIgnIfIcnnfIovoI of Infordopondonco, nIfhough fnr from IdonfIcnI. ThIs IovoI of corroInfIon couId boconsIdorod IIkoIv for fwo numbor sofs fhnf shnro n common orIgIn, ns woII ns shnrIngmnnv of fho snmo dovoIopmonfnI procoduros.'DWD:DYHDQG5DQGRP1XPEHU6HW&RPSDULVRQVOno mofhod for nssossIng fho InformnfIon cnrrvIng pofonfInI of fho Do/o Wote, nndconvIncIng onosoIf fhnf If Is nof n rnndom procoss, Is fo compnro If wIfh n dnfn sof fhnfhns boon rnndomIv gonornfod. SovornI such ronJon uote sofs woro consoquonfIvproducod fo bo compnrod wIfh fho rovIsod nnd sfnndnrd Do/o Wote numbor sofs dIrocfIv,nnd fo nIso uso ns Inpuf fo fho TWZ soffwnro fo gonornfo rnndom soodod TImoWnvos.IIg. l3 Is n grnph of fho rovIsod Do/o Wote wIfh n rnndom wnvo sof ovorInv, nnd IfcIonrIv shows fhnf fhoso numbor sofs bonr IIffIo rosombInnco fo ono nnofhor. CorroInfIonnnnIvsIs of fho fwo sofs shows n corroInfIon of 0.03, or ossonfInIIv un-corroInfod ns onowouId oxpocf for nnv rnndom numbor sof. IIg. l3 nIso npponrs fo show fhnf fho rovIsodDo/o Wote Is n vorv dIfforonf fvpo of numbor sof from fho rnndom wnvo sof, nnd Ifnpponrs fo showIng somo kInd of InformnfIon cnrrvIng procoss. Is fhIs In fncf fho cnso, ordoos If jusf npponr fhnf wnvIxnmInnfIon of fho pouer epec/ro for fho Jo/o nnd ronJon uotee shown In IIgs. l2 nndl3 cnn rovonI somofhIng nbouf fho nnfuro of fhoso fhroo wnvoforms nnd fhoIr34roInfIonshIp. Tho convorsIon of fImo, or spnco domnIn wnvoforms Info froquoncv domnInwnvoforms (froquoncv spocfrum or powor spocfrum) Is porformod usIng n mnfhomnfIcnIopornfIon cnIIod n IourIor frnnsform. WIfh fhIs mofhod, n froquoncv spocfrum cnn boproducod, whIch cnn foII us how much powor Is confnInod In onch of fho froquoncvcompononfs (hnrmonIcs) of n gIvon wnvoform, nnd fhorobv provIdIng fho froquoncvdIsfrIbufIon of fho wnvo powor. ThIs dIsfrIbufIon wouId fvpIcnIIv bo dIfforonf forInformnfIon cnrrvIng wnvoforms fhnn for rnndom, or noIso sIgnnIs. Tho rnndom, or noIsosIgnnI spocfrum Is fvpIcnIIv fInf ovor fho sIgnnI bnndwIdfh, nnd offon dIsfInguIshnbIofrom nn InformnfIon cnrrvIng sIgnnI spocfrum fhnf oxhIbIfs 1 f (f = froquoncv) bohnvIor.)LJXUHIourIor frnnsform opornfIons woro porformod on fho dnfn sofs shown In IIgs. l2 nnd l3,wIfh fho rosuIfs shown In IIg. l4. Tho fop grnph of IIg. l4 IncIudos pIofs for fhoe/onJorJ nnd retieeJ Do/o Wote powor spocfrn, whIIo fho boffom grnph dIspInvs fhoIonJon Wote powor spocfrum. Tho coIorod IInos drnwn fhrough onch of fho spocfrn nropouer func/ion curvo-fIfs, fhnf show fho froquoncv roII-off chnrncforIsfIcs of onch wnvo.ofIco fhnf fho fwo powor spocfrn In fho fop grnph oxhIbIf froquoncv roII-off (powor IovoIdocronsos wIfh IncronsIng froquoncv), whorons fho Iowor grnph powor spocfrum oxhIbIfsn fInf froquoncv rosponso (powor IovoI Is froquoncv Indopondonf). ThIs froquoncv roII-offIs chnrncforIsfIc of InformnfIon cnrrvIng sIgnnIs, whorons fho fInf rosponso IschnrncforIsfIc of noIso or rnndom sIgnnIs.Tho retieeJ Jo/o uote spocfrum, shown In fho fop grnph In groon, Is oxhIbIfIng fhononrIv porfocf 1 f froquoncv rosponso fhnf Is fvpIcnI for nn InformnfIon cnrrvIngwnvoform. On fho ofhor hnnd, fho e/onJorJ Jo/o uote powor spocfrum shown In bIuo,oxhIbIfs froquoncv roII-off, buf wIfh n fInffor rosponso fhnf Is nof 1 f . In fncf, fho fInffor35)LJXUHfroquoncv rosponso of fho e/onJorJ Jo/o uote Is fho IIkoIv rosuIf of hIgh froquoncv noIsofhnf Incronsos fho powor nf fho fnII ond of fho spocfrum nnd provonfs n sfoopor roII-off.ThIs Is somofhIng fhnf shouId bo oxpocfod from fho dIsforfod e/onJorJ Jo/o uote wIfhImboddod mnfhomnfIcnI orrors, whIch wouId fond fo ndd rnndomnoss fo fho wnvo. ThosIgnnfuro of such rnndomnoss cnn bo soon In fho IonJon Wote powor spocfrum, shownIn fho Iowor grnph In rod. ThIs pIof shows fho fvpIcnIIv fInf froquoncv rosponso of n36rnndom, or noIso sIgnnI wIfh no InformnfIon confonf. AppnronfIv, fho grnphs In IIg. l4nro showIng fhnf fho sfnndnrd nnd rovIsod dnfn uotee nro dofInIfo InformnfIon cnrrvIngwnvoforms, buf fhnf fho dIsforfod e/onJorJ Jo/o uote hns Imboddod hIgh froquoncvnoIso fhnf fInffons Ifs rosponso. ThIs Is ossonfInIIv whnf IIgs. l2 nnd l3 nro showIng nswoII.6WDQGDUG5HYLVHGDQG5DQGRP*HQHUDWHG7LPH:DYH5HVXOWV(l) Tho TImoWnvo Zoro Scroon Sof CompnrIsonsOnco fho Do/o Wote, or 384 numbor dnfn sof hns boon gonornfod, If bocomos fho Inpufdnfn for fho TineWote Zero soffwnro pnckngo. As monfIonod provIousIv, fho soffwnroporforms whnf hns boon cnIIod n froc/ol /roneforn, or oxpnnsIon of fho 384 dnfn numborsof fo produco fho TineWote vIowod on fho compufor scroon ns n grnph of Aotel/x. Inordor for fhIs frncfnI oxpnnsIon fo bo porformod proporIv, fho soffwnro roquIros fhnf fho384 numbor dnfn sof shown In IIg. l0 bo rovorsod, such fhnf dnfn poInf 384 bocomosdnfn poInf l nnd dnfn poInf 0 Is dIscnrdod (sInco If`s n dupIIcnfo or wrnp of dnfn poInf384).)LJXUHD37Throo sopnrnfo dnfn sofs woro usod In ordor fo gonornfo fho TineWotee noodod forcompnrIson fho e/onJorJ dnfn sof, fho retieeJ dnfn sof, nnd n ronJon dnfn sof. ThorosuIfs of somo of fhoso TineWote compnrIsons wIII bo shown In fho grnphs fhnf foIIow,bogInnIng wIfh fho dofnuIf TineWote grnphs fhnf nro IncIudod wIfh fho Tine1xplorersoffwnro ns pro-compufod wnvoforms.IIgs. l5n nnd l5b show fho TineWote fhnf Is sforod bv fho soffwnro ns Scroon l, nnd Ifcovors fho porIod bofwoon l942 nnd 20l2. IIg. l5n shows bofh fho TineWote rosuIfIngfrom fho e/onJorJ Jo/o sof on fho Ioff, nnd fhnf for fho retieeJ Jo/o sof on fho rIghf. Onfho ofhor hnnd, IIg. l5b Is fho TineWote gonornfod bv fho ronJon dnfn sof, nnd IfcIonrIv bonrs IIffIo rosombInnco fo fho grnphs of IIg. l5n.ThIs Is fho TineWote grnph fhnf McKonnn hns cnIIod hIsforv`s frncfnI mounfnIn,bocnuso of Ifs mounfnIn-IIko shnpo. Thoro nro sovornI fonfuros fo nofIco horo, wIfh fhofIrsf boIng fhnf fhoso fwo pIofs hnvo romnrknbIv sImIInr shnpos obvIousIv nof IdonfIcnI,buf fhoro Is cIonrIv n common domInnnf procoss nf work. Anofhor common fonfuro ofsIgnIfIcnnco shown In fhoso fwo grnphs, Is fhnf fho mnjor doconf Info Aotel/x (ponk of fhomounfnIn) bogIns somofImo In l96?. IInnIIv, ns monfIonod onrIIor, fho TineWoteproducod bv fho retieeJ Do/o Wote numbor sof, shows n hIghor nvorngo IovoI of Aotel/xfor fhIs fImo porIod (Iowor vnIuos), fhnn doos fho TineWote producod bv fho e/onJorJ38)LJXUHEJo/o sof. ThIs Aotel/x dIfforonco Is fho IIkoIv rosuIf of fho e/onJorJ uote dIsforfIon,cnusod bv fho Imboddod mnfhomnfIcnI orrors fhnf produco sIgnIfIcnnf hIgh froquoncvnoIso In fho wnvo. As shown In IIg. l4, fho hIgh froquoncv compononfs of fho rovIsoddnfn wnvo nro Iowor fhnn fho sfnndnrd wnvo bv nn ordor of mngnIfudo.IIg. l6n shows fho sfnndnrd nnd rovIsod TImoWnvo grnphs for Scroon 4 of fho TWZdIspInv. AgnIn, fhoso fwo pIofs nro quIfo sImIInr In forms of fhoIr npponrnnco, nnd soomfo bo showIng ovIdonco of somo common undorIvIng procoss. Tho dIfforoncos mnv bo duofo fho fncf fhnf fho sfnndnrd numbor sof producos moro hIgh froquoncv noIso bocnuso offho Imboddod orrors In fho numbor sof. Tho corroInfIon bofwoon fhoso fwo grnphs wns)LJXUHDfound fo bo 0.?3l, nof ns hIgh ns Scroon l, buf sfIII n sIgnIfIcnnf corroInfIon nonofhoIoss.On fho ofhor hnnd, fho rnndom dnfn sof TImoWnvo shown In IIg. l6b, shows vorv IIffIocorroInfIon wIfh oIfhor of fho grnphs In IIg. l6n. ThIs Is oxpocfod, sInco rnndom numborsofs nro bv dofInIfIon, un-corroInfod wIfh nnv ofhor numbor sof.A compIofo sof of compnrIsons IIko fhoso shown In IIgs. l5 nnd l6 woro porformod on nIIfho TImoWnvo Zoro scroon sofs (Scroons l-l0) wIfh vorv sImIInr rosuIfs. Tho corroInfIonrosuIfs for fho TWZ Scroon sof compnrIsons rnngod from n Iow of 0.?3 fo n hIgh of 0.9839wIfh nn nvorngo corroInfIon of 0.86, showIng fhnf fho sfnndnrd nnd rovIsod TImoWnvosIn fhIs scroon sof woro romnrknbIv sImIInr. ThIs wns nof fho cnso for ofhor TImoWnvosfhnf woro oxnmInod, whIch wIII bo shown Infor. In ofhor cnsos of TineWote compnrIson,fho dIfforoncos bofwoon fho sfnndnrd nnd rovIsod wnvos, npponrs fo show fhnf fhoretieeJ TineWote oxprossos n Aotel/x procoss hnvIng boffor nIIgnmonf wIfh knownhIsforIcnI procoss somofhIng ono wouId oxpocf from n moro procIso formnIIznfIonprocoss. Moro nnnIvsIs Is corfnInIv In ordor, buf fho dnfn fhus fnr sooms fo mnko fhnfcnso.)LJXUHE(2) CompnrIsons for Ofhor SIgnIfIcnnf HIsforIcnI IorIodsSovornI ofhor TImoWnvo porIods hnvIng hIsforIcnI sIgnIfIcnnco woro oxnmInod forcompnrIson, buf fho fwo roporfod horo nro fho porIods from l895-l925, nnd from l935-l955. Tho fIrsf porIod IncIudos mnjor ndvnncos In phvsIcs nnd fochnoIogv, ns woII ns nworId wnr; nnd fho socond porIod IncIudos fho dovoIopmonf nnd uso of nucIonr wonpons,ns woII ns fwo mnjor wnrs. IIg. l? Is n grnph of fho TImoWnvo compnrIson for fho l895-40l925 porIod, nnd ngnIn fhoso pIofs nro romnrknbIv sImIInr In form. SovornI sIgnIfIcnnfdnfos nro mnrkod wIfh groon nnd rod nrrows fo sIgnIfv Aotel nnd HoIi/uol phonomonn.Tho fIrsf poworod fIIghf hnppons nf KIffvhnwk on ocombor l?, l903; foIIowod bvIInsfoIn`s SpocInI Thoorv of !oInfIvIfv (ST!) on Juno 30, l905; ConornI !oInfIvIfv Inl9l5, nnd fho WorId Wnr I porIod of l9l4-l9l8. Tho ovonfs fhnf wouId bo consIdorodnovoI (mnnnod fIIghf nnd bronkfhroughs In phvsIcs) nII occur nf ovoIfv froughs orovoIfv dosconfs. Tho HnbIfunI phonomonon (wnr), on fho ofhor hnnd, npponrs fo drIvowhnf sooms fo bo n vorv novoI porIod, bnck Info hnbIf. Whon bofh novoI nnd hnbIfunIphonomonon nro occurrIng sImuIfnnoousIv, fhov bofh InfIuonco fho shnpo of fhoTImoWnvo. WWI mnv hnvo drIvon fho wnvo furfhor Info hnbIf fhnn If dId, If If woron`ffor fho sImuIfnnoous occurronco of vorv novoI phonomonn. Ior oxnmpIo, fho work on fhoConornI Thoorv of !oInfIvIfv occurs In fho mIdsf of WorId Wnr I wIfh Ifs snmo 'O!IhnbIfunI nnfuro. Tho moro novoI procoss of n sIgnIfIcnnf ndvnncomonf In scIonfIfIcknowIodgo, ncfunIIv npponrs fo suppross whnf wouId bo n mnjor nsconf Info hnbIf, nndncfunIIv drIvIng fho wnvo Info novoIfv froughs.)LJXUHofIco fhnf fho sfnndnrd TImoWnvo on fho Ioff doosn`f show fho rogrossIon Info hnbIfdurIng fho IIrsf WorId Wnr fho rovIsod TImoWnvo cIonrIv doos. ThIs Is ono cnso InwhIch fho rovIsod TImoWnvo npponrs fo provIdo n boffor doscrIpfIon of fho ovoIfvprocoss fhnn doos fho sfnndnrd TImoWnvo. Howovor, fhIs Is somofhIng fhnf shouId booxpocfod for n procoss wIfh n moro procIso nnd consIsfonf mnfhomnfIcnI modoI.41IIg. l8 shows fho l9l5 fImo porIod, for whIch fho fwo wnvos oxhIbIf n subsfnnfInIdIsngroomonf. WIfh fho oxcopfIon of n brIof fwo-monfh porIod, fho sfnndnrd TImoWnvoshows n sfondv dosconf Info ovoIfv. Tho rovIsod TImoWnvo, howovor, shows moro ofwhnf ono mIghf oxpocf for n pInnof ombroIIod In gIobnI confIIcf. AddIfIonnIIv, fho rovIsodTImoWnvo shows sovornI Insfnncos whoro fho doformInod mnrch Info hnbIf Is oIfhorsIowod or fompornrIIv rovorsod; nnd wIfh fho pubIIcnfIon of fho gonornI fhoorv In onrIvl9l6, fho IovoI of ovoIfv bocomos foo gronf for fho forcos of hnbIf, nnd fho wnvo pIungos.ThIs fIguro provIdos n good oxnmpIo of how fho sfnndnrd nnd rovIsod TImoWnvos cnnoxhIbIf bohnvIornI dIvorgonco, nnd how fhIs dIvorgonco fonds fo nffIrm fho Improvodnccurncv of fho rovIsod wnvoform. !of us now fnko n Iook nf nnofhor porIod fhnf mosf ofus nro fnmIIInr wIfh fho porIod fhnf IncIudos WorId Wnr II, nucIonr onorgvdovoIopmonf, nnd fho Koronn Wnr.)LJXUHIIguro l9 shows fho sfnndnrd nnd rovIsod TImoWnvo compnrIson grnphs for fho porIodl935-l955, nnd fhoro nro obvIous sImIInrIfIos nnd cIonr dIfforoncos bofwoon fho fwownvos. Iofh grnphs show fhnf WWII bogIns nnd onds durIng sfoop nsconfs Info hnbIf,buf fhov doscrIbo somowhnf dIvorgIng procossos, for much of fho mIddIo porIod of fhownr. Tho rovIsod TImoWnvo shows fhnf n vorv novoI procoss Is nppnronfIv nf work formuch of fho porIod of fho wnr. Tho sfnndnrd TImoWnvo doos show novoI InfIuoncos, bufIf Is noIfhor ns consIsfonf nor drnmnfIc ns for fho rovIsod TImoWnvo. Somo vorv pofonfnovoI procoss sooms fo bo occurrIng durIng much of fho wnr porIod, nnd fhnf procoss mnvbo supprossIng n mnjor nsconf Info hnbIf fhnf mIghf ofhorwIso bo hnpponIng. CouId fhIsnovoI procoss bo fho dovoIopmonf of nucIonr scIonco nnd fochnoIogv, ovonfunIIv IondIng42fo fho producfIon nnd uso of nucIonr wonpons Thnf mnv bo nn offonsIvo nofIon, buf Iof`sfnko n cIosor Iook nf If.Tho dovoIopmonf of nucIonr scIonco Is ronIIv nbouf bocomIng moro nwnro nndknowIodgonbIo of n procoss fhnf powors fho sun nnd fho sfnrs moro nwnro of jusf how nvorv poworfuI nspocf of nnfuro works. Whnf ono fhon doos wIfh such knowIodgo Is ndIfforonf procoss onfIroIv nnd InrgoIv n mnffor of conscIousnoss nnd mnfurIfv. As wocnn soo from fho rovIsod TImoWnvo grnph, fho momonf fhnf fhIs knowIodgo Is convorfodfo wonpons fochnoIogv fho nucIonr oxpIosIon nf TrInIfv SIfo In ow MoxIco fho wnvobogIns n sfoop nsconf Info hnbIf.Tho uso of fhIs nwosomo powor ngnInsf ofhor humnn boIngs In HIroshImn nnd ngnsnkIoccurs shorfIv nffor fho fosf nf TrInIfv SIfo, nnd occurs on n vorv sfoop nscondIng sIopo ofhnbIf. Iorhnps fho procoss of bocomIng moro nwnro of nnfuro, nnd oursoIvos Is vorvnovoI Indood. If Is fho sncrod knowIodgo of fho shnmnn, who rofurns from nn ImmorsIonInfo nn nspocf of nnfuro, wIfh guIdnnco or honIIng for hor or hIs poopIo. Wo soom fo hnvoIosf fho sonso of sncrod knowIodgo wIfh Ifs nccompnnvIng rosponsIbIIIfv, somowhoronIong fho wnv. Iorhnps If Is fImo fo rognIn fhnf sonso, nnd rocInIm rosponsIbIIIfv for ourknowIng.)LJXUHTho rovIsod TImoWnvo of IIg. l9 nIso shows fho porIod of fho Koronn wnr ns n vorv sfoopnsconf Info hnbIf, nIfhough somofhIng occurrIng onrIv In l952 dId momonfnrIIv rovorsofho hnbIfunI frond.43&RUUHODWLRQ'DWDDQG7LPH:DYH&RPSDULVRQVCorroInfIon nnnIvsIs wns porformod for nII fho dnfn sofs compnrod In fhIs roporf, ns woIIns fho romnInIng oIghf TWZ scroon sofs nof shown horo, nnd soIocfod fImo porIods. ThIsfvpo of nnnIvsIs nIIows us fo oxnmIno fho roInfIonshIp bofwoon dnfn sofs, nnd osfImnfofhoIr dogroo of Infordopondonco I.o. how sImIInr fhoIr InformnfIon confonf Is. ThorosuIfs of fhoso nnnIvsos nro shown grnphIcnIIv In IIg. 20, nnd fhov IncIudo fho fonTineWote scroons IncIudod wIfh fho TWZ soffwnro, nIno soIocfod hIsforIcnI wIndows,nnd fho 384 numbor dnfn sofs. In nII cnsos shown, fho rovIsod nnd rnndom dnfn sofs nroboIng corroInfod (compnrod) wIfh fho sfnndnrd dnfn sof. SInco nnv numbor sof corroInfodwIfh IfsoIf, hns n corroInfIon cooffIcIonf of ono, fho bIuo IIno nf fho fop of fho grnphroprosonfs fho sfnndnrd dnfn soIf-corroInfIon.!ocnII fhnf n corroInfIon of l sIgnIfIos numbor sofs fhnf hnvo IdonfIcnI InformnfIonconfonf, n corroInfIon of zoro sIgnIfIos no common InformnfIon confonf, nnd n corroInfIonof l monns fhnf fho numbor sofs InformnfIon confonf oxhIbIf mIrror Imngo bohnvIor wnvo ponks fo wnvo vnIIovs ofc. Tho groon IIno In fho grnph shows fho dogroo ofcorroInfIon bofwoon fho rovIsod wnvoform nnd fho sfnndnrd wnvoform, for onch of fhosopnrnfo TImoWnvos fhnf woro oxnmInod. Tho rod IIno shows fho corroInfIon IovoIbofwoon wnvos gonornfod bv fho rnndom soodod dnfn sofs, nnd fhoso gonornfod bv fhosfnndnrd dnfn sof. Tho fIrsf poInf of onch IIno, Is fho corroInfIon cooffIcIonf for onch of fho384 numbor dnfn sofs oxnmInod ronJon, retieeJ, nnd e/onJorJ dnfn sofs.)LJXUH44Tho fIrsf fonfuro fo nofIco nbouf fho retieeJ nnd e/onJorJ dnfn sof corroInfIons shown InIIg. 20, Is fho fncf fhnf fho rovIsod 384 numbor dnfn sof shows n corroInfIon wIfh fhosfnndnrd numbor sof of nbouf 60 - n compnrIson fhnf Is shown In IIg. l2. ThIs Is nsIgnIfIcnnf cross-IInkIng of InformnfIon confonf, buf somofhIng fhnf ono mIghf oxpocf fornumbor sofs wIfh n common bnso nnd vorv sImIInr dovoIopmonfnI procoduros. Tho noxffonfuro of sIgnIfIcnnco Is fho fncf fhnf fho corroInfIon bofwoon fho retieeJ nnd e/onJorJTineWotee, for nII fon TWZ scroon sofs, Is boffor fhnn ?0 nnd ns hIgh ns 98, showIngn vorv hIgh IovoI of Infordopondonco. Tho fImo porIods roprosonfod bv fhoso fonTImoWnvo scroons, rnngos from 4 vonrs fo 36,000 vonrs, whIch Is InboIod on fho grnph.Tho durnfIon of fhoso TImoWnvo porIods mnv hnvo n bonrIng on fho IovoI of corroInfIon,ns wo shnII soo In n momonf.IogInnIng wIfh fho porIod l895-l925, fho grnph shows moro scnffor In fho corroInfIonbofwoon sfnndnrd nnd rovIsod dnfn sofs, whIch rnngos from nbouf 98 down fo 8, wIfhono nnfI-corroInfIon of 95. ofIco fhnf fho corroInfIon npponrs worso for vorv shorffImo porIods, ono fo fwo monfhs or so. Ono possIbIo oxpInnnfIon Is fhnf fho vorv shorffImo porIod TImoWnvos nro gonornfod bv n vorv fow dnfn poInfs In ofhor words n Iowwnvo snmpIIng froquoncv or rnfo. A smnII, nnd undor-snmpIod Inpuf dnfn sof wouId nddn hIghor IovoI of noIso fo fho wnvo sIgnnI, nnd consoquonfIv produco fho hIghor dnfnscnffor obsorvod. Tho snmpIIng fhoorom, from InformnfIon fhoorv, sfnfos fhnf nIInsIng(noIso gonornfIon) bogIns fo occur whon fho sIgnnI snmpIIng rnfo bocomos Ioss fhnn fwIcofho hIghosf froquoncv compononf of fho snmpIod sIgnnI. ThIs Is corfnInIv somofhIng fhnfmnv bo occurrIng In fho mnfhomnfIcs of TImoWnvo gonornfIon.AddIfIonnIIv, ns monfIonod provIousIv, fhIs dIfforonco couId bo fho consoquonco of hnvIngnn Improvod modoI of fho procoss. If Is Imporfnnf fo romombor fhrough nII of fhIscompnrIson nnnIvsIs, fhnf fho sfnndnrd dnfn sof Is gonornfod bv n procoss wIfh ImboddodfInws - nof onough fo dosfrov fho InformnfIon confonf of fho wnvo sIgnnIs, buf onough focnuso somo dIsforfIon of fhnf InformnfIon confonf. ThIs corroInfIon nnnIvsIs IsInforosfIng, prImnrIIv bocnuso If Ionvos fho sfnndnrd TineWote Infncf, moro or Ioss buffho Imporfnnf poInf fo romombor Is fhnf ovon wIfh Iow corroInfIon fho retieeJ Jo/o ee/npponrs fo produco n boffor TineWote.If Is probnbIo fhnf fho vnrInfIons wo obsorvo In IIg. 20 nro fho rosuIf of Io// fhodIsforfIon of fho InformnfIon confonf of fho 384 numbor Jo/o ee/, ns n rosuIf ofmnfhomnfIcnI orrors, onJ fho Iow dnfn wnvo snmpIIng rnfo fhnf occurs for shorf durnfIonTineWotee (nn unoxnmInod buf pInusIbIo fhosIs). If Is nIso Imporfnnf fo poInf ouf horo,fhnf whon wo do soo sIgnIfIcnnf dIfforoncos In fho TImoWnvos gonornfod bv fho e/onJorJnnd retieeJ dnfn sofs, fhoso dIfforoncos hnvo rovonIod n retieeJ TImoWnvo of gronfornccurncv. Howovor, If Is Imporfnnf fhnf wo oxnmIno n sIgnIfIcnnf vnrIofv of nddIfIonnITImoWnvo porIods, fo gnfhor moro sfnfIsfIcs on fho funcfIonIng of fho rovIsod wnvo; buffho dnfn In hnnd so fnr, soom fo bo suggosfIng fhnf fho mnfhomnfIcnI formnIIznfIon of fhodnfn sof gonornfIng procoss, doos Improvo fho TineWote nccurncv.Anofhor sIgnIfIcnnf fonfuro of fho rovIsod dnfn corroInfIon pIof In IIg. 20 fhnf shouId bomonfIonod horo, Is fho fncf fhnf fho corroInfIon cooffIcIonf for fho l9l5 porIod Is nonrIv -l, sIgnIfvIng nn nnfI-corroInfIon or mIrror Imngo roInfIonshIp bofwoon fho wnvos. ThIs Is45fho TImoWnvo compnrIson fhnf Is shown If IIg. l8. If ono woro fo pInco nn ImngInnrvfwo-sIdod mIrror bofwoon fho sfnndnrd nnd rovIsod TImoWnvo grnphs, fhon fhorofIocfIon on oIfhor sIdo of fho mIrror wouId cIosoIv rosombIo fho wnvo fhnf Is on fhoofhor sIdo honco fho doscrIpfIon of nnfI-corroInfIon ns n mIrror Imngo roInfIonshIp.AIso nofIco, fhnf n groon doffod IIno mnrks fho nvorngo of nII fho sfnndnrd/rovIsod wnvocorroInfIons nf nbouf ?0.Tho rod IIno of IIg. 20 shows fho corroInfIon of fho rnndom numbor gonornfod wnvos,wIfh fho sfnndnrd dnfn sof. Iv dofInIfIon, fho rnndom dnfn sofs shouId show IIffIo or nocorroInfIon wIfh oIfhor fho sfnndnrd or rovIsod dnfn sofs, nor wIfh nnv ofhor rnndomnumbor sof. In sovornI cnsos In IIg. 20, fhIs furns ouf fo bo fruo, buf fhoro nro nIsosovornI cnsos In whIch fho rnndom sof corroInfIon Is nof nonr zoro, ns ono wouId oxpocf.In gonornI, fho rod IIno pIof of IIg. 20 shows n much Iowor IovoI of corroInfIon wIfh fhoe/onJorJ numbor sof fhnn doos fho retieeJ sof ns oxpocfod. Inch dnfn poInf on fho rodIIno, howovor, Is ncfunIIv nn nvorngo of oIfhor fwo, or sovon rnndom numbor sofcorroInfIons. In ofhor words, oIfhor fwo or sovon rnndom numbor corroInfIons woronvorngod fo produco onch poInf on fho rod IIno grnph. If furns ouf fhnf mosf of fhosIxfoon corroInfIon poInfs producod bv nvorngIng onIv fwo rnndom sofs, hnvo much moroscnffor fhnn do fho four poInfs producod bv nvorngIng sovon rnndom sof corroInfIons.Tho 384 numbor ronJon Jo/o ee/, nnd fho porIods l895-l925, l905, nnd l9l5, woro nIIproducod bv nvorngIng sovon rnndom sof corroInfIons. Tho vIoIof doffod IIno runnIngfhrough fho rnndom numbor sof corroInfIons, Is fho nvorngo corroInfIon IovoI for nII fhornndom sofs shown, nnd If shows n vorv Iow nvorngo corroInfIon of nbouf 5.If Is nIso possIbIo fhnf fho snmo procoss proposod for producIng fho Inrgor corroInfIonscnffor of fho rovIsod dnfn sof, couId bo nf work for fho rnndom dnfn sofs I.o. shorfdurnfIon fImo porIods wIfh Iow snmpIIng froquoncIos, couId bo cnusIng dnfn scnffor duofo noIso. If n smnII numbor of fho 384 Jo/o file poInfs nro usod fo gonornfo n e/or/ perioJTineWote, fhon fhoro Is n much hIghor probnbIIIfv of corroInfIon bofwoon fho rnndomsofs nnd fho TImoWnvo numbor sofs. WIfhouf furfhor InvosfIgnfIon, howovor, fhIs Is nspocuInfIvo, If pInusIbIo fhosIs.Tho grnphs of IIg. 20 do show fhnf fho e/onJorJ nnd retieeJ dnfn sofs nnd fhoIrdorIvnfIvo TineWotee nro romnrknbIv woII corroInfod. In fho rogIons whoro fhocorroInfIon wonkons, or bronks down onfIroIv, fho rovIsod TineWote npponrs fo show novoIfv procoss fhnf Is In cIosor ngroomonf wIfh known hIsforIcnI procoss. In nddIfIon,fho pIofs In IIg. 20 mnv bo rovonIIng n procoss whorobv shorf porIod TineWotee producosnmpIIng noIso fhnf wonkons fho corroInfIon. ThIs dnfn supporfs fho vIow, fhnf fhoInformnfIon confonf of fho e/onJorJ TineWote Is somowhnf dIsforfod, buf nof dosfrovod;nnd suggosfs fhnf fho retieeJ TineWote nnd Ifs pieceuiee lineor func/ion Is nbIo focorrocf fhIs dIsforfIon, nnd provIdos nn Improvod oxprossIon of fho ovoIfv procoss.&RQFOXGLQJ5HPDUNVTho dovoIopmonf of fho 384 numbor Jo/o ee/ from fho sof of Iire/ OrJer of Difference(IO) Infogors hns boon oxprossod ns n procoss fhnf Is pieceuiee lineor In nnfuro. ThIsprocoss InvoIvos fho combInnfIon nnd oxpnnsIon of sfrnIghf-IIno sogmonfs, whIch cnn bo46oxprossod mnfhomnfIcnIIv ns n pieceuiee lineor func/ion. Tho e/onJorJ Jetelopnen/ hnsboon doscrIbod bv McKonnn nnd Movor In fho TineWote Zero documonfnfIon nnd Inofhor roporfs. Iuf fhIs procoss IncIudos n procodurnI sfop cnIIod fho hnIf fwIsf, fhnf Isnof consIsfonf wIfh fho sfrucfuro of pIocowIso IInonr mnfhomnfIcs; nnd consoquonfIvproducos n dIsforfIon of fho IO InformnfIon confonf. WnfkIns oInbornfod on fhIs Insomo dofnII, In hIs woII-documonfod oxposo on fho nnfuro of fho /olf /uie/, In whIch hodoscrIbod fho dIsforfIons nnd InconsIsfoncIos InvoIvod. Ho fhon concIudod fhnf fhIsdIsforfIon wouId rondor fho TineWote monnIngIoss, ns n ronIIsfIc grnphIcnI dopIcfIon offho Aotel/x procoss ns hnd boon doscrIbod bv McKonnn. I mnInfnIn fhnf fhIs concIusIonwns promnfuro, nnd nppnronfIv Incorrocf.Tho retieeJ Jetelopnen/ of fho 384 numbor Jo/o ee/ IncIudos fho uso of mnfhomnfIcs fhnfcorrocfIv oxprossos fho pieceuiee lineor dovoIopmonf procoss, nnd fhoroforo producos nnundIsforfod oxpnnsIon of fho IO numbor sof. Tho TineWote fhnf rosuIfs from fhIsoxpnnsIon procoss, Is fhon nn nccurnfo rofIocfIon of fho IO numbor sof, provIdod fho sofcnn bo doscrIbod or modoIod bv n pIocowIso IInonr funcfIon. Tho pieceuiee lineor func/iondoscrIbod horo, mnv onIv bo nn npproxImnfIon fo somo moro conplex func/ion fhnf hnsvof fo bo found. In fncf, I wouId nrguo fhnf fhIs Is quIfo IIkoIv for n phonomonon orprocoss of fhIs nnfuro, whIch furfhor sfudv mnv shod somo IIghf on. If wo nssumo fhnffho retieeJ TineWote Is n ronsonnbIv nccurnfo rofIocfIon of fho InformnfIon confonf offho IO numbor sof, fhon fho e/onJorJ TineWote shouId hnvo n dogroo of nccurncvproporfIonnI fo Ifs dogroo of corroInfIon wIfh fho retieeJ TineWote. As wo hnvo soonfhus fnr, fhoso fwo TineWotee show nn oteroge correlo/ion of nbouf ?0, so fhnf fhoe/onJorJ uote hns nn nvorngo nccurncv of nbouf ?0 whon compnrod wIfh fho retieeJuote. Howovor, wo hnvo nIso soon fhIs corroInfIon ns hIgh ns 98, or ns Iow ns 6, wIfhono cnso of n mIrror Imngo or nnfI-corroInfIon of 0.94.ThIs work hns sorvod fo cInrIfv nnd formnIIzo fho procoss bv whIch fho 384 numborTImoWnvo Jo/o ee/ Is gonornfod. ThIs hns boon dono bv showIng fhnf fho procoss IsdoscrIbnbIo wIfhIn fho frnmowork of pIocowIso IInonr mnfhomnfIcs In gonornI, nnd vocformnfhomnfIcs In pnrfIcuInr. Inch sfop hns boon doIInonfod nnd formnIIzodmnfhomnfIcnIIv, fo gIvo fho procoss cInrIfv nnd confInuIfv. Tho formnIIzod nnd rovIsoddnfn sof sorvos ns fho foundnfIon of fho TineWote gonornfod bv fho TineWote Zerosoffwnro, whIch Is vIowod ns n grnphIcnI dopIcfIon of n procoss doscrIbod bv fho obb nndfIow of n phonomonon cnIIod Aotel/x. Aotel/x Is fhoughf fo bo fho bnsIs for fho cronfIonnnd consorvnfIon of hIghor ordorod sfnfos of compIox form In nnfuro nnd fho unIvorso.Tho rosuIfs roporfod horo mnko no fInnI cInIms ns fo fho vnIIdIfv of fho TineWote ns If Isoxprossod bv Aotel/x T/eorx, nor doos If cInIm fhnf fho curronf TineWote Is fho bosfdoscrIpfIon of fhIs Aotel/x procoss. If doos show fhnf fho propor mnfhomnfIcnI fronfmonfof fho IO numbor sof, producos n TineWote fhnf npponrs fo bo moro consIsfonf wIfhknown hIsforIcnI procoss. ThIs consIsfoncv Is gonornI, howovor, nnd moro work noods fobo dono fo oxnmIno fho spocIfIc rofIocfIons or projocfIons fhnf fho TImoWnvo mnv borovonIIng. If Aotel/x T/eorx Is n vnIId hvpofhosIs, rofIocfIng n ronI phonomonon Innnfuro, fhon ono wouId oxpocf fhnf If Is vorIfInbIo In spocIfIc wnvs.If hns nIso soomod npproprInfo fo oxnmIno somo of fho sfops In fhIs wnvo dovoIopmonfprocoss In forms of fhoIr corrospondonco wIfh oIomonfs of phIIosophv nnd scIonco. Tho47fIow of YIn nnd Ynng onorgv rofIocfod In fho oxprossIon of fho forwnrd nnd rovorso bI-dIrocfIonnI wnvos, for oxnmpIo, fInds phIIosophIcnI corrospondonco In n nnfurnI cvcIo ofIIfo-donfh-robIrfh, or In fho procoss of fho shnmnnIc journov ImmorsIon, ongngomonf,nnd rofurn. Corrospondonco cnn nIso bo found In scIonco, In fho fIoIds of cosmoIogv,nsfronomv, nsfrophvsIcs, nnd qunnfum phvsIcs fho IIfo cvcIos nnd mofIon of honvonIvbodIos, qunrks, nnd unIvorsos; fho hnrmonIc nnd hoIogrnphIc nnfuro of IIghf nnd wnvomochnnIcs; nnd fho cvcIIc frnnsformnfIon of mnffor fo onorgv, nnd onorgv fo mnffor. ThorofIocfIon of nII nnfurnI phonomonn nnd procossos ovor fho confInuum of oxIsfonco, fromfho smnIIosf scnIos up fo fho Inrgosf scnIos, musf suroIv IncIudo whnfovor procoss IsoccurrIng In fho I-ChIng ns woII. Tho quosfIon Is, nro wo nro cIovor nnd conscIous onoughfo docIphor nnd oxpross If corrocfIv nnd npproprInfoIv$FNQRZOHGJHPHQWVI wouId IIko fo fhnnk Terence McKenna, for brIngIng fhIs InfrIguIng nnd provocnfIvo nofIonInfo fho coIIocfIvo, nnd for fho courngo nnd forosIghf shown, bv hIs wIIIIngnoss fo oponhImsoIf nnd hIs Idons fo scrufInv nnd boundnrv dIssoIufIon. If fhoro Is nnv roIovnnco ormonnIng fo bo found In fho TineWote or Aotel/x T/eorx, fhon If Is suroIv somofhIng fhnfIs Inrgor fhnn ho, or nnv of us; nnd If Is nIso somofhIng fhnf Is proporIv In fho domnIn ofnII humnn oxporIonco, wIfh onch of us n wIfnoss, pnrfIcIpnnf, nnd confrIbufor.I wouId nIso IIko fo oxpross mv fhnnks nnd npprocInfIon fo Mathew Watkins for hIs work InoxposIng fho mnfhomnfIcnI InconsIsfoncIos, vngnrIos, nnd procodurnI orrors of fhosfnndnrd TineWote Jo/o ee/ dovoIopmonf, nnd chnIIongIng n fhoorv fhnf mnv hnvobocomo fnr foo sodonfnrv nnd Inbrod for Ifs own good. Whnfovor fho fInnI oufcomo of fhIsondonvor of Aotel/x T/eorx, ho hns sof fho onforprIso on Ifs propor courso of opon nndcrIfIcnI InquIrv.I nm nIso gronfIv Indobfod fo Peter Meyer for hIs skIII nnd forosIghf In cronfIng n TWZsoffwnro pnckngo fhnf Is fIoxIbIo, nccossIbIo, nnd frIondIv fo fho sorIous InvosfIgnfor.WIfhouf hIs OS vorsIon of TImoWnvo Zoro soffwnro, fhIs work wouId hnvo boon muchmoro dIffIcuIf If nof ImpossIbIo. Ho hns cronfod n soffwnro pnckngo fhnf mnkos fhosonofIons ronIIsfIcnIIv fosfnbIo, In n roInfIvoIv sfrnIghfforwnrd mnnnor. ThIs mndo IfpossIbIo for mo fo oxnmIno fho offocfs of fho rovIsod dnfn sof on fho TImoWnvo IfsoIf, nswoII ns fncIIIfnfIng fho oxnmInnfIon of fho dofnIIod sfrucfuro of fho wnvo In work fofoIIow.Mv fhnnks nIso fo Dan Levy for hIs offor fo pubIIsh fhIs work on hIs !ovIfv sIfo, ns woII nshosfIng nn upcomIng TineWote mnfhomnfIcnI nnnox fo Aotel/x T/eorx. I wnnf nIso foncknowIodgo Brian Crissey nf IIuo Wnfor IubIIshIng for hIs hoIp In InfogrnfIng fho nowprocoss Info fho TImoWnvo Zoro soffwnro pnckngos nnd documonfnfIon. 1 Computer Software program written by Meyer and others, based on a mathematical relationship exhibited by the I-Ching, formulated and reported by T. McKenna and D. McKenna, the Invisible Landscape, Harper San Francisco, 1993,p. 1212 T. McKenna, the Invisible Landscape, p. 1403 M. Watkins, Autopsy for a Mathematical Hallucination, Terence McKennas Hyperborea at www.levity.com48 4 T. McKenna, Time Explorer Manual, p60, the Invisible Landscape, pp. 140-1425 P. Meyer, http://www.magnet.ch/serendipity/twz/kws.html6 DeltaPoint, Inc., 22 Lower Ragsdale Dr., Monterey, CA 93940, (408) 648-40007 Microsoft Corp., One Microsoft Way, Redmond, WA 980528 McKenna, TimeExplorer Manual, PP. 60-63, http://www.levity.com/eschaton/waveexplain.html9 H.B. Anderson, Analytic Geometry with Vectors, p71, McCutchan Publishing Corp., Berkeley, Ca. 196610 T. McKenna, TimeExplorer software manual, pp. 62-6311 P. Meyer, TimeExplorer software manual, pp. 85-9112 M. Kaku, What Happened BEFORE the Big Bang?, Astronomy, May 1996, pp. 34-41[John Sheliak] sheliak@dsrt.com[Terence McKenna] syzygy@ultraconnect.com[return to Levity] http://www.levity.com/eschaton/Filename: MathWave PaperIIDirectory: D:\DG4\TWZ FilesTemplate: C:\Program Files\MicrosoftOffice\Templates\NORMAL.DOTTitle: Delineation, Specification, and Formalization of the TWZData Set Generation Process - Philosophical, Procedural, and MathematicalSubject:Author: John SheliakKeywords:Comments:Creation Date: 11/11/97 9:50 PMChange Number: 2Last Saved On: 11/11/97 9:50 PMLast Saved By: John SheliakTotal Editing Time: 1 MinuteLast Printed On: 11/11/97 9:51 PMAs of Last Complete PrintingNumber of Pages: 48Number of Words: 13,802 (approx.)Number of Characters: 78,672 (approx.)

McKenna's TimewaveConventional King Wen Tabulation000 110 101 011 111 001 010 100000 1 34 5 26 11 9 14 43110 25 51 3 27 24 42 21 17101 6 40 29 4 7 59 64 47011 33 62 39 52 15 53 56 31111 12 16 8 23 2 20 35 45001 44 32 48 18 46 57 50 28010 13 55 63 22 36 37 30 49100 10 54 60 41 19 61 38 58The I Ching is an ancient chinese oracular system whereinsix coins (or similar) ar consulted to obtain an allegedlymystically-relevant maybe-not-random number in the range0 to 63 inclusive, known as a hexagram.The (binary) bits of this number (or hexagram) areconventionally represented as either broken or unbrokenhoriontal lines stacked vertically. Hexagrams are oftenconsidered as the combination of two three-bit trigrams.The traditional ordering of the sixty four "hexagrams" isusually attributed to King Wen circa 1150 BC.This ordering, essentially one of 64! > 1089 permutations ofthe set Z64 = {0,1,2,....,63} is the numerical starting point ofTerrance McKenna's TimeWave theory. I will write W(i) forthe i'th element of the cyclic King Wen Ordering, startingwith i=0 and with the understanding that W(i) = W(i Mod64) for i > 63 and for i