Mindscapes

Mindscapes and the Plus One Perspectives

**A Problem Understanding**
Few recognize the Reverend Charles Lutwidge Dodgson (Oxford Don and Mathematical Lecturer of Christ Church) as the name of the author of the delightful tales of Alice, who fell down a rabbit hole into a

*Wonderland *where logic and reality were both reversed. The experience changed him so that he became Lewis Carroll. He revisited the world of the Mad Hatter, the White Queen and the Bellman who spoke in languages of poetry, riddles and games. Carroll's "enchanting nonsense" charmed children and critics from the era of Queen Victoria to the 20

^{th} Century.

It also charmed serious mathematicians. For them and Carroll the differences between the ordered world of mathematics and the reasoning of real world people and their leaders were both a tragicomedy and an enigma. Not realizing the order and beauty that knowledge of mathematics could bring to the world was tragic: yet defying its

*laws* of thought could be ridiculously funny. Carroll teamed up with political cartoonist John Tenniel to dramatically illustrate a mathematician's frustration in Alice's return visit to the reversed world in

*Through the Looking Glass*.

His point is better appreciated if you imagine a mathematician carefully framing an important, real world, politically sensitive problem as a puzzle; its solution as a game, all backed up by elegant mathematical equations. Alice's reaction after reading JABBERWOCKY (a poem in the White King's enormous memorandum–book) mocks a typical political response,

"It seems very pretty, " she said when she had finished it, "but it's rather hard to understand! " (You see she didn't like to confess, even to herself, that she couldn't make it out at all. ) "Somehow it seems to fill my head with ideas–only I don't exactly know what they are! However,

*somebody* killed

*something:* that"s clear, at any rate– "

**Mindscapes and Mathematical Psychology**
But real world events in the 20

^{th} Century forced the mathematicians to understand something that politicians were periodically forced to accept, a world the reverse of one governed by revered theorems, strict laws and inflexible rules. Philosophers Bertrand Russell and Alfred North Whitehead built a mirror called meta–mathematics. When mathematicians, with the aid of powerful computers, went through Russell and Whitehead' looking glass they returned to the real world in a state of shock! There were huge holes in the world of numbers and some of the numbers are monsters that do not compute. Rather than divine law manifest, mathematics was only a magnificent artifact of human psychology. What's more, mathematics was subject to the same laws of evidence as any other branch of cognitive psychology. Whether practiced as games, puzzles or rules of thought, mathematics is exclusively psychological in ways that physics and biology are not.

Mindscapes emerged out of the revelation that despite understanding common equations and mathematics, people still had

*irreconcilable differences that precluded cooperation.* Naturally cultural anthropology was the discipline most sensitive to cooperation difficulties on a global scale. Anthropology's formulation of mindscapes used color vision as its psychological metaphor. Psychological topology (a very special kind of geometry) was suggested as the mathematical metaphor. General Systems integration backed up anthropology. See

(Elements). Consequently, genetics, perception, learning, games, language, bio psychology, personality, language, learning and ethics can all be seen to converge in an anthropological formulation. The result is a topological psychology that permits simple description of conflict resolution problems.

**Seven plus One and a Mirror**
Nobody but mathematicians understands topology in five and six dimensions. So in the spirit of Lewis Carroll/John Tenniel, Silverington uses George Lakoff's 21

^{st}; Century linguistics to formulate metaphors that frame complex organization problems and solutions in the form of stories and games. Mindscapes emulate Alice's experience of going through a mirror to a Picasso type world where everything is seen from either four or six perspectives–simultaneously. The tragicomedy of the real world is better appreciated when you return with your new perspective, a perspective called simply "Plus One".

**Organic solutions to cultural problems - brochure**
mindscapes.pdf - 179 Kb

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