WEBVTT - Can Absurdly Big Numbers Be Useful?

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<v Speaker 1>Welcome to brain Stuff. From how Stuff Works, Hey, brain Stuff,

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<v Speaker 1>Lauren Vogelbaum. Here, counting to three is so easy a

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<v Speaker 1>salamander can do it. Seriously. Lab experiments have shown that

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<v Speaker 1>captive salamanders are able to distinguish between piles of two

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<v Speaker 1>fruit flies and piles of three. If you're not impressed,

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<v Speaker 1>when we understand, a human being who had never taken

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<v Speaker 1>a single math class would have no trouble doing the

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<v Speaker 1>same thing. Some single digit numbers like one, two, and

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<v Speaker 1>three are so small that our minds can recognize their

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<v Speaker 1>value without even needing to count. Put a tray of

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<v Speaker 1>three cookies in front of your average adult, and he

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<v Speaker 1>or she will immediately and intuitively know how many. There

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<v Speaker 1>are no fingers or calculators required. Yet as numbers grow bigger,

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<v Speaker 1>our ability to comprehend their values starts to break down.

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<v Speaker 1>The word billion gets tossed around a lot by economists

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<v Speaker 1>and politicians, but it's hard to appreciate just how large

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<v Speaker 1>that some is. For example, have any idea how long

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<v Speaker 1>a billion seconds is? Me? Neither or not until we

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<v Speaker 1>did the math. It's thirty one years, two hundred and

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<v Speaker 1>fifty one days, thirteen hours, and some thirty four point

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<v Speaker 1>nine minutes, not counting leap days and leap seconds. By

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<v Speaker 1>the commonly accepted definition we use today, one billion is

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<v Speaker 1>equal to eight thousand millions. Numerically, it's expressed as a

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<v Speaker 1>one with nine zeros behind it. One trillion is understood

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<v Speaker 1>to be a million millions, or a one with twelve

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<v Speaker 1>zeros behind it. And to put that in perspective, let's

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<v Speaker 1>say you've pulled an H. G. Wells and built a

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<v Speaker 1>functional time machine. If you ordered it to take you

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<v Speaker 1>one trillion seconds back in time, you'd get to hang

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<v Speaker 1>out with mammoths and sabertooth cats, because one trillion seconds

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<v Speaker 1>is the equivalent of thirty one thousand, five hundred and

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<v Speaker 1>forty six years. Okay, so a trillion is a one

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<v Speaker 1>followed by twelve zeros. The next order of magnitude is

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<v Speaker 1>a quadrillion, which contains fifteen zeros. And you may be

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<v Speaker 1>interested to know that a supercomputer that was recently unveiled

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<v Speaker 1>at the Oak Ridge National Laboratory in Tennessee can make

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<v Speaker 1>up to two hundred quadrillion calculations per second. It's roughly

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<v Speaker 1>a million times faster than the average laptop. But regardless,

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<v Speaker 1>if you took a pen, grab some paper, and wrote

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<v Speaker 1>down a nice, tidy row of one hundred individual zeros,

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<v Speaker 1>then put a one in front of them. The massive

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<v Speaker 1>figure you'll see before you is ten to the power

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<v Speaker 1>of one hundred. Mathematician Edward Kastner took a fancy to

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<v Speaker 1>this number in his nine year old nephew, Milton, came

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<v Speaker 1>up with a name for it, calling the super large

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<v Speaker 1>sum a Google. Many years later, a misspelling of this

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<v Speaker 1>term would be used as the name of the Internet

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<v Speaker 1>top search engine. As enormous as a Google is, at

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<v Speaker 1>least you can write it down numerically. By this, we

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<v Speaker 1>mean to say that you could, if you felt so inclined,

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<v Speaker 1>write a one followed by one hundred zeros. The same

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<v Speaker 1>cannot be said of a google plex. That, dear listener,

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<v Speaker 1>is a one followed by a google's worth of zeros.

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<v Speaker 1>No matter how tiny your handwriting is, you'll never be

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<v Speaker 1>able to jot down all those zeros. There are more

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<v Speaker 1>zeros in a googleplex than there are atoms in the

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<v Speaker 1>observable universe. The only way to commit this figure to

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<v Speaker 1>paper is by using exponential notation. Written out that way,

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<v Speaker 1>a googleplex is ten to the tenth to the one

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<v Speaker 1>and If you think a google plex is big, get

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<v Speaker 1>a load of Skews number, which is ten to the

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<v Speaker 1>tenth to the tenth to the thirty four. This one

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<v Speaker 1>derives its name from Stanley Skews, a South African mathematician

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<v Speaker 1>with an interest in prime numbers. You may know that

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<v Speaker 1>a prime is any number that can only be divided

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<v Speaker 1>by itself and by the number one, and therefore three

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<v Speaker 1>is a prime, but four is not, because it's divisible

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<v Speaker 1>by two. To make a long story short, Skews was

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<v Speaker 1>studying a mathematical function that's been used to give rough

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<v Speaker 1>estimates of how many primes there are between zero and

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<v Speaker 1>any number you might care to name. Excuse introduced his

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<v Speaker 1>eponymous number to the world in a nineteen thirty three

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<v Speaker 1>paper and the words of one colleague. This was, at

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<v Speaker 1>the time, at least the largest number has ever served

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<v Speaker 1>any definite purpose in mathematics. It's since lost that distinction

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<v Speaker 1>to still bigger sums like Graham's number and the monstrous

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<v Speaker 1>tree three. Both of these are way too vast for

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<v Speaker 1>the human mind to grasp, yet each is finite and

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<v Speaker 1>mathematically useful in its own way. Before wrapping up this discussion,

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<v Speaker 1>let's take a step back to acknowledge a smaller figure.

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<v Speaker 1>In January, matth enthusiast Jonathan Pace identified what is, to date,

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<v Speaker 1>the biggest known prime number, named M seven seven two

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<v Speaker 1>three seven. It contains more than twenty three million digits

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<v Speaker 1>twenty three million, two hundred thousand, four hundred and twenty

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<v Speaker 1>five of them to be exact. As such, it is

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<v Speaker 1>nine hundred and ten thousand, eight hundred and seven digits

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<v Speaker 1>larger than the previous record holder. To be sure, this

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<v Speaker 1>prime number isn't in the same league as the Google,

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<v Speaker 1>the google Plex, or Skews number, but if you wrote

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<v Speaker 1>it out in its entirety at a rate of five

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<v Speaker 1>digits per inch, the whole thing would seed seventy three miles.

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<v Speaker 1>That's a hundred and eighteen kilometers in length. Sounds like

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<v Speaker 1>a surefire way to get finger cramps. Today's episode was

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<v Speaker 1>written by Mark Mancini and produced by Tyler Clang. For

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<v Speaker 1>more on this and lots of other math magical topics,

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<v Speaker 1>visit our home planet, how Stuff Works dot com.