Speaker 1: Welcome to brain Stuff. From how Stuff Works, Hey, brain Stuff,
Speaker 1: Lauren Vogelbaum. Here, counting to three is so easy a
Speaker 1: salamander can do it. Seriously. Lab experiments have shown that
Speaker 1: captive salamanders are able to distinguish between piles of two
Speaker 1: fruit flies and piles of three. If you're not impressed,
Speaker 1: when we understand, a human being who had never taken
Speaker 1: a single math class would have no trouble doing the
Speaker 1: same thing. Some single digit numbers like one, two, and
Speaker 1: three are so small that our minds can recognize their
Speaker 1: value without even needing to count. Put a tray of
Speaker 1: three cookies in front of your average adult, and he
Speaker 1: or she will immediately and intuitively know how many. There
Speaker 1: are no fingers or calculators required. Yet as numbers grow bigger,
Speaker 1: our ability to comprehend their values starts to break down.
Speaker 1: The word billion gets tossed around a lot by economists
Speaker 1: and politicians, but it's hard to appreciate just how large
Speaker 1: that some is. For example, have any idea how long
Speaker 1: a billion seconds is? Me? Neither or not until we
Speaker 1: did the math. It's thirty one years, two hundred and
Speaker 1: fifty one days, thirteen hours, and some thirty four point
Speaker 1: nine minutes, not counting leap days and leap seconds. By
Speaker 1: the commonly accepted definition we use today, one billion is
Speaker 1: equal to eight thousand millions. Numerically, it's expressed as a
Speaker 1: one with nine zeros behind it. One trillion is understood
Speaker 1: to be a million millions, or a one with twelve
Speaker 1: zeros behind it. And to put that in perspective, let's
Speaker 1: say you've pulled an H. G. Wells and built a
Speaker 1: functional time machine. If you ordered it to take you
Speaker 1: one trillion seconds back in time, you'd get to hang
Speaker 1: out with mammoths and sabertooth cats, because one trillion seconds
Speaker 1: is the equivalent of thirty one thousand, five hundred and
Speaker 1: forty six years. Okay, so a trillion is a one
Speaker 1: followed by twelve zeros. The next order of magnitude is
Speaker 1: a quadrillion, which contains fifteen zeros. And you may be
Speaker 1: interested to know that a supercomputer that was recently unveiled
Speaker 1: at the Oak Ridge National Laboratory in Tennessee can make
Speaker 1: up to two hundred quadrillion calculations per second. It's roughly
Speaker 1: 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, you'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 date,
Speaker 1: the biggest known prime number, named M seven seven two
Speaker 1: three seven. It contains more than twenty three million digits
Speaker 1: twenty three million, two hundred thousand, 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 seed 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 Clang. For
Speaker 1: more on this and lots of other math magical topics,
Speaker 1: visit our home planet, how Stuff Works dot com.