Trichotomists as of July, 19th, 2025
Here is the reply I recieved from Stepanov back in 2014, after supplying him with a link to the Threesology.org site. Like many who are interested in the study of enumeration with respect to historical development, he does not display an awareness of the 3-to-1 ratio as a cognitive expression that is all too often labeled as a pattern-of-four. Such a model of Trichotomization is not on the radar of most number development enthusiasts. (Please take note he is Russian, so English is not his Native language.)
You've got an interesting, useful site, undoubtedly. It's a pity, but I'm not specially engaged in the problem of t(h)reesology for a long time. As concerns to the past, the main interest of me was dynamics of transformation of triple structures into quaternary ones (and vice versa). The both types of structures are very ancient in their genesis. It's unknown which one is more ancient (in one cases the triple ones are previous historically, in other, on the contrary, the quaternary ones appeared earlier).
It's very possible that the most previous were dual structures, i.e. opposites. Structuralism, including anthropology, say so (for example, Claude Lévi-Strauss). It sounds quite plausible psychologically, besides is proved by supervisions over primitive tribes.
Later were two ways:
- 2 + 1 = 3 (for example, an average between two extreme, transition from one to another),
- 2 x 2 = 4 (repetition of dual structure).
- So, both of the structures (3 and 4) were complex and derivative in their genesis.
As it was told, all the structures were transformed one to another. For example, the most ancient were representation of the year consisting of two seasons (warm and cold, or dry and damp). Then three seasons, then four.
For example, ancient Egyptians had three seasons. On the one hand, the culture of ancient Egyptians had a lot of very archaic elements, from the Stone Age. On the other hand, the option of three seasons was natural to Egyptians from the point of view of their environment. Their agricultural life depended on floods of Nile. So, the seasons were:
- 1) before flood,
- 2) flood (some months),
- 3) after flood1.
(Unfortunately, I don't remember exact names now, even less in English. It isn't really difficult to find them in the Internet).
Many triads of ancient deities are known, too. For example, ancient Babylonians had a triad of astral gods: Sin, Shamash, Ishtar (Moon, Sun, planet Venus). Planet Venus is the brightest star in the sky. Compare here night (darkness), day (light) and transition from night to day (morning and evening dawn). The matter is that the planet Venus is visible only just before sunrise and right after sun’s decline. Respectively, there were ideas of the Morning and Evening stars. The Babylon astronomers proved that it is the same star (planet).
But here very deep ancient metaphysics consisted also. Day is life (an activity), night is death (a dream). Transition of the person or the nature from non-existence to life is a birth or revival. Transition from life to non-existence is a dying. The goddess Ishtar is a goddess of fertility (love) and war. That we call planet Venus, Babylonians called planet Ishtar (planet = goddess)2.
Earlier I was surprised very much why the same goddess Ishtar represented both love (fertility), and war. It seemed to me that love and war are incompatible ("make love, not war"). But my representation was too modern. I didn't consider a role of recurrence in ancient thinking. Every year the nature dies and revives. What is "earlier", life or death? In both cases there is a transition from one state to another.
That the death (or non-existence) precedes life (existence) is a very ancient representation. For example, god Marduk creates the world by the murder of the goddess Tiamat ("Chaos"). He split her into two parts. From her top part he created the sky, and from the bottom the earth. Even more ancient representations were in the Paleolith. Ancient hunters believed: if to kill a bear or a deer (to eat them), they will revive then. Really, the food is life for human. But people thought that murder is life for animals and the nature, too.
I can say about these things for a long time, but the main thing for us here is that life and death are connected. In the Bible Adam and Eve as a result of their fall learned sexual love and became mortal.
The Babylon goddess Ishtar became Astarta at Phoenicians. Astarta is a goddess of love and war, too. She is a greatest soldier. Phoenician Astarta, in turn, affected an image of the Greek Aphrodite. Aphrodite is not a murderer anymore. But her lover is Ares, god of war, very blood-thirsty3.
Most important here for us is that quaternary representation passed into the ternary. Initially we have quaternary circular structure:
- 1) death (non-existence),
- 2) transition from non-existence to life (birth),
- 3) the very life,
- 4) transition from life to a non-existence (death).
- But points 2 and 4 were connected in one4.
Morning and Evening stars are one in their essence – the planet Ishtar, the goddess of love and war (conception and death, or murder). Who gives life, that takes it away, as he/she is an owner of life and death. As a matter of fact, we still think so: God is the owner of our life and death (not a goddess anymore, we think patriarchally).
About transformation of quaternary structures into the ternary K. Jung writes also. Though are known many examples of return transitions, too.
Reading various books, I often meet triple structures. Sometimes I write down the most interesting of them. But it is quite impossible now to find it in a lot of my papers (for 14 years I'm working on a book about numbers, already not only about 3 and 4).
But what I can remember at the moment is the following. Ancient idea of the top world (heavenly), the bottom (underground) and the average (earth). In the World tree it is a krone, a trunk, and roots. In many mythologies, a bird lives in the krone, and at roots of the tree lives a dragon (a snake). They meet, and the bird takes down World egg (from which our world is born). Modern scientists still argue, from where came life to Earth:
- 1) from space (sky),
- 2) from Earth (self-generation of life on Earth),
- 3) from their interaction.
One of the options of ancient division of human life: youth, maturity, old age. But there were also other divisions consisting of four, six, seven elements (from what that I met). In general, mythological classifications often are indistinct, change from an era to an era, from one district to another. It is not rare that later various classifications became contemporary in the same culture.
Here one more triad. In modern physics it is a macrocosm, the mesoworld, and a microcosm. The first one is learned by relativistic mechanics (Einstein), the second – by classic (Newton’s) mechanics, the third – by quantum mechanics.
There is a lot of triads in Ancient Greek philosophy. It seems like that this is a general rule: the more rational is a philosophical theory the more triads it has. The philosophy of Proclus (a Greek Neoplatonist philosopher, one of the last major Classical philosophers) is entirely constructed on triads. You can see any good book about Greek philosophy. As to me, I like Losev's works most of all (A.F. Losev). I don’t know if there is a translation in English. He wrote many books on antiquity. For example, there is "History of Antique Esthetics". On my shelf there are eight volumes of it. I don't doubt that there are excellent works on this question in English literature, too.
The huge number of triads is available in the German philosophy, especially by Hegel. As a matter of fact, I had an impression "the more rational is a philosophical theory the more triads it has" because of it. Of course it is not a representative row consisting of two lines: Antique and European philosophies. But the fact is that consistently rational theoretical science arose in the history only two times: in Ancient Greece and Europe. All of us follow these cultures.
Mr. Herb O. Buckland, I am very glad that you are engaged in the matters. Unfortunately, these questions are studied not sufficient for a while. But I am sure that persistence of researchers from different countries will yield its positive fruits, sooner or later (I hope, sooner J). Your country now is the main center of world science. I wish your country and, of course, to you personally a great success in a noble cause of science. Needless to say, I am grateful to you for the link to my modest person. Forgive me for my awful English (generally I read in English, not write).
Sincerely yours, Alexander Stepanov
Footnotes:
- The Egyptian year consisted of three seasons for four months.
- Our tradition to call planets on names of deities occurs from Babylonians. This tradition passed to Greeks then, and from them to Romans. Greeks named the planet Venus Aphrodite (the goddess of love).
- Our culture in many respects comes back to the ancient, and modern scientists say that a sexual inclination and aggression are operated by the same hormone: testosterone. Alpha males are most aggressive, they have more females. Female sexual activity is operated by testosterone, too.
- I don't know, how it was historically. Perhaps, the most ancient people simply didn't distinguish transitions from one to another and from another to the first. Quite often we think the same. For example, the distance from point A to point B is equal to the distance from point B to point A.
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Sorry, as concerns to mythology, I forgot to recommend you one more English author: Robert Ranke Graves (especially his "White Goddess"). He isn't considered an initial scientist, but many of his ideas were picked up by the most serious researchers later. There there are enough examples of triple structures.
Sinserely,
A.S.
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