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Waldo R. Tobler

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Waldo Rudolph Tobler was a highly influential American-Swiss geographer and cartographer.

Tobler Hyperelliptical with Tissot's Indicatrices of Distortion
Tobler Hyperelliptical with Tissot's Indicatrices of Distortion

He lived from November 16, 1930, until February 20, 2018. Tobler is best known for coining the first and second laws of geography. His research profoundly impacted the development of quantitative geography. This field uses mathematical methods to study geographic patterns. He also helped establish the discipline of analytical cartography. This is the study of making maps using mathematical models. His work laid the groundwork for geographic information science, or GIScience.

Tobler hyperelliptical projection SW
Tobler hyperelliptical projection SW

Tobler's interest in geography may have started with his frequent childhood moves. He was born in Portland, Oregon, to Verner Tobler and Hanny Urech Tobler. Because his father was a Swiss consular employee, Waldo held dual citizenship. He was both a citizen of the United States and Switzerland. During World War II, his family moved to Washington, D.C. In 1945, the family traveled by boat and train to Switzerland. He attended boarding school in Zurich and public schools in St. Gall and Bern. Some researchers believe these early travels influenced his passion for studying the world.

University of Washington Quad, Spring 2007
University of Washington Quad, Spring 2007

In 1948, Tobler traveled to France and joined the United States Army. He did this to avoid being drafted into the Swiss Army. The military trained him to speak Russian. He served as an intelligence analyst and an interpreter in Europe. Most of his service took place in Austria during the Korean War. He also interviewed Austrian prisoners of war who had been released from the Soviet Union. After leaving the military in 1952, he used the G.I. Bill for his education. He studied at the University of British Columbia before transferring to the University of Washington.

University of Washington Quad, Spring 2007
University of Washington Quad, Spring 2007

Tobler's early career involved working with advanced computer technology. In 1957, he worked for the System Development Corporation in California. He helped develop the Semi-Automatic Ground Environment, or SAGE, system. This system used radar and computers to detect Soviet bomber aircraft.

SAGE console
SAGE console

His job was to create plastic overlay maps for radar screens. These maps were made manually but printed using computers like the IBM 704. This experience influenced his later research in computer and analytical cartography. He also worked for the Pierce County planning commission. There, he created land-use maps by shading them manually with colored pencils.

Tobler spent much of his professional life in academia. He earned his PhD in geography from the University of Washington in 1961. He then became an assistant professor at the University of Michigan. During this time, he was part of a group called MICMOG. This group included faculty from the University of Michigan and Michigan State University. They discussed quantitative geography and published several papers. Colleagues even gave him the nickname "Ptobler." This was a play on the name of Ptolemy, a famous ancient cartographer. In 1977, he moved to the University of California, Santa Barbara.

UCSB University Center and Storke Tower
UCSB University Center and Storke Tower

He served as a professor of geography and statistics there until his death.

As a cartographer, Tobler invented many new ways to represent the Earth. He was particularly interested in map projections. A map projection is a way to show the curved surface of the Earth on a flat map.

Tobler Hyperelliptical with Tissot's Indicatrices of Distortion
Tobler Hyperelliptical with Tissot's Indicatrices of Distortion

He created the family of Tobler hyperelliptical projections. He also developed the first mathematical equations for area cartograms. A cartogram is a map where the size of areas is changed to show data. He also created a method for smooth, two-dimensional mass-preserving areal data redistribution. Many of his ideas were so advanced they could not be fully used because technology was not yet ready.

Tobler hyperelliptical projection SW
Tobler hyperelliptical projection SW

Tobler's research also looked at how things move across space. He created the "Tobler hiking function."

Tobler's hiking function
Tobler's hiking function

This is a mathematical model that describes human movement. It looks at how walking speed changes based on the slope of the land. His work helped bridge the gap between geography, mathematics, and computer science. He was a principal investigator for the National Science Foundation's National Center for Geographic Information and Analysis.

NSF
NSF

His legacy continues through the many archives of his work held at the Library of Congress and the UC Santa Barbara Library.

UC Santa Barbara Library (36069719981)
UC Santa Barbara Library (36069719981)
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🖼️ Images & Media (13)
File:University of Washington Quad, Spring 2007.jpg
University of Washington Quad, Spring 2007.jpg
File:SAGE console.jpeg
SAGE console.jpeg
File:UCSB University Center and Storke Tower.jpg
UCSB University Center and Storke Tower.jpg
File:NSF.svg
NSF.svg
File:Tobler Hyperelliptical with Tissot's Indicatrices of Distortion.svg
Tobler Hyperelliptical with Tissot's...
File:Tobler hyperelliptical projection SW.jpg
Tobler hyperelliptical projection SW.jpg
File:COVID19 CASES Mar21 May21.gif
COVID19 CASES Mar21 May21.gif
File:Estimated percentage of people below 150% poverty in Contiguous United States Counties, 2020.jpg
Estimated percentage of people below 150%...
File:Q-fig2.jpg
Q-fig2.jpg
File:Tobler's hiking function.svg
Tobler's hiking function.svg
File:GISS DisinguishedLectureInGISCience 2025Speakers.jpg
GISS DisinguishedLectureInGISCience...
File:Millermedal.jpg
Millermedal.jpg

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