omenti

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..

__________

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.

 

2 december 1942 - a half watt

4:00 PM 2-Dec-1942

Compton: The Italian navigator has landed in the New World.

Conant: How were the natives?

Compton: Very friendly

 

Almost exactly 80 years ago the first human-made self sustaining nuclear reaction took place under the stands of a vacant football field at the University of Chicago.  It's a remarkable story and something of a race with Nazi Germany.  Fortunately so many competent physicists had fled Germany that the Nazi bomb project was a failure.  It turns out the wikipedia article on the subject is an accurate and readable summary of the dawn of the pre-manhattan project effort to get a handle on nuclear fission.  The piece  gets a bit technical here and there, but you can skip over those parts if you like.  I'll try and give a high level view of what a sustained reaction is without going into the quantum mechanics of the process.

__________

 

Nuclear fission is the process where the nucleus of an atom breaks apart into smaller pieces releasing energy (often quite a bit) in the process.  The nucleus of an atom is a tight cluster made up of positively charged protons and electrically neutral neutrons.

All of those positive changes packed together - you might ask why don't they fly apart? After all, electromagnetism causes like charges repel.  It turns out a very strong force, cleverly called the strong force, acts on neutrons and protons binding them together.  A difference between the two forces becomes important.  Electromagnetism is a long range force while the strong force only acts over short subatomic distances. To first order you can think of the strong force acting only between immediate neighbors while the electromagnetic force acts on all of the protons.

If the nucleus gets big enough the total repulsive electromagnetic force of all of the protons overcomes the closest-neighbor strong force and breaks the nucleus up in to smaller pieces releasing energy in the process (nuclear fission)

Most of the elements we're used to have nuclei that are too small to break up on their own.  A few are on the borderline. In the case of uranium the addition of a single neutron is enough to undergo fission and in the process it releases energy and, on average somewhat more than two extra neutrons along with a couple of nuclei that are smaller than uranium.¹

In nature uranium usually isn't concentrated and the neutrons from fission are absorbed by other materials.² But if you concentrate uranium you get to a point where each fission has a high probability of striking another uranium nucleus and so on - creating a sustained reaction. Unchecked, with enough purity, and you get an atomic bomb. At lower concentrations and with the ability control the amount of neutron absorption you get a controlled nuclear reactor that liberates a useful amount of energy.

 

A number of interesting characters were involved in these early experiments.  Enrico Fermi was the key player in the first sustained reaction.  Physics was getting specialized and he was probably the last physicist who was both a great theorist and experimentalist. 

__________

¹ I've left out a lot.  I haven't mentioned which isotope of uranium for example.  Also - you may have noticed that adding an extra neutron shouldn't increase the electromagnetic force as the neutron is neutral.  It turns out the uranium nuclei is so close to breaking up that the kinetic energy of the addition neutron adds just enough to break things up.  A nice example is adding a neutron to U-235.  One possible fission chain  n + U-235 → Rb-92 + Cs-140 + 3n + 200 MeV of energy. 

Also details of the strong force weren't known at the time..  A clear hypothesis didn't arrive until about 30 years later and deeper details of the mechanism took almost thirty more..

² A natural formations of uranium t pure enough to initiate sustained nuclear reactions was discovered in Gabon.  It operated for a few hundred thousand years producing less than a megawatt of power.  

 

 

a delightful word

Mr Gross was my high school German teacher.   He was big on learning language through song and would regularly point out a German word or phrase that might be more appropriate than American English. I wasn't a good student of the language, but he made an impact on me.  I still remember and use some of his offerings.  Today I saw one of my favorites used in the New York Times - the first time I've seen it used in America.  

freudenfreude

Mr Gross described it as the opposite of schadenfreude. It's the joy and delight we feel when someone else finds success - even when, particularly when,  their success doesn't involve us.  He used to describe the joy he felt when a blind student from our school won a state piano competition.   It's an important social glue - a gift to be aware of and take delight in.  Mr Gross has been gone for a long time, but thinking about this word turned out to be one of the best things I learned in high school.

 

finding what works

 

It’s a clear winter night as I write these last words. I’ve stepped out to look at the sky. With the stars up above and the blackness of space, I can’t avoid feeling awe.

How could we, Homo sapiens, an insignificant species on an insignificant planet adrift in a middleweight galaxy, have managed to predict how space and time would tremble after two black holes collided in the vastness of the universe a billion light-years away? We knew what that wave should sound like before it got here. And, courtesy of calculus, computers, and Einstein, we were right.

That gravitational wave was the faintest whisper ever heard. That soft little wave had been headed our way from before we were primates, before we were mammals, from a time in our microbial past. When it arrived that day in 2015, because we were listening—and because we knew calculus—we understood what the soft whisper meant.

                 Steve Strogatz 

 

Chatting with a friend the subject of gravity came up.  It isn't a conventional force, but we perceive it as one.  Rather it's connected with the curvature of a four-dimensional object called space-time that we happen to live in.  The fundamental concepts aren't intuitive and the math that describes it is beyond what you might get in an engineering degree.  So how to describe it?  There are very high level books and videos that speak in terms of balls on rubber sheets and then jump to oddities like clocks running faster on mountain tops and blackholes.  I usually find them a bit fluffy and disappointing.  They're bound by assumptions about their audience, so it's not a major criticism. It's just that I was talking with one person and something a bit deeper seemed appropriate.  Just how do you find the right level and where do you go from there?

 

A few years ago Wired produced the 5 Levels series.  An expert would try to explain something about a complex subject to five people:  a child, a teenager, an undergrad majoring in the same subject, a grad student and, finally, a colleague.   My favorite is Donna Strickland on lasers - give it a watch, she's excellent:

I went through something like this just before my Ph.D. thesis defense.  I was to explain my thesis work to a group of high school students. At first I thought it would be easy, but that notion quickly evaporated.  It turned out to be one of the most difficult and embarrassing things I've done.  My advisor stepped in near the end of the talk and summed everything up beautifully.  Afterwards he told me if you understand something deeply, you can explain the gist of it to a high school student.  That's high on the list of the most important things I've learned. 

 

My friend has a BA in biochemistry and knows about differential equations so I figured I should aim for something between the vague videos and what a senior level general relativity course offers.  The more I thought about it I realized it would be best to talk about the history and use a bit of calculus and geometry.  I had the advantage of knowing her well and she can stop and ask questions or give a blank look along the way.  And afterwards she was going to talk about something where she has serious expertise. 

 

Steve Strogatz is an applied math professor at Cornell. He's written several books including the one the opening quote is taken from: Infinite Powers: How Calculus Reveals the Secrets of the Universe.   It's an excellent read that makes no assumption on your mathematical background.¹  Thinking about it gave me some hints of how I might proceed.

 

First why do I have to use math?  Why won't words work?  The laws of nature obey logic that we can make predictions from.  Math, calculus in particular, is a logical calculating tool.  In a way it's a prothesis. Math lets us take a bit of logic, write down and perform logical manipulations that far exceed what we can do in our head, and then interpret the results. The logic can be crafted to represent something about the science.   Every once and awhile the results can make predictions that can lead to new discoveries, but more often they're used to to solve an enormous range of problems.   And why calculus?  Much of the  underlying structure of nature has been successfully expressed with the corner of calculus known as differential equations.  "Why?' is a deeper question.  If one encountered an intelligent alien who understood some aspects of how the Universe worked, I suspect they'd use math.  I suspect, but it's only my suspicion, that it's deeper than an artifact of how we think about things. 

 

I spent a couple of hours writing.  How general relativity came about, a bit on the structure of space-time, what goes into the main equation and how a simple prediction could be calculated.  Then about an hour of chatting that left me with two delightful philosophical questions that will probably lead to more discussions as well as her turn to teach me something. 

 

Whatever your expertise, it can be fun to try and explain the gist and maybe even the beauty of it (those can be he same thing) to someone with a very different background.   If you're like me you'll fail at first, but eventually you'll get to a point where you can find the right grounding, the right words and perhaps the right drawings or even music (some of you are artists and musicians).

__________

¹ By all accounts he's a wonderful teacher and has become a popularizer of math.  Among other things he's created a college course at Cornell for people who think they're afraid of math and have generally put it off until their senior year. 

 

 

 

 

teaching and technological change

On Saturday my niece sent a few photos from her son's robotics competition.  While standardized components and a simple scripting language are used, there's a lot of room for learning and creativity.  Winning teams spend much of their time modifying the basic design along with moving to more sophisticated programming languages.  The basic hardware is quite expensive so many of the groups are sponsored by their schools and sometimes local businesses.  It seems like a great way for kids who like to build things and play computer games to learn a bit of engineering and programming.  My niece's son isn't interested in math or science at school, but loves to build things.  It's a path that has him learning.  Given the right advisor there could be a lot of learning.  It's also a nice example of using technology as a teaching vehicle.

 

Sometimes new technologies are seen as a way to cheat.  I've read that some teachers worry that language models like GPT-3 will give students easy access to ghost-written essays.  Of course there's still the problem of students buying essays from human, but this may be cheaper and easier to get.  One can imagine a number of ways to deal with this.  A teacher might ask something like "based on the debate Adam and Sally were having last Tuesday, how would you.."   Indexicality - pointing to something in the context in which it occurs - is something these language models can't address.  Better still may be to focus on critical thinking in the class and test on something that isn't a simple regurgitation. Essays seem like a very uncreative way to teach writing and critical thinking skills.   And there will probably be teachers who figure out how to involve language models as a tool to teach creative thinking.  That would be a leap similar to using robotics competitions to teach shop, basic engineering and programming skills.

 

I'd like to see changes in how science and math are taught in high school.  Currently there's a push to eliminate areas most students will rarely use.  I'd counter that by teaching the subjects in a way to improve critical thinking.  Pure math may be a way forward, not the "new math" that crashed and burned in the 60s, but big ideas.  It doesn't have to be about formal proofs and calculations (although tools like Mathematica and Maple can be useful experimentation and visualization tools).  I've probably belabored it before, but simple topology, infinity, the continuum, maps, abstraction, inference and model building. None of this has to be taught with rigor, but playing with them can open pathways students have never thought about.   Sure teach some of the regular math, but it doesn't have to be so repetitive. I'd add probability and risk analysis as well as personal finance. The same with science - do away with memorization and focus on the concepts and how we arrived at them.  Of course extra points for making it playful like the robotics competition.

 

But I'm not a k-12 educator so all of this may be silly.

 

And for college here's something by the wonderful Woodie Flowers of MIT on changes he'd made to university engineering curriculum and beyond.  (Woodie was one of the most innovative teachers at MIT)

 

preview season

As many of you know I like to celebrate major accomplishments of friends.  This time I'll offer previews from two good friends as well as another that could have an impact on education.

 

The first is  Juliette Powell's second book.  The A.I. Dilemma: 7 Principles for Responsible Technology is the working title and it's a further development of her dissertation at Columbia.  I've been fortunate enough to have read the nearly-final draft.  Well balanced and accessible to non-specialists, it's going to be an excellent resource for people trying to sort out promises and pitfalls that can impact much of the future.  One person who had an advance look will be using it as required reading for a college course.  Be on the lookout!

 

The second is from Sarah Pavan.  One of the best beach volleyball players in the world, she's also a clear and deep thinker.  As I've aged I've learned to learn from those outside my area.  She's  been a source of ideas. At the elite level women's beach volleyball is a mental game with communication being one of the defining aspects.  A few months ago her teammate of five years decided to quit the team.  Sarah was faced with finding someone with the necessary complementary skill set as well as the drive, passion, ability to communicate and chemistry.  Canada only has a few candidates, but Sarah found the right one in Sophie Bukovec.  I expect to see them developing as a team over the next year as they focus on the Paris Olympics in 2024.

 

 

And finally potential news from what I consider the most important college course in the country. Sense & Sensibility & Science is a course at Berkeley developed and taught by faculty from Physics, Philosophy, and Psychology departments.   Here's an overview:

 

This is a course on the ideas from science that are most widely useful for everyone. Many insights and conceptual tools from scientific thinking are of great utility for all kinds of reasoning, from reading the news critically to making decisions under conditions of uncertainty. The focus in this course is on the errors humans tend to make, and the approaches scientific methodology has developed (and continues to develop) to minimize those errors. The course includes a discussion of the nature of science, what makes science such an effective way of knowing, how both non-scientific thinking and scientific thinking can go awry, and how we can reason more clearly and successfully as individuals, as members of groups, and as citizens of a democracy.

Every day we make decisions that can and should be informed by science. We make decisions as individuals, as voters, and as members of our various communities. We make decisions as students and parents and policy makers. The problem is, we don’t do it so well—a fact sadly apparent in political debates. It’s easy to blame poor decision-making on the greed, irresponsibility, ignorance, or incompetence of other people. But the problem seems to be more basic than that. It seems we face a paradox. Living in a democracy means that everyone’s view counts the same as everyone else’s. But to make decisions informed by science, we often need to defer to those with relevant expertise. Therefore, we shouldn't rely on a democratic system to make the best decisions. Or should we? This basic tension between science and democratic decision-making serves as a unifying theme for Sense & Sensibility & Science (SSS), a course that aims to equip students with basic tools to be better thinkers. We will explore key aspects of scientific thinking that everyone should know, especially the many ways that we humans tend to fool ourselves, and how to avoid them—including how to differentiate signal from noise, evaluate causal claims, and avoid reasoning biases. We’ll then look at the best models for using science to guide decisions, since the rational and arational (e.g., values, fears, and goals) then have to be combined. We will explore these themes experientially, often with in-class activities and discussions, and we will culminate in two open-ended projects to design better methods of deliberation and decision making, first as groups, and then as individuals. Co-taught by faculty from Physics, Philosophy, and Psychology, S&S&S fosters intellectual advancement for interdisciplinary knowledge seekers.

 

Browse through the topics and resources section.  You'll get something reading the recommended materials and thinking about the topics.  It's one of the few places outside the community where I've seen scientific optimism discussed. A book is being developed aimed at college students, although it should be widely applicable.  There's a serious need to put together something like this at the high school level even though many states would probably label thinking about the process of science as 'woke'..

feel free to comment!

a 'I really know better than to post this post...'

a minipost

About this time of year I get a request or two to talk to a high school junior or senior about colleges and majors.  I'll give reasons why I'm not the best the person to talk to, but if they persist I'll spend some time listening and talking.  Curiously there have been three so far this year and two suggested I post something.  Perhaps it can spark you into helping some students - many of you have much richer backgrounds.

 

A caveat is that I came from a position of privilege: white male, reasonably good at math, and from a period of time when great positive change seemed possible.  I didn't view college as training for work.  Somehow I knew what I was curious about from the age of twelve, so it was just following a calling.  I knew I could always get work with the friend of the family in back home who had a thriving HVAC and water softener company. This gave me the freedom to follow a somewhat different path than friends who were thinking about what happened after graduation.   This led to good and bad choices.  I double majored, but the fields were too close to each other and I ended up with a narrow undergrad education. Since then I study a few areas on my own, but I didn't take advantage of a broader education back then.  On a more positive note I got to know several professors as friends and mentors. That part was priceless.

 

° Ask yourself why you want to go to college?  What is your drive?  Many answers are correct, but you should know yours.

 

° A 'what color is your parachute-ish' question: are there any kinds of work you would do for nothing or even pay to do? 

 

° Where may or may not be important.  It's a plus in some fields to attend a famous college, but in many cases the quality of education can be as good at state schools - sometimes even better if you're good at making connections and really dive into the courses.  Famous professors often don't have the time to talk to undergrads. 

 

° Spend some time finding out which professors can teach.  

 

° Double major if you can, but in mostly unrelated areas.  Even if you're focused on employment afterwards - a good ROI on college - choose the second major in a field that you might find fascinating.  The humanities can give you great depth and are underrated for turning you into someone who can think differently down the road.  I've mentored students with a variety of double majors: CS-music, CS-art, physics-philosophy, math-paleontology for example. If you're doing a D-I sport, consider that a major by itself.  It can give a rich training that can serve you down the line too.  If not a double major, make sure your minor is very different from the major.

 

° A benefit of getting to know professors and show an interest is you might be able to get in on some of their projects.  This is often in the form of work-study, which can take a bite out of the debt down the road.  I was lucky enough to get in on a few great projects.  The most interesting seemed boring at first and didn't pay, but it was in an area I hadn't thought about and the professor was brilliant.  There was even an opportunity to have a tiny contribution to a bit of history and I still use some of the learnings. 

 

° Remind yourself that you learn best when it's play.  This won't happen all of the time - or even most of the time - but work on it. 

 

° Learn to witness the immediate world around you in some depth.  I recommend basic drawing and field drawing courses.  There are many other paths, but a bit of time focusing on understanding the natural world around you changes the way you think. 

 

That's pretty much it.  I mainly listen to them. Some of the items I've mentioned cause them to react and think about their own situation.  This year I recommended How to be Perfect by Michael Schur.  It's basically a Philosophy 101 short course done in a brilliantly entertaining manner - the way an engaged professor might go at it.  (If you're interested the audiobook is much better than the printed version as Schur has a stage background.) 

 

design for kids and community in japan

a minipost

 

About twenty years ago I was associated with a human computer interface department. A good deal of the work was associated with this nebulous concept of “community”. The term tends to be defined in the mind of the person talking about it .. like the word god. We had a list of about twenty words that needed rigorous contest when we publishing internally or externally .. community was everyone’s first choice for the list, That said most of us default to a warm and fuzzy concept. How people and neighborhoods should interact. The sort of thing Bob Kraut worries about. (to be fair he also thinks about communities like QAnon)

 

A recent 99% Invisible podcast focused on Japanese community of place design.. deign for the six year old Mixed use zoning, very narrow roads, a school house at the center and very independent kids. Some of us worry about urban and suburban design and traffic - how to you minimize the two or three ton vehicle carrying a driver and a bag of groceries? We often look to the Netherlands snd the Nordics for inspiration Indeed they’re excellent examples of moving from 1970s car-centric design to something better for cyclists and pedestrians. Japan offers a different path - one that seems unlikely in the US.

 

Here’s the a link to the audio, a transcript and a few videos

 

A comment .. most of us of a certain age grew up with kids walking and cycling everywhere - starting around six for walking and seven or eight for cycling. It was the only way a kid could deal with the scale of suburban design with fixed zoning and wide roads. That’s the environment the Dutch and Nordics started with rather than doubling down on complete car dependance.

 

clearing the air

a mini-post

A year ago I managed to help out getting a small grant from the state to build a number of Corsi-Rosenthal boxes with the help of two teachers (science and art) and about twenty high school kids.  It took a Saturday morning to build about eighty of the air cleaners.  All but two are still working and, even though the filters are visually ugly and dirty, they're working just as well.   I won't list all of the learnings - get in touch if you want to know more - but a big benefit besides cutting the viral load is dramatically cutting PM 2.5.  Kids and teachers report fewer allergy and allergy problems and toxic particulate from a nearby highway has been cut.  I suspect these would be great for fires and dusty areas (thinking Arizona and Salt Lake City).   In the past year more clever variants have appeared so check out YouTube if you're curious.  Oh - and filter prices drop if you buy 100 at a time:-)  The only downside was I never want to see duct tape again,

 

The motivation for the post was a fun discussion Andy Slavitt had with Richard Corsi and Jim Rosenthal on his In the Bubble Podcast.   Such a fantastic project for kids and adults!  (there are a number of commercials - Andy donates all profits to charities).

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