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Notes

[Notebook Turkey, DB 55]

[Sunday 17 November 2002 - Saturday 14 November 2002]

[page 110]

Sunday 17 November 2002
Monday 9 November 2002
Tuesday 10 November 2002
Wednesday 11 November 2002
Thursday 12 November 2002

Our basic model of a function is a mapping of the Universe onto itself, ie a mapping of the natural numbers to themselves. The natural numbers here are considered as static labels, and a function is in effect a relabelling of the numbers, which we think of physically as measuring physical acts measured by one quantum of action.

Each function is itself an action, but usually a more complex action that a quantum. Since there are ℵ0 natural numbers representing ℵ0 different quanta, there are ℵ1 possible functions, each requiring a set of ℵ0 actions to complete, one for each relabelling of each of the acts represented by a natural number.

We implement critical points (Casti, p 89) by the transfinite transition, a new world.

Each point in 1 is a function on 0 and so on.

[page 136]

PEER = NOT OWNER = NOT PROPERTY

Most domestic violence arises because people treat one another as possessions rather than peers.

The structure of four space arises from its isomorphism with the quadruple action (time), energy, momentum ? [momentum is a vector, and so may have any number of dimensions?]

Friday 13 November 2002
Saturday 14 November 2002

 

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Further reading

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Casti, John L, Five Golden Rules: Great Theories of 20th-Century Mathematics - and Why They Matter, John Wiley and Sons 1996 Preface: '[this book] is intended to tell the general reader about mathematics by showcasing five of the finest achievements of the mathematician's art in this [20th] century.' p ix. Treats the Minimax theorem (game theory), the Brouwer Fixed-Point theorem (topology), Morse's theorem (singularity theory), the Halting theorem (theory of computation) and the Simplex method (optimisation theory). 
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