8.3: What Thinking Means
“If you’re going to do anything as much as you think, you might just as well learn about it and hone this skill.”
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Thinking is one of those hard-to-pinpoint aspects of life we typically don’t analyze much—like breathing or walking or sleeping. We constantly think, and becoming more attuned to how we think and what we do when we encounter new ideas is an excellent habit to pursue.
“If you’re going to do anything as much as you think, you might just as well learn about it and hone this skill.”
You may have read quotes or inspirational slogans that claim you are what you think. What does that mean? Can you think yourself into a good mood? Can you think you have a million dollars in your pocket? Does that mean you are the next music sensation if you often sing at parties? Not necessarily, but consider Jose, for instance. He isn’t a rock and roll star, but Jose spends a lot of his leisure time thinking about music, analyzing performances, memorizing his favorite musicians’ characteristics, buying fan clothing, and even designing a creative means to explain his excitement for music to his friends through a homemade video. Jose certainly could allow his fascination to seep into other aspects of his life. Do you have a hobby or interest you spend a lot of time thinking about?
Many people go to great lengths to attend a concert by a favorite music star. They think creatively about how to save enough money for tickets; they think analytically about scheduling their other obligations to have time off work to attend or how to make up work in their college classes. This much planning involves a great deal of thinking, and not all about music. In the example about Jose, thinking directs the actions of the person doing the thinking. So, in fact, what we think does influence who we are and how we act. We have many resources available to be more effective thinkers, and learning about these resources gives us options.
Apps and search engines literally bring thinking to our fingertips. Consider how often you visit Google. The use of this familiar site has become so commonplace as to render the proper name of the company into a verb— to google a topic. Basic calculators or word-processing software programs are other simple examples of technology we often use without recognizing them as thinking aids.
While apps, software programs, thinking games, and thought exercises may help you stretch your brain, don’t let their simplicity fool you into thinking that cultivating an inquisitive, thoughtful mind is easy or automatic. Thinking is as complex as it is necessary for our success in life. Some tools you may find useful are applications that provide challenges using mind puzzles are Peak(opens in new window) and Elevate(opens in new window) . These training apps offer brain training that varies from quick matching memory games to more sophisticated thought-processing speed scenarios. You can even use a straightforward tool like a flashcard app, such as Chegg Prep , to create your own thinking games -- using word associations or pictures to help you connect topics and build your skills.
A familiar element of the thinking apps is a progression tracker to help thinkers improve their focus and memory as well as to learn and practice math and verbal skills over time. Researchers are still investigating the correlation between thought-invoking game playing and the decrease in mental agility, memory, and cognitive vitality. Early studies have produced numerous findings, including a long-term investigation of the onset of Alzheimer’s disease conducted with nuns; you can look up the Nun Study to learn more, or go to this article(opens in new window) .


3.1: Diverse Patients Introduction
- Reflect upon personal and cultural values, beliefs, biases, and heritage [1]
- Embrace diversity, equity, inclusivity, health promotion, and health care for individuals of diverse geographic, cultural, ethnic, racial, gender, and spiritual backgrounds across the life span [2]
- Demonstrate respect, equity, and empathy in actions and interactions with all health care consumers [3]
- Participate in life-long learning to understand cultural preferences, worldviews, choices, and decision-making processes of diverse patients [4]
- Protect patient dignity
- Demonstrate principles of patient-centered care and cultural humility
- Make adaptations to patient care to reduce health disparities
- Adhere to the Patient’s Bill of Rights
- Identify strategies to advocate for patients
- Use evidence-based practices
No matter who we are or where we come from, every person belongs to a culture. The impact of culture on a person’s health is profound because it affects many health beliefs, such as perceived causes of illness, ways to prevent illness, and acceptance of medical treatments. Culturally responsive care integrates these cultural beliefs into an individual’s health care. Culturally responsive care is intentional and promotes trust and rapport with patients. At its heart, culturally responsive care is patient-centered care. The American Nurses Association (ANA) states, “The art of nursing is demonstrated by unconditionally accepting the humanity of others, respecting their need for dignity and worth, while providing compassionate, comforting care.” [5]
Nurses provide holistic care when incorporating their patients’ physical, mental, spiritual, cultural, and social needs into their health care (referred to as holism ). As a nursing student, you are undertaking a journey of developing cultural competency with an attitude of cultural humility as you learn how to provide holistic care to your patients. Cultural competency is a lifelong process of applying evidence-based nursing in agreement with the cultural values, beliefs, worldview, and practices of patients to produce improved patient outcomes. [6] , [7] , [8] Cultural humility is defined by the American Nurses Association as, “A humble and respectful attitude toward individuals of other cultures that pushes one to challenge their own cultural biases, realize they cannot know everything about other cultures, and approach learning about other cultures as a life-long goal and process. [9] The bottom line is you will improve the quality of your nursing care by understanding, respecting, and responding to a patient’s experiences, values, beliefs, and preferences. [10]
This chapter will focus on developing culturally competency and cultural humility and providing culturally responsive care.
- American Nurses Association. (2021). Nursing: Scope and standards of practice (4th ed.). American Nurses Association ↵
- American Nurses Association. (2021). Nursing: Scope and standards of practice (4th ed.). American Nurses Association ↵
- American Nurses Association. (2021). Nursing: Scope and standards of practice (4th ed.). American Nurses Association ↵
- American Nurses Association. (2021). Nursing: Scope and standards of practice (4th ed.). American Nurses Association ↵
- American Nurses Association. (2021). Nursing: Scope and standards of practice (4th ed.). American Nurses Association ↵
- Centers for Disease Control and Prevention. (2020, October 21). Cultural competence in health and human services . https://npin.cdc.gov/pages/cultural-competence ↵
- Curtis, E., Jones, R., Tipene-Leach, D., Walker, C., Loring, B., Paine, S.-J., & Reid, P. (2019). Why cultural safety rather than cultural competency is required to achieve health equity: A literature review and recommended definition. International Journal for Equity in Health, 18, 174. https://doi.org/10.1186/s12939-019-1082-3 ↵
- Young, S., & Guo, K. (2016). Cultural diversity training: The necessity for cultural competence for healthcare providers and in nursing practice. The Health Care Manager, 35 (2), 94-102. https://doi.org/10.1097/hcm.0000000000000100 ↵
- American Nurses Association. (2021). Nursing: Scope and standards of practice (4th ed.). American Nurses Association ↵
- U.S. Department of Health and Human Services. (n.d.). Cultural and Linguistically Appropriate Services (CLAS) in Maternal Health Care. https://thinkculturalhealth.hhs.gov/ ↵


8.2: Retribution
Retribution
Retribution , arguably the oldest of the ideologies/philosophies of punishment, is the only backward-looking philosophy of punishment. That is, the primary goal of retribution (in its original form) is to ensure that punishments are proportionate to the seriousness of the crimes committed, regardless of the individual differences between offenders, other than mens rea and an understanding of moral culpability. Thus, retribution focuses on the past offense, rather than the offender. This can be phrased as “a balance of justice for past harm.” People committing the same crime should receive a punishment of the same type and duration that balances out the crime that was committed. The term-backward-looking means that the punishment does not address anything in the future, only for the past harm done.


4.4: Alderian Psychotherapy
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Adler’s approach to psychotherapy has been the topic of numerous books and chapters (e.g., Dinkmeyer, Dinkmeyer, Jr., & Sperry, 1979; Mosak, 1995; Nikelly, 1971a; Watts & Carlson, 1999), including specific books on family therapy and lifestyle counseling for people with disabilities (Rule, 1984; Sherman & Dinkmeyer, 1987). It is generally accepted that Adlerian psychotherapists have no specific technique, but rather are eclectic in their approach. There are, however, a few key elements to Individual Psychology. First is the goal of understanding the style of life. Once the therapist understands the style of life, they can understand most everything the patient does. The therapist then helps the patient to strengthen their social interest. This involves a practical application of social interest: reorienting and readjusting the patient’s style of life. Underlying the success of therapy in Individual Psychology is a supportive therapeutic relationship. Adler believed in facing his clients, on an equal basis. The therapist helps to educate the patient on the nature of therapy and the goals that might be pursued, which involves helping the client to recognize the mistaken style of life and goals they have been pursuing in the past. In this way, the therapist helps the client in their own creative process of personality change (Dinkmeyer, Dinkmeyer, Jr., & Sperry, 1979; Mosak, 1995). This approach shares many similarities with both the client-centered approach popularized by Carl Rogers and the behavioral-cognitive approaches developed by Albert Ellis and Aaron Beck.
Understanding the Style of Life
Psychotherapy is about helping people to change their lives for the better. Thus, it involves looking forward, despite whether or not we need to know what has happened in the past (and different theories consider the importance of the past in radically different ways). According to Adler, “in order to understand a person’s future we must understand his style of life” (pg. 99; Adler, 1929a). The style of life, and the associated scheme of apperception, brings all experience into line with the person’s fictional final goal. So, if we can understand how a person is living their life, if we understand their style of life, we can help them to understand it as well, and then perhaps make changes for the better. So, how might we go about understanding the style of life?
As Freud and Breuer had before him, one area of interest for Adler was the analysis of dreams. However, Adler did not distinguish between the conscious and unconscious, or between waking and sleep. He considered dreams to be a reflection of the style of life, and the individual’s striving for superiority. Thus, dreams do not hold any special meaning (Adler, 1912b/1963, 1928, 1929a, 1932b/1964). As such, their interpretation can be relatively straight-forward:
Take, for instance, our knowledge that mankind as a whole is really cowardly. From this general fact we can presuppose that the largest number of dreams will be dreams of fear, danger, or anxiety. And so if we know a person and see that his goal is to escape the solution of life’s problems, we can guess that he often dreams that he falls down. Such a dream is like a warning to him: “Do not go on - you will be defeated.” (pg. 155; Adler, 1929a)
Of greater interest to Adler was the analysis of early memories . He believed that the earliest childhood recollections provided valuable information, and he did not let a single patient go without having been asked about them:
The information regarding memory is significant. Memory is an activity. It is based on the life style, which here steps in by selecting from old impressions a single one. This leads us to the question, why this single one? In it the entire life style resonates. (pg. 197; Adler, 1932b/1964)
It is not even important if the memory is, in fact, true. A “memory” may be created by a child based on their conscious experience in order to reflect an attitude, or an emotional tone, if that is necessary to pursue their unique, personal goal (Adler, 1928). Accordingly, if we can obtain a person’s earliest memories, we make reasonable predictions regarding the future course of their life. However, early memories are not reasons for behavior, but they are hints. It is also true that some forgotten memories (or unconscious memories) may have played a role in the creation of the style of life, but they are obviously more difficult to obtain, so they defy analysis. But, Adler did not consider them to be any different in content and tone from the conscious memories; the unconscious psyche enacts the same style of life toward the same final goal (as with dreams; Adler, 1929a, 1931a, 1964). There may, however, be some interesting differences in early memories based on culture. For example, Wang (2006b) examined the earliest memories of European American and Taiwanese college students in response to five cue words: self, mother, family, friend, and surroundings. In both groups, memories for ‘mother’ came from an earlier time than memories for ‘self,’ and memories for ‘mother,’ ‘family,’ and ‘friend’ were more socially oriented. The European Americans typically had memories from earlier ages, and their memories tended to report more specific events and to focus on their personal roles and autonomy in those memories. Thus, early memories not only reflect one’s style of life, but do so within a cultural context.
In two major case studies published by Adler, The Case of Miss R. (1929b) and The Case of Mrs. A (1931b), the subtitle of each book refers to the style of life. In the latter book, he concludes by saying: “I have simply wanted to show you the COHERENCE OF A LIFE-STYLE” (pg. 46; Adler, 1931b). Moving well beyond neurosis, both Adler and his son Kurt applied the study of the style of life to patients suffering from psychotic disorders, including schizophrenia and manic phase of bipolar disorder (Adler, 1929/1964; Kurt Adler, 1959). Kurt Adler does an excellent job of summarizing Individual Psychology, and he quotes his father’s description of neurosis and psychosis as attempts by a person to avoid clashing with reality and exposing their weakness and inferiority. However, these are “failed” styles of life, because they lead to an avoidance of social interest, which is necessary for solving life’s challenges in cooperation with others. In the case of a disorder such as schizophrenia, the child begins life with extreme feelings of inferiority, which lead to an exaggerated fictional goal. Subsequently, it is more difficult to achieve any success in life, which creates a vicious cycle of failure and greater distrust of others. Finally, as the individual fails to develop social-emotional capacities, common sense, or logic, they retreat into the private world that accommodates their exaggerated fictional personal goal. The subsequent treatment of psychotic patients is difficult, particularly if the therapist expects too much. Kurt Adler extends his father’s caution that the therapist must be aware of their own style of life, set aside any personal expectations, and never expect anything of the patient (Kurt Adler, 1959). As we will see below, Harry Stack Sullivan also paid special attention to psychodynamic processes in schizophrenia.
Discussion Question: What are your earliest memories, especially of your mother, father, and sense of self? Can you see a clear relationship between the content of those memories and your style of life? How does your life plan fit with those memories?
Strengthening Social Interest and Reorienting the Style of Life
Adler believed that everyone has some degree of social interest, but in neurotic and psychotic patients there is relatively less. He described Freudian transference as an expression of the patient’s social interest, directed toward the therapist. Resistance is simply the patient lacking the courage (i.e., feeling too inferior) to return to social usefulness and cooperation with others. The therapist must, therefore, help the patient to strengthen their social interest and reorient their style of life. Since the style of life is creatively formed, it becomes important to understand how and when the failed style of life began. Just as the individual took time and was selective in the formation of their failed style of life, the therapist must take time to understand it and educate the patient about it (Adler, 1913b/1963, 1929/1964, 1930c, 1932b/1964, 1958).
Individual Psychology stresses enormously that the psychological development of a person can reach a normal condition only when he can achieve the necessary degree of ability to cooperate. (pg. 199; Adler, 1932b/1964)
It is almost impossible to exaggerate the value of an increase in social feeling…The feeling of worth and value is heightened, giving courage and an optimistic view…The individual feels at home in life and feels his existence to be worthwhile just so far as he is useful to others… (pg. 79; Adler, 1929/1964)
There are numerous ways in which a therapist can help a client to increase their social interest. It begins with the therapist openly communicating with and accepting the patient, which is, of course, a social interaction. This is especially effective if the therapist displays social feeling themselves, while also helping the patient to recognize the patient’s value as a human being (as well as the value of other people). The therapist can point out that if other people, including the therapist, had the same values, goals, and cognitive orientation as the patient then others would also have the same problems as the patient. The therapist can then nudge the patient toward their own niche, where they can feel comfortable with others without fearing being the loser in personal interactions. And finally, the therapist can encourage the patient to get involved in concerns outside themselves (Nikelly, 1971b). Each of these ways of encouraging social interest can be a part of the reorientation and readjustment process, the “working-through” phase of therapy, in which the patient gains insight into their style of life, confronts their goals, and realizes that they are capable of making choices and decisions (Nikelly & Bostrom, 1971). The patient must be encouraged to understand and believe that they have the power to implement their insights and change their life.
The client must not be allowed to think of himself as the victim of past circumstances but must come to recognize that the problem is his alone and that he alone will solve it. In contrast, emphasis on past history may lead to rationalization and intellectualization without appropriate action. The client learns more and more about his problem and does less and less about it. (pg. 103; Nikelly & Bostrom, 1971)
Group Psychotherapy and Family Therapy
Our discussion of Adlerian psychotherapy would not be complete without mentioning group psychotherapy , and in the same breath, family therapy . Group psychotherapy probably has multiple origins, having been tried by a variety of independent therapists. In 1921, Adler began interviewing and counseling parents in front of a group of professionals. This fit well within his perspective on the three life tasks and social interest, since he felt that parents, family, and other important people, such as school teachers, needed to be involved in the development of children. Adler soon discovered that these settings led to personal growth in everyone present, establishing a form of group therapy that may be the oldest still in use. Strictly speaking, Individual Psychology does not prescribe any specific techniques for group psychotherapy, but rather, there is Individual Psychology for patients in a private setting as well as for patients receiving therapy in a group setting (Corsini, 1971).
Involving the parents in a child’s therapy is, quite obviously, the beginning of family therapy. However, when Adler established his child guidance centers, they were open for parents, teachers, social workers, and other interested people to be able to observe the process of psychotherapy. Adler felt it was important for everyone involved in the development of children to be educated in the important process of Individual Psychology, and the same was true of Rudolf Dreikurs, a student of Adler who opened family education centers in the United States (the first in Chicago in 1937; see Dreikurs, 1950; Sherman & Dinkmeyer, 1987). This education may be particularly important for the parents, whose attitude can have a profound influence on whether psychotherapy for a child is successful or not. As for teachers, understanding Individual Psychology can help them to put a child’s academic performance into a context that helps to explain it as a style of life aimed toward a particular goal, even if that goal is dysfunctional and interferes with schoolwork (Friedmann, 1930; Spiel & Birnbaum, 1930). Overall, the goal of family therapy is to improve communication and cooperation amongst all members of the family, and to help parents avoid the most difficult problems (Alexandra Adler, 1930a; Adler, 1930d).
In our conversations with the parents we relentlessly try to make them realize that children must not be beaten. Beating can only lead to a discouragement of the child, and we know well enough that this can make the child worse and not better…We always dissuade parents from engaging in warfare with the child, since the child inevitably remains in the end the stronger party. (pp. 110-111; Alexandra Adler, 1930a)
Discussion Question: Have you ever experienced group psychotherapy, family therapy, or anything similar (or know anyone who has)? What advantages did you experience, or what do you think you might experience if you were to work on your relationships with family members or other people?


6.6: Using BEAM
Booker, M. K. (2012). Manufacturing taste: The culture industry, children’s culture, and the globalization of American values. Pop Culture Universe: Icons, Idols, Ideas . ABC-CLIO.
BEAM: Background Sources
Background sources should be noncontroversial—the author accepts information from these sources as being authoritative (and expects readers to, as well). In other words, the sources (and the information gleaned from them) are generally trusted or undisputed. That information can serve as the incontestable foundation for your claims.
Background information is common knowledge (e.g. the sky is blue) and not necessary to cite. It’s recommended that you cite a background source if you’re unsure if it’s common knowledge. It can be difficult to make this determination, so it’s always a good idea to consult your professor.
Let’s look at a statement in the first paragraph of the pop culture essay:
Thus, the corporate giants of the American Culture Industry (themselves now mostly multinational conglomerates) clearly must pay attention to the demands of audiences around the world in formulating, producing, and promoting the specific films, television, music, and other artifacts that are the stuff of popular culture.
How do you know that the “corporate giants are mostly multinational conglomerates” as stated in the first sentence? Or that the items listed are indeed the stuff of popular culture? These are examples of common knowledge.
Looking a little deeper…
Without context, this paragraph could also be the conclusion of a paper about what corporations should do (demonstrating the ongoing nature of knowledge itself). But the paper is not about making recommendations to the American Cultural Industry. This is an assertion that the author uses to help set up his different arguments and is meant to be taken at face value. So it’s an example of how the same source can play different roles in different written assignments—all depending on how writers use them.
There is more about background sources at Background Reading.
BEAM: Exhibit and Evidence Sources
Generally, exhibit and evidence sources are works of literature (or other media), collected data, or some observed phenomenon, etc. that you have been asked to write about. They are what you analyze or interpret.
Looking again at the pop culture essay, the exhibits being examined are pop culture and American (as well as global) values. Specifically, the essay is examining the relationship between the two:
On the other hand, the international success of Toy Story 3, a film that deals with anthropomorphized toys and is thus essentially a consumerist fantasy of commodities come to life, also suggests that global distribution of the products of the American Culture Industry is beginning to have an impact on the tastes and values of audiences even outside the United States.
Exhibit sources are not limited to examples in the humanities; they could also be data that was collected in a scientific experiment or by a website’s user survey. They can also simply serve as examples that help support a claim.
BEAM: Argument Sources
Argument sources provide you with the other voices in the academic conversation about your topic. Who else has done similar research, and how should your paper respond to what they’ve said? Does your paper refine or extend an existing hypothesis someone else has tested? If so, those sources belong in your paper.
Sometimes the purpose of including an argument source is to disagree with it and definitively indicate a different direction.
From our pop culture essay example:
Althusser’s work remains compelling, despite the fact that theorists such as Michel de Certeau and John Fiske have argued that individuals actually have a considerable ability to resist and oppose the messages conveyed to them by official ideology, in popular culture and elsewhere.
The author is taking part and taking a stand in the ongoing scholarly discussion of culture, although this endorsement of Althusser’s work could possibly be considered a method source if the argument in the article went in a different direction.
BEAM: Method Sources
While argument sources help you frame your paper within the larger scholarly discussion about your topic and exhibits provide a focal point, method sources help provide underlying and sometimes implicit assumptions for your argument or analysis.
For some research, these are literally the methods you use to collect data like a focus group or a particular statistical analysis, and they provide justification for them. In other research, your paper might reveal a leaning toward a major attitude or school of thought within a discipline.
As a persuasive piece of writing, the essay has this intrinsic thread of caution and warning that is summed up in its conclusion:
The children’s film industry might not be quite as sinister as the tobacco industry, with its efforts to addict children to cigarettes. […] Meanwhile, the lives of those audiences are now being increasingly saturated by popular culture, making it more and more difficult for individuals to form attitudes, opinions, and values that are independent of the messages promulgated by the Culture Industry.
While this is a subtle example, you would generally cite or at least credit your methods and theories that frame your analysis in your bibliography.


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attachment
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emotional and affective bond between an infant and their primary caregiver
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attention-seeking behavior
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emotion regulation strategy that consists of an effort to obtain a caregiver’s attention for comfort and support
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attentional distraction
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emotion regulation strategy that consists of turning away from a stressful sound, sight, or event
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autonomy
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sense of independence or freedom to control yourself and your actions
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autonomy versus doubt
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second stage in Erikson’s theory of personality development, in which the toddler forms a sense of autonomy based on whether they are encouraged to try new skills and tasks
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blended family
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family that includes stepparents or stepsiblings
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body-as-obstacle test
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test of self-awareness in which an infant needs to move their body to accomplish a goal
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center care
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childcare provided in a commercial center that is regulated and licensed by the government
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commuter family
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family in which one or more family members split their time between households
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difficult temperament (undercontrolled/exuberant)
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temperament in which the infant has an irregular routine, high intensity, and negative mood and is slow to adapt to new experiences
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disorganized attachment
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pattern of behavior in which infants are confused or inconsistent in their response to the absence of their caregiver
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dyadic regulation
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process of calming an infant down through touch, feeding, or distraction
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easy temperament (resilient)
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temperament in which an infant may be more adaptable and able to thrive in a variety of contexts, establishes a routine quickly, and typically has a positive mood
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effortful control
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includes traits related to impulse control and inhibition, including the ability to maintain attention and control responses to experiences
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emotion
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temporary affective state or feeling that influences an individual’s physiology, facial expressions, and motivations
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emotion regulation
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ability to calm ourselves and move from a state of high arousal to a state of lower arousal
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emotional awareness
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insight into one’s own emotional state and that of others
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emotional labeling
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process of recognizing and identifying one’s own current affective state
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escape behavior
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emotion regulation strategy that consists of distancing or removing ourselves from an upsetting event or experience
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family
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two or more persons who are legally or genetically related, who act as a unit, and who share financial resources
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family care
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childcare provided by family members in the child’s home or the relative’s home
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gender socialization
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the process by which individuals are exposed to and learn gender roles and expectations in their culture
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gender stereotypes
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societal expectations and assumptions based on an individual’s sex or gender identity
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goodness of fit
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degree to which an infant’s temperament and their surrounding environment match and complement each other
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home daycare
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childcare provided in another home by another family, either formally or informally
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insecure ambivalent attachment
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pattern of behavior in which infants become especially distressed during both the absence of their caregiver and their return
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insecure avoidant attachment
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pattern of behavior in which infants show indifference to the absence and return of their caregiver
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intergenerational family
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family that includes aunts, uncles, cousins, or grandparents
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internal working model
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infants’ cognitive understanding of how relationships work and their expectations
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involuntary imitation
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immediate, reflexive imitation that occurs in infants between two and four months of age
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joint attention
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when infants focus their attention on the same object, person, or experience as a social partner
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kewpie doll effect
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motivation to care for an infant because of their rounded features
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mirror neurons
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neurons that react when individuals observe another individual and then perform the same action
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mirror test
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(also, rouge test) test of infant visual self-recognition in which the baby is placed in front of a mirror with a red mark on their nose
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moods
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long-lasting dispositions that describe an individual’s level of arousal and pleasure
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nanny services
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childcare provided by a nonfamily member who cares for children at the child’s home
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negative affectivity
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tendency to experience and express distress, discomfort, and avoidance behavior; associated with lower emotion regulation
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nuclear family
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family that includes two caregivers and their children
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object-relations theory
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theory about the way infants begin to understand their world through their relationship with their primary caregiver
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personality
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long-lasting pattern of behavior, attitudes, thoughts, and emotions consistent across childhood, adolescence, and adulthood
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primary caregiver
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individual who spends the most time caring for an infant in the first year of life
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primary emotions
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biologically based feelings that appear early in the first year of life and are associated with distinct and universal facial expressions
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secondary emotions
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situationally specific emotions that start to develop in the second year of life and require infants to have a sense of self
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secure attachment
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pattern of behavior in which infants become distressed during the absence of their caregiver but feel secure and comforted upon the caregiver’s return
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secure base
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safe place the caregiver gives the infant from which to explore the world around them
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self-conscious emotions
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secondary emotions that respond to an individual’s awareness of how others view them
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self-recognition
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ability to visually identify ourselves when looking at a mirror or a photo
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self-soothing
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emotion regulation strategy that consists of calming ourselves through sucking, breathing, and relaxation
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sense of self
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awareness of self as different from others
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separation anxiety
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distress that infants feel when their primary caregiver is absent
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single-parent family
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family that includes one caregiver and their children
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slow-to-warm-up temperament (overcontrolled/inhibited)
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temperament in which infant may be more prone to anxious or fearful behavior and have a lower activity level and lower mood intensity
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social cognition
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ability to understand another person’s thoughts, emotions, or intentions
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social referencing
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strategy of looking at others to see how they are responding during ambiguous and novel situations to inform one’s own reaction
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social smile
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involuntary smile that infants begin to display at approximately two months of age in response to seeing another smiling face
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Strange Situation
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experiment in which infants and primary caregivers are separated and reunited multiple times in a research lab to examine attachment style
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stranger anxiety
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infant’s fear reaction when encountering a new person or someone they do not often see
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surgency (also, extraversion)
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a trait characterized by high levels of physical activity, sociability, and spontaneity
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synchrony
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interaction between caregiver and child involving responding to each other’s emotions in reciprocal and sensitive ways
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temperament
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innate, biological components of individuality present as consistent patterns of behavior shortly after birth
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transgenerational attachment
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attachment patterns passed down through generations of one family
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trust versus mistrust
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first stage in Erikson’s theory of personality development, in which infants form a sense of trust toward others based on how reliably their caregivers meet their needs
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voluntary imitation
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purposeful imitation of others’ gestures and facial expressions that infants begin to display at approximately eight months of age


8.1: Neuronal Organization
- Describe the general organization of the neurons within and outside of the central nervous system.
Central nervous system
The central nervous system (CNS) is made up of the brain, a part of which is shown in Figure 8.1 and spinal cord and is covered with three layers of protective coverings called meninges (from the Greek word for membrane). The outermost layer is the dura mater (Latin for “hard mother”). As the Latin suggests, the primary function of this thick layer is to protect the brain and spinal cord. The dura mater also contains vein-like structures that carry blood from the brain back to the heart. The middle layer is the web-like arachnoid mater . The last layer is the pia mater (Latin for “soft mother”), which directly contacts and covers the brain and spinal cord like plastic wrap. The space between the arachnoid and pia maters is filled with cerebrospinal fluid (CSF) . CSF is produced by a tissue called choroid plexus in fluid-filled compartments in the CNS called ventricles . The brain floats in CSF, which acts as a cushion and shock absorber and makes the brain neutrally buoyant. CSF also functions to circulate chemical substances throughout the brain and into the spinal cord.
The entire brain contains only about 8.5 tablespoons of CSF, but CSF is constantly produced in the ventricles. This creates a problem when a ventricle is blocked—the CSF builds up and creates swelling and the brain is pushed against the skull. This swelling condition is called hydrocephalus (“water head”) and can cause seizures, cognitive problems, and even death if a shunt is not inserted to remove the fluid and pressure.
Autonomic nervous system
Which of the following statements is false?
a. The parasympathetic pathway is responsible for resting the body, while the sympathetic pathway is responsible for preparing for an emergency.
b. Most preganglionic neurons in the sympathetic pathway originate in the spinal cord.
c. Slowing of the heartbeat is a parasympathetic response.
d. Parasympathetic neurons are responsible for releasing norepinephrine on the target organ, while sympathetic neurons are responsible for releasing acetylcholine.
Sympathetic nervous system
The
sympathetic nervous system
is responsible for the “fight or flight” response that occurs when an animal encounters a dangerous situation. One way to remember this is to think of the surprise a person feels when encountering a snake (“snake” and “sympathetic” both begin with “s”). Examples of functions controlled by the sympathetic nervous system include an accelerated heart rate and inhibited digestion. These functions help prepare an organism’s body for the physical strain required to escape a potentially dangerous situation or to fend off a predator.
Most preganglionic neurons in the sympathetic nervous system originate in the spinal cord, as illustrated in Figure 8.3. The axons of these neurons release acetylcholine on postganglionic neurons within the sympathetic ganglia (the sympathetic ganglia form a chain that extends alongside the spinal cord). The acetylcholine activates the postganglionic neurons. Postganglionic neurons then release norepinephrine onto target organs. As anyone who has ever felt a rush before a big test, speech, or athletic event can attest, the effects of the sympathetic nervous system are quite pervasive. This is both because one preganglionic neuron synapses on multiple postganglionic neurons, amplifying the effect of the original synapse, and because the adrenal gland also releases norepinephrine (and the closely related hormone epinephrine) into the bloodstream. The physiological effects of this norepinephrine release include dilating the trachea and bronchi (making it easier for the animal to breathe), increasing heart rate, and moving blood from the skin to the heart, muscles, and brain (so the animal can think and run). The strength and speed of the sympathetic response help an organism avoid danger, and scientists have found evidence that it may also increase LTP—allowing the animal to remember the dangerous situation and avoid it in the future.
Parasympathetic nervous system
While the sympathetic nervous system is activated in stressful situations, the parasympathetic nervous system allows an animal to “rest and digest.” One way to remember this is to think that during a restful situation like a picnic, the parasympathetic nervous system is in control (“picnic” and “parasympathetic” both start with “p”). Parasympathetic preganglionic neurons have cell bodies located in the brainstem and in the sacral (toward the bottom) spinal cord, as shown in Figure 8.3. The axons of the preganglionic neurons release acetylcholine on the postganglionic neurons, which are generally located very near the target organs. Most postganglionic neurons release acetylcholine onto target organs, although some release nitric oxide.
The parasympathetic nervous system resets organ function after the sympathetic nervous system is activated (the common adrenaline dump you feel after a ‘fight-or-flight’ event). Effects of acetylcholine release on target organs include slowing of heart rate, lowered blood pressure, and stimulation of digestion.
Sensory-somatic nervous system
The sensory-somatic nervous system is made up of cranial and spinal nerves and contains both sensory and motor neurons. Sensory neurons transmit sensory information from the skin, skeletal muscle, and sensory organs to the CNS. Motor neurons transmit messages about the desired movement from the CNS to the muscles to make them contract. Without its sensory-somatic nervous system, an animal would be unable to process any information about its environment (what it sees, feels, hears, and so on) and could not control motor movements. Unlike the autonomic nervous system, which has two synapses between the CNS and the target organ, sensory and motor neurons have only one synapse—one ending of the neuron is at the organ and the other directly contacts a CNS neuron. Acetylcholine is the main neurotransmitter released at these synapses.
Humans have 12 cranial nerves , nerves that emerge from or enter the skull (cranium), as opposed to the spinal nerves, which emerge from the vertebral column. Each cranial nerve is accorded a name, which is detailed in Figure 8.4. Some cranial nerves transmit only sensory information. For example, the olfactory nerve transmits information about smells from the nose to the brainstem. Other cranial nerves transmit almost solely motor information. For example, the oculomotor nerve controls the opening and closing of the eyelid and some eye movements. Other cranial nerves contain a mix of sensory and motor fibers. For example, the glossopharyngeal nerve has a role in both taste (sensory) and swallowing (motor).
Spinal nerves transmit sensory and motor information between the spinal cord and the rest of the body. Each of the 31 spinal nerves (in humans) contains both sensory and motor axons. The sensory neuron cell bodies are grouped in structures called dorsal root ganglia and are shown in Figure 8.5. Each sensory neuron has one projection—with a sensory receptor ending in the skin, muscle, or sensory organs—and another that synapses with a neuron in the dorsal spinal cord. Motor neurons have cell bodies in the ventral gray matter of the spinal cord that project to muscle through the ventral root. These neurons are usually stimulated by interneurons within the spinal cord but are sometimes directly stimulated by sensory neurons.
The peripheral nervous system contains both the autonomic and sensory-somatic nervous systems. The autonomic nervous system provides unconscious control over visceral functions and has two divisions: the sympathetic and parasympathetic nervous systems. The sympathetic nervous system is activated in stressful situations to prepare the animal for a “fight or flight” response. The parasympathetic nervous system is active during restful periods. The sensory-somatic nervous system is made of cranial and spinal nerves that transmit sensory information from skin and muscle to the CNS and motor commands from the CNS to the muscles.
When you use a word nerve what does it refer to? What about neuron? How are these terms different and how are they the same in terms of their function


12.7: Rank Randomization Two or More Conditions
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Learning Objectives
The Kruskal-Wallis test is a rank-randomization test that extends the Wilcoxon test to designs with more than two groups. It tests for differences in central tendency in designs with one between-subjects variable. The test is based on a statistic \(H\) that is approximately distributed as Chi Square. The formula for \(H\) is shown below:
\[H = -3(N+1) + \frac{12}{N(N+1)} \sum_{i=1}^{k} \frac{T_{i}^{2}}{n_i}\]
where
The first step is to convert the data to ranks (ignoring group membership) and then find the sum of the ranks for each group. Then, compute \(H\) using the formula above. Finally, the significance test is done using a Chi Square distribution with \(k-1\) degrees of freedom.
For the "Smiles and Leniency" case study, the sums of the ranks for the four conditions are:
Note that since there are "ties" in the data, the mean rank of the ties is used. For example, there were \(10\) scores of \(2.5\) which tied for ranks \(4-13\). The average of the numbers \(4, 5, 6, 7, 8, 9, 10, 11, 12,13\) is \(8.5\). Therefore, all values of \(2.5\) were assigned ranks of \(8.5\).
The sample size for each group is \(34\).
\[H = -3(136+1) + \frac{12}{(136)(137)} \left ( \frac{(2732)^2}{34} + \frac{(2385.5)^2}{34} + \frac{(2424.5)^2}{34} + \frac{(1776)^2}{34} \right ) = 9.28\]
Using the Chi Square Calculator for \(\text{Chi Square} = 9.28\) with \(4-1 = 3\; df\) results in a \(p\) value of \(0.0258\). Thus the null hypothesis of no leniency effect can be rejected.


6.9: The Lavender Scare
During the 1950s, the United States was filled with fear that communism was seeping into the U.S., and the Federal Government began a public campaign to warn citizens that communism had infiltrated the United States. This time period is commonly referred to as the Red Scare. For queer people, this time period coincided with another moral panic, the Lavender Scare. The U.S. government and most notably, Senator Joe McCarthy began to assert that queer people would be more susceptible to blackmail from the enemy, and government employees who were known to be queer were fired from their jobs. During this time, society started to fear and focus on “the homosexual menace” more than prostitution and masturbation as “[they] were, along with communists, the objects of federal witch hunts and purges” (Rubin, 1984).
Around this time, several organizations were created by LGBTQIA+ people to protect their rights. The Library of Congress has a wonderful history on some of these groups in their LGBTQIA+ Studies Resource Guide. The Mattachine Society - LGBTQIA+ Studies: A Resource Guide and The Daughters of Bilitis - LGBTQIA+ Studies: A Resource Guide .


3.9: Peer-Reviewed Sources
Earlier, you read the term “ peer review ”—this term is probably new to you. Peer review means that experts have anonymously reviewed, critiqued, and recommended (or not recommended) an article for publication. It is important to know what this term means, because you should incorporate peer-reviewed sources into your scholarly writing about nursing and health-related issues. Time to delve deeper and better understand the peer-review process.
The peer-review process
The peer-review process typically applies to journals as opposed to books or websites. Journals focus on a specific discipline or a field of study (e.g., nursing) and are published on a regular basis (monthly, quarterly, etc.). The intended reading audience is other experts, usually not the general public. Journals are considered scholarly publications and each issue contains many articles mainly written by professors, researchers, practitioners, and other experts.
In nursing, authors are considered experts based on the following:
- They have a PhD or other graduate education.
- They have specialized in-depth knowledge.
- They have expertise and training in research and analysis and/or nursing practice.
- They are a student or a patient with first-hand experience to share (e.g., a patient narrative)
Many journals are not peer-reviewed, and these sources are generally not considered scholarly. When an author writes an article, they may submit it to a peer-reviewed journal to be published. Before the journal accepts the article, it is reviewed by experts in the same area of study: their peers. If the reviewers consider the research or work to be lacking quality or relevance, the author is asked to make changes or the manuscript is rejected. If the reviewers consider the work to be of high quality and relevant, the manuscript is accepted. This is why some assignments require you to use articles published in peer-reviewed journals —these sources contain rigorous research and/or theoretical work.
Figure 3.9: The peer-review process
Some experts, such as professors, also publish their evidence-informed research in non-peer-reviewed sources like books and newspapers. These sources may still be considered authoritative and contain expert research and are often reviewed by editors for accuracy, but they do not count as peer-reviewed sources. It is important to know the difference, especially if your instructor specifically requests that you use articles from peer-reviewed journals.
The need to remain critical
Overall, even though the peer-review process is used to evaluate research and other scholarly work, you as the reader need to remain critical and conduct your own evaluation of what you are reading. Remember, the CRAAP evaluation tool helps you remain critical.
The peer-review process is the agreed-upon method for checking credibility in the academic world, but it is not without its flaws. Articles with inaccurate research methods, and therefore flawed conclusions, have been published. Fortunately, most of these papers are retracted and the research is removed from the journal. For example, The Lancet (a prominent medical journal) retracted a 1998 study linking vaccines to autism due to ethical misconduct, serious study flaws, and a biased sample. The work of researchers can also be funded by outside corporations, and many journals require authors to state any conflicts of interest within their paper. If you come across an admission of conflict when reading an article, it will be up to you to evaluate whether or not you feel the research was influenced by the corporation’s own agenda.
Student Tip
WARNING: Google and Google Scholar
You also need to be vigilant when using Google and Google Scholar to find peer-reviewed journals, because some non-credible journals falsely claim to be peer reviewed. Your library provides you with access to databases that contain authorized peer-reviewed journals and filter out the non-credible ones.
Attribution statement
Content from this page was remixed with our own original content and adapted with editorial changes from:
Write Here, Right Now by Dr. Paul Chafe, Aaron Tucker with chapters from Dr. Kari Maaren, Dr. Martha Adante, Val Lem, Trina Grover and Kelly Dermody, under a Creative Commons Attribution 4.0 International License. Download this book for free at: https://pressbooks.library.ryerson.ca/writehere/


16.1: Regulation of Gene Expression
Skills to Develop
- Discuss why every cell does not express all of its genes
- Describe how prokaryotic gene regulation occurs at the transcriptional level
- Discuss how eukaryotic gene regulation occurs at the epigenetic, transcriptional, post-transcriptional, translational, and post-translational levels
For a cell to function properly, necessary proteins must be synthesized at the proper time. All cells control or regulate the synthesis of proteins from information encoded in their DNA. The process of turning on a gene to produce RNA and protein is called gene expression . Whether in a simple unicellular organism or a complex multi-cellular organism, each cell controls when and how its genes are expressed. For this to occur, there must be a mechanism to control when a gene is expressed to make RNA and protein, how much of the protein is made, and when it is time to stop making that protein because it is no longer needed.
The regulation of gene expression conserves energy and space. It would require a significant amount of energy for an organism to express every gene at all times, so it is more energy efficient to turn on the genes only when they are required. In addition, only expressing a subset of genes in each cell saves space because DNA must be unwound from its tightly coiled structure to transcribe and translate the DNA. Cells would have to be enormous if every protein were expressed in every cell all the time.
The control of gene expression is extremely complex. Malfunctions in this process are detrimental to the cell and can lead to the development of many diseases, including cancer.
Prokaryotic versus Eukaryotic Gene Expression
To understand how gene expression is regulated, we must first understand how a gene codes for a functional protein in a cell. The process occurs in both prokaryotic and eukaryotic cells, just in slightly different manners.
Prokaryotic organisms are single-celled organisms that lack a cell nucleus, and their DNA therefore floats freely in the cell cytoplasm. To synthesize a protein, the processes of transcription and translation occur almost simultaneously. When the resulting protein is no longer needed, transcription stops. As a result, the primary method to control what type of protein and how much of each protein is expressed in a prokaryotic cell is the regulation of DNA transcription. All of the subsequent steps occur automatically. When more protein is required, more transcription occurs. Therefore, in prokaryotic cells, the control of gene expression is mostly at the transcriptional level.
Eukaryotic cells, in contrast, have intracellular organelles that add to their complexity. In eukaryotic cells, the DNA is contained inside the cell’s nucleus and there it is transcribed into RNA. The newly synthesized RNA is then transported out of the nucleus into the cytoplasm, where ribosomes translate the RNA into protein. The processes of transcription and translation are physically separated by the nuclear membrane; transcription occurs only within the nucleus, and translation occurs only outside the nucleus in the cytoplasm. The regulation of gene expression can occur at all stages of the process (Figure \(\PageIndex{1}\)). Regulation may occur when the DNA is uncoiled and loosened from nucleosomes to bind transcription factors ( epigenetic level), when the RNA is transcribed (transcriptional level), when the RNA is processed and exported to the cytoplasm after it is transcribed ( post-transcriptional level), when the RNA is translated into protein (translational level), or after the protein has been made ( post-translational level).
The differences in the regulation of gene expression between prokaryotes and eukaryotes are summarized below. The regulation of gene expression is discussed in detail in subsequent modules.
Table \(\PageIndex{1}\): Differences in the Regulation of Gene Expression of Prokaryotic and Eukaryotic Organisms
| Prokaryotic organisms | Eukaryotic organisms |
|---|---|
| Lack nucleus | Contain nucleus |
| DNA is found in the cytoplasm | DNA is confined to the nuclear compartment |
| RNA transcription and protein formation occur almost simultaneously | RNA transcription occurs prior to protein formation, and it takes place in the nucleus. Translation of RNA to protein occurs in the cytoplasm. |
| Gene expression is regulated primarily at the transcriptional level | Gene expression is regulated at many levels (epigenetic, transcriptional, nuclear shuttling, post-transcriptional, translational, and post-translational) |
Evolution Connection: Evolution of Gene Regulation
Prokaryotic cells can only regulate gene expression by controlling the amount of transcription. As eukaryotic cells evolved, the complexity of the control of gene expression increased. For example, with the evolution of eukaryotic cells came compartmentalization of important cellular components and cellular processes. A nuclear region that contains the DNA was formed. Transcription and translation were physically separated into two different cellular compartments. It therefore became possible to control gene expression by regulating transcription in the nucleus, and also by controlling the RNA levels and protein translation present outside the nucleus.
Some cellular processes arose from the need of the organism to defend itself. Cellular processes such as gene silencing developed to protect the cell from viral or parasitic infections. If the cell could quickly shut off gene expression for a short period of time, it would be able to survive an infection when other organisms could not. Therefore, the organism evolved a new process that helped it survive, and it was able to pass this new development to offspring.
Summary
While all somatic cells within an organism contain the same DNA, not all cells within that organism express the same proteins. Prokaryotic organisms express the entire DNA they encode in every cell, but not necessarily all at the same time. Proteins are expressed only when they are needed. Eukaryotic organisms express a subset of the DNA that is encoded in any given cell. In each cell type, the type and amount of protein is regulated by controlling gene expression. To express a protein, the DNA is first transcribed into RNA, which is then translated into proteins. In prokaryotic cells, these processes occur almost simultaneously. In eukaryotic cells, transcription occurs in the nucleus and is separate from the translation that occurs in the cytoplasm. Gene expression in prokaryotes is regulated only at the transcriptional level, whereas in eukaryotic cells, gene expression is regulated at the epigenetic, transcriptional, post-transcriptional, translational, and post-translational levels.
Glossary
- epigenetic
- heritable changes that do not involve changes in the DNA sequence
- gene expression
- processes that control the turning on or turning off of a gene
- post-transcriptional
- control of gene expression after the RNA molecule has been created but before it is translated into protein
- post-translational
- control of gene expression after a protein has been created


4.5: Techniques for Modulating Brain Activity
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TMS
History: Transcranial magnetic stimulation (TMS) is an important technique for modulating brain activity. The first modern TMS device was developed by Antony Baker in the year 1985 in Sheffield after 8 years of research. The field has developed rapidly since then with many researchers using TMS in order to study a variety of brain functions. Today, researchers also try to develop clinical applications of TMS, because there are long lasting effects on the brain activity it has been considered as a possible alternative to antidepressant medication.
Method: UMTS utilizes the principle of electromagnetic induction to an isolated brain region. A wire-coil electromagnet is held upon the fixed head of the subject. When inducing small, localized, and reversible changes in the living brain tissue, especially the directly under laying parts of the motor cortex can be effected. By altering the firing-patterns of the neurons, the influenced brain area is disabled. The repetitive TMS (rTMS) describes, as the name reveals, the application of many short electrical stimulations with a high frequency and is more common than TMS. The effects of this procedure last up to weeks and the method is in most cases used in combination with measuring methods, for example: to study the effects in detail.
Application: The TMS-method gives more evidence about the functionality of certain brain areas than measuring methods on their own. It was a very helpful method in mapping the motor cortex. For example: While rTMS is applied to the prefrontal cortex, the patient is not able to build up short term memory. That determines the prefrontal cortex, to be directly involved in the process of short term memory. By contrast measuring methods on their own, can only investigate a correlation between the processes. Since even earlier researches were aware that TMS could cause suppression of visual perception, speech arrest, and paraesthesias, TMS has been used to map specific brain functions in areas other than motor cortex. Several groups have applied TMS to the study of visual information processing, language production, memory, attention, reaction time and even more subtle brain functions such as mood and emotion. Yet long time effects of TMS on the brain have not been investigated properly, Therefore experiments are not yet made in deeper brain regions like the hypothalamus or the hippocampus on humans. Although the potential utility of TMS as a treatment tool in various neuropsychiatric disorders is rapidly increasing, its use in depression is the most extensively studied clinical applications to date. For instance in the year 1994, George and Wassermann hypothesized that intermittent stimulation of important prefrontal cortical brain regions might also cause downstream changes in neuronal function that would result in an antidepressant response. Here again, the methods effects are not clear enough to use it in clinical treatments today. Although it is too early at this point to tell whether TMS has long lasting therapeutic effects, this tool has clearly opened up new hopes for clinical exploration and treatment of various psychiatric conditions. Further work in understanding normal mental phenomena and how TMS affects these areas appears to be crucial for advancement. A critically important area that will ultimately guide clinical parameters is to combine TMS with functional imaging to directly monitor TMS effects on the brain. Since it appears that TMS at different frequencies has divergent effects on brain activity, TMS with functional brain imaging will be helpful to better delineate not only the behavioral neuropsychology of various psychiatric syndromes, but also some of the pathophysiologic circuits in the brain.
tDCS
transcranial Direct Current Stimulation: The principle of tDCS is similar to the technique of TMS. Like TMS this is a non-invasive and painless method of stimulation. The excitability of brain regions is modulated by the application of a weak electrical current.
History and development: It was first observed that electrical current applied to the skull lead to an alleviation of pain. Scribonius Largus, the court physician to the Roman emperor Claudius, found that the current released by the electric ray has positive effects on headaches. In the Middle Ages the same property of another fish, the electrical catfish, was used to treat epilepsy. Around 1800, the so-called galvanism (it was concerned with effects of today’s electrophysiology) came up. Scientists like Giovanni Aldini experimented with electrical effects on the brain. A medical application of his findings was the treatment of melancholy. During the twentieth century among neurologists and psychiatrists electrical stimulation was a controversial but nevertheless wide spread method for the treatment of several kinds of mental disorders (e.g. Electroconvulsive therapy by Ugo Cerletti).
Mechanism: The tDCS works by fixation of two electrodes on the skull. About 50 percent of the direct current applied to the skull reaches the brain. The current applied by a direct current battery usually is around 1 to 2 mA. The modulation of activity of the brain regions is dependent on the value of current, on the duration of stimulation and on the direction of current flow. While the former two mainly have an effect on the strength of modulation and its permanence beyond the actual stimulation, the latter differentiates the modulation itself. The direction of the current (anodic or cathodic) is defined by the polarity and position of the electrodes. Within tDCS two distinct ways of stimulation exist. With the anodal stimulation the anode is put near the brain region to be stimulated and analogue for the cathodal stimulation the cathode is placed near the target region. The effect of the anodal stimulation is that the positive charge leads to depolarization in the membrane potential of the applied brain regions, whereas hyperpolarisation occurs in the case of cathodal stimulation due to the negative charge applied. The brain activity thereby is modulated. Anodal stimulation leads to a generally higher activity in the stimulated brain region. This result can also be verified with MRI scans, where an increased blood flow in the target region indicates a successful anodal stimulation.
Applications: From the description of the TMS method it is should be obvious that there are various fields of appliances. They reach from identifying and pulling together brain regions with cognitive functions to the treatment of mental disorders. Compared to TMS it is an advantage of tDCS to not only is able to modulate brain activity by decreasing it but also to have the possibility to increase the activity of a target brain region. Therefore the method could provide an even better suitable treatment of mental disorders such as depression. The tDCS method has also already proven helpful for apoplectic stroke patients by advancing the motor skills.


2: The Earth System
The Earth system is a complex interaction between its subsystems the atmosphere, hydrosphere, biosphere, and lithosphere. The Earth system around us today is the result of millions of years of evolutionary processes tending toward a stable equilibrium. At times, assaults from within and outside have stressed the system and forced changes. Here you will explore the types of systems found on Earth and the sources of energy that drive them.
By the end of the chapter you should be able to:
- Explain the origin and shape of the Earth.
- Explain how the Earth's orientation to and revolution around the Sun cause seasons.
- Describe the basic features of the continents and oceans.
- Explain how earth "spheres" interact with one another within the Earth system.
- Explain how natural systems are regulated by feedback.
- Demonstrate through the use of a flow chart how positive and negative feedback effect system change.
- Compare and contrast, and provide examples of open and closed systems.
- Draw a simple diagram of the nitrogen, carbon, oxygen, and hydrologic cycles.
- Compare and contrast, and give examples of endogenic and exogenic sources of energy.
- Explain how feedbacks drive global warming and climate change.


7.5: La Boheme
Introduction
La bohème is an opera in four acts, composed by Giacomo Puccini to an Italian libretto by Luigi Illica and Giuseppe Giacosa, based on Scènes de la vie de bohème by Henri Murger. The world premiere performance of La bohème was in Turin on 1 February 1896 at the Teatro Regio, conducted by the young Arturo Toscanini. Since then, La bohème has become part of the standard Italian opera repertory and is one of the most frequently performed operas worldwide.
In 1946, fifty years after the opera’s premiere, Toscanini conducted a performance of it on radio with the NBC Symphony Orchestra. This performance was eventually released on records and on CD. It is the only recording of a Puccini opera by its original conductor (see Recordings below).
Synopsis
Place: Paris
Time: Around 1830
Act 1
In the four bohemians’ garret
Marcello is painting while Rodolfo gazes out of the window. They complain of the cold. In order to keep warm, they burn the manuscript of Rodolfo’s drama. Colline, the philosopher, enters shivering and disgruntled at not having been able to pawn some books. Schaunard, the musician of the group, arrives with food, wine and cigars. He explains the source of his riches: a job with an eccentric English gentleman, who ordered him to play his violin to a parrot until it died. The others hardly listen to his tale as they set up the table to eat and drink. Schaunard interrupts, telling them that they must save the food for the days ahead: tonight they will all celebrate his good fortune by dining at Cafe Momus, and he will pay.
The friends are interrupted by Benoît, the landlord, who arrives to collect the rent. They flatter him and ply him with wine. In his drunkenness, he begins to boast of his amorous adventures, but when he also reveals that he is married, they thrust him from the room—without the rent payment—in comic moral indignation. The rent money is divided for their evening out in the Quartier Latin .
Marcello, Schaunard and Colline go out, but Rodolfo remains alone for a moment in order to finish an article he is writing, promising to join his friends soon. There is a knock at the door. It is a girl who lives in another room in the building. Her candle has blown out, and she has no matches; she asks Rodolfo to light it. She is briefly overcome with faintness, and Rodolfo helps her to a chair and offers her a glass of wine. She thanks him. After a few minutes, she says that she is better and must go. But as she turns to leave, she realizes that she has lost her key.
Her candle goes out in the draught and Rodolfo’s candle goes out too; the pair stumble in the dark. Rodolfo, eager to spend time with the girl, to whom he is already attracted, finds the key and pockets it, feigning innocence. He takes her cold hand ( Che gelida manina – “What a cold little hand”) and tells her of his life as a poet, then asks her to tell him more about her life. The girl says her name is Mimì ( Sì, mi chiamano Mimì – “Yes, they call me Mimì”), and describes her simple life as an embroiderer. Impatiently, the waiting friends call Rodolfo. He answers and turns to see Mimì bathed in moonlight (duet, Rodolfo and Mimì: O soave fanciulla – “Oh lovely girl”). They realize that they have fallen in love. Rodolfo suggests remaining at home with Mimì, but she decides to accompany him to the Cafe Momus. As they leave, they sing of their newfound love.
Listen: Act I
“Sì, mi chiamano Mimì”
An audio element has been excluded from this version of the text. You can listen to it online here: http://pb.libretexts.org/map/?p=314
“O soave fanciulla”
An audio element has been excluded from this version of the text. You can listen to it online here: http://pb.libretexts.org/map/?p=314
“Che gelida manina”
Here are the lyrics , both the original Italian and an English translation, for “Che gelida manina” from Puccini’s La Boheme. This is a commercial site, but the translation will be helpful to understand what Rodofo says when he first meets the woman he falls in love with, Mimi.
“Si, mi chiamano Mimi”
Here are the lyrics , both the original Italian and an English translation, for “Si, mi chiamano Mimi” from Puccini’s La Boheme. This is a commercial site (about.com) so unfortunately there are some ads that get in the way, but the translation will be helpful to understand what Mimi says in response to Rodolfo’s aria “Che gelida manina.”
Contributors and Attributions
- Authored by : Elliott Jones. Provided by : Santa Ana College. Located at : http://www.sac.edu . License : CC BY: Attribution
- La boheme. Provided by : Wikipedia. Located at : http://en.Wikipedia.org/wiki/La_boh%C3%A8me . License : CC BY-SA: Attribution-ShareAlike


3.2: Globalization
What you’ll learn to do: explain why nations and U.S. firms engage in global business
In this section you’ll learn about the drivers of the global economy and how companies and countries evaluate whether or not to pursue global opportunities.
Learning Objectives
- Differentiate between comparative and absolute advantage
- Explain the roles of absolute and comparative advantage in global business
Globalization and Business
Globalization
There was a time when consumers only had access to goods and services that were available locally. Their choices were limited by what they could access on foot, by horse, or by carriage. This is still the case for many people around the world, and in rural and remote parts of the U.S., it’s still necessary for families to make weekly trips to town to stock up on food, household items and other necessities. However, with the rise of Internet-based business (think Amazon), there’s been an explosion of international trade, and more and more consumers essentially have the world at their door. Of course international trade isn’t just a twentieth-century phenomenon. Trade across borders and between cultures has been a feature of human civilization for centuries—there’s evidence of this dating back as far as the nineteenth century BCE. The Silk Road, one of the best-known and most enduring “international” trade routes, began sometime around 200 BCE and for centuries was central to cultural interaction from China through regions of the Asian continent all the way to the Mediterranean Sea.
So, if cultures and nations have been trading with one other for four thousand years, what makes today’s business landscape different? The answer lies in the distinction between international business and globalization .
International business refers to commerce in which goods, services, or resources cross the borders of two or more nations. This is what the Egyptians were doing when they sent goods across the Red Sea to Assyria. Globalization is broader than international business and describes a shift toward a more integrated world economy in which culture, ideas, and beliefs are exchanged in addition to goods, services, and resources. Globalization implies that the world is “getting smaller”: As a result of new transportation and communication technologies, people around the world can more readily connect with one another—both virtually and geographically.
The following video provides a good introduction to the causes and consequences of globalization.
Impact of Globalization on Global Business
The video, above, provides a good bird’s eye view of the affect of globalization on business—from opening up new markets to increasing the level of competition within markets and industries. Let’s take a look at particular example, though, to think through the various implications of conducting business on a global scale. Consider McDonald’s, which was started by two brothers in San Bernadino, California, sixty-eight years ago. As a result of globalization, nearly 69 million people in 118 different countries eat at McDonald’s every day. The first McDonald’s outside the U.S. and Canada was established in Costa Rica in 1970, and since the 1990s, most of the company’s growth has taken place in foreign countries. The process of building a global presence, entering new markets, and capitalizing on growing international demand for American fast food has enabled McDonald’s to expand from a single location to a global corporation with revenues in excess of U.S. $25.4 billion in 2015. [1] However, entering new markets—whether at home or abroad—means contending with increased competition in those markets, including competition with other globally minded companies. In 2010, Subway surpassed McDonald’s to become the largest single-brand restaurant chain and the largest restaurant operator globally.
What is it like for companies that decide to take advantage of global opportunities as McDonald’s and Subway have? Return to the discussion of “external forces” in module 1, but now consider them from a global business perspective. Globalization certainly means that businesses can reach consumers around the word more rapidly and efficiently—thanks to cell phones, airplanes, and the Internet, we are all so much more interconnected and “accessible” now. But globalization also means incredible complexity. The list below sketches out just a few of the complexities and challenges that an American fast-food company like McDonald’s faces when it takes on the global business environment.
The Global Economic Environment
McDonald’s is a corporation based in the United States, where all business transactions are conducted using the U.S. dollar, but there are 167 official national currencies in the world, each with a different value and purchasing power. Imagine trying to balance the corporate checkbook at McDonald’s when your deposits have been made in more than a hundred different currencies.
The Global Legal Environment
In Greece, there is a $650 fine for eating ice cream at certain historic, artistic, and culturally important sites. If you are the operator of a McDonald’s near the Parthenon, should you remove the ice cream cones and McFlurries from your menu to protect your customers against being fined, or not?
The Global Competitive Environment
McKebab, a fast-food restaurant in Slovakia whose name and golden “M” bear a striking resemblance to McDonald’s.
How does McDonald’s recapture the number-one position it lost to Subway in 2010? The company may need to make substantial changes to its operations, menu offerings, and/or marketing tactics. This is a steep, uphill climb in the United States alone, but consider trying to accomplish it in 118 different countries in 188 different markets—where you are competing not only with other global U.S. fast-food companies like Subway and KFC but with local ones, like “McKebab,” as well!
The Global Technological Environment
What does technology have to do with fast food or McDonald’s? Consider the company’s presence in China, where there are nearly 1.3 billion mobile users, and say hello to “McDonald’s Next,” a “modern and progressive” version of the restaurant that first opened in Hong Kong, featuring mobile-phone-charging platforms, free Wi-Fi, and self-ordering kiosks. This next generation of McDonald’s is a response to increased expectations around speed, service, economy, and availability across established and developing economies, mostly fueled by consumers’ growing access to affordable technology. As global businesses respond to demands created by technology, they must also leverage technology to move products, people, and supplies around the globe in a cost-effective and efficient manner.
The Global Social Environment
McDonald’s Maharaja Mac
McDonald’s has had to adapt in countless ways to meet the demands of its customers around the world. While it prides itself on offering a consistent, internationally recognizable menu and brand, the company has also had to cater to local dining preferences and customs. In 1995, for example, the first kosher McDonald’s opened in a Jerusalem suburb. In Arab countries, the restaurant chain offers “halal” menus, which comply with Islamic laws governing the preparation of meat. In 1996, McDonald’s entered India for the first time, where it offered a Big Mac made with lamb called the Maharaja Mac. [2]
McDonald’s is not a complex business—after all, it sells inexpensive burgers and fries, not automobiles or airplanes or pharmaceuticals—but clearly the global environment presents challenges even for them. You may be wondering why nations and businesses decide to take on such challenges, given the ongoing difficulty, risk, and uncertainty. We’ll investigate this question throughout the remainder of this module.
Absolute and Comparative Advantage
Consider the humble banana. Even if you’re not a big fan of this yellow fruit, you’ve surely seen them in the grocery store or in a market somewhere. If you walked through a US city with a banana and asked people to identify it, it’s unlikely you would encounter anyone who had no idea what it was. What if you did the same thing with a picture of a banana tree ? How many people could identify it? Maybe some, but not all. Why is that? In the United States, bananas are grown in Hawaii, and not everyone has been to Hawaii. In fact, most of the bananas in the world are grown in Ecuador. If we Americans love bananas and don’t live in Hawaii and can’t get to Ecuador regularly, without global trade, we’re out of luck: no bananas for cereal in the morning or as snacks during the day and, worse, no banana splits at the local ice cream parlor. Why do Ecuador and Hawaii trade away their bananas instead of keeping them all to themselves? Probably because, although bananas are delicious and nutritious, it’s hard to build houses out of them. Instead, the state of Hawaii and nation of Ecuador choose to trade their bananas for things they lack, while considering the cost and profitability of exporting their product.
Ecuador and Hawaii offer an example of comparative advantage. Because bananas are not grown or readily available everywhere in the world, Ecuador and Hawaii can profitably export theirs to banana-less places like Iowa and Canada. At the same time, Ecuador may need computer systems to keep track of all of those bananas they are selling, but Ecuador is not a technologically advanced economy like the United States. The United States has a comparative advantage in computers, so we sell our computers to Ecuador and let them concentrate on selling us bananas.
The Concept of Advantage
In order to understand why businesses are willing to operate in a complex global environment, we must first understand two fundamental concepts that drive almost all business decisions: absolute and comparative advantage. Countries and companies are willing to assume the risk of engaging in global trade because they believe that they have an advantage over the competition that they can turn into profits. Not all countries have the same natural resources, infrastructure, labor force, or technology. These differences create advantages that can be exploited in global trade, to a country’s (or company’s) benefit.
Absolute Advantage
An entity (country, region, company, or individual) is considered to have an absolute advantage if either of the following conditions exists:
- It is the only source of a particular product, good, or service. This kind of absolute advantage is very rare and usually depends on a particular natural resource being available only within a certain region or country. An example might be the coveted edible red bird’s nests found only in the caves of Thailand (and prized in Chinese cooking as the main ingredient in bird’s nest soup). Similarly, if Ecuador were the only place in the world where bananas could be grown, it would have an absolute advantage. However, suppose some sneaky banana spy goes to Ecuador and pilfers some banana tree seedlings and takes them back to her home country and begins growing and exporting bananas. At that point Ecuador no longer has an absolute advantage on the basis of the “only-source” condition.
- An entity is also considered to have an absolute advantage if it is able to produce more of something than another entity while using the same amount of resources (factors of production). When the sneaky banana spy started growing bananas in her home country, she didn’t actually take away Ecuador’s absolute advantage, because Ecuador can produce more bananas using the same amount of resources (labor, land, water, equipment, etc.). Put another way, Ecuador’s direct cost of producing bananas is lower than the banana spy’s. Assuming that the bananas can be grown in the new country, it will take that country a very long time to match Ecuador’s skill, efficiency, and output level, and until it does, Ecuador will retain its absolute advantage.
Comparative Advantage
An entity (country, region, company, or individual) is considered to have a comparative advantage over another in producing a particular good or service if it can produce the good or service at a lower relative opportunity cost.
You’ll recall from the economic environment module that opportunity cost is the value of the next best alternative . (The video, below, also includes a refresher on this concept.) Since countries and businesses have limited resources, they are forced to make choices about how they allocate those resources. As a student, you understand opportunity cost better than you think. You have a limited amount of time, and you must choose between reading this module and going out with your friends, because you can’t do both. If you choose to go out with your friends, then the opportunity cost might be failure on your next exam because you did not use the time to prepare.
Ecuador has a comparative advantage in bananas over a long list of countries, including the United States. This comparative advantage is even better understood when you consider that their next best alternative product is oil. The Middle Eastern countries have been pumping oil from the ground for as long as Ecuador has been growing bananas. It makes as much sense for Kuwait to attempt to export bananas as it does for Ecuador to export oil. It’s the reality of comparative advantage that encourages countries and businesses to do what they do best—leaving the production of other goods and services to other countries or companies—and in so doing, focusing on producing goods and services where they have advantage, thus maximizing their opportunities in a global environment.
The following video provides an excellent illustration of comparative and absolute advantage and explains why they are such important considerations in how countries decide to specialize and trade.
practice question \(\PageIndex{1}\)
Consider an economy that has an absolute advantage in producing a given product, then it ________ have a comparative advantage in producing that same product.
- must
- might or might not
- definitely
- Answer
-
b. Absolute advantage means the economy can produce a given product with a lower resource cost and comparative advantage means the economy can product a given product with a lower opportunity cost. Absolute advantage meaning being better at something relative to something else. Specialization allows for everyone benefiting from producing under comparative advantage and then trading.
practice question \(\PageIndex{2}\)
If Kate can make more tacos in an hour than Bill, but Bill can make more tacos at a lower opportunity cost then Bill has a(n) ________.
- absolute advantage in making tacos.
- both an absolute and comparative advantage in making tacos.
- comparative advantage in making tacos.
- Answer
-
c . Kate has an absolute advantage because she can make more tacos and Bill has a comparative advantage because he can make more tacos at a lower opportunity cost.
Game: Absolute and Comparative Advantage
It’s one thing to talk and read about global business and another to actually engage in global trade. The following interactive provides a brief introduction to doing just that, with a focus on just how countries behave to create a more productive global economy.
learn more
Now that you’ve learned about specialization, you can try playing this trade game to explore trade in a fictional world: Play the Trade Ruler Game . Note that this game is Flash-based, so you’ll need to enable Flash in your browser in order to see it.
Global Markets
Global Markets and Business Opportunity
Increasingly nations and business use their comparative or absolute advantages to enter global markets driven by the same factor: the immense size of these markets.
Let’s return to the banana for a moment. In 2015, Ecuador exported 6.55 million metric tons of bananas. Without a large global demand for bananas, every man, woman, and child in Ecuador would have to eat 834 pounds of them per year to consume all of the production. Of course that wouldn’t happen: Instead, the country would simply cut back on the production of bananas—but, in so doing, it would lose an export that now accounts for more than 10 percent of its gross domestic product (GDP). Ecuador needs a large and vibrant global market to keep up with its tremendous supply of bananas, and it relies on the revenue from those bananas to purchase the other things it needs (in the same way that you traded cell phones for blue jeans in the island trader simulation).
Later in this module we’ll discuss how nations like Ecuador enter foreign markets, but for now let’s look more closely at the size of the world’s largest markets. The following table shows population and GDP data for the top five economies in the world as of 2015. [3] You’ll recall from the economic environment module that GDP, or gross domestic product, is a monetary measure of the market value of all final goods and services produced in a period, and the GDP growth rate is the increase or decrease in GDP over a period of time, expressed as a percentage.
| Country | GDP | Population | GDP Growth Rate |
| China | $19,390,000,000,000 | 1,367,485,388 | 6.90% |
| European Union | $19,180,000,000,000 | 513,949,445 | 2.20% |
| United States | $17,950,000,000,000 | 321,368,864 | 2.40% |
| India | $7,965,000,000,000 | 1,251,695,584 | 7.30% |
| Japan | $4,830,000,000,000 | 126,919,659 | 0.50% |
Looking at the figures in this table, it isn’t hard to imagine that a country or company would like to have a foothold in one or all of these markets. Taken together, these five economies represent a lot of people, a lot of purchasing power, and a lot of economic growth. However, the immensity of the global market offers more than just new target customers. Consider some of the following benefits nations and firms realize by entering foreign markets.
Access to Factors of Production
You will recall that the factors of production required for a successful business venture are natural resources, capital, human capital, and entrepreneurship. Access to global markets enables countries and companies to acquire these factors of production when they are nonexistent, scarce, or just too costly at home. For example, India is one of the largest providers of telephone-based customer service (labor) worldwide, which makes sense given that its population is second only to China and almost four times that of the United States. In addition, labor costs in India are significantly lower than in the U.S.
Innovation and Ideas
Many companies enter global markets and, once there, discover unmet needs or unique products and services. They are then able to use their discoveries to expand an existing product line or introduce new products in other markets or at home. For example, many people credit the United Kingdom with inspiring the development of the craft beer industry in the United States.
Risk Reduction
Given the complexity of operating a business globally, it may seem like a contradiction that risk reduction is one of the benefits of a large global market, but it’s actually true. If a country or a company trades or does business with multiple foreign partners, they are less dependent on the success of any single partnership. Likewise, if a nation or business has multiple global sources for factors of production, then if one source “dries up,” they will still have access to what they need. For example, in 2010 China halted its export of rare earth minerals to Japan after the two countries were unable to resolve a territory dispute. Japan used these minerals in the production of everything from cars to computer chips, and to say that the Japanese were in a state of distress is an understatement. As a result of this albeit brief reduction in Chinese supply, Japan established a trade agreement with India for the import of the needed materials. They will no longer be totally dependent upon the Chinese for these important resources.
In summary, globalization makes business on a global scale possible, and the size of the global market makes it attractive. By using their absolute and comparative advantages, countries and companies can leverage their resources to produce and trade the things that benefit them the most.
The following video provides a recap of the main reasons why countries and businesses engage in global trade.
- https://en.Wikipedia.org/wiki/McDonald%27s ↵
- en.Wikipedia.org/wiki/History_of_McDonald ↵
- CIA World FactBook https://www.cia.gov/library/publications/the-world-factbook/rankorder/2001rank.html#ch ↵


15.5: Complex Recursive Sequences
We will now explore recursively defined sequences of complex numbers.
A recursive relationship is a formula which relates the next value, \(z_{n+1},\) in a sequence to the previous value, \(z_{n} .\) In addition to the formula, we need an initial value, \(z_{0}\).
The sequence of values produced is the recursive sequence .
Given the recursive relationship \(z_{n+1}=z_{n}+2, \quad z_{0}=4,\) generate several terms of the
recursive sequence.
Solution
We are given the starting value, \(z_{0}=4 .\) The recursive formula holds for any value of \(n,\) so
if \(n=0,\) then \(z_{n+1}=z_{n}+2\) would tell us \(z_{0+1}=z_{0}+2,\) or more simply, \(z_{1}=z_{0}+2\)
Notice this defines \(z_{1}\) in terms of the known \(z_{0},\) so we can compute the value:
\( z_{1}=z_{0}+2=4+2=6 \)
Now letting \(n=1,\) the formula tells us \(z_{1+1}=z_{1}+2,\) or \(z_{2}=z_{1}+2 .\) Again, the formula gives the next value in the sequence in terms of the previous value.
(z_{2}=z_{1}+2=6+2=8\)
Continuing,
\(z_{3}=z_{2}+2=8+2=10\)
\(z_{4}=z_{3}+2=10+2=12\)
The previous example generated a basic linear sequence of real numbers. The same process can be used with complex numbers.
Given the recursive relationship \(z_{n+1}=z_{n} \cdot i+(1-i), \quad z_{0}=4,\) generate several terms of the
recursive sequence.
Solution
We are given \(z_{0}=4 .\) Using the recursive formula:
\(z_{1}=z_{0} \cdot i+(1-i)=4 \cdot i+(1-i)=1+3 i\)
\(z_{2}=z_{1} \cdot i+(1-i)=(1+3 i) \cdot i+(1-i)=i+3 i^{2}+(1-i)=i-3+(1-i)=-2\)
\(z_{3}=z_{2} \cdot i+(1-i)=(-2) \cdot i+(1-i)=-2 i+(1-i)=1-3 i\)
\(z_{4}=z_{3} \cdot i+(1-i)=(1-3 i) \cdot i+(1-i)=i-3 i^{2}+(1-i)=i+3+(1-i)=4\)
\(z_{5}=z_{4} \cdot i+(1-i)=4 \cdot i+(1-i)=1+3 i\)
Notice this sequence is exhibiting an interesting pattern – it began to repeat itself.
Mandelbrot Set
The Mandelbrot Set is a set of numbers defined based on recursive sequences
For any complex number \(c,\) define the sequence \(z_{n+1}=z_{n}^{2}+c, \quad z_{0}=0\)
If this sequence always stays close to the origin (within 2 units), then the number \(c\) is part of the Mandelbrot Set . If the sequence gets far from the origin, then the number \(c\) is not part of the set.
Determine if \(c=1+i\) is part of the Mandelbrot set.
Solution
We start with \(z_{0}=0\). We continue, omitting some detail of the calculations
\(z_{1}=z_{0}^{2}+1+i=0+1+i=1+i\)
\(z_{2}=z_{1}^{2}+1+i=(1+i)^{2}+1+i=1+3 i\)
\(z_{3}=z_{2}^{2}+1+i=(1+3 i)^{2}+1+i=-7+7 i\)
\(z_{4}=z_{3}^{2}+1+i=(-7+7 i)^{2}+1+i=1-97 i\)
We can already see that these values are getting quite large. It does not appear that \(c=1+i\) is part of the Mandelbrot set.
Determine if \(c=0.5 i\) is part of the Mandelbrot set.
Solution
We start with \(z_{0}=0\). We continue, omitting some detail of the calculations
\(z_{1}=z_{0}^{2}+0.5 i=0+0.5 i=0.5 i\)
\(z_{2}=z_{1}^{2}+0.5 i=(0.5 i)^{2}+0.5 i=-0.25+0.5 i\)
\(z_{3}=z_{2}^{2}+0.5 i=(-0.25+0.5 i)^{2}+0.5 i=-0.1875+0.25 i\)
\(z_{4}=z_{3}^{2}+0.5 i=(-0.1875+0.25 i)^{2}+0.5 i=-0.02734+0.40625 i\)
While not definitive with this few iterations, it does appear that this value is remaining small, suggesting that \(0.5 i\) is part of the Mandelbrot set.
Determine if \(c=0.4+0.3 i\) is part of the Mandelbrot set.
- Answer
-
\(z_{1}=z_{0}^{2}+0.4+0.3 i=0+0.4+0.3 i=0.4+0.3 i\)
\(z_{2}=z_{1}^{2}+0.4+0.3 i=(0.4+0.3 i)^{2}+0.4+0.3 i = 0.47+0.54 i\)
\(z_{3}=z_{2}^{2}+0.5 i=(-0.25+0.5 i)^{2}+0.5 i=-0.1875+0.25 i\)
\(z_{4}=z_{3}^{2}+0.5 i=(-0.1875+0.25 i)^{2}+0.5 i=-0.02734+0.40625 i\)
If all complex numbers are tested, and we plot each number that is in the Mandelbrot set on the complex plane, we obtain the shape to the right[1].
The boundary of this shape exhibits quasi-self-similarity, in that portions look very similar to the whole.
In addition to coloring the Mandelbrot set itself black, it is common to the color the points in the complex plane surrounding the set. To create a meaningful coloring, often people count the number of iterations of the recursive sequence that are required for a point to get further than 2 units away from the origin. For example, using \(c=1+i\) above, the sequence was distance 2 from the origin after only two recursions.
For some other numbers, it may take tens or hundreds of iterations for the sequence to get far from the origin. Numbers that get big fast are colored one shade, while colors that are slow to grow are colored another shade. For example, in the image below[2], light blue is used for numbers that get large quickly, while darker shades are used for numbers that grow more slowly. Greens, reds, and purples can be seen when we zoom in – those are used for numbers that grow very slowly.
The Mandelbrot set, for having such a simple definition, exhibits immense complexity. Zooming in on other portions of the set yields fascinating swirling shapes.
[1] en.Wikipedia.org/wiki/File:Mandelset_hires.png
[2] This series was generated using Scott’s Mandelbrot Set Explorer