linguaphiles: Algebra

Joshua the Magnificent (

apollotiger) wrote in

linguaphiles,
@ 2005-09-26 12:10:00

Current mood:

curious

Algebra

As I was doing my math homework this morning, I found myself wondering: what do math books in other languages that use other alphabets use as variables? In American textbooks, the canonical ones are a, b, c, x, y, and n.

Maybe someone who learned their math in Russia or Greece or Korea might be able to help me on this? For example, what are the axes (x-axis, y-axis, z-axis in English) called in other languages?

(Post a new comment)

	oblomov_jerusal 2005-09-26 07:18 pm UTC (link)
	Books in Russian use the same letters as English one (Letters used are always Latin, not Cyrillic.) (Reply to this) (Thread)

	apollotiger 2005-09-26 07:20 pm UTC (link)
	Oh well. That’s decidedly less exciting than I thought it might be. ;) (Reply to this) (Parent)

	dontbeakakke 2005-09-26 07:38 pm UTC (link)
	You need to watch Mean Girls again. - I like math. - Why? - Because it's the same in every language (Reply to this) (Thread)

	apollotiger 2005-09-26 07:40 pm UTC (link)
	<laugh type="nervous/sheepish"/> I actually haven’t watched that movie yet. I’d like to, though, because Tina Fey rocks. (Reply to this) (Parent)

	lakehmm 2005-09-26 10:55 pm UTC (link)
	Yet another display of how Mean Girls holds eternal and infinite wisdom. (Reply to this) (Parent)(Thread)

	dontbeakakke 2005-09-26 11:58 pm UTC (link)
	Basically it's like our generation's Zohar. (Reply to this) (Parent)

sparkofcreation
2005-09-27 12:13 am UTC (link)

Actually that's so far from true it's laughable (and yes, I know you were joking).

Math is really, really, really hard to do in a foreign language—not just the words but the way things are written out. If you write a long-division problem for someone who learned math in Spanish, he/she will do it as a root. And adding large numbers looks like sign language in Spanish, there're about a million hand positions they do that substitute for American "carrying the 1" or whatever.

Rumor has it that's one way to catch spies—if you make someone do math for long enough, they'll always go back to the way they learned in the first place.

(Reply to this) (Parent)(Thread)

joefredette
2005-09-27 06:50 pm UTC (link)

Uh... No? Lol,

Math in it of itself is best thought of as a language, When one does math in a foriegn language, he does it the same way you'd do it in English, because you are not actually "Speaking" your language, but rather the language of mathematics.

In Spanish 2+2 still equals 4, they may read the line as "Dos y dos es quatro" (or something similar, my Spanish is horrible.) but the math concept is still the same.

As for using different characters as variables/constants w/e

Remember that the purpose of a symbol in mathematics is to hold a value, it has no lexical meaning other than what you assign to it (usually.) there are some accepted letters that mean certain things, like Pi or 'x' which are constant and variable, respectively. But these could just as easily be reversed, if I said

Pi = 2
Pi^2 = 4

its just as legitimate as saying

x=2
x^2 = 4

similarly, I could use a cryllic letter to represent some value. This is generally a good idea when you want to seperate different types of variables. say for instance you had an equation that contains both lengths and angles, I may use greek letters for the Angle values, and Latin for the Lengths (this is very commonly done.) Other examples of this include Cantor Set theory, which deals with different sizes of infinity, Cantor used the Hebrew Letter 'aleph' to describe an infinity of some size. (if you're curious how you can have one infinity be bigger than the other, then let me know, I'll see if I can explain it.)

So again, its best not to think of 'x' and 'y' in terms of being letters in the english language, but rather as being symbols that you give meaning to as you need them.

Math is very much like conlanging, only on a much smaller scale, and without have to define grammar, usually.

~~Joe

hoorah WPI-Math Majors!

(Reply to this) (Parent)(Thread)

arsinyk
2005-09-27 09:57 pm UTC (link)

Math itself is universal, but the way people go about doing/talking about math isn't. My friend learned math at a French school and spent a considerable amount of time "relearning" multiplication and division when she switched over to public school (which was teaching in English) because the systems are so different. And then almost failed her first year of math because she still wasn't used to the differences.

(Reply to this) (Parent)

sparkofcreation
2005-09-27 11:30 pm UTC (link)

I'm aware of all that, thank you. However, I can promise you that it is true people who need to do math problems will do them in the language and using the methods that they were taught in school. (This probably applies less at higher levels, esp. when the person's higher math courses were taught in English.)

That has nothing to do with mathematics in its purest form, obviously. Of course writing equations out is the same in any language. But while 2+2=4 in any language, someone whose native language is Spanish will always see the equation and think "dos más dos son cuatro" while someone whose native language is English will think "two plus two is four" and someone whose native language is French will think "deux plus deux sont quatre." Because mathematics is not part of language per se (as you said), it's much harder to make someone whose first language is English think "dos mil y cinco" when they see the year "2005" than it is to make them think "perro" when they see a dog.

Have you ever watched someone who'd learned math in a non-English-speaking country try to do math in English? I have, and I've learned fascinating things about the ways math problems are done in Spain or Colombia or Mexico or Peru or the Dominican Republic or Hong Kong. I can assure you that in every example I can think of, the person reverted to his/her first language in order to do anything much more complicated than 2+2 (adding two two-digit numbers, for example).

I repeat: math is very, very, very hard to do in a foreign languge. If you don't believe me, try it. Have someone ask you to add two numbers together in your second language and see if you can do it without thinking of the English words for them—including not thinking "carry the 1" or anything like that. Bonus points if you can do it using the same techniques as speakers of that language use (for example, Spaniards count on their fingers instead of writing the little 1s or 2s or whatever when they carry a number).

(Reply to this) (Parent)(Thread)

joefredette
2005-09-28 03:38 pm UTC (link)

well, does it count that I did learn math in a foriegn country, in their language (I was an exchange student for most of my math career), and learnt it in the same fashion as the rest of the world learns it?

maybe it was because it was german, which bears some similarity to english (however limited) but I have seen a number of foriegn people (classmates, mostly) doing math in the same way we do.

~~Joe

(Reply to this) (Parent)

boonleong
2005-09-26 08:06 pm UTC (link)

I believe Descartes started the whole thing, using letters at the front of the alphabet (a, b, c) to stand for constants and letters at the back (x, y, z) to stand for unknowns.

Eulerdecided the Latin alphabet wasn't enough for his needs and brought in Greek and Fraktur letters. So the conventional symbols for some mathematical entities are sometimes Greek or Fraktur symbols.

Finally Cantor decided to use א to stand for infinity. (There are different levels of infinity, so it's not all just ∞).

Yeah, that's about it I think.

Math in Chinese uses the same conventional symbols as in English. There was a period, maybe in the 1700s, when it used 甲,乙,丙, etc to stand for variables and equations were written vertically, and stuff like that, but that died out a long time ago.

(Reply to this) (Thread)

	boonleong 2005-09-26 08:07 pm UTC (link)
	Well. You can totally tell I'm a math major now. (Reply to this) (Parent)(Thread)

	purplegenie 2005-09-26 08:16 pm UTC (link)
	Different levels of infinity? I'm intrigued...but how can you possibly have an infinity more infinite than, well, infinity? I guess perhaps this isn't the place for this discussion, but it is interesting. :) (Reply to this) (Parent)(Thread)

co_lum_bus
2005-09-26 08:29 pm UTC (link)

Simple: the total number of integers is infinite, and the total number of rational numbers is infinite, and the total numumber of real numbers is infinite.

Yet one can show that the first two are "equally infinite" - yoo can combine them into pair, so that each pair would have one integer and one rational number, and every integer will enter excatly one pair, and every rational number will enter exactly one pair. Howevere, you cannot to the same with all real numbes - there are too many of them! Thus, the number of real number is not only infinite, but is provably larger than the infinite number or integers.
Mathematician say that the set of real number has a higher cardinality than the set of integer numbers.

(Reply to this) (Parent)(Thread)

sparkofcreation
2005-09-27 12:16 am UTC (link)

I don't follow. Aren't rational numbers any number where the decimal either ends or begins to repeat? Like 1.5 or 8.675 or 31.6666.... So I understand how there're more real numbers than rational numbers or integers, but in the same way, shouldn't there be more rational numbers than integers? Since there's an infinite number of rational numbers between each integer?

(Reply to this) (Parent)(Thread)

co_lum_bus
2005-09-27 12:32 am UTC (link)

Nope, there are as many rational numbers as integers. Let me give you a simpler example. You may think there are more integer numbers than positive integers (whole numbers). Let me prove it is not the case. I will start counting integers starting from zero:

0,-1,1,-2,2,-3,3...

This way I assign to each integer a whole number, thus, their infinities are equivalent. I can do the same trick with all rational numbers, using the fact that each rational number can be written as a ratio of two integres, therefor reprezents a point on a regular grid, so I can start counting from zero and go around in a spiral way, increasing the radius (it is a littel bit more complicated, but in an essential way). One can prove, however that you cannot count all real numbers.

By the way, this is why the sets of the firmer type are called "countable sets". The set of all real numbers is not a countable set.

(Reply to this) (Parent)

	lyssiae 2005-09-26 10:07 pm UTC (link)
	Yup, what he said. There's a whole slew of them. Check out Cantor's diagonal proof that the infinity that describes (for want of a better word) real numbers (that is, every possible number on a number line) is "larger" than the infinity that describes integers. It's the kind of orgasmic maths that makes you feel warm and gooey inside :) (Reply to this) (Parent)(Thread)

more fun than diagonal proof

dseomn
2005-09-27 08:32 pm UTC (link)

There's a riddle that's a lot more fun than the diagonal proof:

Part 1: You run a hotel with ∞ rooms (one room for each counting number), the hotel is full and one more person wants a room, what do you do?

Part 2: Same as part 1, but with an infinite number of people wearing number tags with unique counting numbers.

Part 3 (the different types of infinities part): Same as part 2, but the number tags are all real numbers from 0 to 1 (inclusive or exclusive doesn't matter).

Do not read below this if you don't want the answers.

Answers:

Part 1: Have everybody move up one room, put the person in room 1.

Part 2: Have everybody already in the hotel multiply their room number by 2. Have the people on the bus multiply their number by 2 and subtract 1, put them in the corresponding room.

Part 3: It's not possible, because you don't have enough rooms.

(Reply to this) (Parent)(Thread)

	Re: more fun than diagonal proof apollotiger 2005-09-27 08:42 pm UTC (link)
	I had fun trying to disprove the reflexive property of variables with infinity. :D “Well, see, by definition, if you take an even number, from 0 to that number, half of those numbers will be even and half will be odd. But since there are an infinite number of even numbers and an infinite number of numbers, infinity is less than infinity.” (Reply to this) (Parent)

	Re: more fun than diagonal proof lyssiae 2005-09-27 08:43 pm UTC (link)
	Sorry, but that's nowhere near as fun as the diagonal proof.... (Reply to this) (Parent)

joefredette
2005-09-27 07:12 pm UTC (link)

a good way to think about it is call the "Hilberts grand hotel paradox"

Heres the idea:

What if you had a Hotel with an Infinite number of rooms, and an infinite number of people who wanted to stay at your hotel.

Now, what if you took all those people and put them in all the even numbered rooms. Well, you've filled an infinite number of rooms with an infinite number of people, but yet, you still have rooms left over, right (all the odd numbered rooms.) Similarly, if you have a set of numbers that is infinitely long, but only contains even numbers, it is less than another infinitely long set, that has all the numbers. or even just all the even numbers and 1.

The concept of different levels of infinity is a bit tough to grasp sometimes. So don't feel bad if you don't get it right away, It took me several books about the subject to really understand it.

Btw, Whats the syntax for denoting different Aleph Sets? I don't remember... I generally just use "Aleph " where the ratio indicates what part of infinity is contained in the set. so
"Aleph one-over-two" (A1/2) is the set of all the even numbers. Is this correct? If anyone could post a link or something, it'd be Grand.

~~joe

(Reply to this) (Parent)

	co_lum_bus 2005-09-26 08:25 pm UTC (link)
	One could add that for unknown reasons Cantor called the countable set aleph_0, but the continuum he called C, and not bet or bet_0. so, the only Hebrew letters routinely used is aleph, and only with the subscript 0. Besides, the modern math utilizes some Cyrillic letters as well, namely those that cannot be confused with Latin: Ш, Ю, Я. (Reply to this) (Parent)

	sollersuk 2005-09-27 05:37 am UTC (link)
	This is what gave Diophantus problems - since he was using letters for numbers he was a bit short of symbols to use for unknowns, which may be why he was only able to use one. (Reply to this) (Parent)

	markusn 2005-09-27 09:14 am UTC (link)
	Then there's all the weird d's used in multipla differentials. Icelandic slips in there, I believe. (Reply to this) (Parent)

	joefredette 2005-09-27 06:51 pm UTC (link)
	oh dear, I copied a good portion of what you said in my post, sorry, thats okay though. It's good stuff.. yay for math! (Reply to this) (Parent)

co_lum_bus
2005-09-26 08:34 pm UTC (link)

While the letters are the same in math, their pronunciation differes: in Gremany they prononce letters as approspriate for the German alpahbet, in France correspondingly, and in Russian according to the rules of the Latin language.

also, although the letters are the same, some mathematical symbols are different. Say, the curl of a vector is denoted as curl X in English, but as rot X in German or Russian. Rassians do not write tan for a tangent, but tg; sh, ch, and th, instead of sinh, cosh and tanh, respectively.

The gradient symbol is written the same way, as an upside down delta, but is called nabla in Russian and German, as opposed to del in English.

(Reply to this) (Thread)

	kyrasantae 2005-09-27 03:14 am UTC (link)
	My professor called the gradient symbol "nabla" too! But he does speak with an accent and he might be from Germany. (Reply to this) (Parent)

	boonleong 2005-09-27 03:40 am UTC (link)
	Interesting. I've seen tg before. I knew the upside down triangle was called both del and nabla, but personally I call it div, grad or curl depending on the context. (Reply to this) (Parent)

	tronella 2005-09-26 09:09 pm UTC (link)
	the German exchange student who was in my class for a year always used Greek letters for variables instead. (Reply to this) (Thread)

	tanigawa 2005-09-27 04:27 pm UTC (link)
	This is totally off subject but I think I'm absolutely in love with your icon. It's a Petit Prince and Magritte reference all in one, n'est ce pas? (Reply to this) (Parent)(Thread)

	tronella 2005-09-28 12:55 pm UTC (link)
	it is indeed :) yay, I love when people get both references! (Reply to this) (Parent)

izlude_tingel
2005-09-27 06:32 am UTC (link)

When I was an exchange student in Japan, they used almost all of the same symbols and variables that we did, with one exception that I noticed: In the states, when we write the variable x, we make it by writing two diagonal lines that intersect. ("X") My Japanese friends, however, made two semicircles that intersect (something like ")(", if the lines touched in the middle.) It wasn't a big deal by any means, but it was something interesting.

(Reply to this) (Thread)

	thewhiteowl 2005-09-27 07:35 pm UTC (link)
	I'm Irish and I use the two touching curls. (Reply to this) (Parent)

	boonleong 2005-09-27 08:58 pm UTC (link)
	I use both with the same frequency. It's very useful for distinguishing x from the multiplication symbol. (Yes, I also write my t and z funny, because of + and 2.) (Reply to this) (Parent)(Thread)

joefredette
2005-09-28 03:42 pm UTC (link)

I generally right 'X' in the non curly way. But thats mostly because I used the Raised dot or Asterisk for my multiplication symbol. I right my t similar to the futhork "n" (if memory serves, its a straight line with a slash thru the middle, kind of like juxtaposing a | with a /) or occasionally I just right it upsidedown, or capitalize it.

I also cross my Z's (and n's!), even though they look nothing like my 2's, I just like the way they look better...

(Reply to this) (Parent)

	boonleong 2005-09-29 02:46 am UTC (link)
	Well, what do you know. I was surfing around randomly and my attention was drawn to this article, on Arabic mathematical expressions. (Reply to this)

Username:		Create an Account Forgot your login or password? Login w/ OpenID
Password:
	Remember Me
	English • Español • Deutsch • Русский…

About

Help

Get Involved

Legal

Store

LJ Labs