Waldo Rudolph Tobler (November 16, 1930 – February 20, 2018) was an American-Swiss geographer and cartographer. Tobler is regarded as one of the most influential geographers and cartographers of the late 20th century and early 21st century. He is best known for coining what has come to be referred to as Tobler's first law of geography. He also coined what has come to be referred to as Tobler's second law of geography.

Tobler's career had a major impact on the development of quantitative geography, and his research spanned and influenced the study of any discipline investigating geographic phenomena. He established the discipline of analytical cartography, contributed early to Geographic information systems (GIS), and helped lay the groundwork for geographic information science (GIScience) as a discipline. He had significant contributions to computer cartography and was one of the first geographers to explore using computers in geography. In cartography, he contributed to the literature on map projections, choropleth maps, flow maps, cartograms, and animated mapping. His work with analytical cartography included contributions to the mathematical modeling of geographic phenomena, such as human movement in the creation of Tobler's hiking function. Tobler's work has been described as ahead of its time, and many of his ideas are still unable to be fully implemented due to limitations of technology.

Tobler held the positions of professor of geography and professor of statistics at University of California, Santa Barbara and was an active professor emeritus at the Department of Geography until his death.

Early life

Tobler was born in Portland, Oregon, in 1930 to parents Verner Tobler and Hanny Urech Tobler. His father was a Swiss consular employee, and this granted Waldo Tobler both Swiss and United States citizenship. His father's career resulted in moves to Seattle when Waldo Tobler was young, and later to Washington, D.C., when World War II started. During World War II, his father's duties included reporting on the treatment of German Prisoners of War held in the United States. Tobler attended junior high school in Chevy Chase, Maryland, while his father was stationed in Washington, D.C.

In May 1945, after the Allied victory in Europe, the family returned to Europe by boat from Boston, Massachusetts to Le Havre France, then by train to Paris, and finally to his parents' native Switzerland. His father was then stationed in Budapest, and Tobler attended boarding school for a year in Zurich, where he learned German, then public high school in St. Gall, and Bern. Geographers Pradyumna Prasad Karan and Cotton Mather speculated that this frequent moving in early life may have influenced Tobler's later career choices and passion for geography. Tobler later stated that these early travels may have contributed to a career in geography.

Military service

When Tobler turned 18 in 1948, Switzerland wanted to draft him into the Swiss Army. To avoid the Swiss draft, Tobler traveled to France and joined the United States Army in 1948. A native speaker of English, Swiss German, and French, the military trained him to speak Russian to serve as an interpreter for the Counterintelligence Corps. During his time in the military, he served as both an intelligence analyst and an interpreter in Europe (mostly in Austria) during the Korean War, and participated in interviewing Austrian Prisoners of War who had been released from the Soviet Union. Tobler described this activity as "little more than industrial espionage." He left the military in 1952 and used his G.I. Bill to attend university.

Education and field

After leaving the military, Tobler attended classes at University of British Columbia in Vancouver, Canada. Here, Tobler was introduced to Canadian Geographer John Ross Mackay, who Tobler convinced to allow him to take advanced cartography classes as a freshman. After two years at the University of British Columbia, Tobler transferred to the University of Washington in Seattle, from which he received his B.A. (1955), M.A. (1957), and PhD (1961), all in geography. Tobler returned for his PhD only after receiving a National Science Foundation fellowship to fund his studies.

At the Department of Geography, University of Washington, Tobler participated in the quantitative revolution of the late 1950s, working with geography professors Edward Ullman and William Garrison. Here, he became one of many of Garrison's grad students (dubbed the "space cadets") who would go on to be highly influential geographers. His master's thesis is titled "An Empirical Evaluation of Some Aspects of Hypsometric Colors", and his dissertation "Map Transformations of Geographic Space".

Career and academic organizations

Student jobs

While the GI Bill funded much of Tobler's undergraduate courses, he took on several jobs during this time. As an undergraduate student, Tobler was offered positions on research expeditions to the Arctic. However, he turned down this position for a higher-paying job as a mucker in an underground gold mine in British Columbia. Tobler also worked parking cars part-time in Seattle and as a fire lookout in Seattle's Cedar River watershed. Tobler indicated that his choice to work in these positions rather than participate in research expeditions influenced his later specialization in geography. If he had taken the research position, he likely would have been a physical geographer.

After graduating with his B.S. in geography, Tobler was offered a position as a cartographic assistant at the University of Washington, which enabled him to pursue his master's degree.

System Development Corporation

In 1957, after obtaining his master's degree, Tobler began work for the System Development Corporation (SDC), a spinoff of the RAND Corporation, in Santa Monica, California. Here, Tobler worked on developing the Semi-Automatic Ground Environment (SAGE) system, a system that combined both RADAR and computers to detect Soviet bomber aircraft, coordinate interceptor aircraft, and ultimately prevent a Soviet nuclear first strike. Tobler's job entailed creating plastic overlay maps for Radar screens to train RADAR operators during exercises. These maps were created manually but printed using computers such as the IBM 704. With these, SDC experimented with duplication and generating maps using computers directly. Tobler's experience here influenced his later academic publications and research on computer and analytical cartography.

In 1958, the American Association of Geographer's annual meeting was held in Los Angeles, California. At this meeting, Tobler arranged a tour of the computer facilities that SDC operated. Tobler stated this was his first experience with the AAG.

Pierce County planning commission

After the SDC, Tobler worked for two years for the Pierce County planning commission. During this time, he worked to create land-use maps by manually shading with colored pencils. He left this position after getting an NSF fellowship and returned to school to get his PhD.

University of Michigan

After earning his PhD in 1961, Tobler became an assistant professor at the University of Michigan. While at the University of Michigan, Tobler was a member of the Michigan Inter-University Community of Mathematical Geographers (MICMOG), organized by fellow University of Washington geography PhD graduate William Bunge, which brought together faculty from both the University of Michigan and Michigan State University. These meetings sought to discuss topics related to quantitative geography, and organized joint seminars, which resulted in several discussion papers. At the MICMOG meetings, Tobler was given the nickname "Ptobler", as he was "the greatest cartographer since Ptolemy." The MICMOG seminars and publications eventually led to the creation of the journal Geographical Analysis. Tobler remained at the University of Michigan until 1977.

University of California, Santa Barbara

In 1977, Tobler then moved to the University of California, Santa Barbara 1977, to be closer to the West Coast, where he grew up. Here, he continued his research in applying computers to cartography, flow, and other applications. At UC Santa Barbara, he worked with geographers Reginald Golledge and Michael Frank Goodchild. Until his retirement, he held the positions of Professor of Geography and Professor of Statistics at the University of California, Santa Barbara. He was an active Professor Emeritus here until his death.

Other organizations

Tobler was one of the principal investigators and a senior scientist in the National Science Foundation-sponsored National Center for Geographic Information and Analysis. Tobler served on the National Research Council the Board on Earth Sciences. He has been on the editorial board of several journals, including The American Cartographer, Journal of Regional Science, Geographical Analysis, and the International Journal of Geographical Information Systems. He was a charter member of the Urban and Regional Information Systems Association, a council member of the Regional Science Association, member and chairman of the Mathematical Social Science Board, and served as the United States delegate to the International Geographical Union Commission on Geographical Data Processing and Sensing. Until his retirement, he was a member of the Royal Geographical Society of Great Britain.

Research and publications

While Tobler may have fewer publications than some contemporary geographers, his publications covered a broad range of topics and are considered of exceptional quality. His career in geography profoundly impacted the discipline, and he is perhaps the most influential geographer of the past century. The Library of Congress maintains some of Tobler's early work in "The Waldo Tobler Collection" within the broader "Geographic Information Systems (GIS) & Geospatial Resources," and the UC Santa Barbra Library maintains a collection of his work in "The Waldo Tobler Academic Archives".

Cartography

Waldo Tobler described himself as a "geographical cartographer", and his research interests reflect this. He published the first paper on using computers for making maps, established the discipline of analytical cartography, and contributed to the literature around thematic maps. His early work, including his dissertation, involved map projections, which he continued to work on throughout his life. Tobler's time working at SDC on the SAGE system influenced his development of both computer and analytical cartography, and it is possible much of his work was kept confidential for some time due to military applications. Geographer Mark Monmonier described Tobler as "arguably the twentieth century's most innovative cartographer."

Map projections

One of Tobler's largest interests, especially early in his career, was map projections, with much of his dissertation focusing on them. He is the inventor of novel and unusual map projections, including the family of Tobler hyperelliptical projections and the first derivation of the partial differential equations for area cartograms. He also invented a method for smooth two-dimensional mass-preserving areal data redistribution.

In 1972, Tobler translated and published Johann Heinrich Lambert's 1772 "Notes and comments on the Composition of Terrestrial and Celestial Maps." Tobler served as the third author of a book by Qihe Yang and John P. Snyder titled "Map Projection Transformation: Principles and Applications." This book was based on substantial translations by first author Qihe Yang from his work originally published in Chinese, and Tobler stepped in to help revise and assemble the book after Snyder died.

Computer cartography