omenti

stalking breadth and serendipity

Randall Munroe has this wonderful way of stating depth. (via his wonderful xkcd)

 

It's been fashionable to talk about information overload for some time, but the amount of information we and our machines make is almost infinitesimally small next to the amount information in the natural world. We don't directly experience the world. Rather we rely on heavily filtered senses to feed models our mind creates.  Even the stand types of information we rely on - images and sound - represent only a tiny bit of what's out there. 

 

We've become adept in building models to understand what's going on.  In the late 19th century a few physicists developed statistical mechanics - a mathematical construction that allows you to consider enormous numbers of objects (say the air molecules in a room) and be able to accurately describe what's going on as well as well as what will happen.  It was an enormous leap in thought that directly led to the development of quantum mechanics a few decades later. Here's one of the best introductions to a field I've seen in a textbook: from States of Matter - a sophomore/junior level text by David Goodstein. (image grabbed from the ebook)

 

Science has given us tools and techniques to extend our vision beyond our senses.  The development of lenses for microscopes and telescopes, judged by the avalanche of knowledge they led to, may be the most important invention of the past millennia.

 

We have a difficult time sorting out information we and other people produce.  Generally we use a combination of active and passive filters. These filters change with both experience and technology.  We often find ourselves cutting out more than we should. We often live and work in 'echo chambers', surrounding ourselves with information from similars.  Some sociologists refer to this as cocooning,  a term I prefer. Machine learning produced cocooning is very real and an active area of study.

 

A trick is to create active filters that provide breadth.  The one I practice is regularly read and talk to interesting people outside my area.  There are a lot of smart people out there who are willing to share, but there are a couple of tricks.  First you need to describe what you do in a manner that they can get a good-enough understanding.  They have to do the same.  This can be very difficult - it's like teaching an introductory course or writing a book and often, as a by-product, sharpens your understanding of what you do.  Second you need to develop a working understanding.  I find offering whatever I can bring to work on their problem to be both fascinating and useful. It's one of the main reasons why I tithe my time to 'help' others.  In fact it's a type of homemade university I've created.

 

These conversations or library ramblings sometimes break down.  The secret weapon, should you be lucky enough to know one, is a human impedance match.¹  The rare ability to ensure a good-enough two way information transfer.  I know of two (there may be more) on this list and feel lucky to know them. 

 

Sometimes you can put together a serendipity machine.  I've been around two - possibly three - so far.  A small group of people with a very wide range of backgrounds who know, understand and respect each other and their differences.  Put them in a comfortable place - face to face is important as a good deal of out of channel communication goes on - and let them range. The topics may be concerned with an engineering issue, but somehow jump to 13th century Sicily and that jump, realized a few months later, was the productive insight.  That group was in the spirit of Ted Lasso's Diamond Dogs, although it usually met on Friday afternoons with meetings the ran from four to ten hours.  It isn't terribly efficient, but can be fun and produce very interesting ideas and understandings. 

__________

Finally Pip talked about the need to communicate something positive as a counterpoint to the negative news and social  media message we usually get.   So here goes - a short story of great fun and imagination. Chivalry by Neil Gaiman. It must be listened to rather than read from the page. Only a half hour, the performance I recommend is from the Selected Shorts series with Christina Pickles doing the honors. Simply wonderful! About $3 at the Apple Bookstore and probably the same at Amazon.

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¹ I first came across electronic impedance matches as a teenage amateur radio builder and operator. Without going into detail,  a signal in the form of an alternating current usually has different values in different "boxes".  If  a signal goes from one box to another of differing impedance, there is a loss of signal.  An impedance match minimizes the loss of signal.  The example I fought as a kid was making sure the impedance of my transmitter matched that of my antenna.   (the same analogy works for power transmission)

A human impedance match often probes the two people figuring out what questions to ask and clarifications to add to increase the level of understanding on both ends.  It's a skill I work on, but still lack after all these years.

 

 

 

beyond david mackay?

a minipost

David MacCay was a remarkable fellow.  Curious and cross-disciplinary, he worked in applied math, physics and engineering research at Cambridge.  Passionate about doing something about global warming, he happened to be a great communicator.  I had a few interactions with him: first about thirty years ago playing with neural networks and later in the mid 2000s as he was putting together Sustainable energy – Without the Hot Air - probably the clearest book written on energy production and demand.  You can still buy the book and  proceeds go to support some good charities.  David updated the book online until his early death in 2016.  It's free online, but the printed version is a better experience.

 

The book is written at two levels - one for folks without a mathematical background and a somewhat deeper version that assumes an understanding of high school physics. David goes into depth building easy to understand models and then plugs in numbers from past and present technologies.  The last step is where the book is flawed.  Enormous advances have been made in solar and wind power technology and prices have fallen dramatically.  A few of David's conclusions relevant ten years ago are now dated.  For example he shows that wind power and solar are insufficient for the UK, even in an ideal world without existing infrastructure and bureaucratic inertias. The last two roadblocks still exist almost everywhere, but the underlying story has changed.

 

Brian O'Callaghan's group at THAT other English university have published an updated look at solar and wind energy in the UK and come to the conclusion that they are practical and nearly sufficient at scale.  Here's the summary of their policy paper.  Their technical papers are solid and thorough.   I suspect Sir David would be proud.

 

In addition to getting an important  update, there's an important lesson here.  When describing current and future technology scenarios it's extremely important to lay down some clear thinking that is largely independent of current and future inputs.  The basis of this type of scenario is really just a solid foundation that's waiting for inputs.   It's rare to see ones that work twenty or  more years in the future.   David's did and does... it just needed updated inputs.

 

 

 

gains and loses - should we have a choice?

In the mid 70s a young researcher at Waterloo named Janet Starkes had an insight that changed ideas about why good athletes are good.  It led to a a good deal of work on the acquisition of expertise. She had been a volleyball player as an undergrad and her familiarity with the sport led to her testing perceptual cognitive skills of volleyball players.  In the process she invented the occlusion test.    She showed players on the Canadian National Team brief flashes - sixteen thousandths of a second - of volleyball matches.  Some had the ball in the frame while it had just exited the frame in others.  The players had to say if the ball was visible or not.  Unskilled observers find the task is impossible - all you see is a brief flash of light.  Even studying the image for longer is difficult as the there's a confusion of visual information.  

 

The players were able to correctly score the images at a much greater rate than chance.  A few saw even more.  In indoor volleyball the setter is the person who directs how the play will proceed.   Good setters have what is often called court sense. Elite players seem to know where the players who are important to the developing play are and how they're moving.  This court sense has been measured in elite players in other sports like basketball, soccer, hockey, and cricket.

 

The occlusion experiments  have been repeated in sports like tennis and baseball to understand when a player knows what the near future may bring. They explain why Jenny Finch was able to strike out the best major league baseball players. They didn't understand her pitch and how the ball was moving - even though it was only traveling at 60 to 70 miles per hour. They were reduced to reacting to the moving ball - something that doesn't work in baseball. The elite players generally make their decisions on how to hit the ball around the time the pitcher releases it - sometimes just before.  Much of the information they use comes from observing motions that lead up to and are part of the pitch.  

 

Experiments with chess players show elite players can understand the board and how play is proceeding in a very short time even though, in theory, there are an enormous number of potential moves ahead.  When experimenters then displayed images of boards with impossible or extremely unlikely arrangements of pieces, the elites were reduced to the level of raw beginners.  Just like the major league baseball players facing Jenny Finch.   The view is the chess players and elite athletes break information down into something of a mental shorthand - "chucks" of information.  When they are presented with a chunk or series of chunks they're familiar with they know, usually without thinking,  how to proceed.  

 

The brain is "plastic."  It takes a good deal of time and effort to develop relevant neural libraries of these chunks..  sometimes a childhood of playing and learning at a variety of levels in many activities.  London cabbies are  interesting example.  It may not be the case now with GPS navigation, but cabbies had to pass an extremely difficult test of their knowledge of the city's streets that usually requires over a year of study. MRI scans show the cab drivers have a much larger portion of their hippocampus - an enlargement that came from that study.  Musicians show enlarged regions as do people who learn multiple languages at an early age.   It turns out early music and language skills are useful for certain types of reasoning, so perhaps it's good to encourage these skills.  Or maybe not.  

 

What does it mean when we don't develop certain mental skills - when we don't build the pathways.  It's clear I'll never play, or even react to volleyball at an elite level..  the wiring isn't there even if I had the physical skills.   But what if I had never learned how to navigate using maps and looking for signs in nature where I don't have maps.  There's some evidence those skills are very useful for grappling with geometry - particularly the more abstract kind math and physics majors see in college.  Will an over reliance on GPS damage certain types of abstract thinking?  Does it matter?  

 

As various forms of "AI" take over tasks will it free us for other forms of thinking, or will it damage our ability to excel in some areas?  It's speculation at this point, but given how difficult it is to get good at something and  that getting good at one thing can be useful in other areas, it strikes me as an interesting area of study.  Some technologies may enhance, others may handicap. 

 

And in some areas this chunking of information can get you into trouble when a novel approach is called for.  That's when broad and seemingly unrelated connections become important.  The folks who excel at this are deep enough library of chunks that they recognize this takes something else and manage to patch together something novel.    But that's another story.

 

 

 

when there is elsewhere

There haven't been any extensive use reports of the Apple Vision Pro, but most of the people who had a brief introduction walked away impressed giving a sense that this really is something new.  It's spendy by many measures, but supplies will apparently be heavily constrained as some components are both expensive and very low yield. But with its visual and sound field reconstruction capabilities, one set of use cases may involve real-time remote presence.  A court-side seat at a NBA game or something from a Taylor Swift concert come to mind.

 

But there are questions. Horace is one of the best Apple analysts out there as well as an all-around really smart guy. (If you're interested in tech or micromobility, you need to follow his podcasts, posts and live events.) He recently posted some thoughts on the value of remote presence and how it might be one of the  drivers for Apple's new device.  I would be really surprised if folks at Apple aren't thinking along these lines.

 

I sent a note to him that offered a little pushback that wasn't really pushback..  it's more that value of being there varies a lot and the same for quality of experience.  Sports and music are two very interesting cases.

 

Last night an indoor women's volleyball match between Nebraska and Oklahoma set the attendance record for any women's sporting event.  Normally NCAA games are held indoors in places that rarely seat more than 8,000.  High school and college women's volleyball has the greatest participation of any women's team sport in the US.  This wasn't an important match - Nebraska has a much higher ranking than Oklahoma and it's preseason, but it's an event.  There's a strong passion is that part of the country - one of you is well aware of it.¹ So 92,003 paying fans filled more than the seats.. about 10,000 had to stand as the football stadium was too small.  The view of action was probably terrible for most of the fans, but that wasn't the point.  All of those people in the same place sharing the same passion and seeing it roll out at the same time.

Here's the walkout video for a sense of scale

I'm a beach volleyball fan and regularly find myself waking up at two or three in the morning to follow a match with a player I know or a team I care about on the other side planet. The streaming is sometimes poor and costs $80 a year. Tickets aren't terribly expensive, but travel is so I haven't been to a large number of events.  The sport is extremely friendly, probably because there isn't much money in it, and talking to players and other spectators is at least half of it..  going to dinner with a couple of gold medalists isn't exactly an everyday event.  I wanted to go to Tokyo and had been invited as a friend of a Canadian team, but Covid.  Perhaps Paris. 

 

The BBC had a nice piece on why people care about games. It's a short and worthwhile listen.

 

So would I use an Apple Vision Pro if a steam that offered a court side view with good commentary existed?  Sure!  Well - maybe. How much would I pay?  That's an interesting question.  It would largely rest on how much the streaming experience was improved. It can't replace the physical experience of being part of an event.  It's interesting that American soccer (football to the rest of the world) sometimes go to bars to find a critical mass of likeminded fans when their team is playing.  And there are Super Bowl parties.  For a couple of hours what people do for a living, religion, political  views and so on don't matter.  There's a distributed group bonding.  Do products like the Apple Vision Pro augment or replace that form of interaction?  I don't think so, but I don't have a working crystal ball.

 

And there's music. These days it mostly falls into live streaming, on demand streaming, in person concerts and a small (but growing again) amount of collecting physical media.  The streaming experiences aren't great, but they're cheap with large (for popular genres) catalogs.²  I prefer small live music events. Not only do the musicians connect with each other and the audience, but the audience often connects with the musicians and that can be magical. Depending on the event the interactions within the audience can be important..  Taylor Swift concerts are a prime example, but many other musicians have similar or better "magic", albeit at a smaller scale. (I'd offer Yo-Yo Ma as an example).   

 

There's a scale for each person and each event on the importance of various aspects of these different takes on interaction and consumption. Radio and then television changed the values as did the expansion and, in some cases, contraction of live events. Streaming has made a difference, but it has so many rough edges.  I suspect Apple's new product may offer something very different that will once again bring some change, but probably not for some time.  I'm guessing we'll have a better idea around the time Apple Vision Pro 3 or 4 is announced, You'll know it when you can get NBA games through Apple Vision Pro + service for $20 a month:-)

 

But if anyone wants my reaction next Spring, just buy one for me and I'll review it:-)

 

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¹ Nebraska had two legendary players in the 2000 → 2010 era.  Jordan Larson and Sarah Pavan.  Here's Sarah's college record  and when her number was retired.  Both of them went on to illustrious indoor careers overseas and Jordan has been a key player on the US Olympic Team.  Sarah eventually switched to beach volleyball has had many honors including world champion and two time Olympian.  One of Sarah's awards was the Honda Cup in 2007  - the best college female athlete in any sport that year.  Shortly before the Tokyo Olympics the organization that presented the award interviewed her as part of their podcast series.

² In 1994 two of us probably hold the first time record for streaming non-trivial, live music at reasonable quality over the Internet.  A Utah Phillips concert from the Folk Project in New Jersey at 96 kbps stereo by bonded ISDN lines to a hub in Princeton where it went to the Net where a few people with AAC players could listen.  So I guess I'm familiar with streaming.  It was good, though (for those of you who get the reference:-)

 

 

on moving slowly with your eyes and ears wide open

I work mostly from home and have taken a long walk around noon in almost all forms of weather for the past 20 years.  We have the good fortune to live next to a forested swampy nature preserve.  Within a few weeks you begin to notice the changes in flora and fauna.  A few months and the beginnings of the seasons emerge.  Ten years and differences in the season seasonal patterns emerge and larger scale change shows itself.  

 

It didn't take long for me to appreciate we have six seasons in this part of the world - early spring, spring, summer, early fall, late fall and winter.  They've shifted a fair amount in the time I've been watching with the shift in animal life being alarming.  It turns out the indigenous peoples in the area counted six to eight seasons with six being most common.  Recently, after hearing a piece on two-spirt people in First Nations Peoples and learning the Cree recognize at least twelve genders, I started wondering about the seasons question.

 

As far as I can tell the Japanese calendar used for over 1,000 years until 1872 is the winner.   It referenced seasons and microseasons local to Kyoto.   24 seasons which were then broken further into 72 kō.  It gives a very slow and rich way to observe nature around you.   I love some of the descriptive names:

It's Suzukaze itaru or cool winds blow as I post this.  In two days Higurashi naku or evening cicadas sing begins.

I've started to break down my notes into week long segments to be more sensitive to the longer term change.  Of course the real reason is to move slowly with your eyes and ears open, because we tend to overlook what surrounds us. 

 

spoken, written, and semi-spoken language

a minipost

My wife thinks it's funny when I'm talking with a native-speaking Montanan. After about fifteen minutes my accent shifts towards my almost hidden native accent.  It's still there,  buried under so many years living out of the state.  The funny thing is neither I nor my Montanan friend notice what's happening.  Similarly I can code-switch and fit into the culture of my parents church - at least over the phone as my beard and dress don't conform with the standards. 

 

In high school I spent a lot of time in Alberta and became fascinated by Canadian English.  I didn't realize Albertan, like the Montanan, was a dialect of its own.  There were the obvious Canadianisms comedians emphasize, but my attempts at using them were unconvincing.  Canadians tend to be unusually polite, but deep down inside they know your attempts are clueless. In college I ran into people from all over the world and quickly got to the point where many of the "rules" of spoken English didn't bother me like they did my k-12 teachers.  

 

A friend happens to be a computational linguist specializing in the rhythm and sound of a language - the prosody of language. Getting this part right - good enough to begin to add the meaning in speech that's often missing in text - is one of those hard problems.  I've read a few  of the papers in her field and find them jargon laden and bewildering.  Still, there's something very important that we just do naturally.  There's another branch of linguistics that's more accessible.  Sociolinguists studies how society, including cultural norms, expectations, and context impacts language.   The good stuff all of us use and misuse. Aalthough nothing like earlier changes in the language, there's constant change. The Gen Z meaning of wholesome comes to mind as a  recent shift in progress.

 

One of my most dramatic experiences with the sociology of language came as I was finishing my graduate work. A Chinese professor who didn't speak English was visiting the physics department. Not really an issue as there were several native-born professors and graduate students.  I was working something out on a blackboard and didn't realize he was watching.  He walked up, took a piece of chalk (yes -- we had lovely chalk back then), and gave me a look that asked permission to annotate what I was doing. It turned out he was interested in the same area.  We went back and forth using drawings and equations that were part of the culture we shared and had a lovely conversation for about fifteen minutes.  It occurred to me afterwards that we were relying on facial expressions and posture along with the chalk marks and never spoke a word.  Afterwards I reproduced what remained on the blackboard in my lab notebook.  Not that it was profound, but rather that it was such a nice chat.  He was only around for a few more days, but there were grins every time we saw each other.

 

Two weeks ago a linguist (not the prosody expert) gave me a beginner's tour of sociolinguistics by Valerie Fridland: Like, Literally, Dude  Arguing for the Good in Bad English.   It's great fun! Learn where change in language comes from (hint - it's not upperclass/educated males), how text messaging is entirely different for teens and their 35 year old parents, why ums and uhs in speech are beneficial and much more.   I'd go for the audiobook as she gives acoustic examples.  I'm not good at communication, but now at least I'm a bit more aware.   

 

 

invention

This morning I remembered a quote that would be perfect for a friend as well as many of you.  I'll get to it later, but it made me think about something that I've spent time thinking about for at least a decade.  As an introduction there's a question we like to ask others. 

What's the most important human invention?

Agriculture, towns, fire, cooking, clothing, etc.. tend to come up.   All  are important, but I like turning the question a bit.  Consider a central invention we all do - something that makes us very human.

 We invent tomorrow.  

Our minds create mental models - visions of the future - and give us a kind of time travel.  We run through potential scenarios we might encounter and can plan for.  They're usually in an episodic form and we imagine ourselves and others, often in some other place, experiencing a variety of options.  This time travel can flip and reach into the past.  We call it episodic memory.  These memories aren't perfectly accurate. They're more like screenplays we use to recreate the past with whatever bits of memory and shards of content we can access.  We can also create "what if" scenarios and use them to plan for the future.  It's a fluid time machine that can operate almost simultaneously in the past and future creating past and future episodic memories.  And critically, we separate past and future from each other and the present.

 

People are really good at copying.  Compared to other primates we're supercopiers. But we also experiment doing things like sticking our hands into fire, eating a plant we shouldn't have ..  and we, or those who watched us tempt the Darwin Award, remember and let others know.  We innovate and teach moving this information into our culture - a cultural evolution of sorts.   There's a lot to unpack here.  It's a beautiful subject to think and ask others about, but I want to keep this short and eventually get to the quote.

 

Keeping track of things quickly gets out of hand for our very limited memories.  It appears the first mechanisms were appeared over 20,000 years ago to deal with the information overload of keeping track of herd animals,  seasons.. important things like that.  It was the dawn of humanity creating an external memory system.   Moving forward the Sumerians are usually credited with creating a formal writing system.  At first accounting, but eventually our stories became readable.  And that takes us to a beautiful description by Carl Sagan.

What an astonishing thing a book is. It’s a flat object made from a tree with flexible parts on which are imprinted lots of funny dark squiggles. But one glance at it and you’re inside the mind of another person, maybe somebody dead for thousands of years. Across the millennia, an author is speaking clearly and silently inside your head, directly to you. Writing is perhaps the greatest of human inventions, binding together people who never knew each other, citizens of distant epochs. Books break the shackles of time.

 

beyond abracadabra

More than a few in my line of work, particularly those from the generation before me, are amateur musicians.  The first time it became clear to me was in Gale Dick's living room on Friday evenings. He loved to play the violin and had a nice homemade harpsichord as well as a piano.  Friends would come to play, or in my case just listen to, chamber music.  Regulars included a couple of physicists, a mathematician, a chemist, as well as some real musicians who seemed to enjoy themselves anyway.  It was great fun and the beginning of a life-long addiction to live music, even though I'm just a lurker. 

 

Years later I asked Gale if he understood the connection.  He paused and then replied Bach letting it sink in before elaborating.  Bach ... you see, so much of it has beautiful symmetries...   He recalled when he was coming to grips with group theory in grad school.  The year before he'd come across Noether's Theorem and was blown away.¹  Years later, deep into the thicket of a difficult problem,  he found himself playing a Bach violin sonata in his mind.  

Then magic crackled and the work I was doing connected rather profoundly to those other areas. 

Words came easily to him and new ones, or at least ones I couldn't find in the dictionary, would appear.  As he described the violin sonata sequence, one I hadn't heard before appeared:

You see, Bach's music is this abracadaptor that connects two different kinds of magic giving birth to something that is also magic.

 

That was a long time ago.  Years later I found myself giving a talk at Disney Animation.  After lunch I spent the afternoon chatting with a number of people.  Then it happened.  We were talking about the curious physics that often appears in cartoons.  He said that Walt Disney had a set of rules that defined how things moved in his world building.  The rules are good enough that most survive intact. 

They're the abracadaptor that connects the original story with the artwork.  When it's well done the resulting magic is better than what went into it. 

 

Today I found myself using it in a text message to Sarah.  The beach volleyball season that ultimately determines selection for the Paris Olympics begins in Doha tomorrow.  She and her new partner Sophie have only been playing together for a short time and are still working things out.  

You’re armed with some new knowledge and are likely making great progress putting your abracadaptor into regular operation.°

° abracadaptor. n. - A mechanism or technique that connects two different kinds of magic.

 

There are people who do this: that rare skill that allows them to connect the conversation of those with very different backgrounds creating a deep and wonderful communication.  It's a skill I lack and I'm in awe of the few who can do it.  I like to use some engineering terminology to describe these people - impudence matches.  At its highest level two different magics are connected creating something deeper and an abracadaptor is afoot.

 

__________

¹ Don't worry about either of these if they sound foreign.  Both are important tools in the study of symmetry and deeply connected with physics.

 

types of stupidity

Recently Pip Coburn circulated a note on the importance of finding the right balance of challenge for your skill level to avoid boredom and frustration.  He noted the linkage to Csikszentmihalyi's work on flow, something that's fascinated me for some time as finding states of flow is important to me.¹  

The note made me think about levels of frustration and feelings of 'stupidity' one can have.  For some time I've identified types of stupidity with one being very useful and perhaps necessary in science.  Here's my response:

 

It’s fascinating to think about these things. Your comment on loving the work - “absolutely loving” it - is so important.

I think it’s important finding a field that no one can possibly master but, at the same time, know parts of it well enough to find where you may have a bit of success in if you apply yourself. As a beginning grad student I had no idea how hard it is to do research. It’s much more difficult than the most demanding courses as it’s an immersion into the unknown. Some people just give up and find easier paths. I find it useful to think about how to be productively stupid.

’Stupid’ is an unfortunate word, but I haven’t found anything better. Productive stupidity isn’t the relative stupidity you may feel in a a class where the other students are doing very well. It’s also not where someone who happens to be very bright is working in an area that doesn’t use their talents. (Stephen Hawking would have been a terrible point guard in the NBA even though the position demands strategic and tactical thinking.) Rather it’s a kind of existential fact .. an absolute stupidity. It puts you in the position of being ignorant by choice (here I use 'ignorant' in the 19^th century sense - realizing there's an area you don't know much about and choosing to pursue it). So it’s fine to have failures here and there as you try to find your way. And sometimes, something wonderful is found. The process can generate serendipity. Of course you end up doing many less challenging things as part of the process. They’re often rewarding, but it’s amazing when you find something totally new. It’s what drives a lot of people.

I’ve had some great conversations with people who push their fields and hear the same thing with different words. Yo-Yo Ma, Sarah Pavan (beach volleyball Olympian), a number of physicists and mathematicians as well as several artists.²  The words were different, but the paths were very familiar.

There’s another piece to this.  Bringing together a very diverse set of people who excel at productive stupidity is something of an amplifier. Often there are interesting hints and even keys that you never would have thought of. That and it’s often a lot of fun.

__________

¹ Years ago I attended a talk by Mihaly Csikszentmihalyi.  Afterwards I had a few questions including "how do you pronounce your name?  He said this is good enough for Americans:

Me-high Cheek-sent-me-high

² There are many others who probably do something like this .. these are just the people I've talked about it with.

 

 

six is a surprising number

Ting-Chang Hsien was a dear friend when I was in grad school.  At the time China was beginning to send a few scholars to work with American counterparts and Ting-Chang came to Stony Brook for a few years to work in an area of particle physics the school was noted for.  Near the end of his stay     he decided to see America.  He flew to my parent's home in Montana and, renting a car, spent several weeks traveling through the West.  The day before he flew back to New York my parent's neighbor, Lloyd Erickson, stopped by to chat.  Extroverts by nature, Lloyd and Ting-Chang dove into conversation and homemade ice cream.  Ting-Chang mentioned as a teenager he was a student in Shanghai with an interest in music as well as math.  The school was run by missionaries - his mother was a devout Christian - and his favorite teacher told him he had real talent for math and should give up the piano.  He said "she was from Minnesota .. one of her brothers was technical and worked for a company there."  Lloyd sat up,  "I had an aunt who was a missionary-teacher in China.. she left before the war and and got married."  Ting-Chang mentioned the name of his teacher.  She was in her late 80s and still alive.  Lloyd brought out family photos.  That night old teacher and the physicist talked on the telephone for a long time. 

 

We all know it's a small world.  We find common connections with total strangers even if we don't consider ourselves well connected.  I tend to be shy and don't have that many friends, but continue to be surprised.  Of course there's the Six Degrees of Kevin Bacon.

 

Steven Strogatz does applied math at Cornell.  In the mid 1990s he and his student Duncan Watts were interested in the problem of synchronization.  How is it that some insects like beetles manage to synchronize their sounds at night?  Why is it that types of glowworms blink in unison?  Why is it .. there are many of examples of this in nature ...  They weren't trying to solve the underlying science, but rather were looking to see if there was a deeper mathematical underpinning.  Cornell has lots of beetles in the Summer.  They could make measurements. 

 

They considered two extreme cases.  One is very regular.  Think of a checker board.  Each square on a checker board filled has an immediate group of neighbors - small neighborhood cluster.  To "talk" to square on the other side there are about eight degrees of separation.  Each square is only directly connected to the nearest neighbors.   This kind of model is well-studied in physics where a force may only have a very short range. None of us have connections that limited.    Next consider complete random connections. If you know 150 people, each of them would know a similar number so the total number of people connected by two degrees of separation is about 150² - 22,500.¹  Most of us know that's wrong (except for some early models of Internet connectivity:-) 

 

Their gut feeling was the real answer would le somewhere in between.  Technically they were looking for the phase transition .. the point at which most of the beetles were suddenly in synchronization, or everyone seems to have these seemingly random connections. The small world problem.  What they found was a fairly simple mathematical description that said you only need a small bit of randomness.  In your circle of friends an outlier or two.. or knowing someone with such connections.   

 

Their short paper showed examples ranging from power plant distributions to noise making bugs and is one of the one hundred most cited papers in all of science and math.   They also noted that given connections afforded by travel these days pandemics could spread rapidly.  It's very difficult preventing that phase transition.

 

The small world problem is very beautiful.  It's one of those topics that should be taught in a course that doesn't seem to exist.  In college you get music and art appreciation.  I'll never do good art or music, but 101 level non-major courses gave me a better appreciation for those very human endeavors.  

 

Math is important enough that students in high school get either working on mindless problems they'll never see again or pre-STEM work that only a small percentage will use.  People are properly recommending and even building 'data science' courses.²  These seem like a great idea - familiarity with tools, presentation and interpretation - but I'd like to see a math appreciation path.

 

Math appreciation would have history from a number of civilizations.  Was math the first example of external memory?  Why did people use different number systems?  Why was double-entry accounting so important to Italy?  What about zero?  Imaginary numbers?  The Fibonacci sequence in nature.  Why does a slice of pizza fold the way it does?  What is infinity, are there different kinds?  How are coffee mugs and doughnuts similar? What is the fairest way to vote in a democracy? It's easy to think of dozens of lecture topics that might even inspire a few students and create links to what they finally go into.

 

Just an idle dream I guess..

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¹ Apologies to Robin Dunbar - he'd say the number is almost always used out of context anyway).  

² I hate the term.  Generally anything that adds 'science' to a label isn't science.