Wishful Thinking Reflected in the Sumerian Concept of Numbers
1) Introduction To be better prepared to understand the roots of our numbering conventions, we have proposed to re-imagine the intellectual innovations achieved by the Sumerians, while they introduced the concept of positional notation. This ground-breaking innovation has made, in a - much simplified - example “a,b,c” different to “b,a,c” by the rule: “read the last as the number of single units, the next the number of dozens and the third as the number of grand dozens”: that is, abc translates into our notation as c + b*12 + a*144 and bac as c + a* 12 + b * 144. (They did in fact not use a 12-based system, but the principle they invented remains the same, whether binary, decimal or hexadecimal.) We have offered as a method of accessing the thinking capacity of the ganglions that manage this rule a mental landscape which is easy and emotionally moving. The ganglions can be seen as railroad switches (railway turnouts / points), which are brought into a fixed position by learning. Once one has learnt how to direct the paths of one’s thoughts, one has a much-simplified life. The disadvantages are that one has preconceptions and prejudices, and releasing the switch from its fixed position carries the costs of an experience of frustration. Yet, the regrettable state of affairs is today that we need to re-learn our basic concepts of how things interact with each other in Nature, because the transfer of genetic information, as observed in real life and in vitro, has, in the eyes of many, not yet been explained rationally, comprehensively and exhaustively, and in the eyes of few, the explanation which is in fact rational, comprehensive and exhaustive, cannot be understood by the many, as the ganglions of the many are fixed in their positions as learned in elementary school, and the frustration of re-releasing the switches is just too much for the simple-minded believers of Teachers, who unfortunately lack the long training a psycho-analyst has to go through until she or he loses all belief in authorities and teachings handed down and hopefully learns to think with her or his own head. If we succeed to drip-feed the true believers with the poison of disbelief, which is the elixir of alternative explanations, there may arrive a Darwinian moment, where people say: “it is not nice to un-believe many beliefs, but it does make just too much sense to assume that we are the great-great-great-grandchildren of monkeys”. The goal is in the current case to bring people to the point of saying: “It is not nice to un-believe many beliefs, but it does make just too much sense to assume that there are many ways to arrive at the concept of a number, let alone to that of a sequence”. So, we return to the Sumerian nobles discussing how to build a consistent system of notation for something which is differing to all things sensually perceivable. To un-glue the fixed positions of the switches of the ganglions in the brain, we use the juicy imagination that the Sumerians have abstracted for their idea of “one object as such” from sensually perceivable objects each of them had in a similar fashion, namely ladies of their respective harems. To make the case simple, we imagine each of the scientists to be the proud owner of a harem with 60 ladies each in them, who are normal, healthy women. 2) What they did 1. Enumerate consecutively Astronomers have observed the periodicity of the Earth’s orbit around the Sun and the phases of the Moon well before using positional arithmetic. The 4*7 is connected to phases of the Moon and to some processes of physiological nature in the objects to be abstracted from. One may assume that the 7 days of the week root in these facts. The resulting number line is periodic, roughly on 4*7 and again on 4*7*12. One can deal with the in-exactitudes by means of the two solstices and re-align the calendar if necessary. The resulting number line can be reasonably thought to consist of identical units which follow each other. The mother of N has been born. 1. De-individuate the objects – individuate the places There was no gender or transgender oriented affirmative action thousands of years ago, and no ideas of counting in a politically correct fashion were entertained in those long-gone days. Being morally far inferior to us, the Sumerians created a concept of the object which negates any individuality of the object. In fact, they simply enumerated their women and said that one is just like the next, and the only difference that can be seen between two women is, when they are being put to use. The mathematical concept of a unit predates Kant by about 5 thousand years. If you have many objects-as-such, the only difference they can have among each other is given to them by the place they stand on. This is all very anti-feministic, so far. In a previous posting, a method has been shown, by which the Sumerians could have established an alternative to their place-based system of counting elements of a set, which they had thought into absolute alikeness. They only would have needed a different mind-set, and of course paper, pencil and computers. They could have then established ranking orders among the women of each harem, based on different criteria, and observed the distribution of rank-denoting symbols attached to the individual women. One step farther, and they would have discovered the simple arithmetical rule which is known as “permutations consist of cycles”, and then they could have entered the 21st century – but, lacking paper, pencil and computers, and, before all, a politically correct attitude, they have chosen not to. 3) Wishful thinking The following simplifications have entered the Sumerian idea of units on a number line. Find the wishes associated with the decisions to believe and to teach the concept as established by the Sumerians. 1. All women are alike 2. There is an endless supply of women 3. Whether a woman is a new one or had already been met, is of no relevance 4. Whether my memory works or not, is of no relevance. Discuss, which inner conflicts have been frozen by these instances of pretending not to notice that one has seemingly eliminated contradictory impulses and impressions. To be continued by discussing individuated objects and de-individuated places. Karl
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