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Comment by DEinspanjer | Hacker News Reader

This sounds like an awesome book, and I would probably have loved to have it when my kids were infants. I pointed a few friends at it.

My big experiment with my first born was trying to teach her to count starting with 0 instead of 1. I attempted it for a few months, but ultimately stopped because everyone else around her was counting the typical way and it seemed like it might be confusing to her.. I admit it was a bit embarrassing for me when doing so in the presence of non-geeks.

I'll also go ahead and share a funny anecdote and hope it doesn't come back to haunt her in a decade.. :) We noticed a common side effect of her getting the hiccups whenever we changed her diaper. One day I jokingly said that the first time she ever came home from a date with the hiccups, her boyfriend had better start running.

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My parents taught me to count on my fingers with binary, which lets you get to 31 on one hand, and 1023 on two. I've found that to be a small thing of huge value when doing simple counting tasks, such as counting syllables or words in a short text, where you can't just keep a count in your head.

    ELDERLY LADY: How old are you, little boy?
    YOU: (middle finger)
    ELDERLY LADY: WHAT?!?
    YOU: It's 4 in binary.
    ELDERLY LADY: Oh, for a second, I thought you ...
    YOU: (two middle fingers)
    ELDERLY LADY: WHAT?!?
    YOU: Oh, sorry, I was just guessing your age.

Anyone fascinated by this will find this wikipedia article convenient to get going!

https://en.wikipedia.org/wiki/Finger_binary

Just don't stop at 132 when people are around!

I just tried it and I have the problem that it's very difficult for me to extend only my ring finger. I vaguely remember someone saying that this is because some fraction of the population don't have fully independent 4th and 5th fingers...

I hadn't heard about anyone having naturally occurring fourth and fifth fingers without the linkage. I do remember reading a story about a piano player who devised a set of stretches intended to develop the independence of his ring fingers but it ended up damaging the (tendons|ligaments|<insert medical term here>) and he could no longer effectively play the piano.

http://musicthing.blogspot.de/2006/09/finger-stretching-for-... That was Robert Schumann.

I never thought of that, it's really cool. But I'm not able to show 8 or 9... :(

How have I never thought of this? I am using this from now on...

Thanks for sharing the book with your friends!

I'm intrigued by your 0 vs. 1 experiment. I wonder if there is something fundamentally different in how we learn the concept of ordinal numbers (1, 2, 3) versus, say, integers (-1, 0, 1). Usually we teach numbers by counting physical objects, and perhaps it takes a little longer to understand the concept of zero if you're used to counting objects.

I couldn't hope to determine if the early training had anything to do with it or just the overall attention to early education, but I will say that she developed an affinity for math at a young age and even in preschool tended to be interested in the more advanced concepts of abstract math rather than simple counting of objects.

I did teach both my children to count on their fingers using the pattern taught by ASL. I've noticed that sometimes her friends look at her oddly when she holds up her index, middle, and thumb for the number three, and obviously, they have no clue that holding up the index, middle, and ring fingers might mean either six or three to her depending on to whom she is talking.

I introduced both my children to an awesome game when they were just in kindergarten: http://www.dragonboxapp.com/ it teaches basic algebraic concepts cloaked in the guise of a fun puzzle game.

I find the finger counting (3 with thumb, index, and middle finger) interesting. Here in Asia that could mean 8.

I was first taught to count starting from the index finger as well:

fist = 0

index = 1

index, middle = 2

index, middle, ring = 3

index, middle, ring, pinky = 4

index, middle, ring, pinky, thumb = 5

thumb = 6

thumb, index = 7

thumb, index, middle = 8

thumb, index, middle, ring = 9

(I am from Thailand, but I think this is how counting is taught in America as well?)

I thought this was universal until I went to Singapore. I was quite intrigued that in Singapore a "thumb" is not considered a number but rather a signal for "good" and instead they used thumb + pinky for 6. (The rest seems to be the same.)

Not sure why I brought that up, but I guess I had not realized that there was a difference in even the way we counted all around the world until that point.

EDIT: Formatting

Typically, kids in the USA are taught 1 - 5 the way you describe, but not taught anything further with a single hand. If they want to count to ten, they use both hands in the same manner.

There are a few other fancy ways including even binary which could let you count up to 1024 if you could keep it all in your head. :)

The ASL (American Sign Language) method I mentioned in the parent is described here: http://www.dummies.com/how-to/content/counting-on-numbers-in...

I annoyed my teachers in elementary school demonstrating binary finger counting to 1024 when they were insisting that students stop finger counting because "you could only count to 10"

I was a precocious little shit.

Yeah, my dad taught me to count on my hands in binary when I was young. I tried explaining it to others but that usually broke down when I reached four...

It sounds like (unsurprisingly) Singapore uses the same system used here in Hong Kong. I'm not sure if the same system is used in mainland China.

fist = 0 index = 1 index, middle = 2 index, middle, ring = 3 index, middle, ring, pinky = 4 index, middle, ring, pinky, thumb splayed = 5 thumb, pinky = 6 index, middle, ring, pinky, thumb all held strait with their pads touching, looking a bit like a shadow puppet of a bird's head = 7 thumb, index = 8 just the index finger, bent in half = 9

Yes, the same system is used in mainland China.

Apart from 4 and 5, you can kind of see the link between the written form of the number and the hand signal: 1, 2, 3: obvious because 一二三 6: the thumb and pinky make up the bottom part of the character 六 7: If you look at your own right hand upside-down when making the gesture, the bird's head points in the same direction as the 七 8: Your thumb and index finger are the two lines in 八 9: Your index finger is the second stroke in 九

I don't know whether this is coincidental, or even just my imagination...

My hand cannot do 9 the way you describe. My pinky is too stubborn.

I taught my daughter starting with fist, so zero was natural.

Then, when we started playing board games there was an issue playing games like "Game of Goose" because she started counting with 1 in the occupied space. We "fixed" that starting with 0.

> I've noticed that sometimes her friends look at her oddly when she holds up her index, middle, and thumb for the number three,

Hmm interesting. I have been trying something different as well. I have been counting with fingers with my kid using different fingers every time. The idea is that it doesn't matter to associate a finger with a number as long as the correct number of fingers is up. Like say most people start with the thumb and move left or right. Sometimes I start with the ring finger.

Counting is also fun in general. We count steps, count trees when we drive. I try to never make it about teaching but more about fun.

Thanks for the link, the game seems awesome !!

I always tell my daughter to not forget the number zero when counting and that it is important, without it we can't have the number 10, or 20...and so on...etc

0 is important, but it's not true that without it we can't have the number 10.

In written form, for example, we can represent 10 and 20 without 0 easily, as the 0 is just a syntactic placeholder:

- Roman Numerals: X and XX

- Scientific Notation: 1e1 and 2e1

- Base 16: a and 14

- Set theory: {{{{{{{{{{}}}}}}}}}} and {{{{{{{{{{{{{{{{{{{{}}}}}}}}}}}}}}}}}}}}

But more importantly, the existence of the number 10 is independent of it's representation. Mathematically, the existence of the natural numbers depends on a "unit" (which we often represent with 1) and a method for incrementing or inducing the subsequent number.[1]

0 ensures the existence of groups [2], and by extension many important mathematical structures. I get your point though, and I wonder what would be an accurate, but still relatable, reason for a young person to grasp the importance the number 0?

[1] http://en.wikipedia.org/wiki/Axiom_of_infinity

[2] http://en.wikipedia.org/wiki/Group_(mathematics)

>what would be an accurate, but still relatable, reason for a young person to grasp the importance the number 0?

If you have one cookie, and you eat it, how many cookies do you now have?

I asked my nephew and this was the answer I got back:

1 cookie, in my belly. (And then he demanded a cookie.)

try asking him 'if you have one cookie, and I eat it, how many cookies do you have?'

I think everyone understands the concept of "nothing" or "no cookie" vs "a cookie", just as babies (and, say, birds [1]) have a concept of quantity and even discrete quantity at small values.

I can understand that I have no cookie without counting from the number 0. But why is it important to label nothing, to give it a name and symbol and define its properties?

[1] http://en.wikipedia.org/wiki/Bird_intelligence#Counting

Well, easy, you just apply group theory ;-) and clearly you have the correct amount such that if you keeping eating this amount of cookies, no matter how many cookies you start with, you end up the same number [Identity]

The Romans (and many others) seemed to manage.

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