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  • They say the pen is mightier than the sword,

  • and authorities have often agreed.

  • >From outlawed religious tracts and revolutionary manifestos

  • to censored and burned books,

  • we know the potential power of words to overturn the social order.

  • But as strange as it may seem,

  • some numbers have also been considered dangerous enough to ban.

  • Our distant ancestors long counted objects using simple tally marks.

  • But as they developed agriculture and began living together in larger groups,

  • this was no longer enough.

  • As numbers grew more complex,

  • people began not just using them, but thinking about what they are

  • and how they work.

  • And by 600 B.C.E. in Ancient Greece, the study of numbers was well-developed.

  • The mathematician Pythagoras and his school of followers

  • found numerical patterns in shapes, music, and the stars.

  • For them, mathematics held the deepest secrets of the universe.

  • But one Pythagorean named Hippasus discovered something disturbing.

  • Some quantities, like the diagonal of a square with sides of length one

  • couldn't be expressed by any combination of whole numbers or fractions,

  • no matter how small.

  • These numbers, which we call irrational numbers,

  • were perceived as a threat

  • to the Pythagorean's notion of a perfect universe.

  • They imagined a reality that could be described

  • with rational, numerical patterns.

  • Historians write that Hippasus was exiled for publicizing his findings,

  • while legends claim he was drowned as punishment from the gods.

  • While irrational numbers upset philosophers,

  • later mathematical inventions would draw attention

  • from political and religious authorities, as well.

  • In the Middle Ages, while Europe was still using Roman numerals,

  • other cultures had developed positional systems

  • that included a symbol for zero.

  • When Arab travelers brought this system to the bustling maritime cities of Italy,

  • its advantages for merchants and bankers was clear.

  • But the authorities were more wary.

  • Hindu-Arabic numerals were considered easier to forge or alter,

  • especially since they were less familiar to customers than to merchants.

  • And the concept of zero opened the door to negative numbers

  • and the recording of debt

  • at a time when moneylending was regarded with suspicion.

  • In the 13th century, Florence banned the use of Hindu-Arabic numerals

  • for record keeping.

  • And though they soon proved too useful to ignore,

  • controversies over zero and negative numbers

  • continued for a long time.

  • Negative numbers were dismissed as absurd

  • well into the 19th century.

  • And prominent mathematicians, like Gerolamo Cardano,

  • avoided using zero,

  • even though it would have made it much easier to find solutions

  • to cubic and the quartic equations.

  • Even today it's illegal to use some numbers for different reasons.

  • Some are banned because of what they represent.

  • For example, governments have prohibited the display of numbers

  • that have symbolic meaning,

  • such as the date of a revolution

  • or connections to oppositional political figures or parties.

  • Other numbers are potentially illegal because of the information they carry.

  • Just about any information,

  • whether text,

  • image,

  • video,

  • or executable programs can be translated into a string of numbers.

  • But this means that protected information,

  • whether copyrights,

  • proprietary materials,

  • or state secrets

  • can also be represented as numbers,

  • so possessing or publishing these numbers may be treated as a criminal offense.

  • This idea gathered attention in 2001

  • when code that could be used to decrypt DVDs

  • was widely shared and distributed in the form of a large prime number.

  • The idea of illegal numbers may sound absurd,

  • but like words,

  • written numbers are a way of expressing concepts and information.

  • And in a world where calculations and algorithms

  • shape more and more of our lives,

  • the mathematician's pencil grows stronger by the day.

They say the pen is mightier than the sword,


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B1 中級

TED-ED】禁止番号の簡単な歴史 - アレッサンドラ・キング (【TED-Ed】A brief history of banned numbers - Alessandra King)

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    osmend に公開 2021 年 01 月 14 日