In another generation, I would write in a journal. Perhaps one day someone would take interest, perhaps a child of mine. At this point it does not look that my contribution to the world will be significant enough for anyone to study me. I do think some people would find my ideological biography interesting and I have given a peek of one strand of it elsewhere.
I also realize more and more how much a person must guard their words when you live in a representative role. I am currently Dean of a seminary of a church in which I am ordained. That means my words represent my church, my university, and my denomination all at once. There are also people you don't want to hurt or offend. In short, some thoughts are best not shared until either you or your generation are dead. Sometimes some thoughts would best not be shared until a second generation had also passed.
I post here some thoughts now because I am going to Turkey in a little more than a week, dv. I want to put some thoughts down in a place where they can be found but where they probably won't be found quite so readily. How I tire of my detractors, most of whom probably do not even understand what I am saying half the time. How I have dumbed myself down over the years and hated myself for having to do it. But in case I die, I wanted to sketch my basic understanding of the world.
1. First, I believe there is only one thing of which we can be entirely certain, and that is that something exists. Descartes said, "I think; therefore, I am." Even this statement went too far. It would not have been as snappy, but a more accurate statement would be, "I think; therefore what I am calling 'thought' exists." The notion of an "I" is itself riddled with assumptions.
2. All other claims to truth involve faith of some sort. On the one hand, there are a host of data from the world whose existence works so well that it is worth calling them "facts." Certainly almost everything that can be questioned has been questioned. Am I dreaming right now? Am I a brain in a vat? It is ultimately a matter of faith that I am not a sophisticated computer program, but it is a very reasonable act of faith.
"There is a dog lying on my bed." Given my experience at this moment in time, it is reasonable for me to call this statement a fact. Empiricism is "true" to the extent that the content of my understanding of the world is built out of these facts. Empiricism is not sufficient to account for my understanding of the world because the organization of these facts is a function of my mind, which is a function of my brain. But these data are the materials from which my mind constructs understanding and perspective.
You will recognize in the previous paragraphs the influence of Kant, as well as a hint of Rorty. There are reasonable assumptions to make in this world, reasonable because these assumptions "work." Almost everything can be questioned--and far more than we want to assume is a "warranted basic belief," in the words of Plantinga. But there are data worth calling facts, especially objects that correspond to what Locke called simple impressions.
3. Where things get sticky is in the interpretations of facts, the organizations of our sense experiences in our minds, the "unities of consciousness" our minds create out of the simple impressions we have of the world...
Sunday, May 12, 2013
Friday, June 08, 2012
Monday, March 26, 2012
My father passed today.
My father died this morning. I was walking on the beach in Hilton Head, South Carolina in the morning, taking pictures of jellyfish and crabs, conch and watching bottle nose porpoises slowly making their way to breakfast. At home my father had bought his morning coffee and sausage biscuit from McDonalds and sitting down to eat.
The call came from my sister Debbie to pray. He had a pain in his neck and after my Mom rubbed a little salve as was the custom, he moved chairs, and then slumped over. It was about 8:30, about the time I had been calling them in the morning on my way to work.
Three weeks ago we had a premonitory incident on a Sunday and I was deeply afraid I had lost him without much contact since we'd returned from Germany. I must always regret taking my chances to visit him this weekend. We almost made it, but I had almost daily if brief phone conversations with him and mother these last weeks. Stefanie was able to see him in person two weeks ago and Tom/Sophie were able to speak with him on the phone as well.
He made a quick recovery after that spell and had been fairly well since, apart from some sneezing episodes two weekends ago. All four of my sisters had seen him in the last month, including many nephews and his one great granddaughter.
Our turn was this weekend. We were in South Carolina and were coming down Saturday. Debbie's call this morning was clearly more urgent than any before. We were just about back from our morning walk on the beach. A call to my sister Patricia some twenty minutes later made it clear that it didn't look good. They had shocked him three times and were still having trouble getting a rhythm. They were still in the ambulance in front of the house.
A call to Mom about 9:30, and he was at the hospital. She put on a good voice and had stayed home. Patricia had gone. Maybe 10am and Debbie called to say he was gone.
Angie and I went to tell Tom and Sophie. They had quickly packed while I showered but did not have the final word. They were playing Foosball. On the way across the garden of the Marriott Monarch I saw a magnificent blue heron. It was stately and reminded me of my father, a truly great man.
Much of the timing was providential. We were nearby in South Carolina. My wife's sister Teresa was to drive right by Lakeland that very morning and I could ride with her. The funeral will be later this week while we are already here. It was a good day for eternity.
Sunday, March 25, 2012
Reflections 7
My Dad's father was quite conservative even for my parents' circles. He and some of my dad's siblings actually broke away from my church when they merged with another group in opposition to what they saw as a move in a "liberal" direction. One of my uncles told my dad that he would pray for his soul if he went with the merger.
Another uncle once didn't let my sisters sing special music because one of them had cut her bangs, and hair cutting was not allowed because of 1 Corinthians 11. When my father first bought a black and white TV, my grandfather didn't come visit us for a long time in protest. That was one of his shaming techniques to show his disapproval. He would give you "a good letting alone."
I don't actually think too badly of him. I think you can be so convinced that someone is wrong that you don't feel threatened by them. Of course I mean people who are not in a position to hurt you politically or physically. I have lived a good deal of my teaching life with deep concern for people who disagree with me who might try to sabotage my livelihood.
It wasn't our way to hold these things against them. In fact, we dressed to standard when we visited. Even though my family remained rather conservative, I didn't experience these "standards" as a major concern for our nuclear family in particular.
As I was saying, one song in particular at camp meeting used to bring me inner turmoil. It went through the days of the weeks and you were supposed to stand when it came to the day of the week when you were "saved." "It was on a Sunday, somebody touched me..." You repeated it three times and then ended the stanza with "... must have been the hand of the Lord." Then it moved on to Monday. When the song came to the day you were saved, you were supposed to stand.
To be "saved" meant to have an experience of conversion. You went from being on your way to hell to being on your way to heaven, if you remained faithful. The experience was preached as a somewhat dramatic moment you would definitely know and remember. The picture was one of high emotion, with probable weeping or shouting or some significant sign of emotion. Sure, sure, somewhere someone said that it didn't have to necessarily be dramatic, but that was the image that seemed most given.
There would be multiple verses of a song as part of an "altar call." The altar was a long series of benches stretching across the front of the "tabernacle," as the camp meeting building for services was called, after the holy sanctuary of the Old Testament. In that sense, the altar at the front I suppose was meant to resemble the Holy of Holies where God's presence was, although I don't remember anyone ever saying that.
Everyone knew the ritual. After each verse of a song like "Just as I Am," the song evangelist would implore all of those to come forward who needed to 1) get saved, 2) get sanctified, or 3) something else relating to the sermon (very unusual though for it to be something other than getting saved or sanctified). There would often be, "This is the last verse." Sometimes it was; sometimes it wasn't.
Sometimes the preaching evangelist would get up between verses and tell a story about someone who didn't come to the altar and then died on their way home from the meeting, only to go into the eternity of hell. You could have written up the liturgy of the altar call the same as any Roman Catholic communion. It was followed every night, every year, ever camp meeting.
As I mentioned, I dreaded the "It was on a Sunday song." At first, it was because I did not have a clear moment to say was the real one when I was saved. Mind you, I asked God to forgive my sins repeatedly. I wanted to stand--who wanted to look like they had never been saved. I didn't know what day it was. I was so glad when they added a final verse, "I don't know what day it was but somebody touched me..."
But then there was guilt about not going forward to the altar. I was quite shy and the thought of walking down the length of the sanctuary to pray was terrifying. I would go outside and pray after the service. Once I went and sat on the bench on the front row after the service. Then I felt guilty for not being totally committed to God. If I was really serious about serving God I would have made myself walk down that long aisle to the front.
And at the front, people would pray for you. They would surround you, maybe lay hands on you. They would raise their voices in prayer for you. One or two would be on the other side of the altar, asking you what you were there for, how you wanted them to pray. It was all horribly terrifying to me.
And some people were altar recidivists. I remember a fellow in my home church--I think he might have later turned out to be gay--who was at the altar it seemed almost every week for a while. He never seemed to be able to find peace. I sympathized with him because I never seemed to have those dramatic emotional moments we were led to expect.
Then there was one Sunday morning, I think it was. My sisters were home to visit, maybe from "Brainerd Indian School" in South Dakota. It must have been in the late 70s. Going up that stairway on the outside of our house I felt a peace. Not a big emotion, but it was enough for me to stand up when the camp meeting song came up.
So much of this scene now seems wrong to me...
Another uncle once didn't let my sisters sing special music because one of them had cut her bangs, and hair cutting was not allowed because of 1 Corinthians 11. When my father first bought a black and white TV, my grandfather didn't come visit us for a long time in protest. That was one of his shaming techniques to show his disapproval. He would give you "a good letting alone."
I don't actually think too badly of him. I think you can be so convinced that someone is wrong that you don't feel threatened by them. Of course I mean people who are not in a position to hurt you politically or physically. I have lived a good deal of my teaching life with deep concern for people who disagree with me who might try to sabotage my livelihood.
It wasn't our way to hold these things against them. In fact, we dressed to standard when we visited. Even though my family remained rather conservative, I didn't experience these "standards" as a major concern for our nuclear family in particular.
As I was saying, one song in particular at camp meeting used to bring me inner turmoil. It went through the days of the weeks and you were supposed to stand when it came to the day of the week when you were "saved." "It was on a Sunday, somebody touched me..." You repeated it three times and then ended the stanza with "... must have been the hand of the Lord." Then it moved on to Monday. When the song came to the day you were saved, you were supposed to stand.
To be "saved" meant to have an experience of conversion. You went from being on your way to hell to being on your way to heaven, if you remained faithful. The experience was preached as a somewhat dramatic moment you would definitely know and remember. The picture was one of high emotion, with probable weeping or shouting or some significant sign of emotion. Sure, sure, somewhere someone said that it didn't have to necessarily be dramatic, but that was the image that seemed most given.
There would be multiple verses of a song as part of an "altar call." The altar was a long series of benches stretching across the front of the "tabernacle," as the camp meeting building for services was called, after the holy sanctuary of the Old Testament. In that sense, the altar at the front I suppose was meant to resemble the Holy of Holies where God's presence was, although I don't remember anyone ever saying that.
Everyone knew the ritual. After each verse of a song like "Just as I Am," the song evangelist would implore all of those to come forward who needed to 1) get saved, 2) get sanctified, or 3) something else relating to the sermon (very unusual though for it to be something other than getting saved or sanctified). There would often be, "This is the last verse." Sometimes it was; sometimes it wasn't.
Sometimes the preaching evangelist would get up between verses and tell a story about someone who didn't come to the altar and then died on their way home from the meeting, only to go into the eternity of hell. You could have written up the liturgy of the altar call the same as any Roman Catholic communion. It was followed every night, every year, ever camp meeting.
As I mentioned, I dreaded the "It was on a Sunday song." At first, it was because I did not have a clear moment to say was the real one when I was saved. Mind you, I asked God to forgive my sins repeatedly. I wanted to stand--who wanted to look like they had never been saved. I didn't know what day it was. I was so glad when they added a final verse, "I don't know what day it was but somebody touched me..."
But then there was guilt about not going forward to the altar. I was quite shy and the thought of walking down the length of the sanctuary to pray was terrifying. I would go outside and pray after the service. Once I went and sat on the bench on the front row after the service. Then I felt guilty for not being totally committed to God. If I was really serious about serving God I would have made myself walk down that long aisle to the front.
And at the front, people would pray for you. They would surround you, maybe lay hands on you. They would raise their voices in prayer for you. One or two would be on the other side of the altar, asking you what you were there for, how you wanted them to pray. It was all horribly terrifying to me.
And some people were altar recidivists. I remember a fellow in my home church--I think he might have later turned out to be gay--who was at the altar it seemed almost every week for a while. He never seemed to be able to find peace. I sympathized with him because I never seemed to have those dramatic emotional moments we were led to expect.
Then there was one Sunday morning, I think it was. My sisters were home to visit, maybe from "Brainerd Indian School" in South Dakota. It must have been in the late 70s. Going up that stairway on the outside of our house I felt a peace. Not a big emotion, but it was enough for me to stand up when the camp meeting song came up.
So much of this scene now seems wrong to me...
Sunday, March 18, 2012
Reflections 6
To me, the most coherent view sees God in relational terms. God knows us and wants to rescue us from our alienation. He wants to be reconciled with us. He wants to be in relationship with us.
Relationships can be broken. Any violation of our faithfulness to God damages our relationship to God, not on his side but on ours. We cannot be unloving and not create distance between us and God. A person who is unfaithful in a marriage or friendship cannot be as close to their partner or friend, especially if their friend knows their faithlessness.
But relationships only break instantly with the most major of infidelities. God will take us back if we can bring ourselves to go back--not always possible because our hearts become hardened like cement and we cannot move them any more. We can still move with smaller acts of infidelity, but they can accumulate like plaque in an artery. Eventually we will have a heart attack and the relationship may not survive.
At least these are thoughts I had later. The climate of preaching that led me to fear that I would fry with the smallest of infractions was just plain wrong. It was built off a shallow understanding of God's love, not to mention of relationships. It made God into a poor excuse for a human spouse, let alone a divine one.
The preaching I grew up with was also preoccupied with spiritual events, benchmarks you needed to check off a list. I remember in particular one song they sometimes sang at camp meeting in Frankfort, Indiana. Some families went to the beach or the mountains when they took their vacation. We went to camp meeting or church district conference or, every four years, to church general conference.
Frankfort, Indiana was probably the navel of my childhood universe. Every year at the beginning of August we made pilgrimage back to Indiana. Frankfort was where my mother had largely grown up. There was a Bible college there, Frankfort Pilgrim College.
My mother's father, Harry Shepherd, had taught there most of my mother's life except in the years of the Great Depression. In those years he had pastored and taught at Bible colleges in North Carolina () and Kentucky (Kingswood). Then he had made his way back to southern Indiana pastoring () before finally finishing out his career at Frankfort.
Over the years he taught (dispensational) prophecy, Latin, calculus, and I suspect any number of other classes. He was a graduate of the 190* class of Wabash College and had played baseball there. He was quite a bit older than my grandmother, Verna, and she was his second wife after his first wife passed. Born in 1882, he and his two sisters were orphaned after his father finally succumbed to injuries he sustained in the Civil War. I never met him, since he died about three years before I was born.
So my mother had grown up roaming the campus of Frankfort Pilgrim College. She attended both high school and college there and became quite a good pianist. My three oldest sisters went to college there, although my third oldest sister Sharon had to finish her work at Hobe Sound Bible College in south Florida when the Wesleyan Church closed Frankfort.
But the camp meeting continued there and, although the grounds were sold in 2010, it continues even today. I was born in Indiana, although my father's job took him to Florida in 1971. So while we lived in Ft. Lauderdale, we remained strongly connected to Indiana.
I was born in Indianapolis at Methodist Hospital. At the time we lived on the north side of town, just south of Carmel. My Dad's parents lived in the middle of Indianapolis. My Dad's father, Dorsey, had been a grocery store owner and a church planter. During the Depression he sold his store and worked as a butcher. He was handy with an engine and in general quite unlike me, except perhaps that he was the type of person to speak his mind. That side of me only comes out in writing.
My Dad's father was quite conservative even for my parents' circles...
Relationships can be broken. Any violation of our faithfulness to God damages our relationship to God, not on his side but on ours. We cannot be unloving and not create distance between us and God. A person who is unfaithful in a marriage or friendship cannot be as close to their partner or friend, especially if their friend knows their faithlessness.
But relationships only break instantly with the most major of infidelities. God will take us back if we can bring ourselves to go back--not always possible because our hearts become hardened like cement and we cannot move them any more. We can still move with smaller acts of infidelity, but they can accumulate like plaque in an artery. Eventually we will have a heart attack and the relationship may not survive.
At least these are thoughts I had later. The climate of preaching that led me to fear that I would fry with the smallest of infractions was just plain wrong. It was built off a shallow understanding of God's love, not to mention of relationships. It made God into a poor excuse for a human spouse, let alone a divine one.
The preaching I grew up with was also preoccupied with spiritual events, benchmarks you needed to check off a list. I remember in particular one song they sometimes sang at camp meeting in Frankfort, Indiana. Some families went to the beach or the mountains when they took their vacation. We went to camp meeting or church district conference or, every four years, to church general conference.
Frankfort, Indiana was probably the navel of my childhood universe. Every year at the beginning of August we made pilgrimage back to Indiana. Frankfort was where my mother had largely grown up. There was a Bible college there, Frankfort Pilgrim College.
My mother's father, Harry Shepherd, had taught there most of my mother's life except in the years of the Great Depression. In those years he had pastored and taught at Bible colleges in North Carolina () and Kentucky (Kingswood). Then he had made his way back to southern Indiana pastoring () before finally finishing out his career at Frankfort.
Over the years he taught (dispensational) prophecy, Latin, calculus, and I suspect any number of other classes. He was a graduate of the 190* class of Wabash College and had played baseball there. He was quite a bit older than my grandmother, Verna, and she was his second wife after his first wife passed. Born in 1882, he and his two sisters were orphaned after his father finally succumbed to injuries he sustained in the Civil War. I never met him, since he died about three years before I was born.
So my mother had grown up roaming the campus of Frankfort Pilgrim College. She attended both high school and college there and became quite a good pianist. My three oldest sisters went to college there, although my third oldest sister Sharon had to finish her work at Hobe Sound Bible College in south Florida when the Wesleyan Church closed Frankfort.
But the camp meeting continued there and, although the grounds were sold in 2010, it continues even today. I was born in Indiana, although my father's job took him to Florida in 1971. So while we lived in Ft. Lauderdale, we remained strongly connected to Indiana.
I was born in Indianapolis at Methodist Hospital. At the time we lived on the north side of town, just south of Carmel. My Dad's parents lived in the middle of Indianapolis. My Dad's father, Dorsey, had been a grocery store owner and a church planter. During the Depression he sold his store and worked as a butcher. He was handy with an engine and in general quite unlike me, except perhaps that he was the type of person to speak his mind. That side of me only comes out in writing.
My Dad's father was quite conservative even for my parents' circles...
Sunday, March 11, 2012
Reflections 5
... continued from last Sunday
____________
I have often thought that I might not have struggled with my faith so much if I had grown up with a form of faith that was a little more informed and defensible. When I later studied the Bible and theology, I found myself torn, on the one hand, between loyalty to my childhood faith and those who preached it, and, on the other hand, to truths that became increasingly obvious beyond reasonable doubt. I found myself in completely unnecessary faith crises for no reason whatsoever.
I think the categories of fundamentalism can remain comfortable for a lifetime if you are never exposed to the simple questions or situations that deconstruct it so easily. Then again, there are others who have a strange ability to live with possible explanations rather than probable ones. Perhaps I too might have remained quite satisfied with my childhood fundamentalism if I had become a doctor or a scientist of some sort. There are some questions you just don't ask when you live in a particular paradigm. But once those questions are honestly asked, it is only a matter of time before they unraveled.
But I am getting ahead of myself. I'll have recourse later to give my thoughts on raptures and a rigid sense of what experiences Christians are supposed to have. For now, I want to clarify what a bad concept of God I had in my bones as a child. Mind you, it was not something you could have talked through with me, I don't think. I was in the grip of an irrational fear.
I saw a video in seminary that summed it up well. God was a cowboy to me, a policeman with an itchy trigger finger. He was a "one sin you're out" kind of God. If you died or the rapture happened in the ten seconds between a sin and your repentance, you were toast.
Suffice it to say, this is a horrible picture of God. It pictures God as a legalist, not a truly loving God. I am more loving than this god. In fact almost any average person on the street gets higher grades than this god for love. No doubt there are a lot of people in prison, maybe even some murderers, who come out more loving.
And it is an immature picture of God. It is a god who loves rules for their own sake and gets really ticked off when people break them. He's an insecure god, who cannot handle any infraction of his rules.
If the "eternal security" of some Baptists would allow a "Christian" to commit murder and still go to heaven, my childhood experience was one of continual insecurity. Yet if the word "love" is meaningful at all in relation to God, it surely means that he wants us to make it. And I was raised to believe that he wanted everyone to make it, that the only reason anyone wouldn't make it would be their own doing.
I have also come to reject prevailing ideas about what it means to say that God is a God of justice. So many Christians seem to treat God's justice as something to which he himself is a slave. "I'd really like to have mercy on you," God might say, "but I have to follow the rules."
But doesn't God make the rules? I can believe that God exercises justice for our good. I can believe that God exercises justice for the collective good. I can believe that God exercises justice when a person is beyond redemption. I cannot believe he is just because he has to be or because he just can't hold his temper when people offend his honor.
To me, the most coherent view sees God in relational terms. God knows us and wants to rescue us from our alienation. He wants to be reconciled with us. He wants to be in relationship with us...
____________
I have often thought that I might not have struggled with my faith so much if I had grown up with a form of faith that was a little more informed and defensible. When I later studied the Bible and theology, I found myself torn, on the one hand, between loyalty to my childhood faith and those who preached it, and, on the other hand, to truths that became increasingly obvious beyond reasonable doubt. I found myself in completely unnecessary faith crises for no reason whatsoever.
I think the categories of fundamentalism can remain comfortable for a lifetime if you are never exposed to the simple questions or situations that deconstruct it so easily. Then again, there are others who have a strange ability to live with possible explanations rather than probable ones. Perhaps I too might have remained quite satisfied with my childhood fundamentalism if I had become a doctor or a scientist of some sort. There are some questions you just don't ask when you live in a particular paradigm. But once those questions are honestly asked, it is only a matter of time before they unraveled.
But I am getting ahead of myself. I'll have recourse later to give my thoughts on raptures and a rigid sense of what experiences Christians are supposed to have. For now, I want to clarify what a bad concept of God I had in my bones as a child. Mind you, it was not something you could have talked through with me, I don't think. I was in the grip of an irrational fear.
I saw a video in seminary that summed it up well. God was a cowboy to me, a policeman with an itchy trigger finger. He was a "one sin you're out" kind of God. If you died or the rapture happened in the ten seconds between a sin and your repentance, you were toast.
Suffice it to say, this is a horrible picture of God. It pictures God as a legalist, not a truly loving God. I am more loving than this god. In fact almost any average person on the street gets higher grades than this god for love. No doubt there are a lot of people in prison, maybe even some murderers, who come out more loving.
And it is an immature picture of God. It is a god who loves rules for their own sake and gets really ticked off when people break them. He's an insecure god, who cannot handle any infraction of his rules.
If the "eternal security" of some Baptists would allow a "Christian" to commit murder and still go to heaven, my childhood experience was one of continual insecurity. Yet if the word "love" is meaningful at all in relation to God, it surely means that he wants us to make it. And I was raised to believe that he wanted everyone to make it, that the only reason anyone wouldn't make it would be their own doing.
I have also come to reject prevailing ideas about what it means to say that God is a God of justice. So many Christians seem to treat God's justice as something to which he himself is a slave. "I'd really like to have mercy on you," God might say, "but I have to follow the rules."
But doesn't God make the rules? I can believe that God exercises justice for our good. I can believe that God exercises justice for the collective good. I can believe that God exercises justice when a person is beyond redemption. I cannot believe he is just because he has to be or because he just can't hold his temper when people offend his honor.
To me, the most coherent view sees God in relational terms. God knows us and wants to rescue us from our alienation. He wants to be reconciled with us. He wants to be in relationship with us...
Sunday, March 04, 2012
Reflections 4
So from that moment as a 10 year old when I woke up from that nap, my "conscience" awoke, and I experienced great fears off and on for the next ten years or so. My "rapture" fear put me through quite a bit of torture for a while. I might run back in the house from outside on the sidewalk just to check if my mother was still here.
Mind you, I wasn't confident that anyone at school or in my neighborhood was "saved." I never questioned for a moment whether my family was. But I actually got into such a state in the sixth grade once that they sent me home from school. I had been crying at my desk, desperately afraid that no one was at home because the rapture had happened. I had a slight fever but nothing much. The doctor simply said my spleen was a little enlarged.
My mother gave me a box of promises. They were Bible verses like Joshua 1:9, "Be strong and of a good courage; be not afraid, neither be thou dismayed, for the LORD thy God is with thee whithersoever thou goest." They really didn't help much because I didn't trust that these verses were for me. Did God even listen to the prayers of sinners, unless they were sincere prayers for repentance?
So I constantly asked God to forgive my sins. "Please forgive me if I've sinned. Please forgive me if I've sinned." But did you need to confess every individual sin to be forgiveness? What if I couldn't remember them all? I actually couldn't think of sins to ask God to forgive me. Was I then inevitably condemned?
These all speak of a faulty view of God, a view of God as an unbending judge. I doubt the preachers of my childhood viewed God that way, but that is the way I experienced their preaching. God was a legalist, a policeman, a sheriff who was waiting for you to mess up so he could blow you away.
And I grew up around a lot of legalism. These were people who kicked me off a playground on Sunday because it was a day you didn't work and playing was work for a child. These were people who worried about how long your sleeves were and equated godliness with hair length and the type of clothes you wore. They were, in short, people with no real understanding of God or Christ, let alone the Bible.
I have often thought that I might not have struggled with my faith so much if I had grown up with a form of faith that was a little more informed and defensible...
Mind you, I wasn't confident that anyone at school or in my neighborhood was "saved." I never questioned for a moment whether my family was. But I actually got into such a state in the sixth grade once that they sent me home from school. I had been crying at my desk, desperately afraid that no one was at home because the rapture had happened. I had a slight fever but nothing much. The doctor simply said my spleen was a little enlarged.
My mother gave me a box of promises. They were Bible verses like Joshua 1:9, "Be strong and of a good courage; be not afraid, neither be thou dismayed, for the LORD thy God is with thee whithersoever thou goest." They really didn't help much because I didn't trust that these verses were for me. Did God even listen to the prayers of sinners, unless they were sincere prayers for repentance?
So I constantly asked God to forgive my sins. "Please forgive me if I've sinned. Please forgive me if I've sinned." But did you need to confess every individual sin to be forgiveness? What if I couldn't remember them all? I actually couldn't think of sins to ask God to forgive me. Was I then inevitably condemned?
These all speak of a faulty view of God, a view of God as an unbending judge. I doubt the preachers of my childhood viewed God that way, but that is the way I experienced their preaching. God was a legalist, a policeman, a sheriff who was waiting for you to mess up so he could blow you away.
And I grew up around a lot of legalism. These were people who kicked me off a playground on Sunday because it was a day you didn't work and playing was work for a child. These were people who worried about how long your sleeves were and equated godliness with hair length and the type of clothes you wore. They were, in short, people with no real understanding of God or Christ, let alone the Bible.
I have often thought that I might not have struggled with my faith so much if I had grown up with a form of faith that was a little more informed and defensible...
Sunday, February 26, 2012
Reflections 3
... Imagine joining that to a religious environment that I at least experienced as one that expected moral perfection with a God who would judge those who did not measure up. I don't know that any of the preachers I grew up with would necessarily characterize their preaching in this way, but these were probably the points that stuck out to me as a child.
There was an emphasis on having certain religious experiences. The first was when you were "saved." You needed to be able to pinpoint a moment when you were sure God had saved you. The second was when you were "sanctified." You needed to be able to pinpoint a moment when God filled you with the Spirit like the disciples on the Day of Pentecost in Acts 2.
The preachers of my childhood preached these events in dramatic terms. When I did not have dramatic emotional events to point to, I became uncertain of my "salvation," of my eternal destiny. Eventually I would have some moments when peace followed prayer and angst. I could point to them as these experiences as my moments.
But there was also an emphasis on the need for faithfulness. I was raised with the sense that even one sin returned you to a course toward hell. Whatever experiences I might have had in the past, they were completely contingent on avoiding future sins at all costs. Repentance needed to be immediate, in case something happened, and I would go to hell.
As a child, I was not afraid of sudden death, but I was afraid that Jesus would suddenly return to earth. In the late 1970's end times speculation had returned with a fervor because of books like Hal Lindsey's Late Great Planet Earth. A trilogy of films came out and we saw them as a church. A Thief in the Night pictured a wife waking up to find that her husband had disappeared in the rapture, and she had been left alone to go through a 7 year tribulation with unimaginable suffering for those who had missed the rapture but turned to Christ during that time when the Antichrist would rule on earth.
So from that moment as a 10 year old when I woke up from that nap, my "conscience" awoke, and I experienced great fears off and on for the next ten years or so...
There was an emphasis on having certain religious experiences. The first was when you were "saved." You needed to be able to pinpoint a moment when you were sure God had saved you. The second was when you were "sanctified." You needed to be able to pinpoint a moment when God filled you with the Spirit like the disciples on the Day of Pentecost in Acts 2.
The preachers of my childhood preached these events in dramatic terms. When I did not have dramatic emotional events to point to, I became uncertain of my "salvation," of my eternal destiny. Eventually I would have some moments when peace followed prayer and angst. I could point to them as these experiences as my moments.
But there was also an emphasis on the need for faithfulness. I was raised with the sense that even one sin returned you to a course toward hell. Whatever experiences I might have had in the past, they were completely contingent on avoiding future sins at all costs. Repentance needed to be immediate, in case something happened, and I would go to hell.
As a child, I was not afraid of sudden death, but I was afraid that Jesus would suddenly return to earth. In the late 1970's end times speculation had returned with a fervor because of books like Hal Lindsey's Late Great Planet Earth. A trilogy of films came out and we saw them as a church. A Thief in the Night pictured a wife waking up to find that her husband had disappeared in the rapture, and she had been left alone to go through a 7 year tribulation with unimaginable suffering for those who had missed the rapture but turned to Christ during that time when the Antichrist would rule on earth.
So from that moment as a 10 year old when I woke up from that nap, my "conscience" awoke, and I experienced great fears off and on for the next ten years or so...
Sunday, February 19, 2012
Reflections 2
I experienced those days of fear as torturous. In its most intense times, I would be asking God to forgive me of my sins many times a minute. I can't imagine the fear of a child being separated from his or her parents in a concentration camp. I can't imagine the fear of a child being abducted. But my fear was real to me, despite the fact that I can look back and realize it was not real outside myself.
My youngest daughter Sophie experienced some fear in the first grade. It was nothing like my fears as a child but it reminded me of it. She came home from school a few times afraid of the fact that her teacher at some point would yell at the class because of the problem students. Perhaps there were other elements to her fear then, but it led me to think there was probably something genetic involved that traced to me as well.
I think my fears in part stemmed from a sense of inadequacy I had. In part, that sense of inadequacy stemmed from being an idealist, having perfection as the standard. But I also was bad at attaining my own standards. I am moving a little beyond the sixth grade, I know, as I analyze.
I was never diagnosed as hyperactive, although one "identity-sharing" story we tell is when an elderly woman at a concert turned around from the pew in front of us and asked my mother if I had ever been checked. They didn't diagnose with "attention deficit" back then, but I certainly did have trouble in college and seminary focusing on reading. I'll return to that later.
In any case, I often had overly optimistic goals coupled with an inability to follow through with things I started. So I wanted to build a plane as a child. I think I wanted to be able to fly my Grandma Shepherd back and forth from Indiana. She stayed with us for a short time in the 70's before moving back to Indiana and dying in a nursing home in 1979. She was in a wheelchair by then.
I would not listen to the reason of my parents but stubbornly insisted on starting to nail planks of wood together. They often appeased my unrealistic ambitions. I was not one to listen to reason but was more emotionally driven. I was quite stubbornly persistent about such things. I could build an airplane and no one was going to tell me differently.
My parents of course were always right, but they usually let me find out for myself. They knew little to nothing about electronics or engineering. I was probably above average in intelligence but not smart enough to figure out such things on my own. At one point my father agreed to buy one volume a month of a new Funk and Wagnall's Encyclopedia for me. It was a deal going at the Grand Union grocery store down the street in Wilton Manors, Florida. We had an older set, but I wanted an updated one.
I did use those volumes and still have them today. Encyclopedias were the Google of the day. They were one of my only sources of information on the kinds of scientific things I was interested in.
At various times they agreed to subscriptions to Popular Science, Popular Mechanics, then later Popular Electronics. One Christmas, maybe my senior year of high school, the family went together to buy me the parts to build a hexidecimal computer. Of course it wouldn't have done any thing but display digits. I'm sure that all seemed like so much play and craziness, but they appeased me.
One month I saw an add in the back of Popular Science, I think it was, for an opportunity to raise and sell fishing worms. It was of course ridiculous. Where would I have sold them? I'm not even sure they use worms much to fish in Florida. It's more shrimp and squid.
But my dad went so far as to buy a tub to put the worms in. I think I even tore up some newspaper in preparation. But thankfully for him, was soon on to something else. We never bought a single worm...
My youngest daughter Sophie experienced some fear in the first grade. It was nothing like my fears as a child but it reminded me of it. She came home from school a few times afraid of the fact that her teacher at some point would yell at the class because of the problem students. Perhaps there were other elements to her fear then, but it led me to think there was probably something genetic involved that traced to me as well.
I think my fears in part stemmed from a sense of inadequacy I had. In part, that sense of inadequacy stemmed from being an idealist, having perfection as the standard. But I also was bad at attaining my own standards. I am moving a little beyond the sixth grade, I know, as I analyze.
I was never diagnosed as hyperactive, although one "identity-sharing" story we tell is when an elderly woman at a concert turned around from the pew in front of us and asked my mother if I had ever been checked. They didn't diagnose with "attention deficit" back then, but I certainly did have trouble in college and seminary focusing on reading. I'll return to that later.
In any case, I often had overly optimistic goals coupled with an inability to follow through with things I started. So I wanted to build a plane as a child. I think I wanted to be able to fly my Grandma Shepherd back and forth from Indiana. She stayed with us for a short time in the 70's before moving back to Indiana and dying in a nursing home in 1979. She was in a wheelchair by then.
I would not listen to the reason of my parents but stubbornly insisted on starting to nail planks of wood together. They often appeased my unrealistic ambitions. I was not one to listen to reason but was more emotionally driven. I was quite stubbornly persistent about such things. I could build an airplane and no one was going to tell me differently.
My parents of course were always right, but they usually let me find out for myself. They knew little to nothing about electronics or engineering. I was probably above average in intelligence but not smart enough to figure out such things on my own. At one point my father agreed to buy one volume a month of a new Funk and Wagnall's Encyclopedia for me. It was a deal going at the Grand Union grocery store down the street in Wilton Manors, Florida. We had an older set, but I wanted an updated one.
I did use those volumes and still have them today. Encyclopedias were the Google of the day. They were one of my only sources of information on the kinds of scientific things I was interested in.
At various times they agreed to subscriptions to Popular Science, Popular Mechanics, then later Popular Electronics. One Christmas, maybe my senior year of high school, the family went together to buy me the parts to build a hexidecimal computer. Of course it wouldn't have done any thing but display digits. I'm sure that all seemed like so much play and craziness, but they appeased me.
One month I saw an add in the back of Popular Science, I think it was, for an opportunity to raise and sell fishing worms. It was of course ridiculous. Where would I have sold them? I'm not even sure they use worms much to fish in Florida. It's more shrimp and squid.
But my dad went so far as to buy a tub to put the worms in. I think I even tore up some newspaper in preparation. But thankfully for him, was soon on to something else. We never bought a single worm...
Sunday, February 12, 2012
Reflections on Childhood 1
I think of the first seventeen years of my life with fondness. For that I am very thankful, for I know that many people in the world do not think of their childhood in such idyllic terms. Many try to forget some abuse or neglect they experienced as a child, when they were most vulnerable. Many have childhood memories of need and suffering.
I do not have memories of a concentration camp or being ripped from my parents' arms. I have no memories of growing up in the Depression or of war. I didn't run to a bomb shelter when the sound of planes came overhead. I didn't have drills in school where we pretended nuclear missiles were on their way from the Soviet Union.
Neither of my parents died when I was a child. They never divorced. In fact they are still alive and together today. I never once heard them yell at each other. I was never spanked in rage, and I don't remember them ever even yelling at me. It never occurred to me once growing up to ask whether they loved me.
That is not to say that I did not have fears as a child, at some points almost paralyzing fears. I see these as much a matter of my own genetics and my growing brain as anything else. I do believe the religious context in which I grew up accentuated my own innate tendencies. I grew up in an incredibly religious environment of a particular conservative Christian sort.
I did not experience this environment as oppressive. I was convinced that we did what God wanted us to do. We did have some family practices that I might have wished were different. We did not watch TV on Sundays--when all the best movies premiered on television. We did not go to the movies, so Sunday night was about my only chance to see Star Wars or ET. We also did not go out to eat on Sundays. Sunday was the "Sabbath," and we set it aside as a day of rest.
But again, I did not experience these practices as oppressive. They were a little inconvenient at times. Perhaps I was a little embarrassed to tell my friends at public school some of these things. But by and large I tried to defend them. I was a conformist. If any of these things came up, I swallowed hard and tried to defend the way we did things.
I do not consider my parents legalistic on these issues to this day. A legalist, in my opinion, is someone who likes rules for their own sake. My parents, however, made exceptions. They might make an exception after church Sunday night to let me watch something like Star Wars. They might eat at a restaurant on Sunday if we happened to be travelling. We lived more strictly than others but that, in my view, is something different than legalism.
Nevertheless, the matrix of ideas I grew up around were a cocktail of fear in the hands of my psyche. I was born to doubt myself. Once in college when I playing "Doubting Thomas" in an Easter play, an ex-girlfriend commented jokingly that I had been typecast.
It basically started one afternoon in January at a winter "camp meeting." I don't remember what the revivalist had preached that morning, but I laid down fine for a nap and woke up in desperate fear for my soul. I think I was in the sixth grade, about 10 years old.
Maybe during the nap the last synapse in a key neural passageway was added. Maybe it was the flipping of the switch toward algebra and abstract thinking. Whatever it was, the slightly hyper, always in dreamland boy woke up in a sweat to enter a phase of "hell fear" that would come off and on for the next ten years or so.
I do not have memories of a concentration camp or being ripped from my parents' arms. I have no memories of growing up in the Depression or of war. I didn't run to a bomb shelter when the sound of planes came overhead. I didn't have drills in school where we pretended nuclear missiles were on their way from the Soviet Union.
Neither of my parents died when I was a child. They never divorced. In fact they are still alive and together today. I never once heard them yell at each other. I was never spanked in rage, and I don't remember them ever even yelling at me. It never occurred to me once growing up to ask whether they loved me.
That is not to say that I did not have fears as a child, at some points almost paralyzing fears. I see these as much a matter of my own genetics and my growing brain as anything else. I do believe the religious context in which I grew up accentuated my own innate tendencies. I grew up in an incredibly religious environment of a particular conservative Christian sort.
I did not experience this environment as oppressive. I was convinced that we did what God wanted us to do. We did have some family practices that I might have wished were different. We did not watch TV on Sundays--when all the best movies premiered on television. We did not go to the movies, so Sunday night was about my only chance to see Star Wars or ET. We also did not go out to eat on Sundays. Sunday was the "Sabbath," and we set it aside as a day of rest.
But again, I did not experience these practices as oppressive. They were a little inconvenient at times. Perhaps I was a little embarrassed to tell my friends at public school some of these things. But by and large I tried to defend them. I was a conformist. If any of these things came up, I swallowed hard and tried to defend the way we did things.
I do not consider my parents legalistic on these issues to this day. A legalist, in my opinion, is someone who likes rules for their own sake. My parents, however, made exceptions. They might make an exception after church Sunday night to let me watch something like Star Wars. They might eat at a restaurant on Sunday if we happened to be travelling. We lived more strictly than others but that, in my view, is something different than legalism.
Nevertheless, the matrix of ideas I grew up around were a cocktail of fear in the hands of my psyche. I was born to doubt myself. Once in college when I playing "Doubting Thomas" in an Easter play, an ex-girlfriend commented jokingly that I had been typecast.
It basically started one afternoon in January at a winter "camp meeting." I don't remember what the revivalist had preached that morning, but I laid down fine for a nap and woke up in desperate fear for my soul. I think I was in the sixth grade, about 10 years old.
Maybe during the nap the last synapse in a key neural passageway was added. Maybe it was the flipping of the switch toward algebra and abstract thinking. Whatever it was, the slightly hyper, always in dreamland boy woke up in a sweat to enter a phase of "hell fear" that would come off and on for the next ten years or so.
Thursday, December 23, 2010
Functions and Models
Some time ago I finished walking through chapter one of James Stewart's Calculus, "Functions and Models." Right now I'm snailing through chapter 2 at 2 pages a day. But I wanted to catch-up with myself by making a review sheet for chapter 1.
- Tangent problem and area problem generated calculus (differential the first and integral the second). Sum of a series relates to the second.
- What is a function, domain, range, etc? Basically, exactly one y for each element in x (thus the vertical line test--a vertical line can't ever pass through a function more than once.
- Piecewise functions have parts. An even function is symmetrical with regard to the y axis (f of x=f of -x). An odd function has symmetry with regard to the origin (f of x= negative of f of -x).
- Linear functions are of the form y=mx+b (slope intercept form).
- Polynomial functions involve powers of x beyond the first. Quadratic involves the second degree (x squared). Cubic functions involve the third (x cubed).
- More polynomial functions include power functions of the form x to the a power, where a is a constant. The root function is x raised to the 1/n power (e.g., the 1/2 power is a square root). A reciprocal function is something raised to a negative power, which means one over that x to a positive power.
- Rational functions are of the form P(x)/Q(x).
- Algebraic functions can be put into the form of algebraic operations (add, subtract, etc), such as all those that precede.
- Transcendental functions are non-algebraic and are the ones that follow.
- Trigonometric functions involve things like sine and cosine.
- Exponential functions involve a constant raised to the power x. Logarithmic functions are the inverse y=log base a of x.
- Then we have the translations I think I covered somewhere below from the pre-calculus text. Don't feel like repeating them. Same with stretching and reflecting functions, composite functions.
- The sections I'm seeing on graphing calculators in this book are truly fascinating because it just shows how old I am. We had nothing like this on the Texas Instrument calculators I used to think were off the charts because they did logarithms and the trig. functions.
Sunday, December 12, 2010
Motion in Two or Three Dimensions (Physics)
I actually finished reading chapter 3, "Motion in Two or Three Dimensions," of Young and Freedman's University Physics quite a long time ago. I try to read two pages of either this physics or a calculus text a day. So since I read this chapter I have read the first chapter of Stewart's sixth edition calculus text and am almost done with chapter 4 of Young and Freedman. So I want to catch up with the old before I finish chapter 4.
One observation I've made is that the broad strokes of physics and chemistry are really not too difficult to explain. The Devil is in the details of application. As always, I'm tempted to write something to boil things down without the burden to be technically correct.
This chapter's review list:
One observation I've made is that the broad strokes of physics and chemistry are really not too difficult to explain. The Devil is in the details of application. As always, I'm tempted to write something to boil things down without the burden to be technically correct.
This chapter's review list:
- The main difference between motion in 2 and 3 dimensions from one dimension is simply that one must now use vectors. This is just same old same old, dividing out the x, y, and perhaps z components of displacement, velocity, or acceleration, whether as an average or as an instantaneous derivative.
- Projectile motion is 2 dimensional motion. Using trig, the initial velocity x component in projectile motion will be v0x=v0cosθ while the initial y velocity component will be v0y=v0sinθ.
- The x velocity component is constant because of Newton's first law, Galileo's law of inertia, so the distance, x=(v0cosθ)t very straightforwardly (distance=velocity x time).
- The y velocity component must deal with the constant negative acceleration of gravity, -g, which yields the slightly more involved formula for y=(v0sinθ)t-½gt2, based on the formula, d=vt + ½at2
- Motion in a circle is also 2 dimensional. Although I don't think converting from radians to degrees and visa versa is a big deal, the reasons for radians hasn't quite clicked with me. In circular motion with a constant speed, the acceleration always points inward toward the center of the circle. This "centripetal acceleration" is a=v2/R
- Since speed is distance/time, and in uniform circular motion, the distance around is the circumference, which equals πD (diameter, which is also 2R, radius) = 2πR, the velocity thus equals 2πR/T.
- Accordingly, if we substitute 2Ï€R/T for v in the equation above, we get a=4Ï€2R/T2
- In non-uniform motion, we have to take the derivative of the velocity to get the component of acceleration that is tangent to the circle, and the vector sum of the total acceleration will not point directly toward the center. It will point either ahead or behind, depending on whether we have acceleration or deceleration.
- The final section of the chapter had to do with velocity relative to different reference frames. So the velocity of a point in frame B in relation to frame A is a vector sum--the velocity of point P in relation to B "plus" the velocity of frame B in relation to frame A.
Thursday, November 04, 2010
Chemistry: Chemical Bonds
Trying to catch up in my snails progress through various science and math resources. Here's my review notes for a chemistry chapter on chemical bonds.
- The octet rule is the fact that (except for H and He), the outermost electron shell of Groups 1A-7A want to have eight electrons.
- For those in the outer groups, there will be a tendency to go into ions, so those on the right tend to become cations (positive ions) by losing electrons to end up with the 8 outer electrons of a lower shell. Those on the left tend to gain electrons and become negatively charged anions to fill up the outermost shell they start with.
- Electronegativity is how strongly an atom holds on to its electrons. It increases from left to right on the periodic table and from bottom to top in a column (as does ionization energy).
- An ionic bond forms with a difference in electronegativity of 1.9 or greater between two atoms. A covalent bond forms if less than 1.9. A non-polar covalent bond forms if the difference in electronegativity is below 0.5.
- In an ionic bond, electrons transfer from one atom to another (e.g., from Na to Cl). In a covalent bond, two atoms share electrons (mostly elements toward the middle of the periodic table). In a polar covalent bond (electronegativity between 0.5 and 1.9), electrons are shared but gravitate more toward one atom than another (the one more to the right and top in the table). Such a polarized compound is called a dipole.
- An ion can be one type of element (monatomic, add -ide) to it (choride). An ion can also be polyatomic. To name a binary ionic compound, name the first (cation) element, then the second (anion). "Ous" and "ic" (think ars-en-ic with a British accent) are the lower and higher charged ions of an element that can form more than one ion (e.g., Fe).
- A binary molecular compound will use di- tri- and so forth.
- VSEPR or Valence Shell Electron Pair Repulsion model predicts the structure of a compound. An atom with 4 regions of electron density would be tetrahedral with default angles of 109.5 degrees. Three regions would be pyramidal with a default of 120 degrees. Two regions would be linear (180 degrees).
Thursday, October 07, 2010
Chemistry: Atoms
This is to record for review a summary of my pilgrimage through a chapter of Chemistry:
- element, compound, mixtures homogeneous and heterogeneous...
- Dalton's early 1800 revival of atomism--law of conservation of mass and law of constant composition. Dmitri Mendelev in the 1800s developed the Periodic Table.
- mass number includes both protons and neutrons, atomic number just protons
- Isotopes have differing numbers of neutrons in a particular atom. Atomic weight is the average mass of a particular atom, with 1 amu (atomic mass unit) being the mass of a proton (1.666 x 10-24g).
- The 18 non-metals are on the right side of the Periodic Table (except for Hydrogen). They all conduct electricity except for graphite.
- 6 elements are metalloid: boron, silicon, germanium, arsenic, antimony, and tellurium. The rest are metals.
- Groups are vertical columns. Halogens are Group 7. Alkali metals (except for Hydrogen) are Group 1. Noble gases are Group 8. Periods are horizontal rows.
- The principal energy levels are numbered, 1, 2, 3, 4...
- These "shells" also have potential subshells: s, p, d, and f. Electrons in subshells are paired, but only when all the potential orbitals have at least one electron. The s subshell only takes 2 electrons. The p subshell takes up to 6 (3 orbitals). The d takes 10 (5 orbitals) and f takes 14 (7). s shells are spherical. p shells are like bar bells along an imaginary x, y, and z axis.
- The transition elements are in between the main group elements columns 2 and 3. They include the d shell. The inner transition metals are the f shell and are located in the 6th and 7th periods before the normal transition metals.
- The valence shell is the outermost shell and its electrons are valence electrons. The Lewis-dot structure is very helpful in processing how atoms bond on the basis of their outermost shell.
- Ionization energy, the propensity of an atom to form an ion (to gain or lose electrons in the valence shell), increases as you move up and to the right of the Periodic Table.
Saturday, October 02, 2010
Motion in One Dimension
I think it was about a week ago or so that I declared chapter two of University Physics, by Young and Freeman, dead. I had been sauntering through it for months. The main points are easy, although as usual the application of them into concrete situations is more diffiicult. But here I summarize the main points:
1. Average velocity Δx/Δt or (x2-x1)/(t2-t1).
2. Instantaneous velocity is lim Δt→0 of Δx/Δt, which = dx/dt.
3. Average acceleration Δv/Δt or (v2-v1)/(t2-t1).
4. Instantaneous acceleration is lim Δt→0 of Δv/Δt, which = dv/dt.
Then these equations work for constant acceleration
5. v2 = v1 + at
6. x2 = x1 + vt + ½at2
7. v22 = v12 + 2a(x2-x1)
8. x2 - x1 = [(v2 + v1)/2]t
9. Finally, for varying acceleration, one will have to integrate:
x2 = x1 + ∫0→t of v dt
v2 = v1 +∫0→t of a dt
1. Average velocity Δx/Δt or (x2-x1)/(t2-t1).
2. Instantaneous velocity is lim Δt→0 of Δx/Δt, which = dx/dt.
3. Average acceleration Δv/Δt or (v2-v1)/(t2-t1).
4. Instantaneous acceleration is lim Δt→0 of Δv/Δt, which = dv/dt.
Then these equations work for constant acceleration
5. v2 = v1 + at
6. x2 = x1 + vt + ½at2
7. v22 = v12 + 2a(x2-x1)
8. x2 - x1 = [(v2 + v1)/2]t
9. Finally, for varying acceleration, one will have to integrate:
x2 = x1 + ∫0→t of v dt
v2 = v1 +∫0→t of a dt
Thursday, September 30, 2010
Polynomials Observed
In perhaps the strangest element to my personality, I have eeked my way these last three months through a chapter in a math book on "Polynomial and Rational Functions." Here is my summary for review in perpetuity:
1. Quadratic Functions
- f(x)=ax2+bx+c
- standard form relating to parabola f(x)=a(x-h)2+k
- negative coefficient makes parabola go down; (h, k) is the vertex
- lead coefficient below 1 widens, greater narrows parabola
- x coordinate of vertex is -b/2a
Leading coefficient test: for even powered polynomials, positive is up on both sides; negative is down on both sides.
- Leading coefficient test: for odd powered polynomials, positive is down on left, up on right; negative is reversed.
- Turning points are at most n-1 times (where n is the degree of the polynomial)
- A function only has at most n real zeros
- Intermediate Value Theorem--everything in between two points
- This unit was pretty easy, basically long division with the coefficients of a polynomial.
- Remainder Theorem--divide the coefficients of a polynomial by a number and the remainder is the y point for the number as the x point.
- Factor Theorem--if the remainder is zero, then the number is a factor
- Also an easy section. Standard form is a +bi
- "Complex conjugates" are a+bi and a-bi. Multiplying them removes the imaginary part.
- Fundamental Theorem of Algebra--any polynomial has at least one zero :-)
- Linear Factorization Theorem--polynomials have as many factors as the degrees of n.
- Rational Zero Test--With integer coefficients, every rational zero is a factor of the final number divided by the lead coefficient.
- Complex zeros appear in conjugate pairs
- Descartes' Rule of Signs--# of positive real zeros is equal to the number of changes in sign in the polynomial or less than that by an even integer.
- Descartes continued--# of negative real zeros is equal to the number of changes in sign for f(-x) or less than that by an even integer.
- Upper Bound Rule: With a positive lead coefficient, c is an upper bound if, 1) it is positive and 2) the polynomial, divided by x-c, results in all positives in the bottom row of synthetic division (or all zeros), then c is an upper bound among the real zeros of the function.
- Lower Bound Rule: If 1) c is negative and 2) the numbers in the bottom row alternate between positive and negative (zero counts as an alternation) then c is a lower bound among the real zeros of the function.
- In the form f(x)=N(x)/D(x)
- Domain obviously can't include any D(x) that equals 0 (vertical asymptote there).
- If the degree of the numerator is less than 0, then y=0 is a horizontal asymptote.
- If the degree of numerator and denominator are the same, then y=lead coefficient of numerator/lead coefficient of denominator is the horizontal asymptote.
- If the degree of numerator is more than denominator, no horizontal asymptote.
- If the degree of numerator is one more than denominator, then slant asymptote. Divide the polynomial out with long division and the part before the remainder is the slant asymptote (in the form y=that bit)
- Decomposing rational functions into partial fractions: 1) divide if improper, 2) factor the denominator, 3) for each factor of the denominator (including repeated ones), you should have a rational component broken out, 4) quadratic factors are the hard ones--various (ax+c) in each numerator, the denominators build from the basic (ax2+bx+c) up the various powers of this e.g., (ax2+bx+c)2 and up to the power of the full quadratic. All of course added together.
- The kind of repeatedness of #4 above applies to simple linear factors too. So if (x+2)2 is a factor, then the broken out partial fractions will need to include both a denominator of (x+2) as well as one that is (x+2)2.
- John Bernoulli (1667-1748) developed the method of partial fractions.
Wednesday, June 09, 2010
Chemistry: Matter and Measurement
The chapter covered thigns like chemical versus physical properties and changes, what chemistry is, the scientific method, significant figures and exponential notation, the International System of Units (SI), volume, mass versus weight, factor-label method, kinetic and potential energy, the calorie,
Things I might forget:
1. specific gravity is the density of something divided by 1--basically comparing the density of something to water.
2. specific heat is the amount of energy needed to raise the temperature of 1 gram of something 1 degree C.
Things I might forget:
1. specific gravity is the density of something divided by 1--basically comparing the density of something to water.
2. specific heat is the amount of energy needed to raise the temperature of 1 gram of something 1 degree C.
Pre-Calculus: Functions
This chapter covered symmetries, basic equations of circles and parabolas, intercepts and line equation forms, some basic functions (linear, cubic, square root, reciprocal, step, absolute value, inverse, quadratic, etc), combinations of functions (including the composition of functions), the domains and ranges of functions, and direct and joint variation.
Areas that I will no doubt forget quickly and need to review are:
Areas that I will no doubt forget quickly and need to review are:
- Shifting (adding to the x side shifts up or down-fine; but the horizontal shifts are counterintuitive to me--f(x-c) shifts to the right)
- Reflections (to reflect over the x axis, negate it-fine; but to reflect on the y, you negate within the function f(-x).
- Stretches (a vertical stretch involves a number times the function that is greater than 1; a horizontal stretch is when the coefficient is between 1 and 0)
- Inverse functions involve switching the x and the y.
- The vertical line test tells if something is a function. The horizontal line test tells whether a function has an inverse. Only one-to-one functions can have inverses.
Saturday, May 16, 2009
Coulomb's Law
Coulomb's log: After several weeks of piddling, I've done enough exercises to move on from this section of a chapter of a college physics textbook (1996) on Coulomb's Law. The main take away is Coulomb's Law:
F=k*q1*q2/r squared
The net force from two electric charges equals a constant (9*10 to the 9th) times the absolute value of q1 times q2 (two charges) divided by the distance between the two charge squared.
Following the process of how Coulomb developed this formula, I've understood more clearly than ever how scientists developed these sorts of formulas. They first figured out proportionalities. Is the force proportionate to the charge? To the product of the charges? Is it proportionate to the distance? Inversely proportionate?
Having then arrived at a set of proportions, namely that the force of two charges is directly proportionate to the product of the two charges and inversely proportionate to the square of the distance between the two charges, they then slap a constant to make the proportions into an equality. Then experimentally they figure out what the constant is.
F=k*q1*q2/r squared
The net force from two electric charges equals a constant (9*10 to the 9th) times the absolute value of q1 times q2 (two charges) divided by the distance between the two charge squared.
Following the process of how Coulomb developed this formula, I've understood more clearly than ever how scientists developed these sorts of formulas. They first figured out proportionalities. Is the force proportionate to the charge? To the product of the charges? Is it proportionate to the distance? Inversely proportionate?
Having then arrived at a set of proportions, namely that the force of two charges is directly proportionate to the product of the two charges and inversely proportionate to the square of the distance between the two charges, they then slap a constant to make the proportions into an equality. Then experimentally they figure out what the constant is.
Friday, April 17, 2009
Quantum Physics 1
When I was about twelve, I used to play a game every once and a while to keep me from getting bored--and I have always been very easily bored. I would pretend as if I suddenly developed complete amnesia and had to figure out where I was. Another question I used to ask myself is how much of human knowledge I could recreate if everyone else on the planet suddenly disappeared or if I were stuck on a deserted island. Not much, I always concluded.
So what if I were the last person alive on earth? I'm sure my first order of business would be figuring out food, crops, etc. I'd want to figure out medical type things and be ready for any kind of sickness. Assuming that nothing electrical worked, maybe I would spend some time trying to fix some things along those lines. Sure, I might travel too. I could live in a different ghost city every week if I wanted to.
But eventually, if I had access to all the books humanity had left behind, I would probably start to study things. Let's say one year or two I decide that I want finally to spend the time to learn quantum physics. I'd always wanted to, but didn't have the time. Of course I'd have to review a bunch of physics I hadn't thought about since high school and college, and that was now decades ago.
Where would I start?
So what if I were the last person alive on earth? I'm sure my first order of business would be figuring out food, crops, etc. I'd want to figure out medical type things and be ready for any kind of sickness. Assuming that nothing electrical worked, maybe I would spend some time trying to fix some things along those lines. Sure, I might travel too. I could live in a different ghost city every week if I wanted to.
But eventually, if I had access to all the books humanity had left behind, I would probably start to study things. Let's say one year or two I decide that I want finally to spend the time to learn quantum physics. I'd always wanted to, but didn't have the time. Of course I'd have to review a bunch of physics I hadn't thought about since high school and college, and that was now decades ago.
Where would I start?
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