User:Loekıa/Numbers: Difference between revisions
The&System (talk | contribs) (Fractions must always be accompanying a numerator.) |
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== Background == | == Background == | ||
In previous versions of Toaq, numbers took the form of '''verbs of cardinality''' (e.g. {{T|heı}} was "to be ten in number"). But this system was | In previous versions of Toaq, numbers took the form of '''verbs of cardinality''' (e.g. {{T|heı}} was "to be ten in number"). But this system was limited: it made it awkward to talk about numbers in the abstract, and gave us no natural way to extend the system to more "exotic" numbers like the negative integers, non-integers, or even zero for that matter. | ||
There have been plenty of number system proposals in the past (particularly in the days of Toaq Beta), but now that we have prefixes to play with and special grammar for pronouns, I think Delta has given us the chance to do even better. | |||
== The basics == | == The basics == | ||
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== Counting higher == | == Counting higher == | ||
To form larger numbers | To form larger numbers, the golden rule is "each digit is a word". The tens place is marked with {{Derani||heı}}, and the hundreds place with {{Derani||fue}}. So for example, 123 would be spoken as {{Deranize|shífue guheı saq}}. Note that we never write out {{Deranize|koam}} as a digit, and {{Derani||shıheı}} and {{Deranize|shıfue}} may be abbreviated to simply {{Derani||heı}} and {{Derani||fue}}. | ||
To form ''even larger'' numbers, put the appropriate | To form ''even larger'' numbers, keep going with {{Derani||heı}} and {{Derani||fue}}, but put the appropriate scale word ({{Deranize|bıq}}, {{Deranize|nhoeı}}, {{Derani||gıga}}, {{Derani||tera}}…) after each group of three digits. | ||
{{Example|{{Deranize|Chum bua jẹ́mshı nhoeı cıheı bıq req ní doaq.}}|About one million, fifty thousand people live in this city.}} | |||
{{Example|{{Deranize|Sho cueq Bétatoaq râo kú kọ́gu bıq heı dıaı.}}|Toaq Beta [[Timeline|was released]] in 2017.}} | |||
== Negatives and decimals == | == Negatives and decimals == | ||
Negatives are formed with the prefix {{Deranize|ze-}}. The | Negatives are formed with the prefix {{Deranize|ze-}}. The word {{Deranize|co}} is a spoken decimal point. The resulting numbers are not cardinal numbers, so they're mostly useful as pronouns. | ||
{{Example|{{Deranize|Zıuhuaq zẹ́saq | {{Example|{{Deranize|Zıuhuaq zẹ́saq zẹ́jo co gu.}}|The number −3 is greater than the number −4.2.}} | ||
The | The word {{Deranize|chıo}} marks the start of repeating decimals. | ||
{{Example|{{Deranize| | {{Example|{{Deranize|shí co gu saq chıo jo fe}}|2=1.23(45) = 1.23454545…}} | ||
== Units == | == Units == | ||
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== Fractions == | == Fractions == | ||
The prefix {{Deranize| | The prefix {{Deranize|peo-}} can also form fractions: for example, {{Deranize|fé pẹocı}} is the number 5/6, and {{Deranize|shí pẹofue}} is 1%. Just as a quantity requires both a number and a unit, a fraction requires both a numerator and denominator; {{Deranize|pẹofue}} isn't particularly meaningful on its own. | ||
Fractional units are a little different from units proper, because they form numbers, not quantities. That is, in {{Deranize|róaı | Fractional units are a little different from units proper, because they form numbers, not quantities. That is, in {{Deranize|róaı pẹosaq meta}}, {{Deranize|pẹosaq}} must come ''before'' {{Deranize|meta}} because it belongs to the number part of the quantity. | ||
== | == Sums == | ||
Some things are most naturally expressed as the sum of multiple quantities. Quantities | Some things are most naturally expressed as the sum of multiple quantities. Quantities add together when put next to each other:{{Example|{{Deranize|Fáfuaq mı Taıtanıko bï duo hóq sáq hora heı jo mınu da.}}|The movie Titanic is 3 hours and 14 minutes long.}}You can also combine a whole number and a fraction to produce a '''mixed number'''. Just put {{Deranize|roı}} between the whole number and the fraction:{{Example|{{Deranize|Luı pıe jí shí roı shı pẹogu lıta nao.}}|I've had 1 ½ liters of water.}} | ||
== Pseudo-numbers == | == Pseudo-numbers == | ||
Some words like {{Deranize|puı}} and {{Deranize|tıopuı}} are pseudo-numbers: they can't stand alone as a number pronoun, but can still be used with certain prefixes, such as {{Deranize|ne-}} and {{Deranize|nho-}}. | Some words like {{Deranize|puı}} and {{Deranize|tıopuı}} are pseudo-numbers: they can't stand alone as a number pronoun, but can still be used with certain prefixes, such as {{Deranize|ne-}} and {{Deranize|nho-}}. | ||
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{{Example|{{Deranize|Hẹkıaı nháo nhọ́puı [gochıq].}}|She has many cats.}} | {{Example|{{Deranize|Hẹkıaı nháo nhọ́puı [gochıq].}}|She has many cats.}} | ||
{{Example|{{Deranize|Guache kọtıopuı [mí_Lıqkoq]?}}|The how-many-th president is Lincoln?}} | {{Example|{{Deranize|Guache kọtıopuı [mí_Lıqkoq]?}}|The how-many-th president is Lincoln?}} | ||
== Writing conventions == | |||
Of course, numbers are cumbersome to spell out in full, so we normally just write them with Arabic numerals. Toaq uses the dot "." as a decimal separator and the comma "," to divide groups of three digits, as in "10,000.56". | |||
One challenge when using Arabic numerals is where to put the tone marks: numbers can appear in different tones, and computers in particular have a hard time inserting and displaying diacritics on top of numbers. For this reason, we adopt the following conventions: | |||
* By default, a bare number such as 24 is assumed to be in the rising tone ({{Deranize|gúheı jo}}). | |||
* A verb of cardinality should have its {{Deranize|ne-}} prefix written out explicitly ({{Deranize|guheı jo}} → {{Deranize|nẹ24}}). | |||
* A numeric determiner in the hiatus tone {{Done|4}} should have its {{Deranize|nho-}} prefix written out ({{Deranize|kıaı gû gochıq}} → {{Deranize|kıaı nhộ2 gochıq}}). | |||
* A number pronoun in the hiatus tone {{Done|4}} should have the prefix {{Deranize|no-}} added ({{Deranize|Huaq gû sáq}} → {{Deranize|Huaq nộ2 3}}). | |||
Revision as of 21:10, 2 July 2024
Officially, Toaq Delta has nothing to say about how numbers work. So, here's my unofficial proposal for a number system!
Background
In previous versions of Toaq, numbers took the form of verbs of cardinality (e.g. heı was "to be ten in number"). But this system was limited: it made it awkward to talk about numbers in the abstract, and gave us no natural way to extend the system to more "exotic" numbers like the negative integers, non-integers, or even zero for that matter.
There have been plenty of number system proposals in the past (particularly in the days of Toaq Beta), but now that we have prefixes to play with and special grammar for pronouns, I think Delta has given us the chance to do even better.
The basics
In their most basic form, numbers are pronouns.
| Toaq | English |
|---|---|
| (kóam) | zero |
| (shí) | one |
| (gú) | two |
| (sáq) | three |
| (jó) | four |
| (fé) | five |
| (cí) | six |
| (díaı) | seven |
| (róaı) | eight |
| (néı) | nine |
(Neu fé gú róı sáq.)
Five is the sum of two and three.
By combining a number with a prefix, you can turn it into another part of speech. For example, to get a verb of cardinality, we use the prefix (ne-).
(Eju… Nẹcı áma.)
Let's see… There are six of us. (We are six in number.)
For brevity, when a verb of cardinality appears in the falling tone, we're actually allowed to omit the prefix altogether: (Cı áma.) As linguists, we say that (ne-) has a null allomorph.
Another important prefix is (ko-). It forms ordinals, much like the English suffix '-th'.
(Kọsaq máq ké buajıo tı hû tıeq.)
It's the third house on the street (third out of the houses on the street).
(Bọdana níjuı kộshı túq doaq po ní gua.)
This city was the first in this country to fall.
Finally, the prefix (nho-) turns a number into a determiner:
(Hẹkıaı nháo nhọ́gu gochıq.)
She has two cats.
This prefix also comes with a null allomorph which can be used as long as the determiner has a complement. So, normally we'd see this written as simply (gú gochıq).
Counting higher
To form larger numbers, the golden rule is "each digit is a word". The tens place is marked with (heı), and the hundreds place with (fue). So for example, 123 would be spoken as (shífue guheı saq). Note that we never write out (koam) as a digit, and (shıheı) and (shıfue) may be abbreviated to simply (heı) and (fue).
To form even larger numbers, keep going with (heı) and (fue), but put the appropriate scale word ( (bıq), (nhoeı), (gıga), (tera)…) after each group of three digits.
(Chum bua jẹ́mshı nhoeı cıheı bıq req ní doaq.)
About one million, fifty thousand people live in this city.
(Sho cueq Bétatoaq râo kú kọ́gu bıq heı dıaı.)
Toaq Beta was released in 2017.
Negatives and decimals
Negatives are formed with the prefix (ze-). The word (co) is a spoken decimal point. The resulting numbers are not cardinal numbers, so they're mostly useful as pronouns.
(Zıuhuaq zẹ́saq zẹ́jo co gu.)
The number −3 is greater than the number −4.2.
The word (chıo) marks the start of repeating decimals.
(shí co gu saq chıo jo fe)
1.23(45) = 1.23454545…
Units
Units like (meta) (meter) and (hora) (hour) are also number words. They multiply when put next to each other, and must be paired with a number to form a quantity.
(Buaıne kú sáqheı meta.)
The length is 30 meters.
(Cabaq kú gúcoshı kılobata hora.)
The energy is 2.1 kWh.
They can also be inverted with (peo-). For example, (pẹometa) is the unit m⁻¹. A quantity like 60 km/h is expressed as "sixty kilometer hour⁻¹":
(Suaıne kú cíheı kılometa pẹohora.)
The speed is 60 km/h.
Fractions
The prefix (peo-) can also form fractions: for example, (fé pẹocı) is the number 5/6, and (shí pẹofue) is 1%. Just as a quantity requires both a number and a unit, a fraction requires both a numerator and denominator; (pẹofue) isn't particularly meaningful on its own.
Fractional units are a little different from units proper, because they form numbers, not quantities. That is, in (róaı pẹosaq meta), (pẹosaq) must come before (meta) because it belongs to the number part of the quantity.
Sums
Some things are most naturally expressed as the sum of multiple quantities. Quantities add together when put next to each other:
(Fáfuaq mı Taıtanıko bï duo hóq sáq hora heı jo mınu da.)
The movie Titanic is 3 hours and 14 minutes long.
You can also combine a whole number and a fraction to produce a mixed number. Just put (roı) between the whole number and the fraction:
(Luı pıe jí shí roı shı pẹogu lıta nao.)
I've had 1 ½ liters of water.
Pseudo-numbers
Some words like (puı) and (tıopuı) are pseudo-numbers: they can't stand alone as a number pronoun, but can still be used with certain prefixes, such as (ne-) and (nho-).
(Hẹkıaı nháo nhọ́puı gochıq.)
She has many cats.
(Guache kọtıopuı mí Lıqkoq?)
The how-many-th president is Lincoln?
Writing conventions
Of course, numbers are cumbersome to spell out in full, so we normally just write them with Arabic numerals. Toaq uses the dot "." as a decimal separator and the comma "," to divide groups of three digits, as in "10,000.56".
One challenge when using Arabic numerals is where to put the tone marks: numbers can appear in different tones, and computers in particular have a hard time inserting and displaying diacritics on top of numbers. For this reason, we adopt the following conventions:
- By default, a bare number such as 24 is assumed to be in the rising tone ( (gúheı jo)).
- A verb of cardinality should have its (ne-) prefix written out explicitly ( (guheı jo) → 24 (nẹ24)).
- A numeric determiner in the hiatus tone
should have its (nho-) prefix written out ( (kıaı gû gochıq) → 2 (kıaı nhộ2 gochıq)). - A number pronoun in the hiatus tone should have the prefix (no-) added ( (Huaq gû sáq) → 2 3 (Huaq nộ2 3)).