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Positive psychology

Positive psychology is a field of psychological theory and research of optimal human functioning of people, groups, and institutions. It studies "positive subjective experience, positive individual traits, and positive institutions... it aims to improve quality of life."

Positive psychology began as a new domain of psychology in 1998 when Martin Seligman chose it as the theme for his term as president of the American Psychological Association. It is a reaction against past practices which tended to focus on mental illness and which emphasized maladaptive behavior and negative thinking. It builds on the humanistic movement of Abraham Maslow and Carl Rogers, which encourages an emphasis on happiness, well-being, and purpose.

Positive psychology largely relies on concepts from the Western philosophical tradition, such as the Aristotelian concept of, which is typically rendered in English with the terms "flourishing", "the good life" or "happiness". Positive psychologists study empirically the conditions and processes that contribute to flourishing, subjective well-being, and happiness, often using these terms interchangeably.

Positive psychologists suggest a number of factors that may contribute to happiness and subjective well-being, for example: social ties with a spouse, family, friends, colleagues, and wider networks; membership in clubs or social organizations; physical exercise; and the practice of meditation. Spiritual practice and religious commitment is another possible source for increased well-being. Happiness may rise with increasing income, though it may plateau or even fall when no further gains are made or after a certain cut-off amount.

Definition
Martin Seligman and Mihaly Csikszentmihalyi define positive psychology as "the scientific study of positive human functioning and flourishing on multiple levels that include the biological, personal, relational, institutional, cultural, and global dimensions of life."

Basic concepts
Positive psychology concerns, a word that means human thriving or flourishing. A "good life" is defined by psychologists and philosophers as consisting of authentic expression of self, a sense of well-being, and active engagement in life.

Positive psychology aims to complement and extend traditional problem-focused psychology. It concerns positive states (e.g. happiness), positive traits (e.g. talents, interests, strengths of character), positive relationships, and positive institutions and how these apply to physical health.

Seligman proposes that a person can best promote their well-being by nurturing their character strengths. Seligman identifies other possible goals of positive psychology: families and schools that allow children to grow, workplaces that aim for satisfaction and high productivity, and teaching others about positive psychology.

A basic premise of positive psychology is that human actions arise from our anticipations about the future; these anticipations are informed by our past experiences.

Those who practice positive psychology attempt psychological interventions that foster positive attitudes toward one's subjective experiences, individual traits, and life events. The goal is to minimize pathological thoughts that may arise in a hopeless mindset and to develop a sense of optimism toward life. Positive psychologists seek to encourage acceptance of one's past, excitement and optimism about one's future, and a sense of contentment and well-being in the present.

Happiness
Happiness can be defined in two general ways: an enjoyable state of mind, and the living of an enjoyable life.

Quality of life
Quality of life is how well you are living and functioning in life. It encompasses more than just physical and mental well-being; it can also include socioeconomic factors. This term can be perceived differently in different cultures and regions around the world.

Research topics
According to Seligman and Christopher Peterson, positive psychology addresses three issues: positive emotions, positive individual traits, and positive institutions. Positive emotions concern being content with one's past, being happy in the present, and having hope for the future. Positive individual traits are one's strengths and virtues. Positive institutions are strengths to better a community of people.

According to Peterson, positive psychologists are concerned with four topics: positive experiences, enduring psychological traits, positive relationships, and positive institutions. He also states that topics of interest to researchers in the field are states of pleasure or flow, values, strengths, virtues, talents, as well as the ways that these can be promoted by social systems and institutions.

History
The positive psychology movement was first founded in 1998 by Martin Seligman. He was concerned about the fact that mainstream psychology was too focused on disease, disorders, and disabilities rather than wellbeing, resilience, and recovery. His goal was to apply the methodological, scientific, scholarly and organizational strengths of mainstream psychology to facilitate well-being rather than illness and disease.

The field has been influenced by humanistic as well as psychodynamic approaches to treatment. Predating the use of the term "positive psychology", researchers within the field of psychology had focused on topics that would now be included under this new denomination.

The term "positive psychology" dates at least to 1954, when Abraham Maslow's Motivation and Personality was published with a final chapter titled "Toward a Positive Psychology." In the second edition published in 1970, he removed that chapter, saying in the preface that "a positive psychology is at least available today though not very widely." There have been indications that psychologists since the 1950s have increasingly focused on promoting mental health rather than merely treating mental illness. From the beginning of psychology, the field addressed the human experience using the "Disease model," studying and identifying the dysfunction of a person.

In the opening sentence of his book Authentic Happiness, Seligman claimed: "for the last half century psychology has been consumed with a single topic only—mental illness," expanding on Maslow's comments. He urged psychologists to continue the earlier missions of psychology of nurturing talent and improving normal life.

Development
The first positive psychology summit took place in 1999. The First International Conference on Positive Psychology took place in 2002. In September 2005, the first master's program in applied positive psychology (MAPP) was launched at the University of Pennsylvania. In 2006, a course on positive psychology at Harvard University was one of the most popular courses on offer. In June 2009, the First World Congress on Positive Psychology took place in Philadelphia.

The field of positive psychology today is most advanced in the United States, Canada, Western Europe, and Australia.

Influences
Several humanistic psychologists, most notably Maslow, Carl Rogers, and Erich Fromm, developed theories and practices pertaining to human happiness and flourishing. More recently, positive psychologists have found empirical support for the humanistic theories of flourishing.

In 1984, psychologist Ed Diener published his tripartite model of subjective well-being, which posited "three distinct but often related components of wellbeing: frequent positive affect, infrequent negative affect, and cognitive evaluations such as life satisfaction." In this model, cognitive, affective, and contextual factors contribute to subjective well-being. According to Diener and Suh, subjective well-being is "based on the idea that how each person thinks and feels about his or her life is important."

Carol Ryff's six-factor model of psychological well-being was first published in 1989. It postulates that self-acceptance, personal growth, purpose in life, environmental mastery, autonomy, and positive relations with others are key to well-being.

According to Corey Keyes, who collaborated with Carol Ryff and uses the term flourishing as a central concept, mental well-being has three components: hedonic (i.e. subjective or emotional ), psychological, and social well-being. Hedonic well-being concerns emotional aspects of well-being, whereas psychological and social well-being, e.g. eudaimonic well-being, concerns skills, abilities, and optimal functioning. This tripartite model of mental well-being has received cross-cultural empirical support.

Influences in ancient history

Before the use of the term "positive psychology" there were researchers who focused on topics that would now be included under the umbrella of positive psychology. Some view positive psychology as a meeting of Eastern thought, such as Buddhism, and Western psychodynamic approaches.

The historical roots of positive psychology are found in the teachings of Aristotle, whose Nicomachean Ethics is a description of the theory and practice of human flourishing—which he referred to as —of the tutelage necessary to achieve it, and of the psychological obstacles to its practice. It teaches the cultivation of virtues as the means of attaining happiness and well-being.

Core theory and methods
There is no accepted "gold standard" theory in positive psychology. The work of Seligman is regularly quoted, as is the work of Csikszentmihalyi, and older models of well-being, such as Ryff's six-factor model of psychological well-being and Diener's tripartite model of subjective well-being.

Later, Paul Wong introduced the concept of second-wave positive psychology.

Initial theory: three paths to happiness
In Authentic Happiness (2002) Seligman proposed three kinds of a happy life that can be investigated:
 * 1) Pleasant life: research into the pleasant life, or the "life of enjoyment", examines how people optimally experience, forecast, and savor the positive feelings and emotions that are part of normal and healthy living (e.g., relationships, hobbies, interests, entertainment, etc.). Seligman says this most transient element of happiness may be the least important.
 * 2) Good Life: investigation of the beneficial effects of immersion, absorption, and flow felt by people when optimally engaged with their primary activities, is the study of the Good Life, or the "life of engagement". Flow is experienced when there is a match between a person's strengths and their current task, i.e., when one feels confident of accomplishing a chosen or assigned task. Related concepts include self-efficacy and play.
 * 3) Meaningful Life: inquiry into the meaningful life, or "life of affiliation", questions how people derive a positive sense of well-being, belonging, meaning, and purpose from being part of and contributing back to something larger and more enduring than themselves (e.g., nature, social groups, organizations, movements, traditions, belief systems).

PERMA
In Flourish (2011), Seligman argued that the last category of his proposed three kinds of a happy life, "meaningful life", can be considered as three different categories. The resulting summary for this theory is the mnemonic acronym PERMA: Positive Emotions, Engagement, Relationships, Meaning and purpose, and Accomplishments.
 * Positive emotions : include a wide range of feelings, not just happiness and joy, but excitement, satisfaction, pride, and awe, amongst others. These are connected to positive outcomes, such as longer life and healthier social relationships.
 * Engagement : refers to involvement in activities that draw and build upon one's interests. Csikszentmihalyi explains true engagement as flow, a state of deep effortless involvement, a feeling of intensity that leads to a sense of ecstasy and clarity. The task being done must call upon a particular skill and it should be possible while being a little bit challenging. Engagement involves passion for and concentration on the task at hand—complete absorption and loss of self-consciousness.
 * Relationships : are essential in fueling positive emotions, whether they are work-related, familial, romantic, or platonic. As Peterson puts it, "other people matter." Humans receive, share, and spread positivity to others through relationships. Relationships are important in bad times and good times. Relationships can be strengthened by reacting to one another positively. Typically positive things take place in the presence of other people.
 * Meaning : is also known as purpose, and answers the question of "why?" Discovering a clear "why" puts everything into context from work to relationships to other parts of life. Finding meaning is learning that there is something greater than oneself. Working with meaning drives people to continue striving for a desirable goal.
 * Accomplishments : are the pursuit of success and mastery. Unlike the other parts of PERMA, they are sometimes pursued even when accomplishments do not result in positive emotions, meaning, or relationships. Accomplishments can activate other elements of PERMA, such as pride, under positive emotion. Accomplishments can be individual or community-based, fun-based, or work-based.

Each of the five PERMA elements was selected according to three criteria:
 * 1) It contributes to well-being.
 * 2) It is pursued for its own sake.
 * 3) It is defined and measured independently of the other elements.

Character Strengths and Virtues
The Character Strengths and Virtues (CSV) handbook (2004) was the first attempt by Seligman and Peterson to identify and classify positive psychological traits of human beings. Much like the Diagnostic and Statistical Manual of Mental Disorders (DSM) of general psychology, the CSV provided a theoretical framework to assist in understanding strengths and virtues and for developing practical applications for positive psychology. It identified six classes of virtues (i.e., "core virtues"), underlying 24 measurable character strengths.

The CSV suggested these six virtues have a historical basis in the vast majority of cultures and that they can lead to increased happiness when built upon. Notwithstanding numerous cautions and caveats, this suggestion of universality leads to three theories:
 * 1) The study of positive human qualities broadens the scope of psychological research to include mental wellness.
 * 2) The leaders of the positive psychology movement challenge moral relativism by suggesting people are "evolutionarily predisposed" toward certain virtues.
 * 3) Virtue has a biological basis.

The organization of the six virtues and 24 strengths is as follows:
 * 1) Wisdom and knowledge: creativity, curiosity, open-mindedness, love of learning, perspective, innovation, prudence
 * 2) Courage: bravery, persistence, vitality, zest
 * 3) Humanity: love, kindness, social intelligence
 * 4) Justice: citizenship, fairness, leadership, integrity, excellence
 * 5) Temperance: forgiveness and mercy, humility, self-control
 * 6) Transcendence: appreciation of beauty, gratitude, hope, humor, spirituality

Subsequent research challenged the need for six virtues. Instead, researchers suggested the 24 strengths are more accurately grouped into just three or four categories: Intellectual Strengths, Interpersonal Strengths, and Temperance Strengths, or alternatively, Interpersonal Strengths, Fortitude, Vitality, and Cautiousness. These strengths, and their classifications, have emerged independently elsewhere in literature on values. Paul Thagard described some examples.

Flow
In the 1970s, Csikszentmihalyi began studying flow, a state of absorption in which one's abilities are well-matched to the demands at-hand. He often refers to it as "optimal experience". Flow is characterized by intense concentration, loss of self-awareness, a feeling of being perfectly challenged (neither bored nor overwhelmed), and a sense that "time is flying." Flow is intrinsically rewarding; it can also assist in the achievement of goals (e.g., winning a game) or improving skills (e.g., becoming a better chess player). Anyone can experience flow and it can be felt in different domains, such as play, creativity, and work.

Flow is achieved when the challenge of the situation meets one's personal abilities. A mismatch of challenge for someone of low skills results in a state of anxiety and feeling overwhelmed; insufficient challenge for someone highly skilled results in boredom. A good example of this would be an adult reading a children's book. They would not feel challenged enough to be engaged or motivated in the reading. Csikszentmihalyi explained this using various combinations of challenge and skills to predict psychological states. These four states included the following:

 * Apathy: low challenge and low skill(s)
 * Relaxation: low challenge and high skill(s)
 * Anxiety: high challenge and low skill(s)
 * Flow: high challenge and high skill(s)

Accordingly, an adult reading a children's book would most likely be in the relaxation state. The adult has no need to worry that the task will be more than they can handle. Challenge is a well-founded explanation for how one enters the flow state and employs intense concentration. However, other factors contribute. For example, one must be intrinsically motivated to participate in the activity/challenge. If the person is not interested in the task, then there is no possibility of their being absorbed into the flow state.

Benefits
Flow can help in parenting children. When flow is enhanced parents and children, the parents can better thrive in their roles as a parents. A parenting style that is positively oriented results in children who experience lower levels of stress and improved well-being.

Flow also has benefits in a school setting. When students are in a state of flow they are fully engaged, leading to better retention of information. Students who experience flow have a more enjoyable and rewarding experience. This state can also reduce stress, which helps with students' mental health and well-being. This increases resilience and helps students to overcome challenges or setbacks by teaching them a growth mindset.

Most teachers and parents want students become more engaged and interested in the classroom. The design of the education system was not able to account for such needs. One school implemented a program called PASS. They acknowledged that students needed more challenge and individual advancement; they referred to this as sport culture. This PASS program integrated an elective class into which students could immerse themselves. Such activities included self-paced learning, mastery-based learning, performance learning, and so on.

Flow benefits general well-being. It is a positive and intrinsically motivating experience. It is known to "produce intense feelings of enjoyment". It can improve our lives by making them happier and more meaningful. Csikszentmihalyi discovered that our personal growth and development generates happiness. Flow is positive experience because it promotes that opportunity for personal development.

Negatives
While flow can be beneficial to students, students who experience flow can become overly focused on a particular task. This can lead to students neglecting other important aspects of their learning.

In positive psychology there can be misunderstandings on what clinicians and people define as positive. In certain instances, positive qualities, such as optimism, can be detrimental to health, and therefore appear as a negative quality. Alternatively, negative processes, such as anxiety, can be conducive to health and stability and thus would appear as positive qualities. A second wave of positive psychology has further identified and characterized "positive" and "negative" complexes through the use of critical and dialectical thinking. Researchers in 2016 chose to identify these characteristics via two complexes: post-traumatic growth and love as well as optimism vs. pessimism.

Second-wave positive psychology
Paul Wong introduced the idea of a second wave of positive psychology, focused on the pursuit of meaning in life, which he contrasted with the pursuit of happiness in life. Ivtzan, Lomas, Hefferon, and Worth have recast positive psychology as being about positive outcome or positive mental health, and have explored the positive outcomes of embracing negative emotions and pessimism. Second-wave positive psychology proposes that it is better to accept and transform the meaning of suffering than it is to avoid suffering.

In 2016, Lomas and Itzvan proposed that human flourishing (their goal for positive psychology) is about embracing dialectic interplay of positive and negative. Phenomena cannot be determined to be positive or negative independent of context. Some of their examples included:

 * the dialectic of optimism and pessimism: Optimism is associated with longevity, but strategic pessimism can lead to more effective planning and decision making.
 * the dialectic of self-esteem and humility: Self-esteem is related to well-being, but pursuit of self-esteem can increase depression. Humility can be either low self-opinion or it can lead to prosocial action.
 * the dialectic of forgiveness and anger: Forgiveness has been associated with well-being, but people who are more forgiving of abuse may suffer prolonged abuse. While anger has been presented as a destructive emotion, it can also be a moral emotion and drawn upon to confront injustices.

In 2019, Wong proposed four principles of second-wave positive psychology:

Second-wave positive psychology is sometimes abbreviated as PP 2.0.
 * 1) accepting and confronting with courage the reality that life is full of evil and suffering
 * 2) sustainable wellbeing can only be achieved through overcoming suffering and the dark side of life
 * 3) recognizing that everything in life comes in polarities and the importance of achieving an adaptive balance through dialectics
 * 4) learning from indigenous psychology, such as the ancient wisdom of finding deep joy in bad situations

Third-wave positive psychology
The third wave of positive psychology emphasizes going beyond the individual to take a deeper look at the groups and systems in which we live. It also promotes becoming more interdisciplinary and multicultural and incorporates more methodologies.

In broadening the scope and exploring the systemic and socio-cultural dimensions of people's lived realities, there are four specific things to focus on:

 * 1) The focus of enquiry: becoming more interested in emergent paradigms like "systems-informed positive psychology" which incorporates principles and concepts from the systems sciences to optimize human social systems and the individuals within them.
 * 2) Disciplines: becoming more multi- and interdisciplinary, as reflected in hybrid formulations like positive education, which combines traditional education and research based ways of increasing happiness and overall well-being.
 * 3) Cultural contexts: becoming more multicultural and global
 * 4) Methodologies: embracing other paradigms and ways of knowing, such as qualitative and mixed methods approaches rather than relying solely on quantitative research.

Research advances and applications
Subject-matter and methodology development expanded the field of positive psychology beyond its core theories and methods. Positive psychology is now a global area of study, with various national indices tracking citizens' happiness ratings.

Research findings
Research in positive psychology, well-being, and happiness, and the theories of Diener, Ryff, Keyes, and Seligman cover a broad range of topics including "the biological, personal, relational, institutional, cultural, and global dimensions of life."

A meta-analysis of 49 studies showed that Positive Psychology Interventions (PPI) produced improvements in well-being and lower depression levels; the PPIs studied included writing gratitude letters, learning optimistic thinking, replaying positive life experiences, and socializing with others. In a later meta-analysis of 39 studies with 6,139 participants, the outcomes were positive. Three to six months after a PPI the effects on subjective well-being and psychological well-being were still significant. However the positive effect was weaker than in the earlier meta-analysis; the authors concluded that this was because they only used higher-quality studies. The PPIs they considered included counting blessings, kindness practices, making personal goals, showing gratitude, and focusing on personal strengths. Another review of PPIs found that over 78% of intervention studies were conducted in Western countries.

In the textbook Positive Psychology: The Science of Happiness, authors Compton and Hoffman give the "Top Down Predictors" of well-being as high self esteem, optimism, self efficacy, a sense of meaning in life, and positive relationships with others. The personality traits most associated with well-being are extraversion, agreeability, and low levels of neuroticism.

In a study published in 2020, students were enrolled in a positive psychology course that focused on improving happiness and well-being through teaching about positive psychology. The participants answered questions pertaining to the five PERMA categories. At the end of the semester those same students reported significantly higher scores in all categories (p<.001) except for engagement which was significant at p<.05. The authors stated, “Not only do students learn and get credit, there is also a good chance that many will reap the benefits in what is most important to them—their health, happiness, and well-being.”

Quantitative
Quantitative methods in positive psychology include p-technique factor analysis, dynamic factor analysis, interindividual differences and structural equation modeling, spectral analysis and item response models, dynamic systems analysis, latent growth analysis, latent-class models, hierarchical linear modeling, measurement invariance, experimental methods, behavior genetics, and integration of quantitative and qualitative approaches.

Qualitative
Grant J. Rich explored the use of qualitative methodology to study positive psychology. Rich addresses the popularity of quantitative methods in studying the empirical questions that positive psychology presents. He argues that there is an "overemphasis" on quantitative methods and suggests implementing qualitative methods, such as semi-structured interviews, observations, fieldwork, creative artwork, and focus groups. Rich states that qualitative approaches will further promote the "flourishing of positive psychology" and encourages such practice.

Behavioral interventions
Changing happiness levels through interventions is a further methodological advancement in the study of positive psychology, and has been the focus of various academic and scientific psychological publications. Happiness-enhancing interventions include expressing kindness, gratitude, optimism, humility, awe, and mindfulness.

One behavioral experiment used two six-week interventions: one involving the performance of acts of kindness, and one focused on gratitude which emphasized the counting of one's blessings. The study participants who went through the behavioral interventions reported higher levels of happiness and well-being than those who did not participate in either intervention.

Another study found that the interventions of expressing optimism and expressing gratitude enhanced subjective well-being in participants who took part in the intervention for eight months. The researchers concluded that interventions are "most successful when participants know about, endorse, and commit to the intervention." The article provides support that when people enthusiastically take part in behavioral interventions, such as expression of optimism and gratitude, they may increase happiness and subjective well-being.

Another study examined the interaction effects between gratitude and humility through behavior interventions. The interventions were writing a gratitude letter and writing a 14-day diary. In both interventions, the researchers found that gratitude and humility are connected and are "mutually reinforcing." The study also discusses how gratitude, and its associated humility, may lead to more positive emotional states and subjective well-being.

A series of experiments showed a positive effect of awe on subjective well-being. People who felt awe also reported feeling they had more time, more preference for experiential expenditures than material expenditures, and greater life satisfaction. Experiences that heighten awe may lead to higher levels of life satisfaction and, in turn, higher levels of happiness and subjective well-being.

Mindfulness interventions may also increase subjective well-being in people who mindfully meditate. Being mindful in meditation includes awareness and observation of one's meditation practice, with non-reactive and non-judgmental sentiments during meditation.

National indices of happiness
The creation of various national indices of happiness have expanded the field of positive psychology to a global scale.

In a January 2000 article in American Psychologist, psychologist Ed Diener argued for the creation of a national happiness index in the United States. Such an index could provide measurements of happiness, or subjective well-being, within the United States and across many other countries in the world. Diener argued that national indices would be helpful markers or indicators of population happiness, providing a sense of current ratings and a tracker of happiness across time. Diener proposed that the national index include various sub-measurements of subjective well-being, including "pleasant affect, unpleasant affect, life satisfaction, fulfillment, and more specific states such as stress, affection, trust, and joy." In 2012, the first World Happiness Report was published. The World Happiness Report was initiated by the UN General Assembly in June 2011, when it passed the Bhutanese Resolution. The Bhutanese Resolution called for nations across the world to "give more importance to happiness and well-being in determining how to achieve and measure social and economic development." The data for the World Happiness Reports is collected in partnership with the Gallup World Poll's life evaluations and annual happiness rankings. The World Happiness Report bases its national rankings on how happy constituents believe themselves to be.

The first World Happiness Report, published in 2012, detailed the state of world happiness, the causes of happiness and misery, policy implications from happiness reports, and three case studies of subjective well-being for 1) Bhutan and its Gross National Happiness index, 2) the U.K. Office for National Statistics Experience, and 3) happiness in the member countries within the OECD.

The 2020 World Happiness Report, the eighth in the series of reports, was the first to include happiness rankings of cities across the world, in addition to rankings of 156 countries. The city of Helsinki, Finland was reported as the city with the highest subjective well-being ranking, and the country of Finland was reported as the country with the highest subjective well-being ranking. The 2020 report provided insights on happiness based on environmental conditions, social conditions, urban-rural happiness differentials, and sustainable development. It also provided possible explanations for why Nordic countries have consistently ranked in the top ten happiest countries in the World Happiness Report, such as Nordic countries' high-quality government benefits and protections to its citizens, including welfare benefits and well-operated democratic institutions, as well as social connections, bonding, and trust.

Additional national well-being indices and reported statistics include the Gallup Global Emotions Report, Sharecare Community Well-Being Index, Global Happiness Council's Global Happiness and Well-being Policy Report, Happy Planet Index, OECD Better Life Index, and UN Human Development Reports.

Influences on other academic fields
Positive psychology influenced other academic fields of study and scholarship, notably organizational behavior, education, and psychiatry.

Positive organizational scholarship
Positive organizational scholarship (POS), also referred to as positive organizational behavior (POB), began as an application of positive psychology to the field of organizational behavior. An early use of the term was in Positive Organizational Scholarship: Foundations of a New Discipline (2003), edited by Ross School of Business professors Kim S. Cameron, Jane E. Dutton, and Robert E. Quinn. The editors promote "the best of the human condition", such as goodness, compassion, resilience, and positive human potential, as an organizational goal as important as financial success. The goal of POS is to study the factors that create positive work experiences and successful, people-oriented outcomes.

The 2011 volume The Oxford Handbook of Positive Organizational Scholarship, covers such topics as positive human resource practices, positive organizational practices, and positive leadership and change. It applies positive psychology to the workplace context, covering areas such as positive individual attributes, positive emotions, strengths and virtues, and positive relationships. The editors of that volume define POS this way:"Positive organizational scholarship rigorously seeks to understand what represents the best of the human condition based on scholarly research and theory. Just as positive psychology focuses on exploring optimal individual psychological states rather than pathological ones, organizational scholarship focuses attention on the generative dynamics in organizations that lead to the development of human strength, foster resiliency in employees, enable healing and restoration, and cultivate extraordinary individual and organizational performance. POS emphasizes what elevates individuals and organizations (in addition to what challenges them), what goes right in organizations (in addition to what goes wrong), what is life-giving (in addition to what is problematic or life-depleting), what is experienced as good (in addition to what is objectionable), and what is inspiring (in addition to what is difficult or arduous)."

Psychiatry
Positive psychology influenced psychiatry and led to more widespread promotion of practices including well-being therapy, positive psychotherapy, and an integration of positive psychology in therapeutic practice.

Benefits of positive influences can be seen in practices like positive psychological interventions (PPIs). It is an intervention designed to promote positive outcomes by implying positive activities such as imposing adaptive personality traits to be praised and encouraged. Research has found that PPIs has the potential to improve medical and psychiatric disorders of individuals with depression and suicidal levels. Department of Developmental Services (DDS) did a research on a 52-year-old single gay man with bipolar II disorder and attention deficit hyperactive disorder (ADHD) with low self-esteem. In addition, there were other focuses of this research: promoting kindness behavior, identifying, and encouraging internal strengths to reach a fulfilling life. PPIs increases the individuality's purpose with constant strengthen on personality traits and behavior positivity.

Psychoanalysis can be used to treat mental illnesses such as depression as it focuses on identifying the conscious and unconscious motivations and behaviors affecting one's life. Treatment using psychoanalysis runs in a longer duration by practicing free association to promote personal growth. Cognitive behavioral therapy (CBT), a common type of psychotherapy in America, focuses on both psychoanalysis and behavioral analysis: psychoanalysts focusing on conscious and unconscious motivations, behaviorists focusing on objectively measured behaviors. Therapy such as exposure therapy helps people with specific aspects of depression, or more specific cases like social phobia.

Positive psychology may assist those recovering from traumatic brain injury (TBI). TBI rehabilitation practices rely on bettering the patient's life by getting them to engage (or re-engage) in normal everyday practices, an idea which is related to tenets of positive psychology. While the empirical evidence for positive psychology is limited, positive psychology's focus on small successes, optimism, and prosocial behavior promises to improve the social and emotional well-being of TBI patients.

Popular culture
Positive psychology is a subject of popular books and films, and influences the wellness industry.

Books
Several popular psychology books have been written for a general audience.

Ilona Boniwell's Positive Psychology in a Nutshell provided a summary of the research. According to Boniwell, well-being is related to optimism, extraversion, social connections (i.e., close friendships), being married, having engaging work, religion or spirituality, leisure, good sleep and exercise, social class (through lifestyle differences and better coping methods), and subjective health (what you think about your health). Boniwell writes that well-being is not related to age, physical attractiveness, money (once basic needs are met), gender (women are more often depressed but also more often joyful), educational level, having children, moving to a sunnier climate, crime prevention, housing, and objective health (what doctors say).

Sonja Lyubomirsky's The How of Happiness provides advice on how to improve happiness. According to this book, people should create new habits, seek out new emotions, use variety and timing to prevent hedonic adaptation, and enlist others to support the creation of those new habits. Lyubomirsky recommends twelve happiness activities, including savoring life, learning to forgive, and living in the present.

Stumbling on Happiness by Daniel Gilbert shares positive psychology research suggesting that people are often poor at predicting what will make them happy and that people are prone to misevaluating the causes of their happiness. He notes that the subjectivity of well-being and happiness often is the most difficult challenge to overcome in predicting future happiness, as our future selves may have different perspectives on life than our current selves.

Films
The film industry noticed positive psychology, and films have spurred new research within positive psychology.

Happy is a full-length documentary film covering positive psychology and neuroscience. It highlights case studies on happiness across diverse cultures and geographies. The film features interviews with notable positive psychologists and scholars, including Gilbert, Diener, Lyubomirsky, and Csikszentmihalyi.

For several years, the Positive Psychology News website included a section on Positive Psychology Movie Awards that highlighted feature films that featured messages of positive psychology.

The VIA Institute has researched positive psychology as represented in feature films. Contemporary and popular films that promote or represent character strengths are the basis for various academic articles.

Wellness industry
The growing popularity and attention given to positive psychology research has influenced industry growth, development, and consumption of products and services meant to cater to wellness and well-being.

According to the Global Wellness Institute, as of 2020, the global wellness economy is valued at US$4.4trillion; the key sectors of the industry included Nutrition, Personal Care and Beauty, and Physical activity, while the Mental wellness and Public health sectors made up over US$0.5billion.

Companies highlight happiness and well-being in their marketing strategies. Food and beverage companies such as Coca-Cola and Pocky—whose motto is "Share happiness!" —emphasize happiness in their commercials, branding, and descriptions. CEOs at retail companies such as Zappos have profited by publishing books detailing how they deliver happiness, while Amazon's logo features a dimpled smile.

Criticism
Many aspects of positive psychology have been criticized.

Reality distortion
In 1988, psychologists Shelley E. Taylor and Jonathan D. Brown co-authored a Psychological Bulletin article that coined the phrase positive illusions. Positive illusions are the cognitive processes people engage in when they self-aggrandize or self-enhance. They are unrealistically positive or self-affirming attitudes that individuals hold about themselves, their position, or their environment. They are attitudes of extreme optimism that endure in the face of facts and real conditions.

Taylor and Brown suggest that positive illusions protect people from negative feedback that they might receive, and this, in turn, preserves their psychological adaptation and subjective well-being. However, later research found that positive illusions and related attitudes lead to psychological maladaptive conditions such as poorer social relationships, expressions of narcissism, and negative workplace outcomes, thus reducing the positive effects that positive illusions have on subjective well-being, overall happiness, and life satisfaction.

Kirk Schneider, editor of the Journal of Humanistic Psychology, pointed to research showing high positivity correlates with positive illusion, which distorts reality. High positivity or flourishing could make one incapable of psychological growth, unable to self-reflect, and prone to holding racial biases. By contrast, negativity, sometimes evidenced in mild to moderate depression, is correlated with less distortion of reality. Therefore, Schneider argues, negativity might play an important role: engaging in conflict and acknowledging appropriate negativity, including certain negative emotions like guilt, might better promote flourishing. Schneider wrote: "perhaps genuine happiness is not something you aim at, but is... a by-product of a life well lived—and a life well lived does not settle on the programmed or neatly calibrated."

Narrow focus
In 2003, Ian Sample noted that "Positive psychologists also stand accused of burying their heads in the sand and ignoring that depressed, even merely unhappy people, have real problems that need dealing with." He quoted Steven Wolin, a clinical psychiatrist at George Washington University, as saying that the study of positive psychology is just a reiteration of older ways of thinking, and that there is not much scientific research to support the efficacy of this method.

Psychological researcher Shelly Gable retorts that positive psychology is just bringing a balance to a side of psychology that is glaringly understudied. She points to imbalances favoring research into negative psychological well-being in cognitive psychology, health psychology, and social psychology.

Psychologist Jack Martin maintains that positive psychology is not unique in its optimistic approach to emotional well-being, stating that other forms of psychology, such as counseling and educational psychology, are also interested in positive human fulfillment. He says while positive psychology pushes for schools to be more student-centered and able to foster positive self-images in children, a lack of focus on self-control may prevent children from making full contributions to society. If positive psychology is not implemented correctly, it can cause more harm than good. This is the case, for example, when interventions in school are coercive (in the sense of being imposed on everyone without regard for the child's reason for negativity) and fail to take each student's context into account.

Role of negativity
Barbara S. Held, a professor at Bowdoin College, argues that positive psychology has faults: negative side effects, negativity within the positive psychology movement, and the division in the field of psychology caused by differing opinions of psychologists on positive psychology. She notes the movement's lack of consistency regarding the role of negativity. She also raises issues with the simplistic approach taken by some psychologists in the application of positive psychology. A "one size fits all" approach is arguably not beneficial; she suggests a need for individual differences to be incorporated into its application. By teaching young people that being confident and optimistic leads to success, when they are unsuccessful they may believe this is because they are insecure or pessimistic. This could lead them to believe that any negative internal thought or feeling they may experience is damaging to their happiness and should be steered clear of completely.

Held prefers the Second Wave Positive Psychology message of embracing the dialectic nature of positive and negative, and questions the need to call it "positive" psychology.

Toxic positivity
One critical response to positive psychology concerns "toxic positivity". Toxic positivity is when people do not fully acknowledge, process, or manage the entire spectrum of human emotion, including anger and sadness. This genre of criticism argues that positive psychology places too much importance on "upbeat thinking, while shunting challenging and difficult experiences to the side." People who engage in a constant chase for positive experiences or states of high subjective well-being may inadvertently stigmatize negative emotional conditions such as depression, or may suppress natural emotional responses, such as sadness, regret, or stress. Furthermore, by not allowing negative emotional states to be experienced, or by suppressing and hiding negative emotional responses, people may experience harmful physical, cardiovascular, and respiratory consequences. Opponents of toxic positivity advocate accepting and fully experiencing negative emotional states.

Methodological and philosophical critiques
Richard Lazarus critiqued positive psychology's methodological and philosophical components. He holds that giving more detail and insight into the positive is not bad, but not at the expense of the negative, because the two (positive and negative) are inseparable. Among his critiques:

 * 1) Positive psychology's use of correlational and cross-sectional research designs to indicate causality between the movement's ideas and healthy lives may hide other factors and time differences that account for observed differences.
 * 2) Emotions cannot be categorized dichotomously into positive and negative; emotions are subjective and rich in social/relational meaning. Emotions are fluid, meaning that the context they appear in changes over time. Lazarus states that "all emotions have the potential of being either one or the other, or both, on different occasions, and even on the same occasion when an emotion is experienced by different persons"
 * 3) Individual differences are neglected in most social science research. Many research designs focus on the statistical significance of the groups while overlooking differences among people.
 * 4) Social science researchers' tend to not adequately define and measure emotions. Most assessments are quick checklists and do not provide adequate debriefing. Many researchers do not differentiate between fluid emotional states and relatively stable personality traits.

Lazarus holds that positive psychology claims to be new and innovative but the majority of research on stress and coping theory makes many of the same claims as positive psychology. The movement attempts to uplift and reinforce the positive aspects of one's life, but everyone in life experiences stress and hardship. Coping through these events should not be regarded as adapting to failures but as successfully navigating stress, but the movement doesn't hold that perspective.

Another critique of positive psychology is that it has been developed from a Eurocentric worldview. Intersectionality has become a methodological concern regarding studies within Positive Psychology.

A literature review conducted in 2022 noted several criticisms of the area, including lack of conceptual thinking, problematic measurements, poor replication of results, self-isolation from mainstream psychology, decontextualization, and being used for capitalism.

The US Army's Comprehensive Soldier Fitness program
The Comprehensive Soldier Fitness (CSF) program was established in 2008 by then-Chief of Staff of the United States Army, General George W. Casey, Jr., in an effort to address increasing rates of drug abuse, family violence, PTSD, and suicide among soldiers. The Army contracted with Seligman's Positive Psychology Center at the University of Pennsylvania to supply a program based on the center's Penn Resiliency Program, which was designed for 10- to 14-year-old children. Although Seligman proposed starting with a small-scale pilot-test, General Casey insisted on immediately rolling out the CSF to the entire Army. Interviewed for the journal Monitor on Psychology of the American Psychological Association, Seligman said that "This is the largest study—1.1 million soldiers—psychology has ever been involved in." According to journalist Jesse Singal, "It would become one of the largest mental-health interventions geared at a single population in the history of humanity, and possibly the most expensive."

Some psychologists criticized the CSF for various reasons. Nicholas J.L. Brown wrote: "The idea that techniques that have demonstrated, at best, marginal effects in reducing depressive symptoms in school-age children could also prevent the onset of a condition that is associated with some of the most extreme situations with which humans can be confronted is a remarkable one that does not seem to be backed up by empirical evidence." Stephen Soldz of the Boston Graduate School of Psychoanalysis cited Seligman's acknowledgment that the CSF is a gigantic study rather than a program based on proven techniques, and questioned the ethics of requiring soldiers to participate in research without informed consent. Soldz also criticized the CSF training for trying to build up-beat attitudes toward combat: "Might soldiers who have been trained to resiliently view combat as a growth opportunity be more likely to ignore or under-estimate real dangers, thereby placing themselves, their comrades, or civilians at heightened risk of harm?"

In 2021 the Chronicle of Higher Education carried a debate between Singal and Seligman about whether, with the CSF well into its second decade, there was any solid evidence of its effectiveness. Singal cited studies that, he said, failed to find any measurable benefits from such positive psychology techniques, and he criticized the Army's own reports as methodologically unsound and lacking peer review. Seligman said that Singal had misinterpreted the studies and ignored the Army's positive feedback from soldiers, one of whom told Seligman that "if I had had this training years ago, it would have saved my marriage."

title: Positive psychology


text:
Odyssey (Yngwie Malmsteen album)

Odyssey is the fourth studio album by guitarist Yngwie Malmsteen, released on 8 April 1988 through Polydor Records. The album reached No. 40 on the US Billboard 200 and remained on that chart for eighteen weeks, as well as reaching the top 50 in five other countries. As of 2021 it remains Malmsteen's highest-charting release on the Billboard 200.

Critical reception
Steve Huey at AllMusic gave Odyssey two stars out of five, calling it "a more subdued, polished collection seemingly designed for mainstream radio airplay", but that it "shows little difference in approach from [Malmsteen's] previous output". He praised Joe Lynn Turner's vocals and Malmsteen's guitar work, but remarked that the latter sounds "constrained and passionless" due in part to his recovery from a near-fatal car accident in 1987.

Personnel

 * Yngwie Malmsteen – guitar, Moog Taurus, bass (tracks 3–7, 10–12), arrangement, producer
 * Joe Lynn Turner – vocals
 * Jens Johansson – keyboard
 * Anders Johansson – drums
 * Bob Daisley – bass (tracks 1, 2, 8, 9)
 * Jeff Glixman – engineer, producer
 * John Rolio – engineer
 * Scott Gordon – assistant engineer, assistant mixing engineer
 * Steve Thompson – mixing
 * Michael Barbiero – mixing
 * George Cowan – assistant mixing engineer
 * Jim Lewis – executive producer

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Odyssey (Yngwie Malmsteen album)


text:
Talk:Inverse-square law

Point sources?
Inverse-square laws are about point sources, and yet it sounds like point sources can't actually exist. (Doesn't the Planck length, among other things, imply that things must have a certain minimum size?) In light of this apparent paradox, can someone explain why inverse-square laws are to any extent successful? Perhaps there are empirically-derived bounds along the lines of "if two masses both have volumes less than Vsmall, then Newton's gravitation law will give results that shall not deviate by more than 1x10^(-8) newtons from the true value"? --Ryguasu 17:31 Feb 6, 2003 (UTC)

Partly it's something along those lines. Notice that one of Newton's laws says that if no force acts on an object it continues at the same velocity, but one may object that there has never been an object on which no force acted, and the objection is somewhat parallel to what you're saying. Newton demonstrated mathematically that if the earth has uniform density then its gravitational field outside of the sphere in which its mass exists, is the same as if all the mass were concentrated at the center. So that's another reason. Michael Hardy 00:23 Feb 7, 2003 (UTC)

 * For example, Sol "provides" 9140W at the distance of Mercury (0.387AU); but only 1370W at the distance of Earth (1AU)

It would be useful if the formula to get the above values (9140 and 1370) were given too.

It does not make sense to use watts as the unit here. Perhaps watts-per-square-meter or something like that was intended instead? If so, it needs to say so. Michael Hardy 22:58, 12 Jan 2004 (UTC)

 * Looking at the Principia Mathematica first edition -- it may BE Robert Hooke who advance the Inverse-Square in relation to gravity first... - Sparky 06:01, 18 January 2004
 * Do you mean Philosophiae Naturalis Principia Mathematica? QuentinUK (talk) 23:01, 6 January 2012 (UTC)

The diagram
I just looked at the diagram I drew again and I realised it doesn't look terribly good. I am going to redraw it. Does anybody have some suggestions as to how I can make it better? -- Borb 00:39, 31 December 2005 (UTC)

 * Looks good to me. If you were specific about what you think needs improvement in it, maybe I could say more. Michael Hardy 02:44, 31 December 2005 (UTC)

 * It doesn't look very high quality, I was going to draw it again anyway, I just wondered if there was a different way I should draw it. A diagram could be either showing a quarter of the lines going through the same sized square, as in my diagram, or it could be showing the same number of lines going through a square 4 times the size of the original. Does anybody have a preference on which type I should draw? Also, technically the "squares" should be part of a sphere so I might try making them look like that. -- Borb 20:14, 2 January 2006 (UTC)
 * If you can access a copy of Edgar Allan Poe's Eureka, you will find a perfectly clear visual illustration of this law.Lestrade 15:21, 12 February 2006 (UTC)Lestrade

 * The diagram is wrong. Look at the red lines, one of them is actually going the wrong way, and end up in a completely new place in the 3r area. Irios 11:28, 3 March 2010

Diagram
The first diagram I ever saw of the inverse square law was better, in my opinion. It showed ...

Nevermind, I found some similar ones:  — Omegatron 18:16, 19 February 2006 (UTC)

What about lasers?

- I agree on the diagram comment. Looking at the two linked images here the first did not work. The second is a great diagram. Displaying the four and then nine squares at each of the given distance values displays how the light is being spread out over greater distance.

p. 47 of Bill Bryson's A Short History of Nearly Everything explains that Halley (of Halley's Comet fame) was the one who went to Newton to ask him about a math problem concerning the inverse square law. Halley and Hooke were acquaintances and were involved in a bet to see who could solve the problem first. After Newton started publishing books with his findings, Hooke said he had already discovered the answer and accused Newton of plagiarism.

Light and other electromagnetic radiation
It would be appropriate to add the word "Interestingly" to the start of this section, I am perplexed attempting to explain connection Omeganumber (talk) 02:26, 1 March 2008 (UTC)

citation
how do you cite it? —Preceding unsigned comment added by 24.236.97.242 (talk) 18:34, 7 March 2008 (UTC)

New Diagram!
Well I finally got around to drawing a new diagram of the inverse square law. Comments/Suggestions etc? It's not the easiest law to illustrate... -- Borb (talk) 14:05, 2 April 2008 (UTC)

Hi If you could show the first square as a more intense shade of yellow, and the third as a very pale shade of yellow, that might help to illustrate the fact that intensity has diminished by to one-quarter and then one-ninth. — Preceding unsigned comment added by 116.90.137.88 (talk) 20:10, 7 August 2013 (UTC)

Acoustics section
This is intended as constructive criticism regarding the "acoustics" entries on the inverse square law page. I don't like to see popular misconceptions perpetuated. I guess if I knew how to present what I feel is the correct information on the page I would have edited it rather than posing a comment here, but I am an absolute novice when it comes to Wikipedia editing. But to get to the point…

The propagation of sound *does* obey the inverse square law in exactly the same way as electromagnetic radiation does. Sound *pressure* is not a valid equivalent to electromagnetic radiated power as a source – you are not comparing like with like. As the distance from the source increases, the acoustic *power* fall as the inverse square of the distance – double the distance means a quarter of the power, or 6·02dB; this equates to (and is the cause of) a halving of sound *pressure*, since pressure is proportional to the square root of power times radiation resistance, the latter being constant.

If my knowledge of acoustics is faulty, then please disregard the foregoing comments, if not, then maybe you might consider editing the relevant sections of the page accordingly.

S Sycamore (talk) 19:16, 8 August 2008 (UTC)

Above copied from User_talk:Borb -- Borb (talk) 20:58, 8 August 2008 (UTC)

 * If anything, the section as written is confusing to the layperson, both physically and mathematically. The section reads "In acoustics one usually measures the sound pressure at a given distance r from the source using the 1/r law. Since intensity is proportional to the square of pressure amplitude, this is just a variation on the inverse-square law." On its face, this seems to suggest that this whole section does not belong on this page at all, as it is inversely proportional and not inverse-square. Could someone clarify (for the layman) the difference between "pressure" and "intensity," as that seems to be the sticking point?  NewkirkPlaza (talk) 19:19, 22 October 2014 (UTC)

 * I removed acoustics section - it may be correct, but not explained to a depth that makes it fit (understandable) into the article. I think it would be hard or impossible to fix that, because much depends on the use of dB in that section, which makes the numbers hard to understand. Also, the reader would need to understand the relation of sound power, amplitude, pressure and loudness (or most of it) to make sense of the calculations in terms of perceived sound intensity. (Oh, and the dB is usually referring to a standardized psychoacoustic weighting of frequencies, which complicates it some more.) — Preceding unsigned comment added by Volker Siegel (talk • contribs) 14:10, 29 July 2016 (UTC)

Light Emitting Diodes (LEDs)
Is it possible that the LED device .. designed to remove infrared radiation (IR) from the white light spectrum does not follow the Inverse-square law as is? Sorta meaning IR helps carry light through distance?Greg0658 (talk) 16:42, 9 February 2009 (UTC) More clearly put .. does LED light fall-off at a different rate than full spectrum electromagnetic waves and white light?Greg0658 (talk) 13:58, 13 May 2009 (UTC)
 * No the inverse square law is a spreading function and is independent of the spectrum of radiation. The typical LED has a built in reflector and lenses that direct the light in one direction. Inverse square still applies but it's as if the point source was originated somewhere far to the rear of the actual LED so the fall of is less per unit distance after the LED surface. 12.106.237.2 (talk) 17:15, 15 April 2010 (UTC)

If the light spreads out over some space as it moves away from the source, it spreads over the same amount of space regardless of whether it's from a light-emitting diode or from some other kind of source. Michael Hardy (talk) 17:34, 15 April 2010 (UTC)

accuracy - Point Source Approximation
From ISBN 0-9658356-9-3 Ryer, A, "The Light Measurement Handbook", 1997 : p.26. (The chapter is also available online here)

Under the heading "Point Source Approximation" Ryer describes 1) some practical limitations of the inverse square rule, 2) a more accurate and encompassing alternative formula which includes non-point sources.

If I have interpreted correctly: for illuminance from a non-point-source - ie where the diameter of the light source is more than 1/5th of the distance - the following formula may be more useful: E = Lr2/(r2 + d2); where r= source radius and d= distance.

This would certainly seem like a valid addition to the Inverse-square_law section. Perhaps it would also be applicable in other contexts ? --Redbobblehat (talk) 14:07, 10 February 2009 (UTC)

Watts Versus Candles

 * I was trying to look up a solution to a problem I had run into regarding Inverse Square law calculations given a distance variable of 0 (which would involve division by 0, which is unallowed), although I see someone has made a comment referring to limitations of inverse square law, and that may be one of them.
 * However, much of the work I am doing involves simulated sunlight, and I noticed the potentially useful mention of the relative illumination of the sun at the surfaces of Mercury and the Earth; but I was a bit puzzled as to why this is presented in watts? Watts are a measurement of energy consumption, not illumination: for that reason, it's impossible to convert between watts and candles since energy consumption given an illuminative power is variable: in other words, different lights produce varying amounts of illumination given the same energy consumption. So I can't convert the value to a useful illuminative power. Perhaps this should be given in candles instead? LSmok3 Talk 12:10, 7 December 2009 (UTC)

A clearer summary definition for the layman is needed
This article could greatly benefit by the addition of a clear summary for the layman appended near the beginning. I came away with not much greater an understanding of the concept of the inverse-square law than I had before I read this. Not enough, I had to go to several other web sources to acquire a basic understanding. I am a well-educated person without much mathematics (which is a large demographic). Someone with a thorough grasp of the term and its applications, as well as related concepts, should write a brief non-technical, non-specialist definition and place it near the beginning of the article. The depth and breadth of Wikipedia articles is commendable and very useful, but just as often readers seek to gain a basic grasp of a thoroughly unfamiliar subject. We can do both here, it just needs 50-100 words of cogent definition added.Googlyelmo (talk) 19:06, 22 October 2010 (UTC) Googlyelmo (talk) 19:06, 22 October 2010 (UTC)

Kepler's beliefs
Hi there Wikipedians- I removed the part of the sentence under 'gravitation' which read " instead of the guess of Johannes Kepler at inverse distance dependence"

I'm researching pre-Newtonian gravitation and can't find any other mention that Kepler accepted a 1/d law for gravity. He certianly used a 1/d relation for orbital velocity- but that's not the same thing at all as gravitational attraction. If someone finds a reference then I think it could be reintroduced. In the meantime it shouldn't be there as it's unsubstantiated. 188.220.171.33 (talk) 17:33, 26 November 2010 (UTC)

Hello 188.220.171.33. I wonder if Kepler merits inclusion as it does work out that the inverse of the square of the velocity of a planet is directly proportional to its radius. Uglysses

The Flux Visualisation
I just noticed an error in the introductional picture about the flux behaviour. The intersection points of the three central rays with the third distance sphere are obviously wrong (compared to the first two spheres). If you klick on the image it is presented correctly, so it should be an easy matter to change this. Anyways, i have no idea how to do that. Greetings to all fans of the inverse square law. — Preceding unsigned comment added by 92.224.175.6 (talk) 11:37, 10 September 2011 (UTC)

To do: some mathematics
The article should present a mathematical discussion of the force field of four special cases. The force should be derived – not only from the flux, but also by integrating over an even distribution of charges. -- Petri Krohn (talk) 22:52, 17 January 2012 (UTC)
 * 1) The outside of a spherical charge distribution (equal to a point charge)
 * 2) The inside of a spherical charge distribution (zero)
 * 3) Infinitely long linear charge. (inverse to distance)
 * 4) Infinitely large planar charge. (constant at all distances from plane.)

Entropy and energy density
What is the relation of the ISL to space-time? --TheLastWordSword (talk) 17:37, 3 August 2015 (UTC)

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Non euclidean geometries
The reference to Barrow's 2020 is not an original reference, and there are mathematical problems which would confuse a reader grasping for an understanding, or even a professional for that matter. Hyperbolic geometry in relation to general relativity has been dealt with extensively in the literature i.e. in monograph form. See, for examples, the Wikipedia references. Citing lecture notes (by Guth), which contain no references hardly does the subject of the applications of nun euclidean geometries justice. Why should lecture notes replace a vast literature on the subject? Bernhlav (talk) 15:39, 19 March 2024 (UTC)

title: Talk:Inverse-square law