9.3 The Universal Time Constant Chart

This is the third week of Module 9, "Relationships of Current, Counter EMF, and Voltage in LR Circuits." These modules are part of the Navy Basic Electricity and Electronics series from the 1970s. The third section of this module is titled, "Using the Universal Time Constant Chart."

9.1 Rise and Decay of Current and Voltage
9.2 LR Time Constant

The so called universal time chart gives the percentages of maximum I (current) or E (voltage) for each of the five time constants it takes for a circuit with an inductor in it to reach the maximum when powering up or to reach zero if powering down. The chart is to the right.

The time constant, as we learned in the previous section, is calculated by dividing the inductance by the resistance. So you can see on the chart that TC1, TC2, TC3, and so forth are expressed as L/R, 2L/R, 3L/R and so forth.

The line that starts at zero and increases to 100% is the powering up line. So at one TC (time constant), the voltage or current will be at 63.2% of its maximum value. At T2, it will have reached 86.5% of its maximum value, and so forth.

The line that starts at 100% and decreases to 0 is the counter-EMF coming from the inductor as the circuit powers down (E_L). It has the percentages opposite the percentages on curve A. So at one time constant interval, the circuit will still have 36.8% of what its maximum voltage was. At T2, voltage will be down to 13.5%. At T3 it will be at 5%. At T4 you will have 2% left. Then final at T5 the circuit will have completely powered down.

Friday Science: Adam and the Genome 3

Hit and run this morning with a new book by Dennis Venema and Scot McKnight called, Adam and the Genome: Reading Scripture after Genetic Science. Both are men of strong faith.

Previous posts
Personal Preface
Forward and Introduction

1. Now quickly chapter 1. Chapter 1 is titled, "Evolution as a Scientific Theory." Venema gives a bit of his personal story. Grew up against evolution. Didn't agree with it even through his PhD program. He now teaches biology at Trinity Western University

He spends a section of the first chapter correcting the sense that scientific theories are guesses or conjectures. A hypothesis in science does get to be called a theory until it has produced an extensive body of results that fit with it. In common language, we might say, "It's just a theory." But that is not how theories work in science. "A hypothesis that is not rejected after many, many predictions and tests eventually becomes a broad explanatory framework that has withstood repeated experimentation and that makes accurate predictions about the natural world: in other words, a theory" (4).

He then dismisses the often referenced studies on diet and health. Most of this is not good science. It is rather sensational journalism and people trying to sell you stuff. Don't mistake the fake science from the long, painstaking real stuff.

2. He has a long quote from John Edwards dismissing the idea that the earth goes around the sun. Edwards gives both theological and scientific arguments against it. One argument against it, the absence of a stellar paradox, Venema indicates was shown to be present two hundred years later. His point is that what seems difficult for Christian belief today might not seem difficult to a later generation. And sometimes it takes a little time to show what at first seems counterintuitive.

The latter part of this chapter gives an example. The idea that mammals descended from fish seems odd to say the least, as does the idea that tetrapods came out of the water to land and then that some of them returned to the sea as whales. Darwin suggested the latter and was soundly laughed to scorn for it.

Venema then gives evidence that, while not proving these hypotheses, has made them more plausible and has failed to disprove the theories. Lungfish are an example of a fish that to this day has the breathing apparatus both of water and air. They also have bones in their fins. Paleontological work in this time period has also found fossils of several species that blur the distinction between fish and tetrapod.

Finally, he speaks of fossils of species found around the Indian Ocean that have features that are suitable for water but that are still tetrapods. He follows up with the embryology of whales, which shows that the embryos begin toward developing back legs but then call it off in later development.

These fossils do not prove the hypothesis, but they support it and "fail to reject" it upon further experimentation.

Here endeth the first chapter.

Jamestown 2

From last week
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4. In December of 1606, three ships set sail from Blackwall, at that time just outside of London to the east, on the north side of the River Thames. These were the Susan Constant, the Godspeed, and the Discovery. Christopher Newport captained the largest of the ships, the Susan Constant. Captain John Smith was also on board. John Ratcliffe captained captained the Discovery.

Captain John Smith was one of those personalities who did not do well as a subordinate. Maybe he was smarter than everyone else or maybe he was not, but he certainly found himself repeatedly in trouble with his superiors. He was jailed on the trip over for mutiny, and scheduled to be hanged upon arrival. But when they arrived, instructions from Virginia Company were opened, and Smith was to be on the governing council.

Throughout his time he would repeatedly clash with the leadership of the colony. He probably also was a key player in keeping the colony alive, as opposed to the earlier attempt at Roanoke Island in 1587. When Governor John White returned in 1590, the colony was gone, leaving only the word "Croatoan." Many think the colony moved and, perhaps, blended into some of the surrounding native American groups.

On those first three ships to Jamestown, there were some 105 passengers and 39 crew, all men. Only 38 men were still alive when Captain Newport returned again from England with the "First Supply" in 1608.

5. The three ships made their "first landing" in what they called "Cape Henry" after the son of King James, April 26, 1607. Chaplain Robert Hunt offered a prayer and they set up a cross. He would be dead the next year. His remains have been found on the site of the first church in Jamestown, the first one to be buried in the new church--no coffin, only in a shroud.

On May 4, 1607. they settled on the spot up the "James River" that would become "Jamestown," both named after King James...

Gen Eds 11: The First Humans

The end of my world history posts! And only after ten months.

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. This is the final post in the world history part:

• World History Overview
• From 9-11 to the Present
• From the Cold War to the Millennium
• From Waterloo to World War II
• 5a. The French Revolution
• 5b. The Enlightenment to the American Revolution
• 5c. From Cromwell to the First Industrial Revolution
• 6a. Reformation and Scientific Revolution 
• 6b. The Renaissance and a New World
• 7a. Church Schisms in the Middle Ages
• 7b. Kings Rising in the Middle Ages
• 7c. Medieval Arabia, India, China, and South America
• 8a. The Roman Empire
• 8b. The Roman Republic
• 9a. Greeks and the Hellenistic Age
• 9b. Assyrians, Babylonians, Persians
• 10a. Ancient India
• 10b. Ancient China
• 10c. Ancient Egypt
• 10d. Ancient Mesopotamia

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1. The last post began to delve into some sensitive waters. An Archbishop named James Ussher in 1650 suggested that God created the world in 4004BC. This date fits with a fairly literal reading of the chronologies in Genesis.

However, in my last post I gave some dates from mainstream archaeology that go back further than 4000BC. Archaeologists date the walled city of Jericho back as far as 8500BC and Çatalhöyük as far back as 7000BC. These dates would require at the very least for the genealogies of Genesis to be significantly incomplete.

2. On the one hand, the fingerprints of history in Genesis coincide extremely well with the history of Mesopotamia from the previous post. We have Abraham at the time of Hammurabi. We trace him back to Ur in Sumer. And in the area of Sumer we have the beginnings of civilization. This is the area from which the ziggurat arose, like the Tower of Babel. There is evidence of a devastating flood in this area. Even Genesis points to the Garden of Eden being in the area of the Tigris and Euphrates (Gen. 2:14).

These breadcrumbs point back to about the same time as Ussher in the right region. The birth of human history is exactly where Genesis locates it--in Mesopotamia around the fourth millennium BC.

3. According to our previous post, human "history" began with the beginning of writing in the late 3000s BC in the area of Sumer. However, the current state of archaeology wants us to push back further, back to an "agricultural revolution" around 10,000BC. The current state of paleontology, which goes back beyond that point, wants to push back even further. How are we to fit these dates with the Bible?

In the last two decades, genetics has caused us even more problems. The mapping of the human genome, according to the current state of research, suggests that a common female and common male ancestor might have lived somewhere between 120,000 and 150,000 years ago in Africa. But not at the same time. [1] The current estimate is that "The DNA in current humans could not have come from a pool of fewer than approximately 10,000 humans." [2]

These theories of course are probably not in anything like their final form. We are in a dialog between Scripture and science, between possible interpretations of the Bible and possible interpretations of science. For example, John Walton's proposition is that perhaps Adam and Eve were royal representatives for a community of early humanity at some point in our early history. [3]

According to one theory, all humanity can be traced to East Africa about 70,000 years ago. According to current theory, Homo sapiens left Africa about then. So following Walton's theory, we might speculate that Adam and Eve ruled the Homo sapiens of East Africa some time before 70,000 years ago.

This of course is speculation, a discussion that hasn't hardly even started. For many, it is a conversation that should never start.

4. My goal in the rest of this post is simply to sketch out what seems to be the current dominant timeline for humanity among experts in this area at large, to do with as you will. My dates are based on Yuval Noah Harari's book, Sapiens: A Brief History of Humankind. It is a clearly secular book.

According to the current theory, a female ape had two daughters 6 million years ago. One would become the progenitor of all chimpanzees The other would become the mother of all humanity.

In this theory, about 2.5 million years ago, the genus Homo originated. This is not Homo sapiens or human beings as we are. These were animals in our genus, just as a lion and a tiger are in the same genus Panthera. According to the theory, this new genus Homo emerged from a genus of apes called Australopithecus.

Again, the current theory sees Homo sapiens emerging as a new species in Africa about 150,000 years ago. There were other "humans" around in the world at that time: Homo erectus, Homo neanderthalensis, Homo denisova. According to DNA, about 1-4 percent of Middle Eastern and European DNA is Neanderthal, and about six percent of Aboriginal Australian is Denisovan DNA.

So these "humans" would have intermingled a little, perhaps until as recently as 50,000 years ago. Neanderthals may have lasted until 30,000 years ago.

The success of these broader humans was the use of fire, going back as far as 300,000BC according to the current theory. Because humans could cook their food, they could eat all the needed food for a day in an hour, as opposed to the five hours of chewing raw food that chimpanzees need to do a day.

They were not particularly spectacular in comparison to other predators out there. In fact, some speculate that tools may have developed so that humans could break into bone to eat after the more skilled predators were done eating off all the meat from a kill.

There are no longer any other humans other than Homo sapiens. We apparently eliminated the others, according to the "Replacement" theory.

5. Some then suggest that the real point of origin for humanity as we know it took place about 70,000 years ago in East Africa. Yuval Harari calls this moment the "Cognitive Revolution." According to the current theory, some Homo sapiens had left Africa about 100,000BC for the Middle East, but they had not managed to compete against the Neanderthals, who actually had bigger brains.

But something changes in between 70,000 and 30,000BC, on this theory. Harari calls this chapter, "The Tree of Knowledge." Unlike Neanderthals, so the conjecture goes, Sapiens trade over long distances. Sapiens can coordinate with larger groups than small bands. Most importantly, Sapiens can imagine--they can construct realities like founding stories and legal fictions. They can not only talk about what is. They can talk about what could be.

6. In this theory, these Sapiens were all hunter-gatherers. They did not live in any one fixed location. They traveled to find food where they could. They ate on the spot what they could.

The next revolution, according to Harari, is the "Agricultural Revolution." This is when Sapiens transitioned from being a mostly hunter-gatherer species to becoming a farming species. In one place he mentions 12,000BC, but in another he suggests 9500-8500BC.

"Wheat and goats were domesticated by approximately 9000BC; peas and lentils around 8000BC; olive trees by 5000BC; horses by 4000BC; and gravevines in 3500BC" (77). "By 3500 BC the main wave of domestication was over" (77-78). "By the first century AD the vast majority of people throughout most of the world were agriculturalists" (78).

The rest is history. Agriculture tied down people to locations. Locations prepared the way for cities. Cities expanded the number of people in one place. Once the number moves into the hundreds, we need writing. We need bureaucracy. We need administration. We need collective imagination. We need to control violence. We need to organize warfare.

Here endeth world history.

Next Week: Chapters 1-8 of Sapiens

[1] E.g., Sequencing Y Chromosomes Resolves Discrepancy in Time to Common Ancestor of Males versus Females

[2] Both Tremper Longman III (vi) and Scot McKnight pass this idea along (xi) in Adam and Genome: Reading Scripture after Genetic Science. These are faith-filled biblical scholars who believe in the inspiration of Scripture but also feel the need to take science seriously in the name of truth. See also the faith-filled scientist, Francis Collins, The Language of God.

[3] The Lost World of Adam and Eve: Genesis 2-3 and the Human Origins Debate.

Paul 4.1 Back in Antioch

Prior novel chapters may disappear after transferred into a Word document. While it lasts, here is the link to the last post in chapter 3.
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Chapter 4: Jerusalem Decisions
The whole way back to Antioch, Paul was thinking about what might lie ahead. John Mark had been back in Jerusalem for over a year. Who knows what all he had said to the leaders in Jerusalem? They would of course tend to believe his account because he was one of them.

Paul could hear what he might be whispering into their ears. "Paul hijacked the mission from Barnabas." "Paul has no regard for the Jewish Law." "Paul has abandoned his own people in preference to non-Jews."

Barnabas assured Paul that everything would be fine. Mark was just young and immature. And, with a bit of a smile, "You can be a little overbearing at times, Paul."

Finally, Barnabas had a plan that made sense to Paul. "Let's go down to Jerusalem after we get back," he said. "Let's take one of the Gentile converts from Antioch to show them an actual person. It's hard to argue with a real person in front of you," Barnabas continued. "They'll see that the gospel is for the whole world, Paul. How could they keep such good news all to themselves?"

Paul agreed. It made sense. It would sure be better for the kingdom--and for the churches he had planted--if James and Peter agreed that Gentiles could be saved from the coming judgment without becoming circumcised.

The house churches of Antioch were clearly glad to see them, and they hung on every story Paul and Barnabas told. They were amazed that a Roman governor had believed, although they already knew that part of the story from John Mark. At first they cringed to hear of Paul getting stoned, but then laughed when Barnabas told how Paul "just got up and went into town" while they were looking at his body thinking he was dead.

Paul could tell, though, that there had been some rumblings about his familiarity with non-Jews. Had he started eating pork? "No!" he assured them. Had he succumbed to sexual immorality like the Gentiles? "May it never be!" he protested in anger. "And none of those who have believed do such things either!"

It infuriated him that they would assume a person was sexually immoral, just because he or she was a Gentile!

Friday Science: Adam and the Genome 2

1. I am blogging through a new book by Dennis Venema and Scot McKnight called, Adam and the Genome: Reading Scripture after Genetic Science. Both are men of strong faith. Yesterday, I gave a sort of personal preface.

The Foreword by Tremper Longman III gives a taste of the recent conundrum. If evolution were not already difficult for many Christians to harmonize with the Bible, recent DNA research has suggested that "humanity begins not with a single couple but rather with an original population of some thousands of people" (vii).

2. The Introduction then gives a little more personal detail on the two authors. Dennis Venema wonders "if my path would have been less circuitous if the church had had a better relationship with science to begin with." Venema teaches college biology at Trinity Western University in Vancouver. Interestingly, he did not become convinced that evolution was correct until after he had actually become a college professor (11)!

Venema makes a comment that I have been making for years. The real issue for Christianity and evolution is not in Genesis. That's easy. The real issue is in Paul's writings and, more specifically, with the theological problem of Sin, evil, and death.

Scot McKnight is a New Testament scholar who is coming at the problem from the other side, from the biblical side. He is wrestling with this question that Longman mentions in the Foreword: "The DNA in current humans could not have come from a pool of fewer than approximately 10,000 humans" (xi).

I'll stop there to today, as other things press... See you next Friday, dv.

Preface to Friday Science: My Creation Quest

1. I have decided to blog through a recent book by Dennis Venema and Scot McKnight called, Adam and the Genome: Reading Scripture after Genetic Science. Scot is a faith-filled New Testament scholar and Dennis Venema is a faith-filled scientist.

Perhaps I should start by giving part of my own story on these topics. Ideologically, I grew up fundamentalist. My family did not have the heart of a fundamentalist, but we had the ideas of them. Fundamentalism is a militant version of a religion whose main goal is to combat forces of change coming from the surrounding culture.

I was going through my teens in the decades when Jerry Falwell was working his magic on America. I went to some of the early evolution debates between Henry Morris and Kenneth Miller because I grew up in the shadow of Coral Ridge Presbyterian Church in Fort Lauderdale, Florida. I was quite convinced that evolution was intrinsically antithetical to Christianity.

I was frankly disappointed with Morris as a debater. He seemed to spend most his time quoting people and giving quasi-philosophical arguments. I wanted him to blast the evolutionist with evidence. I was more pleased later with Duane Gish but let's just say that if I hadn't already been convinced, I don't think he would have convinced me. I've more recently watched Ken Ham debate Bill Nye and, again, it seems like his arguments are far more presuppositional than evidentiary.

2. In the meantime, I received a call to ministry in college. Later I felt within that call a call to train ministers in the Bible. So I went on to get a PhD in New Testament. I went through a common process of learning that there were reasons why scholars had some of the "funny ideas" I had once made fun of.

Having started out as a chemistry major and both loving and having an aptitude for math and science, I was well wired by the time I got to seminary to follow the evidence to its most likely conclusions. What I came to conclude is that at least some of my seminary professors were playing a bit of a game. They went through the motions of gathering evidence and making arguments, but it seemed to me that other interests were really guiding their conclusions, unacknowledged preconditions.

To be honest, I have personally found this to be the case for many biblical scholars, both conservative and liberal. And of course I have been accused of "cooking the books" too. The Bible scholars I have always admired are the straight shooters, but they seem few and far between.

I have at least heard that disillusionment is a common tale for faith-filled believers who go on to do graduate degrees in science. Some of them unnecessarily lose their faith in the process because they have been told that certain conclusions are incompatible with Christian faith. Then as those conclusions seem inevitable to them, they draw the logical inference--Christian faith must be wrong.

3. I am not an expert on matters of science. I have the aptitude (or at least did when my brain was nimble) and I have the interest. But I am not qualified to say what science reasonably concludes.

What I am an expert on is the Bible, and I know enough from my field to know that the biblical reasons often given against evolution are often based on shoddy understanding. In my opinion, it would not be good exegesis to read Genesis 1 as a blueprint for scientific creationism. Genesis 1 is poetic in nature and is in dialog with Ancient Near Eastern creation stories, not nineteenth, twentieth or twenty-first century science.

In my opinion, the problem for Christian understanding in relation to evolution is not Genesis 1 but Romans 5 and 1 Corinthians 15. Evolution requires lots of death, so if physical death entered the world through Adam, then evolution presumably contradicts Christian understanding.

There has been some interesting push-back on this line of thinking. What if Paul is talking about spiritual death rather than physical death? In the Garden of Eden, do not Adam and Eve need to eat from the Tree of Life to live forever, meaning that they are not immortal by nature? And whether you understand Sin as a nature or a power, you could say it came into play with Adam and Eve.

4. So in the not too distant past, even fifteen years ago, it was easy to say, "Could not Adam and Eve have been the first humans into which God placed a soul?" This approach would allow us to retain Adam and Eve in their historical form and yet let each individual make up their own mind on whether they were the absolute beginning or the spiritual beginning.

Enter Francis Collins and The Language of God. Collins is clearly a faith-filled individual. But he has also cracked the human genome. As I understand it, the current understanding of DNA is that we cannot identity a single set of parents who converge in the past. The current understanding is apparently that "the DNA in current humans could not have come from a pool of fewer than approximately 10,000 humans" (xi).

Accordingly, we have seen a few books come out very recently trying to grapple with this new conclusion from genetics in relation to Adam and Eve:

• The book I am reading now: Venema and McKnight, Adam and the Genome
• John Walton, The Lost World of Adam and Eve
• Cavanaugh and Smith, Evolution and the Fall

5. I do not assume that the recent finding of genetics is correct. But nor do I assume that our traditional interpretation of Romans is correct. What I assume is that:

• "All truth is God's truth." Once we understand the Bible appropriately and science appropriately, there will be no true contradiction.
• Our understanding of the Bible is hardly infallible. Interpretations come and go. Most of us aren't particularly skilled interpreters of the original meaning.
• There's a lot of truth in science. If I don't believe this, I should probably turn in the computer I'm typing on, as well as my cell phone and car. Most of us aren't particularly skilled at science.

It seems to me that at least some of us need to participate in this discussion. In this age where the democratization of knowledge is reducing Christian expertise to the lowest common denominator, it might be time to bring more advanced discussions out into the open.

Jamestown 1

I novelized my family history for a while a year ago.  It seemed like some people enjoyed it. In the end, I got tired of making stuff up. I've let it sit for about 9 months. Thought I'd try again with a factual approach.
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1. When I was a child, my grandmother passed on a tradition that had been passed down by her mother's family before her. The tradition was that we had an ancestor who had come over to America with Captain John Smith of Pocahontas fame. Such traditions are a matter of pride in a family.

As it is with most traditions, there would seem to be at least a kernel of truth in the story. My mother's mother's mother's mother's father's father's father's father's father's father seems to have settled in Jamestown in the early 1600s. That is my great, great, great, great, great, great, great, great grandfather (8th great grandfather).

In this day when you can connect to other people's genealogical quest, I was intrigued to find another person out there relating a similar family tradition. "It is tradition among VA families that the first Shelburne, Thomas, came to Jamestown in 1607 and settled there." So we have a tradition I can trace to my great, great grandmother that her ancestor came over to Jamestown in 1607, and I have been able to connect it to the family traditions of others who claim the same thing about the same person.

2. So did Thomas Shelburne come over with Captain John Smith in 1607? It would be nice to think so. It is at least possible. The problem is that his name does not appear on any manifest in those early years. The lists were not exhaustive, especially if Thomas were a young cabin boy who was there only to play a subservient role.

Still, we know of other boys. There was a boy named Milman who was the cabin boy of Captain Newport. And another boy named Helyard was cabin boy to Captain Waldo. Both boys would be dead within a year.

According to some memory, Thomas was Welsh. There was a Welshman named Captain Peter Wynne on board. No doubt we could write a novel where a naive young Thomas Shelburne somehow ended up at the last minute serving as Wynne's cabin boy at the age of twelve.

But there is no record of it. There is no record of Thomas in those dark years of Jamestown where so many died. We have so many names from those early years, but Thomas' is not one of them.

So while I would like to think that he came over in 1607 and while it is indeed possible he slipped through the cracks, I have to consider another option as perhaps more likely for the time being. It seems more likely that, as another family's memory has it, he was born in Great Britain during the reign of King James (1603-25). He then emigrated at some point in the 1630s and married Elizabeth Augustine around 1640 in Jamestown.

3. My DNA supports an ancestry that is some 64% British. How a young Welshman found his way to Jamestown is lost to history. We do know that southern Wales faced significant flooding in 1607. If Thomas really was born in 1595 and came to America at the age of twelve, perhaps here was a possible cause.

The London of 1607 was the London of King James I. It was the London of Shakespeare. The King James Version was underway and would be published in 1611. London Bridge at the time not only had houses on it, but the heads of former enemies of kings, like William Wallace of Scotland fame, as well as Thomas More and Thomas Cromwell, both of whom were put to death by Henry VIII.

...

Gen Eds 10d: Ancient Mesopotamia

Ziggurat at Ur

This is the fourth and final post in the Classical Civilizations" unit of my World History series. The first three were India, China, and Egypt.

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:

• World History Overview
• From 9-11 to the Present
• From the Cold War to the Millennium
• From Waterloo to World War II
• 5a. The French Revolution
• 5b. The Enlightenment to the American Revolution
• 5c. From Cromwell to the First Industrial Revolution
• 6a. Reformation and Scientific Revolution 
• 6b. The Renaissance and a New World
• 7a. Church Schisms in the Middle Ages
• 7b. Kings Rising in the Middle Ages
• 7c. Medieval Arabia, India, China, and South America
• 8a. The Roman Empire
• 8b. The Roman Republic
• 9a. Greeks and the Hellenistic Age
• 9b. Assyrians, Babylonians, Persians
• 10a. Ancient India
• 10b. Ancient China
• 10c. Ancient Egypt

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1. It is hard to believe, but we have finally hit the dawn of human history. The oldest walled village of which we know is Jericho, around 8500BC by most reckonings. [1] Perhaps there were only a few hundred inhabitants but it represented a movement that began to take place in the region--the formation of cities.

In this scenario, we humans had not really started farming until around 12,000BC, making the shift from being hunters to being farmers. When you farm, you are stuck to one place. People collect in one place. In 7000BC, the largest city may have been in Turkey, Çatalhöyük in Anatolia. It may have numbered between 5000 and 10,000.

But the first empire was in "Mesopotamia," "between the rivers" of the Tigris and Euphrates, modern day Iraq. Egypt united its lower and upper regions into a united kingdom around 3100BC, as we have seen. But the first empire was at Akkad around 2250BC, the empire of Sargon the Great. This area saw dominant kingdoms and empires for some 4000 years from the time of the Sumerians in lower Mesopotamia to the fall of the Babylonians to the Persians in 539.

2. We might say that humanity crossed the line from the pre-historic to the historic during the Uruk period (4100-2900BC) in Mesopotamia. These are the Sumerians, who called themselves, "black headed people." This area, Sumer, is the biblical area known as "Shinar" in Genesis 11:1.

The city of Uruk, perhaps founded somewhere around 4500BC, seems to be the place where writing really began to develop. At first this writing was a partial script--it was not created to write poetry but to keep count of cattle and taxes. [2] Writing develops to facilitate trading.

cuneiform

The form of writing is cuneiform. Cuneiform largely consisted of lines with triangles at the top. The Sumerians would also develop the 24 hour day and the idea of 360 degrees for a circle.

In Uruk, the cylinder seal was also used as far as we know for the first time, giving authority a reach beyond the presence of the king, a guarantee that you were reading something that was truly from the king. Kings ruled cities at this point, and cities conquered other cities. Empire does not as yet exist, only kings ruling individual cities and networks of cities with some kings more powerful than others (cf. Gen. 14:1-2).

The ziggurat also develops at Uruk. This will become the pyramid in Egypt. The Mayans, Incas and Aztecs also had their versions, making us wonder if there was contact of some sort across these continents. The Tower of Babel in Genesis 11 is perhaps a ziggurat of sorts. In the earliest days, kings were probably priests. Only later would the royal authority be sometimes detached from the religious authority.

Gilgamesh was a legendary king of Uruk, and we know him best from the Mesopotamian flood story, The Gilgamesh Epic. Gilgamesh was thus the Uruk version of Noah. The epic itself was not written down until sometime between 2100 and 1400BC, but this still qualifies it as the oldest human epic.

3. Uruk was not however the first city of the area. Eridu was perhaps founded in 5400BC and the Sumerians considered it the oldest city in the world. It was a city thought by the Sumerians to have predated the flood. This period before Uruk and writing is called the Ubaid period (6500-3800BC). This is the period right before the Bronze Age, often called the Calcolithic or Copper Age.

We have long associated this region with the Garden of Eden, and Genesis mentions the Tigris and Euphrates as two of four rivers in the area of the Garden (Gen. 2:14).

The city of Ur, from which Abraham originated (cf. Gen. 11:31; Josh. 24:2), was another Sumerian city dating from around 3800BC. The oldest wheels were discovered at Ur, on a four wheeled wagon. The kinds of tools that developed in the late 3000s in the Copper and Bronze Age were almost needed to make wheels.

The last period of Sumerian history ended in 1750BC with the third dynasty of Ur. Most famous in this period is Ur-Nammu, who created a law that foreshadowed the more famous law of Hammurabi.

4. Prior to the end of Sumerian history, the Akkadian empire began with Sargon the Great in the year 2334. This is the world's first real empire because it included multiple peoples over a vaster area of land than ever before. The Akkadians, unlike the Sumerians, were a Semitic people. Sargon ruled from Akkad.

The Akkadian language is often considered significant for Old Testament scholars. It is the oldest known Semitic language and thus is in the same family as Hebrew, Aramaic, and Arabic, not to mention Babylonian and Assyrian.

5. The city of Babylon was founded centuries before its most famous king from this period, Hammurabi (1792-50BC). His famous law Code of Hammurabi set down case law whose impact we can see in the Law of Moses. The "law of retribution," for example (the lex talonis) is found there, "An eye for an eye and a tooth for a tooth" (ca. 1776BC).

The Amraphel of Genesis 14:1 has letters strikingly similar to Hammurabi, given that Semitic languages are centered in the consonants rather than the vowels. It is thus no surprise that Abraham is generally dated to about this period of history.

Hammurabi and Abraham were during the Middle Bronze Period (2119-1700). It was probably in this period (ca. 1900) that the city of Ashur was founded, which would be the center of the old Assyrian kingdom. Other cities in that area included Nimrud and Nineveh.

Also during this time was the thriving of the city of Ugarit, in northern Palestine (ca. 1900). Ugaritic is also a Semitic language of great significance in Old Testament studies. Ugaritic literature gives us significant insights into the cultural and literary context of the Old Testament (e.g., what Leviathan might be in Job 41:4).

6. In the middle of the second millennium BC, the Hittites and then the Kassites would rule this area. The Hittites conquered the region in 1595BC. They are mentioned in Genesis (e.g., 23). In the Late Bronze Age (1700-1100BC), the Kassites would come south and conquer the area.

The Kassites have left us the Amarna letters from the 1300s BC, which were sent to Egypt and refer to the Hittites and others. Around 1100BC, the Enuma Elish we have was written down, although it undoubtedly is much earlier. Found in the library at Nineveh, it gives us the Babylonian creation story.

The juncture between the Bronze and the Iron Age, which is happening in the late 1000s BC, is the juncture where Israel is struggling with the Philistines. Israel is a bronze culture; the Philistines use iron. The Trojan War is a bronze war, and thus also dates to this general time.

Next Post in Series: History 11: The First Humans

[1] A book I have found fascinating in writing this post is Yuval Noah Harari, Sapiens: A Brief History of Humankind (San Fransisco: HarperCollins, 2015). The question of fitting the dates normally assumed by archaeologists and a very literal reading of Genesis is a controversial one. However, ancient chronologies were not necessarily exhaustive and we can assume that God's purposes in the genealogies of Genesis were much broader than to give us an exhaustive account of the names. The purpose of such lists at the time was to assure us of the ancientness of the lineage and its origins in God's creation of humanity.

[2] Harari, Sapiens, 122-24.

17 Narrow Misses with Hitler

I've read two more chapters of Konrad Heiden's 1944 book, Der Fuehrer since I last posted. Figured I needed to just say a few words and move on. Previous posts are at the bottom.

Chapter 18 is called, "Hindenburg's Stick," and chapter 19 is called, "The Race with Catastrophe." In these chapters, Hitler seems to advance. Then he faces defeat. Then he inches forward again.

1. I grew up thinking badly of most Germans at the time of Hitler, but it's clear that Hitler did not command majority support in the early 1930s. There were political zig zags and multiple exit ramps when Hitler might have been shown the way off the freeway.

1932 was a bad year for Germany. Much worse would follow, but it was all set in motion during this sad year. The players all played the hands they had. They danced with the devil, thinking they could control him, thinking that they had the power to stop him at a time of their choosing.

At the beginning of 1932, Heinrich Brüning was Chancellor. Paul von Hindenburg was President with Kurt von Schleicher as his close advisor. This would effectively be the last year of the Weimer Republic, German's brief experiment with democracy until after WW2. By the end of 1934, Hindenburg would be dead of lung cancer, Schleicher would be murdered, and Brüning would have left the country to save his own life.

2. You would have thought that with Germany's debt dismissed, the nation would have settled down. But you have two sides who are unwilling to compromise, both of whom want the other dead. One of them is going to win. The other side is going to end up dead. In this case the Communists were the other side.

Missteps. They dissolve the parliament on June 2, 1932, thinking some sort of autocratic control would enable them to establish stability. But the parliament would never return.

Goebbels and Goring try to control Hitler. "He must never be allowed to attend conferences alone" (466).

Papen becomes the Chancellor. He imposes unpopular economic measures to stabilize the economy. Probably a political mistake that would again keep Hitler on the autobahn. In the elections of these years, "the majority was against Hitler, but it was for nothing at all" (477). He would eventually rise not because the people wanted him but because they didn't want anyone else more.

Meanwhile Hitler's people were preparing for the great mass murder, the moment when they would kill their enemies.

Hitler's people are defeated again and he is chastised by Hindenburg. If you ask me, these repeated elections that parliamentary systems have at almost any time often contribute to great instability.

3. Chapter 20, "The Race with Catastrophe," begins with the incredible debt that Hitler and his party had accumulated. They needed to win just so that they could forgive all their own debt.

A good deal of this chapter dealt with a rival of Hitler's within the National Socialist party, Gregor Strasser. In late 1932, the majority of the party expected to lose more and more and had lost faith in the Fuhrer. Here is another moment it seems to me where Germany missed an exit ramp. Strasser seemed almost more popular that Hitler within the Nazi party in late November and December of 1932.

But Strasser resigned and went on vacation on December 7. He gave up the fight. How many catastrophes in history have been the result of people resigning rather than sticking it out in difficult times?

It reflected very poorly on Hitler for a moment, but by morning Hitler had turned it around. Strasser was the loser. Strasser was the betrayer. Instead of undermining Hitler, Hitler solidified his hold on the Nazi party. Hitler set up a central commission over the party, and his private secretary Rudolf Hess emerges as a leader.

But on December 11, the current Chancellor, Schleichter, effectively secured for Germany its ability to rearm. Riding a wave of approval, he easily sets up a government. Papen's economic initiatives were suspended. Hitler is depressed. "This was the darkest Christmas Hitler had had in years" (510).

Previously on Hitler:

• How to Take Over the World
• Bands of Restless Men
• Hitler was a Loser
• Rallies with the Rabid
• Waging War against His People
• The Art of Propaganda
• His Brand Is Crisis
• Big Words for a Coward
• Prophecies of the Antichrist
• Germany's Return from Despair
• Fatherland Security
• Hitler's Philosophy
• Destroying Democracy with Democracy
• He's Horrible to Work With
• Putting on a Show
• Maneuvering Toward Power

Paul 3.6

The next morning, about an hour before dawn, Paul and Barnabas left the city of Lystra and continued east to Derbe. It would take almost two days to get there.

Things seemed to turn around in Derbe. For one, Paul's eyes seemed to get better and better. Not everyone in the synagogue believed the good news, but there wasn't the hostility they had experienced elsewhere either. A number of people believed as Paul shared the good news in the agora while he fixed and made tents and other goods.

After a few weeks, Paul suggested to Barnabas they go back through the cities where they had already been in Galatia. If those house churches were going to survive, they would need stable leaders. Each city would need a group of leaders to keep them on track and oversee the believers there. Like Jewish synagogues, about ten people would be ideal. They proposed to make sure these leaders were in place before they returned to Antioch in Syria.

Probably each house church would have at least one of these leaders, but bigger ones might have more than one. Synagogues often were not in buildings. They were simply places where Jews gathered to pray and worship on the Sabbath. In the same way, followers of the Way might meet near a river or in some open space early on Sunday but then in individual house assemblies during the week to eat together, hear Scripture read, and worship.

When they returned to Lystra, Paul did not return to the marketplace. Paul and Barnabas appointed elders for the assemblies of the city, of which the house of Lois was the chief one. Accordingly, Lois was the elder in the city who held the most influence. Her daughter Eunice also served as an overseer in the city. Paul took note of her son Timothy, seeing in him a future minister or "deacon" to help them on their journeys.

And so they retraced their steps. A two day journey back to Iconium from Lystra. A five day journey up steep hills to get back to Antioch in Pisidia. In each place they appointed overseers for the collective house churches of the city. Five more days down to Perga in Pamphylia, this time much easier going downhill. Another day to the port city of Attalia.

Finally, Barnabas and Paul found a boat traveling to Antioch from Attalia, which took about three days. While Barnabas was glad to be back in familiar territory, Paul was a little sad. He would not want to stay long in Palestine before heading back out to spread the good news even further west.

Paul 3.5

Crowds began to gather. "How can the lame man walk?" Everyone was mystified. "This is not possible."

Soon attention turned to Paul and Barnabas. The formerly lame man kept pointing to Paul and saying in the local tongue, "This man healed me."

"The gods have come to earth again," someone finally shouted. They knew all too well the story of Baucis and Philemon, and they believed it. Long ago, the gods Zeus and Hermes had come to the region of Phrygia, not far from them, to visit the people of that region. But no one gave them any welcome except this one elderly couple.

In judgment, Zeus and Hermes caused a great flood which killed all the people of the region. Not only had they failed to entertain strangers--a high value in a world where it was dangerous to travel. They had treated them with scorn. Like God did to the cities of Sodom and Gomorrah, the Greek gods destroyed the cities that had done such things to visitors.

The city of Lystra would not make the same mistake. For about an hour, they insisted on sacrificing to Paul and Barnabas and throwing a great feast. Since Paul did the speaking, they called him Hermes. Barnabas they called Zeus. Before Paul could stop them, they were already rounding up all the goats and oxen they could find for slaughter. The priest of the temple of Zeus in particular called for sacrifices to Zeus.

Paul was both shocked and infuriated. Not only did he vigorously try to stop the growing crowd from praising him and Barnabas, but soon he started decrying the gods of the people. He began denouncing Zeus as a false god to the priest of Zeus.

"There is no Zeus!" he yelled at the top of his lungs. "There is no Hermes! These are false gods. These are evil demons even!" he shouted. "There is only one God, the God of Israel!"

It did not take very much shouting like this for the priest of Zeus and the crowd to change its tone. Now this foreigner was insulting their gods. This fact clearly showed to the Lycaonians not only that they were not gods but that they were in fact evil men.

Soon instead of praising Paul, they were grabbing whatever stones they could find and throwing them at Paul. Paul fled the agora. He fled down the main thoroughfare of the city with several young and fast men on his heels. Several hard blows found their mark.

He barely made it out of the city when enough of them caught up with him to inflict severe damage to his body. One rock in particular hit him square in the head and knocked him unconscious. His body would tell him for weeks how many other blows they inflicted while he lie there.

Barnabas managed to slip out of the agora without suffering the same fate. He went back to the house of Lois, while Timothy and others ran to the edge of town. There they found Paul's seemingly lifeless body folded over on the grass, just a few feet away from the Via Sebaste leading out of the city toward Derbe. There was no trace of the mob.

What would they do? Should they bury him? What was the point of taking the body back into town?

But before they made any decision, Paul suddenly started moving and, with some help. managed to stand up. Carefully, he managed to hobble back to Lois' house with Timothy and another man propping him up.

Seminary CM5: The Kingdom Core

This is the fifth post on the Contexts of Ministry in my Seminary in a Nutshell series. See the bottom for the previous posts in this unit, "The Person and Contexts of a Minister." I have completed one other unit in this series, The Pastor as Leader.
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1. Cultures differ significantly from each other and the biblical cultures differed significantly from us. Is there not some "kingdom core" that transcends culture? Is there not some timeless truth and practice that applies in all times and all places?

We cannot reiterate enough the fact that all human thought is ensconced in culture and that all biblical thought was incarnated in culture. What we are really talking about here are truths and practices that apply to all cultures rather than ones that transcend culture. We are asking about omni-cultural truths and practices.

Perhaps more importantly, we are asking about standards by which we can judge elements of culture. The danger here is that we so very often cannot distinguish our culture from this kingdom core. It seems beyond question that a large amount of what Christian missionaries from the United States have exported to the world over the last couple centuries has had as much of American culture in it as it has the gospel. No doubt we can attribute some contemporary mission failure to an inability to discern cultural elements in the way the mission was conducted.

2. So what is the kingdom core? It is perhaps easiest to address ethics and practices first, rather than beliefs. The reason is that the New Testament is so clear on what the fundamental Christian ethic is. From Jesus to Paul to John to James, the New Testament is unanimous in its sense that loving God and loving our neighbor/enemy is the kingdom ethic. [1] It is not its core. It is the whole of the ethic.

Any appropriation of the Bible that conflicts with the love of God and the love of neighbor is a misappropriation of Scripture!

Love is a universal human value. All cultures have some sense of what love is. It is thus an omni-cultural ethic. To be sure, different cultures understand it slightly differently. What is considered unloving can differ somewhat from culture to culture. American culture right now probably has a very weak sense of love, one that befits our world of vast convenience and ease. We thus probably under-appreciate the harder aspects of love that are intrinsic to cultures and sub-cultures where life is much more difficult.

Another warning applies to the impulse to use the concept of loving God as a way to wiggle out of loving our enemy or neighbor. Someone might say, "I cannot show love to my enemy at this point because my love of God trumps it here." This is a trick of Satan. Love of God never requires us to act hatefully toward our enemy, although a misinterpretation of the Bible might.

Love has to do with bringing good to others. It has to do with action rather than feeling. I can love someone that I do not like. Justice does not conflict with love. Justice can be redemptive toward an individual. And justice can be protective of a group of people. Finally, justice can be protective of the order of things. In none of these cases is justice unloving.

The love of God is about giving him priority in all things and in letting nothing in our life get in the way of loyalty to him. However, God is not threatened by the disobedience of his creation. In the mystery of his will he has created the world with the possibility of such disobedience. He thus does not always shut down opposition to him immediately, nor does he command us to do so. Nevertheless, the love of others suggests that we will help them find God and will protect others if we can.

3. So the "law of love" is at the essence of the kingdom core--what our attitudes and actions should be. How that love plays itself out will differ somewhat from time to time, culture to culture, sub-culture to sub-culture. For example, it is hard for me to imagine that the law of love can play out very well in American culture in a way that insists men must rule over women. In my world, love insists that husband and wife be of equal value and authority in the home.

Yet it was not universally so in the world of the New Testament. The household codes of Colossians and Ephesians, the instructions of 1 Peter to a persecuted church, these were accommodations to first century culture. The kingdom core suggests that if we find ourselves in a world where we can more fully implement Galatians 3:28, we should.

Yet there are many cultures around the world where the household codes seem to fit the cultural context neatly. Husband-headship in those contexts does not conflict with the love of neighbor. Accordingly, Christians in each time and place must "work out your salvation with fear and trembling" (Phil. 2:12). Those of us from different cultures will often not be able to see what love exactly looks like for them.

4. What of beliefs? Certainly Scripture is a sacrament of transformation for all cultures. No matter where we live, God will help his people see what they need to see in Scripture.

There is however a core, a commonly held set of beliefs derived from Scripture that Christians have agreed on for millennia. These are especially found in the core creeds of Christendom.

• God exists and is active in the world (cf. Heb. 11:6).
• Jesus is the Son of God. Jesus in fact is God (e.g., John 1:1). 
• Jesus is the only mediator between God and humanity (1 Tim. 2:5). Humanity stands under the power of Sin and under the prospect of judgment (Rom. 3:23), but through Christ, God has provided a way of salvation from final judgment (Rom. 6:23; 10:9).
• There is thus eternal life to be gained through Christ (John 3:16).
• Those who have the Spirit of God within them constitute the people of God (1 Cor. 3:16).
• Scripture is the canon, a divinely appointed meeting place for God to inform and by which to form us (2 Tim. 3:16). The Bible is the primary source of our story and our symbols as Christians.

5. The way these beliefs play themselves out in various cultures may differ a little. The symbols that speak the most strongly may differ. Indeed, these things differ from denomination to denomination in my own culture. The impulse to say, "This is the core," is almost always more restrictive than it is for God.

It is ultimately the charge of Christians in a particular culture or sub-culture to determine how the gospel might play out. The importance is that those decisions are made full of faith. And of course, we can be wrong!

Next Sunday: Culture 6: The Church and Culture

[1] Cf. Matt. 22:34-40; 5:43-48; Rom. 13:8-10; Gal. 5:14; 1 John 4:7-8; Jas 2:8.

The Calling of a Minister

• The Domains of Ministry
• The Calling of a Minister
• Ministerial Calling in Scripture
• Ministerial Calling in History
• God can call anyone he wants into ministry.
• A Theology of Calling

The Person of a Pastor

• Intro to the Pastor as Person
• Personal Strengths and Weaknesses
• Sacred Pathways
• Individual Spiritual Disciplines
• Corporate Spiritual Disciplines
• Some Formational Reading

Contexts of Ministry

• Kinds of Context
• The Making of Meaning
• How Culture Works
• The Cultures of the Bible

9.2 LR Time Constant

Last week we began Module 9, "Relationships of Current, Counter EMF, and Voltage in LR Circuits." These modules are part of the Navy Basic Electricity and Electronics series from the 1970s.

9.1 Rise and Decay of Current and Voltage

1. The second unit for this week is called "LR Time Constant." L of course stands for inductance and R for resistance. "In a purely resistive circuit, current reaches its maximum value the instant the circuit is energized" (30). On the other hand, we have seen that inductance in a circuit creates a counter-EMF when a circuit is powered up, meaning that current will take a moment to reach its maximum value.

2. Now enter the notion of a "time constant." The time constant is defined as the inductance in henrys divided by the resistance in ohms, the result of which is in time.

TC = L/R

As it turns out, this constant approximates one fifth of the amount it takes for an LR circuit to energize up to its full current value. So it takes a circuit five time constants to power up. For each passing time constant, a circuit will move 63.2% of its remaining current amount.

So the first TC period, the circuit will go from zero amps to 63.2% of its final amp value. Similarly, when powering down, a circuit will go from 100% to 36.8% of its maximum value. In the second TC period, it will power up 63.2% of its remaining amount or another 23.3% to 86.5% of its maximum value (or down to 13.5% its maximum value if it is decreasing).

From T2 to T3, it will reach 95% of its maximum (or 5% if de-energizing). From T3 to T4 it will reach 98% (or 2%). Then by T5 it will be approximately to its maximum (or zero if de-energizing).

3. The section ends here, but I can mention the mathematical basis for this peculiar set of percentages. The underlying formula from which 63.2% comes is (1 - 1/e).

Friday Gen Eds MS13: Electromagnetism

This is the thirteenth 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 on the home stretch 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:

• Math/Science Overview
• Basic Types of Numbers
• The Atom and Quantum Physics
• The Periodic Table
• Molecules and Ions
• Chemical Reactions
• The Basic Tools of Algebra
• Heat and Thermodynamics
• Basic Geometry and Trigonometry
• The Basics of Calculus
• The Physics of Motion
• The Forces of Motion

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1. In the winter, I will often touch my wife's arm before I kiss her goodnight, because I have given her a shocking kiss more than once. The reason is that I have built up a static charge somehow. It could be my shoes rubbing against the carpet. When it is warmer, the moisture in the air is greater and such charges disperse more easily. But when it is colder, there is less moisture and the charge is vented on my unsuspecting wife serving as a conductor.

A conductor is a material through which electrons move easily. An insulator is a material through which electrons do not move easily. The flow of electrons through a conductor is called current, and this channeling of electrons is electricity. Benjamin Franklin famously demonstrated in 1752 that lightning was a form of electricity, using a kite in a thunderstorm.

Current, Voltage, Resistance
2. The flow of current is measured by how many electrons are passing any given point in a certain amount of time (technically, how much charge is passing that point). The amount of electrons is measured in coulombs. [1] One coulomb is the charge equivalent of 6.2 x 10¹⁸ electrons.

One coulomb of charge moving past a given point in a second is called one ampere. It makes sense that as a current moves through things one by one, the same amount of current goes through each thing, if it doesn't get branched off. Let's say there is a circuit that starts with a power source (like a battery) and goes through a wire and several things (e.g., a light bulb, a heater, etc) but it does so one at a time and never branches off until the wire comes back finally to the power source. We call this a series circuit because the current goes "around" (circuit) through all the elements one by one.

In this case, the amount of "amps" going through each element in that circuit will be the same.

3. The moving charge of electrons always emerges from the power source at its "negative" pole. It thus returns into the source at the "positive" side. Electricity thus flows from negative to positive in a circuit. It is pushed out of the source by an "electromotive force" or EMF. We call the amount of work done by that force on each coulomb of charge a volt. Voltage is thus the work done per coulomb in a circuit.

Unlike current, each element in a series circuit absorbs a certain amount of work. So while every element of a circuit will have the same number of amps, each element in a circuit absorbs some of the work from the electrons. The volts used by each element thus add up to the total voltage at the power source in a series circuit. [2]

4. We might say that each element in the circuit thus provides a certain resistance to the voltage. Without any such resistance, we would have a short circuit and the power source might burn up. The amount of current going through an element is proportional to the amount of work done on that element. That is to say, the more work done on the element, the more current going through it.

This relationship is captured in a law called Ohm's law [3] If E is the voltage and I is the current, then E = I x R, where R is the resistance of an individual element in a circuit. The unit of resistance in electricity is called the ohm and it is the amount of resistance afforded by something that only allows one amp of current to flow through when one volt of force is applied.

So since the current is the same throughout a series circuit and the voltage is the total difference in work done between the poles of a power source, the total resistance in a circuit adds up just like the total voltage does. The total resistance of a series circuit is the sum of all the individual resistances.

5. Power is the amount of work done in a certain amount of time. Electrical power is measured in watts. From every day life, we know that a 100 watt light bulb burns brighter than a 60 watt one. Power equals the voltage times the current, or P = E x I (where E is the voltage and I is the current). So the higher the voltage, the higher the power exerted. The higher the current, the higher the power exerted. And of course if both the voltage and the current are higher, the power exerted is all the higher.

6. I mentioned the rules for series circuits above. As series circuit is one in which there is a single flow of the current. It does not branch at any point. Accordingly, the current is the same throughout. The resistance adds up per element to make up the total resistance. Similarly, the voltage drop across each element adds up to the total voltage in the circuit.

In a parallel circuit, the current branches at some point, perhaps at several points. In this case, it is the voltage that is the same across every branch. Meanwhile, it is the current in each branch that adds up to the total. [4]

The current in each branch depends on the resistance in each branch. As far as the total resistance, it goes down when resistance is added to individual branches, meaning that the total amperage will go up. You can find the current or resistance in any branch using some variation of the E = I x R formula.

Finding the total current or resistance in a parallel circuit is more complicated. If you find the reciprocal (one over x) of the resistance in a branch, then add them together, then take the reciprocal of that sum, you will have the total resistance of the circuit. You can then use the voltage and the total resistance to find the total current.

7. I have assumed that the circuits we have been talking about have been direct current (DC). Direct current is the kind of current that might come from a battery. In a battery, a chemical reaction is used to create the electromotive force that pushes current through a circuit. Direct current is current that is constant, constant in its voltage and amperage unless something interferes with the circuit somehow.

However, the current that comes from a wall plate is alternating current (AC). This is current that alternates between a positive and negative voltage (usually 110 volts), usually at about 60 Hertz or 60 back and forth alternations per second. Another way to think of alternating current is that the flow of current alternates directions.

Alternating current is used because it is more easy to manipulate--for example, to change voltages. It is also easier to generate high voltages in AC rather than in DC. Since high voltage is more suitable for transferring electricity over longer distances, modern societies generate high voltages in AC and then distribute that electricity to local communities where transformers then reduce the voltage and distribute it to houses. Individual devices may then convert the AC to DC so that the device can function.

Magnetism and Induction
8. Most of us know what a magnet is. You can use one to pick up metal. You might touch a screw to a magnet and it will temporarily become magnetized. Then it will stay on your screwdriver more easily. A compass works because the earth has a certain magnetic field. The metal on the compass will turn toward the north pole.

In the early 1800s, a relationship was discovered between electricity and magnetism. When current runs through something, a magnetic field is created around it. Similarly, if a magnet is moved around a conductor, it can generate a current. The rotation of a magnetic field generated by electricity is the cornerstone of the electric motor.

9. Here are some basic facts about magnetism. Magnetic lines form closed loops, the smallest loops possible. Magnetic lines pass through everything, although they can be directed. Like magnetic polarity repels; opposites attract.

10. By coiling a wire around a conductor, you can create an electromagnetic field by running current through the wire. The "left hand rule" expresses how this works. If you picture wrapping your left hand in the way that the wire is wrapped around, then your thumb will point toward what will become the north pole of the artificial magnet (magnetic fields go from north pole out in a closed loop only to re-enter the magnet at its south pole).

By the same token, if you point your left thumb in the direction of the current in a wire (current moves from negative to positive), your fingers will curl in the direction the magnetic field created around the wire moves.

11. Inductance is the property of a circuit that opposes any change of current. When current changes, creating a magnetic field, a counter EMF is created that opposes that change. This is Lenz's Law: "The voltage induced in a circuit by changing current always opposes the change causing it." This is a parallel to Newton's third law. When current is decreasing, inductance wants to maintain it. When current is increasing, inductance wants to resist it.

The unit of inductance is the henry. 1 henry is the amount of inductance that yields one volt when the current is changing at the rate of 1 ampere per second. The symbol for inductance is L.

Induction is the actual creation of a voltage, which requires motion. Inductance does not require current flow. Induction does. Induction is the action of inducing a voltage when current is changing in a circuit.

Charges and Capacitance
12. Coulomb's Law is the analogy to Newton's Law of Gravitation and tells us how to calculate the force of a charge on another charge. The equation looks quite the same!

F_e = k(q₁q₂)/r²    [5]

Any one charge (e.g., q₁) creates a field that travels through space. Any other charge then reacts wit that field, while the initial charge is similarly acted on by the other charge. The main difference between gravity and the electromagnetic force is that the force of gravity only accumulates, while charges are positive and negative and thus can cancel each other out.

13. Capacitance refers to the capacity of two separated plates to retain a certain charge, almost like a battery. Such plates often have some sort of insulator in between them, called a dielectric. The unit of capacitance is a farad. 1 farad is the capacity to store one coulomb of charge when one volt of potential exists across a capacitor.

So C (capacitance) = Q (charge)/E (voltage).

Capacitance is directly proportional to plate area. The bigger the area, the bigger the capacity for storing charge. It is inversely proportional to plate spacing. The bigger the gap, the less the capacity for storing charge.

A vacuum in between the two plates suggests the least capacitance for two plates, so when a vaccuum or air is the "dialectric" between two plates, we say the dialectric constant is 1. Other insulators between the two plates increase capacitance. Pure water, for example, increases capacitance by 81 times!

The equations for calculating capacitance in a circuit are exactly the same as the formulas for resistance and inductance.

Maxwell's Equations
The most fundamental principles of electromagnetism were captured by James Clerk Maxwell (1831-79) in the mid-1800s. In his famous four equations, he captured and built on the work of others before him like Michael Faraday (1791-1867) and Andre-Marie Ampere (1775-1836).

1. Gauss' law for electric fields is named after Carl Friedrich Gauss (1777-1855) and basically says that an electric charge produces an electric field passing through any closed surface around it and that the amount of electric flux passing through that closed surface is proportional to the total charge contained within that surface.

In another form, this law suggests that electric charge is repelled by positive charge and attracted to negative charge.

2. Gauss' law for magnetic fields is closely related to the previous law. It amounts to saying that the total magnetic flux passing through any closed surface is zero.

3. Maxwell's third equation is Faraday's Law, which we have described above but not named. Faraday's law states that a magnetic field passing through a surface induces an electromagnetic force at the boundary of that surface, and a changing magnetic field induces an electric current.

4. Maxwell's fourth equation is the Ampere-Maxwell equation, which we have also encountered above but did not name. An electric current generates a magnetic field.

Next Post: Math/Science 14: Genetics and Evolution

I intent to read through material from a couple books before the next post, so it may take some time to get to the next one, but I will post some review material in the meantime.

[1] After Charles Augustin de Coulomb (1736-1806).

[2] The idea that the voltage difference across each element in a series circuit add up to the total voltage is called "Kirchhoff's law" for voltage.

[3] Named after Georg Ohm (1789-1854).

[4] Kirchhoff's current law.

[5] I have introduced k as a constant to show the similarity with Newton's Law of Gravitation. The constant is usually expressed as 1/4πɛ₀, where ɛ₀ is the "constant of permittivity of free space," approximately, 8.85 x 10^-12 farads/meter.

Paul Novel 3.4

Is life anything more than a rush from deadline to deadline? Here's a Monday post on a Wednesday.
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First they came to Lystra. Paul did find a Jewish doctor there to look at his eyes. He seemed to think that the altitude of the mountains might have made them worse, that Paul mainly needed to rest. But rest was not a word in Paul's vocabulary. As usual, Paul set up shop to sell and fix leather goods, while sharing the good news to anyone who would listen.

He and Barnabas had a fair reception in the synagogue. In particular, the family of a widow named Lois came to faith and opened up her home for believers to gather and worship. Soon Lois' daughter Eunice also believed. Eunice was married to a Greek man and had a son barely thirteen years old named Timothy.

Day blurred into day. His eyes slowly got a little better. As he worked in the agora each day, he was more and more grieved by a lame man who never seemed to move from the same spot. He slept on the same spot and begged for some small morsel of food each day from someone. He was often harassed by children and others.

Paul's heart was stirred more and more with each passing day. Paul began to talk to the man each day about Jesus. He told the man how Jesus had healed the lame and cured the blind. He told the man that if he would only believe, God would heal him too. Even more, God would one day give him a body that would live forever.

Finally, one day two teenagers were troubling the man. One grabbed his right arm and the other his left. "You can walk!" joked one of the teens.

"You can walk," Paul interrupted with the sound of great authority in his voice. Barnabas too was full of faith that this was the day that the man would be healed. "You can walk," Paul repeated, "if you only believe in God!"

"Oh yeah," one of the boys said, and they let go of the man.

But he did not fall. To his own astonishment, he looked down to find himself standing on his own two feet. "I can stand!" the man exclaimed. He moved one of his feet. "I can walk!" he said even louder.

"I can walk!" he said again, louder and louder. He moved his feet, one after the other, each time faster than the time before. "I can walk!" he shouted, moving around the agora, faster and faster.

Everyone was astonished and amazed. "Isn't this the lame man who sits every day in the marketplace begging? Isn't this the man we all make fun of in our homes?"