omenti

the costs of stop and go as well as spinning

If you are ever thinking about buying a rowing machine, we should talk.  I spend something north of six hours a week on one and have come to learn a fair amount about various approaches.   My main machine is a classic Concept II model B that was probably made in 1986.  It was the second generation of the first simulators that were good enough for serious rowing athletes to train on and you can learn a bit of good technique with them.  It is also built extremely well.  You pull a handle attached to a chain that spins a racketed sprocket that is, in turn, attached to a flywheel with some turbine blades cut into its face.  Most of your work goes into swirling the air.  The immediate vicinity of the machine is mostly dust free as a result.

 

This year I added a second machine as something of a splurge.  Nice as the model B is, and there are several newer models but it seems unlikely this one will wear out in my lifetime,  it doesn't go far enough to reproducing the motion of a rower in a shell and you miss some important bits of form as a result.  Most important is the fact that your feet are stationary and your trunk moves back and forth.  Some serious rowing enthusiasts mount their machines on nearly frictionless sliding rails.  Doing this sort of works, but is expensive and takes a lot of room.

 

The folks who make the Concept II machines (they also built most of the racing oars used in competition), came up with a newer design with a clever mechanical system that allows your butt to stay mostly fixed and more closely encourages proper technique.  I splurged and bought one. Lovely and recommended if you intend to also use a proper rowing shell, but more complex and expensive with no real exercise benefit.

 

Why I mention it is that it has a similar flywheel, but adds a shroud with louvers that allow you to control the amount of air the blades can swirl.  This allows you to carefully tailor your training load.  When wide open the air drag is much greater than what the model B produces - as you stop rowing the flywheel comes to a stop much faster than the old design.  One thing you notice right away is that if your strokes are poorly timed or of unequal effort, you end up wasting a good deal of energy.  While this may be ok for exercise, it would be deadly when you are  racing.  There are advantages to a constant speed.

 

Which takes us to the bicycle track.  If you watched the indoor track bike racing event at the Olympics you many have wondered why the riders often travel very slowly and then suddenly burst into wild acceleration as they race to the finish.  You also may have wondered about the unusual disk wheels in some of the events. 

 

It turns out indoor racing is in still air which makes covered wheels practical (no side winds). Smooth wheels have less air resistance than their spoked cousins and  they have a lower moment of inertia than a spoked wheel which gives them a great advantage when accelerating.  

 

When you are riding a bike you have to supply some work to get it up to speed.  Once it is moving there are a couple of forces that try to slow you down - one is friction against the road and the other is air resistance.  At bicyclish speeds the road friction is pretty low - particularly if you are using extremely narrow high pressure track bike tires and pales in comparison to air resistance.  If you stop pedaling and just coast on level ground, you slow and eventually come to a rest.   You can also supply some work to counteract the air resistance (and road friction) and move along at a constant speed.  Most of us have experienced both of these techniques on bicycles (it happens to anything that moves in a fluid, but I happen to love examples that you feel with your own physical exertion).

 

strap in - time for a deeper look

 

To set this up let's look at the energy required to get up to some speed, let's call that v.  Let's call the mass m - in the case of a bike it would be the rider plus her bike, for a runner it is just the person.  You start out with no kinetic energy and end up with E_k = mv²/2.  When you stop you lose all of that energy - mostly in the form of heat.¹  The rate of energy loss (technically power) is just E_k/t, where t is the time it takes to stop.  

 

Let's look at the case where you travel some distance d at a constant speed v and then quickly stop.  You can talk about the average energy loss for that distance as well as the average power loss.  It is just E_k divided by d/v  (d/v is the time it takes to go the distance at a constant velocity).  Substituting you get mv³/2d.  A couple of things to look at ...  this is large when the distance is small and it also grows rapidly with velocity.  So far so good...

 

The other drain is air resistance.  A runner (you can do this for anything moving through a fluid) presents an area towards the wind - let's call that A, and over some time t it sweeps out a volume of air that is just A times the distance she travels or Avt.²  You are pushing a mass of air in front of you away.  The mass is just the density of the air times its volume or m_air = pAvt where p is the density of air (about 1.3 kg/m³ at sea level and average air pressure). ³  When you move through the air the energy you have to supply just moves and swirls the air.  It is just m_airv²/2 or pAtv³/2. Divide by t to get the average rate and t drops out leaving you with pAv³/2.

 

Now it is time to compare the rate of energy loss from braking to the energy loss from air resistance. The ratio is useful:  m/pAd.   If the mass of the runner or vehicle is greater than the mass of the air in the volume tracked out, more energy is lost to braking rather than air resistance.  Another way of looking at it is if this ratio is greater than 1.0 more energy is lost in braking than is spent overcoming air resistance at speed.

 

This is significant.  It tells us when starting and stopping doesn't make sense and can even tell you when an aerodynamic car or bike makes more sense than one that is light weight.  The threshold is just 1 = m/pAd or d = m/pA.  (Note I'm ignoring regenerative braking .. spinning up a generator to stop and storing the energy in a battery, flywheel or capacitor to throw towards starting.  If you know the total conversion efficiency you can just plug it in .. it effectively increases the distances).

 

Plugging in a few numbers you get d ~ 120 meters for a runner, 250 m for a cyclist, and 1,100m for the car.⁴  A useful result.  If you drive with lots of stops and starts it makes sense to get a light weight car and not worry so much about aerodynamics.  If you have a lot of highway driving the weight is not as important as aerodynamics.  Also a cyclist or runner who can easily accelerate (say they are lighter or have more white muscle) can fatigue the competition by setting pace and varying their speed.   

 

Drat - I'm ten minutes over my allotted hour and there isn't time to talk about the inertia in bike wheels.  I'll stop here and pick up there soon.  It adds a bit of complexity, but is quite beautiful and the general concept applies to figure skating, gymnastics, diving and even volleyball.

 

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¹ Two points.  There is another form of energy that goes into spinning the wheels if you have a bike, car or some other wheeled transport.  We'll touch on that later, but I want to keep the argument simple at this point.  Also stopping something can go into sound, flexing a muscle and so on ... but heat is usually the largest sink. 

² A point I'm glossing over.  Here "A" is an effective area that takes into account how aerodynamic the moving body is.  It is the product of a coefficient of drag, a measurable quantity that varies for different shapes - a jetliner or sailplane has a much lower drag coefficient than a runner, bike rider, brick or piano.  So when I say A, I really mean aC_d, where C_d is the drag coefficient and a is the measured cross sectional area you present to the air.  Likewise I should point out that v is the relative air velocity when you are talking about air resistance and the velocity relative to the ground where you are talking about the runner's, biker's or car's kinetic energy.  So we'll just assume there is a perfect calm to keep the equations simple.

³ Rather than track down the html for the greek letter rho, I'll just use p which sort of looks like a rho:-)

⁴ I assume the runner has a mass of 70kg and an effective area A (aC_d) of 0.45m², the rider plus bike has a mass of 80kg and an effective area of 0.25m², and the car and driver have a mass of 1,500kg and an effective area of 1m².

 

 

 

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Recipe corner - two quick tricks

 

Dealing with too much bread

We have a lot of bread from a bit of over experimentation and some of it is getting old.  Rather than talk about making something to begin with, here is my favorite thing to do with slightly older bread (it works on fresh bread too) as long as it still has a bit of moisture.  If the bread is getting really dry, put it in a plastic bag, flit in a bit of water and seal the bag.  In a couple of hours it should be in much better shape unless it is really over the hill.

Cut the bread into half inch thick slices, lay them on a baking sheet and brush one side wit a fair amount of olive oil.  I like using a thyme infused olive oil and, lacking that, I just chop a small bit of fresh thyme into some olive oil awhile before brushing it for a similar effect.  But I love thyme so your mileage may vary.

Pop the pan into a 350°F oven for about five minutes until the bread is slightly toasted and browned - the wonderful Maillard reaction browns the bread and creates dozens of fantastic flavor compounds.  Remove the bread and while it is still warm take a peeled clove of garlic and rub each piece of bread with it as hard as you can without crunching the bread to spread some of the garlicy goodness into a few of the cracks.  Have at it and put as much down as your love of garlic dictates.  Let it them to room temperature. 

I bet you can't eat just one:-)  There are so many possibilities for variations on the theme, so have fun!

 

The simplest "ice cream"

Really simple, really good and not bad for your health either.  The kids can make it too.

Take a few bananas and freeze them.  Break them into smaller pieces and put into a food processor with the standard metal blade.  Switch on and let it run a few minutes stopping every now and again to scrape down the sides.  At some point there will be a neat little phase transition of sorts and it will turn into a semi-frozen mass with the consistency of soft ice cream.  At that point just scoop it out and enjoy it or add some flavorings and spin it for another thirty seconds or so.  I really like throwing in some peanut butter and then adding broken bits of semisweet chocolate afterwards along with some crushed nuts.  Adding a few tablespoons of chocolate syrup is good too.

It turns out bananas have a boatload of pectin.  Pectin is concentrated in the walls of the plant cells and the mechanical action of the blades breaks the cell walls and allows the pectin to form into lovely pectin chains which form the basis for the gel that has the nice ice creamy texture.

 

artifacts of patents and licensing

A friend wrote with a pointer to a piece on how the Apple/Samsung verdict harms consumers.

 

Ah intellectual property ..  

 

I was compelled to reply and perhaps it is worth sharing even though Om said far too much will be written on the subject.

 

I think this is just the nature of how patents and licensing work when a technology is perturbed - something we've had since the time of Watt and have seen repeated over and over. In the end it is probably good, although locally good and bad products will be impacted - some positively and some negatively. Google was way to caviler artificially reducing the mfg cost of its operating system to zero. There were and are numerous patent violations - not much has been written, but I'm told Microsoft makes $8 to $15 on most of the Android phones sold in the US, Europe and Japan. There will be a lot of court action for a few years, but ultimately there will be licensing on the sticky points all around. The marginal mfgs will drop out and new players will have to either have their own innovation (I hate that word - way too fluffy) or be large enough to pay for licensing.

It would be nice if all were robust, but that isn't going to happen with the current system.¹  Individual patents come into play, but  licensing agreements at this level usually involve portfolios and you have to have relevant portfolios to have any standing.  Google had almost none and the purchase of Motorola was probably driven by a desire for an instant portfolio so they could play the game.  Unfortunately for them it appears as though Motorola's portfolio is not terribly relevant and they may have wasted billions of dollars.

I would be surprised if Apple ends up with more than 15% of the market in 5 years (and that would be 15 percent of a billion phones per year or more - still an incredible business if there are any margins). I also believe that Microsoft is the potential big winner in this round. Their OS may be cheaper than Android with its licensing fees and uncertainty and the UI is both clean and novel (Apple and Microsoft, despite the hard words, have elaborate cross licensing agreements and an agreement not to use each other's UI features - both have very competent UI and UX teams - something Google lacks)

Now the bar is raised for what innovation has to be and there will be companies other than Apple doing the original work that appeals to end users.

For me the importance brilliance of the iPhone is it broke the carrier's stranglehold on tech, design and how people used these portable computing devices. Nokia could have built something as good or better, but companies like AT&T and Verizon were their customers and not the end user. They basically wouldn't let Nokia, which had its own stranglehold on much of the mobile market, be creative.²  We would still be in 2006 with only marginal change if the iPhone didn't happen.  

It is extremely important to note that when the iPhone was introduced it was roundly criticized for only having a single button and no hardware keyboard. Most of the tech  pundits as well as its competition predicted it would fail.  A few years later everyone says the design was obvious...  funny how that happens, eh?³

In order to do well Apple needs to figure out how to destroy the iPhone rather than allow the competition to do it. That will be very hard work.

I don't worry much about the impact as people change their phones every few years. What bothers me is the stagnation at the carrier level and the very high degree of lockin on things like spectrum (an artificial concept dictated by tech established by 1930 and reinforced by policy) and enormously high infrastructure costs. Much better things could have happened... We pay far too much for far too few bits per second and are forced to deal with congestion and scarcity that are not dictated by the underlying physics...

 

I'm convinced there will be good competition and real progress, but it is important to remember that this has played out many times before.  The trials will take a few years and produce a lot of smoke - the important things to watch are the licensing agreements and how they shift the game as well as new ideas that happen to be outside the scope of current patents.

 

I'm not happy with the patent system, but it does create a stable framework and can encourage competition.  If you are interested in this sort of thing I recommend reading the history of intellectual property disputes.  The development of the airplane and what happened to the Wright brothers is particularly interesting.  That is a cautionary tale Steve Jobs stressed with associates.

 

It is clear that anyone who wishes to play in this space at a deep level needs to combine social and technical clue.  That is a major change for this industry.  And a final note: while this may seem messy it doesn't hold a candle to the train wreck that is copyright.

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¹ There are two major types of patents that are relevant - design patents and utility patents.  We tend to think of utility patents, but the design of something is also protectable under the system.  Many elements that feed into user experience happen to be design patents, which is almost virgin territory for the tech world.  

² Decoupled customers and end users can be a real problem.  It may be this is ultimately an issue for companies like Google and Facebook and gives an opening to a very clever challenger.  It is certainly a huge issue in American politics.

³ This is historically true for some of the largest ideas and best design.  Often we don't stumble into the really great solutions but, because they are great, they seem completely obvious once we see them. Something like the iPhone's UI and UX is subtle and extremely complex - very difficult to get right.  Most of those elements are missed with quick high level dismissal of how original it seems.  You might say the same thing about something like special relativity, which is based on simple geometryand can be taught to a smart 14 year old.

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Recipe Corner 

 

Well - this is too simple to be a recipe, but it is trivial and turned out very well.   One of my standard breakfasts involves a bowl of steel-cut oatmeal.  I mix various things in and this morning found a winner.  

Cut a plantain into half inch rounds, drizzle with olive oil, sprinkle on some sea salt (non-iodized as heat will be used), some brown sugar and some pumpkin pie spice.  Spread it on a baking sheet and roast it in a 450° F oven for about 25 or 30 minutes turning them roughly half way through.    It really smells good!  Mix it in with a your oatmeal - I topped with some crushed pecans, cinnamon and blueberries and a bit of maple syrup. And had it with milk.  

Wow it was good!

And also food related.  A youtube video on a clever technique for separating egg whites and yolks.  This sort of thing has been done approximately forever in introductory physics demonstrations, but it is still deeply cool.  

 

why lift and separation is important

I was struck by this Louis Vuitton ad with Michael Phelps and Larisa Latynina - two remarkable athletes in the service of formal clothing and quite a shift from the standard attire as well as depiction of athletes from the original ancient games.  

 

Modern athletes wear a wide range of clothing appropriate to the sport.  Some is protective, some only has minor functionality other than basic modest and offering sponsors billboard space for television, but some athletic clothing offers competitive advantage.

 

Running offers interesting examples.  Run fast enough and you will feel a considerable amount of wind resistance.  You want to reduce that force against you as much as possible.  Basically you are moving the air in front of you as you run.  About a year ago I wrote a post with a quick derivation of the power you have to develop to deal with that force.  The force turns out to be  half of the coefficient of drag for your body * the area you present as you run * the density of the air *  the square of your velocity relative to the air.¹  The important bits that you can control are your velocity, your frontal cross sectional area, and your coefficient of drag.  A cyclist can adapt a posture to minimize her frontal area while running generally makes that impossible.  Cyclists use a lot of aerodynamic tricks with bikes, wheels, riding position and even helmets.  And even runners can play with their clothing.  

 

To understand running attire it is useful to consider golf.

 

Sports balls are fascinating objects.  Apart from ping pong balls, few are smooth and spherical.  The shape gives them unusual properties that makes playing with them more interesting.  Balls tend to evolve with a sport and then, at some point, standardize so everyone can play on even terms.  

 

Early golf balls were mostly spherical hardwood.  It was noticed at the time that some balls were better than others, specifically some that we beaten up a bit would go further on a drive, but other beaten up balls performed worse.  Progression eventually led to a realization that small surface imperfections were important for good performance and the modern dimpled ball emerged.

 

The physics is pretty neat.  Two things are going on - one is caused by the spin on the ball and the other is related to the airstream immediately around it.²  The second is the larger effect, so I'll only consider it for the time being.

 

There are two basic types of airflow - laminar and turbulent.  Laminar flow is smooth (think of laminations), while turbulent flow is rough and choppy.  Laminar flow tends to take place at "low" speeds and turbulence becomes dominant as airspeed increases. 

A smooth ball generates a large wake as it pushes air molecules aside. Immediately behind the ball the air molecules are further apart compared to the air around and in front of the ball. A region of low pressure forms just behind the ball sucking it backwards and slowing it in the process. The air immediately around the ball is the boundary layer and one worries about where it separates from the ball - having it separate further behind the ball produces a smaller amount of total separation and the pressure drop behind the ball is smaller.  

. The dimpled ball separates the air less and has a smaller wake. The air behind the ball does not differ in air pressure as much as with the smooth ball so the dimpled ball has a smaller pressure drag and can travel further.

 

If you look at the airflow very close to the dimpled ball you notice they are roughing up the flow a bit and generating a bit of turbulence.  This makes the air stick a bit more to the ball.  It generate a bit of drag, but that turns out to be completely washed out by the fact the boundary layer sticks around a bit longer.  

 

Sweet   Dimpled balls are just better and have been around for a long time, but the effort was mostly trial and error - these days it has been possible to show what is taking place.  

 

But what does this have to do with running?

 

As it happens we create boundary layers when we run.  Our size and speed mean that if we're wearing something smooth - like a lycra bodysuit - the airflow is mostly laminar and there is an early and largish boundary separation that creates a low pressure area behind us.  One can imagine a diet of beans might help, but only for brief moments and the impact wouldn't be that great anyway, so it makes much more sense to make sure the boundary layer doesn't detach as quickly.

 

It turns out the trick is a tight fitting almost smooth body suit (you don't want a loose fit as the flapping fabric would present extra area creating even more drag) covered with a thin ribbing - about a half millimeter high and just enough to rough up the air and get the boundary layer to hang around a bit longer.  The C_d drops and the runner can put more of her power into moving herself rather than wasting it on moving air.  The effect can be dramatic.  The effect is more important as the airspeed goes up and at the very high speeds seen in the 100 meter event such suits are worth as much as a tenth of a second.³  At slower speeds air resistance is much less important (remember the force goes as the square of the relative airspeed and therefore the necessary power required to overcome it goes as the cube).

 

Hair, it turns out, is less of a problem than you might think.  There was a period when sprinters wore hoods, but the heat generated around their heads became excessive.  The head is only about 7% of your total body area and the impact of air resistance is about 3% of the total effort a sprinter must create at top speed.  Seven percent of three percent is under a hundredth of a second and the impact of heat buildup renders that counterproductive.

 

Talk of the Olympics and specialized suits brings up the Speedo LRZ swimsuits see prior to the 2008 competition.  Of all of Olympic sport, more science has probably been devoted to swimming than anything else.  Lowering the drag from moving through water is a big thing - after all - water is nearly 800 times denser than air and the underlying physics is well understood (although the calculations can be very difficult).  Speedo came up with a seamless and wrinkle-free shell of a suit and its shape stayed smooth throughout the swimming stroke. There was also a thin layer of a foamy material that had very small gas pockets that made the swimmer more buoyant.  They rode higher in the water and produced less drag.  

 

The overall effect was pretty dramatic - a 5% to 8% reduction in overall drag - but the cost was high.  The suits were very expensive ($500), took a half hour to put on and only lasted a race or two.  Since their impact was about the same on the top swimmers the decision was made to ban them and records set using them are noted separately.

 

There are many more examples - it turns out shoes are a fascinating area, but it would take pages and pages to describe the current understanding of shoes vs no barefoot as well as the difference between shoes.  So that's it for today.

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¹ The area for this is what only what the oncoming air sees and is often called the frontal cross sectional area.  Also note that the relative velocity is important.  If you are running at 10 mph with a 10 mph tailwind, the effective velocity is 0 - you don't have to move the air that is in your path.  Tailwinds are even better and records have strict limit on how big they can be.

The coefficient of drag, or C_d, is a quantity that represents how easily a shape moves through a fluid.  At a given speed the frontal area times the C_d will tell you the force you have to generate to move the air column before you aside - double the area or C_d and you need twice the force (or power).  C_d range from well under 0.1 for a sailplane, about 0.20 to 0.30 for many sports cars,  0.7 for a cyclist, 1.0 for a runner, 1.4 for the Empire State Building, 1.9 for the Eiffel Tower, and 2.1 for a brick.

² A spinning ball produces lift through the Magnus effect.  I won't go into it, but ping me if you are interested.  I've worked it out for volleyballs and found an interesting result that explains part of the ball's trajectory ..,

³ In his world record 100 meter run Usain Bolt was moving at 12.27 meters per second at the 65 meter point - about 27.3 mph!  He was producing about 3,000 watts of power at the time - about twice what a stove top electric burner consumes.  This is near the human limit for burst power production and can only be maintained for a short amount of time. The body can't sweat out this extra heat immediately and the core body temperature of a sprinter increases rapidly.  If their muscles could be powered a bit longer the increase in body temperature would kill them.

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Recipe corner.

First a technique from shesimmers for making sticky rice that doesn't require much kit.  I just tried it and had excellent results.  recommended!

 

There are a variety of tiger salads.  I don't know where this one originated, but we tried it last night and found it deliciousSim as well as easy to make.

 

Simple Tiger Salad 

 

Ingredients

 

° 1 large bunch cilantro, with the thick stems removed, cut into 3-inch lengths (about 5 cups, loosely packed)

° 1 green bell pepper stemmed, seeded and slivered (cucumber would do nicely too)

° 1 fresh chili pepper, stemmed, seeded and slivered

° 2 scallions, slivered

° 2 tsp vegetable oil

° 1/4 teaspoon salt

° sesame oil and white vinegar, to taste

° a handful of chopped peanuts (optional)

 

Technique

 

° In a bowl, combine cilantro, green pepper, chili pepper and scallions. Add vegetable oil and salt; toss lightly.

° Add peanuts if you like and a few drops of sesame oil, vinegar and more salt to taste; toss again. Pile on a plate and serve immediately as it wilts quickly

 

estimating and measuring the "network effect"

A source of personal frustration since 1995.  Back then I was giving a background talk on some simple basics of the Internet to some business executives at the company I was with.  Someone asked about Metcalfe's Law - something I was unaware of..  I had to ask what it was and was told that it stated the value of a network increased as the square of the number of people in the network.  Standing at the whiteboard for 30 seconds I was able to come up with how they got it and also a big flaw in the statement...

Since then there has been a huge amount of blind belief in Metcalfe's Law and Reed's Law leading to some rather spectacular valuations on building out fiber and and new network connections in the late 90s along with companies that were just looking for users - forget the little issue of being profitable and, more recently, in social networks.

More recently people are wondering about the network effect and the value of investments with the non-performance of some social media companies...

A bit of background is probably in order..

There are three "laws" involved (they really aren't laws, but the people who invoke them treat them as if they are solid truth - usually without understanding what they are based on and what they imply)

• Sarnoff's Law - after David Sarnoff of RCA fame in the 20s and 30s.  It implies the number of possible network connections increases as the number of users.  It usually speaks of broadcast networks where a message is sent via radio or TV and anyone with a receiver can "tune in" ...  The implication is the more viewers, the greater the value.  Note that nothing is said about the strength or value of the individual connection.  Note also that it could be newspaper or magazine subscriptions...

• Metcalfe's Law - after Bob Metcalfe, inventor of ethernet.  It is the number of pairs that can be made in a group.  For n members, it is possible to assemble n*(n-1)/2 distinct pairs.  If n is a large number, this is very close to n²/2, which is the normal statement of the "law" - people also say it increases as n² ...  Since we are used to thinking about communication connections between a pair of people, this is a natural way of thinking about the number of connections on something like a telephone network, but it ignores group conversations.  Note that it says nothing about the strength of the connections - just that they are possible.

• Reed's Law - after David Reed, an MIT prof who is also something of an Internet boffin.  David talks about the number of distinct subgroups that can be formed in a larger set of members.  For a group of n members it is possible to have 2ⁿ distinct subgroups, but n of them have just one member (themselves) and it includes the group with no members (null set).  So the number of subgroups that have at least 2 members is 2ⁿ - (n + 1).  As n gets large, the first term dominates and the number of subgroups gets close to 2ⁿ.  It says nothing about the value of these subgroups to their members, but is just the mathematical limit of the number of possible subgroups.

They aren't wrong - as long as they are carefully restricted to their specific domains, but somehow people interpret these as the value of networks and likelihoods rather than limits.  Additionally Reed's and Metcalfe's "Laws" are frequently confused.

When talking about these it is probably important to mention Dunbar's Number.  The assertion is the maximum number of stable and persistent social relationships you can manage is determined by some cognitive limit and for humans this is about 150.  This determines effective organization size, the scale of your meaningful social network and so on.  It is highly debatable, but it is clear the number of relationships is finite - people don't have 1,000 close personal friends and certainly not 10,000,000 (a few Facebook phenoms have millions of "friends").  More careful analyses suggest we have layers of friends and other social connections and the average limit is on the order of 100 to 300 people.  We usually only have a handful who constitute close personal relationships and maybe a few dozen we might trust.

Back in 1995, and how these "laws" are used today, the question was "what is the value of the network?"  Here one can immediately dismiss Reed's Law - if the value of any subgroup is the same, the value of going from n to n+1 members doubles the total value of the network.  So if 1,000 users was worth - say $10 - 1,001 would be worth $20.  Another 9 members increases the value to a bit over $10,000 and adding another 30 members increases the value by well over a billion times.  It would make real sense to find those additional 20 members.  It wouldn't take too many more to increase the network's value by more than the total economy of the Earth - 2ⁿ gives an exponential growth.  Most of these subgroups will never exist and you need to consider their value on a case by case basis.

Metcalfe's Law doesn't see such a dramatic increase, but it does increase much faster than what is observed as n becomes large.  Back in 1995 I thought a bit about the problem when I was standing at the white board and suggested, half jokingly, that it probably scales as n*log(n) as so much of nature seems to follow a logarithmic increase and we clearly see more "value" than a linearly increasing broadcast network (Sarnoff's Law).

Since then Andrew Odlyzko and others have suggested a limit of value probably increases as - surprise - n*log(n) and show some fairly convincing arguments, but not a proof.

As it happens Juliette Powell¹ mentioned someone objected her use of Reed's Law citing the number of pair combinations that Metcalfe's Law allows.  An apples and oranges argument - perhaps they were thinking on only of the old telecom work where communication almost always took place between a pair of participants and she was thinking of something far broader and more general - the Internet.  In reality we won't see the number of groups that either Metcalfe or Reed suggest is possible, but Reed's model is more relevant for the Internet as it includes all possibilities.

To figure out value, social effects must be included - linkages vary greatly in value.  I'm inclined to believe that, but also belief there is a plateau effect going on - a manifestation of something like Dunbar's Number along with the strength of social connections. There also seems to be a burnout effect - particularly among people who begin to get real lives (although there are a large number of people who just waste their idle time or who look for ways to spend bits of time when everything else seems boring).

In any case it is complex.  Sociology and anthropology are very complex subjects and there is enormous room for discovery.  I suspect that the nature of electronically mediated social connections as well as hybrid connections with machines and real human interactions, will keep evolving.  I think that services like Facebook and Twitter happened to offer an "improvement" over what currently existed for many - but the deep social connections just aren't there and the long term prospects (say 10 or more years) are iffy at best.  

Perhaps the huge number of new services being tried are just an inefficient monte carlo-ish mechanism that, over time, will help us sort out some rather thorny sociology and anthropology.

For some people and organizations these can be useful and effective tools.  For others they can be not terribly useful to wastes of time and money.  There will be an evolution, but if you find something useful by all means do so and work on learning how to increase its value.  But also appreciate there are limits.  If you are in a situation where Sarnoff's broadcast networks are the end of the road there may be value here, but nothing is trivial.

I have worries about the current trend to Balkanization of the Internet reducing it to something very different and much more limited.  The US government is bound up in the concept of promoting "broadband", which has nothing to do with the Internet.  Rather than paying an ISP and being able to just exchange packets with anyone or anything, the telcos and others are moving towards buying access, but then buying certain classes of services - or even specific services - on top of that.  This is extremely unhealthy and will slow down the development of new types of communications and services completely eliminating some possibilities.  

We are only beginning to understand how people communicate - the fundamentals of what makes us the most social of all creatures.  Social communication is more at its beginning than its end and people I know like Juliette, Howard, Nancy and a few more of you are working out how to better adapt current services to the needs of people and organizations as well as thinking about potentially new and even better modes.  It is going to require people and organizations with a broad range of skills - engineering alone with no longer cut it.²  This is a natural and important progression, but we need an Internet to make it happen.  We may be in the process of losing that key piece.

Coming back to the title of the piece.  As long as you clearly define your terms you can come up with an estimate of the potential of the Internet.  Reed's model is based on something that is based on the Internet, while Metcalfe's only covers a more narrow case. Both of them, for any reasonably large n, vastly overestimate the real world case and, in particular, the value of the network.  Other arguments based on economics are possible, but a deeper understanding demands an understanding the sociology and anthropology of social communication.  

So many questions - how perfectly excellent!

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¹ Juliette is a dear friend as well as a great synthesizer and communicator of ideas - I'm in awe of her as communication is a huge weak spot of mine.  When I grow up I want to be half as good as she is.  It is very rare to find someone so adroit at connecting the dots and managing to communicate the result.  She has created some killer metaphors, and metaphor is one of the basic elements of rhetoric and storytelling. 

² A good example of this comes from studies on why many in the third world don't use much better stoves, even when they are available and is very applicable to sanitation and food storage.  

Another example is the inability for 3d avatars to take hold.  An anthropologist friend looked into this and noted many of the early adopters, for a variety of reasons, were software engineers as well as some heavy users of MUDs and MOOs.  These people tend towards shyness and a reasonable percentage show signs of Asperger's Syndrome (not all, but a good proportion).  They tend towards shyness in face to face interactions and are not skilled with out of band communications.  The 3d world gives then a world with a more limited scope of communication removing many of the issues they have in the real world.  On the other hand most users find worlds like Second Place to be artifical and lacking in rich communication.

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Recipe corner 

For the longest time I hated scones.  It seems I only had those my grandmother made - a type of scone popular in Ireland and Wales in the 19^th century and fried in a pan.  She was a great baker and cook - but her scones were an exception.  Years later I had something wonderful and asked what it was.  A scone.  A proper English scone.  So the recipe offering will be the basic scone recipe I use.  Try adding some cherries or berries to it.  My favorite is a handful of wild blueberries along with some chopped pecans. These freeze and microwave at a later date nicely, so don't worry about eating them all at once.

Note that the basic version is vanilla.  If you thow in other ingredients, you should cut back on the vanilla bean.  When I go to blueberries, I just put in the scraping of a half bean.  If you are trying for a citrus flavor I would cut out the beans entirely. 

Basic Scones

Ingredients

° 725 g AP flour (cake flower is probably better)

° 230 g white sugar

° 1 tbl baking powder

° 1 tsp baking soda

° the scrapings of  4 vanilla beans

° 240 g butter, room temp

° 450 g greek plain yogurt (I use Fage plain whole - forget about reduced fat!!)

° 3 large egg yolks

Technique

° pre-heat oven to 375°F with a rack in the middle position

 ° combine the dry ingredients in a mixing bowl and add the butter and mix together at low speed until butter has completely mixed into the dry.  

° add the liquid ingredients and mix until a ball forms.  do not over-mix!

° place on a floured surface and shape into an 8 or 9 inch round, patting it into shape and evening its thickness with your fingers.  cut into wedges or whatever shape tickles your fancy.  you can also back the whole thing and cut it later.

° bake until the scones are firm and begin to brown a bit around the edges (20 minutes for me)  

° glaze them if you like to seal - I like a basic sugar glaze of 1 part brown sugar dissolved in 10 parts water over a gentle heat.   just brush it on with a pastry brush. variations are confectioner's sugar or egg glazes.  pick your poison

(scone image from clockworkgrue)

 

cheating gravity

My Dad has this recurring dream...  He is running impossibly fast and comes on a smooth lake...  "Why not?" - and he starts running across it almost effortlessly getting only the bottom of his feet wet.  He can run for miles like this and wakes up happy and exhilarated.

 

I have flying dreams and a different sort of running dream.  I'm running very fast with longer and longer strides.  I begin to increase the length of my strikes and start to pull my legs up a bit as I'm heading back towards the ground on each so the strides seem longer and longer.  At some point I'm totally avoiding the ground.  

 

Such dreams are probably common, but what about some athletes like basketball players who appear to float in the air for awhile? It can look particularly impressive as part of a slam dunk I've also seen it in soccer, er, football and volleyball.  A volleyball playing friend told me sometimes she does it at the net so to keep herself well positioned to put together a block.  She can touch a bit over 11 feet, so the ability to linger for a few tenths of a second at a slightly lower level can give an advantage.  Plus "it feels neat!"  

 

But the real masters are probably ballet dancers.  

 

There seems to be something a bit wrong here - after all - high school physics teaches us that someone jumping will propel themselves in a parabolic arc.  That is still true for a complicated object like a human body.  The trick is that the its center of mass follows the parabolic path.  You can move the rest of your body into any position you can muster while this is taking place.  The physics is all very simple even though the motion of any of the given points can be very confusing.¹  As its motion slows near the top of the trajectory the dancer can move her limbs so as to keep some of her body in a stationary vertical position.  Adjustments are constantly made as her vertical speed slows, stops and then begins to increase in the other direction. As some point her center of mass is moving too quickly to compensate.  

 

I watched a video of a dancer performing a grand jeté.   In it 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 it 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 and 0.3s still looks startling and even beautiful to the audience.  In volleyball it is more on the order of basketball.  I'm sure it must feel wonderful when probably executed.

 

Using the fine print and the fact that we notice heads a lot to "cheat" gravity.

 

There is another use of this in sport.   If you are standing normally, your center of mass is about 55% of your height from the ground and inside your body. If you bend forward at your hips your center of mass moves forward.  It is possible to move it outside your body.²  A high jumper can arrange for his body to move so that it completely soars above the bar even though the trajectory of his center of mass might pass under the bar (or somehow cause some of him to collide with it).  Dick Fosbury perfected the technique in the late 60s and revolutionized a sport - the Fosbury Flop.

 

Our sense of time is finely tuned to the environment we live in and that includes possible motions of our bodies.  We can discern individual bits of motion down to about three hundreds of a second - our world is viewed at roughly video rate.  A really fast tennis serve is a bit north of 65 meters per second.  Air resistance quickly drops that, but the ball initially is travels about 2 meters before we can take in the next frame³ The receiving player must make a lot of assumptions about where the ball is going to go based on subtle information before the ball is hit.  Clearly a lot of experience in understanding the biomechanics of how the trajectory of a tennis ball is created is built into any experienced player.  The same can be said for many other sports - baseball, even though the ball's speed coming off the bat is somewhat lower than that of a tennis ball, is more dramatic as the ball has enough mass that it does not slow down as quickly..  

 

Athletes are really good at Newtonian physics!

 

I'm better than Colleen sitting down with equations and working something out, but she has a much better ability to execute a series of those equations - equations that can be way to difficult for me to solve analytically - and not only come up with answers in real time, but convert the answers to values her muscles can use adjusting for real time position information of her own body.  Even more impressive is the fact that her senses notice where her body was rather than where it is at any given time.  We all have a neural time lag. Since she is very tall, she lives a bit more in the past than I do making the feat even more impressive.⁴

 

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¹ Take a hammer, or something else with an uneven mass distribution, and toss it with a bit of spin.  (hopefully away from anything that can be damaged)  The tends will form a tumbling pair of paths, but if you carefully watch the motion of the center of mass near its head. That will trace out a smooth parabolic trajectory.  

² You may have tried this as a student trying to pick up a chair with your head against a wall.  Women tend to have lower centers of mass relative to their height than men - the net result can be the men are unable to pick up the chair, but the women can.

³ There is additional time used to register an event, but ignore that and assume you are watching the ball.

⁴ Neural impulses travel at speeds that are slower than you may think anywhere from a few to about 120 meters per second.  Touch generally moves about 50 meters per second and pain much more slowly (hammer your finger and you notice you've done something really stupid fairly quickly, but the pain takes about a second to register - this is really useful to making an unencumbered choice when something really goes wrong)

The body tends to aggregate a few types of perception - touch your nose.  You "feel" the touch with your finger tip and the tip of your nose even though the time delay on the path from your nose to your brain is much less (up to a few tenths of a second).  People with longer bodies and longer neural path lengths perceive reality a bit later than shorter people.  Colleen lives a few hundredths of a second more in the past than I do (probably about 0.05s or so - certainly more than a perceived image frame) and has to adjust the motion of her body appropriately. Of course we never notice any of that, but it is a fascinating new layer of complexity.

 

Anyway - you can probably figure out that I woke up after one of those wonderful dreams where I can adjust my stride so as to rarely touch the ground.  Of course you might actually do that if you could dial back the force of gravity.  For some fun, think about Olympic events on the moon where the force of gravity is about a sixth that of Earth (assume you are in a big stadium that has an atmosphere to make it a bit more interesting) ... what would the record book look like?  And note that your reaction time is suddenly improved relative to how events transpire in some (not all!) sports...

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recipe corner

 

This was really good the other night. Heirloom tomatoes are wonderful now and it  that roasting them might be just wonderful.  Some corn was lurking along with a very flavorful vegetable stock - enough to spark a soup.  The quantities shown are very approximate - use your intuition and don't follow exactly.

 

Corn and Tomato Summer Soup

 

Ingredients

 

° 4 large very ripe heirloom tomatoes

° 2 ears of corn- cut off the kernels

° 4 cloves of garlic minced

° a small yellow onion

° a swish of olive oil 

° a small chili finely chopped (I'll leave it up to you how hot or not, so pick your poison - you can leave it out)

° 700g or so of vegetable stock (about 3 cups)

° salt and pepper

° plain greek yogurt (I like Fage 2%, or the full test if you dare)

 

Technique

 

° Preheat your oven to 400°F

° Heat the olive oil in a large pan over a medium low heat .

° Add the onions, garlic, chili and some salt and sweat the onions (cook them 'til translucent - about 4 or 5 minutes for me)

° In another pot heat the stock

° Slice the tomatoes in half and cut out the cores, drizzle some olive oil on their flat sides and place them flat side down on a cookie sheet.  Roast until they just start to caramelize, but don't let them burn (about 10 minutes for me)

° Dump the tomatoes into the pot with the onion and garlic.  Pour a bit of the stock onto the yummy browned pan scrapings and scrape all of that into the pot.

° Cook on a medium heat for about 5 or 10 minutes until it starts to dry out a bit (depending on how much stock you have ladled onto it)

° Add the corn kernels and cook for another few minutes (maybe 3 or 4)

° Add the stock, bring to a boil and reduce to a simmer and cover. Let it cook "enough" - about 45 minutes for me.

° Put it into a food processor or use an immersion blender (much less dangerous).  Strain off the debris 

° Season to taste.  You will need pepper and possibly more salt.  Some herbs may be appropriate.

° Serve with a bit of yogurt and a drizzle of olive oil on each bowl. I added some chopped basil, but use your imagination.

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Yesterday it was pointed out that it was "eat ice cream all day day" ..  I decided to make something and picked up some heavy cream in the evening and then searched the pantry for inspiration.  I ended up with a tried a true vanilla with some additions.  Recommended.  But try to get pasteurized heavy cream rather than the ultra pasteurized variety if you can (it isn't easy).  Also use pasteurized eggs for safety as this is an uncooked method.

Lots of room for experimentation here!

 

Chocolate, Bing Cherry and Pecan Ice Cream

 

Ingredients

° 2 large pasteurized eggs 

° 185g (about 3/4 cup) granulated white sugar

° 2 cups heavy cream (pasteurized rather than ultrapasteurized if possible)

° 1 cup whole milk 

° half vanilla bean (optional)

° about 50g coarsely chopped semisweet chocolate (a mixture of chocolate types would be great!)

° about 50g bing cherries, pitted and cut into quarters

° about 30g coarsely chopped pecans

 

Technique

 

° chill the chocolate, cherries and nuts in separate bowls and get as close to freezing as you can

° whisk eggs until light and fluffy - a couple of minutes usually

° whisk in the sugar a bit at a time and then completely bend.  Pour in the milk and cream and continue to blend.  

° split and scrape the vanilla bean - mix in the goodstuff  (I didn't have a bean and it worked out, but I think it would be better with)

° add to your ice cream freezer and start freezing

° a minute or so before it is ready add the nuts, chocolate and cherries

 

 

flying through the water

Fifteen feet across and thirty inches deep,  old vinyl swimming pool wasn't terribly useful for swimming.  I was twelve and its novelty had worn off.  The obvious uses were floating or just trying to stay cool in the Summer, but it turned out to make a lovely wind tunnel and general piece of experimental apparatus.

 

My Dad liked ice cream enough that he found five gallon cartons that our freezer could barely hold.  These were very sturdy and the empties were useful.  It turns out you probably don't want to try it, but I though I could launch a model rocket from under water by covering the top with something the rocket could fly through.¹   But somehow the idea of moving through water - flying through water - caught my fancy.

 

Plastic model airplanes were common back then and I had the idea that I might be able to fly once of them.  After all, the better ones had a bit of an airfoil molded into the wing.  What I didn't know at the time was this was a good idea.  Water and air are both fluids and the motion of a body through them is governed by the same fluid dynamics.  The difference is water is about 800 times denser than air.  It took quite a bit of experimentation, but finally I had a nice "wind tunnel" that replaced air with water.²

 

You've probably done the same with your hand out the car's window. The airflow against your hand creates quite a bit of drag, but you can change the shape of your hand by cupping it a bit to resemble an airplane's airfoil and something wonderful happens. There is lift - the same sort of lift that allows flight under the right conditions - enough, depending on the angle of attack, to make it challenging to hold in place when the car is at highway speeds.³   This same airfoil can be used underwater as a hydrofoil when we swim and gives a neat window to examine of some the Olympic swimming events as well as how those of us who are less skilled and athletic manage.

 

Brynne suggested swimming as the next Olympic topic and Jean triggered something about airfoils.  A nice topic as there has been an enormous amount of research into swimming since the 70s.  Computational fluid dynamics, a discipline fueled by the aerospace industry, had advanced to the point where it was possible to study the basics of a human moving through water and competitive swimming has been revolutionized mostly through improvements in technique.⁴  After all - things moving through water behave very much like things moving through really dense air - the sort of thing I was learned from that little vinyl wind tunnel, er, swimming pool when I was twelve.⁵

 

While runners and cyclists go forward by pushing off of solid surfaces, swimmers move forward by pushing against the fluid they are flying through.  You cup your hand a bit and control the angle it makes with the water.  Just like an airfoil there is gravity, drag, lift and propulsion - the propulsion is from the lift pointing mostly forward.  Fortunately the human body has almost the same density as water, so very little work has to be done to support yourself against gravity.

 

There are three basic types of drag that try to hold a swimmer back - friction, pressure and waves.  The first type - friction of the body against the water - varies with the speed and shape of the swimmer.  This is what you feel and have to pay attention to as a recreational swimmer as it is important at all speeds.  For the same body shape it scales linearly with your cross sectional area to the direction of motion and the square of your speed relative to that of the water - just like running or biking through the air.  The power required to counteract this resistive force goes as the cube of your speed.  It takes a lot of muscle and effort to go just a bit faster.

 

As you swim there is a pressure difference between the water immediately in front and behind you - the pressure being higher in front.  This creates another type of drag and one that becomes increasingly important as you move faster.  Most recreational swimmers don't go fast enough for it to dominate, but if you're moving quickly it becomes a real issue in a hurry.

 

Near the surface of the water you have to plow through the waves.  You create your own and have to deal with those of others even in an otherwise perfectly still pool.  As you move faster both their amplitude and their wavelength - the peak to peak distance between swells - increase. If you are going fast enough that the wavelength is a bit longer than your height you can get caught in your own trough which is a natural practical speed limit.  A taller swimmer will have a longer wavelength to break and has a higher speed limit than someone who is shorter.  

 

The amplitude of the waves you generate can be changed with technique and great progress has been made with computational analysis and the application of newly discovered techniques.  Likewise a lot of work has gone into basic swimming technique to supply more thrust.

 

This wave interaction has an interesting story.  If you can swim underwater you don't have to deal with it.  A fast freestyle swimmer will stay submerged as long as they can after a start or when they turn.  In 2010 an American swimmer broke the world record in the 50 meter backstroke by staying underwater the whole time using a dolphin kick and a few other tricks.  In the end he was disqualified and the rules were changed to limit the distance a swimmer can remain submerged.  It is important to come as close to this limit if you can if you want to win at the highest levels as wave drag at high speeds can account for more than half the total drag.

 

World class swimmers tend to have long torsos, very long and powerful arms and relatively short legs with large flippers - er - feet.  Mike Phelps and Missy Franklin are both relatively tall with very long torsos and wingspans greater than their heights - they also have great lungs and an insane ability to capacity to use oxygen - a great VO₂ max .  Both have very large feet and have great arm muscles and big hands.  They were made to swim fast.  Usain Both is very tall, with a short torso and very long legs, an enormous percentage of white muscle, and a very short achilles tendon.  He was made to run fast.  Of course, beyond the genetic gifts there is an enormous amount of dedication and excellent training and coaching...  

 

...but at what level of sport are genetic gifts required?

 

For average k12 and recreational sports I doubt that genetic gifts are required to do well and enjoy yourself.  You should do what you enjoy. I've seen really good 5'7" high school basketball players do very well. Perhaps at state tournaments or in very competitive leagues height starts to be necessary, but you can do a lot with hard work and a love of the game.  Exceptions may be people who have dramatically different red to white muscle ratios.  There are people who just can't jump, but can run forever (that runs in my family) I suspect, for these people as well as for the natural sprinter/jumpers, you will gravitate to sports that seem right to you.  

 

But at the highest level of sport you need everything as well as some luck.  Colleen, at 6'7 and extremely long legs and arms, is one of these people.  Long limbs are good for some sports, but you pay a price when you need to rotate your body.  When she was a pre-teen she really wanted to dive well, but a 6'1 11 year old just can't rotate her body quickly enough.  It would be fascinating to make a silhouette of the a composite average of the top few in the world for each sport and create a poster - gymnasts on one end and basketball players on the other.  It is remarkable that world class bike riders are about the same height and the same is true of distance runners.  But so few of us will compete at these levels that the best advice is undoubtedly what the ad suggests - pick whatever sport you like and - 

 

Just Do It!

 

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¹ I tried three or four different materials for a breakable windows the rocket could puncture.  Unfortunately materials strong enough to submerge to a satisfying depth kept the rocket inside usually resulting in a delayed rupture with a lot of acrid smoke belching to the surface and a water damaged rocket.

² I built a little underwater tow track with a couple of pulleys, a crank and a small scale for making measurements.  I didn't realize that the airfoils on the models weren't terribly accurate, but I was able to "fly" some of the aircraft and even rig them for climbing and banking by bending little control surfaces I added with a bit of tape. 

³ There are four basic forces on an airplane in flight - gravity trying to pull it down, lift counteracting gravity, drag trying to slow the aircraft and thrust from an engine pulling it forward (of course unpowered gliding is possible too and then you just out three forces).  If you carefully examine an airfoil the top surface has a concave surface and the bottom surface usually has a flat or cave surface.  Air meeting the airfoil either goes above it or below it.  The air that travels across the top has a longer path to take and, since the same amount that starts out just in front of  the airfoil has to be the same as that just behind it, the air pressure on top is lower and the pressure on the bottom higher. The net result is an upward lift.  As the aircraft increases its speed relative to the air it is moving through the lift increases.  At some point the lift force exceeds that of gravity and we have flight.

⁴ Checking the records for the men's 100 meter freestyle the progression has been from 52.9s in 1964 to 4.9s today.  The women have gone from 58.9s to 52.1s.  Swimming is about four times slower than running for many events so compare this to the 400m track event which has gone from 44.9s to 42.2s for men and 51s to 47.6s for women - a much smaller rate of progression.  Technique turns out to be much more important than the exotic and very expensive swimsuits seen during the last Olympics.  In sport there is a level where relatively tiny improvements can give an enormous advantage.

⁵ If you want to motivate a teen to learn a bit about math getting them fascinated by aerodynamics and fluid flow is an outstanding gateway drug.  The Navier-Stokes equations are a beautiful way to address fluid dynamics.  Non-linear partial differential equations and a bit of fundamental bedrock of mathematical literacy for the physical, and even some of the biological, sciences.  A motivated teenager can learn quite a bit if there is a strong motivation.

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Recipe corner

 

I love a good granola bar and this chocolate cherry one is a winner.  This is good with a scoop of a rich vanilla ice cream on top or just by themselves.

 

Chocolate Cherry Almond Bars

 

Ingredients

 

° 150g (1-2/3 c) rolled oats

° 115g honey (1/3 c) I like Tupelo these days)

° 40g (1/3 c) whole wheat flour

° 1/2 tsp salt

° 50g (about 2 oz) chocolate bar crushed (about 70% cocoa)

° 75g (1/2 c) dried cherries

° 75g (1/2 c) slivered almonds 

° 1 tsp good vanilla extract

° 55g (1/4 c) butter (you can use coconut or olive oil)

° 50g (1/4 c) dark brown sugar (I have used 1/2 brown sugar, 1/2 molasses too)

 

Technique

 

° set oven to 350° F

° combine everything in a large bowl and mix well

° spread onto a baking sheet and pat down until it is about a half inch thick - cover exposed edges with a bit of foil so they don't get too brown

° bake until the top is golden brown - maybe 25 minutes

° cool and cut into whatever bar shape pleases

 

The second recipe - after all, I didn't post one with the last post, is something I will make in the near future to honor a breakthrough Jean made a few days ago. (isn't it wonderful to celebrate friends like this?).  I've made the vanilla and it is one of my best vanillas ever.  I've also done the fudge and will make the modification I've suggested.  It will be a slam dunk, I'm sure.  I'll leave everything in old units as this is from old notes before I began to weigh ingredients.   If you don't make your own ice cream try this with a super premium vanilla softened, a good fudge and some peanut butter and peanut butter cups.  It should be excellent too:-)

 

Peanut Butter Chocolate Ribbon Ice Cream

 

Ingredients

ice cream

° 1 cup whole milk

° 2/3 cup white sugar

° 2 cups heavy cream in two separate cups - try to get just pasteurized rather than ultrapasteurized if you can

° a bit of salt

° 6 egg yolks from large eggs (odd that large is the standard egg size, isn't it?)

° 2 tsp vanilla extract - highest quality you have

° the scrapings of one vanilla bean

° a couple of handfuls of the smallest peanut butter cups chopped coarsely.  I'm guessing about 5 or 6 ounces.

fudge ribbon

° 1/2 cup white sugar

° 1/3 cup light corn syrup

° 1/2 cup water

° 6 tbl Dutch-process cocoa powder (some of the high end cocoa powers aren't and won't work well here)

° 1/2 tsp vanilla

for the peanut butter ribbon

° 1/3 cup smooth peanut butter (I think the stuff without sugar will be best - but stir it well)

° a bit of whole milk - maybe a couple of tbl

 

Technique

 

° Heat the milk, sugar, 1 cup heavy cream and a pinch of salt in a sauce pan - just warm it

° in another bowl whisk the egg yolks while slowly adding some of the heated mixture

° As the mixture heats to somewhat warm, put the yolk mixture into the sauce pan

° stir constantly over a medium heat until the mixture thickens.  The gold standard is when it coats the spatula - now you have custard

° pour throw a strainer over another bowl you have cleverly pre-positioned and stir in the remaining cup of heavy cream

° stir in the vanilla extract and bean scrapings 

° stir it every now and again until it cools and then chill in the fridge for a few hours

now onto the fudge - 

° mix the water, sugar, corn syrup and cocoa over a medium heat until bubbles just start to form - then boil for a minute or so stirring constantly and remove from the heat.

° stir in the vanilla extract and let cool.  You can pour it into a jar and store it.  Make sure it is chilled before you use it!

now for the ice cream making!

° churn freeze the custard mixture as per the instructions of your ice cream machine

° as this happens whisk the milk and peanut butter together

° when the machine begins to slow add the chopped chocolate peanut butter cups and let it run another minute or so.  

° move some (a third?) of the ice cream to a storage container and drizzle a third of the fudge and the peanut butter/milk mixture and repeat the process until you have have added all of the layers.  

° finish by throwing it in your freezer for a few hours.  I suspect I'll break in well before that as I frequently act my shoe size and I happen to be the "adult supervision" here

 

 

it's a drag...

OK - I've been spending way too much time watching the Olympics.  The fact that all of the events are being streamed has had an impact on the amount of work I've been able to accomplish, so I'm writing off some of this as vacation time.  

 

I tend to be interested in sports I've had some involvement with - either by participation (and never at a terribly athletic level), through the involvement of a friend or relative, or by getting involved in the science behind a sport.¹  

 

I had asked for suggestions of science of sport questions people might have and a few people responded.  Ted asked about the remarkable long jump record set by Bob Beamon.  According to the always infallible Wikipedia, he came to the event as a favorite with a personal best of 8.33 meters - very close to the world record at the time.   Somehow he managed 8.90 meters - 29 feet 2.5 inches - over 21 inches longer than the world record at the time.  This was such a huge increase over everyone else in the world - and himself - that it stood out and remained the record until 1991 when Mike Powell jumped a 8.95 meters.  Beamon still has the second longest jump in history, although a few have approached it.

 

Ted asked about what might be going on - after all - records were falling for jumping and sprinting events, while distance events saw terrible performance.

 

Mexico City is 2,240 meters above sea level and oxygen absorption by the human body is only about 90% what the athlete can manage at sea level.  Athletes who had spent time training at altitude were able to absorb somewhat more than athletes who weren't acclimatized with the distance events being dominated by runners from high altitudes, although the times were not fast compared with sea level performances.  Sprinting events, on the other hand, saw a lot of new records.

 

It turns out oxygen absorption isn't very important in sprinting events.  During the burst of speed of a flat out sprint, the muscles are converting chemical to mechanical energy by anaerobic metabolism.²  In other words it makes sense that anaerobic events shouldn't be degraded, while aerobic events will.

 

The atmosphere has a lower density at greater altitude above sea level.  At  20° C air density is 1.23 kilograms per cubic meter at sea level, but Mexico City is down to 0.98.  Although the density is only 80% of sea level, you will only see a 0.1% drop in your sprint time, while many of the winning sprinters saw improvements in the 1 to 2% range.³  Further analysis suggests the real culprit was the wind.

 

The winds at Mexico City were largely behind the athletes for the 100 and 200 meter events and were high - bordering on, and possibly exceeding, the 2.0 meter per second limit requirement for official Olympic records.   Precise weather data was not recorded and it is impossible to make absolute statements, but tail winds of this speed turn out to be enough to account for the improvements several athletes saw and there was a suspicion that they may have much stronger at times.⁴

 

For all endurance events athletes who had trained at altitude had a big advantage over those who did not.  Since'68 some athletes train at altitude as the body learns to absorb more oxygen at the lower air pressure.  The effect is short-lived and needs to be properly timed for best effect.  Probably more common these days is sleeping in oxygen tents that simulate high altitudes.

 

The wind does have an impact on many events though - and perhaps technique should vary to take it into account.  Imagine a longer race with a windspeed of w and runners pushing along at a constant speed v.  For sake of argument think of them as running a square lap with legs that have a north, west, south and east alignment and have the wind coming from the north.  When a runner is going north she will have an effective windspeed of v+w and when she is going south v-w.  The force she feels will be proportional to (v+w)² on the north leg (v-w)² on the south and just v² on the east and west portions.  As long as the magnitude of v is greater than that of w, the total force for the race will be greater than it would be if the conditions were calm - she has to work harder to keep up the same pace. 

 

Fortunately this is fine and dandy if all of the runners are experiencing the same conditions.  And there are some tricks you can play.  If you run directly behind another runner your effective airspeed, and thus air resistance, is less than that of an exposed runner.  Runners and cyclists often bunch in packs to take advantage of this and the leader is at a big disadvantage.  

 

But what if there is a trailing wind?  I rarely see athletes take advantage of this and I've mentioned it to a couple of Olympic coaches.  The runner (or cyclist) with the most wind at their back has an advantage, but those in the pack no longer benefit from the trailing wind.  A better strategy would seem to be to break out of the pack.  I was told the athletes don't know the wind velocity at any moment and windspeeds in these races is usually too low from them to take chances.  

 

But what about Bob's miracle record-smashing jump? I found a few papers on the subject.  The greater speed from the tail wind he probably had was probably enough to account for about half the extra distance.  The rest probably came from his athleticism and perhaps a variation on his techniques.  The fact that another person was able to better it in a calm shows that the record was humanly possible - he was able to muster the magic of doing it 23 years earlier than improvements in training and technique would suggest.  

 

This is the beauty of sport - when someone manages to tap what seems impossible and astound the world.

__________

¹ I'm very slow, but can have a bit of endurance.  When I actively cycled centuries (100 mile rides) were no big deal.  My niece Magi also is a red muscle (slow twitch) person, but she is a genuine athlete.  She does marathons and is a nationally ranked ultra-marathon runner, racing in the mountains.  Ultra-marathons usually start at 50 miles - yikes!

Pip and Dave - and probably others among you - have run marathons and Jheri is a "purely for the fun of it" runner who knocked off a 2:58 marathon the first time she tried one.  

Colleen is exceptionally athletic having been a Division 1 All American in volleyball when she was in college and then moving on to pro indoor volleyball in Europe and finally pro beach volleyball.  She taught me a lot about the sport and it is one of the main Olympic attractions for me.

² It is a bit beyond a short post, but there are two types of anaerobic (without oxygen) metabolism.  Both provide mechanical energy that greatly exceeds what aerobic metabolism can provide.  Different muscle types are specialized for one or the other.  White muscle is good for anaerobic metabolism, while red muscle (it looks red due to the oxygenated blood in it) is better suited for the long haul.  Most people have 50:50 mixtures - but people good at endurance running can have as much as 80% red muscle, and 100 yard dash specialists can have about 75% white muscle. Usain Bolt could never run a marathon - at least not with a credible amateur time.  This leads to a lot of interesting questions about body type and genetics in sport at the amateur, pro and world class levels.

A note on sub 10 second 100 meter races.  The runners produce power at 2,500 to 3,000 watts.  This is above and beyond the normal 70 or so watts used to keep the body functioning, but not physically moving.  There is no way this heat can be immediately removed (for comparison the electric element on a stovetop is about 1,500 watts) and the internal body temperature soars.  If the race was as long as 20 seconds at that level most of the runners would probably die from heat effects. Fortunately muscles can only function at this level for about 10 seconds.  The 200 meter races are very different from 100 meters, even though both are sprints.

³ Offered without derivation - there is quite a bit of physics behind this number. 

⁴ Again more physics, but a 2 meter/s following wind gives approximately a 0.12 second improvement for a 100 meter dash about twice that for 200 meters.

 

psychological time elasticity

Years ago I was trying to understand if there was any social value in tithing - after all - money is not evenly distributed so the burden varies enormously along with the perceived value of the act.   Instead I decided to tithe my time to the projects of others.  It began as four hours a week, but I enjoyed it so much that I quickly moved to a point where I was donating eleven hours a week - a tithe of my waking hours.¹

 

Special relativity elegantly shows that measured time is not fixed.  For us it is usually fixed and most of us would measure an hour to be exactly the same thing anywhere on Earth and in an century.²  So my practice is still "better" than giving money.

 

So we know that observable time - what we can measure with a clock - is not fixed, but is rather dependent on relative motion even though we live an existence where we live in a strong illusion that it is fixed.

 

When you were in the third grade there were times when a special day never seemed to arrive - time seemed to stretch out forever.  But when you are in high school taking a test that is much too long, a fifty minute period flies by and seems to end about as quickly as it started.  

 

Our perception of time is relative and depends on other  factors.

 

Much has been written about Csíkszentmihályian flow - the psychological state that is so addictive and puts you in a state where your concentration is so great that time appears to move very slowly.  Even now - especially now - many Olympians are experiencing it in London and it is a major factor in sport.  I'm a flow junky and attempt to recreate as often as I can.  But there is another feeling that can alter our perception of the passage of time.

 

Awe

 

One of the gut feelings I've had is that awe is very important to human evolution - the fact that we take delight in such experiences may well be selected as it can fuel curiosity and discovery.  I'll be the first to admit that my feelings are clouded as I love the feeling at a personal level and believe it has been a major driver in my own life.  

I also have wondered how it changes the perception of time.  For me it is similar to flow, but different even though both are immersive.  Both leave me with a strong feeling of time stopping but flow, outside the experience, gives me the sense that time must have zipped by.  With awe it "feels" different and seems to make almost everything that follows special.  I have wondered if this is a mechanism that might work well for parents and very young children.  The awe associated with watching a little kid develop may suppress the more negative aspects and help ensure the child has a lot of parental interaction.  Also, from a child's point of view, there is an enormous amount of awe available in fresh experiences and this may drive curiosity which, in turn, can drive learning.   I wonder if it it may be a driver of religious experience, but real speculation ...

 

I see awe as a "lean back" form of immersion and flow as a lean forward immersion. Both bring delight, change the perception of time and are totally addictive.  

All speculation and gut feeling, but now people are experimenting. I saw a report on a paper out of Stanford on the subject and immediately put on my critical cap as I've seen a lot of garbage on the subject.  This appears to be ok and starts you thinking about more direct questions and experiments. (pdf - a preliminary working paper)

Abstract

When do people feel as if they are rich in time? Not often, research and daily experience suggest.

However, three experiments showed that participants who felt awe, relative to other emotions, felt they had more time available (Experiments 1, 3) and were less impatient (Experiment 2). Participants who experienced awe were also more willing to volunteer their time to help others (Experiment 2), more strongly preferred experiences over material products (Experiment 3), and experienced a greater boost in life satisfaction (Experiment 3). Mediation analyses revealed that these changes in decision making and well-being were due to awe’s ability to alter the subjective experience of time. Experiences of awe bring people into the present moment, which underlies awe’s capacity to adjust time perception, influence decisions, and make life feel more satisfying than it would otherwise. 

Awe Expands People’s Perception of Time, Alters Decision Making, and Enhances Well-Being Time might be the scarcest commodity for many people in modern life. A recent poll of over 1,000 Americans found nearly half (47%) felt they lacked enough time in daily life (Carroll, 2008). This feeling of having too much to do and not enough time to do it—or “time famine” (Perlow, 1999)—has been linked to undesirable side effects including trouble sleeping, stress, difficulty delaying gratification, and postponing seeing a doctor when ill (Lehto, 1998; Vuckovic, 1999; Zhang & DeVoe, 2010). In light of these findings, we asked, what could be done to shift people’s perception of how much time is available?

Three experiments examined whether awe, defined as the emotion that arises when one encounters something so strikingly vast that it provokes a need to update one’s mental schemas (Keltner & Haidt, 2003), can expand perceptions of time availability. Additionally, we investigated whether awe, through engendering the sense that more time is available, would alter prosocial decisions concerning time, consumption preferences, and well-being assessments. We predicted that people induced to feel awe, relative to other states, would be more willing to volunteer their time, prefer experiential goods over material ones, and experience a boost in life satisfaction. 

 

Neat!  Perhaps we not only have the awesome experience that, by itself changes our perception of time, but we may experience a better sense of what is important and have more positive social experiences following these "awesome" moments.  Anecdotally it seems to happen for me and the three good friends I mentioned it to today.  Maybe there is something deep here.  

 

What are those experiences that leave you with a sense of awe?  For me they usually involve a direct interaction with nature or experiencing sometime beautiful.  

It has come when I've been moved past the state of tears by a cellist playing Bach's D Major Suite in a way that is simultaneously completely new and familiar 

it comes during a total solar eclipse

it comes while I dance like a crazy person under a red aurora.

it comes on a cloudless and moonless night in a place a hundred miles from the nearest city with the Milky Way so bright you can't find the constellations

it comes...  

I have to seek it out, but it just comes as long as I'm open to it.

It rarely comes when I'm interacting with a computer, although I regularly achieve flow using a computer.

 

My guess is both are excellent for your mental well-being, but don't take my word for it..  go out and cast your soul out leaning backward in awe of Nature and lean forward as you become the master of your craft.

 

So many questions!!   and that is just as it should be.

___________

¹ My TED^x talk goes into the practice in more depth if you can put up with a not so great talk...

² I won't go into a discussion of Einstein's Special Relativity, but recommend learning about it if you don't know already.  It turns out High School math and a bit of logical thinking is more than enough - that is why it is so beautifully elegant.  You'll struggle a bit with the concept, but when you see why it works - why measurements of length and time aren't fixed for two observers who are moving relative to each other - you'll feel the delight in understanding something rather deep.  

I strongly recommend a classic text on the subject: 

Spacetime Physics: Introduction to Special Relatively by Edwin Tayor and John Wheeler

I think the old 1971 version is the better and it is readily available as a used text for very little.

__________

Recipe corner

Somewhat Smashed Green Peas

Now is the time you can find fresh green peas.  The problem is they rapidly lose their sugar.  If you can't use them within about 12 hours of picking, you are probably better off with a high quality flash frozen pea, but if you have some in your garden or can pick some nearby they can be incredible!

This is really simple and quite wonderful - even with good frozen peas.  As always the amounts are approximate so you don't need to be terribly careful.  You can experiment with adding a bit of cream or season it differently, but I prefer letting the peas just speak for themselves.

 

Ingredients

 

° 450g freshly picked or high quality frozen peas

° 120g scallions - trimmed 

° 2 tbsp extra virgin olive oil

° 2 cloves of garlic, crushed

° finely grated zest of a lemon

° sea salt & freshly ground black pepper

 

Technique

 

° cook the peas in salted boiling water until just tender

° chop the scallions and keep the green and white bits separate. Heat the olive oil in a pan and gently cook the white part of the scallions, but don't let them brown. After a few minutes stir in the garlic and a minute later the green bits of the scallions and lemon zest.  Cook until the green bits just begin to wilt, but no further.

° Drain the peans and reserve a bit of the water - maybe four tablespoons.  With a stick blender or food processor blend half of the peas with the reserved water and onion mixture.  Keep it a bit rough.

° Now mix in the remaining whole peas, season and serve.