omenti

the danger of over simplification

In the early 1990s Anders Ericsson of Florida State University went to a music school in Berlin to test an idea about deliberate practice.  The music school had high standards.  Ericsson suspected practice separated the best of the best from the average.  He asked the eighteen year old violin students to think back on how much practicing they did since they took up the instrument.  Then he had the music professors to divide them into three groups - great, good and average.  Those in the great group averaged about 10,000 hours of practice.  The good, about 8,000 and the average practiced around 5,000 hours.  It seemed like a neat result - practice more and you do better.  He published a paper that wasn't exactly rigorous - it lacked statistical measures like ranges and standard deviations and was more of a discussion than a formal paper.  

 

Prof. Ericsson didn't push the result was a bit to the side of his core work and he didn't heavily promote the result.  But others saw a compelling story around that lovely round hour and a work ethic.   One was Malcolm Gladwell.  Gladwell is a great storyteller, but he often oversimplifies and gets things wrong.  The 10,000 hour result has been disproven by more careful studies over and over, but his books and TED talks are enormously popular and have made the idea something of a cultural meme.  

 

Recently I was thinking about something else he said that was misleading. Great storytelling, but misleading.  The more I thought about it, the more damaging it seemed.  It's partly linked to the 10,000 hour story and some unhealthy forms of training. 

 

In Outliers Gladwell talks about a relative age effect.  He uses sports, but it can apply to academics and other areas.  Say the calendar allowing kids to participate in a sport begins on January 1.  Kids born in the first quarter would be  January → March birthdays.  He noticed that ice hockey players born in the first quarter are over-represented and forth quarter kids are  under-represented.  The pattern appeared in several other sports so he set about writing a compelling sounding story.

 

What happens is when  kids are allowed to try out for a sport - say nine or ten years old - many of the first quarter kids are significantly more developed than forth quarter kids.  Most coaches can't tell the difference between maturity and ability and tend to select the kids who perform the task better.  The rate of change at that age is so great that the majority selected will be the older kids. 

 

A problem is the better players get moved to the better coaches and facilities. The talented ones in the chosen pack progress riding a premium training infrastructure.  There may be very talented kids who are later born who miss the advantages of this training and infrastructure who are lost to the system as they miss a chance to develop and are soon left far behind.

 

Combine this with the 10,000 target (as an exercise figure out how many hours a day you need between the age of nine and seventeen to become expert) and you realize specialization needs come early for the better athletes. I'll admit to oversimplification here - this is a fascinating area that has become something of an arms race as, at least in the US, the goal of a college scholarships can force specialization before a kid becomes a teenager.

 

The funny thing is when you look at more carefully you see sixty to seventy percent of the college age players in many sports are first quarter births, but for professional athletes in the same sports the relative age effect almost goes away.  Almost as at the very elite level there's a slight over abundance of third and forth quarter athletes. What appears to be going on is there's a great weeding of talent from college to pro. In many sports late bloomers - kids who got their growth spurt late for example - finally reached parity, but the fact that they had to work harder and learn the sport better ultimately made them better athletes.

 

There are other complexities I won't go into other than mentioning playing a variety of sports rather than concentrating tends to make better elite athletes.  We have a bias when we hear about prodigies like Tiger Woods and tend to assume they're the norm, but it's not. We also tend to forget about the prodigies that never make it.  One estimate is that only about one percent of sports prodigies identified by the media (written up in a magazine) by the time they're teenagers ever make it into the pros.  

 

So the American and some other systems do manage to train a number of elite athletes in many sports and show it internationally in the Olympics.  What about the potentially elite athletes that were never trained?   It turns out some systems cast a much wider net.  The Nordics, notably Norway, push universal recreation and sport for kids as a healthy way to provide fun and lower healthcare costs. Early specialization is discouraged and good facilities are made available to all.   It appears to work very well.

 

I'm far from athletic and am not recommending changing any system (although I think Norway's goal of a healthy population is excellent).  This is an illustration.  Similar issues of pipelining kids exist in music, art and academics.  Broadly speaking STEM education is an example of exclusion and producing a population that isn't as literate as it could be.

 

Back to the storytellers and  oversimplification.  If something isn't important and you just want to get a tough idea across, it might be appropriate, but anything of importance needs an appropriate level of depth. That places serious demands on the author, teacher - anyone trying to communicate.   It's something I struggle with a lot. 

 

 

 

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.

 

 

coupling constants

The funny thing is I thought I was a good teacher. 

 

First year graduate students are required to spend part of their time teaching.  I drew a two of lab sections of Physics 103/104 -  Physics for the Biological Sciences or, more popularly, physics for pre-meds.  Each lab section had about thirty students and consisted of experiments, quizzes and reviews for tests along with office hours.   I spent quite a bit of time preparing for the classes and the students seemed friendly and interested.  The problem was I didn't appreciate what the students were after.

 

At the time the grade in a physics class was one of the gating factors for admission to medical or dental school and almost as important for nursing school.  My students were strongly motivated to make me feel happy with them as I was a third of their grade.   As long as the labs were done properly I had a lot of freedom and focused on what I thought was important in an introductory course.  

 

That's where it came off the rails. 

 

An undergrad physics degree is partly an introduction to physics at two levels and partly mathematical methods.  You think you're learning physics, but mostly it's problem solving technique and some basic important physics.  There's no sense of the beauty of the frontier.  I find math beautiful, so I was naively happy. Physics has a different way of looking at the world and slowly you begin to adopt that way of thinking.  You're rewiring your brain.  Few know enough to start doing the real thing until the about the second year of grad school. Even then it isn't pretty.   I was trying to teach those poor students what I thought was neat - some math techniques to solve the problems they'd have on their tests.  Fortunately Janos, the professor in charge, beautifully tied the text with real world medical issues and techniques.  He would bring in guest professors from the medical school and he was learning a bit of what they did along the way.  But there was only so much he could do.  As the lab courses were taking place he couldn't teach his grad students how to teach.

 

It took a few years until I realized how beautiful physics, not just the math behind it, really was. About that time I had my second major teaching failure.  I couldn't save myself, but at least I realized I was failing.

 

My advisor required his thesis students to present their work to a class of high school physics students - about the level of an AP high school class.  My thesis was on semileptonic charm production when you slam pions into protons.  You know those examination dreams where you find there's a final in a class you thought you had dropped?  It was worse than that - much worse as I wasn't able to wake up in a sweat.    The next time the class met Paul came in.  In fifteen minutes he gave a beautifully simple and just-correct-enough lecture explaining my work.   The difference was he was a much better physicist and knew the material deeply enough to know what was important and what wasn't at the level of a high school student.  He recognized what could be done with their background.  Anything else and they'd be lost.  I was awestruck.  Later he told me if you're really good, you can do it with eighth graders. 

 

Since then the quality of student teaching has improved.  Stony Brook now requires a course on teaching and physics grad students take Alan Alda's course on science communication. Many of the non-major science courses are more finely tuned to various majors.  I suspect the deepest look at what physics really is would be in one of the history of science or philosophy of science courses.  These things were foreign to me at the time.

 

Wth time I hope I've improved a bit.  It's still difficult finding the right level.  It works best when you're walking with a friend and they know something much more deeply than you and a conversation takes place.  Speaking to a mixed group is more challenging, but perhaps I make myself less of a fool now.  I sometimes worry about this blog and have adopted the approach of treating it like I was talking to a friend.  The problem is it's too one-way, but it is what it is. 

 

Expertise isn't enough.  I was thinking about one of you - an Olympian and an expert in her sport with physical and mental gives along with an enormous amount of hard work.  Is this the right person to teach a beginner in the sport?  Would the best mathematician be the right person to teach a calculus class?  I think the answer is a qualified maybe.  If they've given the thought on how to pull from their depth of experience precisely the right thing for whoever they're trying to teach.   And that brings me to the idea of coupling constants.

 

In physics some of the forces interact in a somewhat similar fashion.  So much so that these forces unify under certain conditions.  Electricity and magnetism are more properly thought as a single force - electromagnetism.  Electromagnetism and the weak interaction can unify and the result can unify with the strong interaction.  This unification is know as the Standard Model in particle physics. Each of the components has something known as a coupling constant that tells you the relative strength of the interactions you're working with.   In teaching the trick is to find the right interaction.  If methods are similar you might even find a coupling constant lurking.  

 

Some people do this brilliantly and in a variety of fields. Carl Zimmer in biology - where I first learned girls are neurologically better predisposed to creative thinking.   The mathematician Steven Strogatz in his book Infinite Powers - a sort of introduction to calculus for people who think they're afraid of math or who took it a long time ago and have forgotten most of what they've learned. Writing a book like this is much more difficult than a technical paper.  You can't have jargon and you need to find ways to connect.  Steven connects.  

 

The other recommedation is for people who can remember their calculus, but are hazy on differential equations.  Differential equations and their partial differential equation relatives are everywhere.  Few things in the technical world can be understood without them.   But solving anything but very easy examples can be hard and a math student can quickly find themselves in the weeds learning odd techniques.  Here Grant Sanderson avoids most of the math and gets to the core of what a simple ordinary differential equation is using a simple pendulum as an example.  It's very beautiful, but skip it if you aren't comfortable with calculus.  This is the level of clarity that an expert can bring to bear.

 

finding the right position for the slider between education and vocation

William Rowan Hamilton had become obsessed with the idea of a three dimensional number system - sort of analogous to complex numbers being a two dimensional system.  The story he later told was every morning his son would say 'papa, can you multiply triples?' to which Hamilton would sadly shake his head and say 'no, I can only add and take away'.   Then, on a walk on the 16^th of October, 1843, he  crossed the Broom Bridge in Dublin and suddenly knew how to do it.  Rather than adding a single dimension to the complex plane, he'd add two giving three imaginary dimensions and one real dimension perpendicular to them.  In his excitement he carved it into the bridge with his knife:  i² =  j² = k² = ijk = -1

 

He called them quaternions.  They had some use in the day, but when people invented linear algebra, the technique fell by the wayside ... that is until quantum mechanics  came along about eighty years later.  And then computer graphics further down the road.

 

It turns out they're a lovely way to think about quantum mechanics and perform real calculations. Erwin Schrödinger knew enough about forgotten math to realize it was a beautiful gem.  Decades later, trying to improve the speed of computer graphics, a physicist realized they could be a key to quickly calculating rotations in space -- and Tomb Raider became the first computer game with smooth graphics on using relatively primitive personal computers.

 

Hamilton had other accomplishments that deeply impacted physics and math, but the quaternion story has a certain romantic element. To this day physicists gather at the Broom Bridge on the 16^th of October to celebrate.

 

The story of physics is that it's extremely important to think broadly and to keep expanding your learning.  It is also is relevant to education and work across many fields today.  That's what I want to get to, but first this wonderful parody of a certain song..  perhaps the best math song ever.

 

What prompted all of this was an email with a link describing the most contrarian college in America.  It's laser focused on a vision of an education seemingly without much a nod to vocation ...  seemingly..   I'd argue that it's too focused on a narrow piece of education, but have no doubt its graduates have learned how to learn..  they have the beginnings of a real education.  Mark Roosevelt, its President, sums it up:

Education should prepare you for all of your life. It should make you a more thoughtful, reflective, self-possessed and authentic citizen, lover, partner, parent and member of the global economy.

It  takes a special kind of student to thrive in a school like that.  I wouldn't have survived - my interests, those that I was motivated to dive into, lay elsewhere.  I'm happy it exists and that there is spectrum of schools for those who look.

 

My belief is a deep education with at least a few focuses creates the second type of person Claude Shannon describes:

“There are some people if you shoot one idea into the brain, you will get a half an idea out. There are other people who are beyond this point at which they produce two ideas for each idea sent in.”

The ability to get multiple ideas is core to serious play and creativity.   I'd claim focusing on education rather than finding the minimally easy path helps create the neural connections that make this possible.

 

A worry is that many, if not most, schools and students tend more towards vocation.  Focus on what is important to get a degree that will get you employed to pay off that mountain of debt.  Many (not all) businesses, on the other hand, would do well to have broader employees who are still learning and growing - those who can think creatively.  There is a disconnect. 

 

I hope this focus on vocation changes.  The rate of real change is great and people will keep up better if they are broader and more adaptable.  When recommending colleges I tend to focus on education ..  often to the consternation of those asking.  Of course I may be a poor example.  My education was far too narrow, but I've been lucky and curious enough to have been able to expand it a bit.  The other note is you can get a wickedly broad experience at many more places than you might imagine.

 

 Finally there's this odd emphasis on over-scheduling many pre-college kids, but I've probably written on how it kills creativity enough.

 

the desire for desires - tapping the power of boredom

About a week ago the Manhattan-bound bus I was on broke down in rush hour traffic.  I had been daydreaming most of the way, and now I had to take out my phone and say I'd be at least an hour late.  The text went out and the phone went back in my pack.  

 

'Why is it our Universe has three dimensions ..  well, three spatial and this crazy one we call time that sets everything in motion?'  One of those fundamental questions that is almost too basic to address, but it reminded me of a problem.  I was about fifteen and Kip was trying to get me to think about spaces and objects with dimensions greater than three.  He asked where the volume was concentrated on a hypersphere with five dimensions and one with a hundred.  I couldn't solve it and somehow remembered it.  Suddenly the answer came out of the blue.  Like so many things it seemed so easy in retrospect.  It led me to think about something I had never thought about - after all, the alternative was sitting on the bus and getting bored.¹

 

More than an hour had passed when the rescue bus came.  Everyone else seemed to be occupied with their smartphones or laptops. It turns out I'm reasonably self-entertaining and quickly got lost in thought again.  By the time I walked out of the Port Authority Bus Terminal it was too late for the meeting and there were two hours to kill before meeting a friend for a walk (the real excuse for the trip). I ordered a bagel in a coffee shop and took out a notepad and pencil.   It could have been that problem or a hundred other things.

 

I was lucky enough to have been bored more often than I'd admit at the time. I was also lucky enough to have ways to deal with it and the desire to do so.  Sometimes boredom was coupled with procrastination.  (I think some procrastination can be a good thing, but that's another subject).  In high school homework would pile up.  I had free time and I'd start feeling guilty.  If I wasn't up against a deadline sometimes it would push me to building something, draw, ride my bike or just daydream.  My father was demanding about chores, but both of my parents gave my sister and I enormous freedom to manage our spare time - probably because they were too busy with making ends meet and keeping up the house. There wasn't a lot of spare money, but somehow money for projects always turned up.²  We had learned to turn our boredom into play.

 

The desire for desires

 

That's how Tolstoy defined boredom in Anna Karenina. Researchers are learning that's how our brains work.  When we get bored, it's looking for novelty.  It appears to be such a strong drive that it can reward us with a dopamine hit..  That can be a problem. When you are in FOMO mode looking at Instagram, Facebook, Twitter, Snapchat, or... you get a little dopamine burst when you find something new.  You move to the next novelty (which is usually really inane) and get another.  We can become numb to the dopamine response so, like a lab rat pushing a lever, we keep going.  Not everyone is equally susceptible, but for some it's a computer mediated addiction.  

 

Perhaps more important is you're always being entertained these days.  It's an easy escape from some types of boredom and can  keeps you from the type of creativity that is now being associated with boredom.  There may be some interesting bottom lines - particularly for kids as they're developing their neural wiring -  how much passive FOMO behavior is reasonable.  Some have called social media the 21^st century tobacco - time will tell, but that may be accurate.

 

Researchers speak of four or five  types of boredom.  Early stages can be healthy leading  to daydreaming and creative dot connecting while others can be toxic.  A continued state of boredom with no outlets can lead to depression, drug addiction and even violence.  In the past few years Iceland has embarked on a major program to fight juvenile drug addiction and alcoholism by making it easy for kids to find other paths.  It isn't inexpensive, but they appear to be making real progress and the alternative is unacceptable.

 

It's fascinating that reactions to boredom are cultural.  Japan, China and the US link boredom with not having enough to do and admitting that you're frequently bored is taken as a bad sign.  It's apparently different in France where it is seen as social commentary and an excuse to shift what you're doing.  

 

Only recently has boredom become an area of active research.  It will be interesting to see how attitudes and perhaps the nature of work and study change as we learn what it really is and how it works.   Maybe more of us will have quiet places and times and the learned ability to let our minds satisfy that desire connect.   Or perhaps not ..  maybe Facebook, Google and the others will have managed capture our attention and reduce creativity. 

 

So many open questions.

__________

 

¹ I won't go into detail unless anyone's interested.  The second item was how spikey (is that a word?) are hypercubes.  It turns out to be not a difficult problem if you know how to compute the volume of a hypersphere for any positive dimension.   There is real pleasure learning about things so foreign we can only know them by their shards and shadows.  

² From the eighth grade on there would always be a check for forty-two dollars in my Christmas stocking with "experiments" written in the comment line.  That was a large sum back then.  It was before Douglas Adams let us know why forty two was important.  He must have liked the number for some reason.

 

how to paint like kandinsky

My artist sister sent a link to this short video from The Tate.  It's not quite what it claims, but that turns out to be useful.  Go ahead..   I'll wait.

 

Without a bit of background in the fine arts this isn't exactly a step-by-step how-to-paint guide.   For most of us it's somewhere between art appreciation and art creation.  It reminds me of learning physics as an undergrad.  You spend a few years learning bits and snatches thinking you're learning physics.  Silly you -  in reality it's just a little background.  Slowly you begin to focus on technique - mostly math - and come to think this must be physics.  It isn't, but you're beginning to get an appreciation.  You can go to serious academic talks without getting totally lost and you start to get the sense that this is much deeper than you had imaged. A talk might give a sense of how someone did something, but rarely offers much where the creative piece came from.    A few more years and you begin to get the hang of it - at least a small corner.  Back to the video.

 

I imagine art students would see some interesting hints.  I like what Sui said about her own inspiration.  That  led me to some notes from The Tate on Kandinsky.

Painted between 1910 and 1911, Cossacks is an expression of Kandinsky’s belief in the power of art “to awaken this capacity for experiencing the spiritual in material and in abstract phenomena.” The dynamic tension between abstract form and concrete content may be read as a manifestation of the wider conflict between the forces of political oppression – Kandinsky had been deeply moved by the strikes and upheavals in Odessa a few years earlier – and the hunger for spiritual rejuvenation consequent upon the rise of soulless modernity. Like his contemporaries Piet Mondrian and Henri Matisse, Kandinsky saw painting as an extension of religion, capable, as he wrote in his Reminiscences (1913), of revealing ‘new perspectives and true truths’ in ‘moments of sudden illumination, resembling a flash of lightning.’ The echo of the Ancient Greek writer Longinus’s notion of sublime speech, which similarly strikes like a bolt of lightning, is carried over into Kandinsky’s description of the spiritual mission of the modern artist. In his 1911 essay On the Spiritual in Art, he compares the life of the spirit to ‘a large, acute-angled triangle,’ at the apex of which stands the solitary artistic genius dispensing spiritual food to the multitudes below.

Impressively deep.

 

It turns out they've done a few of these of how-tos ..  If you want to move a bit beyond art appreciation, even though you may never try painting or printing, there's more here: print like Warhol, paint watercolor like Turner and cast like Whiteread.   They're quite wonderful and I hope they keep making these. 

 

A couple of interesting issues immediately come to mind.  How to you communicate at a variety of levels and why is art so important in unexpected areas?  Since I've written quite a bit about the first, I'll skip to the second.  What is the utility of art? 

 

I find visualization critical my own thinking - particularly at the playful stage that some might call the creative piece.  You get to the point where the questions become visualizations that you manipulate.  A mathematical expression might take the form of a visualization that you play with without formally solving it.  It's part of what some call intuition.  Sometimes these are on paper or a blackboard and sometimes they're in your head and you copy them, or at least their flavor, to move the court you're playing on. 

 

I've been drawing since I was a little kid and still will sit and sketch something on a tree trunk for an hour as exercise.  I'm guessing that the ability to visually focus, something art and photography can teach you, is central to improving your ability to visualize.  It's much more powerful than anything I've seen with a computer and I suspect is very useful in many disciplines. 

 

With all this practice you'd think I'd be an ok artist, but that isn't the case.  No complaints as the practice has undoubtedly shaped my neural connections that let me, for good or not, think how I think.  I believe there are rather deep connections between our perception of beauty and Nature and this can allow us to use visualizations as a rather powerful guide.  That's conjecture, but it keeps popping up over and over.  As a physicist friend says:  If there is a God, it's almost certain she's an artist. 

 

Others have noticed the impact of the visual arts on scientific thinking and a few physics and math programs recommend students take at least a semester of a class that involves drawing.  I'd like to see that practice expanded and have been trying to encourage my undergrad school to link with a nearby art institute.  STEM is only part of an education even if you're working in one of it's fields.  Adding a visual art or music (or .. ?)  may be essential if your goal is to be creative (whatever that means).  So many stories.  It probably doesn't need to be a fine art for everyone, but the current focus on narrowness in hopes of finding employment is approximately wrong. 

 

the magnificent violence hidden in a single raindrop

 

The sound of a skater on thin ice.  Predicting a rainstorm of molten iron on a star fifteen years in the past.  

 

It's been a year since I worried about participating in the first March for Science and two Earth Days have gone by.  I've been thinking a lot about the place of science in society.   Somehow it's often perceived as disengaged, from culture, cold, dispassionate and disconnected from almost all of society.  As if it is irrelevant.   At the same time there is widespread confusion global warming, GMOs, evolution,  the impact of technologies, and vaccines along with confusion about the relationship of religion and science and the big fundamental questions such as the origin of the universe and life, the mind and the fundamental laws of physics. 

 

It isn't that way.  Science is very relevant, but there's a communication and image problem.  While formal science and math education need to be fixed, perhaps fixing science communication is something that needs to happen first. 

 

It takes real work and a good deal of thinking to express ideas usually addressed by equations and dense manipulations of experimental data in such a way they're clear and accurate enough.   There are some people who make it look easy.  My thesis advisor made a big point of it and I've gradually become a bit more adroit, but if someone was to ask about something I haven't thought about translating, I stumble and fail.  

 

Issac Newton was arguably the first mathematical physicist.   As an undergrad I made the mistake of trying to wade through the Principia Mathematica - his magnum opus.  Its notation is obscure and the Latin is approximately  dense.  Asked why he didn't write it in English he replied "to avoid being baited by little smatterers in mathematics" .  He wanted to make it obscure.  

 

It's an easy trap to fall into.  Flying home to Montana at the end of my junior year I found myself sitting next to a pretty girl.  Too shy to start a conversation, I pulled out pencil and paper and worked out a solution to a problem a little more cleverly than in the exam.  The paper filled with what must have been unintelligible scribblings as I killed any chance of conversation.

 

Galileo Galilei had a different approach.  He had a deep conviction that ideas were to be shared and understood by almost everyone.  He created stories with good dialog and characterization and used the tool of metaphor to make his points - the Dialogue Concerning the Two Chief World Systems being a fine example.  His work was readable and interesting enough to become popular and that made him powerful and his science a threat to established dogma.  A few followed in his footsteps as great storytellers  - Darwin and Faraday come to mind.  But science became an institution in the late 19^th century with its own culture and language.  

 

That's the challenge..  to use metaphor, images and even characterization to tell the story.  It has to be accurate enough and not dumbed down.  This is important even when scientists talk to scientists in different fields. You tend to think what you're doing is clear - and it is for anyone who has been working in that field for five or ten years.  Many scientists suffer from imposter syndrome.  Science in other fields can look very hard - much harder than what you're doing.  You fail to realize they've been working at what they do as hard and long as you have and they may feel the same way if you gave a talk.  Science is hard won with a lot of work.  It is the best description we have of how the Universe works and is often how we find ourselves on the threshold of the unknown.  That's the basis for ripping good tales.   It's worth creating them.

 

Years ago there was this wonder public talk as part of a Caltech lecture series.  The speaker described being on the rim of the Grand Canyon and those millions of years of erosion.  Thousands of feet below a river thundered and raged.  In the distance a thunderstorm - the source of those waters. The words of Lauren Isley came to him as he watched:

 

the magnificent violence hidden in a single raindrop

Indeed. 

 

A few people are good at code switching, fluently moving among different descriptions..  I'm working on it.

 

BUT its not enough and this is the problem I've been struggling with for the past year.  Some areas of science have become politicized.  Human-caused global warming is almost universally accepted by the scientific community, but that has an impact of some of the largest businesses in the world and a massive misinformation campaign has been conducted.  Scientists and expertise are actively being ignored and ridiculed in some corners.  Science education in much of the country is under attack and has been damaged. These issues led to the March for Science.  That wasn't enough.  Much more contact than a simple attempt to raise consciousness is required.   I think storytelling is part of the solution, but you have to understand the audience.

 

I'm most comfortable chatting with one curious person.  With a two-way conversation the level of the storytelling can be adjusted and, if I'm really lucky, they'll tell me their story about something that interests them.  This is even true talking with scientists in other fields.  If I'm speaking to a class I have a sense of the expected level.  A general audience?  Let's just say that hopefully can learn from failure. 

 

I thought about dividing up - segmenting - the population so I would know a how to address, or even ignore, different groups.  Looking around I settled on the Six Americas segmentation from the Yale Program on Climate Change Communication and George Mason University.  Designed to ferret out beliefs on global warming, it breaks the US population into six separate groups identified to reasonable accuracy using a 36 question survey.  The nice thing is it works for science in general.

The Alarmed are fully concerned about the danger of global warming and are taking personal and political steps to combat it. The Concerned believe it is real, but isn't that important to them yet - maybe it's a top ten issue, maybe not. The Cautious, Disengaged and Doubtful represent a range understanding and acceptance of the problem and none are meaningfully engaged.  The Disengaged and Doubtful generally will vote against those who want to do something about the problem as they see the fight as wasteful.  The Dismissive are convinced it isn't real for a variety of reasons.  They fight it actively and well-funded powerful groups support their cause.  Dismissal has become part of their personal identify. (this is important as it is true for other areas of science)

 

I've wasted far to much time combating the dismissive with evidence.  They simply will never buy it. The doubtfuls are also a tough group to talk to.    That leaves the concerned, cautious and disengaged as potentially useful audiences and each has different information needs. In fact, when it comes to global warming, the only group seriously interested in actions and steps are the alarmed.  Mentioning that to other groups can be counterproductive.

 

Let's say you have a message and understand which of the six Americas are in the audience.  Now you have to be trusted.  A Ph.D. in physics has negative value in some of the groups that might be important to address.  It has been noted that celebrities taking up the cause can be more impactful if changing minds is the goal.  So if you are an athlete, film star or other person in the public eye...