What cell phones teach us about the power grid

Back in the day the telephone network was a regulated monopoly. As long as the phone company kept the regulator happy, they were permitted to earn rate of profit on their investment. This resulted in a couple of interesting effects.

First of all, the company was incentivized to invest more in infrastructure: The more they invested, the higher their profit (which was a regulated rate times the size of their investment). This is very different from an unregulated company, where investment is viewed as a cost.

Second, while keeping the regulator happy was always a complex dance, the regulator tended to focus on a few key metrics, one of which was network uptime. This incentivized the phone company to use that large infrastructure investment to produce a network of extreme reliability.

And that network was reliable. In my personal experience with wired phones in that era a wired phone always had service: For two decades as a youth I had literally 100% success picking up a phone and getting a dial tone. Likewise, calls did not drop. Service was rated in nines: 99.999% uptime was 5 nines, 99.9999% uptime was 6 nines.

Of course, that sort of reliability is impossible with cell phones. They move around. Worse yet, they go places where radio signals simply can’t reach.

Cell phone reliability is pretty darned good—let’s call it 98%, as long as you’re not trying to get service in places where nobody else cares if there’s service (the middle of the desert, the middle of the ocean, etc.). But people are not surprised when they find a spot where there’s no service, nor are they surprised if a call drops when elevator doors close or they drive into a tunnel.

This is not to say that cell phone service is bad. My point is simply this: To get the advantages of cell phones, people have accepted a drop in telephone service reliability from six nines down to less than two.

I think this is particularly of interest because I see a potential parallel with the power grid.

The big problem with solar and wind power is that they’re crappy at providing baseline power, for obvious reasons: nighttime, cloudy days, calm days, etc.

If you want a power grid to provide five or six nines of availability, you really need to have enough fossil fuel (or nuclear) generation capacity to provide a large fraction of your total power needs—at least 80%, probably more if you don’t have considerable diversity in your renewable sources (both diverse sources: solar and wind, and geographic diversity: the wind is always blowing somewhere and the sun shines different hours different places).

But just as people learned to get by with less than two nines of phone network reliability, people could certainly learn get by with a less reliable power grid as well.

Thinking of household use, there are certain things that really need fairly reliable power (refrigerator, freezer, furnace), but beyond those few things, we only require a high-availability grid because we’ve set things up with the expectation that it would be there.

Just two or three modest changes to the way we use power could easily accommodate a less-reliable grid.

The easiest one would be for each household to have a guaranteed level of power—enough to keep your food fresh, your pipes unfrozen, and a couple of lights turned on—and then make additional power available on an as-available basis. Alternatively, you could go with a market-based measure where power was cheap when it was plentiful and expensive when it was scarce. A third option would be to distribute the resiliency, with each household providing its own backup power storage or generation capability.

My point here is not to solve the issues for a smart grid, but just to make this point: For a big enough payoff—like the payoff of a internet-connected supercomputer that you can carry in your pocket—we would accept a considerable downgrade in reliability from our power grid.

The payoffs from renewable energy arguably are that big. (In particular, not rendering the planet uninhabitable for humans. But that’s a payoff that’s uncertain and diffuse, with the gains—especially the early gains—going to people other than the ones who need to make the sacrifices.) But there are payoffs to everybody: less particulates in the air, fewer pipeline and tanker spills, fewer truck and rail accidents hauling coal and oil through towns and cities, fewer worker deaths in the coal-mining and oil-drilling industries. And then there are the cost savings: Renewable power has the potential to be very cheap and very reliable in the out-years, once the infrastructure has earned out its initial capital costs.

It might well be worth getting past the idea that the power grid should provide near-perfect reliability, given the payoffs involved in accepting a bit less.

Walking past the UofI’s solar farm

There’s a dearth of good walking routes from Winfield Village to Champaign and Urbana.

From west to east, the choices are Prospect, Lyndhurst/Fox Drive, Neil/Route 45, First Street, and Race Street. The first two are okay if we’re heading to western or central Champaign, but are pretty out-of-the-way if we’re headed to campus or to Urbana. The latter two lack sidewalks and entail long walks along busy roads, which makes them pretty unsatisfactory.

A few weeks ago, I saw a pack of cross-country runners turn up a rather faint double-track on this side of the railroad, which alerted me to the fact that it’s possible to go that way.

img_20160409_132552803_25726287304_oI was doubly interested in going that way, both as a possible alternative route north, and because about one mile north of us there’s a large installation of photovoltaic panels that the University has been calling its “solar farm,” and this bit of double-track leads right to it.

The track runs along the west side of what seems to be research crop fields for the University, although that bit of it may be an easement to provide access to a recently constructed line of pylons for some high-tension power lines.

The solar farm seems to producing quite a bit of electricity on sunny days like today.

Having walked to the solar farm we turned east. Having come that far instead of having to walk a mile along First Street, we only had a quarter of that distance to cover before we reached Windsor and were able to get on a proper sidewalk.

We took a nice tour around the more obscure corners of the research park, including a little diversion past the Fire Service Institute’s training facilities. Then we crossed Route 45 and made our way down to Schnuck’s to pick up a couple of groceries and head on home.

Total walking was 7.7 miles, in my case added to a 3.5-mile morning run.

I had not done much running since settling into the low-carb thing. Together with the walk, it’s a bit of a test of whether I’m seeing any of the endurance benefits I’m hoping to see. (Answer: Maybe. I certainly didn’t get hungry or feel a need to fuel up during the walk. But then, neither did Jackie.)

Coal and fossil forests

I spent my lunch hour at an OLLI lunchtime lecture, learning about why we have coal in Illinois, and why sometimes coal formations have fossilized forests on top. The talk by Scott Elrick (of the Illinois State Geological Survey) was absolutely fascinating.

The first part of the talk looked at the history of continental drift, looking at where the land mass that eventually became North America (and the piece of it that became Illinois) was over the last few hundred million years. During the Pennsylvanian period, Illinois was roughly on the equator, which turns out to be important.

To get coal, you need to have lots of plant matter, but very little sediment. If you don’t have the plant material, you’ve got nothing to turn into coal. But even if you have the plant material, if you have any significant amount of sediment—inorganic material washed in by water and deposited on the ground—you don’t end up with coal, you just end up with shale.

There’s an area along the equator called the “convergence zone” where the weather of the northern hemisphere meets the weather of the southern hemisphere. Most of the time, this zone shifts north and south over the course of a year, meaning the tropics experience wet seasons and dry seasons. However, during the period in question there was extensive glaciation, meaning lower sea levels, which turns out to mean much less shifting of the convergence zone. Which means that, for a geologically long period of time, it rained a lot, all year.

That’s the circumstance that lets you get coal. To be more specific, that’s the circumstance that gets you peat.

Lots of plant matter, but very little sediment (because those plants had lots of roots to stabilize the ground, and they never had to die back, because there were no seasons). The plants grow, the plants die, the dead plants end up on the wet ground, they get covered with water, which limits the oxygen that gets to the plant, meaning that more plants can grow on top of them before they decay. Result: peat.

To get coal takes one more thing: Your peat has to get buried. If it gets buried well enough that air never gets in there, and if it ends up buried deep enough that there’s some serious pressure and heat, and stays there for long enough, all the volatile (i.e. non-carbon) elements in the peat get cooked off. Result: coal.

So, in the Pennsylvanian, we had this long period of nothing but rainy season, allowing layers of peat to build up. But eventually the glacial period ended.

It turns out that glacial periods can end really fast. They start slow, with ice building up gradually over decades and centuries. But they can end very quickly, with centuries of ice melting in a matter of years.

The ice melts, the sea levels rise, and the convergence zone starts showing seasonality, moving north and south over the course of the year. Forests full of plants that expected rain every day suddenly had to adapt to tolerate dry seasons.

This produced a lot of changes, of course. The plant species show dramatic shifts. Crucially, they die back during the dry season—meaning that you start to see a lot more sediment.

In the fossil record, you see this as a thick vein of coal with a thick vein of shale on top.

And right here in east-central Illinois, something very interesting happened. Along a fault line, a series of earthquakes caused the ground on one side to sink. In that sunken area the sediment built up even more quickly—quickly enough to cover whole plants. Fallen trees were covered up faster than they could rot away. Branches with leaves were covered before the leaves could fall off.

The result is a thick vein of coal, with a fossil forest on top of it.

Is that cool or what?

This particular forest, near Danville, Illinois, was the first one discovered that was big enough that paleobotanists could study the forest at the level of the forest community. As opposed to just seeing what plants grew near a few other plants, they could see how the plants that grew near one another changed as you moved from one part of the forest to another.

Painting by J. Vriesen and K. Johnson via nature.com

Scott Elrick showed us all kinds of cool stuff. One thing was this artist’s rendition of the forest, showing large, tall trees growing very close to one another, something that would be rare in forest today. Turns out that these trees—Lycopods—had photosynthetic bark, and didn’t grow leaves until they reached their full height. So they didn’t shade out their neighbors the way modern trees do. They also had very long roots that extended many meters from the trunk, but the root systems were quite shallow, going just a few meters down.

He also had pictures taken from within the coal mine, showing the fossils of these trees—trunk and roots—growing right up out of the coal seam: Trees that had been alive when the weather changed and that ended up with a meter or two of sediment covering the bottom of the trunk fast enough that the tree never fell down. It just fossilized in place.

It was a great talk at which I learned all sorts of things about geology and paleobotany. I’m going to have to follow this guy’s work in the future.

The huge win of moderately high-speed trains

Since there scarcely any thought of building them in the US, it’s silly to worry about the downsides of real high-speed trains, but it’s the sort of thing I tend to worry about. After all, the math is kind of scary.

It’s only 135 miles from Champaign’s Illinois Terminal to Chicago’s Union Station. If your trains can average 135 mph, you could make the commute in an hour—a long commute, but well within the range that many people find acceptable.

On a train that fast, you could depart Champaign at 6:45 and get to your desk anywhere in the Loop by 8:00. Another train that left at 7:45 could get you to Union Station in time to be at your desk at 9:00. Combine those with similar trains that departed shortly after the close of business and got you back to Champaign in time for supper, and suddenly Champaign offers all of its regular attractions plus all the attractions of Chicago.

Personally, I think that would be awful. It could easily attract thousands of new residents to Champaign—and Champaign does not need thousands of new residents.

Happily, the high-speed rail network that the US is actually building operates at a top speed of 110 mph—fast compared to highway speeds, but nothing like an average of 135 mph. I don’t know what sort of average speed that would produce, allowing for congestion and stops along the way, but let’s just pick a number and say we could average 90 mph. That would mean that it would take one hour thirty minutes to get to Chicago.

Suddenly the math for making Champaign a bedroom community is much less compelling. At 90 mph, the furthest you could live from Chicago and still have a one-hour commute would be Gilman. As a practical matter, people who found the idea attractive would probably live in Kankakee instead. Not that I have anything against Kankakee, but better they get thousands of downtown Chicago workers than we do.

While averting the downside of turning Champaign into a bedroom community, moderately high-speed rail service is still great for non-commuters. Amtrak service to Chicago is already pretty good—fine for a day trip to Chicago. I can catch the City of New Orleans at 6:00 AM and get to Chicago before the museums open. After a day in the city I can either leave around 4:00 PM on the Illini and get home in time for supper, or I can have an early supper in Chicago, leave around 8:00, and get home by bedtime. Imagine if those trains averaged 90 mph.

Better, imagine a couple of 110 mph trains making evening runs designed to allow people in Champaign to head into the city after work, arrive early enough for a late dinner—or, if they ate dinner on the train, a show—and then return in time to spend the night in their own bed.

The more I think about it, the happier I am with the (objectively pretty lame) moderately high-speed rail taking shape in the US. It has great potential to make Chicago accessible for half-day or evening visits without the downside of turning Champaign into a bedroom community.

(All these meditations prompted by Andrea Mayeux‘s article Researchers say high-speed rail could fuel U.S. real-estate, economic booms, via Tobias Buckell’s post High speed rail could spark a real estate boom in second tier cities.)

Reducing poverty

I’m big on reducing poverty, both locally and globally. (I do worry that more rich people will use more resources, suggesting that reducing poverty isn’t an unalloyed good thing. On yet another hand, only rich people can afford things like sequestering carbon or preserving habitat. It’s complicated.)

Since I’m interested in reducing poverty, I was interested in Lant Pritchett’s recent talk Everything you think you know about poverty is wrong.

Pritchett and I see pretty much eye-to-eye on how to have a rich country, I think.

These well-off countries have a productive economy, a government that is responsive to the citizens, a capable bureaucracy, and the rule of law.

This has interesting implications for global development, because these are all things where it’s very difficult to improve someone else’s situation. If a country has government by-and-for the elites, or a corrupt bureaucracy, it’s going to be poor—and there’s very little outsiders can do to help. One of Pritchett’s points is that things that seem like they might help, such as improving education, seem to do more harm than good—perhaps because well-educated corrupt bureaucrats are worse than ignorant ones.

His solution is for rich countries to create or expand guest worker programs, which I think is a poor idea.

It’s not that I don’t think it would work. A poor worker who came to a rich country and worked a couple of years could both support relatives back in the poor country and save up enough money to return home and start a business. That would relieve poverty both immediately and going forward. It would also produce another person with first-hand experience of the advantages of a less-corrupt society (as opposed to merely seeing the advantages of getting in on the corruption).

The main reason I think it’s a poor idea is that enforcing a guest worker program eventually requires a police state. Somebody has to check all workers—it’s the only way to identify those who aren’t legally entitled to work. Somebody has to make sure those whose permission to work has expired get fired. Those whose permission to live here has expired, but who don’t go home, become an underclass with all the usual problems of an underclass—crime, violence, oppression, disease. I’ve written about this before (see Missing the point on immigration).

There is also the issue of how guest workers affect salaries, wages, and working conditions of citizen workers (short version: I think it makes them worse).

The ideal solution, of course, would be for every country to be rich enough and free enough that people from all over the world would want to move there. But that just brings us back to where we started.

Dressing for . . .

It was on my first trip to England that I came to understand that what we think of as formal wear, business attire, and sports clothing was originally designed to be the most comfortable possible clothing for the circumstances. The circumstances in this case being the climate, technology, and infrastructure of England in the eighteenth and nineteenth century.

Without central heat interiors were going to be chilly, but even if you were quite frugal with your wood or coal they would not have to be really cold.

Given those indoor circumstances, and given that you had to make do with wool, silk, linen, and cotton (because there were no synthetic fibers), you would quite naturally end up with just the sort of garments that we now think of as being part of formal wear—wool coats and vests, silk bands to wrap around your neck, and so on. Sport clothing, of course, was for the sort of sports the English aristocracy engaged in: riding and shooting. Tweed and leather were very practical.

It seems obvious now, but it was something of a revelation to me. When I was younger, I always thought of that sort of clothing as being uncomfortable.

Partially that’s because such clothing is only really comfortable if it really fits. You don’t need a bespoke suit for it to fit correctly; even today good men’s clothing is routinely altered to fit. But clothing purchased for a child will never fit for long (and often never fit at all, because the child knows neither how the garment is supposed to fit nor how to articulate any issues discovered during the fitting).

Perhaps more important, such clothing is only comfortable in the sort of very cool environment for which it was originally designed. If your interior temperatures are around 60°F, you will be more comfortable in a wool coat over a wool vest than you would be in shirtsleeves. At 70°F it will be the other way around.

My attitudes toward such things has also been influenced by Jackie’s work with fiber. In my youth, my experience with wool was that it was scratchy, uncomfortable stuff (totally aside from it being made into garments that didn’t fit and were wrong for the climate). Now I’ve learned about the many different kinds of wool—starting with merino, of course, but by no means ending there—that are not scratchy. Now I have wonderful vests and sweaters, made to fit, from premium materials.

Of course, the top layers are really the last thing to think about. Comfortable clothing begins with the base layer. There again, my experiences as a child turned me against a whole very useful category: long underwear. Any clothing that you’re going to put another layer of clothing on top of needs to fit exactly right. An outer layer that’s too loose can be tolerated. But a too-loose under layer is going to get bunched up and shifted away from where it needs to be: Intolerable.

The ill-fitting hand-me-down long underwear I got as a child turned me against a whole category of garments that doubtless have an important role to play in comfortable dressing. I’m only now, more than two decades after returning to the Midwest, beginning to accumulate items for an appropriate cold-weather base layer. (I’ve made do up to now by having a wide range of top-layer options: spring jackets, fall jackets, winter coats, parkas, my Alaska pipeline coat.)

As a young man, I think I’d have been perfectly happy to wear nothing but shorts and t-shirts, and simply crank up the heat to make up the difference. My attitude has changed. If I had the money, I’d be very pleased to get and wear wool coats and vests, silk cravats, smoking jackets, and the like. Not because of the fashion statement they’d make (which would be a rather silly statement, however much I’ve come to appreciate a fine tweed), but because they’d be very comfortable.

New growing regions less fertile

Prairie plants
Prairie plants

One utterly predictable consequence of climate change is that the price of northern farmland will rise as growing regions shift north.

Tobias Buckell yesterday shared a report that just this sort of price shift is now occurring—interesting to me because this result is not merely predictable: I predicted it my own self, way back when I was in high school.

Global warming was still pretty speculative then (in the 1970s), but people were already talking about the greenhouse effect and trying to figure what the result would be. At the time, I was mainly thinking about the geopolitical implications of  shifting the growing regions north—how things would change if Canada and the (then) Soviet Union were suddenly way more productive of food, while places like the United States, China, and France suddenly less so.

What I discovered, though, was that those northern regions aren’t nearly as fertile as places like Illinois, where 8,000 years of tall grass prairie left an incredibly thick layer of rich soil.

No matter how perfect the climate is, Saskatchewan is not going to produce the bushels per acre of Illinois or Kansas. Their soil is not only less fertile, it’s also much more fragile than the soil of the tall grass prairies. The fertile layer isn’t as deep, so the land must be plowed with greater care, and it will in any case be more quickly depleted.

I’m sure there’s a lot more and better data available now than there was back then, but I doubt if it changes the fundamentals. Shifting growing regions means winners and losers, but it also means less total food production.

Funding the capital costs of household solar power

I was reminded yesterday that I wanted to mention Property Assessed Clean Energy, which came up in the course I’m taking on electric power. (What reminded me was Tobias Buckell’s post about how the real issue for photovoltaics is the capital cost of installing the capacity, which he mentioned in reference to a rather interesting article on issues with solar feed-in tariffs.)

Property Assessed Clean Energy (PACE) is a clever idea for funding homeowner investment in solar power. The way it works is this: The municipality raises money with a bond issue, then lends it to homeowners to invest in solar (or potentially wind) power generating capacity. That investment is then paid back to the municipality over 15 or 20 years via an assessment on the property tax bill. The money is easy for the homeowner to pay back, because the debt repayment is funded by savings on the power bill.

The property tax assessment stays with the house if it is sold, which is reasonable because the photovoltaic system or wind turbine stays with the house as well. This means that the capital is available quite cheaply, because the money is very likely to be paid back.

The really big win of PACE is that it greatly reduces the biggest financial risk that a homeowner takes when making an investment in solar power—the risk that he or she will end up having to move before the rather long payback period, and end up being on the hook to pay the loan back, without enjoying the benefits of the lower power bills.

The problem is, even though about half the states have laws authorizing some form of PACE, the whole scheme has been blocked by the Federal Housing Finance Agency, which instructed Fannie Mae and Freddie Mac not to underwrite mortgages on properties with a PACE assessment.

As I understand it, the issue is that the property tax assessment (like property taxes in general) are senior to the mortgage in the event of a default. But if this regulation is legitimate, the federal mortgage authorities can regulate all municipal activity. They could ban mortgages on houses where the municipality is funding public art through a property tax assessment (or on houses where the municipality isn’t funding public art). If this principle stands, municipal governments will have to do whatever the mortgage authorities demand, or else only people rich enough to pay cash would be able to buy a house in town.

There’s a group called PACENow that’s working various paths to get the prohibition reversed.

Electric power

I’m taking a course on electric power. The instructor, Debbie Insana, lived through the blackouts and brownouts in California produced by the intersection of partial deregulation of the energy markets with corrupt individuals at the (also corrupt) Enron corporation. Prompted by that experience, when she moved to Illinois, she wanted a house that required no net energy inputs to function. That was hard to scale for a single house, so she ended up developing a whole subdivision of energy-efficient houses in Urbana. (The instructor’s title was “The Changing World of Electric Power,” but the people administering it decided pimp it up a little and listed it as Shocking Events in the Changing World of Electric Power. )

It’s of particular interest to me, because I’ve studied much of this same material long ago. Back in 1976, when I was in high school, I attended a National Science Foundation workshop on the energy crisis. The physics hasn’t changed, the politics has probably gotten worse, but the technology has changed, and with it the economics. It’s all very interesting.

Yesterday’s session was on wind power. The installed base of wind power is growing very rapidly (albeit from a low base). A good bit of the installation is happening in Illinois—but for an odd reason. As a source of power, the wind here is rated only fair-to-good. The big win is that we have excellent interconnections to the rest of the country, with major transmission lines that let us deliver power to the east coast and to the Tennessee Valley Authority.

But Illinois is only slipping in here because of an odd intersection of those grid connections, adequate wind, and tax breaks that encourage building now rather than later. The future of wind power going to be off-shore installations. The wind there is stronger and strong closer to the ground. And, it blows strongly during the daytime, when the power is needed, rather than blowing most strongly at night, the way it does on land.

I’m learning about all kinds of new stuff, from technology such as rare-earth magnets making generators smaller and lighter (easier to install on a wind turbine) to lots of obvious-once-you-think-about-it ideas, such as co-siting a wind farm with a gas turbine generating plant: reliable (gas provides electricity when wind isn’t blowing) and cheap (no fuel needed when the wind blows) and flexible (can operate both to serve peak demand).

Wind turbines only function for a certain range of wind speeds—a minimum speed to begin generating power and a maximum speed beyond which wind load can damage the turbine. In excessive winds, they’re designed to feather the blades, brake to a stop, and then lock in place. The teacher shared a video with us of what happens when these mechanisms fail:

I’m looking forward to the next couple of classes in particular, one on solar and one on balancing power in the grid.

Investing for collapse

There’s a whole genre of collapse-oriented investment writing. I’m something of a connoisseur of the form. But one really needs to treat that sort of literature as pornography—interesting to read, if you’re into that sort of thing, but almost nothing in it is stuff you’d actually want to do.

There are two ways most collapse writers go wrong. One is to assume that keen insight into the nature of the problems we face will allow one to make a bunch of smart investment moves in advance—as if there were some advantage to being the richest guy standing in a post-apocalyptic world.

In his recent post Where Should I Put My Money Before Things Collapse? John Robb avoids that trap pretty well. He understands that the systemic nature of the problem makes attempts to align your investments with the underlying trends pointless:

Looking for a safe asset class today, is like a Soviet bureaucrat in 1989, sensing trouble ahead, looking for the directorate with the safest job.

The other is to assume that there will be a collapse event. Those writers seem to suggest that you can spend your time until collapse behaving much as you do now (with some occasional time off to stock your shelter and practice your marksmanship), and then spend the end times hiding out in your shelter. That’s wrong, because there’s no reason to assume that there will be a collapse event. It’s at least as likely that things’ll go on much as they have been, with occasional points where a bunch of people lose their jobs, yet another class of investments suddenly becomes worthless, and various things (such as food or fuel) spike up in price.

John Robb does pretty well avoiding that trap as well. He understands that the only sensible response is to find a lifestyle that works now, and that will continue to work as collapse proceeds.

Just as he indicates, the right responses to problems like peak oil, peak debt, climate change, environmental degradation, habitat loss, and so forth are going to be community-level responses. With that in mind, he’s putting his money into supporting efforts to create that community response and those communities.

Having said all that, four decades of reading collapse literature have convinced me that collapse happens slowly. Very slowly. Slowly enough that we’re going to need to go on investing in ordinary investments for quite some time to come.

It seems like it would make sense to want those investments to be informed by the societal problems that we face, but my experience has been that an understanding of the sources of impending collapse doesn’t lead to useful investment insights.

There are a lot of reasons. First, as I said, collapse happens slowly, meaning that shorter-term trends will end up dominating. Second, a lot of governmental power will be brought to bear in support of pre-collapse norms, meaning the sort of large profits that might be produced if your investments do align with the large trends are prone to being seized or taxed away. Third, the situation is intractably complex, meaning that even a clear understanding of several of the problems may yield predictions that end up being trumped by other problems—no one can say whether peak debt or peak oil will influence the course of the economy more strongly or more suddenly.

The upshot is that investing for collapse is as pointless as Robb points out; I merely disagree with his analogy. Rather than being like a Soviet bureaucrat in 1989, I figure it’s more like being CEO of a department store chain in 1969. There are still opportunities to get ahead following the old arrangements, but all the most powerful forces of society, human nature, and nature itself are arrayed against you. You’d be much better off charting an entirely new course—and Robb’s suggestions are good ones.