7.6: Chapter 7 Review

  1. The value of a new boat depreciates after it is purchased. The value of the boat 7 years after it was purchased is $25,000 and its value has been decreasing at the rate of 8.2% per year.
    1. Find the initial value of the boat when it was purchased.
    2. How many years after it was purchased will the boat’s value be $20,000?
    3. What was its value 3 years after the boat was purchased?
  2. Tony invested $40,000 in 2010; unfortunately his investment has been losing value at the rate of 2.7% per year.
    1. Write the function that gives the value of the investment as a function of time (t) in years after 2010.
    2. Find the value of the investment in 2020, if its value continues to decrease at this rate.
    3. In what year will the investment be worth half its original value?
  3. Rosa invested $25,000 in 2005; its value has been increasing at the rate of 6.4% annually.
    1. Write the function that gives the value of the investment as a function of time (t) in years after 2005.
    2. Find the value of the investment in 2025.
  4. The population of a city is increasing at the rate of 3.2% per year, since the year 2000. Its population in 2015 was 235,000 people.
    1. Find the population of the city in the year 2000.
    2. In what year with the population be 250, 000 if it continues to grow at this rate.
    3. What was the population of this city in the year 2008?
  5. The population of an endangered species has only 5000 animals now. Its population has been decreasing at the rate of 12% per year.
    1. If the population continues to decrease at this rate, how many animals will be in this population 4 years from now.
    2. In what year will there be only 2000 animals remaining in this population?
  6. 300 mg of a medication is administered to a patient. After 5 hours, only 80 mg remains in the bloodstream.
    1. Using an exponential decay model, find the hourly decay rate.
    2. How many hours after the 300 mg dose of medication was administered was there 125 mg in the bloodstream
    3. How much medication remains in the bloodstream after 8 hours?
  7. If (y = 240b^t) and (y = 600) when (t = 6) years, find the annual growth rate. State your answer as a percent.
  8. If the function is given in the form (y = ae^{kt}), rewrite it in the form (y = ab^t).
    If the function is given in the form (y = ab^t), rewrite it in the form (y = ae^{kt}).
    1. (y=375000left(1.125^{t} ight) onumber)
    2. (y=5400 e^{0.127 t} onumber )
    3. (y=230 e^{-0.62 t})
    4. (y=3600left(0.42^{t} ight))

Walk-through of Chapter 7 Elite Stages

If you’ve come this far, you are doing pretty well. Here is the idiot’s guide to owning the challenges in Chapter 7 of Lords Mobile’s Elite Stages. Like the other chapter guides, this strategy is for Free-To-Play players (although I will mention notable P2P heroes when relevant).

Chapter 7 is also known as Way of Fire and Lava Plateau. I have no idea why IGG give these extra names for this chapter when no seems to really notice. They may as well have called it “Way of Ridiculousness” or something else more meaningful. My guess is that whoever came up with these names was sniffing a lot of glue at the time.

Important Note: If a player has reached Elite Stage 7, I hope that I can assume that he already has at least a few gold heroes. The gold heroes aren’t necessary, but they will have to be at least partially advanced. The most important factor will be the hero trophies. The more hero trophies, the better. Focus on collecting as many trophies as you can!

7.6: Chapter 7 Review

When more than one author extracts data from the same reports, there is potential for disagreement.  An explicit procedure or decision rule should be identified in the protocol for identifying and resolving disagreements. Most often, the source of the disagreement is an error by one of the extractors and is easily resolved. Thus, discussion among the authors is a sensible first step. More rarely, a disagreement may require arbitration by another person. Any disagreements that cannot be resolved should be addressed by contacting the study authors if this is unsuccessful, the disagreement should be reported in the review.

The presence and resolution of disagreements should be carefully recorded. Maintaining a copy of the data ‘as extracted’ (in addition to the consensus data) allows assessment of reliability of coding. Examples of ways in which this can be achieved include:

Use one author’s (paper) data collection form and record changes after consensus in a different ink colour.

Use a separate (paper) form for consensus data.

Enter consensus data onto an electronic form.

Agreement of coded items can be quantified, for example using kappa statistics (Orwin 1994) , although this is not routinely done in Cochrane reviews. A simple calculation for agreement between two authors is described in Section 7.2.6 . If agreement is assessed, this should be done only for the most important data (e.g. key risk of bias assessments, or availability of key outcomes).

Informal consideration of the reliability of data extraction should be borne in mind throughout the review process, however.  For example, if after reaching consensus on the first few studies, the authors note a frequent disagreement for specific data, then coding instructions may need modification. Furthermore, an author’s coding strategy may change over time, as the coding rules are forgotten, indicating a need for re-training and, possibly, some re-coding.

7.6: Chapter 7 Review

It is strongly recommended that more than one person extract data from every report to minimize errors and reduce potential biases being introduced by review authors. As a minimum, information that involves subjective interpretation and information that is critical to the interpretation of results (e.g. outcome data) should be extracted independently by at least two people. In common with implementation of the selection process (Section 7.2.4 ), it is preferable that data extractors are from complementary disciplines, for example a methodologist and a topic area specialist. It is important that everyone involved in data extraction has practice using the form and, if the form was designed by someone else, receives appropriate training.

Evidence in support of duplicate data extraction comes from several indirect sources. One study observed that independent data extraction by two authors resulted in fewer errors than a data extraction by a single author followed by verification by a second (Buscemi 2006) . A high prevalence of data extraction errors (errors in 20 out of 34 reviews) has been observed (Jones 2005) . A further study of data extraction to compute standardized mean differences found that a minimum of seven out of 27 reviews had substantial errors (Gøtzsche 2007) .

7.6: Chapter Summary

Conformity refers to the change in beliefs, opinions, and behaviors that occurs as the result of social influence. The typical outcome of conformity is that people&rsquos beliefs and behaviors become more similar to those of others around them.

The change in opinions or behavior that occurs when we conform to people who we believe have accurate information is known as informational social influence. Informational social influence usually results in private acceptance, which is real change in opinions on the part of the individual.

Normative social influence occurs when we express opinions or behave in ways that help us to be accepted or that keep us from being isolated or rejected by those we care about. The outcome of normative social influence is frequently public compliance&mdasha change in behavior that is not accompanied by an actual change in one&rsquos private opinion.

Majority influence occurs when the views or behaviors of a larger number of individuals in the current social group prevail. Majority influence may frequently produce public compliance. One powerful example of majority influence can be found in the line-judging studies of Solomon Asch.

Minority influence occurs when the views of a smaller number of individuals prevail. Although less frequent than majority influence, minority influence can occur if the minority expresses their views consistently and confidently. An example is Moscovici&rsquos color-judgment study. Because minorities force group members to think more fully about a topic, they can produce more creative thinking.

The extent to which we conform is influenced by the size of the majority group. The increase in the amount of conformity that is produced by adding new members to the majority group, known as the social impact of each group member, is greater for initial majority members than it is for later members.

Conformity decreases sharply when there is any disagreement among the members of the group that is trying to create influence. Unanimity is powerful in part because being the only person who is different is potentially embarrassing, and because we want to be liked by others, we may naturally want to avoid this.

Milgram&rsquos study on obedience is an example of the power of an authority to create obedience. Milgram found that when an authority figure accepted responsibility for the behavior of the individuals, 65% of the participants followed his instructions and administered what they thought was a severe and dangerous shock to another person.

The conformity observed in Milgram&rsquos study was due in part to the authority of the experimenter. In a replication when the experimenter had lower status, obedience was reduced. Obedience was also reduced when the experimenter&rsquos ability to express his authority was limited by having him sit in an adjoining room and communicate to the teacher by telephone. Milgram&rsquos studies also confirmed the role of unanimity in producing conformity.

Social power is the ability of one individual to create behavioral or belief changes in another person. Five types of social power&mdashreward, coercive, legitimate, referent, and expert power&mdashvary in terms of whether they are more likely to create private acceptance or public compliance.

Leaders use many types of power to influence others. Some approaches to understanding the nature of leadership have focused on the personality of the leader, finding that variables such as intelligence and sociability are associated with good leaders. Other leadership styles, such as those exhibited by charismatic and transformational leaders, have also been studied. Other approaches, including the contingency model of leadership effectiveness, examine the conditions under which different types of leaders are most likely to be effective.

People with lower self-esteem are more likely to conform than are those with higher self-esteem, and people who are dependent on and who have a strong need for approval from others are also more conforming.

Men, on average, are more concerned about appearing to have high status by acting independently from the opinions of others they are more likely to resist changing their beliefs in public than are women. In contrast, women, on average, are more concerned with connecting to others and maintaining group harmony they are more likely to conform to the opinions of others in order to prevent social disagreement.

Men and women differ in their preferred leadership styles, such that women use more relationship-oriented approaches than men use. Although men are perceived to be better leaders than women, and often are more likely to become leaders, there is no evidence that either men or women are more effective leaders.

When individuals feel that their freedom is being threatened by influence attempts, and yet they also have the ability to resist that persuasion, they may develop psychological reactance and not conform at all. Reactance has been shown to occur in many real-world contexts.

7.6 The Source of Intelligence

A young girl, born of teenage parents, lives with her grandmother in rural Mississippi. They are poor—in serious poverty—but they do their best to get by with what they have. She learns to read when she is just 3 years old. As she grows older, she longs to live with her mother, who now resides in Wisconsin. She moves there at the age of 6 years. At 9 years of age, she is raped. During the next several years, several different male relatives repeatedly molest her. Her life unravels. She turns to drugs and sex to fill the deep, lonely void inside her. Her mother then sends her to Nashville to live with her father, who imposes strict behavioral expectations upon her, and over time, her wild life settles once again. She begins to experience success in school, and at 19 years old, becomes the youngest and first African-American female news anchor (“Dates and Events,” n.d.). The woman—Oprah Winfrey—goes on to become a media giant known for both her intelligence and her empathy.


Where does high intelligence come from? Some researchers believe that intelligence is a trait inherited from a person’s parents. Scientists who research this topic typically use twin studies to determine the heritability of intelligence. The Minnesota Study of Twins Reared Apart is one of the most well-known twin studies. In this investigation, researchers found that identical twins raised together and identical twins raised apart exhibit a higher correlation between their IQ scores than siblings or fraternal twins raised together (Bouchard, Lykken, McGue, Segal, & Tellegen, 1990). The findings from this study reveal a genetic component to intelligence (figure below). At the same time, other psychologists believe that intelligence is shaped by a child’s developmental environment. If parents were to provide their children with intellectual stimuli from before they are born, it is likely that they would absorb the benefits of that stimulation, and it would be reflected in intelligence levels.

Figure 7.07. The correlations of IQs of unrelated versus related persons reared apart or together suggest a genetic component to intelligence.

The reality is that aspects of each idea are probably correct. In fact, one study suggests that although genetics seem to be in control of the level of intelligence, the environmental influences provide both stability and change to trigger manifestation of cognitive abilities (Bartels, Rietveld, Van Baal, & Boomsma, 2002). Certainly, there are behaviors that support the development of intelligence, but the genetic component of high intelligence should not be ignored. As with all heritable traits, however, it is not always possible to isolate how and when high intelligence is passed on to the next generation.

Range of Reaction is the theory that each person responds to the environment in a unique way based on his or her genetic makeup. According to this idea, your genetic potential is a fixed quantity, but whether you reach your full intellectual potential is dependent upon the environmental stimulation you experience, especially in childhood. Think about this scenario: A couple adopts a child who has average genetic intellectual potential. They raise her in an extremely stimulating environment. What will happen to the couple’s new daughter? It is likely that the stimulating environment will improve her intellectual outcomes over the course of her life. But what happens if this experiment is reversed? If a child with an extremely strong genetic background is placed in an environment that does not stimulate him: What happens? Interestingly, according to a longitudinal study of highly gifted individuals, it was found that “the two extremes of optimal and pathological experience are both represented disproportionately in the backgrounds of creative individuals” however, those who experienced supportive family environments were more likely to report being happy (Csikszentmihalyi & Csikszentmihalyi, 1993, p. 187).

Another challenge to determining origins of high intelligence is the confounding nature of our human social structures. It is troubling to note that some ethnic groups perform better on IQ tests than others—and it is likely that the results do not have much to do with the quality of each ethnic group’s intellect. The same is true for socioeconomic status. Children who live in poverty experience more pervasive, daily stress than children who do not worry about the basic needs of safety, shelter, and food. These worries can negatively affect how the brain functions and develops, causing a dip in IQ scores. Mark Kishiyama and his colleagues determined that children living in poverty demonstrated reduced prefrontal brain functioning comparable to children with damage to the lateral prefrontal cortex (Kishyama, Boyce, Jimenez, Perry, & Knight, 2009).

The debate around the foundations and influences on intelligence exploded in 1969, when an educational psychologist named Arthur Jensen published the article “How Much Can We Boost I.Q. and Achievement” in the Harvard Educational Review. Jensen had administered IQ tests to diverse groups of students, and his results led him to the conclusion that IQ is determined by genetics. He also posited that intelligence was made up of two types of abilities: Level I and Level II. In his theory, Level I is responsible for rote memorization, whereas Level II is responsible for conceptual and analytical abilities. According to his findings, Level I remained consistent among the human race. Level II, however, exhibited differences among ethnic groups (Modgil & Routledge, 1987). Jensen’s most controversial conclusion was that Level II intelligence is prevalent among Asians, then Caucasians, then African Americans. Robert Williams was among those who called out racial bias in Jensen’s results (Williams, 1970).

Obviously, Jensen’s interpretation of his own data caused an intense response in a nation that continued to grapple with the effects of racism (Fox, 2012). However, Jensen’s ideas were not solitary or unique rather, they represented one of many examples of psychologists asserting racial differences in IQ and cognitive ability. In fact, Rushton and Jensen (2005) reviewed three decades worth of research on the relationship between race and cognitive ability. Jensen’s belief in the inherited nature of intelligence and the validity of the IQ test to be the truest measure of intelligence are at the core of his conclusions. If, however, you believe that intelligence is more than Levels I and II, or that IQ tests do not control for socioeconomic and cultural differences among people, then perhaps you can dismiss Jensen’s conclusions as a single window that looks out on the complicated and varied landscape of human intelligence.

In a related story, parents of African American students filed a case against the State of California in 1979, because they believed that the testing method used to identify students with learning disabilities was culturally unfair as the tests were normed and standardized using white children (Larry P. v. Riles). The testing method used by the state disproportionately identified African American children as mentally retarded. This resulted in many students being incorrectly classified as “mentally retarded.” According to a summary of the case, Larry P. v. Riles:

In violation of Title VI of the Civil Rights Act of 1964, the Rehabilitation Act of 1973, and the Education for All Handicapped Children Act of 1975, defendants have utilized standardized intelligence tests that are racially and culturally biased, have a discriminatory impact against black children, and have not been validated for the purpose of essentially permanent placements of black children into educationally dead-end, isolated, and stigmatizing classes for the so-called educable mentally retarded. Further, these federal laws have been violated by defendants’ general use of placement mechanisms that, taken together, have not been validated and result in a large over-representation of black children in the special E.M.R. classes. (Larry P. v. Riles, par. 6)

Once again, the limitations of intelligence testing were revealed.


Learning disabilities are cognitive disorders that affect different areas of cognition, particularly language or reading. It should be pointed out that learning disabilities are not the same thing as intellectual disabilities. Learning disabilities are considered specific neurological impairments rather than global intellectual or developmental disabilities. A person with a language disability has difficulty understanding or using spoken language, whereas someone with a reading disability, such as dyslexia, has difficulty processing what he or she is reading.

Often, learning disabilities are not recognized until a child reaches school age. One confounding aspect of learning disabilities is that they often affect children with average to above-average intelligence. At the same time, learning disabilities tend to exhibit comorbidity with other disorders, like attention-deficit hyperactivity disorder (ADHD). Anywhere between 30–70% of individuals with diagnosed cases of ADHD also have some sort of learning disability (Riccio, Gonzales, & Hynd, 1994). Let’s take a look at two examples of common learning disabilities: dysgraphia and dyslexia.


Children with dysgraphia have a learning disability that results in a struggle to write legibly. The physical task of writing with a pen and paper is extremely challenging for the person. These children often have extreme difficulty putting their thoughts down on paper (Smits-Engelsman & Van Galen, 1997). This difficulty is inconsistent with a person’s IQ. That is, based on the child’s IQ and/or abilities in other areas, a child with dysgraphia should be able to write, but can’t. Children with dysgraphia may also have problems with spatial abilities.

Students with dysgraphia need academic accommodations to help them succeed in school. These accommodations can provide students with alternative assessment opportunities to demonstrate what they know (Barton, 2003). For example, a student with dysgraphia might be permitted to take an oral exam rather than a traditional paper-and-pencil test. Treatment is usually provided by an occupational therapist, although there is some question as to how effective such treatment is (Zwicker, 2005).


Dyslexia (also known as Alexia) is the most common learning disability in children. An individual with dyslexia exhibits an inability to correctly process letters. This manifests in a childs’ disruption in their ability to read, while the disruption does not affect their ability to comprehend spoken or aural language. The neurological mechanism for sound processing does not work properly in someone with dyslexia. As a result, dyslexic children may not understand sound-letter correspondence. A child with dyslexia may mix up letters within words and sentences—letter reversals, such as those shown in the figure below, are a hallmark of this learning disability—or skip whole words while reading. A dyslexic child may have difficulty spelling words correctly while writing. Because of the disordered way that the brain processes letters and sound, learning to read is a frustrating experience. Some dyslexic individuals cope by memorizing the shapes of most words, but they never actually learn to read (Berninger, 2008). Surprisingly, there have been some reports of individuals with dyslexia, but without agraphia, as in the individual is able to write fine, but is unable to understand what they are writing (Benson & Geschwind, 1969). In terms of neuroimaging, some work has demonstrated that people with dyslexia show disruptions of left hemisphere posterior neural systems while individuals are performing reading tasks (Shaywitz, Mody & Shaywitz, 2006). Additionally the evidence suggests some people have a genetically based form of dyslexia in which there are problems in the occipital-temporal region (where the occipital and temporal lobes meet) of the left hemisphere, a region that is strongly associated with language processing. There appears to be mainly disruptions in these areas of the brain that make it difficult to assemble letter combinations into words. However other groups with dyslexia show functioning processing of the left occipital-temporal region, but appear to suffer from a dyslexia that is is environmentally based related to poor education and other environmental factors that have separated affects on the development of the right prefrontal region associated with proper memory retrieval. These individuals tend to treat words as wholes instead of sounding them out attempting to retrieve words directly resulting in difficulty processing new words, and persistent reading difficulties that can be separate from what appears to be the more genetic based form of dyslexia (Radvansky & Ashcraft, 2013).

These written words show variations of the word “teapot” as written by individuals with dyslexia.


Genetics and environment affect intelligence and the challenges of certain learning disabilities. The intelligence levels of all individuals seem to benefit from rich stimulation in their early environments. Highly intelligent individuals, however, may have a built-in resiliency that allows them to overcome difficult obstacles in their upbringing. Learning disabilities can cause major challenges for children who are learning to read and write. Unlike developmental disabilities, learning disabilities are strictly neurological in nature and are not related to intelligence levels. Students with dyslexia, for example, may have extreme difficulty learning to read, but their intelligence levels are typically average or above average.

Openstax Psychology text by Kathryn Dumper, William Jenkins, Arlene Lacombe, Marilyn Lovett and Marion Perlmutter licensed under CC BY v4.0.


Review Questions:

1. Where does high intelligence come from?

2. Arthur Jensen believed that ________.

a. genetics was solely responsible for intelligence

b. environment was solely responsible for intelligence

c. intelligence level was determined by race

d. IQ tests do not take socioeconomic status into account

3. What is a learning disability?

a. a developmental disorder

b. a neurological disorder

d. an intellectual disorder

4. Which of the following statements is true?

a. Poverty always affects whether individuals are able to reach their full intellectual potential.

b. An individual’s intelligence is determined solely by the intelligence levels of his siblings.

c. The environment in which an individual is raised is the strongest predictor of her future intelligence

d. There are many factors working together to influence an individual’s intelligence level.

Critical Thinking Questions:

1. What evidence exists for a genetic component to an individual’s IQ?

2. Describe the relationship between learning disabilities and intellectual disabilities to intelligence.

Personal Application Question:

1. Do you believe your level of intelligence was improved because of the stimuli in your childhood environment? Why or why not?

dysgraphia: learning disability that causes extreme difficulty in writing legibly

dyslexia: common learning disability in which letters are not processed properly by the brain

range of reaction: each person’s response to the environment is unique based on his or her genetic make-up

Answers to Exercises

Review Questions:

Critical Thinking Questions:

1. Twin studies are one strong indication that IQ has a genetic component. Another indication is anecdotal evidence in the form of stories about highly intelligent individuals who come from difficult backgrounds yet still become highly successful adults.

2. Learning disabilities are specific neurological problems within the brain and are separate from intelligence. Intellectual disabilities are pervasive and related to intelligence.

dysgraphia: learning disability that causes extreme difficulty in writing legibly

dyslexia: common learning disability in which letters are not processed properly by the brain

range of reaction: each person’s response to the environment is unique based on his or her genetic make-up

7.6: Chapter 7 Review

Ecclesiastes Chapter 7

These sayings are much like those in the Book of Proverbs and demonstrate that Ecclesiastes also supports the wise approach to life. Mourning and sorrow are better than feasting and laughter (verses 1-3), because they cause a man to reflect wisely on the brevity of life. The laughter of the fool is compared to the crackling of thorns (verse 6), since both were characterized by noise, volatility and transience. To talk about the former days (verse 10), or the "good old days," is not wise. Both good and bad days are the work of God and are used, apart from our ability to understand them, in God's sovereign plan (verses 13-14).

Ecclesiastes 7:1 "A good name [is] better than precious ointment and the day of death than the day of one's birth."

Where a man has so lived to earn a good reputation, the day of his death can be a time of honor.

It appears that Solomon is giving some words of wisdom on the value of different things in life. A good name is, probably, the most valuable thing a person can have (in the physical). The only things that are more important are our relationship with God and our families.

It is a blessing to children, when they are left an honorable name by their father and mother. They are one step ahead of creating a good name for themselves. At least, everyone expects them to be of good character, when their parents have a good character. It is very nice to smell good, but more important is a person's character.

The day of death is better than the day of one's birth, because there are a lot of problems and heartaches in this world. When we die (if we are saved), those troubles and heartaches are over.

Revelation 14:13 "And I heard a voice from heaven saying unto me, Write, Blessed [are] the dead which die in the Lord from henceforth: Yea, saith the Spirit, that they may rest from their labors and their works do follow them."

The point of the section (of verses 2-6), is to emphasize that more is learned from adversity than from pleasure. True wisdom is developed in the crucible of life’s trials, though the preacher wishes that were not the case when he writes “this too is futility” (verse 6).

Ecclesiastes 7:2 "[It is] better to go to the house of mourning, than to go to the house of feasting: for that [is] the end of all men and the living will lay [it] to his heart."

Actually, we have this reversed. We rejoice when someone is born, and mourn when they die. Birth brings a lifetime of problems that we must deal with. At death (if we are Christians), we are told there will be no more sorrow.

Revelation 21:4 "And God shall wipe away all tears from their eyes and there shall be no more death, neither sorrow, nor crying, neither shall there be any more pain: for the former things are passed away."

Ecclesiastes 7:3 "Sorrow [is] better than laughter: for by the sadness of the countenance the heart is made better."

I have used the following expression many times: We do not learn anything on the mountain top, we learn in the valley. Problems come to make us strong.

Psalms 119:71 "[It is] good for me that I have been afflicted that I might learn thy statutes."

James 4:8-10 "Draw nigh to God, and he will draw nigh to you. Cleanse [your] hands, [ye] sinners and purify [your] hearts, [ye] double minded." "Be afflicted, and mourn, and weep: let your laughter be turned to mourning, and [your] joy to heaviness." "Humble yourselves in the sight of the Lord, and he shall lift you up."

None of this is saying that laughter is bad. It is, in fact, good. It is speaking of sorrow for our sins causing us to repent and be renewed in our hearts.

Ecclesiastes 7:4 "The heart of the wise [is] in the house of mourning but the heart of fools [is] in the house of mirth."

This is just explaining that what we do with our lives here on this earth is a very serious matter. We cannot just drift through life pleasing our flesh, and have a future. Our future lives are very serious things.

We will spend all of eternity in one of two places. If we never get serious about our relationship with God, we will spend eternity in hell. On the other hand, if we get serious with God, repent of our sins, and become a new creature in Christ, we will inherit eternal life in heaven.

Ecclesiastes 7:5 "[It is] better to hear the rebuke of the wise, than for a man to hear the song of fools."

The "song of fools" is speaking of songs of revelry. This type of song is usually accompanied with drinking or drugs. We find that suggestions in this type of songs encourage one to sin.

The present day rock music has terrible suggestive lyrics. Some of the words spoken are covered with the loud beat. Many young people do not even know what the words are.

The sad thing is that they are recorded in the subconscious mind, even when they do not realize what they are saying. The rebuke of the wise is to cause the person not to sin. We can certainly see that the rebuke is better.

Proverbs 15:32 "He that refuseth instruction despiseth his own soul: but he that heareth reproof getteth understanding."

Ecclesiastes 7:6 "For as the crackling of thorns under a pot, so [is] the laughter of the fool: this also [is] vanity."

The thorns, in this instance, are being burned. The laughter of a fool is as temporary as the thorns which burn. The fool's laughter is soon over, and reality sets in. The most foolish thing a person could do is reject the Lord for earthly pleasure.

Ecclesiastes 7:7 "Surely oppression maketh a wise man mad and a gift destroyeth the heart."

Oppression is an attack on the wise from the outside. It can be an attack from Satan, or from some person under the influence of Satan. It is maddening to be attacked. It is even more terrible to be the oppressor yourself. The truly wise will not be the oppressor.

Isaiah 33:15-16 "He that walketh righteously, and speaketh uprightly he that despiseth the gain of oppressions, that shaketh his hands from holding of bribes, that stoppeth his ears from hearing of blood, and shutteth his eyes from seeing evil" "He shall dwell on high: his place of defense [shall be] the munitions of rocks: bread shall be given him his waters [shall be] sure."

Exodus 23:8 "And thou shalt take no gift: for the gift blindeth the wise, and perverteth the words of the righteous." The "gift that destroys the heart" is speaking of bribery.

Ecclesiastes 7:8 "Better [is] the end of a thing than the beginning thereof: [and] the patient in spirit [is] better than the proud in spirit."

He that shall endure to the end shall be saved. In that particular sense, the end is much better than the beginning. At the beginning of a job, we are uncertain of ourselves. We have many obstacles to overcome. At the end, we have done all of this and have overcome.

The proud in spirit do not receive instruction very well. Those who are patient will make fewer mistakes.

Luke 21:19 "In your patience possess ye your souls."

Ecclesiastes 7:9 "Be not hasty in thy spirit to be angry: for anger resteth in the bosom of fools."

A very common way of describing this person would be to say he was "hot tempered".

Proverbs 14:29 "[He that is] slow to wrath [is] of great understanding: but [he that is] hasty of spirit exalteth folly."

Ephesians 4:26-27 "Be ye angry, and sin not: let not the sun go down upon your wrath:" "Neither give place to the devil."

Ephesians 4:31 "Let all bitterness, and wrath, and anger, and clamor, and evil speaking, be put away from you, with all malice:"

Anger leads to murder and hate which are both forbidden to believers.

Ecclesiastes 7:10 "Say not thou, What is [the cause] that the former days were better than these? for thou dost not inquire wisely concerning this."

Many people look back to the "good old days". They were not "good old days", when they were living them. They are good when you look back, because you have forgotten the problems. It seems (in verse 10 above), he is discontented with things the way they are. He really has no way of knowing that one time is better than another.

God has us in whatever circumstance is best for us at the present. We should be content, whatever is happening. There are times when we look back, that one particular thing was better, but every time has its problems as well.

In the midst of trouble and discontent, it is easy to lose touch with reality.

Ecclesiastes 7:11 "Wisdom [is] good with an inheritance: and [by it there is] profit to them that see the sun."

This is speaking of someone who has inherited money and prestige. His wisdom will be considered quicker than someone of low estate. Men are respecters of persons. Wealth that is used for good purposes is good. Solomon was a good example of that, because his father David was thought so highly of.

Ecclesiastes 7:12 "For wisdom [is] a defense, [and] money [is] a defense: but the excellency of knowledge [is, that] wisdom giveth life to them that have it."

Wisdom and money are a protection for those who have them. Godly wisdom brings eternal life. Knowledge is accumulated learning. The more you study God's Word, the closer you are to receiving Him in His fullness.

John 17:3 "And this is life eternal, that they might know thee the only true God, and Jesus Christ, whom thou hast sent."

7.6: Chapter 7 Review

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The lectures of this course are based on the first 11 chapters of Prof. Raymond Yeung’s textbook entitled Information Theory and Network Coding (Springer 2008). This book and its predecessor, A First Course in Information Theory (Kluwer 2002, essentially the first edition of the 2008 book), have been adopted by over 60 universities around the world as either a textbook or reference text. At the completion of this course, the student should be able to: 1) Demonstrate knowledge and understanding of the fundamentals of information theory. 2) Appreciate the notion of fundamental limits in communication systems and more generally all systems. 3) Develop deeper understanding of communication systems. 4) Apply the concepts of information theory to various disciplines in information science.


Chapter 7 Discrete Memoryless Channels - Part 2


Prof. Raymond W. Yeung

Choh-Ming Li Professor of Information Engineering, and Co-Director, Institute of Network Coding

Текст видео

In section 7.6, we discuss the channel capacity in the presence of feedback. Feedback is commonly used in practical communication systems for correcting possible errors which occur during transmission. Daily examples of feedback in communication includes, phone conversation and also classroom teaching. In data communication, the receiver may request the packets to be re-transmitted if the parity check bits received are incorrect. This is called automatic repeat request or ARQ in short. The transmitter can at any time decide what to transmit next based on the feedback so far. The question is can the use of feedback increase the channel capacity? Surprisingly, the answer is no for the discrete memoryless channel, even with complete feedback. This means that even the transmitter knows exactly what have been received by the receiver so far, it is not possible to transmit information through the channel reliably at a rate higher than without feedback. In the remaining of this section, we are going to see why this counter-intuitive result holds. Definition 7.18 is the definition of a feedback code. An (n,M) code, recall that n is the block length of the code and M is the size of the message set, with complete feedback for a discrete memoryless channel with input alphabet X and output alphabet Y is defined by the encoding functions f_i from the message set <1,2. M>times the output alphabet Y to the power i minus one to the input alphabet X, where i is from one up to n, and a decoding function g, from the output alphabet Y to the power n, to the message set <1,2. M>. We are going to adopt the following notations. We use bold Y^i to denote the sequence (Y_1, Y_2 up to Y_i) and X_i to denote f_i of W and Y^. Here, X_i is the symbol to be transmitted through the channel at time i. The function f_i, is the encoding function for the i-th transmission, which depends on w, the message to be transmitted and Y^, the first i minus 1 symbols received by the channel. Because of this, this code uses complete feedback. Here is the schematic diagram for an (n,M) code with complete feedback. At time i, the symbol X_i is transmitted through the channel and a symbol Y_i is received and fed back to the encoder. This is the dependency graph for a channel code with feedback, which is equivalent to the factorization, q(w, x, y, w hat) equals q(w) times the product from i equals 1 up to n, q(x_i|w,y^) times the product from i equals 1 up to n, p(y_i|x_i) times q(w hat|y), where this factorization is valid whenever the conditional events have non-zero probabilities. [BLANK_AUDIO] Definition 7.19 is the definition of a rate R being achievable with complete feedback. A rate R is achievable with complete feedback for a discrete memoryless channel p(y|x), if for any epsilon greater than zero there exists for sufficiently large n, an (n,M) code, with complete feedback, such that with 1 over n, times log M, that is the rate of the code, is at least R minus epsilon, and at the same time the maximal conditional probability of error is less than epsilon. [BLANK_AUDIO] Definition 7.20 is the definition of the feedback capacity. It says that the feedback capacity, C_ of a discrete memoryless channel is the supremum of all rates achievable by codes with complete feedback. Proposition 7.21 says that the supremum in the definition of the feedback capacity, in definition 7.20, is indeed the maximum. The proof follows directly from definition 7.19. Please see the textbook for details. We remark that since a channel code without feedback is a special case of a channel code with feedback, because the code can ignore the feedback, even if it is available, the feedback capacity is at least equal to the capacity without feedback. We now prove lemma 7.22, which says that for all i, W and Y^ X_i and Y_i forms a Markov chain. We first note that the Markov chain, W, X^ Y^, X_i and Y_i, hold because the channel is memoryless. Note that in the Markov chain in lemma 7.22, the set of random variables on the left hand side, is a subset of the set of random variables on the left hand side of this Markov chain. Thus, intuitively the Markov chain in lemma 7.22 should hold. The proof goes as follows. From the Markov chain in step one we have that, the mutual information between W, X^, Y^ and Y_i, conditioning on X_i, is equal to 0. For the ease of visualization, we temporarily cover X_i, the conditioning random variable. By means of the chain rule, we can expand this mutual information into the sum of two mutual informations. First, the mutual information between W, Y^ and Y_i, and second, the mutual information between X^ Y_i conditioning on W and Y^. Now we restore the conditioning random variable X_i. Because the sum of these two mutual informations is equal to 0, and the mutual information is always non-negative, we see that both mutual informations are equal to 0. In particular, the first mutual information, namely I(W,Y^Y_i|X_i) is equal to 0, which is equivalent to the Markov chain, W, Y^, X_i and Y_i. This proves the lemma. We have seen that the feedback capacity is at least equal to C, the capacity without feedback. Now we prove that the feedback capacity is also less than or equal to C. So from this, we can conclude that the feedback capacity is actually equal to C. Consider any code with complete feedback. Consider log M equals entropy of W because the message is chosen uniformly from the message set, and H(W) is equal to I(WY) plus H(W|Y). For the first term, I(WY) can be written as H(Y) minus H(Y|W). And H(Y|W), can be written as summation i equals 1 up to n, H(Y_i|Y^,W), where this is an application of the chain rule. Now we insert the random variable X_i in the conditioning in the i-th term of the summation. This is valid because in a feedback code, X_i is a function of W and Y^. In other words by inserting X_i we do not add any new information in the conditioning. Now by lemma 7.22, because Y_i is independent of W and Y^ given X_i, we can eliminate Y^, and W in the conditioning in the i-th term. And so, we have H(Y) minus summation i equals 1 up to n, H(Y_i|X_i). By the independence bound, H(Y) is upper bounded by summation i equals 1 up to n, H(Y_i). Now combining H(Y_i) and minus H(Y_i|X_i), we have I(X_iY_i), the mutual information between the input and output of the channel at time i. And by the definition of C, each of these mutual informations is less than or equal to C. And so, we obtain the upper bond n times C. Now, for the second term on the right-hand side in step two, we have H(W|Y) equals H(W|Y,W hat). This is valid, because W hat, which is the estimated message, is a function of the received sequence Y. By removing the sequence Y from the conditioning, we obtain the upper bound H(W|W hat), because conditioning can only reduce entropy. Now H(W|W hat), is very close to zero for reliable communication. So from step two, we have log M equals I(WY) plus H(W|Y), where I(WY) is less than or equal to n times C, and H(W|Y) is very close to 0. And therefore, we obtain that log M, is less than or equal to nC asymptotically. Formally, we apply Fano's inequality to upper bound H(W|W hat). Upon filling in the epsilons and deltas as in the proof of the converse of the channel coding theorem, we conclude that R is less than or equal to C for any rate R achievable with complete feedback. [BLANK_AUDIO] Here are some remarks regarding the feedback capacity. Although feedback does not increase the capacity of a Discrete Memoryless Channel, the availability of feedback often makes coding much simpler. I urge you to go through the example for a binary eraser channel, in example 7.23. In general, if the channel has memory, feedback can increase the capacity.

7.6. The Appeals Process, Standard of Review, and Appellate Decisions

The government cannot appeal a jury’s decision by acquitting the defendant, or finding the defendant not guilty. Thus, most criminal appeals involve defendants who have been found guilty at trial. The government may appeal a court’s pretrial ruling in a criminal matter before the case is tried, for example a decision to suppress evidence obtained in a police search. This is called an interlocutory appeal. Although the defendant is permitted to appeal after entering a guilty plea, the only basis for his or her appeal is to challenge the sentence given. When the defendant appeals, he or she is now referred to as the appellant, and the State is the appellee. (Note that often the court will use the words petitioner and respondent. The petitioner is the party who lost in the last court who is petitioning the next level court for review the respondent is the party who won in the last court). In routine appeals, the primary function of appellate courts is to review the record to discern if errors were made by the trial court before, during, or after the trial. No trial is perfect, so the goal is to ensure there was a fair, albeit imperfect, trial. Accordingly, the appellate courts review for fundamental, prejudicial or plain error. Appellate courts will reverse the conviction and possibly send the case back for a new trial when they find that trial errors affected the outcome of the case. A lower court’s judgment will not be reversed unless the appellant can show that some prejudice resulted from the error and that the outcome of the trial or sentence would have been different if there had been no error. By reviewing for error and then writing opinions that become case law, appellate courts perform dual functions in the criminal process: error correction and lawmaking.

Appellate judges generally sit in panels of three judges. They read the appellant’s brief (a written document filed by the appellant), the reply brief (a written document filed by the the appellee), and any other written work submitted by the parties or friend of the court amicus curiae briefs. Amicus curiae are individuals or groups who have an interest in the case or some sort of expertise but are not parties to the case. The appellate panel will generally listen to very short oral arguments, generally twenty minutes or less, by the parties’ attorneys. During these oral arguments, it is common for the appellate judges to interrupt and ask the attorneys questions about their positions. The judges will then consider the briefs and arguments and the panel will then meet and deliberate and decide based on majority rule. If the appellate court finds that no error was committed at trial, it will affirm the decision, but if it finds there was an error that deprived the losing party of a fair trial, it may issue an order of reversal. When the case is reversed, in most instances, the court simply will require a new trial during which the error will not be repeated. This is called a remand. In some cases, however, the order of reversal might include a direction to dismiss the case completely, for example when the appellate court concludes that the defendant’s behavior does not constitute a crime under the law in that state. When reading an opinion, also known as decisions, from an appellate court, you can tell the procedural history of a case (i.e., a roadmap of where the case has been: what happened at trial, what happened as the case was appealed up from the various appellate courts).

Standards of Review

You have just learned that one function of the appellate courts is to review the trial record and see if there is a prejudicial or fundamental error. Appellate courts do not consider each error in isolation, but instead, they look at the cumulative effect of all the errors during the whole trial. Appellate court judges must sometimes let a decision of a lower court stand, even if they personally don’t agree with it. Sports enthusiasts are familiar with the use of instant/video replay, and it provides us a good analogy. Officials in football, for example, will make a call, a ruling on the field, immediately after a play is made. This decision, when challenged, will be reviewed, and the decision will be upheld unless there is “incontrovertible evidence” that the call was wrong. When dealing with appeals, how much deference to show the lower court is the essence of the standard of review. Sometimes the appellate courts will give great deference to the trial court’s decision, and sometimes the appellate courts will give no deference to the trial court’s decision. How much deference to give is based on what the trial court was deciding—was it a question of fact, a question of law, or a mixed question of law and fact.

The appellate court will allow a trial court’s decision about a factual matter to stand unless the court clearly got it wrong. The appellate court reasons that the judge and jury were in the courtroom listening to and watching the demeanor of the witnesses and examining the physical evidence. They are in a much better position to determine the credibility of the evidence. Thus, the appellate court will not overturn findings of fact unless it is firmly convinced that a mistake has been made and that the trial court’s decision is clearly erroneous or “arbitrary and capricious.” The arbitrary and capricious standard means the trial court’s decision was completely unreasonable and it had no rational connection between the facts found and the decision made. The lower courts finding will be overturned only if it is completely implausible in light of all of the evidence. One court noted, “Where there are two permissible views of the evidence, the fact finder’s choice between them cannot be clearly erroneous.” [1]

Sometimes the law requires, or at the parties’ request, that a trial judge or jury make a special finding of fact. Findings of fact are made on the basis of evidentiary hearings and usually involve credibility determinations that are better made by the trial judge sitting in the courtroom listening to the evidence and observing the demeanor of the witnesses. It is not enough that the appellate court may have weighed the evidence and reached a different conclusion unless the decision was clearly erroneous, the appellate court will defer to the trial judge.

Trial judges often make discretionary rulings., for example, whether to allow a party’s request for a continuance or to allow a party to amend its pleadings or file documents late. In these matters of discretion, the appellate court will only overturn the trial judge if they find such a decision was an abuse of discretion. The lower court’s judgment will be termed an abuse of discretion only if the judge failed to exercise sound, reasonable, and legal decision-making skills. A trial court abuses its discretion, for example, when: it does not apply the correct law, erroneously interprets a law, rests its decision on a clearly inaccurate view of the law, rests its decision on a clearly erroneous finding of a material fact, or rules in a completely irrational manner. Abuse of discretion exists when the record contains no evidence to support the trial court’s decision.

When it comes to questions of law, the appellate courts employ a different standard of review called de novo review. De novo review allows the appellate court to use its own judgment about whether the trial court correctly applied the law. Appellate courts give little or no deference to the trial court’s determinations and may substitute its own judgment on questions of law. Questions of law include interpretation of statutes or contracts, the constitutionality of a statute, the interpretation of rules of criminal and civil procedure. Trial courts presume that laws are valid and do not violate the constitution, and the burden of proving otherwise falls on the defendant. Trial courts sometimes get it wrong. De novo review allows the court to use its own judgment about whether the court correctly applied the law. Appellate judges are perhaps in a better position to decide what the law is as the trial judge since they are not faced with the fast-pace of the trial and have time to research and reflect.

Sometimes the trial court must resolve a question in a case that presents both factual and legal issues. For example, if police stop and question a suspect, there are legal questions, such as whether the police had reasonable suspicion for the stop or whether the questioning constituted an “interrogation”, and factual questions, such as whether police read the suspect the required warnings. Mixed questions of law and fact are generally reviewed de novo. However, factual findings underlying the lower court’s ruling are reviewed for clear error. Thus, if the application of the law to the facts requires an inquiry that is “essentially factual,” review is for clear error.

In reviewing the trial court record, the appellate court may discover an error that parties failed to complain about. Generally, appellate courts will not correct errors that aren’t complained about, but this is not the case when they come upon plain error. Plain error exists “[w]hen a trial court makes an error that is so obvious and substantial that the appellate court should address it, even though the parties failed to object to the error at the time it was made.” [2] If the appellate court determines that the error was evident, obvious, clear and materially prejudiced a substantial right (meaning that it was likely that the mistake affected the outcome of the case below in a significant way), the court may correct the error. Usually, the court will not correct plain error unless it led to a miscarriage of justice.

The selection of the appropriate standard of review depends on the context. For example, the de novo standard applies when issues of law tend to dominate in the lower court’s decision. When a mixed question of law and fact is presented, the standard of review turns on whether factual matters or legal matters tend to dominate or control the court’s decision. The controlling standard of review may determine the outcome of the case. Sometimes the appellate court can substitute its judgment for that of the trial court and overturn a holding it does not agree with, but other times, it must uphold the lower court’s decision even if it would have decided differently.

Appellate Decisions

In most appeals filed in the intermediate courts of appeal, the appellate panel will rule but not write a supporting document called a written opinion stating why it ruled as it did. Instead, the appellate panel will affirm the lower court’s decision without an opinion (colloquially referred to as an AWOP). Sometimes, however, appellate court judges will support their decisions with a written opinion stating why the panel decided as it did and its reasons for affirming (upholding) or reversing (overturning) the lower court’s decision. The position and decision by the majority of the panel (or the entire court when it is a supreme court case), is, not surprisingly, called the majority opinion. Appellate court judges frequently disagree with one another, and a judge may want to issue a written opinion stating why he or she has a different opinion than the one expressed in the majority opinion. If a particular judge agrees with the result reached in the majority opinion but not the reasoning, he or she may write a separate concurring opinion. If a judge disagrees with the result and votes against the majority’s decision, he or she will write a dissenting opinion. Sometimes opinions are unsigned, and these are referred to as per curium opinions. Finally, if not enough justices agree on the result for the same reason, a plurality opinion will be written. A plurality opinion controls only the case currently being decided by the court and does not establish a precedent which judges in later similar cases must follow.

Chapter Summaries: Genesis Chapter 7 Summary

In Genesis chapter seven we go, and the chapter begins with the Lord acknowledging the righteousness of Noah in his generation. Pretty cool and fresh! The Lord commands Noah to take seven clean animals of the earth, a male and female, and the same for the birds of the air.

Noah was also commanded to take two of the unclean beasts, the male, and female. The reason? Within seven days, God was going to bring rain for forty days and nights, destroying every living soul off the face of the earth. Noah obeyed God and built the ark.

The father of Shem, Ham, and Japheth was 600 years old when the rains began. He went into the ark with his family and all the animals. Keep in mind here, the animals were under a covenant, meaning the lions weren’t predators eating meat or flesh.

The Waters Covered the Hills and Mountains

Therefore, Noah and his family had no problems getting the beasts into the ark. The rains begin and everything and one who had the breath of life in their nostrils died (who were not in the ark). Yes, all of the mocking towards Noah literally ceased.

The waters covered the hills and mountains, even if anyone could climb Mount Everest back then, they were going to become overcome with waterfloods. The waters covered the earth for 150 days.

This is the summary of Genesis chapter 7.


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