This is another one that came out of teaching the introductory physics class.
Whenever we cover angular momentum, we always end by discussing gyroscopes. A gyroscope is a wheel with a rigid, low-friction axis. It has most of its weight concentrated on the outside, so it is rotationally "heavy". Angular momentum is a vector (i.e. the direction of rotation matters). The purpose of a gyroscope is to carry a large quantity of angular momentum at safe rotation speeds and to be physically aligned with its angular momentum vector. This sets up a great classroom demonstration of the three-dimensional nature of torque. (Torque is defined as the rate of change of angular momentum; it is also a vector.) Any force used to try to reorient the gyroscope produces a torque that is perpendicular to both the force applied and the axis of the gyroscope. Students have been told that this is true repeatedly and even done homework calculations, but when the whole gyroscope kicks sideways and twists out of their grip it becomes much more real.
The wonky dynamics of a gyroscope when large torques are applied make them fun demonstrations. The other side of constrained angular momentum is that small bumps and twists have almost no effect on the gyroscope's orientation. Even if a gyroscope moves side to side violently, it will usually continue pointing in the same direction. Among other things, this is incredibly useful for navigation. Most planes and ships today have a gyroscope somewhere on board in an isolated environment. The gyroscope is not mechanically tied to the vessel. Instead as the vessel pitches and yaws the apparent motion of the gyroscope indicates the attitude deviance, allowing for rapid and precise corrective action. Attitude (meaning rotational orientation) control is critical to navigation, especially in air travel. If a plane is not flying level, a course correction intended to steer left or right may include a downward component as well, a potentially disastrous error.
We are used to thinking of up as "the direction opposite the pull of gravity" but in stormy seas or high winds this metric loses its meaning. When the world around has lost all of its familiar reference points, a gyrostabilizer acts as an internal "external reference frame". Navigation in any direction remains possible because there is something that is inside the vessel, but unaffected by its turbulent environment, that knows which way is up.
A gyroscope by itself won't keep a plane from crashing. The pilot needs to note that his attitude is out of synch with the reference and take corrective action. Actually, the pilot rarely has to intervene so directly in modern aircraft. The plane's control surfaces (flaps, ailerons, etc.) automatically adjust when an attitude deviation is indicated. Tellingly, this is called "slaving" the controls to the gyroscope. This leaves the pilot free to navigate in the macro sense of deciding where the plane should go and what is the best way to get there. The pilot has increased freedom as a result of making his second-to-second activities slaved to the device inside his plane that points upward.
Maybe this is akin to what is meant by "freedom in Jesus". There are places our Lord wants to go with us, but we'll never get there if we spend all of our time dealing with the storms and temptations of life, just trying to keep from crashing. We need to slave our habits and attitudes, the things we do on automatic, to Jesus. Fortunately, there is a Spirit living inside us who always knows which way is up, even in the midst of the storms. At first, we have to pay close attention to the Spirit's nudging while we try to maintain control ourselves. When we finally submit everything to Him, we find that we are not made completely powerless. Instead, we are free for the first time to really fly.
Sunday, August 30, 2015
Sunday, July 12, 2015
Is There A God? (Methods In Experimental Deity Detection)
Given the immense success of the modern scientific establishment, which has taken on some of the outstanding Big Questions about the world and the people in it, and the equally great popularity of various philosophical frameworks which invoke an omnipotent Creator God, it seems reasonable for scientists to think we might now be in a position to either address or dismiss the question "Is there a God?"
The word 'god' is used to describe a variety of entities, so some clarification is needed. For example the Greek gods, situated on Mt. Olympus and bearing human-like forms, can be sought by satellite imaging. There is a clear test which can be performed to falsify their existence. That test has been done; we looked and found nothing. That makes the Greek theory of gods a scientific theory, but a false one. On the other hand, pantheistic 'God is in everything'-type deities are so ill defined as to be clearly outside the purview of science.
When most Westerners say "I (don't) believe in God" they mean something loosely based on the God of Abraham. At a minimum this means a quasi-omnipotent, omniscient, intangible spirit. On the face of things, the inclusion or non-inclusion of such a God in a scientist's understanding of the world seems like it must be axiomatic. There is no way to empirically distinguish between a well-ordered universe which strictly obeys certain laws because it is subject to the absolute rule of a lawful Creator and one that arose spontaneously in accordance with its own internally-consistent set of rules. In his recent book, A Universe From Nothing, Lawrence Krauss presented a very convincing argument that a Universe could (or must) arise from fluctuations in the quantum vacuum. He was immediately dismissed by those not inclined to his philosophical views for failing to account for the existence of the quantum vacuum. Conversely, in a disordered universe there would be no sure way to detect or dismiss a lawless God who just did whatever seemed right at the time.
In its abstract form, then, the existence of God is not a scientific question. The modern popular understanding of 'God' contains more than enough wiggle room to evade any conceivable attempt at falsification. However, there are a number of large scientific experiments currently in progress which have limited falsification power, but are aimed at detecting something which we think ought to exist. Taking our cue from this kind of science, we might at least be able to test specific claims about God. If you hope or suspect that there is a God but aren't sure how to approach Him, this might be a worthwhile path to pursue.
The key to any detection experiment is to determine what kinds of signals can only originate from the subject and tune an instrument to distinguish that signal from all others. To reduce the complexity of its backgrounds, any deity detection experiment should probably take the approach from direct dark matter searches that an omnipresent entity is easiest to detect locally. If something is everywhere and it has discrete, measurable effects on its surroundings, then the best place to look for it is here. (For most people, a God who doesn't have local effects might as well not exist.) We should also borrow a page from the Search For Extraterrestrial Intelligence (SETI) and assume that God is much more powerful than we are and wants to be found, or at least isn't hiding. "Ask and it will be given to you; seek and you will find; knock and the door will be opened to you." (Matthew 7:7) However like SETI we should expect a certain other-ness from the object of our search. "For my thoughts are not your thoughts, neither are your ways my ways." (Isaiah 55:8) Derivation of the behavior of God from first principles is, almost by definition, impossible. Any concrete information we have must come from revelation (God tells you what He is like), which rather obviates the existence question. Fortunately, there are several extensive books which purport to outline in detail the behavior of God as it relates to people. For this exercise, we will use the text of the Bible to develop tests for the Christian God, although you could presumably start with the Quran, the Torah or other texts.
Following the advice of Matthew 7:7 ("Ask and it will be given to you…"), the simplest possible deity detection experiment is to say out loud "God, do you exist?" If you can summon the confidence to say it aloud and then trust yourself to hear the answer, the Direct Question Method has an anecdotally high success rate. However it may be difficult to interpret the result. The act of performing the experiment is likely to cause feelings of awkwardness and hyper-sensitivity. On top of those emotions, a sudden unexpected thought in your head saying e.g. "Yes, I do." may not be especially convincing. A better question might be "Show me that you exist." That moves the detector out of your head, but opens up the entire world as the signal region. It then becomes necessary to decide over an extended period whether the events of your life might have happened on their own or had to be orchestrated by God. To simplify the analysis, variants on the Gideon Method could be employed:
In principle, by selecting a number of sufficiently unlikely independent tests, God's existence could be established to arbitrary confidence. In practice, there is some biblical record of God frowning on extensive use of this method. In several instances where a risky behavior is suggested purely to show that God is God, the Bible says flat out "Do not put the Lord your God to the test." (Deut 6:16 and Luke 4:12) Instead "...Jesus said, 'If you hold to my teaching, you are really my disciples. Then you will know the truth, and the truth will set you free.'" (John 8:31-32, emphasis added)
The problem here is that the God of the Bible is not primarily interested in being detected. He is interested in positive relationships. "You believe that there is one God. Good! Even the demons believe that--and shudder." (James 2:19) The question of a locally acting deity is important to our immediate lives, so once we have reasonable confidence that God might be trying to get our attention, the expectation is that we play by His rules and take our data from personal interactions.
A Biblical Experiment
So what does it mean to hold to Jesus' teaching? At one point, a religious scholar asked Jesus
Loving God
First, how does one love a God who is unknown and possibly doesn't exist? We can get some help here from other places where people are actively forming new relationships. Dating often begins with a lot of talking and time spent in places where the other person likes to hang out. Talking to God is called prayer. Agnostic prayer usually starts with "God, are you there?" but can quickly move to other things you want to know, concerns, etc. Just like on a date, taking time to be quiet and listen is a plus, as is praise. Since praise implies an established relationship, it may be easier to start with gratitude, ranging from the joys of the day to the wonder of creation. An omniscient deity presumably does not require us to pray aloud, but most people find that vocalization makes communication, including prayer, more concrete and cuts down on distractions.
Where does God like to hang out? Omnipresent beings hang out everywhere by definition, so it could be argued that hanging out with God is simply a matter of cultivating an awareness of His presence all the time. This is a valuable exercise, but one complicated by the open question of God's existence. A more concrete method would be to hang out with other people who are hanging out with God (or, for those still on the fence, people who think they are hanging out with God). "For where two or three gather in my name, there I am with them." (Matt 18:20) In most places in North America, a brief search will turn up many churches within a short distance. These organizations are nominally all part of a single Body of Christ (1 Cor 12:27) tasked with carrying out the work of God on Earth. Matters of denomination are largely irrelevant to the present query, but before investing much time in a church it would be prudent to determine that they believe God is active in their midst and look to the Bible as an authoritative reference. Another clue is found in Galatians 5:22-23: "But the fruit of the Spirit is love, joy, peace, forbearance, kindness, goodness, faithfulness, gentleness and self-control." No one is perfect, but if these things are completely absent from a church, the God described in the Bible should be sought elsewhere.
Loving Your Neighbor
This brings us to loving your neighbor as yourself. In Luke's account of the Greatest Commandment discussion, the follow-up question is "And who is my neighbor?" (Luke 10:29) Jesus responds with a parable about a Jew left for dead my robbers who is rescued by a Samaritan, his cultural enemy. The Samaritan carries him to safety and then pays a large sum of money to have him looked after. Caring for the needs of those unable to care for themselves is a major theme throughout the Bible, as is God's interaction with people engaged in this activity. Giving up our time and money to care for other people, particularly people we dislike, often feels like a giant leap into insanity and almost everyone has deeply-held limits on how far down that road they are willing to go. Since the Bible promises that God will meet us where we are (e.g. James 4:8), it is sufficient for deity-detection purposes to go as far as we are able and make these limits, once discovered, a matter of prayer. If a choice must be made between giving time or giving money, the relational aspect of giving time is an advantage here.
Besides caring for material needs, one of the things Jesus commanded us to do for our neighbor is forgive them. "Forgive" in English has two related definitions:
1) stop feeling angry or resentful toward someone (for an offense, flaw, or mistake)
2) cancel (a debt)
Forgiveness is supposed to be very healthy, but can also be extremely difficult. "Help me forgive <person> for <thing>." is a very common prayer. Considering that "forgive us our debts as we also have forgiven our debtors" (Matt. 6:12) made it into Jesus' 53-word stock prayer, attempts to obey Jesus' teaching should include as much forgiveness as possible.
(This post is now several years old and never got posted. I leave open the question of how to interpret the events of your life during a deity-detection search. For most people, relational intuition will be more valuable than some numerical analysis.)
The word 'god' is used to describe a variety of entities, so some clarification is needed. For example the Greek gods, situated on Mt. Olympus and bearing human-like forms, can be sought by satellite imaging. There is a clear test which can be performed to falsify their existence. That test has been done; we looked and found nothing. That makes the Greek theory of gods a scientific theory, but a false one. On the other hand, pantheistic 'God is in everything'-type deities are so ill defined as to be clearly outside the purview of science.
When most Westerners say "I (don't) believe in God" they mean something loosely based on the God of Abraham. At a minimum this means a quasi-omnipotent, omniscient, intangible spirit. On the face of things, the inclusion or non-inclusion of such a God in a scientist's understanding of the world seems like it must be axiomatic. There is no way to empirically distinguish between a well-ordered universe which strictly obeys certain laws because it is subject to the absolute rule of a lawful Creator and one that arose spontaneously in accordance with its own internally-consistent set of rules. In his recent book, A Universe From Nothing, Lawrence Krauss presented a very convincing argument that a Universe could (or must) arise from fluctuations in the quantum vacuum. He was immediately dismissed by those not inclined to his philosophical views for failing to account for the existence of the quantum vacuum. Conversely, in a disordered universe there would be no sure way to detect or dismiss a lawless God who just did whatever seemed right at the time.
In its abstract form, then, the existence of God is not a scientific question. The modern popular understanding of 'God' contains more than enough wiggle room to evade any conceivable attempt at falsification. However, there are a number of large scientific experiments currently in progress which have limited falsification power, but are aimed at detecting something which we think ought to exist. Taking our cue from this kind of science, we might at least be able to test specific claims about God. If you hope or suspect that there is a God but aren't sure how to approach Him, this might be a worthwhile path to pursue.
The key to any detection experiment is to determine what kinds of signals can only originate from the subject and tune an instrument to distinguish that signal from all others. To reduce the complexity of its backgrounds, any deity detection experiment should probably take the approach from direct dark matter searches that an omnipresent entity is easiest to detect locally. If something is everywhere and it has discrete, measurable effects on its surroundings, then the best place to look for it is here. (For most people, a God who doesn't have local effects might as well not exist.) We should also borrow a page from the Search For Extraterrestrial Intelligence (SETI) and assume that God is much more powerful than we are and wants to be found, or at least isn't hiding. "Ask and it will be given to you; seek and you will find; knock and the door will be opened to you." (Matthew 7:7) However like SETI we should expect a certain other-ness from the object of our search. "For my thoughts are not your thoughts, neither are your ways my ways." (Isaiah 55:8) Derivation of the behavior of God from first principles is, almost by definition, impossible. Any concrete information we have must come from revelation (God tells you what He is like), which rather obviates the existence question. Fortunately, there are several extensive books which purport to outline in detail the behavior of God as it relates to people. For this exercise, we will use the text of the Bible to develop tests for the Christian God, although you could presumably start with the Quran, the Torah or other texts.
Following the advice of Matthew 7:7 ("Ask and it will be given to you…"), the simplest possible deity detection experiment is to say out loud "God, do you exist?" If you can summon the confidence to say it aloud and then trust yourself to hear the answer, the Direct Question Method has an anecdotally high success rate. However it may be difficult to interpret the result. The act of performing the experiment is likely to cause feelings of awkwardness and hyper-sensitivity. On top of those emotions, a sudden unexpected thought in your head saying e.g. "Yes, I do." may not be especially convincing. A better question might be "Show me that you exist." That moves the detector out of your head, but opens up the entire world as the signal region. It then becomes necessary to decide over an extended period whether the events of your life might have happened on their own or had to be orchestrated by God. To simplify the analysis, variants on the Gideon Method could be employed:
Gideon said to God, “If you will save Israel by my hand as you have promised— look, I will place a wool fleece on the threshing floor. If there is dew only on the fleece and all the ground is dry, then I will know that you will save Israel by my hand, as you said.” And that is what happened. Gideon rose early the next day; he squeezed the fleece and wrung out the dew—a bowlful of water. Then Gideon said to God, “Do not be angry with me. Let me make just one more request. Allow me one more test with the fleece, but this time make the fleece dry and let the ground be covered with dew.” That night God did so. Only the fleece was dry; all the ground was covered with dew. (Judges 6:36-40)(Caveat: A well-controlled, successful fleece test will either change your life or result in immediate revocation of your scientist's license. Don't ask questions to which you don't want answers.)
In principle, by selecting a number of sufficiently unlikely independent tests, God's existence could be established to arbitrary confidence. In practice, there is some biblical record of God frowning on extensive use of this method. In several instances where a risky behavior is suggested purely to show that God is God, the Bible says flat out "Do not put the Lord your God to the test." (Deut 6:16 and Luke 4:12) Instead "...Jesus said, 'If you hold to my teaching, you are really my disciples. Then you will know the truth, and the truth will set you free.'" (John 8:31-32, emphasis added)
The problem here is that the God of the Bible is not primarily interested in being detected. He is interested in positive relationships. "You believe that there is one God. Good! Even the demons believe that--and shudder." (James 2:19) The question of a locally acting deity is important to our immediate lives, so once we have reasonable confidence that God might be trying to get our attention, the expectation is that we play by His rules and take our data from personal interactions.
A Biblical Experiment
So what does it mean to hold to Jesus' teaching? At one point, a religious scholar asked Jesus
"Teacher, which is the greatest commandment in the Law?" Jesus replied: "'Love the Lord your God with all your heart and with all your soul and with all your mind.' This is the first and greatest commandment. And the second is like it: 'Love your neighbor as yourself.' All the Law and the Prophets hang on these two commandments.'" (Matt. 22:36-40)Jesus identified Himself as the fulfillment of the Law and the Prophets (Matt. 5:17), so all of His teaching should be contained within these two commandments. Let's take them one at a time.
Loving God
First, how does one love a God who is unknown and possibly doesn't exist? We can get some help here from other places where people are actively forming new relationships. Dating often begins with a lot of talking and time spent in places where the other person likes to hang out. Talking to God is called prayer. Agnostic prayer usually starts with "God, are you there?" but can quickly move to other things you want to know, concerns, etc. Just like on a date, taking time to be quiet and listen is a plus, as is praise. Since praise implies an established relationship, it may be easier to start with gratitude, ranging from the joys of the day to the wonder of creation. An omniscient deity presumably does not require us to pray aloud, but most people find that vocalization makes communication, including prayer, more concrete and cuts down on distractions.
Where does God like to hang out? Omnipresent beings hang out everywhere by definition, so it could be argued that hanging out with God is simply a matter of cultivating an awareness of His presence all the time. This is a valuable exercise, but one complicated by the open question of God's existence. A more concrete method would be to hang out with other people who are hanging out with God (or, for those still on the fence, people who think they are hanging out with God). "For where two or three gather in my name, there I am with them." (Matt 18:20) In most places in North America, a brief search will turn up many churches within a short distance. These organizations are nominally all part of a single Body of Christ (1 Cor 12:27) tasked with carrying out the work of God on Earth. Matters of denomination are largely irrelevant to the present query, but before investing much time in a church it would be prudent to determine that they believe God is active in their midst and look to the Bible as an authoritative reference. Another clue is found in Galatians 5:22-23: "But the fruit of the Spirit is love, joy, peace, forbearance, kindness, goodness, faithfulness, gentleness and self-control." No one is perfect, but if these things are completely absent from a church, the God described in the Bible should be sought elsewhere.
Loving Your Neighbor
This brings us to loving your neighbor as yourself. In Luke's account of the Greatest Commandment discussion, the follow-up question is "And who is my neighbor?" (Luke 10:29) Jesus responds with a parable about a Jew left for dead my robbers who is rescued by a Samaritan, his cultural enemy. The Samaritan carries him to safety and then pays a large sum of money to have him looked after. Caring for the needs of those unable to care for themselves is a major theme throughout the Bible, as is God's interaction with people engaged in this activity. Giving up our time and money to care for other people, particularly people we dislike, often feels like a giant leap into insanity and almost everyone has deeply-held limits on how far down that road they are willing to go. Since the Bible promises that God will meet us where we are (e.g. James 4:8), it is sufficient for deity-detection purposes to go as far as we are able and make these limits, once discovered, a matter of prayer. If a choice must be made between giving time or giving money, the relational aspect of giving time is an advantage here.
Besides caring for material needs, one of the things Jesus commanded us to do for our neighbor is forgive them. "Forgive" in English has two related definitions:
1) stop feeling angry or resentful toward someone (for an offense, flaw, or mistake)
2) cancel (a debt)
Forgiveness is supposed to be very healthy, but can also be extremely difficult. "Help me forgive <person> for <thing>." is a very common prayer. Considering that "forgive us our debts as we also have forgiven our debtors" (Matt. 6:12) made it into Jesus' 53-word stock prayer, attempts to obey Jesus' teaching should include as much forgiveness as possible.
(This post is now several years old and never got posted. I leave open the question of how to interpret the events of your life during a deity-detection search. For most people, relational intuition will be more valuable than some numerical analysis.)
Thursday, July 31, 2014
Studying For Exams
In my first year of graduate school (2008), i TA'd for an introductory electromagnetism class that turned out to be very difficult. Except for the difficulty, i liked a lot of things about the way the course was structured. This letter, then, is advice from a younger me to students dealing with professors like the one i am trying to be.
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Dear Section 2,
A number of you have asked me for study strategies and tips for the final exam. So far i've given only half-answers and promises to think about it. Unfortunately, the number of people i've blown off is slowly approaching the section size. So rather than track you all down with an answer, i'm going to do this all at once. I'm sure there is at least one person who has asked me about a specific situation
that isn't addressed by this e-mail. Whoever you are, i'm sorry, i've forgotten. Ask me again and i'll try to give you a straight answer.
Most of you seem to be having three basic problems:
First, in some instances you just can't get your head around a concept, even in theory. For many, this is your first experience studying phenomena of which you can't immediately form a mental picture, so you are much more scared than you need to be.
Second, you may understand a concept in theory, but don't know when to use it. This issue is characterized by staring blankly at problems while a thousand unusable or unrelated tidbits of information swim through your head.
Third, once you've figured out what concept to use, you discover that you don't really understand it well enough to implement it properly. On exams this tends to manifest itself as a half-credit solution in which you picked random areas, charges, currents, etc. and plugged them into your equation wherever they would fit (or not in some cases).
Finally, as a corollary, several students have complained that they do homework with a group, but on their own they can never reproduce the work. Or they could eventually flail their way to a mostly correct solution, but in an exam there isn't time. These are all problems that are common but somewhat unique to physics. Again, since you have relatively little experience with physics, you are probably more upset than the situation warrants. So calm down, take a deep breath...and let's talk about study strategies.
To start, it might be good to re-read the notes i sent out before the midterm. They contain some tips for right before and during the final that i won't reiterate here. If you need a copy, let me know.
The first problem can only be dealt with by another person. Assuming you've read the lecture notes and the book as they relate to a particular concept, reading them over and over again is unlikely to impart any sudden epiphany. Ask a friend to explain it to you. If that doesn't work, take your friend with you and ask a TA or the professor to explain. I'm always available by e-mail, but basic conceptual questions are much better addressed in person. (Note that you can still use e-mail to make an in-person appointment.) On the flip side, if someone asks you to explain a concept, please make every effort to do so. You might just discover that you don't know it as well as you thought you did. When explaining an equation, if you need math, you don't really understand it. By taking time to just review the theory of the class to each other, you insure yourselves against that sudden feeling of cluelessness when you open the exam.
There is still the question of which concepts in the course are fundamental. If there's a demand for it, i can put together a list, but the part of me that feels responsible doesn't want to risk leaving something off and the physicist in me says it's obvious. Please let me know if this is grossly incorrect. (Update: Nobody asked for this, partly because it was covered in the exam review. If its ever unclear which concepts in my courses are fundamental, please let me know!)
Problem two is basically an inability to DO physics, despite understanding it. The antidote, then, is obviously to do more physics. However it is possible to struggle through many problems without really getting at the underlying skill that makes them look easy in a physicists hands. I've stressed that you can learn faster by working in groups, but there is a danger that part of the group does problems while another part watches. Therefore it is best to work in smaller groups and stay engaged in your group. I've found 2-4 to be about right at this level. That is NOT to say that you can't have more people than that working together. I strongly suggest you make a party of it. Order food, find a place with lots of whiteboard space and invite everyone you know in the class to a physics party. That means someone has to step up and organize it, but you all have to learn the material anyway and this is so much faster and more fun. Some of the best times i had as an undergrad were with some subset of the two dozen people who were just as buried in physics as i was. (Yes, i'm a nerd, but that doesn't make me wrong.) Freshmen: you might even get an RA to organize something for everyone in your dorm.
Several of you have told me that you do practice problems, but they always seem to take forever and/or you're never sure you've got them right. Remember that problems are always written to test one or more of the fundamental concepts. Figure out what those concepts are and you're well on your way to solving the problem. Not by coincidence, the grading rubric usually starts with a couple points just for writing down the relevant concept, often directly from the equation sheet. So in studying and on the exam, start by writing down the concept you are going to use! This will give you something to break into manageable pieces and calm the flutter of other facts running through your head. Once you have a concept, break it down. If it's Gauss' Law, find an appropriate Gaussian surface, calculate it's area and count/calculate the charge it encloses. If you want to integrate the force on a wire from a magnetic field, draw dL and B at some point on your diagram and use the right hand rule to locate the dF vector. At this point, i always wave my hands at the board and say "Do math." From there, you will usually see an obvious, mostly mathematical, path to a solution. If your math skills are a little rusty, group study can be a good time to brush them up.
The third problem is less frightening but more insidious than the first two. It certainly claims the most points. When you understand an equation well enough to see that it applies to your problem, but don't really know what it means or where it came from, you produce a solution that graders politely refer to as 'creative'. This is one of the best reasons to check that you can explain the fundamentals of the course to a fellow student without breaking out any math. This is the reason, when studying, to break each equation into parts and make sure you know what each part is and what it means. This is why every problem should start with a concept, not just an equation. For example: If you know that the voltage around a moving loop is vlB but don't know why or when, you have no idea what length to use and have restricted your knowledge of moving wires to linearly translating loops entering magnetic fields (although you probably don't know that). V=vlB is an equation, Faraday's Law is a concept. The moving wire problem should start with Faraday's Law. The cure to Problem 3 is a combination of the cures to the first two problems. Working problems from their fundamentals will bring out those things that you don't quite understand fully. At that point, it's important not to be afraid of asking about a concept that you thought you had down. In a group, that means asking why the group did what it did. Alone, that means finding a friend or asking a TA. (When you e-mail a TA, remember to tell us what problem you are working on and what you've already done.) Some of you have asked about good problems to study. Obviously old midterm and practice midterms are good. It helps that you have the solution key. But you've seen them before, so they may not build your confidence about fresh problems. Problems from <textbook> are also good, but you don't necessarily have the solutions and they tend to be easier than exam problems. I assume <Head TA> will post practice finals on <course management website>. Those are probably the best material.
I think that covers most of the issues i promised to address. Again, let me know if i've left out something you asked me. Actually, feel free to bring any problems i haven't covered, but hopefully this gets most of them.
Ben
------------------------------------------------------------------------------------------------------------------------------------
Dear Section 2,
A number of you have asked me for study strategies and tips for the final exam. So far i've given only half-answers and promises to think about it. Unfortunately, the number of people i've blown off is slowly approaching the section size. So rather than track you all down with an answer, i'm going to do this all at once. I'm sure there is at least one person who has asked me about a specific situation
that isn't addressed by this e-mail. Whoever you are, i'm sorry, i've forgotten. Ask me again and i'll try to give you a straight answer.
Most of you seem to be having three basic problems:
First, in some instances you just can't get your head around a concept, even in theory. For many, this is your first experience studying phenomena of which you can't immediately form a mental picture, so you are much more scared than you need to be.
Second, you may understand a concept in theory, but don't know when to use it. This issue is characterized by staring blankly at problems while a thousand unusable or unrelated tidbits of information swim through your head.
Third, once you've figured out what concept to use, you discover that you don't really understand it well enough to implement it properly. On exams this tends to manifest itself as a half-credit solution in which you picked random areas, charges, currents, etc. and plugged them into your equation wherever they would fit (or not in some cases).
Finally, as a corollary, several students have complained that they do homework with a group, but on their own they can never reproduce the work. Or they could eventually flail their way to a mostly correct solution, but in an exam there isn't time. These are all problems that are common but somewhat unique to physics. Again, since you have relatively little experience with physics, you are probably more upset than the situation warrants. So calm down, take a deep breath...and let's talk about study strategies.
To start, it might be good to re-read the notes i sent out before the midterm. They contain some tips for right before and during the final that i won't reiterate here. If you need a copy, let me know.
The first problem can only be dealt with by another person. Assuming you've read the lecture notes and the book as they relate to a particular concept, reading them over and over again is unlikely to impart any sudden epiphany. Ask a friend to explain it to you. If that doesn't work, take your friend with you and ask a TA or the professor to explain. I'm always available by e-mail, but basic conceptual questions are much better addressed in person. (Note that you can still use e-mail to make an in-person appointment.) On the flip side, if someone asks you to explain a concept, please make every effort to do so. You might just discover that you don't know it as well as you thought you did. When explaining an equation, if you need math, you don't really understand it. By taking time to just review the theory of the class to each other, you insure yourselves against that sudden feeling of cluelessness when you open the exam.
There is still the question of which concepts in the course are fundamental. If there's a demand for it, i can put together a list, but the part of me that feels responsible doesn't want to risk leaving something off and the physicist in me says it's obvious. Please let me know if this is grossly incorrect. (Update: Nobody asked for this, partly because it was covered in the exam review. If its ever unclear which concepts in my courses are fundamental, please let me know!)
Problem two is basically an inability to DO physics, despite understanding it. The antidote, then, is obviously to do more physics. However it is possible to struggle through many problems without really getting at the underlying skill that makes them look easy in a physicists hands. I've stressed that you can learn faster by working in groups, but there is a danger that part of the group does problems while another part watches. Therefore it is best to work in smaller groups and stay engaged in your group. I've found 2-4 to be about right at this level. That is NOT to say that you can't have more people than that working together. I strongly suggest you make a party of it. Order food, find a place with lots of whiteboard space and invite everyone you know in the class to a physics party. That means someone has to step up and organize it, but you all have to learn the material anyway and this is so much faster and more fun. Some of the best times i had as an undergrad were with some subset of the two dozen people who were just as buried in physics as i was. (Yes, i'm a nerd, but that doesn't make me wrong.) Freshmen: you might even get an RA to organize something for everyone in your dorm.
Several of you have told me that you do practice problems, but they always seem to take forever and/or you're never sure you've got them right. Remember that problems are always written to test one or more of the fundamental concepts. Figure out what those concepts are and you're well on your way to solving the problem. Not by coincidence, the grading rubric usually starts with a couple points just for writing down the relevant concept, often directly from the equation sheet. So in studying and on the exam, start by writing down the concept you are going to use! This will give you something to break into manageable pieces and calm the flutter of other facts running through your head. Once you have a concept, break it down. If it's Gauss' Law, find an appropriate Gaussian surface, calculate it's area and count/calculate the charge it encloses. If you want to integrate the force on a wire from a magnetic field, draw dL and B at some point on your diagram and use the right hand rule to locate the dF vector. At this point, i always wave my hands at the board and say "Do math." From there, you will usually see an obvious, mostly mathematical, path to a solution. If your math skills are a little rusty, group study can be a good time to brush them up.
The third problem is less frightening but more insidious than the first two. It certainly claims the most points. When you understand an equation well enough to see that it applies to your problem, but don't really know what it means or where it came from, you produce a solution that graders politely refer to as 'creative'. This is one of the best reasons to check that you can explain the fundamentals of the course to a fellow student without breaking out any math. This is the reason, when studying, to break each equation into parts and make sure you know what each part is and what it means. This is why every problem should start with a concept, not just an equation. For example: If you know that the voltage around a moving loop is vlB but don't know why or when, you have no idea what length to use and have restricted your knowledge of moving wires to linearly translating loops entering magnetic fields (although you probably don't know that). V=vlB is an equation, Faraday's Law is a concept. The moving wire problem should start with Faraday's Law. The cure to Problem 3 is a combination of the cures to the first two problems. Working problems from their fundamentals will bring out those things that you don't quite understand fully. At that point, it's important not to be afraid of asking about a concept that you thought you had down. In a group, that means asking why the group did what it did. Alone, that means finding a friend or asking a TA. (When you e-mail a TA, remember to tell us what problem you are working on and what you've already done.) Some of you have asked about good problems to study. Obviously old midterm and practice midterms are good. It helps that you have the solution key. But you've seen them before, so they may not build your confidence about fresh problems. Problems from <textbook> are also good, but you don't necessarily have the solutions and they tend to be easier than exam problems. I assume <Head TA> will post practice finals on <course management website>. Those are probably the best material.
I think that covers most of the issues i promised to address. Again, let me know if i've left out something you asked me. Actually, feel free to bring any problems i haven't covered, but hopefully this gets most of them.
Ben
Friday, March 21, 2014
Watts Up?
A while back i was adding instruments to a rack already loaded with sensitive equipment and started to worry about blowing a fuse in the middle of a delicate experiment. A colleague lent me a power monitor made by the Watts Up? Corporation. You plug it into an outlet, then plug your devices into it and it reads out statistics on your power consumption in Volts, Amps, Watts or Dollars. It does peak detection and a number of other sophisticated things, but i was struck by how little i actually know about grid power usage. I consider myself fairly well informed (i work with electronics for a living), but i did not know, for example, that my desktop draws 0.9 A at rest and 1.3 A when working hard. At 120 V, assuming a rate of $0.15/kWh, it costs $0.39/day to leave my computer running ($0.56 if i leave it running an experiment). Good to know.
I suspect i am in the American majority in having a vague sense that i should reduce my power consumption without really knowing how to effectively do that. I'm sure that some of the 'green consumer' advice we get is good and some of it is hogwash, but i've never taken a quiet stroll through the data to decide which is which.
I'll start at the small end. How important is it to unplug chargers when not in use? Any power 'wasted' by a device turns to heat. In the absence of cooling fins, all heat is radiated away. So if we know the surface area of a device and its temperature, we know how much heat is being wasted. In the extreme limit, a charger that was a 4 inch cube heated to the boiling point would be wasting 42 W. But that's unrealistic. My cell phone charger is about 2"x1"x1" and isn't warm to the touch. Even assuming it is 5 ˚C above room temperature, it wastes 0.18 W (costing me $0.24/year). Not worth the hassle of forgetting to plug it in even once a year.
Looking up, i see that each of my labs is lit by 16 32W fluorescent bulbs, or 512 W. This costs $0.61 per room each day if i work 8 hours (ha), and $1.22 per room if i forget to turn them off one night. That's starting to look like real money. Whatever the advertisers say, fluorescent bulbs don't last any longer than incandescents, but each of those 32 W fluorescents probably replaces a 100 W incandescent. Over the 1000 hr life of each bulb, that extra 68 W costs $10.20. So even though they cost a few bucks extra and are heavily over-advertised, i should probably replace my incandescents at home with compact fluorescents. (grumblegrumble)
A quick search of Energy Star ratings tells me that modern home refrigerators use 280-580 kWh/yr at a cost of $42-$87/yr. (1 kWh/yr = 0.114 W) This number does seem to be very time dependent. Refrigerators from the '90s routinely ran over 1000 kWh/yr or $150/yr. Since a new refrigerator can cost $500-$2000 and lasts 10-15 years, i'd say from a cost perspective its probably not worth replacing a nice refrigerator that isn't nearing the end of its life anyway. (Unless the price of electricity goes up.) On the other hand, my parents have an enormous deep freezer that has been in our basement for my entire life. When we become real people and have our own house, my wife and i definitely want one; but that might be a case where buying new actually is cheaper.
Frankly, i suspect all of this logic is wiped out by the cost of heating and cooling a home. The insulative power of materials is a tricky thing to measure, but the standard unit seems to be R-value measured in (m^2*K)/(W*in). This has the advantage that you add the R-values of multiple insulation layers, but its a weird unit to think about. Most decent insulation has an R-value of about 1, so 5 inches of decent insulation lets through about 0.2 W/(m^2*K), which is a nice physics unit that i'm used to. If we imagine a standard 2-story, square, 200 m^2 house with no windows, a flat roof and 2.5 meter ceilings, it would have 200 m^2 of wall and another 100 m^2 of roof. If you try to pull a 10 degC difference between inside and outside, you need to move 300 W of heat. Total cost: $394/year.
Huh. Actually, that's not bad. However...a single square meter of single-pane glass will cost you 70 W = $92/year under those conditions. Glass is effectively a conductor, but it does block convection. Even double-pane glass with radiation coatings only get this down to ~10 W/m^2 = $13/yr/m^2. If you've used fiberglass panels (R = 0.44) instead of, say, polyurethane foam (R ~ 1), you spend an extra $500/year. On the other hand, installing blown foam costs about $15/m^2, or $4500 for our fictitious house. You'd recover your investment in nine years in modest climes. Definitely worth it in extreme climates, but very geography-dependent. Same goes for double-pane windows. They range $200-$500/m^2 and may save around $80/m^2/year.
Of course, this assumes you're running an electric heater. Air conditioning is even trickier. First, cooling power is often rated in 'tons', which apparently means the same cooling power as 1 ton of ice melting over 1 day. This works out to 3517 W or $4620/yr if it ran continuously. Next is efficiency ratings. There seem to be at least four competing systems, most of which mix imperial and metric units. I like the Coefficient of Performance (COP), which is (Watts removed from house) / (Watts of power used). It seems that COP values of 2-5 are common for cooling systems. Of course, if you switch the input and output pipes on your AC, you could theoretically get that same boost to efficiency by 'cooling' the outdoors to warm your house. This arrangement is sold under the name 'heat pump', which i guess makes sense.
This is rapidly becoming too situation-dependent to carry further. The pattern here seems to be that most of the eco-friendly advice makes good economic sense most of the time, but a lot of it is in the margins and many power usage decisions are interlinked. You really can save money every year by installing better insulation, getting a newer fridge or switching to CPFs. But at current electricity prices, you won't recoup your investment for several years. As for the Watt's Up meters, they range $50-200. Its possible that having better information could help a homeowner save $200 in the course of a decade by making better choices. Probably not worth buying for an apartment-dweller.
I suspect i am in the American majority in having a vague sense that i should reduce my power consumption without really knowing how to effectively do that. I'm sure that some of the 'green consumer' advice we get is good and some of it is hogwash, but i've never taken a quiet stroll through the data to decide which is which.
I'll start at the small end. How important is it to unplug chargers when not in use? Any power 'wasted' by a device turns to heat. In the absence of cooling fins, all heat is radiated away. So if we know the surface area of a device and its temperature, we know how much heat is being wasted. In the extreme limit, a charger that was a 4 inch cube heated to the boiling point would be wasting 42 W. But that's unrealistic. My cell phone charger is about 2"x1"x1" and isn't warm to the touch. Even assuming it is 5 ˚C above room temperature, it wastes 0.18 W (costing me $0.24/year). Not worth the hassle of forgetting to plug it in even once a year.
Looking up, i see that each of my labs is lit by 16 32W fluorescent bulbs, or 512 W. This costs $0.61 per room each day if i work 8 hours (ha), and $1.22 per room if i forget to turn them off one night. That's starting to look like real money. Whatever the advertisers say, fluorescent bulbs don't last any longer than incandescents, but each of those 32 W fluorescents probably replaces a 100 W incandescent. Over the 1000 hr life of each bulb, that extra 68 W costs $10.20. So even though they cost a few bucks extra and are heavily over-advertised, i should probably replace my incandescents at home with compact fluorescents. (grumblegrumble)
A quick search of Energy Star ratings tells me that modern home refrigerators use 280-580 kWh/yr at a cost of $42-$87/yr. (1 kWh/yr = 0.114 W) This number does seem to be very time dependent. Refrigerators from the '90s routinely ran over 1000 kWh/yr or $150/yr. Since a new refrigerator can cost $500-$2000 and lasts 10-15 years, i'd say from a cost perspective its probably not worth replacing a nice refrigerator that isn't nearing the end of its life anyway. (Unless the price of electricity goes up.) On the other hand, my parents have an enormous deep freezer that has been in our basement for my entire life. When we become real people and have our own house, my wife and i definitely want one; but that might be a case where buying new actually is cheaper.
Frankly, i suspect all of this logic is wiped out by the cost of heating and cooling a home. The insulative power of materials is a tricky thing to measure, but the standard unit seems to be R-value measured in (m^2*K)/(W*in). This has the advantage that you add the R-values of multiple insulation layers, but its a weird unit to think about. Most decent insulation has an R-value of about 1, so 5 inches of decent insulation lets through about 0.2 W/(m^2*K), which is a nice physics unit that i'm used to. If we imagine a standard 2-story, square, 200 m^2 house with no windows, a flat roof and 2.5 meter ceilings, it would have 200 m^2 of wall and another 100 m^2 of roof. If you try to pull a 10 degC difference between inside and outside, you need to move 300 W of heat. Total cost: $394/year.
Huh. Actually, that's not bad. However...a single square meter of single-pane glass will cost you 70 W = $92/year under those conditions. Glass is effectively a conductor, but it does block convection. Even double-pane glass with radiation coatings only get this down to ~10 W/m^2 = $13/yr/m^2. If you've used fiberglass panels (R = 0.44) instead of, say, polyurethane foam (R ~ 1), you spend an extra $500/year. On the other hand, installing blown foam costs about $15/m^2, or $4500 for our fictitious house. You'd recover your investment in nine years in modest climes. Definitely worth it in extreme climates, but very geography-dependent. Same goes for double-pane windows. They range $200-$500/m^2 and may save around $80/m^2/year.
Of course, this assumes you're running an electric heater. Air conditioning is even trickier. First, cooling power is often rated in 'tons', which apparently means the same cooling power as 1 ton of ice melting over 1 day. This works out to 3517 W or $4620/yr if it ran continuously. Next is efficiency ratings. There seem to be at least four competing systems, most of which mix imperial and metric units. I like the Coefficient of Performance (COP), which is (Watts removed from house) / (Watts of power used). It seems that COP values of 2-5 are common for cooling systems. Of course, if you switch the input and output pipes on your AC, you could theoretically get that same boost to efficiency by 'cooling' the outdoors to warm your house. This arrangement is sold under the name 'heat pump', which i guess makes sense.
This is rapidly becoming too situation-dependent to carry further. The pattern here seems to be that most of the eco-friendly advice makes good economic sense most of the time, but a lot of it is in the margins and many power usage decisions are interlinked. You really can save money every year by installing better insulation, getting a newer fridge or switching to CPFs. But at current electricity prices, you won't recoup your investment for several years. As for the Watt's Up meters, they range $50-200. Its possible that having better information could help a homeowner save $200 in the course of a decade by making better choices. Probably not worth buying for an apartment-dweller.
Thursday, July 18, 2013
I'd Tell You, Kid, But You Wouldn't Believe Me
Even before he can talk, my little boy has started to hum back the lullabies we sing routinely. One of his favorites is "Twinkle, twinkle little star. How i wonder what you are." As comforting as it is to hear a child singing, to lay on your back in the grass and point out tiny diamonds in the sky, a part of me wants to explain. Because of course we know what that little star is. Far out in space, immense nuclear furnaces drive the workhorses of the visible universe. A tiny fraction of the power from one star drives nearly every process on Earth, but ultimately even the stuff we are made of was created in stars, the last stages of giant stars that blasted heavy elements into the vicinity of the proto-Sun in some of the biggest explosions anywhere ever. How cool is that? Bizarrely, though we think of stars as nuclear powered, nuclear fusion actually holds the more energetic gravitational collapse in check; the most powerful force in existence barely restrains the weakest. Even more amazingly, all but one of those stars is so far away that a glowing ball bigger than a million Earths is reduced to a dot. Most are farther away than that. You need advanced optics to even see collections of billions of stars spinning around each other. The scale of the Universe is beyond even the numbers children make up to be ridiculous. A billion trillion miles barely gets you out of our local cluster of galaxies. It may be that there is nothing new under the Sun, but there's an awful lot that we haven't explored yet.
As much as we love Kermit the Frog in this house, he's really flubbed this one. First, rainbows aren't technically illusions. They are exactly what they appear to be, its just that you're seeing different images from many microscopic objects to form the complete picture. That's why rainbows are so amazing! They have nothing to hide because they are themselves a revelation! They are proof that every beam of sunlight is made up of all the colors you can imagine, but its only when refracted through a cloud of tiny water drops that those colors split out so you can see them. But it gets better. Sometimes a color is missing, or sometimes there is more of one color than there ought to be. The things that add or remove colors here in our backyards are the same things that add or remove colors in the sky or on distant stars and planets. By splitting the light coming from far-off places into rainbows, we can tell what they're made of, how far away they are and sometimes where they're going. Closer to home, spectroscopy lets us look into the hearts of molecules and even date fossils. The dreamers have found the rainbow connection. They dreamed of knowledge pouring out from every ray of light and then clothed their dreams in metal and glass. Now they're using it to reach for the stars.
"Why are there so many songs about rainbows and what's on the other side?
Rainbows are visions, but only illusions. Rainbows have nothing to hide.
So we've been told and some choose to believe it. I know they're wrong wait and see.
Someday we'll find it, the rainbow connection, the lovers, the dreamers and me."
As much as we love Kermit the Frog in this house, he's really flubbed this one. First, rainbows aren't technically illusions. They are exactly what they appear to be, its just that you're seeing different images from many microscopic objects to form the complete picture. That's why rainbows are so amazing! They have nothing to hide because they are themselves a revelation! They are proof that every beam of sunlight is made up of all the colors you can imagine, but its only when refracted through a cloud of tiny water drops that those colors split out so you can see them. But it gets better. Sometimes a color is missing, or sometimes there is more of one color than there ought to be. The things that add or remove colors here in our backyards are the same things that add or remove colors in the sky or on distant stars and planets. By splitting the light coming from far-off places into rainbows, we can tell what they're made of, how far away they are and sometimes where they're going. Closer to home, spectroscopy lets us look into the hearts of molecules and even date fossils. The dreamers have found the rainbow connection. They dreamed of knowledge pouring out from every ray of light and then clothed their dreams in metal and glass. Now they're using it to reach for the stars.
Someday i will explain all this. I hope my son develops the expertise to find wonder far beyond what his eyes can see. I hope he learns to fill his mind beyond capacity with the awesomeness of the world around him. But to every thing there is a season. Tonight, we're using non-equilibrium dynamics to solve the "kicking a ball without falling over" problem and finding diamonds in the sky. For tonight, i couldn't ask for more.
Thursday, July 4, 2013
Refined Like Silver, Tested Like Gold
The Bible makes a number of references to God refining us. Here are a few examples:
The people for whom the Old Testament was written are assumed to know how gold and silver are refined. Maybe in a world dominated by gold and silver coins that shouldn't be too surprising. At any rate, most readers from the age of fiat currencies probably gloss over these passages. Below is a briefprimer ramble in metallurgy aimed at illuminating the above metaphors.
Refining refers to the process of drawing impurities out of a material without inducing a chemical change. For metals with fairly high initial purity, this is usually done in the liquid phase. When heavy metals like gold or silver are refined, some impurities burn away, while others float to the surface and must be scraped off.
Silver melts at 962 C (1763 F) which is hot, but not an extraordinary temperature for handling metals. We don't normally think of metals as 'burning', but molten silver will rapidly oxidize if raised much above its melting point under normal atmosphere. This process is irreversible and effectively destroys the melt. For this reason, silversmiths watch their crucibles very carefully, adjusting the heat and skimming off slag over a long period. To say that something is 'refined like silver' implies that, yes, the subject is pushed to an extreme until it loses its old form, but the Refiner is paying very close attention, making sure that the heat never becomes too much and periodically working with the subject to remove undesirable things which have come to the surface. This can be a long process, which is completed when the silver takes on its characteristic mirror finish. When the Refiner can see Himself reflected in the melt, the refining is complete.
Although gold is right below silver on the periodic table, it is handled very differently. It melts at a slightly higher temperature (1064 C, 1947 F), but never oxidizes under normal atmosphere. This means gold can be processed in a blast furnace or (nowadays) an arc furnace. Unlike the carefully regulated flames under the silversmiths crucible, these technologies are designed to spend fuel (coal or electricity, respectively) as quickly and thoroughly as possible with minimal attempt at control. The goldsmith doesn't fiddle around with surface skimming either. Anything that isn't gold in a blast furnace burns or separates. If something is to be 'refined like gold', it should expect intense heat with little or no regard for its safety (hence Jobs' comment). The Refiner is trying to remove contaminants rapidly and really doesn't care what happens to them or whether the subject is highly attached to them. He is only interested in the indestructible essence which gives the subject such immense value and warrants such an extravagant expenditure ofwrath...er, fuel.
How are gold and silver tested? Today, silver is tested by dissolving it in nitric acid. In Biblical times, you tested silver by attempting to refine it. This squares with the interchangeable use of 'testing' and 'refining' in different translations of the above passages. As Proverbs 17:3 implies, gold can also be tested in a furnace, but there are several countertop methods which might be referred to in Zechariah 13:9. First, gold was by far the densest material known to the ancient world.* Even gold alloyed with lead would be considerably lighter than a pure gold object of the same size. So if someone claimed to have a 1 uncia** gold coin, you could check its density against a reference gold uncia to determine its authenticity. Second, pure gold is a good resonator. It makes a clear, rich tone when struck. Heavily alloyed or plated gold usually makes a dull thunk. If something is 'tested like gold', it might be measured against an external standard to see if foreign inclusions have made it less substantial than expected. It might also be perturbed sharply to see if it naturally responds like the thing it is claimed to be.
**A Roman talent (weight) was 32.3 kg. 1 talent = 100 libra = 1200 uncia, so 1 uncia = 27 g. A Roman talent (monetary) meant a talent of silver (or, rarely, gold), about $21,000 (or $1,300,000) at current prices. So Jesus' parable of the servant who owed 10,000 talents in Matthew 18:24 was clearly intended to be a non-physical value, an incalculable debt. But the wealthy man in Matthew 25:14 might have distributed eight talents of silver to trusted servants for investment. His annoyance that $20,000 was buried instead of deposited is understandable.
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What might God be doing with all this silver and gold? The obvious metaphor is their coinage property; they have worth because the King finds them inherently valuable. But precious metals are used for all sorts of things besides coinage. In labs, silver and gold are routinely used for their very high conductance and reflectivity. For example, a common problem in cryogenics is the desire to keep two geometrically-isolated objects at the same temperature, which is equivalent to bringing them very close together on a thermal map. To do this, you need to run a thin wire between them which carries a lot of power very easily. If you can afford it, the best material for this application is ultra-high purity, annealed silver. If God refers to you, who make contact with both Heaven and Earth, as 'refined like silver', it is possible that He wants you to bring together two things which can't be physically co-located by transferring power from one to the other.
To prepare silver for use as a thermal tie, you must first make it into the right shape. This usually means extruding it into rods or sheets and bending those into the desired geometry. Such cold working causes the normally malleable silver to stiffen, pulling sheets of atoms against each other. Internal stress makes it less workable and less conductive, so the silver should be annealed in its final shape before use. Annealing requires heating the piece back to nearly its melting point in a specially prepared atmosphere. The goal is for the silver to let go of its internal strain fields (to fully accept its current shape on a microscopic level) and to chemically alter any trace impurities so they don't impede conduction. Annealing is a shape-specific treatment, so bending the piece through use gradually reduces its effect. Where flexible thermal ties are absolutely necessary, they ought to be removed and re-annealed occasionally. This is generally avoided because it is extraordinarily tedious to extract the part, create an annealing atmosphere, slowly ramp up the power and monitor the anneal so that the part is restored but not damaged.
The maintenance program for the Body of Christ calls for each piece to be routinely pulled out of its working role, isolated from its usual atmosphere and, often, treated to power way beyond its usual load which nevertheless has no external effect. It might seem strange or even offensive to an outsider that mature Christians claim to experience God's power most in their quiet times. This isn't about purification, though that may occur as well. Instead its about reorganizing internal structures, bringing out the stresses incurred with use and letting God reshape us according to our changing place in the whole structure that is the Church. This isn't the sort of treatment you give to bullion coins, however valuable. Its a regimen more suited for flexible parts that need to constantly respond to a changing environment. It implies that God wants to teach us to fully accept the shape He has given us and that we should be prepared to carry His power on a regular basis.
If we can stretch an ancient metaphor to cover modern applications, this says something about how we should expect God's power to work in our lives. The perfect thermal tie is one that is very well anchored at both ends and offers no impedance to power flowing through it. They are valuable because they are compliant, but they don't do anything besides gradually spread out to contact as much of the two endpoints as possible. To be effective, we need to maintain our purity and really accept the configuration we've been given. Both of these tasks require an external power source. We also need to let ourselves flow outward to make as much contact with Heaven and Earth as possible. This means cultivating deep prayer and deep friendships, speaking in tongues and speaking in lecture halls. Then we need not worry about "accessing" God's power. When you bridge a state imbalance with a conductor, power just flows. Until we achieve a state of 'On Earth as it is in Heaven', anybody who touches both carries power all the time. If configured properly it shouldn't be obvious. It ought to manifest as healthy relationships, effective ministry and other distributed effects in the same way that a good heat strap looks completely inert until you check your thermometers. In this model, things that we think of as "displays of God's power" are the equivalent of local welding. It means you encountered something so broken it needed to be melted. This world is broken enough that we should be prepared for this, but we don't need to work to make it happen. It is enough to become the kind of people through whom power flows. The rest will take care of itself.
- And I will put this third into the fire, and refine them as one refines silver, and test them as gold is tested. They will call upon my name, and I will answer them. I will say, ‘They are my people’; and they will say, ‘The Lord is my God.’” (Zechariah 13:9)
- See, I have refined you, though not as silver; I have tested you in the furnace of affliction. (Isaiah 48:10)
- But he knows the way that I take; when he has tried me, I shall come out as gold. (Job 23:10)
- The crucible is for silver and the furnace is for gold, and the Lord tests hearts. (Proverbs 17:3)
The people for whom the Old Testament was written are assumed to know how gold and silver are refined. Maybe in a world dominated by gold and silver coins that shouldn't be too surprising. At any rate, most readers from the age of fiat currencies probably gloss over these passages. Below is a brief
Refining refers to the process of drawing impurities out of a material without inducing a chemical change. For metals with fairly high initial purity, this is usually done in the liquid phase. When heavy metals like gold or silver are refined, some impurities burn away, while others float to the surface and must be scraped off.
Silver melts at 962 C (1763 F) which is hot, but not an extraordinary temperature for handling metals. We don't normally think of metals as 'burning', but molten silver will rapidly oxidize if raised much above its melting point under normal atmosphere. This process is irreversible and effectively destroys the melt. For this reason, silversmiths watch their crucibles very carefully, adjusting the heat and skimming off slag over a long period. To say that something is 'refined like silver' implies that, yes, the subject is pushed to an extreme until it loses its old form, but the Refiner is paying very close attention, making sure that the heat never becomes too much and periodically working with the subject to remove undesirable things which have come to the surface. This can be a long process, which is completed when the silver takes on its characteristic mirror finish. When the Refiner can see Himself reflected in the melt, the refining is complete.
Although gold is right below silver on the periodic table, it is handled very differently. It melts at a slightly higher temperature (1064 C, 1947 F), but never oxidizes under normal atmosphere. This means gold can be processed in a blast furnace or (nowadays) an arc furnace. Unlike the carefully regulated flames under the silversmiths crucible, these technologies are designed to spend fuel (coal or electricity, respectively) as quickly and thoroughly as possible with minimal attempt at control. The goldsmith doesn't fiddle around with surface skimming either. Anything that isn't gold in a blast furnace burns or separates. If something is to be 'refined like gold', it should expect intense heat with little or no regard for its safety (hence Jobs' comment). The Refiner is trying to remove contaminants rapidly and really doesn't care what happens to them or whether the subject is highly attached to them. He is only interested in the indestructible essence which gives the subject such immense value and warrants such an extravagant expenditure of
How are gold and silver tested? Today, silver is tested by dissolving it in nitric acid. In Biblical times, you tested silver by attempting to refine it. This squares with the interchangeable use of 'testing' and 'refining' in different translations of the above passages. As Proverbs 17:3 implies, gold can also be tested in a furnace, but there are several countertop methods which might be referred to in Zechariah 13:9. First, gold was by far the densest material known to the ancient world.* Even gold alloyed with lead would be considerably lighter than a pure gold object of the same size. So if someone claimed to have a 1 uncia** gold coin, you could check its density against a reference gold uncia to determine its authenticity. Second, pure gold is a good resonator. It makes a clear, rich tone when struck. Heavily alloyed or plated gold usually makes a dull thunk. If something is 'tested like gold', it might be measured against an external standard to see if foreign inclusions have made it less substantial than expected. It might also be perturbed sharply to see if it naturally responds like the thing it is claimed to be.
*Modern scam artists will plate gold around a tungsten core to fake the weight. Tungsten was discovered as a pure element in 1781, so that wasn't a risk Biblical readers would consider.
**A Roman talent (weight) was 32.3 kg. 1 talent = 100 libra = 1200 uncia, so 1 uncia = 27 g. A Roman talent (monetary) meant a talent of silver (or, rarely, gold), about $21,000 (or $1,300,000) at current prices. So Jesus' parable of the servant who owed 10,000 talents in Matthew 18:24 was clearly intended to be a non-physical value, an incalculable debt. But the wealthy man in Matthew 25:14 might have distributed eight talents of silver to trusted servants for investment. His annoyance that $20,000 was buried instead of deposited is understandable.
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What might God be doing with all this silver and gold? The obvious metaphor is their coinage property; they have worth because the King finds them inherently valuable. But precious metals are used for all sorts of things besides coinage. In labs, silver and gold are routinely used for their very high conductance and reflectivity. For example, a common problem in cryogenics is the desire to keep two geometrically-isolated objects at the same temperature, which is equivalent to bringing them very close together on a thermal map. To do this, you need to run a thin wire between them which carries a lot of power very easily. If you can afford it, the best material for this application is ultra-high purity, annealed silver. If God refers to you, who make contact with both Heaven and Earth, as 'refined like silver', it is possible that He wants you to bring together two things which can't be physically co-located by transferring power from one to the other.
To prepare silver for use as a thermal tie, you must first make it into the right shape. This usually means extruding it into rods or sheets and bending those into the desired geometry. Such cold working causes the normally malleable silver to stiffen, pulling sheets of atoms against each other. Internal stress makes it less workable and less conductive, so the silver should be annealed in its final shape before use. Annealing requires heating the piece back to nearly its melting point in a specially prepared atmosphere. The goal is for the silver to let go of its internal strain fields (to fully accept its current shape on a microscopic level) and to chemically alter any trace impurities so they don't impede conduction. Annealing is a shape-specific treatment, so bending the piece through use gradually reduces its effect. Where flexible thermal ties are absolutely necessary, they ought to be removed and re-annealed occasionally. This is generally avoided because it is extraordinarily tedious to extract the part, create an annealing atmosphere, slowly ramp up the power and monitor the anneal so that the part is restored but not damaged.
The maintenance program for the Body of Christ calls for each piece to be routinely pulled out of its working role, isolated from its usual atmosphere and, often, treated to power way beyond its usual load which nevertheless has no external effect. It might seem strange or even offensive to an outsider that mature Christians claim to experience God's power most in their quiet times. This isn't about purification, though that may occur as well. Instead its about reorganizing internal structures, bringing out the stresses incurred with use and letting God reshape us according to our changing place in the whole structure that is the Church. This isn't the sort of treatment you give to bullion coins, however valuable. Its a regimen more suited for flexible parts that need to constantly respond to a changing environment. It implies that God wants to teach us to fully accept the shape He has given us and that we should be prepared to carry His power on a regular basis.
If we can stretch an ancient metaphor to cover modern applications, this says something about how we should expect God's power to work in our lives. The perfect thermal tie is one that is very well anchored at both ends and offers no impedance to power flowing through it. They are valuable because they are compliant, but they don't do anything besides gradually spread out to contact as much of the two endpoints as possible. To be effective, we need to maintain our purity and really accept the configuration we've been given. Both of these tasks require an external power source. We also need to let ourselves flow outward to make as much contact with Heaven and Earth as possible. This means cultivating deep prayer and deep friendships, speaking in tongues and speaking in lecture halls. Then we need not worry about "accessing" God's power. When you bridge a state imbalance with a conductor, power just flows. Until we achieve a state of 'On Earth as it is in Heaven', anybody who touches both carries power all the time. If configured properly it shouldn't be obvious. It ought to manifest as healthy relationships, effective ministry and other distributed effects in the same way that a good heat strap looks completely inert until you check your thermometers. In this model, things that we think of as "displays of God's power" are the equivalent of local welding. It means you encountered something so broken it needed to be melted. This world is broken enough that we should be prepared for this, but we don't need to work to make it happen. It is enough to become the kind of people through whom power flows. The rest will take care of itself.
Tuesday, June 11, 2013
Does This Make Sense?
Its the end of the school year. Ordinarily this doesn't mean much to grad students, but for the past few years i have been tutoring two of the most amazing high school students in whatever math or physics they were assigned or could imagine. They were both seniors this year, so i'm dipping back into the pool of sophomores and juniors to cover the gap between stipend and rent. The place where i work is good at attracting good kids, but i'm struck once again by how infrequently high school students are made to answer the question "Does this answer make sense?". I know students enter the college physics sequence with the (dis)ability to grind through an algorithm, get a ridiculous answer and circle it without blinking. They must be picking that up in high school, but it is sufficiently dis-incentivized that it usually doesn't last long. My previous students learned to anticipate the question long ago, so it caught me off guard last week when a new student wrote down a completely nonsensical answer and then waited calmly for my evaluation of his work. This amazes me every time i encounter it because the question "Does this make sense?" is at the heart of the process that turns students into scientists.
At first, when intuition is a pretty good guide to reality, the question forces a check on math skills which are too often subpar or merely misguided. If you calculate the speed of any ball to be in excess of Mach 1, you should realize immediately that you are wrong. This provides a good opportunity to re-examine your work before submitting it for a grade. On the flip side, routine reality-checking helps students anchor the numbers and units they are working with onto familiar things. Humans are 1-2 meters in size and 50-100 kg in weight. Less obviously, 10 seconds is too long for a ball to be in the air, humans can't fall faster than about 50 m/s (120 mph) and "1 g" of horizontal acceleration would take a car from 0 to 60 (mph) in 2.7 seconds, which is only achievable in a road car if you have quite a lot of money. These are the sorts of things students can find out by doing simple problems at home and using them to calibrate their reality-checker. They do what no amount of class time can achieve, pull the world of numbers and formulae down into the real world where they can be used in day-to-day life. Only then will they get into your head and change who you are.
As some point intuition runs out. For some students, magnetism is a completely foreign land. For others, its relativity. Routine, in-class questioning "Does this answer make sense?" is the only way to build up a feel for subjects with which the students can't possibly have any direct experience. They go from using intuition to check their math to building a sense of what reality ought to be using math. This process carries students straight through from the time physics starts to get confusing to the day they ask a question, realize that no one in the world knows the answer and use some combination of intuition, observation and math to push the boundary of knowledge a little bit further. And not just in physics. The whole of science education is based around the question "Does this make sense?".
Why is the single most important question needed to create scientists apparently never asked in the high schools of a nation which prides itself on its scientific excellence? I have to admit i have paid almost no attention to secondary education since i was its recipient. As much as i love teaching smart, motivated teenagers with supportive families as a side job, teaching mandatory classes every day for a career is something else entirely; and i have great respect for people who can do it well. That said, it strikes me as odd and mildly alarming that students coming from very good school systems make it into adulthood without ever coupling mathematics to reality. Maybe there is something about meeting a new tutor which causes students' common sense to shut down, so that i'm seeing a bunch of false negatives? Maybe my standards for common sense are unreasonably high? Normally these posts end with some sort of conclusion, but i am honestly stumped here. Anyone in high school want to comment?
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