omenti

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.