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Graphic comparing highest mountains

Graphic comparing highest mountains

In mountaineering, 8000m peaks are the ultimate test of high-altitude climbing. It so happens that there are 14 Eight-thousanders. In 1986 Reinhold Messner became the first person to have climbed all 14 8000m peaks. It has become a coveted trophy of mountaineering, with only about 30 people having done so since.

A different, but somewhat related challenge is to climb the highest mountain on every continent, the so-called Seven Summits. This was first completed by Dick Bass in 1985. It has become a more mainstream mountaineering challenge, and about 300 people have repeated that feat. That has also lead to significant and often problematic overcrowding on those seven summits.

Interestingly, it was noted that the second highest mountain on each continent is typically harder to climb than the highest. Hence yet another challenge was born to complete the first ascent of the Seven Second Summits. Hans Kammerlander claims to have done so in 2010 – although some doubts have arisen regarding whether he stood on the right summit on Mount Logan, Canada. Others have suggested combining the Seven Summits and the Seven Second Summits, giving again 14 peaks.

On the Wikipedia page I found an interesting graphic comparing the 14 Eight-thousanders with the Seven + Seven Second Summits. It was created by Cmglee and shared on the Wikipedia page.

Comparison of highest mountains (Source: Wikipedia)

This is an interesting chart, created as .svg file and thus rendering in high definition on large wide-format screens. It is also interesting to follow the revision history on the talk page and the suggestions about coloring and labeling coming from interested readers. In some ways, this shows how published charts can be improved collaboratively. Contributor ‘Cmglee’ has contributed several .svg graphics to Wikipedia as per the User talk page, including a 5-set Venn diagram, life-expectancy bubble charts and Earthquake intensity bubble charts.

I have a personal interest in mountaineering. In 2009-2010 I embarked on my own adventure of a lifetime called the ‘Panamerican Peaks’. Cycling between Alaska and Patagonia (Panamerican Highway) and Climbing the highest mountain of every country along the way. You can find out more about that adventure on my Panamerican Peaks website. Coincidentally, there are a minimum of 14 countries and peaks in that set as well: United States, Canada, Mexico, Guatemala, El Salvador, Honduras, Nicaragua, Costa Rica, Panama, Colombia, Ecuador, Peru, Chile, Argentina.

Position and elevation of 14 Panamerican Peaks

Prior to starting my adventure journey I had mapped out the height of those 14 mountains. Interestingly, except for a few peaks in Central America, the country high-points get higher the further North or South they are located.

Heights of 14 Panamerican Peaks

Four of those peaks are included in the Seven (Second) Summit lists above: Denali, Logan (North America) and Aconcagua, Ojos (South America). It would be great to include the other 10 Panamerican Peaks in a similar graphic. About time for me to look into generating .svg graphics…

And sure enough, Wikipedia contributor Cmglee provided me with a version of the above .svg chart comparing the 14 Panamerican Peaks with the 14 Seven (Second) Summits as follows:

Comparison of 14 Panamerican Peaks with Seven (Second) Summits

Thanks to Cmglee for the quick turn-around.

 
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Posted by on June 4, 2012 in Recreational

 

Tube Maps

Tube Maps

I just got back from a combined business and vacation trip around Easter to Germany and Austria. In Europe, public transportation is an important part of the infrastructure. Especially in the big cities many people commute daily by train or subway, some even live without a car.

One of the most important pieces of information for train and subway systems is the tube map. It is a schematic transit map showing the lines, stations and connections of the train or subway system. It’s main element is that it abstracts away geographical detail (where is what) and focuses on topological aspects: How do I need to transit to which other line to get to a particular station?

London Tube Map (Source: Wikipedia)

The Wikipedia tube map article details the origins around the London subway system which was called the tube (hence the name for this type of map) dating back to first schematic maps in 1931 by Harry Beck:

“Beck was a London Underground employee who realised that because the railway ran mostly underground, the physical locations of the stations were irrelevant to the traveller wanting to know how to get to one station from another — only the topology of the railway mattered.”

This style of map has been widely adopted and successively refined. Having grown up in Munich and having used its train (S-Bahn) and subway (U-Bahn) system for some 25 years, I came to realize that it is not only a convenient tool for the traveller. It can form the basis of mental models of the topology of a city. The first lines of the Munich S- and U-Bahn system were built for the Olympic Games in 1972. The history and evolution of the train and subway system over the 40 years since has been documented on this website. Let’s look at the tube maps and their evolution in roughly 10 year time intervals.

Munich Tube Map 1971

1971: Note the basic shape of a central track West-East shared by all S-Bahn lines which then fan out radially to the suburbs. The 45° angles help with the text labels and add simplicity to the layout. This simplicity is one key element for such tube maps to become a mental model of the city topology, i.e. of knowing what is where and how to get to it. Note that initially there are only two U-Bahn lines sharing most of their underground tracks.

Munich tube map 1980

1980: The design of the map evolves to “stretch” out the line-graph to both fill out the entire available rectangular space and to free up some more space in the center; here two additional U-Bahn lines require more space, also due to the fact that U-Bahn stations are closer together than S-Bahn stations in the periphery. The Text label “P+R” is introduced to designate Park & Ride facilities at the stations for commuters.

Munich tube map 1992

1992: Some additional U-Bahn lines and stations fill in the center. One of the S-Bahn lines is renamed (S3 -> S8) and extended to the North to connect to the new Munich airport (Erding). Also a few minor map changes (new color scheme, font and legend).

Munich tube map 2001

2001: S1 now also reaches the new airport, which simplifies travel from the Western part of the city and effectively creates a Northern loop. The map changes in the top section to reflect this new topology; this graphically compresses the U-Bahn system in the upper half. A new color (blue) for the stations represents he inner zone. This together with the new text label “XXL” represents tariff boundaries. (A similar approach with blue font color for inner zone station names was dropped after a brief version in 1997; it looked confusing.)

Munich tube map 2012

2012: The current map adds several graphical aspects such as the concentric rings of background color for tariff boundaries, a new font for cleaner look and less line breaks as well as icons for long distance train connections. It also shows some geographic features such as the Isar river and the two lakes in the South-West as well as icons for tourist attractions or land-marks such as the new soccer stadium, the ‘Deutsches Museum’ or the Zoo. For a hi-res map see this pdf file.

Such a sequence shows the evolution of schematic concepts and visual representations over the decades. When you take away some of the simplifying tube map abstractions such as the 45° angle, you get topographical maps like this:

Topographical map of Munich U-Bahn 2010

While such a map gives you a more precise idea of where you are at any given station in the city, it is much harder to remember and to reconstruct in your head. I believe that this simplicity-by-design of modern tube maps makes it such a strong candidate for forming the basis of mental models of city topology.

Here is an interesting variation of the Munich transit system in a so called isochrone map using colors to display transit times say from the center to other city destinations. Robin Clarke created the following map and describes in this post how he did it.

Munich transit system Isochrone Map (Source: Robin Clarke)

A final example of using tube maps in an interactive graphic comes from Tom Carden. He created an applet that lets you click on any of the 200 London subway stations and get a isochronic map showing transit times from that origin to any other station. While not laid out as clean as the Beck-style tube maps, this interactive graphic represents 200 different maps all in one! (Click on the image to get to the interactive version.)

Interactive London Tube Map (Source: Tom Carden)

See also the more recent Blog post London Tube Map for additional examples of graph visualizations using the London underground as illustration object.

As a traveller arriving in an unknown city we often tend to take such subway infrastructure and its documentation for granted. What amazes me is to think about the amount of cumulative work – plan, design, construction, logistics, etc. – that has gone into building such an infrastructure. A few interesting facts about the Munich U-Bahn (subway) system: 6 lines, 100 stations, 103 km, ~ 1 million passengers /day. (Source: Wikipedia). Building a subway costs in the order of $100 million/km, so this represents an investment of about $10 billion! Think about that the next time you try to find your way through a new city…

 
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Posted by on April 20, 2012 in Industrial, Recreational

 

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Futuristic TouchScreen Visualization

Futuristic TouchScreen Visualization

Glass manufacturer Corning has published the second YouTube video in its series “A Day Made of Glass”. It provides a glimpse into the future of ubiquitous touchscreen glass displays, from the car dashboard to the kitchen refrigerator and wall-to-wall home display, the large school community table to the medical laboratory, even the glass wall in an outdoor theme park.

Corning Day Of Glass 2

Mashable writes in its story about the video that it “will blow your mind”. Hyperbole aside, it is worth watching (click on image above). The script goes through a typical day and shows various display applications; then it pauses the scenes and mentions the underlying technological challenges and whether the depicted displays are possible and feasible with today’s technology. From the video:

“Of course, this is not just a story about glass. It’s a story about a shift in the way we will communicate and use technology in the future. It’s a story about ubiquitous displays, open operating systems, shared applications, cloud media storage and unlimited bandwidth. We know there are many obstacles to be overcome before what we’ve just seen will become an attainable, reliable reality. But at Corning, we believe in this vision – and we are not waiting.”

Besides being a great corporate promotional piece, the 11 min video is a great example of how interactive, even immersive visualizations can change how we consume and interact with information and with one another.
Apple created a video back in 1987 titled “Knowledge Navigator” which seemed similarly futuristic at the time. Today, 25 years later, the iPad is in common use. Interactive touch screens have become the norm for smart phones since Apple launched the iPhone in 2007, just 5 years ago. Larger form factors exist, but are still expensive to build.

Regardless of how long it will take for touch screen displays to get bigger and become ubiquitous, the notion of interactive data visualization will only become more valuable.

 
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Posted by on February 5, 2012 in Industrial, Medical, Recreational, Scientific

 

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Number of Neighbors for World Countries

Number of Neighbors for World Countries

One important geographical aspect in economy is whether a country is land-locked. Another aspect is the number of neighbors a given country shares a border with. If we sort all 239 world countries, 75 (31%, almost one third) of them are island countries such as Madagascar or Australia where this number is zero. On the opposite end are countries with the most border connections. Here are the top 6 countries in descending order: China (16), Russia (14), Brazil (10), Sudan, Germany, and Democratic Republic of Congo (9 each). All other countries have 8 or less neighbors. Here is a visual breakdown:

The histogram shows the high frequency of island states; the range from 1 to 5 neighbors is fairly common, with a steep drop off in the frequency of 6 or more neighbors. Here is a world map with the same color-code:

WorldMap color-coded by number of neighboring countries

Large countries tend to have more neighbors (Russia (14), China (16), Brazil (10)), but there are obvious exceptions to this tendency (Canada (1), United States (2)). The number of neighbors depends not just on the size of the country itself, but on it’s neighbors’ sizes as well; for example, a small country such as Austria (land area size world rank: 116th) has a rather high number of 8 neighbors because many of them in turn are relatively small (Switzerland, Liechtenstein, Slovenia, etc.).

The average number of neighbors is about 2.7 and there are 323 such border relationships. These can be visualized as graphs with countries as vertices and borders as edges. (Note that to simplify the graphs I excluded all 75 islands = disconnected vertices except Australia.) There are two main partitions of this graph following the land-border geography: One with Europe, Asia and Africa and one with the Americas.

Border-Connected Countries in Europe, Asia, Africa

With the graph layout changed from “Spring Embedding” to “Spring Electrical Embedding” one obtains this interesting variation of the same graph which looks like a sword fish:

The "EurAsiAfrica Sword-fish"

The other partition of the Americas can be visualized in a circular embedding layout:

Europe, Asia, Africa (left) and Americas (right)

It is also interesting to look at the numbers for lengths of pairwise borders between two countries:

  • Number: 323 border-pairs
  • Minimum: 0.34 [km]
  • Maximum: 8893 [km]
  • Mean: 789.6 [km]
  • Total: 255048 [km]
  • Most pairwise borders are between 100 – 1000 km long, but they can as short as 1/3 km (China – Macau) or almost 9000 km (Canada – United States).

    When we look at the entire border length for each country, we see familiar names on top of the ranking:
    China: 22147 [km], Russia: 20293 [km], Brazil: 16857 [km], India: 14103 [km], Kazakhstan: 12185 [km], United States: 12034 [km]. It seems likely that the first four, the so called “BRIC” countries, owe part of their economic strength to their geography: Size, length of borders and number of neighbors influence the number of local trading partners and routes to them. There are many more correlations one can analyze such as between border length / number of neighbors and GDP / length of road network etc. One thing seems likely when it comes to the economy of world countries: Size matters, and so does Geography!

    Epilog: This analysis was all performed using Wolfram’s Mathematica 8. The built-in curated CountryData provides access to more than 200 properties of the world countries, including things like Population, Area, GDP, etc. Some cleaning of the borders lengths data was required to deal with different spellings of the same country. (If you’re interested in the data or source-code, please contact me via email.) List manipulation and mathematical operations such as summation are very easy to do in the functional programming paradigm of Mathematica. Graphs are first-order data structures with numerous vertex and edge operators. Charting is also fairly powerful with BarCharts, ListPlots and more advanced graph charting options. Which other software provides all this flexibility in one integrated package?

     
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    Posted by on October 6, 2011 in Recreational, Socioeconomic

     

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    Oregon Coast Bike Map

    Oregon Coast Bike Map

    A good example of visualization for recreational purposes is the Oregon Coast Bike Map created by the Oregon Department of Transportation and published here. Here is a sample page of this 13 page document:

    Sample Page from the Oregon Coast Bike Map

    The map is full of useful information relevant to cyclists such as weather, traffic, campgrounds, attractions, etc. What I find particularly useful is the indication of distances and elevation profile. Unlike motorized traffic hills tend to slow cyclists down a lot, so estimating ride time to a goal not only depends on the distance, but also on the vertical elevation gain en route to that goal. For example, consider this enlarged area (inset C of above page) of the beautiful “3 Capes” region near Tillamook:

    Inset of 3 Capes Region

    Note the use of color to indicate type of road and traffic as well as shaded bands in elevation profile. I think this is a good example of creating insight by visualizing data. I should know, as I was riding this stretch 2 years ago in August of 2009 during my Panamerican Peaks cycling and climbing adventure. Not having the benefit of such a detailed map I decided to embark on the 3 capes route late in the afternoon, only to get caught by sunset in NetArts as the unexpected hills slowed me down…

    Another excellent map also designed by ODOT is the Columbia River Gorge Bike Map. Check it out for another example of good visualization for recreational purposes.

     
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    Posted by on August 30, 2011 in Recreational

     

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