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Revive Volume 7, 2010 Contents In one of the training programmes with primary
school teachers, we were discussing place value and how we put the units’ digit on the right, the
tens’ left of the units, and so on. One teacher shot up
to ask why we needed to put the unit digit on the
right. After a moment’s hesitation, I said that it did
not matter how we put it as far as the math was
concerned. That is, four hundred and thirty seven
could be also written as 734 and not as usual 437 and
be read as sevens, thirties and four hundreds.
46
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Being Conventional
on Numbers, Maps and Magnets ( Download PDF version )
S. Srinivasan
S. Srinivasan (“Chinu”), of the Discovery Science Resource Group, SAHAJ, Baroda, looks at
conventions of languages that we all live with. He cites many examples of conventions and
representations across cultures, opening our eyes to several possibilities and issues. Will learning be
more ‘free’ if we say there are many ways of doing the same thing? The author can be reached
at: sahajbrc@youtele.com
This led to a bit of ruckus in the class. Teachers said
it was unacceptable to write the units’ digits at the
extreme left. After much debate, one or two teachers
grudgingly accepted that I could have a point. And
grudgingly is how we all do (certainly I do) when
anything unconventional is posed to us for the first
time. Understanding and acceptance comes with
familiarity and quiet contemplation during a walk or
when by ourselves. As it probably did with our
teachers who came and told me the next day that
maybe I had a point.
I hope, dear reader, it is clear that as long as everybody
follows the same convention, it does not matter
whether we write from the left or the right. For
example, Hindi and English can be written RTL, from
right to left (i.e., tfel ot thgir morf). It is by acceptance
of convention that we read certain languages from left
to right and some others such as Urdu and Arabic
from right to left. Similarly writing units (ones) on
the right most is a convention that is accepted.
Conventions in writing and maps
The typical map and globes all indicate north on the
top and we all somehow end up believing that the
Himalayas are up there and Australia “down under”.
One can make an “upside down” map[1] and wait for
the reaction from children, teachers and of course the
school administration.
Similarly there is a convention for naming the north
and south poles of a bar magnet. Most science books
tell us that when we freely suspend a bar magnet, the
side pointing to the earth’s North Pole is labelled as “N” or north on the magnet. But we wonder, if
unlike poles attract, the end marked “N” should have
been labelled as “S” or South. It turns out that as a
matter of convention we may have chosen the former
label at the risk of spreading wrong science and
confusing children.
Writing itself has several conventions. LTR (left to
right) and top to bottom (TB) are dominant ones.
There are other systems (see table) where this is not
obvious or natural. Some, like Japanese use both
horizontal and vertical systems depending on the
context. Naturally the way they represent numbers
changes accordingly. The way we write or represent
our communication has an influence on our
perception and acceptance of reality.
Conventions in arithmetic
There are several other conventions in elementary
arithmetic related to negative numbers, decimals,
exponents, etc. We write negative numbers on the left
side of the number line: we may as well write them on the right side. Decimals are written with the whole
number part on the left and the fractional part on the
right. Can 1.5 (i.e., one and a half) also be written as
5.1? Can 23 be written as 23, with the index 3 is a
subscript instead of a superscript?
And multiplying like this instead of the usual way:
x12
______
46
92
______
552
Conventions in telephone numbers
Now a related question: when we are asked our
telephone number we always start from the left. For
example a cell phone number is rattled off as
9998531521, that is, nine, nine …two, one. Why do
we not say one, two, five … nine, nine, nine? It should
not make a difference, especially since cell numbers are
not really numbers in the usual sense. In some Arabic
speaking countries and in Egypt, telephone numbers
(and numbers in arithmetic) are read the usual /
dominant way (left to right) but Arabic numbers are
traditionally read (i.e. in increasing order, for e.g.,
1234 is ‘four and thirty and two hundred and one
thousand’), though this reading has declined of late[2].
Now the above cell phone number can also be written
as 1251358999. So if we write and read from right to left, we get the number as we conventionally hear
it. If you dial it this way, the cell phone company
technology does not recognise this and is unlikely
to in the near future. Since all phone networks are
nowadays connected to not only other countries but
many computers there seems to be some consensus on
reading telephone numbers.
What is the reason then for writing digits as we do?
Apparently the most significant digit is written first
and the less significant digit thereafter. The units fall
last in the hierarchy of writing. It is worth wondering
how much of this convention is because of the
number of right handed people in this world!
Conventions with number names
Now let us look at how the numbers 11- 20 and 21-99
are read in some Indian languages. In Hindi, we know
there are special names for the numbers 11 to 19. A
novice to the language cannot figure out the name for
the number 12, even if they know the name for 11.
But Tamil and Telugu, one could figure it out. Eleven
and twelve are called ‘padinonnu’ and ‘padirendu’
in Tamil (ten and one); and (ten and two), but in
Hindi ‘gyarah’ and ‘barah’ are not as obvious. This
differentiation can be made when comparing
numerals in English and German also. Number sets
21-29 and so on until 99 are decipherable in Tamil,
Telugu, English and German but not altogether in
Hindi or Gujarati or many other languages[3]. For e.g.,
in Hindi, 21 will be read as ‘ekees’ (one and twenty)
and 44 will be ‘chualis’, (four and forty). Similarly, in
Gujarati, also, it takes some practice to discern
whether one is referring to 74 or 76 with terms as
‘chummoter’ and ‘chhoter’. In Hindi we also have the
peculiar practice of heralding the next ten when referring to 19, 29, 39, etc. Even if we have mastered
naming 20-28, 30-38, 40-48, and so on, naming 29,
39, 49 will surprise you. 29 is called ‘untees’ (with a
suffix of 30), instead of being predictable ‘navvees’; 39
is called ‘unchaalis’ (with a suffix of 40), instead of
‘navtees’ etc.’[4] Due to this baffling number naming
system in Hindi, we often come across regular
speakers of Hindi, using number names in English
and dropping Hindi!
Calendar Dates
With respect to calendar dates, we have various
conventions:
• Little-Endian,[5] dd-mm-yyyy common to the
vast majority of the world's countries including India.
• Middle-Endian, mm-dd-yyyy as used in the United States and a few other countries, likely more descriptive with name of the month.
• Big-Endian, yyyy-mm-dd.
Point to ponder
When I married my wife who is from North India
I found her eating rice first and then the rotis whereas
I was used to finishing off the rotis first and savouring
the rice afterwards. This was initially quite a cause
of irritation.
The point I am making is that it is worthwhile to
examine why things are named as they are. Education
must include interrogating and asking the why
and how of accepted ways of doing things. This
acceptance without pausing, questioning, reflecting,
and wondering, serves sometimes as a deterrent in
higher levels of education. Questioning conventions
helps break hard-set thought patterns and open new
windows. I thank the teacher who questioned me.
It set me thinking and helped me to cultivate
appreciation of other ways of doing things and not
take things for granted.
1. Source: http://www.diversophy.com/maps/whatsupsouth.pdf
2. Source: <http://www.101languages.net/arabic/writing_system.html>
3. Hindi, Gujrati, German, Tamil, Telugu, and English are languages known to the author. In many languages such as Hindi, Gujrati, the
logical naming conventions is not usually known and the etymology is lost in history.
4. Incidentally, 89 is also correctly navassi instead of unianve!
5. The terms Endian originally comes from Jonathan Swift's satirical novel Gulliver’s Travels, where tensions are described in Lilliput and
Blefuscu: royal edict in Lilliput requires cracking open one's soft-boiled egg at the small end, inhabitants of the rival kingdom of Blefuscu
crack theirs at the big end.