Parry Moon


Parry Hiram Moon was an American electrical engineer who, with Domina Eberle Spencer, co-wrote eight scientific books and over 200 papers on subjects including electromagnetic field theory, color harmony, nutrition, aesthetic measure and advanced mathematics. He also developed a theory of holors.

Biography

Moon was born in Beaver Dam, Wisconsin, to Ossian C. and Eleanor F. Moon. He received a BSEE from University of Wisconsin in 1922 and an MSEE from MIT in 1924. Unfulfilled with his work in transformer design at Westinghouse, Moon obtained a position as research assistant at MIT under Vannevar Bush. He was hospitalized for six months after sustaining injuries from experimental work in the laboratory. He later continued his teaching and research as an associate professor in MIT's Electrical Engineering Department. He married Harriet Tiffany, with whom he had a son. In 1961, after the death of his first wife, he married his co-author, collaborator and former student, Domina Eberle Spencer, a professor of mathematics. They had one son. Moon retired from full-time teaching in the 1960s, but continued his research until his death in 1988.

Scientific contributions

Moon’s early career focused in optics applications for engineers. Collaborating with Spencer, he began researching electromagnetism and Amperian forces. The quantity of papers that followed culminated in Foundations of Electrodynamics, unique for its physical insights, and two field theory books, which became standard references for many years. Much later, Moon and Spencer unified the approach to collections of data, with a concept they coined "holors". Through their work, they became disillusioned with Albert Einstein's theory of relativity and sought neo-classical explanations for various phenomena.

Holors

Moon and Spencer invented the term "holor" for a mathematical entity that is made up of one or more "independent quantities", or "merates" as they are called in the theory of holors. With the definitions, properties and examples provided by Moon and Spencer, a holor is equivalent to an array of quantities, and any arbitrary array of quantities is a holor. The merates or component quantities themselves may be real or complex numbers or more complicated quantities such as matrices. For example, holors include particular representations of:
Note that Moon and Spencer's usage of the term "tensor" may be more precisely interpreted as "tensorial array", and so the subtitle of their work, Theory of Holors: A Generalization of Tensors, may be more precisely interpreted as "a generalization of tensorial arrays". To explain the usefulness of coining this term, Moon and Spencer wrote the following:
And, as indicated in the promotional blurb on the back of the book, part of the value of holors is the associated notational conventions and terminologies, which can provide a unified setting for a variety of mathematical objects, as well as a general setting that "opens up the possibility to devise a holor for a new... application, without being limited to a few conventional types of holor".
Although the terminology relating to holors is not currently commonly found online, academic and technical books and papers that use this terminology can be found in literature searches. For example, books and papers on general dynamical systems, Fourier transforms in audio signal processing, and topology in computer graphics contain this terminology.
At a high level of abstraction, a holor can be considered as a whole — as a quantitative object without regard to whether it can be broken into parts or not. In some cases, it may be manipulated algebraically or transformed symbolically without needing to know about its inner components. At a lower level of abstraction, one can see or investigate how many independent parts the holor can be separated into, or if it can't be broken into pieces at all. The meaning of "independent" and "separable" may depend upon the context. Although the examples of holors given by Moon and Spencer are all discrete finite sets of merates, holors could conceivably include infinite sets, whether countable or not. At this lower level of abstraction, a particular context for how the parts can be identified and labeled will yield a particular structure for the relationships of merates within and across holors, and different ways that the merates can be organized for display or storage. Different kinds of holors can then be framed as different kinds of general data types or data structures.
Holors include arbitrary arrays. A holor is an array of quantities, possibly a single-element array or a multi-element array with one or more indices to label each element. The context of the usage of the holor will determine what sorts of labels are appropriate, how many indices there should be, and what values the indices will range over. The representing array could be jagged or of uniform dimensionality across indices. A holor can thus be represented with a symbol and zero or more indices, such as —the symbol with the two indices and shown in superscript.
In the theory of holors, the number of indices used to label the merates is called the valence. This term is to remind one of the concept of chemical valence, indicating the "combining power" of a holor. The example holor above,, has a valence of two. For valence equal to 0, 1, 2, 3, etc., a holor can be said to be nilvalent, univalent, bivalent, trivalent, etc., respectively. For each index, there is number of values that the index may range over. That number is called the plethos of that index, indicating the "dimensionality" related to that index. For a holor with uniform dimensionality over all of its indices, the holor itself can be said to have a plethos equal to the plethos of each index. So, in the special case of holors that are represented as arrays of N-cubic shape, they may be classified with respect to their plethos and valence, where the plethos is akin to the length of each edge of the and the number of merates is given by the "volume" of the hypercube.
If proper index conventions are maintained then certain relations of holor algebra are consistent with that of real algebra, i.e., addition and uncontracted multiplication are both commutative and associative. Moon and Spencer classify holors as either nongeometric objects or geometric objects. They further classify the geometric objects as either akinetors or oudors, where the akinetors transform as
and the oudors contain all other geometric objects. The tensor is a special case of the akinetor where. Akinetors correspond to pseudotensors in standard nomenclature.
Moon and Spencer also provide a novel classification of geometric figures in affine space with homogeneous coordinates. For example, a directed line segment that is free to slide along a given line is called a fixed rhabdorGreek ῥάβδος "rod".

Books

  • Parry Moon, The Scientific Basis of Illuminating Engineering, McGraw-Hill, 608pp. .
  • Parry Moon, Lighting Design, Addison-Wesley Press, 191pp. .
  • Parry Moon, A Proposed Musical Notation, .
  • Parry Moon & Domina Eberle Spencer, Foundations of Electrodynamics, D. Van Nostrand Co., 314pp. .
  • Parry Moon & Domina Eberle Spencer, Field Theory for Engineers, D. Van Nostrand Co., 540pp. .
  • Parry Moon & Domina Eberle Spencer, Field Theory Handbook: Including Coordinate Systems, Differential Equations and Their Solutions, Spring Verlag, 236pp. .
  • Parry Moon & Domina Eberle Spencer, Vectors, D. Van Nostrand Co., 334pp. .
  • Parry Moon & Domina Eberle Spencer, Partial Differential Equations, D. C. Heath, 322pp. .
  • Parry Moon, The Abacus: Its History, Its Design, Its Possibilities in the Modern World, D. Gordon & Breach Science Pub., 179pp. .
  • Parry Moon & Domina Eberle Spencer, The Photic Field, MIT Press, 267pp. .
  • Parry Moon & Domina Eberle Spencer, Theory of Holors, Cambridge University Press, 392pp. .

    Papers

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