Lenore Blum - Academia.edu (original) (raw)
Papers by Lenore Blum
Proceedings of the National Academy of Sciences
Significance This paper provides evidence that a theoretical computer science (TCS) perspective c... more Significance This paper provides evidence that a theoretical computer science (TCS) perspective can add to our understanding of consciousness by providing a simple framework for employing tools from computational complexity theory and machine learning. Just as the Turing machine is a simple model to define and explore computation, the Conscious Turing Machine (CTM) is a simple model to define and explore consciousness (and related concepts). The CTM is not a model of the brain or cognition, nor is it intended to be, but a simple substrate-independent computational model of (the admittedly complex concept of) consciousness. This paper is intended to introduce this approach, show its possibilities, and stimulate research in consciousness from a TCS perspective.
14th Annual Symposium on Switching and Automata Theory (swat 1973), 1973
There are several situations that we are trying more or less to model. One arises from the standa... more There are several situations that we are trying more or less to model. One arises from the standard IQ test in which a person is given a finite sequence of integers and asked to produce the next integer in the sequence. Another is provided by the following grossly simplified view of one aspect of physics: Consider a physicist who is
In 1995, the Computer Science Department at Carnegie Mellon University (CMU) began an effort to b... more In 1995, the Computer Science Department at Carnegie Mellon University (CMU) began an effort to bring more women into its undergraduate computer science (CS) program. At that time, just 7% (7 out of 96) of entering freshman computer science majors at Carnegie Mellon were women. Five years later, in 1999, the percentage of women in the entering class had increased fivefold to about 38% (50 out of 130).
Classically, the theories of computation and computational complexity deal with discrete problems... more Classically, the theories of computation and computational complexity deal with discrete problems, for example over the integers, about graphs, etc. On the other hand, most computational problems that arise in numerical analysis and scientific computation, in optimization theory and more recently in robotics and computational geometry, have as natural domains the reals R, or complex numbers C. A variety of ad hoc methods and models have been employed to analyze complexity issues in this realm, but unlike the classical case, a natural and invariant theory has not yet emerged. One would like to develop theoretical foundations for a theory of computational complexity for numerical analysis and scientific computation that might embody some of the naturalness and strengths of the classical theory. Toward this goal, we have been developing a new theory of computation and complexity which attempts to integrate key ideas from the classical theory in a setting more amenable to problems defined over continuous domains. Our approach is both algebraic and concrete; the underlying space is an arbitrary commutative ring (or field) and the basic operations are polynomial (or rational) maps and tests. The theory yields results in the continuous setting analogous to the pivotal classical results of undecidability and NP-completeness over the integers, yet reflecting the special mathematical character of the underlying space. For example, over the reals we have that (1) the Mandelbrot set as well as most Julia sets are undecidable and (2) the problem of deciding if an algebraic variety has a real point is NP -complete. While there are many subtle differences between the new and classical results, the ability to employ mathematical tools of more mainstream mathematics (such as from algebra, analysis, geometry and topology) in the domain of the reals may suggest new approaches for tackling the classical, as well as new, "P = NP ?" questions. The material covered here is based in large part on (Blum, Shub and Smale 1989) denoted in this paper by BSS, (Blum and Smale 1990) and (Blum 1990).
Recruiting Women to Information Technology across Cultures and Continents, 2007
This paper presents a cultural perspective towards thinking about, and acting on, issues concerni... more This paper presents a cultural perspective towards thinking about, and acting on, issues concerning gender and computer science and related fields. We posit and demonstrate that the notion of a gender divide in how men and women relate to computing, traditionally attributed to gender differences, is largely a result of cultural and environmental conditions. Indeed, the reasons for women entering-or not entering-the field of computer science have little to do with gender and a lot to do with environment and culture as well as the perception of the field. Appropriate outreach, education and interventions in the micro-culture can have broad impact, increasing participation in computing and creating environments where both men and women can flourish. Thus, we refute the popular notion that focusing on gender differences will enhance greater participation in computing, and propose an alternative, more constructive approach which focuses on culture. We illustrate the cultural perspective using specific case studies based in different geographical and cultural regions.
ACM SIGCSE Bulletin, 2006
There are some arguments that suggest women need academic handholding, such as a "female fri... more There are some arguments that suggest women need academic handholding, such as a "female friendly" curriculum, in order for them to participate and be successful in computer science and related fields. Then there are other arguments that suggest we need to change the field to suit women or help women adjust to the field. In this paper we present a different perspective that shows none of these may be necessary. The "Women-CS Fit" is already there! Specifically, under certain cultural and environmental conditions we can see that women fit very well into computing fields and what we have been attributing to gender is actually the result of cultural and environmental conditions. The reasons for women participating in -- or not participating in -- the field of computer science have little to do with gender and a lot to do with culture. In other words, we need to recognize that this is a cultural issue, and an issue that concerns us all. Appropriate local intervention...
The classical (Turing) theory of computation has been extraordinarily successful in providing the... more The classical (Turing) theory of computation has been extraordinarily successful in providing the foundations and framework for theoretical computer science. Yet its dependence on 0's and 1's is fundamentally inadequate for providing such a foundation for modern scientific computation where most algorithms --with origins in Newton, Euler, Gauss, et. al. -- are real number algorithms.
Advances in Cryptology, 1983
Complexity and Real Computation, 1998
Classical complexity theory deals primarily with combinatorial (discrete, integer) problems. We e... more Classical complexity theory deals primarily with combinatorial (discrete, integer) problems. We extend the theory here to consider a wider class of problems.
The Collected Papers of Stephen Smale, 2000
Complexity and Real Computation, 1998
The focus of this chapter is on the result that the complexity of a continuation algorithm can be... more The focus of this chapter is on the result that the complexity of a continuation algorithm can be bounded essentially by the square of the condition number of the homotopy.
The Collected Papers of Stephen Smale, 2000
ABSTRACT Two main results of [L. Blum, M. Shub and S. Smale, Bull. Am. Math. Soc. 21, 1–46 (1989;... more ABSTRACT Two main results of [L. Blum, M. Shub and S. Smale, Bull. Am. Math. Soc. 21, 1–46 (1989; Zbl 0681.03020)] are the existence of universal machines and the NP-completeness of several feasibility problems. The latter reaffirmed the importance of equation solving as a computational problem and suggested two lines of research. On the one hand, there is the P≠NP conjecture which implies that even deciding feasibility for systems of equations cannot be done efficiently. On the other hand, while accepting the difficulty of equation solving, one might try to find algorithms which behave well “in general” or with respect to some particular viewpoint. These two problems appear in a list of problems for the next century proposed by S. Smale [Math. Intell. 20, 7–15 (1998; Zbl 0947.01011)] in response to a request from V. I. Arnold (on behalf of the International Mathematical Union). Smale selected 18 problems from which the 3rd exactly asks whether P=NP and the 17th (“Solving polynomial equations”) reads: Can a zero of n complex polynomial equations in n unknowns be found approximately, on the average, in polynomial time with a uniform algorithm? We review some of Smale’s work in relation to the first problem. Then we focus on the second.
Library of Congress Cataloging-in-Publication Data Complexity and real computation / Lenore Blum ... more Library of Congress Cataloging-in-Publication Data Complexity and real computation / Lenore Blum ... [et al.]. p. cm. IncIudes bibliographical references and index.
SIAM Journal on Computing, 1986
If one is interested in the computational complexity of problems whose natural domain of discours... more If one is interested in the computational complexity of problems whose natural domain of discourse is the reals, then one is led to ask: what is the "cost" of obtaining solutions to within a prescribed absolute accuracy e 1/2 (or precision s =-log2 e)? The loss of precision intrinsic to solving a problem, independent of method of solution, gives a lower bound on the cost. It also indicates how realistic it is to assume that basic (arithmetic) operations are exact and/or take one step for complexity analyses. For the relative case, the analogous notion is the loss of significance. Let P(X)! Q(X) be a rational function of degree d, dimension n and real coefficients of absolute value bounded by p. The loss of precision in evaluating P! Q will depend on the input x, and, in general, can be arbitrarily large. We show that, w.r.t, normalized Lebesgue measure on Br, the ball of radius about the origin in R", the average loss is small: loglinear in d, n, p, r; and K, a simple constant. To get this, we use techniques of integral geometry and geometric measure theory to estimate the volume of the set of points causing the denominator values to be small. Suppose e > 0 and d-> 1. Then: THEOREM. Normalized volume {x nrllQ(x)l < } < e/dKdnd(d + 1)/2r. An immediate application is a loglinear upper bound on the average loss of significance for solving systems of linear equations.
SIAM Journal on Computing, 1986
Two closely-related pseudo-random sequence generators are presented: The lIP generator, with inpu... more Two closely-related pseudo-random sequence generators are presented: The lIP generator, with input P a prime, outputs the quotient digits obtained on dividing by P. The x mod N generator with inputs N, Xo (where N P. Q is a product of distinct primes, each congruent to 3 mod 4, and x 0 is a quadratic residue mod N), outputs bob1 b2" where bi parity (xi) and xi+ x mod N. From short seeds each generator efficiently produces long well-distributed sequences. Moreover, both generators have computationally hard problems at their core. The first generator's sequences, however, are completely predictable (from any small segment of 21PI + consecutive digits one can infer the "seed," P, and continue the sequence backwards and forwards), whereas the second, under a certain intractability assumption, is unpredictable in a precise sense. The second generator has additional interesting properties: from knowledge of Xo and N but not P or Q, one can generate the sequence forwards, but, under the above-mentioned intractability assumption, one can not generate the sequence backwards. From the additional knowledge of P and Q, one can generate the sequence backwards; one can even "jump" about from any point in the sequence to any other. Because of these properties, the x mod N generator promises many interesting applications, e.g., to public-key cryptography. To use these generators in practice, an analysis is needed of various properties of these sequences such as their periods. This analysis is begun here.
In 1995, the Computer Science Department at Carnegie Mellon University (CMU) began an effort to b... more In 1995, the Computer Science Department at Carnegie Mellon University (CMU) began an effort to bring more women into its undergraduate computer science (CS) program. At that time, just 7% (7 out of 96) of entering freshman computer science majors at Carnegie Mellon were women. Five years later, the percentage of women in the entering class had increased fivefold. In 1999, women were 38% of the incoming first-year computer science class (50 out of 130),; in the fall of 2000, approximately 40% of the entering class were women. [See Table 1.]
Bulletin of the American Mathematical Society, 1989
We present a model for computation over the reals or an arbitrary (ordered) ring R. In this gener... more We present a model for computation over the reals or an arbitrary (ordered) ring R. In this general setting, we obtain universal machines, partial recursive functions, as well as JVP-complete problems. While our theory reflects the classical over Z (e.g., the computable functions are the recursive functions) it also reflects the special mathematical character of the underlying ring R (e.g., complements of Julia sets provide natural examples of R. E. undecidable sets over the reals) and provides a natural setting for studying foundational issues concerning algorithms in numerical analysis. Introduction. We develop here some ideas for machines and computation over the real numbers R. One motivation for this comes from scientific computation. In this use of the computer, a reasonable idealization has the cost of multiplication independent of the size of the number. This contrasts with the usual theoretical computer science picture which takes into account the number of bits of the numbers. Another motivation is to bring the theory of computation into the domain of analysis, geometry and topology. The mathematics of these subjects can then be put to use in the systematic analysis of algorithms. On the other hand, there is an extensively developed subject of the theory of discrete computation, which we don't wish to lose in our theory. Toward this end we define machines, partial recursive functions, and other objects of study over a ring R. Then in the case where R is the ring of integers Z, we have the same objects (or perhaps equivalent objects) as the classical ones. Computable functions over Z are thus ordinary computable functions. R.E. sets over Z are ordinary R.E. sets. But when the ring is specialized to the real numbers, we have computable functions which are reasonable for the study of algorithms of numerical analysis. R.E. sets over R are no longer countable and include, for example, basins of attraction of complex analytic dynamical systems.
The American Mathematical Monthly, 1980
The American Mathematical Monthly, 1998
ACM SIGCSE Bulletin, 2007
In this paper, we describe a pilot summer workshop (CS4HS) held at Carnegie Mellon University in ... more In this paper, we describe a pilot summer workshop (CS4HS) held at Carnegie Mellon University in July 2006 for high school CS teachers to provide compelling material that the teachers can use in their classes to emphasize computational thinking and the many possibilities of computer science. Diversity and broadening participation was explicitly addressed throughout the workshop. We focused on broadening the image of what CS is -- and who computer scientists are -- since the reasons for under-representation in the field are very much the same as the reasons for the huge decline in interest. We describe the design of the workshop along with results from initial surveys and evaluations. Short-term evaluations show that this workshop was successful in changing the perception of CS for these teachers and giving them the impetus to include broader topics in their programming courses for the upcoming school year. Future surveys will track the long-term effect of this workshop.
Proceedings of the National Academy of Sciences
Significance This paper provides evidence that a theoretical computer science (TCS) perspective c... more Significance This paper provides evidence that a theoretical computer science (TCS) perspective can add to our understanding of consciousness by providing a simple framework for employing tools from computational complexity theory and machine learning. Just as the Turing machine is a simple model to define and explore computation, the Conscious Turing Machine (CTM) is a simple model to define and explore consciousness (and related concepts). The CTM is not a model of the brain or cognition, nor is it intended to be, but a simple substrate-independent computational model of (the admittedly complex concept of) consciousness. This paper is intended to introduce this approach, show its possibilities, and stimulate research in consciousness from a TCS perspective.
14th Annual Symposium on Switching and Automata Theory (swat 1973), 1973
There are several situations that we are trying more or less to model. One arises from the standa... more There are several situations that we are trying more or less to model. One arises from the standard IQ test in which a person is given a finite sequence of integers and asked to produce the next integer in the sequence. Another is provided by the following grossly simplified view of one aspect of physics: Consider a physicist who is
In 1995, the Computer Science Department at Carnegie Mellon University (CMU) began an effort to b... more In 1995, the Computer Science Department at Carnegie Mellon University (CMU) began an effort to bring more women into its undergraduate computer science (CS) program. At that time, just 7% (7 out of 96) of entering freshman computer science majors at Carnegie Mellon were women. Five years later, in 1999, the percentage of women in the entering class had increased fivefold to about 38% (50 out of 130).
Classically, the theories of computation and computational complexity deal with discrete problems... more Classically, the theories of computation and computational complexity deal with discrete problems, for example over the integers, about graphs, etc. On the other hand, most computational problems that arise in numerical analysis and scientific computation, in optimization theory and more recently in robotics and computational geometry, have as natural domains the reals R, or complex numbers C. A variety of ad hoc methods and models have been employed to analyze complexity issues in this realm, but unlike the classical case, a natural and invariant theory has not yet emerged. One would like to develop theoretical foundations for a theory of computational complexity for numerical analysis and scientific computation that might embody some of the naturalness and strengths of the classical theory. Toward this goal, we have been developing a new theory of computation and complexity which attempts to integrate key ideas from the classical theory in a setting more amenable to problems defined over continuous domains. Our approach is both algebraic and concrete; the underlying space is an arbitrary commutative ring (or field) and the basic operations are polynomial (or rational) maps and tests. The theory yields results in the continuous setting analogous to the pivotal classical results of undecidability and NP-completeness over the integers, yet reflecting the special mathematical character of the underlying space. For example, over the reals we have that (1) the Mandelbrot set as well as most Julia sets are undecidable and (2) the problem of deciding if an algebraic variety has a real point is NP -complete. While there are many subtle differences between the new and classical results, the ability to employ mathematical tools of more mainstream mathematics (such as from algebra, analysis, geometry and topology) in the domain of the reals may suggest new approaches for tackling the classical, as well as new, "P = NP ?" questions. The material covered here is based in large part on (Blum, Shub and Smale 1989) denoted in this paper by BSS, (Blum and Smale 1990) and (Blum 1990).
Recruiting Women to Information Technology across Cultures and Continents, 2007
This paper presents a cultural perspective towards thinking about, and acting on, issues concerni... more This paper presents a cultural perspective towards thinking about, and acting on, issues concerning gender and computer science and related fields. We posit and demonstrate that the notion of a gender divide in how men and women relate to computing, traditionally attributed to gender differences, is largely a result of cultural and environmental conditions. Indeed, the reasons for women entering-or not entering-the field of computer science have little to do with gender and a lot to do with environment and culture as well as the perception of the field. Appropriate outreach, education and interventions in the micro-culture can have broad impact, increasing participation in computing and creating environments where both men and women can flourish. Thus, we refute the popular notion that focusing on gender differences will enhance greater participation in computing, and propose an alternative, more constructive approach which focuses on culture. We illustrate the cultural perspective using specific case studies based in different geographical and cultural regions.
ACM SIGCSE Bulletin, 2006
There are some arguments that suggest women need academic handholding, such as a "female fri... more There are some arguments that suggest women need academic handholding, such as a "female friendly" curriculum, in order for them to participate and be successful in computer science and related fields. Then there are other arguments that suggest we need to change the field to suit women or help women adjust to the field. In this paper we present a different perspective that shows none of these may be necessary. The "Women-CS Fit" is already there! Specifically, under certain cultural and environmental conditions we can see that women fit very well into computing fields and what we have been attributing to gender is actually the result of cultural and environmental conditions. The reasons for women participating in -- or not participating in -- the field of computer science have little to do with gender and a lot to do with culture. In other words, we need to recognize that this is a cultural issue, and an issue that concerns us all. Appropriate local intervention...
The classical (Turing) theory of computation has been extraordinarily successful in providing the... more The classical (Turing) theory of computation has been extraordinarily successful in providing the foundations and framework for theoretical computer science. Yet its dependence on 0's and 1's is fundamentally inadequate for providing such a foundation for modern scientific computation where most algorithms --with origins in Newton, Euler, Gauss, et. al. -- are real number algorithms.
Advances in Cryptology, 1983
Complexity and Real Computation, 1998
Classical complexity theory deals primarily with combinatorial (discrete, integer) problems. We e... more Classical complexity theory deals primarily with combinatorial (discrete, integer) problems. We extend the theory here to consider a wider class of problems.
The Collected Papers of Stephen Smale, 2000
Complexity and Real Computation, 1998
The focus of this chapter is on the result that the complexity of a continuation algorithm can be... more The focus of this chapter is on the result that the complexity of a continuation algorithm can be bounded essentially by the square of the condition number of the homotopy.
The Collected Papers of Stephen Smale, 2000
ABSTRACT Two main results of [L. Blum, M. Shub and S. Smale, Bull. Am. Math. Soc. 21, 1–46 (1989;... more ABSTRACT Two main results of [L. Blum, M. Shub and S. Smale, Bull. Am. Math. Soc. 21, 1–46 (1989; Zbl 0681.03020)] are the existence of universal machines and the NP-completeness of several feasibility problems. The latter reaffirmed the importance of equation solving as a computational problem and suggested two lines of research. On the one hand, there is the P≠NP conjecture which implies that even deciding feasibility for systems of equations cannot be done efficiently. On the other hand, while accepting the difficulty of equation solving, one might try to find algorithms which behave well “in general” or with respect to some particular viewpoint. These two problems appear in a list of problems for the next century proposed by S. Smale [Math. Intell. 20, 7–15 (1998; Zbl 0947.01011)] in response to a request from V. I. Arnold (on behalf of the International Mathematical Union). Smale selected 18 problems from which the 3rd exactly asks whether P=NP and the 17th (“Solving polynomial equations”) reads: Can a zero of n complex polynomial equations in n unknowns be found approximately, on the average, in polynomial time with a uniform algorithm? We review some of Smale’s work in relation to the first problem. Then we focus on the second.
Library of Congress Cataloging-in-Publication Data Complexity and real computation / Lenore Blum ... more Library of Congress Cataloging-in-Publication Data Complexity and real computation / Lenore Blum ... [et al.]. p. cm. IncIudes bibliographical references and index.
SIAM Journal on Computing, 1986
If one is interested in the computational complexity of problems whose natural domain of discours... more If one is interested in the computational complexity of problems whose natural domain of discourse is the reals, then one is led to ask: what is the "cost" of obtaining solutions to within a prescribed absolute accuracy e 1/2 (or precision s =-log2 e)? The loss of precision intrinsic to solving a problem, independent of method of solution, gives a lower bound on the cost. It also indicates how realistic it is to assume that basic (arithmetic) operations are exact and/or take one step for complexity analyses. For the relative case, the analogous notion is the loss of significance. Let P(X)! Q(X) be a rational function of degree d, dimension n and real coefficients of absolute value bounded by p. The loss of precision in evaluating P! Q will depend on the input x, and, in general, can be arbitrarily large. We show that, w.r.t, normalized Lebesgue measure on Br, the ball of radius about the origin in R", the average loss is small: loglinear in d, n, p, r; and K, a simple constant. To get this, we use techniques of integral geometry and geometric measure theory to estimate the volume of the set of points causing the denominator values to be small. Suppose e > 0 and d-> 1. Then: THEOREM. Normalized volume {x nrllQ(x)l < } < e/dKdnd(d + 1)/2r. An immediate application is a loglinear upper bound on the average loss of significance for solving systems of linear equations.
SIAM Journal on Computing, 1986
Two closely-related pseudo-random sequence generators are presented: The lIP generator, with inpu... more Two closely-related pseudo-random sequence generators are presented: The lIP generator, with input P a prime, outputs the quotient digits obtained on dividing by P. The x mod N generator with inputs N, Xo (where N P. Q is a product of distinct primes, each congruent to 3 mod 4, and x 0 is a quadratic residue mod N), outputs bob1 b2" where bi parity (xi) and xi+ x mod N. From short seeds each generator efficiently produces long well-distributed sequences. Moreover, both generators have computationally hard problems at their core. The first generator's sequences, however, are completely predictable (from any small segment of 21PI + consecutive digits one can infer the "seed," P, and continue the sequence backwards and forwards), whereas the second, under a certain intractability assumption, is unpredictable in a precise sense. The second generator has additional interesting properties: from knowledge of Xo and N but not P or Q, one can generate the sequence forwards, but, under the above-mentioned intractability assumption, one can not generate the sequence backwards. From the additional knowledge of P and Q, one can generate the sequence backwards; one can even "jump" about from any point in the sequence to any other. Because of these properties, the x mod N generator promises many interesting applications, e.g., to public-key cryptography. To use these generators in practice, an analysis is needed of various properties of these sequences such as their periods. This analysis is begun here.
In 1995, the Computer Science Department at Carnegie Mellon University (CMU) began an effort to b... more In 1995, the Computer Science Department at Carnegie Mellon University (CMU) began an effort to bring more women into its undergraduate computer science (CS) program. At that time, just 7% (7 out of 96) of entering freshman computer science majors at Carnegie Mellon were women. Five years later, the percentage of women in the entering class had increased fivefold. In 1999, women were 38% of the incoming first-year computer science class (50 out of 130),; in the fall of 2000, approximately 40% of the entering class were women. [See Table 1.]
Bulletin of the American Mathematical Society, 1989
We present a model for computation over the reals or an arbitrary (ordered) ring R. In this gener... more We present a model for computation over the reals or an arbitrary (ordered) ring R. In this general setting, we obtain universal machines, partial recursive functions, as well as JVP-complete problems. While our theory reflects the classical over Z (e.g., the computable functions are the recursive functions) it also reflects the special mathematical character of the underlying ring R (e.g., complements of Julia sets provide natural examples of R. E. undecidable sets over the reals) and provides a natural setting for studying foundational issues concerning algorithms in numerical analysis. Introduction. We develop here some ideas for machines and computation over the real numbers R. One motivation for this comes from scientific computation. In this use of the computer, a reasonable idealization has the cost of multiplication independent of the size of the number. This contrasts with the usual theoretical computer science picture which takes into account the number of bits of the numbers. Another motivation is to bring the theory of computation into the domain of analysis, geometry and topology. The mathematics of these subjects can then be put to use in the systematic analysis of algorithms. On the other hand, there is an extensively developed subject of the theory of discrete computation, which we don't wish to lose in our theory. Toward this end we define machines, partial recursive functions, and other objects of study over a ring R. Then in the case where R is the ring of integers Z, we have the same objects (or perhaps equivalent objects) as the classical ones. Computable functions over Z are thus ordinary computable functions. R.E. sets over Z are ordinary R.E. sets. But when the ring is specialized to the real numbers, we have computable functions which are reasonable for the study of algorithms of numerical analysis. R.E. sets over R are no longer countable and include, for example, basins of attraction of complex analytic dynamical systems.
The American Mathematical Monthly, 1980
The American Mathematical Monthly, 1998
ACM SIGCSE Bulletin, 2007
In this paper, we describe a pilot summer workshop (CS4HS) held at Carnegie Mellon University in ... more In this paper, we describe a pilot summer workshop (CS4HS) held at Carnegie Mellon University in July 2006 for high school CS teachers to provide compelling material that the teachers can use in their classes to emphasize computational thinking and the many possibilities of computer science. Diversity and broadening participation was explicitly addressed throughout the workshop. We focused on broadening the image of what CS is -- and who computer scientists are -- since the reasons for under-representation in the field are very much the same as the reasons for the huge decline in interest. We describe the design of the workshop along with results from initial surveys and evaluations. Short-term evaluations show that this workshop was successful in changing the perception of CS for these teachers and giving them the impetus to include broader topics in their programming courses for the upcoming school year. Future surveys will track the long-term effect of this workshop.