In order to gain acceptance, there must be as few changes as possible. So, we need new symbols for ten and eleven, but we should keep the old names for speech.

I would also keep the name twelve. Numbers above twelve would be called twelve and one, twelve and two etc.

Then two twelves, two twelves and one etc. up to a gross.

Thus decimal 143 (my house number incidentally) we should call eleven twelves and eleven.

John Youles

You're even less revolutionary than shibboleth: http://s13.invisionfree.com/DozensOnline/i...hp?showtopic=14
;)

It is certainly a novel approach, but not one that I personally favour. I think that whilst it is best to keep it simple and unchanged, one must simply break the link between certain names and the figure association. That is, when you say "twelve", folks think "12"... which is the kind of mentality we must break*. What does everyone else think?


*but something to ponder: if one said "dek", wouldn't folks still think "10"?

Two years ago, in my Microcomputer Systems class, my lab partner pronounced 0x1000 (dec. 4096) as a "thousand". That is, he associated number names with the figures, not with the values. I wonder if this is true for people in general.

Doesn't a "kilobyte" mean 1024 bytes? In other words "kilo" means not 1000 but 2^10. This is a "binary thousand".

Similarly a megabyte would be 2^20 bytes = 1048576 bytes. A "binary million".

In a similar way 144 could be called a "dozenal hundred"
(or 108 = 9x12?).

And 1782 a "dozenal thousand"
(although 1008 = 84x12 = 7 gross would be an alternative).

So what would a "dozenal million" be? 12^6 = 2985984
(or 1000008 = 83334x12?)

Edit: It seems that 100...0008 = 12x8...3334 is a general result!
Just add 8 to any power of ten and you get a multiple of 12.

18 is not a multiple of 12.

Edit: However, for higher powers of ten, you are right.

Base case: 10² = 100 = *84 is 8 less than a multiple of twelve (*90).

Inductive case: Suppose that 10^k+8 is a multiple of twelve. Equivalently, 10^k mod 12 = 4. Let n=k+1. Then 10^n=10×10^k, so

10^n mod 12 = (10×10^k) mod 12
= ((10 mod 12) × (10^k mod 12)) mod 12
= (10 × 4) mod 12 = *34 mod 12 = 4, as expected

Therefore, by the principle of mathematical induction, 10^n mod 12 = 4 (or equivalently, 10^n+8 mod 12 = 0) for all integers n >= 2, Q.E.D.

Speaking of kilobytes, what would the binary prefixes be under a base-12 system? The term "kilobytes" exists because 2^10 ~= 10^3 (error: 2.4%) is a convenient approximation, but it's less convenient under a non-decimal system. Perhaps in base 12 we would have 2^(*16) = *107854 ~= *100000 (error: 5.3%), and measure memory in units of quarter-megabytes.

This ambiguity was supposed to be corrected by the NEW term kibi. Thus, a "kilobyte" is a "kibibyte".... except there is universal agreement that kibi sounds like a bad joke :D

OK, naming numbers is the first difficult problem. Even in decimals people are arguing over "billions" (10^12 or 10^9?) and so on. We have to find a consistent, easy and logical possibility.

1. I would keep the "ten" for :A and "eleven" for :B . Everything else will just cause still more confusion. Also, in languages like French, if :A should be called "dek" and *10 like decimal 10, it would be very similar to "dix" = *10.

2. Dozen for *10 is absolutely clear. What do we call *20? Twenzy? Twozy? Twozen? Twodo? Two dozen? I would prefer "twozen", it's most consistent with "dozen". There is no particular reason why we should use "twen-" instead of "two-", besides tradition (and traditionally, we could keep the decimal system and spare our efforts).

3. In German, there would be more problems. Dozen means "Dutzend" (speak "dootsent", but with short "oo"), and shortening it to "-zend" sounds bad, because we tend to swallow this "e" and speak only "tsnd". Also, it is too similar to our ten, "zehn" (speak "tsehn"). So there is only the possibility *20 = "zwei Dutzend", which would in English mean "two dozen" and could be shortened (although not in German) to "twozen". That's another reason why I prefer this variant.

4. *100="gross" is clear, also e.g. "five gross" for *500. Additionally, TGM proposes "duna", but mostly for use as a prefix (e.g. "dunafoot"). In German, it is spelled "Gros", but pronounced the same way.

5. Next comes *1000: "great gross", "grand gross" or simply "grand" in English, "Maß" (="measure") in German. Also, TGM proposes "trin".

6. Now we come to big numbers. I've thought of adopting the "billion" system, but of course in long scale (because it has much more logic). But there are two disadvantages: First, there is no Greek or Latin word for eleven, so we will get problems with *10^66 ("elvillion" in long scale). And second, there is no reason why we should give every 6th dozenal power a new name and not, for instance, every 4th or 3rd. The dozenal powers should also have names that are based on recurrences of *10. So *10^10 should be something special and not just the "billion" or "billiad" or whatever name we would choose.

7. Therefore I like the TGM proposal:
*10^2 is duna, *10^3 trin, *10^4 quedra, *10^5 quin, *10^6 hes, *10^7 sev, *10^8 ak, *10^9 neen, *10^ :A dex, *10^ :B lef, and *10^10 is zennil (zen=*10+nil=0).
For *10^23 it is dunatrin, for *10^ :A 5 dexquin and like that. For *10^100 I would adopt the googol and call it "dozenal googol" or just googol, who cares. Then *10^102 is googol duna, *10^120 is googol dunnil and *10^200 is dunagoogol. Like that we will get to *10^ :B :B :B :B "leflefgoogol leflef".

8. For really big numbers, we need a little more effort. In decimals, 10^googol is called "googolplex". So we could use this -plex suffix for "*10 to the power of". Therefore, *10^10000 = *10^(10^4) = quedraplex. *10^(10^10) then is zennilplex, and so on to *10^(10^100) "googolplex", *10^(10^1000) "zengoogolplex" and *10^(10^(10^100)) "googolplexplex or googolduplex. I think, this is now high enough to for everyday use :P .

See, if we adopted the "billion" system, the googol, which is a very "dozenal" number, would not fit in; it would just be *10^100 = *10^(6*20) = "vigintillion". OK, that's not as awkward as in decimal (the decimal googol is somewhere between sedecilliard and septendecillion in long scale or duotrigintillion and trestrigintillion in short scale).

So far,
Ebbe

Let me just say that I've got a real problem with suffixes for numbers between twelve and two dozen and for the first power of twelve.

We already have the word dozen, so why not just use that? What on earth is wrong with "a dozen and one", "a dozen and two"; or with "two dozen", "three dozen", "four dozen and eleven", etc?

Indeed since we use words for higher powers, (hundred, thousand and million, etc in decimal), this system is actually more regular.

"Gross" is also fine for the second power of twelve, so no need to change that, "great gross" isn't as satisfactory, and I prefer "grande" /gran'deh/, I believe "grand" has already been suggested.

Higher powers will still have to be delt with, somehow "magnum", or maybe "magnal" seems to sound right for twelve to the power of six. Not sure about using other champaign sizes, though.

Summary
twelve^1 twelve/dozen
twelve^2 gross
twelve^3 grande
twelve^6 magnum/magnal

in swedish the word Dozen is "Dussin"

i guess in english phonetics this would be doo-sin


i think counting in dozenal should use the german system (as numbers after 20)

1 and twenty, 2 and twenty, etc...

but applying this to all multiples of twelve (dozenal 10)

for example:

one and twelve, two and twelve, three and twelve..............nine and twelve, ten and twelve, eleven and twelve, twenty, etc..

the base factoral names after twelve (20, 30, 40,..100, 1000, million) should remain the same

these factoral names are too burned into our languages to attempt to change them now

with big numbers...
i think the Chuquet system would work best for dozenal - with slight modification

for example...

thousand = 12^3
million = 12^6
milliard = 12^9
billion = 12^12
billiard = 12^15
trillion = 12^18
trilliard = 12^21
quadrillion = 12^24
quadrilliard = 12^27
quintillion = 12^30
quintilliard = 12^33
sextillion = 12^36
sextilliard = 12^39
septillion = 12^42
septilliard = 12^45
octillion = 12^48
octilliard = 12^51
nonillion = 12^54
nonilliard = 12^57
decillion = 12^60
decilliard = 12^63
unilllion = 12^66
unilliard = 12^69
ducillion = 12^72
ducilliard = 12^75
unducillion = 12^78
unducilliard = 12^81
triducillion = 12^84
triducilliard = 12^87
quaducillion = 12^90
quaducilliard = 12^93
sexducillion = 12^96
sexducilliard = 12^99
sepducillion = 12^102
sepducilliard = 12^105
octducillion = 12^108
octducilliard = 12^111
nonducillion = 12^114
nonducilliard = 12^117
decducillion = 12^120
decducilliard = 12^123
enducillion = 12^126
enducilliard = 12^129
vigillion = 12^132
vigilliard = 12^135
unvigillion = 12^138
unvigilliard = 12^141
trivigillion = 12^144
trivigilliard = 12^147
quarvigillion = 12^150
quarvigilliard = 12^153
quintvigillion = 12^156
quintvigilliard = 12^159
sexvigillion = 12^162
sexvigilliard = 12^165
sepvigillion = 12^168
sepvigilliard = 12^171
octvigillion = 12^174
octvigilliard = 12^177
nonvigillion = 12^180
nonvigilliard = 12^183
decvigillion = 12^186
decvigilliard = 12^189
envigillion = 12^192
envigilliard = 12^195
dretillion = 12^198
dretilliard = 12^201
undretillion = 12^204
undretilliard = 12^207
didretillion = 12^210
didretilliard = 12^213
tridetrillion = 12^216
tridetrilliard = 12^219
quadetrillion = 12^222
quadetrilliard = 12^225
quindetrillion = 12^228
quindetrilliard = 12^231
sexdetrillion = 12^234
sexdetrilliard = 12^237
sepdetrillion = 12^240
sepdetrilliard = 12^243
octdetrillion = 12^247
octdetrilliard = 12^250
nondetrillion = 12^253
nondetrilliard = 12^256
decdetrillion = 12^259
decdetrilliard = 12^262
endetrillion = 12^265
endetrilliard = 12^268
tetrillion = 12^271
tetrilliard = 12^274
untetrillion = 12^277
untetrilliard = 12^280
ditetrillion = 12^283
ditetrilliard = 12^286
tritetrillion = 12^289
tritetrilliard = 12^292
quartetrillion = 12^295
quartetrilliard = 12^298
quintetrillion = 12^301
quintetrilliard = 12^304
sextetrillion = 12^307
sextetrilliard = 12^310
octetrillion = 12^313
nontetrillion = 12^316
nontetrilliard = 12^319
dectetrillion = 12^322
dectetrilliard = 12^325
entetrillion = 12^328
entetrilliard = 12^331
pentillion = 12^334
pentilliard = 12^337
unpentillion = 12^340
unpentilliard = 12^343
tripentillion = 12^346
tripentilliard = 12^349
quadpentillion = 12^352
quadpentilliard = 12^355
quinpentillion = 12^358
quinpentilliard = 12^361
sexpentillion = 12^364
sexpentilliard = 12^367
octpentillion = 12^370
octpentilliard = 12^373
nonpentillion = 12^376
nonpentilliard = 12^379
decpentillion = 12^382
decpentilliard = 12^385
enpentillion = 12^388
enpentilliard = 12^391
hexillion = 12^394
hexilliard = 12^397
unhexillion = 12^400
unhexilliard = 12^403
trihexillion = 12^406
trihexilliard = 12^409
quadhexillion = 12^412
quadhexilliard = 12^415
quinhexillion = 12^418
quinhexilliard = 12^421
sexhexillion = 12^424
sexhexilliard = 12^427
sephexillion = 12^430
sephexilliard = 12^433
octhexillion = 12^436
octhexilliard = 12^439
nonhexillion = 12^442
nonhexilliard = 12^445
dechexillion = 12^448
dechexilliard = 12^451
enhexillion = 12^454
enhexilliard = 12^457
heptillion = 12^460
heptilliard = 12^463
unheptillion = 12^466
unheptilliard = 12^469
diheptillion = 12^472
diheptilliard = 12^475
triheptillion = 12^478
triheptilliard = 12^481
quadheptillion = 12^484
quadheptilliard = 12^487
quinheptillion = 12^490
quinheptilliard = 12^493
sexheptillion = 12^496
sexheptilliard = 12^499
septheptillion = 12^502
septheptilliard = 12^505
octheptillion = 12^508
octheptilliard = 12^511
nonheptillion = 12^514
nonheptilliard = 12^517
decheptillion = 12^520
decheptilliard = 12^523
enheptillion = 12^526
enheptilliard = 12^529
actillion = 12^532
actilliard = 12^535
unactillion = 12^538
unactilliard = 12^541
diactillion = 12^544
diactilliard = 12^547
triactillion = 12^550
triactilliard = 12^553
quadactillion = 12^556
quadactilliard = 12^559
quinactillion = 12^562
quinactilliard = 12^565
sexactillion = 12^568
sexactilliard = 12^571
sepactillion = 12^574
sepactilliard = 12^577
octactillion = 12^580
octactilliard = 12^583
nonactillion = 12^586
nonactilliard = 12^589
decactillion = 12^592
decactilliard = 12^595
enactillion = 12^598
enactilliard = 12^601
novillion = 12^604
novilliard = 12^607
unnovillion = 12^610
unnovilliard = 12^613
trinovillion = 12^616
trinovilliard = 12^619
quadnovillion = 12^622
quadnovilliard = 12^625
quinovillion = 12^628
quinovilliard = 12^631
sexnovillion = 12^634
sexnovilliard = 12^637
sepnovillion = 12^640
sepnovilliard = 12^643
octnovillion = 12^646
octnovilliard = 12^649
nonovillion = 12^652
nonovilliard = 12^655
decnovillion = 12^658
decnovilliard = 12^661
enovillion = 12^664
enovilliard = 12^667
centillion = 12^670
centilliard = 12^673
uncentillion = 12^676
uncentilliard = 12^679
dicentillion = 12^682
dicentilliard = 12^685
tricentillion = 12^688
tricentilliard = 12^691
quadcentillion = 12^694
quadcentilliard = 12^697
quincentillion = 12^700
quincentilliard = 12^703
sexcentillion = 12^706
sexcentilliard = 12^709
sepcentillion = 12^712
sepcentilliard = 12^715
octcentillion = 12^718
octcentilliard = 12^721
noncentillion = 12^724
noncentilliard = 12^727
decentillion = 12^730
decentilliard = 12^733
encentillion = 12^736
encentilliard = 12^739
kilotillion = 12^742
kilotilliard = 12^745
unkilotillion = 12^748
unkilotilliard = 12^751
trikilotillion = 12^754
trikilotilliard = 12^757
quadkilotillion = 12^760
quadkilotilliard = 12^763
quinkilotillion = 12^766
quinkilotilliard = 12^769
sexkilotillion = 12^772
sexkilotilliard = 12^775
sepkilotillion = 12^778
sepkilotilliard = 12^781
octkilotillion = 12^784
octkilotilliard = 12^787
nonkilotillion = 12^790
nonkilotilliard = 12^793
deckilotilllion = 12^796
deckilotilliard = 12^799
enkilotilllion = 12^802
enkilotilliard = 12^805
megatillion = 12^808
megatilliard = 12^811
unmegatillion = 12^817
unmegatilliard = 12^820
trimegatillion = 12^823
trimegatilliard = 12^826
quadmegatillion = 12^829
quadmegatilliard = 12^832
quinmegatillion = 12^835
quinmegatilliard = 12^838
sexmegatillion = 12^841
sexmegatilliard = 12^844
sepmegatillion = 12^847
sepmegatilliard = 12^850
octmegatillion = 12^853
octmegatilliard = 12^858
nonmegatillion = 12^861
nonmegatilliard = 12^864
decmegatillion = 12^867
decmegatilliard = 12^870
enmegatillion = 12^873
enmegatilliard = 12^876
gigatillion = 12^879
gigatilliard = 12^882
ungigatillion = 12^885
ungigatilliard = 12^888
trigigatillion = 12^891
trigigatilliard = 12^894
quadgigatillion = 12^897
quadgigatilliard = 12^900
quingigatillion = 12^903
quingigatilliard = 12^906
sexgigatillion = 12^909
sexgigatilliard = 12^912
sepgigatillion= 12^915
sepgigatilliard = 12^918
octgigatillion = 12^921
octgigatilliard = 12^924
nongigatillion = 12^927
nongigatilliard = 12^930
decgigatillion = 12^933
decgigatilliard = 12^936
engigatillion = 12^939
engigatilliard = 12^942
teratillion = 12^945
teratilliard = 12^948
unteratillion = 12^951
unteratilliard = 12^954
diteratillion = 12^957
diteratilliard = 12^960
triteratillion = 12^963
triteratilliard = 12^966
quateratillion = 12^969
quateratilliard = 12^972
quinteratillion = 12^975
quinteratilliard = 12^978
sexteratillion = 12^981
sexteratilliard = 12^984
septeratillion = 12^987
septeratilliard = 12^990
octteratillion = 12^993
octeratilliard = 12^996
nonteratillion = 12^999
nonteratilliard = 12^1002
decteratillion = 12^1005
decteratilliard = 12^1008
enteratillion = 12^1011
enteratilliard = 12^1014
extillion = 12^1017
extillaird = 12^1020
unextillion = 12^1023
unextillaird = 12^1026
diextillion = 12^1029
diextillaird = 12^1032
triextillion = 12^1035
triextillaird = 12^1038
quadextillion = 12^1041
quadextillaird = 12^1044
quintextillion = 12^1047
quintextillaird = 12^1050
sexextillion = 12^1053
sexextillaird = 12^1056
septextillion = 12^1059
septextillaird = 12^1062
octextillion = 12^1065
octextillaird = 12^1068
nonextillion = 12^1071
nonextillaird = 12^1074
decextillion = 12^1077
decextillaird = 12^1080
enextillion = 12^1083
enextillaird = 12^1086
zillion = 12^1089
zilliard = 12^1092
unzillion = 12^1095
unzilliard = 12^1098
dizillion = 12^1101
dizilliard = 12^1104
trizillion = 12^1107
trizilliard = 12^1110
quadzillion = 12^1113
quadzilliard = 12^1116
quinzillion = 12^1119
quinzilliard = 12^1121
sexzillion = 12^1124
sexzilliard = 12^1127
sepzillion = 12^1130
sepzilliard = 12^1133
octzillion = 12^1136
octzilliard = 12^1139
nonzillion = 12^1142
nonzilliard = 12^1145
deczillion = 12^1148
deczilliard = 12^1151
enzillion = 12^1154
enzilliard = 12^1157
godzillion = 12^1160
godzillaplex = 12^godzillion (a big radioactive monster size number with attitude)

växan wrote:

Then went on to suggest that number names be retained while assigning new values.

I wonder what you were thinking here. Nobody uses milliard or billiard these days, and they were never used in British English at all. Modern English usage is that billion is 10^9 and a trillion is 10^12 in all varieties of English. And Million is most certainly 10^6. You are only going to confuse matters here.

German (and I presume other Germanic languages) does give the unit before the tens, but why would you want to retain this system?

It's archaic in English and you'll only hear it in the nursery rhyme, "Four and twenty blackbirds baked in a pie." Furthermore, it moves away from the direction in which the language is evolving. (German on the other hand is more evolved from the viewpoint of sound shift.)

What do you mean by "factoral names"? As far as I know, no number system uses factorials.

I agree that we should propose as few changes as possible. We need symbols for 9+1 & 9+10. but when I first became acquainted with DSGB & DSA the usual proposals were for X & E. The upsidedown 2 & 3 are usually unprintable and sometimes confusing. We already have ocasional difficulties with 6 & 9 on tickets, dials etc. X & E are found on normal keyboards and most fonts. So why not use them? X is familiar. It is not likely to be confused with x in algebra or with the multiplication sign (which perhaps should be replaced by *.)
I would suggest continuing to use dek (if you want it to look more english,you may want to spell it "deck"). You can then use the word "ten" to refer to 1 followed by 0 irrespective of the base used in the same way that in zulu (military) time the word "hundred" is used for any number eding in 00 e.g. six p.m. is called "eighteen hundred hours".
The snag about shortening dozen to zen is that zen is too easily confused in speech with ten.
The real problem then would be showing which base we are using, perhaps by clearly distinguishable type faces

most of europa only use the Chuquet system : million, milliard, etc..

where 1 billion = 1 000 000 000 000

which is twice as efficient as the short scale american system
since a Chuquet Octillion = 10^48 and an american Octillion is only 10^27

britain does not, however english is just 1 of dozens of european languages
the EU has a population of 450 million - 70 million of which are native english speakers

so it's not so important what is or is not used in english

americans have their own language, which sometimes resembles english,
but mostly not - especially when it comes to small details like : spelling, grammar, lexicon, phonetics,

british people count money very similar to germans and swedes

ex: ten pound and twenty p where americans would say "ten-twenty"
or rather "ten-twenny" since there seems to be some problem pronouncing the letter T

for germans "one and twenty" is the normal way to count
and there are about 150 million people in europa speaking german


using this system would be much easier than creating new words for 13 - 23

actually, yes they were.. it was Prime Minister Wilson who adopted the american short scale system in 1974

due to pressure from American finance and government
who decided the world should do as they do, since they intend to buy the planet one piece at a time anyway

you can read more about it here


a brief list of Long Scale countries :

Sweden, Finland, Norway, Danmark, Germany, Austria, Netherlands, Luxembourg, Belgium, France, Spain, Portugal, Italy, Switzerland, Poland, Hungary, Czech Republic, Latvia, Estonia, Romania, Malta, Croatia, Slovenia, Slovakia, Serbia, Cyprus, and Mexico

Short Scale countries :

USA, UK, Ireland, Australia, New Zealand, India, Brazil, Russia, Greece, and Turkey


other scale systems :

China, Japan, Korea

there is no need for new names

the terms hundred, thousand, million, milliard, billion can be applied to any base

once you define the base - the terms are used to designate magnitude and nothing more

a binary thousand = 8

it is still written as 1000 so why not call it a thousand?



how stupid would it be to throw away perfectly good number terms
just for a change of base

It causes confusion. In one of my comp sci courses, I was frequently asking my lab partner, "Did you mean a decimal thousand or a hex thousand [0x1000=4096]?"

Of course, the names could be reused after base ten is forgotten.

Britain used to use the long system but the word "milliard" was rarely if ever used.

We used to say "a thousand million" instead.

aha, now i see what you meant

if you think using the same names causes confusion
just imagine the kaos of introducing 100s of new names into the number system

it would cause massive confusion

base 10 will never be forgotten
any more than binary, hexadecimal, duodecimal, or vigesimal have been forgotten

many different bases are used concurrently throughout the world

in all honesty, i think the odds of dozenal ever replacing decimal are about 1000000:1
given the amount of data that needs to be converted

every textbook, science paper, and numbered document,
in every learning institution and industry would have to be revised,
the cost of new metric standards, and new calculating machines,
industrial machines, education, etc.. would be astronomical

and don't forget that 95% of the world are hardwired for decimal
most of whome would sooner die before ever considering a change of number base

it's going to be a hard sell to say the least

i think the only chance would be to create a parallel dozenal system alongside
decimal, and let the value of dozenal numbering sell itself to more and more people
generation by generation, until those opposing the change have become a minority

Okay, for big numbers, we have several possibilities here:

1. We take the Chuquet system (or even Pelletier/short scale) and *10^6 will be the (dozenal) million, *10^10 the billion, *10^16 trillion and so on. The good news is, it is very easy to learn, because everyone knows the million and has the mental image of 1000000, which would be also correct in dozenal. However, it has some disadvantages:
a) we use bases 6 and 10 for the exponent. For example, *10^100 would be (since *100 = 144 = 6*24) the "quadravigintillion" ... there is no obvious connection between the exponent *100 and this name.
B) we also could invent new latin numbers for eleven and twelve, and therefore add an "elvillion" or something like that. Then we use bases 6 and *10 in the exponent, which is somewhat better than above. For instance, *10^100 would be the "vigintillion", but still you have to calculate *100/6 before spelling the number. This is the variant växän prefers, but in his list, there is something wrong (12^144 should be the vigillion, not 12^132... the "doducillion" and other do- numbers are missing)
c) why use another base not equal to the dozen in the exponent? I see absolutely no reason to do so. Our decimal system only has grown historically to do so (ahm... by the way, I believe that is a rather bad translation of the German sentence...), since the invention of the million.

2. We use a system similar to Donald Knuth's -yllion numbers. He proposes to call 10^4 a myriad (like in Greek), 10^8 a myllion, 10^12 a myriad myllion, 10^16 is the byllion, 10^32 the tryllion and generally 10^(2^(n+2)) an n-yllion. You could easily convert this to dozenal. But a number lika *10^35 would be (since *39=2^5+2^3+2^2+2^0) "a dozen myriad myllion tryllion", which sounds and looks rather ugly. And again, we would use base two for the exponent in spite of being sure that twelve is the best :) .

3. We use a system with dozenal base in the exponent. First, there is the TGM proposal. The names would have to be discussed (I don't like "dex" and "ak" and "quedra"...), but it's perfectly consistent. It has the advantage (or is it a disadvantage?) to give every power of *10 it's own name. For instance, *10^35 is the trinquin. But it is a bit too scientific for everyday use; people would miss an equivalent for million ("hes" does not sound very large). Also, for high exponents >=*10000, the -plex system I proposed is not convenient (for instance, what would you call *10^345600? A "threequin-fourquedra-fivetrin-sixduna-plex"? Hmm...)

4. I like the "magnum" for *10^6 very much. With it, you could easily derive a word for every number <*10^10. *1857 632000 is, of course, a "one grande eight gross five-dozen-seven magnum six gross three-dozen-two grande". Thats very similar to our "million" approach.
For higher numbers, you need a new name for *10^10 (perhaps an "mill-" word), and *10^20 (bill-), *10^30 (trill-) and so on to *10^:B0 (elvill- ?), then *10^100 would be the googol or ducillion? I have to think through that.

5. Why new number names? Because I want to know from the spoken number, if it is a decimal or dozenal. Both bases will always coexist in my head, and I don't want to get confused.


I don't want to mix bases, so I won't use the first possibility. The second is nice for playing around, but not for everyday use. The third is better, but not very obvious. I like it because of its compatiblity with the googol. The fourth is worth thinking of.

That's my opinion, what's yours? B)

the best solution (in my opinion) would be to create new multiple and submultiple exponent prefixes,
and apply these to the number base (any base)

in exactly the same way SI prefixes are used with metric base units

using SI prefixes only as an example...



base 10

multiples

10
decaten
centaten
kiloten
megaten
gigaten
teraten
etc...

submultiples

deciten
centiten
milliten
microten
nanoten

etc...




base 12

multiples

12
decatwelve
centatwelve
kilotwelve
megatwelve
gigatwelve
teratwelve
etc...

submultiples

decitwelve
centitwelve
millitwelve
microtwelve
nanotwelve

etc...


SI prefixes are however too awkward sounding and there aren't enough prefixes
to serve the purpose

so a new, extended (phonetically pleasing) set of prefixes could be created
1 for each exponential power of 3

Perhaps you could name the exponents in multiples of three:

*1,000 = one trizen
*10,000 = twelve trizzen
*100,000 = gross trizzen
*1,000,000 = one hexzen
*10,000,000 = twelve hexzen
*100,000,000 = gross hexzen
*1,000,000,000 = one ninzen

etc.

Thanks ebbe, I'm glad you like the word magnum for a dozen to the power of six.

I like your word ducillion very much, but to me it would sound better for a dozen to the power of nine. du=two after all.

One could derrive a suffix from this word -cillion/'sili:ən/, which is (IMO) sufficiently different to the suffixes -illion/-rillion/-tillion used for powers of ten to stop confusion while retaining their charactor enough to sound natural.

We should remember that numbers above the trillions are very rarely used and that dozenal groupings will be greater again so really big numbers aren't that important but let me just suggest this:

dozen ^1 = dozen
dozen ^2 = gross
dozen ^3 = grande
dozen ^6 = magnum
dozen ^9 = ducillion
dozen ^dozen = tricillion
dozen ^dozen & three = tetracillion
dozen ^dozen & six = pentacillion
dozen ^dozen & nine = hexacillion/hexillion
dozen ^two dozen = septacillion
dozen ^two dozen & three = octacillion/occillion
dozen ^two dozen & six = ennacillion
dozen ^two dozen & nine = decacillion
dozen ^three dozen = aelfacillion/elfəsıli:ən/

I'm not sure that the c in -cillion should be replaced with an s.

For the most part, really big numbers would be written a dozen to the power of x, anyway.

But what's the du=2 got to do with 9? it's a bit like the US billion for 10^9 - billion was bi-million (or 10^12) so wouldn't ducillion be better for an even number of millions rather than an odd number?

thanks!

but why are you telling Ebbe - when Ducillion is my word? <_<

Ebbe took the word from my post...

I want to bring up this topic once more. I still do not know how to call *10^4:

• Quedra (TGM proposal)?
• A Dozen grand(e)?
• Myriad (Greek for 10000)?
• Million (Quadrascale, see below)

I could live with all of these possibilities.

More important is the question *10^10:
1. Trilliad (short scale, so *10^6=Milliad and *10^9=Billiad)
2. Billiad (long scale, *10^6=Milliad, *10^9=grand Milliad)
3. Millzen (dozenal scale, *10^6=Magnum(?), *10^9=grand Magnum, *10^20= Billzen...) or something like that
4. Zennil (TGM proposal)
5. Trilliad (Quadrascale, *10^4=Milliad, *10^8=Billiad, *10^4n=n-illiad)
The "quadrascale" is an idea I got just now, although it is not a very good one.

Consider *10^40 (12^48) in these systems. In my opinion, its name should have something to do with "four" or "four dozen" or "quad-". I also give the names of the (very special) *10^100, the dozenal googol:
1. *10^40=Tredecilliad / *10^100=Novemtrigintilliad
2. Octilliad / Vigintilliad
3. Quadzen / ? (googol would be the best, I think)
4. Quedranil / Zennilnil or googol
5. Decilliad / Trigintilliad

I still think the TGM proposal is best, although the names sound awful. Perhaps we could adopt it with other names. After all, it is the most logical one, because the exponent base is twelve (not 3, 6 or 4 as in short, long or quadrascale) and it is expandable.

Another question: Could we invent some artificial "latin" and "greek" names for eleven and twelve? Or will we need none?

We still need more ideas and opinions!

P.S. @växan: That's right, I did.

I stand corrected, Växan you did write the word "ducillion first but to be honest, I never read your post because it appeared to be more of an exercise in conlanging than a serious proposal. Ask yourself how often you need to use the word "quadrillion" and I mean usefully need to not when you are using it for fun. If you add the GDP's of all the world's nations togeter you'll aget a figure for Gross World Product of about 50 quadrillion dollars and I'm using the short scale here: 50×10^15. There just isn't any need for names for such high numbers. I've even gone too far in my own proposal. When numbers get really big, we tend to say number point whatever times ten to the power of whatever. Substitute times a dozen to the power of.
"Llanfairpwllgwyngyllgogerychwyrndrobwllllantysiliogogogoch" is the longest place name in the UK, but if you want to refer to it, you say, "Llanfair pwll" or "Llanfair PG", the reason is obvious like why we use "to the power of" for very large numbers - it's easier (and even that abbreviated place name isn't easy unless you're Welsh.)

The suffix -cillion/-sillion is however quite euphonious and ducillion sounds great. Du=2, that's right, and it is precisely because it is analagous to the short scale billion that I suggested its alternative use. Frankly, it hardly matters that the powers are odd, you think of the analagy with the short scale billion, and all becomes clear. Where you got the idea for the power of 72, I'll never work out. Likewise, tricillion/trisillion depending on how you want to spell it, also sounds fine. Different enough from trillion to avoid confusion, but somehow instantly familiar and analagous. And tricillion is the largest grouping that I expect to be needed for everyday use.

I think we should not repeat the confusion with long and short scale, and rather take an entirely other system. Perhaps short or long scale is the easiest, but not the most logical.

@Endi: You're right that we need a system only for numbers up to at most *10^20, but when we're inventing it, why not make it expandable to even higher numbers?

And still, I like high numbers. I need to have a name for *10^(10^(10^10)) ! :P
(Hmm, zennilduplex would do, perhaps...)

To me, a magnum is a kind of gun or a 1½-litre champagne bottle, one grand is $1,000 or a concert piano, zen is a school of Buddhism, elf is the name of a curious mythological being or a mischievous child, and deck is what you call the platform of a ship, a pack of playing cards or a device for playing tapes. I think those words are already too meaning-crowded to try to cram new meanings into them.

What do nine and two have to do with each other? Oh, I remember now: 9 equals 3 plus 3 times 2, how easy. <_<

The current million/billion/etc. system for naming the decimal powers is unsatisfactory to say the least, with no obvious way to connect the names with the digits in the power; apart from a complete chaos due to the short/long-scale discrepancies. IMHO, the least desirable thing would be a dozenal imitation of such a lame system, especially when dozenal lends itself easily to a much more coherent naming scheme of the following kind:

(Note: Do not care about the made-up names used in this post, they are mere placeholders to illustrate the scheme, not an actual naming proposal)

Basic set
Numbers up to *10^10 (~ decimal 9 billion/trillion); numbers above this order of magnitude are very rarely used, as Endi has already pointed out.

3-digit style

*10^1 = *10 = dozen
*10^2 = *100 = dundred
*10^3 = *1,000 = douzand

*10^4 = *10,000 = dozen douzand
*10^5 = *100,000 = dundred douzand
*10^6 = *1,000,000 = dozillion

*10^7 = *10,000,000 = dozen dozillion
*10^8 = *100,000,000 = dundred dozillion
*10^9 = *1,000,000,000 = dozilliard

*10^A = *10,000,000,000 = dozen dozilliard
*10^B = *100,000,000,000 = dundred dozilliard
*10^10 = *1,000,000,000,000 = doogol

4-digit style

*10^1 = *10 = dozen
*10^2 = *100 = dundred
*10^3 = *1000 = douzand
*10^4 = *1,0000 = dozyriad

*10^5 = *10,0000 = dozen dozyriad
*10^6 = *100,0000 = dundred dozyriad
*10^7 = *1000,0000 = douzand dozyriad
*10^8 = *1,0000,0000 = dozyrion

*10^9 = *10,0000,0000 = dozen dozyrion
*10^A = *100,0000,0000 = dundred dozyrion
*10^B = *1000,0000,0000 = douzand dozyrion
*10^10 = *1,0000,0000,0000 = doogol

Examples:

3-digit style
*1,012,345,678,9AB = one doogol, one dozen two dozilliard, three dundred four dozen five dozillion, six dundred seven dozen eight douzand, nine dundred ten dozen eleven

4-digit style
*1,0123,4567,89AB = one doogol, one dundred two dozen three dozyrion, four douzand five dundred six dozen seven dozyriad, eight douzand nine dundred ten dozen eleven

Summing up: dozen (*10^1), dundred (*10^2), douzand (*10^3), dozyriad (*10^4), dozillion (*10^6), dozyrion (*10^8), dozilliard (*10^9), doogol (*10^10) (note again these particular made-up names are here merely as placeholders, not as actual name proposals). Of course, an alternative would be to have individual names for each of those twelve powers; either unique names, or a TGM-prefixes-style scheme deriving names from the digit in the power (something of the kind dozen (*10^1), bidozen (*10^2), tridozen (*10^3), quadridozen (*10^4)...).

By comparison, English has the following names for decimal powers within this "everyday" range: ten (10^1), hundred (10^2), thousand (10^3), myriad (10^4), lakh (10^5), million (10^6), crore (10^7), milliard (10^9), billion (10^9/10^12), trillion (10^12/10^18), with two ambiguous names and no special name for such a relevant decimal quantity as the tenth power of ten (10^10) (though it does have a name for the tenth power of the tenth power of ten, i.e. the googol = 10^100 = (10^10)^10).


Extended set
Quantities too large for everyday life (like the decimal "quadrillion", "decillion", "centillion", etc.).

*10^20 = bidoogol
*10^30 = tridoogol
*10^40 = quadridoogol
...
*10^47 = dozen dozillion quadridoogol (*10^(1+6+40)) = douzand dozyriad quadridoogol (*10^(3+4+40))

Pretty straightforward to name once you've learnt the powers of the basic set.
Unlike their decimal analogues:

10^20 = hundred (short) quintillion (10^(2+3+3×5)) = hundred (long) trillion 10^(2+6×3)
10^30 = (short) nonillion (10^(3+3×9)) = (long) quintillion (10^(6×5))
10^40 = ten (short) duodecillion (10^(1+3+3×12)) = ten thousand (long) sextillion / ten sextilliard (10^(1+3+6×6))
...
10^47 = hundred (short) quattuordecillion (10^(2+3+3×14)) = hundred thousand (long) septillion / hundred septilliard (10^(2+3+6×7))

The crazy nomenclature for the decimal zillions could be simplified a lot, if only there was a name for 10^10. <_<

Trillion, not quadrillion.

I said

Dan said

I think Dan's right, I don't know where I got that quadrillion figure. It was off the internet somewhere. I think that they are using the short scale in this link:
http://www.globalpolicy.org/globaliz/chart...adepertable.htm

I quite like uaxuctum's naming system.

Good work, uaxuctum!

Your system is the best and most logical one so far. I like your names dozyriad, dozillion, dozyrion, and dozilliard very much, but would keep the gross and great gross, which have already been in use.
Hmm, doogol is related to the googol, of course. I think it sounds a bit strange... don't know, but I currently have no better idea.

I would like to have names for *10^5, *10^7, *10^:A ... as well, but they are not too important.

Only problem is: how would you abbreviate them?

I clarified those names were merely intended as placeholders, not as actual naming proposals.

However, it wouldn't be difficult to abbreviate them: zyriad, zillion, zyrion and zilliard. In fact, these would be my actual naming proposals. The word "zillion" already exists, but the proposal would only add the specific meaning of *10^6 to its more general meaning of "very large number" (just like "million" can refer to 10^6 or to an indefinite very large quantity).

that's only because i couldn't find a URL to a swedish morse code image :-(

but i can write it out manually ;-)

A · —
B — · · ·
C — · — ·
D — · ·
E ·
F · · — ·
G — — ·
H · · · ·
I · ·
J · — — —
K — · —
L · — · ·
M — —
N — ·
O — — —
P · — — ·
Q — — · —
R · — ·
S · · ·
T —
U · · —
V · · · —
W · — —
X — · · —
Y — · — —
Z — — · ·
Å · — — · —
Ä · — · —
Ö — — — ·

yes, but then you said...

so i had to write something just as punitive :-P

it's not supposed to be in phonetic order %-/
i wrote that it's in alphabetical order
hello, is this thing on??.....testing! testing! 1-2-3


Brits these daze, what are they like! <_<

Just an idea, with two alternatives for each section. I've included the decimal nomenclature for comparison. The -don/ton ending is meant to be pronounced dun/tun (a reduced form from "dozen" duzen > "dozn" duzn > "-don" dun); an additional alternative would be to spell it just like that: -dun/tun (onedun, twidun, fourdun, fiftun, sixtun, sevendun, eightun, ninedun, tendun, elevendun). Both -don/ton and the -doon/toon alternative ending (a reduced form with vowel umlaut, similar to "teen" from "ten"), are meant to carry the primary stress (just like the -teen ending). The endings -da (pronounced as unstressed duh) and -do (pronounced the same as -da when completely unstressed, or as doh with a secondary stress), are, of course, even more reduced forms of "dozen", up to nasal-dropping (just like -ty, reduced from "ten", drops the nasal). The d/t alternation is merely due to consonant harmony (voiced -d gets devoiced into -t when following a voiceless consonant; similarly, the -d in "liked" is actually pronounced -t, even though the orthography doesn't show the change in this case).

The guiding principle is to maintain a certain degree of familiarity and to introduce the fewest changes. This is to reduce the inconvenience of switching to dozenal nomenclature. The more dissimilar to current decimal nomenclature, the more likely it is to be perceived as an alienating invention and to raise opposition and dislike. Therefore, as the maxim goes, in dubio pro traditione. The same principle works for dozenal digits and other mathematical symbols: the current digits from 0 to 9 should be kept, just like +, %, etc. (there's no need to change them, and a whole new set of digits would only make the switch unnecessarily traumatic); and the less digit-like the new digits (i.e. the less similar in shape to existent digits), the more they are likely to be disliked or perceived as "not looking like digits" (the asterisk and hash being a prime example of really bad choices).

I think I've had a better idea for the dozenal teens: end them in -tween (portmanteau of twelve and teen). This way they sound more natural and allow for easy analogues of "a teenager" and "in one's teens": a tweenager and in one's tweens. For the dozens, I'd favour the -do ending over -da because it makes the ordinals look more natural. So summing up:

All due respect, but this is just an exercise in conlanging and I don't know why people keep doing this. The general trend over time is for languages to become more isolating and you want to introduce new suffixes. Stick to words, they are easier. What's wrong with the word "dozen"?
(a/one) dozen (and) one,
(a/one) dozen (and) two,
(a/one) dozen (and) three
.
.
.
(a/one) dozen (and) nine
(a/one) dozen (and) ten
(a/one) dozen (and) eleven
two dozen
two dozen (and) one
two dozen (and) two
two dozen (and) three
.
.
.
ten dozen
.
.
.
ten dozen (and) eleven
.
.
.
eleven dozen (and) five
etc.

Words in parentheses represent optional words just as now (a/one) is optional before "hundred", and British, Irish and Antipodean people tend to say the "and" in hundred and twenty four (usually reduced to 'n'), whereas Americans and Canadians don't.

It's only the higher numbers that we need to wory about.

For the very same reason why people keep "conlanging" everytime a new concept needs to be named, or everytime a previously rare concept becomes common and needs to be named succintly, which is happening almost everyday. Why did they "conlang" that word laser for what could have been named coherent light, or the very words conlang for constructed language and dozenal for duodecimal? Following your logic strictly, we shouldn't "conlang" any new word to fill the gaps of English dozenal nomenclature, not even for the big numbers, and instead stick with expressions like duodecimal million, duodecimal billion, etc. The natural corollary would be that we shouldn't invent new digits either, nor anything; just stick with existent things, because anything else would be just that: inventing. The whole idea of introducing dozenal numeration and dozenal arithmetic into the world at large, and into Western societies in particular, may be called an exercise in "connumbering", as long as no language or culture, except for a few isolated cases in Africa, has developed it "naturally". Even if many measures were twelve-based, the numbering and the arithmetic was performed in decimal, and that's precisely why a full-fledged dozenal nomenclature hasn't evolved in English.

Nothing wrong, nobody talked about abandoning the word dozen. But frequently used expressions are doomed to erode over time, just like two pence came to be pronounced tuppence, have not fused into haven't, etc. That's a natural part of how languages behave and evolve, and that's how the words twenty, thirty, etc. came into existence in the first place.

All due respect, this is simply not true. Why do people keep spreading this myth? Languages keep moving through a neverending cycle from isolation to agglutination to inflection back to isolation and start again. Chinese, after having been almost thoroughly a monosyllablic isolating language during its classical period, is moving back into agglutinating and inflecting. Nowadays Mandarin is already a mostly bisyllabic language with several morphemes behaving as suffixes that were previously independent words. Let alone Shanghainese, which has become a full-fledged polysyllabic inflecting language already, having even lost its tonal character to become a pitch-accent language (like Japanese, Ancient Greek and Swedish). In English, contractions like aren't, won't, etc. are an obvious step back into inflection, and new suffixes pop up from time to time (just think of the -gate craze: Watergate > Monicagate, Nipplegate, Katrinagate, Wiregate...). You can't expect people to keep lengthy common phrases like are not going to unaltered forever; time will erode them into shorter forms (aren't gonna), eventually leading back to agglutination and inflection (there's an interesting conlanging experiment about what might have become of English one thousand years from now, based on trends that are already present in today's English and on how the Old English of a thousand years ago morphed drastically into modern English; see here). Not to talk about what's happening in French, where things like je t'ai dit are actually pronounced as a single word (shteh-DEE), effectively becoming a single complex inflected verb form, after spoken French had lost most of the verbal inflections inherited from Latin. Spanish lost the Latin forms of the future and conditional, but has modernly developed its own forms from a phrasal construction of infinitive+haber: ser he (I have to be) > seré (I will be), ser h[ab]ía (I had to be) > sería (I would be), and the second person formal pronoun usted developed during the past centuries from the erosion of the phrase vuestra merced "your mercy" (its progressive morphing through various intermediate forms, like vuesarced, vuested and the like, is extensively documented, as well as for the analogous developments from vuestra señoría into usía and vuestra excelencia into vuecencia).

:o Uaxuctum, when I re-read my thread, I saw that it was extremely rude, "with all due respect" mmm - I didn't show much of that. I didn't have a lot of time, and should have waited until I did to reply to a thread that I disagreed with, my appologies if I appeared over-terse. I also think that you may well be right when you say that languages cycle through being isolating, agglutinating and inflected rather than necessarily going in one direction. There are simplifying trends and complicating trends. We can see different evolutionary trends within different languages although it is a mute point as to whether any language has yet time to go through any one complete cycle. I had already seen the link you showed me, by the way :D.

I have to say, however, that I still don't like these or indeed any cardinal number suffixes for numbers between twelve and two dozen, or for multiples of one dozen under a gross.

One thing against them is something called parallellism. I am going to appear to go a bit off the point but bare with me, I will come back. This from grammar mudge:
http://www.grammarmudge.cityslide.com/arti...426348/5588.htm

Parallism also exists in (but is sometimes absent from) language itself. It could be argued, for instance, that the irregular verbs of English are a sort of non-parallelism, and accordingly, auxiliary language designers strive hard to eliminate them.

The numbers in English are not parallel.

We count from one to ten but the suffix "-teen" only starts to be used at thirteen leaving eleven and twelve with non-parallel constructions. Then we have a suffix to indicate single powers of ten "-ty" before going to words to indicate the second and third powers of ten - "hundred" and "thousand". Million, the sixth power of ten is a word, too. English almost exclusively uses the short scale for higher numbers so the each additional third power after a million is indicated by a word derrived from a latin numerical prefix and the suffix -illion, which was derrived from "million". "Million", itself then, is not parallel as it comes ultimately from Italian "millione" (now milione), literally "a great thousand," mille, of course means a thousand in both Italian and Latin. Anyway, after a billion, the numbers finally become parallel.

Now the great thing about the word dozen is by using it, we have the chance to make the number names parallel. You would like to introduce a suffix for numbers between a dozen and two dozen well that makes it more parallel than English, and another for single powers of a dozen. OK, just as parallel in English, but then remember the second power of a dozen is a gross - a word not a suffix. "Great gross" is not parallel, and I like the term "grande" for this reason. By retaining the word "dozen" to talk about all numbers between twelve and a gross, everything becomes wonderfully parallel again.

To conclude, I am not against neogalisms or conlangs; or you for that matter, Uaxuctum :D, indeed I have found many of your posts thought-provoking and interesting but to take your example of the laser, the word was invented to serve a need. In fact, a laser, refers to the machine that produces coherent light, although by back-formation, the machine can be said "to lase". Your suffixes, however, do not fulfill a need and I sorry, but I really think this, try to replicate an already defective structure from English, and do so in a somewhat awkward way.

Tisk tisk tisk. No kind of language is more or less complicated than any other. Synthetic inflexional languages are not more complicated than isolating analytic ones (morphologically they may well be, but what about syntactically, for example?)

And to be perfectly frank, I'm not sure I follow your comments on parallelism. What difference does it make if the number system is "parallel" or not? It hasn't been "parallel" for thousands of years. I don't think it makes any difference, to be honest. :)