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Symmetry Under Transformation
Cubical Maze Module
Sommer Cube (S3). What it is. What it does.
The Answers take a little explaining: follow multiple perspectives -- mental and manual rotation: the sciences, art, and music -- with Links.
Informal Reasoning: "Use it or lose it".
S3 is predicated on switchiness (compound switching), juxtaposition of square and circle across three dimensions, and binary opposition, the bit (binary digit), the basic unit of information, which can have only one of two values (0/1), and can be physically implemented with a two-state device; S3 manipulator seeks best paths (optimization) in an unfriendly (blocking), gravity-dependent distributed network. A topology of binary (asynchronous) and analogical reasoning.
Self-reference. Hands and Mind.
Cognitive engagement. Cognitive tool.
Rolling Ball Switch
four bit (0/1) -- nibble Asynchronous Binary Processor (0/1)
The Smart Block. The Upgrade: Hands and Mind.
Binary and Analogical Reasoning.
"Analogy pervades all our thinking, our everyday speech and our trivial conclusions as well as artistic ways of expression and the highest scientific achievements."
G. Polya, How to Solve It (1945)
S3 is a hybrid: combined puzzle and maze and rolling ball device, where intuition, naive commonsense reasoning, is a prerequisite -- logic is necessary but not sufficient. Thinking within a topology of paradox. Reasoning as play: invitation to Double-Loop learning (intrinsically destabilizing).
A simple block and ball networking system which leverages full-spectrum cognitive / perceptual processing, learning algorithms, and the art of design, with an emphasis on advanced thinking and intuition -- and its reflection upon itself (not "mere facts", but principles): functional relations, particularly goals and feedback (What information is relevant? What are my assumptions? Are they justified?)
As Artificial Intelligence’s John McCarthy put it, “the first task is to define even a naive common sense view of the world precisely enough to program a computer [S3] to act accordingly.”
S3 is about the essence of artificial intelligence: the Human in a situation where logic will fail.
S3 is an eminently measurable interface (invites interaction and responds to it), a working definition of that naive commonsense reasoning (in a paradoxical environment) versus logical algorithms. The functionality of machine, the learning of organism.
And it’s fun.