Author: Gregory Pijanowski

The Education of Albert Einstein

Most historic figures have myths attached to them and certainly Albert Einstein is no exception.  Among them, Einstein failed math in high school and did his famous work on relativity in “splendid isolation”.  After reading Walter Isaacson’s biography on Einstein, one can see the social influences that shaped Einstein in his early years and how it enabled him to make advances in physics that others could not.  And much of that is rooted in modern educational theory.

Jean Piaget’s research on child development concluded there are four stages of development.  The final transition usually occurs around age eleven when a child moves from a concrete understanding of the world to an ability to solve abstract and hypothetical problems.  The age this transition occurs can vary with each individual and also with the subject matter.  Contrary to the struggling student myth, Einstein began thinking in abstract terms at a very early age.  A compass given to Einstein at age five demonstrates this.  Rather than thinking of the compass in concrete terms, that is, a mechanical device that points north, Einstein conjectured on the invisible magnetic field that caused the compass to always point north.  And this trend continued in Einstein’s early life.

During the 1930’s, a Ripley’s Believe It or Not! column stated Einstein failed math in high school and has remained part of the Einstein lore.  Truth is, Einstein had learned calculus by age 15.  And physics?  Einstein was at a college level by age 11.  How did this myth begin?  More than likely from Einstein’s days as a student in Germany’s authoritarian educational system.  Einstein thought little of rote learning, and was not afraid to make his teachers aware of that.  In today’s parlance, that bit of acting out probably gave the impression of a troubled student.  So what was it in Einstein’s background that allowed him to advance so quickly in his studies?

The second pillar of modern educational theory is Lev Vygotsky’s theory of learning by social interaction.  Part of that theory is the concept of the zone of proximal development.  Here, a student is placed in contact with a more skilled partner to help master a subject.  In Einstein’s case, his parents provided the first zone of proximal development.  Hermann Einstein, Albert’s father, partnered with his brother Jakob building electric generators and lighting.  This surrounded Albert with a technical/scientific background from the get-go not unlike, say, Bill Belichick growing up in a household with a football coach as a father.  Pauline, Albert’s mother, was a pianist and Albert would play the violin most of his life to catch a break from physics.

Einstein plays the violin during the charity concert in the New Synagogue, Berlin, January 29, 1930. Credit: Institute of Czech Literature, Czech Academy of Science.

At age 10, Einstein was introduced into another zone of proximal development in the person of Max Talmud, a 21-year-old medical student who had dinner with the Einsteins weekly.  Talmud introduced Einstein to many subjects including geometry and Kant’s Critique of Pure Reason.  Talmud’s greatest gift to Einstein may have been Aaron Bernstein’s 21 volume People’s Book on Natural Science.  Bernstein encouraged constructive learning techniques, in particular, thought experiments such as what it would be like to ride along a light beam.  These thought experiments played a crucial role in Einstein’s relativity breakthroughs and his attempt to describe the theory to the public in his book, Relativity:  The Special and General Theory.

As one might imagine, Einstein raced out of Talmud’s zone of proximal development in short order.  Not unlike the first time a student realizes they have raced ahead intellectually of their teacher.  Nonetheless, Talmud served as a rich pipeline of learning resources for Einstein.  In some sense, Talmud was Einstein’s version of the internet without all the negative distractions.  This resource enabled Einstein to think in ways that provided insights to solve problems other physicists were not able to.  Young Albert Einstein also possessed a fierce streak of individuality.

Self-identity is typically formed during high school years, but can be delayed beyond college.  By all indications, Einstein’s self-identity was molded by his family and his ethnicity.  Of the four general parenting characteristics, the Einsteins would fall into authoritative (not to be confused with authoritarian).  This engaged parenting style typically endows a child with high self-esteem and confidence, which certainly Albert Einstein possessed.  As a Jew in Germany, Einstein was an outsider in German society (as Isaacson notes, only 2% of Munich’s population was Jewish) and this reinforced Einstein’s contempt for the German authoritative educational system.  The Swiss educational system was another story.

Aarau, Switzerland. Credit: Roland Zumbuhl/Wiki Commons

Fed up with Germany, Einstein moved to Switzerland at age 16 and spent a year at the Aarau Cantonal School.  This school favored a constructionist educational philosophy where students build their own knowledge rather than simply accepting what was told to them by an authority figure.  Part of the instructional technique at Aarau included an emphasis on visualization of mathematical concepts based on the ideas of Johann Heinrich Pestalozzi who also valued student individuality.  Einstein thrived at Aarau and its visualization techniques played a significant role in Einstein’s breakthroughs in relativity.

Einstein’s Aarau transcript. Grade scale is 1-6 with 6 being best grade. Credit: Wiki Commons. Translation can be found at: https://commons.wikimedia.org/wiki/File:Albert_Einstein%27s_exam_of_maturity_grades_(color2).jpg

However, Einstein’s professional academic career did get off to a slow start.  In fact, he was working at a Swiss patent office in 1905 when he published four landmark papers on special relativity, mass-energy equivalence (E = mc2) the photoelectric effect (proving light acts as particles as well as waves) and Brownian motion (which established the existence of atoms).  Einstein’s anti-authoritarianism during his college years at Zurich Polytechnic rubbed some of his professors the wrong way and he had difficulty obtaining good references.  This has led to the myth of Einstein working in “splendid isolation” during this time.  And in a sense, Einstein was isolated from the heavy hitters in physics.  However, this may have been a godsend as those heavy hitters made discoveries that pointed towards relativity, but lacked the creativity Einstein possessed to put all the pieces together.  In pursuit of this, Einstein found one more learning social component in Zurich.

The Olympia Academy founders Conrad Habicht, Maurice Solovine, and Albert Einstein. Credit: Wiki Commons/Emil Vollenweider und Sohn

Had Einstein been discussing the current problems of physics in academia after the turn of the century, he would have been hamstrung by the Newtonian concept of absolute time.  That is, clocks run at the same pace for every observer in the universe.  Einstein and a group of friends formed what they jokingly dubbed the Olympia Academy.  Of the many topics discussed during these weekly sessions were David Hume’s and Ernst Mach’s rejection of absolute time.  This skepticism of Newtonian absolute time is the linchpin of special relativity, which states the speed of light is constant to all observers in the universe and time is variable as a function of velocity (times moves more slowly the faster you go, reaching a standstill at the speed of light).  Special relativity also put the universal speed limit at light speed leading to general relativity, which redefined gravity as curvatures in space-time which ripple throughout the universe at the speed of light and not instantaneously via Newton’s gravitational fields.

So is there anything we can apply from Einstein’s education?

To begin, don’t expect your students to become Einstein – the human race is lucky to experience such a genius once a century.  Great disasters are usually the result of many little things going wrong, great successes require many little things going right.  Replicating Einstein’s education will not likely produce another Einstein anymore than putting a hockey stick in a child’s hand will make him a Wayne Gretzky.  But to continue the sport’s analogy, Red Auerbach expressed a coaching philosophy that his job was to help his players reach their differing levels of maximum potential.  To illustrate, I am the same height as Larry Bird and Magic Johnson, but my maximum potential as a basketball player is significantly lower.  Rather than concern myself with that, with proper instruction, I should focus on reaching my personal potential level.

For example, if a student is struggling putting the ball in the hoop, rather than give a wedgie George Costanza style, have the player perform a thought experiment Albert Einstein style.  Instead of traveling with a light beam, imagine moving along with a basketball headed for the rim.  Take two scenarios, a shot with a low arc and one with a high arc.  How does the hoop appear as you are headed with the ball towards it?  The ball with the high arc “sees” more area in the hoop to enter, increasing the odds of making two points.  It  might not make the child into Larry Bird, but will move forward into reaching their full basketball potential wherever that may fall.

Techniques such as this allows a student to internally construct knowledge and not simply take a teacher’s word for it.  And student’s can apply these techniques in other subjects.  Also, the social component of learning cannot be ignored.  Ridiculing, instead of providing instruction, for a poor performing student causes social isolation not only in that class, but can cascade throughout the educational experience.  All the educational resources in the world cannot help a student who is socially isolated.  And likewise, lack of community resources in the educational system can thwart good instruction.  Teaching someone to fish may keep them well fed, but it only works if they actually have a fishing rod to use.

To maximize a student’s potential a rich social experience is required where ideas are passed back and forth as well as contact with more experienced learners.  This does not stop after childhood.  As the great economist Alfred Marshall noted, inexperienced workers are more productive when teamed with more experienced workers.  This is also why industries tend to form geographic clusters such as Silicon Valley.  In fact, despite his disdain for Germany, Einstein moved to Berlin in 1914 as that was the center of physics on the continent.  The diaspora of Jewish scientists, including Einstein, in the 1930’s had the opposite effect of diminishing Germany’s physics research.  Also, adequate resources must be available to apply what is learned.  Can a student without computer resources expect to function well in today’s society?  Finally, do not burden the student with unrealistic expectations.  Focus on what the student can do, not what they cannot do, and use that as a base to build upon to reach their own level of maximum potential.

*Image on top of post is Einstein presenting a lecture at American Association for the Advancement of Science in Pittsburgh on December 28, 1934.  Credit:  AP/Public Domain.

Why Go to Jupiter?

At 11:53 P.M. EDT on July 4th, as the last of the fireworks begin to fade, NASA will be eagerly awaiting a signal from the Juno spacecraft that it has entered orbit around Jupiter.  This will commence twenty months of exploration of Jupiter’s polar regions which is the epicenter of the giant planet’s massive magnetic and auroral activity.  It will also signify the beginning of the end of NASA’s second wave of space missions to the gas giants that began in 1989 with the launch of the Jovian Galileo probe.  In September 2017, Cassini will cease operations with a decent into Saturn.  Five months later, Juno will meet the same fate as it plunges into Jupiter.  NASA’s exploration of the outer planets will go dark until the 2020’s.

Juno, named after the Roman goddess wife of Jupiter, was launched in 2011 and embarked on a 1.8 billion mile odyssey to the giant planet that included a flyby past Earth.  Why flyby Earth?  The pull of Earth’s gravity whipped Juno into sufficient velocity to reach Jupiter.  This maneuver, while more time-consuming, saves fuel and cost.  Not an insignificant consideration as Juno was hatched during an era of flatline budgets for NASA.  In all, the Juno mission will cost $1.1 billion or roughly the same as a NFL stadium.  Below is a video of Juno’s trajectory to Jupiter.

Normally, we associate planetary missions with spectacular imagery.  Juno does have a camera on board but that will be used for outreach purposes.  The science of Juno involves magnetometers and particle detectors.  Jupiter has a massive magnetic field that produces aurora activity several times the size of Earth and radio emissions as well.  Juno intends to use its measurements to study the interior of Jupiter which in turn will reveal the processes that drive its magnetic activity and origins.

Jupiter’s aurora was discovered in 1979 by Voyager I.  On Earth, the aurora is created by ionized particles embedded in the solar wind spiraling down Earth’s magnetic field lines towards the poles (charged particles will follow the path of magnetic fields).  Here, in the upper atmosphere, the ionized particles slam into oxygen and nitrogen atoms exciting their electrons to a higher energy level.  As the electrons subside back to a lower energy level, the kinetic energy of these particles are converted to electromagnetic energy in the form of green and red light.

Juno’s elliptical orbits will avoid zones of high radiation surrounding Jupiter. Credit: NASA/JPL/Caltech/Institute for Aeronautics and Astronautics

On Jupiter, the process is a bit different.  The solar wind contributes to the aurora, but there is another major source of ions from the moon Io.  The most volcanic active body in the Solar System, Io spews out oxygen and sulfur ions that travel along Jupiter’s magnetic field to the poles.  The aurora has been viewed by the Hubble which recently released this image.

aurora
Credit: NASA/ESA

When electrons are accelerated, radio waves are transmitted.  This is the principal that radio towers work on.  Electrons are accelerated up and down the transmission tower producing the broadcast received by your radio and converted to sound waves by its speakers.  Around Jupiter, electrons are accelerated as they spiral down the magnetic field lines.  Io also acts to accelerate electrons as its presence distorts Jupiter’s magnetic field. A change in a magnetic field induces an electric field pushing the electrons.  This action creates radio transmissions from Jupiter that are received on Earth in the 8-38 MHz range, the same range shortwave radio is transmitted.

Ham radio operators have received these transmissions from Jupiter and NASA’s Radio Jove project allows schools to purchase receivers for a few hundred dollars to detect Jupiter’s radio waves.    Samples of these radio observations can be heard here.

One might ask, why should we care about Jupiter’s magnetic field and how does it relate to Earth?  The answer lies in the fact that while we can map Earth’s magnetic field as it extends into space, we are unable to map the dynamo process generating the field in Earth’s interior.  Jupiter, being a gaseous planet, will allow Juno to map the magnetic field down to the interior where the dynamo lies.  Jupiter formed before the solar wind blasted away the primordial material of the solar nebula.  The more we learn about Jupiter’s interior, the more we’ll know how the Solar System originated.  The video below describes how Juno will explore Jupiter’s magnetic field.

Juno’s instrument package includes a radio transmitter to detect variations in Juno’s velocity as it orbits Jupiter.  Doppler shifts in the radio waves will allow for measurements of variations in Jupiter’s gravity field providing hints to the make up of its interior.  The Jovian Auroral Distributions Experiment (JADE) and Jupiter Energetic Particle Detector Instrument (JEDI-video below) will measure the ions and electrons traveling along the magnetic field lines that eventually produce Jupiter’s aurora.

The Jovian Infrared Auroral Mapper (JIRAM) will provide images of Jupiter’s aurora.  Juno’s magnetometer will construct a 3-D map of Jupiter’s magnetic field, both the field lines and their magnitude.  The Microwave Radiometer’s (MWR) function is to detect thermal radio emissions from six layers beneath the clouds of Jupiter.  This will provide a 3-D map of the Jovian atmosphere.  The Ultraviolet Imaging Spectrometer’s (UVS) mission is to examine the aurora in ultraviolet allowing for measurements on both the day and night sides of Jupiter.  The aptly named Waves instrument will measure radio waves produced by the magnetic field.  Last, but not least, is the JunoCam which will take the first pictures of Jupiter’s poles and allow for the public to participate on deciding other targets to image.

Image of Antarctica taken by JunoCam during Earth flyby. Credit: NASA.

On February 21, 2018, after completing 37 elliptical orbits of Jupiter, Juno will crash into Jupiter ending its adventure.  The next mission to the outer Solar System is not scheduled until the 2020’s with NASA’s planned Europa mission.  This gap was caused by funding curtailments created by the Great Recession.  This is similar to the gap between the Pioneer and Voyager missions launched in the 1970’s and the Galileo mission launched in 1989.  That first gap was caused by budget cuts during the Reagan administration in the 1981-82 recession. In fact, that gap almost became catastrophic as the administration proposed to terminate Voyager funding before the mission reached Uranus and Neptune.  Fortunately, Voyager was kept alive and is still returning data today.  So, what can we hope for in the meantime?

The Hubble Space Telescope will still take high quality images of the outer planets, and will be joined by the James Webb Space Telescope in 2018.  Of course, both have other mission objectives and are not dedicated to viewing the Solar System.  The next generation of ground telescopes featuring mirrors in the 30-40 meter range will be able to peer deeper with more detail into the Solar System, possibly mapping surface characteristics of Kuiper Belt objects.  New Horizons just received funding approval to visit the Kuiper Belt object 2014 MU69 beyond Pluto on New Year’s Day in 2019.  Despite the upcoming lull in deep space exploration, the future still looks interesting for planetary science.

*Image on top is workers testing the solar panel for Juno prior to launch.  Credit:  NASA.

(Slight) Changes in Latitude

At first glance, Buffalo and New York City would appear as different as two cities can be.  However, over the past two centuries both have been connected by the Erie Canal, the Empire State Express that linked Buffalo’s Central Terminal with Grand Central Terminal, and the New York State Thruway.  Infrastructure joining two cities not only moves people and goods, but ideas.  During the late 1800’s, Buffalo was a proving ground for many innovative architects who transferred their ideas to the big city.  A two-block area in downtown Buffalo has very significant architectural ties to New York City.

ESB1
Ellicott Square Building, Photo: Gregory Pijanowski

Above is the Ellicott Square Building. You may recognize it as the Ellicott Hotel from the movie The Natural. Built in 1896, it was the largest office building in the world at the time. In its basement was the Vitascope Theater, possibly the first movie theater in the United States.

Advertisement for Vitascope Theater.  Ten cents in 1897 is $2.75 in 2016 dollars. November 7, 1897. Credit: Wiki Commons.

On the marble floor of the Ellicott Square Building are several swastikas.  Before Nazi Germany, the swastika symbolized good fortune and is still used for that purpose in India and Indonesia.  The architect for the Ellicott Square Building was Daniel Burnham who six years later designed this building:

Flatiron Building, 1990, Photo: Gregory Pijanowski
Flatiron Building, 1990, Photo: Gregory Pijanowski

That, of course, is the classic Flatiron Building.  The shapes of the respective buildings were both determined by the street layout.  While most of Manhattan is laid out as a grid, the Flatiron Building lies where Broadway diagonally cuts across 5th Avenue necessitating its distinctive shape.  Daniel Burnham’s architecture firm still survives in the form of Graham, Anderson, Probst and White in Chicago.

Next door to the Ellicott Square Building is M&T Plaza:

MandT
M&T Plaza, Photo: Gregory Pijanowski

Does the exterior steel tubing and resultant narrow windows look familiar? The buildings below had the same type of framework:

World Trade Center, 2001. Credit: Jeff Mock, Wiki Commons.

Both M&T Plaza and the World Trade Center were designed by Minoru Yamasaki during the  mid-1960’s. In each building, the exterior steel columns were intended to carry the load of the building’s weight.  This precludes the need for interior columns maximizing floor space.  A century before M&T Plaza was built, Abraham Lincoln’s funeral train stopped in Buffalo and his body laid in state on the site as some 100,000 filed by to pay their respects.

April 27, 1865 – Lincoln’s funeral cortege. Credit: Buffalo & Erie County Public Library.

Minoru Yamasaki passed away in 1986 and his firm Yamasaki & Associates ceased operations in 2010, a victim of the Great Recession.  Of course, we are no longer able to appreciate the World Trade Center in person, but their architect’s legacy lives on in Buffalo which set the stage for his most prominent work.

The 2nd Amendment in the Classroom

The aftermath of another American mass shooting in Orlando means the gun control debate along with the interpretation of the 2nd Amendment is again front and center in the media.  How to handle this in the class?  The best bet is to allow your students to construct an interpretation by going back to the historical roots of the 2nd Amendment.

Before that is done, I would recommend students to be skeptical of the initial reports regarding the motives of a mass shooting.  Amid the confusion, the rush to get the story first, and now the need for everyone to get their hot takes in on social media, an awful lot of misinformation gets flung around the first few days after such an incident.  As documented in Dave Culler’s book Columbine, the initial reports that the shooters were part of the goth clique Trench Coat Mafia turned out false.  In fact, most of the Trench Coat Mafia had graduated the prior year.  However, in a classic case of circular reporting, an erroneous statement by a student was repeated throughout the day of the shooting by several media outlets.  The truth will often take days, weeks, months, sometimes years to illuminate.

That being said, it should be stressed to students that they build their own interpretations of the 2nd Amendment and not rely on someone to do it for them.  The full amendment has to be analyzed by the class:

“A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed.”

An excellent start to this exercise is to have the class read the 29th Federalist Paper by Alexander Hamilton and the 46th Federalist Paper by James Madison.  These papers, written four years before the Bill of Rights were enacted, form the foundation of this amendment.  Before the class embarks on this endeavor, it’s a good idea for the students to discuss their current preconceptions of the 2nd Amendment to give a baseline how their understanding progresses throughout this lesson.

Title page for Federalist Papers. Credit: Library of Congress.

After the students have read the papers, a class discussion should ensue.  I like to compare this to my three stints on jury duty.  Some in the jury always wanted to vote right away.  Its been my experience a discussion first would bring to my attention angles of the case I had not considered.  And that is likely to be the case here as this is the student’s first attempt reading these documents.

The followup discussion should address the following themes:

Do the Federalist papers address individual self-defense or argue the right of states and/or federal government to form standing militias?

What was the importance of public militias during the time the constitution was drafted?  Do those reasons apply today?

In the era of industrialized warfare, could an armed militia protect the public from a tyrannical government given the asymmetry in firepower?  Examine some recent case studies such as the Soviet Union, Syria, and North Korea.

Are the popular arguments, pro or con, for gun control covered in any sort of context in the Federalist Papers?  Are media commentators knowledgeable on the topic?

And finally, ask your students how the assignment has changed their perceptions of the 2nd Amendment?

Having students construct their understanding of the 2nd Amendment does not mean whatever comes to their minds is to be taken as fact.  Their statements should undergo critical review by the rest of the class.  The class has to comprehend any criticism is not intended to be personal, but as a quality control measure on their understanding of the context of the Federalist Papers.  As a teacher, you must address the fact that any criticism should be based on what was read in the assignment and cannot devolve into ad hominem attacks.  The use of such attacks is an admission the student has lost the argument and did not integrate what was read as required to participate in the discussion properly.

The teacher in a sense acts as a referee during the discussion.  The classroom is not intended to be an ideological bubble, the students will get plenty of opportunity to experience that in today’s society.  A conflict of thought and ideas are healthy in the classroom.  The teacher should ensure the student’s arguments exhibit a solid understanding of the Federalist Papers and are not cherry-picking or taking out of context any of the readings.  Unlike social media, a student’s place in the discussion is earned with reading comprehension and a critical understanding of the material.  The loudest voice should not win in the classroom.

History has a certain advantage as original documents can be understood at the high school level.  This is opposed to science where journal articles usually require advanced training to grasp.  The internet makes the Federalist Papers easily available to each student and that was not the case when I was in high school.  In a controversial topic such as gun control, constructionist learning techniques allows the student to build their own understanding rather than rely on an authority figure to do it for them.  And this is a skill set that will serve your students well in the future.

*Image on top of post is an engraving of the Battle of Lexington.  Credit:  John H. Daniels & Son/Library of Congress.

Big Mo

During the nascent age of home computers, the Apple IIe football game Tuesday Morning Quarterback had a momentum indicator that fluctuated in favor of both teams throughout the game.  When momentum was on my side, short gains turned into long gains, touchdowns came easier, and life was good.  When on the opposition’s side, fumbles and interceptions became the norm and the odds of anything else going bad, along with my blood pressure rising, increased.  The concept of momentum in sports is well-known, lesser so, is the physics concept of momentum which has many application in sports and astronomy as well.

Momentum is defined as follows:

p = mv

Where p is momentum, m is mass, and v is velocity (both p and v are in bold as they are vectors with two quantities, magnitude and direction).  Thus, a marble rolling at 1 m/s has more momentum than a freight train at a stop.  And obviously, a freight train moving at 1 m/s has far more momentum than that marble at the same velocity.  A change in momentum over time also tells us how much force has been imparted on an object.  In more formal terms:

F = dp/dt

In other words, force is equal to the rate of change in momentum divided by the rate of change in time.

Safer barrier after a NASCAR crash. Photo: Jared Smith/Wiki Commoms.

Safer barriers in auto racing use this concept.  Fatalities in racing used to be a fairly common occurence.  There were 37 fatalities during the first 57 runnings of the Indianapolis 500.  Improvements in auto design, head restraints, and the safer barriers have dropped those numbers considerably.  The safer barriers act as a cushion to soften the blow of a race car against the wall.  What the barriers do is prolong the time of impact.  Looking at the equation F = dp/dt, doubling the time of impact reduces the force imparted on the race car by one half.  The amount of time of impact is small, we’re talking milliseconds here, but enough to dramatically increase driver safety.  Another sport is grappling with the same concept, but with an impact that occurs inside the body.

Chronic Traumatic Encephalopathy (CTE) is a degenerative brain disease found in football players.  CTE results in memory loss, aggression, and early dementia.  The disease is the result of repetitive concussive blows of the brain against the skull.  The brain has some protection against common bumps in the form of fluid inside your skull, but the fluid gives way when a violent blow, such as often occurs in football, is taken by the head.  In effect, the inside of your skull lacks a safer barrier in these instances.  This shortens the time of impact leading to an increase in force directed to the brain.  And here you can see how problematic this is for football.  You can’t insert a safer barrier inside the skull, the answers lie in changing the game in a manner that reduces these impacts.  Really, the only solution at this point is to eliminate contact in the game, something that would radically alter the nature of football which has become the most popular sport in America.

Momentum also plays a role in rotational movement, which is applicable to a much less violent sport than football.

Angular momentum (L) is defined as:

L =Iω

Where I = moment of inertia and ω = angular or rotational velocity.

I varies by the shape of the spinning object but is proportional to the radius.

As angular momentum is conserved, if the radius of an object is reduced, its rotational velocity increases.  Figure skaters use this principle to create rapid spinning movements in their routines.  As the skater begins to rotate, the arms are drawn towards the body to reduce radius and increase velocity.  You can try this at home on a swivel chair.  Have a friend spin you around with your arms outstretched, then pull your arms inward.  You will note the rate of your spin increasing.  Not as much as a figure skater does, but enough to notice.

Imparting a rotational force on an object is referred to as torque.  If an object is malleable, increasing its angular momentum by adding torque to it will cause it to flatten.  You’ll see this at your local pizzeria when the cook takes a blob of pizza dough and spins it in the air.  The blob becomes flattened into a pie shape that is then cooked in the pizza oven.  Beyond Earth, there are many applications of this principle.

Angular momentum flattens protoplanetary disk around the star HL Tauri Credit: ALMA (ESO/NAOJ/NRAO), Yen et al.

Our Solar System originated when torque was applied to an interstellar gas cloud.  This force most likely came from a nearby supernova.  As the gas cloud began to rotate, it flattened and commenced the process of constructing the Sun in the center and the planets in the disk.  This process has been observed in other planetary systems in the formation stage.  How spiral galaxies originate is not completely understood, but a galaxy’s angular momentum causes it to flatten into the classic spiral shape we see in so many space images.  When galaxies collide, the reverse of this process takes place.

The Antennae Galaxies/NGC 4038-4039
The The Antennae Galaxies/NGC 4038-4039 colliding. Credit: NASA, ESA, and the Hubble Heritage Team (STScI/AURA)-ESA/Hubble Collaboration

When two spiral galaxies collide, the odds of their angular momentum being in the same direction during the collision is slight.  Think of it this way, kids often start a whirlpool in a swimming pool by walking around the perimeter of the pool in the same direction.  This torquing action increases the angular momentum of the water in the pool.  If some other kids jumped in the pool and starting walking in the opposite direction, this torquing action offsets the original whirlpool, causing the rotation of the water to decrease.  This is essentially the same thing that happens to spiral galaxies when they collide.  The result is the two galaxies merge to form a giant elliptical galaxy with little rotation.  In essence, this is pizza effect put in reverse as the two flatten spirals form a blob shape.

And how does this apply to us?  Well, not us directly, but in a few billion years, the Milky Way will collide with its nearest large neighbor, the Andromeda galaxy.  While the two galaxies contain over a trillion stars combined, the odds of the Sun colliding with another star is slim.  That is a consequence of the large distances between the stars.  If the Sun was the size of a basketball, the nearest star would be 4,300 miles away.  However, the collision will eject stars from their respective galaxies and gravitational disturbances could cause incoming comets to collide with planets.  As this event will occur billions of years from now, the Sun will be nearing its red giant phase meaning Earth has become uninhabitable.  Humanity will not contend with this event unless interstellar travel has been achieved.  The video below is a computer simulation of the collision.

So momentum is not just a phrase tossed around in “horse race” punditry, but an actual physics concept with applications in our daily lives and the rest of the universe.

*Image on top of post is Mike Stratton’s tackle of Keith Lincoln in 1964 AFL Championship game.  The tackle was a momentum changer both in the physical and allegorical sense as the play turned the game in Buffalo’s favor.  Credit:  Wiki Commons.

Science and Authoritarianism

With authoritarianism making headway in both Europe and America, it might be instructive to take a look back at what has historically happened to scientists and their supporting institutions when democracy wanes.  Here, I’ll take a look at Nazi Germany.  This might tempt some to invoke Godwin’s law as this is the extreme case study.  However, the Freedom Party of Austria has its roots in the Nazi party while Greece’s Golden Dawn party employs an altered swastika for its emblem inviting the comparison.  In America, the rise of Donald Trump trends more towards the celebrity cult/buffoonery of Gabriele d’Annunzio/Benito Mussolini, but the same can not be said of his most strident Twitter followers.  We’ll focus on the three most prominent German scientists of the era, Albert Einstein, Max Planck, and Wernher von Braun.

The Refugee

Over a decade before Hitler rose to power, Albert Einstein became the most famous scientist in the world during 1919 when the Eddington expedition provided experimental confirmation of general relativity.  Einstein’s troubles in Germany started only a couple of years later as Philipp Lenard and Johannes Stark, Nobel Prize winners in their own right, began to wage an anti-Semitic campaign against Einstein.  Lenard was a fine experimental physicist, but had been left behind in the modern physics revolution.  Stark also had difficulty comprehending the mathematics of the new physics.  Unable to critique relativity on its merits, both referred to modern theoretical physics as “Jewish science” and eventually espoused what was referred to as Deutsche Physik or Aryan Physics.  This politicization of science discarded modern physics and was intended to ride the wave of Nazi power.

Events in Germany came to a head as Hitler became Chancellor in January of 1933.  Shortly afterwards, Jews were forbidden to hold university or research positions.  Einstein had been in Belgium during early 1933 with the intention of returning to Germany.  However, as the situation deteriorated (Einstein’s house had been raided and sailboat confiscated), Einstein appeared at the German consulate and renounced his German citizenship (Einstein was still a Swiss citizen) and resigned his position at the Prussian Academy of Sciences, the same academy where he announced his final general relativity theory in 1916.  During the summer of 1933, while still in Belgium, word was put out that a $5,000 bounty had been placed on Einstein’s life.

On October 3rd, four days before he left Europe never to return, Einstein gave a speech at the Royal Albert Hall.

During the speech, Einstein asked, “How can we save mankind and its spiritual acquisitions of which we are the heirs? How can we save Europe from a new disaster?”  The eventual answer, of course, was at a cost of millions of lives.

After arriving in America, Einstein took up a job offer at Princeton where he had remained until his death in 1955.  Einstein worked to get other unemployed German Jewish physicists jobs in America.  In all, over a thousand Jewish scientists relocated to America including  several Nobel prize winners.  This represented a significant shift in intellectual and innovative resources from Europe to America.  In 1939, Einstein wrote a letter to President Roosevelt warning about the potential for Nazi Germany to produce an atomic bomb.  Many top refugee scientists worked on the Manhattan Project, whose final result would have been used against Germany had it not surrendered a couple months before the first atomic test.

The essential lesson here is that Einstein’s enormous talent did not spare him from Nazi persecution.  Purging or banning an ethnic group, besides the obvious ethical considerations, results in an intellectual drain.  Segregating an ethnic group from educational resources presents a loss of potential economic growth, which is why ideologues need to resort to ethnic stereotyping to deflect attention from the negative by-products of their policies.  Einstein, to his last days, spoke out for civil rights, lectured at black colleges, and was rewarded for his efforts with an 1,800 page FBI file.

As a pacifist, Einstein deeply regretted the letter that started the Manhattan Project.  As a scientist, to this day, his work has held up to every rigorous test experimental physicists have thrown up against it.  Relativity theory has provided us with the Big Bang, black holes, time dilation, and gravitational waves.  Einstein will be long remembered while those who chose the expedient path of supporting Nazism have had their scientific legacy tarnished greatly.  Not everyone in the German scientific establishment jumped aboard the Nazi bandwagon, some tried to mitigate the effects of Nazism by working within the system.

The Statesman

When Hitler ascended to power, Max Planck was president of the Kaiser Wilhelm Society.  Planck had revolutionized physics in 1900 by discovering energy was emitted in discrete packages dubbed quanta.  This would kick-start the quantum mechanics breakthroughs in the decades to follow.  Planck was among the first to recognize the significance of Einstein’s work in 1905 on special relativity, and as editor of the journal Annalen der Physik, published Einstein’s work.  It was Planck, as dean of Berlin University, who opened up a professorship for Einstein in 1913.  It was here that Einstein finished up his work on general relativity.

Max Planck. Credit: Bain News Service/Library of Congress

Max Planck was born in 1858 and his life arced with Germany’s rise from a patchwork of unorganized states to unification as a single nation in 1871, eventually to  rival the British Empire as a European power.  Conservative in temperament, Planck was inclined to be apolitical publicly.  However, Planck was a firm believer in advancing German science and loyalty to the German state.  In May 1933, as Einstein was severing his ties to Germany, Planck announced at the Kaiser Wilhelm Society annual meeting that:

“The Kaiser Wilhelm Society for the Advancement of the Sciences begs leaves to the tender reverential greetings to the Chancellor and its solemn pledge that German science is also ready to cooperate joyously in the reconstruction of the new national state.” 

In reality, Planck thought the Nazi party would moderate its views once in power (sound familiar?) and personally endeavored to continue the high standard of German research.  That did not happen, of course.  Planck met with Hitler personally in 1933 hoping to moderate his policy to stem the exodus of Jewish scientists from Germany.  The meeting ended with a Hitler rant that science would have to suffer.  Not surprising, as that is how discussions with hopeless ideologues tend to go.  At the annual Kaiser Wilhelm Society meeting in 1934, Planck noted while the society was devoted to science in service of the fatherland, pure research was suffering as a result of Nazi policies.  By 1935, Planck openly defied Hitler and attended the funeral service for Fritz Haber, who had been in exile from Germany.

It is difficult to maintain a functional operation when the overall organization is dysfunctional.  Eventually the dam breaks, and the dysfunctionalty takes control.  Planck in 1933 was also playing the role of the extreme centrist, blaming both Nazi and Jewish cultures equally for the situation in Germany.  In this one can see the danger in not recognizing an asymmetric authoritarian movement.  By 1936, Planck had openly stated that intelligence counts more in science than race.  But despite Planck’s efforts, the purging of highly talented Jewish scientists had been complete.  In 1937, Planck retired as president of the society, but not without offering the parting shot that scientific work required opposition to prove its merit, something Nazi supported science would not permit.

Planck’s experience offers the cautionary tale that an authoritative movement must be defeated before it obtains the keys to governance.  There was no reasoning to be had with Hitler in 1933 and access to power offered no motivation for Nazis to moderate their policies towards Jews.  By the end of World War II, Planck’s Berlin house had been destroyed in an Allied air raid, and he lost his son who was put to death for his participation in the plot to kill Hitler.  Planck had previously lost another son in World War I during the battle of Verdun.

Eight days after the surrender of Germany in 1945, at the age of 87, Planck resumed his role as president of the Kaiser Wilhelm Society.  After Planck had passed away in 1947, the Kaiser Wilhelm Society was renamed the Max Planck Institute.  Under a democratic Germany, the institute has produced 18 Nobel prize winners and over 13,000 scientific publications annually.  ESA’s Planck mission measured the cosmic microwave background radiation – the remnants of the Big Bang.  The spectrum of this radiation is that of a blackbody, the same type Planck studied to determine that energy is emitted in packages.  Blackbody spectra are emitted by objects in a hot, dense state, meaning that was the state of the universe when it was 380,000 years old.  Planck’s legacy has enabled us to understand the nature of the electron and the origins of the universe.

In 2007, the Max Planck Institute completed a ten-year study on the history of the Kaiser Wilhelm Society during Hitler’s reign.  The report acknowledged, especially after Planck’s departure in 1937, unethical scientific research during that period.  It was not just party hacks involved in this behavior, some of the most talented scientists engaged in projects that degraded their reputations.

The Opportunist

On July 20, 1969, Neil Armstrong and Buzz Aldrin became the first humans to walk on the lunar surface.  It was the culmination of a decade’s worth of work and $150 billion (2016 dollars) to beat the Soviet Union to the Moon.  At the head of the Saturn V design team was Wernher von Braun, who was director of the Marshall Space Flight Center in Huntsville, Alabama.  During the post World War II era, von Braun was the leading public advocate of space exploration.  In many ways, von Braun was the Carl Sagan or Neil deGrasse Tyson of his era.  Unlike Sagan or deGrasse Tyson, von Braun’s reputation originated on the backs of slave labor.

In some regards, von Braun was similar to Planck in that he was not a Nazi ideologue.  He was loyal to Germany as a nation, but his main focus, obsession really, was space exploration and rocketry.  His childhood dream was to go to Mars, but as Hitler rose to power, only military rocket research was permitted.  During the early 1930’s, von Braun received a government research grant that permitted him to complete his PhD ahead of schedule.  Unlike Planck, he joined the Nazi party in 1937 to advance his career.

Wernher von Braun (in civilian cloths) at the Peenemünde Army Research Center where the V-2 was developed. March 21, 1941. Credit: Wiki Commons/German Federal Archives.

During World War II, von Braun headed up the German V-2 program.  While the V-2 killed 9,000 in its attacks, some 12,000 slave laborers were killed in the V-2 Mittelwerk production plant.  The facility was adjacent to the Dora-Nordhausen concentration camp which supplied the labor.  While von Braun was not stationed near the plant, he did visit it and was aware of the deaths at the plant.  The V-2 program was not enough to stave off the eventual defeat of Germany in 1945.  Von Braun planned to escape to America as he felt that would provide him the best opportunity to advance his career.  Along with about 1,600 other scientists and engineers, von Braun was shepherded to America as valuable assets for the upcoming Cold War against the Soviet Union in a program code named Operation Paperclip.

Von Braun became famous to the American public during the 1950’s.  In 1952, von Braun played a key role in a influential series of articles in Collier’s magazine.  These articles presented to the public a peek at how future space missions to the Moon and Mars as well as a space station might look like.  In 1955, von Braun started work on a series of television programs for Disney promoting space exploration.  A sample of which is below:

Von Braun was a true visionary of space exploration.  It is difficult to reconcile a man who worked for both Adolf Hitler and Walt Disney.  My first lesson on space exploration was an article written by von Braun for the 1969 World Book Encyclopedia.  When NASA was founded in 1958, it got to choose the pick of the litter from the existing military rocket programs, and that was von Braun’s army team.  The rest is history and cemented von Braun as the face of America’s space program.

Von Braun passed away in 1977, about a decade before Operation Paperclip was investigated by the Justice Department.  While von Braun’s work on the V-2 project was common knowledge, his membership in the SS was not well known to the public until 1985.  Arthur Rudolph, whose contributions were crucial to the development of the Saturn V, was also the operations manager at Mittelwerk.  Rudolph was deported in 1984.  Kurt Debus, the first director of the Kennedy Space Center and an ideological Nazi during the war, avoided the investigation by passing away in 1983.  How would have von Braun fared if probed by the Justice Department?

Wherner von Braun and Kurt Debus, roll out of Saturn V, May 26, 1966. Credit: NASA

Von Braun’s supporters point out that he would have been executed had he opposed the working conditions at Mittelwerk.  No doubt, that is the case.  In fact, von Braun was arrested by the SS in 1944 for carelessly opining that the war was a lost cause and the future of rocketry would be space exploration.  However, this is a variation of the I was following orders routine, and von Braun was too high up in the food chain to use that as a passable defense.  Clearly, von Braun had charted his own course in the Nazi apparatus.  It is difficult to imagine a rigorous investigation ending well for von Braun.

What can we take from all this?  Under an oppressive authoritarian regime, you can leave the country, try to maintain institutional integrity within the system, or advance your career regardless of personal debasement.  If you want to leave, you’ll have more difficulty than Einstein securing a visa and a job.  If Max Planck could not preserve the integrity of the Kaiser Wilhelm Society, what are the chances you’ll be able to where you are situated?  As for careerism, if landing a man on the Moon is not enough to cleanse questionable past associations, do you really think you could pull that off?

The easiest solution is simply to reject authoritarianism before it takes power.  Democracy is far easier to sustain by pushing for needed reforms than it is to re-institute it after it falls.  Authoritarianism typically ends in chaos, war in the case of Germany and Japan in 1945 and Syria today, economic in the case of the Soviet Union in the 1990’s or Venezuela today.  Regardless how you navigate your path through it, don’t think you will get out unscathed one way or another.

*Photo at top of post:  Nazi Germany’s loss is America’s gain. Albert Einstein receives from Judge Phillip Forman his certificate of American citizenship.  October 1, 1940.  Credit:  Al Aumuller/Library of Congress.

The American Eclipse of 2017

On November 18, 1805, the Lewis and Clark expedition explored Cape Disappointment off the Pacific coast in what is now Oregon.  This concluded an 18 month journey to reach the Pacific Northwest.  Today, the Cape is home to a state park which includes the Lewis and Clark Interpretive Center.  On August 21, 2017, some 150 miles south, a solar eclipse will begin its race across the United States eastward until it exits into the Atlantic at Charleston, South Carolina.  If you intend to travel to view the eclipse, several spots along the path of totality offer short day trips to some interesting historical spots.  With proper planning, you can combine science and history in your trip.

Google and NASA has put together a neat interactive map for the eclipse that allows you to determine the time of totality for any given location.  Below is how the eclipse enters the United States in Oregon starting at 10:15 A.M. PDT in the morning.

Credit: Google Maps
Credit: Google Maps

“men appear much Satisfied with their trip beholding with estonishment the high waves dashing against the rocks & this emence ocian.” – Lewis and Clark Journal, November 18, 1805.

If you are not from the Northwest, you might think this was a poor spot to view the eclipse as the climate is notorious for rain.  However, most of the rain falls from October to March and the eclipse occurs during the driest month of the year for this region.  Salem averages less than half an inch of rain for the entire month of August compared to over six inches in December.  Salem will experience 1:53 of totality compared to 2:00 in the center of the shadow.  This site has the added benefit of a major airport in Portland 45 miles north.  And north of Portland, you can trace the trail of Lewis and Clark as they reached the Pacific along the Columbia River in the Lewis and Clark National Historical Park.  From there, you can move on to Cape Disappointment to the Lewis and Clark Interpretive Center to take in the Pacific at the North Head Lighthouse.

North Head Lighthouse at Cape Disappointment. Credit: Wiki Commons

After Oregon, the path of totality enters Wyoming just south of Yellowstone National Park then eastward.  The city of Casper is near the center of the path and will experience totality for 2:25.  Casper is also very dry in August, averaging less than an inch a rain during the month.  The airport in Casper is serviced by Delta and United Airlines with the major connections at Denver and Las Vegas.  While in Casper, you can visit the National Historic Trails Interpretive Center which has exhibits on the Oregon, California, Mormon, and Pony Express Trails.  If you are feeling adventurous, there are several spots in Wyoming where the ruts of the wagon trains are still embedded in the ground.  One such spot is the “Parting of the Ways”

Parting of the Ways, Credit: National Park Service.

“If any young man is about to commence the world, we say to him, publicly and privately, Go to the West” – Horace Greeley in the New Yorker, August 25, 1838.

There is a bit of a historical dispute on this spot.  Some claim this is where the Oregon and California trails branched off.  The more accepted version is the right fork was the Sublette Cutoff which was a shortcut, but presented 50 miles of waterless trails.  The left fork led to Fort Bridger and was a longer, but less riskier passage.  Either way, it is an awesome piece of natural preservation.  This is pretty rugged territory and a four wheel drive is recommended along with stocking up on supplies as there won’t be a 7-11 around the corner.  Directions and background on this site can be found here.  The Parting of the Ways is a four hour drive from Casper.

Casper
Credit: Google Maps.

History always has two sides, and the other side of the westward expansion can be found 200 miles north of Casper at Little Bighorn Battlefield National Monument.  Here is where Cheyenne and Lakota forces defeated General Custer’s 7th Calvary Regiment.  The site houses memorials to both sides of the conflict.  Millions of Native Americans were eventually killed as a result of war, disease, and forced relocation over the course of several centuries as European descendants made their way westward into the Americas.

After Wyoming, the path of totality barrels through Nebraska including the town of North Platte, also part of the Oregon Trail.  Then through Missouri, the eclipse travels over the northern part of the Metro Kansas City area including the Harry S.Truman Library and Museum in Independence ten miles east of the city.  Totality lasts about a minute over the museum, to experience over two minutes of totality, you’ll want to head towards the center line in the map below.  St. Joseph will enjoy 2:38 of total darkness.  As you move east, the climate gets wetter, meaning cloud cover becomes more of a possibility.  Kansas City averages almost four inches of rain in August.

KC
Credit: Google Maps

“We must build a new world, a far better world — one in which the eternal dignity of man is respected.” – Harry S. Truman address to the United Nations Conference, April 25, 1945.

The Truman Library has exhibits on the end of World War II, including the decision to drop the atomic bomb, the start of the Cold War, and the upset win in the 1948 election as well as his formative years serving in World War I.  To learn more about Truman’s early life, there is the Harry S. Truman National Historic Site which was his home.  This site preserves over 50,000 objects related to Truman.

Harry S Truman National Historic Site, Credit: National Park Service.

Independence was also the starting point for the Oregon, California, and Santa Fe Trails.  This is commemorated in the National Frontier Trails Museum.  The museum contains pioneer narratives, a public research library, as well as a Lewis and Clark exhibit as the expedition stopped there early in their journey.

From Kansas City, the path of totality heads towards St. Louis and the Gateway Arch.  If you like country music, Nashville will experience totality, then the eclipse moves directly towards the Great Smokey Mountains National Park.  The best way to reach this region is to fly into Knoxville which is less than an hour away.  One caveat here, there’s a reason they are called the Great Smokey Mountains and that is because…they are smokey.  The region receives 50-80 inches of rainfall per year.  And this, of course, can reduce the visibility of the eclipse.

Credit: Gregory Pijanowski
Great Smokey Mountains, Credit: Gregory Pijanowski

Still, if you decide to go this route, you will not be disappointed by the scenery.  This is the most visited national park with over ten million taking in the vistas annually.  There is also no charge to enter the park.

Knoxille
Credit: Google Maps

“We knew the world would not be the same. A few people laughed, a few people cried, most people were silent. I remembered the line from the Hindu scripture, the Bhagavad-Gita. Vishnu is trying to persuade the Prince that he should do his duty and to impress him takes on his multi-armed form and says, “Now, I am become Death, the destroyer of worlds.” I suppose we all thought that one way or another.” – J. Robert Oppenheimer on the first atomic explosion, quote televised in 1965.

Less than a half hour from Knoxville is the formally secret town of Oak Ridge.  Secret in that this was where uranium was enriched during the Manhattan Project for the atomic bomb.  The K-25 gaseous diffusion plant was a U-shaped building a half a mile long with some 2,000,000 square feet of floor space.  Eventually, 12,000 people were employed at the plant and was so designed that they were not aware what they were producing due to the secretive nature of the project.  The plant was demolished in 2014, but the American Museum of Science and Energy offers exhibits on the history of the Manhattan Project and nuclear energy.  The museum offers bus tours of the historic Oak Ridge facilities which are now part of the Oak Ridge National Laboratory.

Finally, the path of totality moves into South Carolina, over Charleston, and out into the Atlantic Ocean at 2:49 P.M. EDT, ninety-three minuets after touching down in Oregon.  Charleston will experience a minute and half of totality, situating yourself towards the center of the path of totality will stretch out total darkness for two and a half minutes.

Charelston
Credit: Google Maps

“The last ray of hope for preserving the Union peaceably expired at the assault upon Fort Sumter.” – Abraham Lincoln, First Annual Message, December 3, 1861.

As anyone who has lived down South can tell you, Summer is the rainy season and Charleston is no exception averaging over six inches of rain in August.  Still, if you make Charleston your destination, there is an excellent historical district downtown and in the harbor, Fort Sumter National Monument where the Civil War started on April 12, 1865 when Confederate forces attacked the fort.

Fort Sumter, Credit: NPS

As the eclipse moves from Oregon, across the Great Plains, and through the South, its path crosses over or near some of the history that helped define the United States as a nation from our westward expansion, the Civil War, to the emerging superpower at the end of World War II.  Not all of the history has been pretty, the push west resulted in the deaths of millions of Native Americans.  Over 700,000 died in the Civil War that abolished slavery, but did not give African-Americans total equality, the atomic bomb ended World War II, but gave humanity the ability to terminate its existence.  Those events also gave us the great cities on the West Coast, our current African American president, and a peaceful relationship with a democratic Japan that has lasted since 1945.  With history, you take the successes alongside the failures.

*Image atop of post is solar eclipse on March 20, 2015.  Credit:  Damien Deltenre/Wiki Commons.

Planets and Dwarf Planets – What’s in a Name?

The term dwarf planet was introduced in 2006, the same year I started teaching astronomy.  It has been a source of confusion for students ever since.  The confusion lies not only with the re-designation of Pluto, but also that an asteroid is considered a dwarf planet while the other four objects so designated lie in the Kuiper Belt outside the orbit of Neptune.  The term dwarf planet was something of a compromise for those reluctant to modify Pluto’s status as a planet.  As the living memory of Pluto as a planet fades, I suspect the term dwarf planet will fade as well.  So how should we categorize the objects that lie in our Solar System?

Rather than looking at the shape and size of these objects, I prefer to examine how they were created in the solar nebula that formed the Solar System.  When we divide the solar nebula into concentric circles, each section formed a distinct type of object.  The solar nebula concept was first hypothesized by Immanuel Kant in The Universal Natural History and Theories of the Heavens published in 1755.  As often is the case in astronomy, it took awhile for the ability to verify the theory to emerge.  In this case, the process spanned some three centuries.

Part of the holdup was determining if the Sun, planets, and asteroids are all the same age as they must be if formed together in the solar nebula.  A model of stellar evolution had to be created and that required Einstein’s relativity theory to explain nuclear fusion.  This model puts the Sun’s age at 4.6 billion years.  The age of the Earth also had to be determined and given the amount of erosion that takes place on the surface, finding rocks from Earth’s early days is difficult.  Nonetheless, radiocarbon dating has put the age of zircon found in Australia at  4.4 billion years.  This result also matches up with the age of the oldest Moon rocks brought back from the Apollo program.  Also during the 1970’s, Russian physicist Victor Safronov formulated a modern solar nebular theory to compare the evidence against.

The Solar System began when a rotating interstellar cloud containing gas and dust grains began to collapse under its gravity.  The rotation of the cloud caused this collapse to create a disk.  The bulk of the matter was still in the center of the solar nebula and this is where the Sun materialized.  Today, the Sun contains 99.8% of the Solar System’s mass.  There is no difficulty categorizing the Sun as a star as nuclear fusion occurs in its core.  The difficulty comes in the layers of the solar nebula outside the Sun.

The first concentric ring around the Sun is where the inner, rocky planets are located.  These would include Mercury, Venus, Earth, and Mars.  In this zone, as the Solar System was forming, the Sun kept temperatures warm enough to keep hydrogen and helium from condensing.  As these two elements comprised 98% of the solar nebula, only trace amounts of heavier elements were left to construct planets.  This explains the smaller size of the rocky planets.  However, they were still large enough to become spherical in shape.  The gravity of the planets pulled equally inward from all sides, overcoming the internal mechanical strength of its constituent material forming a sphere.

At the outer edge of this zone beyond the orbit of Mars lies the asteroid belt.  During the epoch of the solar nebula, there was enough material here to form a planet.  However, the presence of Jupiter’s gravitational influence caused enough disruption to keep this material from coalescing into a single planet.  Today, there is not enough matter here to form a body the mass of the Moon.  Nonetheless, one asteroid, Ceres, was large enough to become spherical in shape.  As such, it was designated as a dwarf planet in 2006.  When discovered in 1801, is was classified as a planet and remained so until the mid-1800’s.  Here you can see the ephemeral nature of this categorizing.  Ceres was in fact the first object discovered in a belt consisting of over 1 million asteroids.  Once it was understood Ceres was simply the most visible of a large number of asteroids, its classification was changed.  In this, Ceres is very similar to Pluto but their point or origin makes their physical makeup very different.

Ceres, Credit: NASA

Between the orbits of Mars and Jupiter lies what is called the frost line.  Beyond the frost line, both heavy elements and hydrogen compounds such as water, methane, and ammonia condensate (convert directly from gas to solid).  As the hydrogen compound ice particles and rocky material began to stick against each other, they eventually grew large enough to gravitationally attract the surrounding hydrogen and helium gas.  In this region, the hydrogen and helium gases’ temperature was colder than inside the frost line.  Colder gases move with slower velocity than hot gases and this enabled planets outside the frost line to trap huge amounts of hydrogen and helium.  Consequently, being outside the frost line allowed the outer planets to grow significantly larger than the inner planets.  Thus, the gas giant planets Jupiter, Saturn, Uranus, and Neptune bear little resemblance to Mercury, Venus, Earth, and Mars as you can see below.

Terrestrial planets have small rocky bodies with thin atmospheres while gas giants have small icy/rocky cores surrounded by large amounts of hydrogen and helium gas. Distance between planets not to scale. Credit: Wiki Commons.

The third concentric ring in the Solar System beyond the orbit of Neptune is the Kuiper Belt, of which Pluto is a member.  Also, short period comets such as Halley’s are thought to originate from the Kuiper Belt.  These objects differ from the asteroid belt in that they are more icy than rocky in nature.  This makes sense as the Kuiper Belt lies beyond the frost line where hydrogen compounds can condensate.  Pluto was the first Kuiper Belt object to be discovered in 1930.  It stood alone until 1992 when the second Kuiper Belt object was found.  While Pluto is highly reflective, most Kuiper Belt objects are dark, in fact, darker than coal.  That, along with their small size makes them difficult to detect.  To date, more that 1,000 Kuiper Belt objects have been discovered giving the Solar System a third zone of objects orbiting the Sun.

Kuiper Belt objects in orange, outer planetary orbits in green. Credit: The Johns Hopkins University Applied Physics Laboratory

Looking at the above image, it is tempting to think that the Kuiper Belt objects were formed beyond the orbit of Neptune.  However, the origins of the Kuiper Belt are still a matter of debate among astronomers.  As these are icy bodies, they originated beyond the frost line, but precisely where is uncertain.  One theory, called the Nice model, postulates these objects are left over remnants from where the gas giant planets formed and pushed outward by the migration of Neptune’s orbit beyond Uranus.  This model explains Kuiper Belt objects that have highly elliptical orbits but not those with circular orbits.  As it is estimated some 200,000 objects exist in the Kuiper Belt, there is quite a bit of discovery and mapping to perform to pin down the origins of these objects.

Beyond the Kuiper Belt is the Oort Cloud where long period (orbits that last thousands of years) comets are thought to originate.  The Oort Cloud consists of trillions of icy bodies ranging from 1-20 km and extends about 1 light year from the Sun.  To date, astronomers have not directly detected the Oort Cloud but we have observed long period comets traveling through the Solar System at different angles indicating an origination point from a spherical cloud.  Like the Kuiper Belt, models have determined these icy objects formed beyond the frost line near the gas giant planets and were ejected by the gravity of these planets to their current location.

Oort cloud relative to the planets. Credit: ESO

If the solar nebula existed 4.6 billion years ago, how can we prove this theory is correct?  We cannot observe the formation of our own Solar System, but we can observe, thanks to the Hubble and the next generation ALMA radio telescope, stellar and planetary systems forming around other stars.  Below is perhaps the most iconic image taken by the Hubble, the Pillars of Creation in the Eagle Nebula located 7,000 light years from Earth.  This is a large (the column on the left is four light years long) interstellar gas cloud acting as a nursery for new stars.  In fact, ultraviolet radiation from newly born stars eats away at the dust cloud which gives it its shape.

Credit: NASA, ESA, STScI, J. Hester and P. Scowen (Arizona State University)

Below is an image of a spinning protoplanetary disk in the Orion Nebula 1,500 light years from Earth.  The spinning motion has flattened the dust cloud to a disk shape.  The disk contains dust grains that will clump together to form planets, asteroids, and small icy bodies such as Kuiper Belt objects.

A Protoplanetary Disk Silhouetted Against the Orion Nebula
Credit: NASA, J. Bally (University of Colorado) and H. Throop (SWRI)

The next image is planet creation in process around HL Tauri 450 light years from Earth.  Taken by the ALMA radio array in Chile, you can see the gaps in a protoplanetary disk cleared of dust by planets forming in the rings.  This is direct evidence of stars and planets creation matching up with the solar nebula theory of how our Solar System formed.

Credit: ALMA (ESO/NAOJ/NRAO)

Getting back to the first point, when thinking how to categorize Solar System objects, it is best to consider how these objects formed.  The term dwarf planet covers objects that originated inside and outside the frost line in the solar nebula and is of little use here.  And as I mentioned before, most likely will be discarded as the collective memory of Pluto as a planet fades.  It is a transition term much like Ceres was referred to as a minor planet between its time as a planet and asteroid.  As such, I do not consider it a good point of emphasis when learning about the Solar System.  Instead, I would summarize as follows:

Objects formed inside the frost line:  Rocky planets with thin atmospheres, rocky asteroids, some of these asteroids are large enough to become spherical in shape, but most are not such as Eros below.

Credit: NASA/JHUAPL

Objects formed outside the frost line:  Gas giant planets with small icy-rocky cores and large atmospheres, small icy bodies such as the Kuiper Belt and Oort Cloud objects.  Some, like Pluto, are large enough to form a spherical shape but most are not.

The Solar System is not static:  After these objects are created and the solar nebula was dissipated by the young Sun’s solar wind, gravitational perturbations caused migration of these objects.  In our Solar System, the orbital resonance of Jupiter and Saturn caused Neptune to migrate outward and took the Kuiper Belt objects with it.  However, around other stars, Jupiter sized gas giants have migrated inwards to occupy orbits closer to their host star than Mercury is to the Sun.  Over the course of 4.6 billion years, the Solar System has been a dynamic place.

Our lifetimes are very small compared to the cosmic time scale and thus, we tend the think of the Solar System as a static system.  Nonetheless, we do see migrations of objects whenever a comet pays us a visit from the outer reaches of the Solar System.  By classifying objects in the Solar System by their composition, it allows you to understand how the Solar System formed and what path those objects took to reach their final destination.  And that is more important than worrying if a celestial body is a planet or a dwarf planet.

*Image atop of post is sunset over the mountains of Pluto taken 15 minutes after New Horizons closest approach. Credits: NASA/JHUAPL/SwRI.

The Two Sides of the Sombrero Galaxy

While in grade school, the classic image (above) of the Sombrero Galaxy was one that perked my interest in astronomy.  The disk with the bright central core gave it a mysterious look, something I wanted to learn more about.  Located 30 million light years from Earth, it is not bright enough to see with the naked eye, but easily captured by amateur astronomers armed with small telescopes.  Although reasonably close as far as galaxies go, it still is an enigma for astronomers.

The Sombrero Galaxy was discovered on May 11, 1781 by Pierre Mechain, who was working with Charles Messier to build a catalog of nebulous objects so astronomers would not mistake for comets.  The Sombrero Galaxy was not included in the original catalog, although Messier hand wrote a description of it in his personal copy.  Mechain announced the discovery in a letter to the Berlin Royal Academy of Sciences and Arts on May 6, 1783.  Eventually, in 1921, the Sombrero Galaxy was entered into the Messier catalog and given the designation M104.

News traveled slow in the 1780’s, and the Sombrero Galaxy was discovered independently by William Herschel on May 9, 1784.  Herschel’s superior optics allowed him to view the dark dust lane in the disk that provided the Sombrero Galaxy with its moniker.  In 1800, Herschel would discover infrared light.  Two centuries later, infrared imaging would allow astronomers to make an important discovery about the Sombrero Galaxy.

During the 1800’s, spiral galaxies were referred to as spiral nebulae.  At the time, it was thought the Milky Way was the sole galaxy to exist and the spiral nebulae were located within.  Telescopes did not have the ability to resolve individual stars in galaxies outside the Milky Way.  During the early 1900’s, astronomers began to challenge this view of the universe and a discovery from the Sombrero Galaxy played a crucial role in this debate.

In 1912, Vesto Slipher of the Lowell Observatory measured the red shift of the Sombrero Galaxy.  If an object is moving away from us, its light waves become elongated, that is, the light shifts towards the red part of the spectrum.  The red shift of the Sombrero Galaxy indicated it was moving away from us at a velocity of 1,000 km/s.  Moving at such a fast rate suggested M104 resided outside the Milky Way, as this is almost twice the escape velocity of our galaxy.  From an observational standpoint, this was among the first clues that the universe was expanding and not static, as was the prevailing wisdom at the time.

On April 26, 1920, what became known in astronomy circles as The Great Debate, took place in the Smithsonian Museum of Natural History between Harlow Shapley and Heber Curtis.  Shapley proposed there was only one galaxy in the universe and that the Solar System was located far from the center of that galaxy.  Curtis countered that we were located near the center of the Milky Way, but the spiral nebulae were galaxies residing outside the Milky Way.  As is often the case with debates such as this, both were right…and both were wrong.

The observations of Edwin Hubble at Mt. Wilson Observatory throughout the 1920’s proved Curtis right in that the spiral nebulae were not gas clouds in the Milky Way, but other galaxies outside the Milky Way.  However, Shapley turned out to be right on the location of Earth residing outside the center of the Milky Way.  We tend to want to confer the status of a winner and loser with debates such as these, but remember, it is the evidence, not the person, that determines if a scientific proposal is correct or not.  You’ll want to keep this in mind with similar debates today on string theory and parallel universes.  The Sombrero Galaxy, like other spiral nebulae, was reclassified as a spiral galaxy outside the Milky Way.

The Sombrero Galaxy lies about 30 million light years from Earth.  If you happen to catch it in a telescope, the light entering your eye started its journey from the galaxy when India began to slam into the Asia continent to form the Himalayan mountains.  North America looked like this 30 million years ago.

Credit: Ancient Earth Globe/Ian Webster and C.R. Scotese

To put a light year in perspective, even though the Sombrero Galaxy is moving away from us at a rate equal to the distance from Paris to Copenhagen every second, it has only receded 1/3 of a light year since its red shift was first measured in 1912.  The nearest star from us is Proxima Centauri at 4.2 light years.  Even traveling at 1,000 km/s, it would take some 1,200 years to reach.  That demonstrates the challenges facing those working on methods of interstellar propulsion.

Over the past two decades, space telescopes have afforded astronomers a better understanding of the internal structure of the Sombrero Galaxy.  The Hubble, of course, is the most famous of these observatories and took this iconic image in 2003.

Credit: NASA and the Space Telescope Science Institute (STScI)

Seen here is the notable bright core of the Sombrero Galaxy, with its signature dust lane across the disk titled only 6 degrees from our vantage point on Earth.  At 50,000 light years, the Sombrero Galaxy is only half as wide as the Milky Way but has more than 10 times the globular clusters with 2,000.  In 1996, Hubble picked up a high rate of rotation near the core of the galaxy, confirming the 1988 ground observations by John Kormendy at the Canada-France-Hawaii Telescope.  This rotation is accelerated by the presence of a black hole with a mass one billion times that of the Sun.  It is one of the largest black holes detected in a nearby galaxy.

By and large, this is the way astronomers have seen the Sombrero Galaxy until recently viewed by other parts of the electromagnetic (EM) spectrum.

Just after the above image was taken by the Hubble, NASA launched the Spitzer Space Telescope.  Named after Lyman Spitzer, Jr., who first proposed an orbiting telescope in 1946, the Sptizer observes in infrared.  Cooler objects such as planets and dust radiate most strongly in infrared.  Certain wavelengths of infrared have the ability to pass through dusty regions without being absorbed.  This gives astronomers the ability to peer behind the curtain of opaque, dusty areas to see what lies behind.  When the Spitzer took a look at the Sombrero Galaxy, this is what it saw.

Credit: NASA/JPL-Caltech/University of Arizona/STSc

The red represents a dust ring in the spiral disk.  This is the area of a spiral galaxy where stars are born.  That was expected, what was unexpected was the blue starlight in the galactic halo.  Prior to this image, it was thought the bright halo was tenuous and small.  Instead, it is an elliptical galaxy with a spiral galaxy embedded within.  The Spitzer enabled astronomers to see stars behind the dust in the halo.  This also explained why the Sombrero has far more globular clusters than spirals normally have.  Elliptical galaxies typically have a couple thousand of these clusters.

Credit: NASA and the Space Telescope Science Institute (STScI)

Besides the Spitzer, the Chandra X-Ray Observatory has imaged the Sombrero Galaxy.  Objects that are very hot will radiate high energy x-rays.  Galactic dust and gas does not generally fall into this category unless it is heated up by a nearby source.  What the Chandra imaged when pointed at M104 was this.

Credit: NASA/UMass/Q.D.Wang et al

With the x-ray image, the spiral disk disappears as it consists of cool dust.  The point sources in this image are high energy stars and background quasars.  The Chandra also picked up halo of hot gas that extends 10,000 light years beyond the spiral disk.  It is thought this gas is disbursed via a galactic wind originating with supernova activity throughout the galaxy.

If you want to look at M104 yourself, May is the optimal month to do so.  Best to seek a dark sky location far from city lights, and while it is too dim to be seen with the naked eye, a pair of binoculars or a small telescope is sufficient to bring it into view.  An 8-10 inch telescope will start to resolve features such as the dust lane.  Below is an image of where M104 will be located on May 14th from my hometown Buffalo, NY.  At 10:30 PM, it will be directly due south in the constellation Virgo.

M104 as seen with Starry Night.
M104 as seen with Starry Night.

It is always a challenge to target a deep space object such as M104, but like anything else, you’ll get better and better with more experience.  Do not get discouraged if unable catch it on the first try and good hunting!

*Image on top of post is the Sombrero Galaxy taken at Mt. Palomar’s 200-inch Hale Telescope.  Credit:  Mt. Palomar/Caltech.

Beware of Outliers

As we currently digest the run-up to the 2016 presidential election, it can be expected that the candidates will present exaggerated claims to promote their agenda.  Often, these claims are abetted by less than objective press outlets.  Now, that’s not supposed to be the press corps job obviously, but it is what it is.  How do we discern fact from exaggeration?  One way to do that is to be on the lookout for the use of outliers to promote falsities.  So what exactly is an outlier?  Merriam-Webster defines it as follows:

A statistical observation that is markedly different in value from the others of the sample.

The Wolfram MathWorld website adds:

Usually, the presence of an outlier indicates some sort of problem. This can be a case which does not fit the model under study, or an error in measurement.

The most simple case of an outlier is a single data point that strays greatly from an overall trend.  An example of this is the United States jobs report from September 1983.

bls
Credit: Bureau of Labor Statistics

In September 1983, the Bureau of Labor Statistics announced a net gain of 1.1 million new jobs.  As you can tell from the graph above, it is the only month since 1980 that has gained 1 million jobs.  And why would we care about a jobs report from three decades ago?  It is often used to promote the stimulus of the Reagan tax cuts.  When you see an outlier such as this being used to support an argument, you should be wary.  As it turned out, there is a simpler explanation for this that has nothing to do, pro or con, with Reagan’s economic policy.  See the job loss immediately preceding September 1983?  In August 1983, there was a net loss of 308,000 jobs.  This was caused by the strike of 650,000 AT&T workers who returned to work the following month.

If you eliminate the statistical noise of the striking workers from both months, you have a gain of over 300,000 jobs in August 1983, and 400,000 jobs in September 1983.  Those are still impressive numbers and require no need for the use of an outlier to exaggerate.  However, it has to be noted, it was the monetary policy of the Fed Chair Paul Volcker, rather than the fiscal policy of the Reagan administration that was the main driver of the economy then.  Volcker pushed the Fed Funds rate as high as 19% in 1981 to choke off inflation causing the recession.  When the Fed eased up on interest rates, the economy rebounded quickly as is the normal response as predicted by standard economic models.  So we really can’t credit Reagan for the recovery, or blame him for the 1981-82 recession, either.  It’s highly suspect to use an outlier to support an argument, it’s even more suspect to assume a correlation.

To present a proper argument, your data has to fit a model consistently.  In this case, the argument is tax cuts alone are the dominant driver determining job creation in the economy.  That argument is clearly falsified in the data above as the 1993 tax increases were followed by a sustained period of job creation in the mid-late 1990’s.  And that is precisely why supporters of the tax cuts equals job creation argument have to rely on an outlier to make their case.  It’s a false argument intended to rely on the fact that, unless one is a trained economist, you are not likely to be aware of what occurred in a monthly jobs report over three decades ago.  Clearly, a more sophisticated model with multiple inputs are required to predict an economy’s ability to create jobs.

When dealing with an outlier, you have to explore whether it is a measurement error, and if not, can it be accounted for with existing models.  If it cannot, you’ll need to determine what type of modification is required to make your model explain it.  In science, the classic case is the orbit of Mercury.  Newton’s Laws do not accurately predict this orbit.  Mercury’s perihelion precesses at a rate of 43 arc seconds per century greater than predicted by Newton’s Laws.  Precession of planetary orbits are caused by the gravitational influence of the other planets.  The orbital precession of the planets besides Mercury are correctly predicted by Newton’s laws.  Explaining this outlier was a key problem for astronomers in the late 1800’s.

At first, astronomers attempted to analyze this outlier within the confines of the Newtonian model.  The most prominent of these solutions was the proposal that a planet, whose orbit resided inside of Mercury’s, perturbed the orbit of Mercury in a manner that explained the extra precession.  This proposed planet was dubbed Vulcan, after the Roman god of fire.  Several attempts were made to observe this planet during solar eclipses and predicted transits of the Sun with no success.  In 1909, William W. Campbell of the Lick Observatory stated no such planet existed and declared the matter closed.  At the same time, Albert Einstein was working on a new model of gravity that would accurately predict the orbit of Mercury.

Vulcan’s Forge by Diego Velázquez, 1630. Apollo pays Vulcan a visit. Instead of having a real planet named after him, Vulcan settled for one of the most famous planets in science fiction.  Credit: Museo del Prado, Madrid.

The general theory of relativity describes the motion of matter in two areas that Newton could not.  That is, when located near a large gravity well such as the Sun or moving at a velocity close to the speed of light.  In all other cases, the solutions of Newton and Einstein match.  Einstein understood that if his new theory could predict the orbit of Mercury, this would pass a key test for his work.  On November 18, 1915, Einstein presented his successful calculation of Mercury’s orbit to the Prussian Academy of Sciences.  This outlier was finally understood and a new theory of gravity was required to do it.  Nearly 100 years later, another outlier was discovered that could have challenged Einstein’s theory.

Relativity puts a velocity limit in the universe at the speed of light.  A measurement of a particle traveling faster than this would, as the orbit of Mercury did to Newton, require a modification to Einstein’s work.  In 2011, a team of physicists announced they had recorded a neutrino with a velocity faster than the speed of light.  The OPERA (Oscillation Project with Emulsion-tRacking Apparatus) team could not find any evidence for a measurement error.  Understanding the ramifications of this conclusion, OPERA asked for outside help in verifying this result.  As it turned out, a loose fiber optic cable caused a delay in firing the neutrinos.  This delay resulted in the measurement error.  Once the cable was repaired, OPERA measured the neutrinos at its proper velocity in accordance with Einstein’s theory.

While the OPERA situation was concluding, another outlier was beginning to gain headlines.  This being the increase in the annual sea ice in Antarctica, seemingly contradicting the claim by climate scientists that global temperatures are on the rise.  Is it possible to reconcile this observation within the confines of a model of global warming?  What has to understood is this measurement is an outlier that cannot be extrapolated globally.  It only pertains to sea ice surrounding the Antarctica continent.

Glaciers on the land mass of Antarctica continue to recede, along with mountain ranges across the globe and in the Arctic as well.  Clearly something interesting is happening in Antarctica, but it is regional in nature and does not overturn current climate change models.  At least, none of the arguments I’ve seen using this phenomenon to rebut global warming models have provided an alternative model that also explains why glaciers are receding on a global scale.

Outliers are found in business as well.  Most notably, carelessly taking an outlier and incorporating it as a statistical average in a forecasting model is dangerous.  Lets take a look at the history of housing prices.

Credit: St. Louis Federal Reserve.
Credit: St. Louis Federal Reserve.

In the period from 2004-06, housing prices climbed over 25% per year.  This was clearly a historic outlier and yet, many assumed this was the new normal and underwrote mortgages and derivative products as such.  An example of this would be balloon mortgages, where it was assumed the homeowner could refinance the large balloon payment at the end of the note with newly acquired equity in the property as a result of rapid appreciation.  Instead, the crash in property values left these homeowners owing more than the property was worth causing high rates of defaults.  Often, the use of outliers for business purposes are justified with slogans such as this is a new era, or the new prosperity.  It turns out to be just another bubble.  Slogans are never enough to justify using an outlier as an average in a model and never be swayed by any outside noise demanding you accept an outlier as the new normal.  Intimidation in the workplace played no small role in the real estate bubble, and if you are a business major, you’ll need to prepare yourself against such a scenario.

If you are a student and have an outlier in your data set, what should you do?  Ask your teachers to start with.  Often outliers have a very simple explanation, such as the 1983 jobs report, that will not interfere with the overall data set.  Look at the long range history of your data.  In the case of economic bubbles, you will note a similar pattern, the “this time is different” syndrome.  Only to eventually find out this time was not different.  More often than not, an outlier can be explained as an anomaly within a current working model.  And if that is not the case, you’ll need to build a new model to explain the data in a manner that predicts the outlier, but also replicates the accurate predictions of the previous model.  It’s a tall order, but that is how science progresses.

*Image on top of post is record Antarctic sea ice from 2014.  This is an outlier as ice levels around the globe recede as temperatures warm.  Credit:  NASA’s Scientific Visualization Studio/Cindy Starr.