omenti

repairability

Growing up our family always had Fords.  For most of grade school through junior high that meant a blue Ford Falcon.  My Dad's reasoning was simple - a neighbor had good mechanical experience with Fords, particularly the straight-6 engine in the Falcon.  He also had a nice set of tools. Much of it was simple enough that I was involved in part of the routine maintenance even before I had my driver's license.  Simple things like changing the oil every 1,500 miles, gapping and replacing the spark plugs, making sure the battery levels were ok, draining the radiator, testing and replacing the antifreeze, and taking off the air cleaner to spray ether in when cold-starting it when it was below -20°F.   

 

By the time I was driving legally  (I drove a pickup on a wheat farm during harvest the year before I had my license. I suspect that was common in Montana.  Learning how to drive a manual transmission amounted to me trying to not stall the pickup while my boss watched laughing for an hour.)  By high school I graduated to more sophisticated work.  Replacing the head gasket on my own and even replacing the rings under the watchful eye of my Dad's friend.  Everything was exposed and simple - most of it was just sorting out fuel, air and spark.   Sometimes, driving to King's Hill on a hot Summer day, the engine would quit.  That meant pouring some cold water on the fuel line near the engine and waiting a few minutes to break the vapor lock.  Each car had a set of peculiar tricks, but makes had personalities.  Changing to a Chevy or Dodge would have a learning curve.

 

While the Falcon was simple and to work on, almost everything was poorly made.  Perhaps not to the eye, but tolerances in the engine and transmission were sloppy.  A careful break-in period was necessary if you wanted an engine and transmission to last.  It was inefficient even though it didn't weigh much by today's standards.  Although it was a compact, it only got 18 miles per gallon on the road and 13 or 14 in town.  Engine and transmission oil had to be replaced regularly.  Tires went about 10,000 miles if you were lucky, brakes needed adjustment every few thousand miles, the chassis needed lubrication regularly and so on.  The body and chassis designs were primitive and non-crashworthy by today's standards.  Cars often remained fairly intact even in fatal collisions.  

 

The seventies brought more efficient designs along with increasing safety regulation.  More sophisticated tooling that produced dramatically improved engine and transmission tolerances that allowed more efficient designs.   They lasted longer, but it was becoming difficult to work on them.   Repair was moving towards replace.  The failure of a wiring harness on the mechanism for an electric window might be a fifty cent part, but the replacement module could cost hundreds and require several hours of work to replace.

 

Home electronics followed a similar path.  Our first TV was a 19" black and white Magnavox from about 1961.  It had a few dozen tubes, a lot of point to point wiring and hand-soldering, and mechanical switches.  If something went wrong the first step was to take off the back of the set and see if any of the tubes weren't glowing.  You'd pull the suspect out and test it at the local drugstore - most had a tube testing kiosk with a stock of replacement tubes.  That happened a few times before we got our first color TV in 1969 - a Motorola "Quasar" which only had two tubes including the picture tube.  It's main selling point was reliability. By the 80s integrated circuits began to invade home electronics and home repairs became next to impossible.  It didn't matter as we perceived our devices were improving faster than their failure rate.  Prices dropped so rapidly that throwing them away became popular.

 

This replace rather than fix mindset applies to many consumer goods, and many aren't engineered for a long life.  During the pandemic our eight year old refrigerator failed.  I was able to get it working again in about a day, but the repair was anything but easy.  The dishwasher also failed.  A gear on the motor, but the replacement module was $260 and special tools are required. It was eight years old so the leap to a new unit was an easy choice.  I probably wouldn't have tried to repair these things if I didn't have the background of repairing things that broke at home.

 

Ten years ago a mechanical engineer friend thought there might be a market for simple good design and quality manufactured items - mostly home appliances.  They would cost more, but last twenty or thirty years and be easily repairable.   He built a few prototypes, but was laughed at.   It turns out we're mostly ok with disposable.

 

The design integration in most smartphones and watches makes repairs difficult.  If compact, rugged and waterproof are goals, replaceable batteries are an issue even though you may need to replace them every few years.  A cynic might say it gives the user a push to get a new device.  

 

More important is the level of software integration across the system.  Apple's walled garden is problematic for many, but the value of more security and privacy (assuming you don't live in China), and mostly well-behaved apps is worth it to many.  Trading price and flexibility for stability and privacy.   

 

This raises the question of what should we be using?  Cars are much safer and efficient, although more expensive to operate, consumer electronics are mostly better and much cheaper.  Thinking of different ways to do things probably makes sense.  Getting rid of a second car and adding an electric cargo bike if your roads are safe enough is an option.  Three very sophisticated friends have traded their smartphones for simple "dumb" phones.  Well-made and designed clothing that lasts a decade.  Not everyone has multiple choices, but the pandemic seems to have people questioning many things. 

 

I'll end with a recommendation that applies almost universally..  staying away from IoT (Internet of Things) devices makes a lot of sense unless you know exactly what the security and privacy issues are in each case.  

 

 

 

bananas, bagels, pizza and gauss

minipost

I watched by the sidelines as a few people managed got in a verbal tangle about what makes proper pizza.  As the religious wars raged I remembered pizza illustrates a deep feature of mathematics - Gaussian curvature and the Theorema Egregium (remarkable theorem). It turns out you can get a good feel of it with a ball, banana, bagel and a slice of pizza.  

The always enthusiastic Cliff Stoll demonstrates:

 

Math, properly taught, is beautiful and not that hard ...  And go out and get some pizza.  I won't judge.

 

a congressman, the sun and the moon

Someone sent this rather bizarre segment of a Congressional hearing involving Rep. Louie Gohmert of Texas.  

 

Rather than being clueless about science (he may be that too), I suspect he's echoing some baseless claims used to claim humans have no impact on global warming.  While the orbits of the Earth and Moon are dynamic, they have no impact on current global warming.   That said, the Moon's orbit is changing at a measurable rate and that's worth a short post.

 

The Moon and the Earth orbit a common center of mass called a barycenter that's about 1,700 kilometers beneath the Earth's surface.  Seen from the Earth, the Moon's orbit is elliptical with a slight wobble. The gravitational interaction between the two bodies raises tides on the Earth, making our days longer and pushing the Moon out a bit less than four centimeters per year - roughly at the rate your fingernails grow. 

 

So the Moon's orbit is changing, but slowly.  Unchecked this process would continue for nearly fifty billion years when the Earth's day would have slowed to nearly fifty of our current days and the Moon would take the same amount of time to orbit the Earth.  At that point we'd be permanently locked with the Moon.  

 

Fifty billion years is a long time and something else will happen long before then.  About five billion years from now the Sun will become a red giant.  There are a few scenarios - here's my favorite.  

 

The Sun's atmosphere, as it heats and expands,  will create drag on the Moon's orbit bringing it closer to Earth.  There's a limit called the Roche limit to how close a gravitationally formed body can hold together before tidal forces rip it apart.  For the Earth-Moon system that's a bit under 19,000 kilometers (say 12,000 miles).  The Moon is ripped apart and scattersinto a Saturn-like ring that might stay around for a few hundred thousand years.

 

If the Sun keeps growing the Earth will eventually be in or near enough to its photosphere that the Earth would spiral into the Sun and be no more.   But that's a long time away.  In the meantime we need to worry about the here and now of global warming - perhaps not as dramatic as the ending five billion years out, but deadly nonetheless. 

 

are athletes getting better?

Olympic minipost

One of Simone Biles' floor routines as seen through a high speed camera. (go full screen)  Many sports have undergone dramatic changes in the past fifty years.  The introduction of springy floors and beams has allowed more dramatic routines that revolutionized gymnastics.  It's a sport where powerful muscles and a short stature are required. Simone's incredible acceleration combined with the strength to jump explosively and change her moment of inertia in mid-air give her claim to the great athlete of our time title.  At times she's experiencing g-forces usually found in aerobatic aircraft.  Here's a short video from Quartz (it won't embed) before the Rio Olympics  explaining a bit of what's going on as well as giving a sense of how far the sport has come. 

 

Three major innovations have changed elite sports - equipment, extreme specialization of body type to match the demands of specific sports, and a much larger gene pool to selection from.  David Epstein gave a nice talk about seven years ago touching on all three:

 

Many sports - particularly Olympic sports - lack the financial rewards seen in the top professional sports, but at the elite level it's clear the expanded gene pool has become important.  Of course none of this applies at the amateur level -  people find a sport or two they like and "just do it."  There's a lot of evidence continuing these activities has a huge positive impact on health - particularly as one ages.  It may be elite athletes encourage many of us to move.  Perhaps the endeavor is cost effective at the societal level - it's both desirable and part of the public health policy in Norway.

 

playing with dimensions

Many occupations develop tricks to get "good enough" answers question.  These range from rules of thumb to shortcuts that are based on some insight.  In physics dimensional analysis - checking to see the technique or answer has the right dimensions - is important. After all - you don't want to measure someone's height and come out with an answer in pounds.   

 

The common shorthand is to use square brackets to denote the dimension of a physical quantity.   For a distance r [r] = L, velocity [v]  = L/T, g (the acceleration of gravity) [g] = L/T².  Generally M is the dimension for mass, L for length, and T for time. 

 

With a bit of additional information you can make quick estimates and even gain some insight.  Consider two athletes of similar build and physicality, but different heights.  One is six feet tall, the other five feet.  If you want to compare the power to weight ratio all you need to know is the power a muscle generates is proportional to its cross sectional area.  Their weights scale as the cube of their height, so  [power/weight] = L²/L³ or 1/L.  The shorter athlete has a twenty percent power to weight advantage.   You can use this type of analysis and freshman level physics to sort out why different sports dictate very specific body types at the elite levels of sport.  

 

Techniques like these are used during the early and very playful part of asking questions.  They can tell you if your approach is plausible or if it's going to be wrong.  Plausible doesn't mean right, but it's very useful to recognize what can't work so you can try something else.  It's a lovely way to learn by failing gently.  With time and experience you develop an intuition for what might work. 

 

One of these quick calculations is legendary.  A series of photos of the Trinity after the end of WWII.   Four stages of the explosion with a length and time indicators.  Details like yield were classified.  A British physicist didn't realize calculations were classified and did his own back of the envelope calculation in a few minutes.  His estimate was published and caused a kerfuffle worrying that secret information had been leaked.  

 

There wasn't a leak. The truth is many of the physicists involved made quick estimates that were good enough - enough to tell them the device's yield was about what they thought it would be.  They just didn't publish for obvious reasons. 

 

Here's my ten minute estimate using dimensional analysis and a bit of physical intuition. I'm avoiding a very difficult set of differential equations with some very messy boundary conditions - not to mention some quantities I have no way of knowing as an outsider.  To make it as simple as possible consider a spherical blast. The ground will have a minimal on the radius of the blast in the atmosphere, so ignore it.  The blast creates an expanding bubble that has to push against air outside the bubble. The most important terms in any expression will include the radius of the blast, the density of the air outside the blast, and the energy of the device.  There are many other things going on - this is just an attempt to see if a very simple high level relation of the relevant variables can be found in a few minutes.

 

Basically rearrange these terms dimensionally to see if you can find radius as a function of time after the device was set off.   Remarkably a simple relationship emerges.  So why not plug some numbers in?   The time and radius can be found in the photos and the density of air is well-known.    My radius measurement is crude - I know the device was on a tower and found a point that looked like the center.. draw some lines on a piece of paper, put it up to the picture and estimate 90 meters... perhaps a bit less.  A bit of arithmetic and a yield of equivalent to fifty thousand tons of TNT falls out.   

 

(pardon the handwriting, but it's much quicker and more natural than trying to typeset it)

 

 

The estimate isn't that far off - it gives you a good sense how the radius scales as the one fifth power of the blast's energy and to the two fifths power of time.  Those relationships are more illuminating than the estimated yield.  Since there are four images you could do something a bit more elaborate measuring all of the photos and making a plot of the growth of the fireball. 

 

 

 

a shot echoed in the dark

   Our guide, the Director of Development for The Cleveland Orchestra, noted how difficult it was to find matching marble for the lavatories.   There were only two of us and we wanted to set up in the main hall, but impressions must be made and little was being spared in the big three year remodeling job. 

 

Cleveland's Severance Hall is a remarkable place.  A odd mash-up of Art Deco and Egyptian Revival architecture, it was finished during the Great Depression and became home to The Cleveland Orchestra.  Like many symphony halls the acoustics were bad boarding on terrible.  Remodeling a few decades later partly fixed the problem, but in addition to rendering the pipe organ unusable,  was architecturally "wrong."  The work underway when we visited would address all of those issues and make the space one of the best concert halls in the world. 

 

Our company was doing quite a bit with digital music at the time.  There was a relationship with the Rock and Roll Hall of Fame and another with the Oberlin Conservatory.  Two of us who were doing much of the Oberlin work developed a relationship with The Cleveland Orchestra and Telarc Records on the side.¹  At the same time work on sound field reproduction was a serious research topic.

 

The idea behind sound field reproduction sounds simple enough. If you've ever been around live music - or even in a recording studio - you've probably noticed your home equipment can't begin to reproduce the acoustic experience.  The problem stems from the fact that the wavelengths of the sounds we hear range over three orders of magnitude and much of it is similar in size to musicians, audience members, seats, curtains, the room itself, etc etc.  These sounds are reflected, refracted and absorbed.  Moving anything causes a change.  It's a difficult problem that the music industry and Hollywood would love to see solved.  Plus it's an interesting problem!

 

The approach we were using had a microphone array on a tripod.  One up, one down and an odd number between them in the same plane as the floor.  Severance was undergoing acoustic tuning and we were going to set up the array to record some music to compare it with other techniques.

 

We were left alone in the open hall. It was very quiet so I did the obvious thing and clapped my hands once.  There was a lovely echo coming from everywhere at slightly different times.   If we recorded an even better "clap" - an impulse function - we could mathematically play with it and create a signature of the room.²  Armed with this we could have some fun.  We needed to create a good enough impulse.

 

Severance Hall is on the grounds of Case Western Reserve University - a lovely area with good restaurants and a lot of art and music.  (if you ever stay in the area get a room in Glidden House - fantastic little hotel).  I figured the school probably had an athletic department and quickly found a track coach.  I was able to talk him into lending me a starter's pistol.

 

Later that night in the darkened hall a shot rang out - only to be captured digitally.  Then a few more just to make sure there was enough.

 

Back at the Labs we had a special acoustically isolated room - an acoustically neutral room (these are rare and not cheap!)   Using the same microphone array that was used in Severance Hall we recorded some live music with musicians in the area.  The music was convolved with Severance Hall's signature and then mixed down to six channels for playback in the room.  

 

It was fairly convincing..  close your eyes and it really felt like the place the shot rang out in the great hall.   Of course you can do better, but it was a great excuse to have a bit of fun.

 

__________

¹ Over the years I’d spent some time worrying about image and sound quality. At one point I thought better was - well - better. My epiphany came in the a perfectly restored 66 red Mustang. It was near Cleveland with the head recording engineer from Telarc Records and a seriously good musician from the Oberlin Conservatory. We were talking about where music reproduction might go with sound field reconstruction and dramatically more information than CDs could provide when a favorite Beatles tune came up on the 8 track (gasp! - it *was* an authentically restoration). The volume came up and the two of them were singing along to the music in pure delight. There is something transcendent about the music - even with awful reproduction in that noisy environment. Portable music players with cheap headphones would be good enough for most. As long as there's a personal touchstone.

²  take its Fourier Transform.

diving into boiling stones

The air you breathe is about 21% oxygen and 78% nitrogen by volume.  People suffering from serious Covid-19 need much higher oxygen concentrations to hopefully buy some time.  Hospitals need to keep local stocks of liquid oxygen or high pressure oxygen tanks filled to provide treatment.   Patients can be treated at home with a portable oxygen supply and lower the burden on the hospital.  Often this means oxygen concentrators.

 

Around 1800 a mineralogist noticed heating stilbite produced steam. The class of materials was called zeolites from the Greek for "to boil" is zeo and lite is a mineralogy shorthand for lithos or stone.  There are a few hundred such materials each with a similar internal structure or framework.  The framework creates tiny pores - pores that can absorb substances and even be used as molecular sieves.  Wikipedia shows a structure for a common zeolite called mordenite.  It's based on a silicate (SiO₄) building block - I show it as this framework is common to zeolites and there's a nice public domain image.

 

 

Now back to oxygen concentrators.  Rather than getting bogged down in their operation just note regular air is passed through a molecular sieve made out of a different zeolite that traps nitrogen and allows oxygen to pass.  Relatively inexpensive machines for home use can produce about 10 liters per minute of enriched air that is 80 to 90 percent pure oxygen.   These are regularly used by people who need oxygen therapy and have kept a lot of people out of the hospital during the pandemic.

 

A wonderful invention, but there's something extremely beautiful about zeolite.

 

Chemists and physicists have their own way of looking at its repeating framework - the one called the secondary building unit.  Mathematicians have their own interesting way.  To get there a bit of a digression is warranted. 

 

Take a deck of cards.  Assuming it's well shuffled (say a dozen shuffles or so) I guarantee the order of the cards has appeared only once and will never appear again.  The reason comes from the fact there are an enormous number of possible combinations of cards: 52!  (52*51*50 ...  *3*2*1) or something over 8 *10⁶⁷ unique orderings!  One way of thinking about it a mathematician might consider each possibility a point in a 52 dimension space.  It's a bit abstract as we are only used to three physical dimensions, so here's a way to think about these configuration spaces.

 

A mathematician looks at a cube and says "that's a three dimension cube..."  A square is a 2 dimension cube, a line is a 1 dimension cube and a point is a cube of 0 dimensions.  She can go in the other direction too..  4 dimension cubes and up.   OK - now back to the cards.  Take three cards labeled 1, 2 and 3.  There are six (3! = 6) possible orderings:    {(1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), (3,2,1)}  Make yourself a 3d grid with an x, y and z axis and plot the six points.²  Now connect them up - pretend you have a rubber band to snap around them.³ 

 

Sweet!  You get a hexagon.  Shine a light on it at the right angle and it will cast a hexagon shadow.  The combinations of the three cards are linked to a shape!  

 

Now take four cards labeled 1,2,3 and 4.  There are 4! = 24 possible ways to order them.  Plotting them on a 4 dimension grid doesn't work for our spatially limited brains, but if you do the same trick of connecting them up you get a 3 dimensioned gem-like shape .. the exact shape of zeolite's framework (the secondary building unit).  If we lived in a place with four physical dimensions the shape of that object would cast a three dimensioned shadow..  

 

Thinking about the structure of an important molecular sieve with four playing cards..  math can be a curious playground.

 

__________

¹ The repeating unit is fairly complex: (Ca, Na₂, K₂)Al₂Si₁₀O₂₄·7H₂O

² you can also do it with two 2d grids..  say x,y and z,y and see the pattern  

³ the convex hull

mother's day

She enjoyed having to wait.  People around her would become characters in stories she'd make up.  Story making was a hobby of hers.  Often she'd invite you to join in.  As you gained experience, she'd take greater leaps.  Simple things on the street would develop complex plot twists and even find themselves in other eras or places.  

 

She was a bit on the quirky creative side and some of that may have rubbed off on me and my sister.  Here are a few lessons I learned:

° It's good to have some boredom in your life. It encourages you to try something new.

° It's fine to not be great at something if you enjoy it.

° You need several very different interests because they'll have conversations with each other if you just listen.

° Don't worry about names and dates in school. "How" and "why" are better.

° chocolate is good, pie is good, ice cream is good.

° Your friends may turn out to be at least as important as your family.  Find the good ones.

 

We were never pushed to do homework school. My parents were busy enough that our upbringing was more semi-supervised free range.  There were a lot of books and trips to the library.  The reward for a good report card we'd get an ice cream cone from Dairy Queen.  Perfect marks scored a banana split or a milk shake.  And even if she didn't understand our interests, Mom would support us how best she could. 

 

When I was about fifteen I read Edwin A. Abbott's Flatland - probably the book that had the biggest impact on me until I went to college.  As I  described the world Abbott created, Mom ran with it and developed a richer story and asked some "how" questions.  Those questions started me down a path  that taught me a little engineering - subjects she was unfamiliar with.  I began to see the value of story telling - particularly those visual stories.

 

Besides stories she enjoyed drawing and painting.  She wasn't very artistic, but spent a lot of her free time at it.  I wondered why as my sister's art was much better.   Then I went off to collage and found myself drawn to sketching.  I'm terrible, but it's a form of play that can take me to a state of flow.  I realized she was probably doing the same thing.  My sister became an accomplished artist - some her pieces have been described as snapshots of quirky short stories.   She obviously picked up a lot from Mom too.

 

We celebrate those important ones through memories and  recognition of how they helped create who we are.  Even now I find myself watching people and imaging stories when I'm waiting.  She would have laughed at how unimaginative smartphones are.

 

Happy Mother's Day Mom.

 

objects and friction

Randall Munroe's xkcd is a necessary visit for anyone doing science, math, or engineering.   Artistically simple, he often sums things up with an almost poetic simplicity. Some have suggested topic ideas - he's taken two of mine and created beautifully distilled views of the underlying concepts that make me envious of his talent.  And he does it about three times a week.   Every now and again he creates something that resonates across a community.    It happened again last week:

 

 

Anyone who reads a lot of scientific papers recognizes this. Dozens of variations emerged overnight.  Some were very specialized - at least three relevant to astrophysics alone and I only know that because I know the community.    Here's one Abeba Birhane posted.¹

 

 

Serious truth!  A good deal of the community is this clueless.

It made me think of friction and objects.

 

One of the most remarkable features of physics is its simplicity.  While it may be non-intuitive and sometimes requires a bit of tricky math, you can remove complexity and discover underlying bedrock.  Once you understand the simple basics you can restore the complicating bits a piece at a time and describe a vast set of physical processes.  The fact that you can deconstruct and reconstruct so effortlessly is unique among the sciences.  It's why a physicist will tell you physics is the simplest science.  

 

Beyond physics complexity and emergent properties become important.  It turns out that asking "what is life?" is one of the most difficult questions. Working backwards from biology to biochemistry to chemistry to physics breaks down along the way.

But back to simplicity 

Students learning about motion and collisions start with a statement like "assume a frictionless surface."  Concepts become clear and it's easy to describe interactions where everything is understood.  Two blocks colliding elastically for example.  Later on you can restore friction.  Mechanical engineers, working in the real world,  are forced to deal with it.  In some of their systems - say a chain and gear bicycle transmission - it's possible to have efficiencies that exceed 99%.  Frictionless is the ideal here.  On the other hand you don't want frictionless tires or brakes - you'd never start and, if somehow put in motion, you couldn't stop.  The bicycle and road system is complicated enough that friction is good in places.  Fortunately good engineers know how to deal with such things.

 

The concept of "frictionless" has extended to interactions between computational objects and people.  In fact people are often treated as objects that contain a long series of properties.  Constructions like these lack the meaningful emergence that social creatures have. Serendipity and insight are often the result of social "frictions" in our interactions with other people.   We can have simple low friction interactions.  Sometimes they're great as we're not looking for much, but they're generally shallow.  A worry is large scale machine learning can create a faux sense that interactions with machines are deeper than they really are.  And many of these interactions are with other parties who make decisions about and for us. 

 

A few who build large scale social platforms have deep backgrounds in the social sciences and the humanities and think deeply about underlying social issues, but much of it is done without much clue by coders who build things quickly and then iterate to make them better - often more frictionless.  

 

Separately I had two wonderful reports from people at a very creative company.  Fully vaccinated people are back at the office with some precaution and maskless outside.  One reported she's had more insight and exciting ideas in the last week than in the last six months - largely through random talks with coworkers where they could "read" each other.  I hope all of you find the light at the end of the tunnel soon.

__________

¹ She's a cognitive scientist from Ethiopia who specializes in critical race theory - a rather important intersection these days.

 

 

 

the power of the liberal arts

a minipost

Tomer Hanuka of the School of Visual Arts in New York asked his third year illustration students to create a post-pandemic New Yorker cover.   Some of the pieces were so moving that he posted them on Twitter where they quickly went viral.   So viral that an article appeared in The Washington Post.

 

The power of art never ceases to amaze me.  I'm clearly not an artist, but think visually.  The few beginner art classes I had in school as a teenage played a big role in how I think abstractly.   I don't understand why art, and for that matter liberal arts in general, are on the cutting block these days.  Somehow they're not seen as relevant for the job market.  I think they're necessary if the student is preparing for life long learning.  Of course I'm biased as I was a liberal arts major (physics and math are liberal arts).

 

I've spent some time trying to link art and physical science programs in a couple of colleges. No details as it's been political and was interrupted by the pandemic, but I'm still enthusiastic.  The fact that one of the physics professors is in a rock band helps..