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, 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's career resulted in moves to Seattle when Waldo Tobler was young, and later to Washington, D.C., when World War II started. 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."

Education and field

thumb|300px| University of Washington "quad" in Spring 2007

After leaving the military, Tobler attended classes at University of British Columbia in Vancouver, Canada. 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. 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. 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. At this meeting, Tobler arranged a tour of the computer facilities that SDC operated. 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." Here, he continued his research in applying computers to cartography, flow, and other applications.

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. Geographer Mark Monmonier described Tobler as "arguably the twentieth century's most innovative cartographer."

Map projections

400px|thumb|The Tobler hyperelliptical projection with [[Tissot's indicatrix of deformation; α = 0, k = 3]]

400px|thumb|The world on Tobler hyperelliptical projection. 15° graticule; α = 0, γ=1.18314; k= 2.5.

One of Tobler's largest interests, especially early in his career, was map projections, with much of his dissertation focusing on them. 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."

Computer cartography

Using his time and experience on the SAGE system, Tobler built upon the concepts and published his work in academic journals. Tobler's research in developing applications for computer cartography is described by Mark Monmonier as occupying "a pivotal place in map history". Analytical cartography is the foundation for many of the developments in Geographic information systems, and shapes how spatial analysis and cartography are taught today. Tobler argued that these maps would increase data density, and avoided many of the issues with Data binning and Statistical classification. There has been significant debate around the best approach to solve this issue with choropleth maps, and most choropleth maps today continue to make use of class breaks. Other approaches to creating classes in choropleth maps include using the Jenks natural breaks optimization, quantile, or equal class intervals.

Cartograms

Tobler's interest in cartograms stemmed from his interest in map projections. A chapter of his dissertation was developed for their creation, later adapted and published in the Geographical Review.

Tobler was among the first to use computers to create cartogram maps, with the rubber sheet method being the first method he proposed for their creation. Tobler's methods for creating cartograms are still employed, however they have some practical problems in implementation that can sometimes ruin topology. Tobler's methods serve as the basis for many other methods to create them. While crude, the result of this research was that Tobler was the first to develop a software approach to creating flow maps in 1987. The first demonstration of this technology by Tobler involved mapping the flow of money through the US Federal Reserve to the various US states. Tobler's flow mapper software, and similar programs, continue to be built upon and applied to new topics. Tobler published several studies on different approaches to spatial interpolation, including an extension of bilinear weighted interpolation and other models.

With regard to spatial resolution Tobler has formulated the following rule of thumb: "The usefulness of a GIS is constrained by its spatial resolution. The size of the smallest detectable feature is twice that of the resolution. The rule is: divide the denominator of the map scale by 1,000 to get the detectable size in meters. The resolution is one half of this amount." This text following the colon in his statement, which was not the main focus of the paper, is now known as "Tobler's First Law of Geography", and is probably what Tobler is most famous for. The first law of geography is widely cited and is relevant today, particularly within the sub-discipline of geographic information science. The Geographic Information Science and Technology Body of Knowledge "Model Curricula" in particular emphasizes the importance of the first law in the section on "Metrical relationships: distance and direction." It is considered the theoretical basis of many statistics in spatial analysis, including those involved in cluster analysis and spatial autocorrelation (such as Moran's I). Spatial autocorrelation, and Tobler's 1970 paper, are considered central to modern approaches in technical geography. Tobler's first law is included in the children's book "ABCs of Geography" under the letter "T" for "Tobler".

In a 1999 paper titled "Linear pycnophylactic reallocation comment on a paper by D. Martin," Tobler stated "Philosophically, the phenomenon external to an area of interest affects what goes on in the inside; a sufficiently common occurrence as to warrant being called the second law of geography." In his 2004 paper "On the First law of Geography: A reply", he discussed this concept again. This has come to be known as Tobler's second law of geography. This has come to be known as Arbia's law of geography.

The laws of geography, particularly Tobler's first law of geography, have been debated heavily in literature, with their status as scientific laws questioned, changes and amendments proposed, exceptions noted, and corresponding defenses by proponents of the laws. Tobler weighed in on this debate surrounding his law, and others, in a 2004 article titled "On the First law of Geography: A reply". While this project had serious limitations, largely due to data limitations, it was the finest scale population set produced to that point. The project was later supported by the Columbia University's Center for International Earth Science Information Network. In this research, Tobler used himself as a subject, and published the results in a 1993 paper. Using the frequency of locations being noted in Cuneiform tablets discussing commercial transactions, he estimated the distance between the towns in Babylonia using a reverse gravity model.

The Austrian Academy of Sciences created the Waldo Tobler Awards, which include the Waldo Tobler GIScience Prize and the Young Researcher Award in Geographic Information Science, to recognize Tobler's contributions to geographic research. The awards seek to "encourage scientific advancement in the disciplines of Geoinformatics and/or Geographic Information Science." It has since been issued to David Mark (2016), Thomas Poiker (2017), Helena Mitasova (2018), Michael Batty (2019), Luc Anselin (2022), and Sara Irina Fabrikant (2023). The Young Researcher Award in Geographic Information Science is awarded to "individuals, typically under the age of 35, acknowledging publications enhancing the body of Geoinformatics or GIScience literature." It has since been issued to Filip Biljecki (2015), Xingjian Liu (2016), Song Gao (2016), Chen Min (2017), Pablo Cabrera Barona (2017), Auriol Degbelo (2018), Wei Luo (2018), Franz-Benjamin Mocnik (2019), Yingjie Hu (2019), Laura Knoth (2020),Yuhao Kang (2023 ), and Weiming Huang (2022). This session honors the legacy of Waldo Tobler by featuring a leading researcher in GIScience.

  • Osborn Maitland Miller Medal, American Geographical Society 1989
  • Meritorious Contributor Medallion, Association of American Geographers, 1971
  • Andrew McNally Award, 1986
  • AAG Microcomputer Specialty Award, 1993.
  • GIS Hall of Fame Inductee, URISA (Urban and Regional Information Systems Association), 2016.

Memorials

thumb|UC Santa Barbara Library where the Waldo Tobler Archives are hosted.

Rachel Tobler (Waldo Tobler's widow) and the Geography department at UC Santa Barbra established the "Waldo Tobler Memorial Lecture Fund" in honor of Waldo Tobler. The fund helps "to support open lectures in the fields of demography, mapping and cartography, and geographic information science." Rachel Tobler donated Waldo Tobler's collection of papers and research materials to the UCSB Library, which now hosts them as "The Waldo Tobler Academic Archives". The journal Cartography and Geographic Information Science honored Tobler with both an obituary authored by Keith C. Clarke and a graphic composite on the cover featuring themes of his work. Two of the International Cartographic Association journals, (The Cartographic Journal, and the International Journal of Cartography), as well as the journals Imago Mundi, Transactions in GIS, and Annals of GIS honored Tobler with obituary articles. The American Association of Geographers published a memorial for him on their website.

See also

Notes

References

  • Waldo R. Tobler at UCSB
  • CSISS/Flow Mapper Software
  • UCSB Geography