There are 5 messages in this issue.
Topics in this digest:
1a. Re: Do people ever make variant numerical systems for non-primitive
From: R A Brown
1b. Re: Do people ever make variant numerical systems for non-primitive
From: MorphemeAddict
2. Of Elves and Mountains (Hesperic etymologies)
From: Jörg Rhiemeier
3a. Re: OT: Math with roman numerals (Was: Do people ever make variant n
From: James Kane
3b. Re: OT: Math with roman numerals (Was: Do people ever make variant n
From: Gary Shannon
Messages
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1a. Re: Do people ever make variant numerical systems for non-primitive
Posted by: "R A Brown" [email protected]
Date: Tue Mar 5, 2013 11:55 am ((PST))
On 05/03/2013 14:43, Daniel Myers wrote:
>> -------- Original Message -------- From: Leonardo
>> Castro Date: Tue, March 05, 2013 6:52 am
[snip]
>>
>> I once affirmed that to a friend and he told me "Let's
>> check!" and started trying to make basic operations
>> with Roman numerals. To my surprise, he succeeded! He
>> succeeded and said: "It's not that difficult...". I
>> watched he performing the operations while analyzing
>> developing the methods himself and it really didn't
>> looked very difficult.
I tried this very many years ago. Certainly addition and
subtraction are not exactly difficult. Multiplication was
also not difficult, just tedious. I could find no
convenient way, however, of doing division, except, of
course, by repeated subtraction. It sounds as tho your
friend probably made a better job of division that I did ;)
>> I don't have time to repeat what he did now, but I
>> challenge you do so.
>
> Agreed. Also, tools were developed to facilitate math
> with Roman numbers - the medieval counting board in
> particular was very successful.
As, indeed, was the old Roman calculus.
> Having used one I can tell you that (with a bit of
> practice) arithmetic computation becomes almost trivial.
Yep.
> There's a good paper describing them and their use here:
> http://www.amatyc.org/publications/Electronic-proceedings/2005SanDiego/Bell.pdf
>
> As long as a society doesn't have a need for calculus,
> they could get along just fine without a decimal number
> system.
The ancient Greeks managed famously just using the letters
of their alphabet, including a couple of obsolete ones.
--
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 (14)
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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 12:13 pm ((PST))
On Tue, Mar 5, 2013 at 2:55 PM, R A Brown <[email protected]> wrote:
> On 05/03/2013 14:43, Daniel Myers wrote:
>
>> -------- Original Message -------- From: Leonardo
>>> Castro Date: Tue, March 05, 2013 6:52 am
>>>
>> [snip]
>
>
>>> I once affirmed that to a friend and he told me "Let's
>>> check!" and started trying to make basic operations
>>> with Roman numerals. To my surprise, he succeeded! He
>>> succeeded and said: "It's not that difficult...". I
>>> watched he performing the operations while analyzing
>>> developing the methods himself and it really didn't
>>> looked very difficult.
>>>
>>
> I tried this very many years ago. Certainly addition and
> subtraction are not exactly difficult. Multiplication was
> also not difficult, just tedious. I could find no
> convenient way, however, of doing division, except, of
> course, by repeated subtraction.
Repeated division by 2, then adding the answers that were even, should
work. (I think.)
Perhaps less tedious than simple repeated subtraction.
Is there any equivalent to the 'law of nines' with Roman numerals?
stevo
> It sounds as tho your
> friend probably made a better job of division that I did ;)
>
>
> I don't have time to repeat what he did now, but I
>>> challenge you do so.
>>>
>>
>> Agreed. Also, tools were developed to facilitate math
>> with Roman numbers - the medieval counting board in
>> particular was very successful.
>>
>
> As, indeed, was the old Roman calculus.
>
>
> Having used one I can tell you that (with a bit of
>> practice) arithmetic computation becomes almost trivial.
>>
>
> Yep.
>
> There's a good paper describing them and their use here:
>> http://www.amatyc.org/**publications/Electronic-**
>> proceedings/2005SanDiego/Bell.**pdf<http://www.amatyc.org/publications/Electronic-proceedings/2005SanDiego/Bell.pdf>
>>
>> As long as a society doesn't have a need for calculus,
>> they could get along just fine without a decimal number
>> system.
>>
>
> The ancient Greeks managed famously just using the letters
> of their alphabet, including a couple of obsolete ones.
>
>
> --
> Ray
> ==============================**====
> http://www.carolandray.plus.**com <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 (14)
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2. Of Elves and Mountains (Hesperic etymologies)
Posted by: "Jörg Rhiemeier" [email protected]
Date: Tue Mar 5, 2013 12:15 pm ((PST))
Hallo conlangers!
I have a new Hesperic etymological finding to report.
On New Year's Day, I had written:
> Also, Alpianic
> *alp- 'mountain' looks like a regular descendant of PH *xalb-,
> perhaps from the notion that high mountains (such as those of
> the Alps where Alpianic languages are spoken) are snow-capped
> and thus "white".
Actually, this is wrong. The Alpianic reflex of PH *xalb- is
*ôpa 'ancestor'. The word *alpa 'mountain' is a cognate of
Old Albic _arb_ < PH *xarb 'hill, mountain' (the shift *r > *l,
counterfeeding *al > *ô, is regular before stops). This is in
turn an extended form of the PH root *xar- 'high' (cf. Old Albic
_ar_ 'high', _aran_ 'up'). So no connection between Elves and
mountains, despite the similarities of the words.
--
... brought to you by the Weeping Elf
http://www.joerg-rhiemeier.de/Conlang/index.html
"Bêsel asa Éam, a Éam atha cvanthal a cvanth atha Éamal." - SiM 1:1
Messages in this topic (1)
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3a. Re: OT: Math with roman numerals (Was: Do people ever make variant n
Posted by: "James Kane" [email protected]
Date: Tue Mar 5, 2013 1:15 pm ((PST))
I think I read somewhere that the subtraction thing, eg XL for forty, is in
fact a later invention and the Romans themselves were quite happy to have four
I's or four V's in a row.
Would this make the maths easier?
On 6/03/2013, at 3:43 AM, Daniel Burgener <[email protected]> wrote:
> On Tue, Mar 5, 2013 at 6:52 AM, Leonardo Castro <[email protected]>wrote:
>
>> 2013/3/4 Matthew George <[email protected]>:
>>> I was thinking about Roman numerals, and how terrible for performing
>>> mathematics that whole system is.
>>
>> I once affirmed that to a friend and he told me "Let's check!" and
>> started trying to make basic operations with Roman numerals. To my
>> surprise, he succeeded! He succeeded and said: "It's not that
>> difficult...". I watched he performing the operations while analyzing
>> developing the methods himself and it really didn't looked very
>> difficult.
>>
>> I don't have time to repeat what he did now, but I challenge you do so.
>
> Interesting! I just tried some basic addition and multiplication with
> roman numerals and it was in fact quite easy. Multiplication got tedious
> quickly and I didn't go far enough to figure out really complicated
> problems. (I could do, for example MXIII * V with little trouble, but I
> haven't tackled MXIII * XVII yet). Addition was easy though.
>
> Here's a simple example of the method I came up with for addition:
>
> CCLXXIV + CXCVII
>
> I did the work in two phases: First, "clump everything together", then
> "rewrite".
>
> Since each roman numeral represents a quantity, I can add them by simply
> grouping those quantities together, with special rules for cases like "IX"
> etc. I, X and C can be prefixed to larger numbers to indicate
> subtraction. In this situation, there are two cases. If there is a
> positive numeral of the same value in the other number, they cancel. If
> not, you can carry the prefix down.
>
> So here's the "clumping" for the above example:
>
> CCCCLXVVI
>
> The prefixed X and I each cancel one in the other number. Now this result
> isn't good because it has four Cs and two Vs, which should become a "CD"
> and an "X" respectively. That's what the "rewrite" phrase is for.
>
> So the end result is:
>
> CDLXXI.
>
> (Note that the second phase may require multiple iterations, if for example
> our "VV" -> "X" transformation resulted in four Xs. There are also
> additional rules to follow if your result has prefixed numerals in it.
>
> So to check in base 10, we did: 274 + 197, and got 471, which is the
> correct answer.
>
> I would wager that once one became familiar with the method, this could be
> faster than addition in modern numerals (although not worth the time to
> convert back and forth to Roman numerals). Multiplication seems easier
> with the modern way though based on my brief experimentation with it.
>
> -Daniel
Messages in this topic (3)
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3b. Re: OT: Math with roman numerals (Was: Do people ever make variant n
Posted by: "Gary Shannon" [email protected]
Date: Tue Mar 5, 2013 1:46 pm ((PST))
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).
>From there it's an easy matter to construct a multiplication table for
pairs of two-digit groups multiplied together since each two-digit group
represents one decimal digit.
01 = 1 or 10 or 100 or 1000 (I, X, C, M)
02 = 2 or 20 or 200 or 2000 (II, XX, CC, MM)
03 = 3 or 30 or 300 or 3000 (III, XXX, CCC, MMM)
04 = 4 or 40 or 400 or 4000 (IIII, XXXX, CCCC, MMMM)
10 = 5 or 50 or 500 or 5000 (V, L, D, V)
11 = 6 or 60 or 600 or 6000 (VI, LX, DC, VM)
12 = 7 or 70 or 700 or 7000 (VII, LXX, DCC, VMM)
13 = 8 or 80 or 800 or 8000 (VIII, LXXX, DCCC, VMMM)
14 = 9 or 90 or 900 or 9000 (VIIII, LXXXX, DCCCC, VMMMM)
--gary
On Tue, Mar 5, 2013 at 1:14 PM, James Kane <[email protected]> wrote:
> I think I read somewhere that the subtraction thing, eg XL for forty, is
> in fact a later invention and the Romans themselves were quite happy to
> have four I's or four V's in a row.
>
> Would this make the maths easier?
>
>
> On 6/03/2013, at 3:43 AM, Daniel Burgener <[email protected]>
> wrote:
>
>
Messages in this topic (3)
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