omenti

the question of getting bent and slowing down

 

(a) Without resorting to equations, why light slows down when it travels from air to sheet of glass and why it speeds up when it exists?

(b) Again without equations, why does light refract?

 

For the past decade and a half a friend in the engineering department of a very large and famous university in the midwest is infamous for asking "unfair" questions of graduating seniors.   The student's grades aren't affected. He's interested in how deeply students thought about everyday phenomena that are fundamentally important to engineering,  He hopes to learn about teaching in and outside of the department as well as the curiosity of the students. 

 

This year's question was a disaster.  Nearly two hundred students took the exam and four got part a correct.  The same four gave the only correct answer for part b.  Refraction is really important - lenses wouldn't be possible, there wouldn't be rainbows.. there wouldn't even be vision.  It has practical use throughout engineering, even finding use in certain types of market trades where gaining an information advantage is important.   I'll answer part a and leave b for another time because it requires a bit more background.

 

In high school you probably learned the index of refraction of a transparent material determines the angle light will bend if it travels from one transparent material to another.  The greater the index, the greater the bending.  Some (approximate) values are:

 

        a vacuum      1.0000

        air                    1.0003

        water               1.33

        glass                1.5  (it can vary from about 1.5 to nearly 1.75)

        polystyrene    1.55

        sapphire          1.77

        diamond          2.417

 

You probably also learned that light slows to the speed of light divided by the index of refraction in a transparent material, If light travels at c - the speed of light - in a vacuum, it slows to c/1.33 or three quarters the speed of light in water and c/1.50 or .two thirds the speed of light in glass.   The illustration shows light moving from air (for most purposes you round the index of refraction of air to 1.000) to a sheet of glass and out the other side. 

 

The answers given by most of the students clumped into two categories - both wrong.  It's interesting to consider them before moving on to what really takes place.

 

One idea was to suggest light bounced from atom to atom (or molecule to molecule) in the glass taking a three dimensional pinball path,  It would effectively travel a longer distance making it appear to take longer to go from one side to the other.  The problem is light would effectively scatter out even in perfectly clear glass.  A narrow beam, say from a laser, would light up a broadening region inside the glass and the would continue as a broad cone once it left. Some of the light would  even bounce backwards creating an undirected glow on the first side. The clearest materials would be blurry and dim to look through with the  blur increasing with thickness of the glass. Crisp images would be impossible. 

 

The second popular answer was to suggest atoms (or molecules) absorbed the light and then re-emitted it.  It takes a bit of time for them to do this, so the effect would be to slow the light down. The problem is when an atom absorbs and then emits light it doesn't remember the direction the light came from and can emit it in any direction.  Now you have the glowing problem again.  There are other issues - among them atoms and molecules have very special and narrow frequencies they absorb an emit (quantum mechanics).  The effect would only happen for a few very narrow colors and some colors would be completely absorbed. 

 

We don't see either of theses, so something else is going on.

 

__________

I think the simplest way to look at this is to consider light as a wave.  As it travels along there are oscillating electric and magnetic fields perpendicular to its motion.  The animation shows the fields happily moving along with the electric field in red and the magnetic field in blue.  

 

 

You've probably come across the superposition of waves.   Take two waves with the same wavelength and add them together.  If the peaks of one line up with the peaks of the other, you get a larger wave with peaks and troughs twice as big.  If the peaks line up with the troughs, they cancel each other.  The next gif shows two waves and the result of summing them .. 

 

This turns out to be what we need conceptually. 

 

The electric field in the light juggles the electron clouds of the glass molecules causing them to move up and down.  They don't move in direct unison as the mass the molecules dampens the motion, But they still jiggle and very rapidly.  If you take a charge and shake it, you get an electric field. The jiggling molecules are producing their own electric field as they feel the light's electric field.

 

That's it!  

 

The electric fields produced by the jiggling molecules as they dance to the tune of the light combine with the electric field of the light.  The math is a bit messy as you have to consider all of the molecules, but the combined field moves below the speed of light -  just like you had divided it by the index of refraction.   When Thomas Young discovered the index of refraction more than two centuries ago he was only able to predict how light would bend, no one knew what was really going on.  The key came later in the 19^th century with an understanding of Maxwell's equations.

    

An acceptable answer could have been something like:  the electric field of light inside the material jiggles the electrons of the material's molecules generating another electric field.  These fields combine to produce an effective field that travels slower than the speed of light in the vacuum. 

 

Of course you could ask embarrassing questions in any department and discipline and that makes you wonder about education. 

 

_________

I should add that there are deeper ways of thinking about this.  Quantum electrodynamics gets at the interaction between photons and electrons, but it gets very messy and for most applications would be overkill.   It's  like Newtonian physics and Relativity ...  for almost everything we do Newtonian physics is good enough.

 

 

an ecology posed by a children's song and multidisciplinary problems

Last week I read Range: Why Generalists Triumph in a Specialized World by David Epstein.  David writes well  I've recommended The Sports Gene as another excellent read.   In Range he talks about real world messy problems that often poorly defined and open-ended.  The really interesting ones usually require a range of backgrounds.  Experts often do worse than generalists.  If you have a group of people, you want a range of expertise and backgrounds.   

 

You've probably heard of Fermi calculations.  Enrico Fermi liked to frame problems in such a way that you might be able to approximate an answer using common sense and a few bits of information.  Things like "how much water flows through the Mississippi River in a year?"  or "how many piano tuners work in New York City?"  They're extremely common in physics and are used to think about how good or bad a conjecture is.  The type of question you can get a handle on in your head or on the blackboard.

 

There are many other approaches to problems. The school where I did my undergrad work has a course that teaches multidisciplinary thinking.  Although it's a physics class, it really isn't about physics - or at least it doesn't have to be.  People get together a couple of times a week for a few hours and a problem is posed to talk about.  Students come from a variety of backgrounds.  What is common is serious motivation and curiosity.  There aren't midterms or finals, but there is a project each student proposes and works on.  They're given some funding and access to other class members, professors and grad students.  And each week they're immersed in the two hour sessions each featuring something that is best approached as a cross-disciplinary problem.  They learn to sort out the various strengths and weaknesses of the other students and the professor.

 

Getting into the course is difficult. About a hundred apply and maybe six are accepted  You have to pass a couple hurdles - problems you spend about four weeks each on showing you can bring a range of thought to the table.  You must show they're capable of cross-disciplinary thinking.¹  A hurdle problem I'm familiar with was  posed as a line from a children's song:²

Mares eat oats, and does eat oaks, and little lambs eat ivy.

The question is:

Considered in an ecological sense, we have three species each of plant and animal life that interact in a finite geographical area. Supposing that we start out this system with roughly equal numbers of the six species, determine the way the system changes with time.

You have four weeks to come up with something clever and compelling.  Then on to the next hurdle.  The class has had extraordinary success over the years and is something of a legend.,

 

Very few people have a great range of background and expertise.  At least in the US we seem to value those who are broad less than those with a very narrow deep expertise.  One of my favorite thinkers was a mathematician some of you knew - Norm. He would sit and listen to ideas coming from a variety of backgrounds.  Later .. a few minutes to a week or two .. he'd stop you and say "Let me see if I understand what you were saying"  Then he'd proceed to give a much deeper and better thought-out version of what everyone had been trying to say, adding his own bit in the process.  Not always, but often enough history or art might be part of the framing.   These sessions were marked by deep play as well as chocolate coated coffee beans.  Play is the glue that allows communication across disciplines .. even if it's in your own head.

 

My own range isn't that great, but Norm and others - friends who have very different backgrounds - have changed the way I think.   I have this habit of "tithing" my time to the projects of friends.  I'm particularly interesting in areas outside of physics and math as I end up learning something and find myself in Norm's shoes at times.   This broader approach of posing and approaching questions strikes me as richer than the traditional expert deep dive as you can always add expertise where you have it when it's useful.

 

I've had a bit of serious insight on a very difficult problem that changed how I saw the world.  Insights came from a forestry program, a couple of sociologists and a professional volleyball player who has a degree in microbiology.  There are dozens of other problems where outside insight has combined with my own contribution to be a bit out of the box. And who would have thought thinking about bats would be just the right analogy for what turned out to be a neurology problem I didn't realize I needed to know about...

 

I don't know if I manage to help others.  If I do it's probably by offering a bit of thinking that might seem novel as their background is different.  At the same time I'm often lost as an outsider in their world until I start working in it for awhile.  I probably don't get very good at it, but it's the diversity that might be useful.

 

I'm very much against the hyper-specialization in STEM focused education we seem to be moving towards.  There's enough change in the world that the humanities, liberal arts and just practical skills are increasingly necessary. There has been some work on teaching cross disciplinary thinking. That strikes me as having great potential. 

__________

¹ As these are freshmen when they work on the hurdles it's interesting to look at their backgrounds. It's a bit of a problem as so few have taken the course, but it's been around for decades.   I won't go into that here, but it's very different from those of kids who focus on standardized tests and assigned activities.  A really interesting question is how much of the ability to acquire cross disciplinary thinking is wired in and how much is learned. I have suspicions, but that's beyond this post.

² Not to be confused with the song "Mairzy Doats and Dozy Doats" from the late 40s:-)  It's sort of a homonymic phrase. 

 

 

making and sparking

"No - we took all of that out years ago.  It's just not relevant anymore."

 

Fifteen or so years ago I visited the local high school to see if they had an adult education program that would let me use the student shop.  We don't have enough space or cash for a proper shop at home and frankly I'm not that good at wood or metal working, but every now and again the urge strikes.  

 

I'm not arguing that shop class was well thought-out or even useful - it wasn't when I was a teenager - but there's something to being able to design and build something.  On my own I did build a few things:  a couple of telescopes, some amateur radio gear, model airplanes and a seismometer.  Although the attempts of a kid, they were enormously powerful learning exercises.  I learned how to solder, how electronics works at the component level work and a bit of practical optics.  I even got to the point where I designed a transmitter and a simple analog computer.  Commercial equivalents were better - they were designed by people who actually knew what they were doing - but I was learning the basics for design and that is much more powerful.  

 

In grad school the ability to design and build was essential - so important even the theory students had to learn a few basics..  I knew enough about electronic design, but had never done any metal work.  Metal shop was wonderful. The shop was well equipped and managed with expert help around most of the time. We were given a couple of simple projects.  Once you made those you had to show you could do it with greater precision.   We were finally given shop keys when  they thought we wouldn't destroy the machines or ourselves. They encouraged us to come in and play. 

 

I remembered a project in an ancient issue of Popular Science that fascinated me when I came across it in the library as a kid - a Stirling engine.  I decided to build one of my own based on a bit of insight into better materials.  The first was very inefficient - about 30 watts at the flywheel using a hot plate for a heat source.  A minor redesign moved it past 100 watts.  The design and construction was a wonderful diversion to the classes I was taking.

 

Times have changed.  While engineers generally know how to build things, Spending a bit of time teaching in Oberlin's Technology in Music and Related Arts I found art majors and music students more adroit at "making"   than computer science students.  Programming is clearly building, but it's useful to tie it to the physical world every now and again.  Some schools stress that more than others.

 

It doesn't happen often, but when someone mentions their kid is interested in learning about computing I recommend simple inexpensive computing modules that interface with the real world.  Arduino and Raspberry Pi for example.  An enormous amount of "how to" videos and documents exist and beginners can start with very cheap kit. They can have quick success getting something working from cookbook like plans.  At first no real skills other than patience and the ability to follow instructions are necessary.  Then, with the application of curiosity,  learning begins,   You change this and that to change what it does.  You can write simple or complex programs and you can buy interface modules, usually called shields, that  interface with the outside world.  

 

People with that spark - the desire or need to do something they can't go out and just buy - make this interesting.. A dance major at Oberlin learned about Raspberry Pis in her computing for arts class.  She sewed an accelerometer to her leotard and connected it to a raspberry Pi on a belt.  Information was liked to her laptop via by bluetooth.  For fun she connected it to lights that changed color with changing acceleration.  A friend on the women's softball team saw it and thought it would be useful in pitching practice.  Another version with software tuned to the needs of softball was built and the coach is thinking. Of course you can do this with an Apple watch, but its much more difficult to make it do just what you want and this way you develop a deeper understanding. 

 

And so these things go..  Which brings me to something exciting.

 

People who build and design get good at it with practice and are on the lookout for new challenges.   A few of you may be familiar with Panic - a tiny company that makes a few very nice applications for developers.  They're profitable by themselves but use some of that profit to fuel their need to explore.  A few years ago, out of nowhere,  they came out with a video game called Firestarter.  It wasn't one of your multi million dollar developments, but many people loved it because it was beautiful, clever and absorbing.  They more than broke even which wsa good enough. There has been anticipation about another game in development called the Untitled Goose Game.  But again out of nowhere came something completely shocking and wonderful.

 

Hardware

 

These guys decided to build a minimal hardware game player called the Playdate. People who have seen it seem to be somewhere between excited and ecstatic. 'Impossible to resist' keeps coming up.  I won't go into details because I'm not a game player and I don't know much other than  care appears to have gone into every step of development.  They even wrote their own operating system. (that actually makes more sense than Linux for a very small game).  They made it for themselves because it was a challenge they couldn't resist.  Maybe it will break even, maybe it won't, but it won't break the company if it flops.  I'll probably get one and I'm not a gamer.  

 

People sometimes ask me why I'm passionate about a few odd things that not many other people find interesting.  Many of us have a spark - a playful spark.  They're all different and that's wonderful.  Some of us aren't very good, others are the opposite, but that's not why we do it. We may or may not get paid, but that probably doesn't matter much.  Sometimes I think it's better to not be paid as there's more freedom (assuming what you do is cheap).  Often you find yourself learning a variety of things you never thought about as part of pursing your spark.  In my case that can mean designing and building.  I'm not very adroit at that part, but it's a useful tool and I slowly improve with experience.  I'm in awe of those who thrill to be beauty of creating design and objects.  

 

About fifteen years ago I found a poem that sums it up .. 

To be alive: not just the carcass
But the spark.
That's crudely put, but…
If we're not supposed to dance,
Why all this music?

                - Gregory Orr

 

the mayor of allentown

You've probably seen this excellent summary of issues associated with the Boeing 737 Max.  The core message seems to be this:

They described a compartmentalized approach, each of them focusing on a small part of the plane. The process left them without a complete view of a critical and ultimately dangerous system." Few people get time to reflect and look at"inessential stuff" and few of those who can care to; they are used to be "focused."

Compartmentalization seems to be the default when it comes to complex systems.  I think it's ingrained in our culture to appreciate specific easily identifiable acts. "Catalysts" and generalists are rarely appreciated.  The move fast and break things mentality in certain quarters combined with interchangeable employees who fit certain descriptions is aspirational in certain quarters and it extends to education.

 

I'm reminded of an internal postmortem of an expensive disaster that occurred in AT&T's Allentown Western Electric facility in the early to mid 1980s.  Western Electric was AT&T's manufacturing arm. The telephone monopoly built a dizzying array of almost everything it used - from relays and wires to telephones and building sized switches.  Digital switches were built around computers and a specialized switching fabric  that required a lot of memory.  Manufacturing capabilities grew with the increasing need and AT&T, along with IBM, was inventing and developing a lot of core manufacturing technology as well as financing key pieces in Silicon Valley and beyond. By the early 80s these two companies were close to the leading edge of IC manufacture.  The Allentown works was Western Electrics cpu, memory and custom silicon location.

 

Western Electric and Bell Laboratories manufacturing and technical directors began to appear for the increasingly specialized subprocesses of a complex larger process.  They'd get together and meet regularly, but they each recognized they owned the most important part of the process. This focus and pride in specialization extended downwards.  In a sense they were sort of right - many of them were critically important.  They optimized their subprocesses measuring what they could find.

 

During the period a guy named Doug (I think) would wander around and talk to people.  Almost no one knew who he reported to, but he was friendly and smart.  Smart enough to let the engineers talk about what was going right and wrong. He'd take doughnuts around and show up at meetings and in the clean rooms.  No one considered him an expert, but the doughnuts were really good.  Every now and again he'd make suggestions being careful to let people feel it was really their idea.  He was given a somewhat derisive nickname - The Mayor of Allentown.

 

Doug worked for an old line director.  Someone who taught other companies how to make transistors in the early 1950s when AT&T, as a monopoly, was required to share their intellectual property.   The director created Doug's position as kind of generalist's glue.  Doug had a master's in electrical engineering and a Ph.D. in anthropology. When the director retired the other directors absorbed his groups.  None of them saw any need for the Mayor. - his skillset wasn't specialized enough to give value to the company.  He was given an insulting offer and quit instead.

 

In a few months a series of process disasters cascaded through the works.  Critical switch and computer components weren't available to the people who needed them.  Other parts of the company had to do frantic redesigns to incorporate external parts.  Losses were well over $40 million in early 1980 dollars.  It took six months and an enormous revamp to get back on track.  Western Electric never regained its position as a leading edge manufacturer. 

 

It turns out you can still find excellent doughnuts in Allentown.