Terence B Allen
Terence B Allen
BA Chemistry University of Calfornia at Santa Cruz 1972; MD University of California San Francisco 1976
About
15
Publications
24,508
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
81
Citations
Introduction
Skills and Expertise
Publications
Publications (15)
Review of Axiomatic Music Theory by Seyyed Mehdi Nemati
Music theory is an example of a regular language produced by a deterministic finite automaton. Wikipedia says music theory has no axiomatic basis in modern mathematics (which absurdly implies music is not consistent or defies Godel's completeness Theorem). I show in my second music topology poster how music theory is axiomized directly in Category...
Find out why frequency and musical pitch are not the same. Pitch is a real valued function that is defined by the curve-lifting map between p = f and p = log 2 f.
Periventricular leukomalacia (PVL) is a form of cerebral infarction occurring in neonates, particularly in low-weight and premature infants. PVL is well-known to neonatologists, but generally considered nonfatal. Many infants with PVL die in the hospital with multiple medical problems. Those infants with PVL who survive because of intensive care wi...
This study reports a method of classifying parathyroid disease based on statistical analysis of the number of abnormal glands.
A 2 1/2 year old boy accidentally ingested the herbicide diquat. Progressive neurologic dysfunction preceded his death 143 hours after poisoning. Brain stem infarction and purpura were noted at post mortem and closely resembled the brain stem pathology in 3 of 7 adults who died after diquat ingestion. Renal, gastrointestinal and pulmonary involveme...
The parathyroid oxyphil cell is apparently capable of parathyroid hormone secretion. To investigate the significance of oxyphil cells in abnormal human parathyroid glands, we compared histologic and clinical features in a retrospective study of 114 cases of hyperparathyroidism, Parathyroid glands were classified by the presence or absence of signif...
To the Editor.—
In the December 1977 issue of the Archives (113:1701-1704), Baden and Alper reported on a possible genetic syndrome that associated ichthyosiform dermatosis, keratitis, and deafness, but ignored the obvious probability that they are a manifestation of late congenital syphilis.Ichthyosis in congenital syphilis is well known and phot...
Questions
Questions (58)
The problem of string vibration boils down to whether the string is open or closed.
I say it is closed and everyone else says it is open.
Quoting physicist V.I. Arnold:
"In formulating the principle of [Galilean] relativity we must keep in mind that it is relevant only to closed physical (in particular mechanical systems), i. e., that we must include in the system all bodies whose interactions play a role in the study of the given phenomena...."
"In the future {chapters in the book], the term "mechanical" will mean a closed system."
So if the string is open, then it is not a mechanical system. The open string has no defined energy. Without energy there can be no physics.
I think it is absolutely certain that no mathematician or physicist can show that an open non-mechanical system that predates Newton can be better than using standard calculus and the calculus of moving surfaces.
It is also clear that mathematicians and physicist do not even understand their own mathematical methods (theory of oscillation with one degree of freedom) when applied to the string.
This raises big questions about the theory of strings in higher dimensions, where strings are both open and closed. These strings are not invariant geometric objects. They have no defined energy level, they do not conserve energy. They are variants that can never be used to establish natural law as a minimum principle.
Note that Mersenne's "law" is not natural because it requires reference to a particular coordinate system in meters and kilograms. A natural law cannot depend on the choice of coordinate systems (under Galilean relativity).
I have made formal statement after formal statement, and so far no mathematician or physicists has responded with a formal statement to contradict me.
Mathematicians and physicists cannot defend their honor. All I get is "Everyone know the string is open." So prove it!
Introduction to Tensor Analysis and the Calculus of Moving Surfaces, Springer 2013 is a wonderful book that contains everything there is to know about the theory of string vibration under one degree of freedom.
We are forced to accept the string has only one degree of freedom because otherwise energy cannot be defined, and so physics does not apply to matter without defined energy.
I can understand the exact mathematics involved, but I am still a bit shaky on tensors and the critical energy equations involve covariant derivatives that I would like to understand better.
I want to distill the parts that are specific to the string perturbation.
The basic point I follow Grinfeld on is the string shape can be constructed without reference to a coordinate system. The domain is the string line which has coordinates on the real line. Then we show how it moves.
The surface of the string under energy conservation is a catenoid.
Using the coordinates of points on the catenoid surface parameterized by time we can understand how the surface of the potential energy surface moves after perturbation.
I invite anyone who understands the calculus of moving surfaces (there are other books) to discuss this with me.
My exploration of the string Euler characteristic made me wonder if the Euler characteristic is related to energy conservation, then why not consider string thermodynamics. Not heat but free energy.
The Gibbs phase rule F = c - p + 2 for the string reads degree of freedom 1 = 1 component - 2 phases +2.
The rule is a tautology on one component because one degree of freedom implies two phases, and two phases implies one degree of freedom.
The string energy can only be defined under one degree of freedom.
So experimental evidence unequivocally shows two distinct energy phases: amplitude expansion and amplitude contraction.
Clearly the two phases are determined by the same closed system.
Note the 1 degree of freedom Lagrangian is E = T + U, not E = T - U
Phase I: When the deformed string is released, the baseline potential energy U is increases to U + U'(t). Energy conservation is the same as volume preservation, so the shape of the manifold minimizes surface area. This forces the excess potential energy U'(t) into kinetic action T(t) so that U + U'(t) > U + T(t).
Phase II When all excess potential energy is transferred to kinesis, the normal curvature of the smooth manifold is restored but with a surface that is moving. Then the kinetic energy T(t) runs down to zero. The base line potential energy cannot run down.
So the time-invariant standing wave has a covariant derivative which gives the string velocity, and therefore the invariant frequency, too.
This proves that the frequency and amplitude are both determined by the Gibbs free energy change which drives amplitude decay.
It is therefore proven that frequency and amplitude are dependent on the same closed potential system.
I have attached sketches of the string energy cycle at rest, deformed, expansion, and contraction.
If anyone would like to help write these equations better, I would appreciate it. My calculus has limits. I think someone could really do some interesting things here. The field is wide open for discovery and original research (in spite of what they tell me on Stack Exchange).
If you do write the string energy equations, go over and lay them on physics stack exchange for me.
