From a stain on the wall to five visual languages

Do you know about the “stain on the wall”  creativity technique of Leonardo da Vinci? Here is a quote [source used]:

I will not forget to insert into these rules, a new theoretical invention for knowledge’s sake, which, although it seems of little import and good for a laugh, is nonetheless, of great utility in bringing out the creativity in some of these inventions.    This is the case if you cast your glance on any walls dirty with such stains or walls made up of rock formations of different types.  If you have to invent some scenes, you will be able to discover them there in diverse forms, in diverse landscapes, adorned with mountains, rivers, rocks, trees, extensive plains, valleys, and hills. You can even see different battle scenes and movements made up of unusual figures,  faces with strange expressions,  and myriad things which you can  transform into a complete and proper form constituting part of similar walls and rocks. These are like the sound of bells, in whose tolling, you hear names and words that your imagination conjures up.

I propose to you  five graphical formalisms, or visual languages, towards the goal of “computing with space”.

They all come from a “stain on the wall”,  reproduced here  (is the beginning of the article What is a space? Computations in emergent algebras and the front end visual system, arXiv:1009.5028),  with  some links  to more detailed explanations and related material which I invite you to follow.

Or better, to threat them as  a stain on the wall. To share, to dream about, to create, to discuss.

In mathematics “spaces” come in many flavours. There are vector spaces, affine spaces, symmetric spaces, groups and so on. We usually take such objects as the stage where the plot of reasoning is laid. But in fact what we use, in many instances,are properties of particular spaces which, I claim, can be seen as coming from a particular class of computations.

There is though a “space” which is “given” almost beyond doubt, namely the physical space where we all live. But as it regards perception of this space, we know now that things are not so simple. As I am writing these notes, here in Baixo Gavea, my eyes are attracted by the wonderful complexity of a tree near my window. The nature of the tree is foreign to me, as are the other smaller beings growing on or around the tree.  I can make some educated guesses about what they are: some are orchids, there is a smaller, iterated version of the big tree. However, somewhere in my brain, at a very fundamental level, the visible space is constructed in my head, before the stage where I a capable of recognizing and naming the objects or beings that I see.

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The five visual languages are to be used with the decentralized computing model called Distributed GLC.  They point to different aspects, or they try to fulfil different goals.

They are:

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