A Wisdom Archive on Numerical Analysis

Cytogenetics - Routine analysis. Routine chromosome analysis refers to analysis of metaphase chromosomes which have been banded using trypsin followed by Giemsa. This created unique banding patterns on the chromosomes. The molecular mechanism and reason for these patterns is unknown, although it likely related to replication timing and chromatin packing. Cells from bone marrow, blood, amniotic fluid, cord blood, tumor, and tissues (including skin, unbilical cord, liver, and many other organs) can b ...

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Cytogenetics - Early years. Barbara McClintock began her career as a maize cytogeneticist. In 1931 McClintock and Harriet Creighton demonstrated that cytological recombination of marked chromosomes correlated with recombination of genetic traits (genes). McClintock continued her career in cytogenetics studying the mechanics and inheritance of broken and ring (circular) chromosomes of maize. During her cytogenic work, McClintock discovered transposons, a find which ev ...

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Nervous Ether The name given by Dr. Benjamin Ward Richardson to a hypothetical fluid or medium regarded by him as intervening between the minute structural elements of the human body and serving as the means of interaction between these elements.
 
Dr. Richardson was a highly honored 19th century English physician, and his views though unorthodox commanded respect. He used the word ether in a way similar to that in which it was used by physicists: if the elements of a body are regarded as separate from one another, a medium of some sort must account for their mutual actions.
 
Such a medium must differ in certain respects from ordinary physical matter, so whether it is a form of matter or of energy is left open. This theory is one of a numerous family -- vital fluid, animal magnetism, odic force -- a loose generalization covering a great many things, or as a first crude guess. It is inadequate compared with the complex analysis of the bodily structure and functions presented by Hindu books.
 
Prana and linga-sarira are general terms for the energic and vehicular aspects of our physical constitution, and Dr. Richardson's nervous ether in many respects fits in with both of them. But the scientist begins with the physical structure, which he assumes as a self-existent basis, and then proceeds to add something to it; while the theosophist begins with the life principle and derives the physical structure from it. For the latter, every cell, every atom, is a living unit, endowed with its own power of movement; and no outside nervous ether need be added for the production of the phenomena of life or vitality.

 
(See also: Nervous Ether, Mysticism, Mysticism Dictionary )

Physical Organs Natural history reveals that the organs of the body acquire a greater individual importance, and in some cases occupy a larger proportion of the organism, as we ascend from the lower to the higher animal forms. G. de Purucker points out that "Every one of the organs of the human physical body, both collectively and distributively, is the organic representative in man''s physical sheath or body of one part or portion of his complex inner and invisible constitution. . . . every one of the monadic centers in man''s being . . . has its own corresponding organ in the physical body, each such organ functioning in the body as much as it can according to the characteristic or type-activity of its inner and invisible cause. Thus the heart, the brain, the liver, the spleen, etc., is, each one, the expression on the physical plane and in the human physical body of a corresponding consciousness-center in the invisible constitution of the sevenfold man" (ET 961-2n).
 
There are manasic as well as kamic organs. The brain and heart are "the organs of a power higher than the Personality" (BCW 12:367; or St in Oc 89). The liver is called the kamic organ; the spleen is the vehicle of the linga-sarira. Of the rhythmic tides of vital air in the chest, it is said: "The primeval current of the life-wave is then the same which assumes in man the form of the inspiratory and expiratory motion of the lungs, and this is the source of the evolution and involution of the universe" (q from Nature''s Finer Forces Rama Prasad, BCW 12:356 or Studies in Occultism 76). The uterus, within which a new manifestation of life appears, corresponds physically to the universal matrix -- cosmic space -- the fertilized cell being the point in the circle where differentiation begins. The eyes, from one standpoint at least, are the most occult of our senses. The fibers of the large optic nerves are interrelated with special organs of the senses and sensations -- optic thalami, pineal and pituitary glands, etc. -- which are grouped around the center of the brain.
 
Further, "every human organ and each cell in the latter has a key-board of its own, like that of a piano, only that it registers and emits sensations instead of sounds. Every key contains the potentiality of good or bad, of producing harmony or disharmony" according as the impulse comes from the higher or lower nature (BCW 12:368-9 or St in Oc 91). Memory has no special organ of its own in the brain, but has seats in every organ of the body. The whole body is a vast sounding board in which each cell bears a long record of impressions connected with its parent organ, and also it has a memory and consciousness of its own kind. These impressions are, according to the nature of the organ, physical, psychic, mental, or again mixed, as they relate to this or another plane, there being states of instinctual, mental, and purely abstract or spiritual consciousness. The physiological functions and reciprocal workings of cells and organs are in the body automatically directed by a "universally diffused mind" throughout that body, which is beyond all material analysis. Because of this intelligence operating throughout the organism, physiology is destined someday "to become the hand-maiden of Occult truths" (BCW 12:139; or Studies in Occultism 105).
 
On a larger scale, each organ has its own rhythm or vibratory rate of response to cosmic eternal motion. The response is animated by a "vital principle without which no molecular combinations could ever have resulted in a living organism, least of all in the so-called ''inorganic'' matter of our plane of consciousness" (SD 1:603). The breaking of the normal rhythm of one organ disturbs that of all the rest, which accounts for the many reflex symptoms that often appear.
 
The general principles of occult physiology underlie and coordinate the numerous details of chemical, microscopic, and biological research. The human organism illustrates the modern scientific view of the electronic nature of matter. In man, the positive and negative phases of the one Life unite to manifest in functional currents of vitality; all of which has a significant bearing on the prevailing medical recourse to organotherapy, the end results of which are not recognized, as such, since they operate on inner lines of force. Each animal body -- human or beast -- is a complex organism whose various parts are vibrating in consonance with the synthetic character of its own evolutionary status of vital matter and conscious force -- its selfhood. Hence, the injection of the physiologic essence of any one creature''s organs into the life-currents of another, aiming to give a certain impetus to functional reaction, inevitably adds a subtly disturbing foreign element. The same physical matter composes all animal bodies, so that the human and beast life-atoms are interchangeable, but such interchange is governed or regulated by extremely occult causal relations which raise their action outside or above the plane of human interference. Organotherapy, as at present understood and practiced, is a divergence from nature''s normal processes, having no analog in nature which, in turn, provides resources of wholesome remedial matter. These artificial mixtures of both physical and superphysical forces, involve vital issues beyond the ken of research laboratories. The end results of unbalanced forces might be sought among the increase in cases of malignant, degenerative, and mental and nervous disorders, with their unequilibrated operation of functioning vitality and of consciousness.
 
Pi The mathematical symbol for the incommensurable ratio of the circumference of a circle to the length of its diameter, and for corresponding ratios in plane and solid geometry. Its incommensurability is a particular instance of the impossibility of expressing geometrical magnitudes exactly in number. Bearing in mind that there is a geometrical key to interpretation of cosmic law and structure, and that the facts of geometry cannot possibly be arbitrary or meaningless but must be faithful representations of general laws; then we shall understand that the ratio {pi sym}, involving such radial and important elements as the straight line and the circle, must be of paramount importance. The figures, either for approximate decimal evaluations or approximate fractional ratios, play an important part in the symbology of the ancient mystery-language. These figures and the numbers which they make are found in the numerical values of letters and words in the Hebrew and Greek alphabets. The problem of squaring the circle by a purely geometrical construction does not involve the use of {pi sym} at all.

 
(See also: Physical Organs, Mysticism, Mysticism Dictionary, Occultism, Occultism Dictionary )

In some forms of cancer, especially hematological malignancies, cytogenetics can determine which chromosomal translocations are present in the malignant cells, facilitating diagnosis and susceptibility to treatment (e.g. imatinib mesylate in the presence of the Philadelphia chromosome). In congenital disorders, such as Down's syndrome, cytogenetics can determine the nature of the chromosomal defect - a "simple" trisomy, a mosaic, "balanced" translocation, a deletion, or an insertion in one - or bo ...

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In mathematics, a large number of methods have been proposed for the summation of divergent series. These generally take the form of some linear functional L with domain contained in some space S of numerical sequences. That is, firstly, a useful method for attributing a sum to a series that doesn't converge should at least be linear. Secondly, the sequence of partial sums of the series is considered, which is an equivalent way of presenting it. For any such L, its abelian theorem is the result that if c ...

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The Abel–Ruffini theorem states that there is no general solution in radicals to polynomial equations of degree five or higher. The content of this theorem is frequently misunderstood. It does not assert that higher-degree polynomial equations are unsolvable. In fact, if the polynomial has real or complex coefficients, and we allow complex solutions, then every polynomial equation has solutions; this is the fundamental theorem of algebra. Although these solutions cannot always be computed exactly, they ca ... Including:

• Abel–Ruffini theorem - History

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