omenti

supplier to the olympics

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The Winter games are over and a disproportionate number of Norwegians and Canadians are homeward bound with precious metals.  Two of you recently won gold medals - one in physics, the other in computer science and another stands an excellent chance of winning gold in beach volleyball in the Tokyo games two years from now.  But a simple question: where does gold come from?

 

Until recently gold's origin was the stuff of speculation.  Nuclear fusion in stars produces elements past helium..  Hydrogen burns to helium, helium burns to carbon and so on.  But the process gets stuck at iron and is unable to produce anything heavier.  To get there you need different mechanisms.

 

Supernovas came to mind and do some of the work, but getting to very heavy elements - the precious metals for example - is difficult . Something wildly powerful is needed.  Kilonovas - the strength of a thousand novas - were theoretically possible if two neutron stars collided, but even then the explosions had to play out in a certain way.  Nothing had been observed.  At least until the 17^th of August last year.

 

The LIGO gravity wave observatory caught the unmistakable signature of two neutron stars spiraling together and finally merging.  At the same time a burst of gamma rays that alerted an orbiting patrol telescope that was sufficient cause to turn optical patrol telescopes to  search a patch of sky about the area of a hundred and forty full moons for a fading point of light about 130 million light years away.  A needle in the haystack, but the needle was fading.  Eleven hours later, after discarding about two thousand candidates,  it was found.  Hundreds of astronomers dropped everything - the game was afoot. The observations took place from gamma ray to radio allowing astrophysicists to study the progression of the event across a good chunk of the electromagnetic spectrum.  Combined with the gravity wave observations it is the first example of what is being called multi-messenger astronomy.

 

The event was not as spectacular as the first two gravity wave observations. They involved the merger of black holes each with masses twenty to thirty times that of the Sun.  In the process they briefly shook the fabric of space-time with about the energy you'd get if you converted three Suns directly into energy - all in about a second.  This new event, unpoetically labled GW170817, involved two neutron stars each with a mass about one and a half times larger than the Sun and roughly the diameter of Manhattan.   The merger still converted a lot of mass into energy, but only about one fortieth the mass of the Sun this time.  Big, but not stupendous.  The violent merger sent a large cloud of matter traveling outward at nearly the speed of light. As it cooled some interesting physics took place and a pot of gold emerged.

 

Astrophysicists had already worked out what the signal for a kilonova and the existence of a process that made heavy metals (the r-process) would look like. At first the light was blue and decaying in a way consistent with the production of lighter heavy elements like silver. Four days out it reddened consistent with the production of the heavier gold, platinum and uranium.  The amount of precious metals blasted out into space was, at least my my count, staggering.  Somewhere between a few dozen and two hundred Earth masses of gold and five hundred of platinum.  It is likely almost all of the gold found on Earth came about from neutron star mergers..  

 

So while the event was not the most energetic ever, it was still impressive and more science has been learned from it than about anything in recently memory.  It suggests this new type of astronomy that requires some of the most intense data analysis known will become very important.

 

And here's what the start of the process that lead to the creation of precious metals and some other heavy elements sounded like - a merger that took about a minute and shook space-time at a frequency in the human hearing range.

 

 

So for those who will win gold and silver .. that's where it came from.

 

a bit of science behind the role of the athlete's brain in sports

My niece Magi ran another 100km race last weekend.  That, combined with the Olympics, made me think a little about some recent work on factors limiting human performance  But firstt here’s something for those of you who are amateur athletes as well as student athletes you might know.  Sarah Pavan is a world-class volleyball player in both beach and indoor games.  She notes that she has been able to stay away from serious injury by taking proper care of her body.  A recent post on her blog has an exceptionally clear video showing her shoulder exercises that should help people stay out of trouble.  Even if you’re not an athlete they're worth looking at and thinking about.  I’ve been through nearly two months of physical therapy recently (bicycle hit me). Videos this clear would have been useful. 

 

Now onto performance.

 

 

Since the 1920s a standard measures for endurance has been vo2max .. roughly the rate at which your body can utilize oxygen during intense exercise.  It is often interpreted as the limit on how much power your body can sustainably generate.  You can use it as a proxy for cardiorespiratory fitness and some physicians are beginning to use it as a vital sign in physicals.  (my last physical included it)   It used to be considered THE magic indicator for endurance performance, but when you take a group of elite athletes it’s clear other factors are at play. 

 

 

There are are a number of other factors, but how we deal with pain and what controls muscles under stress is fascinating.  It turns out your threshold of pain does not appreciably change with fitness level.  What does change is what your body does with it.  Most of us feel pain and use it as a panic signal.  Someone who frequently pushes the boundaries goes beyond the simple panic interpretation.  For them it is information rather than an automatic panic response. .  “I've felt this level before..  I can slow down a bit or keep going at the same pace for another few minutes without injury”.  For the athlete a simple signal has become a rich piece of relevant information.  

 

 

For a long time it was felt there was a built-in mechanism to physically shut down activity under extreme stress..  particularly when the body is running low on oxygen.  A counter example emerged from studies on free divers .. the guys who dive without oxygen tanks.  Try holding your breath.  Most of us start having involuntary diaphragm contractions between two and four minutes.  The record is over 11 minutes (!) and periods longer than six minutes can apparently be learned without relying on being a genetic freak.  What’s going on is carbon dioxide is building in your bloodstream.  The warning comes much sooner than running out of oxygen (probably a good thing) and you can train yourself to recognize the signal and go past it (this seems like a really dumb thing to do, but people do it).  The experts  recognize when they’re about to lose consciousness and start breathing again. (again don’t try this!)  The point is the mind can control some deeply engrained natural responses.

 

 

Figure skating offers another example.  Why can people lean backwards like that and not fall over?  It turns out practice builds new neural maps in the cerebellum.  The map fires neurons to cancel out normal reflex signals.   Something similar goes on when they spin.  Spin around on a chair, stop suddenly and try to get up.  There’s fluid in your inner ear that’s still moving and your brain does that calculation and claims you’re still spinning. One of the feedbacks is to make your eyes move to compensate for the now non-existant motion and the mismatch makes you dizzy. Try and get up and see how that works.  With practice skaters build up and spin resistance neural map - also in the cerebellum - that precisely blocks the sense of motion at the end of the spin.  As a result their eyes don’t move and they don’t get dizzy.

 

 

An emerging view is, while vo2max may tell you who has potential to survive the climbing portions of the Tour de France and who can’t, there’s a lot of mental control that comes with training and practice. Some of the papers refer to perceived effort as being an important controller.  While this is closely tied to the feedback from our muscles and, in the non-athlete probably the same thing most of the time, it is being found that the mind has a significant role in controlling what is perceived effort allowing the body to perform beyond normal levels and the level of perceived effort can be increased with training. Combine this with the ability to create new neural maps and the brain gets more interesting.

 

 

This is very early work and clean experiments are difficult.. but a few solid testable hypotheses are emerging.  I’m sure an athletes like Sarah and Magi know about mental control and toughness instinctively, but it’s real and perhaps people will learn exactly what it is and isn’t and, as a result, learn to train better.

 

 

There’s another potentially important result.  We all have been told that exercise is good for us, but for someone starting out the first ten minutes can be an unpleasant disaster.  They don’t realize it gets easier with experience and that the first few months may be a barrier.  That’s probably a good reason to sign up with a trainer who can encourage you through the process. But it may be other techniques can be found to inhibit the slowdown signals.   Getting more people exercising would have an enormous benefit to public health.  This type of research has a large potential payoff beyond sports.

 

 

visits to the land of csikszentmihalyi

 

Last June I found myself next to the mother-in-law of one of the world's best volleyball players.  She commented on the extreme amount of focus the young woman had during the match.   Only what was necessary, but in great depth and richness.  I found myself wondering if she was in a state of flow.  A few years earlier I talked with another very high level player about his perception of time during a match.  He mentioned times when time seemed to run slowly and he had almost a detached sense of self.  He "knew" exactly where the other three players were and how they were moving even though he could only see one of them.

 

I've been told I'm very good at  focusing.  Sukie tells me when I'm really thinking I'm often in a strange posture on the rug or in a chair and unresponsive - "about like a petit mal seizure except it goes on for ten minutes to an hour."  Sometimes when I'm walking with someone talking about an exciting idea just it and the conversation remain.  A couple of times my walking partner has saved me from traffic.  And sometimes I draw in the air on an imaginary sheet of paper or slate board sometimes going back to look at what I've written or even change it.  It doesn't happen all the time, but often enough.  During the deepest times time goes all wonky and there's a feeling of perfection I find difficult to give words to.  I take this to be the type of flow Mihaly Csikszentmihalyi describes.   It's usually presented in terms of skiing a perfect line with time moving very slowly, but a variety of types have been proposed.  A few days ago I experienced it thinking about the sound of the skater on thin black ice.

 

Watching the video I was taken by the sound - questions began to form. Soon I was almost flying across the ice striking it with a blade of my skate here and then as I glided along.  The scene was like that of the video, only the strides were longer.  I heard the swishing sound of tiny bits of ice being thrown by the blade's motion. I imagined the blade, warm with friction, gliding on the three or four molecule thin layer of liquid water on the surface.  No strange sound yet.  I looked at a single stride starting and the blade came down on the ice.  The collision of steel and ice produced a strong short impulse that shook the thin ice layer.   I saw the vibrations in its frequency domain - a very rich and wide range of acoustic frequencies all color coded ranging from blue for the highest pitches to yellow for the lowest (a mental Fourier Transform of the impulse).  The vibrations made their way out though the clear solid crystal ice lattice and I watched as a ring of acoustic energy advanced outward on the surface at the speed of sound in ice.  All of this in very slow motion.  Think of the ring as a flattened doughnut.  As it moved out it separated into a partial rainbow from blue at the outer to a yellow inner edge.  The separation from outer to inner edge increased as the ring moved grew.  My mind had factoring in frequency dispersion of sound in ice.  As these rings moved outward from each skate strike, now I was above myself watching the rings expand and move towards the shoreline they shook  air molecules hard enough to make a sound loud enough to complete the journey.  Now I was standing on the shore watching the ring expand towards me and listening for a sound. It struck the shore and shook the air making its way to me.  I heard the sound and with it  had a hypothesis.  There was enough information to say something about the frequency dispersion in ice and I tested it in my mind by throwing a rock out where it could make a similar impulse.  Should you find some thin black ice try tossing a rock out onto it - at least fifty feet or so - and listen.  You should hear it. 

 

When the living room came back into focus I realized about ten minutes had passed.  It felt like a few seconds.  The image of the flow was still very clear and now I could think about it numerically.   Often it's an exhilarating feeling - joy and delight come to mind.

 

There are undoubtedly  many methods to encourage flow.  I wonder if that's what a skier is doing as she visualizes a run?   It's rather intense play and it can be structured or unstructured.  I'm no artist, but like to draw imagines I see and hear.   Early in the morning I draw for awhile . An alarm pulls me out if I get carried away.  Sometimes it stimulates flow, but I think it also improves my ability to link different ideas ...  to think differently. For me this usually works best after physical exercise. 

 

Flow can occur  in groups.  Again this is a discussion where athletes probably have much to say.  I suspect elite beach volleyball teams are examples and much has been made of the communal problem solving nature of the Norwegian men's ski team at this year's Olympics.   I've seen it in very small groups where the participants know each other very well.   It's not brainstorming (brainstorming has a well deserved poor reputation), but rather a form of play among experts.  It's well understood there are stupid ideas, but it's the idea that is stupid rather than the person.  In my experience these groups tend to be self selecting.  The best ones have very diverse individuals. They're are a big reason why those people love doing what they do.

 

I've seen them come together for general as well as specific tasks.  Everyone really wants to get something done - in a sense everyone's rowing in the same direction. I've seen them in music, art, the "hard" sciences, engineering and sports and suspect that's a tiny fragment of what can be.

 

I've seen dozens and dozens of teams that stand no chance of ever getting there.  Putting together such teams takes insight that goes beyond experience. The few I've put together were laced with passion.

 

So a definition...   Mihaly Csikszentmihalyi and others have formal descriptions.  For me it's the verb of a playground and the tools and experiences you've built to find delight in focus and depth.  

A favorite Feynman quote  (it applies  to many other endeavors):

Physics is like sex: sure, it may give some practical results, but that's not why we do it.”

  

the sound of skates on very thin black ice

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A reader pointed to this video and asked what's going on:

I’m pretty sure the sound is from an acoustic surface wave on the ice.  A thin rigid sheet is very efficient at transferring acoustic energy.  When the skater strikes the ice with a thin skate blade an impulse is generated.  The ice responds with a very rich range of frequencies (think about Fourier transforms if you have some math under your belt).  In ice the speed of sound is frequency dependent - higher frequencies move faster. A ring of energy moves out from the skate strike, widening as it moves with higher frequencies leading the pack.  The vibrating ice shakes the air as it moves creating sound that travels through the air. By the time it gets to you there is that characteristic star wars sound .. the high pitch that rapidly drops in frequency.  You may hear the air traveling sound later.. but it will be much weaker compared to the very efficient ice transfer.  

It won’t work with thick, bubbly or cracked ice ..  you’d really want black ice.  

If you’re near a lake and get a nice sheet, try throwing a rock out on the ice ..  You should get the same effect.  

 

the olympics: canadian rock stars

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Growing up in North Central Montana, I spent a fair amount of time in Southern Alberta.  One of the things you did with friends was curling - the only regular sport I can think of where a projectile's path is modified on purpose after launch.  Imagine tennis or volleyball where an essential part of the game is having another player offensively or defensively modify the path of the ball..

So let's try a little physics experiment. The rock has a mass of about 20 kilograms with a thin ring on the bottom that contacts the ice.  You'd think you could model this as an upside down glass tumbler moving across a low friction surface.  Give it a try.  Turn a glass upside down and give it a shove with a bit of spin on a smooth surface like a table.   You'll notice it veers in the direction opposite the spin and the amount of veering is related to the rate of spin.  So what's going on?

Take a  counter clockwise spin.  At the front of the glass the motion of the spin is to the left meaning the opposing force of friction is to the right.  At the back of the glass the motion of spin is to the right, so the force of friction is to the left.  If they were equal the glass would go straight, fall of the table and shatter into shards.  But the forces aren't equal.  The glass tips forward a bit putting more force on the front.  As a result the force of friction at the front of the glass is to the right and larger than the force of friction at the rear, which is to the left.  You add these forces and find a net force to the right so the glass moves somewhat to the right before flying off the table and crashing to the floor.  The diagram is for a curling rock and there's a discrepancy, so read on.

A counterclockwise spinning curling rock veers left!  

There are two main hypothesis and reality is probably a combination of the two plus a bit more.  I'll use what I think is the strongest contender.  The higher pressure on the front of the tilting rock differentially melts the ice at the front more than the back creating a slightly slipperier surface at the front.  The force of friction at the front (to the right in our case and properly shown in the illustration) becomes smaller than the leftward frictional force in the back.   Add the forces and the rock veers to the left.  (I'm leaving out quite a bit, but that's the gist)

There are some curious reasons why this can happen. The special pebbling of the ice surface is critically important and ice conditions vary favoring players with a lot of experience.  The brooms?  They have nothing to do with clearing off the ice, rather they heat it a bit making the it a bit slipperier causing a straighter trajectory.

Played properly it's a beautiful sport.  The game has great depth and innovations like smart brooms are revolutionizing technique.   Experience is critical and often the Canadians show the way with the best deep understanding of sheets of ice.

 

the next step in home audio?

 Still cold from the UPS truck the Apple HomePod woke up when I plugged it in and asked my iPhone for a dance.  They spun about and chatted in their local network for a minute or two before Siri introduced herself.  It was completely unexpected surprise from a great friend who  shares the love of music.  A day into the journey I have a few thoughts.

 

I'm a poor musician, but find it an important part of my life.  Grad school was at Stony Brook.  Besides an excellent physics department one of my reasons for doing grad school at Stony Brook was its proximity to music in  New York City..  That wasn't quite enough, so two of us founded a concert series at the university that thrives to this day.  At Bell Labs it became apparent that music might be a significant driver for Internet use and I found myself walking several paths.  One was sound field reconstruction.

 

Sound field reconstruction is just the fancy way of  recreating the sound where it was recorded or engineered in your home.  In theory you record the acoustic signatures of the recording studio and your living room and create a mathematical operation that makes your living room sound like the recording space.  In practice it's approximately hard.  Sound waves are fairly large and get reflected, absorbed and transmitted by and through everything in your room.  Making matters worse the sound field at different spots in the room is usually very different and things in the room move between and during listening sessions.  We made serious progress, but it took exotic microphone and speaker arrays as well as state of the art (for the time) computing to make it sort of work.,

 

One detail is centrally important.  Imagine sitting before a simple speaker cone.  Most of the sound comes straight at you with the volume falling off as you get away from the speaker's central axis.  Speakers have very characteristic patterns showing how loud they are depending on the angle you're sitting at as well as the frequency of the sound they're producing.  If you have two stereo speakers there is usually a sweet spot where the sound reproduction is optimal.  In this area the sound field can be fairly good and you can close your eyes and visualize where the musicians are.

 

Imagine an array of speakers, each with its own amplifier, all controlled by a computer, you can control the phase and amplitude (loudness) of each speaker.  The waves they send out interfere with each other as they expand outwards.   By controlling the phase and loudness (amplitude) of each speaker you can make them interfere in such a way that they create a new wave that can be aimed.  The little animation shows an array of four speakers in a row, but it can be any number and they don't have to be in a line.  The HomePod uses seven small speakers arranged in a ring.  

(you may have to click on the animation to start it)

 

The HomePod also has a ring shaped array of six microphones.  They listen to the room (sample it) at a fairly high rate and decide what parts of the music, from its stereo signature, need to go where and how it needs be modified to interact with the room and everything in it.  An Apple A8 processor, the same two billion transistor processor used in the iPhone 6 and 6 Plus, handles the computational chores.  This is much more power than we had back in the day.  Although I don't know exactly what they're working on, several people I know who are real experts at this have been at Apple for years.

 

 

The HomePod also has a computer controlled single woofer with its own amplifier mounted vertically to handle the low notes.  

 

I'll leave the specsmanship, mechanical and most of the UX discussion to others and just talk about what it sounded like.  I'm not golden eared, but rather a serious listener.   I focus on the music and let it take me where it pleases. 

 

I listened to works across several genres with the HomePod placed at about ear height in a small acoustically complex room.¹   For very small groups - soloists and piano quartets for example - the sound stage was excellent ..  about as good as my stereo pair of conventional speakers (about $3,000 in speakers).  The HomePod didn't match the reference speakers when I was sitting at the sweet spot, but was better when I moved around the room.  That is astounding. 

 

It was creating stereo -a  term has nothing to do with a pair of anything, but rather three dimensional.  Moving  beams of audio around it was painting a sound field in my living room. 

 

As I listened to larger ensembles I found a less accurate sound field.  That said it was still comparable to my reference pair when I was away from  my very small sweet spot - its effective sweet spot was larger.   Note for some pieces of music a good $500 pair of speakers would do a better job if properly installed, but  would love to see what a pair of HomePods placed about two meters apart would do.  Apple has promised the feature will be available later this year.  I've already earmarked the funds for immediately buying a second unit then.  I suspect a pair of HomePods will blow my reference pair away when it comes to sound stage placement.   That will be even more true for those who haven't carefully adjusted their current speakers with test recordings and a spectrum analyzer. 

 

You can control it from an iPhone, iPad or Mac, but Siri is the intended interface.  I've had poor luck with Siri on my iPhone, but here it works much better.  It's also much more robust to interference.  Microphones beamform too and it's clearly listening to you doing its own cocktail party trick.   That said it, and every other interface I've seen are just wrong when it comes to classical music.

 

Comparing it to the networked speakers from Amazon and Google is silly.  Their speakers are terrible and useful only as acoustic wallpaper you listen to in the background.  They're really microphones in your home listening to you assuming you agree to Google's  or Amazon's value proposition (I don't).  Privacy is vastly different - I'll go with Apple's differential privacy rather than Google's "you are the product" flavor.   But if music is secondary and you want a digital assistant with a speech interface, Google and Amazon are the ticket.  Apple is going after the other audio companies along with making its platform stickier in the process

 

I suspect the speaker will be like the Apple TV - fairly stable hardware with the bulk of improvements coming through software updates.   My list of UI and UX issues is growing, but I suspect this will become part of my life. 

 

And a final caveat - speakers involve personal taste.  YMMV

 __________

¹ I'm very familiar with these pieces.  With one exception  I've heard them live and I've even been involved in the recording process on two. 

Ecstacy  Anonymous 4 and Mike Marshall

Us  Regina Spektor 

Seven Swans Al Petteway

The Heart Asks for Pleasure First  Ahn Trio

Black Horse and the Cherry Tree   K.T. Turnstall

The Littlest Birds  The Be Good Tanyas

Submarines The Lumineers

Pipeline (electric and acoustic versions) The Duo Tones

An Spailpin Fanach Connie Dover

The Heroic Conditions of the Universe Pt 7 After the Storm Alexandre Desplat

Turn it Around Lucius

Jolene Mindy Smith's version

Vespro della Beate Vergine: Domine ad Adiuvandum a 6 Monteverdi

Shchedrik Kitka

Our Town Iris DeMent

Sun Will Set Zöe Keating

Don Giovanni Madamina, IL Catalogo and Questo Mozart  (sort of a sign of politics)

Canon a due Violincelli in D Major Gabrielli

Cello Sonata in D Major Op 69 Beethoven

Suite No 6 in D Major  JS Bach (Yo-Yo Ma)

   

a most remarkable instrument

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Let your spectrum analyzer listen to  middle C on a piano and take a look at what comes out. (guess what?  your smartphone can do it)   Most of the acoustic energy, assuming the piano is tuned to a 440 A is concentrated at a tad below 262 hertz (cycles per second), but other things are going on.  Bursts of energy at multiples of the 262 Hz fundamental  frequency paint the spectrum along with a few other bursts.  The integer multiples of the fundamental frequency are called partial harmonics and the others are inharmonic partials.  Together they form a large part of why a piano sounds like a piano - in fact why a specific piano sounds like that particular instrument - it's timbre.

The time development of a note can be very complex with the distribution of energy in the various harmonics changing as the note decays.   A really nice way to study this is with Fourier analysis.  I gave a crude non-mathematical introduction earlier, but I just came across another beautiful illustration. 

Enter Anna-Maria Hefele .  She's  a remarkable singer who has mastered the art of overtone singing.  Thanks to Richard Feynman's life-long fascination with Tuva you're probably aware of Tuvan throat singing.   Her singing is much richer.  Let's start with her voice as an instrument in this lovely version of H.I.F. Biber's Rosary Sonata 1.

 

and now a graphical look into the flexibility she has ..  simply wonderful!  Such a fine way to show off the overtones.

the olympics: spinning through the air

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In figure skating you to convert  some of the kinetic energy from your speed across the ice into air time during which you spin.  You launch yourself skyward using the teeth on front of your blade like the base of a lever (way more inefficient than pole vaulting).  Once it leaves the ice your center of mass follows a simple mostly parabolic trajectory defined by gravity.  You can't change that path, but you have another trick up your sleeves.

To start a spin you need to generate a lot of torque.  This is done by generating large forces in opposite directions against the ice.  (read powerful leg muscles!)   Now the trick.  Physics has several conservation laws.   We'll make use of conservation of angular momentum.  It's the product of the rate of spin and the moment of inertia.  The moment of inertia is basically a measure of how mass is distributed around an axis of rotation.   The further out the mass from the axis of rotation, the higher the moment of inertia.  You can't change your mass, but pull your arms in and your moment of inertia decreases and your rate of spin increases in response. 

I watched about a dozen world class skaters carefully frame by frame doing the same quadruple jump.  The longest flight time I saw was 0.66 seconds - most of the others between 0.63 and 0.65 seconds.  They were spinning a bit over nine times a second during the core part of the flight, but much slower just after takeoff and before landing.  

The 0.66 seconds of airtime resulted from increasing the height of his center of mass by about 53 centimeters.  It is difficult estimating the force of his impact when he hit the ice, but it was probably about eight or nine times his body weight -- all on one skate.

Clearly there's a lot of skill and training.  Training informed by kinesiology - a mix of anatomy, physics and sport,. It's interesting to think what body type is favored and what someone who could easily land quintuple jumps would be like physically.

The physics requirements demand a light and very thin body to optimize range of control over his moment of inertia.  Very powerful legs to get the highest possible speed and liftoff for maximum flight time as well as generating an enormous amount of torque against the ice.  The arms must be strong enough to move in quickly and there is some advantage having longer arms.. eg.. the skater's wingspan is likely to be longer than his height.   I would be surprised if his height is much more than 170 centimeters and his mass greater than about 60 kilograms.  

 

One might dream of what could be done give more air time.  Perhaps an event on the Moon with a sixth the gravity and flight times approaching four seconds.

But wait -  there's a sport for that.  Freestyle skiing.  Similar physics in that you're playing with your moment of inertia, now concentrating on all three axes rather than one, as your body moves through it's Newtonian parabola. 

 

 

the olympics: why is ice slippery?

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One of the questions on my Ph.D. physics prelim was this:

what is a ruby and why is it red? why is the friction so low on a sled?  on a plot of p verses t, plot out the phases of helium-3

We had twenty minutes to impress the readers with whatever depth we could must.  The middle question was a trick to see how foolish we were. 

 

Many smooth surfaces aren't slippery.  Ice can be slippery even if it isn't very smooth.  The normal explanations are the weight of the skater puts pressure on the ice lowering it's melting point and/or the friction of motion heats the surface melting a thin layer.  The problem is even if you use a heavy skater - say 120kg on small skates - you only get a liquid surface down to about -3.5°C.  The friction is only good for a couple of degrees for the fastest speed skaters. I've (stupidly) skated in -30°C weather.  What's up?

A century and a half ago Faraday hytophesized ice forms a thin liquid surface.  His conjectures as to why and his experiments weren't good enough.  Now it is known ice has a very thin layer of liquid water - about four or five molecules thick near freezing and down to two at -35°C where the skating begins to get tough.  The pressure and friction effects are real and contribute, but only on warm ice.

It took an exotic experimental technique to verify and measure the effect and physics behind the pheomea is on the deep side, but we have something.  And that's why, when you stick two ice cubes together and put them back in the freezer they freeze into a single body.

Those ice dancers, hockey players, speed and figure skaters - they're all gliding on a film four atoms thick.

How cool is that?

 (speed skating often warms the air above the ice, but that's for the same reason they do it for indoor cycling - wind resistance)