An inter-disciplinary researcher with a background in mathematics, computer science and the study of religion. I'm particularly interested in the application of Buddhist ethics to the design of technology, as in the Sigala project, research.siga.la.
Many of my ideas are synthesised in my book, Buddhism and Computing: How to Flourish in the Age of Algorithms (Mud Pie Books).
In this paper we survey some of the developments with regards to technology-enhanced support of m... more In this paper we survey some of the developments with regards to technology-enhanced support of mathematics learning and teaching. Coverage is especially given on how to design systems that work effectively on the Web, particularly in the fields of economics and business studies. This is a rapidly evolving landscape in which general trends in e-learning have raised expectations of the electronic tools
In this paper we briefly introduce virtual learning environments, which have become integral to o... more In this paper we briefly introduce virtual learning environments, which have become integral to online learning (or e-learning) in higher education around the world. We describe what they are, the functionality they provide and the kinds of benefits they offer universities, with particular reference to the subject of economics. We also touch on some considerations concerning the e-learning software itself, setting their development in a historical perspective. In our analysis we draw especially on practices in the UK with illustrations from WebLearn, the virtual learning environment used by the University of Oxford.
... In such cases, having a group of student blogs to compare side by side is valuable. Blogs in ... more ... In such cases, having a group of student blogs to compare side by side is valuable. Blogs in an Institutional Setting. Blogs offer considerable potential and so it is natural to ask: How to incorporate blogs in the institutional setting, particularly with existing e-learning systems? ...
An investigation is presented into the use of formal methods for the production of safety-critica... more An investigation is presented into the use of formal methods for the production of safety-critical systems with embedded software. New theory and procedures are tested on an industrial case study, the formal specification and refinement of a communications protocol for medical devices (the Universal Flexport protocol [copyright]). On reviewing the current literature, a strong case emerges for grounding any work within an overall perspective that integrates the experience of safety engineering and the correctness of formal methods. Such a basis, it is argued, is necessary for an effective contribution to the delivery with assurance of life-critical software components. Hence, a safety-oriented framework is proposed which facilitates a natural flow from safety analysis of the entire system through to formal requirements, design, verification and validation for a software model undergoing refinement towards implementation. This framework takes a standard safety lifecycle model and cons...
Whether a design aids or hinders human flourishing depends on architecture: just as a physical en... more Whether a design aids or hinders human flourishing depends on architecture: just as a physical environment affects one’s social development, so too an online environment affects one’s cognitive and spiritual development. This short article responds to the problem of the 'attention economy' by highlighting the need to be heedful in the use of digital systems and, more fundamentally, to properly evaluate the design of such systems in terms of the impact on human agency.
The Internet promised to be a boon for learning — a global library of human knowledge that would ... more The Internet promised to be a boon for learning — a global library of human knowledge that would allow anyone to learn anything. However, very quickly, that resource became a confusing jumble.
How could those of us interested in educational technology improve this situation, bringing the signal out of the noise? We propose using KEPLAIR (Knowledge-based Environment for Personalized Learning using an Artificial Intelligence Recommender), an online platform, currently in initial development, designed to help its users find learning opportunities and materials. Using learning goals chosen by the learner, KEPLAIR will browse the Internet to harvest materials. Then it will filter the result and make recommendations to match the learner’s cognitive level, pre-existing knowledge about the topic, and preferred physical and social environments. Depending on what learners want, KEPLAIR’s recommendations might include a book or video, an online course, a club or community, or even a tutor or learning coach. The intent is not for KEPLAIR to teach, test, or even promote a predetermined curriculum, nor will it require learners to be part of any formal school or learning organisations. KEPLAIR’s purpose is simply to help learners reach their self-chosen goals by highlighting appropriate, attractive, and useful materials so they stand out from the background noise. This will be done in a highly personalized way for each single user, taking into proper account the many aspects involved in recommending, such as needs, background, abilities, aims, interests, tastes, preferences, attitudes, behaviors, motivations, expectations, context, and community.
Obviously, this undertaking poses significant technological, social, and learning challenges. To implement KEPLAIR’s vision, development has begun on an ontology that includes four major learning classes: Goal/Pathway; Learner Profile; Social, Physical, & Digital Environment; and Learning Resource. Based on such an ontology, the AI will draw on semantic analysis of online materials from formal educational institutions, open educational resources (OER), and pre-existing pathways, environments and learning objects. It will engage in conversational dialog with users and user-initiated and user-controlled data uploads to create detailed learner profiles and learning pathways.
This paper will introduce KEPLAIR’s basic structure and mechanisms, offering opportunities to reflect on and respond to the strategies KEPLAIR’s international design team is considering. It will also report on the initial proof-of-concept project currently underway at the University of Bari in Italy.
In this paper we survey some of the developments with regards to technology-enhanced support of m... more In this paper we survey some of the developments with regards to technology-enhanced support of mathematics learning and teaching. Coverage is especially given on how to design systems that work effectively on the Web, particularly in the fields of economics and business studies. This is a rapidly evolving landscape in which general trends in e-learning have raised expectations of the electronic tools to go beyond merely providing mechanical functions: nowadays the teacher expects them to help organise their teaching and even enhance their teaching methods. For the student, there is increasing focus on the learner experience, which seeks a wider range and availability of e-learning support tools together with greater ease of use. Advances in technology mean that options keep changing, setting many challenges for system developers, so this paper seeks to indicate the broad features in these changes, with particular regard to future planning. These general considerations are subsequently brought into focus in later sections of this paper by addressing the question of how e-learning systems may provide judicious support for the uniquely human abilities of solving problems. In this case visualisation is an excellent aid, but any tools provided need to draw on a wide range of online resources that are readily available so as to properly establish the learning context. Finally, we briefly introduce into this context two new systems for teaching mathematics: VisualEconoMath, an integrated environment comprising automated tools for deriving solutions to prescribed mathematical problems and How2SolveIt, which supports the quintessential human learning processes surrounding questions and answers, in this case between students and lecturers.
How mobile blogs for personal reflection may be related to institutional learning environments, d... more How mobile blogs for personal reflection may be related to institutional learning environments, drawing on experiences from the RAMBLE Project at the University of Oxford.
This is a copy of the dissertation (15,000 words) that I submitted during the course of my Master... more This is a copy of the dissertation (15,000 words) that I submitted during the course of my Master's in the Study of Religion(s) at Oxford University, which I completed in October 2009. The analysis of the Fifth Precept, as observed by lay Buddhist followers, covers both textual analysis with reference to the Pali canon followed by its interpretation and actual practice (early 21st century) across different Schools based on findings from an online survey.
This report presents preliminary findings from an online survey conducted in 2009 concerning view... more This report presents preliminary findings from an online survey conducted in 2009 concerning views and practices relating to the Fifth Precept in Buddhism. Respondents were mainly from North America, Europe and Oceania.
This work was carried out just prior to the Master's dissertation, 'Avoiding pamāda: An analysis of the Fifth Precept as Social Protection in Contemporary Contexts with reference to the early Buddhist teachings', available at https://www.academia.edu/34976455/. It was necessary to ascertain current practice and interpretations so as to enable comparison with the canonical texts. Thus whilst not part of the formal assessment, it should be read in conjunction with the dissertation and has been classified as a 'thesis chapter'.
This Master's thesis, 'Norms of Ideals in Direct Sums of Number Fields and Applications to the Ci... more This Master's thesis, 'Norms of Ideals in Direct Sums of Number Fields and Applications to the Circulants Problem of Olga Taussky-Todd', presents original research. As the title suggests, to tackle a problem which was originally posed by Olga Taussky-Todd, who asked what values can be taken by the determinant of a matrix with integer entries where each row is a cyclic shift of the previous one. Hitherto algebraic results for specific cases have been proven by M. Newman using matrix manipulation. To address the general case, the approach here uses a well-known relationship between determinants of matrix transformations and 'absolute' norms of fractional ideals in a direct sum of number fields, using asymptotic methods. This gives an indication of what proportion of integers are values. Some additional new proofs are given for results already presented by Newman.
The research was undertaken at the University of Glasgow, with the thesis originally submitted in 1992. The author has belatedly made the work available here, with some corrections, in the hope that it may be of some value for other researchers and especially to honour the memory of his supervisor, the late Prof. Robert (“Bob”) W. K. Odoni.
This paper addresses from a Buddhist perspective the burgeoning challenges of living and flourish... more This paper addresses from a Buddhist perspective the burgeoning challenges of living and flourishing with digital technology. At its heart are the principles of human agency and a framework for the cultivation of sīla (moral virtue). These allow us respectively to develop criteria for evaluating new technology, such as artificial intelligence, and to design systems that enhance wellbeing and human relationships. Accordingly, we apply them to the design of novel online social networks, where we treat the problem of maintaining heedfulness by deploying thinking routines to strengthen cognitive (and hence moral) functioning.
PLE Position Paper (personal thoughts) prepared for a 'PLE Experts' meeting held in Manchester on... more PLE Position Paper (personal thoughts) prepared for a 'PLE Experts' meeting held in Manchester on 6 June 2006 attended by about 16 e-learning specialists.
A few observations following the meeting are available from the RAMBLE Project blog (archive) posted on 7 June 2006 - see associated link/URL.
In this paper we survey some of the developments with regards to technology-enhanced support of m... more In this paper we survey some of the developments with regards to technology-enhanced support of mathematics learning and teaching. Coverage is especially given on how to design systems that work effectively on the Web, particularly in the fields of economics and business studies. This is a rapidly evolving landscape in which general trends in e-learning have raised expectations of the electronic tools
In this paper we briefly introduce virtual learning environments, which have become integral to o... more In this paper we briefly introduce virtual learning environments, which have become integral to online learning (or e-learning) in higher education around the world. We describe what they are, the functionality they provide and the kinds of benefits they offer universities, with particular reference to the subject of economics. We also touch on some considerations concerning the e-learning software itself, setting their development in a historical perspective. In our analysis we draw especially on practices in the UK with illustrations from WebLearn, the virtual learning environment used by the University of Oxford.
... In such cases, having a group of student blogs to compare side by side is valuable. Blogs in ... more ... In such cases, having a group of student blogs to compare side by side is valuable. Blogs in an Institutional Setting. Blogs offer considerable potential and so it is natural to ask: How to incorporate blogs in the institutional setting, particularly with existing e-learning systems? ...
An investigation is presented into the use of formal methods for the production of safety-critica... more An investigation is presented into the use of formal methods for the production of safety-critical systems with embedded software. New theory and procedures are tested on an industrial case study, the formal specification and refinement of a communications protocol for medical devices (the Universal Flexport protocol [copyright]). On reviewing the current literature, a strong case emerges for grounding any work within an overall perspective that integrates the experience of safety engineering and the correctness of formal methods. Such a basis, it is argued, is necessary for an effective contribution to the delivery with assurance of life-critical software components. Hence, a safety-oriented framework is proposed which facilitates a natural flow from safety analysis of the entire system through to formal requirements, design, verification and validation for a software model undergoing refinement towards implementation. This framework takes a standard safety lifecycle model and cons...
Whether a design aids or hinders human flourishing depends on architecture: just as a physical en... more Whether a design aids or hinders human flourishing depends on architecture: just as a physical environment affects one’s social development, so too an online environment affects one’s cognitive and spiritual development. This short article responds to the problem of the 'attention economy' by highlighting the need to be heedful in the use of digital systems and, more fundamentally, to properly evaluate the design of such systems in terms of the impact on human agency.
The Internet promised to be a boon for learning — a global library of human knowledge that would ... more The Internet promised to be a boon for learning — a global library of human knowledge that would allow anyone to learn anything. However, very quickly, that resource became a confusing jumble.
How could those of us interested in educational technology improve this situation, bringing the signal out of the noise? We propose using KEPLAIR (Knowledge-based Environment for Personalized Learning using an Artificial Intelligence Recommender), an online platform, currently in initial development, designed to help its users find learning opportunities and materials. Using learning goals chosen by the learner, KEPLAIR will browse the Internet to harvest materials. Then it will filter the result and make recommendations to match the learner’s cognitive level, pre-existing knowledge about the topic, and preferred physical and social environments. Depending on what learners want, KEPLAIR’s recommendations might include a book or video, an online course, a club or community, or even a tutor or learning coach. The intent is not for KEPLAIR to teach, test, or even promote a predetermined curriculum, nor will it require learners to be part of any formal school or learning organisations. KEPLAIR’s purpose is simply to help learners reach their self-chosen goals by highlighting appropriate, attractive, and useful materials so they stand out from the background noise. This will be done in a highly personalized way for each single user, taking into proper account the many aspects involved in recommending, such as needs, background, abilities, aims, interests, tastes, preferences, attitudes, behaviors, motivations, expectations, context, and community.
Obviously, this undertaking poses significant technological, social, and learning challenges. To implement KEPLAIR’s vision, development has begun on an ontology that includes four major learning classes: Goal/Pathway; Learner Profile; Social, Physical, & Digital Environment; and Learning Resource. Based on such an ontology, the AI will draw on semantic analysis of online materials from formal educational institutions, open educational resources (OER), and pre-existing pathways, environments and learning objects. It will engage in conversational dialog with users and user-initiated and user-controlled data uploads to create detailed learner profiles and learning pathways.
This paper will introduce KEPLAIR’s basic structure and mechanisms, offering opportunities to reflect on and respond to the strategies KEPLAIR’s international design team is considering. It will also report on the initial proof-of-concept project currently underway at the University of Bari in Italy.
In this paper we survey some of the developments with regards to technology-enhanced support of m... more In this paper we survey some of the developments with regards to technology-enhanced support of mathematics learning and teaching. Coverage is especially given on how to design systems that work effectively on the Web, particularly in the fields of economics and business studies. This is a rapidly evolving landscape in which general trends in e-learning have raised expectations of the electronic tools to go beyond merely providing mechanical functions: nowadays the teacher expects them to help organise their teaching and even enhance their teaching methods. For the student, there is increasing focus on the learner experience, which seeks a wider range and availability of e-learning support tools together with greater ease of use. Advances in technology mean that options keep changing, setting many challenges for system developers, so this paper seeks to indicate the broad features in these changes, with particular regard to future planning. These general considerations are subsequently brought into focus in later sections of this paper by addressing the question of how e-learning systems may provide judicious support for the uniquely human abilities of solving problems. In this case visualisation is an excellent aid, but any tools provided need to draw on a wide range of online resources that are readily available so as to properly establish the learning context. Finally, we briefly introduce into this context two new systems for teaching mathematics: VisualEconoMath, an integrated environment comprising automated tools for deriving solutions to prescribed mathematical problems and How2SolveIt, which supports the quintessential human learning processes surrounding questions and answers, in this case between students and lecturers.
How mobile blogs for personal reflection may be related to institutional learning environments, d... more How mobile blogs for personal reflection may be related to institutional learning environments, drawing on experiences from the RAMBLE Project at the University of Oxford.
This is a copy of the dissertation (15,000 words) that I submitted during the course of my Master... more This is a copy of the dissertation (15,000 words) that I submitted during the course of my Master's in the Study of Religion(s) at Oxford University, which I completed in October 2009. The analysis of the Fifth Precept, as observed by lay Buddhist followers, covers both textual analysis with reference to the Pali canon followed by its interpretation and actual practice (early 21st century) across different Schools based on findings from an online survey.
This report presents preliminary findings from an online survey conducted in 2009 concerning view... more This report presents preliminary findings from an online survey conducted in 2009 concerning views and practices relating to the Fifth Precept in Buddhism. Respondents were mainly from North America, Europe and Oceania.
This work was carried out just prior to the Master's dissertation, 'Avoiding pamāda: An analysis of the Fifth Precept as Social Protection in Contemporary Contexts with reference to the early Buddhist teachings', available at https://www.academia.edu/34976455/. It was necessary to ascertain current practice and interpretations so as to enable comparison with the canonical texts. Thus whilst not part of the formal assessment, it should be read in conjunction with the dissertation and has been classified as a 'thesis chapter'.
This Master's thesis, 'Norms of Ideals in Direct Sums of Number Fields and Applications to the Ci... more This Master's thesis, 'Norms of Ideals in Direct Sums of Number Fields and Applications to the Circulants Problem of Olga Taussky-Todd', presents original research. As the title suggests, to tackle a problem which was originally posed by Olga Taussky-Todd, who asked what values can be taken by the determinant of a matrix with integer entries where each row is a cyclic shift of the previous one. Hitherto algebraic results for specific cases have been proven by M. Newman using matrix manipulation. To address the general case, the approach here uses a well-known relationship between determinants of matrix transformations and 'absolute' norms of fractional ideals in a direct sum of number fields, using asymptotic methods. This gives an indication of what proportion of integers are values. Some additional new proofs are given for results already presented by Newman.
The research was undertaken at the University of Glasgow, with the thesis originally submitted in 1992. The author has belatedly made the work available here, with some corrections, in the hope that it may be of some value for other researchers and especially to honour the memory of his supervisor, the late Prof. Robert (“Bob”) W. K. Odoni.
This paper addresses from a Buddhist perspective the burgeoning challenges of living and flourish... more This paper addresses from a Buddhist perspective the burgeoning challenges of living and flourishing with digital technology. At its heart are the principles of human agency and a framework for the cultivation of sīla (moral virtue). These allow us respectively to develop criteria for evaluating new technology, such as artificial intelligence, and to design systems that enhance wellbeing and human relationships. Accordingly, we apply them to the design of novel online social networks, where we treat the problem of maintaining heedfulness by deploying thinking routines to strengthen cognitive (and hence moral) functioning.
PLE Position Paper (personal thoughts) prepared for a 'PLE Experts' meeting held in Manchester on... more PLE Position Paper (personal thoughts) prepared for a 'PLE Experts' meeting held in Manchester on 6 June 2006 attended by about 16 e-learning specialists.
A few observations following the meeting are available from the RAMBLE Project blog (archive) posted on 7 June 2006 - see associated link/URL.
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Papers by Paul Trafford
How could those of us interested in educational technology improve this situation, bringing the signal out of the noise? We propose using KEPLAIR (Knowledge-based Environment for Personalized Learning using an Artificial Intelligence Recommender), an online platform, currently in initial development, designed to help its users find learning opportunities and materials. Using learning goals chosen by the learner, KEPLAIR will browse the Internet to harvest materials. Then it will filter the result and make recommendations to match the learner’s cognitive level, pre-existing knowledge about the topic, and preferred physical and social environments. Depending on what learners want, KEPLAIR’s recommendations might include a book or video, an online course, a club or community, or even a tutor or learning coach. The intent is not for KEPLAIR to teach, test, or even promote a predetermined curriculum, nor will it require learners to be part of any formal school or learning organisations. KEPLAIR’s purpose is simply to help learners reach their self-chosen goals by highlighting appropriate, attractive, and useful materials so they stand out from the background noise. This will be done in a highly personalized way for each single user, taking into proper account the many aspects involved in recommending, such as needs, background, abilities, aims, interests, tastes, preferences, attitudes, behaviors, motivations, expectations, context, and community.
Obviously, this undertaking poses significant technological, social, and learning challenges. To implement KEPLAIR’s vision, development has begun on an ontology that includes four major learning classes: Goal/Pathway; Learner Profile; Social, Physical, & Digital Environment; and Learning Resource. Based on such an ontology, the AI will draw on semantic analysis of online materials from formal educational institutions, open educational resources (OER), and pre-existing pathways, environments and learning objects. It will engage in conversational dialog with users and user-initiated and user-controlled data uploads to create detailed learner profiles and learning pathways.
This paper will introduce KEPLAIR’s basic structure and mechanisms, offering opportunities to reflect on and respond to the strategies KEPLAIR’s international design team is considering. It will also report on the initial proof-of-concept project currently underway at the University of Bari in Italy.
Thesis Chapters by Paul Trafford
This work was carried out just prior to the Master's dissertation, 'Avoiding pamāda: An analysis of the Fifth Precept as Social Protection in Contemporary Contexts with reference to the early Buddhist teachings', available at https://www.academia.edu/34976455/. It was necessary to ascertain current practice and interpretations so as to enable comparison with the canonical texts. Thus whilst not part of the formal assessment, it should be read in conjunction with the dissertation and has been classified as a 'thesis chapter'.
The research was undertaken at the University of Glasgow, with the thesis originally submitted in 1992. The author has belatedly made the work available here, with some corrections, in the hope that it may be of some value for other researchers and especially to honour the memory of his supervisor, the late Prof. Robert (“Bob”) W. K. Odoni.
Drafts by Paul Trafford
A few observations following the meeting are available from the RAMBLE Project blog (archive) posted on 7 June 2006 - see associated link/URL.
How could those of us interested in educational technology improve this situation, bringing the signal out of the noise? We propose using KEPLAIR (Knowledge-based Environment for Personalized Learning using an Artificial Intelligence Recommender), an online platform, currently in initial development, designed to help its users find learning opportunities and materials. Using learning goals chosen by the learner, KEPLAIR will browse the Internet to harvest materials. Then it will filter the result and make recommendations to match the learner’s cognitive level, pre-existing knowledge about the topic, and preferred physical and social environments. Depending on what learners want, KEPLAIR’s recommendations might include a book or video, an online course, a club or community, or even a tutor or learning coach. The intent is not for KEPLAIR to teach, test, or even promote a predetermined curriculum, nor will it require learners to be part of any formal school or learning organisations. KEPLAIR’s purpose is simply to help learners reach their self-chosen goals by highlighting appropriate, attractive, and useful materials so they stand out from the background noise. This will be done in a highly personalized way for each single user, taking into proper account the many aspects involved in recommending, such as needs, background, abilities, aims, interests, tastes, preferences, attitudes, behaviors, motivations, expectations, context, and community.
Obviously, this undertaking poses significant technological, social, and learning challenges. To implement KEPLAIR’s vision, development has begun on an ontology that includes four major learning classes: Goal/Pathway; Learner Profile; Social, Physical, & Digital Environment; and Learning Resource. Based on such an ontology, the AI will draw on semantic analysis of online materials from formal educational institutions, open educational resources (OER), and pre-existing pathways, environments and learning objects. It will engage in conversational dialog with users and user-initiated and user-controlled data uploads to create detailed learner profiles and learning pathways.
This paper will introduce KEPLAIR’s basic structure and mechanisms, offering opportunities to reflect on and respond to the strategies KEPLAIR’s international design team is considering. It will also report on the initial proof-of-concept project currently underway at the University of Bari in Italy.
This work was carried out just prior to the Master's dissertation, 'Avoiding pamāda: An analysis of the Fifth Precept as Social Protection in Contemporary Contexts with reference to the early Buddhist teachings', available at https://www.academia.edu/34976455/. It was necessary to ascertain current practice and interpretations so as to enable comparison with the canonical texts. Thus whilst not part of the formal assessment, it should be read in conjunction with the dissertation and has been classified as a 'thesis chapter'.
The research was undertaken at the University of Glasgow, with the thesis originally submitted in 1992. The author has belatedly made the work available here, with some corrections, in the hope that it may be of some value for other researchers and especially to honour the memory of his supervisor, the late Prof. Robert (“Bob”) W. K. Odoni.
A few observations following the meeting are available from the RAMBLE Project blog (archive) posted on 7 June 2006 - see associated link/URL.