Thanks for all the suggestions - it's been fun making our own system of numbers for DROD, and the additions have been very innovative.
However, we need one more addition before I can compile the entire system into a single article (perhaps for DROD.net if Matt is interested).
We need to make an extension of the system that thakes the scope past 1 million and (hopefully) into infinity (although going beyond is also a possibility
).
After some thought with my friends, we have come up with two different possible extensions:
1. Continue the sequence using place values of 100
This would continue the system in much the same way as Watcher's addition, using place values of 100. As suggested above, "
1 million times"
will be "
millionce"
, from the English word "
million"
(not "
mille"
meaning "
thousand"
in Latin), plus the ending "
-once"
to make it an Indicatory number. Numbers larger than 1 million will require additional infixes - "
milli"
, "
billi"
, "
trilli"
, etc. from the English words denoting those numbers, "
million"
, "
billion"
, "
trillion"
, etc.
However, since we are working in place values of
100, we need to use the old meanings of "
billion"
, "
trillion"
and so on, not today's modern meanings, which means that 1 billion is a million millions, not a thousand millions as it is today, and a trillion is a million billions, not a thousand billions.
So the infixes will be thus:
10^6 times - milli (From "
million"
)
10^12 times - billi (From "
billion"
)
10^18 times - trilli (From "
trillion"
)
10^24 times - quadrilli (From "
quadrillion"
)
10^30 times - quintilli (From "
quintillion"
)
And so on.
The forming of the numbers is similar to before, except that now, we require the number to be split into six digit groups first before further splitting down to two digit numbers.
Take this example: "
402854639858237 times"
First split the number into groups of six digits starting from the right:
[000]402, 854639, 858237, meaning there are 402 billions, 854639 millions and 858237 units (Remember we are using the old system where 1 billion is a million millions). The million and billion groups will therefore have the infixes "
milli"
and "
billi"
added to their ends.
Now we need to find out exactly how many millions, billions and units we have. To do this, we need to split the groups of six numbers further into two digit numbers:
[00], [0]4, [0]2; (billions)
85, 46, 39; (millions)
85, 82, 37 (units)
Using the same system as Watcher added, translate the two digit numbers by taking the base tens number:
10 - deci
20 - viginti
30 - triginti
40 - quadraginti
50 - quinquaginti
60 - sexaginti
70 - septuaginti
80 - octaginti
90 - nonaginti
And adding the Greek prefix to the start of it (if there is a tens part):
1 - mono
2 - bi
3 - tri
4 - tetra
5 - penta
6 - hexa
7 - hepta
8 - octa
9 - ennea ("
nona"
is Latin, not Greek)
Then, to each of the two digit numbers add the suffixes "
uni"
, "
centi"
and "
myri"
, treating each group of 6 numbers separately.
So we have now the translated number pairs:
tetracenti, biuni; (billions)
pentaoctagintimyri, hexaquadraginticenti, enneatrigintiuni; (millions)
pentaoctagintimyri, bioctaginticenti, heptatrigintiuni (units).
Now reverse the order of the numbers and stick them together, adding "
milli"
to the millions group and "
billi"
to the billions group:
biunitetracentibilli,
enneatrigintiunihexaquadraginticentipentaoctagintimyrimilli,
heptatrigintiunibioctaginticentipentaoctagintimyri
Now reverse the order of these groups, putting units first, millions second, and billions last, adding "
once"
to the end of the number.
So "
402854639858237 times"
translated to an Indicatory Number in this way is:
"
heptatrigintiunibioctaginticentipentaoctagintimyrienneatrigintiunihexaquadraginticentipentaoctagintimyrimillibiunitetracentibillionce"
.
What fun! (Although a little tongue-twistingly repetitive)
Alternatively...
2. Continue the sequence using place values of 10
For this, numbers after 1000000 will be grouped as they are in English - in 1000s, not millions as in above. The infixes will be "
milli"
, "
billi"
, "
trilli"
, etc. again, but this time, the numbers that they correspond to, "
million"
, "
billion"
, "
trillion"
, etc., will have the same meaning as the numbers adopted today. "
billion"
will mean a "
thousand million"
, and "
trillion"
a "
thousand billion"
, and so on. The infixes will then be:
10^6 times - milli
10^9 times - billi
10^12 times - trilli
10^15 times - quadrilli
10^18 times - quintilli
And so on.
To form the numbers this time, the number will need to be split thrice:
First into two parts, one containing the last 6 numbers and the other the rest of the number.
The second involves the splitting of the rest of the number (the first digit to the seventh-to last) into groups of three, beginning from the right.
The final split involves splitting the last six digits into three groups of 2 digits like before.
So for the above example, "
402854639858237 times"
, split the number into two parts, with the last six digits in one, and the rest in the other:
402854639, 858237.
Now split the rest of the number (not the last 6 digits) into groups of three:
402, 854, 639, 858237.
Now split the last 6 digits into groups of 2:
402, 854, 639,
85, 82, 37.
First translate the pairs of numbers (in blue) as described above, adding the Greek prefix to the Latin base tens number, then adding the uni, centi or myri suffix to the corresponding pair.
To translate the groups of three, use a similar technique, translating the last two digits of each like before, adding "
uni"
to the end, and then adding "
centi"
with the necessary Greek prefix to the end as before. So "
506"
will become "
hexaunipentacenti"
. The translated groups are now:
biunitetracenti, tetraquinquagintiunaoctacenti, enneatrigintiunihexacenti,
pentaoctagintimyri, bioctaginticenti, heptatrigintiuni.
Now add the infixes "
milli"
to the millions group, "
billi"
to the billions group and "
trilli"
to the trillions group, reverse the order of the groups, so units come first and trillions come last, stick them together and then add "
once"
to the end like before.
So "
402854639858237 times"
translated to an Indicatory Number in this way is:
"
heptatrigintiunibioctaginticentipentaoctagintimyrienneatrigintiunihexacentimillitetraquinquagintiunaoctacentibillibiunitetracentitrillionce"
Also much fun to speak aloud, we found.
So... I hope that hasn't been
too confusing.
Well, the question is, obviously: Which do you prefer?
[Edited by agaricus5 on 05-22-2004 at 11:34 PM GMT]
[Edited by agaricus5 on 05-23-2004 at 06:30 PM GMT]
____________________________
Resident Medic/Mycologist
This will allow up to count up to a million with indicatory numbers.
