omenti

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.

 

 

it's switches all the way down

The other day I saw something that a few of you might want to consider for a kid or even yourself - the Turing Tumble Mechanical Computer.  

 

It turns out digital computers are mostly switches.  A lot of switches these days - perhaps a trillion in your smartphone. As a teenager I built a very simple relay based digital computer based on a column in an old Scientific American. Later I built an updated version that substituted transistors for the relays using some (free) components from the high school physics teacher.  

 

Playing with these beasts is an excellent introduction to understanding how logic circuits work.  You'd be surprised how many computer programmers are hazy on the subject (of course they work at a level of abstraction far above the silicon - or what old timers called the iron).  The early machines of the 30s were very important and set the stage for the dramatic developments that followed.  Here's an outstanding non-technical short history of those early days. (recommended!)

 

But back to the Turing Tumble.. It's limited, but that's central to its beauty.  The instruction book has about sixty examples to play with and an aha! just might strike leading to out-of-the-book insights.  

It's also great to play around with extremely simple silicon digital computers - particularly those that you can hook up to sensors, lights and other interfaces to the real world.   But getting down to the basics is usually a paper or YouTube exercise or, if you want to do it yourself,  a frustrating experience involving a lot of soldering and a non-trivial amount of money.   The Turning Tumble might be just the ticket.  It is play and that is the best way I know of to learn. I didn't have much of a chance to play with it and can't do a thorough review, but I'll probably end up buying one to give to a kid.  The caveat is that you have to spend some time with it to learn.  If the user doesn't find it fascinating enough to devote time to there won't be any learning.  But the same can be said about so many things.

 

The education link on their site has the following in addition to a set of resources:

 

Appropriate Age Range

Turing Tumble is for ages 8 to adult - and that is not a stretch! We find that kids 8-12 are able to get through the first 20-30 puzzles. Adults get addicted by puzzle 27, and their minds are blown by puzzle 35. Younger kids enjoy the first 10 and building their own computers.

 

 

the arc of the chorus

Imagine that you're from another world and happen upon Earth for the first time.  You have the ability to sense not only the visual, but beyond it.   Soon you discover an arc of sound traveling East to West along the Earth's surface as the planet revolves.  Sweeping along it lights an with bird song for a few minutes each morning.  You've discovered the arc of the chorus - the social network of the birds.

When I first went away to college I decided I'd try to catch as many sunrises as I could. By themselves they're beautiful but there's also the arc of the chorus and other morning  sounds.  Even in cities the noise would be low enough to hear the birds in the trees rather than the rumble of transportation.  There's a rich variety  - even when you try listening a kilometer or so away.  

 

A fun little experiment you can do on your computer or phone is to record a number of sounds:  nature, city noise.. a variety of sounds.  Now mix them together being careful not to throw too much in at a time.  I generally only try three or four tracks at a time.  Now try listening only to frequencies around 2.5 kilohertz - say 2000 to 3000 Hz.  That's close to the resonant frequency of your ears - the range you're naturally turned to.   What you discover is a a lot of birdsong survives the filtering.  It's as if we're tuned to it.  I have to wonder if the proximity of birds was important to our ancestors.  It might mark water, protected areas and even a warning system.  But that's just conjecture.

 

It has taken me a long time to be visually and acoustically observant and I still have a long way to go. (those who know me are laughing as I'm very single tasking and not very observant when walking and talking at the same time).  I suspect with sound a lot of unlearning is necessary.  We're taught at an early age to consider some sounds - particularly talking - much more important than others.  Sometimes it's good to be still and listen to a variety of sounds.  You might be surprised how much depth and variety exists.

 

Tuck your phone away or leave it at home.  Smartphones are okay for investigations - taking photos, using it as a microscope, using it to listen to bat calls - but they represent a task master that wants and sometimes demands your attention. 

 

It isn't just the countryside or wilderness that's interesting.  One hot Summer day I was walking by myself in Manhattan when a thunderstorm moved in.  There was the drama of the wind and rain, but the thunder is what stays with me.   You look at the width of the street and the building heights and do the back of the envelope finding the buildings are tall enough.  Realizing you're safe just get wet and wait.  The echoing up and down the avenue  and off the buildings was amazing. The reverberation time was at least ten seconds.  It wasn't as dramatic as being in a fire lookout in an electrical storm, but it's high on the list.

 

It's an interesting world to explore.  Who knows what you'll find.  Some blind people have even taught themselves a modest ability to echolocate. 

 

why revolutions sometimes need astonishing simplicity

Physics is, by far, the simplest science.

 

I probably have said it too much and it can raise eyebrows. It may not seem that way as we have a reasonably deep understanding and the required knowledge can seem esoteric, but that complexity isn't central and misses the point. What is astonishing is that you can often make seemingly absurd simplifications - spherical bodies, frictionless surfaces, planets that behave as if they were points - and get not only a pretty good answer, but a deep understanding of what is really going on - a hint of how Nature really works.

 

Galileo Galilei was said to have dropped balls of similar size, but different weights from the Leaning Tower of Pizza and summarized that they fell at the same rate.  In fact he probably never did the experiment.  Instead he rolled balls down inclined planes showing their acceleration depended on the angle of the plane rather than their mass.   He suggested a very high angle (vertical) was equivalent to balls of different weights falling at the same rate.   The acceleration from gravity was more important than friction against the plane and air resistance. Assuming you understood air resistance and friction against the plane you could add these effects later and get a better answer.  His insight is probably the most important idea in physics.

 

This realization that physics was fundamentally simple brought together ideas from a variety of sources and led to an idea that went beyond revolutionizing physics to revolutionizing how we think about our place in the Universe - the conversation of momentum as articulated in Newtonian physics.

 

Before Newton and Galileo Aristotle's physics was grounded on natures and causes. Whenever something moved there had to be a mover.  When it stopped it was because the mover gave up.  There were four elements- air, fire, water and earth.  Earth and water's nature was moving down, air and fire went up.  All transformations had some underlying cause.  Push a cup on your desk and it moves.  Stop pushing and it stops.   The conservation of momentum would say give it a push and it starts moving until opposed.  In fact friction opposes its motion. For many of the things people did the Aristotle's model was fine - in fact we often think about the world that way.  But look more closely and it fails to predict what's going on. 

 

It would be natural at this point to talk about Newton and the marriage of math to physics as it started to become a science. I'll skip that and move to someone you may or may not be aware of - Laplace.

 

Pierre-Simon Laplace came about a century after Newton.  Newton was deeply religious, but his God was not as interventionist as earlier thinking required.  God created Heaven and Earth and started everything moving.  Then, thanks to the conversation of momentum, simple things like the motion of the planets went on without any intervention.  He noted there might be some problems every  once and awhile that would demand attention, but God could kick back and do other things.

 

Laplace was probably the first person to understand Newtonian physics at a deep level - certainly much deeper than Newton.  As he advanced the math and physics he had a remarkable insight.  He knew how to answer the question "what determines what happens next?"  The answer appears to be more philosophy than physics, but it's deeply rooted in the later.   It's also simple - "the state of the universe precisely now."

 

Many see this as a contradiction to free will, but it applies to systems simple enough that we have enough information about them.  That happens to include a lot of fundamental physics.   Biology and sociology are far too complex for us to deal with exactly.  Classical physics is, at its core, non-teleological.  What happens is not determined by final goals or causes.  In fact we don't have to know about the past either - just the now.  The fly in the ointment is you have to know a lot of information.  All the relevant information for every point in the Universe.  This led to the idea of fields being important - information attached to every point - which is at the foundation of modern physics. 

 

This insight is often called the conservative of information.  Words are loaded and easily misused out of context and this is a very specialized.  It's the exact state of everything at a given instant of time.  Conservation implies the information that exists is exactly what is needed to determine the next moment allowing you to move ahead in time. 

 

The conservation of momentum and information are deep ideas with an enormous impact on how we think about Nature and all of physics, not to mention the technological byproducts that have changed how we live.  All of this was set in motion by understanding physics - the study of  matter and motion - can be stripped down to a bare simplicity if you're sufficiently clever.  

 

This way of thinking - stripping down to simple enough - is part of the playfulness of the sport. The approach can be useful in some other areas, but only if you have a handle on local limitations. 

 

THE FUTURE™

I'm certainly not a futurist.  Oh - there are some things I can predict with reasonable accuracy: that one of my ferrets will beg for a banana next week and next year, when an eclipse will happen somewhere, roughly when the Sun goes into its red giant stage...  The easy stuff.  Throw in people and culture and all bets are off.  I've made some informed predictions that were heavily dependent on technologies I knew a lot about that seem precent now, but if I'm honest and look at my old lab notebooks.. well..  I'm batting 200 at best.¹

 

Since then I've learned a bit more.   New business ideas can appear and develop rapidly, sometimes in a year or two.  Big technology leaps usually depend on basic research and are less frequent appearing at  twenty to forty year intervals.  They're often difficult to notice early on and are accompanied by widely negative and positive projections.  Then there is culture.  We - our basic needs, desires and dreams - evolve at a very slow rate.  Typically thousands of years.  Understanding this is critically important to thinking about the future.   I like to identify what preoccupies people and where future conflict is likely.

 

My model of the near term - say up to twenty year - future involves four areas.  There are probably more.  

    ° what is technically possible (understanding the combination of multiple technologies and a bit of the basics is important.)

    ° what is economically feasible and what are the externalities

    ° regulations and standards

    ° people, culture and social acceptance

   

There's a forest and trees problem.  You have to understand why a certain product or service is popular to see if it's something fundamental or if it's just a manifestation of the possible.  A few years ago people were running around playing Pokemon Go.   Many got excited about augmented reality games and saw this as the future. In fact it was a fad that quickly died out.  It was made possible when the quality and user cost of wireless networks and smartphones got to a point where enough people had them to allow a novel experience.  The underlying importance was the convergence of a good enough network and smartphones.  

 

When a wheel is invented you have to sort out what is a bicycle and what is a hula hoop.  We have a lot of hula hoops.

 

About ten years ago a few of the titans of Silicon Valley pronounced privacy dead.  Lots of people agreed.  I'm guessing almost none of them had any understanding of what privacy is and how it has developed over the past two hundred years.  It's very complex but anyone making decisions needs to understand the history and conflict and why modern notions are still unsettled.   Now we see two huge chastened firms claiming to go all in on privacy (I don't trust one and only partly trust the others).  I'll go out on a limb and claim it will still be a major issue at least two decades out.. probably more.

 

A few words on externalities, but it can get involved.  You can think of great projects that make enormous financial sense on longer time scales that are problematic.  Dealing with climate change and proper sanitation are two excellent examples.  Technology exists to solve both, but the people who benefit most are not those who invest.  

 

Prediction is difficult.  It takes a smart multi-disciplinary team and a rigorous process. You need to understand the past. There can be good success with the bicycle and hula hoop class questions.  Identifying new wheels are likely to be a once in a career issue if you're lucky.    All of these things are well above my pay grade.  I'm continuously reminded how simple physics is.

 __________

¹ In 1992 using, Moore's law and the notion that the Internet and wireless were so desirable that hundreds of billions in infrastructure investment would happen, I suggested in 2017 people would hold a piece of glass in their hand and have have a video connection with a friend halfway around the world and that "call" would effective be free.  The hardest part, in my mind, was the battery.  There were a few other seemingly clever calls, but more than a few duds.  At least there's the realization that I, along with many colleagues, did better than the very expensive futurists the company hired,

 

 

 

natural beauty

Last week a friend and I were talking about finding Nature.  Is a city a wasteland for a nature-lover?  That's a complicated question that triggered a series of thoughts.  Ultimately it depends on the person, but a few thoughts. 

 

In 1981 interview Richard Feynman talks about how he can appreciate a flower's beauty like an artist, but he can also appreciate a deeper beauty with his understanding of science.

There's both truth and arrogance in what he says.  My sister is an artist.  Over the years she's trained herself to see any number of visual relationships that can startle a non-artist like me.  I see some of them, particularly in her abstracts, but I'm missing quite a bit too.

 

But she's missing a lot too.  Our senses pass only a tiny amount of the information around us to our brain which, in turn, assembles a crude approximation of reality.  This virtual reality seems very rich and deep as it should.  It is, after all, reality to us.  We've learned to probe the real thing by observation with sensors that operate outside the limits of our own. Photographs in the near ultraviolet reveal patterns on flowers that some birds and insects use as a pollination cue.  You can look at your hand, a house or a running engine at wavelengths about fifteen times longer than our eyes are sensitive too and easily spot areas of hot and cold.  You can speed up or slow down time with time-lapse or high speed photography. Telescopes and microscopes let you see big things that are dim and far away and tiny things that you didn't know existed.  The list goes on and on. 

 

New observations have sometimes come with surprises that have forced new thinking about the nature of Nature.  There are aspects that are deeply beautiful.  We see some of them directly.  The parabolic arc a thrown ball travels.  The colors of a rainbow.  The intricacies of a spider web.  I've spent quite a bit of time thinking about what might be fundamental.  Certain relations that keep coming up in almost anything in Nature you examine in Nature's language of math.  Things that are beautiful.¹  It makes you wonder if, as a part of Nature, we've evolved to appreciate these beauties.  

 

But back to finding beauty.

 

I grew up in an extremely beautiful part of the world.  Jeri, Tom,  JoAnn and Jheri know it well.  Somewhat East of the Rockies in Montana (Alberta for Jheri).  Prairie and plain with a few smaller mountain ranges.  My parents would take us to the Bob, Glacier, Banff and Jasper several weeks each Summer.  After turning 15  it was okay to ride the dog up to East Glacier with my pack or take my bike over Going to the Sun. A lot of hiking, but especially watching the sky at night.  Enormous physical beauty even though my senses missed the vast majority. 

 

Since then I've lived mostly in urban or suburban areas.  At first I found myself pining for the mountains.  Gradually I  began to discover what Feynman said.  There's a beauty that comes from observation and it gets richer with understanding.  The ocean was very new to me when I was in California - mostly it was a destination on my bike ride.  No mountains in sight - in those days smog hid them if you faced East.  But then a professor friend asked if I could see regularity in the waves and pointed me to a book.  That was a major gateway drug.  I saw the mathematical beauty of the water before I could appreciate the beauty of the  ocean.  That came in time and I now have both.    It adds to what you can see and provides you questions to ask.  It is very much a lean forward experience.   

 

John Keats was disturbed by what he felt was the reductionism of science.  

Do not all charms fly
At the mere touch of cold philosophy?
There was an awful rainbow once in heaven:
We know her woof, her texture; she is given
In the dull catalogue of common things.
Philosophy will clip an Angel's wings,
Conquer all mysteries by rule and line,
Empty the haunted air, and gnomèd mine—
Unweave a rainbow, as it erewhile made

(from Lamia)

But understanding the nature of light and human vision adds a much deeper view with a beauty of its own.  For example you can get all of the colors of the rainbow from a single color of light merely by moving towards or away from the source at an appropriate speed in your mind.  You can start with a single color and reweave a rainbow. You can be encouraged to look for moonbows and appreciate why sun dogs form where they do.  After a bit of work you can discover for yourself that which you didn't know.

 

I'm taken with walks through a little wooded area near our place.  It isn't wilderness by any stretch of the imagination but I tend to go through around the same time of day most of the days I'm at home no matter what the weather.  After a few years I realized if I go by the trees, we really have six distinct seasons here.  I've seen the emergence of cycles that are longer than a year and am beginning to see the impact of global warming.  It has encouraged me to look and listen more deeply.  Microscopes, an ultrasonic converter to listen to bats, insects and mice, intrusion cameras to watch some of the animals and so on.  The coyotes and some of the deer know me and a vulture sometimes follows me on my walks.  It's a much richer place than I had imagined and I've learned more than I did when I lived near mountains.  Of course I'd be learning there too - just put in the time to observe and ask questions. 

 

There's variety in Nature if you can travel to  interesting areas.  It's a wonderful way to fuel curiosity and discovery if you have the resources.  But Nature is deep and everywhere.  Much deeper than any of us imagine.   A camera, portable microscope or binoculars may just be the gateway from almost anywhere.  It's just finding something curious.  It's so rich you can be captivated with or without math.  

 

You will see things you weren't capable of seeing before. 

__________

¹ I've probably written about some aspects of Nature that seem to be fundamentally beautiful.  It's pure conjecture, but I'd include relativity (not Einstein's - it's a subset), symmetry, invariance and complementarity. They seem to exist in art and music too.  Far too much to write about here, but a good topic for a walk. 

a few gallons of gasoline, black holes, and the state of utah

E = mc²    Perhaps the most recognizable equation in the world.  It says something with mass is equivalent to an enormous amount of energy.  A kilogram of mass has 9 x 10¹⁶ Joules of energy.  A quick back of the envelope says anything with the mass of three gallons of gasoline has enough energy to power the state of Utah for a year.  

 

There's just one little problem.  How do you tap it?

 

You could bring matter and antimatter together.  That's 100% efficient.  Three gallons of gasoline mixed with three gallons of anti-gasoline would liberate enough energy to power Utah for two years.  Unfortunately antimatter isn't easy to come by.  It's created in some nuclear decays (including some that happen in you body naturally) and in physics experiments, but the amounts are tiny and the cost of making it astronomical. More practically we're left with three basic methods:  chemical, nuclear and gravitational.

 

I mention gasoline as it's a chemical reaction and we have a sense of what a gallon can do moving in a car.  To get energy from chemical reactions you need to pick the right chemicals.  But how efficient process when it comes to extracting the available mass energy?  Doing a bit of math you find one of the most efficient chemical reactions - combusting hydrogen and oxygen, burning gasoline is not as good - converts 0.000000001% of the available mass into energy.¹  This is so little we never worry about E = mc² when we're using chemical reactions.

 

Nuclear reactions are much more efficient than chemical reactions.  In regular fission, say uranium235   decaying to krypton and barium, only about 0.08% of the uranium's mass turns into energy.  Fusion is somewhat better.  Combining four hydrogens into one helium is about 0.7% efficient.   Impression and potentially enough to end life on Earth, but peanuts compared to matter-antimatter.  

 

What about gravity?

 

It turns out black holes are very efficient mass-energy converters.  It might seem odd at first as most people have heard black holes as places where anything falling in don't escape.  But not everything falls in.  To see how that works consider a rock in space aimed at the Earth ..  a meteorite for example.  A typical speed as one hits the atmosphere about 50,000 kilometers per hour.  Friction slows it down and the kinetic energy it loses turns into heat.  Most objects smaller than marble size are vaporized leaving a brief streak in the sky.  The  heat is radiated away as infrared and visible light.  Some of the mass is converted to energy.  That works out to about 0.0000001% of its mass converted to energy.    Not much different than a chemical reaction and a poor source of energy.

 

Black holes are special.  They're really dense.  Mind-numbingly dense.  An Earth-mass black hole would be about the size of a grape.  Something falling towards a black hole ends up moving very fast  - often close to the speed of light.   By the time a falling object makes it to the black hole's event horizon it has enormous kinetic energy -which would be lost to the rest of the Universe when it crosses over. But if it slowly spirals in, colliding with stuff as it goes, it heats up and radiates energy to the rest of the Universe.  

 

The type of black hole is important.  I won't get into the physics as it's reasonably thick, but an object spiraling in to a non-rotating black hole radiates about 6% of its mass to the Universe - about ten times better than nuclear fusion that powers stars.  Not too shabby.   Rotating black holes drag space-time around with their rotation and effectly allow the object to fall in further.   If the rotation is as fast as garden variety black holes, about 42% of the mass is converted to energy.  Douglas Adams would have been pleased with the result.

 

So if you use a rotating black hole you can power the state of Utah for a year on a bit over seven gallons of gasoline - or same mass of any matter.

__________

¹ Physicists out there forgive me..  I'm being loose with the notion of converting mass into energy to stay out of the weeds.  Sometimes being correct enough is ok.

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.