omenti

what's lost?

A few weeks ago Nancy and I had a brief exchange that reminded me to something I've been thinking about for years.  Anyone reading this has seen an enormous amount of change in their lives.  Some change has been for the better, some is arguably neutral and. . well.. some has been negative.   I started a list and asked a few others for their comments.  Rather than bore and bias you with my own list, I'll just note a few items and start with the comments of others.

 

I contacted eight people under the age of forty hoping to exclude those of us who had to walk miles through ten foot snow drifts.  All eight mentioned parts of the Internet (something at last as broad as the term AI) as problematic..  six singled out "social media" in one form or another

    wastes time 

    algorithmically addictive that creates a bias

    terrible for self-image and filled with hate

    bots and destabilizing countries

Most said social media was useful for some things, but we'd be better off without it.   "AI" - specifically LLMs and generative tools like ChatGPT were noted by three with worries about ownership, bias and techbro mentality.   Two singled out smartphones as time wasters (one of them has gone back to a flip phone).  One summed it up riffing on Cory D. noting "we are living in the enshittocene..."

Other social areas were mentioned:  the loss of civility, women's rights, increase in hate against others,  and the move to autocracy, but I'll move on.

 

I've written quite a bit about the importance of latency to my teenage math and physics education. The fact that I couldn't get immediate answers - often for a few weeks - forced me to think.  Any tendency I have to think deeply about something probably came out of this period.  If I had wikipedia and YouTube videos I probably would have looked, but not learned at any depth.  (Perhaps others do) It sharpened my sense of wonder.   High latency asynchronous communication had and has its place in my life.  When I read a scientific paper and react to it.  There have been times when months go by as I puzzle things out.   I can still do this, of course, but something can be lost with quick communication.  It's something I am still learning to manage.

 

We seem to have become more interrupt driven. My first non-academic job was with the Bell Telephone Laboratories - I use that distinction as it changed radically about a decade after I joined.  My lab director had us pick a four hour period, morning or afternoon,  where we had near total control over our time. We could shut the phone off and had flags outside our private offices indicating we were in "cave mode", could entertain an interruption from someone working with us, or the office was open.  It wasn't standard Bell Labs practice and I found myself coming in around five am to have time without interruption after moving to a different lab without the policy.  It's important as even a short interruption like a short phone call can cause you lose anywhere from five to fifteen minutes trying to context switch and regain a train of thought.  Some may think we multitask, but when it comes to conscious thought  studies almost universally show we're bad at it.

 

And then there's handwriting. Many schools now focus on keyboarding. Cursive writing has largely disappeared.  It turns out that may be a loss. A number of studies show better retention and linkages with other ideas when we mechanically print or use cursive. The brain is plastic throughout life, but under the age of about 20 it's much more plastic with new neural connections being made along with growth in some parts of the brain.   Recent studies like this one show handwriting is much better neurologically than typing on a keyboard. There's also emerging evidence that people who use handwriting for notes and letters protect themselves from dementia.  The effect appears to be as strong as people who are multilingual or play musical instruments. The evidence is strong enough that Sweden is abandoning keyboard use for non-programming classes and moving back to teaching cursive. 

 

My handwriting is terrible, but that doesn't seem to be important.. it's that use of a fine motor skill while thinking.¹  I'm guessing the same goes for drawing and sketching things you are thinking about for non-artistic reasons.   I've collected a few used books and notebooks over the years from a variety of scientists.  It's stunning to see how many doodles and margin notes fill the pages.  And for me there's something special about the right chalk on a high quality slate or a fine pencil on good paper.  The "feel" seems to help me think, but take that as an anecdote. 

 

I'll stop here - these are a few examples  where I can turn from what I see as a loss and find a path that works better for me.   I add that one person's loss might be another's gain.  In any event I'd be interested in learning what you see as losses over your life as well as steps you may have taken.

 

___________

¹ I have regular handwritten correspondences with two people.  In both cases it's mixed mode.  One is an artist, the other a physicist and drawings are interspersed with the words.   There's a wonderful connection one feels with these physical bits of communication. 

 

 

learnings from some mentorships

When Rutherford introduced me to Bohr, he asked me what I was working on. I told him and he said,

'How is it going?' I said 'I'm in difficulties.' He said 'Are the difficulties mathematical or physical?' I said I don't know.' He said 'That's bad.'
            - J. Robert Oppenheimer

 

I've experienced some wonderful mentorships over the years.  I've written about one of my first a few times.   Growing up in Montana you can fall into the beauty of the nature that's all around.  For me it was the sky at night and during the day.   By thirteen I'd been through  the astronomy books the bookmobile had been stocked with and the librarian suggested I write to a few professors.  Fifty stamps produced two - an incredibly high percentage when you think about it.  They had different styles, but generally would pose interesting questions to work out.  The latency in the US Postal Service meant I needed to spend a week struggling with a letter.  Thankfully there wasn't any way to look up an answer, so I really had to think and try. 

 

Many of the lessons had several levels of complexity.  Of course I only saw the least sophisticated level at the time, but I was slowly developing a physical intuition and linking it with intuitive curiosity.  One of the profs concentrated on paths I found fascinating (one of his gifts was realizing what would be fascinating and how to frame it), the other taught some math disguised as neat tricks. It took a Neil Gaiman level of cleverness to make some of the connections.  Thinking about it years later I realized they gave me something else that turned out to be incredibly useful and powerful.  They taught me it was good to be usefully stupid.¹

 

People speak of the imposter syndrome.  Sometimes even  the jargon in a talk barely outside your field is completely incoherent. One can be left with a feeling of being an imposter for sitting in the room.   It should be a good feeling..  it means you might be able to learn something from these people by asking some good questions.  It also means they've spent as much time toiling in their area as you have in yours.   A close friend is a computer scientist who  knows about as much of physics as I know of computer science.  Mutually assured imposterdom.  Our conversations are fascinating and often productive as we deal with each of our ignorances.  It's just as good, and often better, when you're around people with even less overlap with your background and interests.  Art, music, sport, sociology, history, engineering..  there is so much to learn.

 

School generally fails to teach you how to be usefully stupid. Throughout most of the experience you have to 'get the right answer' or write good papers in a short amount of time.  People are good at gaming the system and the learning is often superficial.  I learned a bit of useful stupidity from my mentors as a teenager, but the message really came home as an undergrad when I was struggling with something on my undergrad thesis.  The professor suggested I talk to one of the experts in the field - someone who had been sprinkled with the holiest water in Stockholm. We talked at the blackboard for a half hour and he told me he had no idea what the answer could be and determining if there was an answer might be difficult.  He said it in a most encouraging way.   If he didn't know how to crack it - no one did.  And here I was working on it.  It meant it must be at the frontier. 

 

To be usefully stupid means that you're working hard with all the tools you've built over the years, but it's at the frontier.  No one knows.   In grad school, or a very good undergrad school, the right way to give an examination in math or the 'hard' sciences (and probably many other areas) is to give an oral exam that asks progressively more difficult questions until the student can't answer.  If they have answered everything, it means the faculty has failed.

 

The formal and informal mentorships I've had have taught me so much more, but learning how to be usefully stupid has been the gateway to the frontier as well beginning to broaden my interests.   And thank you to those of you who have been informal mentors to me!  

__________

 

¹ There's a relative stupidity where the material is well-known. Some students read and understand the material and do well on an exam while those who don't fail.  'Stupid' may be an inappropriate word, but it's one a friend with a Nobel Prize uses to describe himself as he struggles with the frontier.

 

 

 

auteur and other fine words and phrases

About a week ago my friend Paul reported on his walking vacation in Iceland.  Paul happens to be in his late 80s and hasn't lost his knack for physics or interesting words and phrases.  He sent photos and noting some beautiful displays of the lux septentrionalis.  In the 45 or so years I've known him I've picked up a fair amount of Latin, Greek and German.  He bears direct responsibility for some of the phrases I use.. cheating in a way as I'm not fluent in these languages.¹  Auteur is a particularly interesting word, so let's dwell on it.

 

Recognizing creation of a book is easy.  Usually there are one or two authors get the credit even though editors, proof readers, printers and more were involved.   It's similar in scientific papers - at least until you get to collaborations of a half dozen or more.  Music is created by a composer, but orchestral performances are jointly credited to the composer and a conductor.  It's the complexity of something - when more than a few creative people are involved, that the term auteur seems appropriate.  I'd nominate James Murray of the Oxford English Dictionary as one of the first auteurs of a series of books - he went far beyond what normal editors do. 

 

The term auteur is usually associated with film.  Even in the thirties one hundred people might be involved in making a film and more than a handful - actors for example - may have had centrally important roles.  Here the equivalent of the creation of the film  is usually given to the director.  A director may not know how operate a camera, the intricate lighting or be able to perform on stage.  What they bring is vision and the ability to communicate it. 

 

Alfred Hitchcock wanted control over every scene of the movie.  He had to work it out ahead of time and communicate it so he repurposed Walt Disney's invention of story boarding to acted film. Hayao Miyazaki draws or corrects a lead frame of each animation segment of his films and spends a large amount of time with  composer Joe Hisaishi to get the music right. His style is dictatorial, but animators regard him as the best - an auteur among animation auteurs.  Pixar has a handful of internally grown auteurs who have seen remarkable success.  Wes Anderson is so good that name actors fall over themselves to get parts before seeing scripts.   It's an impressive group.

 

In spending time with an animation house as well as having worked on some large scale physics experiments, I see a common thread.  There needs to be a vision. There may be, and probably is, someone in the organization for each of the speciality skills who is better at their skill than the auteur.  The problem is having everyone do their best with limited knowledge of the rest causes project to drift from the goal.  It's the sort of thing David Epstein talks about in Range.   Someone has to have vision and taste and that's a special skill that requires development.  

 

It can apply to business.  Steve Jobs comes to mind and there are certainly others at various levels.  An interesting question is at what point does a project get big enough that an auteur is necessary and how does that vary by project type?  Many of you can come up with interesting examples.

 

Since sport is something of a mirror,  one can think of great coaches as auteurs.  It's certainly true  in team sports like football, soccer, indoor volleyball, etc.  Great coaches have developed a sense of the game and the taste in how it should be played.  Certainly they need a group of good players, but not necessarily all need to be, or even should be, great.  Finding a combination to execute the vision is the important piece.

 

__________

¹   Here's a non-alphabetical list of some that come to mind:

Danish (I know three Danes well)

klap lige hesten   "pat the horse" means shut up

det blæser en halv pelican "it's blowing half a pelikan"  means it's very windy

ingen ko på isen  "no cow on the ice" means  whatever the problem is, it's no big deal

så er den ged barberet  "the goat is shaved"  means the problem has been fixed, or the work is done

gå som katten om den varme grød  "walk as the cat around the hot porridge" means some is avoiding the problem

det regner skomagerdrenge  "it's raining shoemaker's apprentices" means the rain is very heavy

hygge a special coziness - what you might find on a snowy evening with good friends, food and a fire.

Italian

commuovere to be moved by a story to the point of tears

Greek

meraki    throwing yourself into something complete with passion, creativity and love.  This is how Paul approaches physics.

Tagalog

kilig the feeling of butterflies in your stomach as it romance or discovery

Malay

pisan zapra the time it takes to eat a banana - about two minutes

Swedish

fika gathering to talk and take a break from ordinary routines. Coffee must be involved.

resfeber the beating of a traveler's heart at the beginning of a journey. A anxiety with anticipation.

Welsh

hiraeth a homesickness for the time and place to which you can't return

Japanese

komorebi the sunlight filtering through leaves on the trees

boketto gazing into the distance without thinking about anything

wabi-sabi finding beauty in imperfections, an acceptance of the cycle of life

German

kummerspeck 'grief bacon'  the weight you gain from emotional overeating

freudenfreude finding joy in the success of others

Yiddish and Yinglish

shlimazel someone who seems to only have bad luck

(this part of the list is long .. mostly from friends on Long Island and NYC. Leo Rosten's The Joys of Yiddish is a wonderful resource)

Bantu

ubuntu 'I find my worth in you and you find your worth in me'  human kindness

French

flâneur a person who lounges or strolls around in a seemingly aimless way. Often seen as an aloof observer of urban society

sirop de poteau 'pole syrup'  imitation or very low quality maple syrup that must have been harvested from telephone poles.

auteur a person of influence or artistic control - often associated with filmmaking.

I'll stop here..  

 

 

 

 

 

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.

__________

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.

 

 

 

wonderful inefficiency

Today the Nobel Prize in Physiology or Medicine went to Katalin Karikó and Drew Weissman.  Richly deserved, their work has saved millions of lives and has created new pathways.

 

Each one had a key piece to the puzzle.  Normally they wouldn't have crossed paths, but working copy machines were a limited resource on their campus.  Katalin (her career path is amazing NY Times gifted) had the habit of reading very old papers and wanted to copy something when she ran into Drew who was also waiting for the machine. 

They talked

I can't begin to list how many collaborations and information transfers have taken place when disciplines physically collide.  Bell Labs was great at this in the day .. the Murray Hill cafeteria was a rich source as were the walking paths around the campus and the byzantine architecture of the place that randomly collided people with each other.  All wonderfully inefficient by many standards.  By design the main buildings at Pixar have a single large restroom that collides disciplines.  Many research organizations have slate blackboards (important if you have mathematicians and/or physicists) or whiteboards everywhere - restrooms, walking paths, along the walls -  for impromptu discussions. The disorganization of Building 20 at MIT is often cited as a founding example of this, but there are many earlier examples.

 

Creativity requires friction. People need a chance to bump into each other.  I suspect this is true for many disciplines as creativity evaporates when people avoid each other for whatever reason.  With all of the remote work these days it's important to think about, and make time, the create interesting connections. Arturo Casadevall at John Hopkins tells his people to read something or talk with someone outside their field every day.¹

“And most people say, ‘Well, I don’t have time to read outside my field.’ I say, ‘No, you do have time, it’s far more important.’ Your world becomes a bigger world, and maybe there’s a moment in which you make connections.”

But back to today's prize and a comment on the Katalin. Her daughter Zsuzsanna Francia won gold in Rowing Eights in the 2008 and 2012 Olympic games.  There are other notables.  Harold Bohr was on the Danish Football team where he won silver in the 1908 Olympics. He was the mathematician bother of physics laureate Niels, who was solid amateur athlete.  And Olivia Newton-John was the granddaughter of physics laureate Max Born. 

__________

¹ a tip of the hat to David Epstein

 

on approaching problems

Over the weekend I had a chat with a student from twenty five years ago.  He's a computer science professor these days and, while catching up, he thanked me for the note I gave him on problem solving.  He wasn't the first to say the same thing.  

As a freshman I discovered George Pólya's notes on problem solving. Pretty basic stuff, but extremely useful in situations where rigor is expected.  I made a version for myself and updated it over the years.  While this version mostly applies to math and physics, it has some general themes that can be useful in many other areas.  Feel free to steal modify it to your needs if you like.

 

Understand the problem

First. You have to understand the problem.

What is the unknown? What are the data? What is the condition?

Is it possible to satisfy the condition? Is the condition sufficient to determine the unknown? Or is it insufficient? Or redundant? Or contradictory?

Draw a figure. Introduce suitable notation.

Separate the various parts of the condition. Can you write them down?

 

Devise a plan

Second. Find the connection between the data and the unknown. You may be obliged to consider auxiliary problems if an immediate connection cannot be found. You should obtain eventually a plan of the solution.

Have you seen it before? Or have you seen the same problem in a slightly different form?

Do you know a related problem? Do you know a theorem that could be useful?

Look at the unknown! And try to think of a familiar problem having the same or a similar unknown.

Here is a problem related to yours and solved before. Could you use it? Could you use its result? Could you use its method? Should you introduce some auxiliary element in order to make its use possible?

Could you restate the problem? Could you restate it still differently? Go back to definitions.

If you cannot solve the proposed problem try to solve first some related problem. Could you imagine a more accessible related problem? A more general problem? A more special problem? An analogous problem? Could you solve a part of the problem? Keep only a part of the condition, drop the other part; how far is the unknown then determined, how can it vary? Could you derive something useful from the data? Could you think of other data appropriate to determine the unknown? Could you change the unknown or data, or both if necessary, so that the new unknown and the new data are nearer to each other?

Did you use all the data? Did you use the whole condition? Have you taken into account all essential notions involved in the problem?

Consult with others!

Set it aside and work on something else if it is still intractable.  It may be that it has to sit in your mind for a long time.  It's surprising how often this happens with a path forward suddenly appearing in the shower or on a walk!

 

Carry out the plan

Third. Carry out your plan.

Carrying out your plan of the solution, check each step. Can you see clearly that the step is correct? Can you prove that it is correct?

Some problems are intractable!  Be prepared to move on after you've spent what you consider enough time.

 

Consider what you've done

Fourth. Examine the solution obtained.

Can you check the result? Can you check the argument?

Can you derive the solution differently? Can you see it at a glance?

Can you use the result, or the method, for some other problem?

 

 

 

those third places

a mini-post

Recently I spent the better part of an afternoon chatting with an urban sociologist about third places: parks, libraries, pubs, dog parks, gyms, bookstores, coffee shops, churches - those social places separate from home (the first place) and work or school (the second place).  She's particularly interested in what they meant during the pandemic, how they're changing, and how why young people see them differently.   

 

A few notes from the chat.  There isn't any order or story, just  think of them more as points to think about as you look at your own experience.

 

Third place visits have traditionally had a impact on physical and mental health, although it's difficult to tease out specifics.  Researchers have pointed out they can "level" differences like ethnicity, class, religion and age.  Dogs parks and some types of sporting events are used as gold standards for mixing people. (I can personally recommend a beagle)  Churches do a great job within a religion, but often raise barriers to outsiders.  Suburban parks that encourage physical activity tend to be frequented by young well-to-do white people, while parks with benches and picnic tables cater to families and ethnic minorities. 

 

Many small businesses are third places and many went out of business during the pandemic. They're coming back and have become particularly important to those who saw their first and second places collapse into a single place (work from home).  She suggested businesses should encourage work from home employees to find third places they enjoy given the mental and physical health benefits. She also loves that Washington DC has a tax on vacant retail space. Areas are more inviting and offer richer third space potential when there are minimal vacancies. 

 

Researchers sometimes tease out how introverts and extraverts fit into all of this.  Both benefit from third places, although the types of places differ.  She noted something fascinating.  It appears the depth of interaction times the number of interactions may be roughly constant across these personality types.  I'm skeptical of statements like that as studying anything as complex as human relationships is tricky, but it's interesting and may have an impact on business and public space design.

 

 

magnets and a most dramatic moment

The opening ceremony of each Olympic game is filled with pageantry and sometimes, with the lighting of the cauldron, drama.  In my mind the most electrifying occured in the 1992 Barcelona games when Paralympian Antonio Rebollo performed some serious diablerie. 

Across the ocean in New Providence, New Jersey David and Mary watched the scene on a small black and white television as they shared pedaling duties.  David was pedaling at the time and gasped.  Fortunately there was a flywheel.

 

Their parents didn't allow television in the home, but both of them had been involved in competitive kayak and canoe events.  Lynn had been an alternate for the Montreal Olympics.  Introducing Mary and David to the Olympics was a good idea, but Al decided to make it educational. The kids would be given an exercise bike, a generator, access to a television and help from their mechanical engineer father and mathematician mother.  They had a few weeks to work things out.

 

When the the friction wheel generator was finally adjusted and working, they were shown how much power they produced and how much power various televisions used.  A twelve year old could keep a small color set going for a short time, but that was it.  They wisely chose the black and white set.  Through trial and error they ended up with a bicycle chain transmission and abandoned the exercise bike for one of their own on a homemade stand. They could now produce nearly twice the power for the same amount of perceived work.  A flywheel was added to make everything smoother.   They had something by the opening ceremony and the kids spelled each other off and developed an amazing sense of how long the commercials lasted.  They saw the torch lighting.¹

 

It's too bad they had a standard generator.  Something with better magnets would have had increased efficiency.  Not enough to move them into a color set (if they were a few years older and more athletic they probably could have managed), but certainly a better experience.  The strength of the magnetic field in a generator or motor is centrally important.  The strongest fields come from superconducting magnets, but they need to be cooled to near absolute zero rendering them impractical for most applications.

 

Electric vehicles use either induction or permanent magnet motors.  The permanent magnet designs tend to be lighter and are more efficient.²   There's a rub.  You're trying to optimize cost and magnetic field strength (among other things).  Rare earths like neodymium work much better than the cheaper ferrite-based magnets and have generally taken over the medium and high end automotive market.³ 

 

The problem with rare earth materials isn't that they're rare .. they fairly comment.  They are, however, unevenly distributed and difficult and toxic to mine and process.  Most of the active mining and processing is in China and it's an environmental disaster.  The US had a single mine in California in the fifties.  Since then it's had t an up and down existence including being closed for economic and environmental reasons.  With the interest in EVs it's back in operation again  and the US has gone from 0% of the world's production of neodymium to about 15% in about seven years.  In theory the mining and processing and safer and less toxic than the Chinese effort. Production should increase in the future.  The US is also largely unexplored - serious mineral exploration has only just resumed after a 60 year hiatus. 

 

The higher cost has some companies, notably Tesla, talking about going to ferrite permanent magnets.  They'd be heavier, less efficient, but would be cheaper and may be the core of lower-end vehicles.  Another alternative is to use a more efficient vehicle.  Electric bicycles and other micromobility solutions use small motors.  You can build 50 to 200 electric bike motors with the materials from one Tesla-class motor.  Not only that these vehicles are very practical for the short trips that dominate much of our mobility needs.  Sadly some areas have saddled themselves with transportation infrastructures that encourage inefficiency.

__________

¹ Mary continued in the families sport tradition and went to Princeton on a fencing scholarship.  She found she was interested in aeronautical engineering and went on for a Ph.D.  I heard she had something to do with the rotor design on the Ingenuity helicopter currently flying on Mars. 

² There are often questions about how permanent magnets work.  Most people have seen electromagnetic induction in school.  A current flows if you move a magnet in a coil of wire and a current through a wire produces a magnetic field.  Permanent magnets are more difficult to talk about .. I've done it at least once, but this short video is a nice intro.

 

³ There are other rare-earth based magnets, but a neodymium alloy is the most common.  It's an allow of neodymium, iron and boron - Nd₂Fe₁₄B - that forms a crystalline structure.  They have widespread use outside of EVs.. GM and Sumitomo Metals independently developed them about 40 years ago to get away from much more expensive and brittle samarium–cobalt magnets.

There's a lot of talk about tetrataenite (an iron-nickel structure) permanent magnets.  In theory they have better magnetic characteristics than neodymium alloys and should be much cheaper, but they're off in the future.  If they happen, expect some unhappy rare earth mining companies.