Attention inequality is the inequality of distribution of attention across users on social networks, people in general, and for scientific papers. Yun Family Foundation introduced "Attention Inequality Coefficient" as a measure of inequality in attention and arguments it by the close interconnection with wealth inequality. == Relationship to economic inequality == Attention inequality is related to economic inequality since attention is an economically scarce good. The same measures and concepts as in classical economy can be applied for attention economy. The relationship develops also beyond the conceptual level—considering the AIDA process, attention is the prerequisite for real monetary income on the Internet. On data of 2018, a significant relationship between likes and comments on Facebook to donations is proven for non-profit organizations. == Attention economy == The attention economy refers to the practice of maximizing the attention users give to a product for advertising-related reasons. Attention economy remains one of the most common forms of advertising, and has been steadily increasing thanks to new technologies such as television, internet and social media. It is one of the most widely-used approaches to economy for its effectiveness for maximising the noticeability of a certain product. == Attention inequality in social media == In social media, attention inequality refers to the unequal distribution of users' attention on social media platforms. This means that instead of an equal distribution of attention, fewer sources receive a disproportionate share of attention, leaving many unnoticed. This phenomenon is possibly the result of social media algorithms, which are commonly designed to drive maximum engagement. This phenomenon is a large factor in the polarization and creation of echo-chambers. Social media algorithms tend to note content that is already performing well and display it to more users, while content that is equally engaging or well-made is not recommended to users. Posts that trigger strong emotions usually out-perform more "uncontroversial" content. When many users interact with the post, it signals the algorithm that the specific post drives engagement. The algorithm then tends to recommend that type of content to an exponential number of people, potentially outperforming "un-emotional" content. These factors, when combined, tend to create an unequal social media environment. == Attention inequality in science == According to a recent 2025 study about research inequality among scientists published in Information Processing and Management, scientific discourse is restricted to a small group of connected scientists, and is frequently not an accurate representation of the whole scientific community. Using citation-network analysis in the fields of nanoscience and chemical physics, the study claims that a group of connected scientists has a significant notability in the scientific community. The calculated connection strength between these scientists is estimated to be about 4.5, the study also says that these authors cite each other four times more often than would be predicted in a random network, whereas ordinary scientists that exist outside of this group only reach an estimated connection strength of 0.9. The study findings suggest that that scientific attention is not distributed by merit, but rather by the connectedness of the scientists involved in the research. == Extent == As data of 2008 shows, 50% of the attention is concentrated on approximately 0.2% of all hostnames, and 80% on 5% of hostnames. The Gini coefficient of attention distribution lay in 2008 at over 0.921 for such commercial domains names as ac.jp and at 0.985 for .org-domains. The Gini coefficient was measured on Twitter in 2016 for the number of followers as 0.9412, for the number of mentions as 0.9133, and for the number of retweets as 0.9034. For comparison, the world's income Gini coefficient was 0.68 in 2005 and 0.904 in 2018. More than 96% of all followers, 93% of the retweets, and 93% of all mentions are owned by 20% of Twitter. == Causes == At least for scientific papers, today's consensus states that inequality is unexplainable by variations of quality and individual talent. The Matthew effect plays a significant role in the emergence of attention inequality—those who already enjoy large amounts of attention get even more attention, and those who do not lose even more. Ranking algorithms based on relevance to the user have been found to alleviate the inequality of the number of posts across topics.
Workplace robotics safety
Workplace robotics safety is an aspect of occupational safety and health when robots are used in the workplace. This includes traditional industrial robots as well as emerging technologies such as drone aircraft and wearable robotic exoskeletons. Types of accidents include collisions, crushing, and injuries from mechanical parts. Hazard controls include physical barriers, good work practices, and proper maintenance. == Background == Many workplace robots are industrial robots used in manufacturing. According to the International Federation of Robotics, 1.7 million new robots are expected to be used in factories between 2017 and 2020. Emerging robot technologies include collaborative robots, personal care robots, construction robots, exoskeletons, autonomous vehicles, and drone aircraft (also known as unmanned aerial vehicles or UAVs). Advances in automation technologies (e.g. fixed robots, collaborative and mobile robots, and exoskeletons) have the potential to improve work conditions but also to introduce workplace hazards in manufacturing workplaces. Fifty-six percent of robot injuries are classified as pinch injuries and 44% of injuries are classified as impact injuries. A 1987 study found that line workers are at the greatest risk, followed by maintenance workers, and programmers. Poor workplace design and human error caused most injuries. Despite the lack of occupational surveillance data on injuries associated specifically with robots, researchers from the US National Institute for Occupational Safety and Health (NIOSH) identified 61 robot-related deaths between 1992 and 2015 using keyword searches of the Bureau of Labor Statistics (BLS) Census of Fatal Occupational Injuries research database (see info from Center for Occupational Robotics Research). Using data from the Bureau of Labor Statistics, NIOSH and its state partners have investigated 4 robot-related fatalities under the Fatality Assessment and Control Evaluation Program. In addition the Occupational Safety and Health Administration (OSHA) has investigated robot-related deaths and injuries, which can be reviewed at OSHA Accident Search page. Injuries and fatalities could increase over time because of the increasing number of collaborative and co-existing robots, powered exoskeletons, and autonomous vehicles into the work environment. Safety standards are being developed by the Robotic Industries Association (RIA) in conjunction with the American National Standards Institute (ANSI). On October 5, 2017, OSHA, NIOSH and RIA signed an alliance to work together to enhance technical expertise, identify and help address potential workplace hazards associated with traditional industrial robots and the emerging technology of human-robot collaboration installations and systems, and help identify needed research to reduce workplace hazards. On October 16 NIOSH launched the Center for Occupational Robotics Research to "provide scientific leadership to guide the development and use of occupational robots that enhance worker safety, health, and well being". So far, the research needs identified by NIOSH and its partners include: tracking and preventing injuries and fatalities, intervention and dissemination strategies to promote safe machine control and maintenance procedures, and on translating effective evidence-based interventions into workplace practice. == Hazards == Many hazards and injuries can result from the use of robots in the workplace. Some robots, notably those in a traditional industrial environment, are fast and powerful. This increases the potential for injury as one swing from a robotic arm, for example, could cause serious bodily harm. There are additional risks when a robot malfunctions or is in need of maintenance. A worker who is working on the robot may be injured because a malfunctioning robot is typically unpredictable. For example, a robotic arm that is part of a car assembly line may experience a jammed motor. A worker who is working to fix the jam may suddenly get hit by the arm the moment it becomes unjammed. Additionally, if a worker is standing in a zone that is overlapping with nearby robotic arms, he or she may get injured by other moving equipment. There are four types of accidents that can occur with robots: impact or collision accidents, crushing and trapping accidents, mechanical part accidents, and other accidents. Impact or collision accidents occur generally from malfunctions and unpredicted changes. Crushing and trapping accidents occur when a part of a worker's body becomes trapped or caught on robotic equipment. Mechanical part accidents can occur when a robot malfunctions and starts to "break down", where the ejection of parts or exposed wire can cause serious injury. Other accidents at just general accidents that occur from working with robots. There are seven sources of hazards that are associated with human interaction with robots and machines: human errors, control errors, unauthorized access, mechanical failures, environmental sources, power systems, and improper installation. Human errors could be anything from one line of incorrect code to a loose bolt on a robotic arm. Many hazards can stem from human-based error. Control errors are intrinsic and are usually not controllable nor predictable. Unauthorized access hazards occur when a person who is not familiar with the area enters the domain of a robot. Mechanical failures can happen at any time, and a faulty unit is usually unpredictable. Environmental sources are things such as electromagnetic or radio interference in the environment that can cause a robot to malfunction. Power systems are pneumatic, hydraulic, or electrical power sources; these power sources can malfunction and cause fires, leaks, or electrical shocks. Improper installation is fairly self-explanatory; a loose bolt or an exposed wire can lead to inherent hazards. === Emerging technologies === Emerging robotic technologies can reduce hazards to workers, but can also introduce new hazards. For example, robotic exoskeletons can be used in construction to reduce load to the spine, improve posture, and reduce fatigue; however, they can also increase chest pressure, limit mobility when moving out of the way of a falling object, and cause balance problems. Unmanned aerial vehicles are being used in the construction industry to do monitoring and inspections of buildings under construction. This reduces the need for humans to be in hazardous locations, but the risk of a UAV collision presents a hazard to workers. For collaborative robots, isolation is not possible. Possible hazard controls include collision avoidance systems, and making the robot less stiff to lessen the impact force. Robotic tech vest is a wearable device for humans, worn in Amazon warehouses. == Hazard controls == There are a few ways to prevent injuries by implementing hazard controls. There can be risk assessments at each of the various stages of a robot's development. Risk assessments can help gather information about a robot's status, how well it is being maintained, and if repairs are needed soon. By being aware of the status of a robot, injuries can be prevented and hazards reduced. Safeguarding devices can be implemented to reduce the risk of injuries. These can include engineering controls such as physical barriers, guard rails, presence-sensing safeguarding devices, etc. Awareness devices are usually used in conjunction with safeguarding devices. They are usually a system of rope or chain barriers with lights, signs, whistles, and horns. Their purpose it to be able to alert workers or personnel of certain dangers. Operator safeguards can also be in place. These usually utilize safeguarding devices to protect the operator and reduce risk of injury. Additionally, when an operator is within close proximity of a robot, the working speed of the robot can be reduced to ensure that the operator is in full control. This can be done by placing the robot in the manual or teach mode. It is also crucial to inform the programmer of the robot of what type of work the robot will be doing, how it will interact with other robots, and how it will work in relation to an operator. Proper maintenance of robotic equipment is also critical in order to reduce hazards. Maintaining a robot insures that it continues to function properly, thereby reducing the risks associated with a malfunction. One common safeguard used in industrial settings is the installation of robot safety fencing. These barriers, often made from durable materials such as mesh or polycarbonate, prevent accidental interactions between workers and robotic systems, reducing the risk of injury. Robot safety fencing is particularly important in environments where high-speed or powerful robots are used. == Regulations == Some existing regulations regarding robots and robotic systems include: ANSI/RIA R15.06 OSHA 29 CFR 1910.333 OSHA 29 CFR 1910.147 ISO 10218 ISO/TS 15066 ISO/DIS 13482
Clinical quality management system
Clinical quality management systems (CQMS) are systems used in the life sciences sector (primarily in the pharmaceutical, biologics and medical device industries) designed to manage quality management best practices throughout clinical research and clinical study management. A CQMS system is designed to manage all of the documents, activities, tasks, processes, quality events, relationships, audits and training that must be administered and controlled throughout the life of a clinical trial. The premise of a CQMS is to bring together the activities led by two sectors of clinical research, Clinical Quality and Clinical Operations, to facilitate cross-functional activities to improve efficiencies and transparency and to encourage the use of risk mitigation and risk management practices at the clinical study level. Based on the principles of quality management systems (QMS) which are used in many industries to create a framework for defining and delivering quality outcomes, managing risk, and continual improvement. Many guidelines and governance bodies have been established to ensure a common approach within a given industry to a set of parameters used to identify the minimally acceptable standard for that industry. The pharmaceutical industry is no exception, with several trade groups (e.g. PhRMA, EFPIA, RQA, etc.) coming together to enhance collaboration. However, as noted by the Academy of Medical Sciences, there are increasingly complex and bureaucratic legal and ethical frameworks that innovators must work within to develop new medicines for patients. The historical pharmaceutical QMS applies primarily to good manufacturing practice as described in existing ISO (International Organization for Standardization) and ICH (International Committee on Harmonization) guidelines. "Good Manufacturing Practices (GMP) relate to quality control and quality assurance enabling companies in the pharmaceutical sector to minimize or eliminate instances of contamination, mix-ups, and errors. This in turn, protects the customer from purchasing a product which is ineffective or even dangerous." These standards have historically been applied to the manufacturing environment, appropriate to how they have been written. However, according to FDA as well as other regulatory bodies, "Implementation of ICH Q10 throughout the product lifecycle should facilitate innovation and continual improvement", implying that the same standards that apply to the manufacturing environment should also be applied to the clinical research space, earlier in the lifecycle of an investigational or marketed product. Accordingly, a CQMS is any system developed to apply these principles to clinical operations within an organization.
Luciano Floridi
Luciano Floridi (Italian: [luˈtʃaːno ˈflɔːridi]; born 16 November 1964) is an Italian and British philosopher. He is John K. Castle Professor in the Practice of Cognitive Science and Founding Director of the Digital Ethics Center at Yale University. He is also a Professor of Sociology of Culture and Communication at the University of Bologna, Department of Legal Studies, where he is the director of the Centre for Digital Ethics. Furthermore, he is adjunct professor ("distinguished scholar in residence") at the Department of Economics, American University, Washington D.C. He is married to the neuroscientist Anna Christina Nobre. Floridi is best known for his work on two areas of philosophical research: the philosophy of information, and information ethics (also known as digital ethics or computer ethics), for which he received many awards, including the Knight of the Grand Cross of the Order of Merit, Italy's most prestigious honor. According to Scopus, Floridi was the most cited living philosopher in the world in 2020. Between 2008 and 2013, he held the research chair in philosophy of information and the UNESCO Chair in Information and Computer Ethics at the University of Hertfordshire. He was the founder and director of the IEG, an interdepartmental research group on the philosophy of information at the University of Oxford, and of the GPI the research Group in Philosophy of Information at the University of Hertfordshire. He was the founder and director of the SWIF, the Italian e-journal of philosophy (1995–2008). He is a former Governing Body Fellow of St Cross College, Oxford. == Early life and education == Floridi was born in Rome in 1964, and studied at Rome University La Sapienza (laurea, first class with distinction, 1988), where he was originally educated as a historian of philosophy. He soon became interested in analytic philosophy and wrote his tesi di laurea (roughly equivalent to an M.A. thesis) in philosophy of logic, on Michael Dummett's anti-realism. He obtained his Master of Philosophy (1989) and PhD degree (1990) from the University of Warwick, working in epistemology and philosophy of logic with Susan Haack (who was his PhD supervisor) and Michael Dummett. Floridi's early student years are partly recounted in the non-fiction book The Lost Painting: The Quest for a Caravaggio Masterpiece, where he is "Luciano". During his graduate and postdoctoral years, he covered the standard topics in analytic philosophy in search of a new methodology. He sought to approach contemporary problems from a heuristically powerful and intellectually enriching perspective when dealing with lively philosophical issues. During his graduate studies, he began to distance himself from classical analytic philosophy. In his view, the analytic movement had lost its way. For this reason, he worked on pragmatism (especially Peirce) and foundationalist issues in epistemology and philosophy of logic, as well as the history of skepticism. == Academic career and previous positions == Floridi started his academic career as a lecturer in philosophy at the University of Warwick in 1990–1991. He joined the Faculty of Philosophy of the University of Oxford in 1990 and the OUCL (Oxford's Department of Computer Science) in 1999. He was junior research fellow (JRF) in philosophy at Wolfson College, Oxford University (1990–1994), a Frances Yates Fellow in the History of Ideas at the Warburg Institute, University of London (1994–1995) and Research Fellow in philosophy at Wolfson College, Oxford University (1994–2001). During these years in Oxford, he held lectureships in different Colleges. Between 1994 and 1996, he also held a post-doctoral research scholarship at the Department of Philosophy, University of Turin. Between 2001 and 2006, he was Markle Foundation Senior Research Fellow in Information Policy at the Programme in Comparative Media Law and Policy, Oxford University. Between 2002 and 2008, he was associate professor of logic at the Università degli Studi di Bari. In 2006, he became Fellow by Special Election of St Cross College, Oxford University, where he played for the squash team. In 2008, he was appointed full professor of philosophy at the University of Hertfordshire, to hold the newly established research chair in philosophy of information and, in 2009, the UNESCO Chair in Information and Computer Ethics, a position which he held until 2013, when he moved back to Oxford. In 2017, Floridi became a fellow of the Alan Turing Institute and the chair of its Data Ethics Group, holding these positions until 2021 and 2020, respectively. Since 2010 he has been editor-in-chief of Philosophy & Technology (Springer). In January 2023, Floridi announced he would move to Yale at the beginning of the academic year 2023–2024, to take over the position of founding director of the Yale Digital Ethics Center. == Philosophical views == One of Floridi's key contributions is his formulation of the 'Philosophy of Information' (PoI). The PoI provides a framework for understanding the nature of information and its role in the world. According to Floridi, information is a vital resource that shapes our knowledge and understanding of the world. It is not simply a neutral representation of reality but a part of the world, with its own properties, effects, and moral implications. Floridi's PoI has several key components including an 'ontology of information', which defines the nature of information, an 'ethics of information', which provides a framework for evaluating the moral implications of information and information technologies, an 'epistemology of information', that analyses the role of information in the development of knowledge and science, and a 'logic of information', the concentrates on the more formal aspects. The PoI also includes a theory of the 'information environment', the infosphere, which encompasses the physical, social, and cultural contexts in which information is produced, used, and communicated. == Recognitions and awards == 2022 - Knight of the Grand Cross - First Class of the Order of Merit (Cavaliere di Gran Croce Ordine al Merito della Repubblica Italiana, the highest honor in the Italian Republic), awarded through a special decree by the president of the Italian Republic Sergio Mattarella for his work on the philosophy and ethics of information. 2022 - Fellow of the Accademia delle Scienze dell'Istituto di Bologna 2021 - Honorary Doctorate (Laurea honoris causa) in Informatics, University of Skövde, Sweden, for "his groundbreaking work on the philosophy of information". 2020 - Premio Udine Filosofia, Mimesis Festival, for The Logic of Information (OUP, 2019) 2020 - Premio Socrate, Cesare Landa Foundation, for philosophical communication 2019 - CogX Award, for "outstanding achievement in ethics of AI" 2019 - Gilbert Ryle Lectures, Trent University 2019 - Premio Aretè "Maestro della Responsabilità", Nuvolaverde, Confindustria, Gruppo 24 Ore Salone della CSR e dell'innovazione sociale, for ethics of communication 2018 - Thinker Award, IBM, for AI Ethics 2018 - Premio Conoscenza, Conferenza dei Rettori delle Università Italiane (CRUI, equivalent of Universities UK), for achievements in research and communication about digital ethics 2017 - Fellow of the Academy of Social Sciences 2016 - J. Ong Award, Media Ecology Association, for The Fourth Revolution (OUP, 2016) 2016 - Copernicus Scientist Award, Institute for Advanced Studies of the University of Ferrara, in recognition of research in the ethics and philosophy of information 2015 - Fernand Braudel Senior Fellow, European University Institute 2014-15 - Cátedras de Excelencia, University Carlos III of Madrid, for research in philosophy and ethics of information 2013 - Member of the Académie Internationale de Philosophie des Sciences 2013 - Fellow of the British Computer Society 2013 - Weizenbaum Award, International Society for Ethics and Information Technology, for "very significant contribution to the field of information and computer ethics, through his research, service, and vision" 2012 - Covey Award, International Association for Computing and Philosophy, for "outstanding research in computing and philosophy" 2011-12 - Fellow, Center for Information Policy Research, University of Wisconsin–Milwaukee 2011 - Honorary Doctorate (Laurea honoris causa) in philosophy, University of Suceava, Romania, for "his leading research in the philosophy and ethics of information" 2011 - Fellow, World Technology Network, NY, in the category "ethics and technology" 2010 - Vice Chancellor Research Award, University of Hertfordshire 2009 - Fellow of the Society for the Study of Artificial Intelligence and the Simulation of Behaviour (AIBS) 2009-10 - Gauss Professor of the Akademie der Wissenschaften, Göttingen, in recognition of research in the philosophy of information (first philosopher to receive the award, generally given to mathematicians or physicists) 2009 - Barwise Prize, American Philosophical Asso
Dataism
Dataism is a term that has been used to describe the mindset or philosophy created by the emerging significance of big data. It was first used by David Brooks in The New York Times in 2013. The term has been expanded to describe what historian Yuval Noah Harari, in his book Homo Deus: A Brief History of Tomorrow from 2015, calls an emerging ideology or even a new form of religion, in which "information flow" is the "supreme value". In art, the term was used by Albert-Laszlo Barabasi to refer to an artist movement that uses data as its primary source of inspiration. == History == "If you asked me to describe the rising philosophy of the day, I'd say it is Data-ism", wrote David Brooks in The New York Times in February 2013. Brooks argued that in a world of increasing complexity, relying on data could reduce cognitive biases and "illuminate patterns of behavior we haven't yet noticed". In 2015, Steve Lohr's book Data-ism looked at how Big Data is transforming society, using the term to describe the Big Data revolution. In his 2016 book Homo Deus: A Brief History of Tomorrow, Yuval Noah Harari argues that all competing political or social structures can be seen as data processing systems: "Dataism declares that the universe consists of data flows, and the value of any phenomenon or entity is determined by its contribution to data processing" and "we may interpret the entire human species as a single data processing system, with individual humans serving as its chips." According to Harari, a Dataist should want to "maximise dataflow by connecting to more and more media". Harari predicts that the logical conclusion of this process is that, eventually, humans will give algorithms the authority to make the most important decisions in their lives, such as whom to marry and which career to pursue. Harari argues that Aaron Swartz could be called the "first martyr" of Dataism. In 2022, Albert-László Barabási coined the term "Dataism" to define an artistic movement that positions data as the central means of understanding nature, society, technology, and human essence. This movement underscores the necessity for art to integrate with data to stay relevant in contemporary society. Dataism responds to the intricacy and interconnectedness of modern social, economic, and technological realms, which exceed individual understanding. Advocating for the use of methodologies from various fields like science, business, and politics in art, Dataism sees this fusion as essential for art to retain its significance and influence. == Criticism == Commenting on Harari's characterisation of Dataism, security analyst Daniel Miessler believes that Dataism does not present the challenge to the ideology of liberal humanism that Harari claims, because humans will simultaneously be able to believe in their own importance and that of data. Harari himself raises some criticisms, such as the problem of consciousness, which Dataism is unlikely to illuminate. Humans may also find out that organisms are not algorithms, he suggests. Dataism implies that all data is public, even personal data, to make the system work as a whole, which is a factor that's already showing resistance today. Other analysts, such as Terry Ortleib, have looked at the extent to which Dataism poses a dystopian threat to humanity. The Facebook–Cambridge Analytica data scandal showed how political leaders manipulated Facebook's users' data to build specific psychological profiles that went on to manipulate the network. A team of data analysts reproduced the AI technology developed by Cambridge Analytica around Facebook's data and was able to define the following rules: 10 likes enables a machine to know a person like a coworker, 70 likes like a friend would, 150 likes like a parent would, 300 likes like a lover would, and beyond it may be possible to know a people better than they know themselves.
Supertoroid
In geometry and computer graphics, a supertoroid or supertorus is usually understood to be a family of doughnut-like surfaces (technically, a topological torus) whose shape is defined by mathematical formulas similar to those that define the superellipsoids. The plural of "supertorus" is either supertori or supertoruses. The family was described and named by Alan Barr in 1994. Barr's supertoroids have been fairly popular in computer graphics as a convenient model for many objects, such as smooth frames for rectangular things. One quarter of a supertoroid can provide a smooth and seamless 90-degree joint between two superquadric cylinders. However, they are not algebraic surfaces (except in special cases). == Formulas == Alan Barr's supertoroids are defined by parametric equations similar to the trigonometric equations of the torus, except that the sine and cosine terms are raised to arbitrary powers. Namely, the generic point P(u, v) of the surface is given by P ( u , v ) = ( X ( u , v ) Y ( u , v ) Z ( u , v ) ) = ( ( a + C u s ) C v t ( b + C u s ) S v t S u s ) {\displaystyle P(u,v)=\left({\begin{array}{c}X(u,v)\\Y(u,v)\\Z(u,v)\end{array}}\right)=\left({\begin{array}{c}(a+C_{u}^{s})C_{v}^{t}\\(b+C_{u}^{s})S_{v}^{t}\\S_{u}^{s}\end{array}}\right)} where C θ ε = sgn ( cos θ ) | cos θ | ε , S θ ε = sgn ( sin θ ) | sin θ | ε , {\displaystyle {\begin{aligned}C_{\theta }^{\varepsilon }&=\operatorname {sgn} (\cos \theta )\,\left|\,\cos \theta \,\right|^{\varepsilon },\\S_{\theta }^{\varepsilon }&=\operatorname {sgn} (\sin \theta )\ \left|\,\sin \theta \ \right|^{\varepsilon },\end{aligned}}} sgn is the sign function, and the parameters u, v range from 0 to 360 degrees (0 to 2π radians). In these formulas, the parameter s > 0 controls the "squareness" of the vertical sections, t > 0 controls the squareness of the horizontal sections, and a, b ≥ 1 are the major radii in the x and y directions. With s = t = 1 and a = b = R one obtains the ordinary torus with major radius R and minor radius 1, with the center at the origin and rotational symmetry about the z-axis. In general, the supertorus defined as above spans the intervals: − ( a + 1 ) ≤ x ≤ + ( a + 1 ) − ( b + 1 ) ≤ y ≤ + ( b + 1 ) − 1 ≤ z ≤ + 1 {\displaystyle {\begin{array}{rcccl}-(a+1)&\leq &x&\leq &+(a+1)\\[4pt]-(b+1)&\leq &y&\leq &+(b+1)\\[4pt]-1&\leq &z&\leq &+1\end{array}}} The whole shape is symmetric about the planes x = 0, y = 0, and z = 0. The hole runs in the z direction and spans the intervals − ( a − 1 ) ≤ x ≤ + ( a − 1 ) − ( b − 1 ) ≤ y ≤ + ( b − 1 ) − ∞ ≤ z ≤ + ∞ {\displaystyle {\begin{array}{rcccl}-(a-1)&\leq &x&\leq &+(a-1)\\[4pt]-(b-1)&\leq &y&\leq &+(b-1)\\[4pt]-\infty &\leq &z&\leq &+\infty \end{array}}} A curve of constant u on this surface is a horizontal Lamé curve with exponent 2 t , {\displaystyle {\tfrac {2}{t}},} scaled in x and y and displaced in z. A curve of constant v, projected on the plane x = 0 or y = 0, is a Lamé curve with exponent 2 s , {\displaystyle {\tfrac {2}{s}},} scaled and horizontally shifted. If v = 0, the curve is planar and spans the intervals: a − 1 ≤ x ≤ a + 1 − 1 ≤ z ≤ + 1 {\displaystyle {\begin{array}{rcccl}a-1&\leq &x&\leq &a+1\\[4pt]-1&\leq &z&\leq &+1\end{array}}} and similarly if v = 90°, 180°, 270°. The curve is also planar if a = b. In general, if a ≠ b and v is not a multiple of 90 degrees, the curve of constant v will not be planar; and, conversely, a vertical plane section of the supertorus will not be a Lamé curve. The basic supertoroid shape defined above is often modified by non-uniform scaling to yield supertoroids of specific width, length, and vertical thickness. == Plotting code == The following GNU Octave code generates plots of a supertorus:
Feigenbaum test
A Feigenbaum test is a variation of the Turing test where a computer system attempts to replicate an expert in a given field such as chemistry or marketing. It is also known, as a subject matter expert Turing test and was proposed by Edward Feigenbaum in a 2003 paper. The concept is also described by Ray Kurzweil in his 2005 book The Singularity is Near. Kurzweil argues that machines who pass this test are an inevitable consequence of Moore's Law.