1.16: Risk Management Planning
Even the most carefully planned project can run into trouble. No matter how well you plan, your project can always encounter unexpected problems. Team members get sick or quit, resources that you were depending on turn out to be unavailable, even the weather can throw you for a loop (e.g., a snowstorm). So does that mean that you’re helpless against unknown problems? No! You can use risk planning to identify potential problems that could cause trouble for your project, analyze how likely they are to occur, take action to prevent the risks you can avoid, and minimize the ones that you can’t.
A risk is any uncertain event or condition that might affect your project. Not all risks are negative. Some events (like finding an easier way to do an activity) or conditions (like lower prices for certain materials) can help your project. When this happens, we call it an opportunity; but it’s still handled just like a risk.
There are no guarantees on any project. Even the simplest activity can turn into unexpected problems. Anything that might occur to change the outcome of a project activity, we call that a risk. A risk can be an event (like a snowstorm) or it can be a condition (like an important part being unavailable). Either way, it’s something that may or may not happen …but if it does, then it will force you to change the way you and your team work on the project.
If your project requires that you stand on the edge of a cliff, then there’s a risk that you could fall. If it’s very windy out or if the ground is slippery and uneven, then falling is more likely (Figure 16.1).
When you’re planning your project, risks are still uncertain: they haven’t happened yet. But eventually, some of the risks that you plan for do happen, and that’s when you have to deal with them.
- Avoid: The best thing you can do with a risk is avoid it. If you can prevent it from happening, it definitely won’t hurt your project. The easiest way to avoid this risk is to walk away from the cliff, but that may not be an option on this project.
- Mitigate: If you can’t avoid the risk, you can mitigate it. This means taking some sort of action that will cause it to do as little damage to your project as possible.
- Transfer: One effective way to deal with a risk is to pay someone else to accept it for you. The most common way to do this is to buy insurance.
- Accept: When you can’t avoid, mitigate, or transfer a risk, then you have to accept it. But even when you accept a risk, at least you’ve looked at the alternatives and you know what will happen if it occurs. If you can’t avoid the risk, and there’s nothing you can do to reduce its impact, then accepting it is your only choice.
By the time a risk actually occurs on your project, it’s too late to do anything about it. That’s why you need to plan for risks from the beginning and keep coming back to do more planning throughout the project.
The risk management plan tells you how you’re going to handle risk in your project. It documents how you’ll assess risk, who is responsible for doing it, and how often you’ll do risk planning (since you’ll have to meet about risk planning with your team throughout the project).
Some risks are technical, like a component that might turn out to be difficult to use. Others are external, like changes in the market or even problems with the weather.
It’s important to come up with guidelines to help you figure out how big a risk’s potential impact could be. The impact tells you how much damage the risk would cause to your project. Many projects classify impact on a scale from minimal to severe, or from very low to very high. Your risk management plan should give you a scale to help figure out the probability of the risk. Some risks are very likely; others aren’t.
Risk Management Process
Managing risks on projects is a process that includes risk assessment and a mitigation strategy for those risks. Risk assessment includes both the identification of potential risk and the evaluation of the potential impact of the risk. A risk mitigation plan is designed to eliminate or minimize the impact of the risk events —occurrences that have a negative impact on the project. Identifying risk is both a creative and a disciplined process. The creative process includes brainstorming sessions where the team is asked to create a list of everything that could go wrong. All ideas are welcome at this stage with the evaluation of the ideas coming later.
Risk Identification
A more disciplined process involves using checklists of potential risks and evaluating the likelihood that those events might happen on the project. Some companies and industries develop risk checklists based on experience from past projects. These checklists can be helpful to the project manager and project team in identifying both specific risks on the checklist and expanding the thinking of the team. The past experience of the project team, project experience within the company, and experts in the industry can be valuable resources for identifying potential risk on a project.
Identifying the sources of risk by category is another method for exploring potential risk on a project. Some examples of categories for potential risks include the following:
- Technical
- Cost
- Schedule
- Client
- Contractual
- Weather
- Financial
- Political
- Environmental
- People
You can use the same framework as the work breakdown structure (WBS) for developing a risk breakdown structure (RBS) . A risk breakdown structure organizes the risks that have been identified into categories using a table with increasing levels of detail to the right. The people category can be subdivided into different types of risks associated with the people. Examples of people risks include the risk of not finding people with the skills needed to execute the project or the sudden unavailability of key people on the project.
Example: Risks in John’s Move
In John’s move, John makes a list of things that might go wrong with his project and uses his work breakdown structure as a guide. A partial list for the planning portion of the RBS is shown in Table 16.1.
| Task | Risk |
|---|---|
| Contact Dion and Carlita |
|
| Host planning lunch |
|
| Develop and distribute schedule |
|
The result is a clearer understanding of where risks are most concentrated. This approach helps the project team identify known risks, but can be restrictive and less creative in identifying unknown risks and risks not easily found inside the WBS.
Risk Evaluation
After the potential risks have been identified, the project team then evaluates each risk based on the probability that a risk event will occur and the potential loss associated with it. Not all risks are equal. Some risk events are more likely to happen than others, and the cost of a risk can vary greatly. Evaluating the risk for probability of occurrence and the severity or the potential loss to the project is the next step in the risk management process.
Having criteria to determine high-impact risks can help narrow the focus on a few critical risks that require mitigation. For example, suppose high-impact risks are those that could increase the project costs by 5% of the conceptual budget or 2% of the detailed budget. Only a few potential risk events meet these criteria. These are the critical few potential risk events that the project management team should focus on when developing a project risk mitigation or management plan. Risk evaluation is about developing an understanding of which potential risks have the greatest possibility of occurring and can have the greatest negative impact on the project (Figure 16.2). These become the critical few.
There is a positive correlation—both increase or decrease together—between project risk and project complexity. A project with new and emerging technology will have a high-complexity rating and a correspondingly high risk. The project management team will assign the appropriate resources to the technology managers to ensure the accomplishment of project goals. The more complex the technology, the more resources the technology manager typically needs to meet project goals, and each of those resources could face unexpected problems.
Risk evaluation often occurs in a workshop setting. Building on the identification of the risks, each risk event is analyzed to determine the likelihood of occurrence and the potential cost if it did occur. The likelihood and impact are both rated as high, medium, or low. A risk mitigation plan addresses the items that have high ratings on both factors—likelihood and impact.
Example: Risk Analysis of Equipment Delivery
A project team analyzed the risk of some important equipment not arriving at the project on time. The team identified three pieces of equipment that were critical to the project and would significantly increase costs if they were late in arriving. One of the vendors, who was selected to deliver an important piece of equipment, had a history of being late on other projects. The vendor was good and often took on more work than it could deliver on time. This risk event (the identified equipment arriving late) was rated as high likelihood with a high impact. The other two pieces of equipment were potentially a high impact on the project but with a low probability of occurring.
Not all project managers conduct a formal risk assessment on a project. One reason, as found by David Parker and Alison Mobey in their phenomenological study of project managers, was a low understanding of the tools and benefits of a structured analysis of project risks (2004). The lack of formal risk management tools was also seen as a barrier to implementing a risk management program. Additionally, the project manager’s personality and management style play into risk preparation levels. Some project managers are more proactive and develop elaborate risk management programs for their projects. Other managers are reactive and are more confident in their ability to handle unexpected events when they occur. Yet others are risk averse, and prefer to be optimistic and not consider risks or avoid taking risks whenever possible.
On projects with a low-complexity profile, the project manager may informally track items that may be considered risk items. On more complex projects, the project management team may develop a list of items perceived to be higher risk and track them during project reviews. On projects of even greater complexity, the process for evaluating risk is more formal with a risk assessment meeting or series of meetings during the life of the project to assess risks at different phases of the project. On highly complex projects, an outside expert may be included in the risk assessment process, and the risk assessment plan may take a more prominent place in the project implementation plan.
On complex projects, statistical models are sometimes used to evaluate risk because there are too many different possible combinations of risks to calculate them one at a time. One example of the statistical model used on projects is the Monte Carlo simulation, which simulates a possible range of outcomes by trying many different combinations of risks based on their likelihood. The output from a Monte Carlo simulation provides the project team with the probability of an event occurring within a range and for combinations of events. For example, the typical output from a Monte Carlo simulation may indicate a 10% chance that one of the three important pieces of equipment will be late and that the weather will also be unusually bad after the equipment arrives.
Risk Mitigation
After the risk has been identified and evaluated, the project team develops a risk mitigation plan, which is a plan to reduce the impact of an unexpected event. The project team mitigates risks in various ways:
- Risk avoidance
- Risk sharing
- Risk reduction
- Risk transfer
Each of these mitigation techniques can be an effective tool in reducing individual risks and the risk profile of the project. The risk mitigation plan captures the risk mitigation approach for each identified risk event and the actions the project management team will take to reduce or eliminate the risk.
Risk avoidance usually involves developing an alternative strategy that has a higher probability of success but usually at a higher cost associated with accomplishing a project task. A common risk avoidance technique is to use proven and existing technologies rather than adopt new techniques, even though the new techniques may show promise of better performance or lower costs. A project team may choose a vendor with a proven track record over a new vendor that is providing significant price incentives to avoid the risk of working with a new vendor. The project team that requires drug testing for team members is practising risk avoidance by avoiding damage done by someone under the influence of drugs.
Risk sharing involves partnering with others to share responsibility for the risky activities. Many organizations that work on international projects will reduce political, legal, labour, and others risk types associated with international projects by developing a joint venture with a company located in that country. Partnering with another company to share the risk associated with a portion of the project is advantageous when the other company has expertise and experience the project team does not have. If a risk event does occur, then the partnering company absorbs some or all of the negative impact of the event. The company will also derive some of the profit or benefit gained by a successful project.
Risk reduction is an investment of funds to reduce the risk on a project. On international projects, companies will often purchase the guarantee of a currency rate to reduce the risk associated with fluctuations in the currency exchange rate. A project manager may hire an expert to review the technical plans or the cost estimate on a project to increase the confidence in that plan and reduce the project risk. Assigning highly skilled project personnel to manage the high-risk activities is another risk-reduction method. Experts managing a high-risk activity can often predict problems and find solutions that prevent the activities from having a negative impact on the project. Some companies reduce risk by forbidding key executives or technology experts to ride on the same airplane.
Risk transfer is a risk reduction method that shifts the risk from the project to another party. The purchase of insurance on certain items is a risk-transfer method. The risk is transferred from the project to the insurance company. A construction project in the Caribbean may purchase hurricane insurance that would cover the cost of a hurricane damaging the construction site. The purchase of insurance is usually in areas outside the control of the project team. Weather, political unrest, and labour strikes are examples of events that can significantly impact the project and that are outside the control of the project team.
Contingency Plan
The project risk plan balances the investment of the mitigation against the benefit for the project. The project team often develops an alternative method for accomplishing a project goal when a risk event has been identified that may frustrate the accomplishment of that goal. These plans are called contingency plans. The risk of a truck drivers’ strike may be mitigated with a contingency plan that uses a train to transport the needed equipment for the project. If a critical piece of equipment is late, the impact on the schedule can be mitigated by making changes to the schedule to accommodate a late equipment delivery.
Contingency funds are funds set aside by the project team to address unforeseen events that cause the project costs to increase. Projects with a high-risk profile will typically have a large contingency budget. Although the amount of contingency allocated in the project budget is a function of the risks identified in the risk analysis process, contingency is typically managed as one line item in the project budget.
Some project managers allocate the contingency budget to the items in the budget that have high risk rather than developing one line item in the budget for contingencies. This approach allows the project team to track the use of contingency against the risk plan. This approach also allocates the responsibility to manage the risk budget to the managers responsible for those line items. The availability of contingency funds in the line item budget may also increase the use of contingency funds to solve problems rather than finding alternative, less costly solutions. Most project managers, especially on more complex projects, manage contingency funds at the project level, with approval of the project manager required before contingency funds can be used.
Project Risk by Phases
Project risk is dealt with in different ways depending on the phase of the project.
Initiation
Risk is associated with things that are unknown. More things are unknown at the beginning of a project, but risk must be considered in the initiation phase and weighed against the potential benefit of the project’s success in order to decide if the project should be chosen.
Example: Risks by Phase in John’s Move
In the initiation phase of his move, John considers the risk of events that could affect the whole project. Lets assume that John’s move is not just about changing jobs, but also a change of cities. This would certainly incur more risks for the project . He identifies the following risks during the initiation phase that might have a high impact and rates the likelihood of their happening from low to high.
- His new employer might change his mind and take back the job offer after he’s given notice at his old job: Low.
- The current tenants of his apartment might not move out in time for him to move in by the first day of work at the new job: Medium.
- The movers might lose his furniture: Low.
- The movers might be more than a week late delivering his furniture: Medium.
- He might get in an accident driving from Chicago to Atlanta and miss starting his job: Low.
John considers how to mitigate each of the risks.
- During his job hunt, John had more than one offer, and he is confident that he could get another job, but he might lose deposit money on the apartment and the mover. He would also lose wages during the time it took to find the other job. To mitigate the risk of his new employer changing his mind, John makes sure that he keeps his relationships with his alternate employers cordial and writes to each of them thanking for their consideration in his recent interviews.
- John checks the market in Atlanta to determine the weekly cost and availability of extended-stay motels.
- John checks the mover’s contract to confirm that they carry insurance against lost items, but they require the owner to provide a detailed list with value estimates and they limit the maximum total value. John decides to go through his apartment with his digital camera and take pictures of all of his possessions that will be shipped by truck and to keep the camera with him during the move so he has a visual record and won’t have to rely on his memory to make a list. He seals and numbers the boxes so he can tell if a box is missing.
- If the movers are late, John can use his research on extended-stay motels to calculate how much it would cost. He checks the moving company’s contract to see if they compensate the owner for late delivery, and he finds that they do not.
- John checks the estimated driving time from Chicago to Atlanta using an Internet mapping service and gets an estimate of 11 hours of driving time. He decides that it would be too risky to attempt to make the drive by himself in one day, especially if he didn’t leave until after the truck was packed. John plans to spend one night on the road in a motel to reduce the risk of an accident caused by driving while too tired.
John concludes that the medium-risks can be mitigated and the costs from the mitigation would be acceptable in order to get a new job.
Planning Phase
Once the project is approved and it moves into the planning stage, risks are identified with each major group of activities. A risk breakdown structure (RBS) can be used to identify increasing levels of detailed risk analysis.
Example: Risk Breakdown Structure for John’s Move
John decides to ask Dion and Carlita for their help during their first planning meeting to identify risks, rate their impact and likelihood, and suggest mitigation plans. They concentrate on the packing phase of the move. They fill out a table of risks, as shown in Table 16.2.
Legend:
- RA: Risk avoidance
- RS: Risk sharing
- RR: Risk reduction
- RT: Risk transfer
| Task | Risks | Mitigation |
|---|---|---|
| Pack kitchen | Cuts from handling sharp knives | Buy small boxes for packing knives (RR) |
| Cuts from cracked glasses that break while being packed | Discard cracked glasses (RA) | |
| Transporting alcoholic beverages | Give opened bottles to Dion or Carlita (RA) | |
| Packing living room | Damage to antique furniture | Supervise wrapping and loading personally (RR) and require movers to insure against damage (RT) |
| Lose parts while talking apart the entertainment centre | Buy box of large freezer bags with a marker to bag and label parts (RR) | |
| Break most valuable electronics—TV, DVD, Tuner, Speakers | Buy boxes of the right size with sufficient bubble wrap (RR) | |
| Pack bedroom | Break large mirror | Buy or rent a mirror-box with Styrofoam blocks at each corner (RR) |
| Lose prescription drugs or pack them where they cannot be found quickly | Separate prescription drugs for transportation in the car (RA) | |
| Pack remaining items | Damage to house plants | Ask Carlita to care for them and bring them with her in her van when she visits in exchange for half of them (RS) |
| Transportation of flammable liquids from charcoal grill | Give to Dion or Carlita (RA) |
Implementation Phase
As the project progresses and more information becomes available to the project team, the total risk on the project typically reduces, as activities are performed without loss. The risk plan needs to be updated with new information and risks checked off that are related to activities that have been performed.
Understanding where the risks occur on the project is important information for managing the contingency budget and managing cash reserves. Most organizations develop a plan for financing the project from existing organizational resources, including financing the project through a variety of financial instruments. In most cases, there is a cost to the organization to keep these funds available to the project, including the contingency budget. As the risks decrease over the length of the project, if the contingency is not used, then the funds set aside by the organization can be used for other purposes.
To determine the amount of contingency that can be released, the project team will conduct another risk evaluation and determine the amount of risk remaining on the project. If the risk profile is lower, the project team may release contingency funds back to the parent organization. If additional risks are uncovered, a new mitigation plan is developed including the possible addition of contingency funds.
Closeout Phase
During the closeout phase, agreements for risk sharing and risk transfer need to be concluded and the risk breakdown structure examined to be sure all the risk events have been avoided or mitigated. The final estimate of loss due to risk can be made and recorded as part of the project documentation. If a Monte Carlo simulation was done, the result can be compared to the predicted result.
Example: Risk Closeout on John’s Move
To close out the risk mitigation plan for his move, John examines the risk breakdown structure and risk mitigation plan for items that need to be finalized. He makes a checklist to be sure all the risk mitigation plans are completed, as shown in Table 16.3. Risk is not allocated evenly over the life of the project. On projects with a high degree of new technology, the majority of the risks may be in the early phases of the project. On projects with a large equipment budget, the largest amount of risk may be during the procurement of the equipment. On global projects with a large amount of political risk, the highest portion of risk may be toward the end of the project.
| Risk | Mitigation | Closeout |
|---|---|---|
| Items lost by movers | Mover’s insurance plus digital image inventory | Confirm all of the numbered boxes are present and still sealed. |
| Antique furniture damaged | Mover’s insurance plus personal supervision of wrapping and loading | Supervise unloading and unwrapping; visually inspect each piece. |
| House plants | Ask Carlita to bring half of them in her van when she visits. | Confirm that the plants are healthy and that Carlita brought about half of them. |
References
Parker, D., & Mobey, A. (2004). Action Research to Explore Perceptions of Risk in Project Management. International Journal of Productivity and Performance Management 53( 1), 18–32.
Attribution
This chapter of Project Management is a derivative of the following text:
- Project Management for Instructional Designers by Wiley, et al. © CC BY-NC-SA (Attribution-NonCommercial-ShareAlike)
Media Attributions
- Risk Management Options by Barron & Barron Project Management for Scientists and Engineers © CC BY (Attribution)
- Risk and Impact by Wiley, et al. © CC BY-NC-SA (Attribution NonCommercial ShareAlike)


3.6: Where?
Where do early childhood programs take place?
In Chapter 6 (Curriculum) and Chapter 7 (Learning Environments), you will be introduced to different types of programs, which sometimes determines where they occur. For now, here is a list of the most common places for young children to develop and grow:
- The child’s home - this is often a child’s first classroom and many important skills are developed here
- Someone else’s home - often-called home daycare or family childcare, there are a variety of types of programs that are run inside caregivers' homes.
- A church, synagogue, or similar establishment - often built for their own programs that take place on the weekends, these are empty during the week and can accommodate multiple uses. Programs operating in such locations may or may not be affiliated with the establishment that owns the building.
- A school setting - either specifically designed for the age group served or modified to meet the needs of various ages.
- A park or community center – some community spaces are dedicated to serving children in a variety of ways.
- Online - synchronously (at the same time) or asynchronously (at different times independently)
“In my practicum class, I was surprised to learn about all of the different places we could train. I thought a school setting was the only place, but there were so many wonderful options.
COVID 19 meant that our in-person program needed to be moved to an online format. Some teachers got really creative with Zoom, Google Classroom, video chats, and other technology. One of my colleagues started with show and tell where she had each child in the class take a turn sharing whatever they wanted about their home. We saw bedrooms, favorite toys and met so many pets and family members. It was a wonderful way to connect!
Interviewing different places I learned that it is not the building but what goes on inside and outside that makes the magic happen.”
Where do I go to get more involved?
The resources above in the “When” section are a great place to get started. Ask your instructor if you would like to inquire further.


2.1: Legal and Ethical Introduction
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- Ernstmeyer & Christman (Eds.)
- Chippewa Valley Technical College via OpenRN
Learning Objectives
- Identify drug administration guidelines within the State Nurse Practice Act
- Identify nursing responsibilities to prevent and respond to medication errors
- Identify nursing responsibilities associated with controlled substances
- Identify ethical responsibilities as they relate to medication errors
- Explain how nursing response reflects respect for a patient’s rights and responsibilities with drug therapy
- Outline nursing actions within the scope of nursing practice as they relate to the administration of medication
- Demonstrate patient-centered care during medication administration by respecting a patient’s gender and psychosocial and cultural needs
- Identify nursing responsibilities associated with safe medication administration
- Identify nursing responsibilities associated with patient medication education
Medication administration is an essential task nurses perform while providing patient care. However, safe medication administration is more than just a nursing task; it is a process involving several members of the health care team, as well as legal, ethical, social, and cultural issues. The primary focus of effective medication administration by all health professionals is patient safety. Although many measures have been put into place over the past few decades to promote improved patient safety, medication errors, and adverse effects continue to be a common event. The World Health Organization (WHO) estimates, “Unsafe medication practices and medication errors are a leading cause of injury and avoidable harm in health care systems across the world. Globally, the cost associated with medication errors has been estimated at $42 billion USD annually.” [1] This chapter will examine the legal and ethical foundations of medication administration by nurses, as well as the practice standards and cultural and social issues that must be considered to ensure safe and effective administration of medication.
- World Health Organization. (2019). Patient safety. https://www.who.int/patientsafety/medication-safety/en/ . ↵


3.5: Elderly Criminals
An aging population in general coupled with mandatory sentencing laws has caused an explosion in the number. This is an expensive proposition for the American correctional system. A substantial reason for this increased cost is the increased medical attention people tend to require as they grow older. Prisons that rely on prison industry to subsidize the cost of operations find that elderly inmates are less able to work than their younger counterparts. There is also the fear that younger inmates will prey on elderly ones. This phenomenon has caused the federal prison system and many state systems to rethink the policies that contribute to this "graying" of correctional populations.
Substantial growth has also been seen in the number of inmates that are ill. Arthritis and hypertension are the most commonly reported chronic conditions among inmates, but more serious and less easily treated maladies are also common. Many larger jails and prisons have special sections devoted to inmates with medical problems. In addition to the normal security staff, these units must employ medical staff. Recruiting medical staff that are willing to work in confinement with inmates is a constant problem for administrators.
According to many critics of mental health in America, the number of mentally ill inmates has reached crisis level. There has been explosive growth in the incarceration of mentally ill persons since the deinstitutionalization movement of the 1960s.  This problem was exacerbated at the federal level by the passage of the Community Mental Health Act of 1963, which substantially reduced funding of mental health hospitals. With state hospitals gone or severely restricted, communities had to deal with the issue of what to do with mentally ill persons. Most communities responded with the poor solution of criminalizing the mentally ill.


1.1: Lab 1- Anatomical Language
Measurable Outcomes
- Understand what the standard anatomical position is.
- Correctly identify a given plane by its correct name.
- Relate different structures of the body using the directional terms provided.
- Correctly identify the anatomical regions of the body.
- Demonstrate how to properly focus histology slides and identify key structures.
- Demonstrate an adequate understand of the material in this section.
Background
A solid foundation is essential when learning any new skill. Understanding anatomical directions, articulations, planes, and regions are the foundation for learning anatomy.
The standard anatomical position of the human body is facing towards the observer, legs hip-width apart, feet facing forward, arms out slightly at either side with palms facing forward. When determining a structure’s relative position, be sure to use this frame of reference. For example, it can be easy to confuse which side is the anterior aspect of the hands, therefore, one might incorrectly assume that the thumb is medial to the little finger. Remember, the anterior aspect of the hand is the palm, therefore the thumb is furthest from the center of the body and is lateral.
The archetypal body planes are frontal, sagittal and transverse planes. The frontal plane splits the body into anterior and posterior halves. The sagittal plane splits the body into left and right halves. The transverse plane splits the body into superior and inferior (top and bottom) halves. It is important to be able to identify a given plane so that you can orient yourself when a specimen, model or diagram is depicted a certain way. This same reasoning applies to the necessity of understanding directional terms such as anterior, inferior, distal and medial. It is recommended that you read the content prior to attending lab to make the most of your time.
Vocabulary for Anatomical Language on page(s) 160-161.


17.5: Using Spectra to Measure Stellar Radius, Composition, and Motion
By the end of this section, you will be able to:
- Understand how astronomers can learn about a star’s radius and composition by studying its spectrum
- Explain how astronomers can measure the motion and rotation of a star using the Doppler effect
- Describe the proper motion of a star and how it relates to a star’s space velocity
Analyzing the spectrum of a star can teach us all kinds of things in addition to its temperature. We can measure its detailed chemical composition as well as the pressure in its atmosphere. From the pressure, we get clues about its size. We can also measure its motion toward or away from us and estimate its rotation.
Clues to the Size of a Star
As we shall see in The Stars: A Celestial Census, stars come in a wide variety of sizes. At some periods in their lives, stars can expand to enormous dimensions. Stars of such exaggerated size are called giants . Luckily for the astronomer, stellar spectra can be used to distinguish giants from run-of-the-mill stars (such as our Sun).
 A giant star has a large, extended photosphere. Because it is so large, a giant star’s atoms are spread over a great volume, which means that the density of particles in the star’s photosphere is low. As a result, the pressure in a giant star’s photosphere is also low. This low pressure affects the spectrum in two ways. First, a star with a lower-pressure photosphere shows narrower spectral lines than a star of the same temperature with a higher-pressure photosphere (Figure 17.9). The difference is large enough that careful study of spectra can tell which of two stars at the same temperature has a higher pressure (and is thus more compressed) and which has a lower pressure (and thus must be extended). This effect is due to collisions between particles in the star’s photosphere—more collisions lead to broader spectral lines. Collisions will, of course, be more frequent in a higher-density environment. Think about it like traffic—collisions are much more likely during rush hour, when the density of cars is high.
Second, more atoms are ionized in a giant star than in a star like the Sun with the same temperature. The ionization of atoms in a star’s outer layers is caused mainly by photons, and the amount of energy carried by photons is determined by temperature. But how long atoms stay ionized depends in part on pressure. Compared with what happens in the Sun (with its relatively dense photosphere), ionized atoms in a giant star’s photosphere are less likely to pass close enough to electrons to interact and combine with one or more of them, thereby becoming neutral again. Ionized atoms, as we discussed earlier, have different spectra from atoms that are neutral.
Abundances of the Elements
Absorption lines of a majority of the known chemical elements have now been identified in the spectra of the Sun and stars. If we see lines of iron in a star’s spectrum, for example, then we know immediately that the star must contain iron.
Note that the absence of an element’s spectral lines does not necessarily mean that the element itself is absent. As we saw, the temperature and pressure in a star’s atmosphere will determine what types of atoms are able to produce absorption lines. Only if the physical conditions in a star’s photosphere are such that lines of an element should (according to calculations) be there can we conclude that the absence of observable spectral lines implies low abundance of the element.
Suppose two stars have identical temperatures and pressures, but the lines of, say, sodium are stronger in one than in the other. Stronger lines mean that there are more atoms in the stellar photosphere absorbing light. Therefore, we know immediately that the star with stronger sodium lines contains more sodium. Complex calculations are required to determine exactly how much more, but those calculations can be done for any element observed in any star with any temperature and pressure.
Of course, astronomy textbooks such as ours always make these things sound a bit easier than they really are. If you look at the stellar spectra such as those in Figure 17.6, you may get some feeling for how hard it is to decode all of the information contained in the thousands of absorption lines. First of all, it has taken many years of careful laboratory work on Earth to determine the precise wavelengths at which hot gases of each element have their spectral lines. Long books and computer databases have been compiled to show the lines of each element that can be seen at each temperature. Second, stellar spectra usually have many lines from a number of elements, and we must be careful to sort them out correctly. Sometimes nature is unhelpful, and lines of different elements have identical wavelengths, thereby adding to the confusion. And third, as we saw in the chapter on Radiation and Spectra, the motion of the star can change the observed wavelength of each of the lines. So, the observed wavelengths may not match laboratory measurements exactly. In practice, analyzing stellar spectra is a demanding, sometimes frustrating task that requires both training and skill.
Studies of stellar spectra have shown that hydrogen makes up about three-quarters of the mass of most stars. Helium is the second-most abundant element, making up almost a quarter of a star’s mass. Together, hydrogen and helium make up from 96 to 99% of the mass; in some stars, they amount to more than 99.9%. Among the 4% or less of “heavy elements,” oxygen, carbon, neon, iron, nitrogen, silicon, magnesium, and sulfur are among the most abundant. Generally, but not invariably, the elements of lower atomic weight are more abundant than those of higher atomic weight.
Take a careful look at the list of elements in the preceding paragraph. Two of the most abundant are hydrogen and oxygen (which make up water); add carbon and nitrogen and you are starting to write the prescription for the chemistry of an astronomy student. We are made of elements that are common in the universe—just mixed together in a far more sophisticated form (and a much cooler environment) than in a star.
As we mentioned in The Spectra of Stars (and Brown Dwarfs) section, astronomers use the term “metals” to refer to all elements heavier than hydrogen and helium. The fraction of a star’s mass that is composed of these elements is referred to as the star’s metallicity . The metallicity of the Sun, for example, is 0.02, since 2% of the Sun’s mass is made of elements heavier than helium.
Appendix K lists how common each element is in the universe (compared to hydrogen); these estimates are based primarily on investigation of the Sun, which is a typical star. Some very rare elements, however, have not been detected in the Sun. Estimates of the amounts of these elements in the universe are based on laboratory measurements of their abundance in primitive meteorites, which are considered representative of unaltered material condensed from the solar nebula (see the Cosmic Samples and the Origin of the Solar System chapter).
Radial Velocity
When we measure the spectrum of a star, we determine the wavelength of each of its lines. If the star is not moving with respect to the Sun, then the wavelength corresponding to each element will be the same as those we measure in a laboratory here on Earth. But if stars are moving toward or away from us, we must consider the Doppler effect (see The Doppler Effect section). We should see all the spectral lines of moving stars shifted toward the red end of the spectrum if the star is moving away from us, or toward the blue (violet) end if it is moving toward us (Figure 17.10). The greater the shift, the faster the star is moving. Such motion, along the line of sight between the star and the observer, is called radial velocity and is usually measured in kilometers per second.
William Huggins , pioneering yet again, in 1868 made the first radial velocity determination of a star. He observed the Doppler shift in one of the hydrogen lines in the spectrum of Sirius and found that this star is moving toward the solar system. (Better measurements now indicate that Sirius is actually moving away, but Huggins is still celebrated as a pioneer in making such measurements.) Today, radial velocity can be measured for any star bright enough for its spectrum to be observed. As we will see in The Stars: A Celestial Census, radial velocity measurements of double stars are crucial in deriving stellar masses.
In the Spectrum Constructor , you can add absorption lines to the spectrum. Then adjust the velocity; negative indicates the star is moving toward the observer, and positive indicates it is moving away. Explore how the absorption lines are seen to shift to shorter and longer wavelengths.
Proper Motion
There is another type of motion stars can have that cannot be detected with stellar spectra. Unlike radial motion, which is along our line of sight (i.e., toward or away from Earth), this motion, called proper motion , is transverse : that is, across our line of sight. We see it as a change in the relative positions of the stars on the celestial sphere (Figure 17.11). These changes are very slow. Even the star with the largest proper motion takes 200 years to change its position in the sky by an amount equal to the width of the full Moon, and the motions of other stars are smaller yet.
For this reason, with our naked eyes, we do not notice any change in the positions of the bright stars during the course of a human lifetime. If we could live long enough, however, the changes would become obvious. For example, some 50,000 years from now, terrestrial observers will find the handle of the Big Dipper unmistakably more bent than it is now (Figure 17.12).
We measure the proper motion of a star in arcseconds (1/3600 of a degree) per year. That is, the measurement of proper motion tells us only by how much of an angle a star has changed its position on the celestial sphere. If two stars at different distances are moving at the same velocity perpendicular to our line of sight, the closer one will show a larger shift in its position on the celestial sphere in a year’s time. As an analogy, imagine you are standing at the side of a freeway. Cars will appear to whiz past you. If you then watch the traffic from a vantage point half a mile away, the cars will move much more slowly across your field of vision. In order to convert this angular motion to a velocity, we need to know how far away the star is.
To know the true space velocity of a star—that is, its total speed and the direction in which it is moving through space relative to the Sun—we must know its radial velocity, proper motion, and distance (Figure 17.13). A star’s space velocity can also, over time, cause its distance from the Sun to change significantly. Over several hundred thousand years, these changes can be large enough to affect the apparent brightnesses of nearby stars. Today, Sirius , in the constellation Canis Major (the Big Dog) is the brightest star in the sky, but 100,000 years ago, the star Canopus in the constellation Carina (the Keel) was the brightest one. A little over 200,000 years from now, Sirius will have moved away and faded somewhat, and Vega , the bright blue star in Lyra, will take over its place of honor as the brightest star in Earth’s skies.
Rotation
We can also use the Doppler effect to measure how fast a star rotates. If an object is rotating, then one of its sides is approaching us while the other is receding (unless its axis of rotation happens to be pointed exactly toward us). This is clearly the case for the Sun or a planet; we can observe the light from either the approaching or receding edge of these nearby objects and directly measure the Doppler shifts that arise from the rotation.
Stars, however, are so far away that they all appear as unresolved points. The best we can do is to analyze the light from the entire star at once. Due to the Doppler effect, the lines in the light that come from the side of the star rotating toward us are shifted to shorter wavelengths and the lines in the light from the opposite edge of the star are shifted to longer wavelengths. You can think of each spectral line that we observe as the sum or composite of spectral lines originating from different speeds with respect to us. Each point on the star has its own Doppler shift, so the absorption line we see from the whole star is actually much wider than it would be if the star were not rotating. If a star is rotating rapidly, there will be a greater spread of Doppler shifts and all its spectral lines should be quite broad. In fact, astronomers call this effect line broadening , and the amount of broadening can tell us the speed at which the star rotates (Figure 17.14).
Measurements of the widths of spectral lines show that many stars rotate faster than the Sun, some with periods of less than a day! These rapid rotators spin so fast that their shapes are “flattened” into what we call oblate spheroids . An example of this is the star Vega , which rotates once every 12.5 hours. Vega’s rotation flattens its shape so much that its diameter at the equator is 23% wider than its diameter at the poles (Figure 17.15). The Sun, with its rotation period of about a month, rotates rather slowly. Studies have shown that stars decrease their rotational speed as they age. Young stars rotate very quickly, with rotational periods of days or less. Very old stars can have rotation periods of several months.
As you can see, spectroscopy is an extremely powerful technique that helps us learn all kinds of information about stars that we simply could not gather any other way. We will see in later chapters that these same techniques can also teach us about galaxies, which are the most distant objects that can we observe. Without spectroscopy, we would know next to nothing about the universe beyond the solar system.
Throughout the history of astronomy, contributions from wealthy patrons of the science have made an enormous difference in building new instruments and carrying out long-term research projects. Edward Pickering’s stellar classification project, which was to stretch over several decades, was made possible by major donations from Anna Draper . She was the widow of Henry Draper, a physician who was one of the most accomplished amateur astronomers of the nineteenth century and the first person to successfully photograph the spectrum of a star. Anna Draper gave several hundred thousand dollars to Harvard Observatory. As a result, the great spectroscopic survey is still known as the Henry Draper Memorial, and many stars are still referred to by their “HD” numbers in that catalog (such as HD 209458).
In the 1870s, the eccentric piano builder and real estate magnate James Lick (Figure 17.16) decided to leave some of his fortune to build the world’s largest telescope. When, in 1887, the pier to house the telescope was finished, Lick’s body was entombed in it. Atop the foundation rose a 36-inch refractor, which for many years was the main instrument at the Lick Observatory near San Jose.
The Lick telescope remained the largest in the world until 1897, when George Ellery Hale persuaded railroad millionaire Charles Yerkes to finance the construction of a 40-inch telescope near Chicago. More recently, Howard Keck, whose family made its fortune in the oil industry, gave $70 million from his family foundation to the California Institute of Technology to help build the world’s largest telescope atop the 14,000-foot peak of Maunakea in Hawaii (see the chapter on Astronomical Instruments to learn more about these telescopes). The Keck Foundation was so pleased with what is now called the Keck telescope that they gave $74 million more to build Keck II, another 10-meter reflector on the same volcanic peak.
Now, if any of you become millionaires or billionaires, and astronomy has sparked your interest, do keep an astronomical instrument or project in mind as you plan your estate. But frankly, private philanthropy could not possibly support the full enterprise of scientific research in astronomy. Much of our exploration of the universe is financed by federal agencies such as the National Science Foundation and NASA in the United States, and by similar government agencies in the other countries. In this way, all of us, through a very small share of our tax dollars, are philanthropists for astronomy.


<IP_ADDRESS>: The Purpose of Academic Argument
The Purpose of Academic Argument
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Nearly all scholarly writing makes an argument. That’s because its purpose is to create and share new knowledge so it can be debated in order to confirm, dis-confirm, or improve it. That arguing takes place mostly in journals and scholarly books and at conferences. It’s called the scholarly conversation, and it’s that conversation that moves forward what we humans know.
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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=1046
Your scholarly writing for classes should do the same—make an argument—just like your professors’ journal article, scholarly book, and conference presentation writing does. (You may not have realized that the writing you’re required to do mirrors what scholars all over the university, country, and world must do to create new knowledge and debate it. Of course, you may be a beginner at constructing arguments in writing, while most professors have been at it for some time. And your audience (for now) also may be more limited than your professor’s. But the process is much the same.
Making an argument means trying to convince others that you are correct as you describe a thing, situation, relationship, or phenomenon and/or persuade them to take a particular action. Important not just in college, that skill will be necessary for nearly every professional job you hold after college. So learning how to make an argument is good job preparation, even if you do not choose a scholarly career.
Realizing that your final product for your research project is to make an argument gives you a big head start because right off you know the sources you’re going to need are those that will let you write the components of an argument for your reader.
Happily (and not coincidentally), most of those components coincide with the information needs we’ve been talking about. Meeting an information need by using sources will enable you to write the corresponding argument component in your final product.


13.3: Simple Random Samples and Statistics
Simple Random Samples and Statistics
We formulate the notion of a (simple) random sample , which is basic to much of classical statistics. Once formulated, we may apply probability theory to exhibit several basic ideas of statistical analysis.
We begin with the notion of a population distribution . A population may be most any collection of individuals or entities. Associated with each member is a quantity or a feature that can be assigned a number. The quantity varies throughout the population. The population distribution is the distribution of that quantity among the members of the population.
If each member could be observed, the population distribution could be determined completely. However, that is not always feasible. In order to obtain information about the population distribution, we select “at random” a subset of the population and observe how the quantity varies over the sample. Hopefully, the sample distribution will give a useful approximation to the population distribution.
The sampling process
We take a sample of size \(n\), which means we select n members of the population and observe the quantity associated with each. The selection is done in such a manner that on any trial each member is equally likely to be selected. Also, the sampling is done in such a way that the result of any one selection does not affect, and is not affected by, the others. It appears that we are describing a composite trial. We model the sampling process as follows:
Let \(X_i\), \(1 \le i \le n\) be the random variable for the i th component trial. Then the class \(\{X_i: 1 \le i \le n\}\) is iid, with each member having the population distribution.
This provides a model for sampling either from a very large population (often referred to as an infinite population) or sampling with replacement from a small population.
The goal is to determine as much as possible about the character of the population. Two important parameters are the mean and the variance. We want the population mean and the population variance. If the sample is representative of the population, then the sample mean and the sample variance should approximate the population quantities.
- The sampling process is the iid class \(\{X_i: 1 \le i \le n\}\).
- A random sample is an observation, or realization, \((t_1, t_2, \cdot\cdot\cdot, t_n)\) of the sampling process.
The sample average and the population mean
Consider the numerical average of the values in the sample \(\bar{x} = \dfrac{1}{n} \sum_{i = 1}^{n} t_i\). This is an observation of the sample average
\(A_n = \dfrac{1}{n} \sum_{i = 1}^{n} X_i = \dfrac{1}{n} S_n\)
The sample sum \(S_n\) and the sample average \(A_n\) are random variables. If another observation were made (another sample taken), the observed value of these quantities would probably be different. Now \(S_n\) and \(A_n\) are functions of the random variables \(\{X_i: 1 \le i \le n\}\) in the sampling process. As such, they have distributions related to the population distribution (the common distribution of the \(X_i\)). According to the central limit theorem, for any reasonable sized sample they should be approximately normally distributed. As the examples demonstrating the central limit theorem show, the sample size need not be large in many cases. Now if the population mean \(E[X]\) is \(\mu\) and the population variance \(\text{Var} [X]\) is \(\sigma^2\), then
\(E[S_n] = \sum_{i = 1}^{n} E[X_i] = nE[X] = n\mu\) and \(\text{Var}[S_n] = \sum_{i = 1}^{n} \text{Var} [X_i] = n \text{Var} [X] = n \sigma^2\)
so that
\(E[A_n] = \dfrac{1}{n} E[S_n] = \mu\) and \(\text{Var}[A_n] = \dfrac{1}{n^2} \text{Var} [S_n] = \sigma^2/n\)
Herein lies the key to the usefulness of a large sample. The mean of the sample average \(A_n\) is the same as the population mean, but the variance of the sample average is \(1/n\) times the population variance. Thus, for large enough sample, the probability is high that the observed value of the sample average will be close to the population mean . The population standard deviation, as a measure of the variation is reduced by a factor \(1/\sqrt{n}\).
Example \(\PageIndex{1}\) Sample size
Suppose a population has mean \(\mu\) and variance \(\sigma^2\). A sample of size \(n\) is to be taken. There are complementary questions:
- If \(n\) is given, what is the probability the sample average lies within distance a from the population mean?
- What value of \(n\) is required to ensure a probability of at least p that the sample average lies within distance a from the population mean?
Solution
Suppose the sample variance is known or can be approximated reasonably. If the sample size \(n\) is reasonably large, depending on the population distribution (as seen in the previous demonstrations), then \(A_n\) is approximately \(N(\mu, \sigma^2/n)\).
1. Sample size given, probability to be determined.
\(p = P(|A_n - \mu| \le a) = P(|\dfrac{A_n - \mu}{\sigma/\sqrt{n}}| \le \dfrac{a \sqrt{n}}{\sigma} = 2\phi (a \sqrt{n}/\sigma) -1\)
2. Sample size to be determined, probability specified.
\(2 \phi (a \sqrt{n}/\sigma) - 1 \ge p\) iff \(\phi (a\sqrt{n} /\sigma) \ge \dfrac{p + 1}{2}\)
Find from a table or by use of the inverse normal function the value of \(x = a\sqrt{n}/\sigma\) required to make \(\phi (x)\) at least \((p + 1)/2\). Then
\(n \ge \sigma^2 (x/a)^2 = (\dfrac{\sigma}{a})^2 x^2\)
We may use the MATLAB function norminv to calculate values of \(x\) for various \(p\).
p = [0.8 0.9 0.95 0.98 0.99]; x = norminv(0,1,(1+p)/2); disp([p;x;x.^2]') 0.8000 1.2816 1.6424 0.9000 1.6449 2.7055 0.9500 1.9600 3.8415 0.9800 2.3263 5.4119 0.9900 2.5758 6.6349
For \(p = 0.95\), \(\sigma = 2\), \(a = 0.2\), \(n \ge (2/0.2)^2 3.8415 = 384.15\). Use at least 385 or perhaps 400 because of uncertainty about the actual \(\sigma^2\)
The idea of a statistic
As a function of the random variables in the sampling process, the sample average is an example of a statistic.
Definition: statistic
A statistic is a function of the class \(\{X_i: 1 \le i \le n\}\) which uses explicitly no unknown parameters of the population.
Example \(\PageIndex{2}\) Statistics as functions of the sampling progress
The random variable
\(W = \dfrac{1}{n} \sum_{i = 1}^{n} (X_i - \mu)^2\), where \(\mu = E[X]\)
is not a statistic, since it uses the unknown parameter \(\mu\). However, the following is a statistic.
\(V_n^* = \dfrac{1}{n} \sum_{i = 1}^{n} (X_i - A_n)^2 = \dfrac{1}{n} \sum_{i = 1}^{n} X_i^2 - A_n^2\)
It would appear that \(V_n^*\) might be a reasonable estimate of the population variance. However, the following result shows that a slight modification is desirable.
Example \(\PageIndex{3}\) An estimator for the population variance
The statistic
\(V_n = \dfrac{1}{n - 1} \sum_{i = 1}^{n} (X_i - A_n)^2\)
is an estimator for the population variance.
VERIFICATION
Consider the statistic
\(V_n^* = \dfrac{1}{n} \sum_{i = 1}^{n} (X_i - A_n)^2 = \dfrac{1}{n} \sum_{i = 1}^{n} X_i^2 - A_n^2\)
Noting that \(E[X^2] = \sigma^2 + \mu^2\), we use the last expression to show
\(E[V_n^*] = \dfrac{1}{n} n (\sigma^2 + \mu^2) - (\dfrac{\sigma^2}{n} + \mu^2) = \dfrac{n - 1}{n} \sigma^2\)
The quantity has a bias in the average. If we consider
\(V_n = \dfrac{n}{n - 1} V_n^* = \dfrac{1}{n - 1} \sum_{i = 1}^{n} (X_i - A_n)^2\), then \(E[V_n] = \dfrac{n}{n - 1} \dfrac{n - 1}{n} \sigma^2 = \sigma^2\)
The quantity \(V_n\) with \(1/(n - 1)\) rather than \(1/n\) is often called the sample variance to distinguish it from the population variance. If the set of numbers
\((t_1, t_2, \cdot\cdot\cdot, t_N)\)
represent the complete set of values in a population of \(N\) members, the variance for the population would be given by
\(\sigma^2 = \dfrac{1}{N} \sum_{i = 1}^{N} t_i^2 - (\dfrac{1}{N} \sum_{i = 1}^{N} t_i)^2\)
Here we use \(1/N\) rather than \(1/(N -1)\).
Since the statistic \(V_n\) has mean value \(\sigma^2\), it seems a reasonable candidate for an estimator of the population variance. If we ask how good is it, we need to consider its variance. As a random variable, it has a variance. An evaluation similar to that for the mean, but more complicated in detail, shows that
\(\text{Var} [V_n] = \dfrac{1}{n} (\mu_4 - \dfrac{n - 3}{n - 1} \sigma^4)\) where \(\mu_4 = E[(X - \mu)^4]\)
For large \(n\), \(\text{Var} [V_n]\) is small, so that \(V_n\) is a good large-sample estimator for \(\sigma^2\).
Example \(\PageIndex{4}\) A sampling demonstration of the CLT
Consider a population random variable \(X\) ~ uniform [-1, 1]. Then \(E[X] = 0\) and \(\text{Var} [X] = 1/3\). We take 100 samples of size 100, and determine the sample sums. This gives a sample of size 100 of the sample sum random variable \(S_{100}\), which has mean zero and variance 100/3. For each observed value of the sample sum random variable, we plot the fraction of observed sums less than or equal to that value. This yields an experimental distribution function for \(S_{100}\), which is compared with the distribution function for a random variable \(Y\) ~ \(N(0, 100/3)\).
rand('seed',0) % Seeds random number generator for later comparison tappr % Approximation setup Enter matrix [a b] of x-range endpoints [-1 1] Enter number of x approximation points 100 Enter density as a function of t 0.5*(t<=1) Use row matrices X and PX as in the simple case
qsample % Creates sample Enter row matrix of VALUES X Enter row matrix of PROBABILITIES PX Sample size n = 10000 % Master sample size 10,000 Sample average ex = 0.003746 Approximate population mean E(X) = 1.561e-17 Sample variance vx = 0.3344 Approximate population variance V(X) = 0.3333 m = 100; a = reshape(T,m,m); % Forms 100 samples of size 100 A = sum(a); % Matrix A of sample sums [t,f] = csort(A,ones(1,m)); % Sorts A and determines cumulative p = cumsum(f)/m; % fraction of elements <= each value pg = gaussian(0,100/3,t); % Gaussian dbn for sample sum values plot(t,p,'k-',t,pg,'k-.') % Comparative plot % Plotting details (see Figure 13.3.1)
Figure 13.3.1
. The central limit theorem for sample sums.


8.1.1: Introduction
In 2015, Doug Monahan, the CEO and founder of iBackPack of Texas, Inc., introduced a revolutionary technology package encased in a typical backpack.  Monahan promised that the iBackPack would be a “communication hub and corresponding electrical powerhouse for students and business professionals alike.” To bring the project to market, iBackPack sought crowdfunding through an Indiegogo campaign that raised $723,395 from 4,041 backers. An additional $76,694 was raised from 252 Kickstarter backers.
In 2016, iBackPack raised over $800,000 to fulfill investors’ orders, but the product never materialized. The only update from the company was a Facebook post alluding to issues sourcing “safe” batteries. By 2017, the iBackPack crowdfunding campaign failed to deliver the product promised to its investors. According to an article on the website The Verge in August 2018, the founders of iBackPack were under investigation by the Federal Trade Commission. Although crowdfunding can be a great option for startups, those who abuse the system may find themselves subject to legal action.


6.6: Degenerate Solutions
This section can be omitted on a first reading.
At the event horizon of the Schwarzschild spacetime, the timelike and spacelike roles of the Schwarzschild \(r\) and \(t\) coordinates get swapped around, so that the signs in the metric change from +−−− to − + −−. In discussing cases like this, it becomes convenient to define a new usage of the term “signature,” as s = p − q, where p is the number of positive signs and q the number of negative ones. This can also be represented by the pair of numbers (p, q). The example of the Schwarzschild horizon is not too disturbing, both because the funny behavior arises at a singularity that can be removed by a change of coordinates and because the signature stays the same. An observer who free-falls through the horizon observes that the local properties of spacetime stay the same, with |s| = 2, as required by the equivalence principle.
But this only makes us wonder whether there are other examples in which an observer would actually detect a change in the metric’s signature. We are encouraged to think of the signature as something empirically observable because, for example, it has been proposed that our universe may have previously unsuspected additional spacelike dimensions, and these theories make testable predictions. Since we do not notice the extra dimensions in ordinary life, they would have to be wrapped up into a cylindrical topology. Some such theories, like string theory, are attempts to create a theory of quantum gravity, so the cylindrical radius is assumed to be on the order of the Planck length, which corresponds quantum-mechanically to an energy scale that we will not be able to probe using any foreseeable technology. But it is also possible that the radius is large — a possibility that goes by the name of “large extra dimensions” — so that we could see an effect at the Large Hadron Collider. Nothing in the formulation of the Einstein field equations requires a 3+1 (i.e., (1, 3)) signature, and they work equally well if the signature is instead 4+1, 5+1, . . . . Newton’s inverse-square law of gravity is described by general relativity as arising from the three-dimensional nature of space, so on small scales in a theory with n large extra dimensions, the 1/r 2 behavior changes over to 1/r 2+n , and it becomes possible that the LHC could produce microscopic black holes, which would immediately evaporate into Hawking radiation in a characteristic way.
So it appears that the signature of spacetime is something that is not knowable a priori , and must be determined by experiment. When a thing is supposed to be experimentally observable, general relativity tells us that it had better be coordinate-independent. Is this so? A proposition from linear algebra called Sylvester’s law of inertia encourages us to believe that it is. The theorem states that when a real matrix \(A\) is diagonalized by a real, nonsingular change of basis (a similarity transformation S −1 AS), the number of positive, negative, and zero diagonal elements is uniquely determined. Since a change of coordinates has the effect of applying a similarity transformation on the metric, it appears that the signature is coordinate-independent.
This is not quite right, however, as shown by the following paradox. The coordinate invariance of general relativity tells us that if all clocks, everywhere in the universe, were to slow down simultaneously (with simultaneity defined in any way we like), there would be no observable consequences. This implies that the spacetime
\[ds^2 = −t \,dt^2 − d \ell^{2},\]
where
\[d \ell^{2} = dx^2 + dy^2 + dz^2,\]
is empirically indistinguishable from a flat spacetime. Starting from t = \(− \infty\), the positive g tt component of the metric shrinks uniformly, which should be harmless. We can indeed verify by direct evaluation of the Riemann tensor that this is a flat spacetime ( problem 10 ). But for t > 0 the signature of the metric switches from + − −− to − − −−, i.e., from Lorentzian (|s| = 2) to Euclidean (|s| = 4). This is disquieting. For t < 0, the metric is a perfectly valid description of our own universe (which is approximately flat). Time passes, and there is no sign of any impending disaster. Then, suddenly, at some point in time, the entire structure of spacetime undergoes a horrible spasm. This is a paradox, because we could just as well have posed our initial conditions using some other coordinate system, in which the metric had the familiar form ds 2 = dt 2 −d\(\ell^{2}\). General relativity is supposed to be agnostic about coordinates, but a choice of coordinate leads to a differing prediction about the signature, which is a coordinate-independent quantity.
We are led to the resolution of the paradox if we explicitly construct the coordinate transformation involved. In coordinates (t, x, y, z), we have ds 2 = −t dt 2 − d\(\ell^{2}\). We would like to find the relationship between t and some other coordinate u such that we recover the familiar form ds 2 = du 2 −d\(\ell^{2}\) for the metric. The tensor transformation law gives
\[\begin{split} g_{tt} &= \left(\dfrac{\partial u}{\partial t}\right)^{2} g_{uu} \\ -t &= \left(\dfrac{\partial u}{\partial t}\right)^{2} \end{split}\]
with solution
\[u = \pm \frac{2}{3} t^{\frac{3}{2}}, \quad t < 0 \ldotp\]
There is no solution for t > 0.
If physicists living in this universe, at t < 0, for some reason choose t as their time coordinate, there is in fact a way for them to tell that the cataclysmic event at t = 0 is not a reliable prediction. At t = 0, their metric’s time component vanishes, so its signature changes from + − −− to 0 − −−. At that moment, the machinery of the standard tensor formulation of general relativity breaks down. For example, one can no longer raise indices, because g ab is the matrix inverse of g ab , but g ab is not invertible. Since the field equations are ultimately expressed in terms of the metric using machinery that includes raising and lowering of indices, there is no way to apply them at t = 0. They do not make a false prediction of the end of the world; they fail to make any prediction at all. Physicists accustomed to working in terms of the t coordinate can simply throw up their hands and say that they have no way to predict anything at t > 0. But they already know that their spacetime is one whose observables, such as curvature, are all constant with respect to time, so they should ask why this perfect symmetry is broken by singling out t = 0. There is physically nothing that should make one moment in time different than any other, so choosing a particular time to call t = 0 should be interpreted merely as an arbitrary choice of the placement of the origin of the coordinate system. This suggests to the physicists that all of the problems they’ve been having are not problems with any physical meaning, but merely problems arising from a poor choice of coordinates. They carry out the calculation above, and discover the u time coordinate. Expressed in terms of u, the metric is well behaved, and the machinery of prediction never breaks down.
The paradox posed earlier is resolved because Sylvester’s law of inertia only applies to a nonsingular transformation S. If S had been singular, then the S −1 referred to in the theorem wouldn’t even have existed. But the transformation from u to t has \(\frac{\partial t}{\partial u}\) = 0 at u = t = 0, so it is singular. This is all in keeping with the general philosophy of coordinate-invariance in relativity, which is that only smooth, one-to-one coordinate transformations are allowed. Someone who has found a lucky coordinate like u, and who then contemplates transforming to t, should realize that it isn’t a good idea, because the transformation is not smooth and one-to-one. Someone who has started by working with an unlucky coordinate like t finds that the machinery breaks down at t = 0, and concludes that it would be a good idea to search for a more useful set of coordinates. This situation can actually arise in practical calculations.
What about our original question: could the signature of spacetime actually change at some boundary? The answer is now clear. Such a change of signature is something that could conceivably have intrinsic physical meaning, but if so, then the standard formulation of general relativity is not capable of making predictions about it. There are other formulations of general relativity, such as Ashtekar’s, that are ordinarily equivalent to Einstein’s, but that are capable of making predictions about changes of signature. However, there is more than one such formulation, and they do not agree on their predictions about signature changes.


8.20C: Distribution and Importance of Parasitic Worms
- Explain how parasitic worms may be beneficial
Parasitic worms, often the result of horrible illness and disease, appear to have medicinal properties as well. The importance of parasitic worms has come to light in regards to treating various diseases which may benefit from their presence. It is argued that humans have evolved with parasitic worms and there is a mutualistic relationship which mandates the need for parasitic worms to contribute to a healthy immune system. The most common use of parasitic worms for medicinal purposes is in the use against diseases characterized by an overactive immune response. An overactive immune response is often seen in individuals with allergies and hay-fever, specifically in developed countries where parasites have been under strict prevention and control. It is speculated that parasitic worms have the ability to damp down the immune system, which promotes an environment where they can thrive without being attached. In return, the damping down of the immune system is believed to be beneficial, as this may prevent the development of allergies.
An additional study links an increase in metabolic syndrome in the Western world and the success in preventing and eliminating parasites. The study demonstrates that immune system cells, eosinophils, that are present in fat tissue play a role in the prevention of insulin resistance via secretion of interleukin 4. The interleukin 4 is then able to activate macrophages that function in the maintenance of glucose homeostasis. The study showed that parasitic worm infection results in an increase in eosinophils, thus, promoting control of glucose maintenance.
The hypothesis that parasites are necessary for a healthy immune system is currently under investigation and still requires multiple lines of evidence.
Key Points
- Parasitic worms appear to have medicinal properties as well which has opened a new field of research by studying the use of parasitic worms in disease treatment.
- Scientists hypothesize that parasitic worms can be used to combat autoimmune diseases by damping down the immune system of the host by using parasitic worms to active eosinophils and downstream targets.
- Parasitic worms have been linked to a protective role in autoimmune disease development and prevention of metabolic syndrome.
Key Terms
- eosinophils : a type of white blood cell used to fight parasitic infection


27.4A: Pre-Cambrian Animal Life
- Describe the types of animals found in the Ediacaran period
Pre-Cambrian Animal Life
The time before the Cambrian period is known as the Ediacaran period (between 635-543 million years ago), the final period of the late Proterozoic Neoproterozoic Era. It is believed that early animal life, termed Ediacaran biota, evolved from protists at this time. Some protist species called choanoflagellates closely resemble the choanocyte cells in the simplest animals, sponges. In addition to their morphological similarity, molecular analyses have revealed similar sequence homologies in their DNA.
The earliest life comprising Ediacaran biota was long believed to include only tiny, sessile, soft-bodied sea creatures. However, recently there has been increasing scientific evidence suggesting that more varied and complex animal species lived during this time, and possibly even before the Ediacaran period.
Fossils believed to represent the oldest animals with hard body parts were recently discovered in South Australia. These sponge-like fossils, named Coronacollina acula , date back as far as 560 million years. They are believed to show the existence of hard body parts and spicules that extended 20–40 cm from the main body (estimated about 5 cm long). Other organisms, such as Cyclomedusa and Dickinsonia , also evolved during the Ediacaran period.
Another recent fossil discovery may represent the earliest animal species ever found. While the validity of this claim is still under investigation, these primitive fossils appear to be small, one-centimeter long, sponge-like creatures. These fossils from South Australia date back 650 million years, actually placing the putative animal before the great ice age extinction event that marked the transition between the Cryogenian period and the Ediacaran period. Until this discovery, most scientists believed that there was no animal life prior to the Ediacaran period. Many scientists now believe that animals may, in fact, have evolved during the Cryogenian period.
Key Points
- The pre-Cambrian period ( Ediacaran period ) took place between 635-543 million years ago.
- Early animal life, called Ediacaran biota, evolved from protists; it was previously believed early animal life included only tiny, sessile, soft-bodied sea creatures, but scientific evidence suggests more complex animals lived during this time.
- Sponge-like fossils believed to represent the oldest animals with hard body parts, named Coronacollina acula , date back as far as 560 million years.
- The fossils of the earliest animal species ever found were small, one-centimeter long, sponge-like creatures, dating before 650 million years, which predates the Ediacaran period.
- The discovery of the fossils of the earliest animal species provided evidence that animals may have evolved before the Ediacaran period during the Cryogenian period.
Key Terms
- Ediacaran period : period from about 635-543 million years ago; the final period of the late Proterozoic Neoproterozoic Era
- choanoflagellate : any of a group of flagellate protozoa thought to be the closest unicellular ancestors of animals
- Coronacollina acula : sponge-like fossils believed to represent the oldest animals with hard body parts that date back as far as 560 million years


15.4: Visual Anthropology and Ethnographic Film
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- Jennifer Hasty, David G. Lewis, & Marjorie M. Snipes
- OpenStax
Learning Objectives
By the end of this section, you will be able to:
- Give examples of the early use of visual media in ethnographic fieldwork.
- Define the field of visual anthropology.
- Describe two examples of ethnographic film.
- Explain the ethical challenges associated with ethnographic film.
Although the subfield of media anthropology is relatively new, anthropologists have been incorporating media technologies into their methods of research and ethnographic representation since the early 20th century. An early pioneer of visual methods, Margaret Mead took some 200 photographs as part of her first fieldwork project in Samoa (Tiffany 2005). In the 1930s, Mead and Gregory Bateson used both photography and film in their joint fieldwork in Bali and New Guinea. Mead and Bateson embraced visual media as an innovative means of learning about social life and used photos and film to study childhood, public ceremonies, and dance. Together, they took about 33,000 photographs and recorded about 32,600 feet of film as part of their joint research (Jacknis 2020). Focusing on child development and dance, they used these visual materials to produce two photographic ethnographies and seven short films.
Visual anthropology is either the use of visual media as a research method or its study as a research topic. Whether they consider themselves visual anthropologists or not, most anthropologists take photos of the people and places they encounter in their fieldwork. Visual anthropologists go further, using photography and film to document important events for fine-grained future analysis. As moments frozen in time, photographs allow for analytical contemplation and shared consideration. Film can be slowed down or sped up to focus on certain aspects of individual action or group dynamics that might otherwise go unnoticed. Images may be magnified to reveal minute details. Both film and photography allow for images to be placed side by side for comparison.
Visual anthropologists are also interested in how people in the cultures they study produce their own visual representations in the form of art, photography, and film. Visual anthropologists are interested in popular paintings, billboards, and graffiti as well as forms of photography and film.
Early on, cultural anthropologists recognized that visual media made it possible to share the experiences encountered during anthropological research with their colleagues and students, and the general public. One example of many is the film Trance and Dance in Bali (1951), written and narrated by Mead, which features a Balinese dance called the kris. The kris dance dramatizes the story of a witch whose daughter is rejected as a bride to the king. In retaliation, the witch plots to spread chaos and pestilence in the land. When the king sends an emissary with a convoy of servants to stop the nefarious plan, the witch turns the emissary into a dragon. She then causes the followers of the dragon to fall into trance. When the dragon-emissary revives his followers, they emerge in a somnambulant state, stabbing themselves with daggers but inflicting no harm. After dancing the kris dance, the dancers are brought out of their trance with incense and holy water. Included in the US Library of Congress, this stunning early use of film in anthropology can be viewed at the Library of Congress website or on YouTube .
Ethnographic film is the use of film in ethnographic representation as either a method, a record, or a means of reporting on anthropological fieldwork. Like documentary films, ethnographic films are nonfiction films in which live-action shots are edited and shaped into a central narrative drama. While the line between documentary and ethnographic film is blurry, ethnographic film is associated with the work of professional anthropologists and tends to focus explicitly on depictions of sociocultural processes.
Before Mead and Bateson’s professional use of film, several filmmakers had made amateur ethnographic films depicting aspects of non-Western cultures. The very popular film Nanook of the North (1922), made by explorer Robert Flaherty and based on 16 months of living with the Inuit, follows an Inuit family in the Canadian Arctic. The film focuses on the heroism of husband Nanook and wife Nyla as they struggle against the harsh elements to meet their needs and raise their children. The film documents Inuit lifeways such as traveling by dogsled and kayak, hunting walrus, and building an igloo out of glacier ice. In one controversial scene, the family visits a Canadian trading fort, where they express astonishment at instruments of modernity such as a phonograph. Though the film has been praised for its representation of Indigenous peoples as courageous and hardworking, others have criticized Flaherty for staging some of the events and even having his own common-law wife play the role of Nanook’s wife in the film. Like Mead and Bateson’s film, Nanook of the North is now held by the Library of Congress as one of the most significant examples of early documentary filmmaking. While some consider Nanook to be a precursor to ethnographic film, anthropologist Franz Boas dismissed it as completely irrelevant to anthropology due to Flaherty’s use of artifice and staging (Schäuble 2018). The film can be viewed at the Internet Archive or on YouTube .
From its roots in both amateur and professional filmmaking, ethnographic film became an increasingly important tool for teaching and popularizing anthropological research throughout the 20th century. In the 1950s, John Marshall and Timothy Asch pioneered a more objective, naturalist style of ethnographic film, attempting to avoid Western narratives and exoticization. With the development of the ability to simultaneously record sound in the 1960s, the commentary and conversations of people represented in ethnographic films became audible (even if translations still appeared in subtitles). Subjects could now address the camera directly. Around the same time, anthropologists began considering the power dynamics embedded in the production of ethnographic film—in particular, the ethical issues involved in White Western researchers controlling the representation of non-Western peoples.
Responding to these ethical challenges, many ethnographic filmmakers have turned away from the heavily crafted narrative methods of films such as Nanook toward a more purist style that represents unfolding action with little editing. New methods of representation have emerged, revealing the very act of filming itself and highlighting the relationship between filmmakers and those being filmed. Rather than using film as a means of teaching anthropology to students and the public, some experimental filmmakers conceptualize film as the creation of an entirely new sociocultural experience. The experimental ethnographic film Manakamana , for instance, directed by Stephanie Spray and Pacho Velez and released in 2013, comprises 11 long shots of Nepalese pilgrims taking cable car rides to a mountaintop temple in Nepal. Rather than teaching the viewer about an anthropological topic, Manakamana provides live-action portraits of people and their relationships against the backdrop of the rugged landscape passing below them. Spray and Velez are collaborators in Harvard University’s Sensory Ethnography Lab, a project dedicated to the experimental use of multisensory methods to create ethnographic media. You can view a trailer for the film on YouTube .


6.10: VI Glossary
Acetylcholine: A neurotransmitter that stimulates nicotinic and muscarinic receptors in the parasympathetic nervous system.
Adrenergic agonists: Substances that stimulate SNS receptors and cause effects similar to epinephrine and norepinephrine.
Adrenergic antagonists: Substances that block SNS receptors.
Agranulocytosis: Extremely low white blood cell count and an adverse effect of clozapine and antipsychotic medication.
Anticholinergics: Substances that block the effects of PNS receptors.
Black Box Warning: A significant warning from the Food and Drug Administration (FDA) that alerts the public and health care providers to serious side effects, such as injury or death.
Catecholamines: Substances that include epinephrine, norepinephrine, and dopamine and are responsible for the body’s “fight-or-flight” response.
Central nervous system (CNS): The brain and spinal cord.
Cholinergics: Substances that stimulate nicotinic and muscarinic receptors and cause effects similar to acetylcholine (ACh).
Controlled substance: Drugs regulated by federal law that can cause dependence and abuse.
Dopamine: A neurotransmitter that plays an essential role in several brain functions, including learning, motor control, reward, emotion, and executive functions.
Extrapyramidal side effects: Involuntary or uncontrollable movements, tremors, and muscle contractions that can occur with antipsychotic medications.
 Low levels of GABA are associated with seizures, anxiety, mania, and impulse control. Pregabalin is an anticonvulsant that mimics the effects of GABA and is used to treat generalized anxiety disorder.
Glutamate: An excitatory neurotransmitter. Elevated levels of glutamate are associated with psychosis that can occur with schizophrenia, as well as with illicit drug use such as methamphetamines. Conversely, lamotrigine, a medication used to treat bipolar disorder, inhibits glutamate.
Histamine: A substance that mediates homeostatic functions in the body, promotes wakefulness, modulates feeding behavior, and controls motivational behavior. For example, diphenhydramine, a histamine antagonist, causes drowsiness.
Hypertensive crisis: A condition that can be caused by MAOIs with severe hypertension (blood pressure greater than 180/120 mm Hg) and evidence of organ dysfunction. Symptoms may include occipital headache (which may radiate frontally), palpitations, neck stiffness or soreness, nausea or vomiting, sweating, dilated pupils, photophobia, shortness of breath, or confusion.
Lithium toxicity: Lithium has a narrow therapeutic range of 0.8 to 1.2 mEq/L. Levels above this range cause lithium toxicity. Signs of early lithium toxicity include diarrhea, vomiting, drowsiness, muscular weakness, and lack of coordination. At higher levels, giddiness, ataxia, blurred vision, tinnitus, and a large output of dilute urine may occur.
Neuroleptic malignant syndrome (NMS): A rare but fatal adverse effect that can occur at any time during treatment with antipsychotics. It typically develops over a period of days to weeks and resolves in approximately nine days with treatment. Signs include increased temperature, severe muscular rigidity, confusion, agitation, hyperreflexia, elevation in white blood cell count, elevated creatinine phosphokinase, elevated liver enzymes, myoglobinuria, and acute renal failure.
Neurotransmitters: Chemical substances released at the end of a neuron by the arrival of an electrical impulse. They diffuse across the synapse and cause the transfer of the impulse to another nerve fiber, a muscle fiber, or other structure. Neurotransmitters interact with specific receptors like a key and a lock.
Norepinephrine and Epinephrine: Substances that stimulate alpha- and beta-receptors in the sympathetic nervous system.
Opiates: Powerful analgesics prescribed to treat moderate to severe pain (such as morphine and oxycodone). Opiates also include illicit drugs (such as heroin).
Opioid receptors: Mu, delta, and kappa receptors that are stimulated by endogenous peptides released by neurons (such as endorphins) and exogenous opiates.
Opioid system: A system in the brain that controls pain and reward and addictive behaviors.
Parasympathetic Nervous System (PNS) receptors: Nicotinic and muscarinic receptors that are stimulated by acetylcholine (ACh).
Serotonin: A neurotransmitter that modulates multiple neuropsychological processes such as mood, sleep, libido, and temperature regulation. Abnormal levels of serotonin have been linked to many mental health disorders such as depression, bipolar disorder, and anxiety. Many psychotropic medications target serotonin.
Serotonin syndrome: A syndrome caused by the combination of multiple medications that affect serotonin. It typically develops within 24 hours from the combination of medication and can range from mild to a life-threatening syndrome. Signs of serotonin syndrome include mental status changes (e.g., agitation, hallucinations, coma), autonomic instability (e.g., tachycardia, labile blood pressure, hyperthermia), incoordination, or gastrointestinal symptoms (e.g., nausea, vomiting, diarrhea). Serotonin syndrome, in its most severe form, can resemble neuroleptic malignant syndrome (NMS).
SLUDGE: A mnemonic for anticholinergic side effects: Salivation decreased, Lacrimation decreased, Urinary retention, Drowsiness/dizziness, GI upset, Eyes (blurred vision/dry eyes).
Sympathetic Nervous System (SNS) receptors: Alpha-1, Alpha-2, Beta-1, and Beta-2 receptors that are stimulated by epinephrine and norepinephrine.
Tardive dyskinesia: A syndrome of movement disorders associated with antipsychotic medications that persists for at least one month and can last up to several years despite discontinuation of the medications.