New Civilization News: Some Intriguing Mathematical Properties of the Mayan Calendar
 Some Intriguing Mathematical Properties of the Mayan Calendar
4 Aug 2007 @ 18:21, by John Ringland

### Some Intriguing Mathematical Properties of the Mayan Calendar

This is a brief mathematical analysis of the cycles of the "Tun" or the transcendent Mayan 'calendar'. The analysis reveals some very interesting numerical properties, which show that it is certainly not a random concoction but in fact describes a complex and finely tuned process.

The general process relies on a system of cycles where each cycle is 20 times shorter than the previous cycle. Hence it tends asymptotically toward some point in time (year 2012). The cycle periods become shorter and shorter so that as the cycle number tends to infinity the cycle period tends to zero, i.e. the cycles become infinitely fast.

The so called 'calendar' is not a description of linear time like contemporary calendars, it is a model of cycles of creative activity. Hence it describes an evolutionary model where each creative cycle unfolds and produces the basis for the next cycle of creation. In such a process each cycle becomes faster than the previous one, as is seen throughout biological and human history. Initially there were long stretches of time between innovations but as the reservoir of innovations builds up the process of innovation accelerates. This process has been accelerating very noticeably especially in the last few decades.

This article is a purely mathematical analysis of the structure of the cyclic process and it is not synchronised with conventional calendars as you can see below, the year count begins at year zero. Hence this model makes no attempt to predict at what particular date the Mayans propose that the process will reach its asymptote, however according to other predictions it will happen some time in 2012. The purpose of this analysis is to explore the mathematical structure of the cyclic process and it has some very interesting properties.

The basic model was derived from data found at: http://www.mayanmajix.com/David_Icke_newsletter.html However due to the cyclic nature of the process only a small portion of that data was required to construct this model. Whilst the data for the current cycle (the 8th cycle) is seemingly more exact, i.e. from January 5 1999 to February 10 2011, there are complications due to the arbitrary nature of our current calendar system and the fundamental differences between the two calendar systems. For example, our year zero is centred on estimates of the birth of Christ and we also use the Roman 12 moon cycle that requires leap years and other arbitrary corrections whereas the Mayan's used the more accurate 13 moon cycle. Also, the exact times on those days in 1999 and 2011 are not known, hence I used the longest period data to reduce the impact of these differences and uncertainties.

As you can see in the data, the process begins with an initial cycle with a period of exactly 15.580 billion years. The next four cycles are also exact interger numbers of years, where each is 20 times shorter than the previous, hence the first five cycles are multiples of 20. Another interesting property is that for both the periods and the years the decimal numbers end with an alternating pattern of 375 and 875, which continues indefinitely. The other interesting property is that the entire process tends asymptotically towards exactly 16.4 billion years. I have observed this process up to the 4628th cycle at which point the cycle period was approximately 2.1E-6010 and the overall process period was tending extremely close to 16.4E9. Both the period and the year also ended with 875. This cycle is shown at the end of the list.

The basic model relies on the cyclic interplay of the numbers 1558 and 20, which tend toward the number 1640. When 1558 is used any power of ten will give this general behaviour but any slight deviation and the resulting process does not tend toward an integer, however alternating patterns are still to be found. So the numbers [link] define a very finely tuned cyclic process. Note however that if the acceleration factor is changed from 20 to 2 then any integer initial period will result in a process that tends toward an integer value.

Cycle:     Period:                                                             Year:

-------------------------------------------------------------------------------

1           15580000000                                                     0
2           779000000.00                                                    15580000000
3           38950000.0000                                                  16359000000.00
4           1947500.000000                                                16397950000.0000
5           97375.00000000                                                16399897500.000000
6           4868.7500000000                                              16399994875.00000000
7           243.437500000000                                            16399999743.7500000000
8           12.17187500000000                                          16399999987.187500000000
9           0.6085937500000000                                        16399999999.35937500000000
10         0.030429687500000000                                    16399999999.9679687500000000
11         0.00152148437500000000                                16399999999.998398437500000000
12         0.0000760742187500000000                            16399999999.99991992187500000000
13         0.000003803710937500000000                        16399999999.9999959960937500000000
14         1.9018554687500000000E-7                            16399999999.999999799804687500000000
15         9.5092773437500000000E-9                            16399999999.99999998999023437500000000
16         4.75463867187500000000E-10                        16399999999.9999999994995117187500000000
17         2.377319335937500000000E-11                      16399999999.999999999974975585937500000000
18         1.1886596679687500000000E-12                    16399999999.99999999999874877929687500000000
19         5.9432983398437500000000E-14                    16399999999.9999999999999374389648437500000000
20         2.97164916992187500000000E-15                  16399999999.999999999999996871948242187500000000
21         1.485824584960937500000000E-16                16399999999.99999999999999984359741210937500000000
22         7.429122924804687500000000E-18                16399999999.9999999999999999921798706054687500000000
23         3.7145614624023437500000000E-19              16399999999.999999999999999999608993530273437500000000
24         1.85728073120117187500000000E-20            16399999999.99999999999999999998044967651367187500000000
25         9.28640365600585937500000000E-22            16399999999.9999999999999999999990224838256835937500000000
26         4.643201828002929687500000000E-23          16399999999.999999999999999999999951124191284179687500000000
27         2.3216009140014648437500000000E-24        16399999999.9999999999999999999999975562095642089843750000000
28         1.16080045700073242187500000000E-25      16399999999.9999999999999999999999998778104782104492187500000
29         5.80400228500366210937500000000E-27      16399999999.9999999999999999999999999938905239105224609375000
30         2.902001142501831054687500000000E-28    16399999999.9999999999999999999999999996945261955261230468750

cycle: 4628

period:

2.1221570276462814666109204332721675004454470106993527953514643197075692257463244297190947175351245709050
33594282157852403632697072428882497359338336551115427991559444881133292982304075676345584686352252286979
78622574682972532000915678617960782971993603982647623930031787774053092439515179527775507402743844484796
60904828639006929580016570184609632792932321663363881730495283005939900862324079898672248863483854146551
08913486750775965718363010295895781575486601768209381860605152154236639198308506465230529195699466641863
68117211915633128461387039956321888716232342435574033530721900486390668141737012733739878669293175890618
45607204313300504783976287401018217022172904128541614081764271605100570789654704168254970933364711490856
31691344601045801986067089186437375085095269385768746029776686787146682564361560762249950255182273157973
20413328903265131089902298257045414750109756708951734815052742474435005076920239354137445555770903439478
44936571840255856686449656978393176043267291876400493295771583870429279638208648848414438146093841352571
81298049622975800553832264934719442036719559426517495242430739159597744330357809239751796550985247967601
02360922896817117267784458206695345755320161634449820549459532612884405853099381323273195901308620482911
90088316254554285742457652362953279609472512779813658228589138924709146076349556084638194043407109626198
38768300589872724488298896259389228632231552314478471595632745439636141200256946327530951239097618056200
86360256061255423802917988884304084413655389256693992798724850156094463395576458748812762361573215018782
35047394393659017377900181324186908114511510726293902065434346389854163261491132893402435555474899881571
96995147903267551201993015950305744537243068615195263786474325360879227973966673488693007847224311051841
84769688326574989356595380729737000509535370763661885425919139098324821972726836329719914863213701984272
86613995178670397292521806079832456566375949672130777393704612082719656651864020279163454282909672503304
39019087483914214248576205637609700855185985935873365436461357761427530118140156768972690071524866808252
84989665436860580763680353867728203998871701030303846546897050732606287537374240846572148191265144152369
24010605322081267864148036493456400507794963364670688728050285720772959163746272152371909542135335722906
25180872998595468312675296378725827875507384983132891900842261754590598669651662757681705599452457413377
95929441269839587326557542506653991280084371776396972930479359767225554600908359603178895969480154696858
71325955079785970755246234171790190625085368171454685338628707782149347941276895290550864901925913427529
66609970888078910438450936156084733349664613747687156684486996687608145024415356382686310817129286816041
95327526007243171096416250939255846766315517651025681643836812113878186820036697877614528854499227026476
05743493738735920197740581412781432388152083823456407141213924846431612568367119790768473150163344101862
59872939663696410976211257488211734451622153939858806508775843753961750988688907139340644058721595664262
22004019921691452059010614142093916598043664247880914217842256915213443048677174242072706774325202795080
55714193644277983218796509464376065261186582073693307386875926726322904084225812182395998206629883497953
414916992187500000000E-6010

year:

16399999999.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999776615049721
44405614621890176082447363732136729480496891037217687288744992143953371377950341735530832578593744398338
39575123476765864334213305959645735667970535200584335649165281785183498583595066997629171600225025529652
92071577983496191620228450533048439318290599966539185207271116299811023394202733953847910740411528119589
40074126298347174095123375860714038564335020531281046379051723869389580345001196332785108893590384349991
83193980670515478004440446856208665042755936205102995540379791254203720809969267684771955932967187242993
33548988013642151240117140808060594132596283450631066957191429750512911852759295480867483559519924165123
15258122130223788401876818765364075219353598142871994630978116152942980784241122773987904361771670056831
09682119929379803750131489373400646559214705498224434582439405935199197631631310334449307396627228116807
73546221155475518899563420937098201103437036786586869015784129557642785118478362346417432127948036085892
04361382684571601691393638666008551157375478135174873232337222938264370090065109374903839398091599477652
88630995966036910821639961347832182613162902704485095160269125939148168682319420015528455156817253443191
39876560226886098215425520715619332158083632147860407490099102000651238659793788096188965355893807197320
48120271097208038996547779502618126511938706748274816095635709105730437222953638518831972422749807362211
86605801790635516432390913440471247917398320386583747751430315519003865756893432528823098735933049936197
31132839033695911258858511941695519269481264500157730426880636235306580197092250975563138123841606374803
58929075894545974540096721566830814427471510069109063311407093167228533260594152131684335187400051074702
44682945270509525993953118691506720847090751079657514863970553719291064533675950290198892798055055912351
84221729899599231855788937331188669829594288506169370184397923445435442400089617669787384975930378998119
25897586819151494913203614341105608283392217153039912926677208564189179827942860095081575469062956973853
53458685709257223568735941909488488554352172145939198497336717747203401081378872079087570260158003521717
25704459283838033970311580135051547048582582213630807782855223816588582555633482878795629085010414680820
19718037738908954256420518110564879294011865210225557081095617109187208029568903015436081151313885547383
20559670868109075025444341571173701965376946481829732009896137208776044545573053207939564865306005881370
10960708886797361416851284121713919582133757390147613446784630622779365074846347915626634885564989946528
56872889214490345484009868331191398468752275127676018790160061813794430999089576920091128916140947674862
32725854262172467279228052984617107697729805803161381465110500615414334014409666179698088376891289199923
75609372193420063941213930194191946288756164382303038022961242066633813037338047895550498446255331644855
41136633957282723387965907208332817414308272406394898493039401718821272875291420880690419092001337477224
24830551356571065040279524608259010674940517078059206356051590853781958588795727661478248145031536632403
24787306304616692532719370480353423283248191744992720827954685602974482028729711236628636757308271645849
70543980214200563814668146119387290849150119077971867028522016604408229056843993021175265312194824218750
0000000

-------------------------------------------------------------------------

Below is the java code that was used to produce the above output:

```import java.math.*;
public class MayanCalendar {
public static void main(String[] args) {
int numCycles = 30;
BigDecimal multiplier = new BigDecimal("0.05");
BigDecimal period = new BigDecimal("15580000000");
BigDecimal year = new BigDecimal("0");
for(int cycle=1; cycle<numCycles+1; cycle++){
System.out.println(cycle + "\t" + period + "\t" + year);
period = period.multiply(multiplier);
}
}
} ```

Analysis by John Ringland

Working Toward a Holistic Science: http://www.anandavala.info

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