There are 8 messages in this issue.
Topics in this digest:
1a. Re: Do people ever make variant numerical systems for non-primitive
From: Петр Кларк
1b. Re: Do people ever make variant numerical systems for non-primitive
From: MorphemeAddict
1c. Re: Do people ever make variant numerical systems for non-primitive
From: Alex Fink
2a. Re: Online Moten Dictionary
From: MorphemeAddict
2b. Re: Online Moten Dictionary
From: Roger Mills
2c. Re: Online Moten Dictionary
From: Christophe Grandsire-Koevoets
3a. Re: OT: Math with roman numerals (Was: Do people ever make variant n
From: R A Brown
3b. Re: OT: Math with roman numerals (Was: Do people ever make variant n
From: A. da Mek
Messages
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1a. Re: Do people ever make variant numerical systems for non-primitive
Posted by: "Петр Кларк" [email protected]
Date: Tue Mar 5, 2013 9:23 pm ((PST))
On Monday, 04 March 2013 20:44:20 you wrote:
> I haven't looked at all that many systems. Do people ever make clunky,
> irrational, and old-fashioned systems like the Roman numerals? Or are the
> purposes of number systems so practical that most conlangers have no
> interest in making such a complex (no, baroque) method for doing math?
> Most other aspects of conlangs seem to be deliberately elaborated and
> intricate, reflecting how much weirdness is out there and how the
> complexity of a language isn't related to how materially-advanced its
> society is. But historically, most peoples had very basic math skills.
The Enamyn numbering system is based on Greek numerals
(which were actually Greek letters -- see more at
http://en.wikipedia.org/wiki/Greek_numerals), but since the Enamyn numbering
system is octal (1-8, no zero), some Greek numerals were not used:
α = 1 ι = o 11 (d 9) ρ = o 111 (d 73)
β = 2 κ = o 21 (d 17) σ = o 211 (d 137)
γ = 3 λ = o 31 (d 25) τ = o 311 (d 201)
δ = 4 μ = o 41 (d 33) υ = o 411 (d 265)
ε = 5 ν = o 51 (d 41) φ = o 511 (d 329)
ϛ = 6 ξ = o 61 (d 49) χ = o 611 (d 393)
ζ = 7 ο = o 71 (d 57) ψ = o 711 (d 457)
η = 8 π = o 81 (d 65) ω = o 811 (d 521)
Obviously, the values after η differ from their Greek counterparts, which is
likely why the numbering system switched to Enamyn letters in the late fifth
century AD, when the written language switched from Greek letters to a newly
formulated native script which was a significant improvement over the Greek
alphabet.
Side note: I'm aware that this is a really *odd* way of counting, and
I'm
wondering if it's just a little too weird. I know that there are some cultures
that count with base-8, but this way of counting seems pretty unique.
Comments?
Oh, and if you're interested, here's the Python code that will convert
from decimal to octal, Enamyn-style:
def ash(n):
n = int(n) - 1
if n >= 0:
return str(ash(n / 8)) + str((n % 8) + 1)
else: return ""
In case you're wondering, "ash" means "eight".
:Peter
Messages in this topic (17)
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1b. Re: Do people ever make variant numerical systems for non-primitive
Posted by: "MorphemeAddict" [email protected]
Date: Tue Mar 5, 2013 9:33 pm ((PST))
What is the largest number you can write in this system, and how do you
write numerals greater than that?
stevo
On Tue, Mar 5, 2013 at 10:50 PM, Петр Кларк <[email protected]> wrote:
> On Monday, 04 March 2013 20:44:20 you wrote:
> > I haven't looked at all that many systems. Do people ever make clunky,
> > irrational, and old-fashioned systems like the Roman numerals? Or are
> the
> > purposes of number systems so practical that most conlangers have no
> > interest in making such a complex (no, baroque) method for doing math?
> > Most other aspects of conlangs seem to be deliberately elaborated and
> > intricate, reflecting how much weirdness is out there and how the
> > complexity of a language isn't related to how materially-advanced its
> > society is. But historically, most peoples had very basic math skills.
>
> The Enamyn numbering system is based on Greek numerals
> (which were actually Greek letters -- see more at
> http://en.wikipedia.org/wiki/Greek_numerals), but since the Enamyn
> numbering
> system is octal (1-8, no zero), some Greek numerals were not used:
>
> α = 1 ι = o 11 (d 9) ρ = o 111 (d 73)
> β = 2 κ = o 21 (d 17) σ = o 211 (d 137)
> γ = 3 λ = o 31 (d 25) τ = o 311 (d 201)
> δ = 4 μ = o 41 (d 33) υ = o 411 (d 265)
> ε = 5 ν = o 51 (d 41) φ = o 511 (d 329)
> ϛ = 6 ξ = o 61 (d 49) χ = o 611 (d 393)
> ζ = 7 ο = o 71 (d 57) ψ = o 711 (d 457)
> η = 8 π = o 81 (d 65) ω = o 811 (d 521)
>
> Obviously, the values after η differ from their Greek counterparts, which
> is
> likely why the numbering system switched to Enamyn letters in the late
> fifth
> century AD, when the written language switched from Greek letters to a
> newly
> formulated native script which was a significant improvement over the Greek
> alphabet.
> Side note: I'm aware that this is a really *odd* way of counting,
> and I'm
> wondering if it's just a little too weird. I know that there are some
> cultures
> that count with base-8, but this way of counting seems pretty unique.
> Comments?
> Oh, and if you're interested, here's the Python code that will
> convert
> from decimal to octal, Enamyn-style:
>
> def ash(n):
> n = int(n) - 1
> if n >= 0:
> return str(ash(n / 8)) + str((n % 8) + 1)
> else: return ""
>
> In case you're wondering, "ash" means "eight".
> :Peter
>
Messages in this topic (17)
________________________________________________________________________
1c. Re: Do people ever make variant numerical systems for non-primitive
Posted by: "Alex Fink" [email protected]
Date: Tue Mar 5, 2013 9:45 pm ((PST))
On Tue, 5 Mar 2013 22:50:22 -0500, Петр Кларк <[email protected]> wrote:
>On Monday, 04 March 2013 20:44:20 you wrote:
>> I haven't looked at all that many systems. Do people ever make clunky,
>> irrational, and old-fashioned systems like the Roman numerals? Or are the
>> purposes of number systems so practical that most conlangers have no
>> interest in making such a complex (no, baroque) method for doing math?
>> Most other aspects of conlangs seem to be deliberately elaborated and
>> intricate, reflecting how much weirdness is out there and how the
>> complexity of a language isn't related to how materially-advanced its
>> society is. But historically, most peoples had very basic math skills.
>
> The Enamyn numbering system is based on Greek numerals
>(which were actually Greek letters -- see more at
>http://en.wikipedia.org/wiki/Greek_numerals), but since the Enamyn numbering
>system is octal (1-8, no zero), some Greek numerals were not used:
>
>α = 1 ι = o 11 (d 9) ρ = o 111 (d 73)
>β = 2 κ = o 21 (d 17) σ = o 211 (d 137)
>γ = 3 λ = o 31 (d 25) τ = o 311 (d 201)
>δ = 4 μ = o 41 (d 33) υ = o 411 (d 265)
>ε = 5 ν = o 51 (d 41) φ = o 511 (d 329)
>ϛ = 6 ξ = o 61 (d 49) χ = o 611 (d 393)
>ζ = 7 ο = o 71 (d 57) ψ = o 711 (d 457)
>η = 8 π = o 81 (d 65) ω = o 811 (d 521)
I think a more germane question is this: how do you write numbers using this
system if they don't end in a bunch of ones?
The actual Greek system gets to make straightforward use of addition: if you
wish to write 438, well, υ 400 and λ 30 and η 8 appear in the table, and you
catenate them to add and get υλη 438.
But in your system, say I want to write the octal number 438 (= decimal 288).
Do I still write υλη, even though there's no arthmetic sense in which υ means
411 and λ means 31 here? Do I decompose it as 411 + 21 + 6 and write υκϛ, even
though that's not parallel to your expression 438 for it in Arabic digits?
Alex
Messages in this topic (17)
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________________________________________________________________________
2a. Re: Online Moten Dictionary
Posted by: "MorphemeAddict" [email protected]
Date: Tue Mar 5, 2013 9:52 pm ((PST))
On Tue, Mar 5, 2013 at 10:22 PM, Roger Mills <[email protected]> wrote:
> Very interesting. I haven't followed the development of the lang. very
> closely, so from my POV it would have helped to have some slight
> pronunciation guide, particularly of the "|" character, also of "j", which
> I gather is IPA [j] not [dZ], and anything else that might depart from
> "standard" or IPA value. .... Perhaps more important, a list of the
> abbreviations used, e.g. Cpart, sim. and others that aren't immediately
> obvious (but even the obvious ones should be included)..
>
+1
stevo
>
> I know that sort of stuff is scut-work, but needed for complete usability
> without having to hunt hither-and-yon in other online places.
> Roger
>
> --- On Tue, 3/5/13, Christophe Grandsire-Koevoets <[email protected]>
> wrote:
>
> From: Christophe Grandsire-Koevoets <[email protected]>
> Subject: Online Moten Dictionary
> To: [email protected]
> Date: Tuesday, March 5, 2013, 11:33 AM
>
> Hi everyone,
>
> I've been working hard on revising my personal Moten dictionary (in Toolbox
> format) in order to be able to export it in a format readable by others. I
> finally finished and uploaded the resulting PDF in Google Drive. It's
> available with the following link:
>
> https://docs.google.com/file/d/0B4Ba74aEwr57bVQ2V2QtbnJNSk0/edit?usp=sharing
>
> In principle it's set up so that anyone with the link can view (and I think
> also download) the document, but I'd like to hear from others whether
> that's correct.
>
> The document itself is a plain PDF file, without fancy things like
> hyperlinks or anything similar. It's basically the output of the Export
> function of Toolbox, with only minimal post-processing from me (which I
> unfortunately had to do in Microsoft Word, given that's the expectation
> from Toolbox). In the future when I update this document, I will try to see
> whether I can add hyperlinks, but for now you'll have to make do with plain
> browsing and the search function of your PDF viewer.
>
> The dictionary itself is composed of two parts. The first one is the full
> (including morphemes) Moten-English dictionary, with Moten words arranged
> by stem rather than citation form (makes hardly any difference for nouns,
> but at least this way verbs are next to related words rather than
> clustering under the _i_ and _j_ entries :P). I've tried to be exhaustive
> in the definitions, and added all kinds of comments and information like
> words of similar meaning, synonyms and antonyms, counterparts, etc. so that
> the semantics of each entry becomes clear (and to prove that the Moten
> vocabulary isn't just a relex of English and French, hopefully :P).
> The second part is an English-Moten word list, with simple English entries
> and the various Moten stems that cover them. No definitions there, but the
> corresponding Moten glosses include part of speech and sense number in the
> Moten-English dictionary. The idea, naturally, is to look for the
> equivalent of an English word in that list, and then check the
> Moten-English dictionary to see the actual semantic range of that
> equivalent. I know it's unpractical without hyperlinks, which is why I'll
> try to add them in a future version.
>
> Naturally, the dictionary is far from complete (446 entries in the
> Moten-English side, 890 entries in the English-Moten side), but I'd still
> love to get feedback from it. Is it readable, is it understandable, are
> there mistakes in it I missed? Is there anything you'd like to see in it
> that's missing? Comments on the semantics of Moten words are also more than
> welcome :) . Do the semantic ranges make sense, do I need to add some
> explanation somewhere?
>
> BTW, there is no pronunciation guide in this document, and I've put
> phonetic transcriptions only for some onomatopoeia whose pronunciations
> don't follow normal Moten phonology. But you can find a complete
> description of Moten pronunciation in the following link:
>
> http://christophoronomicon.blogspot.co.uk/2009/12/moten-part-i-background-and-phonology.html
>
> So, what do you think?
> --
> Christophe Grandsire-Koevoets.
>
> http://christophoronomicon.blogspot.com/
> http://www.christophoronomicon.nl/
>
Messages in this topic (4)
________________________________________________________________________
2b. Re: Online Moten Dictionary
Posted by: "Roger Mills" [email protected]
Date: Tue Mar 5, 2013 9:54 pm ((PST))
Very interesting. I haven't followed the development of the lang. very closely,
so from my POV it would have helped to have some slight pronunciation guide,
particularly of the "|" character, also of "j", which I gather is IPA [j] not
[dZ], and anything else that might depart from "standard" or IPA value. ....
Perhaps more important, a list of the abbreviations used, e.g. Cpart, sim. and
others that aren't immediately obvious (but even the obvious ones should be
included)..
I know that sort of stuff is scut-work, but needed for complete usability
without having to hunt hither-and-yon in other online places.
Roger
--- On Tue, 3/5/13, Christophe Grandsire-Koevoets <[email protected]> wrote:
From: Christophe Grandsire-Koevoets <[email protected]>
Subject: Online Moten Dictionary
To: [email protected]
Date: Tuesday, March 5, 2013, 11:33 AM
Hi everyone,
I've been working hard on revising my personal Moten dictionary (in Toolbox
format) in order to be able to export it in a format readable by others. I
finally finished and uploaded the resulting PDF in Google Drive. It's
available with the following link:
https://docs.google.com/file/d/0B4Ba74aEwr57bVQ2V2QtbnJNSk0/edit?usp=sharing
In principle it's set up so that anyone with the link can view (and I think
also download) the document, but I'd like to hear from others whether
that's correct.
The document itself is a plain PDF file, without fancy things like
hyperlinks or anything similar. It's basically the output of the Export
function of Toolbox, with only minimal post-processing from me (which I
unfortunately had to do in Microsoft Word, given that's the expectation
from Toolbox). In the future when I update this document, I will try to see
whether I can add hyperlinks, but for now you'll have to make do with plain
browsing and the search function of your PDF viewer.
The dictionary itself is composed of two parts. The first one is the full
(including morphemes) Moten-English dictionary, with Moten words arranged
by stem rather than citation form (makes hardly any difference for nouns,
but at least this way verbs are next to related words rather than
clustering under the _i_ and _j_ entries :P). I've tried to be exhaustive
in the definitions, and added all kinds of comments and information like
words of similar meaning, synonyms and antonyms, counterparts, etc. so that
the semantics of each entry becomes clear (and to prove that the Moten
vocabulary isn't just a relex of English and French, hopefully :P).
The second part is an English-Moten word list, with simple English entries
and the various Moten stems that cover them. No definitions there, but the
corresponding Moten glosses include part of speech and sense number in the
Moten-English dictionary. The idea, naturally, is to look for the
equivalent of an English word in that list, and then check the
Moten-English dictionary to see the actual semantic range of that
equivalent. I know it's unpractical without hyperlinks, which is why I'll
try to add them in a future version.
Naturally, the dictionary is far from complete (446 entries in the
Moten-English side, 890 entries in the English-Moten side), but I'd still
love to get feedback from it. Is it readable, is it understandable, are
there mistakes in it I missed? Is there anything you'd like to see in it
that's missing? Comments on the semantics of Moten words are also more than
welcome :) . Do the semantic ranges make sense, do I need to add some
explanation somewhere?
BTW, there is no pronunciation guide in this document, and I've put
phonetic transcriptions only for some onomatopoeia whose pronunciations
don't follow normal Moten phonology. But you can find a complete
description of Moten pronunciation in the following link:
http://christophoronomicon.blogspot.co.uk/2009/12/moten-part-i-background-and-phonology.html
So, what do you think?
--
Christophe Grandsire-Koevoets.
http://christophoronomicon.blogspot.com/
http://www.christophoronomicon.nl/
Messages in this topic (4)
________________________________________________________________________
2c. Re: Online Moten Dictionary
Posted by: "Christophe Grandsire-Koevoets" [email protected]
Date: Tue Mar 5, 2013 11:31 pm ((PST))
On 6 March 2013 04:22, Roger Mills <[email protected]> wrote:
> Very interesting. I haven't followed the development of the lang. very
> closely, so from my POV it would have helped to have some slight
> pronunciation guide, particularly of the "|" character, also of "j", which
> I gather is IPA [j] not [dZ], and anything else that might depart from
> "standard" or IPA value.
I actually did give a link to the pronunciation guide in my e-mail. It's at
http://christophoronomicon.blogspot.co.uk/2009/12/moten-part-i-background-and-phonology.html:)
. I'm planning to add a pronunciation guide to the document itself,
but
for that I need to streamline the post-processing stuff first, as it's
currently completely manual, and I cannot see myself re-writing the guide
each time I create a new version :) . And I wanted to have a version of the
document out as quickly as possible to see whether everyone could access it
correctly, before I started working on more complex things like that :) .
Anyway, the Moten script is a romanisation rather than a native script
(even within the fiction where the language actually exists), so it's very
phonemic. All letters have their IPA values (barring allophony), except the
four special letters _|l_, _|n_, _|s_ and _|z_ (| isn't a separate
character). Those are respectively /ʎ/, /ɲ/, /ts/ and /dz/ (the last two
are affricates, not clusters). Allophony does change things a bit, but
there's luckily not much of it in Moten.
> .... Perhaps more important, a list of the abbreviations used, e.g. Cpart,
> sim. and others that aren't immediately obvious (but even the obvious ones
> should be included)..
>
You're very right about that, and I'll try to add it in the next version :)
. Here again the issue is about how to streamline the process. Right now
getting the document out in the shape it currently has took me nearly a
whole afternoon, and as you've noticed it's lacking in many ways. I need to
look at a way to streamline that process before I can start adding things
to it.
I'm also a bit unhappy that the process requires me to use Word at the
moment. I wonder whether there's any Toolbox MDF-to-(Xe)LaTeX converter out
there...
>
> I know that sort of stuff is scut-work, but needed for complete usability
> without having to hunt hither-and-yon in other online places.
>
You're right of course, and thanks for pointing it out. I'll see what I can
do for the next version, which should be out by the time the next
instalment of the Moten grammar is ready. Right now, I'm just happy that
you could access the document and read enough of it to notice all these
issues :) .
Cheers,
--
Christophe Grandsire-Koevoets.
http://christophoronomicon.blogspot.com/
http://www.christophoronomicon.nl/
Messages in this topic (4)
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________________________________________________________________________
3a. Re: OT: Math with roman numerals (Was: Do people ever make variant n
Posted by: "R A Brown" [email protected]
Date: Wed Mar 6, 2013 12:00 am ((PST))
On 05/03/2013 21:14, James Kane wrote:
> I think I read somewhere that the subtraction thing, eg
> XL for forty, is in fact a later invention
Basically, correct.
> and the Romans themselves were quite happy to have four
> I's or four V's in a row.
Four Xs that should be. You will never have four Vs in a row.
> Would this make the maths easier?
Yes, IMO.
When I played with doing math(s) using Roman numerals, the
first step I did was to change the post-Roman subtractions.
The system seems to have developed from what we find on
funeral inscriptions where, e.g. IIXXX = duodetriginta =
two-from-thirty, i.e. 28.
From 18, 19 until we reach the hundreds the +8 or +9
numerals were designated in the spoken language a "duode-"
and "unde-" respectively, i.e.
duodeviginti = 18
undeviginti = 19
duodetriginta = 28
undequadraginta = 39
etc.
I suspect, however, that when doing math(s) this was not
done. At any rate, AFAIK 'four' was always written as IIII
in the Classical period, and 'forty' as XXXX etc.
========================================================
On 05/03/2013 21:45, Gary Shannon wrote:
> If you require permitting four symbols in a row and
> forbid subtractive symbols then Roman numbers could be
> rewritten as positional notation like this:
>
> MMDCXXXXIII -> 02 11 04 03 where each two-digit group
> represents a 5's and units digit for the next power of
> ten.
>
> In other words, the rightmost digit of each group is
> base 5 (M, C, X, I) and the leftmost digit is base two
> (V, D, L, V), and the groups are base ten. (I..VIIII,
> X..LXXXX, C..DCCCC, M..VMMMM).
Exactly! That's the way the old Roman abacus worked. The
system is bi-quinary.
PS - I think I referred to the abacus as 'calculus' in an
earlier email. 'Twas an error. Of course the thing was an
'abacus', and _calculi_ ("pebbles") were use as counters.
Hence the verb _calculāre_ = "to calculate", and the nouns:
_calculātor_ = "one who calculates" or "a teacher of arithmetic"
calculō (gen: calculōnis) = "an accountant"
--
Ray
==================================
http://www.carolandray.plus.com
==================================
"language … began with half-musical unanalysed expressions
for individual beings and events."
[Otto Jespersen, Progress in Language, 1895]
Messages in this topic (5)
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3b. Re: OT: Math with roman numerals (Was: Do people ever make variant n
Posted by: "A. da Mek" [email protected]
Date: Wed Mar 6, 2013 3:38 am ((PST))
> From 18, 19 until we reach the hundreds the +8 or +9
numerals were designated in the spoken language a "duode-"
and "unde-" respectively, i.e.
duodeviginti = 18
undeviginti = 19
duodetriginta = 28
undequadraginta = 39
etc.
This may be a remnant of a change from octal to decimal system.
Similarly, a duodecimal system could be expressed using only decimal digits:
10[A] = A = twofrom dozen = IIЖ
11[A] = B = onefrom dozen = IЖ
12[A] =10[C] = dozen = Ж
13[A] = 11[C] = dozen one = ЖI
...
21[A] = 19[C] = dozen nine = ЖΨIII
22[A] = 1A[C] = twofrom twodozen = IIЖЖ
23[A] = 1B[C] = onefrom twodozen = IЖЖ
24[A] = 20[C] = twodozen = ЖЖ
25[A] = 21[C] = twodozen one =ЖЖI
Or a duodecimal system expressed using only octal digits:
8 = foufrom dozen = IIIIЖ
9 = threefrom dozen = IIIЖ
10[A] = A = twofrom dozen = IIЖ
11[A] = B = onefrom dozen = IЖ
12[A] =10[C] = dozen = Ж
13[A] = 11[C] = dozen one = ЖI
...
19[A] = 17[C] = dozen seven = ЖΨI
20[A] = 18[C] = fourfrom twodozen = IIIIЖ
21[A] = 19[C] = threefrom twodozen = IIIЖ
22[A] = 1A[C] = twofrom twodozen = IIЖ
23[A] = 1B[C] = onefrom twodozen = IЖ
24[A] = 20[C] = twodozen = IЖ
25[A] = 21[C] = twodozen one = ЖI
> I suspect, however, that when doing math(s) this was not
done.
It is essentially a system with digits -2 to 7 instead of usuall 0 to 9.
The algorithms for countig with negative digits are the same as the usual;
in both cases the last step is a normalisation of the number.
(1)(9) + (2)(8) = (3)(17) = (4)(7)
XVIIII + XXVIII = XXXVVIIIIIII = XXXXVII
(2)(-1) + (3)(-2) = (5)(-3) = (4)(7)
IXX + IIXXX = IIIXXXXX = XXXXVII
Messages in this topic (5)
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