Taking Care With Creation

Although it is not of direct practical significance, every culture seems to invest significant time deciding for itself where everything came from.  Usually this goes some way toward explaining how things are organized now.  Indeed, it has been claimed that your entire world-view can be derived from your creation myth.  That seems a bit of a stretch to me, but it is prevalent in our culture and has fueled (or at least been used to justify) a particularly divisive culture war.

There are at present two popular stories floating around our culture about how the world and its inhabitants came to be.  The first, largely extracted from the first two chapters of Genesis, is that one day the Creator said "Let there be light" and there was Light, and also Darkness.  In the subsequent five 24-hour periods, He created Sky and Sea; separated Land from Sea and created plants; made Sun, Moon and stars (emphatically lower case); populated the sky and sea with birds and fish; and populated the land with animals.  At the end of the sixth day He scooped up some dust, breathed His own breath into it and made Adam (lit. 'the Man').  He placed Adam in a garden paradise and gave him dominion over all the animals He had created.  Having established holy community and free will, on the seventh day God rested.  (Spoiler alert: Mayhem ensues.)

This version of events is commonly referred to as the 'Genesis' or 'Christian' version for obvious reasons.  It is contrasted to the 'Scientific' or 'Secular' version, which goes something like this:

In the Beginning there was nothing.  And then there was something.  The Big Bang brought time and space into being along with enough energy to make a Universe, but it was completely without form.  Not just chaotic, but Entropy = Zero.  However, the early Universe was quite hot and thermodynamics set in rather quickly.  It took a few millennia to get the fundamental forces sorted out and dispose of some extra anti-matter, but then most of the energy settled out into a large number of protons and electrons bouncing about in a truly enormous pressurized bath of photons.  ("Let there be light" indeed)  At some point, the photon bath cooled enough to let the protons and electrons combine into neutral hydrogen.  Within a couple minutes, the once-charged Universe suddenly became transparent.  The photon bath depressurized and became what we now observe as the Cosmic Microwave Background.  At this point gravity took over, gently intensifying slight over-densities of hydrogen into structures of all sizes: super-clusters, galaxies, stars, but not planets because you can't make a very interesting planet with just hydrogen.  As stars collapsed, gravity eventually tested the 'point-like' nature of atoms to extreme limits and ignited nuclear fusion.  By turning hydrogen to helium, stars can hold gravity at bay for billions of years.  But the Universe is very old.  Eventually the hydrogen supply gave out.  For a while, the dying stars burned helium to make heavier elements, but that process is much hotter and goes much faster.  In their death throes, stars collapsed inward until atomic nuclei were pressed into a solid mass.  The spring force from the rebounding gluons blew the stars apart, scattering heavy elements throughout the galaxy.  When the second generation of stars formed they were orbited by little balls of rock called planets.  On the surface of a planet named Earth, long carbon chains formed shells around tiny droplets of a polarized atom called water.  Because carbon has so many bonding sites, carbon-based molecules can make and break bonds with water with relatively little energy, making these droplets especially chemically active.  In time, these bubbles grew in complexity and formed rudimentary cells.  Once the cells started reproducing, the oceans quickly (in geological terms) became populated by those cells that reproduced and sustained themselves best.  Eventually, interactions between cells created communities that started to function like an organism.  These survived because they were more robust than single cells, although complexity comes at a price.  Once whole organisms could reproduce they continued the natural selection process, filling the Earth with every form of life that could be sustained.  The history of organisms in this planet is a long and winding one, but about 65 million years ago, an asteroid impact wiped out most of the large species and opened new niches for the small, furry animals called mammals.  A few million years ago, natural selection favored a group of mammals with opposeable thumbs, upright stance and large brains. Descendents of these first hominids became, among other things, the species Homo sapiens which has the rather unusual ability to ask questions like "Where did i come from?"

It is unlikely that anyone reading this is unaware of the battle between fervent defenders of these two creation stories.  Any scientist who is also Christian has to think carefully about this because he will have to defend his conclusion to one camp or the other.  After much debate from both sides, i have concluded the following:


1) Genesis is primarily a book about the origin of the Jewish people.  Probably first committed to text during the Babylonian exile, its opening chapters take much of the form of the Babylonian creation myth while turning the content on its head.  The Babylonian version has the Earth created by the god Marduk from the body of his grandmother Tiamat after defeating her army of monsters in battle.  Most of the text is devoted to the battle and subsequent creation of astronomical bodies as homes for various gods.  Regrettably, the Earth was not maintenance-free, so the gods created men to do the tasks none of them wanted to do.  Thus the purpose of man is toil and it is important to bring your sacrifices and taxes to the temple of Marduk situated for your convenience in downtown Babylon.

In a time when the best and brightest of Israel were being selectively re-educated by the conquering Gentiles, the writer of Genesis had to set the record straight before getting to the real business of introducing Abraham and family.  The Pentateuch is very clear that labor is a gift.  Toil is a result of the Fall and much of the promise of the Promised Land revolved around labor becoming a community-building experience and not being toil.  Since the Babylonian creation myth is highly stylized, we should expect Genesis 1-2 to be similarly poetic.  In fact, the Biblical creation story isn't much longer than my extreme summary of the secular account.  If the purpose of Genesis 1 was to provide a mechanistic account with any detail, we should expect it to be longer.


2) There is an overwhelming library of precise technical evidence to support the events reported in the 'Scientific' version, but absolutely no discussion of intent or agency.  To say the Scientific version proves that the universe has no intent or agency is extremely poor logic.  In fact, the Scientific version is much more elegant than the Genesis version from a technical perspective.  Rather than a proliferation of rules established ad hoc to make everything run properly, it has a handful of rules and mechanisms that automatically populate the various structures required.  The Maker who orchestrated such a 14-billion-year project deserves even more praise than one who slapped everything together in six days.

When this debate comes up in lab, which happens periodically, i like to hold up a sample mount sitting on my desk and ask how it came to be.  The correct 'technical' answer would be something like

A 3/16" copper plate was cut with a band saw to slightly larger than  6" x 3 1/2".  Two edges were made parallel using a vise carefully squared by running an edge-finder down its inner face and a 1/2" end-mill spinning at 4000 rpm.  The parallel edges were then set in the vise and the end-mill used to square the other two edges so that the final plate was 6.000" x 3.500" with 1 mil tolerance.  A #30 drill bit was then used to make 4-40 clearance holes centered 0.250" x 0.250" from the corners.  A #43 drill bit made pilot holes at the other positions indicated in the drawing which were finished with a 4-40 tap and light counter-sink.  The edges were then de-burred by hand with a 150/inch file and the plate washed in isopropyl alcohol to remove the machine oil.

The answer i almost always get is "You drew up what you wanted and [machinist] made it for you."  Both answers are correct, but they convey different information.  If i wanted to tell a non-techie how good our machinists are, i wouldn't go into tolerances and cutting techniques.  I would just make a pile of all the complicated things they've made for me and let the work speak for itself.  Similarly, if i wanted to teach the next generation of civil servants about the greatness of the Creator God, i wouldn't start by teaching them astrophysics.  I would enumerate the observable things that God has made and assert that they all reflect His glory.  If i could do it in a repeating poetic framework so they didn't forget large sections of Creation, even better.


3) There is a God who is active in modern times and who claims in no uncertain terms to be the Creator and the God of the Bible.  He is quite well known by many people and, frankly, the Scientific version of events sounds more like His MO.  For example, consider the problem of sin.  Adam and Eve are exiled from the Garden on page 3 of my Bible.  After messing about with various societal structures and lots of water as ways to address the brokenness of mankind, God makes a covenant with a man named Abram.  He promises Abra(ha)m that he will be the father of many nations and that through him all nations will be blessed. (Gen. 18:18)  That happens on page 13.  Abraham's family is then relocated, enslaved, multiplied, rescued and returned to the Promised Land.  They rebel, are rebuked and saved (repeatedly), demand a kingdom, try to rule without God (repeatedly), fall into politics for 200+ years, lose their kingdom(s), are captured, exiled, redeemed, re-instituted and conquered again.  878 pages and three millennia later, we get to "An account of the genealogy of Jesus the Messiah, the son of David, the son of Abraham." (Matt 1:1)  God's approach to making the Church is recorded in the entire Old Testament.  Do we really believe He made the Universe by fiat in six days?

Modern instances of divine creation fall broadly into two categories (based on my observations in healing ministries; i have no training in theology).  Either a created thing is broken and needs restoration or the Kingdom is advancing into new territory and there is an original creation.  Restorative miracles can happen very quickly.  People walk away from prayer sessions pushing their wheelchairs.  But whenever someone says "the Lord gave me a new [job, ministry, family, etc]" they can almost always point to a long list of things that didn't make sense at the time to see how this thing was woven together over a period of time.  Original creations generally take place in the framework of normal causality.  God doesn't seem to be phased by long-term processes; He just starts them earlier so the thing He wants to happen happens when He wants.  So i tend to believe the story about an Original Creation that brought causality into being and proceeded at its own pace according to the rules set forth at the Beginning.


4) If this blog had any readers, someone would say "Don't you believe the Bible is the Word of God?"  Yes, i do.  I also observe that God frequently speaks to us through song.  Hence, i feel no need to physically locate the valley of the shadow of death (Psalm 23:4).  Powerful imagery, not a real place.  Now, the Psalms are explicitly a hymnbook, but the Bible is littered with songs interspersed into otherwise historical accounts.  A quick search on biblegateway turns up Exodus 15, Deuteronomy 32, Judges 5, 2 Samuel 22 and Hosea 2.  Isaiah seems to spend half his time giving detailed warnings, naming cities and times, and the other half singing prophesies that are useless as historical predictions but carry timeless truths.  Guess which half gets quoted more.  Is it unreasonable to believe that this list includes Genesis 1?  Again, the Creation of the Universe is not the central story of the Bible, so it doesn't get much press time.  For a one page summary, it says more powerfully than any technical account that the Earth and the Heavens belong to the Lord, who is still resting (read: located) at the seventh day, the completion or head of Creation.  Compared to that knowledge, the technical details just don't matter.

Active Watching

New students to cryogenics are always in a rush.  When you start cooling a system, there are a set of time constants that govern how fast the various parts get cold.  They are usually measured in hours.  The temptation is to maximize your efficiency by going off and doing other work.  Certainly there's a place for that, but if you never let yourself watch your experiment all the way through, you will never really understand what's going on.  Physics means real things happening.  You can calculate time constants and try to optimize various goals, but in the end there is a real time which must be waited out.  It will not be exactly what you calculated.  Your exchange gases and vacuum ratings are real pressures and they almost certainly won't do in real life exactly what your model says they should.  So watch carefully when everything is working.  That way when they break you will know what is different.

Getting a new student to sit still the first time isn't very hard.  Once they learn how complicated their job is, they are usually happy to step aside and watch you do it for a while.  You may think they are learning patience from you, but as soon as they take the helm chances are they will go back to rushing.  The problem is they are used to doing homework, where progress occurs at the speed of thought.  As soon as they have enough information to paint a picture of what's going on, they act.  But they don't usually have enough information to make a good decision and they fear doing nothing when something is wrong far more than the reverse.

The same is true elsewhere although it isn't usually phrased that way.  Any time you try to change some piece of the world, there is a timescale in play that has nothing to do with your mental or physical speed.  Petitions take time to move through committees.  Children take time to grow up.  Sometimes things change all at once and you have to move fast to keep up; part of wisdom is learning when to act and when to sit.  The time to be seated is not just down time.  Its when you watch how the world works in your absence and what needs your action.  If you want to make a meaningful change, these are very important things to know.  And actually this is what science is all about, really getting immersed in the details and finding out how all the unregarded bits work.  Science starts with watching.

One of the risks of really watching things is that you notice the things that are broken.  And if you watch them be broken every day, you might feel inclined to fix them.  This can lead to a lot of extra work.  Sometimes its an easy fix; re-glue a joint, forgive a friend.  Other times you change the entire course of your life.  Maybe you find a persistent noise source in your microwave array and then spend the rest of your life studying the Cosmic Microwave Background.  Maybe there's a place right nearby where hunger and loneliness are rampant and no one but you seems interested in going there.  Whatever it is, being a watcher first means that when you do act there will be a reason for your action.

Active watching is terrible for your schedule.  I don't know how many times i've popped my head into lab with the intent to spend two minutes watching before going home, only to discover some problem and spend multiple hours fixing it.  In the long run i'm glad i discovered it; my experiment didn't break.  In the short run, i'm tired and wish i was at home.  On the flip side, i remember discovering one morning that my little boy could climb stairs.  I thought i had several weeks to get the baby gate ready.  I was somewhat late for work that day.  Whatever plans you have, active watching means giving the world permission to change them.

Building an intuition and learning to trust it can take years.  That was one of the most frustrating things about grad school for me.  Even if i understood a fridge on paper, i didn't react in the right way when something went wrong in the lab.  Or i thought the right thing and then did the wrong thing.  Over time, watching puts you in tune with the thing being watched so you act appropriately when there is no time to think.  In fact, it gives the world permission to change you.

Dust and Ashes

In the last year of any degree program, its time to start thinking about what comes next.  I'm definitely thinking about academia, but i'm not that interested in the lifestyle of a research professor.  I'm also interested in living somewhere rural.  That means i'm actively seeking out positions that other people in my place might pass up.  At some point in this search, i found myself thinking that i could pretty much do whatever i wanted with my degree.  And the next instant, the Lord was in my head saying "Dust and ashes".

...

Well, that was a bit sobering.  But not immediately clear.  Everything about this search, the degree, the job and ultimately physics itself is dust and ashes.  I'm vehemently not searching for fame and fortune, so why inject that tidbit of humility into the equation?  I think this is actually an instruction about how to use prestigious degrees effectively.  It is probably extensible to all noteworthy accomplishments.

Every book about homesteading has at least a paragraph about ash.  Ash is what's left when all the life has been lived and every last scrap of living energy has been spent.  Even the ever-hungry fireplace has rejected it, but ash is far from useless.  Fine ash is used to make soap, but the majority of a winter's ash build-up is tilled back into the fields in the spring to supply the next year's crop with much needed potash (farmer-speak for water-soluble potassium).  If fields are harvested year after year without getting a coating of ash back now and then, they stop yielding.  So having ash is very important, but you'd be insane to hoard up large piles of it.  Aside from the social awkwardness, stockpiled ash eventually becomes wet and turns to lye, which is toxic and extremely caustic.  Ash turned to lye in a charcoal grill will eat through the steel bottom in a season or two.  It will dissolve skin fairly quickly, but what makes it so dangerous is that it isn't immediately painful.  Fail to treat lye with respect and you can sustain serious injuries before you realize anything is wrong.  For this reason, it is important to sequester ashes in a safe place and disperse them back to the soil as soon as you can.

When you start a new degree program, you typically move to a new place and start a new life.  That life must be lived then.  Days are spent, whether well or poorly, and at the end of them there are no more.  A degree, in a sense, is what is left when all the life of the degree program has been lived.  There will be another life afterward, but you can't save up this one to live later.  So the question is what to do with the degree.  One popular answer is to put it on the wall and let everyone know about it.  Even if you don't openly flaunt it, there's always that temptation to pull the PhD card.  Just a subtle reminder why your opinion is important.  Physicists are notorious for this even when the debate isn't strictly about physics.  While it often wins arguments and earns respect of a sort, this is toxic to the kinds of relationships that will grow Life in your new life.  Worse, the toxicity isn't immediately apparent.  It may be some time before you start to wonder why relationships haven't deepened.  The better approach is to take everything that degree represents: work experience, classes, extracurricular awards, and till it under so that only you know about it.  Of course, share your knowledge freely (when asked) and do everything to the best of your ability, but let that flow out of who you have become instead of trying to transplant a piece of your previous life.

As my program comes to an end, it is important to finish strong so that i have plenty of ash for the next Spring of my life.  It is also important to leave things in such a way that my presence is not required.  By training my replacement, writing documentation and cleaning up the lab i recognize an Autumn, a time to harvest papers and prepare for the Winter between-time ahead.  On my resume, there will be a large section about a PhD with Prof. Famous at Prestigious U.  That is a natural result of building a resume (another Autumn activity), but the goal should be to sequester it there.  In interviews, i should be talking about what work they want done and how i am prepared to do it well.  Just as last year's growth is pruned back and burned to increase this year's yield, it is better to enter a new place as an unknown and become known for the work done there.

I have been greatly blessed in this season of my life, so its closure should yield godly ashes.  (Presumably the way to identify God's ashes is to till them under and see if the enriched man yields more godly fruit?  Hard to assess as the man in question.)  Anyway, the point is they are God's ashes.  While very useful, they are dangerous in a subtle way and they are not mine to put on display or to cast about carelessly.

Physics Exam Tips

A while back, i discovered that almost none of the undergrads in my local Chi Alpha knew about a large amount of education research that i consider pretty basic.  Combing over advice emails i had sent to various students, i assembled a list of things i think every student entering a technical field should know.  This was first published by Glen Davis at http://glenandpaula.com/wordpress/.  I'm moving it here so i can get at it more easily when i have students again.

1. From the first day of class, sit in the front of the room toward the center. At least one study has shown that students who sit in the front are 2–3 times more likely to get an A and 6 times less likely to fail than students sitting in the back even when seats are randomly assigned on the first day of class. We can debate why this is so all day, but it is so, so take advantage of it. (By ‘the front’ i mean the first ten or so rows of Hewlett 200.)
2. Be sure to get plenty of sleep the two nights before the exam. Of all the bad conditions you could be in going into a physics test, being tired is probably the worst one that is legal. Studies indicate that the second night before the test is even more important than the night immediately before. A clear, thinking, creative mind is your single greatest asset for any physics you might encounter. If you have been keeping up with the class, getting two full nights of sleep is probably more important than any amount of studying you might do during those two days.
3. That said you will probably want to do some studying. If you haven’t already, I highly recommend finding someone else in the class to study with. Go over problems together. Go into the later problems in each chapter and pick some that you’re not sure you can both do. Taking an exam well is very similar to teaching the grader how to do the problems, so even if you are teaching a friend how to do something you already know, you are preparing for the test. If you both (or all) get stuck on something, contact a TA.
4. Read every problem at the beginning of the test. Your mind will continue to process problems you are not looking at, provided it is awake. (See Tip 2) Studies show that you are best served loading all the questions into your brain at the start to give yourself maximum time to contemplate. If you get really stuck on a problem, leave plenty of space and move on. Odds are you’ll have better insight when you come back to it.
5. DON’T PANIC. Attempt every question. This sounds really obvious, but we occasionally get blue books that have a few scribbles labeled ‘Problem 1′ and nothing else. As best we can tell, these students are looking at the first question, panicking and staring blankly at the paper for forty-five minutes or just walking out. This is something worth practicing to avoid. If you find yourself in a panic: stop, look away from the paper while slowly counting to ten. If you are feeling calm, you can go back and draw a diagram or write down some possibly relevant equations. If you start panicking again, repeat Steps 1 and 2. If you are not feeling calm, turn a couple pages and start the next question. Things will look better when you come back to this one. Trust me.
6. Now for a few tips on getting the most [points] out of your graders. Grading a midterm takes 4–5 hours. As much as we try to assess each of you according to all the knowledge of physics you demonstrated, we are going to get tired and eventually parts of our brains are going to go on autopilot. If your answers are in clearly marked boxes (preferably near the left side of the page) and they are right, there is a reduced chance of any error in your work being marked off. If an answer is wrong, but it’s in a box near the left side of the page immediately below the work that produced it, then it is very easy for us to find the one little error and give you most of the points. I know having all the answers in one box at the bottom of the page feels concise, but if one of them is wrong we have no idea where on the page to look for the mistake. On a related note, it is better if you work one part of a problem and then work the next one below it. Believe it or not, grad students can get confused if part c is to the right of part b instead of below it. It’s silly, but after a few hours of grading that’s the way we are, so you might as well not let it hurt you. As a general rule, each line on the page should only have one equation or statement on it. (pictures excluded) You may use up more pages that way, but there’s no shortage of blue books.
7. Whenever possible, draw a picture. Not only will it help you think, but it also helps us know what you were thinking. If you are not absolutely confident in your solution, a minute spent drawing a decent picture is probably worth it in terms of partial credit. Too often I’ve suspected a student knew more than their answer indicated, but they didn’t leave a good record of their thought process so I couldn’t grant partial credit. And that makes me sad. (Organizing graphics are also great antidotes to panic, see Tip 5.)
8. When you get an answer, check that it makes sense. Negative lengths and times are often indicators that you’ve made a mistake, as are e.g. megaCoulomb charges and kiloAmp currents. If this happens to you, go look for the error and fix it. If you can’t find it, let us know that you don’t like the answer and why. One of the easiest ways to tell that someone is lost is if they give you a non-physical answer and don’t blink. As a physicist, it is much easier to grade leniently if a student indicates that they understand why the result of their calculation can’t be right. If nothing else, the grading rubric often has a point designated just for having a result that could be true. You’ll at least get that.
9. It is well known that having good handwriting improves the attitude of those grading your exam. What is less well known is that having tiny handwriting can hurt you. Often what is perfectly legible to you while you are curled up with your nose 12 inches from the paper makes our eyes hurt after the third or fourth hour of grading. Obviously this vastly reduces the incentive to hunt for that tiny little math error you made in part a. This is not a small matter. I, for one, tend to get a migraine when I bend over small text for too long. So imagine a three hour migraine and then gauge the incentive to just mark you off so I can stop looking at your paper. Find a test that you have taken recently. If you (or better, a friend) can’t clearly read your text at arm’s length, you might consider consciously writing larger on all tests from now on. Grading fatigue isn’t limited to physics TAs.

Building A Model Of Global Warming

A good friend whose technical credentials i respect recently suggested to me that the reason all the climate scientists agree about global warming is that they are all running the same model that has never been independently developed more than once.  I mentioned this to another technically trained friend who said "Wait, you believe in global warming?"  Until this point, i have kind of figured that the greenhouse effect was probably real because i (mostly) trust the peer review process and it seems like most of the people with the expertise to do so are saying that it exists.  That's not enough anymore.  So here is my attempt to model the atmosphere using the good old physics standbys of rough simplification and convenient assumptions.

(This really is a log of my thoughts.  Its not the shortest path to the answer.  In fact it is much longer than i thought it would be.  Calculation 1 is...not my best work.  I tried to take a shortcut that cost me a couple of stupid assumptions and ended up not being any shorter.  But i found a lot of interesting things along the way so i left it intact.)

First some rules: As of this writing, i have absolutely no training in climate science or geophysics and i have not consulted with anyone in those fields.  I will build my model using whatever physics or chemistry seems best to me as i go along.  Since the goal is to get a non-expert opinion, i will not reference any text making any claim about climate change.  I will source all physical constants from WolframAlpha; if i need another source i will stick to standard reference texts and (inter)national standards offices and i will cite them.

Okay, here we go.  The first thing we need is a model for how the Earth heats up and cools down every day.  Heat comes from the Sun.  I've heard various solar luminosities quoted, but typing (Solar Luminosity)/(4*pi*(1 A.U.)^2) gives me 1368 W/m^2.  Radiation that gets blocked by the atmosphere contributes to the planet's heat load but not to luminosities quoted by ground-dwelling solar enthusiasts (who usually estimate 1 kW/m^2), so i'm going to use my number.  Since the Sun only illuminates a cross-section of the Earth, i type (1368 W/m^2)*pi*(Earth Radius)^2 and get 1.748x10^17 W or 174.8 petawatts as the incident solar energy.  Probably this is high since the Earth is partly reflective, but it shouldn't be radically off.

On the cooling side, i assume the Earth is a black-body radiator with a constant surface temperature.  Obviously the poles are colder, but hopefully this cancels out my assumption that they were black-body absorbers.  The power radiated per unit area for a black body is the Stefan-Boltzmann constant times the temperature to the fourth power.  The area in question is now the surface area of the Earth, 4*pi*R^2.  Typing ((174.833 PW)/((Stefan-Boltzmann Constant)*4*pi*(Earth Radius)^2))^(1/4) gives me 278.68 K, which is 42 °F, a bit chilly but certainly a common surface temperature.  Looking good so far.

Before going on, i need to know some wavelengths so i can get into a little chemistry.  The energy of a photon can be expressed as the Boltzmann constant (k) times its temperature (T) or as Planck's constant (h) times its frequency (f).  In addition, the frequency of any wave is its speed (c) over its wavelength (l).

E = kT = hf = hc/l rearranges to l = hc/kT.

A little math on the black-body intensity curve (formalized as Wien's Displacement Law) tells us that a black body radiates most of its power at 3-10 times its thermodynamic temperature with a peak at 5*T.  For a 280K planet, this makes the wavelengths of interest 5-17 microns with the peak at 10 microns.  This is indeed a good chunk of the middle-to-deep infrared zone.  Out of interest, i do the same thing with the surface temperature of the Sun (5780 K) and find that most of the power is in a band around 250-800 nm with the peak at 500 nm.  That's the entire visible spectrum plus a bit of the ultraviolet range.  Thus, sunsets are red, the daytime sky is blue and we have to wear sunscreen to block UV but we don't worry too much about solar x-rays.  That's a good cross-check.

With wavelengths in hand, we now need to see how carbon dioxide changes the picture.  This turns out to be tricky.  A spectrum taken by Dow Chemical Company in the 1960s (before anyone was thinking about global warming) and kindly digitized by NIST (National Institute of Standards and Technology) shows that CO2 has massive absorption peaks around 15 um and 4.3 um.  A 10 cm path through 200 mmHg of CO2 has an absorbance of 0.01 for the infrared light above 17 microns.  Between 5 and 13 microns the absorbance is more like 0.005 and right around the peak intensity of 10 microns, the absorbance appears to be zero.  This doesn't look good for global warming.  CO2 has some absorbance, but it gets progressively smaller the closer you get to the Earth's peak radiation.

Absorbance is kind of a weird unit, so it needs explanation.   For a monochromatic beam of light of intensity I_in traveling through a sample, Absorbance = LN(I_in/I_out).  The advantage of this arrangement is that if you double the thickness of the sample, the absorbance is doubled rather than having to square a transmission ratio.  Absorbance is always positive and higher values mean more blocked light in the way you would intuitively expect.

If the Dow Corning sample were made 1 meter square (but still 10 cm thick), it would contain (1 mole / 22.4 liters) * (200 mmHg / 1 atm) * (0.1 cubic meters) = 1.17 moles of CO2.  I want to find out how much CO2 would be needed to transmit 1/e of the light so i can calculate the optical depth of the atmosphere.  I_out/I_in = 1/e implies an absorbance value of 1.  So, for example, if 1.17 moles/m^2 has an absorbance of 0.01, the optical depth at that wavelength is 1.17/0.01 = 117 moles/m^2.  If the sample absorbance is 0.005, the optical depth is 1.17/0.005 = 234 moles/m^2.

So how much atmosphere is there and how much CO2 is in it?  The pressure at sea level is 14.7 psi.  Most of that is N2 gas at 28 g/mol.  Typing (1 atm) / (28 grams/mole) / (1 gee) gives me 369,000 moles/m^2.  (Aside: I love that we have standardized on 'gee' as the name for Earth gravity to distinguish it from grams in our shorthand.)  If the CO2 concentration were 1 part per million (ppm), we would have 0.37 moles/m^2 of CO2 and we wouldn't be worried.  The National Oceanic and Atmospheric Administration (NOAA) says that the concentration in recent years is around 390 ppm with some seasonal variation.  (The earliest record is 315 ppm in 1960).  This gives us about 144 moles/m^2 of CO2 over our heads (or 116.5 moles/m^2 in 1960), which is about one optical depth for deep IR radiation.  Interesting...

*************************************(Calculation 1: Playing Around)*************************************

I need to stop and make a model of the atmosphere as a whole.  Oh wait, no i don't! The International Organization for Standardization (ISO) publishes an International Standard Atmosphere (it isn't free, but many free calculators are available online).  To first order, i will assume that blocking more infrared radiation warms up the entire atmosphere evenly without changing the gradients between layers.  This obviously isn't true for large temperature changes, but if this calculation ends in even a 10% change we have much bigger problems.

Since we have some numbers handy, let's test the global warming hypothesis by comparing 1960 with now (~2010).  On average, radiation emitted half an optical depth or less away from space escapes.  Anything emitted from deeper in the atmosphere is blocked.  Adding more CO2 moves the emission layer upward (although not uniformly for all wavelengths).  The density profile of the atmosphere ensures that the ground is always much warmer than the stratosphere.  As radiation is effectively emitted from higher up, the ground will get warmer.  Or at least that's a theory.  Let's try that on with some numbers.

I'll work my way up the energy scale, starting from the deep infrared where the optical depth is 117 moles/m^2.  Half of 117 is 58.5 moles /m^2.  In 1960, deep infrared radiation could penetrate 58.5/116.5 or 50% of our atmosphere.  Since atmospheric pressure is determined by the weight of the air overhead, i will look for a height where the pressure is 0.50 atm.  This turns out to be 5500 meters above sea level.  The calculator tells me that the temperature at this altitude is 252.4 K.  In 2010, the radiation point was at 58.5/144 = 0.406 atm.  This occurs at 7000 meters where the temperature is 242.65 K.  If this were the absorbance across the entire spectrum, each of these levels would get fixed at 278.7 K in their respective years with everything else warming up to match.  In this case the Earth's surface would have warmed by 9.8 °C in 50 years.  The temperature in 1960 would be 312.4 K = 102.6 °F, so its a good thing this isn't the case.

Oddly, when i consider the region of lower absorbance (depth = 234 moles/m^2), i get roughly the same result.  Now the 1960 radiation surface is at sea level (288.15 K on the atmosphere calculator) and the  2010 radiation surface is at 0.812 atm -> 1720 meters -> 277.0 K for a temperature increase of 11.1 °C.  So let me deal with the absorption peaks.  Assuming a sample absorptivity of 0.2, the optical depth is 1.17/0.2 = 5.85 moles/m^2.  This means i'm looking for the temperature at pressures of 0.05 atm in 1960 (20500 m -> 217.15 K) and .0406 atm in 2010 (21810 m -> 218.45 K) for a difference of -1.3 °C.  Bizarrely, above 18000 meters (216 K), the temperature starts to rise again.  The peaks are actually much more absorptive than this, and the scaling down to a surface temperature doesn't work with an inversion.  These regions are going to have a small and unclear contribution anyway, so i'm ignoring them for the rest of this calculation.

This leaves me with some wavelengths with minor absorptivity which would generate a 10 °C difference in the surface temperature and some wavelengths with no absorptivity where adding more CO2 has no effect on the apparent surface temperature.  How do i weight them?  Since we're really worried about total power emitted, i'll weight each region by the integral of the Planck black body intensity spectrum over the frequencies they represent (Wikipedia "Black Body Radiation" for more details, but i'm treating this as common knowledge)  A few minutes with Wolfram Alpha* tells me that for a 280 K planet, 40.0% of the power is radiated at >16.5 microns, 11.4% in the first absorption peak at 14-16.5 microns, 17.6% in the 'greenhouse' region at 11-14 microns, 19.0% in the 'transparent' region at 8-11 microns and 11.6% in the 'greenhouse' region at 4.5-8 microns.  That adds up to 99.6%, so i ignore the wavelengths below 4.5 microns.  (One possible flaw: the Dow Corning spectrum only goes up to 22 microns; 23.5% of the power is radiated above that wavelength.)

*The actual formula to generate a weighting factor for a-b microns is:
(15/pi^4)*Integrate[x^3/(e^x-1),{x,50/b,50/a}]     
(50 microns = 280 K, 15/pi^4 makes the 0->inf integral equal to 1).

Even assuming the deep IR region remains a greenhouse region above 22 microns, i'm still going to assign it an additional weighting factor of (252.4/288.2)^3 = 0.672 because the radiation it emits is at a lower temperature.  The third power is used because that's the exponent for radiation per unit frequency.  So my weighting factors are now 0.4*0.67 = 0.269 for the deep IR region with a 9.8 °C increase, 0.176+0.116 = 0.302 for the near IR greenhouse region with a 11.1 °C increase and 0.19 for the transparent region with 0 °C increase for a combined weighted average of 7.87 °C increase over the past 50 years.  (Housekeeping: If we assume that CO2 is completely transparent to wavelengths above 22 microns, the above calculation gives a 7.36 °C increase)

*****************(Calculation 2: What I Should Have Done From The Beginning)******************

Wow! That's a huge effect.  In Ohio, 7.5 °C is the difference between a hard freeze that kills next year's pests and a ruined harvest.  I'm not really sure i want to believe a result that large that depends so heavily on a published standard atmosphere and hand-wavy assumptions.  Given the data i've already amassed, what if i do a straight power balance?

If the atmosphere is x optical depths thick in a certain range of wavelengths, then it transmits e^-x of the light in that range.  That means it absorbs 1-(e^-x) of the light.  That energy will be re-emitted fairly quickly.  If x is fairly small, half the re-emitted light will go upward to space and half will return to the surface.  So the additional power loading on the surface is (P_emitted)*(1/2)*(1-(e^-x)).  For large x (the absorption peak), i'm going to assume 2/3 of the energy returns to the surface.  One reason for this is that if i divide the atmosphere into many opaque layers and model the radiation between them, each layer sends 1/2 * 1/2 = 1/4 of the radiation from the previous layer back to the surface.  1/2+1/8+1/32+1/128+... = 2/3.  Alternatively, i could just assume that a very opaque atmosphere radiates from its coldest point, which the ISA tells me is 216 K.  Turns out (216/288)^4 = 0.316 ~= 1/3.

I can already see that this method is going to lead to a very warm planet even in 1960.  Up to now, i haven't accounted for anything that reflects visible light back into space which would reduce the overall power that needs to be radiated away as IR.  The technical term for diffusive reflection is albedo, but i can't find any references to Earth's albedo that don't ultimately link back to journals about climate science.  (Astronomers also use albedo to describe planets, but any measurement of Earth's albedo from space quickly gets snapped up by climate journals, which violates the rules of this exercise.)  Since it doesn't affect the question of recent warming, i'm going to pick 0.3 as the Earth's average reflectivity (so 70% visible absorption), which is the most common value i see on the web.  One could imagine that changes in surface temperature could change the albedo, creating feedback effects.  Warmer oceans mean more reflective clouds, but less reflective ice.  Since these effects are very hard to model and presuppose the victory of the warming hypothesis, i will ignore them.

This leaves me with the equation:

(Stephan-Boltzmann)*T_surface ^4 = 0.7*P_incident/Area + (SB)*T^4 * Sum[*f*(1/2)*(1 - e^-x)]

where f is the fraction of energy emitted in bands with optical depth x.  Using the values found in Calculation 1, i get the sum as 0.260 in 1960 and 0.285 in 2010.

Terms In The Sum:
Deep IR                    f = 40%       x = 117/117 in 1960      x = 144/117 in 2010
Shallow IR                f = 29.2%    x = 58.5/117 in 1960     x =   72/117 in 2010
'Window' Region       f = 19%      x = 0 in 1960                 x = 0 in 2010
Absorption Peak       f = 11.4%    Use 2/3 in place of (1/2)*(1 - e^-x)

Plugging these back into the power balance equation (recall P_incident = 1.748x10^17 W and Area = 4*pi*R_Earth^2), i get a surface temperature  ((0.7*1.748x10^17 W/(4*pi*(Earth Radius)^2)) / ((Stephan-Boltzmann Constant)*(1-0.260)))^(1/4) of 274.8 K = 35.0 °F in 1960 and 277.2 K = 39.3 °F in 2010 for a net change of 2.4 °C or 4.3 °F in 50 years.  As far as i know, this is mostly in line with current claims by climate scientists.  My overall temperatures are a little low, but they're pretty close and i'm ignoring the greenhouse effect for water (which NIST has digitized here), methane and various hydrocarbons.  I'm also ignoring tidal action, volcanism and probably a whole host of minor heat sources.

(Housekeeping: If i assume that CO2 is transparent to IR above 22 microns (f = 16.5% for deep IR), i get Sum values of 0.186 in 1960 and 0.2015 in 2010.  This give temperatures of  268.3 K = 23.4 °F in 1960 and 269.6 K = 25.7 °F in 2010 for a change of 1.3 °C or 2.3 °F in 50 years.)

***********************************************************************************

I have a vague memory of seeing somewhere in the news a claim that the average surface temperature of the Earth has raised by 1-2 °C since we started recording it.  If you're reading this and you want to know the details, you should go talk to a climate scientist; they've spent decades on this while i've spent a few hours.  Thinking about other heat-movers, the biggest thing i've left out is convective cooling.  Since the vapor pressure of water changes rapidly with temperature, i could imagine convection currents increasing as the ground/sea warms up, carrying heat above the greenhouse absorbers.  That would have a stabilizing influence, but "convection bubble driven by warm moist air" is meteorologist-speak for "giant storm".  Right now, i'm in favor of anything that causes more rain to fall on the Midwest.  In the long run, i'm not convinced that dumping that much power into hurricanes and thunderstorms is a net gain.

If you think the climate scientists are all toeing a party line, please consider me as an outside adjudicator.  I am a politically and socially conservative, scientifically-trained Christian who can't possibly have been indoctrinated into any sort of grand cover-up because (1) i disagree with almost all of the political and moral statements made in the name of global warming and (2) i haven't been paying enough attention.  I believe the world will end when God is good and ready to end it and not a moment before.  However based on the above calculation, i believe that the science behind the greenhouse effect is sound.  We will not end the world, but we are changing it.

(Aside: I'm all for arguing over the implications of climate change.  For that, please address your complaint to the relevant politicians and activists.  It might be helpful to know how a 1 degree change affects various ecosystems, but i have no idea how to model that.  Probably its hard to separate the warming component from other variables which are more obviously human-driven like toxins and GMOs.)

I'm curious now about the 'anthropogenic' question.  Is the increase in CO2 man-made or natural in origin?  The total recorded increase in the carbon content of the atmosphere is (144-116.5 moles/m^2)*(12g/mole)*4*pi*(Earth Radius)^2 = 169 billion tons.  (The oxygen was already in the air so its mass shouldn't be counted.)  WolframAlpha helpfully tells me that this is "~1.7 x estimated mass of all oil produced since 1850 (upper limit)" although who knows where that information comes from.  Looking around the internet, sites like this one seem to agree that the average global oil consumption in the past 50 years is about 3 billion tons per year for a total of 150 billion tons.  (I can't find an authoritative source that isn't buried in government-speak, but the exercise is over so i can bend the rules)  A lot of petroleum ends up as plastics in landfills, and even the oil that gets burned sheds a little mass as water (which promptly rains out).

On the other hand, we are burning forests at a pretty spectacular rate, which might make up the difference.  Conservationists on the Internet seems to agree on "1.5 acres/second" as the current rate of rainforest destruction.  That works out to 4.6e7 = 46 million acres per year.  A search for timber yield suggests that lumber and paper companies are getting about 100 green tons per acre when they clear-cut U.S. forests.  (Unsurprisingly, no one is publishing how much money they're making by logging rainforest.)  As a rough guide, this suggests that 4-5 billion tons of rainforest are destroyed each year.  That's more carbon than shows up in the atmosphere, but one could imagine scenarios where most of the mass ends up buried or converted to lumber (which is ultimately land-filled) instead of burned.  Anyway, it looks to me like we're emitting carbon at a rate at least comparable to the observed increase.

Given the other unexpected coincidences that happened during this exercise, i'm not going to say that means we are definitely the cause of global warming.  Apparently plankton absorb about 10 billion tons of carbon from the air each year, then die and carry it to the bottom of the ocean.  Since the CO2 concentration continues to rise, there must be other sources that offset this.  So i'll say with some confidence that i think additional atmospheric CO2 is causing a global increase in temperature, and with somewhat less confidence that we are the cause of the additional CO2.
 
Well, that took longer than expected.  In the interest of scientific honesty, i'm going to post this before asking a climate scientist to evaluate it.   I think the blog format lets me comment on my own posts, so we'll see whether this model is even close to theirs.  If so, then yes the model can be independently derived, even by a bumbling physicist like me.

A Light In The Darkness

The very first hike i went on as a Boy Scout was to Daniel Boone National Forest in Kentucky.  We had scheduled a 12 mile course to take 5-6 hours.  It was a beautiful April day, cool and bright, a great day to go hiking.  Unfortunately, a blizzard back in February had brought a number of trees down across the path and then, on this first thaw of the year, melted all at once.  When we weren't hacking through branches we were building bridges across streams whose banks couldn't be reached with a long pole.  'Be prepared' is all well and good, but no one thought this hike would require machetes or hundreds of feet of rope.  Of course, it takes about 5 minutes of bridge planning before a bunch of bored 11-year-olds try to wade across.  It turns out streams have steep banks even when they're not visible.  To make matters worse, many of the trail markers were on downed trees or just washed away, making navigation dicey at times.

After 12 hours of this, we crested the last ridge and stopped to regroup.  With a mile to go and about half an hour of daylight left, we split into groups of kids who could travel at the same speed; when traveling at night, being lost isn't nearly so dangerous as being alone.  Naturally, the Senior Patrol Leader got stuck leading all the new kids to safety.  This guy was one of my childhood heroes, but he was having a rough night.  At the glacial pace of exhausted children, he guided us by fragments of white paint and gut instinct well into dusk.  But eventually the moonless night settled on us and there was just nothing to go by.  We should have been home hours ago; no one in our group had brought a flashlight.

But somebody had.  Off to one side of us, someone kept swinging a light right in our eyes.  The weird thing was, the light was moving around us much faster than we could walk, it only appeared intermittently and it didn't seem to be going in a straight line.  When you're trying to guide by night vision, a light in your face is more than a small annoyance and we learned a lot of new vocabulary from our SPL as he tried to avoid looking at it.  Finally when we couldn't even see each other, we formed a human chain and turned toward the light.  Even if the light-bearer was lost too, at least we wouldn't be alone.  After a very long time (~10 minutes), we emerged in a paved clearing.  There were three older boys there and a kid my age with a MagLite.  His dad had been the leader of the fastest group and they had reached the end point well before dark.  Only one car had been left at the trail-head, so the dads had driven back to base camp, leaving the boys with the light from the glove box and instructions: "Stay here and tell anyone who comes that we'll be back."

In other circumstances, the kid with the flashlight had no credentials as a guide.  He was a squirrelly little guy and this was his first hike as a Boy Scout too.  All he knew was that his dad was coming back here, he had a light and out in the miles of utter darkness all around him were a bunch of lost people.  So he turned on the light and swung it through the trees.  Sort of.  His attention span was pretty limited and the older boys kept yelling at him to stop wasting batteries.  No one came for a long time so he kept turning off the light until he got bored again.

As it turned out, almost no one heeded the light.  I learned much later that one of the dangers of navigating in a forest is that your sense of direction changes much faster than you realize.  If you don't have a distant fixed object to go by, it takes great skill to walk in a straight line just by looking at the trees.  And that's in broad daylight.  What is far more likely is that you will build for yourself a local reference frame with little bearing on reality and put much more confidence in it than is justified.  In those circumstances an external fixed reference that you refuse to acknowledge will appear to drift wildly around a shifting world that you have convinced yourself is stable.  Whatever path you walk, it is important to have a sense of the bigger geography around you so you can decide what ought to be the anchor point(s) of your personal world.  If the light of your world seems inconsistent, you should really think carefully about your local heading.

Eventually, of course, the convoy returned.  Trucks fanned out across the clearing and pointed their high beams into the woods.  Groups of boys appeared from every direction, soaked to the skin and nearly sleeping on their feet.  We didn't actually lose anyone that night, but we'd been lost for less than an hour.  The cost of ignoring the flashlight was a half mile or so of extra walking.  In the grand scheme of things, we failed at a very short navigational challenge and got off fairly light for being unprepared.  A lot of people who ignore their guiding light are nowhere to be found when rescue comes.

When the headlights turned on, it was obvious that that kind of power could only be emitted by a father or a ranger.  All sensible boys turned toward them, but found that they had wandered a long way from safety.  I wonder had the flashlight been more steady how many of us would have been waiting there when the dads returned.  Someday our Father will return with his high beams on.  In the meantime, we have all the problems that come with wielding a flashlight: limited energy, unfocused output, low visibility.  Holding up the light takes effort and there are people yelling at us to turn it off.  Even so, it is vitally important to keep the light turned on and pointed out into the darkness.  There are an awful lot of lost people out there.  Just try not to shine it in their eyes.

No Hidden Variables (Spins Are Not Coins)

I've been dealing with quantum mechanics for a while now and most of the time i feel like i'm pretty comfortable with the basics.  I know wave-functions are fundamentally different from particles even though they sometimes get used interchangeably.  I'm okay with bras and kets and using operators for things like position and momentum.  But every once in a while something reminds me that i'm still glossing over a lot of the weirdness in my head.

There's a famous argument between Einstein and Bohr about wave-functions.  Basically, Einstein argues that the Heisenberg Uncertainty Principle doesn't mean that particles don't have definite positions and momenta, just that we can't measure them.  (Search "Einstein-Podolsky-Rosen" or "EPR Paradox")  The consensus of most of the physics community is that Bohr successfully defended the indefinite nature of quantum mechanics through a series of thought experiments.  (Einstein's assumptions are referred to as 'local reality', giving Bohr's alternative the unhelpful moniker 'non-reality'.)  Thought experiments are all well and good if you already have your Nobel Prize, but a Prof. John Bell of CERN actually proposed a class of experiments to distinguish between a fundamentally classical world and a fundamentally quantum one.  Many of the experiments are quite subtle (and therefore easy for the layman to ignore), but one of them really bothers me.

Suppose you have a black box filled with spin-0 particles which occasionally decay into a pair of spin-1/2 particles.  Each pair will necessarily go in opposite directions (conservation of momentum) and have opposite spin (up or down, conservation of angular momentum).  Until they reach some outside observer, they are 'entangled' because the result of one spin measurement will depend on the result of the other.  This type of system has been constructed and indeed if a pair of observers agree what axis they are using before-hand they always get opposite results.  If Observer 2 rotates his axis by 90 degrees, his measurements are now completely uncorrelated to Observer 1's.  But that's okay; if you had two random vectors pointing in opposite directions, knowing the x-component of one would tell you nothing about the y-component of the other.

Where things get weird is when you let the measurement axes float around.  Suppose you do the same experiment, but for each decay Observer 1 uses a vertical measurement axis while Observer 2 randomly selects an axis which is either vertical or rotated by x or by 2x.  Later they compare their data, only then revealing the relative angle between their measurements.  If the angles are aligned, they get 100% correlation.  If misaligned slightly, the correlation is still large but not 100%.  If you imagine the spins as classical vectors whose orientation is merely unknown (all you can measure is 'up from horizontal' or 'down from horizontal') then the chance of a rotation by x degrees pushing the result through horizontal is x/180.  The chance for a rotation of 2x is 2x/180.  So if the results of measurements skewed by x are correlated 1-a of the time then measurements skewed by 2x will be correlated 1-2a of the time provided x is smaller than 45 degrees.  But if the spins are quantum spins, then you need to calculate the wave-function overlap, which works out to cos(x).  For small x, this makes the correlation for measurements skewed by x equal to 1-(1/2)*x^2 == 1-a, but for a skew of 2x, it is 1-(1/2)*(2x)^2 = 1-4a !  Doubling the angle decreases the correlation 4-fold.

To get how crazy this is, imagine you had a pair of very weighted coins which flipped heads 99% of the time.  If you flip one of them a bunch of times, the results are 99% correlated to 'all heads'.  Now you flip the pair of them a bunch of times and record how often they show the same side.  You would expect the correlation to be at least 98% since the combined incidence of 'not heads' is only 2%.  But if you're flipping quantum mechanical coins, you could get only 96% correlation.  They don't match each other more often than they collectively don't match some third reference flip.  This is a sign that they don't have a definite direction, even a hidden one, until you look at them.  Only the correlation can be measured.

The ideal of 'realism' (that uncertainty doesn't prevent unknowable variables from existing) is closely linked to the idea of 'counterfactual definiteness', the idea that an experiment you didn't perform still has a definite result.  In the case of the coins, this would mean checking that either coin matches 'heads' rather than checking that they match each other.  For quantum spins, counterfactual definiteness says that even though you didn't measure the entangled states along parallel axes, they would have had opposite spins if you had.  Non-reality says that question is meaningless, even though it can be answered in the abstract with no uncertainty.

Why Do We Hold Final Review Sessions

It is fairly well established now that the overview lecture before a final exam does absolutely nothing for students who have been keeping up with the class.  In fact it tends to lead them into a false sense of confidence that may make further studying difficult.  Yet every class i've TAed held multiple sessions where a pair of TAs tried to treat the entire 300-500 person class like a very large section.  Nobody ends up doing much physics and many of the questions boil down to "Can you tell us what's on the exam?"  (Since the professor was once a TA himself, he hasn't even discussed the exam with us.)  If i were running the show, things would be done differently.

The Goal: The only way to learn physics is to do physics.  We want to encourage students to form small groups and do problems together.  We want to minimize getting stuck but encourage doing tricky problems.  The experience should be made enjoyable so they can keep doing it for multiple hours without their brains locking up, which tends to happen around Hour 1 of a traditional review session.

The Space: I'm thinking a big open space, maybe a ballroom or open gallery, with lots of little tables seating no more than 6-8.  There's plenty of space to walk between the tables in straight lines and the occasional double-sided whiteboard scattered throughout.  Nearby, we'll need two or three smaller rooms (maybe seating 30-50?) set up for impromptu lectures.  A central microphone might be nice if you want to announce something to a whole class, but it could easily become more annoying than useful.

The People: All intro physics sections will be invited with students coming and going as they please.  We'll put each class in a different section of the room, but all TAs will be wandering around ready to answer any question from any section. The idea is when you do get stuck, we should minimize the time between raising your hand and the arrival of a TA.  Professor attendance might be nice for a few hours, but optional.

The Problems: By this point in the class students have several past exams, practice exams and old homeworks to go over.  They should be encouraged to bring study material but blank copies of these will be available on request.  I've always thought the idea of making students make their own crib sheets was ridiculous, but it might be an effective learning tool if they could get TA guidance at a session like this.

The Tables: Small.  I'm imagining round, but experiments with a group working at each end of a rectangular table might be worthwhile.  All tables will have extra pencils, scratch paper and water bottles.  Since its annoying to get stuck and hold your hand up until a TA arrives, we should have some sort of signal at the table.  Maybe every table has a white flag on the end of a 3 ft dowel rod.  If you get stuck, stick the flag in a little base on the table and move on to the next problem with both hands free until a TA arrives.  (This is especially important for intro electromagnetism where the Right Hand Rule is so often employed.)

The Time: Ideally as long as possible, but you have limited TA availability.  TA shifts shouldn't be more than 2-3 hours; they have exams too.  If there is a true dead period with no classes before exams, then i would go mid-morning to dinner-time one day.  If not, it will have to be a couple long evenings in a row.

The Food: Either lunch or dinner should be provided along with snacks.  Pizza is traditional at study parties, but it makes your hands greasy.  Maybe small burrito-like food that can be eaten with one hand?  The trick is not to make everything wet or greasy while not tasting dry.  On the tables there should be snacks like pretzels and non-greasy chips.  Soda is known to be bad for concentration, but we want to keep students hydrated and not spill cups of water.  I'm thinking water bottles on the tables which can be refilled at coolers of lemonade, kool-aid, iced tea, etc.  If meal food is cost-prohibitive, hold the session near a restaurant/dining hall and focus on hydration.

Breakout Sections: Every class has certain subjects that always confuse a fair fraction of the students.  Traditional review sessions typically focus on these, but many of the students who are stuck elsewhere are then bored.  At my review session there would be an announcement like "Half hour lecture on two-slit diffraction in Breakout Room 1 in 15 minutes."  Then the students who needed that review lecture would have time to wrap up the problem they were working on and their friends would know how long they would be gone.  Of course in the actual lecture with a pared down class size, you'd revert back to section dynamics with a lot of peer interaction.

All this requires a lot more planning and expense than a traditional review session, but you only have to do one for the whole department and the students might actually learn something.  A lot of this depends on certain resources being available at your school.  I suspect this arrangement might work well for chemistry and engineering courses at least and might even be workable in miniature for midterm exam reviews.  Maybe its worth developing some shared resources wherever i end up.

Asking Stupid Questions

Its more or less mandatory at the start of an introductory physics class to say "In this class there are no stupid questions".  If you don't give some reassurance that you won't judge them, some (most?) students will just clam up when they get confused.  But the line has always bothered me.  Of course there are stupid questions.  Given a rudimentary understanding of the fundamentals, some questions just shouldn't need to be asked.  The problem is if the students had a rudimentary understanding of the fundamentals, they wouldn't be taking the intro class.  Dante Shepherd of Surviving the World said pretty much what i've always wanted to say here last week.  I may have to borrow that line.  Its just such an attention-grabber.  At some point in my future life, i'm (hopefully) going to have to come up with my own lines.  Here's some thoughts:

1. You aren't yet qualified to tell the difference between a stupid question and a profound question.  But neither are the people sitting around you.  So don't judge your classmates and don't worry about them judging you.

2. Some of the most profound questions you can ask have as their answer "That's a meaningless question." To ask a good meaningless question you have to synthesize a lot of material starting from a bad assumption.  The world is a weird enough place that, frankly, if you don't make a bad assumption at some point in this class you're being too careful.  And sometimes the only way to discover where you went wrong is to get to the end of a train of thought and ask a really stupid question.

3. I have asked more stupid questions in the past ten years than you can contemplate.  And now i have a PhD, which makes me a certified smart person.  Pretty much anyone at this university that you think is smart has gotten that way by asking stupid questions.

4. You are not yet the you the world will remember.  You may go on to great feats of insight and knowledge, but you are not yet the person who is able to do those things.  College is supposed to be the place where you become that person.  If you want to let go of your stupid questions, let them out in the open.  Otherwise they'll always be inside you.  (This one may be too subtle to use on new freshmen)

5. Particularly in this class, there are a lot of questions that seem like they should be obvious but aren't.  If you're afraid to ask a question, chances are so are the people around you.  So do everyone a favor and ask it.  The time we waste if it really is a stupid question will be much less than the class time i would waste trying to figure out why you're all confused.

Education, Growth and Discipleship

I was recently reminded of an old study about peer instruction.  I wish i had the reference, but i encountered the paper hanging up in a hallway.  In this study, a group of students were identified who didn't understand a particularly difficult physics concept (something about angular momentum, i think).  They were then taught this concept using as much student-to-student interaction as possible.  A few weeks later, they were asked to teach some other students in a class that was a few weeks behind them in the curriculum.  They did this surprisingly well, often better than the professors, because they understood from experience where the confused students were going wrong.  However six months later, when asked to teach another group of students the same concept, they did very poorly because (and this is what blew me away) they had no idea how to think about the problem in any way other than the right way.  In the intervening months, they had completely digested the new learning and now their natural thought processes led them only to the correct answer.

The obvious moral of the story is that it pays to attack difficult learning experiences in groups so you can help each other over the subtle pitfalls the professors have forgotten.  More interesting, i think, is the implication for how the learning process affects you.  Within a few months of taking on new learning, students' brains had rewired so that they didn't have to think about the concepts anymore; they were 'obvious'.  From these 'obvious' concepts could be built more challenging concepts which in turn became obvious.  After a year or two of this, students begin to think in complicated ways; they are rewarded for thinking like a scientist.  Let this go on long enough and the school will give you a diploma certifying that you are a scientist because what naturally comes to mind when you look at the world is a scientific mode of thinking.

I find this idea that you can, in a sense, change what you are by guided practice fascinating, and particularly so when applied to the task of 'becoming a better Christian'.  Given the colossal failure of very eloquent professors in any sort of controlled study to teach difficult concepts without peer interaction, it seems that listening to sermons is probably not enough.  (I am definitely not saying here that we should skip Biblical instruction any more than we should skip class.)  The education research suggests that if we don't help each other work through real-world, messy problems we will learn at a glacial pace and often what we thought we learned will be wrong.  Fortunately we have a fellowship of believers and a wide selection of temptations, moral choices and holy disciplines (prayer, giving, worship, etc.) to work through.  Since the Church is very large, ideally we should form into smaller units of increasing closeness (say, denominations, congregations, small groups).  If we've done this properly, we should see small groups of people in similar life stages rehearsing everything they've learned together, helping each other apply what they've learned to existing problems and bringing issues to the larger groups.

Okay, so no profound insight there.  This more or less matches an existing practice that is observed to work well.  (Aside: I wonder if there are churches where issues from the small groups get fed back into the larger assembly)  But what have we actually learned and what does success look like?  I sometimes get the impression that churches believe we would behave more like Jesus if we just knew more about Him; if we knew 'What Would Jesus Do' then we'd be all set.  This seems unreasonable to me.  I can't behave like Jesus when confronting overwhelming temptation any more than i can behave like Richard Feynman when confronting quantum field theory.  Yes i have the Holy Spirit living in me, but in practice i can only behave like myself with small perturbations.  Much better, i think, to go through the disciplines and difficulties set before me with a group of fellow believers to help me through the subtleties.  In a few months or years i should find that i act more like Jesus because i am more like Jesus.  Then i won't need to be constantly worried about 'What Would Jesus Do?'; it will be obvious.

What Is Faith?

As much as we try to automate large experiments, sometimes a scientist just has to stay up all night to  watch the data stream.  Of course, most of the time things are fine so the watchers don't have much to do.  A few months ago i was data-watching with some other grad students from my lab when the conversation turned to religion, specifically where Jesus came from and why.  Since it isn't weird in big collaborations for someone with a particular expertise to answer a question with an extended lecture (and because we had all night), i gave a brief summary of the Old Testament starting with Abra(ha)m who by faith believed that his descendents would be a blessing to all people and then tracing his descendents through to Jesus, the Savior of all people.

After digesting this, one of my lab-mates said "You keep using this word, faith. What does 'faith' mean?"  That's a tough question at 2AM.  For a scientific audience, the best i could come up with was "Faith is confidence in a result even when you don't have overwhelming evidence in hand all the time."  For example, suppose you measure a quantity in the lab for the first time.  You don't just publish a number, you include error bars.  At first, you publish large error bars or wide confidence limits.  You have some faith in your abilities and equipment, but you've only done this once and your reputation is on the line.  As you refine the experiment and other people try it in their labs, you begin to zero in on a more precise number; your faith in your technique has grown.  Eventually, your result is included in scientific handbooks and used by people who have never measured it themselves because they have faith that you are a careful researcher and the peer review process has ensured that this is a good number.  In the same way a new Christian starts with faith in a Jesus they've mostly heard about.  They believe the basics, but without much experience they're not going to stake much on specific claims about God's character.  As they spend time with God and gain experience, their faith grows.

My friend thought about this for a minute and replied "That makes sense.  But why do Christians need a separate word for that?  Isn't that just being a person?"  My gut reaction was to defend how Christian faith is special.  But sitting in this group of aspiring scientists, it wasn't.  Every person in that room has personally subjected the things we corporately believe (in this case physics) to intense scrutiny, and then proceeded with a confidence that makes the average Christian's faith look like a toy.  We rehearse our fundamental beliefs as a group on an almost daily basis.  We've all been wrong many times and we've all doubted ourselves when we were right.  But we know we can rely on each other for correction and reassurance.

Many scientists i know are wary of religion in general and Christianity in particular because they think it calls for blind faith, which side-steps the whole experiential refining process.  They understand that what you believe is far more important than how much you believe it and that unexamined beliefs can't grow.  But when it was explained what real faith looks like, the objection of at least this group was the opposite.  Why do Christians make such a big deal about faith when scientists have so much more of it?

This Is a Blog

So this is blogging.  Not really sure why i'm doing this, but its been bugging me for a while.  I'll probably find out why later.  Until the real purpose of this blog becomes apparent, i plan to use it to store developed thoughts that i don't want to lose.

The name: I'm acting right now as Christ's Ambassador (-> Chi Alpha -> XA) to the Low Temperature Detector (LTD) physics community.  Its not a mission field most people would think of, but i enjoy it and there are people here who can't be reached any other way.

About me: I'm in my last year of a doctoral program in physics, specifically cryogenic characterization of ultra-pure particle detectors.  I enjoy teaching a wide range of subjects, but haven't had much chance in recent years.  I'm also a born-again Christian, which is not as uncommon as you might think in technical circles.  I'll probably post mostly about physics, teaching and Christianity.  I have a wife and 8-month-old son, so if i post family-related stuff that's where i'm coming from.

If you somehow found this blog, welcome.  I'm sorry it probably isn't very well organized.  I wasn't expecting company.  I hope something here is useful to you or at least thought-provoking.  (If you're a bot, go away.)