Introduction: The Canonical SI prefixes
You have probably heard of the SI prefixes, which can multiply with existing units ranging from terabytes to centimeters to kilowatts. If you aren't familiar with them here's a quick table listing all the prefixes:
You may also have heard of people extending SI prefixes - such extensions are well-known in googology.
For example, Sbiis Saibian has a numerical-root based system, Aarex has two extensible systems, Jim Blowers has an old and a new system, Andre Joyce has an Italian-based system, Lawrence Hollom has a whimsical system used for naming numbers like brontofaxul, and there are lots and lots more (some of which are hoaxes).
In mid-2014, I then thought, "Why not make my own system?" So here's my own system of extended SI prefixes.
The Prefix System
To start off, I'll list my modified versions of the already existing prefixes:
You may be wondering: Why did I make the changes I made?
Mostly for consistency's sake. With this modification, the system's a little more consistent: all prefixes that increase a unit should end with -a and have a capital symbol, and all prefixes that decrease a unit should have a lowercase symbol and end in -o.
But this doesn't introduce anything new - it's just a modification.
The goal here is to reach a million large prefixes and a million small prefixes (not counting deka-, hecta-, deco-, and cento-), reaching up to 10^3,000,000 and down to 10^-3,000,000.
For starters, what should come after yotta-, and mean 10^27 (one octillion)?
A commonly accepted prefix after yotta- is bronto-, which I don't see much of a problem with using - it matches with the theme of prefixes that mean words, since mega- means large, giga- means giant, tera- means monstrous, and bronto- means thunder. The only problem is that it ends in -o instead of -a like the other large SI prefixes. This is easy to fix - just rename bronto- to bronta-.
In this case, the prefix for one octillion in this system is bronta-, and the symbol is B.
So what should be the next prefix, meaning one nonillion (10^30)? A reasonably common continuation for bronto- is geop-, but naturally I'll want to end it with an A. Therefore, with my system, the prefix for one nonillion is geopa-, which I somewhat arbitarily decided should be pronounced /joh-puh/. In this case, we can called 1000 yottabytes a brontabyte, and 1000 bytes a geopabyte. The symbol here will be O, because G, E, and P are taken.
Now with that, we have prefixes for the first ten powers of 1000 - in order they are kila-, mega-, giga-, tera-, peta-, exa-, zetta-, yotta-, bronta-, and geopa-.
Naturally, we'll want reciprocals of bronta- and geopa-. An idea is to make the reciprocals of the large prefixes similar to their large counterparts. This would work because zetta- and zepto- are similar names, as are yotta- and yocto-.
With this technique, the reciprocals of bronta- and geopa- can be called brimto- and gepto-, respectively. The symbols here will be b and g. So now, here is the table of extended prefixes:
What next? Perhaps we can continue with higher and higher powers of 1000, giving each a unique name. But that would become unwieldy and hard to memorize quickly.
Instead, we'll want to combine prefixes, like Jim Blowers does. The same kind of thing is done in most language's numeral systems (e.g. twenty-one is formed from two unique names), which is part of why this system is elegant.
So the next prefixes after geopa- and gepto-, with the combining technique, go as follows:
* apostrophes are used when two roots cause different vowel sounds to appear next to each other, suggested by Nathan Ho
This system works nicely to recycle names, and some prefixes, like geptozepto-, have a nice ring to them. Apostrophes are used here to separate two vowels that are part of separate parts of the prefix.
But like usual, we'll want to go further. After all, we've only defined two new names, and none of them are all that new.
Maybe the prefix for 10^60, the 20th power of 1000, can be called geopageopa-? I'd rather not, as that name is redundant. Something like dugeopa- would be much better, but kind of dull.
Therefore, my idea is that we continue basing the unique prefix names on hoax prefixes - some include sagan-, pija-, kyra-, amos-, pectrol-, harpi-, nisaba-, and zotza-.
Which one should we use for 10^60? My idea is that out of those prefixes, we start with amos-, and modify it to amosa-, with A as the symbol. Then, we can have amosakila- (AK) for 10^63, which is equal to one vigintillion. The sequence can continue with amosamega- (AM), amosagiga- (AG), etc, all the way up to amosabronta- (AB) for 10^87.
Not bad so far. Of course, we'll want a reciprocal of amosa-. Here, we can make the prefix for 10^-60 amisto-, with i as the symbol. It's now trivial to continue with amistomillo- (im) all the way up to amistobrimto- (ib).
And what should the prefix for 10^-90 be? Let's use the hoax prefix harpi-, and modify it to hapra- (symbol: R). The reciprocal can be called harkto- (symbol: h), and both can be combined with prefixes in the same way we've done previously.
Really, we can name a prefix for each of the first 9 powers of 10^30 and 10^-30 by modifying the hoax prefixes I listed:
So now, we can name 99 large and 99 small prefixes: the largest and smallest are zotzabronta- (10^297, symbol: XB) and zuztobrimto- (10^-297, symbol: xb). Not bad so far!
As an example of how this can work, let's say you wanted to find what prefix to use for a googol (10^100) meters. First, the first power of 10^30 below a googol is 10^90, and the prefix for that is hapra-. So doing the math, a googol meters can be called 10 billion haprameters. However, we can get some further detail and turn billion into giga- allowing us to call a googol meters 10 hapragigameters, or 10 HGm for short.
But where to go from here? My idea is to use Greek letter names from here on out, because Greek letters are cool.
We'll start by using alpha- as the prefix for 10^300. The symbol would be the capital Greek letter alpha (Α), but the letter looks identical to the Latin capital letter A. Therefore we must jump out of the system and make the symbol a lowercase letter alpha (α).
Of course, we can continue with alphakila- (one centillion, 10^303), alphamega-, alphagiga-, alphatera- ... alphabronta-, alphageopa-, alphageopakila- ... alpha'amosa, alphahapra-, alphakyra-, alphapija-, alphasagana-, alphapectra-, alphanisaba-, and alphazotza-. The farthest we can get now is alphazotzabronta- (symbol: αXB).
Then, the 200th power of 1000 (10^600) can have the prefix beta- (symbol: β). Once again, we need to use lowercase beta because uppercase beta is identical to Latin B. From there on we can name a whole 'nother 99 prefixes out of those, starting with betakila- and ending with betazotzabronta-.
And now, we can continue with gamma- (symbol: Γ) = 10^900 and delta- (symbol: Δ) = 10^1200.
However, a continuation with epsilon- doesn't work because epsilon doesn't end with -a, and epsilona- or epsila- doesn't sound all that good. We can't really use zeta- either because it can be confused with zetta-. Eta- doesn't sound all that good, but theta- is a reasonable next prefix.
So we continue, only with the Greek letters that sound good as prefixes:
Theta- (Θ) = 10^1500, iota- (Ι, works because Latin I isn't used for a prefix) = 10^1800, kappa- (κ) = 10^2100, lambda- (Λ) = 10^2400, sigma- (Σ) = 10^2700, and omega- (Ω) = 10^3000.
Omega- sounds pretty awesome as an SI prefix (e.g. omegabyte), and this system can name 1000 SI prefixes now. For example, 10^666 would be beta'amosamega- (βAM), and 1000^666 = 10^1998 = iotasagana'exa- (ΙSE).
Of course, it is now necessary to continue the small prefixes to 10^-3000. Once again, we'll use Greek letters to name the following prefixes:
epsilo- (ε) = 10^-300, nuo- (ν) = 10^-600, xio- (ξ) = 10^-900, omicro- (ο, not to be confused with micro- and pronounced OH-mik-roh, NOT oh-MYK-roh) = 10^-1200, pio- (π) = 10^-1500, tafo- (τ, tafo- because tauo- looks awkward and the letter tau's name is prounced "taf" in Greek) = 10^-1800, upsilo- (υ) = 10^-2100, phio- (φ) = -2400, chio- (χ, not to be confused with x for zuzto-, and pronouncd kee-oh, NOT chee-oh) = 10^-2700, and psio- (ψ) = 10^-3000.
So omega- is the largest prefix with the 2000-prefix system and psio- is the smallest.
But we can go further. We can start with the trivial like omegakila-, omegamega- ... omegageopa- ... omega'alpha- ... up to omegasigmazotzabronta- for 10^5997.
But what next? We can use new multiplier roots to start with megomega- (MΩ) for 10^6000, then with gigomega- (GΩ) for 10^9000, continuing with:
tegomega- = 10^12,000
pegomega- = 10^15,000
exgomega- = 10^18,000
zegomega- = 10^21,000
yogomega- = 10^24,000
brogomega- = 10^27,000
geogomega- (jog-oh-may-guh) = 10^30,000
geogkigomega- = 10^33,000
geogmegomega- = 10^36,000
...
geogbrogomega- = 10^57,000
amgomega- = 10^60,000
hagomega- = 10^90,000
kygomega- (kyg-oh-may-guh) = 10^12,000
pigomega- = 10^150,000
sagomega- = 10^180,000
pregomega- = 10^210,000
nigomega- = 10^240,000
zogomega- = 10^270,000
algomega- = 10^300,000
algkigomega- = 10^303,000
alggeogomega- = 10^330,000
begomega- = 10^600,000
gagomega- = 10^900,000
degomega- = 10^1,200,000
thegomega- = 10^1,500,000
iogomega- = 10^1,800,000
kagomega- = 10^2,100,000
lagomega- = 10^2,400,000
sigomega- = 10^2,700,000
And the prefix for 10^2,999,997 is sigzogbrogomegasigmazotzabronta-. The symbol is ΣXBΩΣXB.
Finally the last prefix is omegomega- (symbol: ΩΩ). The prefix is for 10^3,000,000.
If we go in the other way with the small prefixes we can have the following prefixes:
mikpsio- = 10^-6000
nakpsio- = 10^-9000
pikpsio- = 10^-12,000
fekpsio- = 10^-15,000
atakpsio- = 10^-18,000
zekpsio- = 10^-21,000
yokpsio- = 10^-24,000
brikpsio- = 10^-27,000
gekpsio- = 10^-30,000
gekmilkpsio- = 10^-33,000
gekmekpsio- = 10^-36,000
...
gekbrikpsio- = 10^-57,000
amikpsio- = 10^-60,000
hakpsio- = 10^-90,000
kykpsio- (kike-psee-oh) = 10^-12,000
pekpsio- = 10^-150,000
sakpsio- = 10^-180,000
perkpsio- = 10^-210,000
nikpsio- = 10^-240,000
zukpsio- = 10^-270,000
psekpsio- = 10^-300,000
psekmilkpsio- = 10^-303,000
psekgekpsio- = 10^-330,000
nukpsio- = 10^-600,000
xikpsio- = 10^-900,000
omikpsio- = 10^-1,200,000
piokpsio- = 10^-1,500,000
takpsio- = 10^-1,800,000
psukpsio- = 10^-2,100,000
phikpsio- = 10^-2,400,000
chikpsio (kick-psee-oh) = 10^-2,700,000
and finally: psikpsio- = 10^-3,000,000
Conclusion
Why did I choose the prefixes the way I did? For a few reasons:
1. I wanted to make the prefixes sound as varied as the official SI prefixes, and to do this I had to avoid choosing names that are too numerical because such prefixes sound monotonous
2. I wanted to make the prefixes require not too much memorizing, which is why I used the idea of combining prefixes
3. I think a million prefixes is a good stopping point
Note that some systems have other advantages: for example, Sbiis Saibian's naming system keeps the names very short. However, I myself decided not to do this because it messes with the idea of combining names.