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For the vast majority of mathematics and other uses of numbers, the specific details of [numeral system](https://en.wikipedia.org/wiki/Numeral_system) notation -- how to represent specific numbers -- make surprisingly little difference.

As far as I can tell, there are only 2 differences between [Kaktovik numerals](https://en.wikipedia.org/wiki/Kaktovik_numerals) and the [decimal](https://en.wikipedia.org/wiki/Decimal) numeral system: the base, and the specific shapes of the letters.


Base
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Kaktovik numerals are a base-20 system, so they may be useful for transcribing [numerals in the Iñupiaq language](https://en.wikipedia.org/wiki/I%C3%B1upiaq_numerals)
and other languages that express numbers in words that imply a [base-20 system]( https://en.wikipedia.org/wiki/Base-20).

There has been a lot of thought about improving the traditional base-10 (decimal) system.
I feel that most of the people I've read on this subject would agree that base-20 is theoretically overall better than base-10.
Alas, most of the people I've read on this subject propose some other base that is even better than base-20 in some way -- even worse, they seem to disagree on exactly which base is best.
Perhaps the most popular bases currently are:

* [dozenal](https://en.wikipedia.org/wiki/Dozenal)
has some strong arguments in its favor for human writing and speech: [Dozenal FAQs](https://dozenal.org/articles/DSA-DozenalFAQs.pdf)
* [hexadecimal](https://en.wikipedia.org/wiki/Hexadecimal) is better for finger-counting on human hands (in 2 very different ways)
* [octal](https://en.wikipedia.org/wiki/Octal)
* Base-2 and base-3 usually have the best [radix economy](https://en.wikipedia.org/wiki/Radix_economy) when physically building calculating hardware.


shapes of the digits
----

In my opinion, the 3 most important design characteristics of written digit symbols are (in order of importance):

1. Readability
2. Writability
3. Learnability

Let's start with Learnability:

"They are visually iconic, with shapes that indicate the number being represented." -- [Kaktovik numerals](https://en.wikipedia.org/wiki/Kaktovik_numerals)

That's clearly much better for people *learning* the system than traditional decimal digits, who must spend more time memorizing the apparently arbitrary shapes of the traditional decimal digits and their apparently arbitrary mapping to values.

A few other sets of digit symbols also have this nice property of the symbol logically reflecting the value of the digit:
* Maya numerals (also base-20, like Kaktovik numerals)
* [Pentadic numerals]( https://en.wikipedia.org/wiki/Pentadic_numerals) (base 10)
* [Stargate Ancients numerals](https://en.wikipedia.org/wiki/File:Ancient_alphabet.png) (base 10) (alas, far more difficult to write)
* [Babylonian cuneiform numerals](https://en.wikipedia.org/wiki/Babylonian_cuneiform_numerals) (base 60)
* [Matthew DeBlock](http://www.dscript.org/) has designed such symbols for hexadecimal digits
* [Omniglot](https://www.omniglot.com/) collects a huge variety of natural and constructed writing systems, a few of which have this property
* [r/neography](https://www.reddit.com/r/neography/) is a place for discussing constructed scripts, including written digit symbols, which sometimes have this property.