omenti

medical tests and probabilities

a mini post

 

There are many references in the news to how good viruses tests are and what conclusions you can draw from them.  Unfortunately some are wrong and I haven't seen any easy to understand explanations of how to figure these things out.  It's all conditional probability. The standard approach is to use Bayes' Theorem.  Unfortunately most people have never heard of it or vaguely recall a formula with P's and |'s they once memorized without knowing what it really did  

 

Here's an easy way to think about it in the form of an example.  Imagine a population, say a city, where 1% of the people have a viral disease (I'll call the disease 'virus').  There's a test with a 90% chance of returning a correct result.  So if you have the disease there's a 90% chance the test returns a positive, and if you don't have the test there's a 90% chance the test returns a negative.   So what's the probability that someone who has just been tested has the disease?

 

For simplicity imagine an unbiased group of 1000 people in the city.  Let's screen them and see what happens. Ten people will have the disease, 990 will be disease-free.Of the ten people with the disease the test will correctly identify nine of them and incorrectly identify one.   Looking at the people who do not have the disease 90% of 990 or 891 will correctly test negative, but 10% of the 990 or 99 will incorrectly test positive.

 

 

 

 

So the probability a person who tests positive actually has the disease is the number who test positive and have the disease divided by the total number who test positive:  9/108 or about about an 8% chance.

The example has nothing to do with the specifics of CV-19, but maybe will give you a way to think about how to sort out what the real tests are saying when an accuracy is published.   Going deeper really requires tools like Bayes' theorem, but hopefully this is clear.

 

Armed with this technique perhaps this otherwise well-written piece in the NY Times will make sense.  Also note this is for an unbiased initial sample.  If you're screening on existing conditions before testing (which is common outside of Iceland), additional complications appear. But at least this should give you an idea.

 

 

 

 

sometimes you need one heck of a butterfly

In the early 60s Edward Lorenz was working on one of the first computational weather prediction models.  Many of the early explorers, new to computer programming, were getting bitten by limits of the machines and software.   Lorenz, the story goes, was running a numerical computer model to redo a weather prediction from the middle of the previous run as a shortcut. He entered the initial condition shortening it in a way he didn't think would matter given the accuracy it was measured to (say 0.504 rather than 0.504103)

 

"At one point I decided to repeat some of the computations in order to examine what was happening in greater detail. I stopped the computer, typed in a line of numbers that it had printed out a while earlier, and set it running again. I went down the hall for a cup of coffee and returned after about an hour, during which time the computer had simulated about two months of weather. The numbers being printed were nothing like the old ones. I immediately suspected a weak vacuum tube or some other computer trouble, which was not uncommon, but before calling for service I decided to see just where the mistake had occurred, knowing that this could speed up the servicing process. Instead of a sudden break, I found that the new values at first repeated the old ones, but soon afterward differed by one and then several units in the last decimal place, and then began to differ in the next to the last place and then in the place before that. In fact, the differences more or less steadily doubled in size every four days or so, until all resemblance with the original output disappeared somewhere in the second month. This was enough to tell me what had happened: the numbers that I had typed in were not the exact original numbers, but were the rounded-off values that had appeared in the original printout. The initial round-off errors were the culprits; they were steadily amplifying until they dominated the solution." ¹

 

Small changes to an input that was iterated many times created a big change in the output. He presented it at a conference causing someone in the audience to comment a single flap of a seagull's wings could change the weather forever.  Lorenz started using that in his talk changing it to the more poetic single flap of a butterfly's wings in Brazil setting off a tornado in Texas.

 

The image resonated with many existing notions about complex systems including science fiction where a time traveler steps on a bug and returns to a vastly changed future.  From there it has managed to become an embedded concept - usually used to describe chaotic and large inefficient systems.  The problem is it isn't always true. In fact it's usually false.

 

Chaotic systems are often less sensitive to change than other systems.  Run a stream of water in your sink.  The motion in the flow is extremely chaotic - no computer could keep up with the details.  Stick your finger in for a second.  The overall flow changed while your finger was present, but quickly returned to its normal chaotic level almost immediately after you took it out. 

 

The climate system is extraordinarily complex. Predicting weather in advance has made incredible progress thanks to better models, hardware, and software.  It turns out there's probably a limit to how far models can predict based on fundamental changes in the atmosphere.  They aren't butterflies.  Butterfly wing flaps are quickly dampened out by thermal motions of the surrounding air.  To make a change you need big butterfly - a really big butterfly ..  the equivalent of several massive thunderstorms taking place in areas you can't predict ahead to the necessary accuracy.  A butterfly flap equivalent of several thermonuclear explosions.²

 

Inefficient complex systems tend to heal themselves.  The Internet, the way food used to be grown and distributed .. almost any large scale process before it was made "efficient" .. tend to be much more robust than efficient systems where "wasteful" redundancy has been removed.  I worry we're witnessing some of that now as the result of a large perturbation to numerous systems.

 

People often come away with the idea that you can manipulate a large complex system if you only can figure out what breed of butterfly to use and exactly when and where to turn it loose.  It's a fool's errand.  Instead you need to study these systems to learn if it is possible to steer them and how you might do it.  The real insight may be you need to change the system itself rather than its inputs.  

 

The same is true for complex efficient systems.  A very small change can crash them.  High efficiency can be the enemy of robustness. Of course systems can be too inefficient - the trick is to find the right balance to build robust systems.

 

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It's easy to build simple systems where butterflies are very effective.  Lorenz's weather program was simple and easily influenced and it's really easy to find simple expressions that are hair trigger sensitive.³

 

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¹ E. N. Lorenz, The Essence of Chaos, U. Washington Press, Seattle (1993), page 134

² a few times 10¹⁵ J - several hundred kilotons to one megaton.  A large thunderstorm is in the ballpark.

³ I won't spell it out, but if you're comfortable with differential equations consider y'' - y = 0  (say y(t) is position as a function of time) with the initial conditions y(0) = 1 and y'(0) = -1.  The solution is simple and predictable.  

Now imagine you have a measurement error and y'(0) = -1 ± ε  where ε is small.  Different, eh?  :-)

 

 

the problem of where

a minipost

 

Wandering around in a field we seem to know roughly where we are and can make a plan to get from here to there.  This sense of location takes place deep in the hippocampus and the neighboring entorhinal cortex (full disclosure - I couldn't remember that one and had to look it up).  The hippocampus has place cells that fire individually at different locations.  Grid cells and head direction cells are in the entorhinal cortex and create a virtual map of triangles that provide the hippocampus with additional information of location and heading.  It's a full navigation system that receives additional sensory information from sight and hearing.  

 

Some of us make better use than others.

 

I've been wondering about the "court sense" seen in some elite athletes where it's important to know the position and motion of the ball as well other relevant players at any moment.  Soccer, hockey, rugby and beach volleyball come to mind. Using beach volleyball as an example the best players create an evolving mental map of the other three players including one that may be behind you.  They can't take the time to think about it.   It's interesting talking to a player.  They may be unaware of the uniform or other details of the other players, but are very aware of a few pieces of dynamic spatial information. 

 

Toddlers often take indirect paths getting distracted by any number of interesting waypoints on their path.  As adults we tend to take what we think is the easy path from A to B and these days that information comes from the GPS in our phone or car.  GPS navigation isn't infallible, but the same is true for human navigation.  Are we getting worse at human navigation by relying on these satellite consultations so much or is it just a computational extension of our brain?

 

fMRI experiments have been done with people navigating virtual cities and forests with and without GPS.¹   Compared to those who navigated using their own mental maps there was much less hippocampus activity in those who navigated by following external directions.   The virtual map generated by the hippocampus seems to appear only when you are actively engaged in the act of navigation.  It's like we're bypassing part of our brain when we use a GPS.  It has also been shown that enhanced use of personal active navigation increases the size of the hippocampus while inactivity causes atrophy.²  

 

Make it a game to turn off your GPS and navigation on your own for awhile.  There are numerous natural signs and signals that help you find your orientation and path.  Which side of the tree has moss? What is the sun angle and shadow direction?  Which direction is North at night? .. and hundreds more.  Try it in a city too.  If you get lost you can always pull out your phone for a quick look.  You might even find the fun of discovery that a toddler gets by observing their surroundings more carefully.    There's even some evidence that exercising the hippocampus by building up rich maps through cafeful observation lower dramatic stress.  Perhaps give up the GPS function, but sketch or carefully photograph was you see.  Straight up play and you might be doing your brain a favor. 

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¹ Several studies exist.  Here's a fascinating fMRI study taking place in virtual London.

² London taxi drivers have to spend a large amount of time building a mental virtual map of much of the city.  Brain scans show highly developed hippocampus regions.  Some preliminary work with people genetically disposed to early onset dementia has found people with highly developed hippocampuses may be protected from decline. 

the second order waffle house index

minipost

Waffle House is a mostly Southern restaurant chain offering your basic greasy American breakfast 24 hours a day.  Over 2100 locations. Any Southern town with over about 10,000 people has one.  I've visited one a few times when we were working with Disney and found at least their orange juice safe, but a lot of people love them. What makes them interesting to me is the Waffle House Index.  

 

Waffle House is deservedly famous for being open no matter what.  Power out? .. no problem .. that's the emergency generator.  Tornado cut through town?  Keep the place open for the disaster crews. There's even a central disaster control center to manage massive events like hurricanes.  They've become a legend - so much that FEMA publishes an informal, but often quoted Waffle House Index.  Immediately after a disaster they might report something like 3 of 14 Waffle Houses in the impacted area open.  A few days later progress might be summed up as 8 out of the 14 Waffle Houses are back online.  It's useful a measure of commercial and public resilience just under the level expected for first responders and front line medical people. 

 

Until yesterday all of the Waffle Houses were closed.  Now, in states like Georgia, they're allowed to open and some are.  COVID-19 is a new game.  The nature of the danger is ongoing rather than short-lived. Somehow the Waffle House Index doesn't seem appropriate.  I suspect a more interesting index might be the percentage of normal customers coming in for a normal sit-down meal staying the normal amount of time? Sort of a second order Waffle House Index.   What is the regional perception of danger and how does that play out in personal risk-reward calculations?  

 

As recently as this week national polls suggest over 80% of all Americans don't believe going to a restaurant worth the risk. Sporting events and concerts are over 90%.   How regional are these numbers and how do they change with function, social class, income, risk category,  etc. (football in Texas for example)   It's an interesting question as the economy attempts to come back given insufficient testing and a dysfunctional berserker executive. 

 

The evolution of this index would be most interesting.

 

a g-whiz and an explainer

Jheri tagged me to a challenge making its way around:

 

Tell me something amazing about your field in a sentence and then spend five or ten minutes on something that isn't well known. 

 

It's probably meant to be a video chat challenge, but I'll write and go with astrophysics.  You might want to try this for your own field or maybe a passion.

 

It takes more energy to melt a snowflake than all of the energy received by all of the radio telescopes on Earth since they were invented in 1932. 

 

Now for something that would take about five minutes to talk about. Something most people don't know about black holes using nothing more than a bit of first semester high school physics and your imagination.  (If you don't remember much of that you can skip to the last paragraph.)

 

Let's say you have a rocket and want to escape the Earth's gravity - really escape rather than go into orbit.  There are two energies to consider.  The energy of motion of your rocket - its kinetic energy, and the energy from the gravitational attraction between your rocket and the Earth - the gravitational potential energy.  

 

The kinetic energy is just 1/2 mv², where m is the mass of the rocket and v is its velocity. The gravitational potential energy is -GMm/r  where G is the gravitation constant, M is the mass of the Earth, r is the radius of the Earth (the distance from the center of the Earth to the surface where you launch the rocket from), and m is the mass of your rocket.¹   So the total energy is

 

E = 1/2 mv² - GMm/r

 

If you keep increasing the velocity you get to a point where E becomes is no longer negative.  When that happens you've escape Earth's gravity.  The escape velocity is when the kinetic energy equals the gravitational potential energy.  Setting them equal and a bit of algebra we get.

 

v² = 2GM/r  about 11.2 kilometers per second for Earth.

 

You probably saw this in your physics class and are probably wondering what this Newtonian result has to do with black holes.  This is where it gets interesting.

 

About a century after Newton figured this out an English cleric named John Michell wondered what would happen if you kept increasing the mass M.  He knew the speed of light was large, but not infinite.  If you were on a body that was massive enough there was a point where the escape velocity would be greater than the speed of light!  People didn't know the speed of light was constant or that light could be influenced by a mass, but Michell had discovered idea of a black hole in 1784.  Remarkably the result is within a factor of two of the value you get using General Relativity.

 

Let's play around a bit.  c² = 2GM/r is the classical escape velocity for light.  Rearrange to get (on the path to something interesting)

 

M/r = c²/2G

 

Now consider the density (we're getting close to the fun bit!).  The mass of an object is proportional to its density times its volume or M ~ ρ r³  (ρ is the density).   Now substitute in and solve for density

 

ρ ~ c²/2Gr²

 

You're probably used to thinking of a black hole as  an incredibly dense object.  But density falls as the square of the radius of the black hole.  So as black holes get bigger  the density you need gets smaller!   A black hole with the mass of the Sun has a radius of about 3 kilometers and is extremely dense.  The supermassive black hole at the center of M87 that was imaged about a year ago has a diameter roughly four times that of Neptune's orbit - what we usually think of as our Solar System would easily fit inside - but its density is a bit less than that of water!

 

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¹ The negative sign is from the convention that the Earth has no influence over the rocket at an infinite distance.  The negative potential means the rocket is bound to the planet.  It's trapped until it has enough energy to escape.

 

your partner in efficiency

As an undergrad I developed a serious bicycling habit.  Our club would take longish sixty to one hundred mile rides on weekends. These were tours rather than anything approaching racing so we talked along the way.   One of the members was obsessed with the idea of human powered flight.  His spirt was contagious and several of us volunteered labor and calculations helping to build the first prototype in quest of the Kremer Prize.  It was one of those rare challenges where the goal was just barely possible. 

 

My involvement wasn't that deep, but I quickly learned to appreciate the efficiencies required. Questions arose.  What sort of athlete would be required?  How would power move from muscles to where it could be useful?  What kind of aerodynamic design would be most efficient and what was the flight envelope?    

We knew bicycles were efficient.  A good chain drive was almost 99% efficient and you could match the power output curve of the pilot to the requirements of a propeller. That's when I learned only the pilot's legs would be used... using arms and legs wouldn't work for a couple of reasons.  And what about the nature of the leg motion?  Lots of interesting issues and answers.

 

A bit earlier an article on the cost of transportation appeared in Scientific American.  This is the famous piece that Steve Jobs loved to refer to when he pointed out a person by themselves isn't incredibly efficient, but on a bike they're spectacular.  But why?

 

There are a number of ways to approach the problem, but I'll ask a slightly different question and hopefully cover a bit more ground.  

"Why can you go faster on a bicycle than you can run?"

We have two basic models of bipedal motion: walking and running.  When you walk you straighten your knee which lifts you just a bit as your heel comes up shifting weight to the front of the foot. The other leg swings forward, staying close to the ground most of the time.  One foot doesn't lift completely until the other has landed. You don't move up and down much and most of the work is done by muscles in the upper part of your leg.

 

Running is very different.  Your body lifts further and lower leg muscles become important as the motion makes you rise up on the forward part of your foot.  Runners will go into great detail on what's happening, but basically you're launching yourself with quite a bit of force using more muscles and force than when you walk.  When a foot lands some of the energy used to break the fall is stored in tendons for release during the next launch -  a mechanical battery. Optimizing efficiency is the work of training and genetics. [ An odd thing about the efficiency of running and walking is that walking is most efficient over a very narrow speed range, while running has a much flatter efficiency curve.¹ ]

 

You can go faster running by increasing the length of your strides (or leaps), but there are limits. Your leg is a kind of double pendulum.   It takes energy to accelerate it forward and some energy to brake that motion as it starts to reach its forward limit.  It's worse if your leg is heavy.²

 

Rather than swinging legs a cyclist spins a crank.  The crank's motion is a circle about a third of a meter in diameter. A much smaller distance than walking or running strides.   Circular motion means the cyclist isn't having to waste the kinetic energy of their moving lower leg by slowing it (it does waste a some energy, but not nearly as much). The knees and thighs still need to be stopped and started, but the motion is much smaller.  The end result is less wasted energy from leg motion.³

 

Like running there's an upper limit to how fast a cyclist can move their legs and still generate their greatest power.  That's where gears come into play.  The gears and large rear wheel allow the bike to move a longer distance forward than the distance your feet travel in one revolution of the crank.  And different gear ratios allow you tailor your effort to the conditions - speed, head wind, hills ...

 

On a smooth flat road your speed is usually limited by wind resistance and the power your muscles can develop.  It's amazingly efficient.  With very little effort you can sustain a pace that no marathon runner can keep pace with.   

 

note:  I've skipped over a lot.  Human motion is a rich and not completely understood science, but hopefully this is good enough.

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¹ without going into great detail I show a chart here.

² To think about this consider the leg's moment of inertia and the fact that all parts of the leg aren't moving at the same speed. The upper leg moves slower - this is why fast running animals have their muscle concentrated in the upper leg.  Carbon fiber lower legs can make partial amputees faster than an otherwise similar runner with an intact leg.

Note the power your muscles generate increases as cross sectional area, while the weight increases as the volume.  Larger muscles increase in power more slowly than their weight increases.  This is why most competitive distance runners are of average height and very lean. 

³ The cyclist's center of gravity isn't moving as much either and that saves energy.

 

a covid-19 recovery story and psa

A departure from the norm - something worth the read and potentially useful.

 

This is from an old Bell Labs colleague .. the story of how they helped his 89yr old stepfather in Brooklyn. This is no substitute for real medical advise, but might give a sense of reasonable supporting steps. Pulse oximeters are cheap ($25 to $50) and a good way to check your blood oxygenation level. Finding an oxygen concentrator would be a big challenge these days. If you see low reading early on it may be possible to take early steps and this may be increasingly useful information as more is learned about treatment.

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Sharing a miracle! My 89 year old stepfather Richard, was saved by love, science, creativity, and courage. He tested COVID-19 positive on March 19, with fever, fatigue, and a cough, followed by weeks of extreme exhaustion, spiking fever, and bacterial pneumonia. Now he’s been fever free for ten+ days and is gaining strength daily.

This was a miracle not only because COVID-19 can be so dangerous for any of us but even more so based on his age (he is almost 90!) combined with multiple underlying conditions. We are so grateful to see Richard on a path to recovery now; our goal for this post is to share what we did and what we learned with a goal to help others battling COVID-19.

Below are more than a dozen actions that were taken as an extended family to help Richard fight the virus at home, avoiding the need to go to hospital:

1. Pulse oximeter: we purchased an inexpensive ($25) but essential device in the home to measure blood oxygen levels. Levels need to stay above 90 otherwise a doctor should be consulted; measurements are taken multiple times a day, in tandem with temperature checks.

2. Oxygen concentrator: Richard’s doctor prescribed an oxygen concentrator because his blood oxygen levels were in the 80s. A portable, lightweight, battery powered, multi flow oxygen concentrator (Inogen device) was acquired for him as a result. Think of this as an practical in-home option between normal breathing and a hospital ventilator; it can be used in conjunction with the oximeter for measurement and can be covered by insurance/Medicare, if prescribed by a doctor.

3. Respiratory therapist: A respiratory therapist came to the home to demonstrate how to use the oxygen concentrator; this visit was included as part of receiving the oxygen device.

4. Crowd sourced masks, gloves, and hand sanitizer: hitting roadblocks at pharmacies and online sites, we received a heartwarming response from family, friends, and extended networks sending home made masks, gloves, and hand sanitizer from all over the country.

5. Simulated hospital environment: knowing the severe challenges at NYC hospitals in COVID-19 wards, we did everything we could to keep Richard at home, effectively creating a simulated hospital environment but with the comfort and care of being at home with a loved one.

6. CDC home protocol: my mother followed CDC home protocols for disinfecting and mask usage, ensuring her own safety and physical health, critical for a sustained role operating 24 x 7.

7. Virus warrior mindset: the battle at times was as much psychological as it was physical, and my Mom and Richard were champs of the highest order, mustering extraordinary emotional strength at times to keep going when darkness was pervasive.

8. Breathing and movement exercises: Richard’s doctors recommended a set of breathing, stretching, and walking exercises which he did three times a day. In the beginning it was daunting; over time, he was able to steadily increase the number of repetitions.

9. Virtual Urgent Care: we arranged for my mother to have a virtual urgent care visit, using an iPhone app with video streaming to consult with a doctor on her own health.

10. Real World Urgent Care: we finally found an Urgent Care facility in Brooklyn that would treat COVID-19 patients and had an x-ray machine, after trying more than ten different options at the time; many facilities were closed or refused any one with COVID-19. They did a blood test and a chest x-ray using remote radiologists to read the scans, confirming the bacterial pneumonia diagnosis and prescribing antibiotics (see below); this was much easier than visiting an emergency room at a hospital and a key bridge towards recovery.

11. Nurse/home health aide: we worked with a firm that specializes in home care for COVID-19 patients to bring in an experienced nurse/home health aide at a critical time, to help out for three days in a row.

12. Food and pharmacy delivery, and car services: Family members brought chicken soup to the front door. Delivery services brought food to make it practical to stay in. We had to try more than a dozen car services until one was found that agreed to take COVID-19 patients. A local pharmacy delivered supplies to the home.

13. Hydration and electrolytes: Throughout the height of the virus, Richard had little to no appetite. The doctor impressed upon us how critical it was to drink lots of fluids complemented by drinks with electrolytes such as Gatorade and Pedialyte. For nourishment, a drink such as Ensure can be helpful; for those with diabetes, Glucerna is an easy way to support nourishment.

14. Dual track antibiotics: A combination of Azithromycin and Cefdinir, running for ten days, was effective to battle his bacterial pneumonia. The use of these antibiotics was a key turning point in his recovery. However with viral pneumonia this approach may not be applicable. Note that early on hydroxychloroquine was ruled out due to cardiac risks and limited testing.

We hope that this summary of the approach that we took was useful and can help others battle COVID-19 in the broader war to fight this powerful virus and return to normalcy over time. It’s worth noting that love and care from immediate and extended family, along with friends and colleagues, played a critical role to aid recovery; although this can only go so far with respect to the real world ravages and harsh statistics of this disease, don’t underestimate the role love and care can play in this type of miracle, complemented by the application of science, creativity, and courage.

beyond birding

There are a number of ways to learn about systems, but you're usually stuck with observation and modeling when it comes to complex systems.  Every now and again systems you're interested in get a large wack. Fires in California are an example of localized system perturbations.  Reactions may or may not be what you had expected, but you can learn if you observe carefully.

 

COVID-19 has given a lot of systems that involve humans a major wack.  There has been a major drop in transportation and the power production curves have shifted.  Online education with a large variety of techniques will result in some failures and perhaps some successes. How effective are different appraoches and in what context?  How effective is telemedicine?  What happens when you delay elective surgery?  What is the outcome of delaying treatment for a variety of conditions?  What approaches work for dealing with pandemics?  What forms of government are effective for restoring economies? How much socialization do children and adults require? 

 

We live in a suburban area, but normally crepuscular animals are wandering around in daylight.  Which ones and why?  The sound levels in the woods are very different.  I'll be recording and labeling sound ambient sound levels and seeing how they change as this goes on and as we come out of it.  Many animal populations have been hurt by human activity.  Will some make a comeback and how quickly will they fade as we go back to business as usual.

 

It's easy to make long lists.  If you're so inclined there are any number of activities where amateur observation can be effective. Carefully recorded observations will be important even if you don't know what to do with them now.   Bird watching and amateur astronomy could be a model - amateur observations have turned out to be very important over time.  

 

Some of these activities could be great for curious kids and others may give business and life changing insights to adults.  And it's a lot more fun than sitting back and watching tv.

 

 

 

the sandman and the songs of the sand

Om's fine sand dune images took me back to a spring break during my undergrad days.  I had heard about singing sands and managed to talk someone with a car into an expedition to the Mojave Desert.  First towards Barstow and then onto a short dirt road before we got out and two hours of hiking to the Kelso Dune Field.  

Some of the dunes are several hundred feet high and climbing is something you do when you're young or crazy.  We were both and found a long leeward slope to slide down.  I highly recommend sliding down dunes and this one was special.  As we slid it made a satisfying rumble. I don't have a good sense of pitch, but would judge it somewhere between middle C and the C an octave higher.    Over and over we slid just enjoying the effect.  I poured some of it into a bag and we made it back to the car just around sunset.

 

There are perhaps two dozen examples of singing sands in the world. The effect hasn't been studied carefully enough to sort out exactly what's going on, but the common thread is you need very round grains of silica sand of similar size averaging about a quarter millimeter in diameter.  One hypothesis is these clean, round equally sized grains act as layers that jiggle up and down as the shear force causes them to slide against each other.  There are several other plausible ideas.  Sadly it's been observed that even a little pollution can silence a dune. The Kelso Dunes are apparently a faint whisper of what they once were. 

 

Singing sand is a different animal from the sand you tend to find on beaches and river beds. A few years ago it struck me that the sand found on great beach volleyball beaches doesn't stick to the athletes .. at least not that much.  Sarah told me about - the official sand consultant for the Olympics and other major events Hutcheson Sand and Mixes in Huntsville, Ontario.  Curious, I got in touch with their sandman and asked a few questions. You send them a kilo of your sand from layers down to about a half meter and they'll tell you if it meets the specification or find a source.   The size and shape requirements of the grains (mostly between a half and one millimeter in diameter and naturally weathered to a sub-angular to rounded shape) insure it drains easily and doesn't compact like more angular sands.  Size distribution and shape largely keep it from sticking to bare skin.  The sand used in the London games came from a quarry near Surrey, Copacabana beach sand passed muster as do most Southern California beaches, but China had to import 17,000 tonnes from an island in the South China sea.

 

Much of the sand we normally see has a large distribution of size and tends to look more angular than round.  The angular bits allow it to compact and, with a small bit of water, clump together and stick to skin.  The binding force comes from the surface tension of small amounts of water than form little bridges between angular pieces.  Not good for beach volleyball, but great for making concrete.  A side note is demand has been so great that construction grade sand is getting rare and there are sand pirates.  Desert sand doesn't cut muster, so all of those highrises in the Mideast require imported sand.

 

There are any number of interesting properties of sand, but one one you've probably seen.  You may have noticed walking on sand can dry it out.  Walking on wet sand applies pressure.  The grains push against each other and, if they are angular,  rotate into a new position. The sand had been fairly well packed by the force of wind and water, but many of these rotations force the grains apart a bit. This new configuration has a bit more empty volume and water the drains into it. It's called Reynold's dilatancy - here's a little video showing a simple experiment you can try at home.  

 

head and tailwinds

Today a friend said he was having a difficult time concentrating - ".. like running in circles, but with headwinds."   After hanging up I found myself thinking about running or cycling on a closed course in a wind.  Just how much does a wind cost if you have an equal amount of head and tailwind?   A bit of high school physics is required.

 

Here's a simple model.  Consider a square closed course with the wind blowing at a constant speed w from the left..

 

Let's make it easy.  Rather than thinking about what speed you can run on each leg, imagine a constant speed - say v - on each leg of the course and calculate the amount of power you need to generate to overcome the aerodynamic drag force. Everything else you do running should be the same.  

 

Power is force times velocity. Since your mass isn't changing, just look at what power is proportional to.  Tricks like these are common in physics - just leave out terms that stay constant where we only care about the comparison rather than a number.   The very quick answer would be since the power increases as the cube of the effective wind speed you will never gain as much from a trailing wind as you'll loose going into the wind.   Calling wind speed s

 

sorting it out:

 

for leg 1   required power proportional to (v + s)³

for leg 2   required power proportional to  (v - s)³

 

the crosswind terms are the same:  v(v² + as²)  where a is some constant showing how much extra force you need to use to deal with the crosswind.  It could be very low or high depending..  For now consider the simple case where a is 0 and expand the expressions.

 

leg 1: v³ + 3s²v + 3sv² + s³

leg 3:  v³ + 3s²v - 3sv² - s³

leg 2 = leg 4: v³

 

So if we add these up (we're just doing a comparison) we get 4v³ + 6s²v  (you can get away with this as the running speed v is constant).

 

With no wind the power around the course is proportional to 4v³, so having a wind always requires you to generate more power.  What you gain from the tailwind never compensates for what you lose from the headwind and letting the crosswind term a be greater than zero (it will be) only makes things worse.

 

Perhaps a simpler way to think about it is to consider just the drag force from air resistance.  Let's say you're running at 10 mph and have a 3 mph wind.  Going into the wind you're feeling 13 mph of effective windspeed so the drag force will scale as the square of that or 169. With the tailwind you're feeling 7 mph so the drag force scales as 49.  With zero windspeed the force scales like 100.    You lose 69 going into the wind and pick up 51 running with the wind.  

 

So you want to draft behind other racers going into the wind and try to make sure no one is right behind you when you have tailwind. And if you're worried about record setting it's best not to have a wind on a closed course.