Conlangers

A language in which imaginary numbers (i, 2i, etc…) have their own root words and base 10 number system (or whatever other base suits your fancy). However, there are no root words for real numbers. The number “one” would have to be expressed by saying “i * i * i * i”, “two” by saying “√(2i * 2i * i * i)” , “three” by saying “√(3i * 3i * i * i)”, and so on.

(One can’t cheat by saying “i ^ 4”, as, again, there is no word for “4”).

Betascript got a mathematical notation. I tried to shed off traditional math notation as well as I could from a lifetime of indoctrination. Things that specifically got to go were fractional notation, representing equations as, well, equations, zero, and all the shenanigans with logarithms. The latter was heavily inspired by the Triangle of Power, a very useful notation that helps (YMMV) unify exponentiation, taking roots, and logarithms. So here goes.

The number system is duodecimal (base 12, dozenal) and the digits are slightly uncomfortably simple. 12 would have been small enough of a set to have completely different glyphs, but let's say Beta culture was developed by the kind of people that develop number systems.



The system is bijectional, meaning every numeral corresponds with exactly one number, unlike our system that has has redundancies like 1 = 01 = 001 etc. This is a rather roundabout way of saying that the system doesn't use zero, like Ancient Klingon . This should clear out any confusion, things to pay attention to are underlined:


Decimals are expressed by basically using the equivalent of scientific notation to shift the 'point'


Sums and products can be expressed in a variety of ways, with binary operators or surrounding with different kinds of brackets, or both. Simply stringing symbols together is considered summation.


There is no separate symbols for the reverses, ie. subtraction and division, nor for equalness. The relation is expressed just by writing the result next to the operation. (This probably leads to problems, but let's call this notation a draft...)


The same principle of stating a relation is used to combine exponentiation, taking a root, and logarithms. The default form is <base>⊥<exponent> over <result>, and some additional notation allows you to write the result on the same line, left or right, optionally enclosed in brackets.


If the need arises to refer to one of the variables (ie. as in 'selecting' one of the three types of operation), one can use a dot to denote what is considered the result. The same can be used to denote division and subtraction.


The symbol for e is a square, and it forms a ligature with the exponentiation sign.


Minus one, the ubiquitous unsung constant, has its own symbol. Used with different operations it yields useful things like negative numbers, reciprocals, and another useful constant, namely zero. Ligatures get formed, and the imaginary unit gets a further simplified symbol.


Trigonometry tries to make sense with the circle constant and functions that hint at their meaning. Zero degrees is y-axis, not our x. This might be a bad idea. Again using the idea of expressing a relation, the reverse operations are expressed by omitting the argument of the forward version.


Finally, some familiar formulas rendered in Betascript. The last example adds a simple notation for summing series and a sign for infinity. As I'm a beginner in this notation, there might be mistakes or ambiguities.


I can't say anything about the practicality of this system in actually doing mathematics, but creating it certainly was interesting. Some things like the role of -1 fell nicely into place. I have a hunch that similar clicking might happen if one were to go further with this, like with learning any new way of looking at things, like the aforementioned Triangle of Power, reverse Polish notation, or Haskell.

The logical next steps from here would be a) to test the system on actually doing maths, and b) extending it to calculus. My understanding of the latter is, however, probably too shallow to see clearly enough to be able to create anything interestingly different or logical.
 Comments welcome.

(The font was done in Fontforge, equations typeset in Libreoffice and tweaked in Inkscape.)

(Hello to readers of Conlang Blog Aggregator, first post here!)

Betascript got a mathematical notation. I tried to shed off traditional math notation as well as I could from a lifetime of indoctrination. Things that specifically got to go were fractional notation, representing equations as, well, equations, zero, and all the shenanigans with logarithms. The latter was heavily inspired by the Triangle of Power, a very useful notation that helps (YMMV) unify exponentiation, taking roots, and logarithms. So here goes.

The number system is duodecimal (base 12, dozenal) and the digits are slightly uncomfortably simple. 12 would have been small enough of a set to have completely different glyphs, but let's say Beta culture was developed by the kind of people that develop number systems.



The system is bijectional, meaning every numeral corresponds with exactly one number, unlike our system that has has redundancies like 1 = 01 = 001 etc. This is a rather roundabout way of saying that the system doesn't use zero, like Ancient Klingon . This should clear out any confusion, things to pay attention to are underlined:


Decimals are expressed by basically using the equivalent of scientific notation to shift the 'point'


Sums and products can be expressed in a variety of ways, with binary operators or surrounding with different kinds of brackets, or both. Simply stringing symbols together is considered summation.


There is no separate symbols for the reverses, ie. subtraction and division, nor for equalness. The relation is expressed just by writing the result next to the operation. (This probably leads to problems, but let's call this notation a draft...)


The same principle of stating a relation is used to combine exponentiation, taking a root, and logarithms. The default form is <base>⊥<exponent> over <result>, and some additional notation allows you to write the result on the same line, left or right, optionally enclosed in brackets.


If the need arises to refer to one of the variables (ie. as in 'selecting' one of the three types of operation), one can use a dot to denote what is considered the result. The same can be used to denote division and subtraction.


The symbol for e is a square, and it forms a ligature with the exponentiation sign.


Minus one, the ubiquitous unsung constant, has its own symbol. Used with different operations it yields useful things like negative numbers, reciprocals, and another useful constant, namely zero. Ligatures get formed, and the imaginary unit gets a further simplified symbol.


Trigonometry tries to make sense with the circle constant and functions that hint at their meaning. Zero degrees is y-axis, not our x. This might be a bad idea. Again using the idea of expressing a relation, the reverse operations are expressed by omitting the argument of the forward version.


Finally, some familiar formulas rendered in Betascript. The last example adds a simple notation for summing series and a sign for infinity. As I'm a beginner in this notation, there might be mistakes or ambiguities.


I can't say anything about the practicality of this system in actually doing mathematics, but creating it certainly was interesting. Some things like the role of -1 fell nicely into place. I have a hunch that similar clicking might happen if one were to go further with this, like with learning any new way of looking at things, like the aforementioned Triangle of Power, reverse Polish notation, or Haskell.

The logical next steps from here would be a) to test the system on actually doing maths, and b) extending it to calculus. My understanding of the latter is, however, probably too shallow to see clearly enough to be able to create anything interestingly different or logical.
 Comments welcome.

(The font was done in Fontforge, equations typeset in Libreoffice and tweaked in Inkscape.)

(Hello to readers of Conlang Blog Aggregator, first post here!)

In many languages around the world, numbers beyond 'one' are followed by plurals, because obviously, two, three, four etc are semantically plural. Likewise, in many languages, numbers beyond 'one' are followed by singulars, because a plural marking is superfluous. In some languages, two, and maybe other small numbers are followed by some form of paucal or dual or whatever.

However, some languages mess this up a bit, and I figure it might be of some interest to describe two examples.

1. Finnish
The Normal Noun
If the noun phrase is any other case than nominative or accusative, the noun is in the singular and its expected case, while the number likewise is marked for that case. With the nominative or accusative, the noun itself is in the partitive case (which also is the case when the number is in the partitive), and the number is in the nominative form (or rather, numbers have identical nominatives and accusatives, except for 'one').

The Abnormal Noun
Some nouns lack singular forms, and can thus not abide by the rules laid forth above. Instead, the number adjusts, and is marked for the plural. This even goes for the number 'one', giving us monstrosities like

'yksissä häissä' - 'one-plur-inessive wedding-plur-inessive' - at one wedding

but also

yhde-t bilee-t
one-plur party-plur
a party ("ones parties")

This is even more sick, as ordinals too get this treatment, giving us ugly monstrosities like

kolm-ans-i-ssa festare-i-ssa
three-ORD-plur-inessive festival-plural-inessive
at the third festival

Of course, in Finnish each element of the numeral (except 'toista', roughly "-teen" as in thirteen and such) is inflected for the case of the NP, and each element of a numeral is also inflected for ordinality, etc.

Further, the comitative case lacks formally singular forms, and thus whenever that is used, the numeral also needs to be plural - even if that plural is one.

2. Russian
Russian has a peculiarity going on, whose origin is the defunct dual form. The dual was identical for some nouns in the nominative to the genitive singular (but not for all nouns, e.g. feminines had a distinct dual). This has generalized so almost all nouns, when following the numbers two, three and four, take the genitive (when the numeral is in the nominative, mind you!). With other cases, the noun and the numeral are in the same case and in the plural number.

With accusatives, inanimates behave like in the nominative example above. Animates, however, take the plural genitive from two onwards.

Certain numbers - thousand, million, billion - are really nouns, and the "real noun" is in the genitive plural.

3. Hebrew
In Biblical Hebrew (maybe in modern too; I don't know and will not try to find it out today - no diss of modern Hebrew, but Biblical just is so much more cool) the numbers three to ten take the opposite gender's congruence marker. Thus, 'five lads' would be five-fem.sg lad-masc.plur

There is also a 'construct'-number, which signifies 'n of', but has no gender congruence. These construct numerals can also take possessive suffixes for 'two of us' and the like.

Finally, in modern Hebrew, there is still a dual, but this is used only with:

• nouns that naturally occur in pairs, even for genuinely plural numbers of the noun, and with some pluralia tantum (that also naturally occur in pair-like structures, I guess?)
• units of time