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
Thursday, July 31, 2014
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?
Tuesday, May 14, 2013
Why Does Your Light Shine?
This post goes out to my Chi Alpha pastor, who a few years ago at the end of a weekend conference said "The difference between a flashlight and a laser is focus. Right now, i need you to focus." Although his words had the desired effect, this is strictly speaking not true. A flashlight focused down to a millimeter spot is still a flashlight, and a laser diffused to a meter spot is still a laser. But it did get me thinking about modern humanity's various light sources and what kinds of qualities our Light in the world might have.
1. Incandescents: Here i include traditional filament light bulbs and well as other thermally stimulated light sources, such as candles. The point of an incandescent bulb is to dump so much heat into a small space that the normal infrared emission of all warm objects shifts up into the visible spectrum. Although they can be made quite intense with the right lenses and reflectors, incandescent bulbs are primarily a heat source. This model describes every youth group i have ever encountered. An enormous amount of energy goes in and the atmosphere inside is 'on fire'. This can sometimes be highly visible in the immediate environment but the effect is essentially random. Mostly what is apparent is excitement; the emitted light conveys very little about the bulb or the power source.
2. Fluorescents: Fluorescent bulbs contain a vapor (often mercury) which is electrically excited to emit ultraviolet light. This strikes a phosphorescent compound on the walls of the bulb to produce visible light. This isn't the most efficient process in the world; the activation current is quite large and the two-step process still generates a lot of heat. This mostly characterizes my adult, evangelical experience. The fluorescent understands that it is primarily a light bulb, not a self-heater, but it generally takes a decent kick to get the light going and the flickering can get pretty bad at times. The emitted light is more a function of what the bulb can make than what the bulb-maker wanted. Its only because the creator of the bulb knew how to absorb and re-emit that light that the bulb is effective at all.
3. Light-Emitting Diodes: LEDs are made from semiconductors with a gradient of impurities along their length. Impurities of different charge set up an internal electric field. When enough current is applied, this field collapses, letting electrons combine with empty electron sites, emitting light. LEDs are brighter and more consistent than fluorescents. They can also be switched on and off much faster and with less over-charging. Simple LEDs emit a single frequency of light; while this frequency is fixed for a given LED, it can be altered in the creation process. More sophisticated LEDs have a fluorescent material built in which spreads out the emitted spectrum to produce 'white' light. Many Christians i know strive to be more like LEDs, quick to respond when called, bright, effective and durable.
4. Lasers: Light Amplification by Stimulated Emission of Radiation. To make a laser, place a light-emitting material ('gain medium') between two mirrors and add power. The gain medium will try to emit light in all sorts of frequencies and directions. But rather than emit directly to the outside world, this light is bounced around internally. At first almost all of the emitted light is re-absorbed, feeding back into the power source, but light that is of the right frequency is amplified on each pass. Over time the light bouncing around the laser cavity becomes more and more what it was designed to emit, all the same wavelength, direction and phase. One of the mirrors is usually partially transparent, letting the intense beam of coherent light out into the world. While it is true that lasers are supremely focusable, their defining characteristic is coherence, which is achieved by letting the laser cavity prune away photons that don't match the mission of the laser. The difference between a flashlight and a laser is not focus, but submission to the power source.
1. Incandescents: Here i include traditional filament light bulbs and well as other thermally stimulated light sources, such as candles. The point of an incandescent bulb is to dump so much heat into a small space that the normal infrared emission of all warm objects shifts up into the visible spectrum. Although they can be made quite intense with the right lenses and reflectors, incandescent bulbs are primarily a heat source. This model describes every youth group i have ever encountered. An enormous amount of energy goes in and the atmosphere inside is 'on fire'. This can sometimes be highly visible in the immediate environment but the effect is essentially random. Mostly what is apparent is excitement; the emitted light conveys very little about the bulb or the power source.
2. Fluorescents: Fluorescent bulbs contain a vapor (often mercury) which is electrically excited to emit ultraviolet light. This strikes a phosphorescent compound on the walls of the bulb to produce visible light. This isn't the most efficient process in the world; the activation current is quite large and the two-step process still generates a lot of heat. This mostly characterizes my adult, evangelical experience. The fluorescent understands that it is primarily a light bulb, not a self-heater, but it generally takes a decent kick to get the light going and the flickering can get pretty bad at times. The emitted light is more a function of what the bulb can make than what the bulb-maker wanted. Its only because the creator of the bulb knew how to absorb and re-emit that light that the bulb is effective at all.
3. Light-Emitting Diodes: LEDs are made from semiconductors with a gradient of impurities along their length. Impurities of different charge set up an internal electric field. When enough current is applied, this field collapses, letting electrons combine with empty electron sites, emitting light. LEDs are brighter and more consistent than fluorescents. They can also be switched on and off much faster and with less over-charging. Simple LEDs emit a single frequency of light; while this frequency is fixed for a given LED, it can be altered in the creation process. More sophisticated LEDs have a fluorescent material built in which spreads out the emitted spectrum to produce 'white' light. Many Christians i know strive to be more like LEDs, quick to respond when called, bright, effective and durable.
4. Lasers: Light Amplification by Stimulated Emission of Radiation. To make a laser, place a light-emitting material ('gain medium') between two mirrors and add power. The gain medium will try to emit light in all sorts of frequencies and directions. But rather than emit directly to the outside world, this light is bounced around internally. At first almost all of the emitted light is re-absorbed, feeding back into the power source, but light that is of the right frequency is amplified on each pass. Over time the light bouncing around the laser cavity becomes more and more what it was designed to emit, all the same wavelength, direction and phase. One of the mirrors is usually partially transparent, letting the intense beam of coherent light out into the world. While it is true that lasers are supremely focusable, their defining characteristic is coherence, which is achieved by letting the laser cavity prune away photons that don't match the mission of the laser. The difference between a flashlight and a laser is not focus, but submission to the power source.
Thursday, April 25, 2013
Do You Fear Death or the Dentist?
I recently took a survey aimed at assessing the impact of my personal beliefs about God. Among other things, it asked about my emotions and attitudes toward death. Part of the study was trying to see if reminding people about their religion changed those attitudes, but in either case i honestly don't fear death. I know i will die someday and in the time before then i need to become the person who will joyfully enter Heaven. I know people who have dodged certain death by God's grace, so it just doesn't scare me.
At the end of the study they explained that they were trying to assess the impact of reminding people about their religion and also of making them work through a difficult emotional problem before being asked a series of 'react to this situation' questions. They said half of the participants were asked about difficult subjects like death and the other half were asked about a routine experience like going to the dentist...
At the mere mention of the dentist, i immediately started to feel anxious even though the study was over and i wasn't asked to recount any specific experiences. I don't have a phobia or anything extreme, but the prospect of cavities and fillings makes me nervous. I fear not being able to understand my research. I fear having to uproot my family. And i am always nervous around traffic cops. But i don't fear death and i don't experience any of the feelings of aimlessness or helplessness that the survey was trying to elicit. In the moment, that struck me as odd.
There are certain types of knowledge that are easier to apply to big, universal things than small, everyday things. For example, the principles of mechanics are laughably simple, a few conservation laws and some formalism for counting energy. Their study reveals some profounds insights into the sorts of thing which can and can't happen in a classical Universe. And yet, it is very easy for a novice to write a specific classical mechanics problem that an expert finds difficult to solve (e.g. a pendulum hanging from another pendulum, a top-heavy top). This is a well-known phenomenon in physics, but for some reason it was very strange to encounter it in a spiritual setting. We don't think of our gut reactions as something we have to "work through". They are, by definition, instantaneous. But as i've mentioned before, becoming the kind of person who reacts instantaneously in a godly way is a process we will spend the rest of our lives "working out with fear and trembling" (Phil 2:12). At least for me, its a process that has worked from the top down. Getting from the existence of an almighty, loving God to enough faith to confront death turned out to be comparatively simple. Getting to enough peace to confront the dentist has proven somewhat more challenging.
At the end of the study they explained that they were trying to assess the impact of reminding people about their religion and also of making them work through a difficult emotional problem before being asked a series of 'react to this situation' questions. They said half of the participants were asked about difficult subjects like death and the other half were asked about a routine experience like going to the dentist...
At the mere mention of the dentist, i immediately started to feel anxious even though the study was over and i wasn't asked to recount any specific experiences. I don't have a phobia or anything extreme, but the prospect of cavities and fillings makes me nervous. I fear not being able to understand my research. I fear having to uproot my family. And i am always nervous around traffic cops. But i don't fear death and i don't experience any of the feelings of aimlessness or helplessness that the survey was trying to elicit. In the moment, that struck me as odd.
There are certain types of knowledge that are easier to apply to big, universal things than small, everyday things. For example, the principles of mechanics are laughably simple, a few conservation laws and some formalism for counting energy. Their study reveals some profounds insights into the sorts of thing which can and can't happen in a classical Universe. And yet, it is very easy for a novice to write a specific classical mechanics problem that an expert finds difficult to solve (e.g. a pendulum hanging from another pendulum, a top-heavy top). This is a well-known phenomenon in physics, but for some reason it was very strange to encounter it in a spiritual setting. We don't think of our gut reactions as something we have to "work through". They are, by definition, instantaneous. But as i've mentioned before, becoming the kind of person who reacts instantaneously in a godly way is a process we will spend the rest of our lives "working out with fear and trembling" (Phil 2:12). At least for me, its a process that has worked from the top down. Getting from the existence of an almighty, loving God to enough faith to confront death turned out to be comparatively simple. Getting to enough peace to confront the dentist has proven somewhat more challenging.
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