- Introduction
- Linear resonances: yao and trigrammatic
- Constructing a set of twelve trigrammatic resonances
- Searching for trigrammatic resonances
- Listing resonance points
A study of the timewave by means of this software will reveal that there are parts of the timewave which have a similar shape, that is, the wave pattern looks the same, even though the values on the horizontal and vertical axes are quite different. For example, the first graph below shows a 40-year period of the wave and the second graph shows a 2560-year period, but clearly the two graphs are identical in shape:
A study of periods in resonance with each other reveals that often there are mathematically definable relations between them. A number of different mathematical relationships have been identified, and various kinds of resonance points may thus be defined precisely.
At present it seems there are basically two kinds of resonance points, geometric and linear. The geometric resonance points are more usually termed major resonance points (explained in the next section). There are two kinds of linear resonance points, namely, yao and trigrammatic resonance points (explained in Section 3 below).
The major resonance points of a given point in time form a doubly infinite geometric series extending toward and away from the zero point.
The yao and trigrammatic resonance points of a given point in time fall into an infinite number of levels, and within each level there is a linear sequence of resonance points which is infinite only in the direction of the past.
Formal definitions of the varieties of resonance points will now be given, then an explanation of how to graph the resonances using the software, followed by some remarks on the interpretation of resonance points.
Suppose the zero point has been assigned a particular time and date (e.g. 6 a.m. on 2012-12-21). Let d be a number of days (possibly non-integral, e.g. 1792.123), then d specifies a point A on the wave which is d days prior to the zero point. The "first higher major resonance" A1 of A is the point which is d*64 days prior to the zero point. Generally, the nth higher major resonance An of A is the point d*64^n days prior to the zero point, and the nth lower major resonance Bn of A is the point d/64^n days prior to the zero point. Clearly the nth higher major resonance of A is the (n+m)th higher major resonance of the mth lower major resonance of A.
It turns out that the shape of the wave around each of the higher and lower resonances of a point is the same as the shape of the wave around that point, provided the timespan is multiplied by 64 for each higher level of resonance or divided by 64 for each lower level. This can be seen by doing the following:
(i) Graph any region of the wave.
(ii) Copy the graph to another screen.
(iii) Select I ("Resonances").
(iv) Answer N to the question about trigrammatic resonances.
(v) Select either H ("Higher") or L ("Lower").
(vi) Select M ("Major resonance").
(vii) Enter a number (1 = 1st major resonance, etc.).
(viii) Compare the resulting graph with the graph on the former screen.
The shape of the wave is exactly the same on both screens, only the values on the vertical and horizontal axes change (the timespan is multiplied by 64^n for the nth higher and is divided by 64^n for the nth lower major resonance).
This phenomenon has a clear mathematical basis. Consider any date prior to the zero point, and let the value of the wave at that point be v and let the number of days to the zero date be d. It can be shown mathematically that the value of the wave at the point 64*d days prior to the zero point is equal to 64*v. It can also be shown that the value at the point d/64 days prior to the zero date is v/64.
Although the mathematical basis of resonance is well understood the question remains as to how it is to be interpreted. The currently accepted view is that in a sense history repeats itself in the lower resonances of any given part of the wave. This applies both to major resonances and to the trigrammatic resonances.
For example, consider the European Dark Ages, which are generally considered to extend from the fall of the Roman Empire in the fifth century to the beginning of the Middle Ages in the tenth century. You can see this period of the wave by selecting a target date of 725-01-01 (Julian or Gregorian Calendar) and a timespan of 520 years. If, after graphing the wave, you select option I and graph the first lower major resonance, you will see that this resonance of the Dark Ages is approximately the period October 1988 through November 1996. Novelty Theory asserts that these eight years (coinciding with the Bush presidency and the first term of the Clinton presidency) are, in a sense, the Dark Ages once again, suitably modified in accordance with the state of modern society.
Assuming the standard zero date, the resonance in our time of the European Middle Ages is approximately 1997-2004, and the resonance of the modern age (from the Renaissance to the present) is approximately 2005-2012.
As above let d be a number of days (possibly non-integral) then d specifies a point A on the wave which is d days prior to the zero point. For any natural numbers n and m, the point d ± m*3*64^n is the mth trigrammatic resonance point at the nth level. Further, for any positive integers n and m, the point d ± m*64^n is the mth yao resonance point at the nth level. Clearly every trigrammatic resonance point is a yao resonance point, but not vice-versa. In fact the kth trigrammatic resonance point at the nth level is the 3*kth yao resonance point at that level.
As with major resonances, the trigrammatic and yao resonance points closer to the zero point (corresponding to -m*3*64^n or -m*64*n) are said to be lower resonance points, and those further from the zero point are said to be higher resonance points.
The shape of the wave around the higher and lower trigrammatic resonances of a point is often, but not always, either the same as, or similar to, the shape of the wave around that point for the same timespan. This can be seen by doing the following:
(i) Graph any region of the wave.
(ii) Copy that graph to another screen.
(iii) Select I ("Resonance").
(iv) Answer N to the question about trigrammatic resonances.
(v) Select either H ("Higher") or L ("Lower").
(vi) Select T ("Trigrammatic resonance").
(vii) Enter a number in reply to Which cycle?
(viii) Enter a number in reply to Which point?
(ix) Compare the resulting graph with the graph on the former screen.
Sometimes the two graphs will be exactly the same, sometimes only similar. (To find exact, or true, resonances using the Fractal Time software see Searching for trigrammatic resonances below.)
The software permits exploration only of trigrammatic resonances for levels 0, 1, 2 and 3. These correspond respectively to cycles of 6*64 days (384 days), 6*64^2 days (24,576 days = 67.29 years), 6*64^3 days (1,572,864 days = 4306.36 years) and 6*64^4 days (100,663,296 days = 275,606.74 years). (In accord with the Gregorian Calendar the average length of a year is taken to be 365.2425 days.)
As with the geometric resonances historical parallels should be sought among the linear resonances, especially the trigrammatic ones. The following two screens provide a good example (except that the timewave is the one based on the Kelley 384 numbers, which in orthodox Novelty Theory are now considered erroneous). The first screen covers the years in which men were first launched into space, beginning on 1961-04-12 with the Soviet cosmonaut Yuri Gagarin. 1969-07-16 was the date of launch of the Apollo 11 flight, allegedly carrying the first men to land on the Moon (Neil Armstrong and Buzz Aldrin). In 1973 the three American Skylab missions were launched.
The second screen (below) represents a time when the first sea explorers were venturing into unknown realms. Columbus crossed the Atlantic in 1492 and discovered the Bahamas and Cuba. Labrador was explored by John Cabot in 1498 and by Corte-Real in 1500. Vasco da Gama was exploring India around 1498, and Ojeda, Pinzon and Cabral explored Brazil and Venezuela in 1499-1500. The target dates of these two screens, namely, 1969-07-16 and 1498-07-13, are the 14th trigrammatic resonances of each other at the 67-year cycle level.
The following is the 10th higher trigrammatic (67.29-year) resonance of the timewave segment above:
Superimposition of this with the graph for 1997-12-28 gives:
Close, but not exact. To find an exact resonance we have to go back to 1526 and the 14th higher resonance:
Novelty Theory equates a day with a line in a hexagram of the I Ching, and asserts that there are cycles of 6 days (since there are six lines in a hexagram) and 384 days (6x64, the number of lines in all hexagrams), and posits larger cycles whose length in days is 6 times a power of 64. Thus there is a series of 384-day cycles extending sequentially backwards from the zero point, a series of 67.29-year cycles (67.29 years = 384*64 days), a series of 4306.36-year cycles (= 384*64*64 days), and so on.
Consider a particular target date. It will fall into a particular 384-day cycle, a particular 67.29-year cycle, a particular 4306.27-year cycle, and so on. Just as a hexagram can be divided into two trigrams and also into six individual lines (called yao in Chinese), so can a cycle be divided into two and into six equal parts. Consider then the particular 384-day cycle that the particular target date falls into. It will occur either in the first part or in the second part of the cycle, and in one of the six parts of the cycle. Whether it occurs in the first half of the cycle or the second half there will be a point in the other half of the cycle which occupies the same relative position. This is said to be the trigrammatic resonance point of that target date. More exactly, it is the trigrammatic resonance point in the 384-day cycle. For each cycle of larger duration there is a trigrammatic resonance point within that cycle.
The trigrammatic resonance point of a date within the 384-day cycle always occurs exactly 192 days from that date. There is thus an an extended sense of the term trigrammatic resonance point according to which every point which is a multiple of 192 days from a particular date is a trigrammatic resonance point of that date. Similarly the trigrammatic resonance point of a date within the 67.29-year cycle always occurs exactly 192*64 days from that date, and so in the extended sense of the term every date which is 12,288 days from that date is also a trigrammatic resonance point. Similarly for the cycles of larger duration.
The notion of a yao resonance point can be explained in the same way. Whichever sixth-part of a 384-day cycle a particular date falls in, there will be points in the other five parts of the cycle which occupy the same relative position in those parts, and these are the yao resonance points. There are yao resonance points at each of the 384-day, 67.29-year and 4306.36-year cycles (and also for cycles of larger duration).
As with the case of the idea of a trigrammatic resonance point, there is an extended sense of the idea of a yao resonance point according to which every date which is 64 days, 64^2 days, 64^3 days, etc., from a given date is a yao resonance point of that date on some level.
Yao resonance points seem to be of less interest than trigrammatic resonance points.
Not all pairs of segments of the timewave which have the same shape stand in the relationship of geometric resonance or linear resonance. For example, the following 3-month segment of the timewave centered on 1947-02-02 has exactly the same shape as the 16-year segment (see above) centered on 1968-02-09, yet it is obviously not a geometric resonance, and since the mid-points of the segments are separated by 7677 days (which is not divisible by 6 or 64) these two segments are also not linear resonances.
The Fractal Time software allows construction of twelve trigrammatic resonances in one operation. Upon selection of option I, Resonances, the question appears:
If you wish to graph a major resonance or a single trigrammatic resonance then answer N. Answering Y leads to the question:
These cycles were explained above in Section 3. After selecting a cycle the question appears:
For now answer N. (Answering Y leads to a resonance search, which is explained in the next section.)
When a cycle is selected the dates on the other eleven screens are (or may be) modified so that the previous screen (e.g. Screen 7 if the current screen is Screen 8) contains as the target date the first higher trigrammatic resonance (in the selected cycle) of the target date of the current screen. The screen that is two screens previous to the current screen contains the second higher trigrammatic resonance, and so on, to Screen 1. The relative position of the target date in the derivative screens is the same as in the current screen.
Similarly the next screen (e.g. Screen 9 if the current screen is Screen 8) contains as the target date the first lower trigrammatic resonance (in the selected cycle) of the target date of the current screen. The screen that is two screens after the current screen contains the second lower trigrammatic resonance, and so on, to Screen 12.
Screens are modified only if the new target dates (the higher and lower trigrammatic resonances to the target date of the current screen) would be earlier than the zero date and later than the earliest permissible date (about 7,000,000,000 B.C.).
After the construction of the eleven trigrammatic resonances is performed the current screen (which is the 12th trigrammatic resonance in the set of 12) remains unchanged. By using the function keys or the PgUp and PgDn keys you may, as usual, change to the other screens, where the dates for the trigrammatic resonances will be seen.
For example, if you are viewing Screen 8 with a target date of 1996-03-15 then constructing the set of 12 trigrammatic resonances in the 67-year cycle will produce the following target dates on the other screens:
| Screen | Target date |
| 1 | 1760-09-12 |
| 2 | 1794-05-05 |
| 3 | 1827-12-27 |
| 4 | 1861-08-18 |
| 5 | 1895-04-10 |
| 6 | 1928-12-01 |
| 7 | 1962-07-24 |
(Screens 9, 10 and 11 are not changed, since there is no lower trigrammatic resonance in the 67-year cycle after 1996-03-15.)
In this example, graphical displays for trigrammatic resonances prior to 1760-12-09 can be obtained by copying Screen 1 to Screen 12 and then constructing a new set of 12 trigrammatic resonances from Screen 12, which will produce in Screens 1 to 11 the eleven trigrammatic resonances in the 67-year cycle immediately prior to 1760-12-09.
Note that constructing a set of trigrammatic resonances will modify the target dates on other screens, so be sure that you don't wish to retain data in the other screens. The set of screens can be saved by selecting the L option.
Those who would attribute predictive powers to the Novelty Theory must proceed from an examination of resonances. For example, consider the two-month drop in the wave which begins May 7th 1993 and ends July 10th. Novelty Theory says that time periods in resonance resemble each other (i.e. the same kinds of things occur in them), so if you want to see what might happen in time period T you have to look at the various past (i.e. higher) resonances of T, check what, if anything, of significance happened at those past times, and project that to what might happen in T.
For the period 1993-05-07 through 1993-07-10 there are the following higher resonances:
1st major resonance: years 756-768 (According to the principal school of Timewave theorists the first higher major resonance is the most significant resonance when looking for influences.)
Trigrammatic resonances in 67-year cycle (only the ones, up to the 10th, where the wave is seen to have the same shape as the 1993 period):
2nd: January1926 - March 1926
4th: October 1858 - December 1858
6th: June 1791 - August 1791
8th: March 1724 - May 1724
10th: November 1656 - January 1657
Trigrammatic resonances in 4306-year cycle:
1st: March 161 BC - May 161 BC
2nd: December 2315 BC - February 2314 BC
So now you have to pull out the history books to look at what of significance was going on, if anything, in any of these periods. If you find something significant, e.g. that an Islamic army overran a major garrison of the Byzantine Empire in Syria, then you can look for what happened in May - July of 1993 which would be analogous to that.
With this software it is possible to search for "true" trigrammatic resonances, i.e. resonances which not only satisfy the mathematical requirements for trigrammatic resonances (in the extended sense given in Section 3 above) but also which are graphically similar (i.e., look exactly the same, or at least similar).
Suppose we wish to find all true 67-year trigrammatic resonances (within, say, -2000 to 2012) to the 7-year period centered on 1527-01-01 G (using the Kelley set and 2012-12-21 as the zero date). We set up the graph for this period on Screen 6, then select I for Resonances. We answer the questions as follows:
Construct set of 12 trigrammatic resonances? Y
Which cycle? (1=384-day, 2=67.29-year, 3=4306.36-year, 4=275,607-year) 2
Search for similar trigrammatic resonances? Y
Now we are asked:
If we answer '0' it means that we want to find trigrammatic resonances whose graphs are exactly the same as the current graph. '9' finds resonances which perhaps have significant divergence from the current graph. '5' finds resonances which don't diverge as much but may not be exact.
During the next minute or so the software will test the first 999 higher and the first 999 lower trigrammatic resonances other than those that would be after the zero date and those far enough from the current date not to be found before all screens have been allocated. In this example the first higher resonance found by the software is placed in Screen 5, the second in Screen 4, and so on; the first lower resonance found is placed in Screen 7, and so on.
The result in this case is given completely in the following table (all exact trigrammatic resonances with the graph in Screen 6) and is shown partially in the three graphs below:
| Screen | Resonance | Target Date |
|---|---|---|
| 7 | 14th lower | 1998-01-03 G |
| 6 | Current graph | 1527-01-01 G |
| 5 | 18th higher | 921-06-02 G |
| 4 | 44th higher | 46-09-09 G |
| 3 | 66th higher | -694-07-15 G |
| 2 | 98th higher | -1771-12-12 G |
| 1 | 124th higher | -2645-03-21 G |
It is possible to obtain a printed listing of the resonance points for a given target date (the target date shown on-screen). This is done by means of the J, Print, option. When asked whether you wish to print values, resonance points or screens, press R. You are then asked whether you wish to include the yao resonance points as well as the trigrammatic resonance points (better not to). All of the higher and lower resonances to the target date (and time), including geometric, trigrammatic and (optionally) yao resonances, from 7,000,000,000 years ago to within a few hours of the zero point are listed.
If, having specified a target date, you list the resonance points you will obtain a listing of the higher and lower major resonance points and the closest yao and trigrammatic resonance points for that date in the four cycles of length 384 days, 67.29 years, 4306.27 years and 275,607 years. The zero point (6 a.m. on the zero date) has yao and trigrammatic resonance points, but no higher or lower major resonance points.
There are yao and trigrammatic resonance points for any time on any date (before the zero point). The time of day for the yao and trigrammatic resonance points is always the same as the time of day of the target date, since there is always an integral number of days difference between a date and its yao and trigrammatic resonance points. If you list the resonance points for a target date with a time other than 6 a.m. then the time will be given for the yao and trigrammatic resonance points; otherwise the time will be 6 a.m. and this is not printed in the listing.
It may happen that you wish to see the resonance points for a date specified in the Julian Calendar, for example, the date of the assassination of Julius Caesar, March 15th, 44 B.C. (-43-03-15 according to the astronomical system for numbering years). If the calendrical system is set to the Julian Calendar when you list the resonance points for this date then all dates printed will be Julian dates. To list the dates in the Gregorian Calendar simply change the calendar from Julian to Gregorian after having entered the target date of -43-03-15 with the Julian Calendar selected.
In this particular case there is an interesting connection between the target date and the date of the first lower major resonance. The first lower major resonance of the date of the assassination of Julius Caesar is 1980-11-08 (Gregorian). Interestingly enough this is three days prior to the U.S. presidential election of 1980, in which Jimmy Carter was defeated by Ronald Reagan. Although Jimmy Carter was not assassinated, he was in a sense done in by the "October Surprise" plot widely believed to have been hatched between Reagan, George Bush and CIA Director William Casey, on the one hand, and representatives of the late Ayatollah Khomeini on the other, whereby in return for weapons from the Reagan administration (needed in Iran's war with Iraq) Iran agreed not to release the U.S. hostages in Tehran prior to the election. (The hostages boarded the plane to return to the U.S. ten minutes after Reagan was sworn in as President, presumably as a message from the Ayatollah to those who could understand.)
Finally, if you have done a search for trigrammatic resonances, and wish to print the results, you should select the J, Print, option and when asked whether you wish to print values, resonance points or screens, press S for Screens. This will print out the data for all twelve screens, including the screens containing the trigrammatic resonances which were found in the resonance search.