3.8: Employee Abilities and Skills
How do people with different abilities, skills, and personalities build effective work teams?
We begin with a look at employee abilities and skills . Abilities and skills generally represent those physical and intellectual characteristics that are relatively stable over time and that help determine an employee’s capability to respond. Recognizing them is important in understanding organizational behavior, because they often bound an employee’s ability to do the job. For example, if a clerk-typist simply does not have the manual dexterity to master the fundamentals of typing or keyboard entry, her performance will likely suffer. Similarly, a sales representative who has a hard time with simple numerical calculations will probably not do well on the job.
Mental Abilities
It is possible to divide our discussion of abilities and skills into two sections: mental abilities and physical abilities. Mental abilities are an individual’s intellectual capabilities and are closely linked to how a person makes decisions and processes information. Included here are such factors as verbal comprehension, inductive reasoning, and memory. A summary is shown in Table \(\PageIndex{1}\).
From a managerial standpoint, a key aspect of mental ability is cognitive complexity. Cognitive complexity represents a person’s capacity to acquire and sort through various pieces of information from the environment and organize them in such a way that they make sense. People with high cognitive complexity tend to use more information—and to see the relationships between aspects of this information—than people with low cognitive complexity. For example, if a manager was assigned a particular problem, would she have the capacity to break the problem down into its various facets and understand how these various facets relate to one another? A manager with low cognitive complexity would tend to see only one or two salient aspects of the problem, whereas a manager with higher cognitive complexity would understand more of the nuances and subtleties of the problem as they relate to each other and to other problems.
People with low cognitive complexity typically exhibit the following characteristics: 2
- They tend to be categorical and stereotypical. Cognitive structures that depend upon simple fixed rules of
- integration tend to reduce the possibility of thinking in terms of degrees.
- Internal conflict appears to be minimized with simple structures. Since few alternative relationships are generated, closure is quick.
- Behavior is apparently anchored in external conditions. There is less personal contribution in simple structures.
- Fewer rules cover a wider range of phenomena. There is less distinction between separate situations.
On the other hand, people with high levels of cognitive complexity are typically characterized by the following:3
- Their cognitive system is less deterministic. Numerous alternative relationships are generated and considered.
- The environment is tracked in numerous ways. There is less compartmentalization of the environment.
- The individual utilizes more internal processes. The self as an individual operates on the process.
Research on cognitive complexity has focused on two important areas from a managerial standpoint: leadership style and decision-making.
In the area of leadership, it has been found that managers rated high on cognitive complexity are better able to handle complex situations, such as rapid changes in the external environment. Moreover, such managers also tend to use more resources and information when solving a problem and tend to be somewhat more considerate and consultative in their approach to managing their subordinates. 4
In the area of decision-making, fairly consistent findings show that individuals with high cognitive complexity (1) seek out more information for a decision, (2) actually process or use more information, (3) are better able to integrate discrepant information, (4) consider a greater number of possible solutions to the problem, and (5) employ more complex decision strategies than individuals with low cognitive complexity. 5
Physical Abilities
The second set of variables relates to someone’s physical abilities . Included here are both basic physical abilities (for example, strength) and psychomotor abilities (such as manual dexterity, eye-hand coordination, and manipulation skills). These factors are summarized in Table \(\PageIndex{2}\). 6
Considering both mental and physical abilities helps one understand the behavior of people at work and how they can be better managed. The recognition of such abilities—and the recognition that people have different abilities—has clear implications for employee recruitment and selection decisions; it brings into focus the importance of matching people to jobs. For example, Florida Power has a 16-hour selection process that involves 12 performance tests. Over the test period of a couple of years, 640 individuals applied for “lineperson” jobs. Of these, 259 were hired. As a consequence of the new performance tests and selection process, turnover went from 43 percent to 4.5 percent, and the program saved net $1 million. 7 In addition to selection, knowledge of job requirements and individual differences is also useful in evaluating training and development needs. Because human resources are important to management, it is imperative that managers become more familiar with the basic characteristics of their people.
Exercise \(\PageIndex{1}\)
1. Why should abilities and skills be taken into account when selecting employees?
2. Describe the components of mental abilities, cognitive complexity, physical ability, and psychomotor abilities.
2 R.J. Ebert and T.R. Mitchell, Organization Decision Processes: Concepts and Analysis (New York: Crane, Russak, 1975), p. 81.
3 Ibid.
4 T.R. Mitchell, “Cognitive Complexity and Leadership Style,” Journal of Personality and Social Psychology, 1970, 16, pp. 166–174.
5 H. M. Schroder, M. H. Driver, and S. Streufert, Human Information Processing (New York: Holt, Rinehart and Winston, 1967).
6 E. J. McCormick and J. Tiffin, Industrial Psychology (Englewood Cliffs, N.J.: Prentice-Hall, 1976).
7 Dale Feuer & Chris Lee. 1988. The Kaizen Connection: How Companies Pick Tomorrow’s Workers. Training. May, 23–35.
Table 2.1 (Attribution: Copyright Rice University, OpenStax, under CC BY-NC-SA 4.0 license)
Table 2.2 (Attribution: Copyright Rice University, OpenStax, under CC BY-NC-SA 4.0 license)


8.7: VIII Glossary
Bipolar I Disorder: The most severe bipolar disorder with at least one manic episode; most individuals experience additional hypomanic and depressive episodes.
Bipolar II Disorder: A pattern of depressive episodes and hypomanic episodes, but individuals have never experienced a full-blown manic episode typical of Bipolar I Disorder.
Catatonia: A state of unresponsiveness due to a person’s mental state.
Cyclothymia: A disorder defined by periods of hypomanic symptoms and periods of depressive symptoms lasting for at least two years (1 year in children and adolescents). However, the symptoms do not meet the diagnostic requirements for hypomanic episodes or depressive episodes. [1]
Family-focused therapy: Psychotherapy that focuses on psychoeducation, communication enhancement training, and problem-solving skills. It includes attention to family dynamics and relationships as contributing factors to the client’s mood.
Grandiose delusions: A symptom associated with bipolar disorders of feeling unusually important, talented, or powerful.
Hypomanic episode: Episodes similar to symptoms of a manic episode, but they are less severe and do not cause significant impairment in social or occupational functioning or require hospitalization. [2]
Interpersonal and social rhythm therapy (IPSRT): Psychotherapy that emphasizes the importance of establishing stable daily routines such as sleeping, waking up, working, and eating meals.
Manic episode: A persistently elevated or irritable mood with abnormally increased energy lasting at least one week. The mood disturbance is severe and causes marked impairment in social or occupational function. Severe episodes often require hospitalization to prevent harm to self or others.
Psychotherapy: A variety of treatment techniques that help an individual identify and change troubling emotions, thoughts, and behaviors.
Rapid cycling: At least four mood episodes associated with bipolar disorder occurring in a 12-month period.
- National Institute of Mental Health. (2020, January). Bipolar disorder. National Institutes of Health. https://www.nimh.nih.gov/health/topics/bipolar-disorder ↵
- American Psychiatric Association. (2013). Desk reference to the diagnostic criteria from DSM-5. ↵


1.8: Writing Fractions and Decimals as Percents
Learning Outcome
- Use percent to represent a given fraction or decimal
How many cents are in one dollar? There are \(100\) cents in a dollar. How many years are in a century? There are \(100\) years in a century. Does this give you a clue about what the word “percent” means? It is really two words, “per cent,” and means per one hundred. A percent is a ratio whose denominator is \(100\). We use the percent symbol, \(\%\), to show percent.
Percent
A percent is a ratio whose denominator is \(100\).
For example \(46\%=\Large\frac{46}{100}\)
According to data from the American Association of Community Colleges \(\left(2015\right)\), about \(\text{57%}\) of community college students are female. This means \(57\) out of every \(100\) community college students are female, as the image below shows. Out of the \(100\) squares on the grid, \(57\) are shaded, which we write as the ratio \(\Large\frac{57}{100}\).
Among every \(100\) community college students, \(57\) are female.
Similarly, \(\text{25%}\) means a ratio of \(\Large\frac{25}{100}\normalsize ,\text{3%}\) means a ratio of \(\Large\frac{3}{100}\) and \(\text{100%}\) means a ratio of \(\Large\frac{100}{100}\). In words, “one hundred percent” means the total \(\text{100%}\) is \(\Large\frac{100}{100}\), and since \(\Large\frac{100}{100}\normalsize =1\), we see that \(\text{100%}\) means \(1\) whole.
To convert a decimal to a percent, remember that percent means per hundred. If we change the decimal to a fraction whose denominator is \(100\), it is easy to change that fraction to a percent.
Convert a decimal to a percent
- Write the decimal as a fraction.
- If the denominator of the fraction is not \(100\), rewrite it as an equivalent fraction with denominator \(100\).
- Write this ratio as a percent.
example
Convert each decimal to a percent:
1. \(0.05\)
2.\(0.83\)
Solution
| 1. | |
| \(0.05\) | |
| Write as a fraction. Five hundredths – the denominator is \(100\). | \({\Large\frac{5}{100}}\) |
| Write this ratio as a percent. | \(5\)% |
| 2. | |
| \(0.83\) | |
| Write as a fraction. Eighty-three hundredths – the denominator is \(100\). | \({\Large\frac{83}{100}}\) |
| Write this ratio as a percent. | \(83\)% |
try it
[ohm_question]146666[/ohm_question]
Let’s look at a few more examples of converting decimals to percents, but these aren’t as straight forward!
example
Convert each decimal to a percent:
1. \(0.2\)
2. \(1.05\)
2. \(0.075\)
[reveal-answer q=”740440″]Show Answer[/reveal-answer]
[hidden-answer a=”740440″]
Solution
| 1. | |
| \(0.2\) | |
| Write as a fraction. The denominator is \(10\). | \({\Large\frac{2}{10}}\) |
| Multiply the numerator and denominator by \(10\), so that the denominator is \(100\). | \({\Large\frac{20}{100}}\) |
| Write this ratio as a percent. | \(20\%\) |
Notice that you could also have written \(0.2\) as \(0.20\) and gotten to \({\Large\frac{20}{100}}\) without doing any calculations.
| 2. | |
| \(0.05\) | |
| Write as a fraction. | \(1{\Large\frac{5}{100}}\) |
| Write as an improper fraction. The denominator is \(100\). | \({\Large\frac{105}{100}}\) |
| Write this ratio as a percent. | \(105\%\) |
Notice that since \(1.05>1\), the result is more than \(100\%.\)
| 3. | |
| \(0.075\) | |
| Write as a fraction. The denominator is \(1,000\). | \({\Large\frac{75}{1,000}}\) |
| Divide the numerator and denominator by \(10\), so that the denominator is \(100\). | \({\Large\frac{7.5}{100}}\) |
| Write this ratio as a percent. | \(7.5\%\) |
Notice that any decimal that has value beyond the hundredths place will have a decimal answer when converted to a percent.
[/hidden-answer]
try it
[ohm_question]146667[/ohm_question]
[ohm_question]156959[/ohm_question]
[ohm_question]156964[/ohm_question]
Let’s summarize some of the results from the previous examples in the table below so we can look for a pattern.
| Decimal | Percent |
|---|---|
| \(0.05\) | \(\text{5%}\) |
| \(0.83\) | \(\text{83%}\) |
| \(0.2\) | \(\text{20%}\) |
| \(1.05\) | \(\text{105%}\) |
| \(0.075\) | \(\text{7.5%}\) |
Do you see the pattern? To convert a decimal to a percent, we move the decimal point two places to the right and then add the percent sign.
The next table uses the decimal numbers in the table above and shows visually to convert them to percents by moving the decimal point two places to the right and then writing the \(\%\) sign.
In an earlier lesson, we learned how to convert fractions to decimals. Now we also know how to change decimals to percents. So to convert a fraction to a percent, we first change it to a decimal and then convert that decimal to a percent.
Convert a fraction to a percent
- If possible, convert the fraction to a denominator of \(100\).
- If not, convert the fraction to a decimal by dividing.
- Convert the decimal to a percent.
example
Convert each fraction or mixed number to a percent:
1. \({\Large\frac{3}{4}}\)
2. \({\Large\frac{11}{8}}\)
3. \(2{\Large\frac{1}{5}}\)
[reveal-answer q=”32099″]Show Answer[/reveal-answer]
[hidden-answer a=”32099″]
Solution
To convert a fraction to a decimal, divide the numerator by the denominator.
| 1. | \({\Large\frac{3}{4}}\) |
| Change to a decimal. | |
| Write as a percent by moving the decimal two places. | \(75\)% |
| 2. | \({\Large\frac{11}{8}}\) |
| Change to a decimal. | |
| Write as a percent by moving the decimal two places. | \(137.5\)% |
| 3. | \(2{\Large\frac{1}{5}}\) |
| Write as an improper fraction. | \({\Large\frac{11}{5}}\) |
| Change to a decimal. |
\(2.2\)
|
| Write as a percent. | \(220\)% |
Notice that we sometimes need to add zeros at the end of the number when moving the decimal two places to the right.
[/hidden-answer]
Sometimes when changing a fraction to a decimal, the division continues for many decimal places and we will need to round off the quotient. Typically, you will round before converting to a percent unless instructed otherwise. The number of decimal places we round to will depend on the situation. If the decimal calculation involves money, we round it to the hundredths place. For most other cases, we will round the number to the nearest thousandth, so the percent will be rounded to the nearest tenth.
try it
[ohm_question]146669[/ohm_question]
[ohm_question]146670[/ohm_question]
[ohm_question]146671[/ohm_question]


3.10: 3. 10- Solution of the Least-Squares Problem
View Solution of the Least-Squares Problem by the Normal Equations on YouTube
The problem of least-squares can be cast as the problem of solving an overdetermined matrix equation \(\text{Ax} = \text{b}\) when \(\text{b}\) is not in the column space of \(\text{A}\). By replacing \(\text{b}\) by its orthogonal projection onto the column space of \(\text{A}\), the solution minimizes the norm \(||\text{Ax} − \text{b}||\).
Now \(\text{b} = \text{b}_{\text{proj}_{\text{Col(A)}}} + (\text{b} − \text{b}_{\text{proj}_{\text{Col(A)}}})\), where \(\text{b}_{\text{proj}_{\text{Col(A)}}}\) is the projection of \(\text{b}\) onto the column space of \(\text{A}\). Since \((\text{b} − \text{b}_{\text{proj}_{\text{Col(A)}}})\) is orthogonal to the column space of \(\text{A}\), it is in the nullspace of \(\text{A}^{\text{T}}\). Therefore, \(\text{A}^{\text{T}}(\text{b} − \text{b}_{\text{proj}_{\text{Col(A)}}} ) = 0\), and it pays to multiply \(\text{Ax} = \text{b}\) by \(\text{A}^{\text{T}}\) to obtain
\[\text{A}^{\text{T}}\text{Ax}=\text{A}^{\text{T}}\text{b}.\nonumber \]
These equations, called the normal equations for \(\text{Ax} = \text{b}\), determine the least-squares solution for \(\text{x}\), which can be found by Gaussian elimination. When \(\text{A}\) is an \(m\)-by-\(n\) matrix, then \(\text{A}^{\text{T}}\text{A}\) is an \(n\)-by-\(n\) matrix, and it can be shown that \(\text{A}^{\text{T}}\text{A}\) is invertible when the columns of \(\text{A}\) are linearly independent. When this is the case, one can rewrite the normal equations by multiplying both sides by \(\text{A}(\text{A}^{\text{T}}\text{A})^{−1}\) to obtain
\[\text{Ax}=\text{A}(\text{A}^{\text{T}}\text{A})^{-1}\text{A}^{\text{T}}\text{b},\nonumber \]
where the matrix
\[\text{P}=\text{A}(\text{A}^{\text{T}}\text{A})^{-1}\text{A}^{\text{T}}\nonumber \]
projects a vector onto the column space of \(\text{A}\). It is easy to prove that \(\text{P}^2 = \text{P}\), which states that two projections is the same as one. We have
\[\begin{aligned}\text{P}^2&=(\text{A}(\text{A}^{\text{T}}\text{A})^{-1}\text{A}^{\text{T}})(\text{A}(\text{A}^{\text{T}}\text{A})^{-1}\text{A}^{\text{T}}) \\ &=\text{A}\left[(\text{A}^{\text{T}}\text{A})^{-1}(\text{A}^{\text{T}}\text{A})\right](\text{A}^{\text{T}}\text{A})^{-1}\text{A}^{\text{T}} \\ &=\text{A}(\text{A}^{\text{T}}\text{A})^{-1}\text{A}^{\text{T}}=P.\end{aligned} \nonumber \]
As an example, consider the toy least-squares problem of fitting a line through the three data points \((1, 1),\: (2, 3)\) and \((3, 2)\). With the line given by \(y = \beta_0 + \beta_1x\), the overdetermined system of equations is given by
\[\left(\begin{array}{cc}1&1\\1&2\\1&3\end{array}\right)\left(\begin{array}{c}\beta_0\\ \beta_1\end{array}\right)=\left(\begin{array}{c}1\\3\\2\end{array}\right).\nonumber \]
The least-squares solution is determined by solving
\[\left(\begin{array}{ccc}1&1&1\\1&2&3\end{array}\right)\left(\begin{array}{cc}1&1\\1&2\\1&3\end{array}\right)\left(\begin{array}{c}\beta_0\\ \beta_1\end{array}\right)=\left(\begin{array}{ccc}1&1&1\\1&2&3\end{array}\right)\left(\begin{array}{c}1\\3\\2\end{array}\right),\nonumber \]
or
\[\left(\begin{array}{cc}3&6\\6&14\end{array}\right)\left(\begin{array}{c}\beta_0 \\ \beta_1\end{array}\right)=\left(\begin{array}{c}6\\13\end{array}\right).\nonumber \]
We can solve either by directly inverting the two-by-two matrix or by using Gaussian elimination. Inverting the two-by-two matrix, we have
\[\left(\begin{array}{c}\beta_0 \\ \beta_1\end{array}\right)=\frac{1}{6}\left(\begin{array}{rr}14&-6 \\ -6&3\end{array}\right)\left(\begin{array}{c}6\\13\end{array}\right)=\left(\begin{array}{c}1\\1/2\end{array}\right),\nonumber \]
so that the least-squares line is given by
\[y=1+\frac{1}{2}x.\nonumber \]
The graph of the data and the line is shown below.


4.1: Reddit- The Conversation Starts Here
What is Reddit?
Reddit is a forum-based website that was founded to create a space where communities could collaborate, share information on their lives and interests, and find other interests related to their current experience. The website itself is home to communities called subreddits.
Subreddits are separate forums hosted on the reddit website; each one centralizes on a different topic, brand, identity, or opinion. Reddit also curates a few subreddits for general and administration related topics, like News and Announcements . Users can gain all sorts of opinions, advice, and camaraderie on Reddit from personal finance and legal insight, sharing with their coworkers from Target, Starbucks, or emergency medical services, or just finding primal human entertainment like pictures of cute cats or self-posted pornographic material of all genders.
Moderators are responsible for monitoring individual subreddits under a volunteer position, and administrators handle the website-wide affairs like technical specifications, site rules, and annual site performance, as well as supervising the moderators of different communities.
Users register to the site and can subscribe to different subreddits, which allows them to see a customized feed of posts from their favorite subreddits alongside posts that are popular across reddit.
Reddit defines its mission as “[being] home to thousands of communities, endless conversation, and authentic human connection. Whether you’re into breaking news, sports, TV fan theories, or a never-ending stream of the internet’s cutest animals, there’s a community on Reddit for you” (Reddit).
Who is Reddit?
Reddit was founded in 2005 by partners Alexis Ohanian and Steve Huffman. Throughout the years, the two have left and then rejoined the company, currently serving as co-CEOs.
In 2006, Reddit was sold to Conde Nast, a magazine company under Advance Publications. Conde Nast/Advance Publications also own various local news outlets, and magazines including Allure , GQ , The New Yorker , Vogue , Vanity Fair , and Wired . Since 2011, Reddit operates as an independent subsidiary of Advance Publications. Reddit today is the sixth most visited website in the United States , and twenty-first most visited website across the world.
Who pays for Reddit?
Reddit has only a few main funding methods: investor funding rounds , selling advertisements , premium membership options and returns on investing in other tech companies.
Investor funding rounds allow private companies to use their company’s valuation and strategic plan to solicit funding from individual investors and investment firms, ultimately boosting the valuation and gaining liquid capital. Reddit’s latest funding round, which closed in February 2019, raised $300 million from a variety of investors like Chinese firm Tencent Holdings Ltd, investment firms Sequoia Capital and Fidelity, and individuals including Snoop Dogg. Three prior funding rounds raised a combined $250 million and has over twenty major investors. Reddit’s last round of investor funding was responsible for funding “internal product and business efforts” including new video capabilities, a new desktop design, and hiring to increase their workforce from 140 to 300 at the end of 2017.
Their current market valuation is $3 billion and the last funding type was Series D. The letters used for different funding Series classifies the stage in which the corporation requesting funding is considered. Series D investments are reserved for established companies that have completed other funding rounds or proven themselves as a revenue-generator, and typically see $10+ million in funding.
Another popular type of funding is the sale of advertisement options across the site. Advertisement options on Reddit include either a sponsored post on certain subreddits or types of subreddits, or the front page. Advertisers are charged based on the page views their ads get by the thousands, plus a base fee. Other advertisement use on Reddit includes Google Adsense advertisements on the sidebar.
As the website expands its advertising platform, Reddit has targeted ad sales towards fashion, media, and automotive companies; this raised $85 to 100 million this year. Reddit only started selling structured advertising in 2015 and launched its app in early 2016, limiting the percentage of its revenue that came from advertisements. The company plans to expand its advertising platform in the future to take on Google and Facebook’s ad programs.
Smaller revenue streams include the sale of premium memberships and returns on investment in other tech companies . Reddit’s most notable investment went to Imgur in 2014 for a total of $40 million.
The sale of Reddit Premium memberships and Reddit coins enables premium features to enhance user experience and the ability to turn-off ads. Newly revamped from the old Reddit Gold system in 2018, Reddit Premium costs $5.99/mo and can either be purchased for oneself or gifted to other users for one week or one month by using reddit coins to give their comments or posts a Gold Award or Platinum Award. In 2017, Reddit Premium and coins made the site over $1 million; the site is hoping these numbers are boosted with the aforementioned redesign recently debuting.
Reddit leaders have noted that the company will not seek another common method of financing, an IPO/public offering sale , in which companies sell shares of ownership in the company in exchange for liquid capital. Reddit has never publicly shared revenue figures, but owners have stated multiple times that prior to 2018/19, the site has not been profitable and most funds cover the operating cost of the website and its staff.
What data does it collect from its users?
Reddit collect three types of data which they described as information the consumer provided, information they collect automatically, and information they gather from others.
The information they collect from the user is username, password, email, user account preferences and settings. Reddit may log information when you access and use the Services. This may include your IP address, user-agent string, browser type, operating system, referral URLs, device information (e.g., device IDs), pages visited, links clicked, the requested URL, hardware settings, and search terms.
Reddit may receive information about the consumer from other sources, including from other users and third parties, and combine that information with the other information they have about the consumer. For example, Reddit may receive demographic or interest information about the consumer from third parties, including advertisers, and combine it with Reddit’s own data using a common account identifier such as a hash of an email address or a mobile-device ID.
How does Reddit moderate its contributions?
Reddit uses a metric called karma to represent their contributions to Reddit. There are two kinds of karma: link and comment. Link karma is received when you post a link on Reddit, while comment karma is what you will receive when you post a comment. If others like your post or comment, they will give you upvotes. If others do not like the content you post, they will downvote it. Karma is measured by the total difference between all upvotes and downvotes on every link post or comment that redditors submitted.
Reddit allows its users to post various authentic contents that can either be funny, serious or offensive. However it has a basic guideline on what is prohibited or unwelcome on the platform. Reddit prohibits posting illegal content, involuntary pornography, contents that incite violence, personal information, and spam. All contents that might be banned from accessing at workplace, such as nudity, pornography, profanity must be tagged as NSFW (Not Safe For Work).
Most people follow Reddit for their personal interests, and most subreddits are considered non-news thread. However there are a few subreddits designed to update news around the world, including r/news. R/news claims to contain “real news articles, primarily but not exclusively, news relating to the United States and the rest of the World.” Having more than 18 million followers, its popularity lies among the most subscribed subreddits in the entire domain.
R/news promotes ten different rules to control the flow of articles. For examples, the first rule dictates that any news that is more than a week old is not considered “news,” to maintain the strict up-to-date nature of the page. Discussions regarding news should be kept in r/inthenews, which is another subreddit for opinion pieces.
Interestingly, news related to politics should be moved to R/politics. Therefore, this subreddit is not a suitable place for followers who look for inherently political materials.
Critiques of Reddit
While Reddit does appear to have a platform for everyone’s voice to be heard there is an underlying issue that moderators have the power to censor any subreddits that do not adhere to the views they hold. This may lead to some users having a smaller voice in their community and discourage them in the future from participating.
Currently, Reddit has moderator guidelines with vague definitions of how moderators should behave, like being “around” to answer questions and solve problems, cultivating “healthy communities”, and allowing moderators to review appeals to their own actions.
Reddit also lends itself to be an anonymous forum where violent language could be exchanged, making many of its users fearful of death threats, threats of sexual violence, defamation, etc. Currently Reddit reserves the right to ban subreddits and utilize its quarantine method to limit exposure to subreddits.
Looking towards the future Reddit has the opportunity to change how their moderators work by strengthening the non-partisan ideals of moderatorship and encourage consistent action across subreddits, Reddit should shift the shape of their Moderator Guidelines.
First, converting the guidelines to requirements or another type of document requiring explicit acceptance of the rules would create a stronger infrastructure and sense of commitment to how Reddit would like moderators to behave.
Secondly, the terms of the current moderator guidelines need to be better defined. This could be done through either modeling exceptional subreddit moderator and moderator practices, or providing their own examples of how they would like to see moderation handled. For example, in the guidance for Stable and Active Teams of Moderators, Reddit should provide:
- appropriate frequency of participation on the subreddit,
- reasons acceptable for extended leaves,
- a process in which moderators are required to notify their team about extended leave,
- activity frequency guidelines under which a mod is demoted (for example, being missing for x amount of time, being present but not handling moderator duties for y amount of time, etc.)
A solution to abuses of anonymity on Reddit could be an additional financial sanction added to subreddits designated as free speech applicable, but not recommended for the general population. The financial sanction would require the subreddit to pay, collectively, to remain in existence and be hosted. The fee could be per-subscriber or collectively as a subreddit, and could be due annually or per month. The funds from these collections could be partially donated to causes that support human rights, social welfare, and freedom of speech.
The advantage to per-subscriber is that the financial cost would limit the popularity of said subreddits and would scale in terms of subreddit volume, but imposing a community-wide funding target would allow for the temporary suspension of the subreddit if it cannot “offset” itself by a certain contribution for charity, which creates some social good. An annual collection is a more forgiving method for collection and provides a set expectation, and again, the per-month collection discourages high volumes of traffic to the subreddit and maximizes potential to collect funds for charitable causes.
Recommended Reading
“ Reddit Raised $200 Million in Funding and Is Now Valued at $1.8 Billion ” by Kurt Wagner, Vox , July 21, 2017.
“ Reddit’s Co-Founders Sold the Company at Age 23 For a Fraction of the 1.8 Billion It’s Worth Today – Here’s How the Duo Got Back On Top ,” Melia Robinson, Business Insider , Nov. 24, 2017.


3.6: Electric Potential of a Point Charge
By the end of this section, you will be able to:
- Calculate the potential due to a point charge
- Calculate the potential of a system of multiple point charges
- Calculate the potential of a continuous charge distribution
Point charges, such as electrons, are among the fundamental building blocks of matter. Furthermore, spherical charge distributions (such as charge on a metal sphere) create external electric fields exactly like a point charge. The electric potential due to a point charge is, thus, a case we need to consider.
We can use calculus to find the work needed to move a test charge \(q\) from a large distance away to a distance of \(r\) from a point charge \(q\). Noting the connection between work and potential \(W = -q\Delta V\), as in the last section, we can obtain the following result.
The electric potential \(V\) of a point charge is given by
\[\underbrace{V = \dfrac{kq}{r}}_{\text{point charge}} \label{PointCharge}\]
where \(k\) is a constant equal to \(8.99 \times 10^9 \, \mathrm{N} \cdot \mathrm{m}^2/\mathrm{C}^2\).
The potential in Equation \ref{PointCharge} at infinity is chosen to be zero. Thus, \(V\) for a point charge decreases with distance, whereas \(\vec{E}\) for a point charge decreases with distance squared:
\[E = \dfrac{F}{q_t} = \dfrac{kq}{r^2}\]
Recall that the electric potential \(V\) is a scalar and has no direction, whereas the electric field \(\vec{E}\) is a vector. To find the voltage due to a combination of point charges, you add the individual voltages as numbers. To find the total electric field, you must add the individual fields as vectors, taking magnitude and direction into account. This is consistent with the fact that \(V\) is closely associated with energy, a scalar, whereas \(\vec{E}\) is closely associated with force, a vector.
Charges in static electricity are typically in the nanocoulomb (nC) to microcoulomb \((\mu C)\) range. What is the voltage 5.00 cm away from the center of a 1-cm-diameter solid metal sphere that has a –3.00-nC static charge?
Strategy
As we discussed in Electric Charges and Fields , charge on a metal sphere spreads out uniformly and produces a field like that of a point charge located at its center. Thus, we can find the voltage using the equation \(V = \dfrac{kq}{r}\).
Solution
Entering known values into the expression for the potential of a point charge (Equation \ref{PointCharge}), we obtain
\[\begin{align} V &= k\dfrac{q}{r} \nonumber \\[4pt] &= (9.00 \times 10^9 \, \mathrm{N} \cdot \mathrm{m}^2/\mathrm{C}^2)\left(\dfrac{-3.00 \times 10^{-9}\mathrm{C}}{5.00 \times 10^{-2}\mathrm{m}}\right) \nonumber \\[4pt] &= - 539 \, \mathrm{V}. \nonumber \end{align} \nonumber \]
Significance
The negative value for voltage means a positive charge would be attracted from a larger distance, since the potential is lower (more negative) than at larger distances. Conversely, a negative charge would be repelled, as expected.
A demonstration Van de Graaff generator has a 25.0-cm-diameter metal sphere that produces a voltage of 100 kV near its surface (Figure). What excess charge resides on the sphere? (Assume that each numerical value here is shown with three significant figures.)
Strategy
The potential on the surface is the same as that of a point charge at the center of the sphere, 12.5 cm away. (The radius of the sphere is 12.5 cm.) We can thus determine the excess charge using Equation \ref{PointCharge}
\[V = \dfrac{kq}{r}.\]
Solution
Solving for \(q\) and entering known values gives
\[\begin{align} q &= \dfrac{rV}{k} \nonumber \\[4pt] &= \dfrac{(0.125 \, \mathrm{m})(100 \times 10^3 \, \mathrm{V})}{8.99 \times 10^9\,\mathrm{N} \cdot \mathrm{m}^2/\mathrm{C}^2} \nonumber \\[4pt] &= 1.39 \times 10^{-6}\,\mathrm{C} \nonumber \\[4pt] &= 1.39 \, \mu\mathrm{C}. \nonumber \end{align} \nonumber
Significance
This is a relatively small charge, but it produces a rather large voltage. We have another indication here that it is difficult to store isolated charges.
What is the potential inside the metal sphere in Example \(\PageIndex{1}\)?
- Answer
-
\[\begin{align} V &= k\dfrac{q}{r} \nonumber \\[4pt] &= (8.99 \times 10^9\,\mathrm{N} \cdot \mathrm{m}^2/\mathrm{C}^2) \left(\dfrac{-3.00 \times 10^{-9}\,\mathrm{C}}{5.00 \times 10^{-3}\,\mathrm{m}}\right) \nonumber \\[4pt] &= - 5390 \, \mathrm{V}\nonumber \end{align} \nonumber \]
Recall that the electric field inside a conductor is zero. Hence, any path from a point on the surface to any point in the interior will have an integrand of zero when calculating the change in potential, and thus the potential in the interior of the sphere is identical to that on the surface.
The voltages in both of these examples could be measured with a meter that compares the measured potential with ground potential. Ground potential is often taken to be zero (instead of taking the potential at infinity to be zero). It is the potential difference between two points that is of importance, and very often there is a tacit assumption that some reference point, such as Earth or a very distant point, is at zero potential. As noted earlier, this is analogous to taking sea level as \(h = 0\) when considering gravitational potential energy \(U_g = mgh\).
Systems of Multiple Point Charges
Just as the electric field obeys a superposition principle, so does the electric potential. Consider a system consisting of \(N\) charges \(q_1,q_2,. . ., q_N\). What is the net electric potential \(V\) at a space point \(P\) from these charges? Each of these charges is a source charge that produces its own electric potential at point \(P\), independent of whatever other changes may be doing. Let \(V_1, V_2, . . ., V_N\) be the electric potentials at \(P\) produced by the charges \(q_1,q_2,. . ., q_N\), respectively. Then, the net electric potential \(V_p\) at that point is equal to the sum of these individual electric potentials. You can easily show this by calculating the potential energy of a test charge when you bring the test charge from the reference point at infinity to point \(P\):
\[V_p = V_1 + V_2 + . . . + V_N = \sum_1^N V_i.\]
Note that electric potential follows the same principle of superposition as electric field and electric potential energy. To show this more explicitly, note that a test charge \(q_i\) at the point \(P\) in space has distances of \(r_1,r_2, . . . ,r_N\) from the \(N\), charges fixed in space above, as shown in Figure \(\PageIndex{2}\). Using our formula for the potential of a point charge for each of these (assumed to be point) charges, we find that
\[V_p = \sum_1^N k\dfrac{q_i}{r_i} = k\sum_1^N \dfrac{q_i}{r_i}. \label{eq20}\]
Therefore, the electric potential energy of the test charge is
\[U_p = q_tV_p = q_tk\sum_1^N \dfrac{q_i}{r_i},\] which is the same as the work to bring the test charge into the system, as found in the first section of the chapter.
An electric dipole is a system of two equal but opposite charges a fixed distance apart. This system is used to model many real-world systems, including atomic and molecular interactions. One of these systems is the water molecule, under certain circumstances. These circumstances are met inside a microwave oven, where electric fields with alternating directions make the water molecules change orientation. This vibration is the same as heat at the molecular level.
Consider the dipole in Figure \(\PageIndex{3}\) with the charge magnitude of \(q = 3.0 \, \mu \mathrm{C}\) and separation distance \(d = 4.0 \, \mathrm{cm}.\) What is the potential at the following locations in space? (a) (0, 0, 1.0 cm); (b) (0, 0, –5.0 cm); (c) (3.0 cm, 0, 2.0 cm).
Strategy
Apply \(V_p = k \sum_1^N \dfrac{q_i}{r_i}\) to each of these three points.
Solution
a. \(V_p = k \sum_1^N \dfrac{q_i}{r_i} = (9.0 \times 10^9 \,\textrm{N} \cdot \textrm{m}^2/\textrm{C}^2) \left(\dfrac{3.0\space \textrm{nC}}{0.010 \, \textrm{m}} - \dfrac{3.0\space \textrm{nC}}{0.030 \, \textrm{m}}\right) = 1.8 \times 10^3 \, \textrm{V}\)
b. \(V_p = k \sum_1^N \dfrac{q_i}{r_i} = (9.0 \times 10^9 \, \textrm{N} \cdot \textrm{m}^2/\textrm{C}^2) \left(\dfrac{3.0\space \textrm{nC}}{0.070 \, \textrm{m}} - \dfrac{3.0\space \textrm{nC}}{0.030 \, \textrm{m}}\right) = -5.1 \times 10^2 \, \textrm{V}\)
c. \(V_p = k \sum_1^N \dfrac{q_i}{r_i} = (9.0 \times 10^9 \, \textrm{N} \cdot \textrm{m}^2/\textrm{C}^2) \left(\dfrac{3.0\space \textrm{nC}}{0.030 \, \textrm{m}} - \dfrac{3.0\space \textrm{nC}}{0.050 \, \textrm{m}}\right) = 3.6 \times 10^2 \, \textrm{V}\)
Significance
Note that evaluating potential is significantly simpler than electric field, due to potential being a scalar instead of a vector.
What is the potential on the \(x\)-axis? The \(z\)-axis?
- Answer
-
The \(x\)-axis the potential is zero, due to the equal and opposite charges the same distance from it. On the \(z\)-axis, we may superimpose the two potentials; we will find that for \(z > > d\), again the potential goes to zero due to cancellation.


6.2: Assignment- Three Research Topic Ideas
In the group discussions recently you’ve been chatting about initial topic ideas. You’ve probably gotten a better idea of what you’d actually like to pursue, and perhaps even had new ideas in the meantime.
Assignment Requirements
For this assignment, I’d like you to narrow your options down to 3. For each of these 3 potential research topics, draft a paragraph of exploration including the following:
- what the topic is, and why it appeals to you
- questions you have about the topic you didn’t already know the answers to
- an overview of some initial quick research you’ve done on the topic (Google & Wikipedia are fine for our purposes here), including at least one new discovery for you about the issue
- what you’d hope to be able to prove to your reader about this issue in a research essay about it
This is an informal assignment, though matters of proofreading and grammar are always helpful to check over before submitting.
These 3 topics can come straight from your list of 5 that you submitted to the weekly discussion, OR you can come up with 3 new ideas, or any combination of the two.
If you know for sure what topic you’d like to pursue for your essay, I’d still like to see three different potential sub-topics explored here. For instance, if you know you want to write about scuba diving, divide that into three directions you might then take: how scuba diving affects tourism, how scuba divers help or hurt natural underwater environments, what safety training scuba divers should have to complete for certification.
A sample paragraph: I’d like to consider writing my essay about Cheezits, because I’m always snacking on them while I work on my online classwork. I didn’t really know who made them or how popular a snack food they were, beyond the fact that they are readily available in grocery stores. A Google search led me to the brand’s website, where I learned they were made by Sunshine, and had a variety called “Scrabble Junior” that I’d never seen before, with letters printed on each cracker. In an essay about Cheezits, I’d like to be able to prove to myself and my readers that these are a better cheese-flavored snack than other options available right now.Contributors and Attributions
- Composition II. Authored by : Alexis McMillan-Clifton. Provided by : Tacoma Community College. Located at : http://www.tacomacc.edu . Project : Kaleidoscope Open Course Project. License : CC BY: Attribution


11.3A: Blood-Brain Barrier
Tight junctions present in the blood-brain barrier separate circulating blood from cerebrospinal fluid, regulating diffusion into the brain.
- Describe the function of the blood-brain barrier
Key Points
- The blood – brain barrier (BBB) endothelial cells restrict the passage of substances from the bloodstream to a greater extent than endothelial cells in capillaries elsewhere in the body.
- The BBB results from the selectivity of the tight junctions between endothelial cells in central nervous system (CNS) vessels that restrict the passage of solutes.
- Several areas of the human brain are not protected by the BBB, including the circumventricular organs.
- Tight junctions are composed of transmembrane proteins such as occludin and the claudins.
- The BBB effectively protects the brain from many common bacterial infections. However, since antibodies and antibiotics are too large to cross the BBB, infections of the brain that do occur are often difficult to treat.
Key Terms
- astrocyte : A star-shaped neuroglial cell.
- claudins : This family of proteins is the most important component of tight junctions, where they establish the paracellular barrier that controls the flow of molecules in the intercellular space between the cells of an epithelium.
- blood-brain barrier : A structure in the CNS that keeps substances found in the bloodstream out of the brain while allowing in substances essential to metabolic function such asoxygen.
- occludin : A protein forming the main component of the tight junctions, along with the claudin group of proteins.
EXAMPLES
- An exception to the bacterial exclusion are the diseases caused by spirochetes, such as Borrelia , which causes Lyme disease, and Treponema pallidum , which causes syphilis. These harmful bacteria seem to breach the BBB by physically tunneling through the blood vessel walls.
- Modalities for drug delivery through the BBB entail its disruption by osmotic means, biochemically by the use of vasoactive substances, or by localized exposure to high-intensity focused ultrasound.
The blood-brain barrier (BBB) is a separation of circulating blood from the brain extracellular fluid in the central nervous system (CNS). Bacteriologist Paul Ehrlich observed that chemical dye injected into an animal would stain all of its organs except for the brain. In a later experiment, his student Edwin Goldmann found that when dye is directly injected into the cerebrospinal fluid (CSF) of animals’ brains, the brains were dyed while the rest of the organs were unaffected. This clearly demonstrated the existence of some sort of compartmentalization between the brain and the rest of the body. The concept of the BBB (then termed hematoencephalic barrier) was proposed by Lewandowsky in 1900. It was not until the introduction of the scanning electron microscope that the actual membrane could be observed and proven to exist.
Blood-Brain Barrier Structure
The Blood Brain Barrier at the Small Scale : Astrocytes send projections to completely encircle capillaries. This allows tight regulation of passage of molecules into and out of the CNS.
The BBB results from the selectivity of the tight junctions between endothelial cells in CNS vessels that restrict the passage of solutes. At the interface between blood and the brain, endothelial cells are joined by these tight junctions, which are composed of smaller subunits, frequently biochemical dimers that are transmembrane proteins such as occludin, claudins, and junctional adhesion molecule. Each of these transmembrane proteins is anchored into the endothelial cells by another protein complex. This barrier also includes a thick basement membrane and astrocyte cell projections called astrocytic feet (forming the thin barrier called the glia limitans) that surround the endothelial cells of the BBB, providing biochemical support to those cells.
Function and Importance of the Blood-Brain Barrier
The BBB endothelial cells restrict the passage of substances from the bloodstream to a greater extent than endothelial cells in capillaries elsewhere in the body. The diffusion of microscopic particles (e.g., bacteria), large molecules, and hydrophilic molecules into the CSF is restricted, while the diffusion of small hydrophobic molecules (O2, CO2, hormones ) is permitted. Also, BBB cells actively transport metabolic products such as glucose across the barrier.
Non-Protected Areas of the Brain
Several areas of the human brain are not protected by the BBB. These include the circumventricular organs such as the area postrema, median eminence of the hypothalamus, pineal gland, and the posterior pituitary. The posterior pituitary and pineal gland are not covered by the BBB because they secrete hormones into circulation. The median eminence is not covered by BBB because the pituitary secretions collect in this area before release into circulation. The area postrema detects noxious substances present in the blood and is therefore not covered by the BBB.
Role of Blood-Brain Barrier in Infectious Processes
The BBB effectively protects the brain from many common bacterial infections, so brain infections are very rare. However, since antibodies and antibiotics are too large to cross the BBB, brain infections that do occur are often very serious and difficult to treat. However, the BBB becomes more permeable during inflammation. This allows some antibiotics and phagocytes to move across the BBB, but also allows bacteria and virus to cross. Diseases caused by spirochetes are exceptions to this bacterial exclusion. These include Borrelia (the cause of Lyme disease), and Treponema pallidum, which causes syphilis. These harmful bacteria seem to breach the BBB by physically tunneling through the blood vessel walls. Some toxins are made up of large molecules that cannot pass through the BBB. Neurotoxins such as botulinum toxin in food might affect peripheral nerves, but the BBB can often prevent such toxins from reaching the CNS, where they could cause serious or fatal damage.