Can Absurdly Big Numbers Be Useful?

The bigger that numbers get, the harder they are for us to conceive of -- but that doesn't mean they can't be useful. Learn about some just ridiculously huge numbers in this episode of BrainStuff.

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Episode Transcript

Speaker 1 (00:02):
Welcome to brain Stuff. From how Stuff Works, Hey, brain Stuff,
Lauren Vogelbaum. Here, counting to three is so easy a
salamander can do it. Seriously. Lab experiments have shown that
captive salamanders are able to distinguish between piles of two
fruit flies and piles of three. If you're not impressed,
when we understand, a human being who had never taken

(00:23):
a single math class would have no trouble doing the
same thing. Some single digit numbers like one, two, and
three are so small that our minds can recognize their
value without even needing to count. Put a tray of
three cookies in front of your average adult, and he
or she will immediately and intuitively know how many. There
are no fingers or calculators required. Yet as numbers grow bigger,

(00:46):
our ability to comprehend their values starts to break down.
The word billion gets tossed around a lot by economists
and politicians, but it's hard to appreciate just how large
that some is. For example, have any idea how long
a billion seconds is? Me? Neither or not until we
did the math. It's thirty one years, two hundred and

(01:06):
fifty one days, thirteen hours, and some thirty four point
nine minutes, not counting leap days and leap seconds. By
the commonly accepted definition we use today, one billion is
equal to eight thousand millions. Numerically, it's expressed as a
one with nine zeros behind it. One trillion is understood

(01:27):
to be a million millions, or a one with twelve
zeros behind it. And to put that in perspective, let's
say you've pulled an H. G. Wells and built a
functional time machine. If you ordered it to take you
one trillion seconds back in time, you'd get to hang
out with mammoths and sabertooth cats, because one trillion seconds
is the equivalent of thirty one thousand, five hundred and
forty six years. Okay, so a trillion is a one

(01:51):
followed by twelve zeros. The next order of magnitude is
a quadrillion, which contains fifteen zeros. And you may be
interested to know that a supercomputer that was recently unveiled
at the Oak Ridge National Laboratory in Tennessee can make
up to two hundred quadrillion calculations per second. It's roughly
a million times faster than the average laptop. But regardless,

(02:12):
if you took a pen, grab some paper, and wrote
down a nice, tidy row of one hundred individual zeros,
then put a one in front of them. The massive
figure you'll see before you is ten to the power
of one hundred. Mathematician Edward Kastner took a fancy to
this number in his nine year old nephew, Milton, came
up with a name for it, calling the super large
sum a Google. Many years later, a misspelling of this

(02:36):
term would be used as the name of the Internet
top search engine. As enormous as a Google is, at
least you can write it down numerically. By this, we
mean to say that you could, if you felt so inclined,
write a one followed by one hundred zeros. The same
cannot be said of a google plex. That, dear listener,
is a one followed by a google's worth of zeros.

(02:57):
No matter how tiny your handwriting is, you'll never be
able to jot down all those zeros. There are more
zeros in a googleplex than there are atoms in the
observable universe. The only way to commit this figure to
paper is by using exponential notation. Written out that way,
a googleplex is ten to the tenth to the one
and If you think a google plex is big, get

(03:19):
a load of Skews number, which is ten to the
tenth to the tenth to the thirty four. This one
derives its name from Stanley Skews, a South African mathematician
with an interest in prime numbers. You may know that
a prime is any number that can only be divided
by itself and by the number one, and therefore three
is a prime, but four is not, because it's divisible

(03:39):
by two. To make a long story short, Skews was
studying a mathematical function that's been used to give rough
estimates of how many primes there are between zero and
any number you might care to name. Excuse introduced his
eponymous number to the world in a nineteen thirty three
paper and the words of one colleague. This was, at
the time, at least the largest number has ever served

(04:00):
any definite purpose in mathematics. It's since lost that distinction
to still bigger sums like Graham's number and the monstrous
tree three. Both of these are way too vast for
the human mind to grasp, yet each is finite and
mathematically useful in its own way. Before wrapping up this discussion,
let's take a step back to acknowledge a smaller figure.

(04:22):
In January, matth enthusiast Jonathan Pace identified what is, to date,
the biggest known prime number, named M seven seven two
three seven. It contains more than twenty three million digits
twenty three million, two hundred thousand, four hundred and twenty
five of them to be exact. As such, it is

(04:43):
nine hundred and ten thousand, eight hundred and seven digits
larger than the previous record holder. To be sure, this
prime number isn't in the same league as the Google,
the google Plex, or Skews number, but if you wrote
it out in its entirety at a rate of five
digits per inch, the whole thing would seed seventy three miles.
That's a hundred and eighteen kilometers in length. Sounds like

(05:05):
a surefire way to get finger cramps. Today's episode was
written by Mark Mancini and produced by Tyler Clang. For
more on this and lots of other math magical topics,
visit our home planet, how Stuff Works dot com.