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.
I’m of the opinion that almost every technology that touches, directly or indirectly, society is not neutral. This may not be apparent at first to users at large even though some of the risks are known early on. A case in point is coal in the industrial revolution. Tyndall and even Fourier recognized the climate changing potential of pumping CO2 into the atmosphere. A larger number of people recognized the health issues from pollution in the air and water. And there was an enormous economic displacement that took a few generations to iron out (pardon the pun). So what was the major problem from the point of view of governments (especially the military branches) and industry? That coal could run out in as little as 50 years.
We’re in an age of running fast and breaking things and well as laws. ‘AI’ has emerged as something seen as an existential threat by some (a diversionary tactic largely for castle wall-building imho) and direct harm that is taking place now by others. I put ‘AI’ in scare quotes as it covers so many very different technologies. Now generative pre-trained transformers - LLMs - like ChatGPT are hot. It has a few lovely uses, but there’s a good deal of misapplication, legal issues and cases of direct harm. Machine learning is another branch (although it’s used in the GPTs) with it’s own shiny wins and pitfalls. And there are embedded bits in the devices, programs and services we use all the time.
So how do you navigate these and potentially avoid mistakes? Very few people can hope keep up on with the technical side.
Juliette Powell (caveat - a close friend of mine) has a new book out on Tuesday co-written with her business partner, Art Kleiner. The AI Dilemma: 7 Principles for Responsible Technology is a distillation of s her work at Columbia. The first part is a non-technical look at the systems and how they might be improved to minimize harm. The next part focuses on what uses - businesses, etc - can do to minimize risks to themselves and others.
A number of people from the tech and society and tech world have seen it and given enthusiastic thumbs up signals. People ranging from Ester Dyson, who wrote the forward, to deep legal and social thinker Brett Frischmann. I’ve been involved in building a few systems that have some severe constraints - mostly machine learning in astrophysics and cosmology. I’m clearly not a technologist or social scientist, but I actively follow those who are trying to understand these systems more deeply.
I followed her work at Columbia and this is a nice summary and extension. Thumbs up!!
If you prefer audio books, Juliette took on the narration task. She has an excellent reading voice.
I've been following Ben Blonder for some time. He's a young career ecologist at Berkeley. Along the way he's been involved in projects teaching kids science. He's just published a new book on teaching science to kids outside. Trust me - Ben knows what he's doing and has involved some of his collaborators in the book. (I know his dad well .. Greg describes this as a true labor of love, and it shows)
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.
About ten years ago I devoted a good deal of time to learning a bit of category theory - an area of abstract mathematics that's become important to physics. It deals with relationships rather than objects, abstractions and analogies, context, sameness, equivalence rather than equality, how you see patterns, and much more. It can impact thinking in many areas beyond mathematics. It provides a rigorous framework that gives choice in how problems are approached and take you beyond putting things in boxes that don't always make sense.
It's very technical, but Eugenia Cheng has written an excellent non-major freshman level book with the goal of getting art students to think about the world differently. I suspect it will work for many other people - particularly those who have to deal with complexity and seeing curious patterns that are otherwise missed. The Joy of Abstraction is one of those rare books that can change how you see the world. I'd recommend getting a physical version and doing the exercises. (I don't buy books from Amazon and recommend you support local bookstores)
Steve Strogatz chatted with her on this episode of his Joy of Wh(y) podcast. Listen even if the book doesn't strike you as interesting!
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.
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'..
Reading an obscure paper from the 1880s a word stopped me - apricity. It seemed like I had come across it before and there were hints from the context, but it was time for the OED.1 I pulled out the first volume of my old compact edition - the one with the magnifying glass - and found it. An obscure word dating to 1623 meaning the warmth of the Sun in the Winter.
The warmth of a bright Sun in on a clear cold Winter day. That's something that captures most of us know - the radiant heat of the Sun isn't isn't perturbed by the cold air and can be quite comfortable. Then it hit me I heard the word in a John McPhee lecture in Princeton.2 A few decades had passed since he wrote Coming into the Country, but it was about three Alaskas including a look at the Winter. A perfect word for some of the days.
A day of apricity can make snow melt in subzero air temperatures on Southern-facing roofs only to freeze into beautifully clear long icicles at the edge. This type of ice formation is often free of bubbles producing beautifully clear ice. If you have wide enough icicles you might try making an ice lens and starting a fire.
Such days are made for outdoor recreation if there isn't any wind. Perhaps more importantly the basic principle - heat transfer by radiation - can keep heating expenses down. Heating and moving air to fill rooms is enormously inefficient. If you aren't moving around much you might try a small radiant heater and point it at the area where you are. Heat what you need to heat with infrared light. Direct sunlight is the same... sit in the Sun. These measures, plus wearing warm indoor clothing and being somewhat active lets you get away with low thermostat settings. And be on the lookout for aprocity as that can give a big psychological boost!
Another Winter word I like is tingilinde. It's a constructed word based on J.R.R. Tolkien's elfin language Quenya meaning the sparkle of the starlight reflecting on the snow on a dark moonless Winter night. Such sights could be spectacular in Montana away from town when it was really cold and a bit of new snow had fallen as tiny ice crystals. Another great spot is Yellowstone .. super cold air forms the right kind of ice crystal snow near the hot springs and geysers. Once it was magical - the cold starlight reflecting from millions of tiny diamonds along with the greens and reds of a bright aurora dancing overhead. On such nights you don't notice that it's really cold.
__________
1The Compact Edition of the Oxford English Dictionary is the 1928 edition. Devilishly small print that requires a magnifying glass, but the real OED and only about $80 (still a lot back then!) rather than the fortune the full dictionary went for. There's a lovely bit of historical fiction on the dictionary and the people who made it happen: The Dictionary of Lost Words by Pip Williams. It's set in the time and place with many of the characters, but focuses on what was left out.. those who weren't white, male and of a certain class. Recommended!
2 McPhee is a great writer - a master of the creative non-fiction genre.
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.)
His parents were Danish, hers Swedish. By some measures it was a mixed marriage with any number of small cultural differences. He noted and took delight in these small differences and ambiguities. Rather than hunting, fishing or bowling he'd hike in the Summer and take long walks the rest of the year. He liked to walk by himself and I suspect thinking about the stories he'd tell to friends and family about once a week. He said storytelling was in his family and he had a great voice for it. We'd sit in his yard and listen. Some were short, some took a half hour. They were imaginative with emotional moments coming in unsuspecting places. They weren't the polished work of a writer, but left you wondering how he made those connections. Only years later did I learn what an amazingly varied background he had and continually sought out.
My sister is a visual storyteller. It took her half a lifetime to come to a place where she realized a single frame made of many images could be a short story that left you with questions and an open invitation to wonder. She's extremely creative. The stories come to her quickly, but require a week or two to realize. I suspect my Dad was a big influence. He believed the best answers were incomplete and led to deeper questions. He believed breadth was required to see simple answers weren't simple. Corinne went for breadth, unfortunately I started down a path that was deeper than broad.
A trigger for this post was a recent newsletter from David Epstein (The Sports Gene, Range). He begins by talking about Emma Raducanu at the US Open:
Earlier this month, 18-year-old British tennis player Emma Raducanu won her first Grand Slam title. It was a shock; she entered the tournament with 400-to-1 odds. One of my favorite sportswriters, the Guardian’s Sean Ingle, asked Raducanu’s former coach about the factors that helped her talent blossom. Here’s what the coach said:
“From my perspective one of the best things with Emma is that she was exposed to a lot of sports from a young age, and didn’t go too specific into tennis straight away. I see that on court. When she’s learning a new skill, or trying something a little bit different, she has the ability and coordination to pick things up very quickly, even if it’s quite a big technical change.”
Raducanu added this:
“I was initially in ballet, then my dad hijacked me from ballet and threw me into every sport you could imagine. I was doing horse riding, swimming, tap dancing, basketball, skiing, golf and, from the age of five to eight, I was go-karting…From the age of nine I started motocross in a forest somewhere for a year. This was all alongside tennis.”
Although there are a few athletic geniuses like Tiger Woods who focus early, most elite athletes follow a very different path building a broad set of varied skills before specializing. Epstein goes into depth in both of his books. Outside of athletics, the generalists he focuses on in Range have richly diverse backgrounds. Something very different that the experience many have in trade school and college programs. These people have built the tools they need to think creatively. They're often better than narrow experts when confronted with a novel challenge.
I'm sometimes asked to speak on the importance of STEM education at a local school and am doing it again. I tell them STEM ok, but overemphasized in K12. I think a broader liberal arts education leads to flexibility and creativity later on in life. Unfortunately that isn't reflected in many (most?) hiring practices. The lack of intellectual flexibility and diversity has lead to serous problems in some companies (tech in particular). One can always add breadth later, but that can be inefficient once you're out of school.
I don't mean to disrespect STEM subjects. Assuming the curriculum allows, they can be made relevant and exciting to those who won't use them in their work. They add to breadth and can be a starting point for depth. There are wonderful math and science books and teaching approaches that unlock wonder without getting bogged down in minutia. Enough information and wonder that perhaps students will become citizens who can make informed choices.
Over the decades I've slowly broadened muself by talking to people and getting involved with their ideas and projects. Many of you have your own diverse lists. My short and incomplete list includes human powered airplanes, done strange things with sound, learned a little about animated film making, been around story tellers, learned a bit of anthropology and sociology, done art history research, learned about fashion and how clothes are made, learned a bit about diabetes, been involved in sandbending, the mental side of elite sport, and even know a bit about the fluid dynamics of balls used in sports. Many of my guides and friends see this blog and I need to say thank you! It amazes me how some of this triggers a thought in something I'm working on later. You find yourself becoming more creative with age. Who would have thought that the math for thinking about boundary layer separation on an almost non-spinning beach volleyball would help thinking about neutron star atmospheres. Or the linkage between animation and fabric design, or... the list goes on and on...
Depth is great, but you need breadth to be creative.
an almost lost word from the dictionary
The warmth of a bright Sun in on a clear cold Winter day. That's something that captures most of us know - the radiant heat of the Sun isn't isn't perturbed by the cold air and can be quite comfortable. Then it hit me I heard the word in a John McPhee lecture in Princeton.2 A few decades had passed since he wrote Coming into the Country, but it was about three Alaskas including a look at the Winter. A perfect word for some of the days.
A day of apricity can make snow melt in subzero air temperatures on Southern-facing roofs only to freeze into beautifully clear long icicles at the edge. This type of ice formation is often free of bubbles producing beautifully clear ice. If you have wide enough icicles you might try making an ice lens and starting a fire.
Such days are made for outdoor recreation if there isn't any wind. Perhaps more importantly the basic principle - heat transfer by radiation - can keep heating expenses down. Heating and moving air to fill rooms is enormously inefficient. If you aren't moving around much you might try a small radiant heater and point it at the area where you are. Heat what you need to heat with infrared light. Direct sunlight is the same... sit in the Sun. These measures, plus wearing warm indoor clothing and being somewhat active lets you get away with low thermostat settings. And be on the lookout for aprocity as that can give a big psychological boost!
Another Winter word I like is tingilinde. It's a constructed word based on J.R.R. Tolkien's elfin language Quenya meaning the sparkle of the starlight reflecting on the snow on a dark moonless Winter night. Such sights could be spectacular in Montana away from town when it was really cold and a bit of new snow had fallen as tiny ice crystals. Another great spot is Yellowstone .. super cold air forms the right kind of ice crystal snow near the hot springs and geysers. Once it was magical - the cold starlight reflecting from millions of tiny diamonds along with the greens and reds of a bright aurora dancing overhead. On such nights you don't notice that it's really cold.
__________
1 The Compact Edition of the Oxford English Dictionary is the 1928 edition. Devilishly small print that requires a magnifying glass, but the real OED and only about $80 (still a lot back then!) rather than the fortune the full dictionary went for. There's a lovely bit of historical fiction on the dictionary and the people who made it happen: The Dictionary of Lost Words by Pip Williams. It's set in the time and place with many of the characters, but focuses on what was left out.. those who weren't white, male and of a certain class. Recommended!
2 McPhee is a great writer - a master of the creative non-fiction genre.
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