1.4: Human Needs and Developmental Stages
It is important to understand human needs and developmental stages to communicate effectively and provide holistic care.
Maslow’s Hierarchy of Needs
Maslow’s Hierarchy of Needs was created in 1943 by American psychologist Abraham Maslow. Maslow’s theory is based on the ranking of the importance of human needs and the belief that human actions are based on motivation to meet these needs. See an illustration of Maslow’s Hierarchy of Needs in Figure 1.5. [1]
Maslow’s theory states that unless the basic needs in the lower levels of the hierarchy are met, humans cannot experience the higher levels of psychological and self-fulfillment needs. The levels of Maslow’s Hierarchy of Needs have the following definitions [2] :
- Physiological needs: This is the most important level with basic needs humans must have to stay alive and function, including air, food, drink, shelter, clothing, warmth, sex, and sleep.
- Safety needs: People want to experience order, predictability, and control in their lives. This includes emotional security, freedom from fear, and health and well-being (such as safety against falls and injury). For new residents in a long-term care facility, this level includes becoming comfortable in familiar surroundings as opposed to feeling apprehension when experiencing a new environment.
- Love and belongingness: After physiological and safety needs have been fulfilled, the third level of human needs is social and involves feelings of belongingness. Belongingness refers to a human emotional need for interpersonal relationships, connectedness, and being part of a group. A group may mean biological families, friends, or other supporters. It may also include physical intimacy and romantic relationships.
- Esteem needs: Esteem needs include self-worth and feelings of accomplishment and respect. It includes how one views oneself and the feeling of contributing to something of importance.
- Self-actualization: Self-actualization is the highest level and refers to the realization of a person’s potential and self-fulfillment. This level refers to the desire to attain life goals and being truly satisfied in being the most one can be.
Maslow theorized that one cannot attain a higher level in any of these categories if the levels below are not met. For example, one is not motivated by a sense of belonging if they are focused on obtaining basic needs such as food, water, and shelter. The hierarchy is subjective because each individual determines what each level means for them. For instance, for one person, safety may mean living in the neighborhood where they grew up, whereas for another individual it means having a daily routine. Belongingness to one person may mean being a part of a community group whereas to another it may mean having one very close friend. Self-esteem and feelings of accomplishment may be defined by one person as successfully graduating from high school, whereas to another it is defined by being able to run a mile without stopping. Self-actualization is defined by each individual and can mean things such as being a good parent, graduating from college, or achieving one’s dream of becoming a nurse.
The levels of belongingness and self-actualization also include a person’s spirituality and how they find meaning and purpose in life. Spirituality is often mistakenly equated with religion, but spirituality is a broader concept that includes how people seek meaning and purpose in life, as well as establish relationships with family, their community, nature, and/or a higher power. [3]
Maslow’s Hierarchy of Needs is a good basis for providing holistic care and communicating with clients based on their needs and preferences. For example, in nursing, priorities of care are based on physiological needs and safety. Additionally, knowing that a newly admitted resident may have difficulty reaching a higher level of needs if their basic needs are not met is a good starting point for providing care.
Strategies that integrate Maslow’s Hierarchy of Needs when providing care to residents include the following:
- Following the nursing plan of care to meet physiological needs.
- Implementing fall precautions to keep residents safe.
- Answering call lights promptly and consistently providing a calm, comfortable environment to make residents feel secure.
- Respecting residents’ belongings and asking their preferences for grooming, bathing, and meals to satisfy self-esteem needs.
- Encouraging interaction among residents with similar interests to promote a feeling of belongingness.
- Offering to bring residents to on-site religious activities or referring them to social services for a chaplain visit to promote self-actualization and a feeling of belongingness.
Maslow’s Hierarchy of Needs can also be applied to the work environment to enhance professionalism by doing the following:
- Offering assistance to coworkers when able to promote a feeling of security and belongingness and also maintaining residents’ physiological needs and safety as a team.
- Participating fully in the reporting and documentation process of the facility to meet residents’ physiological and safety needs.
- Accurately following training and agency policies and procedures to encourage feelings of self-esteem in the health care worker.
- Being accountable for one’s actions and job responsibilities to promote a feeling of self-actualization by meeting one’s potential.
Erikson’s Stages of Development
Another psychologist named Erik Erikson created a theory of psychosocial development that also describes how one’s personality is developed. It theorizes there are eight stages of development based on a person’s chronological age. Development occurs based on the main conflict or challenge confronted during that period of time. Each stage can create either a virtue/strength or a maladaptive tendency. Erikson proposed that those who have a stronger sense of identity from resolving these conflicts over time have fewer conflicts within themselves and with others and, subsequently, a decreased level of anxiety. [4]
Erikson’s stages of development are defined as trust versus mistrust, autonomy versus shame, initiative versus guilt, industry versus inferiority, identity versus identity confusion, intimacy versus isolation, generativity versus stagnation, and integrity versus despair [5] :
- Trust vs. Mistrust
The first stage establishes trust (or mistrust) that basic needs, such as nourishment and affection, will be met. Trust is the basis of our development during infancy (birth to 12 months). Infants are dependent on their caregivers, so caregivers who are responsive and sensitive to their infant’s needs help their baby to develop a sense of trust; their baby will see the world as a safe, predictable place. Unresponsive caregivers who do not meet their baby’s needs can engender feelings of anxiety, fear, and mistrust; their baby may see the world as unpredictable. [6]
- Autonomy vs. Shame
Toddlers begin to explore their world and learn that they can control their actions and act on the environment to get results. They begin to show clear preferences for certain elements of the environment, such as food, toys, and clothing. A toddler’s main task is to resolve the issue of autonomy versus shame and doubt by working to establish independence. For example, we might observe a budding sense of autonomy in a two-year-old child who wants to choose her clothes and dress herself. Although her outfits might not be appropriate for the situation, her input in such basic decisions has an effect on her sense of independence. If denied the opportunity to act on her environment, she may begin to doubt her abilities, which could lead to low self-esteem and feelings of shame. [7]
- Initiative vs. Guilt
Once children reach the preschool stage (ages 3–6 years), they are capable of initiating activities and asserting control over their world through social interactions and play. By learning to plan and achieve goals while interacting with others, preschool children can master this task. Those who do will develop self-confidence and feel a sense of purpose. Those who are unsuccessful at this stage may develop feelings of guilt. [8]
- Industry vs. Inferiority
During the elementary school stage (ages 7–11), children begin to compare themselves to their peers to see how they measure up. They either develop a sense of pride and accomplishment in their schoolwork, sports, social activities, and family life, or they feel inferior and inadequate when they don’t measure up. [9]
- Identity vs. Identity Confusion
In adolescence (ages 12–18), children develop a sense of self. Adolescents struggle with questions such as “Who am I?” and “What do I want to do with my life?” Along the way, most adolescents try on many different selves to see which ones fit. Adolescents who are successful at this stage have a strong sense of identity and are able to remain true to their beliefs and values in the face of problems and other people’s perspectives. Teens who do not make a conscious search for identity or those who are pressured to conform to their parents’ ideas for the future may have a weak sense of self and experience role confusion as they are unsure of their identity and confused about the future. [10]
- Intimacy vs. Isolation
People in early adulthood (i.e., 20s through early 40s) are ready to share their lives with others after they have developed a sense of self. Adults who do not develop a positive self-concept in adolescence may experience feelings of loneliness and emotional isolation. [11]
- Generativity vs. Stagnation
When people reach their 40s, they enter a time period known as middle adulthood that extends to the mid-60s. The social task of middle adulthood is generativity versus stagnation. Generativity involves finding your life’s work and contributing to the development of others, through activities such as volunteering, mentoring, and raising children. Those who do not master this task may experience stagnation, having little connection with others and little interest in productivity and self-improvement. [12]
- Integrity vs. Despair
The mid-60s to the end of life is a period of development known as late adulthood. People in late adulthood reflect on their lives and feel either a sense of satisfaction or a sense of failure. People who feel proud of their accomplishments feel a sense of integrity and often look back on their lives with few regrets. However, people who are not successful at this stage may feel as if their life has been wasted. They focus on what “would have,” “should have,” or “could have” been. They face the end of their lives with feelings of bitterness, depression, and despair. [13]
By combining Maslow’s and Erickson’s theories of development and motivation, we can begin to understand why some patients need more encouragement, space, or time to allow caregivers to provide assistance with their ADLs to maintain physical and emotional health.
View the following YouTube video [14] for more information about Erikson’s theory of development: Erikson’s Psychosocial Development | Individuals and Society.
Assisting With Spiritual Needs
When clients experience a serious illness or injury, they often grapple with the existential question, “Why is this happening to me?” This question can be a sign of spiritual distress defined as, “A state of suffering related to the inability to experience meaning in life through connections with self, others, the world, or a superior being.” Spiritual well-being is a pattern of experiencing meaning and purpose in life through connectedness with self, others, art, music, literature, nature, and/or a power greater than oneself. Spirituality is often mistakenly equated with religion, but spirituality is a broader concept. Elements of spirituality include faith, meaning, love, belonging, forgiveness, and connectedness. [15] Spirituality and religion can change over a person’s lifetime and vary greatly between people. Some people who are very spiritual may not belong to a specific religion.
Religion is frequently defined as an institutionalized set of beliefs and practices. Many religions have specific rules about food, religious rituals, clothing, and touching. Supporting these rules when they are meaningful part of a resident’s spirituality is an effective way to support the resident and maintain a caring, professional relationship. The nursing assistant should discuss these aspects with the nurse to assure they support the plan of care for the resident and encourage other staff members to provide support. Many nursing homes and assisted living facilities offer religious or spiritual opportunities through their Activities departments.
Many hospitals, nursing homes, assisted living facilities, and hospices employ professionally trained chaplains to assist with the spiritual, religious, and emotional needs of clients, family members, and staff. In these settings, chaplains support and encourage people of all religious faiths and cultures and customize their approach to each individual’s background, age, and medical condition. Chaplains can meet with any individual regardless of their belief, or lack of belief, in a higher power and can be very helpful in reducing anxiety and distress. [16] NAs may suggest chaplain services for their clients.
An important way to assist a client with their spiritual well-being is to ask them what they need to feel supported in their faith and then try to accommodate their requests, if possible. Explain that spiritual health helps the healing process. For example, perhaps they would like to speak to their clergy, spend some quiet time in meditation or prayer without interruption, or go to the on-site chapel. Many agencies have chaplains onsite that can be offered to patients as a spiritual resource. [17]
If the client or family member requests a nursing assistant to pray with them, it is acceptable to pray with them or find someone who will. Some nursing assistants may feel reluctant to pray with patients when they are asked for various reasons; they may feel underprepared, uncomfortable, or unsure if they are “allowed to.” Nursing assistants, nurses, and other health care team members are encouraged to pray with their patients to support their spiritual health, as long as the focus is on the patient’s preferences and beliefs, not their own preferences. Having a short, simple prayer ready that is appropriate for any faith may help a health care professional feel prepared for this situation. However, if the nursing assistant does not feel comfortable praying with the patient as requested, the nurse should be notified so the chaplain can be requested to participate in prayer with the patient. [18]
It is important to support clients within their own faith tradition, but it is not appropriate for the nursing assistant to take this opportunity to attempt to persuade a patient towards a preferred religion or belief system. The role of the nursing assistant is to respect and support the client’s values and beliefs, not promote the nursing assistant’s values and beliefs. [19]
- “ Maslow%27s_Hierarchy_of_Needs2.svg ” by Androidmarsexpress is licensed under CC.BY-SA 4.0 ↵
- McLeod, S. (2020, March 20). Maslow’s hierarchy of needs . Simply Psychology. https://www.simplypsychology.org/maslow.html ↵
- Puchalski, C. M., Vitillo, R., Hull, S. K., & Reller, N. (2014). Improving the spiritual dimension of whole person care: Reaching national and international consensus. Journal of Palliative Medicine, 17 (6), 642–656. https://doi.org/10.1089/jpm.2014.9427 ↵
- This work is a derivative of StatPearls by Orenstein and Lewis and is licensed under CC BY 4.0 ↵
- This work is a derivative of Psychology 2e by OpenStax and is licensed under CC BY 4.0 . Access for free at https://openstax.org/books/psychology-2e/pages/1-introduction ↵
- This work is a derivative of Psychology 2e by OpenStax and is licensed under CC BY 4.0 . Access for free at https://openstax.org/books/psychology-2e/pages/1-introduction ↵
- This work is a derivative of Psychology 2e by OpenStax and is licensed under CC BY 4.0 . Access for free at https://openstax.org/books/psychology-2e/pages/1-introduction ↵
- This work is a derivative of Psychology 2e by OpenStax and is licensed under CC BY 4.0 . Access for free at https://openstax.org/books/psychology-2e/pages/1-introduction ↵
- This work is a derivative of Psychology 2e by OpenStax and is licensed under CC BY 4.0 . Access for free at https://openstax.org/books/psychology-2e/pages/1-introduction ↵
- This work is a derivative of Psychology 2e by OpenStax and is licensed under CC BY 4.0 . Access for free at https://openstax.org/books/psychology-2e/pages/1-introduction ↵
- This work is a derivative of Psychology 2e by OpenStax and is licensed under CC BY 4.0 . Access for free at https://openstax.org/books/psychology-2e/pages/1-introduction ↵
- This work is a derivative of Psychology 2e by OpenStax and is licensed under CC BY 4.0 . Access for free at https://openstax.org/books/psychology-2e/pages/1-introduction ↵
- This work is a derivative of Psychology 2e by OpenStax and is licensed under CC BY 4.0 . Access for free at https://openstax.org/books/psychology-2e/pages/1-introduction ↵
- Desai, S. (2014, February 25). Erikson’s psychosocial development | Individuals and society | MCAT | Khan Academy [Video]. YouTube. Licensed under CC BY-NC-SA . https://youtu.be/SIoKwUcmivk ↵
- Herdman, T. H., & Kamitsuru, S. (Eds.). (2018). Nursing diagnoses: Definitions and classification, 2018-2020. Thieme Publishers New York, pp. 365, 372-377. ↵
- This work is a derivative of Nursing Fundamentals by Chippewa Valley Technical College and is licensed under CC BY 4.0 ↵
- This work is a derivative of Nursing Fundamentals by Chippewa Valley Technical College and is licensed under CC BY 4.0 ↵
- This work is a derivative of Nursing Fundamentals by Chippewa Valley Technical College and is licensed under CC BY 4.0 ↵
- This work is a derivative of Nursing Fundamentals by Chippewa Valley Technical College and is licensed under CC BY 4.0 ↵


2.2: Types of Operating Systems
What are the Types of Operating Systems
An Operating System performs all the basic tasks like managing file,process, and memory. Thus operating system acts as manager of all the resources, i.e. resource manager . Thus operating system becomes an interface between user and machine.
Types of Operating Systems: Some of the widely used operating systems are as follows-
1. Batch Operating System
This type of operating system does not interact with the computer directly. There is an operator which takes similar jobs having same requirement and group them into batches. It is the responsibility of operator to sort the jobs with similar needs.
Advantages of Batch Operating System:
- It is very difficult to guess or know the time required by any job to complete. Processors of the batch systems know how long the job would be when it is in queue
- Multiple users can share the batch systems
- The idle time for batch system is very less
- It is easy to manage large work repeatedly in batch systems
Disadvantages of Batch Operating System:
- The computer operators should be well known with batch systems
- Batch systems are hard to debug
- It is sometime costly
- The other jobs will have to wait for an unknown time if any job fails
Examples of Batch based Operating System: Payroll System, Bank Statements etc.
2. Time-Sharing Operating Systems
Each task is given some time to execute, so that all the tasks work smoothly. Each user gets time of CPU as they use single system. These systems are also known as Multitasking Systems. The task can be from single user or from different users also. The time that each task gets to execute is called quantum. After this time interval is over OS switches over to next task.
Advantages of Time-Sharing OS:
- Each task gets an equal opportunity
- Less chances of duplication of software
- CPU idle time can be reduced
Disadvantages of Time-Sharing OS:
- Reliability problem
- One must have to take care of security and integrity of user programs and data
- Data communication problem
Examples of Time-Sharing OSs are: Linux, Unix etc.
Adapted from:
"Types of Operating Systems"
by
akash1295
,
Geeks for Geeks
is licensed under
CC BY-SA 4.0


31.13: Star Chart and Sky Event Resources Index (Appendix M)
Star Charts
To obtain graphic charts of the sky over your head tonight, there are a number of free online resources.
- One of the easiest is at the Skymaps website: http://www.skymaps.com/downloads.html . Here you can print out a free PDF version of the northern sky (for roughly latitude 40°, which is reasonable for much of the United States). Maps of the sky from the equator and the southern hemisphere can also be printed.
- Sky charts and other summaries of astronomical information can also be found at http://www.heavens-above.com/ .
- A free, open-source computer application that shows the sky at any time from any place is called Stellarium. You can find it at http://www.stellarium.org/ .
- Appendix B provides a section of information for finding astronomy apps for cell phones and tablets. Many of these also provide star charts. If you have a smartphone, you can find a variety of inexpensive apps that allow you to simply hold your phone upward to see what is in the sky behind your phone.
-
A
planisphere
is a sky chart that turns inside a round frame and can show you the night sky at your latitude on any date and time of the year. You can buy them at science supply and telescope stores or online. Or you can construct your own from templates at these two websites:
- Dennis Schatz’s AstroAdventures Star Finder: http://dennisschatz.org/activities/Star%20Finder.pdf
- Uncle Al’s Star Wheel: http://www.lawrencehallofscience.org/do_science_now/science_apps_and_activities/starwheels
Calendars of Night Sky Events
The following resources offer calendars of night sky events.
- Sea and Sky: http://www.seasky.org/astronomy/astronomy.html (click on the fourth menu button)
- Sky & Telescope’s This Week’s Sky at a Glance: www.skyandtelescope.com/observing/sky-at-a-glance/
- Astronomy Magazine’s The Sky This Week: http://www.astronomy.com/observing/sky-this-week
- Dr. Fred Espenak’s Year by Year Tables of Events: http://astropixels.com/ephemeris/ephemeris.html
- Night Sky Network Sky Planner: https://nightsky.jpl.nasa.gov/planner.cfm


11: The Damped, Driven Pendulum
The simple pendulum is the mathematical idealization of a frictionless pendulum. We now consider the effects of friction as well as an externally imposed periodic force. The frictional force is modeled as
\[F_{f}=-\gamma l \dot{\theta}, \nonumber \]
where the frictional force is opposite in sign to the velocity, and thus opposes motion. The positive parameter \(\gamma\) is called the coefficient of friction. The external periodic force is modeled as
\[\nonumber F_{e}=F \cos \Omega t, \nonumber \]
where \(F\) is the force’s amplitude and \(\Omega\) is the force’s angular frequency. If we also include the gravitational force given by \((10.1)\) , Newton’s equation can then be written as
\[\ddot{\theta}+\lambda \dot{\theta}+\omega^{2} \sin \theta=f \cos \Omega t \nonumber \]
where \(\lambda=\gamma / m, f=F / m l\) , and \(\omega\) is defined in (10.3). An analytical solution of (11.1) is possible only for small oscillations. Indeed, the damped, driven pendulum can be chaotic when oscillations are large.
The linear pendulum
Damped pendulum
Here, we exclude the external force, and consider the damped pendulum using the small amplitude approximation \(\sin \theta \approx \theta\) . The governing equation becomes the linear, second-order, homogeneous differential equation given
\[\ddot{\theta}+\lambda \dot{\theta}+\omega^{2} \theta=0 \nonumber \]
which is usually discussed in detail in a first course on differential equations.
The characteristic equation of \((11.2)\) is obtained by the ansatz \(\theta(t)=\exp (\alpha t)\) , which yields
\[\alpha^{2}+\lambda \alpha+\omega^{2}=0 \nonumber \]
with solution
\[\alpha_{\pm}=-\frac{1}{2} \lambda \pm \frac{1}{2} \sqrt{\lambda^{2}-4 \omega^{2}} \nonumber \]
For convenience, we define \(\beta=\lambda / 2\) so that (11.4) becomes
\[\alpha_{\pm}=-\beta \pm \sqrt{\beta^{2}-\omega^{2}} \nonumber \]
The discriminant of \((11.5)\) is \(\beta^{2}-\omega^{2}\) , and its sign determines the nature of the damped oscillations.
The underdamped pendulum satisfies \(\beta<\omega\) , and we write
\[\nonumber \alpha_{\pm}=-\beta \pm i \omega_{* \prime} \nonumber \]
where \(\omega_{*}=\sqrt{\omega^{2}-\beta^{2}}\) and \(i=\sqrt{-1}\) . In this case, the general solution of (11.2) is a damped oscillation given by
\[\nonumber \theta(t)=e^{-\beta t}\left(A \cos \omega_{*} t+B \sin \omega_{*} t\right) . \nonumber \]
The overdamped pendulum satisfies \(\beta>\omega\) , and the general solution is an exponential decay and is given by
\[\nonumber \theta(t)=c_{1} e^{\alpha_{+} t}+c_{2} e^{\alpha_{-} t} \nonumber \]
where both \(\alpha_{+}\) and \(\alpha_{-}\) are negative.
The critically damped pendulum corresponds to the special case when \(\beta=\omega\) , and with \(\alpha_{+}=\alpha_{-}=\alpha<0\) , the general solution is given by
\[\nonumber \theta(t)=\left(c_{1}+c_{2} t\right) e^{\alpha t} . \nonumber \]
Driven pendulum
Here, we neglect friction but include the external periodic force. The small amplitude approximation results in the governing equation
\[\ddot{\theta}+\omega^{2} \theta=f \cos \Omega t . \nonumber \]
An interesting solution occurs exactly at resonance, when the external forcing frequency \(\Omega\) exactly matches the frequency \(\omega\) of the unforced oscillator. Here, the inhomogeneous term of the differential equation is a solution of the homogeneous equation. With the initial conditions \(\theta(0)=\theta_{0}\) and \(\theta(0)=0\) , the solution at resonance can be determined to be
\[\nonumber \theta(t)=\theta_{0} \cos \omega t+\frac{f}{2 \omega} t \sin \omega t \nonumber \]
which is a sum of a homogeneous solution (with coefficients determined to satisfy the initial conditions) plus the particular solution. The particular solution is an oscillation with an amplitude that increases linearly with time. Eventually, the small amplitude approximation used to derive (11.6) will become invalid.
An interesting computation solves the pendulum equation at resonance-replacing \(\omega^{2} \theta\) in (11.6) by \(\omega^{2} \sin \theta\) -with the pendulum initially at rest at the bottom \(\left(\theta_{0}=0\right)\) . What happens to the amplitude of the oscillation after its initial linear increase?
Damped, driven pendulum
Here, we consider both friction and an external periodic force. The small amplitude approximation of (11.1) is given by
\[\ddot{\theta}+\lambda \dot{\theta}+\omega^{2} \theta=f \cos \Omega t \nonumber \]
The general solution to \((11.7)\) is determined by adding a particular solution to the general solution of the homogeneous equation. Because of friction, the homogeneous solutions decay to zero leaving at long times only the non-decaying particular solution. To find this particular solution, we note that the complex ode given by
\[\ddot{z}+\lambda \dot{z}+\omega^{2} z=f e^{i \Omega t}, \nonumber \]
With \(z=x+i y\) , represents two real odes given by
\[\nonumber \ddot{x}+\lambda \dot{x}+\omega^{2} x=f \cos \Omega t, \quad \ddot{y}+\lambda \dot{y}+\omega^{2} y=f \sin \Omega t, \nonumber \]
where the first equation is the same as (11.7). We can therefore solve the complex ode (11.8) for \(z(t)\) , and then take as our solution \(\theta(t)=\operatorname{Re}(z) .\) With the ansatz \(z_{p}=A e^{i \Omega t}\) , we have from (11.8)
\[\nonumber -\Omega^{2} A+i \lambda \Omega A+\omega^{2} A=f \nonumber \]
or solving for \(A\) ,
\[A=\frac{f}{\left(\omega^{2}-\Omega^{2}\right)+i \lambda \Omega} \nonumber \]
The complex coefficient \(A\) determines both the amplitude and the phase of the oscillation. We first rewrite \(A\) by multiplying the numerator and denominator by the complex conjugate of the denominator:
\[\nonumber A=\frac{f\left(\left(\omega^{2}-\Omega^{2}\right)-i \lambda \Omega\right)}{\left(\omega^{2}-\Omega^{2}\right)^{2}+\lambda^{2} \Omega^{2}} . \nonumber \]
Now, using the polar form of a complex number, we have
\[\nonumber \left(\omega^{2}-\Omega^{2}\right)-i \lambda \Omega=\sqrt{\left(\omega^{2}-\Omega^{2}\right)^{2}+\lambda^{2} \Omega^{2}} e^{i \phi}, \nonumber \]
where \(\tan \phi=\lambda \Omega /\left(\Omega^{2}-\omega^{2}\right) .\) Therefore, \(A\) can be rewritten as
\[\nonumber A=\frac{f e^{i \phi}}{\sqrt{\left(\omega^{2}-\Omega^{2}\right)^{2}+\lambda^{2} \Omega^{2}}} \nonumber \]
With the particular solution given by \(\theta(t)=\operatorname{Re}\left(A e^{i \omega t}\right)\) , we have
\[\begin{align} \theta(t) &=\left(\frac{f}{\sqrt{\left(\omega^{2}-\Omega^{2}\right)^{2}+\lambda^{2} \Omega^{2}}}\right) \operatorname{Re}\left(e^{i(\Omega t+\phi)}\right) \\ &=\left(\frac{f}{\sqrt{\left(\omega^{2}-\Omega^{2}\right)^{2}+\lambda^{2} \Omega^{2}}}\right) \cos (\Omega t+\phi) \end{align} \nonumber \]
The amplitude of the pendulum’s oscillation at long times is therefore given by
\[\nonumber \frac{f}{\sqrt{\left(\omega^{2}-\Omega^{2}\right)^{2}+\lambda^{2} \Omega^{2}}} \nonumber \]
and the phase shift of the oscillation relative to the external periodic force is given by \(\phi\) .
For example, if the external forcing frequency is tuned to match the frequency of the unforced oscillator, that is, \(\Omega=\omega\) , then one obtains directly from \((11.9)\) that \(A=f /(i \lambda \omega)\) , so that the asymptotic solution for \(\theta(t)\) is given by
\[\theta(t)=\frac{f}{\lambda \omega} \sin \omega t . \nonumber \]
The oscillator is observed to be \(\pi / 2\) out of phase with the external force, or in other words, the velocity of the oscillator, not the position, is in phase with the force.
The solution given by (11.12) shows that large amplitude oscillations can result by either increasing \(f\) , or decreasing \(\lambda\) or \(\omega\) . As the amplitude of oscillation becomes large, the small amplitude approximation \(\sin \theta \approx \theta\) may become inaccurate and the true pendulum solution may diverge from (11.12).
The nonlinear pendulum
As we already eluded, the fully nonlinear damped, driven pendulum can become chaotic. To study (11.1) numerically, or for that matter any other equation, the number of free parameters should be reduced to a minimum. This usually means that the governing equations should be nondimensionalized, and the dimensional parameters should be grouped into a minimum number of dimensionless parameters. How many dimensionless parameters will there be? The answer to this question is called the Buckingham II Theorem.
The Buckingham I Theorem: If an equation involves \(n\) dimensional parameters that are specified in terms of \(k\) independent units, then the equation can be nondimensionalized to one involving \(n-k\) dimensionless parameters.
Now, the damped, driven pendulum equation (11.1) contains four dimensional parameters, \(\lambda\) , \(f, \omega\) , and \(\Omega\) , and has a single independent unit, namely time. Therefore, this equation can be nondimensionalized to an equation with only three dimensionless parameters. Namely, we nondimensionalize time using one of the dimensional parameters. Here, we choose \(\omega\) , with units of inverse time, and write
\[\nonumber \tau=\omega t \nonumber \]
where \(\tau\) is now the dimensionless time. The damped, driven pendulum equation (11.1) therefore nondimensionalizes to
\[\frac{d^{2} \theta}{d \tau^{2}}+\left(\frac{\lambda}{\omega}\right) \frac{d \theta}{d \tau}+\sin \theta=\left(\frac{f}{\omega^{2}}\right) \cos \left(\left(\frac{\Omega}{\omega}\right) \tau\right), \nonumber \]
and the remaining three dimensionless groupings of parameters are evidently
\[\nonumber \frac{\lambda}{\omega}, \quad \frac{f}{\omega^{2}}, \quad \frac{\Omega}{\omega} \nonumber \]
We may give these three dimensionless groupings new names. Rather than introduce even more named parameters into the problem, I will now call the dimensionless time \(t\) , and reuse some of the other parameter names, with the understanding that the damped, driven pendulum equation that we will now study numerically is dimensionless. We will therefore study the equation
\[\ddot{\theta}+\frac{1}{q} \dot{\theta}+\sin \theta=f \cos \omega t \nonumber \]
with the now dimensionless parameters named \(q, f\) and \(\omega\) .
Equation (11.14) is called a non-autonomous equation. For a differential equation to be called autonomous, the independent variable \(t\) must not appear explicitly. It is possible to write this second-order non-autonomous differential equation as a system of three first-order autonomous equations by introducing the dependent variable \(\psi=\omega t\) . We therefore have
\[\begin{align} \nonumber \dot{\theta} &=u, \\ \dot{u} &=-\frac{1}{q} u-\sin \theta+f \cos \psi, \\ \dot{\psi} &=\omega .\nonumber \end{align} \nonumber \]
The necessary conditions for an autonomous system of differential equations to admit chaotic solutions are (1) the system has at least three independent dynamical variables, and; (2) the system contains at least one nonlinear coupling. Here, we see that the damped, driven pendulum equation satisfies these conditions, where the three independent dynamical variables are \(\theta, u\) and \(\psi\) , and there are two nonlinear couplings, \(\sin \theta\) and \(\cos \psi\) , where we already know that the first nonlinear coupling is required for chaotic solutions.
But what exactly is chaos? What we are considering here is called deterministic chaos, that is chaotic solutions to deterministic equations such as a non-stochastic differential equation. Although there is no definitive definition of chaos, perhaps its most important characteristic is a solution’s sensitivity to initial conditions. A small change in initial conditions can lead to a large deviation in a solution’s behavior. A solution’s sensitivity to initial conditions has been called the Butterfly Effect, where the image of a butterfly appeared in the title of a talk that one of the founders of the field, Edward Lorenz, gave in 1972: "Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?"
We can easily observe that the small amplitude approximation of (11.14) can not admit chaotic solutions. Suppose we consider two solutions \(\theta_{1}(t)\) and \(\theta_{2}(t)\) to the approximate equations, these two solutions differing only in their initial conditions. We therefore have
\[\begin{aligned} &\ddot{\theta}_{1}+\frac{1}{q} \dot{\theta}_{1}+\theta_{1}=f \cos \omega t \\ &\ddot{\theta}_{2}+\frac{1}{q} \dot{\theta}_{2}+\theta_{2}=f \cos \omega t \end{aligned} \nonumber \]
If we define \(\delta=\theta_{2}-\theta_{1}\) , then the equation satisfied by \(\delta=\delta(t)\) is given by
\[\nonumber \ddot{\delta}+\frac{1}{q} \dot{\delta}+\delta=0 \nonumber \]
which is the undriven, damped pendulum equation. Therefore, \(\delta(t) \rightarrow 0\) for large times, and the solution for \(\theta_{2}\) and \(\theta_{1}\) eventually converge, despite different initial conditions. In other words, there is no sensitivity to initial conditions in the solution. Only for large amplitudes where the approximation \(\sin \theta \approx \theta\) becomes invalid, are chaotic solutions possible.
We will next learn some of the concepts and tools required for a numerical exploration of chaos in dynamical systems.


By the end of this chapter, you should be able to:
Summarize what goes into child and staff health records.
Describe the process of daily health checks.
Explain good dental hygiene practices in the classroom.
Discuss the importance of sleep.
Licensing Regulations
Title 22 Regulations that relate to this chapter include:
101220
CHILD’S MEDICAL ASSESSMENTS
Prior to, or within 30 calendar days following enrollment, the licensee will obtain a licensed physician’s written medical assessment of the child. The assessment must be less than one year old.
101220.1
IMMUNIZATIONS
Prior to admission to a Child Care Center, children shall be immunized against diseases as required by the California Code of Regulations, Title 17.
A child who does not meet any of these requirements shall not be admitted to a Child Care Center.
The licensee must document and maintain each child’s immunizations records for as long as the child is enrolled.
101221
CHILD’S RECORDS
A separate, complete and current record for each child must be maintained.
101226.1
DAILY INSPECTION FOR ILLNESS
The licensee shall be responsible for ensuring the children with obvious symptoms of illness are not accepted.
No child shall be accepted without contact between center staff and the person bringing the child to the center.
Introduction
Healthy development continues to support learning throughout childhood and later life. “Health in the earliest years…lays the groundwork for a lifetime of well-being…”
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To promote the health of children in early care and education programs, it’s important to keep records of both children's and staff’s health. Programs can support children’s oral health and healthy sleep habits. And they can help identify developmental and health concerns with screening.
Children’s Health Records
“The health and safety of individual children requires that information regarding each child in care be kept and available when needed. Children’s records consist of various documentation such as a child’s medical and immunization history, emergency medical care information, and parental permission to participate in specific activities…Each child care facility must keep accurate records on each child receiving care in child care.”
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Health records can help early care and education programs identify preventative health measures, develop care plans for children with special needs, and determine whether or not a child should be excluded from care due to illness.
California Title 22 Child Care licensing requirements list the following health-related items to include in the child’s records:
Medical assessment and the following health information:
Dietary restrictions and allergies.
Instructions for action to be taken in case the child's authorized representative, or the physician designated by the authorized representative, cannot be reached in an emergency.
A signed consent form for emergency medical treatment
Record of any illness or injury requiring treatment by a physician or dentist and for which the center provided assistance to the child in meeting his/her necessary medical or dental needs.
Record of current medications, including the name of the prescribing physician, and instructions, if any, regarding control and custody of medications.
Current and updated immunization records
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The National Health and Safety Standards recommends that the following also be included in the child’s records:
A health history completed by the family at admission
The child’s health insurance information
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Staff Health Records
It is also important for records to be kept to document the health of all staff in an early care and education program. Licensing requires the following health-related items to be in staff records:
Health Screening Report
TB Clearance
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In September of 2016, Senate Bill 792 was passed that requires staff or volunteers in an early care and education program to provide records of immunizations (or immunity) for
Pertussis
Measles
Influenza (annually between August 1 and December 1 of each year; can decline in writing)
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The Importance of Keeping Staff Healthy
A culture of wellness is a working environment where an employee's health and safety is valued, supported, and promoted through worksite, health and wellness programs, policies, benefits, and environmental supports. A culture of wellness for staff is really going to be the foundation for creating a culture of health and safety for children.
Staff have health problems such as obesity and depression at rates above the national average. Early care and education salaries are often low, creating personal financial stress. Staff turnover rates are high. In general, early childhood educators are undervalued for the important and high-demand work they do.
Staff wellness and stability will affect the quality of services a program is able to deliver to families and children. Children need consistent, sensitive, caring, and stable relationships with adults. Adults who are well, physically and mentally, are more likely to engage in positive relationships. When we support staff well-being, we strengthen early care and education.
Programs can use the CDC’s Workplace Health Model to support the health of their staff.
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It is outlined in this image (and a link is provided in the Further Resources to Explore feature at the end of the chapter).
planning and management, implementation, and evaluation.
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Pause to Reflect
What does staying healthy mean to you? What do you do (or could you do) to manage your stress, reinforce your resilience, and keep yourself physically healthy (nutrition, activity, etc.)? How could your employer help you stay healthy?
Daily Health Checks
Every day an informal, observation-based quick health check should be performed on every child (before the parent/caregiver leaves). Early childhood educators should use their knowledge about what is normal for a child to identify any concerns about the child’s well-being (but not as an attempt to formally diagnose illness). It is not a process that formally excludes children from illness, but following up concerns noticed at a health check may find reasons to exclude children.
“In a child care setting where lots of people are coming at the same time, it is hard to take a moment with each child. However, this welcoming routine can establish many things and is a good child development policy. This contact will help [teachers] better understand each child, help the children feel comfortable and good about themselves, reduce the spread of illness by excluding children with obvious signs of illness, and foster better communications with [families].”
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Conducting the Daily Health Check
Teachers should use all of their senses to check for signs of illness. This includes:
Listening to what families tell you about how their child is feeling and what the child sounds like (hoarse voice, coughing, wheezing, etc.)
Looking at the child from head to toe (with a quick scan) to see if the child looks flushed, pale, has a rash, has a runny nose or mucus in the eyes
Feeling the child’s cheek or neck (as part of a greeting) for warmth or clamminess
Smelling the child for unusual smelling breath or a bowel movement.
Here are the signs to observe for:
General mood and atypical behavior
Fever (elevated temperature)
Rashes or unusual spots, itching, swelling, and bruising
Complaints of not feeling well
Symptoms of illness (coughing, sneezing, runny nose, eye or ear discharge, diarrhea, vomiting, etc.)
Reported illness in child or family members
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,
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Dental Hygiene
Dental hygiene is important to prevent Early Childhood Caries (ECC), which is a term used to describe tooth decay, including filled or extracted teeth due to decay, in the primary teeth (baby teeth). It is important to rethink the way we “treat” dental caries. Traditionally, we would wait until a child had a cavity and “treat” the cavity with a filling. In order to prevent ECC, we must intervene before the first cavity develops.
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Early care and education programs can teach children and families about dental hygiene and oral care as well as implement good dental hygiene practices. Here are some ideas:
Use teaching practices that engage children and promoting thinking critically. Consider asking questions such as:
How do you brush your teeth?
Why do you brush your teeth?

Tell me about your last visit to the dentist.
Integrate oral health into activities (in addition to tooth brushing). Some possibilities include:
Having children separate pictures of foods that are good for oral health from pictures of foods that are high in sugar.
Reading books with positive oral health messages to children.
Having children pretend they are visiting a dental office.
Singing songs about oral health
Engage families in promoting oral health at home. Some ways to do this include:
Working with families to find the best ways to position their child for tooth brushing. Remind families that young children cannot brush their teeth well until age 7 to 8. It is also important for a parent to brush their child’s teeth or help them with brushing.
Asking families to take photographs of their child brushing his teeth and helping the child write stories about his experience.
Helping families choose and prepare foods that promote good oral health.
Encouraging families to ask their child what she learned about oral health in school that day.
Offering families suggestions for at-home activities that support what children are learning about oral health at school.
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Classroom Tooth Brushing Steps
Sitting at a table in a circle, children brush teeth as a group activity every day.
Give each child a small paper cup, a paper towel, and a soft-bristled, child-sized toothbrush.
Put a small (pea-sized) dab of fluoride toothpaste on the inside rim of each cup, and have children use their toothbrushes to pick up the dabs of toothpaste.
Brush together for two minutes, using an egg timer or a song that lasts for about two minutes.
Brush your teeth with the children to set an example, and remind them to brush all of their teeth, on all sides.
When the two minutes are up, have the children spit any extra toothpaste into their cups, wipe their mouths and throw the cups and paper towels away.
Children can go to the sink in groups to rinse their toothbrushes and put the toothbrushes in holders to dry.
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Sleep Hygiene
It's important to get enough sleep. Sleep supports mind and body health. Getting enough sleep isn’t only about total hours of sleep. It’s also important to get good quality sleep on a regular schedule to feel rested upon waking.
Sleep is an important part of life! Young children spend around half of their time asleep.
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Babies need to sleep between 12 and 16 hours a day (including naps).
Toddlers need to sleep between 11 and 14 hours a day (including naps).
Preschoolers need to sleep between 10 and 13 hours a day (including naps).
School-aged children need 9 to 12 hours of sleep each night.
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We know how busy they are when they are awake, but what are they doing during all of those restful hours? Actually, sleep has many purposes.
Growth: Growth hormone is released when children sleep (Berk 2002, 302). Young children are growing in their sleep, and since they have a lot of growing to do, they need all the sleep they can get.
Restoration: Some sleep researchers have found that sleep is important for letting the brain relax and restore some of the hormones and nutrients it needs (Jenni & O’Conner 1995, 205).
Memory: Sleep is also a time when the brain is figuring out what experiences from the day are important to remember (Jenni & O’Conner 1995, 205).
Health: One study found that infants and toddlers need at least 12 hours of sleep in a 24 hour day. When infants and toddlers had less than 12 hours they were more likely to be obese by the age of 3 (Taveras et. al. 2008, 305).
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The Culture of Sleep and Child Care
Across the world people sleep in different ways. Some people sleep inside, some sleep outside. Some people sleep in beds, others in hammocks or on mats on the floor. Some people sleep alone, some sleep with a spouse or children or both. Some people sleep only at night, while others value a nap during the day. How, when, and where people choose to sleep has a lot to do with their culture, traditions, and customs. This can include where they live, how their family sleeps, even how many bedrooms are in their home. Teachers have a role in providing a sleep environment that is comfortable and safe for the children in their care, while honoring families’ cultural beliefs.
What can teachers do to help young children feel more “at home” when it is time for them to rest?
Think of sleep and sleep routines as part of the child’s individualized curriculum.
 This is an opportunity to find out about a child’s sleep habits before they join the classroom. When you know how a baby sleeps at home, you can use that information to plan for how they might sleep best in your care.
Brainstorm ways to adapt your classroom to help a child feel “at home” during rest times. For example, a baby who is used to sleeping in a busy environment might nap better if you roll a crib into the classroom. Some mobile infants and toddlers might have a hard time sleeping in child care because they think they will miss something fun! These children benefit from having a very quiet place to fall asleep. When you have a positive relationship with a baby it will be easier to know what will help them relax into sleep.
Encourage families to bring in “a little bit of home” to the program – like a stuffed animal or special blanket. A comfort item from home can help children feel connected to their families. They might want that comfort all day. The comfort item from home can also help children make the transition to sleep while in your care. Make sure that infants under one year of age do not have any extra toys or blankets in the crib with them.
Share with families what you learn about their child. Use pick up and drop off times to ask questions about sleep at home. Families can share information that could make their child more comfortable in your care. You can be a resource for families about sleep and their child. Remember that families are the experts about their child.
Napping and Individual Differences
Have you noticed that some children will fall asleep every day at the same time no matter what else is going on? These kids could fall asleep into their lunch if it is served too late! Have you known children who seem to fall asleep easily some days and other times just can’t settle into sleep? These children might need a very stable routine. Some toddlers nap less and sleep more at night while others need to have a long sleep during the day.
Temperament and Sleep
Some of the different patterns in children’s sleep has to do with their temperament (Jenni & O’Connor 2005, 204). Temperament is like the personality we are born with. Some children are naturally easy-going and adapt to new situations while others really need a routine that is the same every day. One child might fall asleep easily just by putting her in her crib or cot when she is drifting off to sleep. Another child might fall asleep in your arms but startle awake the moment he realizes he has been laid down alone.
Circadian Rhythms and Sleep
Something else that can make nap time easy or difficult for young children has to do with their natural sleep cycles. Everyone has a kind of “clock” inside of their bodies that tells them when they are hungry or sleepy. The cycle of this clock is called circadian rhythms. Circadian rhythms are the patterns of sleeping, waking, eating, body temperature and even hormone releases in your body over a twenty-four hour period. How much children need to sleep, when they feel tired, and how easily they can fall asleep are all related to their circadian rhythms (Ferber 2006, 31).
Meeting Each Individual Child’s Sleep Needs
Thinking about the circadian rhythms and temperament reminds us how each child is different. That is why it is important to have nap times that meet the needs of all children in your care. Helping young children to learn to recognize their bodies’ needs and find ways to meet those needs is the very important skill of self-regulation.
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Individualizing Nap Schedules
Creating a space for sleepy children can allow them to relax or nap when their body tells them they are tired. It can take some creativity to figure out how to let a young child nap or rest when they are tired.
What do you do if a child won’t nap when others are? How does one child rest quietly in a busy classroom?
Two-and-a-half-year-old Henry is new to your classroom. His mother has shared with you that he does not nap during the day with her. When nap time comes around you can tell that Henry does not seem very tired.
What can you do for Henry, or other children like him, while the rest of the class sleeps?
Do you have a “cozy corner” that could also be a one child nap area?
Are there soft places to sit and relax with a book or stuffed animal?
Are books or other quiet activities provided if a child isn’t able to rest or settle when other children are?
Are children provided techniques and strategies for calming their bodies e.g. deep breathing, tensing and relaxing their bodies, feeling their heartbeat, etc?
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Summary
By keeping accurate records, conducting daily health checks, supporting children’s development of good dental hygiene, and by providing for individual children’s sleep needs early care and education programs can help promote good health on a daily basis. When programs monitor and screen children, they can ensure that conditions or situations that might interfere with a child’s health or well-being can be identified and supports put in place to mitigate potential negative effects.


4: Strategies and Interface I/O
Learning Objectives
At the end of this unit, the learners will
- Explain the Strategies of Interface I/O
- Distinguish between handshaking and buffering
- Understand the programmed IO mode of data transfer
- Describe a DMA transfer.
This section introduces the learners to the strategies of I/O interfaces. They include: polled, interrupt driven and DMA.
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- 4.4: Unit 4 Summary
- At the end of this unit, the learners will be conversant with the strategies of I/O interfaces. This involves accessibility of devices connected to the processor and where I/O transfers must take place between them and the processor. the various access methods, e.g. polling, interrupt and DMA. The interrupt process is also learned in this section.


7.1.6: Sole Proprietorships
Learning Objectives
By the end of this section, you will be able to:
- Describe the ownership structure of a sole proprietorship
- Explain the advantages and disadvantages of operating as a sole proprietor
A sole proprietorship is a business entity that is owned and managed by one individual and has very little formal structure and no mandatory filing/registration with the state. This type of business is very popular because it is easy and inexpensive to form. The owner, called a sole proprietor, is synonymous with the business and is therefore personally liable for all debts of the business. Sole proprietors do not pay separate income tax on the company, instead reporting all losses and profits on their individual tax returns.
Overview of Sole Proprietorships
Entrepreneurs solely operating their own businesses are called sole proprietors. According to the Tax Foundation, there are more than 23 million sole proprietorships in the US, far more than any other type of business entity. This statistic means that the sole proprietorship is by far the most common business structure, even though the business is not legally separate from its owner. The primary reason that many entrepreneurs choose the sole proprietorship format is that they do not have to make a choice, get professional advice, or spend any money. An entrepreneur who just starts doing business is automatically a sole proprietorship unless they elect to become a different type of entity and file that paperwork. An entrepreneur who becomes a sole proprietor does not necessarily have to go to an attorney or an accountant, or file any documents, making a sole proprietorship quick, easy, and cheap to form and operate.
Another development related to the decision to be a sole proprietor is the rapid growth of the gig economy. Some individuals prefer to work on their own rather than become a full-time employee. Being a gig worker falls somewhere between being a business owner and being an employee, so many gig workers, ranging from drivers for a ride-sharing company to instructional designers, operate as de facto contractors who are sole proprietors.
However, there remains a debate about whether these gig workers should be deemed sole proprietors. Recently, California passed a new law, signed by Governor Gavin Newsom, which extends wage and benefit protections to many thousands of workers who were previously self-employed sole proprietors working in the gig economy. The new law is based on the presumption that when workers are misclassified as independent contractors rather than as employees, they lose basic benefits such as a minimum wage, paid sick days, and health insurance.
The sole proprietorship is the simplest method to operate a business—often under the owner’s name—and the owner is typically taxed directly by the IRS by attaching a Schedule C (Profit or Loss) form to the owner’s individual tax return. In order to document one’s income, instead of being provided a Form W-2 from one’s employer, many self-employed individuals receive one or more 1099-MISC (Miscellaneous Income) forms from clients, which typically demonstrate that the taxpayer is operating a sole proprietorship. Sole proprietors are allowed to deduct their business expenses related to their income and, as both employer and employee, are required to pay the full amount of employment taxes for Social Security and Medicare.
An owner can also operate under a DBA or “doing business as” filing. A DBA is filed at the relevant state or local government office where the sole proprietor wants to operate under an assumed name. Technically, this is not a new organization: It is just a different name. Any business entity may file for a DBA to operate under an assumed name, and many individuals operate under a DBA to indicate the type of services they are providing, such as Smith’s Roofing Company. It is not uncommon for an individual to name a sole proprietorship using LLC or Co. in its name; however, an individual operating under a DBA or assumed name is not provided any of the protections provided to a corporation of LLC, even if Inc. or LLC is used in the assumed name. A sole proprietor needs to consider the impact of using an assumed name prior to creating a DBA.
Advantages and Disadvantages of Sole Proprietorships
The sole proprietor is personally liable for everything. A sole proprietor is the investor, owner, and manager of the business enterprise. The sole proprietor is personally liable for all of the taxes and any unpaid debts of the business venture. The sole proprietor also has no business to sell and can sell only assets related to the business. The sole proprietorship is the easiest business to start but has almost no differentiation from the individual starting the business.
Taxation of Sole Proprietorships
A sole proprietorship is not taxed as an entity. All profits pass through to the owner who pays individual income taxes on all profits earned. It does not matter whether the owner takes the money out of the business or leaves it in the business; all profits are taxed to the individual owner. This is an area that requires significant planning and may be a potential disadvantage, depending on how the individual owner’s personal rate compares to the corporate rate.
Other Low-Risk Entry Structures in Entrepreneurship
Over the past decade, various alternatives to traditional employment have become popular, leading many to become entrepreneurs rather than employees. The US Bureau of Labor Statistics reported that, in 2019, there are 55 million people in who are “gig workers,” which is more than 35 percent of the US workforce. That percentage is expected to increase to 43 percent by 2020. This offers both an opportunity and a challenge. There is a modicum of security when one is an employee of a company, which may not exist in the same way for someone who is freelancing or working as a contractor. There are many examples today of people becoming small entrepreneurs. This process goes by a variety of names, such as the sharing economy, the gig economy, the peer economy, or the collaborative economy. Maybe it means driving for a company such as Lyft, Uber, or GrubHub, or perhaps offering services through TaskRabbit, UpWork, or LivePerson.

Online Resources for the Gig Economy
The website business UpWork provides a platform for individuals to offer their services to large companies on a freelance or contract basis. Do you have skills as a web, mobile, or software developer, or perhaps in the area of data analytics? The UpWork website says that over 5 million businesses use people listed on UpWork, including companies such as Microsoft and General Electric.
Offering your services in this new manner is not controlling of what type of entrepreneurial enterprise you want to be. You can do most of these types of things as a sole proprietor, an LLC, or an S corporation. According to the Tax Foundation, over the past thirty-five years, the number of C corporations has declined significantly, while the total number of pass-through businesses including LLCs, S corporations, partnerships, and sole proprietorships has tripled to over 30 million. According to estimates, there are only 1.7 million C corporations, whereas there are 7.4 million LLCs, partnerships, and S corporations, and a whopping 23 million sole proprietorships. The explanation for these statistics is really quite simple. LLCs have quickly become one of the most popular business structures due to ease of formation and operation. Likewise, sole proprietorships are quick, easy, and low cost compared to corporations, which are more difficult and expensive to form and operate. The choice is open and depends on the variables discussed in this chapter.
ENTREPRENEUR IN ACTION
Nic & Luc Jam
In an interview with the Balance, entrepreneur Leroy Bautista summarized his path to becoming a small business owner. He worked in high-end restaurants and successful catering companies for two decades before he was laid off during the economic downturn. Bautista didn’t sulk or settle for a lousy job. Rather, he saw it as a chance to finally do what his coworkers and friends had been telling him to do: go out on his own, making his sauces and vinaigrettes, and selling them at local markets. It was out of necessity that the Nic & Luc company was born.
Originally selling just a few flavors, he now sells almost twenty flavors. For many small businesses, the word “local” is used as a marketing ploy, but for Nic & Luc, it is part of the business purpose and a core value. Bautista thinks it is important to support other local businesses like himself.
This is not a story that someone like Bezos or Gates might tell: It is much more basic, but it demonstrates how people at all levels are becoming business owners. Each one of them, including Leroy Bautista in this story, must make decisions about mundane things such as taxes, and liability; it can’t be all about jam.


8.9: Magnetism in Matter
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Learning Objectives
By the end of this section, you will be able to:
- Classify magnetic materials as paramagnetic, diamagnetic, or ferromagnetic, based on their response to a magnetic field
- Sketch how magnetic dipoles align with the magnetic field in each type of substance
- Define hysteresis and magnetic susceptibility, which determines the type of magnetic material
Why are certain materials magnetic and others not? And why do certain substances become magnetized by a field, whereas others are unaffected? To answer such questions, we need an understanding of magnetism on a microscopic level.
Within an atom, every electron travels in an orbit and spins on an internal axis. Both types of motion produce current loops and therefore magnetic dipoles. For a particular atom, the net magnetic dipole moment is the vector sum of the magnetic dipole moments. Values of \(\mu\) for several types of atoms are given in Table \(\PageIndex{1}\). Notice that some atoms have a zero net dipole moment and that the magnitudes of the nonvanishing moments are typically \(10^{23} \, A \cdot m^2\).
| Atom | Magnetic Moment \((10^{-24} \, A \cdot m^2)\) |
|---|---|
| H | 9.27 |
| He | 0 |
| Li | 9.27 |
| O | 13.9 |
| Na | 9.27 |
| S | 13.9 |
A handful of matter has approximately \(10^{26}\) atoms and ions, each with its magnetic dipole moment. If no external magnetic field is present, the magnetic dipoles are randomly oriented—as many are pointed up as down, as many are pointed east as west, and so on. Consequently, the net magnetic dipole moment of the sample is zero. However, if the sample is placed in a magnetic field, these dipoles tend to align with the field, and this alignment determines how the sample responds to the field. On the basis of this response, a material is said to be either paramagnetic, ferromagnetic, or diamagnetic.
In a paramagnetic material , only a small fraction (roughly one-third) of the magnetic dipoles are aligned with the applied field. Since each dipole produces its own magnetic field, this alignment contributes an extra magnetic field, which enhances the applied field. When a ferromagnetic material is placed in a magnetic field, its magnetic dipoles also become aligned; furthermore, they become locked together so that a permanent magnetization results, even when the field is turned off or reversed. This permanent magnetization happens in ferromagnetic materials but not paramagnetic materials. Diamagnetic materials are composed of atoms that have no net magnetic dipole moment. However, when a diamagnetic material is placed in a magnetic field, a magnetic dipole moment is directed opposite to the applied field and therefore produces a magnetic field that opposes the applied field. We now consider each type of material in greater detail.
Paramagnetic Materials
For simplicity, we assume our sample is a long, cylindrical piece that completely fills the interior of a long, tightly wound solenoid. When there is no current in the solenoid, the magnetic dipoles in the sample are randomly oriented and produce no net magnetic field. With a solenoid current, the magnetic field due to the solenoid exerts a torque on the dipoles that tends to align them with the field. In competition with the aligning torque are thermal collisions that tend to randomize the orientations of the dipoles. The relative importance of these two competing processes can be estimated by comparing the energies involved. The energy difference between a magnetic dipole aligned with and against a magnetic field is \(U_B = 2\mu B\). If \(\mu = 9.3 \times 10^{-24} A \cdot m^2\) (the value of atomic hydrogen) and B = 1.0 T, then
\[U_B = 1.9 \times 10^{-23}J. \nonumber \]
At a room temperature of \(27^o C\) the thermal energy per atom is
\[U_T \approx kT = (1.38 \times 10^{-23} J/K)(300 \, K) = 4.1 \times 10^{-21}J, \nonumber \]
which is about 220 times greater than \(U_B\). Clearly, energy exchanges in thermal collisions can seriously interfere with the alignment of the magnetic dipoles. As a result, only a small fraction of the dipoles is aligned at any instant.
The four sketches of Figure \(\PageIndex{1}\) furnish a simple model of this alignment process. In part (a), before the field of the solenoid (not shown) containing the paramagnetic sample is applied, the magnetic dipoles are randomly oriented and there is no net magnetic dipole moment associated with the material. With the introduction of the field, a partial alignment of the dipoles takes place, as depicted in part (b). The component of the net magnetic dipole moment that is perpendicular to the field vanishes. We may then represent the sample by part (c), which shows a collection of magnetic dipoles completely aligned with the field. By treating these dipoles as current loops, we can picture the dipole alignment as equivalent to a current around the surface of the material, as in part (d). This fictitious surface current produces its own magnetic field, which enhances the field of the solenoid.
We can express the total magnetic field \(\vec{B}\) in the material as
\[\vec{B} = \vec{B}_0 + \vec{B}_m, \label{eq3} \]
where \(\vec{B}_0\) is the field due to the current \(I_0\) in the solenoid and \(\vec{B}_m\) is the field due to the surface current \(I_m\) around the sample. Now \(\vec{B}_m\) is usually proportional to \(\vec{B}_0\) a fact we express by
\[\vec{B}_m = \chi \vec{B}_0, \label{eq4} \]
where \(\chi\) is a dimensionless quantity called the magnetic susceptibility . Values of \(\chi\) for some paramagnetic materials are given in Table \(\PageIndex{2}\). Since the alignment of magnetic dipoles is so weak, \(\chi\) is very small for paramagnetic materials. By combining Equation \ref{eq3} and Equation \ref{eq4}, we obtain:
\[\vec{B} = \vec{B}_0 + \chi \vec{B}_0 = (1 + \chi)\vec{B}_0. \label{eq4b} \]
For a sample within an infinite solenoid, this becomes
\[B = (1 + \chi)\mu_0 nI. \label{eq5} \]
This expression tells us that the insertion of a paramagnetic material into a solenoid increases the field by a factor of \((1 + \chi)\). However, since \(\chi\) is so small, the field isn’t enhanced very much.
The quantity
\[\mu = (1 + \chi)\mu_0. \label{eq6} \]
is called the magnetic permeability of a material . In terms of \(\mu\), Equation \ref{eq5} can be written as
\[B = \mu nI \label{eq7} \]
for the filled solenoid.
| Paramagnetic Materials | \(\chi\) | Diamagnetic Materials | \(\chi\) |
|---|---|---|---|
| Aluminum | \(2.2 \times 10^{-5}\) | Bismuth | \(-1.7 \times 10^{-5}\) |
| Calcium | \(1.4 \times 10^{-5}\) | Carbon (diamond) | \(-2.2 \times 10^{-5}\) |
| Chromium | \(3.1 \times 10^{-4}\) | Copper | \(-9.7 \times 10^{-6}\) |
| Magnesium | \(1.2 \times 10^{-5}\) | Lead | \(-1.8 \times 10^{-5}\) |
| Oxygen gas (1 atm) | \(1.8 \times 10^{-6}\) | Mercury | \(-2.8 \times 10^{-5}\) |
| Oxygen liquid (90 K) | \(3.5 \times 10^{-3}\) | Hydrogen gas (1 atm) | \(-2.2 \times 10^{-9}\) |
| Tungsten | \(6.8 \times 10^{-5}\) | Nitrogen gas (1 atm) | \(-6.7 \times 10^{-9}\) |
| Air (1 atm) | \(3.6 \times 10^{-7}\) | Water | \(-9.1 \times 10^{-6}\) |
Diamagnetic Materials
A magnetic field always induces a magnetic dipole in an atom. This induced dipole points opposite to the applied field, so its magnetic field is also directed opposite to the applied field. In paramagnetic and ferromagnetic materials, the induced magnetic dipole is masked by much stronger permanent magnetic dipoles of the atoms. However, in diamagnetic materials, whose atoms have no permanent magnetic dipole moments, the effect of the induced dipole is observable.
We can now describe the magnetic effects of diamagnetic materials with the same model developed for paramagnetic materials. In this case, however, the fictitious surface current flows opposite to the solenoid current, and the magnetic susceptibility \(\chi\) is negative. Values of \(\chi\) for some diamagnetic materials are also given in Table \(\PageIndex{2}\).
Water is a common diamagnetic material. Animals are mostly composed of water. Experiments have been performed on frogs and mice in diverging magnetic fields. The water molecules are repelled from the applied magnetic field against gravity until the animal reaches an equilibrium. The result is that the animal is levitated by the magnetic field.
Ferromagnetic Materials
Common magnets are made of a ferromagnetic material such as iron or one of its alloys. Experiments reveal that a ferromagnetic material consists of tiny regions known as magnetic domains . Their volumes typically range from \(10^{-12}\) to \(10^{-8} m^3\), and they contain about \(10^{17}\) to \(10^{21}\) atoms. Within a domain, the magnetic dipoles are rigidly aligned in the same direction by coupling among the atoms. This coupling, which is due to quantum mechanical effects, is so strong that even thermal agitation at room temperature cannot break it. The result is that each domain has a net dipole moment. Some materials have weaker coupling and are ferromagnetic only at lower temperatures.
If the domains in a ferromagnetic sample are randomly oriented, as shown in Figure \(\PageIndex{1a}\), the sample has no net magnetic dipole moment and is said to be unmagnetized. Suppose that we fill the volume of a solenoid with an unmagnetized ferromagnetic sample. When the magnetic field \(\vec{B}_0\) of the solenoid is turned on, the dipole moments of the domains rotate so that they align somewhat with the field, as depicted in Figure \(\PageIndex{1}b\). In addition, the aligned domains tend to increase in size at the expense of unaligned ones. The net effect of these two processes is the creation of a net magnetic dipole moment for the ferromagnet that is directed along the applied magnetic field. This net magnetic dipole moment is much larger than that of a paramagnetic sample, and the domains, with their large numbers of atoms, do not become misaligned by thermal agitation. Consequently, the field due to the alignment of the domains is quite large.
Besides iron, only four elements contain the magnetic domains needed to exhibit ferromagnetic behavior: cobalt, nickel, gadolinium, and dysprosium. Many alloys of these elements are also ferromagnetic. Ferromagnetic materials can be described using Equation \ref{eq4b} through Equation \ref{eq7}, the paramagnetic equations. However, the value of \(\chi\) for ferromagnetic material is usually on the order of \(10^3\) to \(10^4\), and it also depends on the history of the magnetic field to which the material has been subject. A typical plot of B (the total field in the material) versus \(B_0\) (the applied field) for an initially unmagnetized piece of iron is shown in Figure \(\PageIndex{2c}\). Some sample numbers are (1) for \(B_0 = 1.0 \times 10^{-4}T\), \(B = 0.60 \, T\), and \(\chi = (^{0.60}/_{1.0 \times 10^{-4}}) - 1 \approx 6.0 \times 10^3\); for (2) for \(B_0 = 6.0 \times 10^{-4}T\), \(B = 1.5 \, T\), and \(\chi = (^{1.5}/_{6.0 \times 10^{-4}}) - 1 \approx 2.5 \times 10^3\).
When \(B_0\) is varied over a range of positive and negative values, B is found to behave as shown in Figure \(\PageIndex{3}\). Note that the same \(B_0\) (corresponding to the same current in the solenoid) can produce different values of B in the material. The magnetic field B produced in a ferromagnetic material by an applied field \(B_0\) depends on the magnetic history of the material. This effect is called hysteresis , and the curve of Figure \(\PageIndex{4}\) is called a hysteresis loop. Notice that B does not disappear when \(B_0 = 0\) (i.e., when the current in the solenoid is turned off). The iron stays magnetized, which means that it has become a permanent magnet.
Like the paramagnetic sample of Figure \(\PageIndex{2}\), the partial alignment of the domains in a ferromagnet is equivalent to a current flowing around the surface. A bar magnet can therefore be pictured as a tightly wound solenoid with a large current circulating through its coils (the surface current). You can see in Figure \(\PageIndex{5}\) that this model fits quite well. The fields of the bar magnet and the finite solenoid are strikingly similar. The figure also shows how the poles of the bar magnet are identified. To form closed loops, the field lines outside the magnet leave the north (N) pole and enter the south (S) pole, whereas inside the magnet, they leave S and enter N.
Ferromagnetic materials are found in computer hard disk drives and permanent data storage devices (Figure \(\PageIndex{6}\)). A material used in your hard disk drives is called a spin valve, which has alternating layers of ferromagnetic (aligning with the external magnetic field) and antiferromagnetic (each atom is aligned opposite to the next) metals. It was observed that a significant change in resistance was discovered based on whether an applied magnetic field was on the spin valve or not. This large change in resistance creates a quick and consistent way for recording or reading information by an applied current.
Example \(\PageIndex{1}\): Iron Core in a Coil
A long coil is tightly wound around an iron cylinder whose magnetization curve is shown in Figure \(\PageIndex{3}\). (a) If \(n = 20\) turns per centimeter, what is the applied field \(B_0\) when \(I_0 = 0.20 \, A\)? (b) What is the net magnetic field for this same current? (c) What is the magnetic susceptibility in this case?
Strategy
(a) The magnetic field of a solenoid is calculated using \(\vec{B} = \mu_0 n I \hat{j}\). (b) The graph is read to determine the net magnetic field for this same current. (c) The magnetic susceptibility is calculated using Equation \ref{eq5} .
Solution
- The applied field \(B_0\) of the coil is \[B_0 = \mu_0 nI_0 = (4\pi \times 10^{-7} T \cdot m/A)(2000 / m)(0.20 \, A) \nonumber \]\[B_0 = 5.0 \times 10^{-4}T. \nonumber \]
- From inspection of the magnetization curve of Figure \(\PageIndex{3}\), we see that, for this value of \(B_0, \, B = 1.4 \, T\). Notice that the internal field of the aligned atoms is much larger than the externally applied field.
- The magnetic susceptibility is calculated to be \[\chi = \frac{B}{B_0} - 1 = \frac{1.4 \, T}{5.0 \times 10^{-4}T} - 1 = 2.8 \times 10^3. \nonumber \]
Significance
Ferromagnetic materials have susceptibilities in the range of \(10^3\) which compares well to our results here. Paramagnetic materials have fractional susceptibilities, so their applied field of the coil is much greater than the magnetic field generated by the material.
Exercise \(\PageIndex{1}\)
Repeat the calculations from the previous example for \(I_0 = 0.040 \, A.\)
- Answer
-
a. \(1.0 \times 10^{-4} T\); b. 0.60 T; c. \(6.0 \times 10^3\)


7.2: The Productivity Paradox
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- Ly-Huong T. Pham, Tejal Desai-Naik, Laurie Hammond, & Wael Abdeljabbar
- ASCCC Open Educational Resources Initiative (OERI)
In 1991, Erik Brynjolfsson wrote an article, published in the Communications of the ACM, entitled “ The Productivity Paradox of Information Technology: Review and Assessment ” By reviewing studies about the impact of IT investment on productivity, Brynjolfsson was able to conclude that the addition of information technology to business had not improved productivity at all – the “productivity paradox.” He concluded that this paradox resulted from our inability to unequivocally document any contribution after so much effort due to the lack of quantitative measures.
In 1998, Brynjolfsson and Lorin Hitt published a follow-up paper entitled “ Beyond the Productivity Paradox . ” In this paper, the authors utilized new data that had been collected and found that IT did, indeed, provide a positive result for businesses. Further, they found that sometimes the true advantages in using technology were not directly relatable to higher productivity but to “softer” measures, such as the impact on organizational structure. They also found that the impact of information technology can vary widely between companies.
IT Doesn’t Matter
Just as a consensus was forming about IT's value, the Internet stock market bubble burst; two years later, in 2003, Harvard professor Nicholas Carr wrote his article “ IT Doesn’t Matter ” in the Harvard Business Review. In this article, Carr asserts that as information technology has become more ubiquitous, it has also become less of a differentiator. In other words: because information technology is so readily available and the software used so easily copied, businesses cannot hope to implement these tools to provide any competitive advantage. IT is essentially a commodity, and it should be managed like one: low cost, low risk. IT management should see themselves as a utility within the company and work to keep costs down. For IT, providing the best service with minimal downtime is the goal. As you can imagine, this article caused quite an uproar, especially from IT companies. Many articles were written in defense of IT; many others in support of Carr.
The best thing to come out of the article and the subsequent book was that it opened up discussion on IT's place in a business strategy and exactly what role IT could play in competitive advantage. It is that question that we want to address in the rest of this chapter.
References
Brynjolfsson, E. and Hitt, L. (1998). Beyond the Productivity Paradox . Communications of the ACM. Retrieved August 16, 2020, from https://doi.org/10.1145/280324.280332
Brynjolfsson, E. (1992). The Productivity Paradox of Information Technology: Review and Assessment . Center for Coordination Science MIT Sloan School of Management Cambridge, MA. Retrieved from August 16, 2020, from http://ccs.mit.edu/papers/CCSWP130/ccswp130.html
Carr, Nicholas G (2003) IT Doesn’t Matter . Retrieved August 20 from https://hbr.org/2003/05/it-doesnt-matter


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While climate change is often thought of as a future challenge, we can already see its impacts today, as shown by record-high temperatures and changing rainfall patterns. These changes are happening because human activities release large amounts of greenhouse gases into the atmosphere on a daily basis.
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Habitat loss contributes to climate change directly through the destruction of complex ecosystems (i.e. carbon sinks) which releases stored CO
2
, and indirectly through the loss of vegetation that would otherwise sequester CO
2
from the atmosphere.
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Some climatic shifts are predicted to be so rapid in coming decades that many species will be unable to adjust their ranges to keep up with environmental changes. Species with dispersal limitations, special habitat requirements, and important mutualistic relationships are at especially high risk of extinction.
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Mitigating the negative impacts of climate change will require an international multi-pronged approach that includes ecosystem protection and restoration, direct species management, and legislative action.
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Species are seldom exposed to only one threat; rather, different threats interact with climate change so that their combined impact is greater than their individual effects. A successful conservation strategy needs to deal with these threats collectively.


9.4: Themes
Learning Outcomes
- Change the theme on a presentation.
A theme is the overall visual look and scheme to a presentation in PowerPoint. Like many other features, it is quite easy to change the theme after a presentation has been created.
- Click on the Design tab.
- Select a new theme from the available options.
- Double-click on this theme.
The overall look and color scheme of your presentation will change. Compare the first screenshot to the one below.
You can also change the color scheme of a theme, before or after you apply it to a presentation. This is done from the Variants and Customize groups of the Design tab.
Below are just a few of the options available in the Variants menu.
Contributors and Attributions
CC licensed content, Original
- Themes. Authored by : Shelli Carter. Provided by : Lumen Learning. License : CC BY: Attribution


36.6: Absolute Value of Numbers
Lesson
Let's explore distances from zero more closely.
Exercise \(\PageIndex{1}\): Number Talk: Closer to Zero
For each pair of expressions, decide mentally which one has a value that is closer to 0.
\(\frac{9}{11}\) or \(\frac{15}{11}\)
\(\frac{1}{5}\) or \(\frac{1}{9}\)
\(1.25\) or \(\frac{5}{4}\)
\(0.01\) or \(0.001\)
Exercise \(\PageIndex{2}\): Jumping Flea
Move the bug to a starting point, choose a jump distance, and press the jump button. You may need to zoom in or out if your bug jumps off the screen.
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A bug is jumping around on a number line.
- If the bug starts at 1 and jumps 4 units to the right, where does it end up? How far away from 0 is this?
- If the bug starts at 1 and jumps 4 units to the left, where does it end up? How far away from 0 is this?
- If the bug starts at 0 and jumps 3 units away, where might it land?
- If the bug jumps 7 units and lands at 0, where could it have started?
- The absolute value of a number is the distance it is from 0. The bug is currently to the left of 0 and the absolute value of its location is 4. Where on the number line is it?
- If the bug is to the left of 0 and the absolute value of its location is 5, where on the number line is it?
- If the bug is to the right of 0 and the absolute value of its location is 2.5, where on the number line is it?
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We use the notation \(|-2|\) to say “the absolute value of -2,” which means “the distance of -2 from 0 on the number line.”
- What does \(|-7|\) mean and what is its value?
- What does \(|-1.8|\) mean and what is its value?
Exercise \(\PageIndex{3}\): Absolute Elevation and Temperature
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A part of the city of New Orleans is 6 feet below sea level. We can use “-6 feet” to describe its elevation, and “\(|-6|\) feet” to describe its vertical distance from sea level. In the context of elevation, what would each of the following numbers describe?
- \(25\) feet
- \(|25|\) feet
- \(-8\) feet
- \(|-8|\) feet
- The elevation of a city is different from sea level by 10 feet. Name the two elevations that the city could have.
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We write “\(-5^{\circ}\text{C}\)” to describe a temperature that is \(5\) degrees Celsius below freezing point and “\(6^{\circ}\text{C}\)” for a temperature that is \(5\) degrees above freezing. In this context, what do each of the following numbers describe?
- \(1^{\circ}\text{C}\)
- \(-4^{\circ}\text{C}\)
- \(|12|^{\circ}\text{C}\)
- \(|-7|^{\circ}\text{C}\)
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- Which temperature is colder: \(-6^{\circ}\text{C}\) or \(3^{\circ}\text{C}\)?
- Which temperature is closer to freezing temperature: \(-6^{\circ}\text{C}\) or \(3^{\circ}\text{C}\)?
- Which temperature has a smaller absolute value? Explain how you know.
- Are you ready for more?
Summary
We compare numbers by comparing their positions on the number line: the one farther to the right is greater; the one farther to the left is less.
Sometimes we wish to compare which one is closer to or farther from 0. For example, we may want to know how far away the temperature is from the freezing point of \(0^{\circ}\text{C}\), regardless of whether it is above or below freezing.
The absolute value of a number tells us its distance from 0.
The absolute value of -4 is 4, because -4 is 4 units to the left of 0. The absolute value of 4 is also 4, because 4 is 4 units to the right of 0. Opposites always have the same absolute value because they both have the same distance from 0.
The distance from 0 to itself is 0, so the absolute value of 0 is 0. Zero is the only number whose distance to 0 is 0. For all other absolute values, there are always two numbers—one positive and one negative—that have that distance from 0.
To say “the absolute value of 4,” we write: \(|4|\)
To say that “the absolute value of -8 is 8,” we write: \(|-8|=|8|\)
Glossary Entries
Definition: Absolute Value
The absolute value of a number is its distance from 0 on the number line.
The absolute value of -7 is 7, because it is 7 units away from 0. The absolute value of 5 is 5, because it is 5 units away from 0.
Definition: Negative Number
A negative number is a number that is less than zero. On a horizontal number line, negative numbers are usually shown to the left of 0.
Definition: Opposite
Two numbers are opposites if they are the same distance from 0 and on different sides of the number line.
For example, 4 is the opposite of -4, and -4 is the opposite of 4. They are both the same distance from 0. One is negative, and the other is positive.
Definition: Positive Number
A positive number is a number that is greater than zero. On a horizontal number line, positive numbers are usually shown to the right of 0.
Definition: Rational Number
A rational number is a fraction or the opposite of a fraction.
For example, 8 and -8 are rational numbers because they can be written as \(\frac{8}{1}\) and \(-\frac{8}{1}\).
Also, 0.75 and -0.75 are rational numbers because they can be written as \(\frac{75}{100}\) and \(-\frac{75}{100}\).
Definition: Sign
The sign of any number other than 0 is either positive or negative.
For example, the sign of 6 is positive. The sign of -6 is negative. Zero does not have a sign, because it is not positive or negative.
Practice
Exercise \(\PageIndex{4}\)
On the number line, plot and label all numbers with an absolute value of \(\frac{3}{2}\).
Exercise \(\PageIndex{5}\)
The temperature at dawn is \(6^{\circ}\text{C}\) away from 0. Select all the temperatures that are possible.
- \(-12^{\circ}\text{C}\)
- \(-6^{\circ}\text{C}\)
- \(0^{\circ}\text{C}\)
- \(6^{\circ}\text{C}\)
- \(12^{\circ}\text{C}\)
Exercise \(\PageIndex{6}\)
Put these numbers in order, from least to greatest.
\(|-2.7|\qquad 0\qquad 1.3\qquad |-1|\qquad 2\)
Exercise \(\PageIndex{7}\)
Lin’s family needs to travel 325 miles to reach her grandmother’s house.
- At 26 miles, what percentage of the trip’s distance have they completed?
- How far have they traveled when they have completed 72% of the trip’s distance?
- At 377 miles, what percentage of the trip’s distance have they completed?
(From Unit 5.4.3)
Exercise \(\PageIndex{8}\)
Elena donates some money to charity whenever she earns money as a babysitter. The table shows how much money, \(d\), she donates for different amounts of money, \(m\), that she earns.
| \(d\) | \(4.44\) | \(1.80\) | \(3.12\) | \(3.60\) | \(2.16\) |
|---|---|---|---|---|---|
| \(m\) | \(37\) | \(15\) | \(26\) | \(30\) | \(18\) |
- What percent of her income does Elena donate to charity? Explain or show your work.
- Which quantity, \(m\) or \(d\), would be the better choice for the dependent variable in an equation describing the relationship between \(m\) and \(d\)? Explain your reasoning.
- Use your choice from the second question to write an equation that relates \(m\) and \(d\).
(From Unit 6.4.1)
Exercise \(\PageIndex{9}\)
How many times larger is the first number in the pair than the second?
- \(3^{4}\) is _____ times larger than \(3^{3}\).
- \(5^{3}\) is _____ times larger than \(5^{2}\).
- \(7^{10}\) is _____ times larger than \(7^{8}\).
- \(17^{6}\) is _____ times larger than \(17^{4}\).
- \(5^{10}\) is _____ times larger than \(5^{4}\).
(From Unit 6.3.1)


4.1.7: Personality Theory in Real Life
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Synchronicity - Coincidence or an Experience with Mystical Spirituality?
Many people are deeply religious and many others consider themselves to be just as deeply spiritual, though not connected to any specific religion. As important as religion and spirituality are in the lives of many people, psychology has tended to avoid these topics, primarily because they do not lend themselves readily to scientific investigation. Jung certainly did not avoid these topics, and he studied a wide range of spiritual topics. For example, he wrote the foreword for Richard Wilhelm’s translation of the I Ching (Wilhelm, 1950), he wrote psychological commentary for a translation of The Tibetan Book of the Great Liberation (Evans-Wentz & Jung, 1954), he discussed the psychology of evil in Answer to Job (Jung, 1954), he wrote about Gnostic traditions at length (see Segal, 1992), and one of the volumes of his collected works is entitled Psychology and Religion: West and East (Jung, 1958). In addition to his varied spiritual interests, Jung became interested in psychological phenomena that could not be explained in scientific terms. Such phenomena do not necessarily require a spiritual explanation, but in the absence of any other way to explain them, they are often thought of in spiritual terms. One such topic is synchronicity .
Jung uses the term synchronicity to describe the “coincidence in time of two or more causally unrelated events which have the same or a similar meaning” (Jung & Pauli, 1955). In particular, it refers to the simultaneous occurrence of a particular psychic state with one or more external events that have a meaningful parallel to one’s current experience or state of mind. I would like to share with you two experiences of synchronicity from my own life. Having a Ph.D. in physiological psychology, and having spent a number of years conducting biomedical research, it seems rather strange to be sharing experiences that can be classified as extrasensory perception, or ESP. Jung also found it difficult to address this topic:
…If I have now conquered my hesitation and at last come to grips with my theme, it is chiefly because my experiences of the phenomenon of synchronicity have multiplied themselves over the decades…As a psychiatrist and psychotherapist I have often come up against the phenomena in question and could convince myself how much these inner experiences meant to my patients. In most cases they were things which people do not talk about for fear of exposing themselves to thoughtless ridicule. I was amazed to see how many people have had experiences of this kind and how carefully the secret was guarded. So my interest in this problem has a human as well as a scientific foundation. (pp. 5-6; Jung, in Jung & Pauli, 1955)
Synchronicity Experience #1: In February, 1992, our first son, Mark David Kelland, Jr., died at birth. Later that year, I was traveling across the country, taking a whole week to get to a neuroscience convention in California, and I decided to hike up Wheeler Peak, the highest point in New Mexico (13,161 feet). I arrived a little late in the day, but decided I had enough time to make the climb and get back down off the ridge before dark. I just made it, but still had a few miles to go on the jeep trail down to the parking lot. Along the way, I stopped and looked back up at Wheeler Peak. I turned off my flashlight, and in the dark I could just make out the outline of the mountain against the night sky. I prayed to God for a sign that our son was in Heaven. The instant I said “Amen,” a brilliant shooting star streaked across the sky and descended behind Wheeler Peak! I took it to be the sign I had asked for.
Synchronicity Experience #2: While growing up, we lived next door to Bill and Jackie O’Reilly, who co-owned the corner drugstore in the center of Foxborough, MA. When I was young I mowed their lawn in the summer and shoveled their driveway in the winter. When I was old enough to get a regular job, I asked Mr. O’Reilly for a letter of recommendation for a job at the local newspaper. He declined, saying he wanted me to work at their drugstore. But he didn’t say anything else, until Mrs. O’Reilly told him to give me a job. So, I worked at the drugstore from the age of 15 to 20 years old. I even began college at the same school they had attended: the Massachusetts College of Pharmacy. Although I changed schools and switched my major to psychology, I was always hopeful that the O’Reilly’s would be proud of me. Unfortunately, Bill O’Reilly died a week after I graduated from college. Jackie O’Reilly retired and sold their building, and the old corner drugstore in the center of town ceased to exist.
Eventually I moved away, pursued my career in psychology, got married and had children, and visits to Massachusetts became few and far between. One night, about 25 years after I had worked at the drugstore, I had a very vivid and moving dream. I was standing in the center of Foxborough, looking at the building where the drugstore had been. I was overwhelmed by a profound sense of sadness, sad that things must change with time and cannot remain the same, no matter how much we may long for the past. I awoke from that dream astonished by its sense of reality and its emotional impact. The next morning my mother called me, and told me that Jackie O’Reilly had died during the night! Was it merely a coincidence that I dreamt about O’Reilly’s Pharmacy and felt the sadness of watching time pass away, while Jackie O’Reilly was in reality passing away, or was it something more? There can be no scientific explanation. I searched my mind for anything that might have coincidentally caused me to think about the drugstore the day before, but nothing came to mind except for an alternative explanation, which was not at all scientific. Had Jackie O’Reilly’s spirit passed by and said goodbye, on her way to the great beyond?
In the quote cited above, Jung wrote that he was amazed by how many people have had experiences of synchronicity. The questions I would pose to you are quite simple. Have you ever experienced synchronicity? If you have not, do you consider it possible that such events occur as something more than simple (if improbable) coincidence?
Before dismissing synchronicity as non-scientific, keep in mind the circumstances that led Jung to this theory. In addition to personally knowing Wolfgang Pauli, Jung also knew Nils Bohr and Albert Einstein (both of whom, like Pauli, had won a Nobel Prize in physics). Although these men are considered among the greatest scientists of modern times, Einstein perhaps the greatest, consider some of their theories. For instance, Einstein proposed that time isn’t time, it’s relative, except for the speed of light, which alone is always constant. In recent years, experimental physicists have exceeded the speed of light, broken Heisenberg’s Uncertainty Principle (which, by definition, couldn’t be broken), and proposed that it might be possible to get something colder than absolute zero. How can we accept things that cannot be observed or proved as scientific, while rejecting something that Jung and many others have observed time and time again? Jung was impressed by the possibility of splitting atoms, and wondered if such a thing might be possible with the psyche. As physics suggested strange new possibilities, Jung held out the same hope for humanity (Progoff, 1973).
Regardless of whether the strangest of Jung’s theories are ever proven right or wrong, at the very least they provide an opportunity for interesting discussions! There also happens to be another well-known person in the history of psychology who has experienced synchronicity and who talked about many of her patients having had out-of-body and near-death experiences: Elisabeth Kubler-Ross. In her book On Children and Death (Kubler-Ross, 1983), Kubler-Ross describes even more serious concerns than Jung about discussing this topic, but as with Jung, she has also met many, many patients who have had these experiences:
…I have been called every possible name, from Antichrist to Satan himself; I have been labeled, reviled, and otherwise denounced…But it is impossible to ignore the thousands of stories that patients - children and adults alike - have shared with me. These illuminations cannot be explained in scientific language. Listening to these experiences and sharing many of them myself, it would seem hypocritical and dishonest to me not to mention them in my lectures and workshops. So I have shared all of what I have learned from my patients for the last two decades, and I intend to continue to do so. (pg. 106; Kubler-Ross, 1983)
discussion question \(\PageIndex{1}\)
Jung studied and wrote about topics as diverse as alchemy, astrology, flying saucers, ESP, the prophecies of Nostradamus, and synchronicity . Does this make it difficult for you to believe any of his theories? If you don’t believe anything about any of these topics, are you still able to find value in other theories proposed by Jung?