A Study of the Threes Phenomena
Visitors as of May 17th, 2025
Some readers may be familiar with the old counting theme that was used in childhood. Even though I spent some of my childhood in Germany during my Father's duty assignment, I spent the bulk of it in different places in the U.S. As such, my knowledge of the counting rhyme is reflected in the following two lines:
Five Potato, Six Potato, Seven Potato... More.
I don't recall anyone going beyond the "More". However, in seeking out some internet reference, I came upon the following variation:
Five potatoes, six potatoes, seven potatoes - more
Eight potatoes, nine potatoes, ten potatoes - all
One, two, three, four, five, six, seven, eight, nine, ten
One potato, two potatoes, three potatoes - four
Five potatoes, six potatoes, seven potatoes - more
Eight potatoes, nine potatoes, ten potatoes - all
Since I am not familiar with the culture in which the author writes from, and not knowing whether such a version is a standard when they were growing up, I can not say for certain if this variation is a later born creation of an earlier theme with fewer lines, or if the author themselves created an embellishment.
From a Cultural Anthropology perspective involving cognitive psychology and the History of Mathematics, I want to focus on the two lines as I remember them being used in all the U.S. neighborhoods I lived in.(I use the letter "U.S." and not the word "America or American"), since those living in South America may view themselves as Americans as well.
As I took a walk this morning prior to sitting at the computer, I was reflecting on the usage and development of enumeration. Whereas the general theme is to think along the lines that somewhere in the past one or more human-like creatures developed the notion of a single (one) quantity, it is thought that this remained the sole model of a quantitative value that was later associated with some value of multiplicity, whereby the counting sequence was "1-Many". While our language uses some equivalent to designate the value of "1" and more than one, I do not know what these may have been to some ancient form of human whose mind engaged in the contemplation of enumeration, regardless of how crude their conceptualization may have been to our present day collective acceptances and agreements.
Though we of today may say "one" and use the symbol "1", these probably were not the exact figures used by a primitive person. A single notch on a bone or stone or in the sand may have sufficed for some ancient person. And instead of their language of grunting or whatever, they may have uttered a sound or physically expressed the idea of multiplicity by referencing some notion of more, many, much, heap, pile, etc...
The point is, the old "Potato" counting theme suggests to me that it references early human cognition in its efforts of developing a number system. Let's take a look at it again:
Five Potato, Six Potato, Seven Potato... More.
The first three have both singular and a collective distinction, just as do the bases in baseball. Whereas we do not typically say "forth base", neither do we designate the "four" with the same "potato" distinction. In both cases they are a separate reference without the same distinction, just as we see in the first three amino acids for both DNA and RNA:
RNA: Adenosine - Cytosine- Guanine (Uracil)
Each of the examples is a 3 to 1 ratio: (with others included)
- One Potato, Two Potato, Three Potato... Four (number value for the last item but no name)
- 1st base, 2nd base, 3rd base... Home [sometimes used with: base/plate] (name value for the last item but no number)
- Adenosine - Cytosine- Guanine... T/U (name values for all, but no number)
- Papa bear- Mama bear - Baby bear... Goldilocks (name values for all, but no number)
- 3 little Pigs and the Wolf (I have always heard of this story as there being "3" pigs but no names were attached. There was also a wolf but it was never labeled as being "one" in quantity. However it appears the did have names and the houses were not always made of hay, sticks and stones/bricks: 3 little pigs)
- 3 Fiddlers and Old King Cole (name value for the last item but no number)
It is though that early counting went like this:
- 1 (then sometime later...) Plurality (many, much, heap, etc...)
- 1, Plurality was followed by 1, 2
- The 1, 2 was followed by 1, 2, Plurality
- Then the 1, 2, Plurality was followed by 1, 2, 3
- Then the 1, 2, 3, Plurality changed to 1, 2, 3, 4, Plurality...
In some later cases the word "plurality" may be referenced with some high enumeration such as 10,000. In the earlier instances, such as the 1- 2 count, the value "2" was used by some for the next singular quantity after "1" but for others it represented the notion of multiplicity. Similarly, we of today may use the phrase "1 or more, 2 or more, 3 or more..."
In some ancient instances, the notion of plurality may well have preceded the use of any notion of singularity. Hence, the early development of counting in the minds of primitives may have went something like this:
- plurality
- one (which also is plurality)
- one- plurality
- one, two (two also is plurality)
- one, two, plurality (such as the "one- two- many" theme)
- one, two, three (three also is plurality)
- one, two, three, plurality... etc...
- Multiplicities by way of conducting arithmetical variations of singular number values such as 1+ 2, 3 + 2, 3 + 4, 3 X 2, 6 ÷ 2, etc...
It is a scenario of thought that occurs every day, even among educated people. For example, if I ask someone to make a list of references to their favorite number, invariably they at sometime during the conversation reach a point of limitation and may something something to the effect of "there's lots of them", "there's a whole bunch of them", etc... In other words, they are using the primitive valuation of "plurality" as a generality. This is what we see having occurred in the history of religious deities as well. For example, it is not difficult to see differences of cognitive enumeration in religious/spiritual/metaphysical interests.. as well as structures in business, government, military stratifications, musical scores, artist renderings, academic/psychological testing, etc...:
- The plurality of animism, of Nature, of stars... governments, businesses...
- The singularity of the Sun or Moon... kings, queens, sports teams...
- Duality (good/bad, evil/good, light/dark, hot/cold... male/female, twins, master/slave...)
- Pantheons (frequently viewed as some enumeration such as
- Triads, triplets, triangulations...
- Trinities as 3 -in- 1/ 1 -in- 3 themes (Hinduism, Christianity/ Many+One)...
While most of us take the "Potato" counting theme for granted, it appears to reflect a resemblance of early human attempts at developing a system of enumeration that we can generalize as a "One- Two- Many" script which plays out in multiple instances in everyday conversation as well as the varying complexities of individualized "calculuses" ("calculi" is the common plural form of calculus).
As a student or interested person in multiple subjects, such as cultural anthropology, psychology and mathematics, with a particular inclination towards understanding origination, you may well have come across references to enumeration usage by different cultures. In other words, someone may have written or spoken about this or another culture which appears to have a dominant preference for this or that number and as well emphasizing that different cultures have different favorite numbers such as described by the information at the following examples:
- Numbers are Interpreted Differently in Different Cultures
- The Meaning of Numbers Among Different Cultures
- Numbers and their Meanings among Different Cultures by Nisar Nikzad
Several of the sites I found referencing numbers and culture were directed towards business themes of advertisement and sells. The few anthropological sources I encountered were mere sales pitches to purchase a book. I bought "The Anthropology of Numbers" by Thomas Crump, but found it rather uninformative for my eclectic tastes of thinking divergently among different subject areas. While it is an attempt to portray the idea of numbers as a psychological theme, it is too narrowly focused for my interests. Nonetheless, you may find it invaluable for your specific interests.
In all the examples of cultural references of numbers, which includes the multiple references found at all Numerology sites, let us note that only a handful of number patterns are consistently repeated. In so doing, we must differentiate between numbers used in different eras and cultures. For example, when we encounter the tale of seven dwarves in the story of Snow White, let us note that the story has different variations and that the seven dwarves apparently first appeared in the recitation of the tale by the Brother's Grimm which did not contain any names for the dwarves. Apparently, according to this article: The changing names of the Seven Dwarfs, the naming of the seven occurred in 1912 as Blick, Flick, Glick, Pick, Quee, Snick and Whick; after which Disney renamed the dwarfs for its movie to Bashful, Doc, Dopey, Grumpy, Happy, Sleepy and Sneezy.
While Snow White appears to be an old tale, it is not with any certainty when the first mention of "7 dwarves" came into reference before the catalogued version Grimm's Brothers. The fairy tale thought to be the oldest: Smith and the Devil has basic themes of human concern and basic enumerations which need a deeper exploration of cognitive activity. This article: Fairy Tales Could Be Older Than You Ever Imagined is a basic reference to considerations about how deep into history various themes of repeating cognitive activity take place, even though most examinations are interested in what I view as soap opera types of narrative, and not the use of number as an expression of quantity and quality. However, we of today just don't know what a given number or symbol actually meant to a given person telling the tale for the first time and how later renditions may have been altered by the word-of-mouth chain of events from one culture to the next over vast distances of time.
When we say the Beauty is in the eye of the beholder, so is the word "Beauty" itself. For example, when I call my younger brother an idiot (though his IQ is over 200), it is different when I call Donald Trump and idiot. Likewise, if I label Einstein a genius, it is different when I reference Leonardo Da Vinci a genius. Similarly, if you say there are a few items, I may count an exact value of "3" items. It simple is not as claiming we are engaging in semantics such as when saying Potato (with a long a sound) and Potato (with a short a sound.) We don't actually know when the first Fairy tale originated because our definitions of what constitute a fairy tale may differ. Likewise, at what point of linguistic and cognitive sophistication did the first fairy tale contain some number quality and/or quality? If the number twelve (12) was a dominant theme in a given culture (for whatever reason), then one might consider it to show up in conversations more than others. Unless of course a number used to reference something bad or ominous is used such as in the case of the number 13 and its association with the occult.
It may be of interest for some readers to see a short list of children's rhymes and their apparent date of origination. The following list comes from here: Classic Nursery Rhymes
- Jack Sprat (1639)
- Pat-a-cake, Pat-a-cake, Baker’s Man (1698)
- Baa, Baa, Black Sheep (1744)
- Hickory, Dickory Dock (1744)
- Mary, Mary, Quite Contrary (1744)
- This Little Piggy (1760)
- Simple Simon (1760)
- Hey Diddle Diddle (1765)
- Jack and Jill (1765)
- Rock-a-bye Baby (1765)
- Humpty Dumpty (1797)
- Little Miss Muffet (1805)
- One, Two, Buckle My Shoe (1805)
- Hush, Little Baby, or the Mockingbird Song (unknown)
- Twinkle, Twinkle, Little Star (1806)
- Little Bo Peep (1810)
- Mary Had a Little Lamb (1830)
- This Old Man (1906)
- The Itsy Bitsy Spider (1910)
The Dark and Surprising Origins of 5 Nursery Rhymes (Some children's poems have ominous undertones.:
- Ring around the Rosey (1600s? concerning the Plague?)
- Rock-a-bye Baby (early 19th century concerning a smuggled baby?)
- Frere Jacques (1780, concerning an oversleeping Friar?; Friar Jack)
- Mary Had a Little Lamb (1830, concerning an actual event)
- London Bridge (14th century, concerning old interment practice of sacrificed adults and children)
Along with those stories called fairy tales, lullabies and rhymes, we can place terms such as legends, myths, ghost stories, songs, poems and perhaps the "literature" seen on cave walls that we call paintings, and perhaps even all artefacts are to be included as stores. For example, who can say that the placement of a rose every year on a grave doesn't have some elaborate tale behind the practice? Or the story about the wearing of a given piece of clothing, how the hair is worn, or style of boots/shoots, and kind of weapon that was forged or used in battle? No less, which of the artefacts have an attached enumeration of quality or quantity, even if we of today have no idea? Indeed, how many undeciphered languages have some particularized enumerative value that, if known about in the given context, would supply a greater understanding of what was being expressed?
If you were to remove all accounts of enumeration from all tales, how might their value be deduced if the writer was thinking in terms of enumeration but never explicitly expressed such? Indeed, how much of one's life today is defined in terms of a numerical value pertaining to the date, time of day, one's age, financial status and numerous other number-involved valuations that most of us today take for granted but may well have been absent from the cognitive activity of past peoples who related time to the Sun, Moon, stars and seasons, but we of today are appreciably oblivious to because we are more concerned with what time we have to be at work, at an appointment, or a favorite radio/television program is aired?
While one's daily schedule is not called a counting rhyme, many of us nonetheless repeat a given sequence of enumerations of when to dress, eat, sleep, work, read, etc... There is no great model of algebra, geometry, or calculus being used by today's standards, but if we would ask an ancient human to follow the sequence, they might well think of us as being crazy or engaged in some pattern of superstition that none today can recognize as a ritual of ceremony and particularized attire. Then again, we of today might consider the day to day routines of someone in the deep past to be similarly crazy if we had to clean a chamber pot, try to reason with a Roman soldier or berserker, and spend several hours hunting for food, making weapons/hunting tools, or sit among odor-reeking others at some public event worshiping some totemic model of Mr. Potato head?
Origination: Saturday, May 17th, 2025... 5:11 AM
Initial Posting: Saturday, Math 17th, 2025... 11:20 AM