An Ear for Pythagorean Harmonics: the complete technical paper

The complete technical Timing Devices paper is available for download, a .pdf file, 460 kB.

...   Abstract of the Paper

...   Contents of the Paper

...   Related Works by the Author

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Abstract of the Paper

"Timing devices" are proposed electronic inventions to be used in operating models of brains. Timing device designs, e.g., "an Ear for Pythagorean harmonics," resemble schematic diagrams for standard electronic circuits - but the principles are new and different. A "primal timing device" is defined and developed into a kit of complex timing devices. Proposed assemblies of timing devices detect stimuli, control muscle-like action and perform mathematical operations.

Signals in timing device assemblies are made up of "pulses," each lasting for only an instant. Device specifications and operational variables are stated in terms of "timing intervals." Pulse patterns and timing intervals control and change each other. Some patterns change abruptly and others go through gradual changes. Pulses and the timing of pulses make up all the phenomena.

A pulse is an idealization of an "action potential" that operates in nerves. Assemblies of neuron-like timing devices generate, organize and direct pulses. Timing device projects are stages in development of "engineered organisms" that perform activities similar to behaviors of animals, especially quick switching between behaviors, e.g., like a flock of birds that is startled into flight.

In an Ear for Pythagorean harmonics, "difference devices" perform frequency subtractions on pulse streams. Repeated subtractions generate an array of internal signals from a pair of input signals. "Balancing units" can produce a net null signal - silence - that opens a "gate" and denotes a specific ratio of input frequencies.

Simple ratios identify "Pythagorean harmonics." For example, if the two input tones are 660 Hz (pulses per second) and 440 Hz, the Ear detects and signals the presence of a "perfect fifth" based on the ratio of 3/2; and the same result occurs if the two input tones are 900 Hz and 600 Hz. If, however, the two input tones are 880 Hz and 660 Hz, the Ear detects and signals the presence of a "perfect fourth" based on the ratio of 4/3.

Operational features of the Ear parallel aspects of human auditory experience. Design features of the Ear suggest further ways to use timing devices to model behaviors of animals and the capacities of animals to select and switch behaviors.

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Contents of the Paper

  1. Introduction:  Timing Devices Are a New Way to Make Models of Brains.

  2. The Primal Timing Device
    1. Definition of the primal timing device.
    2. Cycles: simple assemblies of primal timing devices.
    3. Pulse wave in a string of primal timing devices.

  3. Complex Timing Devices
    1. Timing devices that operate according to the one-pulse trigger rule
      1. Pulse train generator; coupled timing devices.
      2. Pulse waves in a string of coupled timing devices.
    2. Timing devices that operate according to the two-pulse trigger rule
      1. Frequency detector.
      2. Frequency analyzer.
    3. Timing devices with modulation junctions
      1. Gate modulation: silence detector.
      2. Graded modulation: sensitive hair.
      3. Delay modulation: summation device.

  4. Timing Device Signals
    1. Signals in timing devices occur in several forms, including ideal pulse trains, ideal pulse bundles and irregular approximations of ideal signals.
    2. In the models, pulse bundles drive twitches of muscle-like fibers.
    3. A streaming device uses a ratio (n/m) to calculate output pulse periods from those of an input pulse stream, serving as a frequency multiplier.
    4. Modified streaming devices convert signals between forms:
      1. Converting pulse bundles into a train-like sequence of segments.
      2. Converting pulse bundles into pulse bundles related by a ratio (n/m).
      3. Generating pulse bundles from pulse trains.

  5. Differences and Balances in Timing Device Systems
    1. Difference devices and balancing units.
    2. Engineered organisms that move and sense from a position of balance.
    3. Delays and matches, echoes and beats.
    4. An Ear for Pythagorean harmonics:
      1. The phenomena of Pythagorean harmonics.
      2. Design for the Ear.
      3. Human experience is congruent with operating principles of the Ear.

  6. Conclusion: The Leading Power of Silence

The complete Timing Devices paper is available for download, a .pdf file, 460 kB.

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Related Works by the Author

An Ear for Pythagorean Harmonics is part of the my larger work, where device designs for brains are the basis of a psychological model and the psychological model is used to investigate institutional activities, including physics and natural science, the laws of the courts and the Christian religion. The focus of interest in the larger work is personal freedom, especially as expressed through choices and selections made by persons in institutional situations. Of course, we exercise freedom in wilderness too, but institutional situations are more susceptible to analysis.

The engineering and scientific works set forth principles of device design that can be developed in several directions. Writings about psychological, philosophical, institutional, personal and spiritual matters are more tentative and even sketchy  – but they provide long-range motivation and have suggested particular inventions and pathways of development. For example, the design of the Ear for Pythagorean harmonics had its inception in my personal auditory investigations into "Duo Seraphim" by Claudio Monteverdi, discussed on the Shimmering Silences website, linked below.

I.    Engineering and Scientific Works
Quad Nets (2006)-- Quad Nets is the chief engineering and scientific presentation of my "device models of brains." Timing Devices, discussed here, began as a simplified version of the Quad Net Model.

Quad Nets website -- separately organized

web page on the full paper titled Quad Nets: Material Foundations for Thermal Device Models of Brains

download Quad Nets paper. (.pdf format, 1.1 Mb)
Timing Devices (2007-2009) has developed from a simplified version of the Quad Net Model into an independent area of investigation. The course of development includes possible future projects.

The complete Timing Devices paper is available for download, a .pdf file, 460 kB. Another web page presents the Abstract of the paper and the listing of Contents.

The separate website, link, Shimmering Silences in Beautiful Music (2009) presented initial investigations and original constructions that developed into the present Ear for Pythagorean Harmonics, along with an earlier version of the Timing Devices paper, titled An Ear for Pythagorean Harmonics: Mathematical Processing in Brain Models Built From "Timing Devices," (2009), a .pdf file 212 kB.

The separate web page, "Timing Devices or Why Brains Are Not Computers," link, is now the setting for the first, 2007, version of the Timing Devices paper, .pdf file, 363 kB.

The separate web page, Dancer - Shimmering Gaits of a Six-Legged Engineered Organism link, contains a proposed series of projects for construction of systems for engineered organisms (artificial animals) to be built from timing devices and Quad Net assemblies, starting with a "Utricle" that detects the orientation of an organism with respect to gravity and progressively leading upwards to a six-legged organism that uses a variety of coordination patterns ("gaits") in attempts to navigate a broken and obstructed terrain.

See also "Advanced Note: Convolution Timing Devices," a .pdf file (68 kB) link, preparatory for the present Timing Devices paper.

II.    Philosophy of Science
"Brains are computers" is part of a belief system that I call the Mechanical Cosmology and that includes other propositions: "all things are made of atoms" and "the Universe is governed by laws of physics, like the law of conservation of energy."

Beliefs about atoms and laws of physics have been developmentally productive and wonderfully fruitful in practical ways  – in contrast to "brains are computers"  – but they are also false and misleading. There are no "atoms." Atoms are mental constructions and they do not appear in reality. It is possible to buy materials, such as minerals, metals, refined chemical reagents, vegetable materials, animal materials and synthetic materials; but it is not possible to buy "atoms." The material that is closest to "atoms," refined helium, shows complex, collective, "non-atomic" properties when the temperature gets very low and the helium liquifies.

Energy is never "conserved." "Conservation of energy" is an ideal that is never attained, although billiard tables, vaccuum chambers and ball bearings rather approach it and make exact calculations possible under some circumstances.

Physicists believe that all of reality is made up of particles and laws of physics. Some parts of reality are well modeled by methods based on this belief but other parts of reality  – e.g., the reality of persons and the reality of conflicting principles of social organization  – cannot even be recognized. The physicists' belief is formed through study of imaginary conservative systems of atoms that can never be realized and that do not apply at all to situations that are most important to persons living their lives.

My works on these subjects are not as compactly organized as my engineering and scientific works and the themes run through many diverse works

Works related to Philosophy of Science

Please see a separate web page, "Facts About Snowflakes," about the generation of snowflakes from gaseous water vapor. Snowflakes can be beautifully symmetrical. Physicists are unable to account for this phenomenon because the proposed atomic processes are independent of one another and distant from each spatially. I argue that the attempt to explain the phenomenon by means of atomic processes is a failure. This failure is exemplary of the failures of physics to explain classes of phenomena of phase changes, of which the change from water to ice is the most familiar. I hold that important brain activities are phase changes and outside the reach of the Mechanical Cosmology.

A Patchwork of Limits: Physics Viewed From an Indirect Approach (2000), a .pdf file (157 kB), is discussed on a separate web page The paper is a statement of my "alternative view of physics" that includes technical analysis of the thermodynamic critical state, the conceptual basis of Quad Nets.

A broad statement of my alternative view accessible to the lay reader, with a critical analysis of conventional physics, is in § 6 of "An Objective Kind of Freedom," an archival paper in the form of a .pdf file (618 kB.). The paper was published online in January of 2005 and the first six sections were foundational of my development of Quad Nets later in the year.

"On Cosmological Principles in Natural Science," a .pdf file (23 kB), link, is suggestive of future approaches.
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III.    Large-scale Works

Testimony of Freedom
A separate website, under development, that establishes scientific and engineering foundations for investigations into social and spiritual matters.

Embodiment of Freedom
A separate website that was a prior stage of development, now superseded in large part by Testimony of Freedom. This site contains the Archive of my work that was done prior to May of 2005 and that led up to Quad Nets.

Copyright © 2009 Robert Kovsky