Speaker 1: Welcome to brain Stuff production of I Heart Radio. Hey
Speaker 1: brain Stuff, Lauren Vogelbaum. Here, counting to three is so
Speaker 1: easy a salamander can do it seriously. Lab experiments have
Speaker 1: shown that captive salamanders are able to distinguish between piles
Speaker 1: of two fruit flies and piles of three. If you're
Speaker 1: not impressed, when we understand, a human being who had
Speaker 1: never taken a single math class would have no trouble
Speaker 1: doing the same thing. Some single digit numbers like one, two,
Speaker 1: and three are so small that our minds can recognize
Speaker 1: their value without even needing to count. Put a tray
Speaker 1: of three cookies in front of your average adult, and
Speaker 1: he or she will immediately and intuitively know how many.
Speaker 1: There are no fingers or calculators required. Yet as numbers
Speaker 1: grow bigger, our ability to comprehend their values starts to
Speaker 1: break down. The word billion gets tossed around a lot
Speaker 1: by economists and politicians, but it's hard to appreciate just
Speaker 1: how large that some is. For example, have any idea
Speaker 1: how long a billion seconds is? Me? Neither or not
Speaker 1: until we did the math. It's thirty one years, two
Speaker 1: hundred and fifty one days, thirteen hours, and some thirty
Speaker 1: four point nine minutes, not counting leap days and leap seconds.
Speaker 1: By the commonly accepted definition we use today, one billion
Speaker 1: is equal to eight thousand millions. Numerically, it's expressed as
Speaker 1: a one with nine zeros behind it. One trillion is
Speaker 1: understood to be a million millions, or a one with
Speaker 1: twelve zeros behind it. And to put that in perspective,
Speaker 1: let's say you've pulled an H. G. Wells and built
Speaker 1: a functional time machine. If you ordered it to take
Speaker 1: you one trillion seconds back in time, you'd get to
Speaker 1: hang out with mammoths and sabertooth cats, because one trillion
Speaker 1: seconds is the equivalent of thirty one thousand, five hundred
Speaker 1: and forty six years. Okay, so a trillion is a
Speaker 1: one followed by twelve zeros. The next order of magnitude
Speaker 1: is a quadrillion, which contains fifteen zeros. And you may
Speaker 1: be interested to know that a supercomputer that was recently
Speaker 1: unveiled at the Oak Ridge National Laboratory in Tennessee can
Speaker 1: make up to two hundred quadrillion calculations per second. It's
Speaker 1: roughly a million times faster than the average laptop. But regardless,
Speaker 1: if you took a pen, grab some paper, and wrote
Speaker 1: down a nice tidy row of one hundred individual zeros,
Speaker 1: then put a one in front of them. The massive
Speaker 1: figure you'll see before you is ten to the power
Speaker 1: of one hundred. Mathematician Edward Kastner took a fancy to
Speaker 1: this number. In his nine year old nephew, Milton, came
Speaker 1: up with a name for it, calling the super large
Speaker 1: sum a Google. Many years later, a misspelling of this
Speaker 1: term would be used as the name of the Internet
Speaker 1: top search engine. As enormous as a Google is, at
Speaker 1: least you can write it down numerically. By this, we
Speaker 1: mean to say that you could, if you felt so inclined,
Speaker 1: write a one followed by one hundred zeros. The same
Speaker 1: cannot be said of a google plex. That, dear listener,
Speaker 1: is a one followed by a google's worth of zeros.
Speaker 1: No matter how tiny your handwriting is, e'll never be
Speaker 1: able to jot down all those zeros. There are more
Speaker 1: zeros in a googleplex than there are atoms in the
Speaker 1: observable universe. The only way to commit this figure to
Speaker 1: paper is by using exponential notation. Written out that way,
Speaker 1: a googleplex is ten to the tenth to the one,
Speaker 1: and if you think a google plex is big, get
Speaker 1: a load of Skews number, which is ten to the
Speaker 1: tenth to the tenth to the thirty four. This one
Speaker 1: derives its name from Stanley Skews, a South African mathematician
Speaker 1: with an interest in prime numbers. You may know that
Speaker 1: a prime is any number that can only be divided
Speaker 1: by itself and by the number one, and therefore three
Speaker 1: is a prime, but four is not, because it's divisible
Speaker 1: by two. To make a long story short, Skews was
Speaker 1: studying a mathematical function that's been used to give rough
Speaker 1: estimates of how many primes there are between zero and
Speaker 1: any number you might care to name. Excuse introduced his
Speaker 1: eponymous number to the world in a nineteen thirty three
Speaker 1: paper and the words of one colleague. This was, at
Speaker 1: the time at least the largest number has ever served
Speaker 1: any definite purpose in mathematics. It's since lost that distinction
Speaker 1: to still bigger sums like Graham's number and the monstrous
Speaker 1: tree three. Both of these are way too vast for
Speaker 1: the human mind to grasp, yet each is finite and
Speaker 1: mathematically useful in its own way. Before wrapping up this discussion,
Speaker 1: let's take a step back to acknowledge a smaller figure.
Speaker 1: In January, matth enthusiast Jonathan Pace identified what is, to
Speaker 1: date the biggest known prime number, named M seven seven
Speaker 1: two three seven. It contains more than twenty three million
Speaker 1: digits twenty three million, two hundred four hundred and twenty
Speaker 1: five of them to be exact. As such, it is
Speaker 1: nine hundred and ten thousand, eight hundred and seven digits
Speaker 1: larger than the previous record holder. To be sure, this
Speaker 1: prime number isn't in the same league as the Google,
Speaker 1: the google Plex, or Skews number, but if you wrote
Speaker 1: it out in its entirety at a rate of five
Speaker 1: digits per inch, the whole thing would exeed seventy three miles.
Speaker 1: That's a hundred and eighteen kilometers in length. Sounds like
Speaker 1: a surefire way to get finger cramps. Today's episode was
Speaker 1: written by Mark Mancini and produced by Tyler Klang. For
Speaker 1: more on this and lots of other math magical topics,
Speaker 1: visit our home planet how stuff works dot com. Brain
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