omenti

diverted imagineering

Sometimes when it was really dark - those clear moonless night where the Milky Way stood out - Brian and I would load the binoculars and telescope into my parent's station wagon and either go East on Highwood Road or North on the Bootlegger Trail past Benton Lake to get away from the town lights.  It could be impressively dark.  The kind of dark where the ground disappeared.  We covered a low powered flashlight with red plastic.  Dim red light didn't damage your night vision as much as white light did.   But you could do a lot better.

 

When you're in a very dark place try using your rod-based vision.   Give your eyes at least ten minutes to begin to adapt - twenty minutes will be even better.  You won't see any colors, but your eyes will be somewhere between one thousand and ten thousands times more sensitive to light.  You can navigate with just the light from the Milky Way. 

 

A friend read something about the art of defamiliarizing yourself to gain a new perspective.  Artists might concentrate on the empty space between objects.  A few years ago Frans Blok played with geography by inverting elevations on a map of the Earth.  Everest became the deepest trench in an ocean and the Marianas Trench became the highest peak.  He tweaked place names and came up with something that makes you think. 

 

People noted for artistic creativity often do it.  Just change something to see what you're working on from a different perspective. Haruki Murakami wrote rough drafts in English and then translated back into his native Japanese. Margaret Atwood likes to change an opening sentence or paragraph to hunt for new perspectives.  She uses the example of a change to Little Red Riding Hood where the first sentence becomes: "It was dark inside the wolf." Some writers pin segments of what they're working on to a wall and ponder how the flow changes if you move them around.  Some film people use storyboarding in the same way.   Artists play with negative space - the space between the physical subjects in their paintings and sculptures.   A cute trick some musicians use is to invert music. There are even pianos where the keys are arranged backwards for this kind of play.  

 

Awhile back I taught an intro physics course to non-STEM majors. Hoping to make it a bit more interesting I found examples in sports.  I think all of us learned something.  At one point we were playing with the idea of what a sport would be like on a different world.  Different atmosphere and different gravity  and more unusual possibilities like cartoon physics.  We found many of our assumptions broke. We came to a more fundamental question - what makes a sport interesting on Earth.   Then how could you modify existing sports or invent new ones.  Why current rules of sports are what they are?  How deeply are they based in physics?  It even led to a guest lecture by a neurologist who seemed delighted by the play. 

 

Trying to explain a central concept to someone with your background is both difficult and useful.  Wired had a fascinating series of videos on the theme.   My thesis advisor required his students to explain their work in a period to high school students.  One of the most difficult things I've tried and it completely changed my thinking about teaching. 

 

 

If you're stuck on a particular problem sometimes it's useful to try something else - perhaps something very different.   Problem solving by singing in the shower, running, or doing something else physical is real for some people.  

 

I usually find it's best to change one thing and think about what happens as a result.   find it incredibly useful to talk with folks who do very different things - musicians, writers, filmmakers, artists, business people, athletes and so on.  Sometimes you get involved in a project that leads to a bit of insight that may seem completely unrelated.  Last year I found some thinking on the aerodynamics of spinning volleyballs led to thinking about something curious about neutron stars.   Through that interaction I learned a bit about the "chess" of a sport with just two players on a side and that led to some questions for a neurologist.   

 

Finally it's a fundamental part of humor..  So why not end with a bad joke?

 

A priest, a rabbit and a minister walk into a bar. The priest and minister both order a beer, but the rabbit looks confused.  The bartender asks the rabbit "what'll ya have? "The rabbit says "I dunno. I'm only here because of autocorrect."

 

 

invention

a minipost

I've heard Yasmin Williams a few times  She's an exceptionally inventive guitarist and NPR's Tiny Desk Concert series has featured her a few times.  Here's her latest visit.  

 

(definitely go fullscreen to watch her technique.  Fullscreen doesn't work in some browsers, so go to the NPR link above for their version.)

 

Invention is often a mixture of curiosity and just playing around with things.  The process can seem opaque if it's outside your field, but it's basically playfulness. It's at the heart of art, literature, music, science, technology, sports and much more.  It moves civilization.  

 

 

chindōgu

a minipost

Several people have written asking for educational projects to occupy their kids during the pandemic.  I've answered with a number of ideas, but it hit me chindōgu could be the perfect ticket for many.  It's the absurd Japanese art of useless inventions aimed at solving everyday problems with roots in Rube Goldberg machines and the art of the kludge - a clever but inelegant solution to a problem.   A number of good examples are shown here.  I've recommended this approach to a number of middle and high school teachers.  At least one has had a lot of fun with it making a "how to program things" module more fun.  It's also become a recreational art form at an animation studio you've heard about.

 

Thinking that way can be unexpected powerful.  It cuts through barriers combining critical thinking and play with the goal of humor.  Failure is fine and can be a powerful learning experience. Simone Giertz has been credited with getting more teenage girls interested in engineering than other person or program.  She's famous for useless robots - "shitty robots" as she calls them.   Here's her TED talk (one of the few useful TED talks I've seen).  

 Here's her YouTube channel.  Earlier pieces may be more accessible to beginners as she's become more sophisticated in her craziness.  And she has done much of this with brain cancer.  A remarkable inspiration. 

 

So start off small with supplies around the house and just have fun.  There aren't any downsides and you can spend as much or as little as you want.  You're only limited by your imagination and sense of humor.  And if you are building them, you can draw or write about them.   

 

 

place and time

There was a bowl of M&Ms for after the oral exams  Our grades were based on homework assignments and three oral exams. Four of us would take our turn at the blackboard. The professor had this natural ability to ask question you hadn't thought about, but should be able to solve.

 

Mr Crandall:  Does a clock at the center of the Earth run faster or slower than one on the surface?  If so how big is the difference since the Earth was formed?

(It wasn't as bad as that might sound - he was nothing like John Houseman.)

 

First a little diversion is in order.  You've probably heard the Global Positioning System needs to account for relativity.  Two effects are going on.  In one the satellites are moving with respect to GPS receiver on the ground.  Each satellite has a very stable atomic clock that is synchronized with the other GPS satellites.  Your receiver look at position and time information from at least four satellites to determine your position.  To get the necessary level of accuracy the system needs to account for the effects of both special and general relativity.   

 

Special relativity tells us moving clock appears to run a bit slower than one at rest.  Almost everything around us moves too slowly for this to be important , but a clock on a GPS satellite would lose about seven microseconds a day.  That may not seem like much, but that's enough to cause a position error that increases by about two kilometers a day. 

 

The curvature of spacetime is the bigger problem.   A result of general relativity is the direction where time runs more slowly.¹ The further a clock is from a mass, the faster it runs.  Clocks on orbiting GPS satellites gain about forty six microseconds a day.  Add the special and general relativistic effects and the satellite clocks gain a bit under thirty nine microseconds a day. Left uncorrected the system would be useless in a few minutes and the error would increase by  over seven miles in a day.   The satellites correct for both of these effects before the signal is transmitted.

 

All of this is key to the original question.  Time at the center of the Earth will pass more slowly.  The question is how much?

 

The purpose of these oral exams was not so much to test if you had learned the course material, but to encourage you to quickly frame a problem and come up with a ballpark estimate.  In the spirt of the type of education pioneered by Comenius it was  supposed to be playful and even fun.  This type of thinking with a piece of chalk is core to thinking through new ideas and working with others on certain stages of problems.  A few marks of chalk might represent dozens of pages of calculations if done in detail.  Unfortunately its protrayal on television and in movies can make the field seem artificially difficult to outsiders.

 

A quick calculation showed the center of the Earth is about 1.4 years "younger" than the surface.²  Long lived radioactive elements at the core decay slightly less than their counterparts at the surface. I can still remember the "wow" in my mind as took a handful of M&Ms. A not very great fountain of youth is under your feet. Since then I've learned exercise and eating right are better approaches to aging.

 

Since then I've done a more accurate calculation.  The inner Earth isn't homogeneous.  I found an estimate of how density changes and came up with about 2.5 years.  The initial estimate was ten or fifteen minutes with a piece of chalk vs at least a day's worth of work.   In the process I found  time dilation due to special relativity was a thousand times smaller and reasonable to ignore.  Moving to the Sun I got about 30,000 years with the simple estimate for the Sun's density.

 

The more important point is many fields develop mechanisms for dealing with either too much or too little data by coming up with simple ways to reframe and think about the task.  I've seen it in math, art and sports and assume it's a common approach to playful problem solving - probably so common you don't think about it.  The playful and fun part is key.  That's a space where you can be creative. 

 

__________

¹ You can learn special relativity with high school math and a bit of logic.  It's not at all difficult.  General relativity, on the other hand, requires much deeper math.  And a tip.  "Down is the direction where time runs more slowly" on a t-shirt is a good way to find other physicists in a crowd.

The effect is known as gravitational redshift as you usually measure this by looking at frequency shifts.  Atomic clocks are so good these days that you can measure the effect in a lab by raising one a few meters.  

2 If you want the details send me a note. First derive an equation for the gravitational potential inside a homogeneous sphere.  Next think about the frequency of a photon in a gravitation well to get change as a function of change in gravitational potential.  Then it's just remembering some constants to get the number. 

 

 

 

making and sparking

"No - we took all of that out years ago.  It's just not relevant anymore."

 

Fifteen or so years ago I visited the local high school to see if they had an adult education program that would let me use the student shop.  We don't have enough space or cash for a proper shop at home and frankly I'm not that good at wood or metal working, but every now and again the urge strikes.  

 

I'm not arguing that shop class was well thought-out or even useful - it wasn't when I was a teenager - but there's something to being able to design and build something.  On my own I did build a few things:  a couple of telescopes, some amateur radio gear, model airplanes and a seismometer.  Although the attempts of a kid, they were enormously powerful learning exercises.  I learned how to solder, how electronics works at the component level work and a bit of practical optics.  I even got to the point where I designed a transmitter and a simple analog computer.  Commercial equivalents were better - they were designed by people who actually knew what they were doing - but I was learning the basics for design and that is much more powerful.  

 

In grad school the ability to design and build was essential - so important even the theory students had to learn a few basics..  I knew enough about electronic design, but had never done any metal work.  Metal shop was wonderful. The shop was well equipped and managed with expert help around most of the time. We were given a couple of simple projects.  Once you made those you had to show you could do it with greater precision.   We were finally given shop keys when  they thought we wouldn't destroy the machines or ourselves. They encouraged us to come in and play. 

 

I remembered a project in an ancient issue of Popular Science that fascinated me when I came across it in the library as a kid - a Stirling engine.  I decided to build one of my own based on a bit of insight into better materials.  The first was very inefficient - about 30 watts at the flywheel using a hot plate for a heat source.  A minor redesign moved it past 100 watts.  The design and construction was a wonderful diversion to the classes I was taking.

 

Times have changed.  While engineers generally know how to build things, Spending a bit of time teaching in Oberlin's Technology in Music and Related Arts I found art majors and music students more adroit at "making"   than computer science students.  Programming is clearly building, but it's useful to tie it to the physical world every now and again.  Some schools stress that more than others.

 

It doesn't happen often, but when someone mentions their kid is interested in learning about computing I recommend simple inexpensive computing modules that interface with the real world.  Arduino and Raspberry Pi for example.  An enormous amount of "how to" videos and documents exist and beginners can start with very cheap kit. They can have quick success getting something working from cookbook like plans.  At first no real skills other than patience and the ability to follow instructions are necessary.  Then, with the application of curiosity,  learning begins,   You change this and that to change what it does.  You can write simple or complex programs and you can buy interface modules, usually called shields, that  interface with the outside world.  

 

People with that spark - the desire or need to do something they can't go out and just buy - make this interesting.. A dance major at Oberlin learned about Raspberry Pis in her computing for arts class.  She sewed an accelerometer to her leotard and connected it to a raspberry Pi on a belt.  Information was liked to her laptop via by bluetooth.  For fun she connected it to lights that changed color with changing acceleration.  A friend on the women's softball team saw it and thought it would be useful in pitching practice.  Another version with software tuned to the needs of softball was built and the coach is thinking. Of course you can do this with an Apple watch, but its much more difficult to make it do just what you want and this way you develop a deeper understanding. 

 

And so these things go..  Which brings me to something exciting.

 

People who build and design get good at it with practice and are on the lookout for new challenges.   A few of you may be familiar with Panic - a tiny company that makes a few very nice applications for developers.  They're profitable by themselves but use some of that profit to fuel their need to explore.  A few years ago, out of nowhere,  they came out with a video game called Firestarter.  It wasn't one of your multi million dollar developments, but many people loved it because it was beautiful, clever and absorbing.  They more than broke even which wsa good enough. There has been anticipation about another game in development called the Untitled Goose Game.  But again out of nowhere came something completely shocking and wonderful.

 

Hardware

 

These guys decided to build a minimal hardware game player called the Playdate. People who have seen it seem to be somewhere between excited and ecstatic. 'Impossible to resist' keeps coming up.  I won't go into details because I'm not a game player and I don't know much other than  care appears to have gone into every step of development.  They even wrote their own operating system. (that actually makes more sense than Linux for a very small game).  They made it for themselves because it was a challenge they couldn't resist.  Maybe it will break even, maybe it won't, but it won't break the company if it flops.  I'll probably get one and I'm not a gamer.  

 

People sometimes ask me why I'm passionate about a few odd things that not many other people find interesting.  Many of us have a spark - a playful spark.  They're all different and that's wonderful.  Some of us aren't very good, others are the opposite, but that's not why we do it. We may or may not get paid, but that probably doesn't matter much.  Sometimes I think it's better to not be paid as there's more freedom (assuming what you do is cheap).  Often you find yourself learning a variety of things you never thought about as part of pursing your spark.  In my case that can mean designing and building.  I'm not very adroit at that part, but it's a useful tool and I slowly improve with experience.  I'm in awe of those who thrill to be beauty of creating design and objects.  

 

About fifteen years ago I found a poem that sums it up .. 

To be alive: not just the carcass
But the spark.
That's crudely put, but…
If we're not supposed to dance,
Why all this music?

                - Gregory Orr

 

it's switches all the way down

The other day I saw something that a few of you might want to consider for a kid or even yourself - the Turing Tumble Mechanical Computer.  

 

It turns out digital computers are mostly switches.  A lot of switches these days - perhaps a trillion in your smartphone. As a teenager I built a very simple relay based digital computer based on a column in an old Scientific American. Later I built an updated version that substituted transistors for the relays using some (free) components from the high school physics teacher.  

 

Playing with these beasts is an excellent introduction to understanding how logic circuits work.  You'd be surprised how many computer programmers are hazy on the subject (of course they work at a level of abstraction far above the silicon - or what old timers called the iron).  The early machines of the 30s were very important and set the stage for the dramatic developments that followed.  Here's an outstanding non-technical short history of those early days. (recommended!)

 

But back to the Turing Tumble.. It's limited, but that's central to its beauty.  The instruction book has about sixty examples to play with and an aha! just might strike leading to out-of-the-book insights.  

It's also great to play around with extremely simple silicon digital computers - particularly those that you can hook up to sensors, lights and other interfaces to the real world.   But getting down to the basics is usually a paper or YouTube exercise or, if you want to do it yourself,  a frustrating experience involving a lot of soldering and a non-trivial amount of money.   The Turning Tumble might be just the ticket.  It is play and that is the best way I know of to learn. I didn't have much of a chance to play with it and can't do a thorough review, but I'll probably end up buying one to give to a kid.  The caveat is that you have to spend some time with it to learn.  If the user doesn't find it fascinating enough to devote time to there won't be any learning.  But the same can be said about so many things.

 

The education link on their site has the following in addition to a set of resources:

 

Appropriate Age Range

Turing Tumble is for ages 8 to adult - and that is not a stretch! We find that kids 8-12 are able to get through the first 20-30 puzzles. Adults get addicted by puzzle 27, and their minds are blown by puzzle 35. Younger kids enjoy the first 10 and building their own computers.

 

 

hacking your vision

It was really stupid - not quite Darwin Award stupid - but close.  Now that my parents are gone I can write about it.

 

As a teen I became fascinated with the sensitivity of the human eye.  It turns there are a lot of tricks you can use - I've written about playing with a few subtleties of your color vision to see colors in the night sky as well as my practice of night walking on dark nights without a light.  Moonbows (like a rainbow, only from moonlight), very dim luminescent beetles, the phosphorescent decay of organic matter in still ponds and the reflection of light from the eyes of animals in starlight.  There is a certain thrill in tapping your inner owl and walking around in near darkness.   If you're a bit on the teenager side of the risk curve you can try running or cross country skiing without lights.  And then the stupid thing I tried.

 

The night was exceptionally clear with only starlight.  The hills were just black regions without stars.  Night walking had opened up part of the outdoors I didn't know, but it made me wonder.  Armed with a brand new driver's license and my Dad's old Ford Falcon,  I had driven North of town past Benton Lake on Bootlegger Trail  - far enough to be away from the light glow of town.   I pulled over to the side of the road, taped over the instrument panel so none of the light came though and let my eyes adjust to the dark.  I started the car without the lights and used averted vision to drive.  It was easy to see where the road and even the center stripe was, but everything went away if you accidentally slipped and used the center of your eye.   That's the hard part - you see a something and tend to focus on it.   Suddenly your sensitivity drops off to less than a tenth of a percent of what it was and everything vanishes.

 

I probably drove that way for three or four minutes at up to thirty miles an hour.  I did it again about a month later with a friend.  He didn't have experience with averted vision so he didn't try, but I had a witness. 

 

Don't ever try anything that stupid!  But learning how to use your averted vision is a nice way to extend your view into the natural world.  The world becomes a richer place when you learn how to see it a bit different.  It is one of my forms of travel and particularly interesting when I'm visiting dark places for the first time. 

 

You have three flavors of cones that are each sensitive to different "color" ranges.  A total of about seven million and they're mostly in an area called the fovea near the center of your retina.  There are also rods.  One hundred and fifty million - approximately a boatload. They're generally more than a thousand times as sensitive than your cones  and in some cases can be sensitive to individual photons.  Learning how to use just the cones is the trick.  

 

The fovea is small and densely packed giving you your detailed and color vision.  It's what you usually think about when you consider vision.  At it's center is a very small region about the size of a small dot of ink - about 0.3 millimeters or 300 microns.  The thinnest blonde human hair is about 40 microns in diameter and the coarsest black hair about 120 microns, so its really small!  It's all cones.  If you plot the density of rods and cones on the retina going radially out from the center (the fovea centralis) you see the density of cones drop dramatically around twenty degrees out.  The density of rods, on the other hand, is very low inside this area, and rapidly increases to a maximum around 20 to 25° out and then slowly drops off.¹  Averted vision involves looking away from the center part of your vision.  Ideally you want to be looking at least twenty five or so degrees out.  Further out the density drops, but not that fast..  I aim for about 40° to prevent accidentally falling back into central vision.  I can't do it without biting my lip - find your own technique:)

 

You can also use a camera to extend your range.  Serious photography forces you to take careful note of what's in an image and you have any number of adjustments to  play with. You can play with different wavelength ranges and see what is normally hidden to us.  I like to play with different slices of time from  tiny fractions of a second to minutes long.  

 

We have fireflies around here in the Summer. Here's a simple 30 second time exposure.  (f3.5, ASA 400 for what it's worth).  Flashing signatures vary with species and I've found four in our area. It is relatively straight forward to analyze the signals and do serious observation.   For something so beautiful it isn't deeply studied as one might think so you might discover new behavior!

 

Before stopping it seems reasonable to mention you can hack how your mind synthesizes and uses the vision it generations.  Our brains turn out to be quite "plastic".  Usage patterns can create new connections and destroy old ones.  Playing a musical instrument develops certain regions in the brain as does speaking multiple languages fluently.  Certain types of online interactions are currently under heavy study - it appears that multitasking leads to different neural optimizations along with easily finding answers without reflection.  Jheri is mostly deaf - I've never met anyone as visually aware.  She does an enormous amount of visual tracking and lip reads to the point where you don't realize she's hearing impaired.  

 

Sports are another way to hack your sense of the world.  People who are good at sports that require "field sense"- knowing the position and movement of others on the court and field- develop certain regions associated with orientation, but on a massive scale.  They're doing it for multiple moving objects.  I wonder if some people who are wonderfully athletic but aren't very good players in field and court sports have problems with this? (of course there are dozens of other areas that must work well too) 

 

All of these changes seem quite normal to their owners - after all, we can't easily know what someone else experiences.    A lot of questions arise.   A few months ago a reader mentioned she was interested in how smell interacts with the body.  It is certainly part of our interoception system and represents a nearly blue sky research area.  There must be room for hacking.   I've been talking to a neurologist and reading about dogs.  But I'm out of time.

___________

 

¹ the heights of the curves are different, but you get the idea - artistic license:-)  This is from memory, but in the ballpark.  

 

 

playful thinking

There is this dairy farmer with a problem.  He's tried everything he can think of, but milk production from his herd just won't budge.  The dairy new online push hormones, but no ..  it was time for something unconventional.  He hired three consultants - a mechanical engineer, a psychologist and a physicist.

A week went by and the engineer came back with a stack of papers.  The problem, according to the engineer, is the farmer's milking machines don't develop enough vacuum and the tubes to the storage tank have too many bends.  A special machine is proposed, but the farmer decides to talk to the next consultant.

The psychologist takes a lot of photographs and makes some sound recordings.  He compares these with those of benchmark barns and after a week reports the barn is too disorderly and the sounds from the nearby highway make things worse.  The recommendation is to hire an interior decorator and subscribe to Moozak.  

Nope .. time to listen to the physicist.

The physicist listens to the farmer describe the problem.  "hmmm..." she says as she pulls a half used Fieldnotes pad, pencil and slide rule from her backpack.  Gazing up at the sky focused on nothing in particular she says...

consider a spherical cow

 

You've probably heard some variation of this.  I like it as it describes how a lot of physics is done.  Physics and the other sciences are usually poorly taught - it's anything but facts and equations to memorize and somehow apply.  Rather it's mostly play at it core - at least how you think.  You strip away anything that isn't necessary and see what you can learn.  If the answer doesn't make sense you try a different approach.  The trick is knowing how much to strip away and what to leave in and how to mix in other questions along the way.  Ideally you're left with new insight.

 

A regular reader told me he was curious about my thinking process and asked if I could describe it.    At first I ignored the request, but then decided to give it a try with a little real time play. Using the spherical cow joke as a seed I took a walk with a very smart friend as a sanity check.  This isn't a transcript, but here's roughly how it unfolded.

 

First let's draw a picture of a cow.  Consider a spherical cow of radius 1.  I don't care what the units are and for now a sphere is the simplest shape to get started with.

Now draw another  sphere of radius 2 - this will be our gigantic cow. What kind of milk production can we expect.  Any linear dimension will be twice as big so we can see if barn door heights and widths will work.  The udder will be part of the sphere.  It will be 8 times as large as the regular cow ..  the volume of any part of the cow scale as the radius cubed - it doesn't matter what part of the original spherical cow I choose, as long as the part on the larger sphere has the same shape, its volume will be r³ or 2³ = 8 times as much.

Already a problem looms.  What is the pressure in the udder?  Pressure is just a force spread over an area (think pounds per square inch).  The force in this case is the weight the udder has to support, which increases as the cube of radius. The area of a section of the sphere is  4πr² times the fraction of the sphere the udder takes up.  Now the udder fraction and the  4π are the same for a spherical cow of any radius.  We'll be comparing the two by dividing so they'll cancel out.  The pressure will be proportional (a physicist would say "goes like..") to r³ divided by r² -- or just the radus r.  Our giant cow has twice the pressure on it's udder as the standard cow.  This may be a serious cow design problem and we would need to know more to make progress.  But it gives a hint of another direction.

 

Now draw a more accurate picture of a cow and giant cow.  A small sphere connected by a cylinder to the larger sphere. What about the force on the neck?  The important innards of the neck are the spine and muscle. Strength goes as the cross sectional area.  So if the double sized cow is a perfectly scaled version of a regular cow, it's neck will be r² or 4 times stronger.  It must support itself and the head, both of which will see their weight go up by the cube.  The ratio of weight to strength is simply r or 2 in this case.  Another design issue for giant cattle breeders.

But what of really big animals - like a dinosaur?   If the head is much bigger than the neck it will be the limiting factor.  Imagine something like a cow scaled up eight times in length.  The head would quickly become too heavy.  Something like a big dinosaur walking on four feet with a long neck would need a very small head.  

Now it's clear why the dinosaurs went extinct.

Their brains were too small. This handicap meant they never developed a space program and were unable to deal with the asteroid. 

 

Of course this is tongue in cheek, but this sort of playful approach is exactly how a lot of physics gets done.  As you proceed detail and more critical questions are added.  One gets to point where measurements of Nature are needed and then you see if you can predict -- if not it's just storytelling and not science.

 

Back to the example.  It's an interesting approach to begin thinking about sports.  What kind of body types are more suited to one sport or the other?  People on the list range in height from something under five foot zero to six foot eight.  One might consider gymnastics and the other basketball or volleyball.  Neither would be a good distance runner...  Soon you need to drill deeper, but the thought process stays the same.  As detail enters, calculations need to be more robust.  The observation and experimentation part can be very difficult to implement.  LIGO - the twin observatories for measuring gravity waves are simple to describe conceptually, but making it work took over thirty years of hard work and invention of new instrumentation and techniques (some of which has had impact in engineering and medicine).  This simple concept is a few minutes at a blackboard with no equations and a string of playful questions eventually led to an entirely new form of astronomy.

 

The approach works in many areas where there is enough information to form some kind of a question - often one that sets limits.  There are times when an hour of thinking gets you within a factor of two of a difficult problem that requires huge resources to answer to any precision.  This is a good way for picking paths to follow.  I've been called on to do this in scenario planning style exercises.

 

And for fun ..  what about the folklore that the breath you just took at least one molecule from Julius Caesar's last breath.  A minute or two of thinking gives the answer, but it raises some really interesting questions about the atmosphere..  The first time I thought about the problem as a teenager I was struck by the notion that the atmosphere for a plant is like a salty sea and the thirsty sailor.  That leads you to think about fertilizer and the enormous scale of the process - probably the primary reason for the planet being able to sustain more than two billion people.  Then you think about the energy costs and other natural limiters.  This style of thinking is a great exercise for anyone who likes to discover dot connections.

 

Clearly one doesn't do this all the time, but it's great fun and I encourage folks to try it out. When you do it with others it's not brainstorming - brainstorming doesn't work.  Rather it's a form of play.  It can get addictive and can be physically dangerous for those of us who can't walk and chew gum at the same time.  I naturally fall into this with one of you who has saved me from Manhattan traffic on several occasions.  

 

 

 

23 1407

A few years ago I was walking through the parking lot of JPL in Pasadena when a license plate caught my eye.  It took me a few seconds to figure it out, but it had to be a vanity plate and one I wouldn't mind having.  I pointed and exclaimed something like 'how brilliant' to a rather perplexed friend.  Just a few days ago someone set a rather amazing Internet ad.   It had an easter egg that grabbed my eye for the same reason, although this was much more explicit.  There is a connection between the license plate and the ad.  I'll get to that, but first I need to talk about some playful tools that physics and astrophysics types use.  

 

Any sort of creative work needs a playful component. Its how you develop your intuition.  I'm sure many fields have their own power tools for play and you may want to think about yours as mostly they are so natural that they become part of how we think.  You need to try and discard a large number of ideas without fear of failure. Some of these can be rather silly.  Often you build toy models in your head or at the blackboard.  Typically they aren't practical ..  if someone were to ask how many cattle are required to provide shoes for New York City you might say to yourself 'consider a spherical cow'..  Physics problems tend to exclude much of the real world so you can focus on just the bit of interest.  Mental or blackboard math rules.  You aren't worried about exact answer.  I love the power of computer simulations but anything you have to type into would just slow you down and break the flow during the play stage.  You want to create little visual models that seem like an extension of your mind so you can dance with them.  People develop a certain affinity for numbers and you carry around a few rough rules of thumb.  Things like π² ≈ 10 to about 1.3% .. when you're only worried about 10% errors the arithmetic is easy.  Some bits of Nature are stored in this fashion:

 

° there are π × 10⁷ seconds in a year to better than a half percent

° the speed of light in a vacuum is close to 3 × 10⁸ meters/second.  An interesting coincidence is the original definition of a meter was 1/10,000,000 of the distance from the pole to a point on the equator. Distances can be measured in the time light takes to travel the distance.  We're used to light days and light years, but light goes about a foot in a billionth of a second or a nanosecond. A very tall friend sometimes gives her height as six and two thirds nanoseconds .. about the time light takes to traverse her length.¹ 

° a light foot is sort of practical when thinking about connecting parts of a computer.  If modules are separated by 10 feet, a delay of at least 10 nanoseconds is introduced.  This gets interesting when you're using a lot of fiber optics or physical wire as the speed of light is slower.²  The speed of light in the fiber is about 2/3s that of in a vacuum or air.  A signal will traverse 1000 km in about 5 thousandths of a second, while a radio wave going through the air only requires  3.3 thousandths of a second.  A very long time for a computer.  The difference was large enough to justify the construction of a specialized microwave network between Chicago and New York City to give some traders an advantage based on the difference between the index of refraction of air and optical fiber. 

 ° the acceleration caused by Earth's gravity is denoted by g and is roughly 10 meters per second².  It varies depending where you are on the surface, but unless you want to weigh a pound less or more, the rough figure works for quick calculations.  

° the diameter of the Sun divided by the height of a person is roughly the same as the height of a person divided by the diameter of a hydrogen atom.

° it takes about 500 seconds for light to travel from the surface of the Sun to the Earth

° photosynthesis in crops and trees is usually under 0.5% efficient

° a cow requires about 10 times as much energy as the plants it eats to produce the same amount of energy 

° ...

 

There are hundreds of little relations like this and a few curious numbers too.  One of the most famous is the fine structure constant which describes the strength of electromagnetic interactions between charged particles.  It is close to 1/137 and appears in enough calculations that every physicist knows it.  If you want to flag one down in a stream of people (airports for example), just write 137 or 1/137 on a piece of paper and hold it in view.  I've experimentally found this to be remarkably effective.

 

Some of the relationships aren't directly connected with Nature, but are just fun and sometimes are even useful.  There are too many to list, but here are two..

 

° e is the base of the natural logarithms and is of fundamental importance to economics and science.   It happens to be irrational and transcendental, but the first few digits are easy to remember:  2.7 1828 1828 45 90 45  (1828 repeats twice, and the angles in a right angled isosceles triangle)

° of course there is Hardy–Ramanujan number.  The story goes that G. H. Hardy was visiting his friend and colleague Srinivasa Ramanujan in the hospital. He had ridden in cab number 1729 and remarked that it was such a boring number.  Ramanujan counted, pointing out that it was the smallest number you can express by cubes in two ways:  1³ + 12³ and 9³ + 10³.  This has slipped into popular culture and has appeared in both the Simpsons and Futurama in the form of easter eggs.  But then again some of the principals of those shows are mathematicians. 

 

And number on a taxi brings us back to the number on a vanity plate.  My eye was probably caught by the initial 23, which happens to be my favorite prime, but  it looked suspicious - something close to 20 plus π ...  I remembered e^π - π is just a bit less than 20.  The number on the plate had to be an approximation of e^π.  The connection with the ad is perhaps the most beautiful relation in mathematics : ³

 

e^iπ + 1 = 0

 

While e^π isn't the real thing, it is suggestive enough to bring a smile.  Of course there is the possibility the owner just considered e^π cool without thinking of e^iπ, but this was the JPL parking lot.  

 

If only vanity plates allowed superscripts...

 

 

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¹ again an approximation.  If you want to do this more exactly the speed is about 0.984 ft/ns .. 

² the speed of light in a material is c/n, where n is the index of refraction.  n is close to 1.0 for air, but about 1.5 for optical fiber

In physics experiments signals are delayed with respect others to make logic gates work properly.  You develop a sense that 8 inches or 20 centimeters is about a nanosecond in coax.

³ It links the two most important irrational numerical constants e and π, number i which is the base of the imaginary numbers which gives us complex numbers, the additive identity 0 and the multiplicative identity 1.  It also answers the question "how many mathematicians does it take to change a light bulb?"  Then answer, of course, is -e^iπ...   

If it seems strange that the exponential of a complex number could be equal to 1, consider what the number e is.  It is closely related to compound interest ...  e^z is the limit of (1 + z/N)^N as N goes to ∞. If you set z = iπ and do the math you get -1 + 0i or just -1.  Here's an animated gif: 

 

 

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Recipe Corner

 

Caramelized Carrots

 

Ingredients

 

° 3 pounds of carrots - go for the fancy colored ones if you want it to look good

° salt and freshly ground pepper

° 2 clementines or one large orange

° 1 tbl red wine vinegar

° 3 tbl butter or vegan margarine 

° half a bunch of fresh thyme

 

Technique

 

° peel the carrots. you can quarter of halve them, but if they're pretty whole carrots with a bit of the tops on are beautiful

° put carrots in a large pan and just cover with water.  Add a bit of salt and ground pepper and the clementine juice, the vinegar and butter

° bring to a boil and cook until nearly all the liquid has evaporated

° add the thyme sprigs, reduce heat to low and cook for about 5 minutes to caramelize 

 

a legacy behind and beyond a legacy and an exhibit

In 1958 Willy Higinbotham of Brookhaven National Laboratory cooked up a bit of kit and created Tennis for Two - perhaps the first video game to engage kids at a laboratory open house. 

 

Peter Takacs of BNL has recreated the game for exhibit. If you are in the area catch it at the New York Historical Society through April - the history of technology created in the New York City metropolitan area.  

 

Although interesting and cool, it is unfortunate this has become his legacy.  He was head of the instrumentation division at BNL for many years and was responsible for a large amount of innovation in high energy physics apparatus - innovation that had a profound impact on medicine and other aspects of human life.  He was also a passionate force for nuclear non-proliferation.  As a young scientist he was part of the Manhattan Project and, like many others, pushed for the elimination of the weapon.  He went beyond the ordinary and cofounded the Federation of American Scientists.

 

 

The spinoff from experimental physics has been enormous. Physicists have to invent techniques to make their measurements.  Although developments are often a historical chain, most of the instrumentation used in medicine has a direct link to physics.  In the past few decades medical imagining comes directly from nuclear and high energy physics techniques.  Perhaps the most direct example is positron emission tomography which was largely developed at BNL. 

 

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recipe corner

 

This was really good, but I have a weakness for sweet potatoes 

 

 

Sweet Potatoes with Mustard

 

 

Ingredients

 

 

° 2 large or 3 medium sweet potatoes

 

° 2 tbl vegetable oil

 

° 1 tsp brown mustard seeds

 

° 1/2 tsp cayenne 

 

° 1/2 tsp tumeric

 

° some chopped fresh cilantro - one or two tbl

 

° salt

 

 

 

Technique

 

 

° bake the sweet potatoes in a 350°F oven for about 30 minutes.  Let them cool a bit, peel and cut into half inchish chunks

 

° fry the mustard seeds in oil in a skillet on high heat until the seeds begin to pop.  Cut the heat to medium 

 

° mix in the potatoes, turmeric, cayenne and salt to taste

 

° cook about ten minutes until a crust starts to form. 

 

° garnish with cilantro