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Klaus Bung:
Regularities in Hindi-Urdu numerals
Part F: Rows vs Columns

Rows vs columns

I have examined numerous Urdu courses and textbooks to see if they make any comment on numerals, if only to state that they are unusually complicated, or any attempt to organise them into anything better than an unstructured list from 1 to 99. I have found none, except Schmidt 1999, but have, of course, more searching to do, especially in Hindi books.

Bright 1972 seems to have been the first person to question whether native speakers of Hindi-Urdu produce numerals as indivisible units or psychologically perceive them as pairs of morphemes put together in a specific order, whether they are aware that they have "four-and-twenty black goats" rather than "twenty-four black goats". Bright was not a teacher or textbook author, but an academic linguist, and he did not publish a matrix, even though having one in front of him would have served him well during his investigations.

Schmidt 1999, p 230f, is the only author known to me who presents the numerals in the form of a matrix. She has the multiples of 10 (10, 20, 30, ...) in the right-most column which makes it easy to understand the ekuna numbers. She then observes: "The first syllables of the numbers in the vertical columns, while not identical, are often similar. Some students find it easier to learn the numbers by memorizing the vertical columns, rather than the horizontal ones."

Schmidt's Number Matrix

Click on the image to make it larger. Click here to make it even larger.

This is a refreshingly insightful approach to numerals, as opposed to, on the one hand, countless shoddy and uninfluential, or populist (BBC TV) approaches to Urdu not worth quoting, and, on the other hand, some solid practical Urdu courses produced by renowned linguists, such as Matthews and Dalvi 2003 and Bailey, Firth and Harley 1956.

Bailey, Firth and Harley 1956, p 20 f, simply list the numerals from 1 to 99 in one long column without a warning, and without either expressing surprise that these numerals are resistant to analysis or stating that they can, or cannot, be analysed.

Matthews and Dalvi 2003, p 316 ff, also present the numbers, without any comment about analysis or otherwise, in blocks of 10 at a time (0-10, 11-20, ...) in neither rows nor columns, and tell the students to practise "reading" them. These seem to be intended for practising numeral script (which admittedly is also a skill that has to be learnt) rather than as an exercise in knowing the numerals and using them.

Neither Bailey nor Matthews (nor our class teacher, for that matter) pointed out that Hindi-Urdu employs the blackbird sequence (four-and-twenty, rather than twenty-four). I find that astonishing.

Schmidt does not say why some students find the columns easier to learn than the rows, but it seems to be because of the similarities she observes in the "first syllables" throughout a column.

Schmidt has missed the fact that what she says about "first syllables in a column" is also true of "second syllables in a row". But, unless hyphens are employed to separate the first from the second morpheme, as I have done, these similarities are much more difficult to notice in the rows than in the columns.

Even with hyphens, these similarities are more difficult to see in a row then in a column. To make them absolutely unmissable, even for the dimmest donkey (as opposed to the smartest ass), I have presented the rows as exploded columns, and lo and behold: no longer shall "darkness cover the earth and gross darkness the people", but now order and clarity reign.

Schmidt's assertion that the columns are easier to learn than the rows turns out to be plainly wrong, wrong for all students. Rows are easier to learn, but the numerals have to be hyphenated, and the students have to see the rows as column diagrams as well.

I must not miss this opportunity to draw attention to Schmidt's intriguing concept of "horizontal columns" which, no doubt, refers to the ruins of Carthage, amongst which the proverbial "colourless green ideas sleep furiously".

The importance of fluency

Finally it should be pointed out to teachers and learners alike that being able to recite numerals in a row or in a column does not mean that student "knows" the numbers. When Schmidt says colums are easier than rows, no matter whether true or false, it does not mean that a student can stop learning the numbers when he has mastered one sequence or the other.

Reciting numbers is hardly ever required unless the student decides to join al-Qaeda and has to learn to count down (reverse order, horizontally!) before he shoots his victim, or, even better for the world, blows himself up in the Rub' al Khali ("the empty quarter" in the huge Saudi deserts).

If he hesitates during the count-down, either his victim may not take him seriously or his mentors may think he is not fully committed to their noble cause (perhaps even a double-agent) and therefore dispose of him. This shows that knowing Urdu numbers to perfection can be a matter of life and death.

But not all of us will ever have the chance to risk our life, or to die, in such a noble cause.

For most of us, the Urdu numbers may be needed when we have to haggle over a taxi fare or the price of ten bananas, especially when small amounts are involved. Haggling over the price of a steel mill in terms of lakhs or crores is more likely to be done in English.

For more information about what is required in mastering numerals, at random and in context, whenever they are required, see "Learning foreign language numerals" (soon to be published on this website).

What Schmidt means when she talks about reciting numerals in columns or rows therefore is only intended to decide which is the very first, the most primitive, step in the long process of learning the numerals.

Rows presented as columns

Schmidt's remark about similarities showing in columns has another fortunate implication which can be exploited for teaching and learning purposes.

In this paper, and elsewhere, I have frequently used the technique of "exploded words" to make etymological relationships (similarities), even distant ones, obvious, even to the layman. This technique works with columns but not with rows. Therefore, when required, rows have to be converted into columns first.

Warning: Always use a monospaced font, such as Courier New, and not a proportional font, for exploded words; otherwise the letters will not align.

Once we have constructed the number matrix, for any language, and used it in order to gain insights into regularities and to come to grips with the number system as a whole, there is nothing to stop us from presenting each row in a separate table, as one column, and to utilise the technique of exploded words.

This is what I will do now, in yet another attempt to make the elusive similarities in the rows apparent. We will see that the similarities, even in the second syllables (morphemes) are blindingly obvious. It is only a matter of a helpful diagrammatic display (for which both Descartes and Gilbert argued so forcefully). In our display, three features are of critical importance:

marking the morpheme boundaries by hyphens
displaying even "the rows" of the matrix vertically
exploding the words and arranging related letters so that they form colums of letters

Rows exploded

Note similarities in second morpheme.

Row 10	Row 20	Row 30
10 da s 11 giaa - ra 12 baa - ra 13 te - ra 14 cau - da 15 pand - ra 16 so - la 17 sat - ra 18 aTThaa - ra	19 unn - iis 20 biis 21 ikk - iis 22 baa - iis 23 te - iis 24 cau - biis 25 pacc - iis 26 cha - bbiis 27 sattaa - iis 28 aTThaa - iis	29 una - ttiis 30 tiis 31 ike - ttiis 32 ba - ttiis 33 tê - tiis 34 cau - tiis 35 paî - tiis 36 cha - ttiis 37 saî - tiis 38 aR - tiis

Row 40	Row 50	Row 60
39 un - taal iis 4 caar 40 caal iis 41 ik - taal iis 42 be - aal iis 43 tê - taal iis 44 cau - aal iis 45 paî - taal iis 46 che - aal iis 47 saî - taal iis 48 aR - taal iis	49 un - caas 50 pac - aas 51 ikiaa - van 52 baa - van 53 tre - pan 54 cau - van 55 pac - pan 56 cha - ppan 57 sataa - van 58 aTThaa - van	59 un - saTh 60 saaTh 61 ik - saTh 62 baa - saTh 63 tre - saTh 64 caû - saTh 65 paî - saTh 66 che -aa- saTh 67 sar - saTh 68 aR - saTh

Row 70	Row 80	Row 90
69 un - hattar 70 sattar 71 ik - hattar 72 ba - hattar 73 ti - hattar 74 cau - hattar 75 pac - hattar 76 chi - hattar 77 sat - hattar 78 aT - hattar	79 un - aasii 80 assii 81 ik - aasii 82 be - aasii 83 tir - aasii 84 caur - aasii 85 pic - aasii 86 chi - aasii 87 sat - aasii 88 aTh - aasii 89 nau - aasii	90 nav-ve 91 ik - aanve 92 baa - aanve 93 tiir - aanve 94 caur - aanve 95 pic - aanve 96 chi - aanve 97 satt - aanve 98 aTTh - aanve 99 ninn - aanve

Columns exploded

Note similarities in the first morpheme.

Column 10	Column 11	Column 12
10 das 20 b-iis 30 t-iis 40 caal-iis 50 pac-aas 60 saaTh 70 sattar 80 assii 90 nav-ve	11 g iaa - ra 21 ikk - iis 31 ike - ttiis 41 ik - taaliis 51 ik iaa - van 61 ik - saTh 71 ik - hattar 81 ik - aasii 91 ik - aanve	12 baa - ra 22 baa - iis 32 ba - ttiis 42 be - aaliis 52 baa - van 62 baa - saTh 72 ba - hattar 82 be - aasii 92 baa - aanve

Column 13	Column 14	Column 15
13 te - ra 23 te - iis 33 tê - tiis 43 tê - taaliis 53 tre - pan 63 tre - saTh 73 ti - hattar 83 tir - aasii 93 tiir - aanve	14 cau - da 24 cau - biis 34 cau - tiis 44 cau - aaliis 54 cau - van 64 caû - saTh 74 cau - hattar 84 caur - aasii 94 caur - aanve	15 pand - ra 25 pacc - iis 35 paî - tiis 45 paî - taaliis 55 pac - pan 65 paî - saTh 75 pac - hattar 85 pic - aasii 95 pic - aanve

Column 16	Column 17	Column 18
16 so - la 26 cha - bbiis 36 cha - ttiis 46 che - aaliis 56 cha - ppan 66 che - aa-saTh 76 chi - hattar 86 chi - aasii 96 chi - aanve	17 sat - ra 27 sattaa - iis 37 saî - tiis 47 saî - taaliis 57 sataa - van 67 sar - saTh 77 sat - hattar 87 sat - aasii 97 satt - aanve	18 aTThaa - ra 28 aTThaa - iis 38 aR - tiis 48 aR - taaliis 58 aTThaa - van 68 aR - saTh 78 aT - hattar 88 aTh - aasii 98 aTTh - aanve

Column 19
19 unn - iis 29 una - ttiis 39 un - taaliis 49 un - caas 59 un - saTh 69 un - hattar 79 un - aasii 89 nau - aasii 99 ninn - aanve

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