Complexity of Old Tagalog Counting System
Would you rather practice saying your dalawang libo dalawampu’t tatlong taon, or be sent back in time to say it the old way?
Pre-colonial Philippine societies are involved in trades with neighboring islands, so it is no wonder that they have units of measurements and counting system of their own. However, without numerals even in baybayin, how simple (or complex) do you think would the number system be?
Modern Tagalog Counting Concept
In a book published by Potet (1992) about Numerical Expressions in Tagalog, he divided the numerical expressions of the modern counting system into two parts: multipliers (numbers 1–9) and multiplicands (powers of ten). This suggests that bigger numbers are expressed by obtaining the product of the multiplier and the multiplicand. For instance, we can say that 9 (siyam) x 10 (pu) = 90 (siyam na pu).
This system is influenced by Spanish counting system where multipliers and multiplicands are needed to express bigger numbers. But how would our ancestors do it?
To know that, we need to understand first its principles as stated by Potet (1992), which I synthesized into 3 parts: Basic Numerals, Powers of Ten, and Sets of Ten.
Basic Numerals
In Old Tagalog, basic numerals are composed of numbers 1–9, the same way as they are today. These numerals are needed for us to express larger numbers later on.
Powers of Ten
In addition, we also have the powers of ten, which serve as the multiplicands mentioned earlier. Since powers of ten are expressed in exponents, we need to memorize its Tagalog equivalent. Many Filipinos today are not aware of the multiplicands beyond libo (thousand), but instead milyon (10⁶) and bilyon (10⁹) are used.
If we combine a basic numeral and a power of ten, we will get a “multiplier x multiplicand” concept.
Example:
Sets of Ten
In contrast with powers of ten, sets of ten refer to the set by which numbers are organized by ten. The first set of ten are the numbers from 0 to 9. Being the first set, they don’t have a set name because these are the basic numerals.
However, the second set of ten is labi (Proto-Austronesian *labiq, meaning excess). This has been retained in the modern counting system. In Old Tagalog, however, labi means “more than.” Being the second set, the numbers after 10 are called labing-isa (1 more than ten), labindalawa (2 more than ten), labintatlo (3 more than ten), and so on. This set of labi stops until the number 19 (or 9 more than 10).
The third set, on the other hand, uses the prefix mayka- all throughout the ninth set. The prefix mayka- was correlated by Potet (1992) with another Tagalog numeral prefix ika- (which is used for ikalawa, ikatlo, ikaapat, etc.). However, mayka- means “minus 1.” Every time mayka- is used, it means you have to subtract 1 from the attached number. Thus, maykatlo means “minus 1 on 3” or 20 (not 2, because maykatlo is in tens).
How to express numbers
Now that we know the three (3) main principles in the Old Tagalog Number System, let us try to express numbers from Tagalog.
Example 1: Express “maykalimang isa” in numerical form.
Explanation:
Remember that mayka- means “minus 1 on the attached number.” Since maykalima is a combination of mayka- and lima, this means “minus 1 on 5.” Don’t be confused with 10¹. This is just used for you to visualize that the number 5 is part of the power of ten, particularly pu (10¹). Hence “minus 1 on 5” is 40 and not 4.
To give you a detailed explanation on minus 1 on 5.10¹, take a look at the sample below:
Maykalimang isa makes perfect sense now as 40+1=41.
Example 2: Express “maykaraang apat” in numerical form.
Explanation:
Again, mayka- means “minus 1 on the attached number.” Since mayraan is a combination of mayka- and daan, this means “minus 1 on 10².”
Here, when the multiplier is 9, the expression has to advance forward from puo (10¹) to daan (10²). Take note that this advancement does not make the value of 10² into 100, but is only used as the label for the multiplier 9.
You may observe from the table of Sets of Ten that 80 is maykasiyam, hence 90 advances forward to the next set (the hundred), maykaraan. There is no such thing as maykasampu from the records of Potet (1992) and Morrow (2010).
Maykaraang apat makes perfect sense now as 90+4=94.
Example 3: Express “labi sa raang pito” in numerical form.
Explanation:
Remember that “labi sa” means “more than.” It is used in the second set of hundred. Hence, labi sa raan means that number is anything from 101–109. You may check on the table for Sets of Ten.
We cannot use labing raan because “labi” alone is only used for the 2nd set of ten. Once “labi sa” is used, this pertains to the second set of hundred as shown in the table for Sets of Ten.
Example 4: Express “maykalibong maykaraang siyam” in numerical form.
For expressing larger numbers, we need to break the numbers down into terms. maykalibong maykaraang siyam are three terms altogether.
Explanation:
Maykalibo is 900. We know that when mayka- is attached to any powers of ten, that means that there is a multiplier 9. This means that number 9 advanced forward from daan (10²) to libo (10³) in order to become a maykalibo (900).
The same for maykaraan. When mayka- is attached to any powers of ten, that means that there is a multiplier 9. Hence number 9 advanced forward from puo (10) to daan (10²) in order to become a maykaraan (90).
Siyam is a basic numeral. Overall, maykalibong maykaraang siyam means 999.
Summary of Old Tagalog Counting System
Notice that numbers in bold are expressed the same way in Modern Tagalog counting: dalawampu (20), dalawang daan (200), and isang libo (1000). This is based from a study by Morrow (2010) who explained that each multiple of ten, hundred, thousand and million were the same as they are today. However, from the book published by Potet (1992), there are some examples where this is not applied, and instead uses maykatlo (20), maykatlong daan (200), and labi sa libo (1000).
It is unclear why Morrow (2010) and Potet (1992) have dissimilar findings on that matter, but I will look into other literatures to make sure.
As of writing, I am compiling Verbal Representation and Formulaic Representation of numbers in Old Tagalog. Here, I followed Morrow’s (2010) notes on the Old Tagalog Counting System as my basis as it is more detailed than that of Potet’s (1992).
I labeled Verbal Representation to refer to the numbers expressed in words while Formulaic Representation to refer to the detailed break down of each term.
Example:
Conclusion
Perhaps, counting the old way is more complicated than we realized, but let’s recognize what this could mean for our pre-colonial ancestors, who were once labeled as illiterate by the Spaniards. Despite its intricacy and ingenuity, it’s still a mystery why our ancestors spelled out their numbers instead of using a numerical system. I, personally, have lots of questions on how exponentially large numbers were used in the context of trade, but maybe that’s reserved for another research.
Sources
Potet, J.P. (1992). Numeral expressions in Tagalog. Persee. doi: www.persee.fr/doc/arch_0044-8613_1992_num_44_1_2860
Morrow, P. (2010). Counting the old way. Pilipino Express. Retrieved from https://www.pilipino-express.com/history-a-culture/in-other-words/847-counting-the-old-way.html#:~:text=Pre%2DHispanic%20people%20of%20the,numerals%20the%20same%20as%20words.
