If you are new here and like what you read, consider subscribing.

Thursday, June 17, 2010

Hindi count approximation number pair

Categories: , ,
This post is based on Hindi colloquial/conversational number pairs used in approximating a quantity. Knowledge of colloquial Hindi is requisite.

Hindi conversational numbering follows Hindu-Arabic Decimal Number System with Hindi pronunciations. One (1) becomes Ek, Two (2) becomes Do, Three (3) becomes Teen and so on. When asked to approximate a quantifiable noun viz. in response to “how many minutes before the dad comes home?”, Hindi speakers often speak in number pairs such as Ek-Do (1-2). Not all pairs are acceptable and feel “right” when you say them aloud. This post will try to discern if there is a mathematical pattern in acceptable set of pairings.

Table: List (partial) of acceptable pairs
Pair Type
1-2 Next
2-1 One
2-3 Next
2-4 Double, Next 2x
2-5 Plus 3
3-1 One
3-4 Next
4-1 One
4-5 Next
4-6 Next 2x
5-1 One
5-6 Next
5-10 Double, Next 5x
6-1 One
6-7 Next
7-1 One
7-8 Next
8-1 One
8-9 Next
8-10 Next 2x
9-1 One
9-10 Next
10-1 One
10-11 Next
10-12 Next 2x
10-15 Next 5x
10-20 Double, Next 10x
11-1 One
11-12 Next
12-1 One
12-13 Next
12-15 Plus 3
13-1 One
13-14 Next
14-1 One
14-15 Next
15-1 One
15-16 Next
15-20 Next 5x
16-1 One
16-17 Next
17-1 One
17-18 Next
18-1 One
18-19 Next
18-20 Next 2x
19-1 One
19-20 Next
20-1 One
20-21 Next
20-22 Next 2x
20-25 Next 5x
20-30 Next 10x
21-1 One
21-22 Next
22-1 One
22-23 Next
22-25 Plus 3
23-1 One
23-24 Next
24-1 One
24-25 Next
25-1 One
25-26 Next
25-30 Next 5x
25-50 Double
26-1 One
26-27 Next
27-1 One
27-28 Next
28-1 One
28-29 Next
28-30 Next 2x
29-1 One
29-30 Next
30-1 One
30-31 Next
30-32 Next 2x
30-35 Next 5x
30-40 Next 10x
31-1 One
31-32 Next
32-1 One
32-33 Next
32-35 Plus 3
33-1 One
33-34 Next
34-1 One
34-35 Next
35-1 One
35-36 Next
35-40 Next 5x
36-1 One
36-37 Next
37-1 One
37-38 Next
38-1 One
38-39 Next
39-1 One
39-40 Next
40-1 One
40-41 Next
40-42 Next 2x
40-45 Next 5x
40-50 Next 10x

After manual enumeration of all such pairs where first number is up to 40, we can observe following seven type of pairings:
  1. Next: This is the most common type of pair in which each number is paired with next whole number following it.
  2. One: This is the second most common type of pair in which each number is paired with number One, except, of course, number One itself.
  3. Next 2x: Numbers 2, 4, 8, 10, 18, 20, 28, 30 and 40 pair with next number which is multiple of 2 i.e. next even number. Primarily, numbers ending in 0 seem to follow this pairing. There is temporary pairing of this type for numbers ending in 8 but this doesn’t continue long since after 38 this doesn’t work. 2 and 4 are obvious exceptions.
  4. Plus 3: 2, 12, 22 and 32 seem to follow this type of pairing. Projecting further, it appears that all numbers ending in 2 would following this pairing.
  5. Next 5x: 5, 10, 15, 20, 35 and 40 predictably follow pattern of paring with next number which is multiple of 5. These numbers themselves are multiple of 5 clearly following a pattern.
  6. Next 10x: 10, 20, 30 and 40 again following pattern of pairing with next number which is multiple of 10 while themselves being multiple of 10.
  7. Double: Numbers 2, 5, 10 and 25 pair with numbers twice them though 2, 5 and 10 be also be categorized to other pairing types which makes more sense. Projecting beyond 40, we see that while 50 doesn’t follow this pairing, 100, 150, 200, 500 do so. There doesn’t seem to be any identifiable pattern here.

I also tried to find pattern in sum, product and ratio of numbers in these pairs and in ratio of consecutive sums and consecutive products without success. Possibly, enumerating pairs after 40 may identify more types of pairings. What are your thoughts and observations?

(Peculiarity of such pairings have been in mind for quite many years but this post on Futility Closet — which, by the way, is a recommended read blog — propelled me to write this post.)
There was an error in this gadget