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Post a Comment On: Steve Sailer: iSteve

"Math Mania"

26 Comments -

1 – 26 of 26
Anonymous Varangy said...

(Bilinguals, it has been found, revert to the language they used in school when doing multiplication.)

So true. As a complete, natural bilingual (vocabulary, grammar, and accent) I have to revert to the language I learned mathematics in to do any sort of multiplication/division. My (non-bilingual) friends think I am retarded when they see me painfully using the other language to compute.

2/27/08, 12:36 AM

Anonymous daveg said...

Interesting.

Spanish numbers are very long winded, many having three syllables.

The Spanish are not known for being math-centric.

2/27/08, 1:35 AM

Anonymous Anonymous said...

Another interesting feature of Cantonese is that you can cover all of its tones by just reciting the numbers from 0-9. Each digit therefore has an additional distinguishing characteristic that takes no additional time to say. Whether this makes any difference or not, I have no idea, but as someone who's struggled with learning Cantonese for years (I live in Hong Kong) I can testify:

numbers=easy

all the other words=hard.

There's also a lot of numerological stuff deeply embedded in Chinese culture as well, so being quick with numbers therefore has high value.

2/27/08, 1:49 AM

Anonymous braindead said...

As an engineer I work with math all day long, and study it to boot. Somehow I did not feel like reading the article, even though I consume most iSteve posts. I wonder why?

2/27/08, 2:55 AM

Anonymous daveg said...

Could you test this by providing lists of numbers and measuring the rate of memorization with the verbal complexity of that list?

Might not be enough difference in the numbers (in English at least) to detect a difference.

There is only one single digit number with two syllables (seven) and the double digit number are pretty much the same (eleven and seventeen are longer tho).

Perhaps you could do the test in another language with more variety.

The first 20 French numbers are short, and they were great mathematicians.

2/27/08, 3:01 AM

Blogger Hibernia Girl said...

...multiplication facts must be stored in the brain verbally, as strings of words....

Not true for everybody -- at least it's not true for me.

The multiplication tables -- which I learned by rote memorization -- are burned into my brain visually. At school we had these maths workbooks that included little pictorial representations of the numbers -- dots like on a die. That's how I recall my times tables -- e.g. 8 (dots) x 8 (dots) = 64 (dots).

I haven't stored the multiplication facts verbally -- I've stored them visually -- the same way that my thinking process works -- pictures first, words afterwards.

And I'm not East Asian. ;-)

Not surprisingly, I didn't do very well in higher maths courses! Basic algebra ok -- geometry & trig, terrific -- beyond that, not so good.

2/27/08, 4:07 AM

Blogger Kai Carver said...

French digits are also mono-syllabic: un, deux, trois, quatre, cinq, six, sept, huit, neuf, dix, better than English (seven) and German (sieben). And France has a great mathematical tradition! QED.

Of course, Russian has almost as many polysyllabic digits (adin, tchetirye, vosiem, dieviat, diesiat) as Spanish (uno, cuatro, cinco, siete, ocho, nueve), yet they also have a great mathematical tradition. And anyway, mathematicians don't deal with digits much. Plus, if you take zéro into account, French is tied by German, which has the lovely monosyllabic null.

Clearly, further study is needed :-)

2/27/08, 6:01 AM

Anonymous IMR said...

I'm pretty sure it was the British psychologist Alan Baddeley who did experiments comparing the short-term-memory digit spans of Cantonese and English-speaking Hong Kong schoolkids. The Cantonese speakers could recall an average of 9 or 10 digits, against an average of 7 for the English-speakers. The Cantonese-speakers also had better school grades in maths and showed better scores on simple tests of mental arithmetic.

2/27/08, 6:52 AM

Anonymous Topiary Utopia said...

The stuff about number names sounds like a limited version of the Sapir-Whorf hypothesis.

2/27/08, 7:19 AM

Anonymous Jeremiah said...

I would imagine another factor that creeps in as the math becomes more complex is working memory - the ability to mentally track a series of items and manipulate them without losing the data due to delay. This is one of the four smaller factors assessed by the WAIS-III (the most common IQ test administered by psychologists in the clinical setting). The other three are verbal comprehension, perceptual organization, and processing speed. The two subtests that load most heavily on working memory are "Digit Span" (being given a series of numbers, which you have to repeat - first forwards, then backwards), and "Matrix Reasoning." This is a relatively new subtest, in which a scrambled series of numbers and letters are provided, and the examinee has to mentally rearrange the items and give them back, with numbers first (in sequential order), then letters (in alphabetical order). As you can imagine, the most important ability is to be able to "hold" the data, and be able to manipulate it, without losing any due to memory erosion. This taps memory more than mathematics, but I'd imagine its quite important when discussing more complicated math problems (though the use of paper, chalkboard, etc. would reduce its importance).

What's fascinating to watch when administering these tests are the strategies people will employee in order to attempt to provide answers (harder to assess for the tests administered only verbally, but still occasionally observable). The more intelligent people tend to recognize they need to memorize the data first, before they can manipulate it. You can see them mouthing the original data to themselves over and over until they've "got it," then they go about moving the data into the proper order.

2/27/08, 7:32 AM

Anonymous Eric said...

I doubt gambling is a big help to mathmatics. I used to play a lot of poker, and the number of Asian "scientific" players is very small. Far outnumbered by the ones who think bringing a little golden frog figurine will guarentee a winning session.

Eastern Europeans and Russians, though... almost all of them are mathmatical players. Eventually I realized what happended to all those unemployed nuclear engineers in the '90s. Who knew a PhD in nuclear physics would be such good training for calculating pot odds?

Maybe I should get back into the game now that the Russians are gearing up for Cold War II and those guys are safely ensconced back in Siberian weapons factories.

2/27/08, 9:15 AM

Blogger Truth said...

Steve:

You just insinuated that David Robinson, with his 1300 SAT and Naval Academy degree was smart. You know what that means.

2/27/08, 9:41 AM

Anonymous Bill said...

If I learned a phone number in Chinese, I had to think in Chinese to remember it.

As for the visual/verbal aspects of math, I think there must be a lot of idiosyncracies. I scored higher on the verbal than math SAT, but I was clearly stronger in visual math like geometry than in algebra, which I detested. Actually, I had no problem rotating graphs or shapes in my head, but writing out the proofs was not easy. But that might be related to a mild disability I have (neurological in origin -- go figure) that makes it painful to write with pencil and paper.

Anyway, I believe I read something recently that suggested that apes' mathematical skills are on par with humans'.

Ah, here it is:

"It shows when you take language away from a human, they end up looking just like monkeys in terms of their performance,"

2/27/08, 10:43 AM

Anonymous Anonymous said...


Another interesting feature of Cantonese is that you can cover all of its tones by just reciting the numbers from 0-9.


Ummm, the same is true in Mandarin.

I daresay the same is true in Thai and Laotian. (Although I cannot be sure.)

Your point?

I know a Cantonese speaker who is also a math teacher in the US and I am pretty sure that she does multiplication in English.

However, when she and I count Mahjong scores, we do so in Cantonese (and I am a native English speaker).

2/27/08, 10:56 AM

Anonymous Anonymous said...


If I learned a phone number in Chinese, I had to think in Chinese to remember it.


The same here.

However, if I concentrate, I can translate them from English to Cantonese and vice versa.

2/27/08, 10:58 AM

Anonymous Sideways said...

Interesting, my wife is quadingual, with Chinese being her first language and English being her fourth. She learned math in Indonesian. She still does math entirely in Chinese, which would seem to make her an exception.


You just insinuated that David Robinson, with his 1300 SAT and Naval Academy degree was smart. You know what that means.


I suspect it means your understanding of Steve's motivations are deeply flawed.

2/27/08, 11:02 AM

Anonymous Anonymous said...

If you are strongly analytical, there is no way you are satisfied with rote learning. You want to know why, what are the patterns and principles. Rote I suspect, produces people who do not connect the dots very well, but are competent at mid brow tasks and professions.

2/27/08, 11:08 AM

Anonymous David Davenport said...

Steve,

There's also a divergence between arithmetic skill and quickness versus adeptness in geometry or map reading, and between grasp of more abstract mathematics and deftness in arithmetic -- i.e., adding, dividing, multiplying, and dividing.

This divergence tends to split along male/female lines.

Some math professors are vulnerable to arithmetic errors, and I once took a course taught by a Mechanical Engineering prof. who was great at multiplying or dividing large numbers in his head, but who didn't fully grasp the tensor algebra he was trying to teach. I suppose the gender stereotype doesn't always hold.

2/27/08, 11:17 AM

Anonymous Reg Cæsar said...

This number-name business would suggest the Danes are the worst mathematicians in Europe, an idea which has no other evidence. The sons of Gorm manage to combine the place-swapping "four-and-twenty" quirk of the Germans, Dutch and old English, with the "score" system of French and Italian (quatre-vingt for 80.) So 55 comes out as "five-and-half-the-third-score". Swedes and Norwegians have told me they can understand Danish quite easily but can't count at all in it.

Don't forget the Japanese, with their three-syllable native numbers-- hitotsu, futotsu, etc. Those are the mathephobes who miniaturized the world! Overcompensation, perhaps?

2/27/08, 11:33 AM

Anonymous canson said...

"If you are strongly analytical, there is no way you are satisfied with rote learning. You want to know why, what are the patterns and principles. Rote I suspect, produces people who do not connect the dots very well, but are competent at mid brow tasks and professions."

I disagree. Rote learning if correctly applied will benefit everyone. Those that aren't so bright get some useful knowledge and disciplne. The brighter sort are able to increase speed and accuracy for routine tasks allowing time for more elevated thinking. Memorization saves time on the basics.

2/27/08, 12:06 PM

Blogger KlaosOldanburg said...

"If you are strongly analytical, there is no way you are satisfied with rote learning. You want to know why, what are the patterns and principles. Rote I suspect, produces people who do not connect the dots very well, but are competent at mid brow tasks and professions."

i disagree. go to a higher math class (set theory, linear algebra, differential equations etc.). it's all purely theoretical, abstract material (just like sociology, har dee har har). you will find students who know their multiplication tables (know them because they've been burned into memory) better than anyone else on campus.

linux nerds, who memorize enormous amounts of obscure technical details about the kernel, and how to use a command line interface to manipulate it, also excel at computer programming, which is extremely abstract as well.

if your thesis were correct, the janitor would be better at multiplication than the calculus teacher.

it's sad how afraid we've become of hard work.

2/27/08, 12:29 PM

Anonymous dearieme said...

I was tested for number-memory as a freshman. Mine was lousy and I was told I'd never get a degree. But I, forgive me, proved to be a star undergraduate. Perhaps my result related to the fact that I came from a tiny town where the phone numbers had just three digits? I had never in my life had to remember a number of any length.

2/27/08, 2:29 PM

Anonymous Anonymous said...

Don't forget the Japanese, with their three-syllable native numbers-- hitotsu, futotsu, etc.

hitotsu, futotsu,... mean first, second,... not generally used in calculations

i*chi, ni, san, shi, go, ro*ku, shi*chi, ha*chi, kyu, ju are the Japanese words for 1-10 used in calculations

2/27/08, 4:17 PM

Blogger Justin Halter said...

The guy was totally wrong about kids using calculators.

Don't let your children use calculators in elementary school, and don't let your kid's teacher allow them in the classroom either. Learning algebra is about a zillion times easier if you know the basic algorithms for numbers, especially fraction operations and even long division.

Using calculators raises mathematical cripples who can't even estimate or check for reasonableness. I taught junior high math, I saw first hand the damage that calculators can do to children's math abilities.

2/27/08, 5:07 PM

Anonymous Chris said...

>"But aren't the East Asian advantages in math ability rooted more on the visual side?"

>"i*chi, ni, san, shi, go, ro*ku, shi*chi, ha*chi, kyu, ju are the Japanese words for 1-10 used in calculations"

So, the Japanese have the same superior math ability as the Chinese while using a number system even more cumbersome than English. That would kind of cast doubt on the article's implication that the math facility disparity is linguistic in origin, and suggest that it might be innate.

2/27/08, 9:49 PM

Blogger Markku said...

a*b = min(a,b)*10 - min(a,b)*(10-max(a,b))

That's my algoritm.

For example,

7*8 = 7*10 - 7*(10-8) = 70-14=56.

Or,

14*12 = 12*10 - (10-14)*12 = 12*10 - (-4)*12 = 120 + 48 = 168.

Or,

765*34 = (700+60+5)*(30+4)=
= 21000 + 1400 + 1800 + 20
= 21000 + 3200 + 20
= 24220

Now it is obvious why having the multiplication table burned in your memory is extremely useful. Otherwise you run out of short-term memory slots very fast when multiplying even two- or three digit numbers.

2/29/08, 6:43 AM

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