Category Archives: howardcounty

RIP Dennis Lane

I knew Dennis Lane only slightly: I occasionally commented on his blog, he commented on mine once or twice, and I met and talked to him several times at Howard County blogger meetups and other events. I can’t speak to his life as a private person and how he came to a violent end, and even if I could I wouldn’t: I don’t blog about my own private and family life, and won’t do so about others. However I did want to say a few words to mark his death.

What I admired most about Dennis as a blogger was his ability to write frequently and seemingly extemporaneously on a variety of topics: local politics, real estate and business affairs, and just the normal goings-on of daily life. He mentioned recently that he hadn’t had time to blog as much as normal, but (as I commented on the post), even his “infrequent” blogging way outpaced my own truly infrequent offerings. I also enjoyed reading his Business Monthly columns, whenever I picked up a copy at a local establishment; it was one of the few things I read on paper rather than online. Leaving aside all his other contributions to Howard County, he’ll be sorely missed in the local blogging community, of which he was a founder and guiding light.

A couple of other points: In 2012 four people were murdered in Howard County and I was acquainted with two of them, Mary-Marguerite Kohn and Brenda Brewington, who were shot at St Peters Episcopal Church in Ellicott City almost exactly a year ago. This year I think there have been two homicides in Howard County thus far, and I’m acquainted with one of the victims. Strange that in a placid suburban county of 300,000 violent death should so disproportionately strike people I know.

FInally, it’s fitting that I first learned of Dennis’s death while reading a blog post, in this case by TJ Mayotte. It’s a measure of how much I rely on local blogs and hyper-local sites like Ellicott City Patch and Explore Howard for my knowledge of Howard County affairs. I guess one way to honor Dennis and what he meant to our local online community is to get off my rear end and blog some more myself.

The long game in Columbia

One political faction obtains a solid majority and uses it to push through a far-reaching initiative, only to have their dominance threatened in a subsequent election marked by newly-energized opposition and relatively low turnout. The 2010 mid-term victories of the Republican party? No, it’s the “Pioneers strike back” victories in the just-concluded elections for the Columbia Association Board of Directors.

Tom Coale has already done a good wrap-up, so I’ll confine myself to a couple of thoughts continuing the analogy above. First, what I’ll call the “anti-Arbor” faction faces a decision on strategy similar to that of the anti-Obamacare GOP post-2010: They apparently don’t have the votes to reverse the decision outright, so they face a choice between trying to shape the Inner Arbor plan more to their liking, making compromises where they can find them, or throwing sand in the gears of CA governance to try to delay things until they can re-take a board majority and kill the plan then.

I have no idea which strategy they’ll choose, and in one sense I don’t care—they’ll do what they want to do regardless of what I think. I’m more concerned about the strategy of those who favor the Inner Arbor plan and the accompanying 21st century redevelopment of Columbia. In a recent post unsuccessful candidate Julia McCready rues the “sliminess” in the electoral process. I understand her being upset, especially about untruths allegedly spread by the incumbent. Tom Coale also writes of “blatant and intentional lies” from Inner Arbor opponents. Going back to the GOP analogy, it sounds like someone’s been exercising their inner Karl Rove (or Lee Atwater, to use an example for an older generation). However I think the operative advice here is, “Don’t get mad, get even.”

How to do that? In another post Julia looks to the passing of the Pioneer generation: “… none of us are immortal. The time will come when those in power are gone.” Unfortunately I think this is like the Democratic party looking to demographic change for its salvation. Consider that even 70-ish Inner Arbor opponents can expect to live another 16 years or so if male, and almost 19 years if female, and they may attract younger proteges and supporters in the meantime. Waiting in and of itself is not going to win the day.

What will? I think Tom Coale has the right idea: “forward-thinking candidates” are going to have to build their own networks of dedicated supporters, people who will turn out reliably to testify at CA board meetings and vote in CA and village board elections. This will require not just online activism but old-fashioned offline relationship building and dues-paying, not just for a year or two leading up to the next CA elections but for the long term.

Which leaves me with a final question: Are there enough competent and energetic people who have the patience and stamina for that, especially in an era when Columbia is no longer the “new city upon a hill” but a suburb much like any other? The Columbia Pioneers have spent over thirty years promoting their vision of Columbia; is the next generation of Columbians prepared to spend the next thirty years promoting theirs?

Martin O’Malley has his eyes on the prize and off the ball

I don’t usually comment on Maryland politics beyond Howard County, but this Washington Post story on Martin O’Malley’s approval rating reinforces an opinion I’ve held for a while: O’Malley seems to be frittering away his second term trying to make himself into a national figure, as opposed to actually doing the hard work of preparing Maryland for success in the 21st century. Maybe this is an unfair characterization; maybe (as with the college tuition and school funding issues mentioned in the article) he’s just had a problem “communicating his accomplishments”.

But it’s a simple fact that the public has a limited attention span, and they can be forgiven for thinking that O’Malley’s top priorities right now are things like gun control and repealing the death penalty, given that those have been most in the news with his name attached. I doubt that either of these issues is on the average voter’s top 10 list of critical problems facing Maryland, and so I’m not surprised that voters are lukewarm in their feelings about O’Malley.

The simple fact is that Maryland voters have no desire to see Martin O’Malley run for president in 2016, and nobody else does either. So why spend the next few years polishing his liberal credentials for the benefit of Democratic activists and primary voters? Why not spend the time building a reputation as someone willing to take on hard long-term issues, like growing Maryland’s economy in the coming age of Federal austerity, ensuring that Maryland’s health care system works well as implementation of the Affordable Care Act goes into high gear, and putting the state on a sound financial footing without resorting to excessive taxes or gimmicks like casino expansion?

Unlike Barack Obama, O’Malley doesn’t have the excuse of facing an implacable Republican opposition capable of blocking his political agenda. If a Democratic governor can’t be effective in Maryland, where can they be effective? And though as a registered Democrat it pains me to say this, right now I’d count both Robert McDonnell in Virginia and Chris Christie in New Jersey (plus Andrew Cuomo on the Democratic side in New York) as doing a better job of actually governing their states than Martin O’Malley.

The library as spiritual experience

I think this is a record for me: Three posts in one day, and all about libraries to boot, to mark the occasion of the “Evening in the Stacks” fundraising event at the Miller Branch of the Howard County Library System.

After finishing my last post I happened to be thinking of the role that libraries play in the life of their communities and how libraries are portrayed in TV and films: as just another setting for sitcom wisecracking and rom-com “meeting cute”, or perhaps as a place to go to discover mysterious dark secrets leading to overblown action sequences—what I’ll call the “Indiana Jones” or Da Vinci Code perspective.

As an antidote to all that I present possibly the most beautiful cinematic scene ever set in a library, from the Wim Wenders film Wings of Desire (Der Himmel über Berlin), as angels (the men and women in long coats and scarves) visit the Berlin State Library (Staatsbibliothek zu Berlin) and overhear the thoughts of the patrons as they read.

Turbocharging downtown Columbia with a new Central Branch library

I couldn’t stop thinking about the possibilities that might be opened by a new Central Branch of the Howard County Library System, so I’m taking the unprecedented step of posting twice in one day. In my last post I proposed building a new Central Branch facility that included at least a dedicated co-working space and business resource center, and possibly having it also host the Innovation Catalyst program run by the Howard County Economic Development Authority in the same building, just as the Miller Branch currently hosts the Howard County Historical Society.

Unfortunately though the space requirements to do this are much greater: The Historical Society occupies less than 5% of the Miller Branch building (3,000 square feet out of 63,000 square feet), while the iCat facility is 25,000 square feet vs. less than 50,000 square feet for the current Central Branch facility. Assuming that a new Central Branch facility would have roughly the same footprint as the present one, that’s a major obstacle.

Then while lying in bed last night I thought: The Miller Branch is two stories, an appropriate size because it’s in a relatively rural setting. So is the current Central Branch. But a new Central Branch is going to be at the center of what will be an increasingly urban area; why not make it a three-story facility instead? Assume that the library portion would be roughly the size of the Miller Branch at about 60,000 square feet spread over two stories. Then add an additional 30,000 square feet in the form of a third story to house the co-working space, business resource center, and iCat program. I’m no developer or architect, but looking at an aerial view of the current Central Branch it seems like there’s be more than enough room to increase the building’s footprint to accommodate a three-story facility with 90,000 (or even up to 100,000) square feet.

Howard County Central Branch library

This would be a significantly larger building than the current Central Branch, but I think it would be quite in character with its surroundings: Across Little Patuxent Parkway are office buildings at least twice as tall, and a three-story building would be a nice transition to the future CA headquarters in Symphony Woods.

But what about parking? The new Miller Branch has 470 parking spaces spread across three parking lots (for the Miller Branch proper, the old Miller Branch facility now used at the HCLS central office, and the Ellicott City senior center); 250 of those spaces are next to the new Miller Branch building. In comparison the current Central Branch has less than 150 parking spaces by my count. (I couldn’t find any figures on this, so I resorted to counting spaces by hand in the Google Maps image.) As anyone who’s visited Central Branch knows, parking can be very hard to find there, and almost doubling the size of the building would make it worse.

However, there’s an obvious solution at hand: Part of the Inner Arbor plan is a 1,750-space multi-level parking garage. I haven’t seen anything about the intended uses for that garage, but one possibility is to use it for overflow parking from a future Central Branch facility, and maintain the ground-level parking lot at the new Central Branch at around 100-150 spaces.

Would adding a co-working space and iCat space to a new Central Branch greatly increase vehicular traffic in the downtown area? I don’t think so: Typical library traffic is characterized by many relatively short visits as people drop by to return books or check out new ones; even more extended uses like kids doing homework after school might last only a couple of hours. People using a co-working space or an iCat office would likely stay there for most if not all of the day, so the incremental traffic from increasing the library space by 50% for those uses would likely be less than one would think.

Let’s tie all this together and look at the overall vision. A new Central Branch facility with dedicated co-working space and a co-located facility for the Innovation Catalyst program could be a driver for entrepreneurial vibrancy in the new Columbia downtown:

  • Downstairs high school students could participate in educational activities like the HiTech program focusing on science, technology, engineering, and mathematics, along with business education focused on that same population.
  • Upstairs free-lancers young and old could use the co-working space and learn more about business and small-scale entrepreneurship (e.g., starting and operating successful “lifestyle businesses”).
  • Those wanting to “take it up a notch” could participate in the iCat program and try to launch innovative new startups.
  • If they’re successful then there would be plenty of prime office space nearby into which they could expand their businesses.

And of course all this would be happening right next to a beautiful urban park and arts district, with cafés and an upscale grocery nearby, a major regional shopping center across the street, and attractive apartment and condominium complexes within walking distance. It’s a classic live/work/play (and learn!) combination, and I think might go a long way toward attracting and retaining the sort of bright ambitious young people who could contribute a lot toward the future economy and culture of Howard County.

Could Howard County libraries help grow Howard County’s economy?

Unfortunately I won’t be able to attend the Evening in the Stacks fundraiser at the Miller Branch of the Howard County Library System. However that won’t stop me from doing a library-themed blog post to mark the occasion:

Recently the Howard County Times published an article highlighting the HiTech program at the Savage Branch. To quote from the library’s web site, HiTech is a “new digital media lab for teens centering on science, technology, engineering and math”. It’s part and parcel of the library’s expanding role as an educational resource for Howard County residents.

But what happens when all those teens graduate from the HiTech program and go out into the world of work? Could the Howard County Library System play a role not just in educating young people, but in helping those young people and others put their education to work as entrepreneurs? The Atlantic Cities, a companion site to the Atlantic Monthly’s online presence, recently published an article explaining “Why libraries should be the next great startup incubators”:

Would-be entrepreneurs everywhere are looking for business know-how and physical space to incubate their start-ups. Libraries meanwhile may be associated today with an outmoded product in paper books. But they also happen to have just about everything a 21st century innovator could need: Internet access, work space, reference materials, professional guidance.

Why not … put these two ideas together?

The article goes on to discuss a program in which Arizona State University will partner with the local library system to provide “dedicated co-working spaces … as well as both formal classes and informal mentoring from the university’s start-up resources … everything, in short, but seed money”. In essence it’s a step up from the current common practice of people hanging around the library to work on their laptops and access reference material, while not substituting for a full-fledged incubator program that provides startup funding.

Would something like this work in Howard County? For some time now I’ve been interested in the idea of co-working spaces in Howard County—in fact, it’s what first got me involved in the hoCo blog scene, via commenting on Jessie Newburn’s blog and then doing a guest post on the topic. I’m still skeptical on the idea, for reasons stated in the post. However I think it’s worth taking another look at, and along those lines here’s an idea I’ll throw out there:

With the redevelopment of downtown Columbia and the implementation of the new Inner Arbor plan, one key element will be replacing the Central Branch of the Howard County library system with a new facility along the lines of the new Miller Branch. Why not make a key element of that new facility a co-working space cum business resource center along the lines described in the Atlantic Cities article? In fact, let’s think even bigger: Why not take the current Innovation Catalyst (iCat) program (run by the Howard County Economic Development Authority’s Maryland Center for Entrepreneurship), move it from its current (rather obscure) location off Route 108, and make it a part of an expanded Central Branch as well? The iCat facility and associated coworking space could be to the new Central Branch what the Howard County Historical Center is to the Miller Branch: something that adds value to the library and can leverage the library’s resources.

Now I can see real problems with fitting all this stuff in: The Howard County Historical Center is only 3,000 square feet out of the 63,000 square feet at Miller Branch, while the current iCat office is 25,000 square feet. (By comparison the current Central Branch is just under 50,000 square feet.) But I still like the idea of expanding the idea of the library from a place to learn things to also be a place to do things, and have it do its part to help drive economic growth in Howard County. Now that the Inner Arbor plan is starting down the road to being realized, let’s think about what else can be done to add life and vibrancy to the new downtown.

Columbia is not a gated community

Over at Columbia Compass Bill Santos has written a great post that brought into focus some of my thoughts around the proposed Inner Arbor project for Symphony Woods. I really like what I’ve heard and seen of the project and I hope it comes to fruition. But… I live in Ellicott City, not in Columbia, and when Ian Kennedy asked people to sign a petition in support of the project I was at first hesitant to do so. After all, I’m not a Columbia property owner, I don’t vote for the Columbia Association board of directors, and whatever money CA chooses to spend in support of the Inner Arbor project is not going to come out of my pocket. Should I just stay out of the controversy and leave Columbia-related matters to the “real Columbians”?

In the end I signed the petition (with the encouragement of Tom Coale), but I still had some residual concerns about doing so. However Bill’s post has dispelled all of those. In particular he demolishes the argument of two Columbia residents that CA is nothing more than a homeowners association and as such has “no business serving others with our monies” by “[putting] CA’s residents’ property (i.e. Symphony Woods) … to the regular service of patrons spanning a widespread geographic area, not just Columbians”. As Bill points out, CA is a tax-exempt organization whose exemption from taxation is specifically conditioned on its “promoting in some way the common good and general welfare of the people of the community” and making its “common areas or facilities” available “for the use and enjoyment of the general public”.

In other words, Columbia is not and cannot be the equivalent of a gated community operated for the sole benefit of Columbia lien payers. To put it bluntly, Columbians have no business telling me that the decisions of CA are none of my business. As a taxpayer I’m in my own small way having to make up for the lost tax revenues due to CA’s tax-exempt status—and of course I’ll also be helping to pay for any county-funded amenities (like a new library) that might be built to supplement the CA-funded Inner Arbor facilities.

Beyond the legalities, I can’t understand why right-thinking Columbians would want to put up a metaphorical wall around Columbia and Symphony Woods. Even leaving aside the original Columbia vision of diversity and inclusivity, the health and well-being of Columbia as a community, not to mention the value of Columbians’ properties, are ultimately dependent on the ability of Columbia to attract the custom and patronage not just of Columbians, but of residents of the rest of Howard County and central Maryland in general.

As I’ve written before, Symphony Woods is not a remote wilderness to be preserved in a pristine state of nature with minimal human presence, it is a park—and as Columbia’s downtown evolves, it will be very much an urban park—whose continued existence ultimately depends on the benefits it provides to members of the community within which it is situated. Declaring it off-limits to compatible uses like an arts district is a recipe for its long-term decline into irrelevance. As Symphony Woods is to Columbia, so is Columbia to the rest of Howard County. If Columbia can’t evolve to meet the challenges of a new time—or more correctly, if Columbians are unwilling to let it thus evolve—then that’s a recipe for Columbia’s own long-term decline into irrelevance. And as Bill points out, that’s a violation not only of the spirit of Columbia but also of the letter of the law under which Columbia and CA are organized.

From Symphony Woods to the Commonwealth of Belle Isle

For the most part I’ve stayed out of the debate over the “Inner Arbor” plan proposed for consideration by the Columbia Association Board of Directors. For the record, I think the idea of having an everyday “there there” in Symphony Woods (i.e., not just Merriweather Post Pavilion) is a good idea; I especially like the idea of building a new Central Branch library as part of an overall Symphony Woods cultural complex. Bottom line: I like the proposal, have signed the petition to support it, and encourage others to do so as well.

However I take partial exception to Wordbones’s declaration that this proposal is an example of the dictum “make no little plans”. At its heart the Inner Arbor plan basically involves constructing an office building, a couple of theaters, a parking garage, and some additional indoor and outdoor amenities. It’s big in comparison to what was previously proposed for Symphony Woods, namely a fountain and a small cafe, but it’s fairly small potatoes in the grand scheme of things.

For an example of truly gonzo development ideas we have to leave present-day Columbia and go elsewhere, in particular to Detroit, the symbol of American urban decay and now the proposed location of the Commonwealth of Belle Isle. Belle Isle is an island in the Detroit River currently used as an urban park; at 982 acres it is about 25 times the size of Symphony Woods and almost three times the size of the area covered by the Downtown Columbia plan. Like most of Detroit it’s fallen on hard times, and the city is trying to figure out what to do with it. A local real estate developer, Rodney Lockwood, has offered the city $1 billion to buy the island and develop it. And not just any old development either—Lockwood proposes to turn Belle Isle into a separate 35,000-person “commonwealth” within the United States, with its own independent (and relatively minimal) government, an almost total exemption from Federal taxes, separate citizenship requirements, and eventually its own currency, the Rand.1

As the name of the currency might have told you, the Commonwealth of Belle Isle is another in a string of proposed schemes to establish a libertarian society free of government meddling and dedicated to the principles of liberty and free enterprise—the successor to (among others) space colonies, seasteading, and the Free State Project. It also has connections with the Charter Cities movement promoted by economist Paul Romer, which in turn was inspired by the real-life examples of city-states like Hong Kong and Singapore.2 And of course—though Lockwood goes to some lengths to deny it—the Commonwealth of Belle Isle could also function as an on-shore tax haven, the chilly equivalent of those sunny Caribbean islands where wealthy people park their assets and U.S. corporations establish shell entities to limit their overall corporate tax burden.

An ambitious plan requires an ambitious approach to promote it. The Columbia Association has provided us with a typical slide presentation, while Lockwood has written a 158-page book set 30 years in the future, as a former resident of Detroit returns to marvel at the transformation of Belle Isle and the consequent revitalization of the regional economy. Admittedly it’s not high on drama or conflict; in one fairly typical conversation the two main characters discuss the fine points of Belle Isle’s real estate tax structure (a variant of 19th-century reformer Henry George’s “single tax”). I doubt that Belle Isle the book will achieve the best-seller status of the works of Lockwood’s hero Ayn Rand.3

Lockwood’s book reminds me not so much of Atlas Shrugged or The Fountainhead but rather Edward Bellamy’s Looking Backward, a 19th-century tract-disguised-as-fiction in which the protagonist goes to sleep in Boston in 1887 and wakes up in the year 2000 to find it transformed into a socialist paradise.4 Bellamy’s book was surprisingly popular; according to Wikipedia, “It was the third-largest bestseller of its time, after Uncle Tom’s Cabin and Ben-Hur: A Tale of the Christ. … In the United States alone, over 162 ‘Bellamy Clubs’ sprang up to discuss and propagate the book’s ideas.”

All forgotten now, of course, but not written in vain: The ideas of Bellamy and others eventually were toned down, adapted, and transmuted into the welfare-state capitalism of the New Deal and the Great Society, the milieu from which an idealistic real estate developer named James Rouse emerged bearing the dream of a place that would be “not a perfect city or a utopia, but rather an effort to simply develop a better city”. I suspect the libertarian Belle Isle of 2043, like Bellamy’s socialist Boston of 2000, is a fantasy that is doomed to stay within the pages of a book. But although I’ve been a bit snarky about the concept (though not nearly as snarky as some) I’m loath to dismiss or denigrate the spirit behind it.

I think we could use more experiments in urban living and governance, even somewhat oddball ones. Columbia was a noble experiment, though I think ultimately a failed one: In an America in love with suburbia it inevitably assumed a fairly typical suburban character, and (as I’ve written elsewhere) its relative prosperity and socioeconomic equality is arguably less due to its founding ideals and more a function of its role as a bedroom community for an ever-growing Federal government presence in Maryland.

In a sense the Commonwealth of Belle Isle is a 21st century version of Columbia, projected through the lens of a free market ideology. If any part of the Belle Isle vision comes to fruition it’s possible it will simply become a gated community for the 1% and their domestic servants (or “home managers” as the book has it), a supersized and urbanized version of Gibson Island. But who knows? And if Belle Isle does turn out to be more than that perhaps it will hold lessons for the rest of us. At some point in the future Columbia, Howard County, and Maryland may find that Uncle Sam doesn’t come round with presents as often as he used to. In preparation for that day we need more and better ideas on how to promote private sector economic growth, and we shouldn’t be picky on where we look for them. If an idea is a good one then who cares where we steal it from?


1. According to the Commonwealth of Belle Isle FAQ, individuals seeking to move to Belle Isle “will have to post a citizenship fee, which will probably be in the $300,000 range, plus have a working command of English.” In comparison the total wealth of the median US household is around $60,000, with liquid assets much lower. Although it’s not mentioned in the FAQ, Lockwood has separately proposed reserving 20% of the citizenship slots for non-wealthy but deserving applicants.

2. I should note that Professor Romer’s main foray into real-world charter cities, a proposed venture in Honduras, didn’t go too well; see for example this blog post at Reason.com. However hope springs eternal.

3. It may however be of interest to at least some Columbians: Just as the Columbia Association has been characterized as an over-grown homeowners association, the fictional government of the Commonwealth of Belle Isle resembles nothing so much as a CA on steroids, with its own police force, judiciary, tax system, and currency, but still concerned about the fine details of urban planning, down to the building materials used. This can get a bit absurd sometimes: In the course of giving his friend a tour of Belle Isle one character remarks, “Concrete doesn’t meet our aesthetic test. So we don’t allow any use of it. … In the Soviet era the Russians built the ugliest buildings in the world using primarily concrete. So we figure communism and concrete are linked. Not here! In our free-market world, we go the other direction.”

4. I realize that some may think the real-life Boston of the year 2000 was a bastion of socialism (though no paradise). All I can say to those folks is that they should read the works of Bellamy and others of that time to see the sort of system actual American socialists wanted to establish.

Calculating growth rates (for Howard County or otherwise), part 5

In part 4 of this series I discussed the general problem of estimating growth rates for periods less than a year, and using Howard County’s population in the 21st century as an example calculated estimated monthly, week, daily, and even hourly growth rates for the county based on the Census population figures for 2000 and 2010.

The problem with those calculations is that it’s hard to get a sense for the relative magnitude of the growth rates. For example, how much different is a growth rate of 0.12256% per month from a growth rate of 1.4807% per year? It would be nice to express the growth rates according to a common time period, just as (for example) we use “miles per hour” to refer to the speed of our cars even when we’re just driving 2 minutes to the grocery.

However we have to be careful about this, since a percentage increase that occurs (say) every hour on the hour leads to different results than a percentage increase that is conceived to occur but once a month or once a year. (This is exactly what tripped me up when doing my original estimates of growth rates.)

The solution is to multiply the various rates appropriately to express them as an annual rate, but then to qualify the result by referencing the period over which the growth is assumed to occur. The standard way to do this is to speak of growth being “compounded” at particular intervals. For example, we can take the monthly growth rate of 0.12256% estimated in part 4, multiply it by 12 (the number of months in a year), and express it as an annual growth rate of 1.4707% “compounded monthly”. The following table does this for all the growth rates I calculated in part 4:

Period Per-period growth rate Annual growth rate (with compounding)
Decade 15.384% 1.5384% (compounded per decade)
Year 1.4807% 1.4807% (compounded yearly)
Month 0.12256% 1.4707% (compounded monthly)
Week 0.028271% 1.4701% (compounded weekly)
Day 0.0040271% 1.4699% (compounded daily)
Hour 0.00016779% 1.4698% (compounded hourly)

There are several points worth noting here. First, the idea of compounding in this context is exactly the same as that used in financial calculations: For example, if you have a savings account, your bank will periodically credit you with whatever interest you’ve earned on the money in your account; this is the compounding period.

Second, as compounding periods get shorter the same amount of growth can be produced with a lower nominal rate: In our example a 1.4698% rate compounded hourly produced the same growth over a decade as a 1.4807% rate compounded yearly. Or to put it another way, in a financial context you are better off having a shorter compounding period for a given nominal rate: If the rate on your savings account is nominally 2% per year then you are better off with daily compounding than with monthly.

However there is a limit to how much shorter compounding can affect growth: In the table above moving from yearly to monthly compounding reduced the needed growth rate from 1.4807% to 1.4707%, a difference of 0.01%, but moving from monthly to weekly compounding reduced it only to 1.4701%, a difference of 0.0006%.

As compounding periods get shorter and shorter (per minute, per second, and so on), it appears as if the estimated growth rate will reach some sort of limit, around 1.4698% or 1.4699% in our example. We can refer to this as an annual growth rate compounded continuously or, more simply, as a continuous growth rate. A continuous growth rate isn’t that applicable to your savings account (since your bank isn’t going to credit you with new interest earned every nanosecond) or even to Howard County’s population (since it doesn’t grow every nanosecond either, and you can’t add fractional people like you can fractional dollars).

However continuous or near-continuous growth is very common in nature: Think of bacteria multiplying in a fresh petri dish or (more ominously) in your body after you’re infected with something. The mathematics of continuous growth is also simpler and more elegant than that used for growth compounded on a periodic basis. For example, to compute a continuous growth rate for our Howard County population example I don’t need to do calculations for compounding per minute, per second, and so on in order to find the limit. I can do a quick calculation on my iPhone and tell you that the continuous growth rate in our example is 1.4698689% expressed to 8 significant figures.1

How did I do that? If anyone out there is still reading and (more important) if I can find a good way to explain it, I’ll address that question in a possible part 6.


1. Note that this is higher than the figure of 1.4698% we calculated for hourly compounding, when we would expect the limit to be slightly smaller. As it turns out we’re the victims of rounding in computing the growth rate per hour; expressed to 8 digits the estimated hourly growth rate is actually 0.00016779340%, which corresponds to an annual rate of 1.4698701% compounded hourly, slightly larger than the continuous growth rate of 1.4698689%.

Calculating growth rates (for Howard County or otherwise), part 4

In part 3 of this series I recapped the method derived in part 2 for estimating growth rates (using Howard County’s population in the 21st century as an example) and discussed how to use such estimates to project growth in future years.

Now let’s go back to a question I asked at the end of part 2: Can we calculate a more accurate estimate for the growth rate? We can begin exploring this question by going back to my original inaccurate estimate in part 1 and considering where I went wrong. To get that estimate I simply took the final population in 2010, divided it by the initial population in 2000, then divided that by 10 to get an annual growth rate (which I then converted to a percentage value). That initial estimate was too high: When I used that value to estimate the population in 2001, 2002, and so on, it produced a final population estimate for 2010 that was well in excess of the actual 2010 population.

In making my original estimate I saw that the population in 2010 was 15.834% higher than the population in 2000. The additional population didn’t get added all at once; some population growth occurred in each of the 10 years. I tried to account for that ongoing growth by dividing 15.384% by 10 and assuming 1.5384% growth per year. But that corresponded to adding 1.5384% of the 2000 population each year, and that was my mistake. In actuality an annual growth rate as applied to (say) estimating the 2006 population produces a percentage increase relative to the 2005 population, not the 2000 population.

The 2005 population was larger than the 2000 population because it reflected population growth in the years since 2000. Thus using our initial estimated growth rate of 1.5384% (based on a percentage of the 2000 population) produced too high an estimate of the population growth when we computed population growth year by year (and as part of that process applied that growth rate to the 2005 population). Or, to put it another way, a smaller growth rate than 1.5384% was able to produce 15.384% growth from 2000 to 2010 when applied on a year-by-year basis. In fact, a growth rate of about 1.4807% (vs. 1.5384%) is sufficient to produce 15.384% growth over the 10-year period, as I showed in part 2.

Let’s now turn to a new but (as we’ll see) related question: What if instead of projecting population growth on a year-by-year basis, we wanted to project it on a month-to-month basis? For example,  the 2010 population figure of 287,085 was for April of that year (actually April 1). How could we project the population in May 2010, June 2010, and so on? Could we simply divide our estimated annual growth rate of 1.4807% by 12 to calculate a monthly growth rate?

Based on the discussion above, we should suspect the answer is no. Let’s work out the numbers though just to be sure: We divide 1.4807% by 12 to obtain an initial estimate of 0.12339% growth per month. Using this estimate the population for May 2010 (i.e., on May 1) would be 287,085 times 1.0012339 (converting 0.12339% to non-percentage form and adding 1), or 287,439. Per our discussion in part 3, the population for April 2011 (12 months later) would be 287,085 times 1.0012339 raised to the 12th power, which equals 287,085 times 1.014908, or 291,365.

But wait: according to our estimated annual growth rate of 1.4807% the population for April 2011 (1 year later) should be 287,085 times 1.014807 or 291,336. It’s not a big difference (29 people), but it’s still significant. Again our initial estimated growth rate produced estimated population figures that are too high, and for a similar reason as previously: Our estimated monthly growth rate assumed that for each month we’re adding a given percentage of the population as of April 2010, but in actuality the increase in each month is based on the prior month’s population, which in our example is always higher that that (since we’re making estimates for later in 2010 and 2011).

How can we get a better estimate? We simply go back to our approach in part 2 for computing a growth rate using the actual Census population figures for 2000 and 2010, this time computing everything on a monthly (rather than yearly) basis:1

  1. We again start by dividing the population in (April) 2010 by the population in (April) 2000. This gives 287,085 divided by 247,842, or 1.158339.
  2. Since there are 120 months between the starting and ending population figures, this time we take the 120th root of the result from step 1 to find the growth factor. The 120th root of 1.158339 is 1.0012256.
  3. Again we subtract 1 from the growth factor to find the growth rate, which this time is a monthly growth rate. This gives 1.0012256 minus 1, or 0.0012256.
  4. Again we multiply the growth rate by 100 to convert it into percentage form. This gives 100 times 0.0012256, or 0.12256% per month.

So the more correct estimate for a monthly growth rate is 0.12256% instead of 0.12339%.

Can we go further, and estimate weekly growth rates or even daily growth rates? Of course we can: It’s simply a matter of finding the number of time periods (days, weeks, months, or years) between the initial and final populations, and then using that number when we take the root in step 3 of our general method.

The results are shown in the following table, each expressed to 5 significant figures; just for fun I’ve added entries for a growth rate per decade and growth rate per hour. As an example, the daily growth rate is computed by dividing the population on April 1, 2010 (287,085) by the population on April 1, 2000 (247,842), taking the 3650th root of the result to get the daily growth factor (since there are 10 years of 365 days each), subtracting 1 to get the daily growth rate, and then multiplying by 100 to put the daily growth rate in percentage terms.2

Growth Rate Period Number of periods Estimated Growth Rate
Decade 1 15.384%
Year 10 1.4807%
Month 120 0.12256%
Week 520 0.028271%
Day 3,650 0.0040271%
Hour 87,600 0.00016779%

The above is all well and good, but the way the growth rates are expressed makes it hard to compare them. What would be nice would be to express all rates as annual rates, just as (for example) we talk of driving 50 miles per hour whether our trip lasts for 2 minutes, 2 hours, or 2 days. However we’ve seen enough thus far to know we have to be careful in how we do this, and since this post is long enough as it is I’ll postpone discussion of this topic until part 5.


1. I’m implicitly assuming that each month has equal length. This is not true (at 31 days the month of January is more than 10% longer than February in non-leap years), but it doesn’t affect my overall argument.

2. For simplicity I’ve assumed that each year is exactly 52 weeks (actually a year is about 52.1 weeks), and that there are no leap years (actually there was an extra day in both 2004 and 2008). Correcting these would change the weekly, daily, and hourly growth rates very slightly.