bluuebunny/crossref_metadata_2025_split huggingface dataset:
Act natural, because of Benford’s Law
Authors: D'Agostino Susan 
Published: April 2020

Abstract
“Act natural, because of Benford’s Law” explains how and why large data sets generated as a result of human behavior concerning health records, population counts, tax returns, stock prices, national debts, election data, and more, have numbers whose first digits are unevenly distributed, with Benford’s Law offering percentages. When an individual tampers with a naturally generated data set, they often introduce fake numbers whose first digits are (more or less) evenly distributed from one to nine. Often, a subsequent investigation reveals that someone has tampered with the data set. Mathematics students and enthusiasts are encouraged to act natural so as to avoid looking like a fraudulent data set that does not observe Benford’s Law. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.
Resist comparison, because of chaos theory
Authors: D'Agostino Susan 
Published: April 2020

Abstract
“Resist comparison, because of chaos theory” tells the story of Massachusetts Institute of Technology meteorologist Edward Lorenz who, while working on long-term weather forecasting in 1961, inadvertently upended notions of a Newtonian universe and ignited a scientific revolution by discovering chaos theory. The discussion of how a small change in an initial condition may effect a dramatic change in outcome is enhanced by numerous hand-drawn sketches. Also included are popular culture references to the “butterfly effect” in which the flap of a butterfly’s wings sets off a far-off tornado. Mathematics students and enthusiasts are encouraged to resist comparing mathematical paths when working with a friend as small differences in starting places may lead to different outcomes. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.
Consider all options, as the shortest path between two points is not always straight
Authors: D'Agostino Susan 
Published: April 2020

Abstract
“Consider all options, as the shortest path between two points is not always straight” explains how to find the shortest path between two points on the globe by way of a “great circle”—an equator-like circle that goes around the widest part of a sphere. The discussion is enhanced with numerous hand-drawn sketches. Mathematics students and enthusiasts are encouraged to consider all options in mathematical and life pursuits, especially when a straight or straightforward path is unavailable. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.
Divide and conquer, just like Riemann sums in calculus
Authors: D'Agostino Susan 
Published: April 2020

Abstract
“Divide and conquer, just like Riemann sums in calculus” offers a basic introduction for how to estimate—with any desired non-zero margin of error—the area of an irregular shape. For an initial underestimate, readers are encouraged to draw a large rectangle that fits inside the irregular shape and then use the grade school formula to calculate the rectangle’s area: area equals length times width. To refine this underestimate, readers learn to draw multiple smaller rectangles inside the shape whose areas they also sum. An analogous method is provided for overestimates. The discussion concerning how to obtain underestimates or overestimates with any desired margin of error is illustrated with numerous hand-drawn sketches. Mathematics students and enthusiasts are encouraged to consider dividing and conquering in all challenges they face in mathematics or life. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.
Embrace change, considering non-Euclidean geometry
Authors: D'Agostino Susan 
Published: April 2020

Abstract
“Embrace change, considering non-Euclidean geometry” offers a basic introduction to the geometry of curved surfaces in which the sum of the degrees of a triangle may equal more or less than 180°. The discussion is enhanced by numerous hand-drawn sketches, including triangles on spheres and saddles. Mathematics students and enthusiasts are encouraged to embrace change as a way to alleviate boredom, understand one’s strengths, and uncover new opportunities and modes of thinking. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.
Make an educated guess, like Kepler with his Sphere-Packing Conjecture
Authors: D'Agostino Susan 
Published: April 2020

Abstract
“Make an educated guess, like Kepler with his Sphere-Packing Conjecture” provides an accessible discussion of the history and mathematics behind Johannes Kepler’s Sphere-Packing Conjecture—a statement concerning the densest way to pack spheres such as oranges. The discussion is illustrated with numerous hand-drawn sketches. Though Kepler died before proving his conjecture, his legacy demonstrates the power of conjecture in mathematics. Hordes of mathematicians continued work on his claim for four centuries until Thomas Hales provided a proof of Kepler’s conjecture running to over 250 pages. Upon noting real-life sphere-packing applications in internet messaging, satellite broadcasting, and deep-space telecommunications, readers learn that Kepler’s guess changed the world for the better. Mathematics students and enthusiasts are encouraged to let conjecture serve as a catalyst in their mathematical and life pursuits. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.
Join the community, with Hilbert’s twenty-three problems
Authors: D'Agostino Susan 
Published: April 2020

Abstract
“Join the community, with Hilbert’s twenty-three problems” tells the story of German mathematician David Hilbert who, in 1900 at the International Congress of Mathematicians in Paris, presented twenty-three problems in a first serious effort by any mathematician to curate a list of important open problems across mathematical subfields. In a speech accompanying his offering, he challenged mathematicians to solve all twenty-three problems in the next century. This chapter offers highlights and explanations of some of the twenty-three problems, including the Continuum Hypothesis, the Riemann Hypothesis, and Kepler’s Sphere-Packing Conjecture. With his broad reach, Hilbert understood the value of articulating community-wide mathematical goals, as well as the unifying effect that keeping score might have. Mathematics students and enthusiasts learn that they are part of a community of “zealous and enthusiastic disciples” of mathematics. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.
Enjoy the pursuit, as Andrew Wiles did with Fermat’s Last Theorem
Authors: D'Agostino Susan 
Published: April 2020

Abstract
“Enjoy the pursuit, as Andrew Wiles did with Fermat’s Last Theorem” recounts the story of how mathematician Andrew Wiles was undaunted in the face of 350 years’ worth of mathematicians’ failed efforts at attempting to solve Fermat’s Last Theorem. He believed in his abilities and ultimately succeeded in providing a proof. Along the way, he satisfied a human longing to seek knowledge and energized the mathematics community. Mathematics students and enthusiasts are encouraged to remember to value the journey in mathematical and life pursuits, even when they struggle. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.
Change your perspective, with Viviani’s Theorem
Authors: D'Agostino Susan 
Published: April 2020

Abstract
“Change your perspective, with Viviani’s Theorem” explains a visual proof of Viviani’s Theorem which states that the sum of the distances from any point in an equilateral triangle to its edges by way of perpendicular lines is equal to the altitude of the given equilateral triangle. The discussion is enhanced with numerous hand-drawn sketches. Mathematics students and enthusiasts are encouraged to consider the possibility that a change in perspective need not radically alter circumstances in mathematical and life pursuits. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.
Be contradictory, because of the infinitude of primes
Authors: D'Agostino Susan 
Published: April 2020

Abstract
“Be contradictory, because of the infinitude of primes” offers encouragement and practice with the “proof-by-contradiction” method of mathematical proof. Any mathematician will tell you that the collection of prime numbers is infinite. However, readers are guided in proving this statement by contradicting it. The activity pushes readers to engage deeply with the reasons supporting the fact that there are an infinite number of primes. Mathematics students and enthusiasts are encouraged to debate with enthusiasm in their mathematical and life pursuits. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.
Consider the less traveled path, because of the Jordan Curve Theorem
Authors: D'Agostino Susan 
Published: April 2020

Abstract
“Consider the less traveled path, because of the Jordan Curve Theorem” offers a basic introduction to simple, closed curves and explains why the theorem asserting that every simple closed curve in the plane separates the plane into an “inside” and an “outside” is best appreciated when considering pathological curves. A pathological curve, such as a space-filling curve or the Koch snowflake, is one that lacks features of so-called well-behaved curves. The discussion is enhanced by numerous hand-drawn sketches and a reference to “The Road Not Taken” by poet Robert Frost. Mathematics students and enthusiasts are encouraged to consider the less traveled path in mathematical and life pursuits. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.
Investigate, because of the golden rectangle
Authors: D'Agostino Susan 
Published: April 2020

Abstract
“Investigate, because of the golden rectangle” offers mathematics students and enthusiasts inspiration for mathematical play by way of a guided construction of the golden rectangle. The discussion is illustrated with numerous hand-drawn sketches. A golden rectangle is a rectangle whose side lengths are in the golden ratio, which is, where the Greek letter (pronounced “phi”) is approximately equal to. Readers learn that an indirect, even haphazard, approach in mathematical play may lead to unanticipated discoveries. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.
Draw a picture, as in proofs without words
Authors: D'Agostino Susan 
Published: April 2020

Abstract
“Draw a picture, as in proofs without words” provides a short, wordless illustration proving that. The hand-drawn sketches invoke an earlier time in the reader’s life spent playing with blocks and making quiet yet important mathematical observations. Readers also learn of the story of young Carl Friedrich Gauss whose elementary teacher tried to keep the class busy by asking that they sum the first one hundred integers. Most of the students began the time-consuming process of adding but Gauss drew a few quick sketches that offered a shortcut to the solution: 5,050. Mathematics students and enthusiasts are encouraged to consider play and drawing as methods for eliciting mathematical thoughts. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.
Keep an open mind, because imaginary numbers exist
Authors: D'Agostino Susan 
Published: April 2020

Abstract
“Keep an open mind, because imaginary numbers exist” offers a basic introduction to imaginary numbers, including their history and some real-life applications. In the 1500s, Italian mathematician Rafael Bombelli considered the possibility that an equation such as had a solution. Later, in the 1600s, Rene Descartes defined a new number with the property. He selected the letter for “imaginary”—a word that betrayed his discomfort with the idea. The number is a solution to the equation. In general, an imaginary number may be written as, where and are real numbers and. Mathematics students and enthusiasts who feel bewildered by any mathematical concept are encouraged to work to uncover mysteries in mathematical and life pursuits. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.
Fail more often, just like Albert Einstein did with E=mc2
Authors: D'Agostino Susan 
Published: April 2020

Abstract
“Fail more often, just like Albert Einstein did with not only explains Einstein’s famous equation but tells the little-known story of how he experienced failure along the way. As Einstein worked to correct his mistakes, he not only gained a deeper understanding into the equation, but the entire field of special relativity. Many years later, in a letter to a young girl included in this chapter, he referenced his struggles when he wrote, “Do not worry about your difficulties in mathematics; I can assure you that mine are still greater.” Mathematics students and enthusiasts learn that mistakes are an essential part of the mathematical process. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.
Follow your curiosity, along a space-filling curve
Authors: D'Agostino Susan 
Published: April 2020

Abstract
“Follow your curiosity, along a space-filling curve” tells the story of Italian mathematician Giuseppe Peano’s quest for and discovery of a space-filling curve—a curve that completely fills a space such as a square—that most mathematicians and scientists at the time did not believe existed. For example, Isaac Newton, in his Philosophiae Naturalis Principia Mathematica, tried to ban space-filling curves. The discussion of space-filling curves is enhanced with numerous hand-drawn sketches showing how to construct German mathematician David Hilbert’s space-filling curve. Mathematics students and enthusiasts are encouraged to foster a Peano-like curiosity in mathematical and life pursuits. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.
Exercise your imagination, with fractional dimensions
Authors: D'Agostino Susan 
Published: April 2020

Abstract
“Exercise your imagination, with fractional dimensions” offers a basic introduction to fractional dimensional objects. Unlike a one-dimensional line, a two-dimensional piece of paper, or a three-dimensional box, the dimension of a fractional dimensional object may not be represented by a whole number. The fractional dimensional Koch curve, for example, has approximately 1.26185 dimensions. The discussion is enhanced with numerous hand-drawn sketches providing instruction on how to construct and compute the dimension of the Koch curve. Mathematics students and enthusiasts are encouraged to exercise their imaginations in mathematical and life pursuits as a way of opening themselves up to more of life’s unusual possibilities. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.
Proceed with care, because some infinities are larger than others
Authors: D'Agostino Susan 
Published: April 2020

Abstract
“Proceed with care, because some infinities are larger than others” explains in detail why the infinite set of real numbers—all of the numbers on the number line—represents a far larger infinity than the infinite set of natural numbers—the counting numbers. Readers learn to distinguish between countable infinity and uncountable infinity by way of a method known as a “one-to-one correspondence.” Mathematics students and enthusiasts are encouraged to proceed with care in both mathematics and life, lest they confuse countable infinity with uncountable infinity, large with unfathomably large, or order with disorder. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.
Constitutive relativity in Plato
Authors: Duncombe Matthew 
Published: April 2020

Abstract
This chapter argues that key passages in Plato, which discuss relativity, assume a constitutive view. The formal features—exclusivity, reciprocity, aliorelativity, and existential symmetry—are identified in those passages. These principles are not confined to one dialogue, philosophical topic, or speaker. But they all follow from constitutive relativity. So we can see some of the role constitutive relativity plays. The chapter argues that Plato assumes a constitutive view of relativity by showing that the formal features of constitutive relativity are present across his writing. Section 2.1 discusses Symposium 199d–e and Sophist 255c. Section 2.2 argues for exclusivity in the Symposium 200a–201c and Theaetetus 204b–205a. Section 2.3 argues for reciprocity in Statesman 283d–e. Section 2.4 argues for existential symmetry in Theaetetus 156a–157c. Section 2.5 analyses aliorelativity in Charmides 167c–169a.
Relativity and separation in the theory of Forms
Authors: Duncombe Matthew 
Published: April 2020

Abstract
At Parmenides 133c–134e, Parmenides presents what he calls the ‘Greatest Difficulty’ with Socrates’ inchoate theory of Forms. Although many scholars have recognized that Parmenides’ objection relies on relativity, they have not been able to offer a satisfactory account of the Greatest Difficulty. This chapter shows that once we understand that Plato’s constitutive understanding of relativity is in play, we can give a satisfactory reading. This adds further evidence that Plato assumes a constitutive view of relativity. Section 3.1 introduces the texts of the Greatest Difficulty. Sections 3.2–3.4 discuss the main existing approaches to the argument in the literature. Scholars generally think that the Greatest Difficulty does not pose a threat to the theory of Forms, either because it is not formally valid, or, if it is formally valid, because it begs the question against the Platonist. However, this chapter argues that the Greatest Difficulty poses a genuine challenge to the theory of Forms. Furthermore, the existing approaches assume that Plato holds an incompleteness view of relativity. The chapter argues that, in fact, the Greatest Difficulty assumes a constitutive view of relativity. Section 3.5 shows how it is possible to properly understand the Greatest Difficulty, with the constitutive view of relativity assumed in the background.
Relativity against dogmatism in Sextus Empiricus
Authors: Duncombe Matthew 
Published: April 2020

Abstract
Sextus often tells us that relativity underpins Pyrrhonian Scepticism. Some scholarship focuses on the role of relativity in overarching Pyrrhonist sceptical strategies. Much less scholarship addresses relativity in Sextus’ criticism of particular dogmatic concepts. This chapter argues that Sextus invokes conceptual relativity—a version of constitutive relativity—in his treatment of three dogmatic concepts: signs, causes, and demonstration. However, as a Pyrrhonist, Sextus would likely resist committing himself to a certain concept of relativity, even a conceptual one. This chapter argues that Sextus employs conceptual relativity dialectically against his dogmatic opponents. First, the chapter sets up the two readings of Sextus’ view of relativity. The chapter then presents direct and indirect evidence that the conceptual view is present in Sextus.
Homer’s Intelligent Machines
Authors: Liveley Genevieve , Thomas Sam 
Published: April 2020

Abstract
Through close literary analysis of Homer’s Iliad and Odyssey, this chapter traces the various gradations of weak to strong machine ‘intelligence’ that these ancient poems describe and the mind models that they assume. Beginning with a re-examination of the weak AI evinced in Homer’s descriptions of relatively simple automata, it goes on to analyse Homer’s autonomous vehicles and golden slave girls, considering the more sophisticated models of artificial mind and machine cognition attributed to Homer’s stronger, embodied AI. Throughout, this chapter asks: What kinds of priorities and paradigms do we find in AI stories from Homeric epic and how do these still resonate in contemporary discourse on AI? In particular, what distinctions does Homer draw between artificial and human minds and intelligences? And what is the legacy of Homer’s intelligent machines and the ancient narrative history of AI?
‘A Push-Button Type of Thinking’
Authors: Matthews Graham 
Published: April 2020

Abstract
Midcentury experiments in AI soon resulted in machines that could devise logical proofs, and solve calculus and visual analogy problems; for the first time in human history, AI moved from the realm of myth to become a real possibility. These technological developments catalysed the publication of numerous AI narratives that explored its impact on contemporary issues such as the labour market, centralization, heuristics, and global communication networks. This chapter contends that midcentury AI narratives must be situated in relation to concomitant technological developments in automation and cybernetics that stimulated widespread concern among government institutions, businesses, and the public. It analyses the varied representation of AI in midcentury novels such as Michael Frayn’s The Tin Men (1965), Len Deighton’s Billion-Dollar Brain (1966), and Arthur C. Clarke’s 2001: A Space Odyssey (1968). These novels problematize AI narrative tropes by resisting anthropomorphic tendencies and implausible utopian and dystopian scenarios; instead, they address the societal ramifications—both positive and negative—for humans faced with technological breakthroughs in AI.
AI: Artificial Immortality and Narratives of Mind Uploading
Authors: Cave Stephen 
Published: April 2020

Abstract
AI promises to be a master technology that can solve any problem—including the problem of death. There are two main contemporary narratives describing how AI might achieve this: cyborgization and mind uploading. This chapter focuses on the latter. It examines how works of nonfiction by influential technologists, in particular Hans Moravec and Ray Kurzweil, have framed this possibility. It pays particular attention to three narrative elements: the promise of boundless wish fulfilment, the assumption of exponential technological progress, and the assumption of personal survival through the mind-uploading process. It then examines how works of fiction, including those of William Gibson, Greg Egan, Pat Cadigan, Robert Sawyer, Rudy Rucker, and Cory Doctorow, offer problematized accounts of these claims. It focuses on three problems in particular, which I call the problems of identity, stability, and substrate. It concludes that science fiction offers a particularly important site of critique and response to techno-utopian narratives.
The Uses of Philosophy
Authors: Moriarty Michael 
Published: April 2020

Abstract
This chapter gives an account of the reported conversation between Pascal and Isaac Le Maître de Sacy, one of the leading presences in the Port-Royal community, in which Pascal explains his views about Montaigne (considered as a representative of scepticism) and Epictetus the Stoic. Pascal’s reduction of all philosophy to a contest between these opposed views is discussed. Both writers have insights of value to the Christian. Montaigne destroys an excessive confidence in human reason, and Epictetus preaches lofty moral ideals and submission to Providence; but Montaigne can encourage moral and religious laziness, and Epictetus pride in human capacities. In different ways, they have failed to take account of the truth proclaimed by Christianity: that humanity is a fallen race.