Arnold Kling  

Arithmetic and Language

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This is interesting, if only tenuously related to economics.


English-speaking children, who are prone to such errors as “twenty-eight, twenty-nine, twenty-ten, twenty-eleven.” French is just as bad, with vestigial base-twenty monstrosities, like quatre-vingt-dix-neuf (“four twenty ten nine”) for 99. Chinese, by contrast, is simplicity itself; its number syntax perfectly mirrors the base-ten form of Arabic numerals, with a minimum of terms. Consequently, the average Chinese four-year-old can count up to forty, whereas American children of the same age struggle to get to fifteen. And the advantages extend to adults. Because Chinese number words are so brief—they take less than a quarter of a second to say, on average, compared with a third of a second for English—the average Chinese speaker has a memory span of nine digits, versus seven digits for English speakers.


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COMMENTS (16 to date)
Andrew writes:

this is acually true of most Asian languages Thai also features a simple base ten series of words and lacks twenties and the teens etc. It does create questions about Japanese though which contains 3 different counting systems for different types of objects and also taken the diversity of Chinese spoken in China (Shanghai vernacular is essentially a language with in itself) u have to wander if these gains are really countrywide or only found in metropolitian areas.

8 writes:

All well a good until you reach the big numbers, where the old imperial system relied on 10,000 (wan4) as as a number. Then there's yi4, for 100,000,000. I still get lost when people start talking in the millions and billions.

8 writes:

As an example, to say 27 million 500 thousand, Chinese say 2,750 ten thousands.
二千七百五十萬

To say 1 billion 250 million, they say twelve 100 millions 5,000 ten thousands.
一十二億五千萬

Acad Ronin writes:

English still retains a trace of the old Celtic base twenty system: "Four score and seven years ago..."

The Belgians have improved the French system by inventing the words septante (70) and nenante (90) (note: spelling was never my strong suit), to replace the French soixante dix (60+10) and quatre-vingt dix (4X20 + 10).

As far as Chinese and Japanese are concerned, though the numbers work well until you get to 10,000. Then you have to work in multiples of 10,000 until you get to 100,000,000 (which is 10,000 x 10,000). However, the very need to learn 1800 characters in Japanese and 4000 +/- in Chinese to attain basic literacy slows down other learning. It is also difficult to retain the ability to write without constant practice. Japanese acquaintances of mine have remarked that word processing has given them a larger written vocabulary for computer produced text, but has eroded their ability to write free-hand because they no longer remember the strokes to reproduce the characters.

Troy Camplin writes:

Part of the problem is the idiotic way we teach our children how to count -- especially with the number charts we use in our schools. We typically see the number charts as follows:

_1__2_3__4__5_6_7_8_9_10
11 12 13 14 15 16 17 18 19 20
etc.

The problem with this is that is partially masks the number pattern. After I read a book on number theory, I proposed the following number chart, which my wife used in her pre-K class:

_0_1_2__3__4_5__6_7__8_9
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29
etc.

As you can see, we have the single digits, all the tens, all the twenties, etc. Lined up. The result? In past years, she had only been able to get about half the students to about 20 by year's end (most could get to ten). The year she used my number chart, she was able to get 75% of her students counting to 100 in only 2 months, and all of her students could make significant progress through the numbers by year's end. She even taught them all how to add and subtract, and was beginning to teach them how to add double digit numbers.

The problem with teaching counting has much to do with the fact that the people teaching counting and first math themselves have no understanding of numbers or math at all.

mensarefugee writes:

I actually read that book "The Number Sense".
But the author doesnt control for IQ. Seeing that the average E.Asian is supposed to have an IQ of 103-105 and the average white 100, with the majority of the difference in the mathematical sphere, how does Stanislas know its language caused or IQ caused?

He would have to test E.Asians of completely American descent - even that would have mild problems (selective immigration) but way better than a bald outright assertion.

AMW writes:
Consequently, the average Chinese four-year-old can count up to forty, whereas American children of the same age struggle to get to fifteen

Really? My oldest was counting to twenty by the time he turned three (he's almost four now). Admittedly, he tends to skip over 15, but still.

Brandon Berg writes:

I doubt that the Chinese four-digit grouping system is inherently more confusing than the English three-digit grouping system. It's just confusing to us because the numbers we use as reference points are based on three-digit grouping, so we have to do mental conversions in order to appreciate the scale of Chinese numbers.

If you had grown up using numbers with four-digit grouping as reference points, you wouldn't have to do these conversions.

Brandon Berg writes:

Also, I suspect that the statement "the average Chinese four-year-old can count up to forty" is misleading. If you can count to forty in Chinese, there's no reason you can't count to one hundred. So I suspect a bimodal distribution--maybe a third can count to a hundred and the rest can barely make it to ten.

8 writes:

I'm sure the Chinese are used to it, but it still confuses them occasionally, because they swith from counting 10, 100, 1000 (by 10s) to counting 10,000, 100,000,000 (by 10,000s). I think it goes back to what Arnold wrote about numbers in the ancient world. After 10,000 there's "a lot"; they created a word for 100,000,000 to described the population of the Empire.

caveat bettor writes:

Of course the small advantage in expressing positive integers in Chinese is offset--and then some--by pictographic instead of alphabetic words.

Ever try to type out a simple note in Chinese? It's a huge disadvantage to English--just ask anyone who regularly does both.

Maybe we will see the convergence when something written in Chinese gets deposited on the moon.

Lord writes:

Since numbers can be strung together as single syllable digits, I have difficulty seeing why this would affect memory. We dial 9-1-1, not 911. Counting would be the only difference, but counting is relatively uncommon but when done usually some shortcut is performed such as fingers or notation. The verbal addition when identifying numbers to encode redundant information so it is less likely to be lost in communication.

mk writes:

Random personal anecdote on this:

The article mentions that Chinese numbers have short names, so they're easier to remember.

I have always had this weird (but useful) habit of shortening the number names when I'm counting. I think I only do it if I need to be thinking about something -- if there's a lot of cognitive load going on during the counting.

So, you'd count:

"One, two, three, four, five, six, sev, eight, nine, ten, len, twel, thir, four, fif, si, sen, eigh, nigh, twen"

and so forth. It sounds trivial but it really makes it easier to keep in your head as you're counting.

Troy Camplin writes:

Seriously, people. It's patterned vs. nonpatterned teaching. The brain works on patterns. It is designed to detect patterns, predict patterns, and learn using patterns. If you ignore the number patterns, as we do in pre-K and K, then students have a harder time learning to count than if they are shown the patterns, as noted above.

Brandon Berg writes:

8:
I'm sure the Chinese are used to it, but it still confuses them occasionally, because they swith from counting 10, 100, 1000 (by 10s) to counting 10,000, 100,000,000 (by 10,000s).

No more, I would expect, than we do when switching from counting 10, 100, 1,000 (by 10s) to counting 1,000, 1,000,000 (by 1,000s). Also, digits are usually grouped by fours in Chinese counting, so it would be 1,0000, 1,0000,0000, etc., not 10,000, 100,000,000, etc. There's no reason why this should be inherently more difficult. It's just a question of what you're used to.

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