The nature of avidyÄ in Buddhism and VedÄ nta

This thesis deals with the nature of ignorance as it was interpreted in the Upani~adic tradition, specifically in Advaita Vedanta, and in early and Mahayana Buddhism , e specially in the Madhyamika school of Buddhism. The approach i s a historical and comparative one. It examines the early thoughts of both the upanis.a ds and Buddhism abou t avidya (ignorance), shows how the notion was treated by the more speculative and philosphically oriented schools which base d themselves on the e arly works, and sees how their views differ. The thesis will show that the Vedinta tended to treat avidya as a topic for metaphysical s peculation as t he s chool developed, drifting from its initial e xistential concerns, while the Madhyamika remained in contact with the e xistential concerns evident in the first discourses of the Buddha. The word "notion" has been chosen for use in referring t o avidya, even though it may have non-intellectual and emotional connotations, to avoid more popular a lternatives such as "concept" or "idea". In neither the Upani,ads, Advaita Vedanta, or Buddhism is ignorance merely a concept or an idea. Only in a secondary sense, in texts and speech , does it become one. Avidya has more to do with the lived situation in which man finds himself, with the subjectobject separation in which he f eels he exists, than with i i i intel lect ual constr ucts . Western thought has begun to r ealize the same with concerns such as being in modern ontology, and has chosen to speak about i t i n terms of the question of being . Avidya, however, i s not a 'question' . If q ue stions we r e to be put regarding the nature of a vidya , they would be more of t he sort "What is not avidya?", though e ven here l anguage bestows a status t o i t which avidya does not have. In considering a work of the Eastern tradition, we f ace t he danger of imposing Western concepts on it. Granted t hat avidya is customari ly r endered i n English as ignorance, the ways i n which the East and West view i gno rance di f f er. Pedagogically , the European cultures, grounded in the ancient Greek culture, view ignorance as a l ack or an emptiness. A child is i gnorant o f certain t hings and the purpose o f f ormal education , in f act if not in theory, is to fill him with enough knowledge so that he can cope wit h t he complexities and the e xpectations of s ociety. On another level, we feel t hat study and research will l ead t o the discovery o f solutions, which we now lack , for problems now defying solut i on . The East, on the o t her hand, sees avidya in a d i fferent light.Ignorance isn't a lack, but a presence. Religious and philosophical l iterature directs its efforts not towards acquiring something new, but at removing t.he ideas and opinions that individuals have formed about themselves and the world. When that is fully accomplished, say the sages , t hen Wisdom, which has been obscured by those opinions, will present itself. Nothing new has to be learned, t hough we do have t o 'learn' that much. The growing interest in t he West with Eastern religions and philosophies may, in time, influence our theoretical and practical approaches to education and learning, not only in the established educati onal institutions, but in religious , p sychological, and spiritual activities as well. However, the requirements o f this thesis do no t permit a formulation of revolutionary method or a call to action. It focuses instead on the textual arguments which attempt to convince readers that t he world in which they take themselves to exist is not, in essence, real, on the ways i n which the l imitations of language are disclosed, and on the provisional and limited schemes that are built up to help students see through their ignorance. The metaphysic s are provisional because they act only as spurs and guides. Both the Upanisadic and Buddhist traditions that will be dealt with here stress that language constantly fails to encompass the Real. So even terms s uch as 'the Real', 'Absolute', etc., serve only to lead to a transcendent experience . The sections dealing with the Upanisads and Advaita Vedanta show some of the historical evolution of the notion of avidya, how it was dealt with as maya , and the q uestions that arose as t o its locus. With Gau?apada we see the beginnings of a more abstract treatment of the topic, and , the influence of Buddhism. Though Sankhara' S interest was primarily directed towards constructing a philosophy to help others attain mok~a ( l iberation), he too introduced t echnica l t e rminology not found in the works of his predecessors. His work is impressive , but areas of it are incomplete. Numbers of his followers tried to complete the systematic presentation of his insi ghts . Their work focuses on expl anat i ons of adhyasa (superimposition ) , t he locus and object of ignorance , and the means by which Brahman takes itself to be the jiva and the world. The section on early Buddhism examines avidya in the context o f the four truths, together with dubkha (suffering), the r ole it p l ays in t he chain of dependent c ausation , a nd t he p r oblems that arise with t he doctrine of anatman. With t he doct rines of e arly Buddhism as a base, the Madhyamika elaborated questions that the Buddha had said t e nded not t o edi f ication. One of these had to do with own - being or svabhava. Thi s serves a s a centr e around which a discussion o f i gnorance unfolds, both i ndividual and coll ective ignorance. There follows a treatment of the cessation of ignorance as it is discussed within this school . The final secti on tries to present t he similarities and differences i n the natures o f ignorance i n t he two traditions and discusses the factors responsible for t hem . ACKNOWLEDGEMENTS I would like to thank Dr. Sinha for the time spent II and suggestions made on the section dealing with Sankara and the Advait.a Vedanta oommentators, and Dr. Sprung, who supervised, direoted, corrected and encouraged the thesis as a whole, but especially the section on Madhyamika, and the final comparison.

Zero-sum problems in finite cyclic groups

The purpose of this thesis is to investigate some open problems in the area of combinatorial number theory referred to as zero-sum theory. A zero-sequence in a finite cyclic group G is said to have the basic property if it is equivalent under group automorphism to one which has sum precisely IGI when this sum is viewed as an integer. This thesis investigates two major problems, the first of which is referred to as the basic pair problem. This problem seeks to determine conditions for which every zero-sequence of a given length in a finite abelian group has the basic property. We resolve an open problem regarding basic pairs in cyclic groups by demonstrating that every sequence of length four in Zp has the basic property, and we conjecture on the complete solution of this problem. The second problem is a 1988 conjecture of Kleitman and Lemke, part of which claims that every sequence of length n in Zn has a subsequence with the basic property. If one considers the special case where n is an odd integer we believe this conjecture to hold true. We verify this is the case for all prime integers less than 40, and all odd integers less than 26. In addition, we resolve the Kleitman-Lemke conjecture for general n in the negative. That is, we demonstrate a sequence in any finite abelian group isomorphic to Z2p (for p ~ 11 a prime) containing no subsequence with the basic property. These results, as well as the results found along the way, contribute to many other problems in zero-sum theory.

Repertory grid adaptations in detecting connotative trends and social behaviour problems in education

Please consult the paper edition of this thesis to read. It is available on the 5th Floor of the Library at Call Number: Z 9999 E38 K66 1983

Square Root Finding In Graphs

Abstract: Root and root finding are concepts familiar to most branches of mathematics. In graph theory, H is a square root of G and G is the square of H if two vertices x,y have an edge in G if and only if x,y are of distance at most two in H. Graph square is a basic operation with a number of results about its properties in the literature. We study the characterization and recognition problems of graph powers. There are algorithmic and computational approaches to answer the decision problem of whether a given graph is a certain power of any graph. There are polynomial time algorithms to solve this problem for square of graphs with girth at least six while the NP-completeness is proven for square of graphs with girth at most four. The girth-parameterized problem of root fining has been open in the case of square of graphs with girth five. We settle the conjecture that recognition of square of graphs with girth 5 is NP-complete. This result is providing the complete dichotomy theorem for square root finding problem.

Region Connection Calculus: Composition Tables and Constraint Satisfaction Problems

Qualitative spatial reasoning (QSR) is an important field of AI that deals with qualitative aspects of spatial entities. Regions and their relationships are described in qualitative terms instead of numerical values. This approach models human based reasoning about such entities closer than other approaches. Any relationships between regions that we encounter in our daily life situations are normally formulated in natural language. For example, one can outline one's room plan to an expert by indicating which rooms should be connected to each other. Mereotopology as an area of QSR combines mereology, topology and algebraic methods. As mereotopology plays an important role in region based theories of space, our focus is on one of the most widely referenced formalisms for QSR, the region connection calculus (RCC). RCC is a first order theory based on a primitive connectedness relation, which is a binary symmetric relation satisfying some additional properties. By using this relation we can define a set of basic binary relations which have the property of being jointly exhaustive and pairwise disjoint (JEPD), which means that between any two spatial entities exactly one of the basic relations hold. Basic reasoning can now be done by using the composition operation on relations whose results are stored in a composition table. Relation algebras (RAs) have become a main entity for spatial reasoning in the area of QSR. These algebras are based on equational reasoning which can be used to derive further relations between regions in a certain situation. Any of those algebras describe the relation between regions up to a certain degree of detail. In this thesis we will use the method of splitting atoms in a RA in order to reproduce known algebras such as RCC15 and RCC25 systematically and to generate new algebras, and hence a more detailed description of regions, beyond RCC25.

A Study of Ordered Gene Problems Featuring DNA Error Correction and DNA Fragment Assembly with a Variety of Heuristics, Genetic Algorithm Variations, and Dynamic Representations

Ordered gene problems are a very common classification of optimization problems. Because of their popularity countless algorithms have been developed in an attempt to find high quality solutions to the problems. It is also common to see many different types of problems reduced to ordered gene style problems as there are many popular heuristics and metaheuristics for them due to their popularity. Multiple ordered gene problems are studied, namely, the travelling salesman problem, bin packing problem, and graph colouring problem. In addition, two bioinformatics problems not traditionally seen as ordered gene problems are studied: DNA error correction and DNA fragment assembly. These problems are studied with multiple variations and combinations of heuristics and metaheuristics with two distinct types or representations. The majority of the algorithms are built around the Recentering- Restarting Genetic Algorithm. The algorithm variations were successful on all problems studied, and particularly for the two bioinformatics problems. For DNA Error Correction multiple cases were found with 100% of the codes being corrected. The algorithm variations were also able to beat all other state-of-the-art DNA Fragment Assemblers on 13 out of 16 benchmark problem instances.

Palmer's Pocket Scale with Rules for its Use in Solving Arithmetical and Geometrical Problems

The book is signed by S.D. Woodruff. A label the book indicates that it was also owned by "Band, of De Vere Gardens in Toronto".

An Abstract Algebraic Theory of L-Fuzzy Relations for Relational Databases

Classical relational databases lack proper ways to manage certain real-world situations including imprecise or uncertain data. Fuzzy databases overcome this limitation by allowing each entry in the table to be a fuzzy set where each element of the corresponding domain is assigned a membership degree from the real interval [0…1]. But this fuzzy mechanism becomes inappropriate in modelling scenarios where data might be incomparable. Therefore, we become interested in further generalization of fuzzy database into L-fuzzy database. In such a database, the characteristic function for a fuzzy set maps to an arbitrary complete Brouwerian lattice L. From the query language perspectives, the language of fuzzy database, FSQL extends the regular Structured Query Language (SQL) by adding fuzzy specific constructions. In addition to that, L-fuzzy query language LFSQL introduces appropriate linguistic operations to define and manipulate inexact data in an L-fuzzy database. This research mainly focuses on defining the semantics of LFSQL. However, it requires an abstract algebraic theory which can be used to prove all the properties of, and operations on, L-fuzzy relations. In our study, we show that the theory of arrow categories forms a suitable framework for that. Therefore, we define the semantics of LFSQL in the abstract notion of an arrow category. In addition, we implement the operations of L-fuzzy relations in Haskell and develop a parser that translates algebraic expressions into our implementation.

Abstract of title of part of Lots no. 12 and 13 in the 8th Concession in the Township of Grantham

Abstract of title of parts of lots nos. 12 and 13 in the 8th Concession in the Township of Grantham – Orsen Phelps to Owen Cifford and abstract of title of parts of Lots nos. 10 and 11 in the 9th Concession in the Township of Grantham – David Grass to Owen Clifford. This is a handwritten 2 page summary. This is part of the Owen Clifford Estate signed by W.W. Powell, registrar, Feb. 20, 1871.

Application for Loan, Mortgage Loan Envelope, and Abstract of Title

Atkins, Sarah A. and Carlisle A. Gardner includes: Application for Loan, July 26, 1884; Mortgage Loan Envelope no. 255 for July 1, 1884 – July 1, 1889 and Abstract of Title, August 28, 1884.

Crew, Isaac M., includes: Application for Loan, Mortgage Loan Envelope, and Abstract of Title

Crew, Isaac M., includes: Application for Loan, March 10, 1885; Mortgage Loan Envelope no. 679 for Jan. 1, 1885 – Jan. 1, 1890 and Abstract of Title, April 13, 1885.

Dennis, George W. and Mary E. Dennis, includes: Application for Loan on Real Estate, and Abstract of Title

Dennis, George W. and Mary E. Dennis, includes: Application for Loan on Real Estate, July 10, 1882; and Abstract of Title, Sept. 2, 1882.

Schmidt, John, includes: Application for Loan, and Mortgage Loan Envelope, and Abstract of Title

Schmidt, John, includes: Application for Loan, Aug. 8, 1884 and Mortgage Loan Envelope no. 302 for July 1, 1884 – July 1, 1889 and Abstract of Title, Sept. 6, 1884.

Letter which was enclosed with the application, bond mortgage and abstract of the Jones and Mater accounts to Samuel Woodruff from Jarvis, Conklin and Co.

Letter which was enclosed with the application, bond mortgage and abstract of the Jones and Mater accounts to Samuel Woodruff from Jarvis, Conklin and Co., May 4, 1882.