Above all, the Kutachi Project attempts to marry two notions of geometry. One is the accessibility that visually working with three dimensional geometric objects and relations allows. We seem to reason comfortably about space and use spatial affordances in reasoning in general. At the same time, the models of the world we use in Topoiesis are deeply geometric, but in more abstractly mathematical ways.
These two worlds already meet in elementary particle physics, and perhaps no more clear introduction to this is available than Yuval Ne’eman’s personal overview. His paper follows an informal talk he gave at the Haifa Congress, which he co- hosted. That talk was quite a bit more frank than this paper, frank about what is needed for next steps in physics. We believe those next steps apply to concept modeling as well.
The paper walks through a succinct history of geometry as the foundation of physics, and in particular the concept of symmetry. By this he means a specific notion using invariance and action-related translation, what we call cause. And he should know; using these principles of symmetry as a metatheory, he contributed mightily to our current insights into the nature of matter and action. He co-invented the standard model.
In the talk, he was more open about a battle raging for the soul of the next metatheory among physicists. He believed the future lies with the geometry he described and uses, but perhaps — he speculated — we need a more pure version than we can get with current group theory.
I believe this exactly mirrors the situation in logic, with both historical and mathematical parallels. In our case, our metatheory has to merge with our theory as they are both reasoning systems. Ne’eman and colleagues did not have this challenge, and could keep the two systems separate. That is, physicists could use group theory to model cause without having to assert that particles ‘understood’ the world that way.
Henning Genz in an earlier paper quotes Eugene Wigner, who had a hand in the Society: ‘the relation of the symmetries of the laws of nature to these laws is the same as the relation of the laws to the phenomena.’ For a practical example of this, see our FilmsFolded study.
This said, I believe it to be very likely that key visualizations in particle physics can be adapted from use by the Kutachi Project.
The Relationship to Kutachi
We exploit one of the most intuitive tools in physics, the Feynman Diagram, using category theory and adapted for our Bow-Tie user interface.
Links
Symmetries and their Breaking. Henning Genz. 1989. [Symmetry of Structure]
Symmetry as the Leitmotif at the Fundamental Level in the Twentieth Century Physics. Yuval Ne’eman. 1999. [Culture & Science v10] (not online yet)
The Kutachi essay on Feynman Diagrams. (not online yet)
The Kutachi essay on Quantum Clouds. (not online yet)