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PROf ECTTNG TIME:IOHN PARR SNYDER AND THE DEVETOPMENT

OF THESPACE OBLTQUE MERCATOR PROf ECTION

By

John W. Hessler

PHILIP LEE PHILLIPS SOCIETY

OCCASIONAL PAPER SERIES, NO. 5

GEOGRAPHY AND MAP DIVISIONLIBRARY OF CONCRESS

WASHINCTON, D.C.

Qor(qorAs) x

2004

Library of Congress Philip Lee Phillips Map Society

Geography and Map Division

Library of Congress Philip Lee Phillips Map Society

Geography and Map Division

Table of Contents

Acknowledgements v

lntroduction 1

Early Cartographic Steps 3

Darelopment of the Space Oblique Mercator Projection . . . . . 6

Mathemat ical Methodologiesand Calculator Programs.. . . . . . ' 'a2

Conc lus ion . . . .18

Endnotes . . 19

Anrptated Inventory and Description of the John Parr Snyder Papers . . . . .20

Cor respondence . . . .20

Mathemat ical and Project ion Studies . . . . .2 ' l

h rb l i shedand Unpub l ishedWr i t ings . . . . .2 'a

Gunputer Programs . . . . . .22

hof tss ional Mater ia ls . . . .23

Engineer ingMater ia ls . . . .23

nference Reprints . ..23

Misellaneous . .23

B1|lrynp]ry . . .24

Library of Congress Philip Lee Phillips Map Society

Geography and Map Division

Library of Congress Philip Lee Phillips Map Society

Geography and Map Division

Acknowledgements

I would l ike to express my special thanks to Jeanne Snyder for saving and donating her latehusband's papers, manuscripts, and reference materials to the Ceography and Map Division of theLibrary of Congress and for her helpful encouragement throughout my inventorying and studying of

fohn's papers. Thanks also go to Dr. Alden Colvocoresses, "father" of the Space Oblique MercatorProjection. "Colvo," as he likes to be called, has shared with me hours of conversation and has dedicatedhis intellectual energies over many years furthering the mapping of the earth's surface from space andpromoting the unmanned exploration of the planets in our solar system. This paper greatly benefitedfrom his helpful suggestions and his memories of the formative years of mapping from space.

lwould also l ike to thank some of my col leagues in the Geography and Map Divis ion. JamesFf atness for f irst showing me the pile of unopened boxes that comprised the uninventoried Snyder

Collection; Dr. John H6bertfor suggesting several changes tothe paper; Myra Laird for her precise copyediting; Dr. Ronald Grim for l istening to and then delivering my paper on John Snyder at the 2003International Conference on the History of Cartography; and Patricia Molen van Ee for suggesting thatl rvr i te this monograph and then pat ient ly making i t readable. Final ly, lwould l ike to thank my wifeDr. Katia Sainson, whose consistent and determined scholarship is always an inspiration for my own.

Library of Congress Philip Lee Phillips Map Society

Geography and Map Division

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Library of Congress Philip Lee Phillips Map Society

Geography and Map Division

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PROJECTING TIME:JOHN ST{YDERAI\D THE SPACE OBLIQUE MERCATOR PROJECTION

John W. Hessler

We can only substitute a clear mathemati-cal symbolism for an imprecise one byinspecting the phenomena that we want todescribe, thus trying to understand theirlogical multiplicity-not by conjecturingabout a priori possibilities.

-Ludwig Wittgenstein 1

Introduction

John Parr Snyder (1926-1997) was by all measures one of the most important twentiethcentu4r cartographers. The significance and the influence of his work has been compared to thatof Gerardus Mercator,'a characterization that is well desenred. Snyder's derivation of the equa-tions for the Space Oblique Mercator projection (SOM) and his contributions to the mathemati-cal theory of coordinate transformations rank among the most important developments in thelong history of cartographic science.

The SOM projection, like Mercator's, ushered in a new era of cartography, providing theability to continuously map the earth's surface using satellite data. In 1977, working mostlyalone, and as an amateur, Snyder developed the equations for the SOM, which is one of the mostcomplex projections ever devised. Although the SOM was invented and described geometricallyin fairly simple terms by Alden Colvocoresses of the United States Geological Survey (USGS),the fact that the projection had to account for the rotation of the earth and the orbital motionof the satellite itself made it mathematically complex. The SOM turned out to be so complex, infact, that its solution eluded both National Aeronautics and Space Administration (NASA) andthe USGS staff for many years before John Snyder's frnal solution.

The Snyder Family Trust generously donated John Snyder's unpublished papers, manu-scripts, and annotated reference library to the Geography and Map Division shortly after hisdeath in 1997. Recently, I have inventoried this collection and produced an annotated frndingaid to his manuscripts that is published here for the first time. The importance of this collectionfor scholars and for the history of cartography is twofold. First, it represents a case study in thehistory of cartography for a period when computers and satellites were just beginning to trans-form the discipline into the form that we recognize today. It is the moment in time that saw theinvention of new computational and numerical methods, many of which Snyder experimentedrrith in his manuscripts and used in innovative ways in his projection research. He performedmuch of his most creative work on early programmable calculators, struggling with problems ofmemory allocation and calculating speed. The programs that he wrote for these calculators werestored on small magnetic strips, shown with his calculators in Figure 2.

In order to presenre the program code in a way that would make the programs useable tofuture researchers, I first had to learn the programming language for the long obsolete TexasInstrument 59 anc 56 programmable calculators, and then search through Snyder's mathe-matical notes and manuscripts for clues to his programming techniques. Using retrograde analy-sis and backrvard induction, I was able to reconstruct many of his programs. Although this processposed challenging problems, the code of these programs has yielded deep insights into Snyder'sthinking and the difficulties inherent in programming these early devices.

Library of Congress Philip Lee Phillips Map Society

Geography and Map Division

OccmroNel, PRppR Sunms. No. b

Figure 2. Magnetic programming strips and Snyder's TI-59 and TI-56 calculators

- Second, a-nd-{ore gener4ly, the Snyder collection challenges our conception of the contentand scope of the historiograph.v q_f cartography. Most of the *iitinj rna -oAels that currentlydefine this historiography are built a"orrnd_. ptiori definitionr of *?pr-ur printed artifacts thatare to be contextualized as to their use and pioduction. The."_ur.nrnttions, and the knowledgebase of the historians who m-qk9 t_hem, are in_creasingly insuffrcient as we begin to examine thec?rtgflaphy of the second half of the twentieth century-and beyond. The mathematical and tech-nical knowledge needed to preserve and inte{pjgt the Snyder paper" girr". us a glimpse into thefuture of cartographic history. This history wijt ue ro-ptired noi *"rtly of artifacdbut ratherof complex mathematics and computer pi_ograms, whoise visuali"uiio"'as printed maps is sec-ondary compared with the conceplual ana tfreoretical knowledg" thui prodrr."d them. Unlesscartographic historians recogruze this and begin to think of mapJitt t"r*s of other formats thanthose currently most familiar to the librariari, collector, and pri"r .o"r"*rtor, much of the his-tory of modern cartography may be lost.

Mathematical cartography, more than anything_else, was John Snyder's life, his refuge, andhis inspiration. In order to understand the man, th; legacy that he lefi and the future researchthat his work spawned, it is necessary to discuss his iotion of .aJog.phv and to look deeplyinto his mathematical and programming methods. Some of these meThods cannot be discussedwithout entry into some mathematical and technical details, but I h;;; tried to keep these to aminimum and have provided a large bibliography in those areas where the read"t t"illlffih

Library of Congress Philip Lee Phillips Map Society

Geography and Map Division

PRo.lncrnc Tnur-,IouN PRRR Sttvonn

to explore further. Snyder was not only a cartographer, although that is our focus here, but alsoan engineer, a lover of music, and a Quaker. He was deeply concerned about civil rights and theinjustices of the human condition. He was humble, quiet, and unassuming. He was a husbandand a father and to some of us who manrel at the mathematical insights present in his work,he is a legend.

This paper consists of four parts. The first is a brief biography of John Snyder's life focus-ing on his interest in maps and his involvement in cartographic history up to the time when hebegan his work on the Space Oblique Mercator Projection. Snyder's early intellectual develop-ment was full of mathematics and some of the earliest papers in his collection are projectionnotebooks dating from the time when he was sixteen years old. In this sense, he truly was aprodiry. The second part consists of a history of the development of the Space Oblique MercatorProjection and Snyder's derivation of its analytical equations. The third part concentrates onSnyder's mature mathematical work and the programming methodologies that he employedthroughou