You’ve probably heard about the football player Troy Polamalu whose long locks are, as of today, insured for $1,000,000 dollars. The silly stunt is just the chance we need to talk big — bigger than a million. How big? Let’s see how big.

A “million” is literally Latin for “a great thousand” (*mille* is “thousand,” *-ion* is “largeness” or “greatness.”) A “billion” is literally “two or twice millions,” (*bi-* is “two”), but convention interprets the word to mean ”a thousand millions.” Ready for some messiness? There are two different meanings of a billion, the long and short scales. The simple answer is that the short scale predominates today, and the short scale version of a billion is one with nine zeros. A trillion has twelve.

Here’s where things become exciting. The so-called “standard dictionary numbers” are terms for numerals that go up to centillion, which is basically 1 followed by 303 zeros. Here’s a fun number: quattuordecillion, or 1 followed by 45 zeros.

At this point, the dictionary stops including numerals. You are now entering googol territory. The legend goes that mathematician Edward Kasner asked his nine-year-old son to think of the name for a very big number. His reply is now famous. A googol is equal to 1 followed by 100 zeros. A googolplex is 1 followed by a googol of zeros. Beyond that, we are in pretty abstract territory.

Contrary to what you may have been told, infinity is not a number, it is a quality or concept: “the assumed limit of a sequence, series, etc., that increases without bound.”

And with that, let’s return to something a little humbler, but no less interesting: What do the “twen” and “-ty” of *twenty* literally mean? Here’s the answer.

## 26 Comments

Somehow you all missed “tree”, which is unimaginably larger than even Graham’s number. Just thought you’d like to know.

How come googol reminds me soo much of google?

And it’s not in the dictionary either.

I serendipitously stumbled on to this old link, just as I was musing to myself that after 400 years of sententious speculation, so arcane that only the theorists themselves could refute their own derivations, a few years ago a homeless paranoid former typist who once worked for an ostensibly populist pamphleteer with a circulation of 300 a week (which was subsequently exposed and discredited as the mendacious mouthpiece and fascist propaganda promulgated by a handful of conspiring vigilante control freaks, motivated by fear and an authoritarian zeal, who envisioned in their bucolic town a utopian Meta Police State, where of course, they would be the arbiters of a Kafka-esque/Libertarian notion of justice that encourages others to inform on anyone at all, at the drop of a hat (as finely distinguished from mere arbitrary snitching) unfettered by effete and expendable extravagances such as the good and separate offices of due process; an enlightened realm where axiomatic fundamental human rights, more ineffably inalienable and less subject to squabbling interpretation than mere documents, no matter how venerable such as the Constitution or the Bible, could go opposed in favor of a less circumspect and more Draconian ethos. but I digress…

It was this former typist, now unemployed with plenty of time to contemplate, who finally proved the famous Fermat’s last Theorem, all with nothing more than a divining rod, a barometer and the invaluable actual brain power of an ingenious unemployed IT expert. The mathematical proof was incidental to the initial intention, which was to demonstrate that all obtuse angles are recursive interpolations of irrational numbness. Lacking access to “all obtuse angles”, they- or rather, the brainier one- cleverly created a theoretical set to contain and represent “all obtuse angles” and in so doing, solved the former and provided the means for solving the latter.

based on a true story

I find the use of the word “billion” extremely confusing. I know it as it is literally, a million millions; this unit of measurement is still used. I don’t know when the milliard became the billion but I discovered this only recently. I really wish that people would explain which scale they are using, before they decide to throw figure at us, as I, for one, can never be sure of what they mean. When did we in England start calling a “thousand millions” a “billion”? Nobody told me!

I dont care much for math…but that was an intereesting blog post!

I didnt know there was such a LOONG number and a word for it!

Before i read that, the farthest i could go was septillion…

Ray,

Good post. I’ve never really thought about it that way. I’d always thought the use of short scale was just a case of popular use of a convention even though that convention was technically wrong. My understanding was long scale was more common in the commonwealth whereas the United States almost solely used short scale and eventually most of the english speaking world just accepted the US way of doing things being that the US is a large and influential country.

@Saf

I think that reference to the “ever-increasing/ever-expanding/etc…” aspect of infinite entities is meant to preclude boundaries. (IE: if an entity is not growing, then it must have some static outer limit which is boundable, and is therefore not infinite.)

But I could be wrong…

What about ghosts? Aren’t they so too?

I’ve always thought that the word “infinite” should refer to something that simply isn’t finite, not necessarily ever-increasing/ever-expanding or immeasurably large.

Shouldn’t something that is ever-changing or impossible to predict or confine be considered infinite?

To think of a really large number, just think of the U.S. national debt!

In the face of the burst of the internet communication technological era, what would be a form of a subject, I wonder. No either magic or Jung as if I am not ruling them out.

In the movie I.A. by Spilberg, the child is longing for Mother in the place where even a lion weeps. I am not sure if I recall it right.

Tomorrow I will get the DVD to watch again.

Be nice.

There certainly are infinite numbers in mathematics. Georg Cantor introduced the concept of transfinite numbers and defined them clearly. There are several transfinite numbers, and the simplest one is what you get if you start 1, 2, 3… and go on forever. Whether there is an infinite number of anything in the physical universe is hard to say, but in the world of concepts, we can easily define infinities – like 1, 2, 3…

[...] “MILLION DOLLAR HAIR” — “BETTY DAVIS EYES” OK — NUMBERS and EXISTENCE without further contemplation in the context of a game — is just another theory for why we’re too weak and weary to make up another name — with not understanding 1s and 0s but perceiving why we don’t care — cause sooner or later they’ll pay this POLAMALULU dude 5 million to cut off his stinky hair.–>>Rupert L.T.Rhyme [...]

That is why we have Scientific Notations.

define the infinity or show me your smile, which I have never seen. HaHa.

Y won’t ya’ll just make the numbers people can afford or save up to, Cash wise.

(Or Quatrillions, of which it falls short…)

That long-scale billion that is a million-millions, had a name for the lesser between, called, a milliard, (a short billion), and while that may now be passé the next-larger lesser between is a billiard but which is not–passé…!

(The game of Billiards falls slightly short of a billiard combinations. Yet now it must be officially Trillions … Did the Queen sign on this?)

I think it’s rather obvious how the discrepancy came to be: The choice was between, whether, the prefix applied first, or the suffix first:

(BI + ILLE) + ION = (1000^2) * 1000.

BI + (ILLE + ION) = (1000 * 1000)^2.

–where, Mono + ILLE = 1000^1.

So, We have bill-ion’s, but not b-illion’s…!

However,–

We should also note the original meaning of M- Me- was a hundred not thousand in the Sumerian: cf the Me was one-hundred-laws… So the -ill was probably some amplification-by-ten….

Ray.

oh please! really? what a fake

zers must mean minus 203 and is the same as googol.

But we still have infinity that has yet to have another term….

Its spelled right on my computer….zeros.

also, i’ve seen my own errors above, shush.

I revently looked up the answer to the story about how much rice you would get out of a chessboard, if you put one grain on the first square, 2 on the second, 4 andhte next, and so on, doubling each time.

Ends up being 18,446,744,073,709,551,615. (Eightteen Quintillion, Four hundred and 46 quadrillion, seven hundred fourty-four trillion, seventy three biillion, seven hundred and nine million, five hundred and fifty one thousand, six hundred and fifteen.

By far my favorite number.

Shouldn’t that be an even number?

Inconceivably for an article about really, really big numbers, you somehow managed to miss Graham’s Number, which is the largest value ever given a formal definition. It is unimaginably larger than even Skewe’s Number. AND, unlike Skewes Number (of which there are several) Graham’s Number has only a single value.

http://en.wikipedia.org/wiki/Graham%27s_number

“The so-called “standard dictionary numbers” are terms for numerals that go up to centillion, which is basically 1 followed by 303 zers.”

Was that a typo or is there such a thing as zers?