This one is simple.
The idea is that preliterate or other-literate cultures did not consist of dummies. They were sophisticated thinkers, more or less like us. A challenge then is to discover the forms they used to shape their analytical imaginations. The folks that study this by and large are anthropologists who want to understand variouscultures.
Some of the founders of the symmetry society mentioned here, were ethnomathematicians and a good dip into the subject are the papers by Paul Gerdes on our symmetry site. The reason ethnomathematics and symmetry are so bound is that symmetric forms seem to universally be preferred by cultures that don't use our notational system. One could infer from this alone that symmetry is somehow basic to either the order in the universe or ourability to see it.
This matters to us because we are all about communicating deep, abstract concepts by form. We have three models to study.
- We have a number of pictorial designs: sand paintings, rock painting and carving, objects of one kind and another. Some of these carry the simple grace of katachi, and we can tell by simple viewing that there is something deep going on. Others are patterns, sometimes beyond order, like the dots of Australian Aborigines.
- We have a special class of objects in knots. This is an interest of mine, because we almost certainly had knots well before we had language as we understand today. We know of knots for affixing stone tools as old as 125,000 years ago. We can see elaborate hair braiding in 35,000 year old sculpture. Some of the crossmarks over animals on cave paintings could designate how to cut continuous loops of leather for closed-loop knots (like we know in Cat's Cradle. In fact string figures are so common world-wide they must be quite ancient. In Europe, we have lace that tells stories through a knot grammar. In Central America, we have histories recorded in knot arrangements.
- And we have gesture. We know that early non-modern humans taught each other complex skills millions of years ago. Millions! Compare that to probably less than 4,000 years of written language. We don't know how they communicated but a consensus is that the physiological capability for language is modern, possibly as recent as 60,000 years ago. Some theorize that it was collaboration by language that put Neanderthals at a disadvantage. At any case, there was a period where the language had to be gestural (and demonstrative).
I propose all of these as inspirations for some Kutachi-influenced metaphors.
- String figures
- Gestural calligraphic knots
- Body shapes and movement
Takaki and Petroglyphs
Polymath advisor Ryuji Takaki has a few influences on this project. One is his studies of of kanji/hansi toward creating a new system.
Of interest in this context is his study of petroglyphs, images carved into rock. They are found everywhere, with the apparent range of 40,000 -3,000 years old. Some common elements appear across the globe, especially in the range of 5- 6,000 years old, prompting speculation that they indicate some common tendency of the brain in managing concepts.
Takaki studies those in the southeastern former Soviet republics. decoding the grammar he perceives, he speculates they are distributed narratives about the area. He has developed a set of form metrics to help analyze them.
A small but growing group feel this way about our not so distant ancestors as well. early modern European humans of 35,000 years ago may well have been as sophisticated as us. In fact, their brains were a bit bigger.
The missing piece of course is that they had no way of externally recording insights. Ideas could not promulgate to others, much less to us.
I personally find the idea that they had rich lives attractive, and I can well imagine that they many of them have far better perceptive abilities, cognitive structures and imaginations than we do. Language is a great thing, including the language of mathematics. But it makes it too easy for us to stop when we absorb an idea that is good enough and in any case is the default for everyone we know.
I'm best when I ignore the scholars who went before, no matter how brilliant. The tools you make yourself are always better than those you inherit from folks who make the wrong things.
Workers in this field generally have no stance on whether the mathematics we use today is a naturally revealed part of the raw universe, or a set of imperfect conventions based on constraints of the brain, the need to communicate and/or arbitrary notions of coherence.
It doesn't matter to the Kutachi Project. But once you free yourself from binding technology to insight, and once you place yourself in a vocabulary of pure form, it is easy to believe that all three of those constraints are at work.