Talk:Maya numerals

2001 text

The author of this article says: "The numerals are made up of three symbols; zero (egg shape), one (a dot) and five (a bar)" but then lists 31 as
:
=

which I think according to the above would likely be read as "12." Apparently it's not meant to be 12, but there's no indication of why in this article. Could someone explain further? --KQ

---

Now I get it, 12 would look something like this:

..
_____
_____

First of all, note that the two dots are next to each other. In the author's example, the two dots are above each other. To really do the system properly, you would need a fixed height for each numeral, or a convention where the top line of a number is always represented as dots, or an egg, to make clear the dividing line between numbers. Anyway, the author's number breaks down like this:

.                = 1 × 201
**************
.                
_____            = (1 + 5 + 5) × 200
_____            

add it all up, and you get 31.

It's kind of interesting the way that the Mayans mix an additive number system (like Roman Numerals) and a base X number system (like binary and decimal). I wonder what doing math under this system was like. Perhaps our system would be easier to teach if there was some rationale behind the value of the numerals (like the Mayan system) instead of purely abstract (like our Arabic system).

Arithmatics should be very easy with an abacus. Some sources indicate that earlier European explorers found abacus in use in Puru. I would imagine a Puruian abacus would have 4 beads on the upper deck (to represent 0 to 4 counts of 1) and 3 beads on the lower deck (to represent 0 to 3 counts of 5), compared to 1 bead for the Japanese Soroban's upper deck. You would move one bead on the upper deck for each dot you read off the number. And one bead on the lower deck for each bar in the number. Whenever the upper deck overflow, one bead on the lower deck is added, whenever the lower deck is overflow, one bead on the upper deck on the next column is moved. It works very similar to the Chinese numerals system except the fives are marked on the bottom instead of the top. It works exactly like the add and carry system in decimal number, but instead of doing a carry with every 10 count, the abacus would do a carry to the lower deck for every 5, then do a carry to the adjacent digit for every 4 counts on the upper deck. So it is a system of 5-4-5-4 alternating base. You can also see addition is very simple even without an abacus, just add the dot and bar separately and do the carry whenever necessary. Every 5 dots carry to a bar. Every 4 bars carry to a dot to the next digit. Many Chinese abacus operators can do arithmetics faster than anyone can punch the numbers on a calculator. I would imagine the Mayan could also do arithmatics faster than any westerner because it is an easier system than the arabic.

---

I still don't get it. Why wouldn't 31 be the following:

.
_____
_____
_____
_____
_____
_____

Also, how much is "1 * 20⁰"? Or "1 * 20¹"?

---

because the system is base 20, the most any set of lines can be worth is 19. So any number can be up to:

....
_____
_____
_____

After that, you start above with another number that is worth 20X the first, and you place that number above the first, so 20 =

.
0

(if 0 were egg shaped). The thing to keep in mind is that this isn't quite like Roman numerals, were you simply add/subtract the values of all the symbols. This system has a base like Arabic numbers (the ones we use). Unlike arabic numbers, however, the symbols are related in a logical manner, rather than just abstractly connected. My only qualm with is is that you need to use: fixed height numbers, a separator for each number, or have the top of every number be comprised of dots to make the divistion between the unit, 20, 20², etc. rows.

Also, I've fixed the mathematical notation above, I originally meant, "one times twenty to the power of zero," etc. (which is, by the way, 1). I was basically trying to break down the Mayan numbers the way we break down Arabic numbers in math classes (i.e. 527 = 5 × 10² + 2 × 10¹ + 7 × 10⁰). Clearer now?

---

Yes, much. It was the base 20 that had me. Should the following part also go on the main page, or is that just necessary to explain base 20 to people who didn't get it?

because the system is base 20, the most any set of lines can be worth is 19. So any number can be up to:

....

_____

_____

_____

After that, you start above with another number that is worth 20X the first, and you place that number above the first, so 20 =

.

0

(if 0 were egg shaped).

Mistakes

Did the Maya people make many mistakes between, say, 6 and 25? Sabbut 08:04, 26 May 2004 (UTC)

No. Our current illustration is perhaps not that good at showing how the place value is seperated. More usually the numbers were rotated 90 degrees from what is shown, while the place value seperation was vertical.

So, for example, using a "0" as a dot and a "I" as a bar, six would be:

0I

Where as 25 would be:

0

I

Cheers, -- Infrogmation 15:40, 26 May 2004 (UTC)

In glyphic representation of the numbers, the shape of each glyph being roughly the same size is enough to distinguish between various levels of the vegisimal system. I believe that during calculations, they used beads in some sort of abacus. Dylanwhs 20:32, 26 May 2004 (UTC)

Gnomon edits

I started to make some clean-up edits to User:Gnomon's recent additions to this page, but on consideration I am going to revert much of it. A good deal of it seems to me to be wrong. Thanks for your work here, Gnomon, but could we please have a source for some of this? For example:

"Most of what we know about Mayan numbers comes from a single document, the Dresden Codex"

What about the other pre-Columbian codicies, the stelae and other stone monuments, painting, and pottery which also use Maya numbers? They were still in use in the early colonial era, and for example Landa wrote about the numbers.

That the calendar uses non-vigesimal values IMO no more justifies claiming the system was not base 20 than the fact that we use clock faces with 12 digits means we don't really use base 10. -- Infrogmation 15:17, 9 Feb 2005 (UTC)

I'll check my sources and get back to you -- Gnomon.

I've looked into this and find that there were two systems in use by the Mayans. A pure base-20 system was used for normal purposes, but it did not use the numerals given here in this article. (Unfortunately, the numerals used have been destroyed by the invading Spanish, but it would have used a single symbol repeated as many times as necessary for 1's, another symbol repeated as many times as necessary for 10's, another for 100's and so on). The system described here was only used in the calendar codices and in stone inscriptions, and always used a mixed 18/20. Source: A Universal History of Numbers, Georges Ifrah.

I'll try and write that up and get it into the article.

Sacred numbers

I've heard that there were sacred numbers in Mayan numbers. If this is true please tell me the numbers.

I'd say all numbers were sacred, with their own associated deities. -- Infrogmation 05:10, 13 August 2005 (UTC)

Removed simple add/subtact section

I've removed the following section, as it gives a misleading account which implies add & subtract operations can be achieved simply by shuffling around the dots and bars of the operands:

Obviously, this method only works for certain combinations of operands- while for example 5 + 8 works as indicated, 4 + 8 does not (you would end up with a bar and seven dots, five of which would need to be converted to a bar to get the correct representation of the result, 12).

Similarly, if the operation was 13 - 4, the result cannot be achieved simply by 'taking away' four dots.--cjllw ʘ TALK 03:58, 20 April 2007 (UTC)

Mayan numerals in modern writing

Mayan numerals can be represented in modern writing similar to hexadecimal as:

0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F,G,H,I,J,10,11,12,13,14,15,16,17,18,19,1A,1B,1C,1D,1E,1F,1G,1H,1I,1J,20

and so on. 83.5.64.57 17:43, 10 May 2007 (UTC)

Perhaps so, but they would then not be 'Maya numerals', but a representation of (any) base-20 system.--cjllw ʘ TALK 08:41, 11 May 2007 (UTC)

Multiplication Division?

Was there a way to multiply or divide using this sytem? Maybe adding together one row at a time with the second column? (Example 21 Two dots ontop of one another time just two dots on the bottom the bottom dot goes with the other bottom dot to make 2 then that dot goes up (to nothing) and becomes a dot ontop of ther other dot, then you move on to the 20's row and get that dot move up the second column and add it together so you have two dots on the second row in the third column? .. x : = ::?) --199.227.86.10 14:49, 23 August 2007 (UTC)14:48, 23 August 2007 (UTC)

In a television show in Norway 2011-09-11 a very simple Maya way of multiplication was presented. Does anybody know this method? Hogne (talk) 12:44, 13 September 2011 (UTC)

mayan number 0

The mayan number system did the '0' 300 years before the hindu-arabic. The zero is one concha —Preceding unsigned comment added by 189.69.29.89 (talk) 22:42, 23 March 2009 (UTC)

6 vs. 25

What's the difference between 6 and 25 in this system?? Both are a dot above a line. Georgia guy (talk) 23:12, 28 May 2009 (UTC)

See the answer given previously above. To represent the number 6, both the dot and bar occupy the 'same' position (the lowest unit position). For 25, the dot occupies the next-highest position, while the bar the lowest position. See this crude illustration, here the first-place units (base-20) are on the bottom row, while row above that one contains coefficients (n) for the next-highest place (n × 20 ):

place-value	06	25
n × 201		•
n × 200	•

However, the vast majority of numbers appearing in Maya inscriptions are in the context of calendrical data and calculations, and for those they did not need to go above 19.--cjllw ʘ TALK 01:06, 29 May 2009 (UTC)

more on add/subtract

I added a rough sentence, and I don't have the time to expand, but I think it's worth noting that the basic rules for addition/subtraction/etc described are the same in mayan numerals compared to traditional base-10 math. That might help people to see that this isn't such a "strange" system after all. I'll leave it up to you folks to find sources/whatever, and expand/elaborate/etc if you deem it necessary. 97.122.97.134 (talk) 05:58, 12 April 2010 (UTC)

Number Representation

As far as I am aware, the Mayan number system was not entirely base 20. This page does not accurately reflect that. Numbers were represented as: ___ x 18 x 20^2 + ___ x 18 x 20 + ___ x 20 + ___ I see that this is represented in the calendar section, but believe it only adds confusion about the entire number system. Surely there is a solid reference to clarify if they used the strict base-20 system more often? Source: Crest of the Peacock, 3rd edition, page 67 (can be seen on Google Books) Levells (talk) 16:10, 7 May 2011 (UTC)

No. The number system was indeed base 20. The calendar made an exception for an approximation of the number of days in the year. Infrogmation (talk) 20:45, 7 May 2011 (UTC)

That's right, don't confuse calendrics with the actual arithmetic. Dylanwhs (talk) 09:18, 9 May 2011 (UTC)

I'M JUST LIEINGABOUT THIS WHOLE THING — Preceding unsigned comment added by 121.217.72.201 (talk) 05:52, 28 February 2013 (UTC)

Concerning the calendar arithmetic I would agree that the base was NOT 20. In the German version of this article is written that the Maya only used signs representing values from 0 to 17 on the second stage (20¹) to end up at 360. To me this makes no sense at all. Moreover I think the Maya were to advanced in mathematics to implement such a foolish trick to their calendar, which was kind of major scope for their research politics. To me it is more reasonable that they used 20^i-2*20^(i-1) as the base for their calendar, starting with i=0. Thus, the basic numeric digits 0-19 could be used on every stage whithout a problem. In fact they had a good understanding of working with the power, i.e. 20⁰ is defined as 1 (which is the first stage base of their simple arithmetic system) and 20^(-1) is defined as 0,05 which could simply be calculated by division. The calendar base I introduced here enabled them to work with fractional digits without using a special comma glyph. They could easily adjust the zero glyph in the second stage to round the fractional digit (which in terms of accurancy and irregularities in the solar year was quite useful), as one could see in the dresden codex, different glyphs for the zero existed. Just a thought came up as I read the German and this article. — Preceding unsigned comment added by 2001:4DD0:FF00:178D:0:0:0:2 (talk) 21:11, 11 September 2014 (UTC)

(Coincidental?) connection with D.C. flag

The D.C. flag bears a resemblance to the Mayan numeral for 13, ·̲̲·̲̲·̲̲ . This may be connected to the 13 colonies or 13 original states. However, this may be coincidental, as the D.C. flag was (also?) based off of Washington's coat of arms. — Preceding unsigned comment added by 184.152.75.156 (talk) 03:37, 21 November 2013 (UTC)

History

When did this numeral system first appear? One of the columns on List of numeral systems contains this information. -- Beland (talk) 21:37, 6 March 2014 (UTC)

Seeking knowledgable help

Commons:Commons:Help_desk#Maya_Numerals: someone watching this article may be able to help out. If so, please come by, certainly not something where I have a clue. - Jmabel | Talk 17:03, 20 February 2016 (UTC)