[Fis] Are there 3 kinds of motions in physics and biology?

[Michel Petitjean]

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.javorszky at 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
>