Mesopotamian and Germanic numbers
When did the Scandinavians get the numerals and did they come from Mesopotamia? This essay is a short revival on what we know and speculate about when it comes to origin of numbers and numerals
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Three step year symbolism Isturizt Haute Pyrenées and in Skaane Sweden we have similar find 10000 years later. There are finds of sticks with notches that are 10000 - 30000 years old
Sometimes I like to make an inverse superposition to pretend the nature of things. Let us pretend a tribe far from what we call civilisation. The tribe does not have numerals in their language. Then one day a man gets the idea "count on fingers". Like all inventors the idea fascinates him so he counts like a nerd for days without end. The children in the settlement soon follows and no works are done.
There are rules even in small tribes so the elders' council decides to ban him to a far place within their territory. Occasionally a white anthropologist come to the wilderness and sees this counting man. He is astonished to meet such a civilised man. We westerners learn in the beginning that we are intellectual giants the day we can count to 10 = ten.
In fact it is an achievement because no one have ever seen numerals so they are like the bubbles of speech we make. Do they exist when we do not speak about them? Even white children learn to count on fingers until the mechanic rows of sounds are formed in the brains.
The Counter-man feels encouraged and learns fast. He takes the White Man to his tribe so he can show that he is the educated and understood that all other are fools. It is in that manner the educated sees intellectual inventions. It could be a mean for prestige and domination.
The elder' council are not fond of the event when the White Man tell about civilised numerals. They see he thinks they are primitive not knowing numbers. They can not see the numbers and they can not see any use of them. They are proud of being masters of their environment and they know they know more about it than any civilised man.
They are not afraid, since they know they can shorten the White Man whenever they want. They can not understand what the man does with his paper and pencil. The Video camera they understand since it reproduce their environment as it is. But those secret marks on the paper feel like a threat. Not thinking about how difficult it would be to live in the sustainable way of the tribe. White man's is used to destroy or alter the environment and can not live with nature.
The white threat is real but the aborigines do not know that in academic manner the anthropologist make his valuation. He sees the tribe as primitive in fact since he can not grasp the World Order needed to live in a hash environment. He is the primitive and uneducated in fact since he unmasks that he does not really understand. The same is case with other disparaging words used in science such as cult, shamanism, barbarian and pagan. The last word is the most stupid in our equal world.
In the example we see different layers of reality the academic man naturally thinks he is in the upper layer. The Counting-man thinks he is above his tribe and on his way to the upper layer. The tribe is satisfied with that life have been good as long as anyone can remember.
Before we continue let us look at another superposition. We are all born as a dwarf intellectually and in size. The giants do their best to educate and refine the little wild thing. It starts with teaching the dwarf to scream less and smile more. Only if the dwarf is slow in learning they say openly that he is dumb and primitive.
My first teacher was almost of the "Sumerian School". He used his pointer at the head and shoulders when we did not catch his teaching fast enough. When learning the alphabet he alternated between giving the bright youngsters small bricks as award for right answer like a competition. The pointer hit the others. The system made me answer almost before I knew the question. It became like a handicap in my life. I do not think the system would work on dogs since they learn fastest if they get praise all the time. Best if it a game is on same level. Still today I think dogs overall are treated better than children.
We can also say that we all are taught the most important things of civilisation that our ancestors invented ... even things the experts call "primitive". First of all the real scientific method is seeing a new thing, compare it with what we already know and make conclusions about the thing. This implies also all the conventions of name on things and rules in the society.
Logically we must have some space in our brains for memory of our entire experience and another for working with new things. It is much like the computer. We could speculate in the beginning that they compared with their surrounding. Naturally humankind always makes the first comparison with himself. But to get food and hunt they had to learn how nature behave and what there is in it The hunters tried to get under the skin of the predator and they followed roughly variations in seasons.
The world is like chaos and when we think about it we need to abstract and simplify our description. Most difficult are abstract things such as the fertility of rain and soil that gives the food. As soon as we want to think and discuss timespace we need words and symbols. To grasp time we need to count and refer to some reference. It was natural for early ancestors to use the brains of the collective to get greatest intellectual power.
It was a kind of genius that use the starry sky as reference and memory of the collective. That was like placing a grid and paths on the sky as well as in the memory of mankind. Man is like a prism between upper space and our environment including the soil/ underworld. The upper world is as stable as folk memory while the biosphere is living and changing with seasons and time.
For counting and time can use physical reference as for instance notches in some material. In intimate situations we can use our fingers, sticks, small stones, pebbles and tokens. If we want it to be eternal we can use arrangement of big stones that are almost eternal. These methods make counting visible. What does a number or a god look like? …for instance the fertility and force in rain that I want to use?
I am not so sure that science has pretended the beginning of civilisation from the viewpoint of our ancestors. Their brains were of the same size but they had not yet got all the knowledge later generations invented. Maybe we should get under the skin of our ancestors. However the most important thing is what conclusions they made from their world. Next we could look at which conclusions we still use.
Anthropologist have investigated some "primitive" tribes of today and they draw the "primitive" conclusion that the first counting of mankind was just "one- two - many" or "man, wife, others" and that is just what we find in some places in the Bible. They naturally think that people with no numbers are "behind the mainstream". Maybe it is better to think about natural development of needs in the particular society.
Firstly general statements do not say anything about proportions and that every local culture develop according to the needs. That is up to the law of relativity tied to every locality. I think that there is some confusion depending on poor definition of number configurations in language. The general number case is in today's language contends singular and plural word classes. This is easily mixed with numerals that is a separate class of adjectives.
The early logic of language in symbolism and syllable languages have A) one syllable A = infinitive description of the function "wet" B) two syllables AA = verbal action "flow, stream" C) three syllables AAA = fullness, noun. Arabian language has still singular, dual and plural and I think we have some indications of the use in old Nordic language. That is then a question about grammatical forms and not about numerals that are adjective numbers.
It was used on other aspects of logic. We still say, "all good things are three" But there are other possibilities in handling quantities and qualities.
"Three furrows in Thor (Mars)"
The earliest Sumerian myth we can connect to agriculture ritual and it is about Enlil, Ninlil and Sin their son. In "Advises for farmers" we learn about "breaking the surface - going through the soil - to the wet bottom of the furrow where the seed should be sown. It is the simple rule farmers' use also today. The Sumerian often made rules with 3 aspects since is the natural state of things. Later we see that the deities always took seven steps to underworld and 7 is used as ritual number and a sort of cardinal numbers.
Adjective numerals are divided in cardinal and ordinary numerals. Only mathematicians and school children are counting/ using numbers just "for fun". In the real world the numerals are attached or related to physical things. It was a big step for mankind to think in abstract terms. That includes so-called gods but also numerals. Other adjectives like colours and quality of things we can see but not the numerals as such. Cardinal numerals are used about quantities while ordinals bring order in quantities. It is much like using suites with specified ordinals for the members in time and sequence to get an order. Suite was used to picture time and individual quantities/ idols tied to time or a base ... for instance a week or a year…. SeeFollow in Suite
Thinking is creating a symbolic parallel world and in the beginning it is good to have a physical reference like when we are playing with dolls and other things as a child. In counting they probably used the fingers as reference and the early merchants use small stones and tokens to calculate and work with quantities. Next step was to connect the suite and the stones to the abacus. The oldest find of an abacus is from ca 300 BC at Salamis Greece.
Snorre Sturluson tell us in Advises for poets in Prose Edda:
"LXVI. "Each one singly is called man; it is twain if they are two; three are a thorp; four are a group; a band is five men; if there are six, it is a squad; seven complete a crew; eight men make a panel; nine are 'good fellows;' ten are a gang; eleven form an embassy; it is a dozen if twelve go together; thirteen. are a crowd; fourteen are an expedition; it is a gathering, when fifteen meet; sixteen make a garrison; seventeen are a congregation; to him who meets eighteen, they seem enemies enough. He who has nineteen men has a company; twenty men are a posse; thirty are a squadron; forty, a community; fifty are a shire; sixty are an assembly; seventy are a line; eighty are a people; one hundred is a host"
I am not so sure this has been reality. It sounds more like poetic use. But it is an example that there are other ways of talking about qualities. From the measures we know that they started from the body. They could also associate to the real word when they used rod and rope with standardised length. From the beginning we have also the tokens, small twigs and small stones that could be used in calculation as well as documents. Calculating became necessary in bookkeeping and trade.
Some suggest that they counted on their fingers and toes. Fingers maybe, but I am not so sure about toes. My friend Kenneth showed how we could use the fingers as physical reference for counting. Use right hand for the base 6 and count on left hand and jump to right hand for 6, 12, 18, 24 and 30 and continue with next number each time. After that continue the next 30 by bending the fingers on the base hand to 60. This system could also be used to show quantities by the hands.
In Scandinavian we use the word vecka/ week for original 1/4 of 28. The etymologists thinks it ha the root "to fold" / vika. The method would be similar in counting that they fold in the sequence of the base. The word SI-EX or SE-KS have the SI/SE mean "other side" and X or KS means "to cross" for the base 6 and even 'seven / sieben, sibun' has the jump to next 6 since it mean "one more than six" like eleven is written "one more than ten. Twelve is "two more than ten". Here ends the 2 x 6 and seemingly in an older tradition than 10 as base since next 13 = 3 + 10; 4 + 10 …. But the examples show that maybe they use parallel 5 and 6 as base too.
This comb fromGullrum Gotland they think is import from Elam/ ancient Persia around 3000 BC. The motif "comb with two heads" is found also on pottery. It is the only known Swedish cultural artefact besides the double edge axe from that time and now at http://www.historiska.se/collections/treasures/stoneage/gullrum.html
Normally they only mention the Sumer/ Babylonian system as sexagisemal system. But in Anglo-Scandinavian we have mixed system with base 6; 2 x 6 and 6 x 20 an origin we can maybe find in early Elamite
The Sumerian numerals are 1 = as; 2 = min; 3 = es; 4 = limmu and 5 = ia and we get the help base 5. The row continues 6 = ia-as; 7 = ia-min; 8 = issu; 9 ilimmu (ia-lim) and 10 = u; 20 = nis; 30 = usu (es-u 3 x 10); 40 nin (nin-min 2 x 20); 50 = ninu ( nin-min-u 2 x 20 + 10) and 60 = ges.
"The recognition that the procedure of counting "one, two, three, four, ..." can be performed intransitively, in other words, that when counting it is not necessary to be actually counting something, is likely to have been instrumental in establishing the universality of the number concept. Indeed, it has been suggested that the art of counting arose in connection with primitive religious ritual and that the counting or ordinal aspect of number preceded the emergence of the quantitative or cardinal aspect.
Whatever its origin, the procedure of counting naturally imposes an order on numbers, and it must have been grasped very early on that this order corresponds faithfully to the relative sizes of the collections that numbers are used to count. …sequence of numbers, or number names are much alike since they are attribute to something."
As stated the adjective "primitive" is unnecessary here. If so we should also use the pseudo-value when we are stumbling ahead with our new projects. Some of the oldest evidence of counting so far discovered comes from ancient artefacts belonging to groups of hunters and gatherers. For example, a wolf bone, dated about 30,000 BC, has been discovered with a series of notches carved in it, which seem to represent a tally of some kind.
The modern mathematics have in details defined all operators in mathematics and that is the way of making satellites and precise thingsLeibniz’s Law – First Form
identicals are indistinguishable
i.e.: if x and y are identical , then x and y are indistinguishable
i.e.: if x and y are numerically identical ,
then x and y are qualitatively identical.
i.e.: if x is y, then x and y have precisely the same properties
His second law is the other way round.This is the first step of defining two set of adjectives and the correspondence to reality. We see the same tendency to define things precisely in Sumerian culture. However in the manifold we find different methods.
On the Max Planck institute they have analysed 1600 early 3000 BC early-Elamite/ Persian clay tablets that solely are about accounting. They find that they used at least three number systems sexagesimal (used when counting important persons), bisexagisemal (rationing system) and decimal (discrete animal objects and laborers). In proto-Elamite there was also the capacity system used for grains and cereal products.
The fourth system was mixed and it could be compared to old counting where specific product use specific series of units for counting. It seems that they chose names from their ritual world order to the numbers. It was maybe easier to remember and could be used in other connections. We know from our measuring systems that they used specific numbers and relations depending on the product. Tylft = twelve for timber, tjog = 20 for egg and so on.
I have thought about it before that in our Germanic languages we have individual names for integers from 1 to 12 and we can see it also as 2 x 6 system. In old counting "hundred" = 120 and that fits the bisexagisemal system. The oldest base in Finnish is 6 and later 10 and probably the economy was smaller. The word "first" = ensin and then it is easy to think of Sumerian Ensi = first, leader
In Danish numbers we have nearly full evidence for the 'times twenty' system --- tyve/ snes 20 … fyrre 40 … treds 60 …80 firs …"hundre?"100 … hundred 120 (called 'long hundred' in English.) Tredve 30 and 40 are a bit odd and then we have halvtreds 50 (half-treds 60) and halvfjers 70 (half firs 80). We see they mixed 2 x 10 to 6 x 20.
In French we find just one integer from the "Good Old Days" since 80 = quatre-vingts and denote the 20-system.
Standards are very old. I have an old almanac from 1877. It is worn out but I get the important pages about the official step from the old measures to the decimal system in every area. There is the old rope and rod that originally was used for measuring allotment for growing cereals in Mesopotamia. In the collective field every family got a lot and then they also knew how much seed they needed.
From Sumerian symbolism we have some relief with the priest king wearing "rope and rod". He was the ritual leader and made the first furrow in spring. We also know about stela / mound marking the owner of a land and boundary stone "kudurru" used to mark that the allotment was occupied for the season. The finds tell us about the procession double axe during 4th millennium and later. Surely the "rope and rod" came at the same time and it was a part of the instructions hove to grow cereals in the name of the New Moon goddess.
At the Farmer's almanac Haugsbyn Bronze Age there is a rectangle parted in 3 x 5 = 15 parts and I suppose that is denoting the system of collective allotment. In West Gautland there is a "Celtic field" at Levene with 25 bits of land separated by stone strings. The name could be translated "bread meadow". Maybe the place was once an institute for learning agriculture.? The oldest tribe names from West Gautland are Levoni and Hill-levioni and that sounds much like the know growers from Levene
Normally we would guess that we got most of the influence to Scandinavia during Bronze Age. We have the figurative rock-carvings showing some of the tools. But the rock-carvings at Evenstorp and Haugsbyn are from around 2300 BC and they are about agriculture ritual. We have less evidence from the first period of agriculture in middle 4th millennium. But we have the double axe telling about early Inanna ritual and she was the one in head of the growers. However I do not think we can generalise and say there were agriculture everywhere. But we know for sure that at least in some places they learnt about culture. And in that period they got the corn and that means beer and pure drinking water.