Number sense 1

¡¦Do you like mathematics? I don¡Çt think the answer to this question would be ¡ÈYes¡É,

because most people find it difficult. Unfortunately, it is true that human brain isn't suited for mathematics. Our only intrinsic talent concerning number sense is to judge which is larger between two things, and other talents are all extrinsic. I¡Çd like to write about
recognitions of numbers.

¡¡Until three and Beyond three
                           

¡¦It is mysterious that we can recognize small numbers until 3 easily, but it suddenly
becomes difficult to do beyond three. Imagine numbers around you. For example, 6 is
divided into two ¡ÈThree¡É groups on the surface of the dice. The arrangement of playing
cards is similar to the dice¡Çs one. These arbitrary arrangements show that numbers until
three are easy to recognize.

Memory of number letters works as the same principle. Letters until three are almost
same, but beyond three they are various. Examples as follows.

1 2 3¡¡¡¡¡¡ 4

Chinese: °ì¡¡ Æó¡¡ »°¡¡ »Í
Rome : ­µ ­¶¡¡ ­·¡¡ ­¸

  How many digits can we retain at a glance?
                                         

¡¦It is said that average retention of digits is about seven in America. However, it isn¡Çt
universal. Japanese is nine, Chinese is ten. What caused this difference? The secret is the
length of sound. I can count number words until ten within 2 seconds, but it is difficult to
do English number words even within 3 seconds, because the English sound is longer than Japanese. If you compared syllables, it is clear that Chinese is the shortest among
three. This champions them. (It is said that Kantonese is the shortest in the world, so their retention must be more than ten.)
Japanese: iti ni san si go roku nana hati kyuu juu
English : one two three four five six seven eight nine ten
Chinese: ii ar san su: u: ryu: chi pa ju si
¡¡

Complexity of number system has nothing to do with the retention. Iceland¡Çs number system

is simpler than English one, but their retention is worse than English. Iceland had had a
similar system to the English one, for example eleven, twelve, but they simplified it by
inventing new number words which were longer than former ones.
I¡Çd like to mention a side story. A governor criticized French by saying that it couldn¡Çt be an international language because its number system is irrational. However, he overlooked two facts. First, there is a dialect which has a normal number system similar to Japanese in south France. Most French thinks that this dialect is by far rational than usual one.

Second, French number words are longer than Japanese ones. It is unfair to compare Japanese with French without taking this into account. It is natural that French are worse at counting numbers than Japanese, because they are disadvantaged in their language. If they fixed their number words to suit themselves to natural number system, they could be better.

Next time, I¡Çm going to argue about our false common sense concerning numbers and
mathematics.