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Topic: Transcendence (mathematics)

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	Wolff
		For the mathematical path to be effective in uniting a mathematician with the transcendent, according to Merrell-Wolff, there must be a change of attitude from "self-withholding" to "self-giving." Indeed, according to Merrell-Wolff, through proper practice of mathematics and philosophy one can reach the door to the transcendent but cannot force it to open.
		In particular, as stated in the epigraph for this paper, mathematics is that portion of introceptive knowledge that is available to determinate-indeterminate thought with a minimum of distortion, and hence is the most direct path of return to the transcendent.
		I think that it is this sense of the development of understanding, as the manner in which mathematics is to be done, that Merrell-Wolff had in mind in saying that philosophy must accompany the practice of mathematics if it is to be effective for bridging the gap to the indeterminate.
	www.cejournal.org /GRD/Wolff.htm (3289 words)

	20th WCP: Theory and Praxis in Aristotle and Heidegger
		Transcendence precedes every possible mode of activity in general, prior to nóésis, but also prior to órexis" (GA26: 236\183); it is prior to any noetic intentional relation to the world, and prior to any sort of erotic relationship also.
		Transcendence, being-in-the-world as attempting to understand the world in relation to its own possibilities, is the primordial praxis of Dasein that roots theory and practical comportment.
		Transcendence always takes place within a "horizonal unity", within, that is, a field of possible significance that is limited by what we already are.
	www.bu.edu /wcp/Papers/Acti/ActiHanl.htm (3339 words)

	Mathematical Poetics of Enlightenment
		The remarkable effectiveness of mathematics in the physical sciences suggests that there is, indeed, a deep connection between the manifested world and this logos, or fundamental vibration, that is involved in the poesis of all form.
		Mathematics is a bridge to the Transcendent, an image in form of the universal and absolute ground of form, a symbolic language that can reveal or translate the subtle, or “higher”, conscious experiences into form.
		Mathematics is also of service to the contemplative by virtue of its inherent abstractness, rather than due to the particular meaning associated with its symbols.
	www.integralscience.org /mathpoetics.html (6938 words)

	WHAT EVER HAPPENED TO TRUE/TRUTH/ Revival of Truth in Our Postmodern Culture (Cultural Consequences of the ...
		One of the fundamental presuppositions in any mathematical philosophy is the assumed relationship between the constructive ability of the mathematician to create mathematical relationships and the "objective status" of their relationships prior to or apart from human constriction of them.
		Descartes sought to transcend the disciplines of algebra and geometry, i.e., "universal mathematics" (mathesis universalis).
		The question of which mathematical content is most appropriate for the ground of mathematics has profound consequences toward the development of our foundationaless postmodern culture.
	www.worldvieweyes.org /resources/Strauss/True-Truth.htm (5337 words)

	Jacques Maritain Center: Juan Jose Sanguineti
		Mathematics is not knowledge but a pure method of calculating, and with its fictional clarity it perfectly provides, according to Kant, the model of a deductive and well-defined science.
		However, we must remember that mathematical demonstrations start from hypotheses, and that Aristotle is reluctant, as we have said, to reduce all science to mathematical necessity.
		Undoubtedly, the predominance of mathematical scrutiny in physical methodology contributes partly to this non-ontological view which is the core of pragmatistic epistemology.
	www.nd.edu /~afreddos/papers/sanguin.htm (6674 words)

	Miracle and Transcendence
		The otherness of the transcendent God was so intense that the seraphs could not bear to look at him, and Isaiah's brief glimpse almost cost him his life and the life of his people.
		First, it was a miracle to see a transcendent God, and secondly, a further miracle was required in order for Isaiah to know that his experience was caused by a transcendent God rather than a finite reality.
		God in his transcendent self is God the Father who creates from nothing, his speaking to Isaiah is God the Word or Son, and his acting in subsequent history to confirm that Word is God the Holy Spirit.
	users.iglide.net /rjsanders/theo/tranmir.htm (5323 words)

	WHAT DOES MATHEMATICS REPRESENT
		Public understanding of mathematics with a human face then comes to be about demonstrating the limits of mathematics and science, the ease of learning these traditionally esoteric subjects, and the all too human qualities of their practitioners.
		Mathematical knowledge is not simply a "parade of syntactic variations," a set of "structural transformations," or "concatenations of pure form" (adapted from Geertz’, 1973).
		In the history of mathematics, the 1800s is a period during which self-reflexivity engages and mathematics leaves physical representation behind to an extent unknown in earlier periods.
	www.ioe.ac.uk /esrcmaths/sal.html (4567 words)

	[No title] (Site not responding. Last check: 2007-10-10)
		It was finally proved a couple of years ago, but using a new approach to mathematical proof, which is to break down the problem into thousands of special cases and prove each case with computers.
		Probably the most famous proof in mathematics is the ancient Greek proof that some numbers, like square roots, cannot possibly be expressed as a ratio of whole numbers.
		Cantor expanded the mathematical universe to accommodate an infinity of infinities: a labyrinth of caves.
	www.cbu.edu /~bbbeard/art_thou.txt (6490 words)

	Feldman biography
		Feldman proved in his thesis Borel type results (called the measure of transcendence) for logarithms of algebraic numbers, obtaining estimates for the lower bound depending (as did Gelfond) on both the degree of P and the maximum modulus of its coefficients.
		In addition to his work on the measure of transcendence of numbers, Feldman also produced many results strengthening Liouville's theorem on the rational approximation of algebraic numbers.
		Hilbert's seventh problem asked for a proof of the transcendence of a to the power b when a is an algebraic number and b is an irrational algebraic number.
	www-groups.dcs.st-and.ac.uk /~history/Biographies/Feldman.html (1109 words)

	The Spiritual Function of Mathematics, by Thomas J McFarlane
		Mathematics, according to Wolff, functions as a bridge between the relative and transcendent states of consciousness.
		Mathematics thus constitutes a thread to the Beyond that has never been lost."[71] Moreover, "for him who penetrates deeply into the roots of logic itself, the Recognition can be aroused.
		Mathematics is not only a thread by which we may know the Beyond, but also a means by which we may commune with it.
	www.integralscience.org /sacredscience/SS_spiritual.html (3319 words)

	Transcendence - Wikipedia, the free encyclopedia
		Transcendence (philosophy), climbing or going beyond some philosophical concept or limit
		Transcendence (religion), the concept that God is a being who is entirely above the created universe.
		Transcendent (novel), a science-fiction novel by Stephen Baxter
	en.wikipedia.org /wiki/Transcendence (190 words)

	icem (Site not responding. Last check: 2007-10-10)
		The chief organizer was Maria Luisa Oliveras, a Professor in the Department of Didactics of Mathematics at the University of Granada and Vice-President of the International Study Group on Ethnomathematics (ISGEm).
		History of Mathematics can hardly be distinguished from the broad history of human behavior in definite regional contexts, recognizing the dynamics of population exchanges.
		They are "mathematics" of different natural and cultural environments, all motivated by the drives for survival and transcendence.
	vello.sites.uol.com.br /icem.htm (2874 words)

	Jim Tseng's Work (Site not responding. Last check: 2007-10-10)
		Dynamics is one of those fields of mathematics that seems to use or can be applied to a host of other fields of mathematics.
		It is this strand that is the touchstone of mathematics, and it signifies the essential unity of mathematics.
		I think it is this unity that provides the greatest evidence of the transcendence of mathematics, that mathematics is not merely a human endeavor, not merely a history of human thoughts, but an aspect of the sublime.
	people.brandeis.edu /~jtseng/WORK/work.html (275 words)

	[No title]
		The idea that mathematics is pure or transcendent is “an expression of the felt autonomy of the inner activities of the intellectual network” (Collins, 1998: 878).
		Mathematics, like any discourse, like any language, “is to some degree a jargon, but it is also a language of control and a set of institutions within the culture over what it constitutes as its special domain” (Said, 1983: 219).
		Mathematical knowledge is not simply a “parade of syntactic variations,” a set of “structural transformations,” or “concatenations of pure form” (adapted from Geertz, 1983).
	www.rpi.edu /~eglash/isgem.dir/texts.dir/WillToMath.00.doc (5339 words)

	Vedic Math and the Spiritual Dimension: Index
		Spiritually advanced cultures were not ignorant of the principles of mathematics, but they saw no necessity to explore those principles beyond that which was helpful in the advancement of God realization.
		The Shulba Sutras have preserved only that part of Vedic mathematics which was used for constructing the altars and for computing the calendar to regulate the performance of religious rituals.
		The mathematics of the Vedas lacks the cold, clear, geometric precision of the West; rather, it is cloaked in the poetic language which so distinguishes the East.
	www.gosai.com /chaitanya/saranagati/html/vishnu_mjs/math/math.html (3807 words)

	Why Study Mathematics? -- Paulos
		Nevertheless, enrollment in college-level mathematics is down, and fewer and fewer American students are majoring in math or in the growing number of fields that require it.
		Or consider Lani Guinier's mathematical suggestions regarding the Voting Rights Act, or the possible economic and ecological implications of chaos theory, or the statistical snares inherent in the interpreting of test results, whether they be for academic achievement or the presence of drugs.
		Regarding the third class of reasons, I think it's only fair to say that the "cost" of the philosophical impoverishment resulting from mathematical illiteracy is one that millions of Americans gleefully assume, Still, there is evidence that people respond enthusiastically to mathematical topics as long as they are not labeled as such.
	www.uiowa.edu /~030116/prelaw/whymath.htm (945 words)

	VI(b). New Foundations for Objectivity
		Mathematics has often sent such maps across the generations to future physicists, but, in modern times, not before Whitehead do we have one so clearly addressed to future philosophers.
		Whitehead's method of extensive abstraction, because it employs ideas after the fashion of mathematics, distills for thinking an unequaled perspective upon what ideas on their own terms are qualified to bring to thinking.
		What is meant by transcendence in that context is found as that light verges toward an intensity which fuses the relative Many into an Absolute One (transcendence) or illuminates forms of experience which are Absolutely ambivalent in their alternative status as 'internal' or 'external' (transcendental - as in Kant and Hegel).
	www.differnet.com /experience/sec6b.htm (1889 words)

	[No title]
		The extent of the mathematical knowledge of the average middle school student reaches basic geometry (formulas of areas and perimeters), and perhaps algebra (solving for unknowns in simple equations).
		Geometry as a branch of mathematics is nearly as old as formal mathematics itself.
		His mathematical ability is generally accepted as pure genius; modern mathematicians have yet to fully understand his insights.
	www.ocf.berkeley.edu /~chsu/pi.doc (3043 words)

	Jing Yu (Site not responding. Last check: 2007-10-10)
		Transcendence and Drinfeld modules II, Proceeding of the summer research conference, NSC(1986), 172-181.
		Transcendence and special zeta values in characteristics p, Annals of Mathematics, 134(1991), 1-23.
		Transcendence in finite characteristics, The Arithmetic of Function Fields, ed.
	www.sinica.edu.tw /math/html/research/JY-e.html (401 words)

	Dept. of Mathematics: Academic Programs
		Logical connectives, qualifiers, mathematical proof, basic set operations, relations, functions, cardinality, axioms of set theory, natural number and induction, ordered fields.
		Methods of Applied Mathematics I. Principles and techniques of modern applied mathematics with case studies involving deterministic problems, random problems, and Fourier analysis.
		Further topics in applied mathematics to be selected by the instructor.
	www.coas.howard.edu /mathematics/programs_graduate_courses.html (1023 words)

	[No title]
		The first part of my examination is entitled "The transcendence of discipline" and the second, "The discipline of immanence".
		All of these classifications are based on a theological, metaphysical, mathematical, physical or biological doctrine (from "docere": teaching) and its dogmas (or its dogmatic of doctrinal points) and they are not necessarily realized in university disciplines: there is no confusion between discipline and science or philosophy.
		This principle is also a theoretical principle of classification and hierarchical organization or a double principle: a metaphorical principle of resemblance and a metonymical principle of descent or genealogy [see Kant and Tort], metaphor being to metonymy what paradigm is to syntagm, what condensation is to transfer, what schizophrenia is to paranoia...
	www.ucs.mun.ca /~lemelin/discipline.htm (886 words)

	MATH5535 - Irrationality and Transcendence (Site not responding. Last check: 2007-10-10)
		MATH5535 Irrationality and Transcendence is a course whose roots go back to about 500 B.C., when Pythagoras or one of his followers proved that, contrary to "common sense", some numbers cannot be expressed as a ratio of integers.
		Ideas concerning such automata can be used to investigate the transcendence of numbers which display some sort of "pattern" in their decimal expansions or continued fractions.
		One of the most exciting aspects of this subject is that it uses techniques from widely diverse areas of mathematics: number theory, calculus, set theory, complex analysis, linear algebra and the theory of computation will all be touched upon.
	web.maths.unsw.edu.au /~angell/5535 (383 words)

	ACMS Online - Journal of the ACMS
		This paper addresses the growing popularity of views of mathematics that see it primarily as a social entity and that reject Platonism.
		It affirms the insight of Davis and Hersch that mathematics is indeed a social entity.
		However, it argues that belief in God enables a fuller understanding of mathematics – one that accounts for the apparent transcendence of mathematics and its power to explain concepts in the physical world.
	www.acmsonline.org /Zwier83.htm (140 words)

	Vedic Ganita
		His work shows that the potential of Ganita Sutras is much higher than what appears in the book “Vedic Mathematics” and the mathematical structure of Ganita Sutras is similar to that of Samved indicating that Ganita Sturas belong to Vedic family.
		Transition from one space to another space is to be had in terms of unlocking of the seals of the origin points of all the four folds of the manifestation.
		These two concepts deserves to be studied in detail as transcendence to the higher dimensional spaces is possible only in terms of their understanding.
	www.vedicganita.org /glimpses.htm (1208 words)

	The 23 Paris Problems
		Hilbert concentrated much of his effort in the mathematical interpretation of the statistical theory of radiation, but since radiation theory was relatively new in Hilbert's time, he had little effect on modern radiation theory.
		An updated hit-list can be found at the Clay Mathematics Institute's site, which offers a one million dollar reward for each of the six problems presented.
		...The organic unity of mathematics is inherent in the nature of this science, for mathematics is the foundation of all exact knowledge of natural phenomena.
	www.math.umn.edu /~wittman/problems2.html (2827 words)

	Read This: Briefly Noted, February 2006
		Classics in Mathematics Education Research is an excellent read for any mathematician transitioning into the field of mathematics education or for someone who is interested in learning more about this field.
		The authors of the research articles are prominent mathematics education researchers whose works have greatly contributed to the field of mathematics education.
		July, 2003: mathematical circles, the Scottish Café, and the zeta function.
	www.maa.org /reviews/brief_feb06.html (1419 words)

	Neoreality and the Quest for Transcendence
		Note, however, that the scientists' "God" may not be the God of the Israelites, who smites the wicked, but rather a God that established various mathematical and physical parameters that permitted life to evolve in the universe.
		In light of the possibility of multiple universes, perhaps the term "omniscient" takes on a new meaning, and the God of the Old Testament might be omniscient only in the sense that He knows all that can be known about a single universe and not all universes.
		Pickover is a prolific inventor with dozens of patents, is the associate editor for several journals, the author of colorful puzzle calendars, and puzzle contributor to magazines geared to children and adults.
	sprott.physics.wisc.edu /pickover/neotrans.html (2131 words)

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