million, billion, trillion... then what?

[cosmictraveler]

Teraflop:



A teraflop is a measure of a computer's speed and can be expressed as:
A trillion floating point operations per second
10 to the 12th power floating-point operations per second
2 to the 40th power flops
Today's fastest parallel computing operations are capable of teraflop speeds. Scientists have begun to envision computers operating at petaflop speeds.

Petaflop:


A petaflop is a measure of a computer's processing speed and can be expressed as:
A thousand trillion floating point operations per second (FLOPS)
A thousand teraflops
10 to the 15th power FLOPS
2 to the 50th power FLOPS
Today's fastest parallel computing operations are capable of teraflop speeds. The National Science Foundation, together with NASA and DARPA, has funded eight research projects for envisioning a petaflop computer. Cray says that its X1 supercomputer is "a major milestone en route to Cray's goal of delivering, by 2010, the world's first supercomputer able to sustain petaflops speeds...on a variety of challenging applications." A petaflop computer would actually require a massive number of computers working in parallel on the same problem. Applications might include real-time nuclear magnetic resonance imaging during surgery, computer-based drug design, astrophysical simulation, the modeling of environmental pollution, and the study of long-term climate changes.

Read more about it at:
Cray provides more information about the X1.

More information on the projects can be obtained from the National Science Foundation .

[guthrie]

England does not use this terminology, to them 1,000,000,000,000,000,000,000 is simply "one thousand trillion". (See below for their problem with the word "billion," which is why I didn't use billion in this example.)



What we call the "American" system (billion = million x 1000) is now in use in North America, Holland, and France. What we call the "European" system (billion = million x 1,000,000) is used in all other countries.

With one exception. Because of the influence of the American financial press, the British press now calls 1,000,000,000 "one billion," instead of "one thousand million." But they have not changed their names for the rest of the powers of ten. Once again, the Brits blaze their own trail and it's a lot more crooked and bumpy than anyone else's! Still, wouldn't it be awkward to call George Soros a "billiardaire" or a "thousand-millionaire."

Nope, for once you are wrong. I have never come across anyone or any publication using milliard or billion in the "correct" british usage, in my 5 years at university (science degree) and 3.5 years since in work. Everyone just uses the billion = 10^9, trillion = 10^12, etc.

[TruthSeeker]

The terminology does differ. Use Giga for billion and you won't get it wrong (eg 1 Gyr=1000000000).

Also, in some coutries they write like this:
1,000,000,000 and 0.1

While in others they do the opposite:
1.000.000.000 and 0,1

I came across that when I moved from Brasil to Canada...
Man... was that confusing...?

[Fraggle Rocker]

Nope, for once you are wrong. I have never come across anyone or any publication using milliard or billion in the "correct" british usage, in my 5 years at university (science degree) and 3.5 years since in work. Everyone just uses the billion = 10^9, trillion = 10^12, etc.

Anglophone countries never used the "milliard" series. In the old days they just stuck with "thousand million" etc. But the rest of the European languages (save French and Dutch) used milliarde or its gramatically compatible equivalent.

Interesting that even the American meaning of trillion and the whole series has finally caught on. I wondered how long England would be able to remain schizophrenic about it. If a billion were 10**9 but a trillion were 10**18, what would the numbers in between be? A thousand billion and a million billion? Must have been awkward.

Some of the websites on which I found this were not entirely current, which means they could be as much as five years old, and their data could be five years further out of date. (Although Doctor Math is generally more hip than that.) Your first-hand experience correlates with that. I'm sure the pressure to normalize with our meaning of "a billion dollars" started building as far back as ten or fifteen years ago, when the list of the world's "billionaires" became too long to memorize.

I certainly remember being warned by my professors forty years ago to be careful of the difference when reading British texts. I think Howard Hughes was the world's only "billionaire" then and I doubt that he was big news in the U.K.

[guthrie]

*cough cough* Britain. (behind hand "england? ohh dear.")
I cant rememebr exactly, and i can only really speak for the UK, but I think the pressure towards billion etc started further back than that. (but im only 26, so...) I think ive seen evidence for it in books several decades old, but i really cant remember where. But yes it is likley more to do with money than anything else. Scientists have been using 10^9 etc for donkeys years.

[Vidd]

Hmm actually I mistated it, I just checked and it is ((10)^10)^100 not (10^100)^(10^100). But irregardless it is supposed to be larger than the number of atoms in the universe and thus it is unwritable in long form base ten.

Aye. My dad once told me that if I wanted to think about a large number, to take the number of different ways that every single particle of matter in the universe could be arranged (...in the universe). I thought once, which would be bigger, that number, or the fabled google plex? Now, most people would stick with the former, but I'm not so sure. I did some calculating recently and if you wrote out the number - that is, a 1 followed by a google 0s - and entered it into enough iPods to carry the whole thing, and then lay the iPods back-to-back-to-back-to-back, they'd overshoot the Andromeda galaxy by a factor of about 200,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000. (2*10^50) (two hundred quindecillion)

[Hypercane]

Here is John Conway and Richard Guy's system for nameing -illion numbers.

x 10^3 x 10^30 x 10^300 x 10^3000 x
0 - - -
1 un (n) deci (nx) centi milli
2 duo (ms) viginti (n) ducenti
3 tre (s) (ns) triginta (ns) trecenti
4 quattuor (ns) quadraginta (ns) quadringenti
5 quinqua (ns) quinquaginta (ns) quingenti
6 se (sx) (n) sexaginta (n) sescenti
7 septe (mn) (n) septuaginta (n) septingenti
8 octo (mx) octoginta (mx) octingenti
9 nove (mn) nonaginta nongenti

Of course, if you want the largest numbers known to man, try researching upon Transfinite Cardinals.

[Fraggle Rocker]

I understand the Latin and the Italian just fine. But I don't understand the math. Are you saying that in this system 10^24000 is one octingentillion?

We're already confused enough with the mixture of Latin and Greek prefixes in the metric system. (Greek kilometer vs. Latin millimeter.) And most scientists have a passing familiarity with what they call "scientific" Latin and Greek. I wonder how sanguine they'll b about having to learn Italian numbers as well. Hitting up Hebrew for Aleph sub null was already going over the top for a lot of people.

We have a couple of species of cardinals in the US and even a baseball team by that name, but none of them are transfinite. ^_^

[Hypercane]

Lmao. Transfinite Cardinal Numbers to be specified.

[Vidd]

I've looked up transfinite cardinal numbers before - I don't really see how they're anything other than a more complicated way of expressing ∞. (Is that even considered a number?)

[Hypercane]

I'm not sure, but some people may consider it a number. Its not just a more complicated way of explaining infity, it just starts out complicated because counting and measuring transfinite numbers in relation with other transfinite numbers isnt as easy as 1-10. If you buy the book "Infinity and the Mind" im sure you will get an ensured view of some of the highest numbers in the kingdom of numbers.

[Vidd]

Right, well, what I heard was that since ∞+x (where x is anything other than -∞)=∞, it wasn't technically a number. I wouldn't know though.

My reasoning though is that transfinite cardinals are like "A1 is every even number in existence" "A2 is every odd number in existence..." etc. (I know that's not right but I think that's about the gist of it) And since infinity is infinity is infinity... <shrugs>

[Fraggle Rocker]

I've looked up transfinite cardinal numbers before - I don't really see how they're anything other than a more complicated way of expressing ∞. (Is that even considered a number?)

Whether infinity is a number is more a philosophical question than a mathematical one. It participates in many mathematical processes and it is even the solution to many equations. Still, that doesn't necessarily qualify it as a "number."

There isn't just one infinity, there is a whole hierarchy of them. The Aleph sub null that I spoke of is one of them. Presumably then, there ought to also be Aleph sub 1, sub 2, etc., or why bother with the subscript in the first place.

I'm way over my head already, I stopped studying math when I couldn't see either the joy or the usefulness of being able to solve a partial differential equation.

[John Connellan]

If the number were written out it might extend from one end of the universe to the other. Pretty trippy, huh?

No, it cannot be written out because there is not enough atoms!

[slotty]

Nope, for once you are wrong. I have never come across anyone or any publication using milliard or billion in the "correct" british usage, in my 5 years at university (science degree) and 3.5 years since in work. Everyone just uses the billion = 10^9, trillion = 10^12, etc.

In the UK a billion is 1,000,000 multiplyed by a 1,000,000. If the US system is quoted, its usually stated after the figures ie 24 billion (US)

[Facial]

It says in the Guiness Book of Records that the largest lexicographically accepted number is the centillion, I think it was 10^600 or something like that.

10^100 is known as a google.

Someone mentioned on the first page "hexillion." I've only heard of sextillion and septillions, but not the hex's and the hep's.

[Fraggle Rocker]

It says in the Guiness Book of Records that the largest lexicographically accepted number is the centillion, I think it was 10^600 or something like that.

10^100 is known as a google.

Someone mentioned on the first page "hexillion." I've only heard of sextillion and septillions, but not the hex's and the hep's.

In the American system the Latin number n is used as a prefix to mean 10^(3(n+1)). Bis, "twice," in "billion" means 10^(3(2+1)) = 10^9 = 1,000,000,000. So a centillion would be 10^(3(100+1)) = 10^303.

In the English system it would indeed be 10^600.

You're right that the Latin (ordinal) numbers are used for prefixes, not the Greek. Quadrillion, quintillion, sextillion, septillion -- not tetrillion, pentillion, hexillion, heptillion. The exception would seem to be million, which seems to be formed from Greek mono- instead of Latin uni-. However, million was invented by the Romans themselves before anyone ever thought of a number a thousand times larger. It's just mille, one thousand, with the augmentative suffix -on, which is still used in the modern Romance languages. Italian calzone, shoe; Spanish raton, rat.

[Dreamwalker]

Well, I grew up with the sytem containing Milliard (10^9) and Billiard and so on. But thanks to the Americans, Billion is used for Milliard sometimes, mostly in english speaking countries. But many countries still use Million->Milliard->Billion->Billiard....

[Hypercane]

I think the highest -illion number you could name, well according to Conway and Guy's system, Millillion which is 10^3003.

[GuessWho]

Actually one Billion is a disputed sum.

It seems most of the world has one Billion as:

1,000,000,000,000

But I think (correct me If I'm wrong) America has it down as:

1,000,000,000

Thats why when I saw $50 Billion worth of bonds it wasn't worth any more than £35 Thousand Million's (which is are also called Billion's)

So an English Billionaire is actually richer than his American counterpart even if they have the same number of differnt billions.

This is interesting. I did not know that the world's Billion is 1000 greater than the US's Billion.

However, this makes it impossible to be an English billionare unless there is actually someone who has almost 20 times more money than Bill Gates. Last time I check the richest person on earth was Ingva Camprad who has $53,000,000,000 in wealth.