A Kind of a New Music Box

Some remarks how to use the new toy: Box PPSVB x.11

This entry tries to give an access to an interesting tool that easily allows to compare the sonic and graphic deep-structure of basic computational concepts.

I mentioned before that morphograms are not just pre-semiotic structures but are at the same time also to be conceived as rules.

Some of those rules are applied to define the production rules of morphic cellular auto mata (CA).

Independently of the heavy stuff of conceptualization, the proposed Box PPSVB x.11 is also a very entertaining device: 

A Tool Box for sonic and visual deep-structural adventures.

http://transhumanism.memristics.com/CA-Comparatistics/PPSVB.x11D.html 

You are invited to download tracks at
https://soundcloud.com/morphicalgorithms/tracks

The intention is in no sense to simulate any kind of human sonic or conceptual achievements.

Maybe, the algorithms are manifesting themselves without such recourse to the human history of music and graphics.

Comparition of

classical, indicational and morphic Cellular Automata

If words are not going to be listened to and notions are not  going to be understood, there is still a chance of showing some pictures and making some noise, combined with an offer to motivate to enjoy or to conceive their differences and also to try to overcome the attitude of blind and deaf denial of concepts and other structurations.

This little exercise concentrates on just 3 fundamentally different ways of writing as they are involved in the general concept of 1 D cellular automata and are thematically, at first, restricted to the study of the single archetypical figure of Sierpiński triangles.

Firstly, the classical CA,
secondly, the indicational CA,
thirdly, the morphogrammatic CA.

Therefore I introduce a new kind of an epistemological comparatistics, i.e. a comparison of graphic and sound systems in respect of their paradigmatical structures based on different kinds of writing systems and their CA rule sets.

Aspects of the dynamics of CA systems are not yet in the focus.

Furthermore, the proposed approach to a formalization of morphogrammatic CA is still more a simulation than a genuine implementation of the very concept.

The classical paradigm is well studied, mathematically and philosophically, and got a decisive elaboration with the Opus Magnum of Stephen Wolfram's A New Kind of Science (NKS).

Here, for the classical paradigm, I refer just to some 1D CA examples with the set of CA rules.

The indicational way of writing and thinking, introduced by George Spencer Brown with his Laws of Form, is not specially well elaborated and got a very controverse reception from the side of mathematicians and logicians.

Indicational CAs are divided into:
a) first-order indCA (in the sense of the Calculus of Indication (CI), ruled by the set of ruleCI,
b) as second-order (enactional) rules ruleCIR,
c) as third-order rules ruleRCI, and
d) the rules of ruleCIRT.

ruleCI[{a_,b_,c_,d_}] :=
       Flatten[{rca[{a}],rca[{b}],rca[{c}],rca[{d}]}]

ruleCIR[{a_,b_,c_,d_,e_, f_,g_,h_,i_, k_}] :=
       Flatten[
{cir[{a}],cir[{b}],cir[{c}],cir[{d}],
cir[{e}], cir[{f}], cir[{g}],
cir[{h}], cir[{i}], cir[{k}]}]

ruleRCI[{a_,b_,c_,d_,e_, f_,g_,h_,i_, j_,
             k_,h_,l_,m_,n_,o_,p_,q_,r_,s_}] :=
   Flatten[{
rci[{a}],rci[{b}],rci[{c}],rci[{d}],
rci[{e}],rci[{f}],rci[{g}],rci[{h}],
rci[{i}],rci[{j}],rci[{k}],rci[{h}],
rci[{l}],rci[{m}],rci[{n}],rci[{o}],
rci[{p}],rci[{q}],rci[{r}],rci[{s}]
}]

ruleCIRT[{a_ }] :=
   Flatten[{
ruleCIRT[{a}]
}]
Morphogrammatic CAs are divided into:

a) classical morpho CAs,CA^(3,2), ruled by ruleCl, with complexity 4
b) trans-contextural CAs, CA^(3,3), ruled by ruleM, with complexity 5
c) trans-contextural CAs, CA^(3,4), ruled by ruleMN, with complexity 6 and
d) trans-contextural CAs, CA^(3,4), over-determined, ruled by ruleMNP, with complexity 7, additionally,
e) trans-contextural CAs, CA^(4,2), over-determined, ruled by ruleM42, with complexity 8.

ruleCl[{a_,b_,c_,d_}] :=
       Flatten[{rca[{a}],rca[{b}] ,rca[{c}], rca[{d}]}]

ruleM[{a_,b_,c_,d_,e_}] :=
       Flatten[{rca[{a}],rca[{b}],rca[{c}],rca[{d}],rca[{e}]}]
 
ruleMN[{a_,b_,c_,d_,e_,f_}] :=
       Flatten[{rca[{a}],rca[{b}],rca[{c}],rca[{d}],rca[{e}], rca[{f}]}]

ruleMNP[{a_,b_,c_,d_,e_,f_, g_}] :=
       Flatten[{rca[{a}],rca[{b}],rca[{c}],rca[{d}],
rca[{e}],     rca[{f}], rca[{g}]}]

ruleM42[{a_,b_,c_,d_,e_,f_,g_,h_}] :=
       Flatten[{rlc[{a}],rlc[{b}],rlc[{c}],rlc[{d}],
                      rlc[{e}], rlc[{f}],rlc[{g}],rlc[{h}]
 }]  
After Niklas Luhmann got mesmerized by the actions of the magician Heinz von Foerster (Second Order Cybernetics), it nevertheles nurtured a whole movement over decades of mainly German theoretical sociologists.
 

Finally, the morphogrammatic endeavor is more or less unknown to the academic public.

It is certainly not my aim to enter into this 'debate' about 'deviant' or 'cranky' (Hao Wang) formal languages.

There is also no need to go back to the Ancient Chinese, Pythagoras or Kepler to connect conceptions with numbers and sound.

It suffice to reduce the apparatus to an elementary construct that has shown to be quite powerful.

Cellular automata have a long history but might have come to the public awareness only by computer-supported experiences.

The challenge is to hear and see concepts, i.e. structurations, and not just to perceive sounds and pictures.
This seems to be possible mainly by a comparison of the (deep)structure of different sound and graphic systems.

Epistemologically, different perceptive systems are not properly defined by their internal differences but by the difference between their deep-structural differentiations.

A nice, and well developed structuration is established with the difference of classical, indicational and morphogrammatic writing systems as proposed in my texts towards a general theory of writing systems, called graphematics.

Also sounds of different graphematical systems are heard and pictures are seen, there is nevertheless a crucial difference in their mode of production.

The slogan, What you see is what you get, applies properly for classical approaches of a visualization of concepts and a way to present sound.

The indicational approach is still in the framework of the classical semiotic conceptualizations and modes of writing. Because the fundamental 'topological invariance' of its mode of writing which is not directly perceivable it demands for some combinatorial manipulations of the notation to be possible to perceive in a classical mode of perception its genuine abstraction properly.

The morphogrammatic approach is denying the obvious WYSIWIYG concept. Therefore, What you see and hear is not what it is. Morphogrammatics is a part of kenogrammatics. The term 'keno' in kenogrammatics derived from the Greek kenoma (\[Kappa]έ\[Nu]\[Omega]\[Mu]\[Alpha], emptiness) says it all: there is nothing to tell.

The WYSHINWIS, "What You See and Hear Is Not What It iS", challenges towards a new kind of perception: the cognitive perception, that is at once, a perceptive cognition.

The set of paradigms, the classical, the indicational and the morphogrammatic, is certainly not exclusive. There are other kinds too of conceptualizations and writing systems to recognize. This is explicitly developed in the research field of graphematics, the morphosphere(s).

Hence, the aim of this little exercise presented here, is to learn and to train the brain to recognize the difference between different conceptual systems as they are presented to our perception by sounds and graphics and not their intrinsic beauty or lack of it.

Neither are there any mathematical or philosophical considerations included in this proposal of an exercise.                            

The exercise is, at first, concentrated on the single form of Sierpiński triangles, and its variations in graphic and sonic environments. 

What do we have to do to follow this invitation?

Compare, contemplate and analyze your experiences.


The presented code for the Sound Box is based on David Burraston's program "Music Box Toy with Elementary Cellular Automata". 

http : // demonstrations.wolfram.com/MusicBoxToyWithElementaryCellularAutomata/Wolfram Demonstrations Project 
The rules of the presented CA had been introduced by the author as an experimentation to deal with morphogrammatic and indicational CA.