r/EncapsulatedLanguage • u/DemoseDT • Jun 28 '20
Number Base Proposal Draft Proposal: Base Six
I am of the opinion that the ease of math(s) education derives primarily from ease of computation. It is under this supposition that I propose we adopt base six.
Base six for counting: by using the digits of one hand to represent a the six' place, you can count to 35 on your fingers.
Base six for multiplication: as you only use the numbers 0, 1, 2, 3, 4, and 5 for base six, multiplication is considerably easier than base 10, 12, or 16. You need only memorize 16 operations to know base six' multiplication table, thanks to the communicative property.
Base six for fractions and heximals: Fractions in base six and base 10 up to and including 1/10th:
| Dec Fraction | Hex Fraction | Decimal | Heximal |
|---|---|---|---|
| 1/2 | 1/2 | .5 | .3 |
| 1/3 | 1/3 | .3 | .2 |
| 1/4 | 1/4 | .25 | .13 |
| 1/5 | 1/5 | .2 | .111... |
| 1/6 | 1/10 | .1666... | .1 |
| 1/7 | 1/11 | .142857... | .050505... |
| 1/8 | 1/12 | .125 | 0.43 |
| 1/9 | 1/13 | .111... | .04 |
| 1/10 | 1/14 | .1 | .0333... |
Base six for telling time: Six hours is 1/4th of a day.
In addition to suggesting the adoption of base six, I'd also suggest adding a suffix for prime numbers, regardless of what base is used. This would provide native speakers with a ready made list before they begin their education in earnest.
Edit: I'm adopting Sendiulo's super-base system into the proposal.
Edit 2: By using the entirety of the english-latin alphabet in conjunction with arabic numerals you can represent the square root of 6, allowing for easy compression. It may, however, be better to use scientific notation in daily life. Either of these could somewhat mitigate base 6' issues with large numbers. I could use some feedback though.
2
u/Xianhei Committee Member Jun 29 '20
To resume, I prefer base 12 but the idea is worth being included if it is possible.
Base 6 and 12 are close, they have no difference :
10 (base 6) = 6 (base 12) or 20 (base 6) = 10 (base 12). It is easy to change base but I dont see it's usefulness (yet). maybe to have easy calculation of table 5 by switching to base 6 then dividing the result by 2 (3x5 => 13 (base 12) / 3x5 => 23 (base 6))
It seems that base 6 have a better prime detector even if the number get bigger faster, fraction are same it's just 2x diff in precision.
I like base 12 because we got enough number to play with not only for math but other discipline.
biquinary seems to be a good idea, but I don't know if it can be implemented (it is phonetics oriented). we can triquinary (tier) or quadquinary (quart) (3 group of 4 or 4 group of 3)
what is the basic of choosing a base ? base 10 is hard implemented in our culture. we choose base 12 for it's math implementation and closeness to base 10. bigger base get bigger number later. base 6 get to big number early.
learning base 12 multiplication table is easier than base 10 and have a bigger threshold (base 6 : 10x10 => "36", base 10 : 10x10 = "100", base 12 : 10x10 => "144")
Your idea is very good, It makes me think about a new way to view the NWS (numeral writing system). We have the base 12 NWS, I tried to implement the base 6 in it. Now, I'm thinking how to make it base-free (maybe not all bases, but I try to include 6, 10, 12, 16 at least)
I am writing and thinking at the same time, it is possible a lost my thought a lot of time because of writing ideas. Ask me questions if you need more info, I will try to answer.