Dual Use: Sometimes Technology Helps, Sometimes It Hurts

D.In the first half of the 20th century, mathematicians faced a difficult problem. They applauded the breakthrough in purely mathematical thinking, but lamented that its success also enabled devastating improvements in weapons technology since the two world wars. Addressing these questions in 1942, Lillian R. Lieber, professor of mathematics at Long Island University, finally described mathematics as towers. At the top of the tower is a pure (and good) abstraction, connected to, and often rooted in, both good applications and applications. bad.

Another way to describe the extremes of the Reaver’s Tower is the term: Dual-use technology: Technology with both civilian and military applications. For example, improvements to all-terrain vehicles will change how such machines are used not only for military purposes, but also for recreational purposes. Studies experimentally exploring ways to suppress the virulence of infectious agents not only provide insights into the treatment and prevention of infections, but also how pathogens can be modified to do more damage. can also be revealed. Whether mechanical or molecular, innovation can have both beneficial and detrimental consequences. Mathematical innovation can produce the poetic beauty of a series of logical steps. Moreover, the same innovations can also enable critical steps in the development of weapons or define the optimal distribution of biological agents to maximize harm.

originally, Dual-use technology It would apply only to the dichotomy between military and civilian use. However, in the wake of the 9/11 terrorist attacks in the United States, the term has evolved to refer to pathogen-like research, yielding new insights that can either help or hinder military or civilian applications. it was done. Now, the question of age may or may not exist. Dual use idea. Can mathematical innovation do both beauty and harm? Can computational algorithms accelerate resume rankings, but also potentially amplify past biases in hiring?

The dangers of dual use of mathematics and machine learning are explored in three books, two recent and one from the mid-20th century: Lieber’s 1942. TC Mitz education, Alma Steingart’s 2023 axiomBrian Christian’s 2020 Alignment problem. Taken together, these books show that although breakthroughs in mathematical and computational thinking are often believed to outweigh the potential for misuse, there is always a dark shadow immediately behind them. increase. Eight decades after his first critical thinking on modern dual-use, these documents clearly show his AI and algorithm champions one thing. That said, rapid development doesn’t eliminate the need to be aware of exploits.

In mathematics, we move from a set of postulated truths (axioms) to a set of derived truths (theorems) proven by the logical consequences of the axioms and their interactions. This is the logical foundation of mathematics. And this foundation suggests that mathematics is a science based on discoveries of truths that already exist, but were merely previously unknown.In this sense, the goal of the mathematics field is simply teeth.

or is it? Despite such lofty ideals, mathematical thinking occurs within historical and cultural contexts. Moreover, mathematical results and their applications can have cultural implications. Contrary to the protests of some students, mathematics does have ‘real world’ implications.

The history of mathematical thought and thought considers both the history of mathematics itself and the history of the motivations that have driven mathematicians at different times. Alma Steingart provides a history of mathematical thought spanning the 20th century. A persuasive review of the increasing abstraction of mathematical thought and its embrace of deeper exploration of alternative axiom systems.

Historically, Steingart points out, the axioms from which mathematical inferences were derived were connected to observable, often physical, systems. For example, the ancient Greek Euclidean geometry is based on a set of axioms related to a man’s physical sense of his two-dimensional and his three-dimensional space.

However, in the late nineteenth and early twentieth centuries, mathematicians began to explore truths and theorems that often stem from a set of new axioms, often not directly related to physical objects and relationships. Euclidean geometry is based on axioms such as “two parallel lines never intersect” and “non-parallel lines intersect at one point”, while the field of non-Euclidean geometry is similar but It is based on a radically different set of axioms. do cross. These axioms have little basis in the reality we observe, but mathematical logic can define and prove theorems from them, and in a sense create new types of geometry. This new geometry is self-consistent and found application in the theory of relativity in the early 20th century.

Mathematical thinking occurs within historical and cultural contexts. Moreover, mathematical results and their applications can have cultural implications.

In a way, each system of axioms defines its own reality, waiting to be discovered through the development and proof of theorems.This kind of work is called public theory, is a type of mathematical study that delves into different systems defined by different basic sets of axioms. Mathematicians responded enthusiastically to the challenge, and, as detailed by Steingart, axiology rapidly dominated mathematical research and graduate teaching throughout much of his twentieth century. The growth, expansion, and influence of axiology has driven the development of thinking in both pure and applied mathematical research, and has also driven the “mathification” of other areas of study in biology, physics, and the social sciences.

By World War II, however, the field of mathematics (due largely to axioms) was confronted with the excitement of discovery and the dismay of its exploitation in wartime applications. This battle was won by Lieber in his 1942 account of modern mathematics in a distinctive style and pseudo-free poetry. Education of TC Mitz (famous in town). Her target audience is a fictional character named TC Mitz (an acronym for “The Celebrated Man in the Street”), and she skillfully presents a highly readable and accessible account of axiomatic thinking and non-Euclidean geometry. I’m here.

Lieber’s books are truly unique and fun to read. An extensive review of complex axiomatic mathematical concepts (such as non-Euclidean geometry) reveals the struggle directly. Her husband, also a mathematician, illustrated the text using cartoons in the style of mid-century contemporary art (a form of axiomatic thinking that was itself ‘mathematicized’, as discussed in Steingart). covered) [2023]). The illustrations capture the tension of the beauty of pure mathematical thinking and the terror of applying it to war.

---

The struggle between using mathematical thinking for good and bad purposes continues with the development, extension, hype, and practice of machine learning algorithms that drive current artificial intelligence (AI) research and applications. . Brian Christian captures the arc of history from the last quarter of the 20th century to the first quarter of his 21st century. The thrill of researchers pushing the envelope with new breakthroughs in thinking and computational techniques is, in many ways, well-documented in Steingart’s record of the rapid growth and enthusiasm of axiology in the mathematical community some fifty years ago. similar.

Christian highlights both technological and algorithmic developments in AI, along with its promise and dangers. In doing so, he reflects Lieber’s own excitement and despondency (but certainly none of the creative poetry/prose structures that make Lieber’s books uniquely appealing). (Both books were published by the same publisher due to the twists and turns of publishing history.)

Christian’s writings document advances in computing, data availability, algorithmic structures, and, importantly, the way of thinking of the people who define the development of machine learning. computer scientist ( people) reveled in the rapid advances and breakthroughs of the second half of the 20th century, which paralleled the excitement of mathematicians about axiomatic thinking in the first half of the 20th century.

In both situations, the pace of development fueled optimism about new thinking. Progress has been spotlighted. Concerns about negative applications, consciously or unconsciously, have long been put on the backburner.

Those hectic days soon came to an end. In mathematics, World War II brings solemn reflection, and the text and illustrations in Lieber’s book, as well as the tower metaphor, serve as snapshots of this moment. While axiomatic thinking continues to dominate mathematical theory, full extension of the core axiomatic concept to other fields (biology, art, etc.) has proven elusive and creates backlash. The “mathematicization” and “axiomatization” of these other fields have slipped further down the Lieber tower.

And the Tower of the Reaver is still among us. Machine learning is now rapidly improving algorithms for image classification and text translation. However, such success is currently offset by instances of racial and gender bias in facial recognition and resume recommendations. Worrying examples like this raise awareness that seemingly neutral AI algorithms based on historical data can identify and amplify patterns of historical bias.

Such a combination of help and harm resembles the dual-use technology of yesteryear, and Lieber argues that while the technology may have lofty ideals, it is still a reality that can involve harm and violence. He pointed out that it remains tied to the world’s uses. Still, while both mathematics and machine learning tend to be dual-use, it’s reassuring to know that this doesn’t mean innovations are equally likely to have beneficial or malicious consequences. . Positive applications are usually more important than negative applications, and the problem-solving nature of mathematics and machine learning often motivates the search for positive solutions once a problem is identified. In short, this brief summary serves as a reminder that practitioners in these areas should use their talents for good, not evil.