On the relationship between plane and solid geometry

Traditional geometry concerns itself with planimetric and stereometric considerations, which are at the root of the division between plane and solid geometry. To raise the issue of the relation between these two areas brings with it a host of different problems that pertain to mathematical practice, epistemology, semantics, ontology, methodology, and logic. In addition, issues of psychology and pedagogy are also important here. To our knowledge there is no single contribution that studies in detail even one of the aforementioned area

A new Systemic Taxonomy of Cyber Criminal activity

Cybercrime commonly refers to a broad range of different criminal activities that involve computers and information systems, either as primary tools or as primary targets. Cybercrime Science combines the methodology of Crime Science with the technology of Information Security. The few existing taxonomies of Cybercrime provide only general insights into the benefits of information structures; they are neither complete nor elaborated in a systemic manner to provide a proper framework guided by real system-principles. The main problem with such taxonomies is the inability to dynamically upgrade, which is why there is no timely cybersecurity actions. The current and past approaches were based mainly on the technical nature of cyberattacks and such approaches classified the impact of the activities from a criminological perspective. In this article, we present a systemic taxonomy of Cybercrime, based on definitions of the field items and the related data specifications. We develop a new method for estimating the fractal dimension of networks to explore a new taxonomy of Cybercrime activity. This method can serve to dynamically upgrade taxonomy and thus accelerate the prevention of cybercrime

Axiomatic Architecture of Scientific Theories

The received concepts of axiomatic theory and axiomatic method, which stem from David Hilbert, need a systematic revision in view of more recent mathematical and scientific axiomatic practices, which do not fully follow in Hilbert’s steps and re-establish some older historical patterns of axiomatic thinking in unexpected new forms. In this work I motivate, formulate and justify such a revised concept of axiomatic theory, which for a variety of reasons I call constructive, and then argue that it can better serve as a formal representational tool in mathematics and science than the received concept

A theoretical reflection on smart shape modeling

This paper presents, as far as the authors are aware, a complete and extended new taxonomy of shape specification modeling techniques and a characterization of shape design systems, all based on the relationship of users’ knowledge to the modeling system they use to generate shapes. In-depth knowledge of this relationship is not usually revealed in the regular university training courses such as bachelor’s, master’s and continuing education. For this reason, we believe that it is necessary to modify the learning process, offering a more global vision of all the currently existing techniques and extending training in those related to algorithmic modeling techniques. We consider the latter to be the most powerful current techniques for modeling complex shapes that cannot be modeled with the usual techniques known to date. Therefore, the most complete training should include everything from the usual geometry to textual programming. This would take us a step further along the way to more powerful design environments. The proposed taxonomy could serve as a guideline to help improve the learning process of students and designers in a complex environment with increasingly powerful requirements and tools. The term “smart” is widely used nowadays, e.g. smart phones, smart cars, smart homes, smart cities... and similar terms such as “smart shape modeling”. Nowadays, the term smart is applied from a marketing point of view, whenever an innovation is used to solve a complex problem. This is the case for what is currently called smart shape modeling. However, in the future; this concept should mean a much better design environment than today. The smart future requires better trained and skilled engineers, architects, designers or technical students. This means that they must be prepared to be able to contribute to the creation of new knowledge, to the use of innovations to solve complex problems of form, and to the extraction of the relevant pieces of intelligence from the growing volume of knowledge and technologies accessible today. Our taxonomy is presented from the point of view of methods that are possibly furthest away from what is considered today as “intelligent shape modeling” to the limit of what is achievable today and which the authors call “Generic Shape Algorithm”. Finally, we discuss the characteristics that a shape modeling system must have to be truly “intelligent”: it must be “proactive” in applying innovative ideas to achieve a solution to a complex problem

Proposal For a Study of Commonsense Physical Reasoning

This report describes research done at the Artificial Intelligence Laboratory of the Massachusetts Institute of Technology. Support for the laboratory's artificial intelligence research is provided in part by the Advanced Research Projects Agency of the Department of Defense under Office of Naval Research contract N00014-80-C-0505.Our common sense views of physics are the first coin in our intellectual capital; understanding precisely what they contain could be very important both for understanding ourselves and for making machines more like us. This proposal describes a domain that has been designed for studying reasoning about constrained motion and describes my theories about performing such reasoning. The issues examined include qualitative reasoning about shape and physical processes, as well as ways of using knowledge about motion other than "envisioning". Being a proposal, the treatment of these issues is necessarily cursory and incomplete.MIT Artificial Intelligence Laboratory Department of Defense Advanced Research Projects Agenc

Workshop on Verification and Theorem Proving for Continuous Systems (NetCA Workshop 2005)

Oxford, UK, 26 August 200

Computational universes

Suspicions that the world might be some sort of a machine or algorithm existing ``in the mind'' of some symbolic number cruncher have lingered from antiquity. Although popular at times, the most radical forms of this idea never reached mainstream. Modern developments in physics and computer science have lent support to the thesis, but empirical evidence is needed before it can begin to replace our contemporary world view.Comment: Several corrections of typos and smaller revisions, final versio

The Twist Representation of Shape

We give a contribution to the representation problem of free-form curves and surfaces. Our proposal is an operational or kinematic approach based on the Lie group SE(3). While in Euclidean space the modelling of shape as orbit of a point under the action of SE(3) is limited, we are embedding our problem into the conformal geometric algebra R_4,1 of the Euclidean space R^3. This embedding results in a number of advantages which makes the proposed method a universal and flexible one with respect to applications. Especially advantagous is the equivalence of the proposed shape model to that of the Fourier representations