Dear Karl, Yes I can hear you. About symmetry, I shall soon send you an explaining email, privately, because I do not want to bother the FISers with long explanations (unless I am required to do it). However, I confess that many posts that I receive from the FIS list are very hard to read, and often I do not understand their deep content :) In fact, that should not be shocking: few people are able to read texts from very diverse fields (as it occurs in the FIS forum), and I am not one of them. Even the post of Sung was unclear for me, and it is exactly why I asked him questions, but only on the points that I may have a chance to understand (may be). Best regards, Michel.

2018-05-07 17:55 GMT+02:00 Karl Javorszky <karl.javors...@gmail.com>: > Dear Michel and Sung, > > Your discussion is way above my head in the jargon and background knowledge. > Please bear with me while a non-mathematician tries to express some > observations that regard symmetry. > > Two almost symmetrical spaces appear as Gestalts, expressed by numbers, if > one orders and reorders the expression a+b=c. One uses natural numbers – in > the range of 1..16 – to create a demo collection, which one then sorts and > re-sorts ad libitum / ad nauseam. The setup of the whole exercise does not > take longer than 1, max 2 hours. Then one can observe patterns. > > The patterns here specifically referred to are two – almost – symmetrical > rectangular, orthogonal spaces. As these patterns are derived from simple > sorting operations on natural numbers, one can well argue that they represent > fundamental pictures. > > The generating algorithm is 5 lines of code. Here it is. > > #d=16 > > begin outer loop, i:1,d > begin inner loop, j:i,d > append new record > write > a=i, b=j, c=a+b, k=b-2a, u=b-a, t=2b-3a, > q=a-2b, s=(d+1)-(a+b), w=2a-3b > end inner loop > end outer loop > > The next step is to sequence (sort, order) the rows. We use 2 sorting > criteria: as first, any one of {a,b,c,k,u,t,q,s,w}, and as 2nd sorting > criterium any of the remaining 8. This makes each of the 9 aspects of a+b=c > to be once a first, and once a second sorting key. We register the linear > sequential number of each element in a column for each of the 72 catalogued > sorting orders.. > > Do you think the idea of symmetry is somehow connected to some very basic > truths of logic? Then maybe the small effort to create a database with 136 > rows and 9+72 columns is possible. > > The trick begins with the next step: > > We go through the 72 sorting orders and re-sort from each of them into all > and each of the remaining 71. We register the sequential place of the element > in the order αβ while being resorted into order γδ. This gives each element a > value (a linear place, 1..136) “from” and a value “to”. The element is given > the attributes: Element: a,b, “Old Order”: αβ, from place nr i, “New Order” > γδ, to place nr. j. While doing this, one will realise, that reorganisations > happen by means of cycles, and will add attributes : > Cycle nr: k, Within cycle step nr:. l. This is simple counting and using > logical flags. > > The cycles, that we have now arrived at, give a very useful skeleton for any > and all theories about order. You will find the two Euclid-type spaces by > filtering out those reorganisations that consist of 46 cycles, of which 45 > have 3 elements in their corpus, where each of the 45 cycles has Σa=18, Σb=33. > > The two rectangular spaces – created by paths of elements during resorting – > are not quite symmetrical. As an outsider, I’d believe that there is > something to awake the natural curiosity of mathematicians. > > Hoping to have caught your interest. > > Karl > _______________________________________________ Fis mailing list Fis@listas.unizar.es http://listas.unizar.es/cgi-bin/mailman/listinfo/fis