Zero, corrected

My lovely bride pointed out to me yesterday that I was wrong. This is not news around here. She keeps records of things like low temperatures and she showed me at least two instances where we were well below the ten degrees Fahrenheit I mentioned.

In December of 2013 we had back-to-back nights of -5 ºF and in January of 2017 we bottomed out at -10 ºF.

A negative ten degrees, or ten degrees below zero, would be -23 on the Celsius scale!

Our Founding Fathers did not know about negative numbers, or if they did, they considered them nonsensical. Negative numbers had been around for a thousand years and had been used by Indian and Arabic mathematicians for centuries but did not really gain much traction in the West until the 18th century.

Numbers are more than just quantities. When you put them on a number line you now have something more than just size or magnitude, you now have direction.

A negative number has the same magnitude but it is the opposite of a positive number. On a temperature scale the change in direction is up or down and on a number line it is left or right but the concept is the same.

Beyond that, negative numbers occur in algebraic solutions (remember the quadratic formula?) and along with imaginary (complex) numbers are essential in engineering and science. You just can’t do enough stuff if you only have positive, real numbers.

The obvious use of negatives to represent debts, losses, and outflows in accounting did not become a common practice until modern times.

My sister-in-law pointed out to me that the new vaccine from Pfizer for COVID-19 has to be stored at -80 ºC (-112 ºF). Brrr! Imagine if we could not talk about such things like eighty degrees below the freezing point of water or that such notions were not a commonplace part of a child’s education. That’s weird to think about. Many of the profoundest minds in our history would have been bewildered by something we teach in elementary school! As a race, humanity is a hell of a lot smarter now than we were in the past. That’s not to say we’ll always act smart, just that we are smarter.


It is just past one o’clock here and the thermometer says zero. That’s Celsius, of course, and it sounds worse than it is. In our more familiar Fahrenheit system the air temperature is a balmy thirty-two degrees on the plus side of zero.

The centi-grade system is based on one hundred degrees as you would expect. Water freezes at zero and boils at one hundred.

Fahrenheit’s scale uses one hundred-eighty degrees for the same span: water freezes at thirty-two and boils at two hundred-twelve.

Both are arbitrary. The thing I like about Fahrenheit is when the temperature climbs into triple digits, from the 90s to the 100s, you know it is really hot. The Celsius scale has you going from the mid 30s to the low 40s and it just isn’t the same. Our body temperature of 98.6º F translates to 37 ºC and so a jump to 100 ºF, which is dramatic, seems less so when it is only a jump to 38 ºC.

Other than that you can get used to the Celsius scale easily enough. I like to remember a couple of key points like room temperature which at 68 ºF is 20 ºC. That’s a good point to start. Every five Celsius degrees is equal to nine Fahrenheit degrees so you can just count by fives on one side and add nine on the other.

25 ºC is (68+9) 77 ºF and 30 ºC is (77+9) 86 ºF and so on. You can go down as well. Remembering that 20 ºC equals 68 ºF means that 15 ºC is (68-9) 59 ºF and 10 ºC is (59-9) 50 ºF and so on.

I suppose that is only handy if you are travelling in England or whatnot and they give the weather forecast in Celsius. By the way if you use my subtraction method above all the way down to -40 on the Celsius side you will find that it will equal -40 on the Fahrenheit side! Just a little quirk in the two systems—they are offset by thirty-two degrees and a Celsius degree is 1.8 (9/5) times bigger than a Fahrenheit degree. If the two temperature scales are plotted on a graph the slopes of the lines will be different and that means they have to intersect somewhere.

Thirty-two degrees Fahrenheit (zero Celsius) isn’t all that inviting for a walk around the block but is pretty mild overall. We can get days that are below freezing, in the teens and 20s, which puts you into negative numbers in Celsius (-5 ºC = 23 ºF and -10 ºC = 14 ºF).

It seems like negative numbers should be reserved for the really cold days and the Fahrenheit scale works like that. Anything below zero Fahrenheit (-18 ºC) is really cold, something on the scale of winters in North Dakota. The coldest temperature we have recorded living here thirty-plus years is 10 ºF (or -12 ºC). People in Nebraska get that kind of stuff all the time which makes me happy I live here and not there.

Speaking of variation, you probably know from experience that water boils at different temperatures depending on the altitude (elevation above sea level). That kind of thing, plus the arbitrary nature of the temperature scales, has scientists in search of a more absolute way to measure temperature. The Kelvin scale is based on the idea of absolute zero, when molecular motion is so insignificant it cannot be measured as heat. This scale zeroes out at about -459 ºF (-273 ºC).

If I convert today’s 32 ºF (that is, 0 ºC) to the Kelvin scale I get, interestingly, 273 Kelvins (you don’t say “degrees Kelvin”, just “Kelvins”). A Kelvin, it turns out, is the same size as a Celsius degree, but the scale starts at a different place, absolute zero.


The Weather Service says we might get up to a quarter-inch of rain today. It got me thinking: how much is that?

An inch of rain is just what it says, enough water on the ground to make a depth of one inch. But that’s just one axis of the problem. How much water is that, really?

Let’s imagine a square yard of land, three feet long and three feet wide. Rain falls to some depth, like a quarter-inch or half-inch. If we have to put everything in inches that’s a 36-inch by 36-inch plot, or 362 or 1296 square inches.

If our precipitation is one inch, that’s 1296 x 1 or 1296 cubic inches of water.

If our precipitation is a half-inch, that’s 1296 x (1/2) or 648 cubic inches of water. Thus a quarter-inch of rain would be 324 cubic inches.

But that’s no help. No one thinks about water in cubic inches. We need pints and quarts and gallons! A quick trip to Wolfram Alpha reveals that a gallon of water is 231 cubic inches.

So an inch of rain on a square yard (1296/231) is 5.6 gallons, or five gallons plus five pints. And a half inch is 2.8 gallons and a quarter-inch is 1.4 gallons, or one gallon plus one quart plus one pint.

Let’s translate that to an acre. An acre is 660 feet by 66 feet (do you know why?*) or 43,560 square feet. That’s 220 yards (one furlong) by 22 yards or 4840 square yards.

4840 multiplied by 1.4 gallons gives me 6776 or almost 7000 gallons of water. I live on about one-third of an acre here in town and that means we should get well over two thousand gallons today! The water trucks you see at construction sites carry anywhere from 2000 to 4000 gallons, so that’s a way to visualize the amount.

It has been raining steadily since before sunrise so I think we might get more than is forecast, or at least be closer to the upper end.

California is perpetually short of water. The notion of seasonal drought is a quaint anachronism—supply will always fail to meet demand and that means drought is a permanent condition, just temporarily (and locally) relieved by precipitation.

Some of this water will make its way to the streams and some of it will fill lakes and ponds and some of it will recharge aquifers and some of it will be taken up by plants (even this late in the year) but most of it will evaporate and/or find its way back to the ocean. And the cycle will start all over again.

And some time around May the rains will stop and we’ll have to make do with what’s left over to get us through October and back to the wet season. I remember telling my Irish cousin that we could go six months without rain in California and she was literally open-mouthed with astonishment. She kept shaking her head and saying “can you imagine that?” to her kids. They get over 100 inches of rain per year in Galway which means they average well over a quarter-inch per day.

Now THAT’S a lot of rain!

*An acre is 10 square chains, that is, a piece of land 10 chains long by one chain wide. A chain is 66 feet so 10 x 1 is 660 x 66 and thus 43560. A square mile is 640 acres. Can you see why? (Hint: a mile is 80 chains long.)

SNOW . . . and a president

This morning we were treated to our first-of-the-season snowfall:

It’s wasn’t much, but in the water-starved State of Jefferson it is a thing of beauty. Let’s hope it is a harbinger of colder and wetter times!

It wasn’t until yesterday that everyone agreed to call the election. The Founding Fathers did not want the people to select the president, they wanted the states to select the president. That means we have to sit around and wait for razor-thin margins in places like Pennsylvania or Georgia or Arizona to get settled before we get a result. The popular vote was a clear win for Biden, but like 2016, a few thousand votes in a few dozen counties in a handful of states decided the outcome. Trump was able to eke out an electoral win last time with that math, despite losing the popular vote, but this time the coin flipped the other way.

And I don’t know about you, but I think a coin flip is a lousy way to decide things. I suppose, in a politically divided country, close national elections will be the new norm.

Biden’s lead over Trump is a little over four million votes, which is about the difference in the California vote alone. Californians cast about fourteen million votes in total, roughly one-tenth of the national total.

I’m not sure whether to be embarrassed by the painfully antiquated voting systems in our country or charmed by their rustic quaintness. I suppose a slick, new system where everyone could vote from their phone, laptop, or a computer at the public library would come with its own set of problems, so let’s just do the best job we can with what we have. Everyone does banking and other personal stuff via the world wide web these days, I suspect at some point we’ll vote that way too, but that’s probably farther away than I think.

I was in the 8th grade in 1972 and that was the first national election I paid any real attention to. I was too young to vote in 1976 and cast my first ballot in the 1978 gubernatorial contest (for Jerry Brown!). I’ve voted for a president eleven times (’80, ’84, ’88, ’92, ’96, ’00, ’04, ’08, ’12, ’16, ’20) since then, with my candidate winning five of those contests. What was it I was saying about coin flips? I like those odds better.

Meanwhile, with the race decided we can get back to other things. Like watching the weather and hoping for lots more snow!


The first of Mr. O’Connor’s Three Rules of Science™ is:

all measurements are uncertain.

It’s the size of the uncertainty that matters. How much uncertainty can you live with?

Some phenomena can be measured quite precisely. Others, not so much.

Measuring people’s feelings, for example, or their intentions, is difficult. Even when faced with a binary choice like Trump v. Biden people equivocate when asked about their decisions.

This creates uncertainties in polling. We all KNOW there are such uncertainties but we don’t talk about them. We look at a poll or a survey and it says “47% of people support . . .” and we don’t think “oh that means it could be 42% or even 52%” or somesuch. We get stuck on the number as a fixed thing.

It’s not. It’s just a stop on a continuum. The polls all have ranges attached to their numbers like “+/- 3%” and that means that’s the most likely set of outcomes in their model.

Polling and pollsters are going to get a lot of heat in this election, much like the last one, but it is misplaced. Consumers of polling information should focus on the uncertainties in the polling results and the biases in the polling methods and not assume the models are predictive. They are just models after all, and even good models need to be continuously tweaked.

A “surprise” in an election is often just dissonance with the polls. An expectation of an election result is formed by the pre-election information presented by the polls. If you did not have that information in the first place you might not consider the outcome a surprise!

We expect a lot from these polls. We expect them to give us knowledge about the future when they can only guess at a cluster of possibilities. It’s the process of making those predictions that’s exciting, not the predictions themselves. Building robust, powerful models is foundational work in science. That can only be done with continuous trial-and-error. If the pollsters get it “wrong” then they have a new challenge to work on for the next go-round.

It stinks to have this much uncertainty in our national election. It’s hard to live with. What matters at this point, of course, is not what anyone said beforehand, but reducing, as much as possible, the uncertainly in the final vote counts. Even something as apparently simple as counting and tallying has uncertainty, and I’m not sure any of us knows how much of that there is, and I’m also not sure we really want to find out.

Wood, fire, heat, and smoke

Summers here in the arid West are punctuated by smoky stretches that can last days or even weeks. No one likes the smoky skies and no one wants to breathe the polluted air.

And yes, wildfire smoke is a pollutant. Perhaps I should say it contains many long-recognized polluting chemicals. You’ve heard of them: carbon monoxide, benzene, sulfur and nitrogen oxides, dioxins, formaldehyde, etc. Add in the particulates, especially the small ones (less than 2.5 microns), and weird stuff like mold spores, and you have a nasty brew that is NOT good to breathe.

Now that autumnal weather is here and winter is approaching temperatures are dropping and the heaters are coming on.

That means more wood smoke. It’s almost de rigueur in the rural West to heat your home with wood. It’s a rite of passage to, at the very least, split and stack firewood every fall. Some folks go out and get their own from the vast quantities available in our nearby National Forests. But the majority of people with wood stoves get their fuel delivered. Split, seasoned firewood is sold by the cord (a stack four feet wide, four feet high, and eight feet long) in various lengths (usually 12 to 18 inches). A good quality cord of hardwood like oak can set you back well over two hundred dollars.

There’s nothing quite as satisfying on a cold winter day than a roaring wood fire. The radiant, penetrating heat put out by a wood stove cannot be replicated by more modern heat sources.

But it comes at a cost. Wood is messy. It takes a lot of time and energy to maintain a fire and keep a home heated. The fuel quality varies greatly, as does availability. Wood piles are sources of insect infestations and potential fire hazards. Creosotes, which are by-products of wood combustion, build up in chimneys which require frequent cleaning to reduce the additional hazard of flue fires.

In our home we have both electric heat (via heat exchangers) and a fuel oil furnace. We don’t have natural gas here in Siskiyou County because the pipeline is too far to the east of us and thus we don’t enjoy the benefits of that energy source. We do have town gas (a propane mixture) that runs on an antiquated underground system, but we un-installed that in our home due to its high cost. Bottled gas like propane can run heaters but can’t compete with kerosene-type fuels for efficiency.

As a result we almost never use the wood stove to heat the house any more. We are glad to have it in case there is a power outage (very rare here) in the depths of winter. But the time, effort, and mess associated with a wood fire can’t compete with the ease and convenience of a modern system that one can “set and forget.”

One of the problems with wood heat is that it is almost impossible to regulate. Wood should be burned hot, and completely, in order to reduce emissions. But folks who want a fire in the morning “damp down” their stoves at night, that is, reduce the air intake so that the logs smolder and burn slowly. That keeps them from being consumed and keeps the fire from going out which makes it easier to re-start. This of course is terribly polluting. And it is a matter of guesswork as it depends on how well-seasoned the logs are, the type of wood, the size of the stove, the drop in night-time temperature, even the relative humidity and the outside barometric pressure. Everyone with a wood stove knows the particular quirks of their situation. I’ve been in wood-heated homes when the output of the stove was so ferocious that doors and windows were left open so the heat could escape! That happens sometimes when you get a big fire going—it heats the stove up so much that the box will continue to radiate even as the fire wanes in intensity.

Like all things, wood heat is a trade-off. Many folks appreciate that wood is abundant locally and can be a cost-effective (if you don’t consider the labor costs) alternative to fuel oil and/or electric heat. Many older houses don’t have another heat source. Lots of mountain municipalities regulate wood-burning due to the pollution but have exemptions for low-income people and homes without other options. Wintertime atmospheric inversions are very common in alpine regions and the valleys and basins which hold the bulk of the population can get as polluted from wood smoke as any diesel truck- and passenger car-choked urban area.

And there’s the rub. Because wood smoke, be it from wildfires or hearth fires, is natural, it is not always perceived as a hazard.

That’s nonsense, of course. A poison, be it made by the Hand of God or the Hand of Man, is still a poison. Our ancestors harnessed the fire from wood. Then they harnessed the fire from peat and coal. Then oil and gas. And now we harness fire from the atom.

All of those fires are both good and bad. There is no pure, perfect, “natural” fire. They all come with costs along with the benefits.

I’m looking forward to winter, I always do. I like the cold weather and the opportunities to go skiing and even perhaps do some snow-shoeing. But I can’t say I’m going to enjoy all the seasonal wood smoke. It was easier when the summers weren’t so bad. Now we breathe that stuff all year!

Lots of active weather patterns with frequent storms will be good. Those will keep the air moving and well-mixed and help the pollutants disperse. The crisp, clean mountain air, especially on a brisk January day, is one the best things about living here. Let’s hope we get lots of days like that.

Cedars of Yreka

A few days ago we were sitting at the patio table and watching the trees in the backyard swaying gently in the breeze. We noticed puffs of what looked like yellow smoke coming off the Deodar cedar.

It was pollen, of course.

Here’s what the estimable Sunset Western Garden Book had to say under the entry for Cedrus (true cedars including C. deodara):

Male catkins produce prodigious amounts of pollen that may cover you with yellow dust on windy day

3rd printing May 1989, p. 272

I’ve had to hose off the table twice more since then!

According to botanists there are only four true cedars. One is this species, C. deodara, also known as the Himalayan cedar (its native range). The famous Cedars of Lebanon (C. libani), mentioned in the Bible, are also in the genus Cedrus. The other two are also Mediterranean, the Atlas cedar (C. atlantica) and the Cyprus cedar (C. brevifolia). True cedars are members of the pine family (Pinaceae).

European naturalists encountering new plants in the Americas named them with systems imported from overseas. There are no true cedars in the Western Hemisphere but there are cedar-like trees that were tagged with the name. Ubiquitous in California forests is the incense-cedar or Calocedrus decurrens, a member of the cypress family (Cupressaceae). We have one in our yard. Heading north into Oregon, Washington, British Columbia, and Alaska you find the widespread Western red cedar (Thuja plicata), also in the cypress family. If, like us, you have an arborvitae among your plantings, that’s a relative—Thuja occidentalis.

Back here at home we moved the patio table from outside to under the overhang to keep it free of pollen. Tree pollens are particularly fine and dry compared to flower pollens and are thus easily spread far and wide. Although Deodar cedar pollen is not classified as an allergen, I’m convinced that my runny nose, itchy eyes, and hacking cough last week had something to do with all that yellow stuff floating around my back yard.

Lately the days have been beautiful and smoke-free, so I’m not complaining!

Cold, Rain, and Snow

It’s not bad to be wrong. Sometimes being wrong is the only way to find out how to be right.

Or at least get closer.

The forecasts for the upcoming winter here in the West are not encouraging:

There is literally a “sliver of hope” in the map above for us here: the tan-colored triangle in northwest California along the Oregon border just might include Yreka!

This is a little less depressing. We may get our usual precipitation, which of course isn’t much, but it doesn’t look like a banner year.

Here’s the one that spooks me a bit:

I don’t want “warmer than normal” I want “cooler than normal”!

Despite our best effort, weather and climate forecasting is still pretty tough. The models are saying the chances are good we will have a warmer, drier winter.

Meteorologists and other scientists have to remind themselves that all models are wrong. They are just models after all, no matter how sophisticated, and a model is not reality.

Models get corrected and updated frequently precisely because they are wrong, and like I said earlier sometimes that’s the only way to get closer to being right.

So I sure hope the models are wrong for this winter. Bring on the cold, rain, and snow!


A little, anyway. Not hardly enough, of course.

It’s knocked down the smoke some, perhaps the wind can take care of the rest.

Summer in the Golden State is losing its luster. It was never my favorite time of year, despite being a schoolteacher and a baseball fan! I like the rainy time which is from November to April in most of the state.

There are mountains between me and the Pacific. The Shasta Valley and environs are in the rain shadow of the Klamaths. Suffice to say it is dry here, like much of California.

Like most California cities, Yreka is an oasis sustained by plumbing. We have a water source, Fall Creek, that is a few dozen miles from here so we need a pipeline. Our green lawns and healthy gardens are an illusion. Left to itself, the land here would support juniper, ceanothus, and star-thistle!

Fires have ravaged the West this year. You’ll hear lots of reasons for it, and they are all true. Years of aggressive fire suppression have built up impossible fuel loads in the forests. Logging cutbacks have multiplied that effect. Arguments over policy and bureaucratic inertia have stymied progress. Population growth has put more people on the wild land interface. Climate change has increased the frequency and severity of weather and fire events.

Whenever you are presented with a complex problem, be suspicious when presented with a simple solution. A complex problem is one that can be approached from a variety of perspectives which yield a variety of potential solution paths. At the very least, a complex problem requires a multiplicity of solutions.

Most of the time we solve complex problems by just pushing ahead and seeing what happens, then adjusting on the fly. The problem now is that things are moving too fast. When we just push ahead without forethought, without at least an attempt at planning and problem-solving, we fall back on old habits, old biases, and outmoded ways of doing things.

Engineers often write impossible-to-solve equations for phenomena they study. So they have to make good approximations instead, and that helps guide their work. We need to do the same thing as a society. We don’t know the best way, but we can make models from what we do know, and use those to generate ideas.

And we need the poets on these things, too. They don’t work with differential equations, but they solve equally thorny problems like how to express truth and beauty in the fewest words possible. So they know how to imagine, and see beyond the limits of the language. We will need that to fuel innovation.

The future of life here in the Golden State will likely require an entirely new aesthetic. The California Dream is transforming before our eyes. Let’s get creative and build anew, and stop worrying about what went on before. The most important question is “what shall we do next?”

In the meantime we could use some more goddamn rain!

A truckload

I don’t like to go outside on the really smoky days and today is one of those really smoky days. Here’s the AirNow monitor:

So it got me to thinking, how much air do we breathe every day?

I took a number from HowStuffWorks to get an estimate. They use 11,000 Liters per person per day. The American Lung Association says 2,000 gallons per person per day. That converts to 7571 Liters. I expect there will be a lot of variation in this estimate.

I found I could easily mostly fill a 4-gallon trash bag exhaling normally in one minute. The bag was not at capacity as I had my hand holding a twist in the top few inches, so I estimated the amount with a little geometry. The full part of the bag was a weird, pointy, oblong shape, so I imagined it as a right circular cylinder. I set 12 inches as the average height, 4 inches as the average radius, and used the formula Area = πr2h and got 603 cubic inches. A gallon is 231 cubic inches, so that’s about 2.6 gallons.

If I breathe air at a rate of 2.6 gallons per minute that’s 156 gallons per hour or 3744 gallons per day. That’s over 14,000 Liters. I guess I’m a “heavy breather”!

I don’t think much of my estimate, but I note that it aligns with the other estimates so I will assume their estimates are reasonable. I suspect I would breathe at about half the rate when I sleep, so my 14,000 Liters would then be closer to 10,000 Liters.

So how big is 10,000 Liters? Is 2600 gallons easier to visualize? How about 350 cubic feet?

The cube root of 350 is about seven (7 x 7 x 7 = 343). Imagine a box 7 feet on a side: height, length, and width all about seven feet. That’s how much air you need every day.

Another way to imagine it is in cubic yards, which is about thirteen. Our local garden supply outfit can deliver 10 cubic yards of rock in one load with their ten-wheeler dump truck. Those concrete mixers you see hold about 8 cubic yards.

So if you want to know how much air you need each day, it is at least one truckload!