6.6: Surveillance
Surveillance may seem like an ominous term, but it is one of the most important roles of epidemiology. Disease surveillance is simply gathering data from different sources on the prevalence and incidence of different diseases and conditions. This allows health departments to get both a historical and current picture of the health status of the populations they serve. They can use surveillance to support decision making on funding particular research projects, allocating resources for hospitals or different community programs, or responding to outbreaks quickly. This data for metrics other than infectious diseases can also be used to determine if particular targets are being met - such as those set in the Healthy People initiatives.
How is surveillance conducted? Are health officers bugging phones and sitting in stakeouts like an old FBI movie? Disease surveillance originally began with boots-on-the-ground investigation, and in some places this is still the best method. However, new technologies and cutting-edge strategies help health departments keep tabs on the health of much larger populations.
There are two primary ways that health departments can conduct surveillance: active surveillance and passive surveillance. Active surveillance is a more traditional method of door-knocking and interviewing residents of a community, or perhaps conducting telephone interviews. This is how surveillance had to be done in the early years. John Snow famously visited houses in the Soho district of London. By interviewing residents in this area, he was able to record the number of cholera cases and deaths, and which houses were supplied by the two major water suppliers. This led him to the discovery that those houses fed water from one company (which collected its water from a particularly polluted area of the Thames river,) had significantly higher rates of the disease. Even though no one knew about the bacteria that causes cholera and how it is spread, there was still enough evidence collected by Snow to convince officials to remove the handle of the Broad Street pump - thereby removing the contaminated water source.
Active surveillance can be more accurate than passive surveillance in detecting each case that has developed over a period of time. It can also help with developing an understanding of community spread and potential sources of spread. However, active surveillance requiring door-knocking and interviews is rarely done in modern times due to the significant financial and personnel costs it requires. Instead, passive surveillance is relied on by health departments via reporting of certain diseases that doctors and laboratories come across in practice. For example, a doctor might see a patient complaining of symptoms which the doctor suspects are due to Hepatitis A. The doctor may ask for a stool sample and send that off to a laboratory to confirm results. The laboratory tests the sample and confirms that it is indeed a case of Hepatitis A and reports this case to the local health department, which in turn reports to the state health department and the CDC.
There are a few challenges with passive surveillance - one of them being the fact that not everyone goes to a doctor or clinic for symptoms that they have. Illnesses like influenza are often managed at home, so if a person feels like they have the flu, they won’t go to the office and no official case is recorded or reported. Health departments have found other ways to monitor potential increases in influenza, such as gathering data from Google searches for flu-like symptoms - which tend to go up consistently before doctor visits and hospitalizations increase for influenza. A spike in symptom searches may indicate that the flu is spreading in the community among folks who will probably not visit the doctor for themselves, but may spread it to those who will experience more severe illness and end up in the hospital. One way that active surveillance was used most recently during the COVID-19 pandemic was through taking samples of wastewater (sewage) and testing it for the presence of the virus. This allowed for non-invasive testing and tracking for COVID-19, particularly when home-tests became available and fewer people were reporting illness (CDC, 2023). Thus, more modern data collection may allow health departments to utilize active surveillance in more cost-effective ways.


6.4: Introduction to Le di las maletas a su hijo
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An indirect object is someone or something that is affected by the action of a transitive verb, but is not the direct object. If I give the keys to my friend, the keys are the direct object (what do I give? The keys). My friend, then, is the indirect object (to whom do I give the keys? To my friend). We can use pronouns here as well: I give him the keys. In this section, we’ll start to learn about using indirect object pronouns in Spanish. Don’t panic, though. You’ve already seen this in action. Did you like the verb gustar ? Me gusta esa palabra . That word (subject) is pleasing (verb) to me (indirect object pronoun!).


13.5: Rituals of Transition and Conformity
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- Last updated
- Save as PDF
- Jennifer Hasty, David G. Lewis, & Marjorie M. Snipes
- OpenStax
Learning Objectives
By the end of this section, you will be able to:
- Identify the characteristics of ritual.
- Describe how ritual reinforces social solidarity.
- Distinguish between the different types of ritual.
- Explain the social forces of liminality and communitas.
- Identify the stages of rites of passage.
The Varieties of Ritual Experience in Religion
Rituals , also called rites , are performative acts by which we carry out our religious beliefs, public and private. As sociologist Émile Durkheim noted, they follow a formal order or sequence, called a liturgical order; are performed in a place that is set apart and sacred during the time of the performance; and are inherently social. Unlike idiosyncratic behaviors that an individual may practice on their own, rituals are learned and shared. They foster social solidarity and identity within a community of believers (this a focus of Durkheim’s). Even when performing a religious ritual alone, such as walking a labyrinth during meditation, the ritual itself, because it is learned as part of a larger body of religious practices, connects the individual to the larger community.
Rituals tend to have a common structure even though ritual and ritual performance can be quite variable. In his work Ritual (1993), West African writer and ritual scholar Malidoma Somé ([1993] 1997, 68) outlines the major stages of most ritual acts:
- Opening: “setting the stage” by designating the purpose of the ritual and gathering the human participants
- Invocation: calling upon the spirit world to join the group
- Dialogue: establishing an open connection/communication between participants and the spirit world
- Repetition: fixed sequences, prayers, and/or acts that are required to legitimize the ritual’s purpose
- Closure: a blessing or other form of official dismissal for both human and spirit participants
Even when rituals are scripted and parts are carefully read and followed, individual participation and collaboration will subtly change a ritual each time it is enacted or performed. Rituals are never exactly duplicated, and not all rituals serve the same purpose. Some are primarily performed to affirm, strengthen, and maintain solidarity within the group; some are social markers of life transformations for individuals, families, or groups; and others address healing and the need for renewal. There are many categories of ritual: commemoration feasts or rituals (e.g., Christmas or Hannukah), which are usually held over a calendrical cycle, usually a year; divinatory rites to find the causes of illness, ask for healing, or prophesy about the future, which usually occur on an as-needed basis; and rites of rebellion, in which social rules and norms may be inverted to emphasize their value within a society. Incwala, a ritual found among the Swazi, a group in southern Africa, is a national holiday during which many social rules are suspended or inverted, allowing women to take on men’s public roles and men to take on women’s household duties in a public farce. Among the Swazi, this ritual is understood to illustrate the value of different gender roles in society as well as the importance of social norms in reducing social disorder. In the United States, Halloween is also a rite of rebellion, one in which children go out at night to beg for candy from neighbors. Among the most common broad types of religious ritual, though, are rites of intensification, rites of passage, and rites of affliction.
Rites of Intensification
Called by various names, such as rites of affirmation and calendrical rites, rites of intensification are performed to affirm, strengthen, and maintain bonds of solidarity. Most of the repetitive religious services that are offered through churches, synagogues, and mosques are rites of intensification. These rituals tend to have a rather stable and repetitive structure that allows practitioners to follow along easily. If you attend or participant in any kind of repetitive daily, weekly, or monthly religious ritual, it is likely a rite of intensification. These rites define and indoctrinate individuals so that they identify as a religious community, even though there may be other ritual acts accompanying it. It is not unusual in state religions for these rites to create unity among believers across cultures and nation-states. A good example is the daily practice of Islamic prayer, or salat . Salat involves praying in the direction of the holy city of Mecca at dawn, noon, midafternoon, sunset, and evening every day, regardless of where the believer is located or even what they are doing. Salat establishes a direct relationship between the believer and God and affirms one’s membership in a global community of Muslims.
Rites of Passage
First identified by anthropologist Arnold van Gennep in 1909, rites of passage mark social transformations in people’s lives and establish a change in social status within their communities. Associated most commonly with birth, puberty, marriage, and death, these rituals can be prolonged ceremonies during which the individual receives instruction and preparation for this change in their lives. Gennep noted that there are three stages in a rite of passage—separation, transition, and incorporation—and that during the transition stage, the individual must traverse a threshold ( limen in Latin) from their old social position or status to a new one.
- Separation (pre-limen). The separation phase is marked by detachment from one’s previous status. While the person or people involved may be physically separated and held in a special place, the separation normally occurs within daily life over a period of time and is always marked symbolically. Some examples of separation are the formal engagement of a couple with rings and a period of preparation for the upcoming marriage; the process of catechesis, or formal religious instruction, for young people planning to be baptized or confirmed in a Christian church; and wearing special clothing or colors while mourning the death of a family member.
- Transition (liminality). The transition phase is marked by an ambiguity of status and associated with instruction and teaching. This phase is usually restricted to the period in which an active and public ritual transformation is taking place. The person or people involved, already separated from their previous status and identity, are now transformed into a new status. This is the most active phase of a rite of passage. It is highly scripted and almost always involves teachers, guides, or mentors who usher the individuals through the proper steps to a new social status. Some examples of transition are the marriage ceremony itself, the actual baptism or confirmation ritual in the church, and the funeral service for a loved one.
- Incorporation (post-limen). The incorporation phase is marked by a formal public presentation of the person or people who have gone through the ritual. During incorporation, different symbols are used to express a new social status and identity. In this last stage, those going through the transformation begin to assume the rights, privileges, and responsibilities of their new social status. This might include changing their names, moving to a new location, or wearing different clothing. In many rites of passage, this is an extended period that can last from months to years.
Anthropologist Victor Turner (1969) discusses in detail the significance of liminality in rites of passage. During liminality, an individual is what Turner calls “betwixt and between” (95), without social status or standing, outside of the structure, and in transition from one social stage to another. It is a form of social death. Often, the individual will be dressed in uniform, unmarked clothing and follow behaviors associated with humility and anonymity in their culture. There is also an expectation of total obedience during the change of status, as the individual depends on ritual leaders (gatekeepers) to teach, coach, and mentor them through the passage. If there is a cohort of individuals participating in the rite of passage, such as an age grade going through puberty rites, the participants will share a strong sense of equality and social bonding among themselves, referred to as communitas . Through Turner’s research on the Ndembu of Zambia, anthropologists were better able to understand these common mechanisms of social change.
One example of a rite of passage among the Navajo of the southwestern United States is the Kinaaldá. The Kinaaldá is a traditional coming-of-age ceremony (a puberty rite) for young Navajo women that occurs shortly after a girl’s first menstrual cycle and involves her extended family and community (Carey 2010; Meza 2019). Typically, the ceremony lasts four days and occurs both inside a traditional Navajo house, called a hogan, and in the surrounding area, where the girl will periodically run to ensure that she has a strong and healthy life. At the beginning of the ceremony, as separation begins, the girl lies down and her family straightens her limbs and helps dress her and prepare her for the transition. During the days of seclusion, there are many different tasks as the girl is initiated into womanhood. On the third day, she and her mother will bake a corn cake called an alkaan , and then, led by a Navajo medicine man or woman, they will sing prayer songs all night until the sunrise. During the final stage of the Kinaaldá, in the morning of the fourth day, the mother washes her daughter’s hair and dries it with cornmeal (corn is a Navajo deity). The young woman will then take her last run toward the east, now followed by many young children, so that she might eventually become a loving mother whom her children will always follow. After the ceremony, she is reintroduced to her community as a woman and not a child; she is now considered a young adult.
Not all rites of passage are religious. There are also secular rites of passage, such as graduation or quinceañera, a celebratory birthday for 15-year-old girls in many Latin American communities. And sometimes the religious and the secular are intermingled, as in a marriage ceremony that is both civil and religious. Societies use both secular and religious rites of passage to mark changes in the life cycle of their members.
Rites of Affliction
Unlike rites of intensification and many rites of passage, rites of affliction are usually non-calendrical and unplanned. Normally classified as healing rituals or petitions for supernatural intervention, these rites seek remedy or compensation for the affliction. Whether directly through a shamanic journey or through the mediation of a religious leader, communities petition the spirits or deity for healing or a blessing. While illness and health in most Western societies are understood to be biomedical phenomena based on empirical evidence, in non-Western societies and in localized religious traditions across cultures, well-being is viewed as a relationship between body and soul and thus is believed to have a religious component.
While nonbelievers might refer to rites of affliction as superstition , a belief or practice that has no credible evidence for its efficacy, for believers, these religious rites allow them to plead for help and sometimes control the outcome of threatening life events. Rites of affliction, first described by vary greatly depending on the need. People may perform witchcraft and sorcery to determine the source of affliction, exorcism to remove the presence of an adverse spirit, or divination to identify the source of harm. Divination is a practice or test intended to gain understanding, guidance, or advice about an event or situation. There are literally hundreds of different methods of divination. Some examples include scapulimancy (burning the shoulder blade of a cow or antelope and reading a message in the burn pattern), tasseomancy (reading tea leaves at the bottom of a cup), oomancy (rubbing an egg over an area of illness or pain and then breaking it open to read a pattern), bibliomancy (randomly opening the Bible or another book and seeking a message in whatever passage is on that page), reading tarot cards, and checking astrological signs.
One common rite of affliction in the Christian tradition is the laying on of hands. This ritual appears in the Bible, used both as a means of conveying the Holy Spirit (Num. 27:15-23; Acts 8:14–19) and as an act of healing by Christ (Luke 4:40). Today, in many Pentecostal and Evangelical churches, congregations practice the ritual of laying on of hands. Believers place their hands on the shoulders or head of the congregant who seeks healing—whether from social, mental, or physical distress—in the belief that with fervent prayer and physical contact, the Holy Spirit can move from one individual to another to strengthen, heal, and anoint them with God’s grace. Sometimes the “helpers” stand face-to-face or bend over the individual seeking help. Sometimes believers walk behind the individual in need, who sits in a chair, and then lay hands on their shoulders and pray, either silently or aloud so that the afflicted individual can hear the prayer being offered. In these acts, the religious community pools its spiritual and social resources and encourages the afflicted member—a powerful antidote to illness no matter the faith tradition.
Although they are not exclusively associated with rites of affliction and are sometimes performed as acts of obedience, celebration, spiritual merit, enlightenment, or even penance, pilgrimage is often practiced as a rite to seek redress and healing. A sacred journey to a shrine or holy place, pilgrimage is practiced in many religions. Some of the most famous pilgrimages are the hajj, an Islamic pilgrimage to Saudi Arabia; the Christian pilgrimage to the Sanctuary of Our Lady of Lourdes, a site in France where Mary is believed to have appeared; and the Hindu pilgrimage to the River Ganges in India.
The hajj is one of the five pillars, or primary tenets, of Islam. For believers with the physical ability and financial means, completing the hajj to Mecca, Saudi Arabia, is essential to their faith. While the pilgrimage itself may occur at any time during the last three months of the Islamic calendar, the last five to six days of the 12th month are those on which the most significant rituals occur. Based on the lunar calendar, the hajj is a movable feast, meaning it is a celebration whose dates vary each year and will occur in different seasons over a cycle of years. Because the Islamic calendar is a lunar calendar, it does not coincide annually with the Gregorian calendar followed by most of the Western world today.
Historically, pilgrims arrived by walking, using the travel time and its accompanying struggles to focus on growing in their faith. Some individuals continue this traditional means of completing the hajj, but other devotees arrive by boat, bus, or plane, dedicating themselves to contemplation once they arrive. Mecca is an important symbolic place for Muslims because it was the birthplace of the Prophet Muhammad. During the hajj ritual, the pilgrims will perform many faith acts, including circling the Ka’aba, a building at the center of the mosque representing the most sacred place, seven times clockwise to open the ritual; praying; running between the nearby hills of Safa and Marwah; clipping their hair; going east of Mecca to confess their sins and seek atonement; gathering pebbles to perform a symbolic stoning of the devil; buying sacrifice vouchers so that an animal will be sacrificed on their behalf; and then again circling the Ka’aba seven times, this time counterclockwise, to close the hajj.


4.5: Module 21 Competency Test No. 4 Open Book
21
Module 21 Competency Test No. 4 Open Book
Wally Baumback
Learning Outcomes
When you have completed this module, you will be able to:
- Within a two hour time limit, complete a written exam and a lab exercise.
The Inventor book was written with competency based modules. What that means is that you have not completed each module until you have mastered it. The Competency Test module contains multiple choice questions and a comprehensive lab exercise to test your mastery of the set of modules that you completed. There are no answers or keys supplied in a Competency Test module since it is meant to be checked by your instructor. If there are any parts of this module that you have trouble completing, you should go back and reread the module or modules containing the information that you are having trouble with. If necessary, redo as many lab exercises required until you fully understand the material.
If you are Completing this book:
- Without the aid of an instructor, complete the written test and the lab exercise.
- In a classroom with an instructor, the instructor will give instructions on what to do after you have completed this module.
Multiple Choice Questions
Select the BEST answer.
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When you are selecting objects with a window, which window selects all the objects that are totally inside it and the ones that it crosses?
- Square Window
- Crossing Window
- Extruded Window
- Rectangular Window
- Polygon Window
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What is the name for two or more objects that are connected at their endpoints and then treated as one object in the OFFSET command?
- Loop
- Continuous
- Area
- Polyloop
- Window
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What are the basic sketching planes (XY, XZ, YZ), the three axis (X, Y, Z) and the Center Point called?
- Work Planes
- Work Points
- Work Features
- Work Sketches
- Work Axis
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What is the maximum number of sides that the POLYGON command can draw a regular polygon?
- 20
- 100
- 120
- 180
- 256
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When the graphic cursor appears as a ruler, what units are you measuring in? Select the BEST answer.
- English Units
- Document Units
- System Units
- Metric Units
- Actual Units
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What command is used to extend the length of an existing line or an arc?
- LENGTHEN
- EXTEND
- LINE
- LENGTH
- STRETCH
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What does an aligned dimension measure?
- The delta X or delta Y distance between two points.
- The diameter of circle or radius of an arc.
- The true length of a line or the true distance between two points.
- The horizontal or vertical distance between two points.
- The angle between two lines or the angle between the imaginary lines between three points.
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What best describes the threads created using the THREAD command?
- Graphical representations of the actual thread.
- A texture
- The actual thread.
- They are enlarged to look better.
- Center
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What is a parametric construction plane inserted on the model or in model space called?
- A Work Plane
- A Work Point
- A Work Feature
- A Work Sketch
- A Work Model
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What is an angular dimension measuring?
- The delta X or delta Y distance between two points.
- The diameter of circle or radius of an arc.
- The true length of a line or the true distance between two points.
- The horizontal or vertical distance between two points.
- The angle between two lines or the angle between the imaginary lines between three points.
Lab Exercise 21-1
Time allowed: 2 hours.
| Part Name | Project | Units | Template | Color | Material |
| Inventor Lab 21-1 | Inventor Course | Millimeters | Metric-Modules Part (mm).ipt | Machined-Aluminum | Aluminum-6061 |
Step 1
Project the Center Point onto the Base plane.
Step 2
Note the location of X0Y0Z0. Draw the necessary sketches and extrude them to produce the solid model shown below. Apply all of the necessary geometrical and dimensional constraints to maintain the objects shape and size. All sketches must be fully constrained. (Figure Step 2A and 2B)
Step 3
Create the fillets and chamfers after the model is totally constructed.
Step 4
Apply the colour shown above. (Figure Step 4)
Step 5
Move the End of Part Icon up above the fillets as shown in the figure. Suppress all of the threaded features. (Figure Step 5)
Step 6
Find the following to a precision of 6 decimal points: (Figure Step 6)
A The XYZ coordinates of corner D.
____________________________
B The length of the edge from corner A to corner B.
____________________________
C The distance from corner A to corner C.
____________________________
D The distance from corner C to corner D.
____________________________
E The angle between the edges B to C and B
____________________________
Step 8
The area of the shaded area of Figure Step 8. Do NOT include the area of features on the plane.
____________________________
Step 9
The perimeter of the shaded plane in Figure Step 9.
____________________________
Step 10
The area of the shaded area of Figure Step 10. The area should include the complete surface without any features.
____________________________
Step 11
Using the three figures below, change the colors of the faces shown to: Aluminum – Polished .
- If you are an online student doing this course by correspondence, send an email to your instructor with the answers from the measurement questions in this module. For example:
| 7A | The XYZ coordinates of corner D is ___________ . |
| 7B | The length of the edge from corner A to corner B is ___________ . |
| 7C | The distance from corner A to corner C is ___________ . |
| 7D | The distance from corner C to corner D is ___________ . |
| 7E | The angle between the edges B to C and B to A is ___________ . |
| 8 | The area of the shaded area of Figure Step 8 is ___________ . |
| 9 | The perimeter of the shaded plane in Figure Step 9 is ___________ . |
| 10 | The area of the shaded area of Figure Step 10 is ___________ . |
| 12A | The mass of the solid model in grams is ___________ . |
| 12B | The mass of the solid model in pounds is ___________ . |
The answers in the email can be given as follows:
| 7A | ___________ . |
| 7B | ___________ . |
| 7C | ___________ . |
| 7D | ___________ . |
| 7E | ___________ . |
| 8 | ___________ . |
| 9 | ___________ . |
| 10 | ___________ . |
| 12A | ___________ . |
| 12B | ___________ . |


5: Thesis Statements, Topic Sentences and the First Draft Last updated Save as PDF Page ID 34201 Athena Kashyap & Erika Dyquisto City College of San Francisco via ASCCC Open Educational Resources Initiative 5.1: Developing a Strong, Clear Thesis Statement This page covers a number of strategies to develop, refine, and finalize a strong college-level thesis. 5.2: Topic Sentences This page identifies the components of a good topic sentence, discusses their placement, and provides practice on developing strong topic sentences. 5.3: Writing the Essay Draft This page presents the basics about developing an essay with an extended example. 5.4: Writing Introductory and Concluding Paragraphs This page explains the basic essay structure with strategies for developing the different parts of the essay. 5.5: Key Takeaways


1.3: The Case of Phineas Gage- Connecting Brain to Behavior
- Discuss the Case of Phineas Gage and its contribution to biological psychology.
Overview
While experiments are necessary to establish cause and effect relationships, in-depth studies of unique individuals or groups of people who share an experience can be used to inform our understanding of things that we can not study experimentally. Surgical errors, extreme mistreatment, and tragic accidents are impactful events that can alter individuals significantly, providing unique opportunities to study the effects of experiences which can not be ethically studied experimentally. There have been a number of these case studies which have revealed the role of different parts of the brain on our thinking and behavior. One such case is Phineas Gage. Gage lived 12 years after a rod pierced his skull, damaging his left frontal lobe. Researchers were able to gather information about his functioning before and observe his cognitive ability and personality after the accident. His case enabled the field to understand the role of frontal lobe in personality and mental processes.
The Tale of Phineas Gage
The case of Phineas Gage is worthy of expanded coverage as his tragic accident establishes a clear connection between the brain and who we are. Gage, a 25-year-old man, was employed in railroad construction at the time of the accident. As the company's most capable employee, with a well-balanced mind and a sense of leadership, he was directing a rock-splitting workgroup while preparing the bed of the Rutland and Burlington Railroad south of Cavendish, Vermont, USA. At 4:30 PM on September 13, 1848, he and his group were blasting a rock, and Gage was assigned to put gunpowder in a deep hole inside it.
The moment he pressed the gunpowder into the hole with a bar, the friction caused sparks, and the powder exploded. The resulting blast projected the meter-long bar, which was 1.25 inches in diameter and weighed about 13.2 pounds, through his skull at high speed. The bar entered his left cheek, destroyed his eye, passed through the left front of his brain, and left his head at the top of the skull on the right side. Gage was thrown on his back and had some brief convulsions, but he woke up and spoke in a few minutes, walked with a little help, and sat in an ox cart for the 0.7-mile trip to where he was living.
About 30 minutes after the accident, a doctor arrived to provide medical care. Gage had lost a lot of blood, and the next days that followed were quite difficult. The wound became infected, and Phineas was anemic and remained semi-comatose for more than two weeks. He also developed a fungal infection in the exposed brain that needed to be surgically removed. His condition slowly improved after doses of calomel and beaver oil. By mid-November he was already walking around the city.
The Consequences
For three weeks after the accident, the wound was treated by doctors. During this time, he was assisted by Dr. John Harlow, who covered the head wound and then reported the case in the Boston Medical Surgery Journal. In November 1849, invited by the professor of surgery at Harvard Medical School, Henry Jacob Bigelow, Harlow took Gage to Boston and introduced him to a meeting of the Boston Society for Medical Improvement .
In his reports, Harlow described that the physical injury profoundly altered Gage's personality. Although his memory, cognition, and strength had not been altered, his once gentle personality slowly degraded. He became a man of bad and rude ways, disrespectful to colleagues, and unable to accept advice. His plans for the future were abandoned, and he acted without thinking about the consequences. And here was the main point of this curious story: Gage became irritable, irreverent, rude and profane, aspects that were not part of his way of being. His mind had changed radically. His transformation was so great that everyone said that “Gage is no longer himself.”
As a result of this personality change, he was fired and could no longer hold a steady job. He became a circus attraction and even tried life in Chile, later returning to the United States. However, there is something still little known about Gage: his personality changes lasted for about four years, slowly reverting later. As a proof of this, he worked as a long-haul driver in Chile, a job that required considerable planning and focus skills. He died on May 21, 1861, 12 years after the accident, from an epileptic seizure that was almost certainly related to his brain injury.
After his body was removed from its grave, Gage's mother donated his skull to Dr. Harlow who in turn donated it to Harvard University.
The Legacy
Gage's case is considered to be one of the first examples of scientific evidence indicating that damage to the frontal lobes may alter personality, emotions, and social interaction. Prior to this case, the frontal lobes were considered silent structures, without function and unrelated to human behavior. Scottish neurologist, David Ferrier, was motivated by this fact to investigate the role of frontal lobes in brain function. Ferrier removed the frontal lobes in monkeys and noted that there were no major physiological changes, but the character and behavior of the animals were altered. In other words, he confirmed the role of the frontal lobes that was suggested by Gage's accident in an experiment with a non-human animal.
Knowledge that the frontal lobe was involved with emotions continued to be studied. The surgeon Burkhardt in 1894 performed a series of surgeries in which he selectively destroyed the frontal lobes of several patients in whom he sought to control psychotic symptoms, being the modern prototype of what was later known through Antonio Egas Moniz as psychosurgery. Today, it is well understood that the prefrontal cortex of the brain controls the organization of behavior, including emotions and inhibitions.
Folkloric as it may be, but nonetheless remarkable, the contribution of Phineas Gage's case should not be overlooked, as it provided scientists the baseline for the promotion of studies in neuropsychiatry, and a source of inspiration for world medicine. In 2012, a team of neuroscientists used computer tomography of Gage's skull with typical brain MRI scans to simulate how extensive Gage's brain damage was. They confirmed that most of the damaged area was the left frontal lobe. However, surrounding areas and their neural network were also extensively severed. And it is not just the researchers who keep coming back to Gage. Medical and psychology students still learn about Gage from their history lessons. Neurosurgeons and neurologists still sometimes use Gage as a reference when evaluating certain cases. The final chapter of his life also offers us a thought-provoking discovery about cases of massive brain damage, indicating that rehabilitation may be possible.
Summary
Phineas Gage made a huge contribution to our understanding of the frontal lobe damage and its subsequent change in personality. Furthermore, his case expanded knowledge in neurology in several areas, including the study of brain topography in behavioral disorders, the development of psychosurgery, and finally the study of brain rehabilitation. Also, Gage's case had a tremendous influence on early neuropsychiatry. The specific changes observed in his behavior pointed to theories about the localization of brain function and correlated with cognitive and behavioral sequelae, thereby acquainting us with the role of the frontal cortex in higher-order actions such as reasoning, behavior and social cognition. In those years, while neuropsychiatry was in its infancy, Gage's extraordinary story served as one of the first pillars of evidence that the frontal lobe is involved in personality, which helped solidify his remarkable legacy in world medical history.
Attributions
Adapted from Phineas Gage’s Great Legacy by Vieira Teles Filho, Ricardo. Licensed CC BY 4.0 .


3: Behavior Near Trajectories and Invariant Sets - Stability
Consider the general nonautonomous vector field in n dimensions:
\[\dot{x} = f(x, t), x \in \mathbb{R}^n, \label{3.1}\]
and let \(\bar{x}(t, t_{0}, x_{0})\) be a solution of this vector field.
Many questions in ODEs concern understanding the behavior of neighboring solutions near a given, chosen solution. We will develop the general framework for considering such questions by transforming Equation \ref{3.1} to a form that allows us to explicitly consider these issues.
We consider the following (time dependent) transformation of variables:
\[x = y+\bar{x}(t, t_{0}, x_{0}). \label{3.2}\]
We wish to express Equation \ref{3.1} in terms of the y variables. It is important to understand what this will mean in terms of Equation \ref{3.2}. For y small it means that x is near the solution of interest, \(\bar{x}(t, t_{0}, x_{0})\). In other words, expressing the vector field in terms of y will provide us with an explicit form of the vector field for studying the behavior near \(\bar{x}(t, t_{0}, x_{0})\). Towards this end, we begin by transforming Equation \ref{3.1} using Equation \ref{3.2} as follows:
\[\dot{x} = \dot{y}+ \dot{\bar{x}} = f(x, t) = f(y+\bar{x}, t), \label{3.3}\]
or
\(\dot{y} = f(y+\bar{x}, t)-\dot{\bar{x}}\),
\[= f(y+\bar{x}, t)-f(\bar{x}, t) \equiv g(y, t), g(0, t) = 0. \label{3.4}\]
Hence, we have shown that solutions of Equation \ref{3.1} near \(\bar{x}(t, t_{0}, x_{0})\) are equivalent to solutions of Equation \ref{3.4} near y = 0.
The first question we want to ask related to the behavior near \(\bar{x}(t, t_{0}, x_{0})\) is whether or not this solution is stable? However, first we need to mathematically define what is meant by this term ''stable''. Now we should know that, without loss of generality, we can discuss this question in terms of the zero solution of Equation \ref{3.4}.
We begin by defining the notion of ''Lyapunov stability'' (or just "stability").
Definition 13 (LYAPUNOV STABILITY)
y = 0 is said to be Lyapunov stable at \(t_{0}\) if given \(\epsilon > 0\) there exists a \(\delta = \delta (t_{0}, \epsilon)\) such that
\[|y(t_{0})|<\delta \Rightarrow |y(t)|<\epsilon, \forall t>t_{0} \label{3.5}\]
If a solution is not Lyapunov stable, then it is said to be unstable.
Definition 14 (UNSTABLE)
If y = 0 is not Lyapunov stable, then it is said to be unstable.
Then we have the notion of asymptotic stability.
Definition 15 (ASYMPTOTIC STABILITY)
y = 0 is said to be asymptotically stable at \(t_{0}\) if:
- it is Lyapunov stable at \(t_{0}\),
-
there exists \(\delta = \delta(t_{0}) > 0\) such that:
\[|y(t_{0})| < \delta \Rightarrow lim_{t \rightarrow \infty} |y(t)| = 0 \label{3.6}\]
We have several comments about these Definitions.
- Roughly speaking, a Lyapunov stable solution means that if you start close to that solution, you stay close–forever. Asymptotic stability not only means that you start close and stay close forever, but that you actually get "closer and closer" to the solution.
- Stability is an infinite time concept.
- If the ODE is autonomous, then the quantity \(\delta = \delta(t_{0}, \epsilon)\) can be chosen to be independent of \(t_{0}\).
- The Definitions of stability do not tell us how to prove that a solution is stable (or unstable). We will learn two techniques for analyzing this question–linearization and Lyapunov’s (second) method.
- Why is Lyapunov stability included in the Definition of asymptotic stability? Because it is possible to construct examples where nearby solutions do get closer and closer to the given solution as \(t \rightarrow \infty\), but in the process there are intermediate intervals of time where nearby solutions make "large excursions" away from the given solution.
"Stability" is a notion that applies to a "neighborhood" of a trajectory. At this point we want to formalize various notions related to distance and neighborhoods in phase space. For simplicity in expressing these ideas we will take as our phase space Rn. Points in this phase space are denoted \(x \in \mathbb{R}^n\), \(x \equiv (x_{1}, ..., x_{n})\). The norm, or length, of x, denoted |x| is defined as:
\[|x| = \sqrt{x_{1}^{2}+x_{2}^{2}+ \cdots + x_{n}^{2}} = \sqrt{\sum_{i=1}^{n} x_{i}^{2}}.\]
The distance between two points in \(x, y \in \mathbb{R}^n\) is defined as:
\[ d(x,y) \equiv |x-y| = \sqrt{(x_{1}-y_{1})^2 + \cdots + (x_{n}-y_{n})^2} \]
\[= \sqrt{\sum_{i=1}^{n} \sqrt{(x_{i}-y_{i})^2}. \label{3.7}\]
Distance between points in \(\mathbb{R}^n\) should be somewhat familiar, but now we introduce a new concept, the distance between a point and a set. Consider a set M, \(M \subset \mathbb{R}^n\), let \(p \in \mathbb{R}^n\). Then the distance from p to M is defined as follows:
\[dist(p, M) \equiv inf_{x \in M}|p-x|. \label{3.8}\]
We remark that it follows from the Definition that if \(p \in M\), then dist(p, M) = 0.
We have previously defined the notion of an invariant set. Roughly speaking, invariant sets are comprised of trajectories. We now have the background to discuss the notion of . Recall, that the notion of invariant set was only developed for autonomous vector fields. So we consider an autonomous vector field:
\[\dot{x} = f(x), x \in \mathbb{R}^n, \label{3.9}\]
and denote the flow generated by this vector field by \(\phi_{t}(\cdot)\). Let M be a closed invariant set (in many applications we may also require M to be bounded) and let U M denoted a neighborhood of M.
The definition of Lyapunov stability of an invariant set is as follows.
DEFINITION 16 (LYAPUNOV STABILITY OF M)
M is said to be Lyapunov stable if for any neighborhood \(U \supset M, x \in U \Rightarrow \phi_{t}(x) \in U, \forall t > 0\).
Similarly, we have the following definition of asymptotic stability of an invariant set.
DEFINITION 17 (ASYMPTOTIC STABILITY OF M)
M is said to be asymptotically stable if
- it is Lyapunov stable,
- there exists a neighborhood \(U \supset M\) such that \(\forall x \in U, dist((\phi_{t}x), M) \rightarrow 0\) as \(t \rightarrow \infty\).
In the dynamical systems approach to ordinary differential equations some alternative terminology is typically used.
DEFINITION 18 (ATTRACTING SET)
If M is asymptotically stable it is said to be an attracting set.
The significance of attracting sets is that they are the "observable" regions in phase space since they are regions to which trajectories evolve in time. The set of points that evolve towards a specific attracting set is referred to as the basin of attraction for that invariant set.
DEFINITION 19 (BASIN OF ATTRACTION)
Let \(B \subset \mathbb{R}^n\) denote the set of all points, \(x \in B \subset \mathbb{R}^n\) such that
\(dist(\phi_{t}(x), M) \rightarrow 0\) as \(t \rightarrow \infty\)
Then call B is called the basin of attraction of M.
We now consider an example that allows us to explicitly explore these ideas.
Example \(\PageIndex{9}\)
Consider the following autonomous vector field on the plane:
\(\dot{x} = x\),
\[\dot{y} = y^{2}(1-y^2) \equiv f(y), (x, y) \in \mathbb{R}^2. \label{3.10}\]
First, it is useful to note that the x and y components of Equation \ref{3.10} are independent. Consequently, this may seem like a trivial example. However, we will see that such examples provide a great deal of insight, especially since they allow for simple computations of many of the mathematical ideas.
In Fig. 3.1 we illustrate the flow of the x and y components of Equation \ref{3.10} separately.
The two dimensional vector field Equation \ref{3.10} has equilibrium points at: (x, y) = (0, 0), (0, 1), \((0, -1)\).
In this example it is easy to identify three invariant horizontal lines (examples of invariant sets). Since y = 0 implies that \(\dot{y} = 0\), this implies that the x axis is invariant. Since y = 1 implies that \(\dot{y} = 0\), this implies that the line y = 1 is invariant. Since \(y = -1\) implies that \(\dot{y} = 0\), which implies that the line \(y = -1\) is invariant. This is illustrated in Fig. 3.2. Below we provide some additional invariant sets for (3.10). It is instructive to understand why they are invariant, and whether or not there are other invariant sets.


7.6: Direct Democracy
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Learning Objectives
By the end of this section, you will be able to:
- Identify the different forms of and reasons for direct democracy
- Summarize the steps needed to place initiatives on a ballot
- Explain why some policies are made by elected representatives and others by voters
The majority of elections in the United States are held to facilitate indirect democracy. Elections allow the people to pick representatives to serve in government and make decisions on the citizens’ behalf. Representatives pass laws, implement taxes, and carry out decisions. Although direct democracy had been used in some of the colonies, the framers of the Constitution granted voters no legislative or executive powers, because they feared the masses would make poor decisions and be susceptible to whims. During the Progressive Era, however, governments began granting citizens more direct political power. States that formed and joined the United States after the Civil War often assigned their citizens some methods of directly implementing laws or removing corrupt politicians. Citizens now use these powers at the ballot to change laws and direct public policy in their states.
Direct Democracy Defined
Direct democracy occurs when policy questions go directly to the voters for a decision. These decisions include funding, budgets, candidate removal, candidate approval, policy changes, and constitutional amendments. Not all states allow direct democracy, nor does the United States government.
Direct democracy takes many forms. It may occur locally or statewide. Local direct democracy allows citizens to propose and pass laws that affect local towns or counties. Towns in Massachusetts, for example, may choose to use town meetings, which is a meeting comprised of the town’s eligible voters, to make decisions on budgets, salaries, and local laws. 122
Link to Learning
To learn more about what type of direct democracy is practiced in your state, visit the University of Southern California’s Initiative & Referendum Institute. This site also allows you to look up initiatives and measures that have appeared on state ballots.
Statewide direct democracy allows citizens to propose and pass laws that affect state constitutions, state budgets, and more. Most states in the western half of the country allow citizens all forms of direct democracy, while most states on the eastern and southern regions allow few or none of these forms (Figure 7.20). States that joined the United States after the Civil War are more likely to have direct democracy, possibly due to the influence of Progressives during the late 1800s and early 1900s. Progressives believed citizens should be more active in government and democracy, a hallmark of direct democracy.
There are three forms of direct democracy used in the United States. A referendum asks citizens to confirm or repeal a decision made by the government. A legislative referendum occurs when a legislature passes a law or a series of constitutional amendments and presents them to the voters to ratify with a yes or no vote. A judicial appointment to a state supreme court may require voters to confirm whether the judge should remain on the bench. Popular referendums occur when citizens petition to place a referendum on a ballot to repeal legislation enacted by their state government. This form of direct democracy gives citizens a limited amount of power, but it does not allow them to overhaul policy or circumvent the government.
The most common form of direct democracy is the initiative, or proposition. An initiative is normally a law or constitutional amendment proposed and passed by the citizens of a state. Initiatives completely bypass the legislatures and governor, but they are subject to review by the state courts if they are not consistent with the state or national constitution. The process to pass an initiative is not easy and varies from state to state. Most states require that a petitioner or the organizers supporting an initiative file paperwork with the state and include the proposed text of the initiative. This allows the state or local office to determine whether the measure is legal, as well as estimate the cost of implementing it. This approval may come at the beginning of the process or after organizers have collected signatures. The initiative may be reviewed by the state attorney general, as in Oregon’s procedures, or by another state official or office. In Utah, the lieutenant governor reviews measures to ensure they are constitutional.
Next, organizers gather registered voters’ signatures on a petition. The number of signatures required is often a percentage of the number of votes from a past election. In California, for example, the required numbers are 5 percent (law) and 8 percent (amendment) of the votes in the last gubernatorial election. This means through 2022, it will take 623,212 signatures to place a law on the ballot and 997,139 to place a constitutional amendment on the ballot. 123
Once the petition has enough signatures from registered voters, it is approved by a state agency or the secretary of state for placement on the ballot. Signatures are verified by the state or a county elections office to ensure the signatures are valid. If the petition is approved, the initiative is then placed on the next ballot, and the organization campaigns to voters.
While the process is relatively clear, each step can take a lot of time and effort. First, most states place a time limit on the signature collection period. Organizations may have only 150 days to collect signatures, as in California, or as long as two years, as in Arizona. For larger states, the time limit may pose a dilemma if the organization is trying to collect more than 500,000 signatures from registered voters. Second, the state may limit who may circulate the petition and collect signatures. Some states, like Colorado, restrict what a signature collector may earn, while Oregon bans payments to signature-collecting groups. And the minimum number of signatures required affects the number of ballot measures. California had twelve ballot measures on the 2020 general election ballot, because the state requires fewer signatures to get a constitutional amendment or initiative on the ballot than in a state like Oklahoma, where the number of required signatures is higher. In Oklahoma, the required numbers are almost double those of California—8 percent (law) and 15 percent (amendment) of the votes in the last gubernatorial election. California voters may also have an equally high number of local ballot initiatives. For example, a San Francisco voter in the 2016 election had a total of forty-two ballot measures to consider, seventeen at the state level and twenty-five at the city and county level.
Another consideration is that, as we’ve seen, voters in primaries are more ideological and more likely to research the issues. Measures that are complex or require a lot of research, such as a lend-lease bond or changes in the state’s eminent-domain language, may do better on a primary ballot. Measures that deal with social policy, such as laws preventing animal cruelty, may do better on a general election ballot, when more of the general population comes out to vote. Proponents for the amendments or laws will take this into consideration as they plan.
Finally, the recall is one of the more unusual forms of direct democracy; it allows voters to decide whether to remove a government official from office. All states have ways to remove officials, but removal by voters is less common. The recall of California Governor Gray Davis in 2003 and his replacement by Arnold Schwarzenegger is perhaps one of the more famous such recalls. The 2012 attempt by voters in Wisconsin to recall Governor Scott Walker shows how contentious and expensive a recall can be. Walker spent over $60 million in the election to retain his seat. 124
Policymaking Through Direct Democracy
Politicians are often unwilling to wade into highly political waters if they fear it will harm their chances for reelection. When a legislature refuses to act or change current policy, initiatives allow citizens to take part in the policy process and end the impasse. In Colorado, Amendment 64 allowed the recreational use of marijuana by adults, despite concerns that state law would then conflict with national law. Colorado and Washington’s legalization of recreational marijuana use started a trend, leading to more states adopting similar laws.
Finding a Middle Ground
Too Much Democracy?
How much direct democracy is too much? When citizens want one policy direction and government prefers another, who should prevail?
Consider recent laws and decisions about marijuana. California was the first state to allow the use of medical marijuana, after the passage of Proposition 215 in 1996. Just a few years later, however, in Gonzales v. Raich (2005), the Supreme Court ruled that the U.S. government had the authority to criminalize the use of marijuana. In 2009, Attorney General Eric Holder said the federal government would not seek to prosecute patients using marijuana medically, citing limited resources and other priorities. Perhaps emboldened by the national government’s stance, Colorado voters approved recreational marijuana use in 2012. Since then, other states have followed. Forty-two states and the District of Columbia now have laws in place that legalize the use of marijuana to varying degrees. In a number of these cases, the decision was made by voters through initiatives and direct democracy (Figure 7.21).
So where is the problem? First, while citizens of these states believe smoking or consuming marijuana should be legal, the U.S. government does not. The Controlled Substances Act (CSA), passed by Congress in 1970, declares marijuana a dangerous drug and makes its sale a prosecutable act. And despite Holder’s statement, a 2013 memo by James Cole, the deputy attorney general, reminded states that marijuana use is still illegal. 125 But the federal government cannot enforce the CSA on its own; it relies on the states’ help. And while Congress has decided not to prosecute patients using marijuana for medical reasons, it has not waived the Justice Department’s right to prosecute recreational use. 126
Direct democracy has placed the states and its citizens in an interesting position. States have a legal obligation to enforce state laws and the state constitution, yet they also must follow the laws of the United States. Citizens who use marijuana legally in their state are not using it legally in their country. This leads many to question whether direct democracy gives citizens too much power.
Is it a good idea to give citizens the power to pass laws? Or should this power be subjected to checks and balances, as legislative bills are? Why or why not?
Direct democracy has drawbacks, however. One is that it requires more of voters. Instead of voting based on party, the voter is expected to read and become informed to make smart decisions. Initiatives can fundamentally change a constitution or raise taxes. Recalls remove politicians from office. These are not small decisions. Most citizens, however, do not have the time to perform a lot of research before voting. Given the high number of measures on some ballots, this may explain why many citizens simply skip ballot measures they do not understand. Direct democracy ballot items regularly earn fewer votes than the choice of a governor or president.
When citizens rely on television ads, initiative titles, or advice from others in determining how to vote, they can become confused and make the wrong decisions. In 2008, Californians voted on Proposition 8, titled “Eliminates Rights of Same-Sex Couples to Marry.” A yes vote meant a voter wanted to define marriage as only between a woman and man. Even though the information was clear and the law was one of the shortest in memory, many voters were confused. Some thought of the amendment as the same-sex marriage amendment. In short, some people voted for the initiative because they thought they were voting for same-sex marriage. Others voted against it because they were against same-sex marriage. 127
Direct democracy also opens the door to special interests funding personal projects. Any group can create an organization to spearhead an initiative or referendum. And because the cost of collecting signatures can be high in many states, signature collection may be backed by interest groups or wealthy individuals wishing to use the initiative to pass pet projects. The 2003 recall of California governor Gray Davis faced difficulties during the signature collection phase, but $2 million in donations by Representative Darrell Issa (R-CA) helped the organization attain nearly one million signatures. 128 Many commentators argued that this example showed direct democracy is not always a process by the people, but rather a process used by the wealthy and business.


5.1: Friction
Learning Objectives
By the end of this section, you will be able to:
- Discuss the general characteristics of friction.
- Describe the various types of friction.
- Calculate the magnitude of static and kinetic friction.
Friction is a force that is around us all the time that opposes relative motion between systems in contact but also allows us to move (which you have discovered if you have ever tried to walk on ice). While a common force, the behavior of friction is actually very complicated and is still not completely understood. We have to rely heavily on observations for whatever understandings we can gain. However, we can still deal with its more elementary general characteristics and understand the circumstances in which it behaves.
Friction
Friction is a force that opposes relative motion between systems in contact.
One of the simpler characteristics of friction is that it is parallel to the contact surface between systems and always in a direction that opposes motion or attempted motion of the systems relative to each other. If two systems are in contact and moving relative to one another, then the friction between them is called kinetic friction . For example, friction slows a hockey puck sliding on ice. But when objects are stationary , static friction can act between them; the static friction is usually greater than the kinetic friction between the objects.
Kinetic Friction
If two systems are in contact and moving relative to one another, then the friction between them is called kinetic friction.
Imagine, for example, trying to slide a heavy crate across a concrete floor—you may push harder and harder on the crate and not move it at all. This means that the static friction responds to what you do—it increases to be equal to and in the opposite direction of your push. But if you finally push hard enough, the crate seems to slip suddenly and starts to move. Once in motion it is easier to keep it in motion than it was to get it started, indicating that the kinetic friction force is less than the static friction force. If you add mass to the crate, say by placing a box on top of it, you need to push even harder to get it started and also to keep it moving. Furthermore, if you oiled the concrete you would find it to be easier to get the crate started and keep it going (as you might expect).
Figure is a crude pictorial representation of how friction occurs at the interface between two objects. Close-up inspection of these surfaces shows them to be rough. So when you push to get an object moving (in this case, a crate), you must raise the object until it can skip along with just the tips of the surface hitting, break off the points, or do both. A considerable force can be resisted by friction with no apparent motion. The harder the surfaces are pushed together (such as if another box is placed on the crate), the more force is nearly independent of speed.
\(\displaystyle \PageIndex{1}\):
Frictional forces, such as \(\displaystyle f\), always oppose motion or attempted motion between objects in contact. Friction arises in part because of the roughness of the surfaces in contact, as seen in the expanded view. In order for the object to move, it must rise to where the peaks can skip along the bottom surface. Thus a force is required just to set the object in motion. Some of the peaks will be broken off, also requiring a force to maintain motion. Much of the friction is actually due to attractive forces between molecules making up the two objects, so that even perfectly smooth surfaces are not friction-free. Such adhesive forces also depend on the substances the surfaces are made of, explaining, for example, why rubber-soled shoes slip less than those with leather soles.
The magnitude of the frictional force has two forms: one for static situations (static friction), the other for when there is motion (kinetic friction).
When there is no motion between the objects, the magnitude of static friction \(\displaystyle f_s\) is
\(\displaystyle f_s≤μ_sN,\)
where \(\displaystyle μ_s\) is the coefficient of static friction and \(\displaystyle N\) is the magnitude of the normal force (the force perpendicular to the surface).
MAGNITUDE OF STATIC FRICTION
Magnitude of static friction \(\displaystyle f_s\) is
\(\displaystyle f_s≤μ_sN\),
where \(\displaystyle μ_s\) is the coefficient of static friction and \(\displaystyle N\) is the magnitude of the normal force.
The symbol \(\displaystyle ≤\) means less than or equal to , implying that static friction can have a minimum and a maximum value of μsN. Static friction is a responsive force that increases to be equal and opposite to whatever force is exerted, up to its maximum limit. Once the applied force exceeds fs(max), the object will move. Thus
\(\displaystyle f_{s(max)}=μ_sN\).
Once an object is moving, the magnitude of kinetic friction \(\displaystyle f_k\) is given by
\(\displaystyle f_k=μ_kN\),
where \(\displaystyle μ_k\) is the coefficient of kinetic friction. A system in which \(\displaystyle f_k=μ_kN\) is described as a system in which friction behaves simply.
MAGNITUDE OF KINETIC FRICTION
The magnitude of kinetic friction \(\displaystyle f_k\) is given by
\(\displaystyle f_k=μ_kN\),
where \(\displaystyle μ_k\) is the coefficient of kinetic friction.
As seen in Table, the coefficients of kinetic friction are less than their static counterparts. That values of \(\displaystyle μ\) in Table are stated to only one or, at most, two digits is an indication of the approximate description of friction given by the above two equations.
| Static Friction | Kinetic Friction | |
| System | \(\displaystyle μ_s\) | \(\displaystyle μ_k\) |
| Rubber on dry concrete | 1.0 | 0.7 |
| Rubber on wet concrete | 0.7 | 0.5 |
| Wood on wood | 0.5 | 0.3 |
| Waxed wood on wet snow | 0.14 | 0.1 |
| Metal on wood | 0.5 | 0.3 |
| Steel on steel (dry) | 0.6 | 0.3 |
| Steel on steel (oiled) | 0.05 | 0.063 |
| Teflon on steel | 0.04 | 0.04 |
| Bone lubricated by synovial fluid | 0.016 | 0.015 |
| Shoes on wood | 0.9 | 0.7 |
| Shoes on ice | 0.1 | 0.05 |
| Ice on ice | 0.1 | 0.03 |
| Steel on ice | 0.04 | 0.02 |
Coefficients of Static and Kinetic Friction
The equations given earlier include the dependence of friction on materials and the normal force. The direction of friction is always opposite that of motion, parallel to the surface between objects, and perpendicular to the normal force. For example, if the crate you try to push (with a force parallel to the floor) has a mass of 100 kg, then the normal force would be equal to its weight, \(\displaystyle W=mg=(100 kg)(9.80m/s^2)=980 N\), perpendicular to the floor. If the coefficient of static friction is 0.45, you would have to exert a force parallel to the floor greater than \(\displaystyle f_{s(max)}=μ_sN=(0.45)(980N)=440N\) to move the crate. Once there is motion, friction is less and the coefficient of kinetic friction might be 0.30, so that a force of only 290 N \(\displaystyle (f_k=μ_kN=(0.30)(980N)=290N)\) would keep it moving at a constant speed. If the floor is lubricated, both coefficients are considerably less than they would be without lubrication. Coefficient of friction is a unit less quantity with a magnitude usually between 0 and 1.0. The coefficient of the friction depends on the two surfaces that are in contact.
TAKE-HOME EXPERIMENT
Find a small plastic object (such as a food container) and slide it on a kitchen table by giving it a gentle tap. Now spray water on the table, simulating a light shower of rain. What happens now when you give the object the same-sized tap? Now add a few drops of (vegetable or olive) oil on the surface of the water and give the same tap. What happens now? This latter situation is particularly important for drivers to note, especially after a light rain shower. Why?
Many people have experienced the slipperiness of walking on ice. However, many parts of the body, especially the joints, have much smaller coefficients of friction—often three or four times less than ice. A joint is formed by the ends of two bones, which are connected by thick tissues. The knee joint is formed by the lower leg bone (the tibia) and the thighbone (the femur). The hip is a ball (at the end of the femur) and socket (part of the pelvis) joint. The ends of the bones in the joint are covered by cartilage, which provides a smooth, almost glassy surface. The joints also produce a fluid (synovial fluid) that reduces friction and wear. A damaged or arthritic joint can be replaced by an artificial joint (Figure). These replacements can be made of metals (stainless steel or titanium) or plastic (polyethylene), also with very small coefficients of friction.
\(\displaystyle \PageIndex{2}\):
Artificial knee replacement is a procedure that has been performed for more than 20 years. In this figure, we see the post-op x rays of the right knee joint replacement. (credit: Mike Baird, Flickr)
Other natural lubricants include saliva produced in our mouths to aid in the swallowing process, and the slippery mucus found between organs in the body, allowing them to move freely past each other during heartbeats, during breathing, and when a person moves. Artificial lubricants are also common in hospitals and doctor’s clinics. For example, when ultrasonic imaging is carried out, the gel that couples the transducer to the skin also serves to lubricate the surface between the transducer and the skin—thereby reducing the coefficient of friction between the two surfaces. This allows the transducer to move freely over the skin.
Exercise \(\displaystyle \PageIndex{1}\): Skiing Exercise
A skier with a mass of 62 kg is sliding down a snowy slope. Find the coefficient of kinetic friction for the skier if friction is known to be 45.0 N.
Strategy
The magnitude of kinetic friction was given in to be 45.0 N. Kinetic friction is related to the normal force \(\displaystyle N\) as \(\displaystyle f_k=μ_kN\); thus, the coefficient of kinetic friction can be found if we can find the normal force of the skier on a slope. The normal force is always perpendicular to the surface, and since there is no motion perpendicular to the surface, the normal force should equal the component of the skier’s weight perpendicular to the slope. (See the skier and free-body diagram in Figure.)
\(\displaystyle \PageIndex{3}\): The motion of the skier and friction are parallel to the slope and so it is most convenient to project all forces onto a coordinate system where one axis is parallel to the slope and the other is perpendicular (axes shown to left of skier). \(\displaystyle N\) (the normal force) is perpendicular to the slope, and \(\displaystyle f\) (the friction) is parallel to the slope, but \(\displaystyle w\) (the skier’s weight) has components along both axes, namely \(\displaystyle w_⊥\) and \(\displaystyle W_{//}\). \(\displaystyle N\) is equal in magnitude to \(\displaystyle w_⊥\), so there is no motion perpendicular to the slope. However, \(\displaystyle f\) is less than \(\displaystyle W_{//}\) in magnitude, so there is acceleration down the slope (along the x-axis).
That is,
\(\displaystyle N=w_⊥=wcos25º=mgcos25º.\)
Substituting this into our expression for kinetic friction, we get
\(\displaystyle f_k=μ_kmgcos25º,\)
which can now be solved for the coefficient of kinetic friction \(\displaystyle μ_k\).
Solution
Solving for \(\displaystyle μ_k\) gives
\(\displaystyle μ_k=\frac{f_k}{N}=\frac{f_k}{wcos25º}=\frac{f_k}{mgcos25º}\)
Substituting known values on the right-hand side of the equation,
\(\displaystyle μ_k=\frac{45.0 N}{(62 kg)(9.80 m/s^2)(0.906)}=0.082\).
Discussion
This result is a little smaller than the coefficient listed in Table for waxed wood on snow, but it is still reasonable since values of the coefficients of friction can vary greatly. In situations like this, where an object of mass m slides down a slope that makes an angle \(\displaystyle θ\) with the horizontal, friction is given by \(\displaystyle f_k=μ_kmgcosθ\). All objects will slide down a slope with constant acceleration under these circumstances. Proof of this is left for this chapter’s Problems and Exercises.
TAKE-HOME EXPERIMENT
An object will slide down an inclined plane at a constant velocity if the net force on the object is zero. We can use this fact to measure the coefficient of kinetic friction between two objects. As shown in Example, the kinetic friction on a slope \(\displaystyle f_k=μ_kmgcosθ\). The component of the weight down the slope is equal to \(\displaystyle mgsinθ\) (see the free-body diagram in Figure). These forces act in opposite directions, so when they have equal magnitude, the acceleration is zero. Writing these out:
\(\displaystyle f_k=Fg_x\)
\(\displaystyle μ_kmgcosθ=mgsinθ\).
Solving for \(\displaystyle μ_k\), we find that
\(\displaystyle μ_k=\frac{mgsinθ}{mgcosθ}=tanθ\).
Put a coin on a book and tilt it until the coin slides at a constant velocity down the book. You might need to tap the book lightly to get the coin to move. Measure the angle of tilt relative to the horizontal and find \(\displaystyle μ_k\). Note that the coin will not start to slide at all until an angle greater than \(\displaystyle θ\) is attained, since the coefficient of static friction is larger than the coefficient of kinetic friction. Discuss how this may affect the value for \(\displaystyle μ_k\) and its uncertainty.
We have discussed that when an object rests on a horizontal surface, there is a normal force supporting it equal in magnitude to its weight. Furthermore, simple friction is always proportional to the normal force.
MAKING CONNECTIONS: SUBMICROSCOPIC EXPLANATIONS OF FRICTION
The simpler aspects of friction dealt with so far are its macroscopic (large-scale) characteristics. Great strides have been made in the atomic-scale explanation of friction during the past several decades. Researchers are finding that the atomic nature of friction seems to have several fundamental characteristics. These characteristics not only explain some of the simpler aspects of friction—they also hold the potential for the development of nearly friction-free environments that could save hundreds of billions of dollars in energy which is currently being converted (unnecessarily) to heat.
Figure illustrates one macroscopic characteristic of friction that is explained by microscopic (small-scale) research. We have noted that friction is proportional to the normal force, but not to the area in contact, a somewhat counterintuitive notion. When two rough surfaces are in contact, the actual contact area is a tiny fraction of the total area since only high spots touch. When a greater normal force is exerted, the actual contact area increases, and it is found that the friction is proportional to this area.
\(\displaystyle \PageIndex{4}\):
Two rough surfaces in contact have a much smaller area of actual contact than their total area. When there is a greater normal force as a result of a greater applied force, the area of actual contact increases as does friction.
But the atomic-scale view promises to explain far more than the simpler features of friction. The mechanism for how heat is generated is now being determined. In other words, why do surfaces get warmer when rubbed? Essentially, atoms are linked with one another to form lattices. When surfaces rub, the surface atoms adhere and cause atomic lattices to vibrate—essentially creating sound waves that penetrate the material. The sound waves diminish with distance and their energy is converted into heat. Chemical reactions that are related to frictional wear can also occur between atoms and molecules on the surfaces. Figure shows how the tip of a probe drawn across another material is deformed by atomic-scale friction. The force needed to drag the tip can be measured and is found to be related to shear stress, which will be discussed later in this chapter. The variation in shear stress is remarkable (more than a factor of \(\displaystyle 10^{12}\) ) and difficult to predict theoretically, but shear stress is yielding a fundamental understanding of a large-scale phenomenon known since ancient times—friction.
\(\displaystyle \PageIndex{5}\):
The tip of a probe is deformed sideways by frictional force as the probe is dragged across a surface. Measurements of how the force varies for different materials are yielding fundamental insights into the atomic nature of friction.
PHET EXPLORATIONS: FORCES AND MOTION
Explore the forces at work when you try to push a filing cabinet. Create an applied force and see the resulting friction force and total force acting on the cabinet. Charts show the forces, position, velocity, and acceleration vs. time. Draw a free-body diagram of all the forces (including gravitational and normal forces).
\(\displaystyle \PageIndex{6}\): Forces and Motion
Summary
- Friction is a contact force between systems that opposes the motion or attempted motion between them. Simple friction is proportional to the normal force \(\displaystyle N\) pushing the systems together. (A normal force is always perpendicular to the contact surface between systems.) Friction depends on both of the materials involved. The magnitude of static friction \(\displaystyle f_s\) between systems stationary relative to one another is given by
\(\displaystyle f_s≤μ_sN\),
where \(\displaystyle μ_s\) is the coefficient of static friction, which depends on both of the materials.
- The kinetic friction force \(\displaystyle f_k\) between systems moving relative to one another is given by
\(\displaystyle f_k=μ_kN\),
where \(\displaystyle μ_k\) is the coefficient of kinetic friction, which also depends on both materials.


13.5: Potential Pitfalls and How to Avoid Them
Recently, a few papers have been published that are critical of state-dependent diversification models (Rabosky and Goldberg 2015, Maddison and FitzJohn (2015) ) . These papers raise substantive critiques that are important to address when applying the methods described in this chapter to empirical data. In this section I will attempt to describe the critiques and their potential remedies.
The most serious limitation of state-dependent models as currently implemented is that they consider only a relatively small set of possible models. In particular, the approach we describe above compares two models: first, a model where birth and death rates are constant and do not depend on the state of the character; and second, a model where birth and death rates depend only on the character state (Maddison et al. 2007) . But there is another possibility that might be (in general) more common than either of the models we consider: birth and death rates vary, but in a way that is not dependent on the particular character we have chosen to analyze. I say that this is probably a common pattern because we know that birth and death rates vary tremendously across lineages in the tree of life (Alfaro et al. 2009) , and it seems probable to me that many of our hypotheses about which characters might contribute to that variation are, at this point, stabs in the dark.
This issue is a normal one for statistical analyses – after all, there are always other models outside of our set of considered possibilities. However, in this case, the fact that state-dependent diversification models fail to consider the possibility outlined above causes a very particular – and peculiar – problem: if we apply the tests to empirical phylogenetic trees, even with made-up data, we almost always find statistically significant results (Rabosky and Goldberg 2015) . For example, Rabosky and Goldberg (2015) found that there is very often a statistically significant “signal” that the number of letters in a species name is significantly associated with speciation rates across a range of empirical datasets. This result might seem ridiculous and puzzling, as there is no way that species name length should be associated with the diversification processes. However, if we return to our alternative model above, then the results make sense. Rabosky and Goldberg (2015) simulated character evolution on real phylogenetic trees, and their results do not hold when the trees are simulated along with the characters (this is also why Rabosky and Goldberg’s (2015) results do not represent “type I errors,” contra their paper, because the data are not simulated under the null hypothesis). On these real trees, speciation and/or extinction rates vary across clades. Among the two models that the authors consider, both are wrong; speciation and extinction are independent of the character but not constant through time. Of the two alternatives, the state-dependent model tends to fit better because, from a statistical point of view, it is important for the model to capture some variation in birth and death rates across clades. Even a random character will pick up some of this variation, so that the alternative model tends to fit better than the null – even though, in this case, the character has nothing to do with diversification!
Fortunately, there are a number of ways to deal with this problem. First, one can compare the statistical support for the state-dependent model with the support that one obtains for random data. The random data could be simulated on the tree, or one could permute the tips or draw random data from a multinomial distribution (Rabosky and Goldberg 2015) . One can then compare, for example, the distribution of Δ A I C c scores obtained from these permutations to the Δ A I C c for the original data. There are also semi-parametric methods based on permutations that have similar statistical properties (Rabosky and Goldberg 2017) . Alternatively, we could explicitly consider the possibility that some unmeasured character is actually the thing that is influencing diversification rates (Beaulieu and O’Meara 2016) . This latter approach is the most elegant as we can directly add the model described in this section to our list of candidates (see Beaulieu and O’Meara 2016) .
A more general critique of state-dependent models of diversification was raised by Maddison and Fitzjohn (Maddison and FitzJohn 2015) . This paper pointed out that statistically significant results for these tests can be driven by an event on a single branch of a tree, and therefore be unreplicated. This is a good criticism that applies equally well to a range of comparative methods. We can deal with this critique, in part, by making sure the events we test are replicated in our data. Together, both of these critiques argue for a stronger set of model adequacy approaches in comparative methods.


13.10: Conclusion
These case studies have explored the expansive definitions of “good music” offered by recent Pulitzer committees, a leading art music ensemble, and one of the most famous living classical musicians. All have agreed that quality can be found in many genres and traditions. We might sum up their values according to the five criteria presented in the introduction.
Was every example in this chapter successful at fulfilling its stated purpose? We’ve looked at a lot of dance music—did it inspire you to dance? Did Shaw’s Partita change the way you think about the possible uses for the human voice? Did Marsalis’s “Work Song” cause you to feel the suffering of his oratorio’s protagonists? Was each of these examples exceptional when compared to others of its type?
Is Lamar the best hip-hop artist, and was DAMN. the best hip-hop album of 2017? Is Tehillim a particularly compelling example of minimalist composition? Are the works of Aphex Twin superior to those of other electronic music artists?
Were this examples particularly original? Do they stand out from the field? Is there something about the musical details of Libertango that make it stick in your head? Does the originality of the vision behind Ellington’s Far East Suite qualify it as “better” than other jazz compositions of the era?
The skill of the performer—whether we are talking about Lamar’s accomplished rapping, Roomful of Teeth’s polished singing, Alarm Will Sound’s clever orchestrating, or Ma’s exquisite cello playing—certainly contributes to the quality of each of these examples. Ma in particular has exhibited singular dedication to identify and collaborating with the most accomplished performers from each global tradition. Flawless execution is central to his cross-cultural vision. But what about the skill of the composers? How can we judge that?
Finally, what impact has this music had on society? As an enormously popular performer, Lamar has certainly had an impact—will his legacy shape the future of hip-hop? Copland certainly defined the sound of “Americanness” for generations of composers. That makes him important, but does it make him good? Shaw is still at the beginning of her career—will her future influence determine the quality of Partita in some way?
This book ends as it began: with a long list of questions. None of these questions can be definitively answered, but they are all worth asking. They are worth asking because we listen to music every day, meaning that every day we have the opportunity to engage with an art form that human beings have used to communicate, entertain, and even shape the course of history for tens of thousands of years. We can either listen passively or we can ask questions of what we hear. These questions lead us to listen with greater care, extract more from the music in our lives, and discover new things about the world around us.


5.23: Skills Checklist- Choking Maneuver
- Call out for help or tell another staff member to get the nurse if you think a resident is choking. If no nurse is available, direct someone to call 911 while proceeding with the following steps.
- Until help arrives, stand behind the victim with one leg forward between the victim’s legs.
- For a child, move down to their level and keep your head to one side.
- Reach around their abdomen and locate the navel.
- Place the thumb side of your fist against their abdomen just above the navel.
- Grasp your fist with your other hand and thrust inward and upward into the victim’s abdomen with quick jerks.
- For a responsive pregnant victim, any victim you cannot get your arms around, or for anyone in whom abdominal thrusts are not effective, give chest thrusts while standing behind them. Avoid squeezing the ribs with your arms.
- Continue thrusts until the victim expels the object or becomes unresponsive.
- If the person becomes unconscious, notify the nurse. If no nurse is available, call 911.
View a YouTube video [1] of an instructor demonstrating the c hoking maneuver:
- Chippewa Valley Technical College. (2022, December 3). Choking Maneuver. [Video]. YouTube. Video licensed under CC BY 4.0 . https://youtu.be/HMtwmw5Vaoo ↵


10.3: Random Triangles
Preliminaries
Statement of the Problem
Suppose that a stick is randomly broken in two places. What is the probability that the three pieces form a triangle?
Without looking below, make a guess.
Run the triangle experiment 50 times. Do not be concerned with all of the information displayed in the app, but just note whether the pieces form a triangle. Would you like to revise your guess?
Mathematical Formulation
As usual, the first step is to model the random experiment mathematically. We will take the length of the stick as our unit of length, so that we can identify the stick with the interval \([0, 1]\). To break the stick into three pieces, we just need to select two points in the interval. Thus, let \(X\) denote the first point chosen and \(Y\) the second point chosen. Note that \(X\) and \(Y\) are random variables and hence the sample space of our experiment is \( S = [0, 1]^2 \). Now, to model the statement that the points are chosen at random , let us assume, as in the previous sections, that \(X\) and \(Y\) are independent and each is uniformly distributed on \([0, 1]\).
The random point \((X, Y)\) is uniformly distributed on \(S = [0, 1]^2\).
Hence \[ \P\left[(X, Y) \in A\right] = \frac{\area(A)}{\area(S)} \]
Triangles
The Probability of a Triangle
The three pieces form a triangle if and only if the triangle inequalities hold: the sum of the lengths of any two pieces must be greater than the length of the third piece.
The event that the pieces form a triangle is \(T_1 \cup T_2\) where
- \(T_1 = \left\{ (x, y) \in S: y \gt \frac{1}{2}, \; x \lt \frac{1}{2}, \; y - x \lt \frac{1}{2} \right\}\)
- \(T_2 = \left\{ (x, y) \in S: x \gt \frac{1}{2}, \; y \lt \frac{1}{2}, \; x - y \lt \frac{1}{2} \right\}\)
A sketch of the event \(T\) is given below. Curiously, \(T\) is composed of triangles!
The probability that the pieces form a triangle is \(\P(T) = \frac{1}{4}\).
How close did you come with your initial guess? The relative low value of \( \P(T) \) is a bit surprising.
Run the triangle experiment 1000 times and compare the empirical probability of \(T^c\) to the true probability.
Triangles of Different Types
Now let us compute the probability that the pieces form a triangle of a given type. Recall that in an acute triangle all three angles are less than 90°, while an obtuse triangle has one angle (and only one) that is greater than 90°. A right triangle, of course, has one 90° angle.
Suppose that a triangle has side lengths \(a\), \(b\), and \(c\), where \(c\) is the largest of these. The triangle is
- acute if and only if \(c^2 \lt a^2 + b^2\).
- obtuse if and only if \(c^2 \gt a^2 + b^2\).
- right if and only if \(c^2 = a^2 + b^2\).
Part (c), of course, is the famous Pythagorean theorem, named for the ancient Greek mathematician Pythagoras.
The right triangle equations for the stick pieces are
- \((y - x)^2 = x^2 + (1 - y)^2\) in \(T_1\)
- \((1 - x)^2 = x^2 + (y - x)^2\) in \(T_1\)
- \(x^2 = (y - x)^2 + (1 - y)^2\) in \(T_1\)
- \((x - y)^2 = y^2 + (1 - x)^2\) in \(T_2\)
- \((1 - x)^2 = y^2 + (x - y)^2\) in \(T_2\)
- \(y^2 = (x - y)^2 + (1 - x)^2\) in \(T_2\)
Let \(R\) denote the event that the pieces form a right triangle. Then \(\P(R) = 0\).
The event that the pieces form an acute triangle is \(A = A_1 \cup A_2\) where
- \(A_1\) is the region inside curves (a), (b), and (c) of the right triangle equations .
- \(A_2\) is the region inside curves (d), (e), and (f) of the right triangle equations .
The event that the pieces form an obtuse triangle is \(B = B_1 \cup B_2 \cup B_3 \cup B_4 \cup B_5 \cup B_6\) where
- \(B_1\), \(B_2\), and \(B_3\) are the regions inside \(T_1\) and outside of curves (a), (b), and (c) of the right triangle equations , respectively.
- \(B_4\), \(B_5\), and \(B_6\) are the regions inside \(T_2\) and outside of curves (d), (e), and (f) of the right triangle equations , respectively.
The probability that the pieces form an obtuse triangle is \[ \P(B) = \frac{9}{4} - 3 \ln(2) \approx 0.1706 \]
Proof
Simple calculus shows that \(\P(B_i) = 3/8 - \ln(2) / 2\) for each \(i \in \{1, 2, 3, 4, 5, 6\}\). For example \begin{align} \P(B_1) & = \int_0^{1/2} \frac{x \, (1 - 2 \, x)}{2 - 2 \, x} \, dx \\ \P(B_3) & = \int_0^{1/2} \left(y + \frac{1}{2 \, y} - \frac{3}{2} \right) \, dy \end{align} From symmetry it also follows that \(\P(B_i)\) is the same for each \(i\).
The probability that the pieces form an acute triangle is \[ \P(A) = 3 \ln(2) - 2 \approx 0.07944 \]
Proof
Note that \(A \cup B \cup R = T\), and \(A\), \(B\), and \(R\) are disjoint.
Run the triangle experiment 1000 times and compare the empirical probabilities to the true probabilities.


14.2A: Normal Microbiota and Host Relationships
- Explain the relationship between the normal microbiota and the host upon infection of a pathogen
Normal Microbiota
The phrase “normal microbiota” refers to the microorganisms that reside on the surface and deep layers of skin, in the saliva and oral mucosa, in the conjunctiva, and in the gastrointestinal tracts of every human being. These microorganisms are not harmful to humans; in fact, some are even beneficial and all help maintain our health. Our normal microbiota consists of various bacteria, fungi, and archaea. An example of our bacterial microbiota is E. coli . Many people think of E. coli as the bacteria that makes you sick; however while it has that capacity, it can also remain dormant and benign in your gastrointestinal tract for your entire life. All humans actually acquire E. coli shortly after birth with the intake of food or water. Other forms of bacteria present in the human gut are necessary for proper digestion of carbohydrates.
Host Relationships
While our bodies are happy to host the array of microbiota that are considered “normal,” the human body does not take a back seat when infection tries to use it as a host. Interestingly, normal microbiota can be key players helping the body fight off infection. Resistance to and recovery from viral infections depends on the interactions that occur between the virus and its host. The host has a variety of defenses that it uses to prevent infection. One of the first lines of defense is mucus, which has a range of normal microbiota that compete with and may even attack invading bacteria and virae.
Once a virus or bacteria makes its way past the skin and mucosa, there may be changes that occur in the host to diminish the invader’s effectiveness. An example of such a change is a fever. There are a number of other humoral components of the nonspecific immune system as well. Specific immune responses are produced by antibodies. Different interferons (IgA, IgG, IgM, etc. ) play roles in defeating viruses located in our membranes. The body does not easily become a host to infection; it has a line up of defenses to try to protect you from harm.
Key Points
- The phrase “normal microbiota ” refers to the microorganisms that reside on the surface and deep layers of skin, in the saliva and oral mucosa, in the conjunctiva, and in the gastrointestinal tracts of every human being.
- These microbiota are not harmful to humans; some are even beneficial and most help maintain our health.
- Our normal microbiota consists of various bacteria, fungi, and archaea.
- While our bodies are happy to host the array of microbiota that are considered “normal,” the human body does not take a back seat when infection tries to use it as a host.
- Resistance to and recovery from viral infections depends on the interactions that occur between virus and host. The host has a variety of barriers that it uses to prevent infection. One of the first lines of defense is mucus, which has a range of normal microbiota.
- There are a number of other humoral components of the nonspecific immune system as well.
Key Terms
- host : A cell or organism which harbors another organism or biological entity, usually a parasite.
- microorganism : An organism that is too small to be seen by the unaided eye, especially a single-celled organism, such as a bacterium.
- interferon : Any of a group of glycoproteins, produced by the immune system, that prevent viral replication in infected cells.


3.9: Test Yourself
Now that you have completed this chapter, it’s time to test your knowledge. Try to answer the following questions (you may want to review parts of the chapter before answering). Write your answers down on a piece of paper.
1. What is the apical pulse rate?
Listen to the audio clip of the apical pulse. Count the pulse for 30 seconds and report the rate as beats per minute (NOTE: although this clip only allows you to count for 30 seconds, remember, it is best to count the apical pulse for one minute).
An interactive or media element has been excluded from this version of the text. You can view it online here: pb.libretexts.org/vitalsign/?p=137
Audio clip 3.2: Apical pulse
Alternatively, if viewing textbook as a pdf, use this link: https://www.youtube.com/embed/znhbVRZRLfM?rel=0
2. What is the apical pulse rate?
Listen to the audio clip of the apical pulse. Count the pulse for 30 seconds and report the rate as beats per minute (NOTE: although this clip only allows you to count for 30 seconds, remember, it is best to count the apical pulse for one minute).
An interactive or media element has been excluded from this version of the text. You can view it online here: pb.libretexts.org/vitalsign/?p=137
Audio clip 3.3: Apical pulse
Alternatively, if viewing textbook as a pdf, use this link: https://www.youtube.com/embed/Hxd68qJfzhQ?rel=0
3. How should a healthcare provider respond when a newborn has an apical heart rate of 120 beats per minute?
a. Re-take the rate at the brachial location
b. Document the rate and assess it as normal
c. Document the rate and identify it as tachycardia
d. Notify the physician and identify it as bradycardia
4. Which findings should be of most concern to the healthcare provider in an adolescent client?
a. Pulse 40 bpm and respiration 34
b. Respiration 16 and pulse 82 bpm
c. Pulse 68 bpm and sinus arrhythmia
d. Pulse 2+, 78 bpm, and regular rhythm
5. Match the findings that are typically normal for the person listed:
Sinus arrhythmia Athlete
Bradycardia Newborn
Abdominal breather Adolescent


1.3: Hardware
Learning Objectives
- Discuss the role hardware plays in computing
Computer hardware (usually simply called hardware when a computing context is concerned) is the collection of physical elements that constitutes a computer system. Computer hardware is the physical parts or components of a computer, such as the monitor, mouse, keyboard, computer data storage, hard disk drive (HDD), graphic cards, sound cards, memory, motherboard, and so on, all of which are physical objects that are tangible.
Mainboard
The motherboard is the main component of a computer. It is a large rectangular board with integrated circuitry that connects the other parts of the computer including the CPU, the RAM, the disk drives (CD, DVD, hard disk, or any others) as well as any peripherals connected via the ports or the expansion slots.
Components directly attached to or part of the motherboard include:
- The CPU (Central Processing Unit) performs most of the calculations which enable a computer to function, and is sometimes referred to as the “brain” of the computer. It is usually cooled by a heat sink and fan. Most newer CPUs include an on-die Graphics Processing Unit (GPU).
- The Chipset , which includes the north bridge, mediates communication between the CPU and the other components of the system, including main memory.
- The Random-Access Memory (RAM) stores the code and data that are being actively accessed by the CPU.
- The Read-Only Memory (ROM) stores the BIOS that runs when the computer is powered on or otherwise begins execution, a process known as Bootstrapping, or “booting” or “booting up.”
- The BIOS (Basic Input Output System) includes boot firmware and power management firmware. Newer motherboards use Unified Extensible Firmware Interface (UEFI) instead of BIOS.
- Buses connect the CPU to various internal components and to expand cards for graphics and sound.
- The CMOS battery is also attached to the motherboard. This battery is the same as a watch battery or a battery for a remote to a car’s central locking system. Most batteries are CR2032, which powers the memory for date and time in the BIOS chip.
Storage
Computer data storage, often called storage, refers to computer components and recording media that retain digital data. Data storage is a core function and fundamental component of computers. The price of solid-state drives (SSD), which store data on flash memory, has dropped a lot in recent years, making them a better choice than ever to add to a computer to make booting up and accessing files faster.
Fixed media
Data is stored by a computer using a variety of media. Hard disk drives are found in virtually all older computers, due to their high capacity and low cost, but solid-state drives are faster and more power efficient, although currently more expensive than hard drives, so are often found in more expensive computers. Some systems may use a disk array controller for greater performance or reliability.
Removable media
To transfer data between computers, a USB flash drive or Optical disc may be used. Their usefulness depends on being readable by other systems; the majority of machines have an optical disk drive, and virtually all have a USB port.
Practice Question
Input and Output
Input and output devices are typically housed externally to the main computer chassis. The following are either standard or very common to many computer systems.
Input
Input devices allow the user to enter information into the system, or control its operation. Most personal computers have a mouse and keyboard, but laptop systems typically use a touchpad instead of a mouse. Other input devices include webcams, microphones, joysticks, and image scanners.
Output device
Output devices display information in a human readable form. Such devices could include printers, speakers, monitors or a Braille embosser.
Contributors and Attributions
- Practice Question. Authored by : Sherri Pendleton. Provided by : Lumen Learning. License : CC BY: Attribution
- Modification of Computer Hardware. Provided by : Northern Virginia Community Collegeu2019s Extended Learning Institute. Located at : https://courses.lumenlearning.com/zeliite115/chapter/reading-hardware-2/ . License : CC BY-SA: Attribution-ShareAlike
- Untitled. Authored by : Editors Keys. Provided by : Unsplash. Located at : https://unsplash.com/photos/CtDrd7mWW6M . License : CC0: No Rights Reserved . License Terms : Unsplash License