Zero: The Biography of a Dangerous Idea: Chapter 2

by Charles Seife
Science journalist Charles Seife discusses the history of the number zero, from its origin as an Eastern philosophical concept to its rise as an important tool in mathematics to its current threat to modern physics.

Here are links to our lists for the book: Chapters 0–1, Chapter 2, Chapters 3–4, Chapters 5–6, Chapter 7–∞
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Full list of words from this list:

words only definitions & notes
  1. dictum
    an authoritative declaration
    Zero clashed with one of the central tenets of Western philosophy, a dictum whose roots were in the number-philosophy of Pythagoras and whose importance came from the paradoxes of Zeno.
  2. stifle
    smother or suppress
    Zero’s absence would stunt the growth of mathematics, stifle innovation in science, and, incidentally, make a mess of the calendar.
  3. retinue
    the group following and attending to some important person
    Students flocked to him, and he soon acquired a retinue of followers who wanted to learn from the master.
  4. tenet
    a basic principle or belief that is accepted as true
    But at the center of their philosophy was the most important tenet of the Pythagoreans: all is number.
  5. dub
    give a nickname to
    The discordant tritone, for instance, was dubbed the "devil in music” and was rejected by medieval musicians.
  6. dissonant
    lacking in harmony
    Oddly enough, when Pythagoras put the bridge at a place that did not divide the string into a simple ratio, the plucked notes did not meld well. The sound was usually dissonant and sometimes even worse.
  7. imbue
    give qualities or abilities to; endow
    Achieving this blissful mean is a matter of dividing a line in a special way: divide it in two so that the ratio of the small part to the large part is the same as the ratio of the large part to the whole. In words, it doesn’t seem particularly special, but figures imbued with this golden ratio seem to be the most beautiful objects.
  8. aesthetics
    the branch of philosophy dealing with beauty and taste
    The supernatural link between aesthetics, ratios, and the universe became one of the central and long-lasting tenets of Western civilization.
  9. preclude
    make impossible, especially beforehand
    The equivalence of numbers and shapes made the ancient Greeks the masters of geometry, yet it had a serious drawback. It precluded anyone from treating zero as a number. What shape, after all, could zero be?
  10. conjecture
    a hypothesis that has been formed by speculating
    Nowadays the great unsolved problems in mathematics are stated in terms of conjectures that mathematicians are unable to prove.
  11. squelch
    suppress or crush completely
    Indeed, the Pythagoreans had tried to squelch another troublesome mathematical concept—the irrational. This concept was the first challenge to the Pythagorean point of view, and the brotherhood tried to keep it secret.
  12. tantamount
    being essentially equal to something
    Thanks to the number-shape duality, to the Greeks counting was tantamount to measuring a line.
  13. confound
    be confusing or perplexing to
    How could nature be governed by ratios and proportions when something as simple as a square can confound the language of ratios?
  14. incontrovertible
    impossible to deny or disprove
    This idea was hard for the Pythagoreans to believe, but it was incontrovertible—a consequence of the mathematical laws that they held so dear. One of the first mathematical proofs in history was about the incommensurability/irrationality of the square’s diagonal.
  15. commensurate
    corresponding in size or degree or extent
    To keep these horrible numbers from ruining the Pythagorean doctrine, the irrationals were kept secret. Everyone in the Pythagorean brotherhood was already tight-lipped—nobody was allowed even to take written notes—and the incommensurability of the square root of two became the deepest, darkest secret of the Pythagorean order.
  16. hapless
    unfortunate and deserving pity
    Mathematicians to this day tell of the hapless man who revealed the secret of the irrational to the world. Some say that the Pythagoreans tossed Hippasus overboard, drowning him, a just punishment for ruining a beautiful theory with harsh facts.
  17. impiety
    unrighteousness by virtue of lacking respect for a god
    Ancient sources talk about his perishing at sea for his impiety, or alternatively, say that the brotherhood banished him and constructed a tomb for him, expelling him from the world of human beings.
  18. revile
    spread negative information about
    But whatever Hippasus’s true fate was, there is little doubt that he was reviled by his brothers.
  19. anomaly
    deviation from the normal or common order, form, or rule
    The secret he revealed shook the very foundations of the Pythagorean doctrine, but by considering the irrational an anomaly, the Pythagoreans could keep the irrationals from contaminating their view of the universe.
  20. duality
    a classification into two opposed parts or subclasses
    Zero would clash with this doctrine, and unlike the irrational, zero could be ignored. The number-shape duality in Greek numbers made it easy; after all, zero didn’t have a shape and could thus not be a number.
  21. intractable
    difficult to manage or mold
    Greece would defeat the Persians; Greek philosophy would never quite defeat Zeno—for Zeno had a paradox, a logical puzzle that seemed intractable to the reasoning of Greek philosophers. It was the most troubling argument in Greece: Zeno had proved the impossible.
  22. underlying
    in the nature of something though not readily apparent
    He was a member of the Eleatic school of thought, whose founder, Parmenides, held that the underlying nature of the universe was changeless and immobile.
  23. elusive
    skillful at evading capture
    Achilles would finally catch up to the elusive turtle.
  24. vie
    compete for something
    Another philosophy vied with the atomic theory, and instead of posing such bizarre concepts as the infinite vacuum, it turned the universe into a cozy nutshell.
  25. ensconce
    fix firmly
    The universe was contained in a nutshell, ensconced comfortably within the sphere of fixed stars; the cosmos was finite in extent, and entirely filled with matter.
  26. refutation
    evidence that helps to establish the falsity of something
    Void/zero destroys Aristotle’s neat argument, his refutation of Zeno, and his proof of God. So as Aristotle’s arguments were accepted, the Greeks were forced to reject zero, void, the infinite, and infinity.
  27. conversely
    with the terms of the relation reversed
    Thus, there must be a first event: creation. But what existed before creation? Void? That was unacceptable to Aristotle. Conversely, if there was not a first event, then the universe must have always existed—and will always exist in the future. You’ve got to have either infinity or zero; a universe without both of them makes no sense.
  28. hegemony
    the dominance or leadership of one social group over others
    In the third century BC the era of Greek hegemony was over. Alexander’s empire had collapsed into bickering states, and a new power was flexing its muscles in the West: Rome.
  29. ken
    range of what one can know or understand
    Triangles and circles were easy to measure, but slightly more irregular curves like the parabola were beyond the ken of the Greek mathematicians of the day.
  30. accession
    the act of attaining a new office or right or position
    One dating system had the year 1 based upon the founding of the city of Rome, and the other was based on the accession of the emperor Diocletian.
  31. penchant
    a strong liking or preference
    To the Christian monk, the birth of his Savior was a more important event than the foundation of a city that had been sacked by Vandals and Goths a few times—or, for that matter, the beginning of the reign of an emperor who had an unfortunate penchant for maintaining his menagerie of exotic animals on a diet of Christians.
  32. inconsequential
    lacking worth or importance
    When choosing the first year of a calendar, it really doesn’t matter which year is chosen, so long as everything is consistent after that. A four-year error is inconsequential if everyone agrees to make the same mistake, as, indeed, we have.
  33. heyday
    the period of greatest prosperity or productivity
    Even during the heyday of Rome, the Romans were not exactly math whizzes.
  34. ensuing
    following immediately and as a result of what went before
    Pope John died, and in the ensuing power shift all the philosophers and mathematicians like Dionysius were kicked out of office.
  35. tract
    a brief treatise on a subject of interest
    Boethius is not remembered for his math but for his Consolation of Philosophy, a tract in which he comforts himself with Aristotelian-style philosophy.
  36. languish
    fail to progress or succeed
    In any case, the new calendar languished for years.
  37. venerable
    profoundly honored
    In 731 AD, about the time Dionysius’s Easter tables were set to run out, Bede, a soon-to-be- venerable monk from the northern part of England, extended them again.
  38. ecclesiastical
    of or associated with a church
    When Bede wrote a history of the church in Britain, the Ecclesiastical History of the English People, he used the new calendar.
  39. arbiter
    someone chosen to judge and decide a disputed issue
    Everybody celebrated the turn of the millennium on the wrong date. Even the Royal Greenwich Observatory, the official keeper of the world’s time and arbiter of all things chronological, planned to be swamped by the revelers.
  40. assimilate
    take up mentally
    Though we count with the ordinals (first, second, third), we mark time with the cardinals (0, 1, 2). All of us have assimilated this way of thinking, whether we appreciate it or not.
Created on Sun Feb 06 12:50:29 EST 2022 (updated Tue Aug 23 09:22:36 EDT 2022)

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