omenti

giving time a hand

Hold out your palm and point it skyward.  Every second about one muon will strike it.  Muons are the most common remnant of cosmic ray collisions with the upper atmosphere that make it to sea level.  They're responsible for some genetic mutations and even cancers, but the levels are low enough that we really don't have to think or worry about them much.

 

When I was about thirteen I came across a cosmic ray experiment near the summit of Sulphur Mountain in the Canadian Rockies.  I've described the experience before - two young physicists had the patience to explain what they were doing to a kid. When comic rays collide with molecules in the upper atmosphere a lot of debris is produced - mostly in the form of subatomic particles.  Some have very short lifetimes and don't make it far.  Muons live long enough to make it down to sea level.  But there's a twist.  The half life of a muon is about two point two millionths of a second.  Even if it traveled at the speed of light it would have traveled about six hundred and sixty meters.  Most of these collisions take place a few tens of thousands of meters up. The trick is when we look at something moving very fast, time for it appears to run slowly.  The number of muons making it to your hand is a manifestation that time is relative. 

 

My mind was blown

People put up Stonehenge type markers in the prehistory to note seasons and other special dates.  Moving closer to historical times a variety of sundials were developed.  Clouds and night made them problematic and, depending on design and the skill of the observer, they were frequently only good to an hour or so.  Even so the some Romans had no trouble complaining about them forcing a structure on life.  The Romans moved a bit further  timing devices in the form of water clocks and hour glasses.  Water clocks were used to limit debate in the Roman Senate as well as arguments in legal proceedings.  But time was still mostly for special occasions and localized.  Most people relied on an approximate natural rhythm from cues from the sun and stars.

 

The thirteenth century saw the invention most associated with modern time. The mechanical escapement is a bit of cleverness that converts an oscillation into a ratcheted advancement in one direction.  In a clock a pendulum's swing causes a gear to turn one notch at a time.  The first use was in the church with pendulum driven bells to call the monks to prayer.  Several decades went by and dials appeared allowing the visual estimation of time and a key driver of the Industrial Revolution had appeared a few hundred years early.

 

Since then mechanical time managed to penetrate deeper and deeper into society.  The Industrial Revolution demanded workers at factories at certain hours.  Home clocks were affordable to some households, but reliable alarm clocks were still expensive enough that the profession of the knocker-upper - someone you would hire to wake you up by a certain time - persisted in England until the twentieth century.

 

Now we have accurate portable time and increasingly an expectation to make use of our time. And now if clocks were limited to an accuracy of a second every century, much of our modern technology would no longer work.  Sometimes it seems as if we're to be optimizing the time we have.  We're admonished - or we admonish ourselves - against "wasting" time.  For many being bored or having idle thoughts is somehow wrong.

 

Our sense time in our brain is very non-linear and irregular and an active area of study.  Almost certainly there is no master clock.  We seem to have individual interactions.   I find I require a fair amount of idle time to daydream, think and make associations that don't seem to happen when I'm filling my time "slots."  I can only be creative if I'm bored at some level.  

 

When I began to work out of the home I made it a point to take a walk in the woods across the street every day I was around.  You begin to notice the cycle of the seasons, and after a few years other patterns emerge.  It's been about fifteen years now and the experience grows richer with time. Some of this Summer seems to echo with one eleven years ago and other parts seem unique.   There are cycles for the trees, flowers, weeds, deer, wild turkeys, coyotes, bats, weasels and so much more.  You experience some visually, some with sound and some at time and audio scales we normally don't notice (I often take along a microscope or a box that allows me to listen to ultrasound.)

 

Hold your arms out side to side.  Imagine the distance from the furthest tips to be the age of the Earth - something like four point five billion years.  Now take an emery file and take a few swipes from the fingernail that is touching the present.   Now look at that fingernail.   You've completely eliminated the period of human civilization. 

 

I worry that humanity is failing the marshmallow test -  where you give a little kid a marshmallow and tell him there will be two if he can save the one he has for wait for your return.  Many key countries can't visualize the generation or two ahead to confront global warming.  Perhaps we'd be better off if more of us moved a bit away from the forced regulation of our clocks and allowed more opportunity to consider the broader world.

abigail van allen's layer cake - catalyst for the last half of the 20th century

I was in my second year of grad school and had gone to dinner at my advisor's house.  These dinners were always interesting and the deserts were a near match.  That night we had a wonderful homemade cake.  A layer cake rolled in the shape of a log, filled with fresh fruit and coated with a thin layer of bitter chocolate.  One of the guests - James Van Allen - yes the guy the Van Allen belts are named after - remarked on the cake and told us the story about Sputnik starting the space race was all wrong.  The real beginning came years earlier in his living room over his wife's excellent layer cake.  Reality is often more fascinating than the recent history we hear in school.

 

It was around 1953.  Van Allen and a group of physicists were at his home after a formal meeting.  This night a critical step was taken.  After talking about new learnings from balloon and sounding rocket explorations of the ionosphere.  Someone suggested maybe an Earth orbiting satellite would be possible soon.  After all - this von Braun guy was making a lot of noise about space travel being practical.

 

Indeed Wernher von Braun had been trying to popularize space travel.  He had teamed up with science fiction writers and later with Disney and Collier's trying to convince the public. Although von Braun was charismatic, he wasn't taken that seriously.  The only thing the government wanted him for was leading the Army's program to be rockets that could deliver nuclear weapons.

 

Enjoying the excellent cake was someone who could make a difference.  Lloyd Berkner was one of the most respected scientists in the United States.  He had the ear of generals and even the President.  He made an interesting suggestion.  Maybe the way to learn more about near space would be a multination collaboration like one that explored Antarctica.   Given global tensions it could be useful for political reasons and would spread the costs. Larger sounding rockets could be built along with expeditions to the poles.  Maybe even a satellite.   Everyone at the dinner loved the idea and the International Geophysical Year was proposed soon afterwards.  Ultimately dozens of countries and hundreds of scientists were involved.  The target year would be 1957.

 

Van Allen and the other near space guys kept proposing satellites with no luck.  Then, a few years later, Berkner found the key.  President Eisenhower was focused on avoiding WWIII and countering the Soviets.  Something like a satellite for science was nothing but a distraction.  Berkner had used the "it will shock the other side" argument without luck.  Then he changed gears and suggested it could lead to spy satellites.

 

Eisenhower was a general.   Having great surveillance is deeply embedded in military DNA.  Spies on the ground, high altitude aircraft, code breakers .. whatever it took.  The only trick with a satellite, Berkner said, would be to establish Earth orbit as neutral territory.  A small scientific satellite could set a precedent.   Eisenhower agreed and the Navy ultimately won a competition to work on Project Vanguard - a satellite to be instrumented by Van Allen's team. 

 

The Soviet Union's ICBM project was led by a scientist more interested in space flight than ICBMs.  He realized an ICBM would make a dandy satellite launcher and when Khrushchev took power managed to convince him on an ICBM program and added an Earth orbiting satellite would have a great political impact.  Khrushchev agreed, but what he really wanted was a big ICBM.

 

Through the International Geophysical Year interactions it had become clear that the Soviets were building a satellite - indeed that it would launch in the Fall of 1957.  It seemed like a fantastic cap to the year, but the knowledge and excitement didn't go beyond far that group.

 

When Sputnik (fellow traveler) launched it was mostly ignored by the Americans - certainly the government.  The New York Times made a big announcement and people went out to look.  Satellite tracking became almost a hobby for some (that was the genesis for a global positioning system, but that's another story), but America wasn't quaking in fear.

 

The American government was happy - perhaps delighted.  They weren't first, but this little Soviet metal sphere orbited over American territory several times a day.  Precedent had been established. It would take time, but the Americans would get their spy satellites.

 

The story most of us know came from Texas.  Lyndon Banes Johnson worried whoever controlled space could control Earth - an old sci-fi trope.  LBJ also happened to be the Senate Majority Leader.  He gave impassioned speeches about falling behind.  His words resonated with the public and early American rocket failures only increased public anxiety.  

 

And what about Van Allen and the other scientists?  Johnson managed to open the serious money spigot.  It became clear that ICBMs made great satellite launchers with modest changes.  The scientific study of space was a dandy idea to help prove in new rocket technology.    STEM education in the public schools sprang up largely out of Berkeley and MIT.  The world was changing.

 

The Van Allen Belts?  They were discovered using the early Explorer series of satellites in 1958.  The interaction of the Earth's magnetic field and the solar wind was beginning to sort out. 

 

So that's the secret .. really good layer cake.

 

the danger of over simplification

In the early 1990s Anders Ericsson of Florida State University went to a music school in Berlin to test an idea about deliberate practice.  The music school had high standards.  Ericsson suspected practice separated the best of the best from the average.  He asked the eighteen year old violin students to think back on how much practicing they did since they took up the instrument.  Then he had the music professors to divide them into three groups - great, good and average.  Those in the great group averaged about 10,000 hours of practice.  The good, about 8,000 and the average practiced around 5,000 hours.  It seemed like a neat result - practice more and you do better.  He published a paper that wasn't exactly rigorous - it lacked statistical measures like ranges and standard deviations and was more of a discussion than a formal paper.  

 

Prof. Ericsson didn't push the result was a bit to the side of his core work and he didn't heavily promote the result.  But others saw a compelling story around that lovely round hour and a work ethic.   One was Malcolm Gladwell.  Gladwell is a great storyteller, but he often oversimplifies and gets things wrong.  The 10,000 hour result has been disproven by more careful studies over and over, but his books and TED talks are enormously popular and have made the idea something of a cultural meme.  

 

Recently I was thinking about something else he said that was misleading. Great storytelling, but misleading.  The more I thought about it, the more damaging it seemed.  It's partly linked to the 10,000 hour story and some unhealthy forms of training. 

 

In Outliers Gladwell talks about a relative age effect.  He uses sports, but it can apply to academics and other areas.  Say the calendar allowing kids to participate in a sport begins on January 1.  Kids born in the first quarter would be  January → March birthdays.  He noticed that ice hockey players born in the first quarter are over-represented and forth quarter kids are  under-represented.  The pattern appeared in several other sports so he set about writing a compelling sounding story.

 

What happens is when  kids are allowed to try out for a sport - say nine or ten years old - many of the first quarter kids are significantly more developed than forth quarter kids.  Most coaches can't tell the difference between maturity and ability and tend to select the kids who perform the task better.  The rate of change at that age is so great that the majority selected will be the older kids. 

 

A problem is the better players get moved to the better coaches and facilities. The talented ones in the chosen pack progress riding a premium training infrastructure.  There may be very talented kids who are later born who miss the advantages of this training and infrastructure who are lost to the system as they miss a chance to develop and are soon left far behind.

 

Combine this with the 10,000 target (as an exercise figure out how many hours a day you need between the age of nine and seventeen to become expert) and you realize specialization needs come early for the better athletes. I'll admit to oversimplification here - this is a fascinating area that has become something of an arms race as, at least in the US, the goal of a college scholarships can force specialization before a kid becomes a teenager.

 

The funny thing is when you look at more carefully you see sixty to seventy percent of the college age players in many sports are first quarter births, but for professional athletes in the same sports the relative age effect almost goes away.  Almost as at the very elite level there's a slight over abundance of third and forth quarter athletes. What appears to be going on is there's a great weeding of talent from college to pro. In many sports late bloomers - kids who got their growth spurt late for example - finally reached parity, but the fact that they had to work harder and learn the sport better ultimately made them better athletes.

 

There are other complexities I won't go into other than mentioning playing a variety of sports rather than concentrating tends to make better elite athletes.  We have a bias when we hear about prodigies like Tiger Woods and tend to assume they're the norm, but it's not. We also tend to forget about the prodigies that never make it.  One estimate is that only about one percent of sports prodigies identified by the media (written up in a magazine) by the time they're teenagers ever make it into the pros.  

 

So the American and some other systems do manage to train a number of elite athletes in many sports and show it internationally in the Olympics.  What about the potentially elite athletes that were never trained?   It turns out some systems cast a much wider net.  The Nordics, notably Norway, push universal recreation and sport for kids as a healthy way to provide fun and lower healthcare costs. Early specialization is discouraged and good facilities are made available to all.   It appears to work very well.

 

I'm far from athletic and am not recommending changing any system (although I think Norway's goal of a healthy population is excellent).  This is an illustration.  Similar issues of pipelining kids exist in music, art and academics.  Broadly speaking STEM education is an example of exclusion and producing a population that isn't as literate as it could be.

 

Back to the storytellers and  oversimplification.  If something isn't important and you just want to get a tough idea across, it might be appropriate, but anything of importance needs an appropriate level of depth. That places serious demands on the author, teacher - anyone trying to communicate.   It's something I struggle with a lot. 

 

 

 

staying upright

minipost

 

Over the weekend many of you probably saw highlights of Simone Biles' extreme athleticism. Gymnastics has a lot of interesting science going on, but balance is a central element.  It's important in many sports.  Athletes need to deal with dynamic situations that place their bodies in positions the rest of us wouldn't be able to recover from.   Here's a little exercise to check your balance and muscle control.   No equations or math.

 

Stand still with one foot in front of the other - the heel of your left foot touching the toe of your right.  With your hands relaxed at your sides shift your weight to one of your feet.   See how well you're doing at thirty seconds and then at a minute. How are your calf muscles doing?  It can be surprisingly difficult.  Spreading your arms out sideways should make it easier.   Arms in again and lean to your left or your right.  Not exactly stable is it?  Try again with your arms out..  An improvement, but probably not by a lot.

 

Try a normal standing position like you are talking to someone .. feet side by side.  Even with your arms at your side, you're much more stable. 

 

Now go back to one foot in front of the other again and crouch down as low as you can.  You'll probably find balancing gets easier the lower you go.

 

I won't do the physics, but when a vertical line through your center of gravity falls outside the base of support created by your feet you're out of equilibrium and your body has to figure out how to compensate or suffer the consequences. As you move your feet further apart you broaden your base of support and become more stable Divers often start their dives by leaning forward and moving their center of gravity away from their standing base of support.

 

You can also increase your inertia by spreading your limbs out.  This slows your wobbling giving your body a better chance of dealing with the situation.  The killer way of doing this is to carry a tightrope walker's pole.  This dramatically increasing their moment of inertia (in one axis) slowing what would be dangerous wobbles to the point where their reflexes can deal with them.

 

A few days ago I saw this.  I'm not a fan of scooters as the physics is wrong for stability,.  At the same time I'd hazard Simone has the balance to handle one.  Not to mention her four foot eight inch frame gives a low center of gravity.   I asked a physical therapist who has to deal with balance about scooters.  The advice: you shouldn't be on one unless you can close your eyes and balance on one foot for thirty seconds.  The ability to do this drops dramatically with age.   I won't say much more about scooters as I'm negative and will get flames, but if you must ride one make sure you wear a helmet and don't go fast.  

 

 

order! - a minipost

Apparently a math puzzler became something of a theme on the Internet..  a half dozen people asked me what I thought the answer was

8÷2(2+2)=?

Some came up with 1, others with 16.  Apparently there were near-religious arguments. A mathematician would tell you both are incorrect - the question posed is ambiguous and not an answerable bit of math ..  at least not generally.

 

The problem is the order in which one evaluates expressions.  It turns out the one you learned in grade school is a bit different from the one you may have had when you learned algebra. If you remembered grade school you probably get 16.. algebra people are more likely to get 1.¹  If your algebra teacher was more careful they would have said the expression is wrong - you need to add parenthesis to make it unambiguous. The exception would be if the only people you communicate with agree on representation. That can be a big if..

 

Taking it a bit further, the simple rules you learn in secondary education don't cover don't cover unary ±, which implicitly have lower precedence than exponents on one side and higher on the other!  For example

-x³ → -(x³)
x^-3 → x(^-3)

This is so well agreed upon that no one uses parenthesis in this case.  Historically juxtaposition was treated as implicit multiplication, but that led to ugliness like

1/3x →  1/3*x →  (1/3)*x
a^2x →  a^2*x →  (a²)*x

uck! 

People decided juxtaposition of numeric literals is like a unary operator ..  so the 2 in 2x is attached to the x like the - in  -x.  

 

Back to the original problem. The fact that people had different interpretations and mentioned rules from school meant a better rule was required.  The problem needs to be unambiguous to anyone who might encounter it.  This is an issue for computer languages - different languages can parse the same written expression differently and come to different results.  Agreement on standards is an issue too ..  the Mars Climate Orbiter was lost as  teams at JPL and Lockheed Martin had different takes on a single critical bit of data - one used metric units, the other english..   when the retrorockets on the spacecraft were fired to go into Martian orbit the spacecraft burned up in the Martian atmosphere - it was literally lost in translation.  And this was code that passed multiple very careful reviews - code written for space probes is some of the carefully crafted software period.  Just wait for complex coordination systems and things that move with people nearby or inside.

 

That said there are some areas were common agreement among practitioners creates a local set of standards..  Einstein summation notation in physics is confusing to outsiders, but all physicists know it. And then there's my favorite - the double factorial.  In math (n!)! is not n!! ...  (note that I also have the problem of people interpreting ! as an exclamation point:-)

 

This local agreement is probably true in most fields - even descriptions of an action in a sport are local to the sport.  We all use local shorthand - it's a form of jargon, but we need to know when we can use it and when we need to be more general even it it's awkward.

__________

¹ In one case 8÷2(2+2) → (8÷2)*(2+2) = 4*4 =16

   in the other 8÷2(2+2) → 8÷(2*(2+2)) = 8÷(8) = 1