Caryn Navy
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Caryn Linda Navy (born July 5, 1953) is an American
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...
and
computer scientist A computer scientist is a person who is trained in the academic study of computer science. Computer scientists typically work on the theoretical side of computation, as opposed to the hardware side on which computer engineers mainly focus (al ...
. Blind since childhood, she is chiefly known for her work in
set-theoretic topology In mathematics, set-theoretic topology is a subject that combines set theory and general topology. It focuses on topological questions that are independence (mathematical logic), independent of Zermelo–Fraenkel set theory (ZFC). Objects studied ...
and
Braille technology Braille technology is assistive technology which allows blind or visually impaired people to do common tasks such as writing, browsing the Internet, typing in Braille and printing in text, engaging in chat, downloading files, music, using electro ...
.


Early life

Navy was born in
Brooklyn Brooklyn () is a borough of New York City, coextensive with Kings County, in the U.S. state of New York. Kings County is the most populous county in the State of New York, and the second-most densely populated county in the United States, be ...
,
New York New York most commonly refers to: * New York City, the most populous city in the United States, located in the state of New York * New York (state), a state in the northeastern United States New York may also refer to: Film and television * '' ...
in 1953. Born
premature Premature may refer to: * ''Premature'' (2014 film), an American comedy film * ''Premature'' (2019 film), an American romantic drama film * ''PREMature'', a 2015 British television drama miniseries See also * Premature aging, of an organism * P ...
, she was diagnosed as totally blind from
retinopathy of prematurity Retinopathy of prematurity (ROP), also called retrolental fibroplasia (RLF) and Terry syndrome, is a disease of the eye affecting prematurely born babies generally having received neonatal intensive care, in which oxygen therapy is used due to ...
. Her family soon discovered that she could actually see from the corner of one eye, but at age 10 she lost all sight due to
retinal detachment Retinal detachment is a disorder of the eye in which the retina peels away from its underlying layer of support tissue. Initial detachment may be localized, but without rapid treatment the entire retina may detach, leading to vision loss and blin ...
. The next year, in sixth grade, Navy began learning to read and write
Braille Braille (Pronounced: ) is a tactile writing system used by people who are visually impaired, including people who are Blindness, blind, Deafblindness, deafblind or who have low vision. It can be read either on Paper embossing, embossed paper ...
at school. She also learned the
Nemeth Braille The Nemeth Braille Code for Mathematics is a Braille code for encoding mathematical and scientific notation linearly using standard six-dot Braille cells for tactile reading by the visually impaired. The code was developed by Abraham Nemeth. Th ...
system for writing
mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
, which became her favorite subject. She enjoyed team math competitions, and at age 14 independently rediscovered
Euclid Euclid (; grc-gre, Wikt:Εὐκλείδης, Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the ''Euclid's Elements, Elements'' trea ...
's formula for even
perfect number In number theory, a perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself. For instance, 6 has divisors 1, 2 and 3 (excluding itself), and 1 + 2 + 3 = 6, so 6 is a perfect number. T ...
s. She also learned
Hebrew Braille Hebrew Braille ( he, ברייל עברי) is the braille alphabet for Hebrew. The International Hebrew Braille Code is widely used. It was devised in the 1930s and completed in 1944. It is based on international norms, with additional letters dev ...
in preparation for her bat mitzvah service. At age 16 Navy was hired for her first job, as a
Dictaphone Dictaphone was an American company founded by Alexander Graham Bell that produced dictation machines. It is now a division of Nuance Communications, based in Burlington, Massachusetts. Although the name "Dictaphone" is a trademark, it has bec ...
typist in
New York City New York, often called New York City or NYC, is the List of United States cities by population, most populous city in the United States. With a 2020 population of 8,804,190 distributed over , New York City is also the L ...
. She took a class to learn to travel the
New York City Subway The New York City Subway is a rapid transit system owned by the government of New York City and leased to the New York City Transit Authority, an affiliate agency of the state-run Metropolitan Transportation Authority (MTA). Opened on October 2 ...
.


Education

Navy attended the
Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the ...
1971–1975, majoring in mathematics. The only textbook she had in Braille was her calculus book. All her other books were obtained as
audiobook An audiobook (or a talking book) is a recording of a book or other work being read out loud. A reading of the complete text is described as "unabridged", while readings of shorter versions are abridgements. Spoken audio has been available in sc ...
s from Recording for the Blind. At MIT, her undergraduate advisor
James Munkres James Raymond Munkres (born August 18, 1930) is a Professor Emeritus of mathematics at MIT and the author of several texts in the area of topology, including ''Topology'' (an undergraduate-level text), ''Analysis on Manifolds'', ''Elements of Algeb ...
introduced her to the subject of
topology In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such ...
. Upon her graduation with a bachelor's degree in mathematics in 1975, she received the AMITA Senior Academic Award from the Association of MIT Alumnae. Early in her undergraduate career, Navy met David Holladay, an
electrical engineering Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the l ...
student. He looked up enough Braille to write her a note after their first meeting. They were married after graduation. Navy attended graduate school at the
University of Wisconsin–Madison A university () is an educational institution, institution of higher education, higher (or Tertiary education, tertiary) education and research which awards academic degrees in several Discipline (academia), academic disciplines. Universities ty ...
, majoring in mathematics, with a minor in
computer science Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical discipli ...
. During her graduate education, she used an
Optacon The Optacon (OPtical to TActile CONverter) is an electromechanical device that enables blind people to read printed material that has not been transcribed into Braille. The device consists of two parts: a scanner which the user runs over the mater ...
device to read textbooks that were not available in Braille or as audiobooks. She received her
M.A. A Master of Arts ( la, Magister Artium or ''Artium Magister''; abbreviated MA, M.A., AM, or A.M.) is the holder of a master's degree awarded by universities in many countries. The degree is usually contrasted with that of Master of Science. Tho ...
in 1977, and her Ph.D. in 1981 under the supervision of topologist
Mary Ellen Rudin Mary Ellen Rudin (December 7, 1924 – March 18, 2013) was an American mathematician known for her work in set-theoretic topology. In 2013, Elsevier established the Mary Ellen Rudin Young Researcher Award, which is awarded annually to a young rese ...
.


Mathematics

Navy's doctoral thesis, "Nonparacompactness in Para-Lindelöf Spaces", was important in the development of metrizability theory. The paper examines the properties of para-Lindelöf
topological space In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance. More specifically, a topological space is a set whose elements are called points ...
s, which are a generalization of both
Lindelöf space In mathematics, a Lindelöf space is a topological space in which every open cover has a countable subcover. The Lindelöf property is a weakening of the more commonly used notion of '' compactness'', which requires the existence of a ''finite'' sub ...
s and
paracompact space In mathematics, a paracompact space is a topological space in which every open cover has an open refinement that is locally finite. These spaces were introduced by . Every compact space is paracompact. Every paracompact Hausdorff space is normal, ...
s. In a para-Lindelöf space, every
open cover In mathematics, and more particularly in set theory, a cover (or covering) of a set X is a collection of subsets of X whose union is all of X. More formally, if C = \lbrace U_\alpha : \alpha \in A \rbrace is an indexed family of subsets U_\alpha\s ...
has a locally countable open
refinement Refinement may refer to: Mathematics * Equilibrium refinement, the identification of actualized equilibria in game theory * Refinement of an equivalence relation, in mathematics ** Refinement (topology), the refinement of an open cover in mathem ...
, that is, one such that each point of the space has a
neighborhood A neighbourhood (British English, Irish English, Australian English and Canadian English) or neighborhood (American English; see spelling differences) is a geographically localised community within a larger city, town, suburb or rural area, ...
that intersects only
countably many In mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers. Equivalently, a set is ''countable'' if there exists an injective function from it into the natural number ...
elements of the refinement. The spaces constructed by Navy are
counterexample A counterexample is any exception to a generalization. In logic a counterexample disproves the generalization, and does so rigorously in the fields of mathematics and philosophy. For example, the fact that "John Smith is not a lazy student" is a ...
s to the conjecture that all para-Lindelöf spaces are paracompact. Some of her spaces are even
normal Normal(s) or The Normal(s) may refer to: Film and television * ''Normal'' (2003 film), starring Jessica Lange and Tom Wilkinson * ''Normal'' (2007 film), starring Carrie-Anne Moss, Kevin Zegers, Callum Keith Rennie, and Andrew Airlie * ''Norma ...
Moore spaces under suitable set-theoretic assumptions. Since every metrizable space is paracompact, these are counterexamples to the normal Moore space conjecture. Stephen Watson called Navy's construction "a rather general one that permitted quite a lot of latitude" and said, "No other way of getting para-Lindelöf is known. I don't think another way of getting para-Lindelöf is even possible—Navy's method looks quite
canonical The adjective canonical is applied in many contexts to mean "according to the canon" the standard, rule or primary source that is accepted as authoritative for the body of knowledge or literature in that context. In mathematics, "canonical example ...
to me." In 1983, William Fleissner modified one of her spaces to be a normal Moore space under the assumption of a particular covering property. Fleissner's examples finally resolved the normal Moore space conjecture by showing that it requires
large cardinal axiom In the mathematical field of set theory, a large cardinal property is a certain kind of property of transfinite cardinal numbers. Cardinals with such properties are, as the name suggests, generally very "large" (for example, bigger than the least ...
s.


Career

After graduate school, Navy took a position as a visiting
assistant professor Assistant Professor is an academic rank just below the rank of an associate professor used in universities or colleges, mainly in the United States and Canada. Overview This position is generally taken after earning a doctoral degree and general ...
in the mathematics department of
Bucknell University Bucknell University is a private liberal arts college in Lewisburg, Pennsylvania. Founded in 1846 as the University at Lewisburg, it now consists of the College of Arts and Sciences, Freeman College of Management, and the College of Engineering. ...
in 1981. While they were living in
Lewisburg, Pennsylvania Lewisburg is a borough in Union County, Pennsylvania, United States, south by southeast of Williamsport and north of Harrisburg. In the past, it was the commercial center for a fertile grain and general farming region. The population was 5,1 ...
, Holladay started a software company called Raised Dot Computing, focused on computer Braille technology. He was inspired by Navy's need for Braille translation to help with her math teaching. She was an important consultant for the company, helping with software ideas and testing products in her university work. In December 1981, Raised Dot Computing released its first major product, BRAILLE-EDIT, a
word processor A word processor (WP) is a device or computer program that provides for input, editing, formatting, and output of text, often with some additional features. Word processor (electronic device), Early word processors were stand-alone devices ded ...
and two-way
Braille translator A braille translator is a software program that translates a script into braille and sends it to a braille embosser, which produces a hard copy of the original print text. Only the ''script'' is transformed, not the ''language''. Description Fo ...
program for the
Apple II The Apple II (stylized as ) is an 8-bit home computer and one of the world's first highly successful mass-produced microcomputer products. It was designed primarily by Steve Wozniak; Jerry Manock developed the design of Apple II's foam-m ...
. Navy left the university in 1984 to work for the company, and the couple and the company moved back to
Madison, Wisconsin Madison is the county seat of Dane County and the capital city of the U.S. state of Wisconsin. As of the 2020 census the population was 269,840, making it the second-largest city in Wisconsin by population, after Milwaukee, and the 80th-lar ...
in July 1984. Navy applied her computer skills to improving Raised Dot Computing's assistive software, producing enhanced versions of BRAILLE-EDIT and utility programs to handle textbook-format Braille and other special formats. In 1985 they added a line of
MS-DOS MS-DOS ( ; acronym for Microsoft Disk Operating System, also known as Microsoft DOS) is an operating system for x86-based personal computers mostly developed by Microsoft. Collectively, MS-DOS, its rebranding as IBM PC DOS, and a few ope ...
software, culminating in the company's most successful product, MegaDots. Released in August 1992 and still in production, MegaDots provides Braille translation and word processing for the PC. Raised Dot Computing was transferred in September 1998 to a Wisconsin
nonprofit organization A nonprofit organization (NPO) or non-profit organisation, also known as a non-business entity, not-for-profit organization, or nonprofit institution, is a legal entity organized and operated for a collective, public or social benefit, in co ...
called Braille Planet, which was then bought out in August 1999 by
Duxbury Systems Duxbury (alternative older spelling: "Duxborough") is a historic seaside town in Plymouth County, Massachusetts, United States. A suburb located on the South Shore approximately to the southeast of Boston, the population was 16,090 at the 20 ...
. Navy and Holladay live in
Westford, Massachusetts Westford is a town in Middlesex County, Massachusetts, United States. The population was at 24,643 at the time of the 2020 Census. History Westford began as 'West Chelmsford', a village in the town of Chelmsford. The village of West Chelmsfor ...
, and they still work on MegaDots at Duxbury. Navy is a member of the
Braille Authority of North America The Braille Authority of North America (BANA) is the standardizing body of English Braille orthography in the United States and Canada. It consists of a number of member organizations, such as the Braille Institute of America, the National Braille ...
, where she has chaired the Refreshable Braille Technical Committee since 2004.


References


External links


David Holladay and Caryn Navy Oral History

David Holladay and Caryn Navy's Personal Page
{{DEFAULTSORT:Navy, Caryn Living people 1953 births 20th-century American mathematicians Blind academics Bucknell University faculty Jewish American scientists Massachusetts Institute of Technology School of Science alumni People from Brooklyn Topologists University of Wisconsin–Madison College of Letters and Science alumni American women computer scientists American women mathematicians 20th-century women mathematicians Mathematicians from New York (state) American computer scientists 20th-century American women 21st-century American Jews 21st-century American women