1.2: Fundamental Theories of Disaster
Over the centuries, there have been four fundamental theories about disasters. These four theories have conceived of disasters as:
· Acts of fate/acts of God,
· Acts of nature,
· Joint effects of nature and society, and
· Social constructions.
Acts of Fate/Acts of God
For millennia, disasters were considered to arise from impersonal and uncontrollable forces—either from unfortunate alignments of stars and planets or as acts of God that were beyond human understanding. Both forms of this theory viewed a disaster as predetermined and, thus, completely beyond the victim’s control. A variation on this theory was that disasters were cosmic or divine retribution for human failings—personal disasters for personal failings and collective disasters for societal failings.
Acts of Nature
Over time, increased scientific knowledge led many people to substitute natural causes for supernatural ones. Thus, floods occurred because the large amount of rainfall from a severe storm exceeded the soil’s capacity to absorb it. The rapid runoff exceeded the river basin’s capacity, so the excess spilled over the river banks, flooded buildings, and drowned people and animals. Accordingly, the term natural disaster came to refer to “an outside attack upon social systems that ‘broke down’ in the face of such an assault from outside” (Quarantelli, 1998, p. 266). The resulting conception of man against nature has been especially potent as the driving force behind attempts to “tame” rivers by straightening their channels and building dams and levees.
Interactive Effects of Nature and Society
Still later, it was proposed that hazards arise from the interaction of a physical event system and a human use system. Thus, it takes both a hazardous physical event system and a vulnerable human use system to produce disasters. If either one is missing, disasters do not occur. According to Carr (1932, p. 211)
Not every windstorm, earth-tremor, or rush of water is a catastrophe. [S]o long as the levees hold, there is no disaster. It is the collapse of the cultural protections that constitutes the disaster proper.
According to this view, human societies adapt to the prevailing environmental conditions (e.g., temperature, wind speed, precipitation, seismic activity) at a given location. Unfortunately, they fail to anticipate the variation in those environmental conditions. Consequently, their adaptation to normal conditions usually is inadequate for extreme events—blizzards, heat waves, tornadoes, hurricanes, and floods. This perspective is perhaps best illustrated by earthquake damage and casualties.  According to this view, people can avoid disasters if they stay out of seismically active locations or, if they do move there, they must build structures that resist the extreme environmental events that will eventually occur.
Social Constructions
Most recently, researchers have recognized that disasters are quite systematic in the types of people they harm, as well as the types of geographic locations and human use systems they strike. To the interactive effects theory’s concerns about hazard exposure at specific locations and physical vulnerability of specific structures, social construction theory calls attention to the social vulnerability of specific population segments. To say that hazard vulnerability is socially constructed does not mean people are vulnerable because they think the wrong thoughts—as most people would now categorize the belief that floods are caused by the alignment of the planets and stars. Rather, socially vulnerable population segments emerge because our psychological, demographic, economic, and political processes tend to produce them. Of course these processes have produced many good things. Many residents of the US, in particular, have good jobs, comfortable lives, and we have enjoyed one of the most democratic governments in the world. Nonetheless, all of these conditions have changed over time—life now is much improved from what it was a century ago and there are many ways in which it can be improved still further. Of particular concern to emergency managers should be the many ways in which our institutions can reduce the hazard vulnerability of those who have the least psychological resilience, social support, political power, and are the poorest economically.
Theoretical Comparisons
These theories have, in one sense, succeeded each other over time as scholars have found later theories to provide a better account of the data from their research. However, scientific acceptance is different from popular acceptance. Each of the four theories is currently believed by at least some members of society. Indeed, the most cynical version of the Acts of fate/acts of God theory uses it to avoid responsibility for actions that are substantially within human control. For example, representatives of the coal company that built a dam across Buffalo Creek West Virginia claimed the dam’s collapse was an “Act of God” because the dam was “incapable of holding the water God poured into it” (Erikson, 1976, p. 19). This was clearly a feeble attempt to avoid admitting the company negligently built a non-engineered dam from unstable materials, thus risking the lives of downstream residents to maintain company profits.
Each community throughout the world probably has at least some believers in each theory. Because each theory has different implications for environmental hazard management, the prevalence of each theory has significant implications for policy at the local, state, national, and international levels.


6.2.1: The Propagation of Light
Learning Objectives
By the end of this section, you will be able to:
- Determine the index of refraction, given the speed of light in a medium
- List the ways in which light travels from a source to another location
The Speed of Light: Early Measurements
The first measurement of the speed of light was made by the Danish astronomer Ole Roemer (1644–1710) in 1675. He studied the orbit of Io, one of the four large moons of Jupiter, and found that it had a period of revolution of 42.5 h around Jupiter. He also discovered that this value fluctuated by a few seconds, depending on the position of Earth in its orbit around the Sun. Roemer realized that this fluctuation was due to the finite speed of light and could be used to determine c .
Roemer found the period of revolution of Io by measuring the time interval between successive eclipses by Jupiter. Figure \(\PageIndex{1a}\) shows the planetary configurations when such a measurement is made from Earth in the part of its orbit where it is receding from Jupiter. When Earth is at point A , Earth, Jupiter, and Io are aligned. The next time this alignment occurs, Earth is at point B , and the light carrying that information to Earth must travel to that point. Since B is farther from Jupiter than A , light takes more time to reach Earth when Earth is at B . Now imagine it is about 6 months later, and the planets are arranged as in Figure \(\PageIndex{1b}\). The measurement of Io’s period begins with Earth at point A' and Io eclipsed by Jupiter. The next eclipse then occurs when Earth is at point B', to which the light carrying the information of this eclipse must travel. Since B' is closer to Jupiter than A', light takes less time to reach Earth when it is at B'. This time interval between the successive eclipses of Io seen at A' and B' is therefore less than the time interval between the eclipses seen at A and B . By measuring the difference in these time intervals and with appropriate knowledge of the distance between Jupiter and Earth, Roemer calculated that the speed of light was \(2.0 \times 10^8\,m/s\), which is only 33% below the value accepted today.
The first successful terrestrial measurement of the speed of light was made by Armand Fizeau (1819–1896) in 1849. He placed a toothed wheel that could be rotated very rapidly on one hilltop and a mirror on a second hilltop 8 km away (Figure \(\PageIndex{2}\)). An intense light source was placed behind the wheel, so that when the wheel rotated, it chopped the light beam into a succession of pulses. The speed of the wheel was then adjusted until no light returned to the observer located behind the wheel. This could only happen if the wheel rotated through an angle corresponding to a displacement of (n+½) teeth, while the pulses traveled down to the mirror and back. Knowing the rotational speed of the wheel, the number of teeth on the wheel, and the distance to the mirror, Fizeau determined the speed of light to be \(3.15 \times 10^8\,m/s\), which is only 5% too high.
The French physicist Jean Bernard Léon Foucault (1819–1868) modified Fizeau’s apparatus by replacing the toothed wheel with a rotating mirror. In 1862, he measured the speed of light to be 2.98×10 8 m/s, which is within 0.6% of the presently accepted value. Albert Michelson (1852–1931) also used Foucault’s method on several occasions to measure the speed of light. His first experiments were performed in 1878; by 1926, he had refined the technique so well that he found c to be (2.99796±4)×10 8 m/s.
Today, the speed of light is known to great precision. In fact, the speed of light in a vacuum c is so important that it is accepted as one of the basic physical quantities and has the value
\[c=2.99792458\times 10^8m/s \equiv 3.00\times 10^8m/s \label{speed}\]
where the approximate value of 3.00×10 8 m/s is used whenever three-digit accuracy is sufficient.
Speed of Light in Matter
The speed of light through matter is less than it is in a vacuum, because light interacts with atoms in a material. The speed of light depends strongly on the type of material, since its interaction varies with different atoms, crystal lattices, and other substructures. We can define a constant of a material that describes the speed of light in it, called the index of refraction \(\eta\) :
\[\eta=\dfrac{c}{v} \label{index}\]
where \(v\) is the observed speed of light in the material.
Since the speed of light is always less than c in matter and equals c only in a vacuum, the index of refraction is always greater than or equal to one; that is, \(\eta\) ≥ 1. Table \(\PageIndex{1}\) gives the indices of refraction for some representative substances. The values are listed for a particular wavelength of light, because they vary slightly with wavelength. (This can have important effects, such as colors separated by a prism, as we will see in Dispersion .) Note that for gases, \(\eta\) is close to 1.0. This seems reasonable, since atoms in gases are widely separated, and light travels at c in the vacuum between atoms. It is common to take \(n=1\) for gases unless great precision is needed. Although the speed of light v in a medium varies considerably from its value c in a vacuum, it is still a large speed.
Example \(\PageIndex{1}\): Speed of Light in Jewelry
Calculate the speed of light in zircon, a material used in jewelry to imitate diamond.
Strategy
We can calculate the speed of light in a material \(v\) from the index of refraction \(\eta\) of the material, using Equation \red{index}
Solution
Rearranging Equation \ref{index} for \(v\) gives us
\[v=\dfrac{c}{n}.\]
The index of refraction for zircon is given as 1.923 in Table \(\PageIndex{1}\), and \(c\) is given in Equation \ref{speed}. Entering these values in the equation gives
\[\begin{align*} v &=\dfrac{3.00×10^8m/s}{1.923} \\[4pt] &=1.56×10^8m/s. \end{align*}\]
Significance
This speed is slightly larger than half the speed of light in a vacuum and is still high compared with speeds we normally experience. The only substance listed in Table \(\PageIndex{1}\) that has a greater index of refraction than zircon is diamond. We shall see later that the large index of refraction for zircon makes it sparkle more than glass, but less than diamond.
Exercise \(\PageIndex{1}\)
Table \(\PageIndex{1}\) shows that ethanol and fresh water have very similar indices of refraction. By what percentage do the speeds of light in these liquids differ?
- Answer
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2.1% (to two significant figures)
The Ray Model of Light
You have already studied some of the wave characteristics of light in the previous chapter on Electromagnetic Waves . In this chapter, we start mainly with the ray characteristics. There are three ways in which light can travel from a source to another location (Figure \(\PageIndex{1}\)). It can come directly from the source through empty space, such as from the Sun to Earth. Or light can travel through various media, such as air and glass, to the observer. Light can also arrive after being reflected, such as by a mirror. In all of these cases, we can model the path of light as a straight line called a ray.
Experiments show that when light interacts with an object several times larger than its wavelength, it travels in straight lines and acts like a ray. Its wave characteristics are not pronounced in such situations. Since the wavelength of visible light is less than a micron (a thousandth of a millimeter), it acts like a ray in the many common situations in which it encounters objects larger than a micron. For example, when visible light encounters anything large enough that we can observe it with unaided eyes, such as a coin, it acts like a ray, with generally negligible wave characteristics.
In all of these cases, we can model the path of light as straight lines. Light may change direction when it encounters objects (such as a mirror) or in passing from one material to another (such as in passing from air to glass), but it then continues in a straight line or as a ray. The word “ray” comes from mathematics and here means a straight line that originates at some point. It is acceptable to visualize light rays as laser rays. The ray model of light describes the path of light as straight lines.
Since light moves in straight lines, changing directions when it interacts with materials, its path is described by geometry and simple trigonometry. This part of optics, where the ray aspect of light dominates, is therefore called geometric optics. Two laws govern how light changes direction when it interacts with matter. These are the law of reflection , for situations in which light bounces off matter, and the law of refraction , for situations in which light passes through matter. We will examine more about each of these laws in upcoming sections of this chapter.


7.2: Sensory Impairments Basic Concepts
Interpreting Sensations
Before learning about sensory function, it is important to understand how the nervous system works. An intact nervous system is necessary for information to be delivered from the environment to the brain to trigger responses from the body. For neurons to transmit these messages, they are in the form of an action potential. Sensory receptors perceive a stimulus and then change the sensation to an electrical signal so that it can be transmitted to the brain and then out to the body.  The signal is transmitted to the brain where it is interpreted, and then signals are quickly sent to the hand to pull away from the hot stimuli. [1]
Our bodies interpret sensations through a process using reception, perception, and reaction. Reception is the first part of the sensory process when a nerve cell or sensory receptor is stimulated by a sensation. Sensory receptors are activated by mechanical, chemical, or temperature stimuli. In addition to our five senses, we also have somatosensation. Somatosensation refers to sensory receptors that respond to stimuli such as pain, pressure, temperature, and vibration. It also includes vestibular sensation , a sense of spatial orientation and balance, and proprioception , the sense of the position of our bones, joints, and muscles. Although these sensory systems are all very different, they share a common purpose. They change a stimulus into an electrical signal that is transmitted in the nervous system. [2]
The sensory receptors for each of our senses work differently from one another. Light receptors, sound receptors, and touch receptors are each activated by different stimuli with specialized receptor specificity. For example, touch receptors are sensitive to pressure but do not have sensitivity to sound or light. Nerve impulses from sensory receptors travel along pathways to the spinal cord or directly to the brain. Some stimuli are also combined in the brain, such as our sense of smell that can affect our sense of taste. [3]
As an individual becomes aware of a stimulus and it is transmitted to the brain, perception occurs. Perception is the interpretation of a sensation. All sensory signals, except olfactory system input, are transmitted to the thalamus and to the appropriate region of the cortex of the brain. The thalamus, which is in the forebrain, acts as a relay station for sensory and motor signals. When a sensory signal leaves the thalamus, it is sent to the specific area of the cortex that processes that sense. [4] However, conditions that affect a person’s consciousness also affect the ability to perceive and interpret stimuli.
Reaction is the response that individuals have to a perception of a received stimulus. The brain determines what sensations are significant because it is impossible to react to all stimuli that are constantly received from our environment. A healthy brain maintains a balance between sensory stimuli received and those reaching awareness. However, sensory overload can occur if the amount of stimuli the brain is receiving is overwhelming to an individual. Sensory deprivation can also occur if there are insufficient sensations from the environment. [5]
Sensory Impairment
Alterations in sensory function include sensory impairment, sensory overload, and sensory deprivation. Sensory impairment includes any type of difficulty that an individual has with one of their five senses. When an individual experiences loss of a sensory function, such as vision, the way they interact with the environment is affected. For example, when an individual gradually loses their vision, their reliance on other senses to receive information from the environment is often enhanced.
Safety is always a nursing consideration for a patient with a sensory impairment. Intact senses are required to make decisions about functioning safely within the environment. For example, an individual who has impaired hearing may not be able to hear a smoke alarm and requires visual indicators when the alarm is triggered.
Sensory impairments are very common in older adults. Most older adults develop impaired near vision called presbyopia. See Figure 7.2 [6] for an image of simulated presbyopia.
Deficits in taste and smell are also prevalent in this age group. Additionally, kinesthetic impairment (an altered sense of touch) can occur in adults as young as 55. Kinesthetic impairment can cause difficulty in daily functioning, such as buttoning one’s shirt or performing other fine motor tasks. These sensory losses can greatly impact how older adults live and function. [7]
Vision Impairments
Several types of visual impairments commonly occur in older adults, including macular degeneration, cataracts, glaucoma, diabetic retinopathy, and presbyopia. See Table 7.2 for more information about each of these visual conditions.
| Macular Degeneration | Macular degeneration is the leading cause of legal blindness in individuals over 60 years of age. Risk factors include advancing age, a positive family history, hypertension, and smoking. In macular degeneration, there is loss of central vision with classic symptoms such as blurred central vision, distorted vision that causes difficulty driving and reading, and the requirement for brighter lights and magnification for close-up visual activities. [8] |
|---|---|
| Cataracts | Cataracts are the opacity of the lens of the eye that causes clouded, blurred, or dimmed vision. About half of individuals ages 65 to 75 will develop cataracts, with further incidence occurring after age 75. Cataracts can be removed with surgery that replaces the lens with an artificial lens. [9] |
| Glaucoma | Glaucoma is caused by elevated intraocular pressure that leads to progressive damage to the optic nerve, resulting in gradual loss of peripheral vision. It affects about 4% of individuals over age 70. [10] |
| Diabetic Retinopathy | Diabetic retinopathy is the leading cause of blindness in adults diagnosed with type 1 and type 2 diabetes mellitus. Diabetic retinopathy is a complication of diabetes mellitus due to damaged blood vessels in the retina causing vision loss. [11] Patients with diabetes are encouraged to receive annual eye exams so that retinopathy can be discovered and treated early. Treatments, such as laser treatment that can help shrink blood vessels, injections that can reduce swelling, or surgery, can prevent permanent vision loss. [12] |
| Presbyopia | As a person ages, the lens of the eye gradually becomes thicker and loses flexibility. It stops focusing light on the retina correctly, causing impaired near vision and accommodation at all distances. Presbyopia starts in the early to mid-forties and worsens with aging. It can lead to significant visual impairment but does not usually cause blindness. [13] |
See simulated images of these visual conditions in the “ Eye and Ear Basic Concepts ” section of the “Eye and Ear Assessment” chapter of the Open RN Nursing Skills book.
Hearing Loss and Ear Problems
Approximately one third of individuals aged 70 and older have hearing loss. Good hearing depends on a series of events that change sound waves in the air into electrical signals. The auditory nerve conducts these electrical signals from the ear to the brain through a series of steps. The structures of the ear, such as the tympanic membrane and cochlea, must be intact and functioning appropriately for conduction of sound to occur. Age-related hearing loss ( presbycusis ) gradually occurs in most individuals as they age. [14] Typically, low-pitched sounds are easiest to hear, but it often becomes increasingly difficult to hear normal conversation, especially over loud background noise. Hearing aids are commonly used to enhance hearing. See Figure 7.3 [15] for an image of common hearing aids used to treat hearing loss.
Hearing loss can be caused by other factors in addition to aging. A build-up of ear wax in the ear canal can cause temporary hearing loss. Sounds that are too loud or long-term exposure to loud noises can cause noise-induced hearing loss. For example, a loud explosion or employment using loud machinery without ear protection can damage the sensory hair cells in the ear. After these hair cells are damaged, the ability to hear is permanently diminished. Tinnitus , a medical term for ringing in the ears, can also occur. Some medications, such as high doses of aspirin or loop diuretics, can cause toxic effects to the sensory cells in the ear and lead to hearing loss or tinnitus. [16] , [17] In addition to hearing loss, ear problems can also cause problems with balance, dizziness, and vertigo due to vestibular dysfunction.
Kinesthetic Impairments
Kinesthetic impairments, such as peripheral neuropathy, affect the ability to feel sensations. Symptoms of peripheral neuropathy include sensations of pain, burning, tingling, and numbness in the extremities that decrease a person’s ability to feel touch, pressure, and vibration. Position sense can also be affected and makes it difficult to coordinate complex movements, such as walking, fastening buttons, or maintaining balance when one’s eyes are closed. Peripheral neuropathy is caused by nerve damage that commonly occurs in patients with diabetes mellitus or peripheral vascular disease. It can also be caused by physical injuries, infections, autoimmune diseases, vitamin deficiencies, kidney diseases, liver diseases, and some medications. [18]
Life Span Considerations
Impaired sensory functioning increases the risk for social isolation in older adults. For example, when individuals are not able to hear well, they may pretend to hear in an attempt to avoid embarrassment when asking for the information to be repeated. They may begin to avoid noisy environments or stop participating socially in conversations around them.
Infants and children are also at risk for vision and hearing impairments related to genetic or prenatal conditions. Early determination of sensory impairments is crucial so that problems can be addressed with accommodations to minimize the impact on a child’s development. For example, a screening hearing test is completed on all newborns before discharge to evaluate for hearing impairments that can affect their speech development.
Sensory Overload and Sensory Deprivation
Stimuli are continually received from a variety of sources in our environment and from within our bodies. When an individual receives too many stimuli or cannot selectively filter out meaningful stimuli, sensory overload can occur. Symptoms of sensory overload include irritability, restlessness, covering ears or eyes to shield them from sensory input, and increased sensitivity to tactile input (i.e., scratchy fabric or sensations of medical equipment). [19] Sensory overload affects an individual’s ability to interpret stimuli from their environment and can lead to confusion and agitation. See Figure 7.4 [20] of an image of a patient reacting to sensory overload.
The health care environment with its frequent noisy alarms, treatments, staff interruptions, and noisy hallway conversations can cause sensory overload for patients. Individuals have different tolerances for the amount of stimuli that will affect them adversely. Tolerance to stimuli is impacted by factors such as pain, stress levels, sleep patterns, physical health, and emotional health. When sensory overload occurs in a hospitalized patient, it can lead to delirium and acute confusion. It is important for the nurse to limit unnecessary awakenings and interactions with the health care team members when a patient is experiencing sensory overload.
Conversely, symptoms of sensory deprivation may occur when there are a lack of stimuli. People experiencing sensory deprivation often report perceptual disturbances such as hallucinations. Symptoms of sensory deprivation can mimic delirium, so it is important for a nurse to further investigate new perceptual disturbances. [21]
- This work is a derivative of StatPearls by Gadhvi & Waseem and is licensed under CC BY 4.0 ↵
- This work is a derivative of Sensory Processes by Lumen Learning and is licensed under CC BY-SA 4.0 ↵
- This work is a derivative of Sensory Processes by Lumen Learning and is licensed under CC BY-SA 4.0 ↵
- This work is a derivative of Sensory Processes by Lumen Learning and is licensed under CC BY-SA 4.0 ↵
- This work is a derivative of Sensory Processes by Lumen Learning and is licensed under CC BY-SA 4.0 ↵
- “ Pesto ingredients - blurred.jpg ” by Colin is licensed under CC BY-SA 4.0 ↵
- Correia, C., Lopez, K. J., Wroblewski, K. E., Huisingh-Scheetz, M., Kern, D. W., Chen, R. C., Schumm, L. P., Dale, W., McClintock, M. K., & Pinto, J. M. (2016). Global sensory impairment in older adults in the United States. Journal of the American Geriatrics Society, 64 (2), 306–313. https://doi.org/10.1111/jgs.13955 ↵
- Loh, K. Y., & Ogle, J. (2004). Age related visual impairment in the elderly. The Medical Journal of Malaysia, 59 (4), 562–569. https://pubmed.ncbi.nlm.nih.gov/15779599/ ↵
- Loh, K. Y., & Ogle, J. (2004). Age related visual impairment in the elderly. The Medical Journal of Malaysia, 59 (4), 562–569. https://pubmed.ncbi.nlm.nih.gov/15779599/ ↵
- Loh, K. Y., & Ogle, J. (2004). Age related visual impairment in the elderly. The Medical Journal of Malaysia, 59 (4), 562–569. https://pubmed.ncbi.nlm.nih.gov/15779599/ ↵
- Loh, K. Y., & Ogle, J. (2004). Age related visual impairment in the elderly. The Medical Journal of Malaysia, 59 (4), 562–569. https://pubmed.ncbi.nlm.nih.gov/15779599 / ↵
- Centers for Disease Control and Prevention. (2018, November 5). Watch out for diabetic retinopathy. https://www.cdc.gov/features/diabetic-retinopathy/index.html ↵
- Loh, K. Y., & Ogle, J. (2004). Age related visual impairment in the elderly. The Medical Journal of Malaysia, 59 (4), 562–569. https://pubmed.ncbi.nlm.nih.gov/15779599/ ↵
- National Institute on Deafness and Other Communication Disorders. (2018, July 17). Age-related hearing loss . https://www.nidcd.nih.gov/health/age-related-hearing-los s ↵
- " Traditional_hearing_aids.jpg ” by ikesters is licensed under CC BY-SA 2.0 ↵
- National Institute on Deafness and Other Communication Disorders. (2018, July 17). Age-related hearing loss . https://www.nidcd.nih.gov/health/age-related-hearing-loss ↵
- American Speech-Language-Hearing Association. (n.d.). Causes of hearing loss in adults . https://www.asha.org/public/hearing/causes-of-hearing-loss-in-adults/ ↵
- National Institute of Neurological Disorders and Stroke. (2020, March 16). Peripheral neuropathy fact shee t. https://www.ninds.nih.gov/Disorders/Patient-Caregiver-Education/Fact-Sheets/Peripheral-Neuropathy-Fact-Sheet ↵
- Watson, K. (2018, September 27). What is sensory overload? https://www.healthline.com/health/sensory-overload#causes ↵
- “ Sensory_Overload.jpg ” by Stewart Black is licensed under CC BY 2.0 ↵
- Mason, O., & Brady, F. (2009). The psychotomimetic effects of short-term sensory deprivation. The Journal of Nervous and Mental Disease, 197 (10), 783-785. https://doi.org/10.1097/nmd.0b013e3181b9760b ↵


2: Derivatives
The derivative of a function \(f\) is another function, \(f'\) , defined as \[f'(x) \;\equiv\; \frac{df}{dx} \;\equiv\; \lim_{\delta x \rightarrow 0} \, \frac{f(x + \delta x) - f(x)}{\delta x}.\] This kind of expression is called a limit expression because it involves a limit (in this case, the limit where \(\delta x\) goes to zero).
If the derivative exists within some domain of \(x\) (i.e., the above limit expression is mathematically well-defined), then we say \(f\) is differentiable in that domain. It can be shown that a differentiable function is automatically continuous.
Graphically, the derivative represents the slope of the graph of \(f(x)\) , as shown below:
If \(f\) is differentiable, we can define its second-order derivative \(f''\) as the derivative of \(f'\) . Third-order and higher-order derivatives are defined similarly.
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- 2.4: Partial Derivatives
- Functions can also take multiple inputs; for instance, a function f(x,y) maps two input numbers, x and y , and outputs a number. In general, the inputs are allowed to vary independently of one another. The partial derivative of such a function is its derivative with respect to one of its inputs, keeping the others fixed.


6.3C: Making Decisions
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Decision-making is the mental processes resulting in the selection of a course of action among several alternative scenarios.
Learning Objectives
- Describe three examples of voting which can be used to come to a decision
Key Points
- Groups face unique challenges in decision-making, and as a result there are various decision-making strategies used by groups.
- Consensus decision-making requires that a majority approve a given course of action, but that the minority agrees to go along with the course of action.
- When a consensus is impossible or impractical, voting can be used to come to a decision. Range voting, majority voting, and plurality voting are three examples of this type of decision-making.
- Group polarization refers to the tendency for groups to make decisions that are more extreme than the initial inclination of its members.
- Groupthink is the mode of thinking that happens when the desire for harmony in a decision-making group overrides a realistic appraisal of alternatives. Group members try to minimize conflict and reach a consensus decision without critical evaluation of alternative ideas or viewpoints.
- Groupthinking is the mode of thinking that happens when the desire for harmony in a decision-making group overrides a realistic appraisal of alternatives.
- Group polarization refers to the tendency for groups to make decisions that are more extreme than the initial inclination of its members.
Key Terms
- Consensus decision-making : It is a group decision making process that seeks the consent, not necessarily the agreement of participants and the resolution of objections.
- groupthink : A process of reasoning or decision making by a group, especially one characterized by uncritical acceptance or conformity to a perceived majority view.
- Group polarization : It refers to the tendency for groups to make decisions that are more extreme than the initial inclination of its members.
Decision-making is the mental process resulting in the selection of a course of action among several alternative scenarios. Every decision-making process produces a final choice. Group decision-making is the process used when individuals are brought together in a group to solve problems. According to the idea of synergy, decisions made collectively tend to be more effective than decisions made by a single individual. However, there are situations in which the decisions made by a collection of individuals are riddled with error, or poor judgment. For example, groups high in cohesion have been noted to have a negative effect on group decision making and hence on group effectiveness.
Formal Systems for Making Decisions
Consensus decision-making tries to avoid “winners” and “losers”. Consensus requires that a majority approve a given course of action, but that the minority agrees to go along with the course of action. In other words, if the minority opposes the course of action, consensus requires that the course of action be modified to remove objectionable features.
When a consensus is impossible, impractical, or undesirable, different voting systems can be used for a group to decide on an outcome. Three examples are range voting, majority voting, and plurality voting. Range voting lets each member score one or more of the available options. The option with the highest average is chosen. Majority voting requires support from more than 50% of the members of the group. Plurality voting is where the largest block in a group decides, even if it falls short of a majority.
Social Settings
Decision making in groups is sometimes examined separately as process and outcome. Groupthink is a psychological phenomenon that occurs within groups of people. It is the mode of thinking that happens when the desire for harmony in a decision-making group overrides a realistic appraisal of alternatives. Group members try to minimize conflict and reach a consensus decision without critical evaluation of alternative ideas or viewpoints.
Similarly, group polarization refers to the tendency for groups to make decisions that are more extreme than the initial inclination of its members. These more extreme decisions are towards greater risk if the individual’s initial tendency is to be risky and towards greater caution if individual’s initial tendency is to be cautious. In 2009, an interesting occurrence of group polarization was found in a study conducted by Luhan, Kocher, and Sutter, in which subjects played a ‘dictator game’. In this game, both individual and group decision-making was observed to see how individual preferences with respect to the allocation of money between a dictator and a recipient are transformed into a team decision. Their main finding was that team decisions were more selfish and competitive, less trusting and less altruistic than individual decisions. This study therefore offers evidence of group polarization, where the actions of individuals when in a group were more extreme than when the individual acted individually.


11.5: Free Soil or Slave? The Dilemma of the West
The 1848 treaty with Mexico did not bring the United States domestic peace. Instead, the acquisition of new territory revived and intensified the debate over the future of slavery in the western territories, widening the growing division between North and South and leading to the creation of new single-issue parties. Increasingly, the South came to regard itself as under attack by radical northern abolitionists, and many northerners began to speak ominously of a southern drive to dominate American politics for the purpose of protecting slaveholders’ human property. As tensions mounted and both sides hurled accusations, national unity frayed. Compromise became nearly impossible and antagonistic sectional rivalries replaced the idea of a unified, democratic republic.
THE LIBERTY PARTY, THE WILMOT PROVISO, AND THE ANTISLAVERY MOVEMENT
Committed to protecting white workers by keeping slavery out of the lands taken from Mexico, Pennsylvania congressman David Wilmot attached to an 1846 revenue bill an amendment that would prohibit slavery in the new territory. The Wilmot Proviso was not entirely new. Other congressmen had drafted similar legislation, and Wilmot’s language was largely copied from the 1787 Northwest Ordinance that had banned slavery in that territory. His ideas were very controversial in the 1840s, however, because his proposals would prevent American slaveholders from bringing what they viewed as their lawful property, their slaves, into the western lands. The measure passed the House but was defeated in the Senate. When Polk tried again to raise revenue the following year (to pay for lands taken from Mexico), the Wilmot Proviso was reintroduced, this time calling for the prohibition of slavery not only in the Mexican Cession but in all U.S. territories. The revenue bill passed, but without the proviso.
That Wilmot, a loyal Democrat, should attempt to counter the actions of a Democratic president hinted at the party divisions that were to come. The 1840s were a particularly active time in the creation and reorganization of political parties and constituencies, mainly because of discontent with the positions of the mainstream Whig and Democratic Parties in regard to slavery and its extension into the territories. The first new party, the small and politically weak Liberty Party founded in 1840, was a single-issue party, as were many of those that followed it. Its members were abolitionists who fervently believed slavery was evil and should be ended, and that this was best accomplished by political means.
The Wilmot Proviso captured the “antislavery” sentiments during and after the Mexican War. Antislavery advocates differed from the abolitionists. While abolitionists called for the end of slavery everywhere, antislavery advocates, for various reasons, did not challenge the presence of slavery in the states where it already existed. Those who supported antislavery fervently opposed its expansion westward because, they argued, slavery would degrade white labor and reduce its value, cast a stigma upon hard-working whites, and deprive them of a chance to advance economically. The western lands, they argued, should be open to white men only—small farmers and urban workers for whom the West held the promise of economic advancement. Where slavery was entrenched, according to antislavery advocates, there was little land left for small farmers to purchase, and such men could not compete fairly with slaveholders who held large farms and gangs of slaves.  When labor was associated with loss of freedom, antislavery supporters argued, all white workers carried a stigma that marked them as little better than slaves.
Wilmot opposed the extension of slavery into the Mexican Cession not because of his concern for African Americans, but because of his belief that slavery hurt white workers, and that lands acquired by the government should be used to better the position of white small farmers and laborers. Work was not simply something that people did; it gave them dignity, but in a slave society, labor had no dignity. In response to these arguments, southerners maintained that laborers in northern factories were treated worse than slaves. Their work was tedious and low paid. Their meager income was spent on inadequate food, clothing, and shelter.  In contrast, they argued, southern slaves were provided with a home, the necessities of life, and the protection of their masters. Factory owners did not care for or protect their employees in the same way.
THE FREE-SOIL PARTY AND THE ELECTION OF 1848
The Wilmot Proviso was an issue of great importance to the Democrats. Would they pledge to support it? At the party’s New York State convention in Buffalo, Martin Van Buren’s antislavery supporters—called Barnburners because they were likened to farmers who were willing to burn down their own barn to get rid of a rat infestation—spoke in favor of the proviso. Their opponents, known as Hunkers, refused to support it. Angered, the Barnburners organized their own convention, where they chose antislavery, pro–Wilmot Proviso delegates to send to the Democrats’ national convention in Baltimore. In this way, the controversy over the expansion of slavery divided the Democratic Party.
At the national convention, both sets of delegates were seated—the pro-proviso ones chosen by the Barnburners and the anti-proviso ones chosen by the Hunkers. When it came time to vote for the party’s presidential nominee, the majority of votes were for Lewis Cass, an advocate of popular sovereignty. Popular sovereignty was the belief that citizens should be able to decide issues based on the principle of majority rule; in this case, residents of a territory should have the right to decide whether slavery would be allowed in it. Theoretically, this doctrine would allow slavery to become established in any U.S. territory, including those from which it had been banned by earlier laws.
Disgusted by the result, the Barnburners united with antislavery Whigs and former members of the Liberty Party to form a new political party—the Free-Soil Party, which took as its slogan “Free Soil, Free Speech, Free Labor, and Free Men.” The party had one real goal—to oppose the extension of slavery into the territories (Figure 11.5.1). In the minds of its members and many other northerners of the time, southern slaveholders had marshaled their wealth and power to control national politics for the purpose of protecting the institution of slavery and extending it into the territories. Many in the Free-Soil Party believed in this far-reaching conspiracy of the slaveholding elite to control both foreign affairs and domestic policies for their own ends, a cabal that came to be known as the Slave Power.
In the wake of the Mexican War, antislavery sentiment entered mainstream American politics when the new Free-Soil party promptly selected Martin Van Buren as its presidential candidate. For the first time, a national political party committed itself to the goal of stopping the expansion of slavery. The Democrats chose Lewis Cass, and the Whigs nominated General Zachary Taylor, as Polk had assumed they would. On Election Day, Democrats split their votes between Van Buren and Cass. With the strength of the Democratic vote diluted, Taylor won. His popularity with the American people served him well, and his status as a slaveholder helped him win the South.
Visit the archives of the Gilder Lehrman Institute to read an August 1848 letter from Gerrit Smith, a staunch abolitionist, regarding the Free-Soil candidate, Martin Van Buren. Smith played a major role in the Liberty Party and was their presidential candidate in 1848.
THE COMPROMISE OF 1850
The election of 1848 did nothing to quell the controversy over whether slavery would advance into the Mexican Cession. Some slaveholders, like President Taylor, considered the question a moot point because the lands acquired from Mexico were far too dry for growing cotton and therefore, they thought, no slaveholder would want to move there. Other southerners, however, argued that the question was not whether slaveholders would want to move to the lands of the Mexican Cession, but whether they could and still retain control of their slave property. Denying them the right to freely relocate with their lawful property was, they maintained, unfair and unconstitutional. Northerners argued, just as fervidly, that because Mexico had abolished slavery, no slaves currently lived in the Mexican Cession, and to introduce slavery there would extend it to a new territory, thus furthering the institution and giving the Slave Power more control over the United States. The strong current of antislavery sentiment—that is, the desire to protect white labor—only increased the opposition to the expansion of slavery into the West.
Most northerners, except members of the Free-Soil Party, favored popular sovereignty for California and the New Mexico territory. Many southerners opposed this position, however, for they feared residents of these regions might choose to outlaw slavery. Some southern politicians spoke ominously of secession from the United States. Free-Soilers rejected popular sovereignty and demanded that slavery be permanently excluded from the territories.
Beginning in January 1850, Congress worked for eight months on a compromise that might quiet the growing sectional conflict. Led by the aged Henry Clay, members finally agreed to the following:
1. California, which was ready to enter the Union, was admitted as a free state in accordance with its state constitution.
2. Popular sovereignty was to determine the status of slavery in New Mexico and Utah, even though Utah and part of New Mexico were north of the Missouri Compromise line.
3. The slave trade was banned in the nation’s capital. Slavery, however, was allowed to remain.
4. Under a new fugitive slave law, those who helped runaway slaves or refused to assist in their return would be fined and possibly imprisoned.
5. The border between Texas and New Mexico was established.
The Compromise of 1850 brought temporary relief. It resolved the issue of slavery in the territories for the moment and prevented secession. The peace would not last, however. Instead of relieving tensions between North and South, it had actually made them worse.
Section Summary
The acquisition of lands from Mexico in 1848 reawakened debates regarding slavery. The suggestion that slavery be barred from the Mexican Cession caused rancorous debate between North and South and split the Democratic Party when many northern members left to create the Free-Soil Party. Although the Compromise of 1850 resolved the question of whether slavery would be allowed in the new territories, the solution pleased no one. The peace brought by the compromise was short-lived, and the debate over slavery continued.
Review Questions
The practice of allowing residents of territories to decide whether their land should be slave or free was called ________.
the democratic process
the Wilmot Proviso
popular sovereignty
the Free Soil solution
C
Which of the following was not a provision of the Compromise of 1850?
California was admitted as a free state.
Slavery was abolished in Washington, DC.
A stronger fugitive slave law was passed.
Residents of New Mexico and Utah were to decide for themselves whether their territories would be slave or free.
B
Describe the events leading up to the formation of the Free-Soil Party.
At the party’s national convention in 1848, the majority of Democrats voted for a candidate who supported popular sovereignty. A faction of the party was dismayed by this outcome; they opposed popular sovereignty and wanted to restrict the expansion of slavery in order to protect the value of white workers’ labor. They united with antislavery Whigs and former members of the Liberty Party to form a new political party—the Free-Soil Party—which had one goal, to oppose the extension of slavery into the territories.
Critical Thinking Questions
Consider the role of filibusters in American expansion. What are some arguments in favor of filibustering? What are some arguments against it?
What are the economic and political issues raised by having an imbalance between free and slave states? Why did the balance of free and slave states matter?
How did Anglo-American settlers in Texas see themselves? Did they adopt a Mexican identity because they were living in Mexican territory? Why or why not?
Consider the annexation of Texas and the Mexican-American War from a Mexican perspective. What would you find objectionable about American actions, foreign policy, and attitudes in the 1840s?
Describe the place of Texas in the history of American westward expansion by comparing Texas’s early history to the Missouri Crisis in 1819–1820. What are the similarities and what are the differences?
Consider the arguments over the expansion of slavery made by both northerners and southerners in the aftermath of the U.S. victory over Mexico. Who had the more compelling case? Or did each side make equally significant arguments?
Glossary
- Barnburners
- northern Democrats loyal to Martin Van Buren who opposed the extension of slavery into the territories and broke away from the main party when it nominated a pro-popular sovereignty candidate
- Compromise of 1850
- five separate laws passed by Congress in September 1850 to resolve issues stemming from the Mexican Cession and the sectional crisis
- Free-Soil Party
- a political party that sought to exclude slavery from the western territories, leaving these areas open for settlement by white farmers and ensuring that white laborers would not have to compete with slaves
- Liberty Party
- a political party formed in 1840 by those who believed political measures were the best means by which abolition could be accomplished
- Slave Power
- a term northerners used to describe the disproportionate influence that they felt elite southern slaveholders wielded in both domestic and international affairs
- Wilmot Proviso
- an amendment to a revenue bill that would have barred slavery from all the territory acquired from Mexico


36.5: Review of the Male Reproductive System
By the end of this section, you should be able to:
- 36.5.1 Describe the structure and function of the male reproductive system.
- 36.5.2 Discuss common conditions that affect the male reproductive system.
Structure and Function of the Male Reproductive System
The male reproductive system (also referred to as the testicular reproductive system ) is made up of internal and external organs (see Figure 36.5). The external organs include the scrotum, testes, epididymis, and penis. The internal organs are the vas deferens, prostate gland, ejaculatory ducts, seminal vesicles, bulbourethral (Cowper’s) glands, and urethra (Betts et al., 2023; Netter, 2022).
The scrotum is a loose, sac-like cavity that holds the testicles and provides a controlled temperature for them since temperature within the scrotum is lower than in the body itself. The testicles produce sperm, which fertilize an egg from a female. The epididymis carries the formed sperm into the vas deferens, which then empties the sperm into the ejaculatory duct in the body of the prostate gland. Two seminal vesicles, one on each side of the prostate, also empty into the ejaculatory duct. From the ejaculatory duct, the sperm enter the urethra. The bulbourethral (Cowper’s) glands secrete mucus into the urethra, and both the mucus and sperm are carried outside the body through the urethra.  Contractions of the penis allow the sperm, along with other secretions, to empty outside the body. The primary target would be the uterus where the sperm fertilizes the egg, creating the embryo that implants into the uterus and further develops into the fetus (Betts et al., 2023; Netter, 2022). (Refer to Section 36.1.)
Hormones
Some of the same hormones that are produced in individuals assigned female at birth are also produced in those assigned males at birth, and those include GnRH and the gonadotropins, LH and FSH. As discussed in Review of the Female Reproductive System, GnRH is produced in the hypothalamus. When GnRH is secreted, it acts on the anterior pituitary to secrete FSH and LH, which regulate sex steroid production from the gonads. In males, the gonads are the testes (ovaries in females) which produce testosterone (also considered an androgen).  Additionally, testosterone can self-limit its own secretion through the negative feedback loop. When levels of testosterone are high, feedback to the hypothalamus inhibits the secretion of GnRH. Negative feedback to the anterior pituitary renders it less responsive to GnRH stimuli (Casteel & Singh, 2023; Nassar, 2023).
Andropause
Andropause occurs with aging and represents a time of decreased production of testosterone, atrophy of interstitial cells, and lessened sexual activity. Andropause is comparable to female menopause. The decrease of testosterone can produce depression, fat redistribution, and decreased libido. Not all male clients experience andropause.
Link to Learning
What is “male menopause”? An expert breaks down everything clients need to know about andropause in this Daily Mail video.


6.5: An Example of a Polar Reaction - Addition of HBr to Ethylene
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Objectives
After completing this section, you should be able to
- give an example of a simple polar reaction (e.g., a electrophilic addition).
- identify the electrophile and nucleophile in a simple polar reaction.
Key Terms
Make certain that you can define, and use in context, the key terms below.
- electrophilic addition
- carbocation
Study Notes
The curved arrows introduced in this section are used throughout the course to indicate the movement of electron pairs. It takes practice for the beginning student to feel comfortable using these arrows. Remember that the head of the arrow indicates where the electron pair moves to; its tail shows where the electron pair comes from. (Chemists often refer to the use of curved arrows as “electron pushing.")
This page looks at the reaction of the carbon-carbon double bond in alkenes such as ethene with hydrogen halides such as hydrogen chloride and hydrogen bromide. Symmetrical alkenes (like ethene or but-2-ene) are dealt with first. These are alkenes where identical groups are attached to each end of the carbon-carbon double bond.
Addition to symmetrical alkenes
All alkenes undergo addition reactions with the hydrogen halides. A hydrogen atom joins to one of the carbon atoms originally in the double bond, and a halogen atom to the other. For example, with ethene and hydrogen chloride, you get chloroethane:
With but-2-ene you get 2-chlorobutane:
What happens if you add the hydrogen to the carbon atom at the right-hand end of the double bond, and the chlorine to the left-hand end? You would still have the same product. The chlorine would be on a carbon atom next to the end of the chain - you would simply have drawn the molecule flipped over in space. That would be different of the alkene was unsymmetrical - that's why we have to look at them separately.
Mechanism
The addition of hydrogen halides is one of the easiest electrophilic addition reactions because it uses the simplest electrophile: the proton. Hydrogen halides provide both an electrophile (proton) and a nucleophile (halide). First, the electrophile will attack the double bond and take up a set o f pi elec trons, attaching it to the molecule (1). This is basically the reverse of the last step in the E1 reaction (deprotonation step). The resulting molecule will have a single carbon-carbon bond with a positive charge on one of them (carbocation). The next step is when the nucleophile (halide) bonds to the carbocation, producing a new molecule with both the original hydrogen and halide attached to the organic reactant (2). The second step will only occur if a good nucleophile is used.
Mechanism of Electrophilic Addition of Hydrogen Halide to Ethene
Mechanism of Electrophilic Addition of Hydrogen Halide to Propene
All of the halides (HBr, HCl, HI, HF) can participate in this reaction and add on in the same manner. Although different halides do have different rates of reaction, due to the H-X bond getting weaker as X gets larger (poor overlap of orbitals)s.
Reaction rates
Reaction rates increase in the order HF - HCl - HBr - HI. Hydrogen fluoride reacts much more slowly than the other three, and is normally ignored in talking about these reactions. When the hydrogen halides react with alkenes, the hydrogen-halogen bond has to be broken. The bond strength falls as you go from HF to HI, and the hydrogen-fluorine bond is particularly strong. Because it is difficult to break the bond between the hydrogen and the fluorine, the addition of HF is bound to be slow.
This applies to unsymmetrical alkenes as well as to symmetrical ones. For simplicity the examples given below are all symmetrical ones- but they don't have to be. Reaction rates increase as the alkene gets more complicated - in the sense of the number of alkyl groups (such as methyl groups) attached to the carbon atoms at either end of the double bond. For example:
There are two ways of looking at the reasons for this - both of which need you to know about the mechanism for the reactions.
Alkenes react because the electrons in the pi bond attract things with any degree of positive charge. Anything which increases the electron density around the double bond will help this. Alkyl groups have a tendency to "push" electrons away from themselves towards the double bond. The more alkyl groups you have, the more negative the area around the double bonds becomes.
The more negatively charged that region becomes, the more it will attract molecules like hydrogen chloride. The more important reason, though, lies in the stability of the intermediate ion formed during the reaction. The three examples given above produce these carbocations (carbonium ions) at the half-way stage of the reaction:
The stability of the intermediate ions governs the activation energy for the reaction. As you go towards the more complicated alkenes, the activation energy for the reaction falls. That means that the reactions become faster.
Addition to unsymmetrical alkenes
In terms of reaction conditions and the factors affecting the rates of the reaction, there is no difference whatsoever between these alkenes and the symmetrical ones described above. The problem comes with the orientation of the addition - in other words, which way around the hydrogen and the halogen add across the double bond.
If HCl adds to an unsymmetrical alkene like propene, there are two possible ways it could add. However, in practice, there is only one major product.
This is in line with Markovnikov's Rule which says:
When a compound HX is added to an unsymmetrical alkene, the hydrogen becomes attached to the carbon with the most hydrogens attached to it already.
In this case, the hydrogen becomes attached to the CH 2 group, because the CH 2 group has more hydrogens than the CH group. Notice that only the hydrogens directly attached to the carbon atoms at either end of the double bond count. The ones in the CH 3 group are totally irrelevant.
Exercise \(\PageIndex{1}\)
Supply the missing curved arrows in the equations given below.
- Answer
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Exercise \(\PageIndex{2}\)
Predict the product of the following reactions :
- Answer
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<IP_ADDRESS>: Data as Sources
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Data as Sources
Using data as sources can help with all of your research project’s information needs:- Learn more background information.
- Answer your research question. (The evidence that data provide can help you decide on the best answer for your question.)
- Convince your audience that your answer is correct. (Data often give you ecidence that your answer that your answer is correct. (Data often give you evidence that your answer to your research question is correct or at least a reasonable answer.)
- Describe the situation surrounding your research question.
- Report what others have said about your research question.
Activity: Example of Data
Check out this very detailed data about frozen lasagna. Did you ever think this much data was available? Are there elements new to you? How might you use such data?
Movie: Reinterpreting Little Red Riding Hood
An interactive or media element has been excluded from this version of the text. You can view it online here: https://ohiostate.pressbooks.pub/choosingsources/?p=843
What is data? The word means many things to many people. (Consider “data” as it relates to your phone contract, for instance!) For our purposes, a definition we like is “units of information observed, collected, or created in the course of research.”
Erway, Ricky. 2013. Starting the Conversation: University-wide Research Data Management Policy. Dublin, Ohio: OCLC Research.
http://www.oclc.org/content/dam/rese...13/2013-08.pdf
Data observed, collected, or cerated for research purposes can be numbers , text , images , audio clips , and video clips . But in this section on using data as sources, we’re going to concentrate on numerical data.
Data is the plural of datum. (It’s similar to how media is the plural of medium.)
Sometimes data is actually necessary to answer research questions, particularly in the social sciences and life and physical sciences. For instance, data would be necessary to support or rule out these hypotheses:
- More women than men voted in the last presidential election in a majority of states.
- A certain drugs shows promising results in the treatment of pancreatic cancer.
- Listening to certain genres of music lowers blood pressure.
- People of certain religious denominations are more likely to find a specific television program objectionable.
- The average weight of house cats in the United States has increased over the past 30 years.
- The average square footage of supermarkets in the United States has increased in the past 20 years.
- More tomatoes were consumed per person in the United Kingdom in 2015 than in 1962.
- Exploding volcanoes can help cool the planet by spewing sulfur dioxide, which combines with water vapor to make reflective aerosols.
So using numeric data in those portions of your final product that require evidence can really strengthen your argument for your argument for your answer to your research question. At other times, even if data is not actually necessary, numeric data can be particularly persuasive and sharpen the points you want to make in other portions of your final product devoted to, say, describing the situation surrounding your research question. (See Making an Argument)
For example, for a term paper about the research question “Why is there a gap in the number of people who qualify for food from foodbanks and the number of people who use foodbanks?,” you could find data on the website of Feeding America, the nation’s largest network of foodbanks. Some of that data may be the number of people who get food from a foodbank annually, with the number of seniors and children broken out. Those data won’t answer your research question, but they will help you describe the situation around that question and help your audience develop a fuller understanding.
Similarly, for a project with the research question “How do some birds in Australia use “smart” hunting techniques to flush out prey, including starting fires?,” you might find a journal article with data about how many people have observed these techniques and estimates of how frequently the techniques are used and by how many bird species.
Obtaining Data
There are two ways of obtaining data:
- Obtain data that already has been collected and analyzed. That’s what this section will cover.
- Collect data yourself. This can include activities such as making observations about your environment, conducting surveys or interviews, directly recording measurements in a lab or in the field, or even receiving electronic data recorded by computers/machines that gather the data. You will explore these activities in courses you take.
Finding Data in Articles, Books, Web Pages, and More
Numeric search data can be found all over the place. A lot of it can be found as part of another source- such as books; journal, newspaper, and magazine articles; and web pages. In these cases, the data do not stand alone as a distinct element, but instead are part of the larger work.
When searching for data in books and articles and on web pages, terms such as statistics or data may or may not be useful search terms. That’s because many writers don’t use those terms in their scholarly writing. They tend to use the words findings or results when talking about the data that could be useful to you. In addition, statistics is a separate discipline and using that term will turn up lots of journals in that area, which won’t be helpful to you. So use the search terms data and statistics with caution, especially when searching library catalogs. (See information on the Library Catalog . More information on searching is at Precision Searching .)
Even without using those search terms, many scholarly sources you turn up are likely to contain data. Once you find potential sources, skim them for tables, graphs, or charts. These items are displays or illustrations of data gathered by researchers. However, sometimes data and interpretations are solely in the body of the narrative text and may be included in sections called “Results” or “Findings.” (That shouldn’t keep you from displaying the data in charts, graphs, or tables as you like in your own work, though. See Data Visualization later in this section.)
If the data you find in a book, article, or web page is particularly helpful and you want more, you could contact the author to request additional numeric research data. Researchers will often discuss their data and its analysis – and sometimes provide some of it (or occasionally, all). Some may link to a larger numeric research data set. However, if a researcher shares his or her data with you, it may be in a raw form. This means that you might have to do additional analysis to make it useful in answering your question.
Depending on your research question, you may need to gather data from multiple sources to get everything you need to answer your research question and make your argument for it. (See Making an Argument.)
For instance, in our example related to foodbanks above, we suggested where you could find statistics about the number of people who get food from American foodbanks. But with that research question (“Why is there a gap in the number of people who qualify for food from foodbanks and the number of people who use foodbanks?”), you would also need to find out from another source how many people qualify for foodbanks based on their income and compare that number with how many people actually use foodbanks.
Finding Data, Data Depositories, and Directories
Sometimes the numeric research data you need may not be in the articles, books, and web sites that you’ve found. But that doesn’t mean that it hasn’t been collected and packaged in a useable format. Governments and research institutions often publish data they have collected in discipline-specific data depositories that make data available online. Here are some examples:
- United States Census Bureau
- Budget of the United States Government
- U.S. Bureau of Justice Statistics
- National Center for Education Statistics
- Daily Weather Maps NOAA)
- GeoData.gov
- The World Factbook (CIA)
- OSU Knowledge Bank
The United Nations and just about every country provide information as numeric data available online. Free and accessible data like this is called open data. The U.S. federal government, all states, and many local governments provide open data. You can find them (among other places) at site: .gov.
Other data are available through vendors who publish the data collected by researchers. Here are some examples:
- Hoover’s Online (OSU Only)
- International Monetary Fund Statistical Databases
- World Health Organization Statistical Information System
- Envirofacts
- Census of Agriculture (OSU only)
- OECD Education at a Glance
- Corruption Perceptions Index
Don’t know if a depository that could contain data in your discipline? Check out a data directory such as re3data.org
Evaluating Data as Sources
Evaluating data for relevance and credibility is just as important as evaluating any other source. Another thing that is the same with data is that there is never a 100% perfect source. So just as is pointed out in Evaluating Sources, you’ll have to make educated guesses (inferences) about whether the data are good enough for your purpose.
Critical thinking as you evaluate sources is something your professors will expect. But you’ll benefit in other ways, too, because you’ll be practicing a skill necessary for the rest of your life, both in the workplace and in your personal life.
To evaluate data, you’ll need to find out how the data were collected. If the data are in another source, such as a book; web page; or newspaper, magazine, or research journal article, evaluate that source in the usual way (see Evaluating Sources). If the book or newspaper, magazine, or web page got the data from somewhere else, do the same evaluation of the source from which the book or article got the data. The article, book, or web page should cite where the data came from. If it doesn’t, then that is a black mark against using that data. (The data in a research journal article are often the work of the authors of the article. But you’ll want to be sure they provide information about how they collected the data.)
In addition, if the data are in a research journal article , read the entire article, including the section called Methodology, which tells how the data were collected. Then determine the data’s relevance to your research question by considering such questions as:
- Were the data collected recently enough?
- Is the data cross-sectional (based on information from people at any one time) or longitudinal (based on information from the same people over time)? If one is more appropriate for your research question than the other, is there information that you can still logically infer from this data?
- Were the types of people from whom the data were collected the same type of people your research question addresses? The more representative the study’s sample is of the group your research question addresses, the more confident you can be in using the data to make your argument in your final product.
- Was the data analysis done at the right level for your research question? For instance, it may have been done at the individual, family, business, state, or zip code level. But if that doesn’t relate to your research question, can you still logically make inferences that will help your argument? Here’s an example: Imagine that your research question asks whether participation in high school sports in Columbus City Schools is positively associated with enrolling in college. But the data you are evaluating is analyzed at the state level. So you have data about the whole state of Ohio’s schools and not Columbus in particular. In this case, ask yourself whether there is still any inference you can make from the data.
Research articles are sometimes difficult to read until you get used to them. Here’s a helpful PDF: violentmetaphors.files.wordp...-article.pdfTo evaluate the credibility of the data in a research journal article you have already read, take the steps recommended in Evaluating Sources, plus consider these questions:
- Is the article in a peer reviewed journal? (Look at the journal’s instructions for authors, which are often located on the journal’s website, to see if it talks about peers reviewing the article and asking for changes [revisions] before publishing.) If it is a peer reviewed journal, consider that a plus for the article’s credibility. Being peer reviewed doesn’t mean it’s perfect; just more likely to be credible.
- Do the authors discuss causation or correlation? Be wary of claims of causation; it is very difficult to determine a causal effect. While research studies often find relationships (correlation) between various variables in the data, this does not equal causation. For instance, let’s return to our example above: If the study of Ohio high schools students’ sports participation showed a positive correlation between sports participation and college enrollment, the researcher cannot say that participation caused college enrollment. If it were designed to show cause and effect, the study would not have resulted in a correlation. Instead, it would have had to have been designed as an experiment or quasi-experiment, used different statistical analyses, and would have supported or not supported its hypotheses.
Data Visualization
Modern software can help you display your data in ways that are striking and often even beautiful. But the best criterion for judging whatever display you use is whether it helps you and your audience understand your data better than only text, maybe even noticing points that you would have otherwise missed.
Specific kinds of charts and graphs accomplish different things, which is important to keep in mind as you evaluate data and data sources. For instance:
- Line charts are usually used to show trends, comparing data over time.
- Scatter plots show the distribution of data points.
- Bar graphs usually compare categories of data.
- Pie charts show proportions of a whole.
It’s important to decide what you want a display to do before making your final choice. Studying your data first so you know what you have will help you make that decision. Also, it may also be conventional in your discipline to display your data in certain ways. Examining the sources you were assigned to read in your course or asking your professor will help you learn what’s considered conventional.
Your professors will be examining your visual display to make sure you did not misrepresent the data. For example, the proportions of slices in a pie chart all have to add up to 100%. If yours don’t, you’ve done something wrong.
It’s easy to get overwhelmed by all the choices to be made between potential displays and what each can do: Here are two sites to help you sort them out once you know your data :
If you aren’t ready yet to use some of the specialized tools for display, make it a point to learn how to use the data display capabilities in Microsoft Word and/or Excel. You can find helpful tutorials on the Web. Good search statements to find those tutorials are:
- “Microsoft Word” (charts OR graphs)
- “Microsoft Excel” (charts OR graphs).
If you are OSU staff, students, or faculty, OSU Libraries’ Research Commons can help you choose a display, recommend a tool to accomplish it, and check out your finished data visualization before you have to turn it in. Contact the data visualization specialist.
If you are interested in displaying geospatial data on a map, consider how the Research Commons also helps OSU students, staff, and faculty find geospatial data and choose tools to display them.
Citing Data
Data is not copyrightable, but the expression of data is. So as with any other information source, you should cite any data you use from a source, whether it appeared in an article or you downloaded the data from a repository on the Web.
Unfortunately, data citation standards do not exist in many disciplines, although the DataCite initiative is working on them. Current workarounds include:
- Citing a “data paper,” where available.
- Citing a journal article that describes the dataset.
- Citing a book that includes the data.
- Citing the dataset as a website, where possible.
Examples: Citing Data
Data from a research database:
- APA: Department of Agriculture (USDA) (2008). “Crops Harvested”, Crop Production [data file]. Data Planet, (09/15/2009).
- MLA: “Crops Harvested”, Department of Agriculture (USDA) [data file] (2008). Data Planet, (09/15/2009).
Data from a file found on the open Web:
- APA: Center for Health Statistics, Washington State Department of Health. (2012, November). Mortality Table D1. Age-Adjusted Rates for Leading Causes of Cancer for Residents, 2002-2011. [Microsoft Excel file]. Washington State Department of Health. Retrieved from http://www.doh.wa.gov/
- MLA: Center for Health Statistics, Washington State Department of Health. Mortality Table D1. Age-Adjusted Rates for Leading Causes of Cancer for Residents, 2002-2011. Washington State Department of Health, Nov. 2012. Microsoft Excel file. Retrieved from http://www.doh.wa.gov/
Proper Use of Data
Once you have your data, you can examine them and make an interpretation. Sometimes, you can do so easily. But not always.
What if…
…you had a lot of information? Sometimes data can be very complicated and may include thousands (or millions…or billions…or more!) of data points. Suppose you only have a date and the high temperature for Columbus – but you have this for 20 years’ worth of days. Do you want to calculate the average highs for each month based upon 20 years’ worth of data by hand or even with a calculator?
…you want to be able to prove a relationship? Perhaps your theory is that social sciences students do better in a certain class than arts and humanities or life and physical science students. You may have a huge spreadsheet of data from 20 years’ worth of this course’s sections and would need to use statistical methods to see if a relationship between major and course grade exist.
You may find yourself using special software, such as Excel, SAS, and SPSS, in such situations.
Many people may have a tendency to look for data to prove their hypothesis or idea, as opposed to really answering their research questions. However, you may find that the opposite happens: the data may actually disprove your hypothesis. You should never try to manipulate data so that it gives credence to your desired outcome. While it may not be the answer you wanted to find, it is the answer that exists. You may, of course, look for other sources of data – perhaps there are multiple sources of data for the same topic with differing results. Inconclusive or conflicting findings do happen and can be the answer (even if it’s not the one you wanted!).
Conflicting results on the same topic are common. This is the reality of research because, after all, the questions researchers are studying are complicated. When you have conflicting results you can’t just ignore the differences—you’ll have to do your best to explain why the differences occurred.


1.24.3: Uninstalling Applications
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When you install an app, including the ones that come by default in Windows 10, it takes up storage space on your computer or mobile device. If space becomes limited or you just don’t use an app anymore, you can uninstall it to free up storage space.
You can uninstall Windows Store Applications from the Start menu by navigating to the application, right-clicking on the application, and selecting uninstall. After uninstallation is complete, Windows will notify you.
Other older programs may be uninstalled by visiting the Control Panel, clicking on “Programs” and “Uninstall Program”. Follow the directions on the screen to complete this process.


11: Magnetic Forces and Fields
For the past few chapters, we have been studying electrostatic forces and fields, which are caused by electric charges at rest. These electric fields can move other free charges, such as producing a current in a circuit; however, the electrostatic forces and fields themselves come from other static charges. In this chapter, we see that when an electric charge moves, it generates other forces and fields. These additional forces and fields are what we commonly call magnetism.
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- 11.1: Prelude to Magnetic Forces and Fields
- Before we examine the origins of magnetism, we first describe what it is and how magnetic fields behave. Once we are more familiar with magnetic effects, we can explain how they arise from the behavior of atoms and molecules, and how magnetism is related to electricity. The connection between electricity and magnetism is fascinating from a theoretical point of view, but it is also immensely practical, as shown by an industrial electromagnet that can lift thousands of pounds of metal.
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- 11.2: Magnetism and Its Historical Discoveries
- Magnetism has been known since the time of the ancient Greeks, but it has always been a bit mysterious. You can see electricity in the flash of a lightning bolt, but when a compass needle points to magnetic north, you can’t see any force causing it to rotate. People learned about magnetic properties gradually, over many years, before several physicists of the nineteenth century connected magnetism with electricity.
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- 11.3: Magnetic Fields and Lines
- Even though there are no such things as isolated magnetic charges, we can still define the attraction and repulsion of magnets as based on a field. In this section, we define the magnetic field, determine its direction based on the right-hand rule, and discuss how to draw magnetic field lines.
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- 11.4: Motion of a Charged Particle in a Magnetic Field
- A charged particle experiences a force when moving through a magnetic field. What happens if this field is uniform over the motion of the charged particle? What path does the particle follow? In this section, we discuss the circular motion of the charged particle as well as other motion that results from a charged particle entering a magnetic field.
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- 11.5: Magnetic Force on a Current-Carrying Conductor
- Moving charges experience a force in a magnetic field. If these moving charges are in a wire—that is, if the wire is carrying a current—the wire should also experience a force. However, before we discuss the force exerted on a current by a magnetic field, we first examine the magnetic field generated by an electric current. We are studying two separate effects here that interact closely: A current-carrying wire generates a magnetic field and the magnetic field exerts a force on the wire.
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- 11.6: Force and Torque on a Current Loop
- Motors are the most common application of magnetic force on current-carrying wires. Motors contain loops of wire in a magnetic field. When current is passed through the loops, the magnetic field exerts torque on the loops, which rotates a shaft. Electrical energy is converted into mechanical work in the process.
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- 11.8: Applications of Magnetic Forces and Fields
- Being able to manipulate and sort charged particles allows deeper experimentation to understand what matter is made of. We first look at a mass spectrometer to see how we can separate ions by their charge-to-mass ratio. Then we discuss cyclotrons as a method to accelerate charges to very high energies.