Posts Tagged ‘topology’

Greek To Me: Mapping Mutual Incomprehension (StrangeMaps)

Wednesday, March 11th, 2009

[Editor’s note: This cartogram shows which languages cultures point to when they “just don’t get it”. Thanks Michael!]

Republished from StrangeMaps.
Originally published February 26, 2009.

greektome

“When an English speaker doesn’t understand a word of what someone says, he or she states that it’s ‘Greek to me’. When a Hebrew speaker encounters this difficulty, it ’sounds like Chinese’. I’ve been told the Korean equivalent is ’sounds like Hebrew’,” says Yuval Pinter (here on the excellent Languagelog).

Which begs the question: “Has there been a study of this phrase phenomenon, relating different languages on some kind of Directed Graph?” Well apparently there has, even if only perfunctorily, and the result is this cartogram.

Continue reading at StrangeMaps . . .

Key to Eliminating U.S. Flight Delays? Redesign the Sky Over New York City (Wired)

Tuesday, March 10th, 2009
[Editor's note: Maps show off the poor network topology for air traffic in and out of New York city and how to optimize the system to reduce flight delays across the US.]
Republished from Wired magazine.
By Andrew Blum Email 02.23.09

Two million flights pass through the New York area airspace each year.
Illustration: Aaron Koblin

Inbound JFK. The turns start while you’re still in the clouds. Engines howling, flaps down, the plane lurches and dives, jerky as a taxi in Midtown. Seatback upright and tray table locked, you’re oblivious to the crowded flight paths around you. But the air above New York City is mapped: a dense and nuanced geography nearly as complicated as the city below.

More than 2 million flights pass over the city every year, most traveling to and from the metropolitan area’s three busiest airports: John F. Kennedy, Newark, and LaGuardia. And all that traffic squeezes through a network of aerial routes first laid out for the mail planes of the 1920s. Aircraft are tracked by antiquated, ground-based radar and guided by verbal instructions issued over simplex radios, technology that predates the pocket calculator. The system is extremely safe—no commercial flight has been in a midair collision over the US in 22 years—but, because the Federal Aviation Administration treats each plane as if it were a 2,000-foot-tall, 6- by 6-mile block lumbering through the troposphere, New York is running out of air.

This is a nightmare for New York travelers; delays affect about a third of the area’s flights. The problem also ripples out to create a bigger logjam: Because so many aircraft pass through New York’s airspace, three-quarters of all holdups nationwide can be traced back to that tangled swath of East Coast sky.

Six years ago, Congress green-lit a plan to solve this problem. The Century of Aviation Reauthorization Act calls for a new system, dubbed NextGen, that uses GPS to create a sort of real-time social network in the skies. In theory, it should give pilots the data they need to route themselves—minus the huge safety cushions.

But NextGen needs some serious hardware: roughly $300,000 in new avionics equipment for every cockpit. That’s a lot of peanuts for the struggling airlines. Add to the tab nearly 800 new federally funded ground stations to relay each plane’s location and trajectory to every other plane in the sky and—by the time NextGen finally launches in 2025—the price tag could reach $42 billion.

Jetliner Photos: Jeffrey Milstein

In the meantime, the New York-area skies have seen a huge traffic bump over the past two decades—including a 48 percent increase between 1994 and 2004. So the FAA has set out to coax new efficiency from old technology.

To help reorganize this airspace, the FAA called on Mitre, a Beltway R&D firm that works exclusively for the government. Mitre’s scientists and mathematicians, in cooperation with some of the region’s air traffic controllers, are completely rethinking the flow of aircraft in and out of New York City. Current flight patterns evolved like a rabbit warren, with additions tacked on to an existing architecture. As airports grew busier and airplanes started flying higher and faster, that architecture became increasingly inefficient. The plan, the unfortunately named New York/New Jersey/Philadelphia Metropolitan Area Airspace Redesign, aims to bring order to the air.

Think of it as a redrawn map of the roadways in the sky. While planes used to chug in and out of the city on a few packed roads, the redesign spreads out the aircraft by adding new arrival posts (exit ramps), departure gates (on-ramps), and takeoff headings (streets leading up to the intercity highways). But the biggest move will be making the space for all these additions. Mitre’s proposal is to extend the boundaries of this airborne city into a 31,180-square-mile area that stretches from Philadelphia to Albany to Montauk.

Unclogging the Skies

A new FAA plan—the New York/New Jersey/Philadelphia Metropolitan Area Airspace Redesign—aims to streamline the air traffic over New York. Here are two highlights.

Adding Lanes
Flights heading west out of New York have to squeeze onto two airborne highways over New Jersey before they merge with air traffic from the rest of the country. The redesign adds more lanes, allowing more planes to take off per hour.

Expanding Control
The New York regional air traffic control center is the busiest in the world. The redesign integrates its authority with other regional centers so controllers can direct planes that are farther away, clearing the high-altitude flight paths for through-traffic

The FAA started implementing the first part of the plan—the new takeoff headings—in December 2007 and should have the full strategy in place by 2012. By then the agencies hope to have reduced delays in New York by an average of three minutes per flight. And in a system as interconnected as the US air traffic network, those few minutes could quickly cascade into hours.

Continue reading at Wired . . .

Molecular Frameworks, the Building Blocks of All Life (Wired mag)

Monday, March 9th, 2009

[Editor's note: Blast from your chemistry class, Wired profiles the 30 most common molecular shapes, nature's "shape alphabet".]

Republished from Wired magazine.
By Erin Biba Email 02.23.09

Sure, the world is complicated, but not as complicated as you might think. It turns out that most organic molecules—the kind of chemicals that make food tasty, perfumes fragrant, and life alive—derive from a few relatively simple architectures.

Together with a bunch of data-minded colleagues, Alan Lipkus of the Chemical Abstracts Service took a deep dive into his organization’s century-old library of 24 million organic compounds—most of them synthetic. They found that more than half are built from just 143 basic shapes, or “frameworks.” And the rest? Well, building those requires the other 836,565 cataloged frameworks.

Why do a handful of fundamental shapes get all the work? In part because chemists typically create new molecules—in the search, say, for potential new drugs—from the ones they’re familiar with. It’s cheaper. But Lipkus hopes that showcasing this lopsided approach will encourage researchers to work farther out on the long tail of molecular geometry. “A lot of structures have not been fully explored,” he says. “There could be interesting things to discover.” Here’s a snapshot of the newly discovered shape-alphabet.

Top 30 Molecular Shapes

Molecules are clusters of atoms joined like Tinkertoys. The range of possible structures is vast, but they can all be categorized by “molecular framework”—the underlying rings and connectors. Most common by far is the hexagon—a ring of six atoms, with one at each corner, that’s the basis for nearly 10 percent of known organic compounds. Here are the top 30 most common frameworks, with frequency of occurrence in parentheses.

Continue reading a Wired . . .

Housing Market State by State (Wash Post)

Friday, March 6th, 2009

[Editor's note: This graphic mixes a free-form Dorling cartogram with a bar chart. Both examine the same nominal geographic data but the bar chart shows "underwater" mortgages as a percent of all mortgages while the cartogram shows the same by total per state. Since most US state choropleth maps are simply visual lists, this graphic dispenses with the map entirely and examines the thematic data through two lenses to show two different results.]

Republished from The Washington Post.
March 5, 2009.
Graphic by Todd Lindeman and Laura Stanton.
Related story >>

At least one in five U.S. mortgage holders – or about 8.3 million households – owed more on their mortgages by the end of 2008 than their homes were worth, sometimes called “underwater.”

SOURCE: First American CoreLogic | The Washington Post – March 5, 2009

U.S. Launches Wide-Ranging Plan to Steady Housing Market
$75 Billion Plan Would Help Borrowers Avoid Foreclosure

Washington Post Staff Writers
Thursday, March 5, 2009; Page A01

The Obama administration yesterday sketched in the details of its most ambitious attempt to reduce foreclosures and stabilize the beleaguered housing market at the root of the economic meltdown.

The program has two key elements: a refinancing program for borrowers with little equity in their homes but current on their loans, and a $75 billion program to help reduce mortgage payments for struggling borrowers.

Several large lenders praised the program, including Bank of America and Wells Fargo. There were also converts among those outside the industry. “I was skeptical at first, but I think these guidelines are helpful in a lot of ways,” said John Taylor, president of the National Community Reinvestment Coalition, a nonprofit group that has been critical of industry efforts to modify mortgages.

Homeowners with loans as large as $729,750 could see their interest rates temporarily cut to as low as 2 percent under the program. The administration also said it will add new incentives to persuade lenders that hold second mortgages to give up their claims, further lowering homeowners’ debt obligations. While the Obama administration initially said it would focus on owner-occupied properties, Fannie Mae and Freddie Mac said they would refinance loans for some second homes and investment properties, too.

That the programs would apply to mortgages worth up to $729,750 throughout the country and not just in high-priced regions surprised some industry officials who praised the move. “It will allow us to help more borrowers, especially those who have been hit hardest by the current crisis,” said John A. Courson, chief executive of the Mortgage Bankers Association.

Continue reading at The Washington Post . . .

Taking the Train: The Most Used Subway Systems in the US and Around the World (Good Magazine)

Thursday, March 5th, 2009

[Editor’s note: This chart needs a per capita analysis and comparable accounting of subway milages but is super fun any how. Click image above for larger view, or follow link below. Happy birthday Katie Rose!]

Republished from Good magazine.
Orig pub date: Feb. 17, 2009.

Even though subways are a fuel-efficent way to move people around congested urban areas, Americans make poor use of them, probably because they are poorly funded and often don’t travel where we want to go. Right now, of the five most-used subway systems in the country, only New York City’s attracts as many riders as the five largest foreign subway systems.

A collaboration between GOOD and Robert A. Di Ieso, Jr.

View the original graphic | blog post.

Per Capita Cartograms from ShowUSA

Thursday, March 5th, 2009

[Editor’s note: I promoted ShowUSA’s animated cartograms last week. This week I show off some of their new per capita cartograms and compare them to the raw number versions. Thanks Rick!]

CO2 emissions – per capita version
Click the interactive on the circular arrow to resize.

CO2 emissions – raw numbers version
Click the interactive on the circular arrow to resize.

Compare CO2 Emissions with Coal Fired Electric Power – raw numbers version
Click the interactive on the circular arrow to resize.

Stimulus Bill – per capita version
Click the interactive on the circular arrow to resize.

Stimulus Bill – raw numbers version
Click the interactive on the circular arrow to resize.

Tag Cloud: How Words Could End a War (NY Time)

Tuesday, March 3rd, 2009

[Editor's note: This op-editorial art piece (above) from the New York Times shows how a simple tag cloud can show an idea topology in a simple, powerful format. Full op-ed below.]

Republished from the New York Times.
By SCOTT ATRAN and JEREMY GINGES
Orig published: January 24, 2009

AS diplomats stitch together a cease-fire between Hamas and Israel, the most depressing feature of the conflict is the sense that future fighting is inevitable. Rational calculation suggests that neither side can win these wars. The thousands of lives and billions of dollars sacrificed in fighting demonstrate the advantages of peace and coexistence; yet still both sides opt to fight.

This small territory is the world’s great symbolic knot. “Palestine is the mother of all problems” is a common refrain among people we have interviewed across the Muslim world: from Middle Eastern leaders to fighters in the remote island jungles of Indonesia; from Islamist senators in Pakistan to volunteers for martyrdom on the move from Morocco to Iraq.

Some analysts see this as a testament to the essentially religious nature of the conflict. But research we recently undertook suggests a way to go beyond that. For there is a moral logic to seemingly intractable religious and cultural disputes. These conflicts cannot be reduced to secular calculations of interest but must be dealt with on their own terms, a logic very different from the marketplace or realpolitik.

Across the world, people believe that devotion to sacred or core values that incorporate moral beliefs — like the welfare of family and country, or commitment to religion and honor — are, or ought to be, absolute and inviolable. Our studies, carried out with the support of the National Science Foundation and the Defense Department, suggest that people will reject material compensation for dropping their commitment to sacred values and will defend those values regardless of the costs.

In our research, we surveyed nearly 4,000 Palestinians and Israelis from 2004 to 2008, questioning citizens across the political spectrum including refugees, supporters of Hamas and Israeli settlers in the West Bank. We asked them to react to hypothetical but realistic compromises in which their side would be required to give away something it valued in return for a lasting peace.

All those surveyed responded to the same set of deals. First they would be given a straight-up offer in which each side would make difficult concessions in exchange for peace; next they were given a scenario in which their side was granted an additional material incentive; and last came a proposal in which the other side agreed to a symbolic sacrifice of one of its sacred values.

Continue reading at New York Times . . .

Noncontiguous Area Cartograms (IndieMaps)

Monday, March 2nd, 2009

[Editor's note: Zach Johnson promotes his Actionscript 3 class for producing non-continuous cartograms and gives background on why these are better (and easier to construct) than Gaster-Newman continuous cartograms.]

Excerpted from IndieMaps blog by Zach Johnson.
View full blog post from Dec. 4, 2008.

Fully contiguous cartograms have stretched and distorted borders but perfectly maintained topologies. Like the Gastner-Newman diffusion-based cartograms we see all over the place. Though all sorts of cartogram designs have been produced, those with perfect topology preservation (fully contiguous cartograms) receive the majority of academic and popular press attention.

< snip >

Judy Olson (Wisconsin Geography alum natch) wrote the only academic article to focus specifically on this cartogram symbology in 1976. She believed noncontiguous cartograms held three potential advantages over contiguous cartograms (I’ve three more below):

  1. “the empty areas, or gaps, between observation units are meaningful representations of discrepancies of values, these discrepancies generally being a major reason for constructing a cartogram”
  2. production of noncontiguous cartograms involves “only the discrete units for which information is available and only the lines which can be accurately relocated on the original map appear on the noncontiguous cartogram”
  3. because of perfect shape preservation, “recognition of the units represented is relatively uncomplicated for the reader”

Despite these inherent advantages (along with ease of production), all the early value-by-area cartograms I’ve seen maintain contiguity. Some took the radical step of abstracting features to geometric primitives, like Levasseur’s early French examples (which may not have been cartograms) and Erwin Raisz’s early American “rectangular statistical cartograms”. But in many ways the noncontiguous design is the more radical cartogram, as it actually breaks the basemap apart — rather than skewing shared borders it abandons them.

my [his] AS3 classes

Olson outlines a technique — the projector method — for manually producing such cartograms. A projector capable of precise numeric reduction/enlargement was required, but not much else, and accurate cartograms could be produced in minutes. A scaling factor was calculated for each enumeration unit, the projector was set to this value, and the projected borders were traced, keeping units centered on their original centers.

My [his] AS3 NoncontiguousCartogram class works similarly. It takes an array of objects containing geometry and attribute properties and creates a noncontiguous cartogram. I include methods for creating the input array from a shapefile/dbf combo, but using KML, WKT, or geoJSON representations wouldn’t be too hard. Methods are included for projecting this lat/long linework (to Lambert’s Conformal Conic projection at least). The NoncontiguousCartogram class draws the input geography, figures the area of each feature, and scales figures according to their density in the chosen thematic variable.

It’s all good/in ActionScript 3, so can be used in Flash or Flex. The zip distribution includes the following:

  • the main NoncontiguousCartogram.as class
  • two example applications and the data needed to run them
  • utility classes, including some that make creating cartograms from shp/dbf input quite easy
  • Edwin Van Rijkom’s SHP and DBF libraries, which are used to load the shapefiles in both of the included examples
  • Keith Peters’ MinimalComps AS3 component library, for the components used in one of the examples
  • Grant Skinner’s gTween class, which is required by the NoncontiguousCartogram class for tween transitions

Browse all the above or download the zip.

<snip>

more advantages

In my thesis research last spring, noncontiguous cartograms performed quite well: subjects rated them highly on aesthetics and could locate and estimate the areas of features with relatively high accuracy. I would add the following to Olson’s list of noncontiguous cartogram advantages.

  1. Olson concentrates on the perfect shape preservation of noncontiguous cartograms. The form (well, those with units centered on the original enumeration unit centroids, as in Olson’s projector method) also perfectly preserves the location of the features on the resultant transformed cartogram. Not only are features easier to recognize, but locations within the transformed units can be accurately located as well (cities or mountain ranges from the original geography can be accurately plotted on the transformed cartogram).
  2. Because units are separate on the transformed cartogram, their figure-ground is increased and areas of features can therefore be more accurately estimated.
  3. Many cartogram designs (including most manual cartograms and the Gastner-Newman-produced cartograms) sacrifice some accuracy for shape recognition. This is a defensible tradeoff, especially as area estimation is notoriously inaccurate and nonlinear. Yet it’s a tradeoff that noncontigous cartograms need not make, as they can always perfectly represent the data with relative areas without sacrificing shape preservation.

Thus, noncontiguous cartograms seem to excel at the cartogram’s two main map-reading tasks: shape recognition and area estimation. This is mediated somewhat by the chief advantage of contiguous cartograms: compactness. Because no space is created between enumeration units, contiguous cartogram enumeration units can be larger than those on noncontiguous cartograms, all other things equal. The increased size on contiguous cartograms may improves their legibility.

Read the full entry over at Indie Maps . . .

E00Parser, an ActionScript 3 Parser for the Arc/Info Export Topological GIS Format (IndieMaps)

Monday, March 2nd, 2009

[Editor's note: Zach Johnson promo's his ActionScript 3 class for reading in .e00 GIS files to Flash. Useful for creating cartograms and other graphic representations reliant on topological relationships. Originally posted there Feb. 21, 2009.]

First off, why mess with such a retro format as Arc/Info Export (.e00)?– any code written for this ASCII file type in the last few years has been on how to go from e00 to pretty much anything (especially to the non-topological data format, the shapefile).

Put simply, topological information makes a lot of things possible for the intrepid ActionScripter.

Read more at IndieMaps . . .
Get the code . . .

Animated Cartograms via Show®USA and Show®World (MappingWorlds)

Thursday, February 26th, 2009

[Editor’s note: These new DC-based websites display a wealth of information about the fifty U.S. states and around the world. Maps are presented both as simple choropleth (color by area) and animated non-continuous area cartograms of the type promoted by Zach Johnson over at IndieMapping. Click on the map above to see it animated to the cartogram view. Thanks Rick!

Quibbles: I wish the US map was projected into a conic like Albers and the World maps were projected, too. Some of the maps deserve a per capita view to best show their thematic data. That would be more telling than a simple cartogram. Or a cartogram that was based on per capita measure would be even better.]

Republished from SHOW®USA from MappingWorlds.com
Originally published: 4 Feb. 2009.

From Spanish speakers to bales of cotton produced to number of UFO sightings, SHOW®USA (show.mappingworlds.com) displays each state’s numbers in animated, easy-to-understand maps that resize the state to the data rather than geographical area. The results are cartograms that bring the numbers to life–and reveal a few surprises.

“Look at our Tornado Deaths map, for instance,” says the site’s creator, Desmond Spruijt. “The most people killed last year by tornadoes were in Florida. It makes you wonder why it wasn’t in the Midwest, where our Tornadoes map shows the most storms. It turns out states like Oklahoma have better warning systems and more storm shelters, not to mention fewer people. The visual presentation makes you think about the data, to understand it better.”

Spruijt is founder of MappingWorlds, a company that helps government, non-profit, and business clients worldwide create innovative maps and cartograms. SHOW®USA is the sister site of SHOW®WORLD, which presents maps with data on the countries of the world in the same way.

SHOW®USA and SHOW®WORLD are free for public use, with no registration or personal information collected. Users can download the numbers behind the maps, which come from dozens of sources like the U.S. Census Bureau, capture and use an image of a map with animation, hyperlink to any map, and post comments about each one–all at no charge.

“To us, maps are more than pictures, they are communication and education tools,” says Spruijt. “We want people to use the SHOW®USA maps in slide shows or research papers, in the classroom–wherever our maps can make simple numbers come alive–and also to start conversations about them on our site. SHOW®USA and SHOW®WORLD also show off the kind of innovative maps we create for our clients at MappingWorlds.”

Spruijt founded MappingWorlds in Amsterdam, The Netherlands, in 2004. The company’s clients include the United Nations, the World Bank, and the International Monetary Fund.

The maps available on SHOW®USA touch on nearly every aspect of the land and people of America. Some of the current maps include: Hispanics, rural population, people with disabilities, drunk driving deaths, U.S. military deaths in Iraq, people without health insurance, strawberry production, natural gas reserves, casinos, federal farm support received, electoral college votes, food stamp recipients, gay marriages, murders, hate crimes, immigrants, charitable contributions, foreclosures, roller coasters, number of presidents born in each state, and Bigfoot sightings. With 141 maps so far, the site is still adding data and plans to have several hundred maps on display.

For those without Flash, JPG versions of the embedded SWF above: