cols ← {base←1} ##.mayan numb ⍝ Mayan numbers. As the Pre-Columbian people of Central America used their toes as well as their fingers for counting, they wound up with a base 20 (vigesimal) number system. In earlier writings, distinct symbols were used to represent different powers of 20: 1 - dot 20 - hatchet or flag 400 - feather 8000 - purse or incense pouch For example, if ⍟, ⍞, ↑, $ represent pictograms of dot, hatchet, feather and purse respectively, then $ $ ↑ ⍞ ⍞ ⍞ ⍟ ⍟ ⍟ ⍟ → 20⊥2 1 3 4 → 16464 An APL function to decode such strings might be: deco←{20⊥+/'$↑⍞⍟'∘.=⍵~' '} deco'$ $ ↑ ⍞ ⍞ ⍞ ⍟ ⍟ ⍟ ⍟' 16464 By the 10th century AD, this had evolved into a positional system in which dig- its 1-19 were expressed as dots '⍟' arranged in 4 rows (hands/feet) of 5 (fing- ers/toes). For legibility, completed rows of 5 were drawn as a solid line '⌹⌹⌹⌹⌹' and multi-digit numbers were written in columns with more significant digit-blocks (higher powers of 20) uppermost. For example, the number 258 (20⊥12 18) would be written: ┌───────┐ │ ⍟ ⍟ │ │ ⌹⌹⌹⌹⌹ │ (2+5+5)×20 │ ⌹⌹⌹⌹⌹ │ │ │ + │ ⍟⍟⍟ │ │ ⌹⌹⌹⌹⌹ │ (3+5+5+5)×1 │ ⌹⌹⌹⌹⌹ │ │ ⌹⌹⌹⌹⌹ │ └───────┘ The system boasted a Zero (represented by a snail or sea shell pictogram) and when used for date calculations, had a curious irregularity in the third place (and only the third place) in that items in this position represented 18×20, rather than 20×20. In APL terms, this means we use ··· 20 20 18 20 to encode into Mayan calendrical numbers. Function mayan's optional left argument selects 0: regular ··· 20 20 20 base, 1: calendar ··· 20 18 20 base (default). As the principal use of arithmetic was astronomical and calendrical, it is prob- able that the 18×20 (=360) irregularity was introduced as a simplification. The Mayan calendar year had 360 regular days together with 5 extra "null" days in the short month of Wayeb (see below). We should not infer any vagueness about the length of a Mayan year: The Priest- Astronomers managed to calculate Sun, Moon and planet cycles to an astonishing accuracy; for example, the length of a year was calculated to a precision better than we manage with our Gregorian leap year system, even with its no-it-isn't, yes-it-is adjustment at 100 and 400 years: Modern "accurate" solar year · 365.242198 days Mayan calculation of solar year · 365.242 days (-0.000054% error) Gregorian leap year system · · 365.2425 days (+0.000083% error) ( The Mayan calendar uses the following units of time: days ×\ Kin 1 1 (day) Uinal 20 20 (month) Tun 360 18 (year) Katun 7,200 20 (a "score" of years) Baktun 144,000 20 Piktun 2,880,000 20 Kalabtun 57,600,000 20 Kinchiltun 1,152,000,000 20 Alautun 23,040,000,000 20 Hablatun 460,800,000,000 20 ) ( The names of cardinal numbers reveal a vestigial decimal system: 0 xix im 10 lahun 20 hun kal 1 hun 11 buluc 40 ca kal 2 caa 12 lahca 60 ox kal 3 ox 13 oxlahun 80 can kal 4 can 14 canlahun 100 hoo kal 5 hoo 15 hoolahun 120 uac kal 6 uac 16 uaclahun 140 uuc kal 7 uuc 17 uuclahun 200 ka hoo kal 8 uaxac 18 uaxaclahun 400 hun bak 9 bolon 19 bolonlahun 800 ca bak 1,200 ox bak 1,600 can bak 2,000 hoo bak 8,000 hun pic 160,000 hun calab 3,200,000 hun kinchil 64,000,000 hun alau ( The name for 10 "lahun" appears to include the word for 1 "hun", which means it might translate into English as something like "one-ty". This would imply that the Maya had distinct words for the numbers 0-9, where- as English has distinct words for 1-10 (with Zero following later). Mayan months and weeks both start with day 0. All of this suggests that the Maya were ⎕IO←0 people. Yay Maya! ) ) ( Positional number systems lend themselves to calculation using various types of abacus. An example "Nepohualtzitzin" dates from 900-1000 AD. See: eval.dws/notes.soroban ) To convert decimal number 86,672 to (calendrical) Mayan, we would use: 20 20 18 20⊤86627 12 0 11 7 Which, using Mayan-style digits, becomes: ⍟ ⍟ 12 × 7200 ⌹⌹⌹⌹⌹ ⌹⌹⌹⌹⌹ + _@/ 0 × 360 (_@/ is a picture of a snail) + ⍟ 11 × 20 ⌹⌹⌹⌹⌹ ⌹⌹⌹⌹⌹ + ⍟ ⍟ 7 × 1 ⌹⌹⌹⌹⌹ Examples: mayan 6386 ⍝ (20 18 20⊤6386 → 17 13 6) ⍟ ⍟ ⌹⌹⌹⌹⌹ ⌹⌹⌹⌹⌹ ⌹⌹⌹⌹⌹ ⍟⍟⍟ ⌹⌹⌹⌹⌹ ⌹⌹⌹⌹⌹ ⍟ ⌹⌹⌹⌹⌹ mayan 4321 ⍝ (20 18 20⊤4321 → 12 0 1) ⍟ ⍟ ⌹⌹⌹⌹⌹ ⌹⌹⌹⌹⌹ _@/ ⍟ mayan 70 ⍝ "Three score years and ten". ⍟⍟⍟ ⌹⌹⌹⌹⌹ ⌹⌹⌹⌹⌹ disp∘mayan¨ ⎕ ⍝ various numbers: ⎕: 1234 2345 3456 4567 5678 360 7200 ┌─────┐ ┌─────┐ ┌─────┐ ┌─────┐ ┌─────┐ ┌─────┐ ┌─────┐ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ⍟⍟⍟ │ │ ⍟ │ │⍟⍟⍟⍟ │ │ ⍟ ⍟ │ │⌹⌹⌹⌹⌹│ │ ⍟ │ │ ⍟ │ ├─────┤ │⌹⌹⌹⌹⌹│ │⌹⌹⌹⌹⌹│ │⌹⌹⌹⌹⌹│ │⌹⌹⌹⌹⌹│ ├─────┤ ├─────┤ │ │ ├─────┤ ├─────┤ │⌹⌹⌹⌹⌹│ │⌹⌹⌹⌹⌹│ │ │ │ │ │ ⍟ ⍟ │ │ │ │ │ ├─────┤ ├─────┤ │ _@/ │ │ _@/ │ │⌹⌹⌹⌹⌹│ │⍟⍟⍟⍟ │ │⌹⌹⌹⌹⌹│ │ │ │ │ ├─────┤ ├─────┤ ├─────┤ │⌹⌹⌹⌹⌹│ │⌹⌹⌹⌹⌹│ │ ⍟ ⍟ │ │ ⍟⍟⍟ │ │ │ │ │ │ │ ├─────┤ ├─────┤ │⌹⌹⌹⌹⌹│ │⌹⌹⌹⌹⌹│ │ _@/ │ │ _@/ │ │⍟⍟⍟⍟ │ │ │ │ │ │⌹⌹⌹⌹⌹│ │⌹⌹⌹⌹⌹│ └─────┘ ├─────┤ │⌹⌹⌹⌹⌹│ │⌹⌹⌹⌹⌹│ │ ⍟ │ ├─────┤ ├─────┤ │ │ │⌹⌹⌹⌹⌹│ └─────┘ │⌹⌹⌹⌹⌹│ │ │ │ │ │ _@/ │ └─────┘ │⌹⌹⌹⌹⌹│ │ ⍟ ⍟ │ │ ⍟⍟⍟ │ └─────┘ │⌹⌹⌹⌹⌹│ │⌹⌹⌹⌹⌹│ │⌹⌹⌹⌹⌹│ └─────┘ └─────┘ │⌹⌹⌹⌹⌹│ │⌹⌹⌹⌹⌹│ └─────┘ ⍝ The following function converts ⎕TS-style dates into Mayan "Long Count" form, ⍝ assuming that the Long Count epoch started August 11th, 3114 BCE. long_count←{ ⍝ Mayan Long Count from Gregorian (⎕TS) date. ⍺←584283 ⍝ default GMT correlation: 0.0.0.0.0 ≡ JD:584283. G←⌊days ⍵ ⍝ Gregorian day. J←2415020+G ⍝ Julian day. mayan J-⍺ ⍝ Mayan from Julian. } long_count 2003 12 25 ⍝ 2003-12-25 ≡ 12.19.10.15.16 ⍟ ⍟ ⌹⌹⌹⌹⌹ ⌹⌹⌹⌹⌹ ⍟⍟⍟⍟ ⌹⌹⌹⌹⌹ ⌹⌹⌹⌹⌹ ⌹⌹⌹⌹⌹ ⌹⌹⌹⌹⌹ ⌹⌹⌹⌹⌹ ⌹⌹⌹⌹⌹ ⌹⌹⌹⌹⌹ ⌹⌹⌹⌹⌹ ⍟ ⌹⌹⌹⌹⌹ ⌹⌹⌹⌹⌹ ⌹⌹⌹⌹⌹ long_count 2012 12 21 ⍝ First day of 14th Baktun. ⍟⍟⍟ ⌹⌹⌹⌹⌹ ⌹⌹⌹⌹⌹ _@/ _@/ _@/ _@/ ⍝ This stand-alone version converts a YYYY MM DD vector into the equivalent ⍝ n.n.n.n.n vector: long_vec←{ ⍝ Raw long-count vector. ⍺←584283 ⍝ default GMT correlation: 0.0.0.0.0 ≡ JD:584283. G←⌊days ⍵ ⍝ Gregorian day. J←2415020+G ⍝ Julian day. M←J-⍺ ⍝ Mayan from Julian. n←1+⌈18⍟1⌈M ⍝ generous number of digits. b←20-2⌽n↑2 ⍝ encoding base. v←b⊤M ⍝ long-count vector. (∨\v≠0)/v ⍝ without leading 0s. } long_vec 2012 12 21 ⍝ first day of 14th Backtun 13 0 0 0 0 Correlation with Modern Dates ----------------------------- There is overwhelming evidence that the Maya maintained a rigorous calendar. However, as this ceased with the decline of the civilisation, it has been diff- icult to determine how Mayan dates correspond to the Julian or Gregorian calend- ars. Two correlations seem to be favoured: The first, known as "GMT" (Goodman, Martinez, Thompson), suggests that Mayan date 0.0.0.0.0 corresponds to Julian date 584,283. This is based on studies of some contemporary Central American communities, whose calendar seems to be in- herited from the Maya. The argument is that (unless the population of such peoples dwindled to a critical number at some point in the past before recover- ing) it is inconceivable that their calendar should have missed or gained days; it would be as unthinkable as western civilisation's missing or duplicating a couple of Wednesdays. The second "GMT+2", which uses relatively recent evidence, is based upon Mayan recorded observations of eclipses. We can date such events with extreme accuracy, and they suggest a correlation with Julian date 584,285. If the astronomical recording was accurate, an explanation of the discrepency might be that the 584,285 calendar was subsequently adjusted to realign with the seasons in the same way the Gregorian calendar skipped 3-13 September in 1752. The functions shown here use the 584,283 (GMT) correlation, which now appears to be the more generally accepted one. Cycles ------ Today almost all of the civilised world enjoys a 7-day week. This cycle, which is independent of month and year, is so universal that we forget why we decided upon seven. (muse: There are many suggestions as to the origin of the 7-day week, and no single theory is widely accepted as the definitive answer. One example is that the concept of the week arose in primitive agricultural societies, where seven days was about the right interval for a farmer to prepare and bring his goods to market. A shorter interval would waste too much time away from production, and a longer one might risk goods perishing between market days. Note firstly, that there are strong reasons for market days to occur at ex- actly regular intervals: every so-many days, rather than being constantly re-negotiated. With a regular "week", there is much more chance of everyone showing up on the same day; a prerequisite for successful trading. It is tempting to speculate whether widespread acceptance of an interval of seven days might have come about by a form of natural selection, rather than as a collective or bureaucratic conscious decision: A farmer returning from his local market might have found on occasion, that his figs, chickens and so-forth were ready again after six days. If his local market did not fall on the following day, he might have felt inclined to take his goods to a neighbouring village's market even though it was slightly farther to travel. Villages whose market days just happened to accommodate natural agricultural cycles would tend to retain regular trade as well as to attract occasional additional visitors, whereas those with slightly more inconvenient cycles would tend to decline. In this way, farmer-friendly market cycles would tend automatically to become the norm. ( Having established same-length cycles in adjacent villages, there may have been a second mechanism that selected for staggered market days, while reinforcing their regularity. Service providers such as pot-menders and tooth-pullers, who needed no time to prepare between market days, would probably have toured markets on different days in nearby locations. In the case of a collision, the trader would probably have chosen the better-attended market, and his presence there would in turn have made that market marginally more at- tractive to shoppers, tending to increase its size, ... and so on. Looking at the larger picture, these rotating service providers (axe- grinders, sooth-sayers, hair-cutters, entertainers, ...) could be seen as the teeth on the interlocking cogs of an expanding economic machine, which absorbed adjacent communities, synchronising them into the 7-day cycle. ( If this were the case, we might expect the names of the days of the week (in a particular locale) to indicate the locations of the more important markets in that area: "Oxford-day", "Banbury-day", and so forth, rather than being named after deities. ) ) That the Mayan civilization chose a week with thirteen days (see below), as opposed to one with seven, does not, of itself, detract from this theory, as the Mayan agricultural profile was quite different from that of Eurasia's "Fertile Crescent". See "Guns, Germs, and Steel: The Fates of Human Societ- ies", Jared Diamond. But all of this is merely conjecture ... ) The Mayan calendar included several cycles, two of which often accompany a Long Count date. Combinations such as these are similar to our compound date format: Wednesday, November 5, 2003. │ │ │ └──── Month 12-cycle. └─────────────── Weekday 7-cycle. "Haab" is a cycle of 18 × 20-day months. "Tzolkin" is a cycle of 20 × 13-day weeks. Haab has 18 × 20-day months together with one 5-day month making a total of 365 days in the year: Pop Wo Sip Sotz' Tzek Xul Yaxk'in Mol Ch'en Yax Sak Keh Mak K'ank'in Muwan Pax K'ayab Kumk'u Wayeb (5) Months←'Pop' 'Wo' 'Sip' 'Sotz''' 'Tzek' 'Xul' 'Yaxk''in' 'Mol' 'Ch''en' 'Yax' 'Sak' 'Keh' 'Mak' 'K''ank''in' 'Muwan' 'Pax' 'K''ayab' 'Kumk''u' 'Wayeb' The short month of Wayeb is inauspicious; one should refrain from washing, hair combing and nit-picking during Wayeb. Day-within-month and Month name can be extracted by: haab←{⎕IO←0 ⍝ Mayan day within month. ⍺←245 ⍝ align Gregorian and Maya cycles. mon day←0 20⊤365|⍺+⌊days ⍵ ⍝ month index and day number. name←mon⊃Months ⍝ name of month. day name ⍝ origin-0 day within month. } haab 2003 12 25 ⍝ Christmas day 2003 fell on the fourth day of K'ank'in. 4 K'ank'in haab 2003 12 26 ⍝ Boxing day fell on the fifth day of K'ank'in. 5 K'ank'in haab 2003 12 27 ⍝ ... etc. 6 K'ank'in The names of the 20 Tzolkin days are as follows: Imix Ik' Ak'bal K'an Chikchan Kimi Manik' Lamat Muluk Ok Chuwen Eb Ben Ix Men Kib Kaban Etz'nab Kawak Ahaw Days←'Imix' 'Ik''' 'Ak''bal' 'K''an' 'Chikchan' 'Kimi' 'Manik''' 'Lamat' 'Muluk' 'Ok' 'Chuwen' 'Eb' 'Ben' 'Ix' 'Men' 'Kib' 'Kaban' 'Etz''nab' 'Kawak' 'Ahaw' The 20 Tzolkin days are reused cyclically for successive 13-day weeks. This means that a particular day number (0-12) coincides with a particular day name (Imix-Ahaw) only every 20×13 = 260 days. The Tzolkin date can be extracted using: tzolkin←{⎕IO←0 ⍝ Mayan Tzolkin number and day. ⍺←2 16 ⍝ align Gregorian and Maya cycles. num day←13 20|⍺+⌊days ⍵ ⍝ day number and name index. name←day⊃Days ⍝ day name. (num+1)name ⍝ origin-1 day within cycle. } tzolkin 2003 12 25 ⍝ Christmas day 2003 fell on day 9, a Kib-day. 9 Kib tzolkin 2003 12 26 ⍝ Boxing day fell on day 10, a Kaban-day. 10 Kaban tzolkin 2003 12 27 ⍝ ... etc. 11 Etz'nab An Attractive Gift ------------------ Print the result of the following function on a stone tablet or gold pendant to make an attractive "Stela" of a loved one's date of birth. The final (lower) two digits show Tzolkin and Haab dates, the Mayan cultural equivalent of an astro- logical star sign. time_units←'Kin' 'Uinal' 'Tun' 'Katun' 'Baktun' 'Piktun' 'Kalabtun' 'Kinchiltun' 'Alautun' 'Hablatun' stela←{ ⍝ Stela for date ⍵ (yyyy mm dd). long←long_count ⍵ ⍝ Long Count days. hnum hname←haab ⍵ ⍝ month and day. tnum tname←tzolkin ⍵ ⍝ week and day. digits←long⍪↑,∘mayan¨tnum hnum ⍝ maya-style digits. lft←1 0∘↓¨digits ⍝ left-side column: numbers. rgt←⌽7↑hname tname,time_units ⍝ right-side column: names. disp lft,rgt ⍝ collected stela. } Here are Stelae for Victoria and David Beckham, together with little Brooklyn, Romeo, Cruz and Harper. Notice how Brooklyn and Cruz share the same star signs. david←1974 04 17 victoria←1975 05 02 brooklyn←1999 03 04 romeo←2002 09 01 cruz←2005 02 20 harper7←2011 07 10 stela¨¨(david victoria)(brooklyn romeo cruz harper7) ┌─────┬──────┐ ┌─────┬──────┐ ┌─────┬──────┐ ┌─────┬──────┐ ┌─────┬──────┐ ┌─────┬──────┐ │ ⍟ ⍟ │ │ │ ⍟ ⍟ │ │ │ ⍟ ⍟ │ │ │ ⍟ ⍟ │ │ │ ⍟ ⍟ │ │ │ ⍟ ⍟ │ │ │⌹⌹⌹⌹⌹│Baktun│ │⌹⌹⌹⌹⌹│Baktun│ │⌹⌹⌹⌹⌹│Baktun│ │⌹⌹⌹⌹⌹│Baktun│ │⌹⌹⌹⌹⌹│Baktun│ │⌹⌹⌹⌹⌹│Baktun│ │⌹⌹⌹⌹⌹│ │ │⌹⌹⌹⌹⌹│ │ │⌹⌹⌹⌹⌹│ │ │⌹⌹⌹⌹⌹│ │ │⌹⌹⌹⌹⌹│ │ │⌹⌹⌹⌹⌹│ │ ├─────┼──────┤ ├─────┼──────┤ ├─────┼──────┤ ├─────┼──────┤ ├─────┼──────┤ ├─────┼──────┤ │ ⍟⍟⍟ │ │ │ ⍟⍟⍟ │ │ │⍟⍟⍟⍟ │ │ │⍟⍟⍟⍟ │ │ │⍟⍟⍟⍟ │ │ │⍟⍟⍟⍟ │ │ │⌹⌹⌹⌹⌹│Katun │ │⌹⌹⌹⌹⌹│Katun │ │⌹⌹⌹⌹⌹│Katun │ │⌹⌹⌹⌹⌹│Katun │ │⌹⌹⌹⌹⌹│Katun │ │⌹⌹⌹⌹⌹│Katun │ │⌹⌹⌹⌹⌹│ │ │⌹⌹⌹⌹⌹│ │ │⌹⌹⌹⌹⌹│ │ │⌹⌹⌹⌹⌹│ │ │⌹⌹⌹⌹⌹│ │ │⌹⌹⌹⌹⌹│ │ │⌹⌹⌹⌹⌹│ │ │⌹⌹⌹⌹⌹│ │ │⌹⌹⌹⌹⌹│ │ │⌹⌹⌹⌹⌹│ │ │⌹⌹⌹⌹⌹│ │ │⌹⌹⌹⌹⌹│ │ ├─────┼──────┤ ├─────┼──────┤ ├─────┼──────┤ ├─────┼──────┤ ├─────┼──────┤ ├─────┼──────┤ │ _@/ │ Tun │ │ ⍟ │ Tun │ │⌹⌹⌹⌹⌹│ Tun │ │⍟⍟⍟⍟ │ Tun │ │ ⍟ ⍟ │ │ │ ⍟⍟⍟ │ │ ├─────┼──────┤ ├─────┼──────┤ ├─────┼──────┤ │⌹⌹⌹⌹⌹│ │ │⌹⌹⌹⌹⌹│ Tun │ │⌹⌹⌹⌹⌹│ Tun │ │ ⍟⍟⍟ │ │ │⍟⍟⍟⍟ │ │ │ ⍟ ⍟ │ │ ├─────┼──────┤ │⌹⌹⌹⌹⌹│ │ │⌹⌹⌹⌹⌹│ │ │⌹⌹⌹⌹⌹│Uinal │ │⌹⌹⌹⌹⌹│Uinal │ │⌹⌹⌹⌹⌹│Uinal │ │⍟⍟⍟⍟ │Uinal │ ├─────┼──────┤ │⌹⌹⌹⌹⌹│ │ │⌹⌹⌹⌹⌹│ │ │⌹⌹⌹⌹⌹│ │ │⌹⌹⌹⌹⌹│ │ │⌹⌹⌹⌹⌹│ │ │ _@/ │Uinal │ ├─────┼──────┤ ├─────┼──────┤ ├─────┼──────┤ │⌹⌹⌹⌹⌹│ │ ├─────┼──────┤ ├─────┼──────┤ │⍟⍟⍟⍟ │Uinal │ │ ⍟ ⍟ │ │ │ ⍟ ⍟ │ │ ├─────┼──────┤ │ ⍟ │ │ │⍟⍟⍟⍟ │ │ │⌹⌹⌹⌹⌹│ │ │⌹⌹⌹⌹⌹│ Kin │ │⌹⌹⌹⌹⌹│ Kin │ │⍟⍟⍟⍟ │ │ │⌹⌹⌹⌹⌹│ Kin │ │⌹⌹⌹⌹⌹│ Kin │ ├─────┼──────┤ │⌹⌹⌹⌹⌹│ │ │⌹⌹⌹⌹⌹│ │ │⌹⌹⌹⌹⌹│ Kin │ │⌹⌹⌹⌹⌹│ │ │⌹⌹⌹⌹⌹│ │ │⌹⌹⌹⌹⌹│ Kin │ ├─────┼──────┤ ├─────┼──────┤ │⌹⌹⌹⌹⌹│ │ │⌹⌹⌹⌹⌹│ │ │⌹⌹⌹⌹⌹│ │ │⌹⌹⌹⌹⌹│ │ │ ⍟ ⍟ │ Eb │ │⌹⌹⌹⌹⌹│ Eb │ │⌹⌹⌹⌹⌹│ │ ├─────┼──────┤ ├─────┼──────┤ ├─────┼──────┤ │⌹⌹⌹⌹⌹│ │ │⌹⌹⌹⌹⌹│ │ ├─────┼──────┤ │⌹⌹⌹⌹⌹│ Kib │ │ ⍟⍟⍟ │Kawak │ │ ⍟ ⍟ │ Ok │ ├─────┼──────┤ ├─────┼──────┤ │ ⍟ ⍟ │Kawak │ │⌹⌹⌹⌹⌹│ │ ├─────┼──────┤ │⌹⌹⌹⌹⌹│ │ │⌹⌹⌹⌹⌹│ Pop │ │ _@/ │ Wo │ │⌹⌹⌹⌹⌹│ │ ├─────┼──────┤ │ ⍟ ⍟ │K'ayab│ ├─────┼──────┤ └─────┴──────┘ └─────┴──────┘ ├─────┼──────┤ │⍟⍟⍟⍟ │ Mol │ └─────┴──────┘ │ ⍟⍟⍟ │ │ │ ⍟ ⍟ │ │ │⌹⌹⌹⌹⌹│ │ │⌹⌹⌹⌹⌹│ Tzek │ │⌹⌹⌹⌹⌹│K'ayab│ └─────┴──────┘ │⌹⌹⌹⌹⌹│ │ │⌹⌹⌹⌹⌹│ │ │⌹⌹⌹⌹⌹│ │ └─────┴──────┘ └─────┴──────┘ References: http://en.wikipedia.org/wiki/Maya_numerals http://en.wikipedia.org/wiki/Mesoamerican_Long_Count_calendar Ifrah, G. "The Universal History of Numbers". Diamond, J. "Guns, Germs, and Steel: The Fates of Human Societies". http://mayan-calendar.com/calc.html See also: eval.dws/notes.soroban. See also: roman days Dates ary Back to: contents Back to: Workspaces