I'm going to have to disagree. We should be using base 7.
It pretty much has all the good points (or at least not-bad points) of base 6. It has significant ease of determining "divisible by 2" or "divisible by 3" - add the digits. Get an even number, it's divisible by 2. Get a 3 or multiple of 3 - it's divisible by 3, just like base 10 representations are. There's also a counting trick using 2 sets of 4 fingers:
1. Hold out both hands, palms toward you. Fold in thumbs. You have four fingers on each hand.
2. Count one for left pinkie.
3. Count two for right pinkie.
4. Count three for left ring finger.
5. Count four for right ring finger.
6 And so on, until count 6 for right middle finger.
7. Count ten for left index.
8. Count eleven for right pinkie.
9. Count twelve for left pinkie.
10. Count thirteen for right ring finger
11. And so on, until you count sixteen for left middle finger.
12. Count twenty for right index finger.
Even numbers are on the right fingers, odd on the left. Even multiples of 10 (base 7) are right index, odd multiples of 10 (base 7) on left index finger.
Even numbers have even parity (sum digits is even), odd numbers have odd sum of digits.
Simple and handy, even if fractions aren't worth it. We shouldn't use fractions anyway, except as a jumping off point for rational numbers. Decimal representation all the way, baby!
It pretty much has all the good points (or at least not-bad points) of base 6. It has significant ease of determining "divisible by 2" or "divisible by 3" - add the digits. Get an even number, it's divisible by 2. Get a 3 or multiple of 3 - it's divisible by 3, just like base 10 representations are. There's also a counting trick using 2 sets of 4 fingers:
1. Hold out both hands, palms toward you. Fold in thumbs. You have four fingers on each hand.
2. Count one for left pinkie.
3. Count two for right pinkie.
4. Count three for left ring finger.
5. Count four for right ring finger.
6 And so on, until count 6 for right middle finger.
7. Count ten for left index.
8. Count eleven for right pinkie.
9. Count twelve for left pinkie.
10. Count thirteen for right ring finger
11. And so on, until you count sixteen for left middle finger.
12. Count twenty for right index finger.
Even numbers are on the right fingers, odd on the left. Even multiples of 10 (base 7) are right index, odd multiples of 10 (base 7) on left index finger.
Even numbers have even parity (sum digits is even), odd numbers have odd sum of digits.
Simple and handy, even if fractions aren't worth it. We shouldn't use fractions anyway, except as a jumping off point for rational numbers. Decimal representation all the way, baby!