Does one method have any inherent advantage over the other?

[rug]

[PoliticAverse]

1. I find the tally method faster/easier. n/t

[rug]

2. I never tried the dot method, although it does save space.

Hmmm, space versus time.

[Sirveri]

3. It's probably easier to make a line than a dot.

hence you just tick off as you count, and it's more automatic. Rather than having to dot the first four counts, then start making slashes, all of which are at different directions.

[rug]

5. That's probably it, although habit plays a role.

I wonder, if we used the dot method in the first place, if it would seem more natural.

[Sirveri]

7. It's possible that some ancient cultures did use such a method.

Though I doubt they used the one above. Sumeria, and our time system, is based off of the number six, and using dots you can make a group of six into a pyramid shape...

I suspect the real reason is that ball point pens and pencils don't mark well unless they are moved on the paper.

[krispos42]

11. Not to mention that pencils and ballpoint pens don't make good dots.

Generally speaking. Markers would work good, but then the lines are a lot thicker.

[Igel]

4. Define your use, define what's "good"--and what's an advantage.

Given a ball-point pen, I'd go with the lines. Those little dots are all but invisible.

If the paper's not pure white--or if there are extraneous marks on it--the dots+square will be more difficult.

Also if you have to look and interpret the numbers fast. Or if it might smear or be copied poorly.


If the goal is to save space, then the dots+squares have an advantage. Assuming that people make the squares as small as you represent them. Otherwise ... no.

[rug]

6. Let's assume one goal, precision and accuracy without doublechecking.

[Tien1985]

8. I didn't know the

Dot method was a thing! I've been doing that my whole life self taught. I've always found lines hard to count. That's really neat

[rug]

9. I never heard of it before.

Your latent genius has been revealed!

[DetlefK]

10. I think, I found an even faster method.

None of those methods offers has an inherent mathematical advantage over the other.
Dots: higher areal data-density. Tally: faster in writing down.

In one method you end up counting 10s, in the other you end up counting 5s. As an algorithm, both methods have a linear relationship between the amounts of data and time.

If we used another basis for counting, one that has a natural square-root, like 16->4 or 9->3, we could arrange the marks in a square geometric structure, reducing the calculation-time to sqrt(n).

1 1 1
1 1 1 becomes 9
1 1 1

9 9 9
9 9 9 becomes 81
9 9 9

81 81 81
81 81 81 becomes 729
81 81 81

And so on.

[rug]

12. I knew I'd get an intelligent math answer in here.

[truedelphi]

13. And thent here is Daniel Tammet's method of counting -

He speaks of numbers as being colors, having the properties of swirling droplets of waters:

#at=474

[rug]

14. Fascinating. And he can learn a language in a week.

Bookmarked. I think I'll pick up his book.