Dear Friends, these last months my role in the group dynamics in Fis has been a destructive one. Ever so often, my contribution had an irritating effect, as the idea has been proposed that the current discussion is in itself useless, because the underlying concepts are inexact, due to a coarse rounding we do in connection with the additions. This is a message that needs selling.
Let me try to sell the idea of a sea change by telling a tale about the Sumerians. (Excuses to the Chinese and Indians who have learnt it otherwise.) Those Sumerians have invented science and rationalism by observing the heavenly bodies and invented the calendar, that is: the counting of time. Imagine being a Sumerian and trying to figure out the movements of the planets and tabulate them. It must have been a heroic task of several generations, writing up and comparing and hunting for patterns. Every sane man at that time knew that the firmament is punctured by holes behind which the Creator's light shone. We have a similar attitude towards the numbering system today, too. We can gain immensely from the idea that the numbers (and their pairs, the additions) are not on a fixed place in the firmament but move around. They do have movement patterns and follow rules while they move. There is a general, logical, abstract movement connected to the abstract idea of additions. Additions are not stable, they move in groups of three. There is a nice, clear and evident logical fact worth mentioning. Nature uses plain common sense and maintains - among other of Her marvels - an Euclid space of which the axes are: x: the sum of a,b; y: the double of one relative to the other (that is b-2a); z: the double of the other relative to the first (that is: a-2b). This is a rather working-day approach to space: the two together and the two doubles give a rough idea about how a is relative to b, and this across sizes. Now the trick is that three of these additions together generate a unit of mass, so that what remains is the place of the three-some in a three-dimensional space. So, every addition - in union with two others - is concurrently a place in a perfectly rectangular space with axes: a+b, b-2a, a-2a. Now this is something the old Sumerians would have thought useful; and they would have found it, too, if only they had the computers. Karl
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