omenti

the natural language of growth

A ninth grader asked me what e was all about.  She had seen it looking through her brother's calculus book.  I took out my iPhone and opened a calculator (rpn of course;-) and rambled on more or less like this...

 

Imagine you're going to deposit a dollar in an extremely generous bank that gives 100% interest a year.  At the end of the year you have your original dollar plus a dollar interest.  Now imagine a slightly different rate ...  50% interest, but now every six months..  At the end of six months you have $1.50 and at the end of the year that increases another 50% giving you $2.25 ... not bad.  Now you're interested so you inquire about the monthly rate.  You see they offer 8-1/3% interest - a twelfth interest - compounded monthly.  So at the end of the first month you have $(1 + 1/12) or   $1.083..  One the second month it is (1 + 1/12)*(1+1/12) = (1 + 1/12)² .. a bit over $1.17 ..   You see the pattern.  At year's end your total is $(1 +1/12)¹² .  $2.613 .. things are getting better.  

 

They don't offer daily interest, but you figure it out anyway and add it to the little table you've been making

 

(1 + 1) = 2  

(1 + 1/2)² = 2.25

(1 + 1/12)¹² = 2.613

(1 + 1/365) ³⁶⁵  = 2.7146

 

You're doing better, but the rate of increase is slowing down.  What about every hour - ( 1 + 1/8760)8760 ?  Your calculator shows $2.7181.  A slight improvement.  You could try every second, every microsecond, every femtosecond...  but what if the bank compounded every instant?  

What is (1 + 1/n)ⁿ if n is infinity?

Euler worked it out.  It is the irrational constant e.  He didn't name it after himself, but it's a convenient way to remember who did it .  There are a variety ways to calculate it.. he showed 1 + 1/2 + 1/6 + 1/24 + ... + 1/n!    He managed to work it out eighteen digits 2.71828182845904523536028...  

 

Some of the important numbers are buried in geometry ..  π is the ratio of the circumference of a circle to it's diameter, √2 is the hypotenuse of right triangle with side lengths of one.  The Greeks loved geometry and found rich pickings.    e, on the other hand, is not geometrical.  Rather it is fundamentally associated with growth.  

 

Try plotting y = e^x ..  Notice y =1 at x =0 and e  at x =e .  If you look a little deeper the gradient of the curve at e turns out to be e and the area under the curve up to e is, you guessed it, e.  In fact for e^x the gradient is e^x and the area under the curve is e^x.   Remarkable - this is the only function with the value, gradient and area under the curve is the same at every point.  This property makes it the natural language of calculus - the math of rate of change, areas, etc.  So if you study anything involving area, or growth .. finance, physics, biology...  e has a deep and fundamental importance.  It makes the math much easier.  If you force yourself to avoid it the math gets complicated in the most ugly way imaginable.

 

You can use it for geekspeak...  A friend would indicate something is huge by saying "e to the something"    brrr ... it's e to the cold outside.  Or "Trump is e to the narcissistic"...  

 

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Recipe Corner

 

How to roast potatoes.  Some tricks.  Chop them into golf ball or smaller sized chunks and parboil them in salted water for about ten minutes. Drain in a colander and shake them up to rough up the edges a little.  Toss in  some olive oil (I used about three tablespoons per kilogram of potatoes) and roast at 425°F or so for about 40 minutes turning a few times as you go.  The real trick is the parboil and roughing step.

 

Here's a seasonal recipe with another trick

 

Ingredients

 

° about four pounds potatoes  ( I like red potatoes . use what you like to roast)

° two oranges

° bunch of sage

° 6 tbl olive oil

° 8 cloves of garlic

 

Technique

 

º oven to 425, chop potatoes to golf ball size chunks

° parboil for 10 min in salted water, drain and rough up a bit

° peel long strips of orange peel  (use a spread peeler!) and pick the sage leaves

° pour the oil on a large roasting tray over a couple of range elements or burners on low heat and add the sage and garlic and orange peel.  Let them fry for about a half minute .. now add the potatoes and toss everything with tongs.  Pop in the oven and broil for 40 to 50 minutes get them crip and golden. 

 

 

364.4 ± an εar

In October of 1958 Oliver Smoot became a measurement's namesake and part of MIT lore.  As part of his fraternity pledge task his body was to be used to measure the Harvard Bridge - a span connecting Cambridge and MIT with Boston proper.   At five foot seven Smoot was the shortest of the pledges - a feature that would create the most labor.  An added advantage that smoot sounded like a proper unit of measure.  

 

The plan was to have Oliver lie down a few times - perhaps ten - and mark the distance with chalk.  This would calibrate a string which would be used to finish the measurement.  An onlooker stumbled onto this and, given an audience,  the plan was abandoned for something more insane ..  Smoot the ruler would lay down for each sixty seven inches of the way.  This went on for about half the bridge's span with a line marking every ten smoots.  Oliver was now exhausted, so his fraternity brothers carried and dragged him to each new point along the way.  In the end he had to move or be moved three hundred and sixty four times with about another forty percent of his height remaining.  Being proper engineers they added an error estimate of an ear written as εar - epsilon is often used to denote an error measurement. Being beginning engineers they were wrong.. but it became famous and is maintained to the day.  The smoot is a non-standard unit of measure set exactly to 67 inches or about 170.28 centimeters.  If you query Google for length you can request the answer in smoots.  Siri doesn't measure up (yet)...

 

Oliver Smoot went on to a career technical standards and measurements and became the chair of the American National Standards Institute before becoming President of the International Organization for Standardization.  Another Smoot, George, is known for one of the most beautiful measurements in all of science - the anisotropy of the cosmic background radiation.  It is generally regarded as the point where cosmology - a field with roots thousands of years long across many cultures - became a precision science.  George's other cool factor is that he was one of two contestants to win the million dollar prize on the game show Are You Smarter than a 5th Grader?  Oh ... he also won the Nobel Prize in physics. 

 

Oliver's smoot is undoubtedly wrong although the unofficial definition is fine.  They should have sorted out the error in using Smoot as a ruler.  What about his posture?  What about his height laying down during the measurements?  What about his angle with respect to a straight shot across the bridge? You're probably one to two centimeters taller if your height is measured in the hour hour or so before gravity compresses your spine after you wake up. Lots of what ifs to consider.  To do this properly an error has to be estimated for each component of the measurement and a grand totaling know as the error propagation that considers them as a whole.  Part of the coursework of anyone early on the a natural sciences course.  

 

How the errors are presented and judgements made can be problematic.  People talk about a crises in science where measurements, usually in the social and medical sciences, are often not repeatable.  I don't think there's a real crisis, but perhaps it is fodder for another post down the road.¹  It applies in many places -- I have worries that some of what has become to be known as data science is done without regard to understanding errors...  It's presentation is often beautiful and can lure people towards misjudging the result.  One I did some post mortem work caused over a hundred million dollars of hurt.

 

A hallmarks of trade has been the standardization of measurements.  If you find yourself in a good reference library track down the history and evolution of a measurement.  A few years ago I hunted the foot in the stacks of the New York City Library with the help of a great reference librarian who specialized in technology and math.    In recent history - about the time the smoot was defined - the foot became standardized and tied to the meter - 0.3048 meters exactly.  It has been part of many systems for obvious reasons.  What surprised me is it varied from city to city from about 250 to 330 millimeters!  Merchants had to carry around books full of conversion factors (some beautiful examples exist in the library).  In one case a despot wanted to take tall young men from a recently suppressed area in Poland for his army.  His region defined a larger foot than the area with soldiers who appeared to be much taller on paper than they really were.  If you are six modern feet your height could be anything from nearly seven foot three to a bit over five foot six.  And that is in the areas that divided a foot into twelve inches .. some used sixteen digits..  

 

The enlightenment gave us the metric system - official adopted everywhere except the United States, Myanmar and Liberia..  We may as well use smoots.

 

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¹ It has much to do with how science deals with and learns from failure - also that medicine and social sciences are extremely messy given human subjects that are often impossible to completely control for.  Many, myself included, feel they are real sciences (yet).  That doesn't mean they aren't worth doing! Math isn't a science and neither is engineering.  

 

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Recipe Corner

 

I love brussels sprouts, but in a pan or the oven..  never a microwave.  Until now.  If you're pressed for time try this (sent by Chris).  It isn't too bad...

 

I would clean the sprouts, cut part of the bottom stem off, then slice them in half. Then, I would get a small glass rectangular dish that was about 1 1/2 inches deep. I would place the sprouts cut side up in the bottom of the dish along with a tablespoon of water. Now, I would melt some butter in the microwave oven and spoon a little over each of the sprouts. A very slight pinch of sea salt and white pepper over the butter. Now, the most important part - the wrap you cover the dish with. I do not use a lid for reasons I will explain. I use a good clingy wrap (Stretch - Tite, available at Costco), and place it tightly over the dish and down the sides. Then I place them in the microwave (one that has a rotating platter), set it on a medium - high heat (65 to 70 percent), and cook them for about 2 to 2 1/2 minutes, depending on the power of your microwave. I let them sit for about three minutes, then set the microwave at the same heat for about a minute and a half. You should see the stretch wrap rising like a bubble above the dish. Watch them to make sure they do not brown. When cooking is finished, remove them from the microwave and the stretch wrap will suck itself down around the sprouts, almost like they were vacuum sealed. Leave them like this for a few minutes - it is at this point that the butter, salt, and pepper will be forced into the sprouts by the apparent vacuum. Cooking them this way retains most of the color of the sprouts and retains their wonderful flavor without the smell during cooking. If one has to watch their sodium intake, leave the salt off, as the butter has a small amount 

 

 

 

 

accepting nature's invitation to play

The latest iPhone’s ability to simulate bokeh - a lovely effect you can get with larger cameras and careful attention to settings - has people excited about smartphones replacing DSLRs … While that may be the effect, something much larger is going on.

 

What excites me most about photography is getting away from the tiny window we view nature from.. we only see light in a narrow range from 0.4 to 0.7 microns and witness events over a limited size range and time scale. Furthermore our brains only process an extremely filtered view… you can say the same for our dozen or so other senses. But we’re ace at building instruments that break these boundaries .. in some sense a photography of nature. I see the detectors at CERN as cameras of sort and the same can be said for microscopes, telescopes, radio antenna, etc, etc. Amateurs outside of the sciences don’t do much with it yet - it is often expensive in money, time and imagination. Some of us play around with time and infrared sensing, some play with sound and others with scale .. but really powerful, mostly standardized, portable communication-enabled computational sensor platforms like the iPhone will change all of that.

 

I like to go into the woods with a couple of microscopes - one about 15x and the other 100x - to get a startling different view of nature. Now it is easy to attach an iPhone for even better images at less expense. I listen to bats by time shifting their calls and doing a bit of Fourier analysis - an external device with the iPhone doing the computation. As a teen I built telescopes, but now I rely on larger installations for my fix of the very old and very far exotica in the sky.

 

We’ll go beyond light and sound. Chemical sensing will become inexpensive and, critically, match the population distribution of people. You’ll have very inexpensive calibrated sensors to sniff and communicate with other local sensors to build and image of - for example - pollution. That will change attitudes.  But change will go in a thousand directions and some will be exotic.  Why not use the distributions of tens of thousands of the tiny camera sensors to detect the signature of cosmic rays, or accelerometers for earthquake early warning system … upwards and downwards the sky’s the limit.

It is still wonderful and necessary to revel in nature and humanity with our bare senses, but that can be enhanced. Perhaps it will encourage more of us, particularly kids, to play with the wonders around us.

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Almost exactly five years ago I wrote a piece on my frustration with camera UX, but a brief glance at the future.  It features my first attempt at digital photograph with a homebrew camera and a ferret named in honor of a nuclear disaster. 

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recipe corner..

 

Just a trick this time.  A neat variation on spaghetti is to make your sauce and, when it is almost done, put the dry or fresh pasta on top with just a bit of water - enough to cover it. Let as the water boils off the pasta cooks and steams a bit.  The flavor can be richer than the traditional gallons of salty water method - different, but a change and you may even prefer it...  I do for some sauces, not so much with others..  the point is experiment!

 

 

a determined bug and it's useful if mysterious result

Let's say you find a determined bug - a bug with the singular ambition of walking in one direction.  It covers no more and no less than one centimeter every second.  You also have an unusual band a meter in circumference.  You make a mark on it and start the bug at the mark.  At the end of the first second you stretch the band so it adds another meter to its circumference, and so on...  does the bug ever make it all the way around?  

 

Most people guess that it can't - after all, the band is growing by a meter for every centimeter the bug travels.  But let's analyze what's going on.  The first insight is the band is expanding uniformly so it's expanding behind as well as in front of the bug.  In the first second the bug travels  one centimeter divided by one meter of the way around ..  one percent.  At the end of the second second it adds a centimeter, but the total distance is now two meters..  it has traveled an additional half percent of the total circumference,  at the third second it has added another third of a percent, then a fourth and so on...      If we add up the percentages we get a sum:

 

1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + ... + 1/n    basically the sum of 1/n for all integers from n = 1 to infinity if the bug walks forever...  

 

If you've had some physics or math, this is the harmonic series related to overtones of musical notes.  Now on to the sum...  does it converge to some number or is it unbounded running off to infinity?

 

Let's see if we can bound the series from above and below with series that are easier to calculate.  Here's a really clever way to answer the question first proposed by the 13^th century monk Nicolas Oresme.  He made series where each element was less than or equal to each element in the harmonic series. By asking what is the largest power of one half that is less than or equal to the number you're looking at.    

 

Consider the first term:  the largest power of 1/2 that is less than or equal to 1 is (1/2)⁰ so the first term of the series is 1

the largest power of 1/2 that is less than or equal to 1/2  is (1/2)¹ or 1/2 so the second term is 1/2

the largest power of 1/2 that is less than or equal to 1/3 is (1/2)² or 1/4 ..  the third term is 1/4

the larger power of 1/2 less than or equal to 1/4 is (1/2)² or 1/4 .. the fourth term is 1/4

the largest power of 1/2 less than or equal to 1/5 is (1/2)³ or 1/8 .. the fifth term is 1/8

the largest power of 1/2 less than or equal to 1/6 is (1/2)³ or 1/8 .. our sixth term is 1/8

  work out a few more for yourself and a pattern emerges

1 + 1/2 + 1/4 + 1/4 + 1/8 + 1/8 + 1/8 + 1/8 + 1/16 + 1/16 + 1/16 + 1/16 + 1/16 + 1/16 + 1/16 + 1/16 + 1/16 + 1/16 + ...

gathering the 1/2s

1 + 1/2 + (1/4 + 1/4) + (1/8 + 1/8 + 1/8 + 1/8) + ...  = 1 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 ...

1 + an infinite number of 1/2s equals infinity...

 

Every term in this series is less than or equal to each corresponding term of the harmonic series.  Since it diverges, the larger harmonic series has to diverge.  Given enough time our singularly determined bug only has to go 100 percent of the way around which is less than infinity so it eventually completes the trip.  Working out how long it takes is a bit more involved, but a long time - about e¹⁰⁰ seconds or about 10⁵⁰ years..

 

This slow growth is logarithmic ..   Using that as a hunch take the harmonic series to some number n and then subtract then natural log(n) 

1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + ... + 1/n - ln(n) ..    or the [sum(1/n)] from 1 to n - ln(n)

as n goes to infinity we have an infinite number subtracted from an infinite number.   The amazing thing is it converges to a rather small number.  It's known as the Euler–Mascheroni constant and has been calculated to over 120 billion decimal digits .. the first few are: 0.5772156649...

 

It's called γ and turns up all over the place in physics and math.  It's in quantum electrodynamics and the standard model - calculate corrections to the mass of the Higgs or the electron and there it is.  e^γ is used to explore products of prime numbers.  It's not as famous as e, i, π, 1, 0, or ∞ .. but is one of the small list of important numbers used in our equations.   Very little is known about it ... it is suspected to be transcendental, but that hasn't been proven. It isn't known if it is irrational..  There are other important numbers - fundamental constants for example, and the deep mystery of why math works so well in describing Nature.  Way too deep for the blog, but perhaps something to frame up at some point.

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Recipe Corner

 

Thai Carrot Soup

 

Ingredients

 

° tbl vegetable oil

° 1 medium onion roughly chopped

° 1 garlic clove chopped

° 1 stalk lemongrass stalk chopped

° 1 piece of ginger grated ..  use your taste.. I did about an inch

° 1 pound of carrots peeled and chopped

° 1 six oz can of whole coconut milk

° 2-1/2 cups vegetable stock

° 1 lime zested and juiced

 

Technique

 

° heat the oil in a pan and cook garlic, onion, lemongrass and ginger for 4 or 5 minutes on medium high heat.  Add carrots and go another 5

° reserve a few tbl of coconut milk and add the rest to the carrot mix.  Simmer until carrots are soft  

° throw in a blender or use a blender stick (I like the later) 'til smooth

° stir in lime juice and zest and then serve..  

 

° drizzle with the left over coconut milk

 

144.17

On September 17^th Canadian engineer Todd Reichert squeezed into the cockpit while his crew installed the aerodynamic shell around him.  A rather tight fit, it does allow for the centimeter or two height variation a human body can experience during the day.  He switched on the GPS, pedal ergs and other instrumentation,  twin video screens and the radio.  A crewman gave a push to get Eta rolling... 

 

Engineering - the best engineering - is an elegant set of compromises to accomplish some task as best you can manage.  There is a certain beauty when the task is aimed at a limit.   Human powered vehicles offer delicious challenges.  I was fortunate enough to have had a modest involvement in early human powered flight, but the land speed record is special as bicycles are the most efficient means to move a human on a hard, mostly smooth surface.  

 

An adult in good physical shape can easily ride a bike at twenty kilometers per hour at an equivalent fuel economy of about a thousand miles per gallon.¹ A Tour de France class bicycle can level speed of about 60 km/h with the strongest riders.  At such speeds an athlete, and an elite bicycle rider has the highest power to weight ratio of any athlete for periods over a few minutes, is delivering about six hundred watts to the pedals.  The problem is wind resistance - about ninety percent of his effort goes into moving and swirling air.  To go faster you need to attack air resistance.  The same for moving an average person on a bike faster for the same amount of power.  Aerodynamics dominate.

 

If you look at the kinetic energy involved in moving air a simple model  shows power required is linear with the frontal area of the vehicle and air density, but increases as the cube of velocity.   If you want use as little power as possible, speed is your enemy, but if you want to go fast or be efficient at speed, beating air resistance is where you focus.  Going a bit more deeply the area confronting the air flow is an effective area... namely the area you physically measure times the coefficient of drag or C_d for the vehicle.  You can think of the C_d as a number that describes the aerodynamic slipperiness of the vehicle.  A falling piano or brick has a large C_d while a car typically has one that is much lower.  A falling human before opening her parachute has a C_d of about 0.8 to 1.2 depending on how she holds her body.  A person sitting upright on a bike is about 1.0, a TdF racer in full crouch about 0.7.  A Ford Model T is about 0.95 while many of the best cars are about 0.24 to 0.26.²  The VW One Liter was about 0.18 .. probably close to the limit for a street legal multi-passenger four wheeled automobile.   

 

Todd's Eta has a C_d of about 0.03. 

 

Todd is an outstanding, but not,  elite athlete.  The Eta needs about 265 watts to go 100 km/h on level ground.  Your car's air conditioner needs about 2,000 to 4,000 watts on a warm humid day.  The numbers quoted for the Eta vary a bit depending on the development of the product, but figure over 9,000 mpg equivalent at a legal highway speed in the US.³

 

So a few weeks ago he opened it up and went an honest 144.17 km/h ... just under 90 mph.  Just his muscles using the just plain food for fuel.  

 

Take a look at their video from a year ago:

 

I suspect they can push further even without going to an elite athlete.  I wouldn't be surprised to see 100 mph some day - that would be like breaking the two hour marathon .. everything has to come together, but it is theoretically possible.

 

This has implications for velomobiles - the rare streamlined bikes you see mostly in Holland and Germany.  It would be easy to install a three hundred watt electric motor with a very small battery - one or two kilowatt-hours would give great range and cost almost nothing - and have a vehicle capable of highway speeds. Of course you'd need safer highways..  On the other hand thirty or forty km/h speed limits with streamlined human-electric hybrids may be practical in some areas.  

 

You probably don't want to get me started on the merits of active transportation though...  The transportation we have is based on legacy standards that go back over two hundred years.  We're left with cars of a certain width, footprint and now even speed.  There has been a large improvement in nearly everything about the car, but I wonder what it would be like if we had standardized on 500 or 1,000 kg vehicles and 50 km/h rather than 110 - 130?  On the other hand we could have standardized on 4,000 kg tanks - the shape of cites and suburbs would be a different animal indeed.

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¹ This is the food energy burned and makes the assumption that a gallon of gas has about 36.6 kWh of energy.  Since the human body is only 20 to 25 percent efficient riding a bike, the power delivered to the pedals is much less and replacing the person's legs with an electric motor would improve the equivalent fuel economy by a factor of three or four.

² The reason why oil changes aren't easy is cars now have aerodynamic pans and farings under their body to clean up the airflow.

³ This is power delivered to the crank.  Factoring in human efficiency reduces this to somewhat under 3,000 mpg - how sad.  Of course you get get exercise riding any bike, so it isn't necessarily a bad thing.

 

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Recipe Corner

Nothing for now..  I'm playing with my new immersion cooker (improperly called sous vide cooking).  I had a homemade unit a few years ago, but it was too frustrating to use.  It interests me as 99% of the cooking done in them centers around meat - cooking produce is a poorly explored area, so I'm playing and making mistakes.  

Something real next time

 

 

 

making sparks

 Tell me a bit about your favorite trips?

 

Forty minutes into the interview and Bill hadn't asked anything about my specific work.  We touched  tracker action pipe organs, color vision, and several topics I can't remember.  Here was a famous Bell Labs director asking about trips.  

 

Road trips..  I like road trips without a destination.  I like taking the backroads, learning from breakdowns and generally getting lost.  I love doing it slowly on a bike.  Arriving is usually less interesting.

 

I had no idea what he'd think, but it was honest.  He told me he only interviewed candidates who were considered capable of the work.  His task was more difficult - building and encouraging an origination that could function creatively in the research environment.  How do you find a group that sparks off each other and improve the chances of serendipity of the entire organization.

 

A madman can spew a random stream of novel words and phrases and most of the useful things and ideas in our lives are far from novel.  Creativity is the combination - something novel and useful.  It also has to be useful to society at the time - at least to be recognized as creative. 

 

It is often assumed that creativity is part of intelligence or that the two are somehow part of something larger, but that doesn't hold up.  Creative networks in the brain turn out to be different from those linked with intelligence.  With intelligence is is all about more neurons and connectivity between them.  Strong paths between regions of the brain.  It is as if there is a network of superhighways that allow you to get from one part of the brain to another.   

 

Creative networks are a different beast.  They're backroads that wander all over sometimes taking seemingly random paths, stopping and starting.  It is like going from the Autobahn to village pathways in pre-industrial times.  These are very high friction paths and rapid information processing just doesn't happen.  But something remarkable does.  Ideas are linked together.  It's as if less is better - in particular activity in the frontal lobes drops dramatically.   Very creative people regular enter a state where activity in the frontal lobes drops for awhile - a self-induced transient hypofrontality.

 

I'm struck by the importance of random influences ... that's probably why Bill was probing for interests outside of math and physics.  He had a reputation for putting together groups of people each with a diverse set of interests to increase the probability of chance interaction.  Architecture plays an important role - the rabbit warren layout of Bell Labs at Murray Hill came close to that of MIT's legendary Building 20.  Physicists would run into mechanical engineers, social scientists into mathematicians, computer scientists into artists and partnerships no one would have predicted emerged.  Occasionally people would have difficulty describing what they were doing as they were in the process of doing something outside the regular boundaries of existing fields. Figuring out the social chemistry to make this happen is - well - non-trivial.¹  Being part of a regulated monopoly is part of it success, but Bell Labs pulled off the creative part for about seven decades.

 

Some organizations, mine was one, wanted members to spend part of their time working in an entirely different discipline. Others were more focused.  This extended to the cafeteria..  tables were somewhat fixed, but some people would float around connecting ideas.  Of course much of it wasn't useful, but the practice and the careful bit of HR at hiring,  led to a creative organization with about seven decades of greatness.

 

 

I'm struck by how new ideas seem to occur during down time after a period of very hard work.  For me it can be during a walk, while sketching or in an exercise session - all times when my mind is completely unfocused.  They seem to appear out of nowhere and seem completely obvious and trivial at the time.  A fair number - certainly well over half - are complete garbage when you look deeper, but there have been a few real gems that I can't imagine where the link came from.  The transient hypofrontality hypothesis seems correct.²

 

Creativity takes many forms across many fields, but being able to find downtime and play with ideas appears to be common.   Boredom is emerging as  important - particularly as a training ground for kids who develop the capacity for creative thinking.  It's not that they're smart and things are easy, but rather that the conditions conditions creative processes to wander, link and leap through the brain.  There is evidence developing tricks to deal with the boredom leads to techniques to trigger transient hypofrontal periods.  Knowledge acquisition by itself by itself fails..  teaching kids to efficiently fill in the correct ovals with number two pencils may lead to great crank turning, but is counterproductive if creativity is a goal.

 

We're all getting older and around the age of forty demyelination takes place - the wiring in our brain slowly gets a bit frayed and leaky.  The smooth superhighway structures no longer support fast and efficient movement.  We still think, but calling up information or normal fast judgements require more time.  But there may be a positive side if we take advantage of it.  It appears our capacity for creating rich transient hypofrontality events increases.  Combine this with the increasing evidence for neuroplasticity and perhaps we can make our older brains more powerful, more creative, with age.

 

I'm just skimming but again this is an area that one can talk about for days.  I've spent more than a little time learning from neurologists and have been thinking more and more about the stability of creative organizations.  But there appear to be some rules that are well grounded in science as well as some widely practiced folklore that is counterproductive (brainstorms sessions for example).  Here are some well-known approaches (you need all of them)

 

° Work intensely and practice, practice, practice in the  field(s) you're interested in.  You're building neural connections that make thinking easier courtesy of neural plasticity.  You're also given your mind difficult problems that it can't solve using the superhighway approach.

° playfulness with downtime to provide opportunities for hypofrontal events.  Learn what works for you.  Yoga, long showers, long walks looking at nature (a favorite of Beethoven), playing a musical instrument (Einstein's path), whatever works..  The point is your mind can't be occupied with what you've been working on.

° have lots of random interactions with people and ideas...  

° keep at it.  creative people put out a huge number of ideas.  many are stinkers, but that doesn't matter.  

 

Again this is just a very high level introduction - I know some of you have been doing this for decades.  I've seen it in so many areas  - recently I had a great discussion with some athletic coaches about it in sport. It can and does appear in the most unexpected places.   It certainly isn't necessary for a good and happy life, but it can be learned and encouraged.  

__________

¹ I strongly recommend Creativity Inc by Ed Catmull and Amy Wallace describing the process of building and encouraging a creative organization at Pixar.  It's style isn't standard, but I don't know of a better description of the process.

² It is still a research hypothesis, but it is holding up well so far as the science progresses and some of the competing explanations have fallen to the wayside.

 

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Recipe corner

I'm a huge fan of okra ..  roasted or fried mostly..

 

Okra Stir Fry

 

Ingredients

 

° 1 tbl vegetable oil

° 2 cups chopped okra

° 1 medium onion finely sliced

° 1/2 tsp turmeric

° 1 green chili finely chopped

°  sea salt  to taste

° red chili powder (if you like)

 

Technique

 

° take the oil to medium heat in a pan

° cook the green chili for a couple of minutes

° add the onion, cut the heat a bit and cook until transparent 

° add the okra and turmeric - cook over medium low uncovered for about a half hour stirring a couple of times

° salt to taste and pull from the heat

° add chili powder if you like (I do) .. I also added a bit of garam masala last time which was great

 

how much is enough? - homer simpson and olympic swimming events

It turns out The Simpsons has little math and science jokes making their way into the show - usually as very short sequences that fans can stop and study.  In a favorite episode Homer scribbles on the blackboard leaving four items.¹    3987¹² + 4365¹² - 4472¹² immediately caught my eye ..  it smelled like they were hinting at Fermat's Last Theorem.

 

There are an infinite number of equations of the form x² + y² = z² ..  like 3² + 4² = 5². Fermat hunted in vain for x³ + y³ = z³ and later claimed xⁿ + yⁿ = zⁿ  has no solution for whole numbers n > 2.  In the margin of a book he stated there are no whole number solutions for the infinite number of equations of that form and then added Cuius rei demonstrationem mirabilem sane detexi, hanc marginis exiguitas non ca- peret - 'I have discovered a truly marvelous proof of this, which this margin is too narrow to contain'.    Nasty.    Frustrated mathematicians toiled for hundreds of years until it was finally proved in a very non-trivial fashion in the mid 1990s .. indeed it wouldn't fit in the margin of a book:)

 

I pulled out my old HP calculator and tapped in the numbers.  Sure enough it worked.  It appeared to be a counterexample .. enough to disprove the proposition.  You suspect a near miss .. something lost as a rounding error.  The next step was to go beyond the ten digit accuracy of the calculator.  I reached for the laptop and fired up Mathematica

the first suggests the first two terms equal the third, but the second shows they aren't in the twelfth digit ..  looking at the first fifteen digits gives a bit more.  For most purposes it isn't necessary to have that many digits of accuracy .. but there are times when the question requires a bit of deeper knowledge - in this case the precision of a calculator.   But swimming pools?

 

There was a bit of a kerfuffle in Rio trying to explain ties in swimming events.  Tightly spaced finishes - often to within a few hundredths of a second are not uncommon and every once and awhile you get two and even three way ties (Phelps, Le Clos, and Cseh in the 100 meter Butterfly).   Identical right down to the hundredth of a second.  That can't be right can it?  Someone must have touched first.  The media mostly butchered the explanation.  Going to thousandths of a second like speed skating and a few other events - seems to be the way to go, but closer examination turns up a flaw.  

 

It turns out swimming pools aren't rigid.  They can't be or they'd break given what they're made of.  The ground around them shifts as does the water.  Even a degree change of water temperature causes a change of size.   In a 50 meter pool the time of the fastest event has a swimmer moving at about 2.39 meters per second.  In a thousandth of a second - a millisecond - the swimmer would travel about 2.4 millimeters.  It turns out the allowable tolerance of the length of a lane is 3 centimeters - something that has to be re-established several times a day during an important event. The pool can vary by more than ten times the distance the swimmer travels in a millisecond ..  timing at that level becomes meaningless.  Records couldn't be compared with each other at that precision and even the lengths of lanes in the pool can't be guaranteed. ² 

 

Which brings up another problem.  How do you have a fair start?  A starting gun goes off and runners or swimmers start out.  The bang of a gun travels at the speed of sound - you probably know the rule of thumb of counting seconds between the flash of lightning and its thunder and multiplying by one thousand feet.  The speed of sound varies with temperature, pressure and humidity, with the standardized value of about 343 meters per second.  Sound travels a about meter in three milliseconds.  Imagine a starting gun at the side of a track.  The path from the gun to a runner can vary by up to fifteen meters in some situations - that's 45 milliseconds .. over four hundredths of a second and a big deal in some of the shorter events.  

 

You might get around that by flashing a light, but the problem is we're wired in such a way that we respond to sound faster than to light - and by a lot ... like 50 milliseconds.  The solution is to put a speaker under each starting block and connect it to an electronic gun.  But another interesting question comes up.  How do you judge a misstart?  That one works out nicely.  Elite runners have a reaction to the starting gun of about 145 milliseconds and remarkably similar to each other.  A misstart is judged at something shorter than what reaction time would allow .. usually 100 milliseconds.   Some runners have very slow starts - reaction time and just getting the muscles going .. Usain Bolt is one of the slowest, so go figure... 

 

And for fun consider a problem I've given to students...  we all know refrigeration is inefficient and that opening the door of a refrigerator is a way to heat a room.  What would it take to detect the effect of a refrigerator in an average house?  What would it take to detect the impact of a single refrigerator on the power grid?  The first case isn't too difficult .. the second case demands some very specialized knowledge.

 

A thread connects these examples.  If you want to make an accurate measurement you need to understand something about what you're measuring and how you're measuring it.   The measuring tool, what you're measuring, its environment and even how they interact over time.  There are limits and when you bump into them it is useful to realize something is amiss so you know if you need to fix it or not - or if the situation needs a complete rethinking.

 

^__________

¹ I suspect this was aimed at physicists as the two physics jokes are a bit deeper than the math jokes.    two math and two physics.  The first has terms you'd see in particle physics - and suggest they predict the mass of the Higgs boson (this was fifteen years before it was confirmed).  The terms may look normal, but the equation don't make sense.  If you plug in numbers it does give about 775 GeV which isn't terribly far from the real figure of 125 GeV. (admission - I did just that immediately)  The third, Ω(t0) > 1,  suggests the universe will implode ..  when things in the room start rushing in on each other Homer replaces the > with a <  which causes a major explosions.  The fourth is a topology joke.  A circle and a triangle are the same, technically homeomorphic, in topology.  Consider a circle made of a perfectly pliable rubber.  You could easily stretch it into a square, pentagon and almost anything else without holes (that's a bit of a stretch, but you get the idea:-)  An object with a hole in it, a doughnut for example, can be stretched into a coffee cup - one hole that goes all the way through is the distinguishing characteristic.  A doughnut is not homeomorphic with a sphere.  Homer suggests that taking a bite out of a doughnut leaves it a doughnut, but you're removed the hole and destroyed its doughtnutness in the process.

For those who love math there are other gems scattered through the shows.

In one a screen comes up in the Springfield stadium:

Tonight's Attendance:

a. 8128

b. 8208

c. 8191

d. no way to tell 

(a perfect number, a narcissistic number and an Mersenne prime)

at one point the spine of one of Lisa's books reads e^iπ + 1 = 0

great stuff... to see this on tv is astonishing.

Futurama has some cultural and writing overlap and tends to leave techie trailings..  

 

² There are other problems with swimming that get a bit complex and pool dependent, but suffice it to say some lanes are better than others and the faster swimmers usually are given the best. 

 

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Recipe Corner

 

Grilled Sweet Potatoes

 

Ingredients

 

° 1 tbl cumin seeds

° about 2 pounds or a kilo of sweet potatoes cut into inchish wedges

° 2 tbl olive oil 

° 1 tbl maple syrup

° salt and pepper

dip

° 1/4 cup tahini

° 1 tbl maple syrup

° 1 tbl lemon juice

° 2 tbl water

° fresh cilantro

 

Technique

 

° get the grill to a good medium high heat

° toast cumin seeds to light brown in a small pan while the grill is heating. Then move them to a chopping board and crush them until fine

° toss the sweet potatoes and everything else up to dip

° make a half dozen aluminum foil packets with two large pieces of foil each (cut it off roughly square) brush the inside with a bit of olive oil

° lay the wedges in a line in each packet and fold tightly

° grill till tender .. about 15 minutes for me, but my grill isn't great.  check in a packet and look for the beginnings of charring.  Flip the packets a couple of times during the process

° remove and carefully open .. let them cool.

° whisk the dip ingredients and drizzle..

° garnish with cilantro 

 

 

 

when swing is a poem of motion

1900 at the Olympics in Paris

François Brandt and Roelof Klein had qualified in the coxed pairs, but had lost a race to a French pair.  Thinking it over with an unspecified amount of alcohol they came to the conclusion they couldn't change their rowing performance, but perhaps Hermanus Brockmann was overweight.  Brockmann was their coxswain.  In the early days the cox was largely responsible for steering and sometimes setting the rhythm of the strokes, but they were frequently seen as dead weight.  Brockmann weighed sixty kilograms.  The pair spotted a young boy in the crowd and ran a trial.  He only weighed thirty-three kilos and they had to attach another five kilos of lead to their shell to make the rudder set properly in the water.

 

The flying Dutchmen leapt to an early lead but couldn't keep their initial pace. Halfway into the race the French started their move, but at the finish the Dutch were still ahead - but by less than a meter. A dramatic race by any measure, but more curious is the fact that the cox disappeared into the crowd never to be awarded his gold medal.

 

That brings me to the trigger for the post.  American Experience in PBS recently aired a piece on the 1936 US men's Olympic rowing team - one of the most amazing bits of magic ever seen at the Olympics.  You can watch it here.

 

How important is that dead weight? In theory a cox aims the boat in the straightest possible line, gives pacing and coaching, and removes the effects of uneven thrust as much as possible. But he or she also adds to the load.  We can easily make an estimate.  

 

In doing very quick calculations to test ideas dimensional analysis is frequently invoked. The kid destined to be a natural scientist would look at the units and note that gallons is a volume or a mass. Assuming you are using the same liquid in your comparisons - at least liquids of similar densities - it doesn't matter ... take your pick. Let's pick volume .. the dimension of volume is a length cubed - L³. Miles are easy - just a length. So miles per gallon is dimensionally L/L³ or 1/L² - an inverse area.  It could be inverse square meters, inverse square feet, or ... hey .. inverse acres has a nice rural feel to it.

 

The question is how much does it cost for a racing skull to carry a cox? Rather than a boat with two rowers let's consider the more general case with N rowers. A four man boat has twice the power of a two man, but its weight is about twice as much. Does having twice the engine and almost twice the weight help or hinder?

 

I've received some complaints about being a tad too technical.  I'll indent and highlight the reasoning behind the estimate.  You can skip it if you like.  It turns out to be about two or three minutes of work at the blackboard and a good example of how physicists play.  You make simple estimates, often little more than dimensional analyses, to build a simple model.  That can give you some insight into the problem and further questions.  It is a very quick method for going through dozens of ideas when you're in conjecture and hypothesis land.  Here it gives a quick and dirty answer to the question.

 

 

The power the rowers deliver mostly is used to overcome the drag on the hull.  It is

p = f_d * v

where p is power, f_d is the force of drag, and v is the boat's velocity relative to the water

The force of drag is reasonably complex and would require some careful measurements that depend on the shape of the hull and some other factors.  The important thing to realize it is proportional to the wetted area - something that goes as a length squared - and the square of the velocity.   So 

f_d ∝ L² * v²

the power needed is 

p_d ∝ L² v² * v or L²v³ 

The power to overcome the drag is supplied by N rowers (assuming all are about equally strong).  A racing shell is pretty minimal, but its volume needs to increase to float with the heavier load.  The volume goes as L³ and also is proportional to N, so L ∝ N^1/3.  Getting tricky we substitute

p_d ∝ L²v³ ∝ N^2/3v³

getting to the end! ....  We know power supplied is proportional to N so 

N ∝ v³ N^2/3

solving for velocity we see

v ∝ N^1/9

 

The speed of the boat only increases slightly with an increasing number of rowers.  

 

For those of you who have rejoined us it only increases at the one ninth power of the rowers or N^0.111.   Try plugging some numbers into your calculator and see!  The time is just to the inverse of the speed over similar distances so t ∝N^-1/9. If you look at world record times over similar distances this holds for one to four person coxless skulls reasonably well and is a good enough model for this purpose. 

 

You can play with some numbers yourself - assuming the cox is just along for the ride the impact of having one decreases with crew number. Since races are tight you don't want to race coxed vs uncoxed boats and you don't want a heavy cox. Hopefully they add more value and perhaps you can get a sense of quantifying that value in real vs expected times.

 

 

The original question was what is the impact of the cox - the little guy or gal with the rudder and the loud voice?  I did a similar analysis increasing the size of the boat, and thus its drag, by going to N + 1 crew members, but assuming only N are contributing to the power.  I won't go through the reasoning as it takes much more time to type than to think about it, but it is very similar.  The predicted time with a cox, t_cox is:

t_cox ∝ (N + 1)^2/9/N^1/3 

To get something that is easy to think about look at the ratio of cox and coxless times and apply a bit of rearranging

t_cox/t ∝ ((N + 1)/N)^2/9

(N + 1) is always bigger than N, so the cox always slows things down ...  not by a lot and the effect decreases with increasing N.  A two man boat should be about nine percent slower if the weight of the cox is similar to the rowers.  But it isn't.  The Dutch used a kid who was about a third the weight of each rower, so a reasonable guess would be about (2.33/2)^2/9 or something over two percent slower - probably several percent faster than an equal muscled crew with a cox that weighed as much as poor Hermanus Brockmann.

 

These days coxswains have much greater value.  They steer the boat and usually run the strategy.  Recently I was thinking about four man (or women) boats - there are coxed and coxless events.  Thinking about the pattern of the rowers led to a slightly veiled surprise. 

 

The pattern of the rowers is called the rig of the the boat.  It looks very symmetric - right, left, right, left for the four and twice that for the eight (note that left, right, left, right is the same by symmetry).  Assuming the crew are evenly matched you would expect the shell to move straight ahead without the intervention of the cox.  If this was true the uncoxed four should be a bit faster with the cox only offering on-bard coaching.  Of course crew members aren't evenly matched so the cox has to work the rudder.  

 

A bit of thinking about the forces on the oarlocks leads to a slightly hidden asymmetry.

 

High school physics tells us we can decompose forces into vector components - when examining the flight of a ball you can break the motion into horizontal and vertical components allowing you to isolate the effect of gravity.  On a shell there is an oscillating force at each of the oarlocks.  When the oar is in the water there is a strong force on the oarlock in the forward direction of the boat's motion.  Assume each crew member is equally strong with the same form and perfect timing.  In a four man boat we get four times this force to move the boat ahead.  Dandy - that's what you usually think about when you calculate the potential speed of a racing shell.  

 

There is another force at the oarlock perpendicular to the forward force.  At the first half of the stroke it is directed towards the shell and in the second half it is directed away.  The force drops to zero at the midway position of the oar - a sinusoidal force.  It is smaller than the forward force and at first glance appears to be balanced by the fact that every oar has an opposing oar on the other side of the shell. Two oscillating forces that are mirror images of each other at any moment.  They should cancel each other so we might be tempted to move on.

 

Here's the nut of the question.  The forces act over a distance.  We're not concerned with a force on the left balancing a force on the right, but rather each oar produces a torque on the rudder.   Now things get interesting.

 

The torque is just a force on a long arm.  Imagine the sideways force is F at any moment in time.  If you are distance L from the rudder, the torque at the rudder is F*L (foot-pounds, newton-meters...).  Let's give our model a distance r  from the rudder - essentially the cox -  to the first oarsman.  Let the oarsmen be separate by the same distance - call it d.  The total torque at any given moment (note I'm just looking at instantaneous torque rather than worrying about a messy integral) for a four man shell with the rig shown would be:

T = rF - (r + d)F + (r +2d)F - (r - 3d)F

 this = -2Fd  certainly not zero over most of the stroke!  This wiggle-waggle torque, remember F is oscillating in magnitude over ⁺/_- its maximum value, either goes into a wasteful motion of the shell or the cox can counteract it.  Both outcomes waste energy.

 

So you wonder about other patterns.  Consider these rigs.  The first is what we just examined and the second is the standard eight which alternates between ⁺/_- 4d as you might expect (check my arithmetic).

 

The third rig is interesting.  Performing a similar calculation I get:

T = rF - (r + d)F - (r + 2d)F + (r + 3d)F

 Now we get zero.  By a clever arrangement we can balance out the torque at every instant.  It turns out this has been tried and successfully, although there isn't any mention they understood what was going on.  

 

Moving to the eight- man gives a trivial wiggle-waggleless rig - 4a is just a couple of the rigs used in example 3.  For fun I found three more and showed that is all that exists. 4b gives zero - you may want to check the arithmetic again.  I found two more in short order and won't give the solution for those of you who find pleasure in figuring things out.  Ping me if you want my solution.  

 

In the real world the forces aren't equal and timing and form are less than perfect - mostly that is.  There is this notion of swing in rowing.  It happens rarely and is the result of near perfect timing and application of force.  Even in world class crews it isn't that common although you may see it in one or two of the races in Rio.  An eight-man boat is producing something over five kilowatts most of the time and can burst much higher. Individual differences on the order of a few watts can destroy swing.  It is a dramatic thing to see and crew members who have been there cite it as something amazing - a very special kind of flow.  You can see it in the motion of the boat and in the expressions of the crew.   Quite literally a poem of motion.

__________

Recipe Corner

 

From an athlete friend:-)

 

Peanut Butter Smoothies

 

Ingredients

 

° 2 sliced bananas - frozen

° 3/4 cup milk or soy milk

° 3 tbl peanut butter

° 2 tbl unsweetened cocoa powder

° 1/4 tsp vanilla extract

 

Technique

 

° surely you jest - blend until smooth and server

 

 

 

 

controlling what you can - the art of the high jump

I while back I asked  if there was interest in a few Olympic themed posts - after all, sport is a gateway to many other areas.  Charlie replied:

 

How about the high jump? I was fascinated by Randall Cunningham's 18 year old daughter's comment on getting her head over the bar and her body would follow. Also, her body didn’t look like it had the right muscles for her accomplishments. Anything interesting there?

 

Vashti Cunningham is a world class high jump athlete. The highest levels of competition in hotly contested sports select ideal body types - while body type is important, it is required.  Vashti is currently listed at something over 6-foot-1 and weighs 121 pounds.  She probably has an extremely high proportion of fast twitch muscle and other genetic gifts, not to mention determination, and for events like this you don't need huge muscle mass as long as its the right kind of muscle but more on that later.

 

The high school physics approach to the high jump would be to recognize you can turn kinetic energy into potential energy in much the way a roller coaster works - you trade speed to fight gravity to altitude and visa versa.  Her kinetic energy depends on her mass and the square of her velocity:  E_kin = 1/2 * mv².and her potential energy depends on how high she is: E_pot = mgh where g is the acceleration due to gravity.   Set these equal and mass drops out leaving height =  v²/2g.  She is probably something over 10 meters per second as she transitions to her jump - 22 to 23 mph.  This gives around 5 meters of altitude gain - much higher than any high jump record. 

 

Fundamentally high jump is not an efficient way to turn kinetic into potential energy.  You want to stop quickly converting all of the energy of motion into throwing your body skyward.  To do that you need a machine - a lever in the form of a pole.  

 

High jumping is a pure sport - no apparatus, just see how high you can jump.   And it it has its tricks and surprises.  Vashti, like most high jumpers, makes use of the changeable shape of her body and physics.   Her motion can be described as the motion of her center of mass - the unique point around which her mass is distributed.¹  If she's standing, given her body type, Vashti's center of mass is about 55 percent of her height - a bit over a meter in her case.  In the high jump she launches her center of mass in an arc.   All work she does goes into raising her center of mass hopefully about the bar.

 

A body's center of mass is not necessarily inside of it.   Throw a horseshoe or boomerang and you see a dramatic illustration as the center of mass follows a smooth path with the body spinning around it.   You can bend your body and move your center of mass outside of it.  This allows for innovation discovered by Dick Fosbury - the Fosbury Flop.  Vashti bends her body around the bar - her center of mass clears the bar, but her body only does when it has to. ²

 

Now she's using physics properly, but there is more going on.  Her center of mass is high in the first place.  Her limbs are long and light making it easier to bend her body.  Height is generally bad for distance, but a plus for sprints.   Sprinters don't need huge muscle mass - just enough to get up to speed and launch.   The muscles in her back are probably very well developed.  She'd probably be good at yoga. 

 

Now it gets into technique.  I talked with a Division-I track coach who didn't want his name used.  Much of what she wants to do is in the run-up and takeoff. The run-up develops speed - a lot of speed - and positions the body so the foot hits the right place for takeoff to begin.  She plants her foot ahead of her body which is traveling over twenty miles per hour at this point.  Her leg is mostly firm but she's fighting its flexion.  That builds up enormous forces in her takeoff leg's muscles allowing her to create a large downward force as her forward momentum comes almost to zero in well under two tenths of a second (she's decelerating at well over six gs - peaking much higher).³

 

This phase is complex.  She's also swinging her arms upwards - hard - along with her other leg.  This pushes her core body down compressing the muscles in her takeoff leg even more.   During the run-up she want to have a low position - that big vertical push needs a build up over the takeoff phase. She's adding more swinging her non-contact limbs up and the low position at plant and high position at take-off usually means a long contact time to get as much of the muscle force to the ground as possible.   Jumpers run very fast with their hips in a low position - a few centimeters can make a big difference.

  

___________
¹ A bit more technically the center of mass of a distribution of mass (planet, ball, person, car, ... anything with mass) is the unique point where the weighted relative position of the distributed mass sums to zero or the point where if a force is applied causes it to move in direction of force without rotation.  Note that center of gravity is often used in place of center of mass if the acceleration due to gravity does not vary (much) over the body.

² You see this in ballet when a great dancer pulls off a flawless grand jeté.  She raises her legs into a nearly horizontal position and raises her arms above her head dropping the level of her head relative to her center of mass as it rises. She reverses the process as she begins to fall earthward again. I timed one at 0.44 seconds - a very long illusion. I also timed a basketball player in a slam dunk contest at about 0.3 seconds. In theory he could probably do it longer with his longer limbs, but he lacked her technique.  Three tenths of a second still looks startling - even beautiful to the audience.  Hang time in volleyball is more on the order of basketball - I've timed some centers at a bit over 0.3 seconds.  It must feel wonderful when properly executed.

³ For simplicity I'm avoiding talking about tendons.  They act as springs - mechanical batteries that store energy and able to release it very quickly.  Their size and stiffness make enormous differences and have a large genetic component. 

__________

Recipe Corner

It is high Summer and we're getting a wide variety of everything including great tomatoes!  Nothing specific, but there has been some discussion about less than perfect looking produce - the so-called ugly fruits and vegetables.  

Consumers demand cosmetically perfect examples - we seem to equate quality with visual appearance (as we do with too many things we don't understand well). Large amounts are discarded by markets and even larger amounts are simply not harvested by farmers as they don’t believe there is a market. Wastage is about 40% - driving up prices and making healthy eating more difficult as a result.

Generally ugly produce is just fine. In fact - it may even be better for you.  (the link is to NPR's The Salt)

 

batteries

A somewhat past prime lemon was sitting around making me wonder..  Let's say you're a Florida citrus baron and your car's battery is run down.  You remembered the lemon battery you helped your kid make for a sixth grade science project and wonder how many lemons would it take to crank the car?

 

A lemon battery is pure simplicity.  Push a galvanized nail and a copper wire into the unsuspecting piece of fruit and connect it to something like a light emitting diode current flows through the completed circuit and the bulb glows.  The flow of electrons from the zinc to the copper only happens when the circuit completes.  In theory the battery could provide power as long as there is zinc and an acidic enough environment to keep the reaction going.  In reality there are many factors that shut things down before the zinc is completely dissolved.   

 

I had never made the measurement.   A minute playing around and the Zn-Cu battery measured 0.82 volts at 1.2 milliamps - just under a milliwatt.   A average car starter needs about 3 kilowatts of power to crank an engine.  Assuming you have some way to connect your fruit without loss, you'll need about three million lemons.  Calling AAA is a bit more practical.   Lemon batteries score high as science education demos, but low on almost every other battery metric you can imagine.

 

You can almost go to the periodic table, pick a couple of elements, and make a battery. Most will be even worse than even our lemon Zn-Cu battery, but a few will stand out in one way or another.   Depending on the application you are interested in six major criteria: how much energy can be stored (energy density), how much power can be delivered (power density), lifetime (how many charge/discharge cycles), charging rate, cost, and safety.  Unfortunately no single chemistry is optimal across more than one or two criteria.  But then good engineering has always been about finding a good-enough optimization.

 

 

Smartphones and cars make us think of lithium ion batteries.   If you're building a space probe nickel-hydrogen is your friend.  It doesn't match lithium-ion in most criteria -  it costs several hundred times as much per kilowatt-hour - but it can go through tens of thousands of charge-discharge cycles.  Not having to replace a battery after a few hundred cycles when you're in deep space makes it seem cheap.  Flow batteries are relatively inexpensive and can go through a large number of charge/discharge cycles, but have a low energy density that relegates them to stationary use. Some lithium-ion chemistries have low costs, but tend to be highly flammable. Power densities - how quickly energy can be transferred from the battery - vary widely ... a very important automotive consideration. Energy and power densities are stronger functions of temperature in some chemistries. This may be ok if your battery is in an indoor power farm, but a serious problem in cars and smartphones.  Dozens of other battery chemistries have their niches, but a lithium-ion comes closer to satisfying more of the criteria than most competitors for many consumer applications.

 

Lithium-ion is a catchall term describing dozens of chemistries. It only tells you the charge is carried by a lithium ion.  The important bits that define a battery - its anode, cathode and electrolyte - are not specified.  The graphite-cobalt oxide battery in your smartphone has very different characteristics from the graphite-lithium manganese oxide battery in your portable drill.  The battery in your smartphone is not ideal for automotive use, but the fact billions are manufactured made them cheap enough to balance some of their other problems.  Tesla felt the wide availability of consumer electric class batteries was enough of an advantage that they could accept some of its issues.  So far that seems to be working well.

 

 

Although smartphones are the current major user of lithium-ion batteries we'll see a transition to automotive use rather soon.  A plug-in EV requires about 5,000 times as much power storage as a smartphone.  Two hundred thousand EVs is about a gigaphone of batteries.  For automobiles it is far from clear which chemistry will win in the short or medium term.  The hope is that entirely different chemistries will become practical in the long term.  I'm also hoping for improvements in smartphone class batteries.  We may see a factor of two in power density in the next decade, but I'm getting ahead of myself.

 

In principle a lithium ion rechargeable battery is simple.²  Generically they consist of two electrodes separated by a thin membrane and an electrolyte that allows ions to freely pass from electrode to electrode.  When the battery is charges lithium ions are released from the positive electrode, the cathode, which is a lithium alloy such as lithium cobalt oxide.  The ions move towards the negatively charged electrode, the anode.  Anodes are usually made from graphite and the ions find spots between the carbon atoms to settle in.  This process requires power electric power to drive it.  

 

To use the power just complete the circuit  by connecting the electrodes to something like a motor.  The lithium atoms embedded in the graphite give up electrons which travel through the circuit running car's electric motor.  At the same time lithium ions leave the graphite and travel through the electrolyte and membrane to the cathode where they meet up with electrons that have made the trip.  That's it - a nice reversible system.  

 

Graphite is used as an anode largely because its a good conductor, but it isn't efficient at storing lithium ions during charging - it takes six carbon atoms to hold one lithium ion.  Silicon seems more attractive - in theory one silicon atom can hold four lithium ions.  A silicon anode can, in theory, store much more energy.  Unfortunately material science hasn't come up with a good way to make a stable anode that can take many charges and the rigors of movement.   Well - perhaps that is temporary.  There have been a few exciting laboratory developments that might yield at least a factor of two better energy density and perhaps at a lower cost.  You could double the range of the Bolt or Model 3 to four hundred miles. Assuming one of the developments work out a viable automobile battery is probably a decade out, but there are signs of progress.³  Currently lithium-ion batteries have about 1/80th the energy density of gasoline.  In automotive use it isn't quite as bad as it sounds as electric drive trains are more than three times as efficient as internal combustion drive trains and you can get away with some extra weight.  A factor of two would be an enormous improvement that would answer most range anxiety worries.  Do it at a low enough cost and you have to worry about ramping manufacturing and charging infrastructure quickly enough to meet consumer demand.

 

The long term may move beyond lithium-ion chemistries entirely.  Metal air batteries use metals like aluminum, lithium, magnesium, silicon and the oxygen in air along with aqueous electrolyte.  In theory they have energy densities approaching gasoline when you factor in the efficiency of the electric drive train. Non-rechargeable primary batteries have been built, but a practical rechargeable is only a dream at this point.

 

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¹ If you've done it right citric acid causes  zinc on the nail into the lemony pulp as charged ions leaving electrons behind in the metal.  ( Zn → Zn²⁺ + 2e^- )  Positively charged hydrogen ions in the pulp, technically the electrolyte, combine with a couple of electrons at the copper surface forming hydrogen ( 2H⁺ + 2E^- → H₂ ).  The oxidized state of Zn has lower energy and the energy released provides the power that flows through the circuit lighting the light emitting diode.

² Rechargeable batteries are called secondary batteries, non-recharcables are primaries.  Although primaries often have much better energy densities than secondaries, replacing them ranges from very expensive to impractical.  An iPhone 6 Plus battery stores about 15 watt-hours - that would be nine AAA alkaline batteries.  The iPhone's battery should be good for about three years of charges.  If you need to recharge your phone every day you'd pay about eight dollars a day for three years - $2,800 - just for batteries! Imagine the landfill and production issues.

³ I'm partial to a novel silicon approach that uses nanoparticles.  It should be stressed there are several very serious approaches underway with a dizzying press release schedule.  Most of them will not amount to anything commercial, but are adding to the knowledge base - at least those that are published.   There is no guarantee solutions exist.   An area where software is not eating the world...

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Recipe Corner

 

Nothing to report foodwise other than my seasonal shift to my pressure cooker.  They're safe and much faster than normal cooking - just the trick for keeping the kitchen cool.  

The reason they work is not their higher temperature (250°F is not that much above boiling).  Steaming is efficient as a huge amount of energy is released in the  form of latest heat.  But the mechanism is often confused ...  It isn't forcing liquid into the food - that turns out to be a very slow process.  It turns out to be the density of the steam.  Density increases by a factor of two so the steam contains twice as many water molecules to deposit their latent heat.

You don't need to know how a pressure cooker works - just know modern cookers do a fabulous job.  I even have hiked with a lightweight model.  When you're in an area where you have to pack your fuel, being able to speed up cooking dramatically quickly reduces your fuel need and the total weight of your pack.