omenti

why revolutions sometimes need astonishing simplicity

Physics is, by far, the simplest science.

 

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

 

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

 

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

 

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

 

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

 

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

 

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

 

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

 

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

 

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

 

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

 

why are we here?

The professor drew a box around the words and added "do not erase" at the bottom.  That marked the opening of a two semester course in General Relativity.  He never commented directly, but its presence was anything but subtle . 

 

The circumstances under which Karl Schwarzchild wrote three significant papers in 1915 were a mixture of ideal and and anything but.  An artillery lieutenant in the German army on the Russian front, he had contracted a disease that would kill him a year later  Before the war he was a physicist and astronomer.   In the army he managed to find access to current papers and had become fascinated with Albert Einstein's brand new General Theory of Relativity.   The formula for General Relativity had written looks simple, but each symbol represents some very complex mathematical objects.  Einstein was unable to solve them exactly and his prediction of the precession of the perihelion of Mercury's orbit was only an approximation.

 

It seems strange that Einstein, with his beautiful geometric approach to General Relativity, tried to solve the problem in rectangular coordinates.  In a few months Schwarzschild created a novel coordinate system and was able to solve a simple system exactly with what is now known as the Schwarzschild metric.  Schwarzschild sent it to Einstein for comments with this preface.

 

As you see, the war treated me kindly enough, in spite of the heavy gunfire, to allow me to get away from it all and take this walk in the land of your ideas.

Einstein was delighted

I have read your paper with the utmost interest. I had not expected that one could formulate the exact solution of the problem in such a simple way. I liked very much your mathematical treatment of the subject. Next Thursday I shall present the work to the Academy with a few words of explanation.

 

The simple case was simple indeed - a non-rotating spherically symmetric mass.   Still there were remarkable conclusions.  At long distances it reduced to Newton's gravitation equation, but close to a large mass there was a point where nothing - not even light - could escape from its surface.  Any number of crazy things would happen as you neared this event horizon. Inside everything would collapse to a point - a singularity.  Furthermore any initial configuration of matter (dust for example) would gravitationally attract and, if there was enough of it, collapse into a black hole.

 

About two weeks into the course we had enough differential geometry under our belts to look at the Schwarzschild metric.  I remember looking up at the words on the upper right hand corner of the board and wondering why our Universe hadn't collapsed into a black hole - like almost instantly after it was formed.  Wasn't there an enormous mass in a tiny space?  I worked out the Schwartzschild radius for a mass the size of the universe in my notebook margin.  Why didn't this happen?

 

The next week it became apparent why.  The metric was for a static universe. General Relativity had a lot to say about non-static universes although that wasn't accepted until the next decade.  There are a number of other metrics that apply to more complex, eg. realistic, universes that do things like expand or contract.  One of these had major contributions from a Catholic priest who basically laid out the mathematical underpinnings of the expanding universe Hubble discovered in 1929, but that's another story.

 

Now it was easy to rule out a static universe .. immediately after the Big Bang (which turns out not to be the beginning) the new universe would find itself within a black hole and would have collapsed into itself.    Or so I thought

 

There's something interesting about General Relativity - you've probably heard the presence of energy and matter curves spacetime.  It turns out there's more -  it also impacts the evolution of spacetime itself.  There are three possibilities that depend on the initial expansion rate.  

 

Too small for the amount of matter and energy and the universe would expand for awhile - perhaps the tiniest fraction of a second - and then collapse on itself.  It's tempting to call it a black hole, but it's worse. Spacetime itself would collapse with it.  Not very promising for life. 

 If the expansion rate was too high, matter would separate so quickly stars wouldn't form.. in fact atoms wouldn't form either.  It's a bad sign if you can't make it to chemistry.   Not good if you want life down the road.

 There's an intermediate case.  There's an exceedingly fine line between collapse into nothingness or expansion into a nearly void.  Here the expansion rate eventually drops to zero with stars, galaxies, planets an us developing along the way.  You want this one.

 

What we now know is a bit more complex.  It's the third case, the goldilocks universe, but dark energy which is causing an accelerating expansion.   It has been slow enough to allow the formation of everything we have.  What really astounds me is the balance.  The fine tuning of the right amount of expansion for the amount of mass energy is precise..   If there had been an extra hydrogen nucleus it would have collapsed.  One less and the infinite expansion would have prevented the formation of complexity.  The words on the blackboard seem much deeper to me now than they did at the time.

 

And if your name becomes associated with something in the public imagination there are always the joke.  Einstein and Schrödinger both mentioned cats so...

northward and beyond!

Yesterday a friend asked for comments on a piece about the recent movement of the magnetic north pole.  The article referred to an update to officially published information about the Earth's magnetic field.  Unfortunately it was both confusing and inaccurate so I typed out a reply on my iPhone.  He suggested I turn it into a blog post.  I'm leaving it unedited and adding a bit on the North Star.

 

This is poorly written. The model is not used for GPS, but rather for compasses… smartphones and cars have compasses, but the accuracy is poor- a few degrees.. this wander is, at middle latitudes, only a fraction of a degree. There are folks who need very accurate compasses (submarines for example) and using them at high latitudes demands a very accurate map. Also GPS denial is a major worry of the military.

The standard model for the planet’s magnetic field is fairly well accepted, but some aspects are not well known.

It’s exceptionally important.. our form of life certainly wouldn’t exist without it as it builds a shield that keeps energetic particles largely from the Sun from reaching the surface. The core of the Earth is mostly iron and a few other heavy elements. It’s about the size of the moon and very hot - about 5700°C if memory serves - but under enormous pressure so it’s a solid. . Just outside is a 1500 or so thick liquid that is mostly iron with a good deal of nickel. This is also a hot zone, although not quite as hellish, and the pressure is now low enough that it’s a non-homogeneous fluid. There’s a lot of movement - in very very slow motion - with slightly warmer plumes rising and the cooling and falling and getting mixed put into circular motions as from the Earth’s rotation (the Coriolis force). The flow of the hot liquid iron generates huge electric currents which, in turn, make magnetic fields. These separate magnetic field regions roughly align along the Earth’s spin axis and produce the planet’s magnetic field.

The motion of the poles is caused by large scale flows going on deep below. To our time scale it appears slow, but it’s been going since the formation of the planet.

Something dramatic takes place every half million years or so although the timing is statistically random. The poles swap. The last was about 700 or 800k years ago (I could be wrong… the number sticks with me) and probably happened very quickly — in a few hundred years or less. There have been short lived reversals since then.. one was during the last glacial period and only lasted for a few hundred years. The Earth’s field dropped to a very low level - like under 10% of the current level - and filled for awhile before going back to something stable.

The strength of the field has been dropping for a few hundred years and there is speculation it might lead to one of these mini events or perhaps even a complete reversal. There are people who feel it is very likely in the “near” future — like the next 5,000 or 10,000 years.

 

On dark and starry nights most people can find Ursa Major - the constellation know as The Big Dipper.  Fewer can find Polaris - the North Star.  The trick is to use the outermost stars of the Little Dipper's bowl as a pointer.  Extend the end of the bowl upwards five times its length and the bright star is Polaris.  It's close to the north celestial pole - the point in the sky you'd find if you extended the axis the Earth spins on straight up.  Polaris is within a degree - roughly the width of your little finger at arm's length and close enough for simple navigation.¹ 

 

Finding North is fundamentally important to navigation.  If you want to be accurate with a compass you need the magnetic corrections.  And to navigate  by the stars you need the celestial north pole.   Literature is full of references.

But I am constant as the northern star,
Of whose true-fixed and resting quality
There is no fellow in the firmament.  (Julius Caesar III i)

A guiding star is mentioned in Iceland sagas 800 years ago.  But it hasn't always been Polaris.  

 

You've probably played with toy gyroscopes.  Spin one up and points in one direction even when you move it around.  But perturb it you  and it can wobble in a circle.  Its spin axis is said to be precessing. The Earth's slightly  non-spherical shape and the gravitational influence of the Sun and Moon conspire to give the Earth a wobble that takes about 25,800 years to complete.   Polaris has been roughy the north star for about a thousand years and is currently about as close to the celestial pole as it gets.  Vikings were navigating in the 8th and 9th century used Polaris even though it was about seven degrees off - enough for large errors if they didn't make corrections.  At the time of Christ a collection of stars in the Little Dipper was used and it was about three degrees off for Columbus.   Shakespeare's Julius Caesar was using a bad metaphor - the North Star isn't North over time.   But it's even less reliable in another way and that makes it fascinating.

 

Polaris is a bright and fat yellow star about two thousand times brighter than the Sun and nearly fifty times the Sun's diameter.  There are two smaller companion stars making it wobble back and forth a bit..  If you can make accurate position measurements it isn't steady.  Even more dramatic is the fact that its brightness changes on a regular basis . well, sort of regular. (did I mention it was fascinating?)

 

A bit over a hundred years ago Henrietta Swan Leavitt made a discovery that revolutionized astrophysics and astronomy.  She showed the intrinsic brightness of a certain type of variable stars called Cepheids was directly related to the time it took to change brightness.  She ha given astronomers an important method to measure stellar distances.  The fact she didn't receive a Nobel Prize is an astonishing example of sexism. As Nobels go this would have been one of the more important.

 

Polaris is about 450 light years away - the closest Cepheid.  Think of it as a nuclear powered internal combustion reciprocating engine (although technically there isn't any combustion).  In Cepheids a carbon core is surround by thin shells of fusing helium and hydrogen.  The cycle starts with the helium  being singly ionized - the temperature is such that one electron is missing (He^-) . Gravity pulls the shell inward compressing and heating it.  Enough heat that the second electron is stripped away.  Doubly ionized helium  (He^{- -}) is more opaque to heat transfer than the singly ionized variety so it heats up in a hurry.  As it heats it expands beginning to cool in the process.  Finally it's cold enough that electrons from the plasma soup in the layer re-attach and He^{- -} is becoming the He^- variety. Radiation now flows more easily and the star gets brighter as it expands.  But now enough radiation is getting through that gravity begins to pull in the He^- and the cycle repeats.  A huge engine chugging away.  When the largest engines on Earth were at around ten thousand horsepower, Henrietta had worked out the secret of vastly larger engines.

 

Polaris isn't exactly your garden variety Cepheid.  In addition it's getting brighter - ten percent brighter in the last century.  (this would be a true disaster if it happened to the Sun..  most life would be snuffed out in a hundred years and the oceans would boil away a hundred years later)  To make things more interesting the change in brightness throughout the star's period got much weaker almost vanishing in the 1990s - but now it's returning. There are some interesting hints and more than a few conjectures, but it's still a mysterious object. Curiously it was discovered to be emitting X-rays.  That usually implies a super hot atmosphere driven by an extremely strong magnetic field.  Where it would come from is still a mystery,.

 

It's humbling to realize how much we can learn by looking at these tiny points of light in the sky and asking really good questions.

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¹ As seen from Earth the Moon is about thirty minutes of arc in diameter - a half degree.  Here are some rules of thumb that are close enough for most people.  If you're really tall with long arms your hands and fingers are usually a bit larger.  If you like you can calibrate your hand.  These are all at arms length

1 degree - the width of your little finger

5 degrees - the width of your three middle fingers side by side

10 degrees - make a fist and hold it with the back of your hand facing you.  

25 degrees -  stretch your thumb and little finger as far away from each other as they'll go. Tip to tip is about 25 degrees

15 degrees - a bit out of order .. like the 25 degree measurement, but between your index and middle finger.

 

smoke rings, sports and beyond

Canals saw explosive growth in England during the first few decades of the Industrial Revolution allowing raw materials like iron and coal to fall in price by as much as eighty percent.   Improving canals became a major industry - they became straighter with locks and aqueducts coming into wide-spread use to deal with changes in elevation.  Then, around 1840, railroads became the thing and many of the canals were purchased for their right of way.  The expansion of railways led to two of the more dramatic financial bubbles in history, but that's another story.  The story here is about something really interesting that happened just before the railroads started taking over.

 

James Scott Russell found himself working on a large canal near Edinburgh, Scotland.  A newly minted engineer, he had been hired to investigate the movement of barges in the hope of making them more efficient.  Russell spent a lot of time observing and making measurements.  One day the tow rope between the mules and the barge snapped and the barge came to a sudden stop.  He watched in amazement watching mass of water in front of the barge's front bow 

“I was observing the motion of a boat which was rapidly drawn along a narrow channel by a pair of horses, when the boat sud- denly stoppednot so the mass of water in the channel which it had put in motion; it accumulated round the prow of the vessel in a state of violent agitation, then suddenly leaving it behind, rolled forward with great velocity, assuming the form of a large solitary elevation, a rounded, smooth and well-defined heap of water, which continued its course ong the channel apparently without change of form or diminution of speed. I followed it on horseback, and overtook it still rolling on at a rate of some eight or nine miles an hour, preserving its original figure some thirty feet long and a foot to a foot and a half in height. Its height gradually diminished, and after a chase of one or two miles I lost it in the windings of the channel. Such, in the month of August 1834, was my first chance interview with that singular and beau- tiful phenomenon which I have called the Wave of Translation.”

Afterwards he built a tank in a laboratory to conduct controlled experiments. In 1844 he published his results noting four things about these solitons.

° The waves are stable, and can travel over very large distances (normal waves tend to either flatten or steepen and topple.

° The speed depends on the size of the wave, and its width on the depth of water.

° The waves do not merge, larger waves overtake smaller ones rather than combining.

° If a wave is too big for the depth of water, it splits into two waves, one big and one small.

A few decades later  physicists began to work out the physics leading off in unimaginable directions.  But back to that wave moving down the canal.  If it was large enough you could surf on it.  And, with enough study and money you could build very repeatable waves to your liking.  It turns out a surfer named Kelly Slater did just that.  The December 17^th, 2018 issue of The New Yorker has a great article. 

 

It turns out solitons exist throughout the physical world - smoke rings, packets of light in fiber optic strands and much more.  On light packets - high speed data communication using optical fibers simply wouldn't work without solitons - the bits of information would blur into a muddle at high data rates. The math is a tad beyond the level of this blog - you'd see it in a second year undergrad physics class.  As people continued to work out why it is stable some insight came from that radical moment in 1953 when the computer went beyond a bicycle for the mind to becoming both a telescope and microscope.

 

Physics 101 classes usually have a vortex ring demonstration to illustrate some of the properties of vortex ring solitons.  Smoke ring guns are a lot of fun and fairly easy to build.  Turning them into a really great demonstration takes some effort. Dianna Cowern recently posted her version.  Her enthusiasm is pure wonderfulness.

Recipe Corner

 

The return of recipe corner - at least for today.  This was great last night

 Roasted Brussels Sprouts

 

Ingredients

° 1 pound Brussels sprouts - remove the outer leaves

° 1 medium sized onion - I had a sweet onion (Vidalia)

° 1 largish baking apple (Granny Smith) cut into half inch chunks 

° 1 tbl olive oil (doesn't have to be a great EVOO)

° 1/2 tsp grated nutmeg

° salt

° ground black pepper

° 1 cup apple cider

° 2 tsp butter

° 1 tsp brown sugar

Technique

° preheat oven to 350°F

° everything through the olive oil into a large baking pan.  salt and pepper to taste and toss to coat.  Cover with aluminum foil. 

° roast for about 25 minutes, uncover and stir

° temp up to 375°F and roast with no foil 'til the sprouts brown a bit - 10 minutes for me

° when the roasting begins bring the cider to a boil in a sauce pan over medium-high heat.  Add butter and brown sugar and stir 'til dissolved. Cook at a boil until it is reduced to the consistency of a syrup .. about 15 minutes for me.  I had about 4 tbl remaining. 

° Put the Brussels sprouts into a serving bowl, add the syrup and toss.. you probably need to adjust salt and pepper a bit before serving.

 

about two hundred miles north of roswell, new mexico...

As Edward Teller, Emil Konopinski, Enrico Fermi and Herbert York walked to lunch one of them noticed a New Yorker cartoon taped to a door blaming trashcan thefts on aliens.  It was 1950 and the country was in something of a UFO craze.  They laughed and continued.  

 

Unidentified flying objects have been a thing in the US since the late 1880s.  As soon as flying machines captured imaginations UFO sightings were reported.  Sometimes explained as foreign war machines, more often they were from other planets in the solar system falling in line with science fiction in the penny press and dime novels.  Jules Verne and HG Wells created more sophisticated aliens and UFO sightings reported rockets and flying saucers during the Great Depression.  The movie comic book industries picked up on it and fanned the enthusiasm.  

 

After WWII the atom bomb - something right out of science fiction for most people - and conspiracy theories growing out of secret government programs gave a sense to many in the public that these events were real.  The four physicists knew everything so far had a down-to-earth explanation - and if there was something, they'd probably be among the first to know. 

 

They sat down to lunch and physics talk when Fermi, who had been uncharacteristically quiet, suddenly exclaimed "where are they?"  Everyone at the table knew what he was talking about.  He scribbled away with some guesses about life supporting planets, the probability of life and the probability of interstellar travel.

 

° there are billions of stars similar to the Sun.  Many are much older than the Sun

° Many probably have planets and some are probably Earth-like.

° Some must have developed intelligent life.  Some of these civilizations are likely to be much more advanced than us.

° even at conservative interstellar travel speed of a half of one percent of the speed of light it would be possible to spread life from one location throughout the out galaxy in under 100 million years.  Not a huge amount of time compared to the geological age of the Earth.

 

We should have been visited .. regularly, in fact.  But where are they?  Although it's not a paradox it is commonly called the Fermi Paradox.   A large number of explanations have been given.  Here's an unordered partial list of the top of my head:

 

° extraterrestrial life is very rare..  we indeed may be alone

° life might be common, but evolution to intelligent life is very rare.

° intelligent life destroys itself before it develops interstellar travel - a popular conjecture during the Cold War and one Carl Sagan warned about.

° civilizations are too far apart in space-time 

° it's too expensive to mount such expeditions.  

° AIs will replace biological intelligent life and they may be focused elsewhere.

° we don't know how to look

° they're not interested in us or they purposely are avoiding us

° they're already here .. or their sensors are

° they're too alien

° and on and on

 

Frank Drake modified a technique particle physicists use to create the first serious attempt to quantify how common life is in the Milky Way galaxy.¹  The Drake Equation differs from the Fermi Paradox in that physical contact isn't necessary.. it's a counting rather than a visit.  It's easy to criticize as many of the terms are little more than educated guesses and some of them depend on poorly defined terms like life and intelligence.  It was also conceived before the Big Bang was established and assumed a steady state universe.  Lots of issues,  nut it fires the imagination and encourages dialog to the point where some progress has been made.

 

In its original form there are seven terms that are multiplied together .. note the fractions f are between 0 and 1.0.

R_*     the rate of star formation

f_p     fraction of stars with planets

n_e     number of planets that might allow life to evolve per star

f_l     fraction of planets that could have life that have life

f_i     fraction of planets with life that evolves to intelligent life

f_c     fraction of planets with intelligent life that have the capability of interstellar communication

L     the length of time such a civilization can broadcast and listen

 

As you might imagine there's some serious guesswork involved.  The last three terms in particular give such a spread that it has been criticized as an exercise in personal bias.   But we've learned a lot since 1961.   Now we have a good estimate of the probability a star has planets .. it's very common.  Furthermore there's been a good deal of work on the signatures of life and physically where to look - so called goldilocks zones.  One of the goals of the James Webb Space Telescope - the follow-on to the Hubble Space Telescope - is probing for signs of life.   That's for one of the next posts.

 

My own view, admittedly not worth much as I don't have enough empirical evidence, is that life must be very common, but intelligent life (whatever that means) is fairly rare.  Still the Universe is so large that I think there must be many civilizations.    But I also like to think we may be very rare and that humanity is special and worth preserving.   My belief is that Elon Musk and Stephen Hawking are very wrong when they say we need to leave Earth very soon to preserve humanity.  We have a very special and amazing place that is worth saving.

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¹ The form has its roots in 19th century system efficiency calculations. If a machine or process has parts each with their own efficiency and everything connected together you simply multiply the efficiencies to get the total system efficiency.  You can use the same technique to estimate the probability of finding a potential mate:-)

 

 

 

 

the other scientific revolution of 1953 that radically accelerated knowledge

In the Winter of 1953 Francis Crick interrupted the lunchtime patrons of the Eagle in Cambridge to announce he and James Watson had discovered the secret of life.   In fact it wasn't far from hyperbole - they had discovered the structure of DNA and the world was forever changed.¹  Something else world-changing happened later that year.  Without it we  wouldn't have advanced past the technologies of the 1960s.  Surprisingly one of the people behind it thought it cute, but hardly worth publishing.  

 

But first a bit of historical context

 

The Manhattan project began with blackboards and experiments.  Individual researchers had their desk calculators, but it soon became necessary to work out how neutrons diffused when a critical mass of fissile material came together. A group of scientist's wives came together to perform the repetitive calculations.  Next came IBM card reading calculators and then von Neumann became interested in developments in electronic computing at Harvard, Bell Labs and the University of Pennsylvania.  There's a deep and rich history from this time on, but the important point was the meaning of "computer" was shifting from a woman with a mechanical calculator to an electronic machine.²

 

In 1953  electronic computers were still rare, mostly one-off machines that were expensive and temperamental.   It was still a world of research and development. A few people recognized practical applications, but the machines mostly weren't ready.  Except for physics.

 

Physicists were heavily involved in the birthing of electronic computers focusing on specific problems that tended to involve military projects or fundamental research to drive the hardware.  Fundamental research was seen as the tip of the R&D effort and was often funded from military budgets which were large enough to support these efforts.   Enrico Fermi  had an interesting idea.

 

He was interested in nonlinear systems thinking they might have something fundamental to do with entropy and why time only flows in one direction.  He, John Pasta and Stanislav Ulam conceived a simple toy problem - sixty four identical masses representing the atoms in a lattice connected end to end by little springs representing chemical bonds. Unfortunately calculating the restoring forces is a beast of a problem.

 

A linear system is one that can be described by a straight line on a graph.  Consider a spring.  Pull it twice as far and it exerts twice as much force. The same is true when you pluck a string on a guitar.³  Nonlinear systems have a more complex behavior.  With linear systems you just add up the contributions of each element without considering the others.  Nonlinear systems are nasty - you need to consider everything at once.  You might be able to calculate very simple systems with a few elements, but after things become very complex.

 

The three physicists wrote down a mathematical description of the physics. Think of it as a strange sort of string that you pluck and then listen to as time goes on.  Solving it would require a lot of computer time.  The big iron at Los Alamos was called the Mathematical Analyzer, Numerical Integrator, and Computer or MANAIC-1 for short.  It had been built for thermonuclear calculations, but this trio had an enormous amount of credibility and it was clearly fundamental research. 

 

The three had no experience with programming, but Mary Tsingou was a mathematical physicist who knew how to reason with  MANAIC-1.  She set to work creating a program that became an experiment simulating how the lattice behaved for sixteen, thirty two and sixty four "atoms" with various spring forces.⁴  

 

Imagine of the frequencies coming out of the system in terms of sound.  They had expected a pure note that would shift  over to more chaotic noises and finally the equivalent of just a hiss.  That didn't happen. 

 

The lattice was "plucked" and a series of overtones appeared and dissolved into each other creating a complex mixture.   Then the whole process reversed and the overtones disappeared in reverse order until the original pure note reappeared and the whole process started over again.  

 

 

Here's an illustration.  Consider the top graph.  The purple points are just the first vibration mode of a simple string - think of it as showing what would happen if it was just a simple string.  The system we're talking about with equal masses and springs is in blue.

 

Even this simple little problem that had baffled some of the greatest minds had a beautiful and completely unexpected result and a new way of doing science had been developed - the computational experiment.  The computer had become not just a bicycle, but rather a telescope for the mind.

 

Much of science is impenetrable without computer experiments like these.  It's so common, I've done thousands, that you tend to think it's natural.  But it had a beginning and without it much of what we've seen from science after the mid 1950s and the resulting technologies wouldn't have been possible.  Inefficient cars and airplanes, no electronic revolution, no cellphones, no ....

 

Fermi thought it was cute, but not fundamentally important.  That may be true for the hypothesis they tested, but how they did it changed the world.

 

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¹ There were many others who were in on this, but Crick and Watson weren't exactly the sharing kind.  Most notably the x-ray diffraction work of Rosalind Franklin.  But she was a women and died before the Nobel was awarded anyway.  

² George Dyson (Freeman Dyson's son) penned Turing's Cathedral.  An excellent and very readable history of the efforts at Princeton.  That may be the most important early thread as the computer architecture used today was developed there.  Much of the slightly later development came out of Cambridge in England. 

³ Sort of ..  you can get it to behave non-linearly, but for now consider a spring that behaves like F = kx where x is the displacement, F is force and k is a constant that tells you about the spring's stiffness.

⁴ I don't know for sure, but have been told she programmed down to the iron in machine language. 

 

 

rain acceleration

He scoffed at the pluviculturists who preceded him as he set his brew of twenty three chemicals aflame on the tower to the East of San Diego.  They had no idea what they were doing with their canons and exploding balloons...  they were more likely to start prairie fires than bring rain.  He claimed to be beyond such pseudo-science.

 

In December of 1915 San Diego's long drought continued with no end in sight.  The expanding city relied mostly on the Morena Reservoir about fifty miles to the East.  A reservoir that was getting dangerously low.  A worried civic club pressed the local government for action and brought in Charles Hatfield - a sewing machine salesman who had a rain-making business on the side.

 

Hatfield had some successes and failures.  It wasn't science - his real ability was timing storms and knowing how to publicize success and downplay failure.  He played customers like lottery players..  hearing a few successes convinced them they'd win too.    He offered to raise the reservoir level by ten inches for a thousand dollars an inch .. payable after the rains fell.  It seemed like a reasonable deal and before the end of the year he shock hands with city officials.

 

By the beginning of 1916 he had a twenty foot tower near the reservoir and started to burn what observers described as "smelling if a Limburger cheese factory had set on fire".  What no one knew was a weather pattern was setting up that would bring a river of water - over forty inches -  to the mountains of Southern California over the next month.

 

In a few days light rains began to fall. Hatfield continued burning his chemicals.  By mid-month the rains had become intense.  The reservoir passed the agreed upon goal - at least for awhile until the dam broke with a wall of water killing dozens of people.  Separately the San Diego river left its bank with the flood destroying homes, businesses, railroad tracks and stock and farmland.

 

Hatfield couldn't understand why the city didn't want to pay.  After all, he had met his goal.  But the agreement was just a verbal handshake.  The city offered a counter proposal..  damage was estimated at over ten million dollars.  He could take credit and they'd pay him the ten thousand, but he'd have to pay the ten million in damages.    It went to the courts. Weather, they ruled, was an act of God.

 

Except it isn't.

 

The human-caused component of global warming has been on a dramatic rise for the past forty years and is now pushing past normal variation.   The weird weather we've been seeing for the past few years is likely to only intensify.  It raises an interesting question.  Some of the poorest parts of the world have done the least to cause it, but will take the worst damage over the next few decades.  Do we think about responsibility for individual events? 

 

Until recently scientists have been careful to not link any single weather event to global warming.  They talk in terms of variation with a rising mean - something lost on most people.  But now it is possible to create attributions using historic data and computer models.  Recently the German weather agency was able to show last month's heatwave was twice as likely to have been explained by global warming than by natural variation.  The work was one in three days.  The approach is sound and the European Centre for Medium-Range Weather Forecasts will attribute extreme events like heatwaves and floods to human caused global warming offering reports within a few days of the event.

 

Some of the attribution can be done with better than 90% confidence .. much better than many medical diagnoses.  Localized events like tornadoes are too challenging at this point and many parts of the world lack rich enough histories, but we're on the edge of solid and sobering results.   It could be very useful in countries that accept empirical results.

 

she ruled the known universe

By the late 19th century astronomy had been revolutionized by photography.  Long exposures accurately produced much more detail than the best human eyes could hope to record and spectrography lead to the creation of astrophysics.  A real revolution was underway and large sums of money were going into new telescopes.

 

There was a fly in the ointment.  A night's worth of human observations were equivalent to a few kilobytes of information.  A good photographic plate contained thousands of times more.  Astronomy was entering its first age of big data. Finding items of interest and making accurate measurements required a lot of computation.  That meant human computers.

 

To create a catalog of the location, brightness and color of every star in the observable universe Edward Pickering created of the first computer centers at the Harvard College Observatory  The first computers were Harvard students, but Pickering found the young men unreliable.  He switched to female computers .. largely educated women who were unmarriageable for one reason or another, allowing them to have a full time job.  Pay was a bit more than a female school teacher made -  twenty cents an hour.  This group became one of most remarkable computer centers of all time.

 

Henrietta Leavitt  studied music at Oberlin and went on to the Harvard Annex (now Radcliffe) to get a college degree.  She enjoyed astronomy so much that her well-to-do family supported her volunteer work at the Harvard Observatory for a few years.  Her speciality was variable stars - the oddballs that changed in brightness over relatively short amounts of time.

 

She went back to her family taking a position as an arts assistant at a local college, but continued to work on a paper based on her observations.  She became ill and became deaf making marriage and work in music unlikely.   Henrietta got in touch with Pickering.  She could come back, but he couldn't pay her.  She went back to work without a salary - after all, her family was expected to support her.  Years later he started to pay her. 

 

She set out to characterize about 1800 variable stars in the Large and Small Magellaniac  Clouds.  As she worked something started to stand out in her mind.  If she assumed these stars were a similar distance away, after all, they were in the same cluster,  she deduced the period over which their brightness changed was related to their brightness. 

 

The apparent brightness of a light changes by the inverse square of its distance.  Double the distance to a light and it appears a quarter as bright.    Henrietta had discovered if two of these variables - known as Cepheid variables - had the same period, but one was one hundred times dimmer, you could deduce it was ten times farther away than the brighter star.  

 

Measuring the distance to objects in the Universe is core to astronomy and cosmology.  Distances to nearby objects - out to about fifty light years away - could be measured using parallax.  Hold a finger in front of your face and look at it with your left eye.  Now your right.  You'll notice a shift in position.  In astronomy you note a position at one part of the Earth's orbit and measure again six months later. Knowing the diameter of the Earth's orbit and the angular difference between the two measurements allows you to calculate the distance with trigonometry.  Unfortunately the technique  only works for nearby objects as the angles become too small to measure with increasing distance. 

 

By the early teens distances to several nearby Cepheids had been measured using parallax. Leavitt's yardstick had been calibrated.  Her result was one of the most important developments in astronomy - certainly worthy of the Nobel Prize.   She was unknown outside of astronomy, but was finally nominated for the Nobel Prize in Physics.  When information was being collected by the Nobel committee it was discovered cancer had taken her a few years earlier.

 

In the mid twenties Edwin Hubble used the Hooker telescope and Leavitt's relation to measure the distance to Cepheid variables in what was then called the Andromeda nebulae. The distances he found were mind blowing - about a million light years.¹  Andromeda was much farther away than anyone had imaging and couldn't be in the Milky Way.  It was a galaxy and the Universe was made of more than just the Milky Way. 

 

The physics of the how Cepheids work took decades to work out, but her relation didn't require a detailed knowledge of the mechanism.²  It became a workhorse and is still regularly used out to distances where you can still see Cepheids.  Over time a series of other yardsticks have been created all using her notion of a knowable absolute  brightness and the inverse square law.  It's how science advances, but someone has to take that first huge leap.  Someone should make a movie about these remarkable computers, particularly the deaf one who figured out how to measure from here to the stars. 

 

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¹ The currently measured distance is something over twice as far out - well within his measurement error.  The million light year distance was mind blowing at the time.

A small detail.  Astronomers often use the parsec as a unit of length rather than light-years.  A parsec is a parallax-second - the distance one astronomical unit (the radius of the Earth's orbit) subtends an angle of one arc second..   it's about 3.26 light-years.  Everyone else seems used to light years so I use them here.

² Cepheids are bright  yellow giants - anywhere from 4 to 20 times the mass of the Sun and up to 100,000 times as luminous.  During their period they see their radius change about as much as 25 percent.   They have a lot of helium in an outer layer.  Helium changes in opacity depending on how ionized it is.  Doubly ionized helium - helium missing both electrons - is more opaque than singly ionized helium.  As helium heats up it becomes more ionized.  At the dimmest part of the star's cycle the outer layer of helium is most opaque.  It absorbs heat from the star's radiation and expands.  As it expands it cools and the helium layer becomes more transparent.  At some point it begins to contract due to gravitation getting hotter as it goes.  The transparent mostly singly ionized helium becomes doubly ionized and opaque and the cycle starts over.  It's a huge fusion powered heat engine.

 

the hike that changed pasadena and human knowledge

On a clear day there it is.  Five or six miles East-North-East of Pasadena and  a tempting climb if you were raised around mountains.  Mt Wilson's summit is a bit over 5,700 feet and the view is remarkable in more ways than one. A trail out of Chantry Flat is fine, but tends to be crowded.  It's more strenuous but I'm partial to the Mt Wilson trail.  You can also drive up ..  assuming your car can handle the nest of television, radio and microwave antennas at the summit.

 

Around 1903 George Hale, a young astrophysics professor from the University of Chicago,  took the hike to see if it was the place for his dream telescope.  Up until around the Civil War astronomy had become a nearly dead subject.  Its main purpose had drifted from science to commercial and military celestial navigation.  But something radical had taken place mostly in America.  Physicists attached prisms to telescopes and began to analyze the spectra of light from the stars.  Photographic film had advanced and was better than the human eye at recording dim images.  It was possible to learn much more about the stars and discoveries grew exponentially.

 

Astrophysics was probably the first scientific field that America took the lead in. Gathering the most light possible was essential and big light buckets were expensive.  Hale came from a well-heeled family and had been able to connect with and inspire wealthy industrialists to fund the emerging field.  At Chicago he was able to talk a streetcar magnate into funding the largest refracting telescope - the 40 inch Yerkes Observatory.  Important work was done, but it soon became clear better observing sites than semi-rural Wisconsin were necessary.

 

It was recognized Mt Wilson had potential in the late 1890s.  Harvard tried to operate a small observatory, but it failed for a number of reasons.  Hale wanted to build a much larger telescope of a radically different design..  a 60 inch reflecting telescope with a novel mount.   The trip to Mt  Wilson in the pre-light and automobile pollution days. He loved it .. the view to the ocean was fine, but the view to the stars convinced him this was the place.  He went to Andrew Carnegie and described the potential of the best instrument in the world.

 

Building and getting a 60 inch telescope up the mountain was an effort, but it was a brilliant instrument exceeding all expectations. Harlow Shapley was able to use it to discover the Sun was not the center of the Milky Way and a few other discoveries followed.   It also became clear that an even larger telescope would be useful and Hale managed to persuade  John Hooker and Andrew Carnegie into funding a 100 inch instrument - the Hooker telescope.

 

It has been argued the Hooker was the most successful telescope in history.  Edwin Hubble discovered not only that there were galaxies beyond the Milky Way, but that the universe was expanding.  Shapley was able to measure the size of our galaxy and Fritz Zwicky found the first evidence for dark matter -- back in the early 1930s!  Our perception of our place in the Universe and evidence its fundamental nature radically changed. 

 

Hale still had yet another telescope in him.  Mt Wilson was becoming victim to light and atmospheric pollution.  The 200 inch Hale telescope was installed on Mt Palomar, seeing first light in 1948.   Its observations made it clear how elements were made in stars and indirect observations of black holes were made. People had been thinking about cosmology from the beginning of recorded history and with observations made with this telescope it finally  had become a real science.

 

If you make it to the summit both of the old telescopes are still there along with a solar telescope. The location doesn't allow serious research, but amateur astronomers can rent time on them and there are small public observation nights on the 60 inch using an eyepiece.  I did it once on a very un-pristine night, OMG!

 

It turns out Hale did much more.  When he moved out to Pasadena he became a trustee of a very small and sleepy technical school - the Throop College of Technology.  It could produce engineers to help build the telescopes, but Hale saw had larger ambitions.  He brought in two very well known scientists - Arthur Noyes and Robert Millikan. The three of them conspired to build an institution that would be small - tiny even - but would hire the best and focus on work that would have a long term impact.  Probably several institutions had mission statements like that, but these people pulled it off.  They created an interesting culture of curious play, depth, rigor and collaboration.

 

Hale befriended Henry Huntington - a railroad and real estate tycoon.  Huntington is fascinating in his own right - the sprawl of Los Angeles and much of it's culture has roots in his projects. He helped with the funding of this emerging technical school and brought in cultural amenities.  By now it had been renamed the California Institute of Technology.

   

That may well have been Hale's greatest contribution to humanity.  For decades Caltech's taste in problem spaces, their cross-disciplinary nature and remarkable students have changed the world. They came a bit too late to participate in the electrification of America, but the type of fundamental and applied science that came from the place changed everything.

 

Hale would have been 150 last week.  He would have been thrilled that he created something special.  Caltech is still at the leading edge of astrophysics and cosmology .. and so much more he couldn't have dreamed.  

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¹ Without a doubt it was one of the watershed instruments - that list might include the Galileo telescope, the Hooker, Karl Jansky's radio telescope, the Hubble Space Telescope and LIGO.

 

 

 

 

(almost) in the beginning

I love it when a scientist or science writer gives  jargon-free explanations.  Carl Sagan, Stephen Jay Gould, E.O. Wilson, Jane Goodall  and Neil deGrasse Tyson come over as superstars and  a handful of new stars have emerged on YouTube.  The work of these explainers is important to society going well beyond science education.  

 

 

A few days back I was given a new cosmology book aimed at a general audience.  The writing was almost jargon-free and respected the audience.  The artwork was outstanding as was the layout of the book.  But I had to give it up.   There were a couple of glaring errors so large to be a post-worthy.  I'll write about the one that bothers me most.

 

You probably learned the Universe began with an event called the Big Bang.  The evidence goes back a long way.   About 90 years ago it was discovered that most of the Universe was moving away from us and that the further away something was, the faster it was moving.  The idea of a static steady-state Universe was in serious trouble.   If everything was expanding it implied they were closer in the past..  much much closer in the very distant past.  It implied a beginning .. perhaps a beginning time.

 

As the Universe expands it stretches the wavelength of existing light.  Blue light becomes redder.  The energy of a photon - the particle of light - depends on it's wavelength.  The shorter the wavelength, the higher the energy.  Going backwards in time photons of existing light were more energetic.  The Universe was hotter.  As you go back in time it gets so hot atoms can't form.  Keep going and you get to a singularity - a super dense and hot region at the beginning of time.   The Big Bang happens and a Universe is set in motion.  You should be able to look in the sky and see the remnants of this event.  By now the expansion had been so great all that was left over was a cool glow of microwave radiation a few degrees warmer than absolute zero^.1  Two Bell Labs astronomers detected it in 1964 and the Big Bang was accepted.  The steady state Universe was dead.

 

There were some curious technical problems left to describe.  In the late 70s the notion of inflation came about to explain them.  Explaining cosmic inflation is a big too much for now, but think of it was the Universe expanding from an tiny size at an unbelievably fast rate for a short amount of time. Much faster than the speed of light (which turns out not to be a problem as information isn't exchanged between parts of the inflating Universe).  

 

The explanation was satisfying and compelling.  Now the Big Bang was seen as a singularity.. essentially a mathematical point of infinite density.  It happened and then the Universe inflated followed by the comparatively gentle expansion we see today.  Nobel prize worthy observations shortly afterwards dispelled that notion.  Inflation had to come first.  The Universe didn't begin as a superhot, superdense point, but more likely began without matter or radiation.  All of the energy was in the fabric of space-time itself - what physicists call a vacuum energy.  After about about a trillionth of a trillionth of a trillionth of a second,  inflation came to an end with the energy converted to matter and radiation somewhere between the size of a grape and a volleyball.  That glob and the expansion that immediately followed was the Big Bang.    

 

You might ask what set off inflation at the beginning of time?  Or was there a beginning of time? Or is was there time?   There are conjectures, but they're just that - conjectures.  There's nothing that can be addressed by physics (yet).   More to learn.

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¹ This background radiation fills the Universe.  If you have an old non-digital TV and tune it to an unused UHF channel, about one percent of the snow on the screen is that leftover from the Big Bang.  It's not from the Big Bang directly, but rather from the time when the Universe cooled to a point where it first became transparent..  about 380,000 years after the Big Bang.