omenti

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.   

 

 

manpo-kei, gold plated teaspoons and home runs

A friend had been struggling to find regular physical activity for a few years.  She complained enough about a lack of motivation that her brother gave her a low-end Fitbit for Christmas.  Somehow the pedometer function clicked for her.  Being able to see the numbers of steps was as motivating for her as filling in circles on an Apple Watch is for other people.  On top of this she'd heard about the magic 10,000 step number.  Initially the goal was beyond her, but she was motivated and within a couple of weeks she was there.  She's kept it up and regularly does 15,000 a day along with increasing her speed.  Her blood pressure is down from last year's number and she feels healthier.

 

In the 60s a Japanese company marketed a pedometer known as the Manpo-kei - which translates to the ten thousand step meter.  The pedometer became a fad and somehow the 10,000 step goal was enshrined in popular culture.  There's no reason why the number means anything other than being something like five miles of walking for most people.  That's over an hour of walking and good exercise. So people who aim for the number are getting a good benefit because the general direction of walking a lot is healthy rather than the number being the "right" target. 

 

The NY Times recently ran an article on some inaccuracies in smart watches.  It doesn't surprise me.  I've been around Olympic programs and athletes for a few years and know some horror stories about the over-reliance of data when you don't know it's accuracy or the context of the measurement or its use.  Like anything else with data, you need to know why, what and how you're measuring, manipulating, and finally interpreting and using the information.  In sport that turns out to be difficult.  There are a number of interesting approaches to deal with the issues, but that's another post. 

 

The NY Times piece and elite training experience suggest broad trends over time are much more important than local accuracy and precision  If you're trying to improve your fitness level or play amateur level sports, the motivation from a smartwatch can make a big difference.  If you're an elite athlete there are many other things to consider and it's likely you're taking advantage of them.

 

The notion of broad trend over local accuracy has utility in many areas.  One that frustrates me is building  carbon dioxide removal technology.  It's something of a delaying tactic being cheerleaded by the petrochemical and coal industries.  In reality it's extremely expensive, requires a large amount of energy and diverts funding from much more effective technologies and behaviors.  Currently four 1 million ton  class plants are on the drawing board.  With luck each could remove a million tons of carbon from the atmosphere by 2030 or so with a projected cost of about a billion dollars each.  So how much of an impact is that?

 

A million tons of carbon dioxide is about 1/40,000 of current yearly emissions.  That's roughly the same ratio as a teaspoon to a bathtub full of water.  Imagine running the tub and in the time it takes to fill it, you can remove a teaspoon of water.  The bathtub keeps running..  in the time another tub of water comes out of the spigot, you can remove a second teaspoon.  And then a third, forth and so on.  

 

We currently have many deployable technologies and behaviors that will turn the tap down much more than a teaspoon worth for far less money.  When we're finally down to the point where we're only putting a gallon or so of water into the tub each year, then it might make sense to deploy a number of teaspoons to make a difference for where it's difficult to turn the tap (aviation and shipping for example) 

 

Spend some money and talent learning how to improve the process, but don't count on it in the near term as it isn't, and will never be,  a silver bullet.  Nothing it.  all we can hope for is silver buckshot and using as much as we can possibly afford.  It makes sense to use the buckshot with the greatest cost/benefit ratio - things like wind, solar, better power grids, efficient transportation (full sized EVs don't count!), and any number of energy thrifty behaviors. 

 

And finally home runs and climate change.  Recently a paper made the major news outlets with projections that climate change will have an impact on Major League Baseball home runs: "Several hundred additional home runs per season are projected due to future warming."  The paper is poorly done .. basically a sensitivity analysis based on a single variable. I won't give it the credibility of a link.  Something that doesn't work in the real world with something as complex as baseball.  I have a some expertise in the fluid dynamics of balls flying through the air and would argue the effect is small.  In fact they note the same thing, but word the conclusion to make it appear there is an effect and climate change impacts everything.  This is pure clickbait for news organizations and probably has the impact of diverting attention from much more serious issues associated with global warming.  It's trivial to see the home run impact is insignificant, but a poorly done analysis can lead to fuzzy thinking and even harm.

 

something deeply profound

David Epstein mentioned Hillel Einhorn's epiphany about happiness - something triggered by a fortune cookie.

befrending the imposter syndrome

[A minipost from my reply to Pip Coburn on his recent piece on student-mindedness]

 

The lesson came as I prepared for my thesis defense.  The Stony Brook physics department has three examiners:  two physicists - a theorist and an experimentalist (one is your advisor)  - and someone external to the department who is outside your field.  How I found mine is a long story, but the choice made a huge difference. He was a surgery professor and an accomplished violinist, which seemed reasonably remote from the semileptonic decay mode of charmed particles. The committee members get a draft of the thesis a few months before the defense. Ideally that's when major issues generally uncovered. I thought the surgeon wouldn’t have much to say, but he *really* wanted to understand what it was about.  He was a serious and intensely curious student, with a range far beyond medicine. His particle physics was about on par with my surgical skills, so I had to describe my work to extremely bright student who had a very different background. Spread over two months we spent at least twenty hours together.  His "dumb" (the label he chose) questions gifted me with a deeper insight into what I'd done.  There was so much I hadn’t thought deeply enough about.  

 

Over a good meal one night he said he used to be intimidated by experts outside his field until he discovered they were often intimidated by him. If you feel intimidated it’s a sign there's something to learn and perhaps you can learn something.  Over those two months I learned a bit about surgery and Bach violin sonatas, but the real learning was to to welcome and appreciate the imposter syndrome (I didn’t know to term until much later). Also I learned something about communication.  What I didn’t learn was how to effectively communicate the work to high school students - but that’s another story.

 

Since then I’ve been on a number of defense committees. Only one was physics. The rest have been all over the place and have been fantastic opportunities to learn and get a bit of insight from a developing expert. Hopefully some of my dumb questions help them as much as my surgeon friend's dumb questions helped me. 

 

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.

 

 

on the visualization of reality

The chunks of plastic held the ghosts of magnetic fields produced by some of our gadgets and appliances.  Shuli's pieces were quite beautiful and had me thinking about visualization on the train ride back home.   

We only see fragments of the real world, but our brain stitches what it can find together into a fleeting proxy for reality.  It's turned out to be good enough of what we do, but I recommend An Immense World by Ed Yong for a look at how evolution has equipped other lifeforms.  (It's a wonderful science for a general audience book - my favorite for 2022)  Science tries to sort out what is real and physics often seems foreign to what we're used to. On the train ride home I was thinking about how we visualize electromagnetic radiation - specifically a question someone had asked a few years back.

What would wifi look like if we could see it?

It seems relevant if you're trying to figure out how walls, refrigerators and other objects in a house or office interact so we know what the signal strength might be.  People who do this either just measure and plot signal strength or have simple models to give them a heat map that hopefully approximates what they would measure.   None of these gets at the real question.. what do wifi signals .. and all the other electromagnetic radiation that surrounds us look like?

 

The equations are straightforward and I suspect many imagine what it might look like when doing calculations - at least the parts we're looking at.  But these representations aren't rich enough.  The real appreciation is in the mathematics.  Feynman commented on it back in the 60s:

I have asked you to imagine these electric and magnetic fields. What do you do? Do you know how? How do I imagine the electric and magnetic field? What do I actually see? What are the demands of scientific imagination? Is it any different from trying to imagine that the room is full of invisible angels? No, it is not like imagining invisible angels. It requires a much higher degree of imagination to understand the electromagnetic field than to understand invisible angels. Why? Because to make invisible angels understandable, all I have to do is to alter their properties a little bit-I make them slightly visible, and then I can see the shapes of their wings, and bodies, and halos. Once I succeed in imagining a visible angel, the abstraction required-which is to take almost invisible angels and imagine them completely invisible- is relatively easy. So you say, "Professor, please give me an approximate description of the electromagnetic waves, even though it may be slightly inaccurate, so that I too can see them as well as I can see almost invisible angels. Then I will modify the picture to the necessary abstraction."

I'm sorry I can't do that for you. I don't know how. I have no picture of this electromagnetic field that is in any sense accurate. I have known about the electromagnetic field a long time I was in the same position 25 years ago that you are now, and I have had 25 years more of experience thinking about these wiggling waves. When I start describing the magnetic field moving through space, I speak of the E and B fields and wave my arms and you may imagine that I can see them. I'lI tell you what I see. I see some kind of vague shadow, wiggling lines-here and there is an E and B written on them somehow, and perhaps some of the lines have arrows on them -an arrow here or there which disappears when I look too closely at it. When I talk about the fields swishing through space, I have a terrible confusion between the symbols I use to describe the objects and the objects themselves. I cannot really make a picture that is even nearly like the true waves. So if you have some difficulty in making such a picture, you should not be worried that your difficulty is unusual.

Our science makes terrific demands on the imagination. The degree of imagination that is required is much more extreme than that required for some of the ancient ideas. The modern ideas are much harder to imagine. We use a lot of tools, though. We use mathematical equations and rules, and make a lot of pictures. What I realize now is that when I talk about the electromagnetic field in space, I see some kind of a superposition of all of the diagrams which I've ever seen drawn about them. I don't see little bundles of field lines running about because it worries me that if I ran at a different speed the bundles would disappear, I don't even always see the electric and magnetic fields because sometimes I think I should have made a picture with the vector potential and the scalar potential, for those were perhaps the more physically significant things that were wiggling.

That said I find myself using my mind to fly through through these abstractions of reality that experience and imagination provides.  I suspect people do this differently.  It isn't something that lends itself to drawing as it's often dynamic and, even though I consider myself extremely visual, not entirely visual. While I find many computer visualizations useful, they don't keep up with the imagination.   I suspect no two people imagine quite the same. 

 

A few nights ago Sukie and I were startled to learn something about her visualization. I was listening to The Case of the Blind Mind's Eye - an episode of an excellent BBC science and math podcast.  I strongly recommend listening to the episode.  They were talking about the mind's eye .. how we conjure up images in our mind.  If I ask you to think about an orange giraffe with purple spots, an image appears in your mind.  Or at least it does for most people.   Aphantasia is a semi-rare condition of people who are unable to generate these images.  It's completely fascinating and you need to listen to the show.  Sukie heard a few comments and had me go back to the beginning.  It turned out she has aphantasia - she's unable to form mental images and is startled that others can.  She's suspected comments about the ability are just a figure of speech.   

 

Aphantasia is more of a difference than a defect.  Sukie is extremely clever and has done impactful work in a few areas.  It turns out there are benefits..  it's another way the brain can imagine.  Ed Catmul (Pixar) has it and managed to create a revolution in how computers create images.  The same for Glen Keane - the Disney character artist who created Rapunzel, Ariel and a score of other important characters.  He describes his process as "thinking with a pencil". The shapes and forms come as he draws in a very fluid and gestural motion. 

 

It may be a spark, perhaps a necessary one, for very out of the box thinking.  In the meantime artists and the process of doing art can unlock the imagination.  It's not a full representation and perhaps that's what makes it so powerful.  It raises so many questions!

 

 

 

unexpected arcs

Three weeks ago breathless reports on the 'breakeven' fusion event at the National Ignition Facility began to appear.  While a remarkable achievement, it's more a marker of progress along a long and difficult path rather than an event promising a hopeful turn in decarbonizing the energy supply. 

 

Nuclear fusion has been hyped since the late 1950s.  Fission based reactors turned out to be straightforward.  All you had to do was refine uranium ore and then control a reaction to heat water and run an otherwise conventional power plant.  The cold war led to any number of atoms for peace projects suggesting a nuclear everything future.  The realization that nuclear fusion was much more efficient and "cleaner" than fission led to optimism and work on controlled fusion.  After all, it happens all the time in stars doesn't it?

 

Power from nuclear fusion has been twenty years in the future ever since.   Science and technology have made serious progress, but the challenges are great.  There's also the issue of cost per kilowatt-hour. If you build a plant that produces more power than it takes to run it, will it be economically competitive with other low or no-carbon solutions? 

 

There's a simple invention → development → application → change arc of technology mindset that doesn't describe the real world. It turns out you can travel a good distance along the arc only to see failure.  The garage-worthy helicopter, supersonic airliners and dirigibles have all be built and commercialized, but have failed for a number of reasons that are likely to keep new versions failing for the foreseeable future.  Somehow the dream factor persists in many of these and new failures continue to rhyme.

 

There are hugely successful inventions that have solved a problem, but turn out to have a deadly flaw that caused great harm.  DDT,  chlorofluorocarbons and leaded gasoline are obvious examples.  Less obvious are inefficient transportation.  Standardizing on 3,500+ pound vehicles to move people a handful of miles on average trips has led to millions of traffic deaths, a large pollution toll and a structuring of infrastructure and where and how people live that is proving difficult to change even though much better choices exist.  Sometimes tend to fire, aim and then look for damage around the target.  Sometimes it takes decades and change is expensive. 

 

There are a wishlist class of inventions where some progress is made, but effective deployment is a long way off (fusion power plants)  or unlikely as the underlying approaches are flawed at this point (self-driving cars, hyperloops, neural implants, space elevators, nuclear powered cars and airplanes, etc.)

 

It's very easy for an imaginative artist or writer to sketch an idea that is technically impossible.  We have a tendency to sort through the chaff and find amazing predictions from a hundred years ago.  It's useful to realize how much noise there is and that these things didn't happen in the author's or their children's lifetimes.  Still - every now and again you run across something that stops you.  This is one of my favorites - not only because it suggests wireless video communications, but it also nails the social element of two people ignoring each other so they can look at a screen.

 

Then there's a class of necessary arcs that we need to get past application and into wide-spread use.  Flexible power distribution to move power from generation to where it can be stored or used.  An advanced worldwide pandemic monitoring system.  Water management and treatment to deal with changing local climates as well as use needs.  More efficient agriculture that can deal with changing climates.  Changes to transportation and housing infrastructures that are less damaging.  Some of these aren't terribly sexy, but require social and political will - areas where progress is often very difficult.  And in the background there needs to be investment in fundamental science.  While progress can be difficult to predict, historically it's easy to predict that there will be unexpected discovery that can lead to something useful down the road.

 

It's fun to enjoy the stories writers and artists weave.  Creating your own is a great way to work with the imagination of a nine year old on a rainy day. Time and interstellar travel won't come along with scores of other ideas that help move stories along.  

 

 

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.