Author: Tom

We the Landowners

Montana Senate Bill 379 gives a few landowners veto power over zoning. I used GIS data to do a quick calculation of how that would play out in some Gallatin County zoning districts:

Zoning District Distinct owners Owners of 40% of Land Share of owners required to protest zoning acts
Bear Canyon District 84 5 6.0%
Bridger Canyon 885 10 1.1%
Middle Cottonwood 242 81 33.5%
River Rock 938 41 4.4%
Springhill 200 27 13.5%
Sypes Canyon #1 24 7 29.2%
Trail Creek District 339 10 2.9%

In remaining Gallatin County, 263 out of 42,576 distinct owners (less than 1%) could block zoning, but my calculations are incorrect because of missing data and the presence of Bozeman in the middle, but the truth is probably not too different from the calculations above.

In fact, the table above understates how dramatically this legislation moves toward a principle of “one acre, one vote.” First, represented “owners” in each district aren’t necessarily people; corporations and trusts get a vote in zoning protests too. Second, non-landowners are completely disenfranchised, even though as residents and citizens they still have an interest in land use policy.

Since MT legislators have already tried to override federal powers in a number of bills this session, perhaps next session they can introduce a MT-specific preamble to the US Constitution,

We the People Landowners of the United States, in Order to form a more perfect Union Subdivision, establish Justice, insure domestic Tranquility Profitability, provide for the common aristocracy’s defence, promote the general Welfare Subservience, and secure the Blessings of Liberty Property to ourselves and our Posterity, do ordain and establish this Constitution for the United States of America, LLC.

I hope that there is in fact some valid underlying intent to SB379. My guess is that it’s fear of a fairness issue: that the rabble will acquire their small lots, then seek to use zoning to lock up all land remaining in large undeveloped parcels, to preserve views and resources. So far, this is a strictly theoretical problem. County commissions, and a lot of MT voters, are a conservative lot, which militates against such developments, and agriculture and forestry are protected from zoning anyway. If there’s any real need for policy here, surely there is a means to achieve it that doesn’t do such violence to democracy.

If the real goal is to create a de facto zoning ban, by making it impossible to create districts or amend regulations, then the legislature should simply de-authorize zoning. But, following the wingwalker’s rule (don’t let go of one thing until you’ve got hold of another), they should first come up with an incentive  system that achieves the purposes of zoning more flexibly.

Crazy orbital dynamics

An asteroid has been discovered sharing earth’s orbit, with a horseshoe-shaped orbit (from an earthbound reference frame).

asteroid

The arXiv blog has a nice summary:

Near-Earth asteroids are common but SO16 is in a category of its own. First and foremost, it has an exotic horseshoe-shaped orbit (see diagram above) which astronomers believe to be very rare.

Its worth taking a few moments to think about horseshoe orbits. Two points are worth bearing in mind. First, objects further from the Sun than Earth, orbit more slowly. Second, objects that are closer to the Sun orbit more quickly than Earth.

So imagine an asteroid with an orbit around the Sun that is just a little bit smaller than Earth’s. Because it is orbiting more quickly, this asteroid will gradually catch up with Earth.

When it approaches Earth, the larger planet’s gravity will tend to pull the asteroid towards it and away from the Sun. This makes the asteroid orbit more slowly and if the asteroid ends up in a orbit that is slightly bigger than Earth’s, it will orbit the Sun more slowly than Earth and fall behind.

After that, the Earth will catch up with the slower asteroid in the bigger orbit, pulling it back into the small faster orbit and process begins again.

So from the point of view of the Earth, the asteroid has a horseshoe-shaped orbit, constantly moving towards and away from the Earth without ever passing it. (However, from the asteroid’s point of view, it orbits the Sun continuously in the same direction, sometimes more quickly in smaller orbits and sometimes more slowly in bigger orbits.)

For SO16, the period of this effect is about 350 years.

Even simple systems like the three-body problem can yield analytically intractable and surprising solutions, but this is the weirdest I’ve yet seen (and the competition is stiff this week). It even inspires poetry in the comments.

Production functions – so pretty, so unphysical

I’m rediscovering my old frustrations with aggregate production functions like the CES. They’re handy, but I have a nagging suspicion, never quite formalized, that they just don’t capture the engineering/thermodynamic realities of substitution. Anyone know any papers on that? I’m aware of critiques of KLEM applications, but not interfuel aggregation.

prodFimages

Click to enlarge. From a google images search for production function.

Candy Causality Confusion

Candy Professor is confused:

Contagious Cavities

One of the favorite themes of the candy alarmists is dental decay: candy causes cavities! How many times have you heard that one? But it just ain’t so.

From no less an authority than the New York Times, this week’s Science section:

While candy and sugar get all the blame, cavities are caused primarily by bacteria that cling to teeth and feast on particles of food from your last meal.

Your last meal. Did you hear that? Not candy, not at all. It’s food, just plain old food, that those cavity-causing bacteria crave.

This is just what we’d all like to hear – cavities are a random act of bacterial promiscuity, so we can gorge on candy as much as we want without dental repercussions!

Unfortunately, this is highly misleading.

The NYT article mentions that streptococcus mutans is one of the common cavity precursor bacteria. A quick trip to wikipedia and microbe wiki reveals all. Here’s a rough picture of the process:

candy

click to enlarge

At top left, food (including candy) goes in. The output of this system that we’re interested in is healthy tooth enamel – i.e. the opposite of cavities. There are many causal pathways between candy and cavities. The simplest (in red) starts when candy (i.e. sugars) goes into the mouth. There, in the presence of bacteria, it’s metabolized to acid, which is neutralized by eroding enamel. That’s bad.

Things get worse if the candy contains sucrose. Sucrose is enzymatically degraded to fructose and glucose (green path), directly fueling the acid process. More importantly, S. mutans preferentially hijacks sucrose, consuming the fructose for energy and using the glucose to make a sticky polysacharide scaffolding for its colonies, which we come to know as plaque. That plaque becomes a home for other less hardy bacteria (orange path). The existence of food and housing allows bacterial populations of all sorts to flourish (blue paths). All of this increases enamel-eroding acid metabolism.

Admittedly, none of this would happen without bacteria around to metabolize sugars. But that’s a feedback loop – sugar intake fuels the growth of the bacterial populations. The idea that “It’s food, just plain old food, that those cavity-causing bacteria crave” is surely nonsense, because there’s a metabolic penalty and a delay in converting complex carbohydrates into cavity-causing sugars. That delay means that the shorter time constant, of chewing and swallowing your food, dominates, so that the primary fuel for bacteria must be simpler (or stickier) carbohydrates.

The existence of at least half a dozen causal pathways from candy intake to loss of tooth enamel gives the lie to the notion that it’s “Not candy, not at all.” You can blame the bacteria if you like, but that’s a victim’s approach to policy. Absent an S. mutans vaccine or similar innovations, there’s not much we can do about our resident bacteria. We can, however, choose not to feed them substances that are uniquely suited to fueling their populations and the destructive processes that result.

April Fools in the MT Legislature

I was planning an April Fool’s Day post to mock the Montana legislature, but I really can’t top what’s actually been going on in Helena over the past few days. One bar-owning legislator proposed rolling back DUI laws, to preserve the sacred small town rite of driving home drunk from the bar. The same day, they seriously debated putting the state on the gold standard, which drew open laughter and an amendment to permit paying state transactions in coal. The gold bugs, who fancy themselves constitutional scholars, evidently weren’t around when the proposal to assert eminent domain power over federal lands was drafted. I could go on and on… It’s troubling, because I keep getting my news reader feed mixed up with The Onion.

A comment at the Bozeman Daily Chronicle captured widespread sentiment around here better than I can:

Hey members of the house- Thanks for wasting our money. Try to do something productive up there instead of making all Montanans look like a bunch of idiots. If I was as worthless as you I’d kick my own a_$. Put that in your cowboy code…

Dynamics of Fukushima Radiation

I like maps, but I love time series.

ScienceInsider has a nice roundup of radiation maps. I visited a few, and found current readings, but got curious about the dynamics, which were not evident.

So, I grabbed Marian Steinbach’s scraped data and filtered it to a manageable size. Here’s what I got for the 9 radiation measurement stations in Ibaraki prefecture, where the Fukushima-Daiichi reactors are located:

IbarakiStationRadiation

The time series above (click it to enlarge) shows about 10 days of background readings, pre-quake, followed by some intense spikes of radiation, with periods of what looks like classic exponential decay behavior. “Intense” is relative, because fortunately those numbers are in nanoGrays, which are small.

The cumulative dose at these sites is not yet high, but climbing:

IbarakiStationCumDose

The Fukushima contribution to cumulative dose is about .15 milliGrays – according to this chart, roughly a chest x-ray. Of course, if you extrapolate to long exposure from living there, that’s not good, but fortunately the decay process is also underway.

The interesting thing about the decay process is that it shows signs of having multiple time constants. That’s exactly what you’d expect, given that there’s a mix of isotopes with different half lives and a mix of processes (radioactive decay and physical transport of deposited material through the environment).

IbarakiRadHalfLife

The linear increases in the time constant during the long, smooth periods of decay presumably arise as fast processes play themselves out, leaving the longer time constants to dominate. For example, if you have a patch of soil with cesium and iodine in it, the iodine – half life 8 days – will be 95% gone in a little over a month, leaving the cesium – half life 30 years – to dominate the local radiation, with a vastly slower rate of decay.

Since the longer-lived isotopes will dominate the future around the plant, the key question then is what the environmental transport processes do with the stuff.

Update: Here’s the Steinbach data, aggregated to hourly (from 10min) frequency, with -888 and -888 entries removed, and trimmed in latitude range. Station_data Query hourly (.zip)

The Secret of the Universe in 6 sentences

Niall Palfreyman wrote this on the board to introduce a course in differential equations:

  1. The Secret of the Universe in 6 sentences
  2. Nature always integrates flows over time
  3. Flows always differentiate fields over space
  4. Structure determines behaviour
  5. Algebra is the study of structure
  6. Dynamics is the study of behaviour

I like it.

A little explanation is in order. I have my morning coffee in hand. It’s warmer than the room, so it’s cooling off. It’s heat winds up in the room. If I want to manage my coffee well, neither burning my tongue nor gagging down cold sludge, I need to be able to make some predictions about the future behavior of my cuppa joe. I won’t get far by postulating demons randomly stealing calorics from my cup, though that might provide a soothingly fatalistic outlook. I’m much better off if I understand how and why coffee cools.

#2, the “nature integrates flows” part of the system looks like this:

coffeeCooling

Each box represents an accumulation of heat (that’s the integral). Each pipe represents a flow of heat from one place to another. The heat currently in the house is simply the net result of all the inflows from coffee cups, and all the losses to the outside world, over all time (of course, there are other flows to consider, like my computers warming the room, and losses to the snowy outside).

In the same way, the number of people in a room is the net accumulation of all the people who ever entered, less all those who ever left. A neat thing about this is that the current heat in the cup, or count of people in a room, is a complete description of the state of the system. You don’t need to know the detailed history of inflows and outflows, because you can simply take the temperature of the cup or count the people in the room to measure the accumulated effects of all the past events.

The next question is, why does the heat flow? That’s what #3 is about. Heat follows temperature gradients, as water flows downhill. Here’s a temperature field for a coffee cup:

Coffee_applepie_infrared

wikimedia commons

Heat will flow from the hot (red) cup into the cool (green) environment. The flow will be fastest where the gradient is steepest – i.e. where there’s the greatest temperature difference over a unit of space. That’s the “flows differentiate fields” part. Other properties also matter, like the thermal conductivity of the cup, air currents in the room, insulation in the wall, and heat capacity of coffee, and these can also be described as distributions over space or fields. That adds the blue to the model above:

CoffeeStructure

The blue arrows describe why the flows flow. These are algebraic expressions, like Heat Transfer from Cup to Room = Cup to Room Gradient/Cup-Room Heat Transfer Coefficient. They describe the structure – the “why” – of the system (#5).

The behavior of the system, i.e. how fast my coffee cools, is determined by the structure described above (#4). If you change the structure, by using an insulated mug to change the cup-room heat transfer coefficient for example, you change the behavior – the coffee cools more slowly.* The search for understanding about coffee cups, nuclear reactors, and climate is essentially an effort to identify structures that explain the dynamics or patterns of behavior that we observe in the world.

* Update: added a sentence for clarification, and corrected numbering.

Then & Now

Time has an interesting article on the climate policy positions of the GOP front runners. It’s amazing how far we’ve backed away from regulating greenhouse emissions:

Then Now
Pawlenty signed the Next Generation Energy Act of 2007 in Minnesota, which called for a plan to “recommend how the state could adopt a regulatory system that imposes a cap on the aggregate air pollutant emissions of a group of sources.” The current Tim Pawlenty line on carbon is that “cap and trade would be a disaster.”
Here he is in Iowa in 2007, voicing concern about man-made global warming while supporting more government subsidies for new energy sources, new efficiency standards, and a new global carbon treaty. Mitt Romney regularly attacks Barack Obama for pushing a cap and trade system through Congress.

And so on…

I can’t say that I’ve ever been much of a cap and trade fan, and I’d lay a little of the blame for our current sorry state at the door of cap and trade supporters who were willing to ignore what a bloated beast the bills had become. Not much, though. Most of the blame falls to the anti-science and let’s pretend externalities don’t exist crowds, who wouldn’t give a carbon tax the time of day either.

Vensim Compiled Simulation on the Mac

Speed freaks on Windows have long had access to 2 to 5x speed improvements from compiled simulations. Now that’s available on the Mac in the latest Vensim release.

Here’s how to do it, in three easy steps:

  • Get a Mac.
  • Get the gcc compiler. The only way I know to get this is to sign up as an Apple Developer (free) and download Xcode (I grabbed 3.2.2, which is much smaller than the 3.2.6+iOS SDK, but version shouldn’t matter much). There may be other ways, but this was easy.
  • Get Vensim DSS. After you install (checking the Install external function and compiled simulation support to: box), launch the program and go to Vensim DSS>Preferences…>Startup and set the Compiled simulation path to /Users/Shared/Vensim/comp. Now move to the advanced tab and set the compilation options to Query or Compile (you may want to skip this for normal Simulation, and just do it for Optimization and Sensitivity, where speed really counts).

OK, so I cheated a little on the step count, but it really is pretty easy. It’s worth it, too: I can run World3 1000 times in about 8 seconds interpreted; compiled gets that down to about 2.

Update: It turns out that an installer bug prevents 5.10d on the Mac from installing a needed file; you can get it here.