Monad

The second axiom, which is reminiscent of Mach s principle, also contains the seeds of Leibniz s Monads [reschQl]. All is process. That is to say, there is no thing in the universe. Things, objects, entities, are abstractions of what is relatively constant from a process of movement and transformation. They are like the shapes that children like to see in the clouds. The Einstein-Podolsky-Rosen correlations (see section 12.7.1) remind us that what we empirically accept as fundamental particles - electrons, atoms, molecules, etc. - actually never exist in total isolation. Moreover, recalling von Neumann s uniqueness theorem for canonical commutation relations (which asserts that for locally compact phase spaces all Hilbert-space representations of the canonical commutation relations are physically equivalent), we note that for systems with non-locally-compact phase spaces, the uniqueness theorem fails, and therefore there must be infinitely many physically inequivalent and... 

As the result of theoretical consideration of polycondensation of an arbitrary mixture of such monomers it was proved [55,56] that the alternation of monomeric units along polymer molecules obey the Markovian statistics. If all initial monomers are symmetric, i.e. they resemble AaScrAa, units Sa(a=l,...,m) will correspond to the transient states of the Markov chain. The probability vap of transition from state Sa to is the ratio Q /v of two quantities Qa/9 and va which represent, respectively, the number of dyads (SaSp) and monads (Sa) per one monomeric unit. Clearly, Qa(S is merely a ratio of the concentration of chemical bonds of the u/i-ih type, formed as a result of the reaction between group Aa and Ap, to the overall concentration of monomeric units. The probability va0 of a transition from the transient state Sa to an absorbing state S0 equals l-pa where pa represents the conversion of groups Aa. 

Dee, John. [Hieroglyphic monad]. The Hieroglyphic Monad. rhttp //www.alchemvlab.com/hieroglyphic monad.html. 

Dee, John.[Hieroglyphic monad]. The hieroglyphic monad translated by J. W. Hamilton-Jones. Edited by J.W. Hamilton- Jones. London Watkins, 1947. 76p. 

Norrgren, Hilde. Interpretation and the Hieroglyphic Monad John Dee s Reading of Pantheus s Voarchadumia. Ambix 52, no. 3 (Nov 2005) 217-245. 

Nature philosophers were conspicuously influenced by the monad and routinely developed their concepts of life around these irreducible units. 

On the other hand, the cells which Caspar Friedrich Wolff (1738- 1794) all but discovered in the chick embryo were rejected by determinists as lacking qualities required of monads.1 Following the early Eighteenth century ... 

Rudolf Virchow (1821- 1902) proceeded to replace tissues with cells as the dominant materialist monads of life and disease. According to his cell doctrine, all cells, and hence all life, came from cells No developed tissue can be traced back either to any large or small simple element, unless it be to a cell (quoted from Libby, 1922, p. 267). (The phrase, Omnis cellula e cellula , however, frequently attributed to Virchow, seems to have been first used as an epigraph by Francois Raspail (1794-1878) (Harris, 1999, P- 33)). 

The standard of testability (vulnerability to negation in the framework of a working hypothesis in the hypothetico-deductive mode or of simultaneous adjustment in the framework of Bayesian modeling) is probably the toughest standard demanded in science. Ideas as old as the monad are not necessarily tested and validated by repeated corroboration. Indeed, they may be untested and powered by inertia. Ideas which are testable are those for which there are alternatives otherwise ideas are either unnecessary or untestable. Since Dennett has already asserted that reductionism permits no alternative, monophyly as such would have to be untestable, but, before condemning it to the rank of scientific dogma, let me cite two cases in which monophyly was tested as the alternative to a different (polyphylic) hypothesis. 

A preferable system is poly(p-fluorostyrene) doped into poly(styrene). Since rotations about the 1,4 phenyl axis do not alter the position of the fluorine, the F spin may be regarded as being at the end of a long "bond" to the backbone carbon. In standard RIS theory, this polymer would be treated with dyad statistical weights to automatically take into account conformations of the vinyl monomer unit which are excluded on steric grounds. We have found it more convenient to retain the monad statistical weight structure employed for the poly(methylene) calculations. The calculations reproduce the experimental unperturbed dimensions quite well when a reasonable set of hard sphere exclusion distances is employed. 

More specifically, the basic notions of a Turing Machine, of computable functions and of undecidable properties are needed for Chapter VI (Decision Problems) the definitions of recursive, primitive recursive and partial recursive functions are helpful for Section F of Chapter IV and two of the proofs in Chapter VI. The basic facts regarding regular sets, context-free languages and pushdown store automata are helpful in Chapter VIII (Monadic Recursion Schemes) and in the proof of Theorem 3.14. For Chapter V (Correctness and Program Verification) it is useful to know the basic notation and ideas of the first order predicate calculus a highly abbreviated version of this material appears as Appendix A. 

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