Saturday, December 31, 2016

6.4 Troubleshooting Parallel Circuits

This is the final section of Module 6 in the Navy Basic Electricity and Electronics series, a module on parallel circuits. The sections so far are:

6.1 Rules for Voltage and Current
6.2 Rules for Resistance and Power
6.3 Variational Analysis

This final section is on troubleshooting problems with parallel circuits and is rather short. It consists of five experiments.

1. The first experiment involves voltage and shows that the voltage drop in each parallel branch is the same as the applied voltage at the source.

2. The second experiment has to do with current and shows that the total amperage is the sum of all the branch currents.

3-4. The fourth experiment has to do with a short in one of the branches of a parallel circuit. "Current follows the path of least resistance" (104). Accordingly, if there is a short, then all the current will go through that path. This will blow a fuse if one is in play.

If there is an open in one branch, it effectively disappears from the system. The voltage and resistance in other individual branches stays the same, but the total current will drop (and thus total resistance will go up).

5. A short can cause considerable damage to the other components of a circuit. The ohmmeter function of a multimeter can help locate a short, as there will be no resistance in that branch. (Fire and smoke may also help :-) De-energize circuit before measuring.

Top Ten Posts of 2016

1. This is the best accounting I can give of my top ten posts for this year. It's often surprising to me what is widely read and what isn't.
2. Going by hits, I went back five years and these are the top ten posts since 2011:
Here was last year's top ten post.

3. I looked at my top tweets this year. Aside from a mocking political one in September ("She started it"), my number one tweet of the year was in November after the election: "The term evangelical should now be abandoned by any group wanting to bring millennials or non-whites to Christ."

4. As far as YouTube is concerned, my top ten watched videos by minutes watched this year were:

Friday, December 30, 2016

Friday Gen Eds MS11: The Physics of Motion

This is the eleventh post in the math/science part of my "Gen Eds in a Nutshell" series. The Gen Ed series consists of ten subjects you might study in a general education or "liberal arts" core at a university or college. I've already done the subject of philosophy, and I'm over half way through the world history subject on Wednesdays. I'm combining the last two on math and science into one series on Fridays.

Thus far in the math/science subjects:
1. Physics is the study of the "laws" of nature as they relate to matter and energy. We can roughly divide it into 1) mechanics, which has to do with motion and its related forces, 2) thermodynamics, which has to do with heat and its associated dynamics, 3) electromagnetism, and what I might call 4) fundamental physics, such as relativity and quantum mechanics.

Mechanics also roughly divides into two basic types of discussion: 1) the description of motion (kinematics) and 2) the forces of motion (dynamics). This entry has to do with the first--kinematics, the description of motion. The next entry will deal with the forces of motion.

Straight Line Motion
2. If you have been driving for a while, you will know that if you are driving 60 miles/hour for an hour, you will have driven 60 miles. We can put this into a formula: d = vt. You can find the distance you have traveled by multiplying the velocity at which you are traveling by the amount of time you are going at that velocity.

There are some details we might mention. First, you have to use the right units for this equation to work. So if you are using "miles per hour" for the velocity, you have to use hours for the time. Otherwise, you're not ready to multiply the two together. What you're trying to do is cancel out the "per hour" part with the number of hours. So if you had minutes or seconds in one place and hours in the others, it wouldn't cancel right.

A physicist might also want to clarify that there is technically a difference between speed and velocity. When we talk about "speed," we don't care what direction you're moving in. Who knows, you might be driving back and forth between two points for an hour. In physics, when we talk of velocity, we are talking about speed in a specific direction. [1]

We might also make the formula a little more detailed by adding a starting point d1, the place where you started. Then the formula is d2 = d1 + vt .

3. Acceleration is the change in velocity over time. We know it from driving in a car or taking off in a plane. So if speed is distance per time, then acceleration is distance per time per time or distance per time squared. Just as we easily derived an equation for distance in relation to velocity, we can imagine a similar one for velocity in relation to acceleration"

v2 = v1 + at

So if you had an acceleration in meters/second squared and you multiplied it by seconds. One of the seconds in the bottom would cancel with the seconds you were multiplying by. And you would be left with meters/second, which is a velocity.

4. If you understood calculus and integration in the previous entry, we can integrate this equation to get another equation for distance traveled when an object is not moving at a constant speed but at a constant acceleration. It turns out to be:

d2 = d1 + v1t + 1/2at2

Another equation finds the distance by multiplying the average velocity by the amount of time. It looks like this:
Finally, if we take this last equation and move the variables around to come up with an equation for t and then substitute this into the second equation above, we end up with the last of the primary motion equations of physics:

5. These are the primary equations for motion in a straight line, such as if you were driving on a straight road, a line in what we might think of as a horizontal direction. A falling body is another kind of "straight-line motion." As it turns out, when a body is relatively close to the surface of the earth, the acceleration due to gravity is constant.

The acceleration of any body near the surface of the earth is 9.8 meters/second squared (or 32 feet/second squared). If we give this constant (meaning a value that doesn't change) the symbol g , we can express the equations above in relation to a body falling in a straight line.

So the distance something will drop in a given amount of time (treating the initial distance and velocity as zero) is

d = 1/2gt2

Implied in this equation is the fact that all objects fall at the same rate of acceleration, no matter how much they weigh. [2]

6. Projectile motion is a motion in two dimensions. If you hit a baseball into the air, there is motion going on in two different directions, driven by two different forces. First, there is a motion in a horizontal direction, an "x" direction. Then there is a motion in the vertical or "y" direction. Gravity is the force at work in the y direction. The force of the bat drove the ball initially both forward and upward.

You can analyze the initial trajectory of the ball in terms of these two components, the x and y components, using trigonometry. So you hit the ball at a certain angle from the horizontal. If you know the velocity at which the ball leaves the bat at this angle, then you can find the "component" of that velocity that is vertical and the component of that velocity that is horizontal.

The "sine" of that angle is the ratio of the opposite side or y component to the hypotenuse or overall velocity. The "cosine" of that angle is the ratio of the adjacent side or x component to the hypotenuse. The bottom line is that if you multiply the sine of the angle by the overall velocity, you will know the initial vertical velocity component for the ball. And if you multiple the cosine of that angle times the initial velocity, you will know the initial horizontal velocity component for the ball.

Now you can analyze these two components of the ball's trajectory separately. For the horizontal component of the ball's trajectory, we have Newton's first law, which we will discuss in the next post: "a body in motion wants to stay in motion." So the ball would continue forward indefinitely if it could (leaving wind resistance out of consideration for the moment).

What makes the ball's time in the air limited is the fact that gravity will pull the ball back down to the ground. By using the velocity equations above, we can figure out first how much time it will take for the ball's upward motion to stop and for it to start falling back down (v2 = v1 - gt), remembering that v2 will be zero. We know v1the initial upward velocity. We know g which is -9.8 m/s (negative because it's pulling downwards). So we can solve for t, the time in the air.

We can then find the distance the ball will travel upward by using the equation d2 = d1 + v1t - 1/2gt2. We now know t. We know the initial vertical velocity. We know g. d1 is however far above the ground the bat hit the ball. After we solve for d2, then we know how high the ball will go before it starts to fall back down.

Circular Motion
A special kind of motion is circular motion. In popular language, we talk about "centrifugal force," which we relate to the way a body wants to fly off of a merry-go-round or the way our bodies crash into the car door if the driver takes two sharp of a curve or the way a rock flies off a sling if you are spinning it around.

Technically, this is not a force but Newton's first law in action--a body in motion wants to stay in motion. Our body wants to continue in the same direction off the merry-go-round or into the car door or off the sling. Therefore, in order to stay on our circular trajectory, we need a force pulling us toward the center of the circle, called a "centripetal" force.

It turns out that a constant acceleration toward the center of a circle is necessary to keep an object moving in constant circular motion. If you spin a yo-yo in a circle, you must constantly apply a centripetal force with your hand. The formula for that constant "radial" acceleration equals v2/r, where r is the radius of the circle and v is the velocity of the object as it would fly tangentially off its circular path if you were to let go.

Periodic Motion
Another kind of motion that has become extremely important for our understanding of electromagnetism and the quantum world is periodic motion. This is a recurring motion such as when a weight is bouncing back and forth on a spring. It is fundamental to clocks of many kinds, such as when a pendulum swings back and forth or the old watches with springs in them. This back and forth motion is called "oscillation."

Some basic terms here are the "frequency" of the back and forth motion (e.g., how many "cycles per second") and the "period" of one back and forth motion (how much time it takes for one cycle). There is also the "amplitude" of the cycle, how big the displacement is from the resting point.

As it turns out, periodic motion can be quantified in terms of circular motion, since the back and forth happens in a cycle, like a point traveling around a circle. The relationship in its simplest form turns out to be:

x = A cos ωt

In this equation, x is the amount of displacement from the rest point at any time t. A is the amplitude or the maximum displacement. "cos" means the cosine of ωt. ω is then something called the "angular frequency." It is 2π times the frequency (cycles per second). [3]

Next Week: Math/Science 12: The Forces of Motion

[1] We say that velocity is a "vector" quantity because it implies motion in a particular direction, while speed is a directionless "scalar" quantity.

[2] Of course not taking into account the fact that something like a feather will experience an air resistance that will make it fall slower than a truck. However, in a vacuum, a feather and a truck would fall at the same acceleration.

[3] The reason for the 2π is to get the frequency into "radian" units, which measure a circle in terms of how many radiuses along the circle you are. The angular frequency ω is thus measured in radians traveled per second.

Thursday, December 29, 2016

The Unending Israeli-Palestinian Puzzle

1. With the recent US abstention at the UN firmly in mind, the Israeli-Palestinian debate is back in the news. The US abstained on a vote condemning Jewish settlements on Palestinian land. The US has always vetoed those sorts of votes before.

If there were a simple solution, someone would have brought it about a long time ago. My own sense is that the Palestinians and their advocates have stubbornly persisted in an all-or-nothing approach, which has not only left them consistently with nothing, but with increasingly less than they had to begin with. In the meantime, Israel slowly creeps deeper and deeper into Palestinian territory with settlements, having found ways to keep Palestinians from succeeding with terrorism.

2. Historically, the beginnings of this situation go back to 1918, when the Ottoman Turks were defeated in World War I, and Britain became the protector of what today is Syria, Palestine, and Iraq. Britain was to watch over these territories "until such time as they are able to stand alone." This territory was known at that time as the "British Mandate," set to expire in 1948.

The British got it from both Arab and Jewish sides in this period. From 1936-39 there was an Arab Revolt against the British and the increasing Jewish population. [1] From 1939-38 especially there were underground Jewish groups that carried out actions against the British, the most famous of which was the bombing of the King David Hotel in 1946. [2]

1947 UN Partition Plan
As early as 1937, a two state solution was proposed, at first by Britain. The Jews supported it as a first step; the Palestinian Arabs refused. This has been the perennial problem on the Palestinian side. It continually refused to compromise at first on the existence of Israel and then later on realistic boundaries. In consequence, it has lost more and more territory to Israel.

3. Partitioning increasingly seemed the only viable option. After World War II, the United Nations proposed a Partition Plan for Palestine: two states, one Jewish and one Arab, with Jerusalem and Bethlehem under international oversight. But the day after the Mandate came to an end, on May 15, 1948, there was a scramble.

The Jews were prepared and organized. They immediately declared themselves a state and moved to occupy parts of Jerusalem. Palestinian Arabs fled central Palestine in large numbers. The Arab League launched the 1948 Arab-Israeli War. A year later, Israel had 60% of the territory that the United Nations had intended for an Arab state.

4. In 1967, as Egypt was amassing forces in the Sinai peninsula, Israel launched a preemptive strike that was incredibly successful. After this Six-Day War, Israel effectively occupied the Sinai peninsula, the West Bank, and the Gaza strip. Most calls for a two-state solution since have pushed Israel to return to its pre-1967 boundaries and yield these occupied territories to the Palestinians.

In 1973, Egypt and Syria fought back in the Yom Kippur War. Egypt sought to regain the Sinai Peninsula, while Syria tried to restore the northeastern Golan Heights. Although the war largely ended with the Israelis still in control of this territory, it helped drive both sides to the negotiating table.

In 1978, Jimmy Carter negotiated the Peace Accords that resulted in a planned withdrawal of Israel from the Sinai peninsula and its return to Egypt (Anwar Sadat, the president of Egypt, was assassinated by his own as a result), which was completed in 1982. Egypt became the first Arab state to recognize Israel as a nation. The Golan Heights were incorporated into Israel.

In 1994, the country of Jordan finally recognized Israel as a country, the second Arab state to do so.

5. An "intifada" was launched by Palestinians against the Israelis in 2000. From 2000 to 2003 there were some 73 suicide bombings. As a result, the construction of a wall was begun. From 2003 to 2006 there were only 12 attacks. The wall cuts at points into what was considered Palestinian territory before 1967, that is, across the green line.

6. In 2005, Ariel Sharon unilaterally withdrew Israelis from settlements in the Gaza strip back to the 1967 green line, and Israel abandoned four settlements in northern Samaria. Then in 2007 Hamas took over Gaza, resulting in mortars and rockets frequently being fired into Israeli territory.

7. In the last decade, Israel has effectively been expanding its territory by building settlements all over the West Bank and to the east of Jerusalem. The triangles in the map to the left show all the settlements for which the UN resolution reprimanded Israel with the US abstaining.

You can see what John Kerry was thinking when he said that the UN resolution is the only hope for a two-state solution. Many would consider there now only a one state eventuality likely--Israel in control of all these lands. Jimmy Carter has urged Obama to unilaterally recognize the Palestinian state before leaving office.

8. Christian theology and pre-millennial interpretation has played a dominant role in US support for Israel over the Palestinians, even though there are far more Palestinian Christians than Israeli ones. Nazareth is within Israel but is primarily Palestinian Christian. Bethlehem is outside Israel, outside the wall, but is predominantly Palestinian Christian.

Nevertheless, the re-establishment of Israel is often considered a fulfillment of biblical prophecy. This could certainly be true. Others would say it was a self-fulfilling prophecy. God sometimes "reinspires" Scripture with new meanings too, so it could be a fulfillment even if it wasn't an original meaning to various biblical passages.

What does the Bible teach?

9. Old Testament Scriptures relating to the reestablishment of Israel were originally dealing with the Babylonian captivity, not with the present day. These were fulfilled in 538BC when Cyrus allowed the Jews to return to Jerusalem (e.g., Isa. 45:1; Ezra 1). Similarly, the temple was already rebuilt in 516BC. The wall was rebuilt in the 400s by Nehemiah.

It is not clear that any prophecy about the temple in the OT remains to be fulfilled, not least because Jesus has atoned for all sins. The Jerusalem of eternity will have no temple (Rev. 21:22).

There is no straightforward prediction of a rebuilt temple in the New Testament. Again, Hebrews indicates that there is no need for an earthly sanctuary. If Hebrews dates to the time after the temple was destroyed, one of its purposes would actually have been to tell Christians not to grieve over the absence of a temple because no earthly sanctuary was ever really able to take away sin.

Mark 13 in context was primarily about the destruction of Jerusalem in AD70 rather than end times. Some material relates to the return of Christ, but this is unexpected, since Jesus was clearly talking about the temple of his day, not in the future (13:1-4). Revelation says nothing about a rebuilt temple or Jerusalem, other than the heavenly Jerusalem that comes down at the beginning of eternity.

10. The only possible hint about a rebuilt temple is 2 Thessalonians 2:3, but anyone reading this verse originally would have thought Paul was talking about the temple that was still standing at the time in his day. Nothing is said about a rebuilt temple, although I won't say it won't happen. We generally understand fulfillments in hindsight, not in foresight.

11. The clearest statement about Israel's future is Romans 11:26, which probably implied that, around the time of Christ's return, there will be a mass conversion of Jews to Christ. This obviously hasn't happened, since Israel is not Christian in belief (about 2% of Jews in Israel are Christian). About 40% of the Jews in Israel are secular Jews even in relation to Judaism. So current Israel is not yet the fulfillment of this statement.

Nevertheless, we do get a hint that Jerusalem will not always be in the possession of Gentiles. Luke 21:24 speaks of Jerusalem being trampled on the Gentiles until the times of the Gentiles are fulfilled. That suggests that Luke believed there would come a time when Jerusalem would be in Jewish control again. But he was surely thinking it would be in Christian Jewish control at that time.

Revelation 21 speaks of a new Jerusalem coming down from heaven. In the meantime, Hebrews 12:22 contrasts the true Mt. Zion and Jerusalem in heaven with any earthly Jerusalem or earthly sanctuary (cf. Heb. 13:14). Similarly, Galatians 4:25 compares the earthly Jerusalem to Hagar, while Paul distances the earthly Jerusalem from the heavenly Jerusalem, which compares to Sarah (4:26).

12. All that is to say that it is quite possible that the reestablishment of Israel was part of God's plan. It is quite possible that Israel will become Christian. But the key prophecies haven't happened. Biblically speaking, current Israel remains the unbelieving Israel of Romans 9 and Acts 28.

[1] Jewish emigration to Palestine had been taking place as part of the Zionist movement that started in 1898.

[2] These groups were reacting particularly to the British "White Paper of 1939," which reduced the number of Jews who could immigrate to Palestine and the amount of land that could be purchased by Jews in Palestine.

Wednesday, December 28, 2016

Gen Eds H8a: The Roman Empire

Arch of Titus,
celebrating victory over Jews
The eighth unit of world history in this series is "The Age of Rome."

This is part of my "General Education in a Nutshell" series. The series consists of ten subjects you might study in a general education or "liberal arts" core at a university or college. The first topic in the overall series was philosophy. So far in the world history section:
Caesar Augustus
1. After some five hundred years as a republic, the Roman elite traded in their right to self-govern for the security and potential peace of an emperor. [1] In 27BC, Augustus became the first emperor of Rome. After decades of civil war, he ushered in a peace that came to be known as the Pax Romana or the Pax Augusta, the "peace of Augustus."

Augustus did largely clear the Mediterranean of pirates and the Roman roads of thieves and highwaymen. He extended the Roman roads which shot straight as an arrow around the empire. Under his reign, the Romans added Egypt to their control and completed the conquest of Spain. They also inched northward into Germania.

Perhaps of most interest to Christians is the fact that Jesus was born during his reign, in about 6BC.

2. The first five emperors of Rome were Augustus (27BC-AD14), Tiberius (14-37), Caligula (37-41), Claudius (41-54), and Nero (54-68). [2] These are probably the five kings mentioned in Revelation 17:10. Jesus conducted his earthly ministry under the reign of Tiberius, as did John the Baptist. He was the specific Caesar in view when Jesus said, "Give to Caesar what is Caesar's and to God what is God's" (Matt.22:21).

Caligula was assassinated. In 39 he had the insane idea of setting up a statue of himself in the temple of Jerusalem. The Roman governor wisely procrastinated. The order for Petronius to commit suicide only arrived after Caligula was dead.

Paul's mission took place under the rules of Claudius and Nero. Under Claudius, Christian Jews were expelled from Rome, including Priscilla and Aquila, who were part of the Pauline mission. 1 Thessalonians, 1 Corinthians, and Galatians seem certainly written during Claudius' reign. His other writings would then have come during the reign of Nero.

Nero is likely the king that Revelation refers to as one who had a fatal wound that had healed (Rev. 13:12; 17:11). [3] The title "Caesar Nero" adds up to 666 if you treat the letters as numbers rather than letters (Rev. 13:18). It was Nero that crucified the apostle Peter and beheaded Paul. And Nero was emperor when Paul wrote Romans 13:1. And anyone reading 1 Peter 2:17 would have initially thought of Nero.

He committed suicide in the year 68.

The Flavians
3. The Jewish War took place from 66-72. It was a revolt of the Jews against Rome, an attempt to free themselves from its rule. It failed of course, effectively ending in the destruction of Jerusalem in AD70. [4] Much of Mark 13 likely refers to various events of this war. There is a tradition, for example, that the believers of Jerusalem did flee to Pella in keeping with Mark 13:14. Luke understands this verse to refer to the destruction of Jerusalem (Luke 21:20). [5]

After the death of Nero, 69 was the Year of Four Emperors. Two were murdered and one committed suicide. This made way for Vespasian to become emperor (69-79), who at the time had surrounded Jerusalem with the Roman army. His son Titus would complete the siege and destroy Jerusalem and the temple. Mark and Matthew were likely finished during the time of Vespasian, Hebrews also in my dating.

Titus then reigned after his father (79-81), and then his other son Domitian (81-96). Luke-Acts was likely written during these reigns. John and Revelation are traditionally dated to the reign of Domitian (or we might suggest they reached their current form at that time). 79 was the year when the volcano Vesuvius erupted, freezing the city of Pompeii in time.

From Nerva to Commodus (96-192)
4. The next five emperors enjoyed relatively peaceful reigns (the Five Good Emperors), although it is during this era that we begin to see a rise in the martyrdom of early Christians. Ignatius of Antioch was put to death around 110 by Trajan (98-117). A governor by the name of Pliny the Younger would write Trajan about that time about how Christianity had permeated the countryside of Pontus where he was governing. He put to death those who were too stubborn to renounce their allegiance to this competing king, Christ.

The early Christian Polycarp died during the reign of Antoninus Pius (138-61), although he was put to death by a governor for refusing to burn incense to the emperor. He was 86 years old at the time. Emperor worship had become standard during this time and is possibly alluded to in Revelation 16:2.

Hadrian's Wall (AD122)
Justin "Martyr" was put to death under Marcus Aurelius (161-180). Marcus Aurelius is famous for his grand Stoic philosophy in the secular world, but we might know him better for his actions toward this famous Christian. The reign of Commodus (177-92) is often thought to be a turning point in the history of the empire, perhaps the beginning of its decline. [6]

Under the emperor Hadrian (117-38), the famed "Hadrian's Wall" was built in Britannia. The Romans had ruled southern Britain from the days of Claudius. They would continue to dominate there until 410, the year when Rome was sacked by the Visigoths.

6. Commodus was strangled to death. After him, twenty-five of the next twenty-six emperors died violently, mostly by murder, although a small number were either executed, died in war, or committed suicide. One of the only ones to die of natural causes was Septimus Severus (193-211). [7]

This political instability clearly was part of Rome's decline. In addition, it was overstretched, with an empire that stretched from Britain to Egypt. It's population began to decline, not least because of plague in the 200s. In 212, the emperor Caracella granted Roman citizenship to everyone in the empire, in an attempt to increase the Roman base. Many soldiers were foreigners, who lacked the loyalty or chance of advancement leading them to fight as earlier generations had.

But the emperors could not administrate the empire's wide holdings, and Germanic tribes increasingly became a preoccupation to the north. Trade declined significantly. The historian Edward Gibbon (1737-94) controversially suggested that Christianity weakened the empire because it undermined traditional devotion to the state. Many, however, disagree with this hypothesis.

In general, this part of Roman history is sometimes called the "crisis of the third century." In 284, the Roman empire was more or less split into three different empires: Gaul (France), Palmyra (Turkey, Palestine, Egypt), and the Roman center (including Spain). Aurelian (270-75) reunited it in 284, marking what is sometimes considered the dividing point between the time of classical and late antiquity.

An important year from a Christian perspective was 250, when the emperor Decius (249-51) made an edict requiring all Romans to offer a sacrifice to the gods in the presence of a Roman magistrate. Decius was trying to restore traditional Roman values, attempting to revive the empire. It of course created a crisis for Christians, who could not in good conscience do so. The result was the worst persecution of Christians yet. Decius was killed in battle the next year against the Goths.

7. Christians enjoyed about 40 years of tolerance until the emperor Diocletian (284-305). In 303 he initiated the last and most intense of the Roman persecutions. He purged the Roman military of all Christians, burned copies of Scriptures, forbade public worship, and demanded sacrifices to Roman gods. Perhaps some 3000 Christians were put to death.

One effort Diocletian made to try to save the empire was to divide it into two administrative jurisdictions. In 285, he appointed Maximian as a subordinate co-ruler in Rome, while he focused his his rule from Byzantium in the east.

Constantine the Great (306-337)
8. Constantine was in Britain on a military campaign when his soldiers acclaimed him as emperor in 306. In the year 312 at the Battle of the Milvian Bridge, Constantine is reputed to have seen a vision of the cross in the sky with the words, "In this sign you will conquer" written beneath. After the battle, he had solidified his status as emperor in the west. In 324 he beat the claimant to rule in the east, becoming the sole emperor of the whole empire.

He shifted the capital of the Roman empire to Byzantium, which he renamed Constantinople in 330. This half of the Roman Empire would become the Byzantine Empire and continue to exist until the Ottoman Turks took the city in 1453.

Constantine is perhaps better known for the imprint he left on Christianity, although whether that impact was ultimately more positive or negative is a matter of dispute. On the one hand, he made Christianity a legal religion with the Edict of Milan in 313. In the year 325, he summoned the Council of Nicaea in hope that Christians might come to some agreement on the relationship between God the Father and Jesus Christ. The result would become official in the Nicene Creed that was finalized in 381 at the Council of Constantinople.

Constantine himself was not baptized until his deathbed, perhaps because he was unsure whether sins committed after baptism could be forgiven.

9. In 381, Theodosius 1 (379-95) made Nicene Christianity the only legal religion of the empire. Contrary to popular belief, Constantine did not force the Roman empire to become Christian. It was Theodosius, 44 years after his death, who did so.

For a brief time, Julian the Apostate (360-63), half-brother of Constantine, tried to reverse the Christian trajectory of the empire. He revoked all the monies and lands Constantine had given to the church and forbade "Galileans" (Christians) from being teachers of rhetoric and grammar. In Julian is the lesson that often before a trajectory of history reaches its final destination, there is a final gasp of the dying resistance. So it was that after Nicaea, Arianism had a massive resurgence before it finally lost the historical battle.

Fall of Rome
Rome was sacked by the Visigoths in 410. The sacking would not stop until the final emperor (at least in name), Romulus, was overthrown by Odoacer. This event, in 479, is often considered the end of the Western Roman empire.

A final push to restore the Roman empire took place under the eastern emperor Justinian I (527-65), who is sometimes called "the last Roman." His soldiers retook Italy from the Visigoths, North Africa from the Vandals, and even the southernmost part of Spain. But the problem of over-extension simply returned, and these lands fell away again in the years after his death.

Justinian enacted legal reforms that are still part of civil law in the modern age, the so called Code of Justinian. At the same time, Justinian is known for finally closing Plato's Academy in 529, considered by some to be the beginning of the Dark Ages. An outbreak of bubonic plague largely ended the cultural flourishing of his reign in the 540s.

  • In times of great danger or conflict, people will often surrender their freedoms or core values for security.
  • Over-extension, especially when coupled with oppressive taxation, is a frequent characteristic of empires and organizations right before their final decline.
  • Persecution sometimes strengthens your enemy. What doesn't kill them makes them stronger.
  • If you can't beat 'em, join 'em.
  • There is often a final gasp of opposition before a historical trajectory is definitively established.
  • A comfortable movement often becomes a weak movement.
Next Week: History 8b: The Roman Republic

[1] The imagery of Star Wars partially comes from this transition from republic to empire.

[2] The Julio-Claudian line.

[3] Anyone reading Revelation 17:9 initially would have thought of Rome when it mentions a city of kings with seven hills. Similarly, "Babylon" was a well-known cipher for Rome after Rome destroyed Jerusalem as Babylon had six hundred years earlier (cf. Rev. 18).

[4] Although technically we might say it officially ended with the taking of Masada in AD72.

[5] There are a number of places where I consider some evangelical scholarship to come up lacking on obvious conclusions because of putting tradition over evidence. In my opinion, no one putting the emphasis on the evidence will conclude that Luke-Acts was written before the destruction of the temple. Similarly, the way Matthew 22:7 is presented seems to confirm that Matthew was also written after the destruction of the temple.

[6] The movie Gladiator fictionally has Commodus poison his father Marcus Aurelius. However, there is no evidence of this.

[7] I feel quite confident that the character Severus Snape in Harry Potter was named after him.

Tuesday, December 27, 2016

5. Waging War against His People

I'm reading through Konrad Heiden's 1944 book, Der Fuehrer. The first five chapters were:
1. The chapter this week roughly covers the period till 1923. We have been flying around this period in the last few chapters. It is the period when Röhm's "patriotic murder clubs" were going around murdering people while the leadership of Bavaria was turning a blind eye. These were the "storm troopers" (SA). Meanwhile, Hitler's rallies were meant to work the German people up into a frenzy.

It was a civil war of sorts. You had these bands of angry men conducting war against their own people. Locally, they made "enemies" of their Germany disappear. Nationally, they meant to get rid of the democratic government, which they thought allowed for communism and was controlled by Jews.

Hitler said in 1922, "We want nothing to do with parliaments. Anyone who goes into a swamp sinks into the muck... A minority suffices to overthrow a state when the majority of the population has gone soft and lost its direction... We do not want the thing they call unity" (112). He compared himself to Jesus going into the temple with a whip, and he thought of himself in such grandiose terms.

In a time of chaos, public opinion is the true source of power. Hitler expressed the speechless panic of the masses. "His speeches are day-dreams of this mass soul; they are chaotic, full of contradictions" (106).

2. One of the leaders of Germany as a whole, for a short while, was actually Jewish--Walter Rathenau. He was actually making strong inroads to decreasing dramatically the amount of war reparations the Allies were expecting from Germany. He was killed by some petty racists in a drive by. If he had lived, perhaps Germany would have turned around.

There were some laws passed as a result against extreme agitation from the right. After a change in the administration of Bavaria, Hitler himself was put in jail for a month for beating a speaker off a platform with a club. His greatest fear was deportation, since he was an Austrian and not a German by citizenship. Deportation was what he feared the worst.

In all of his agitation, Hitler was obsessed with the Jews, calling on Aryans and anti-Semites of all nations to unite in a struggle against the Jewish race, whom he saw as exploiters and oppressors.

3. As a final note, we are introduced to Hermann Göring in this chapter, who would become Hitler's second in command. At the time Hitler met him, he was a morphine addict.

Sunday, December 25, 2016

Luke's Story of Jesus' Birth

I was delighted to encounter an article this year (HT: Anthony Le Donne) that suggests the following story line in Luke's birth story. [1]
  • Mary becomes pregnant of the Holy Spirit in Nazareth before she and Joseph get married.
  • He returns to his family's home in Bethlehem for a census. He takes her with him.
  • They get married in Bethlehem--he takes her into his house. 
  • Following the normal practice, a small make-shift room, a marital chamber, is added to the family's house, often on the roof as a kind of attic addition. This would perhaps only be big enough for the pregnant Mary and Joseph to sleep in.
  • She gives birth in the main room of the house, since there was not room for birth in the "place" (katalyma) of the marital chamber. 
  • Many "farm houses" of this sort had a manger, with animals on the lower part of what was effectively a split level (with about a one meter height difference). They lay Jesus in this manager.
  • Forty days later, they return to Nazareth.
  • Merry Christmas all!
[1] Stephen Carlson's 2010 article from New Testament Studies: "The Accommodations of Joseph and Mary in Bethlehem: katalyma in Luke 2:7."

Friday, December 23, 2016

Friday Gen Eds MS10: The Basics of Calculus

This is the tenth post in the math/science part of my "Gen Eds in a Nutshell" series. The Gen Ed series consists of ten subjects you might study in a general education or "liberal arts" core at a university or college. I've already done the subject of philosophy, and I'm over half way through the world history subject on Wednesdays. I'm combining the last two on math and science into one series on Fridays.

Thus far in the math/science subjects:
1. The calculus was invented in the 1600s. Isaac Newton (1643-1727) usually gets the credit, but Gottfried Leibniz (1646-1716) developed it independently at the same time. Calculus was invented to address two problems, namely, the tangent problem and the area problem.

2. We might introduce the tangent problem in this way. If you drive from location x to location y in 60 minutes and the roadway between is 60 miles, we know that you have driven an average of 1 mile per minute.

But what about the instantaneous speed? How might we know how fast you were driving 29 minutes into the trip?

We might plot your trip on a graph. We might put distance on the y-axis and time on the x-axis. Perhaps we could come up with an equation that expressed the graph.

The average speed between any two points is the difference in distance divided by the difference in time, or the "rise" (y- y1) divided by the "run" (x- x1). In other words, the average speed is the slope of the graph between those two points. And if we wanted to know the speed at any instant, it would be the slope of the tangent to the initial equation at that point.

3. What Newton and Leibniz invented was, first, a way to determine the equation of this tangent line, the instantaneous slope at a point on an equation. More broadly, they found a way to derive an equation for the tangent to an equation at every point along the equation.

Their idea is really very simple. The slope between two points, as we have said, is the rise (of y) divided by the run (of x). So the rise is the y value of the equation (or function) at x2 minus the y value of the equation at x1. Another way to put this is f(x + Δx) - f(x). The symbol Δ means the change in x, and f(x) means the value of the equation (or function) at x.

If we divide f(x + Δx) - f(x) by Δx (the change in x), then we have divided the change in y by the change in x, which is the slope.

Differential Calculus
4. Newton's idea was to take Δx to zero. When the change in x was infinitesimally small, the "limit" as the difference in x approached zero would approach the equation of the tangent line to the equation. We can write the process in this way:
The expression f'(x) is called the derivative of x. If we take an equation and plug in x and x + Δx and go through the process of simplifying it, the Δx part always cancels out and we are left with the equation for the tangents to the initial equation at every point. As we will see in the next post, this allows us to do all sorts of things in science, economics, and in any field that involves change.

5. The branch of calculus that has to do with finding the instantaneous rate of change in this way is called differential calculus. There are some basic patterns for the derivatives of certain kinds of equations. For example, the derivative of a polynomial (an equation with x raised to some power) is very predictable.
The expression dy/dx is a way of saying "the derivative of y." In this case, y = an + b. To find an equation for a line that is tangent to this equation, you multiply the power (n) times whatever number is in front of a. Then you lower the power of n down by 1. [1]

6. You can take the derivative of a derivative, called a second order derivative. In fact, you can keep taking derivatives of derivatives as long as you still have elements left of which to take the derivative.

For example, if you have an equation for the distance you've traveled in a certain amount of time, the derivative of that equation (the first order derivative) gives you an equation for the speed in relation to time. Then if you take the derivative of that equation, the second order derivative is an equation for the acceleration in relation to time. Acceleration is the change in speed in relation to time.

7. This all may sound complicated, but it can be used to do a lot of things. For example, when an equation reaches a maximum or a minimum, its slope will be zero at that point (because the graph changes directions at that point). So if you make the equation of the derivative equal to zero and solve for x, then you will have identified points where the initial equation hits maxima and minima.

If you look at whether the second derivative is positive or negative, you can decide whether it is a maximum or minimum. If the second derivative is negative, then its graph is concave down and the point where the slope equals 0 is a minimum. Otherwise, it's a maximum.

Integral Calculus
8. The opposite problem to the tangent problem might be called the area problem. Let's say you have an equation again that you have graphed. How do you find the area under the graph?

The answer is similar. You slice up the area under the graph into smaller and smaller rectangles and add up their areas. As the width of the rectangles becomes infinitesimal (approaches zero), the sum of all the rectangles approaches the area under the equation.

The way we might write this situation up is:
What this means is that we are going to slice up the area under the equation into "n" number of rectangles. As the number of them approaches infinity (the limit as n approaches infinity), the sum approaches the area. The big symbol is the summation sign. The Δx refers to the little x part of each rectangle and the f(xi) refers to the y part of each rectangle. i = 1 just refers to the fact that we start adding with the first rectangle and we keep adding till we get to the "nth" one.

We call this operation, "integrating" or "finding the integral" of an equation. An "indefinite integral" finds the equation for the area under the entire equation. A "definite integral" finds the area under a specific part of the equation.

9. As it turns out, differentiation and integration are opposite operations. In fact, this is the fundamental theorem of calculus. If you take the derivative of an equation, you can get back to the initial equation by integrating the derivative. Or if you take the integral of an equation, you can get back to the original equation by "differentiating" it.

For example, the derivative of a distance equation is a speed equation, and the derivative of a speed equation is an acceleration equation. But it works the other way too. The integral of an acceleration equation is a speed equation, and the integral of a speed equation is a distance equation.

10. The tools of calculus are immensely helpful in countless fields, especially physics, but also fields like economics, population growth--any topic that involves change.

Next Week: Math/Science 11: The Physics of Motion

[1] The b disappears because it was times an x to the 0 power (1). Zero times b is zero. When taking a derivative, all "constants" like b disappear.

Wednesday, December 21, 2016

Gen Eds H7c: Medieval Arabia, India, China, and South America

The Hajj in Mecca
This is the third and final post in my seventh unit of world history: "The Age of the Church and Jihad."

These are posts in the World History part of my "General Education in a Nutshell" series. This series involves ten subjects you might study in a general education or "liberal arts" core at a university or college. The first topic in the overall series was philosophy. So far in the world history section:
The Rise of Islam
1. Mohammed was born around 570 in what is Mecca, Saudi Arabia today. At the time, the Arabian peninsula was a combination of Jews, Christians, and polytheists who believed in many gods. It was a place of competing tribes.

When he was in his forties, Muhammed thought he began to receive revelations from the angel Gabriel, and he would receive them until his death in 632. Like most in his day, he was illiterate, so these teachings were collected and written down by others. Today we know these teachings as the Qu'ran.

There are "five pillars of Islam." They are:
  • The profession of faith--"There is no god but Allah and Mohammed is his prophet."
  • prayer, five times a day toward Mecca
  • giving to the poor (originally a tax or tribute to Mohammed, the zakat)
  • the month of fasting (Ramadan)
  • pilgrimage to Mecca (Hajj)
2. The material of the Quran is not presented in chronological order, but can be divided into two basic time periods. The earlier material of the Quran relates to the time when Mohammed was in his home town of Mecca. This is the more peaceful material to which moderate Muslims often appeal today when they are in dialog with other religious groups. At that time Mohammed enjoyed a life of relative ease.

But in 622 Mohammed was forced out of Mecca and took up residence in Medina, a move known as the Hijra. The Muslim calendar starts in this year. The material in the Qu'ran dating from this later period is much more combative, and it is from this part of the Qu'ran that militant Islamists draw their notions of jihad.

In this phase of Mohammed's life, his followers began to fight against competing tribes and they would eventually take Mecca itself in 629. Some of Mohammed's opponents in Medina were Jewish tribes, leading to some of his clarifications on the relationship between Islam and Judaism. Islam was thought to give a more accurate understanding of God's promises to Abraham through Ishmael rather than Isaac. Mohammed would also clarify his sense that while Jesus was a prophet, he was not as great a prophet as Mohammed.

3. Islam was radically expansionist in the days immediately following Mohammed's death. Even in the final years of Mohammed's life, treaties were entered into with northern Arabian tribes whereby they agreed to pay the "zakat" to Mohammed. In the two years after his death, Abu Bakr, Mohammed's political successor, would be in control of the entire Arabian peninsula.

The successors of Mohammed divide into two basic groups, the Shia who claim that Mohammed's son-in-law Ali was chosen by God to be the first caliph of Islam. The other group are the majority Sunni, who look to Abu Bakr as the first caliph. Since history is told by the winners, the majority of Muslims are Sunni and look to Abu Bakr as the true successor. Ali was assassinated in 661. [1]

There is no doubt that Abu Bakr was the one who dominated Islam in the first two years after Mohammad's death. Tradition has it that it was he who directed the oral teachings of Mohammed to be written down in the Qu'ran. In his brief period, Islam began to eye an expansion into the Persian empire to the east and the Byzantine empire to the north and west.

This expansion especially took place during the ten year caliphate of Umar [2]. He would take over two-thirds of the Byzantine empire (the remaining Roman empire ruled from Constantinople). And he would conquer the Persian empire of the day (modern day Iran), the Sassanian Empire. This was a vast territory that included territory from northern Africa in the west to Persia in the east to eastern Turkey in the north. It included Egypt, effectively ending Alexandria as a primary center of Christianity. He took Syria, effectively ending Jerusalem and Antioch as major centers of Christianity. [3] At his death, he ruled from Libya to the Indus River (in modern day India).

Islam came upon these regions soon after the two empires had just finished warring against each other, when they were depleted in strength. The Muslim fighters were united in a common cause with a common religious fervor. Those who were conquered could either convert to Islam or, if they were a Jew or a Christian, be a "dhimmi," a "protected one" who paid a tax.

4. By 713, most of Iberia (Spain) was taken from the Visigoths by the Berbers, seeing an opportunity and pushing north from Tangiers. As we mentioned in the previous post, Charles Martel would stop their advance north in 732 at the Battle of Tours.

The Muslim "Moors" would hold territory in the Iberian peninsula for almost 800 years, until Grenada was finally retaken in 1492. Jews and Christians were again allowed to live under the Moors as dhimmis, as long as they paid the zakat. Jews fared much better under Muslims than under the conquering Christians, who insisted they convert or die.

The Moors were pushed back steadily over the centuries, the "reconquista," especially after the Church declared a crusade against them. Portugal became its own kingdom in 1139, for example.

The Golden Age of Islam
5. From a Western perspective, we might call the centuries from the late 700s to the Mongol invasions of the mid-1200s the "Golden Age" of Islam. [4] During this period, Baghdad was the center of Islam, a city founded by the Abassid caliphate or dynasty in 762, just north of where the ancient city of Babylon had stood.

The "House of Wisdom" was founded in Baghdad, and the goal was set to translate all the world's wisdom into Arabic. Greek, Indian, and Persian texts were translated in subjects like mathematics, astronomy, medicine, chemistry, and so forth. Baghdad was the largest city in the world and the Abassid kingdom the largest kingdom in the world at the time.

The greatest thinkers of the early medieval period were not in Christian Europe. The works of Aristotle were preserved largely by Muslim scholars (Christianity at this time was largely Platonic). ibn Sina (Avicenna, 980-1037) wrote on a host of subjects from Persia. ibn Rushd (Averroes, 1126-98) wrote from Spain.

These writers would influence Christian thinkers in France, and Aristotle's influence on Christianity would be sealed through Thomas Aquinas (1225-74). These thinkers also influenced Judaism through the most important Jewish thinker of the age, Maimonides (1135-1204), who lived out his life under Muslim rule.

This flourishing of human thought in the Muslim world would soon come to an end, however. The religious revivals of the eleventh and twelfth centuries largely shut down scientific and philosophical investigation.

6. We have already encountered the Seljuk Turks, who prompted the Crusades because of their advance in Turkey, taking over much of the Byzantine empire. Saladin (1137-93) is the most famous of their leaders and the one who stopped the Crusader advance against Palestine. The Seljuk Turks buffered Europe from the Mongol invasions of the 1200s.

The Ottoman Turks took over the caliphate in 1517 from the Abassids, and had already ruled in Turkey for a couple hundred years before. They conquered Constantinople in 1453 and were only stopped in their westward advance at the Battle of Vienna in 1683. The Ottoman's continued their reign until their kingdom was parceled up after World War I.

7. Islam reached into sub-Saharan Africa as early as the late 600s. The Mali Empire in particular was a key Muslim center in Africa below the Sahara Desert. [5] The famed Timbuktu was a major center of individualized study in the late Middle Ages.

Medieval India
In India, the Golden Age is usually placed from the 300s to the 500s AD, during the Gupta dynasty. This was an era where extensive study of mathematics, science, astronomy, art, and many other fields we now recognize as central to civilization were studied and developed. It is here that the decimal system we currently used was invented. The number symbols we use today (1, 2, 3, 4) came to us from the Indians to the Arabs to us, which is why we call them Arabic numbers.

Slightly later to the south, Brahmagupta (598-late 600s) would use the concept of zero to advance mathematics as well. He was probably the greatest mind of his day in the whole world. What we used to think of as Indian culture reached a kind of mature form during this period. This would include the caste system. The Mahabharata, the longest epic poem in existence, reached its final form at about this time.

The Gupta dynasty came to an end with the invasion of the Huns from the east in 550. The most famous Hun is of course Attila the Hun (406-53), who invaded as far west as Gaul (France) and Italy.

Medieval China
Two main dynasties dominated this period of history in China: the Tang dynasty (618-907) and the Song dynasty (960-1279). The Tang dynasty had its capital at Xian, and was a period of flourishing as far as Chinese poetry is concerned. Du Fu (712-77) is often concerned the greatest Chinese poet of all times, and others such as Li Bai and Wang Wei date from this period. Buddhism was well-established as the dominant religious influence by this time.

The Song dynasty established the first paper currency. Gunpowder and the compass both came from this period of Chinese history. It was put to an end, however, by the Mongol invasions of the 1200s. Kublai Khan destroyed the last Song emperor in 1279.

The Mongol Empire itself started with Genghis Khan (1162-1227). We mentioned him above as the one who ended the rule of the Abassid caliphate in Baghdad. He was brutal and genocidal. One benefit of his rule was the unification of the Silk Road between China and Europe. Marco Polo (1254-1324) would later popularize this trade route with China.

  • No kingdom lasts forever.
  • Most religions have both peaceful and horrific followers.
  • The fanatical and militant almost always find a way to destroy the advance of civilization. The intellectual eventually falls before the violent.
  • Every culture has its day. Every culture has its geniuses.
Next Week: History 8a: The Roman Empire

[1] Sunnis consider Ali to be the fourth caliph.

[2] The Shia of course consider Ali to be the true caliph during this entire period.

[3] Umar allowed Jews to return to Jerusalem. The Romans had kicked Jews out of the city after the bar-Kokhba revolt of 132-35 and built a temple to Jupiter on the Temple Mount.

[4] Muslims divide up the early history of Islam into "caliphates," periods when various dynasties ruled. The first were the immediate successors of Mohammed, the Rashidun (632-61), including Abu Bakr, Umar, Uthman, and Ali. The second caliphate were the Umayyads (661-750), who ruled from Damascus in Syria. The third caliphate were the Abassids (750-1517), who first ruled from Baghdad, which they founded in what is now Iraq. Rule from that location ended in 1258 when the Mongols sacked the city. Then from 1261 they ruled from Cairo, Egypt. The Abassids did not control the entire Muslim world after the early 900s. Parallel caliphates arose in north Africa and Spain.

[5] Tunisia was also a key center of Muslim culture in north Africa from the late 600s. It had a center of learning at Kairouan that has been compared to the medieval university in Paris.

Tuesday, December 20, 2016

4. Rallies with the Rabid

Upper room of the Hofbrauhaus, Munich
I've been reading Konrad Heiden's 1944 story of Hitler's rise to power, Der Fuehrer. The first three chapters were:
1. I read two chapters today. The first had to do with Hitler's service in World War I and the title of the chapter is, "Hitler Finds His Home." The thesis of the author in this chapter is that Hitler had no home, no real sense of purpose or belonging in life... until war happened upon him.

As in the days when, in his mind, he thought himself the grand artist among a world of nothings, now he is the great leader among other soldiers--at least in his imagination. Actually, he was an inconspicuous courier, an orderly who did minor jobs for superior officers, a private who was never promoted. He did earn the Iron Cross twice, once when he stumbled upon a group of more than a dozen French soldiers and took them into custody. [1]

He was one of very few to survive from the "List Regiment," a group badly led, largely made up of students. He was a good soldier, apparently, when it comes to following orders in the heat of battle. But he was apparently too mentally unstable to be put in leadership. In fact, he had contempt for most leaders, whom he didn't think knew how to inspire. Perhaps to him, many were afraid to go all in with war, to incur the big losses that go with success. While others wrote home hoping for the war to end, Hitler was more at home than he had ever been.

He ended the war in a hospital, having gone blind from gas for a short spell. Interestingly, he does not turn in some Navy deserters who wander through his hospital. Perhaps part of him is still hiding in the corner when he doesn't have someone with a gun at his side. I picture him like the sniveling Penguin in his early days in the series, Gotham.

2. The gas left him with a permanent hoarseness in his throat. It would make him sound powerful in the days to come, for he couldn't overcome it without force of voice.

Insert here the Munich intrigues of the second chapter. Hitler and a few others join and take over a nothing group calling themselves the "German Workers' Party." All they have is a briefcase. Ernst Röhm from chapter 2 is part. He likes a small group because only there can he be great.

The first public meeting of this German Workers' Party in the Hofbrauhaus was the hardest for him. Hitler is not the main speaker, but he feels that a wolf is born that February 24, 1920. There are people with side-arms to "escort" anyone out that interrupts or objects. Cold steel will keep his rallies in order.

3. His 25 points are a mixture of the passions of the four main leaders who have taken over the group. The main one is his call for a Greater Germany, a centralized Germany, with only true Germans as its citizens.

Here we see the power of someone who can manipulate the masses. With his words, he plays on Bavarian hatred for Berlin, but his true goal is to rule Bavaria and all German lands from Berlin. [2] He says what works to get the crowds riled up, but he is working against them behind the scenes.

He speaks the socialist language--the state will take over all corporate enterprises. But he nudges to business that what he is really talking about is the Jewish bankers. He will eliminate them.

He speaks of upholding positive Christianity. But he is not talking about biblical Christianity or any church Christianity.

Give the crowds what they want with your words, do what you really want with your actions.

4. It is also at some point during this period that he meets Rudolf Hess, although Hitler is so insignificant that Hess doesn't remember him being part of this movement at the beginning.

[1] He says they were English.

[2] "A deep-seated, often humorous hatred for the more progressive, more industrial, far larger, richer, more powerful, and predominantly Protestant Prussia, which for generations had been leading Germany, was one of the oldest national sentiments of Catholic Bavaria" (95). But Hitler aimed industrial, powerful, centralized Berlin to be the center of pan-Germania.

Sunday, December 18, 2016

Seminary PL31: From Out Group to One Group

This is the seventeenth and last post on church management in my "Seminary in a Nutshell" series. In this series, I first did a section on the Person and Calling of a Minister. Now this is the thirty-first post in a section on the Pastor as a Leader (see at the bottom).

The previous post was about preventing group exit and splits. This post gives some general thoughts and principles of group integration
1. Human nature is tribal. We are born to herd, and we herd with people who are like us. In terms of church growth, Donald McGavran called this the "homogeneous unit principle," where a homogeneous unit is "a section of society in which all members have some characteristic in common." [1] McGavran observed that a group has synergy--and thus is more likely to grow--when the group is made up of people who are alike.

Understandably, the homogeneous principle has come under immense attack in recent days. It is abhorrent to think of some group saying, "We don't want anyone who isn't white" or "We don't want anyone who isn't African-American" or "We don't want anyone who isn't Hispanic" here! Thankfully, the principle hasn't usually been used in that way in the church. The current "segregation" of American congregations is hopefully more an unthinking phenomenon than an intentional one. [2]

But the natural tendency is for groups to congeal that hold some factor in common. Groups of "like" are more likely to grow than groups of "different." Human nature is such that "make us great" is usually a more powerful sentiment than "unite everyone together."

2. Unless, of course, the thing that holds a group together is the value of cross-group unity. Bob Whitesel has insightfully recognized that multi-cultural churches are actually a subtle form of homogeneity. [3] Those who worship at multi-ethnic churches are usually individuals who value the unity of the church across ethnic barriers!

We have a natural tendency to pull toward our "in-group," the group to which we belong. We have a tendency to exclude, alienate, persecute, fight, or at the very least "not see" the out-group or the other group. [3] There are many different ways to be out-group. You could argue that the 2016 election was in part the ignored blue collar worker pushing back, a group that has felt ignored or "not seen" by the "elite" of established national leadership.

I was part of a group once where I was amazed at the unity of the group, only to find out later that some others had always felt on the outside. This is the least offensive form of bias against an out-group, when we don't even realize we are alienating or excluding. But the out-group is keenly aware. The in-group is usually shocked--even indignant--if the out-group finally boils over and asserts itself. The in-group may not even realize the role it played in the creation of the crisis.

3. If some might not agree with this analysis, most Christians would agree with the goal to which I am pushing. If the church is being the church, then it needs to be a church for everyone, not a church for some in-group or subset. As Paul put it, "Now I appeal to you, brothers and sisters, by the name of our Lord Jesus Christ, that all of you be in agreement and that there be no divisions among you, but that you be united in the same mind and the same purpose" (1 Cor. 1:10). Cliques are not supposed to be part of the church.

This was the problem with the Corinthian church that Paul addressed in 1 Corinthians: "it has been reported to me by Chloe’s people that there are quarrels among you" (1:11). Similarly in chapter 11: "I hear that there are divisions among you" (11:18). At Corinth, there was a group loyal to Paul and there was a group that was using Apollos as an excuse to push against Paul. Paul writes Corinth to try to get everyone on the same page.

If it grows unabated, factionalism can result in church splits. It clearly pulls against the mission of the church. The goal of the church is for it to be a place where there is "neither Jew nor Greek, neither slave nor free, not 'male and female'" (Gal. 3:28). The goal of the church is a place where people are present "from every nation, from all tribes and peoples and languages" (Rev. 7:9).

4. So how can a church go from "out-group" to "one group"? Let me suggest three stages of unification of a congregation in this respect:
  • Agree on the value of unity and full inclusion.
  • Take steps to look like your community and, even better, the kingdom of God.
  • Shift from "us-them" language and thinking to "us" language.
5. When I say, agree on the value of full inclusion, I am not simply talking about race or gender. I mean all the cliques and factions that can take place even in a generally homogeneous church. After all, this is the last post in the section on conflict management. Having groups with "favored status" in the church is begging for conflict.

So it goes without saying that everyone in the church should be treated as being of equal worth. The children of the board or of wealthy givers should not be shown favoritism over any other child. Some will always think they are being treated unfairly, but we can only do our best.

We need to notice everyone who is our churches. Out-group conflict can simmer, sometimes for years, under the surface because of inadvertent exclusion. Then some other trigger can bring it to the surface.

Occasionally, there are people in our churches who actually do not want outsiders coming or do not want certain types of people in "their" church. This is so obviously unChristian that it should not even need mentioned. But Jesus makes it clear from the Parable of the Good Samaritan that our neighbor is precisely the person from the group we do not like. Today, this may include people of other races and nationalities, people of other religions, whatever the group is today that we want to hate.

What about the sinner? What about the law-breaker? True, the presence of those who disagree with our values or understandings can be a corrupting influence. But most of the time we will want in church the person whom we believe needs spiritual help.

6. So hopefully we believe that we are all equal in the eyes of the Lord: "For just as the body is one and has many members, and all the members of the body, though many, are one body, so it is with Christ. For in the one Spirit we were all baptized into one body—Jews or Greeks, slaves or free—and we were all made to drink of one Spirit" (1 Cor. 12:12-13).

It is harder actually to draw a mixture of people to our churches. Humans herd. Our church may be located in a diverse community, but it is no easy task to lead a church to look like its location. And even if new people come, there is a fair chance there will be "in-group/out-group" conflict over the new individuals. It is human nature to resist change, especially as we get older.

The question of how to move toward a more diverse church is a subject for another time.

7. What we are concerned with today is how to see out-group or minority group individuals integrated once they are in your church. First, as we have said, the value of inclusion needs to be unbending. We need to be committed to everyone in the church being a full member and participant.

But there is an awkward stage of this process, the final stage, where we shift from "us-them" language to "us" language. Before we final get there, there is often a stage where the "in-group" thinks of itself as the host of the minority group, the new group. They are the ones doing the including, the ones being hospitable. They still assume a dominant role in relation to the "other." The value of inclusion is there, but it is "dominant group including subordinate group."

The final stage of inclusion is when we stop thinking in "us-them" terms at all and we are all simply the one group of the church. There is no host. There is no hospitality toward the other. There is simply "us."

8. There will always be different friend groups in a church. As long as these do not become exclusive or "us-them," they are natural. But it's worthwhile to mix it up every once and a while, get the members of one group talking to members of the other. Get people together who would not naturally do so.

But caution is also appropriate. Introverts don't enjoy forced mixing, while extroverts thrive off it. We should be careful not to make a certain personality a virtue. Go slow as necessary, or you will lose people. Almost any major change that happens, some people will leave anyway.

Next Week: Pastor as Leader 32: The Habits of Effective Administrators

[1] Understanding Church Growth (Grand Rapids: Eerdmans, 1980), 95.

[2] Martin Luther King Jr. once called Sunday morning "the most segregated hour in America."

[3] See his recent book with Mark DeYmaz, re:Mix: Transitioning Your Church to Living Color (Nashville: Abingdon, 2016).

[4] The idea of "white privilege" has at its core this idea of not seeing. I don't see that I didn't get stopped for speeding when a person of color was. I don't see people watching me in a store, paranoid that I will steal something, while a person of color does. I do not experience a place as racist because I was considered "in," while someone else who is "out" feels it every day.

"White" itself is an artificial category. There is no real ethnicity that is "white" or "black." This is
a categorization created by the slave trade. My personal ethnicity is a mixture of English, Scotch-Irish, Dutch, and German. "White" is a category that evolved in American history as new waves of immigrants came to America. For example, Irish and Italians were not initially white because they were an out-group just arriving.

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