omenti

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.

 

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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 milk shake.  And even if she didn't understand our interests, she'd 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 playing with projects.  I wondered why as my sister's art was much better.   Then I went off to college and found myself drawn to sketching.   I was and still am 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 picked up a lot from Mom too.

 

We celebrate those important ones through memories and  recognition of how they helped us become who we are.  Even now I find myself watching people and imaging stories when I'm waiting and everyone else is studying their phone.  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.