Sorry for the delay, Karl. Here it is. ---Pedro
----- Mensaje original -----
De: Karl Javorszky <karl.javors...@gmail.com>
Fecha: Martes, 18 de Diciembre de 2012, 3:55 pm
Asunto: spam filter
A: "Pedro C. Marijuan" <pcmarijuan.i...@aragon.es>
> Hi Pedro,
>
> happy Xmas and New Year!
>
> The spam filter has rejected Step Six. Maybe you could ask it to
> publish it?
>
> Best:
> Karl
> -----------------------------
>
Step Six of Learn to
> Count in Twelve Easy StepsWhat happened
> previously: Step 1.:We have introduced
> additional describing aspects of the logical sentence a+b=c. Next to a,b,c, we
> also make use of u=b-a, k=b-2a, t=2b-3a, q=a-2b, s=17-(a+b|c), w=2a-3b.Step
> 2.:We have introduced the
> collection of additions we shall use. We have generated the aspects
> {a,b,c,k,u,t,q,s,w} of the 136 smallest pairs of a,b.> Step 3.:We have shown
> that a sort
> on the data set – with any of the aspects as first, a different aspect as the
> second sorting argument – assigns a place to an addition; different sorts may
> assign different places.Step 4.:Ordering the data set on
> all pairs of aspects brings forth 72 variants of realisations of the order
> principle based on {<|=|>}. Some of the sorting orders are identical,
> some contradictory. The contradictions are visible on
> {place|amount|frequency|order}. The task is to consolidate the
> contradictions.Step 5.:Those sorting orders which
> to each addition assign identical sequential numbers build a common “clan”
> together. In the version of the Table presented here, 20 clans are visible.
> Members of a clan can differ on their number of teeth; the place of an element
> within a tie is not quite indeterminable but is rather dependent of how finely
> has the preceding sorting order had sorted previously.Step
> 6.:Reordering:After having eliminated the
> easy cases, where no reordering is needed, we now confront the mechanics of
> transforming the sequence alphabeta into the sequence gammadelta. (V[alfabeta,
> gammadelta]=.f.) This procedure is called “reordering” and as its effect, an
> element j that previously had the sequential place p1 has now the
> sequential place p2. (p1 {=|#} p2)Of specific interest is the
> case, wherein during a reorder, several elements have to move together in the
> course of a reordering. This is the main concept of the Twelve
> Steps.Explaining the main
> concept: The central concept can be
> pointed out exactly, by deictic methods. Before doing so, let us try to
> explicate the idea in colloquial speech. One knows from everyday life that a
> change of places may be an intricate business, as oftentimes someone has to
> vacate first the place in which a different person will come to sit, while the
> person expelled has to ask a 3rd one to liberate his place in turn,
> etc. This can get quite complicated, but normally people don’t talk much about
> it, as it normally has a solution that is evident to all. Rubik’s cube shows
> a specific instance of the
> central concept at work. (Please see 6.graph.Rubik). The concept presented
> here
> is similar to that made visible in the cube, but for the following points:
> there, 6 planes are given and 24 elements move while 6 are fixed; the task is
> deducting from the known results of the planes the collection and the sequence
> of the repetitive procedures (“operations”) that will result in the goal being
> achieved. Here, we have 136 elements, none of them fixed and the number of
> planes can be a subject of a spirited debate. The task here is to deduct the
> appearance of the planes after having gone thru all repetitive procedures
> (“operations”). In the case of the cube, the pleasure of having solved the
> puzzle encounters one as soon as one understands the procedures of which the
> resulting planes are an implication; here, success comes from having
> understood
> the planes that result from the applications of the procedures.In logistics
> one
> would speak of “merchandise in transit”, where one will use effective and
> expected matches between material and spatial references.Names for the main
> concept:Wittgenstein calls the idea
> discussed here a Sachverhalt (pls see around 2.01 in
> http://people.umass.edu/phil335-klement-2/tlp/tlp.html#bodytext).
> It appears ok to interpret, that the Sachverhalt is that “amount j is on
> place p”, while the Zusammenhang is that “j moves together within
> {j,j’,j’’,...etc} during a reorder from alphabeta into gammadelta”.
Heraclit has predicted the
> dynamic interdependence among realisations of the order without giving a
> specific name to it. He points out the “upward-downward path”
> (http://en.wikipedia.org/wiki/Heraclitus#Panta_rhei.2C_.22everything_flows.22).
Here, we may make use of
> the ideas – and the names – of the connotations of a convoy, chain, string or
> rhythm for the Zusammenhang and step or tact for the Sachverhalt.Data:The
> deictic definition is
> done by presenting a fragment of Table T (please see 6.num). Each line in
> Table
> T is one step in the process of reordering. We publish – next to the
> permutation of the first-level arguments that were used at the creation of the
> Table – order alphabeta (the “previous” order), order gammadelta (the “new”
> order), arguments (a,b), the sequential number for the Zusammenhang i,
> the step number j within string No. i [tact j in rhythm i],
> and sequential place previous (“from”) and sequential place new
> (“to”).Statistics:There is a quite wide range
> of properties for the chains. Interactive Figure 6.graph.1 shows the
> properties
> of convoys within a reorder, to discuss, how many strings are necessary for a
> reorder and how the number of tacts of the rhythms are distributed;6.graph.2
> shows in the form
> of a circle, which places are connected into a chain during a reorder;One may
> select and deselect
> specific chains to see the additions that are connected by a Zusammenhang in
> the form of points in the plane built by the axes x: alphabeta, y: gammadelta
> (6.graph.3); We keep track of the
> “carry” in the form of “carry_a” and “carry_b” (not shown here). The carry is
> the sum of the argument over all j in chain i.In the next Step (to appear
> 8th of January, 2013) we shall propose a type of chains to be used
> as standard units; in Steps 8 and 9 we build spaces with rectangular axes by
> using properties of the standard chains.Please allow me to wish you
> a nice Midwinter Break.
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