If you've looked at numerology at all, you will know about the way that positive numbers are reduced by adding together digits to make new numbers until there is only one digit left.

For example, the number 561 is first reduced to 5+6+1=12, and then to 1+2=3.

often, a numerologist will take the digits in your birthday and reduce you to a number, or take the letters of your name, and number them with A being 1, and Z being 26, and similarly reducing you to a single number.

In my case, I was born 6/7/1974, which reduces to 6+7+1+9+7+4=34, which then reduces even farther down to 3+4=7.

So, I am, as they say, a "7".

Also, in numerology, a number that is a multiple of 3 will always reduce to a 3, 6, or 9 (a multiple of 3), and a multiple of 9 will always reduce to 9.

All this is well and good, and conveniently works with our base ten number system.

But let us investigate Alternate Base Numerology, to check for the "3" rule and the "9" rule.

Starting in base 2, it quickly becomes obvious that all numbers are numerologically reduced to 1. There is no other result. For example, the number 111100(60 decimal), is reduced to 100(4 decimal), which is reduced to 1.

So, in Base 2, no 3 rule and no 9 rule, and in fact the only rule is that everything gets reduced to 1.

In base 3, we will get values 1 or 2, so no 3 or 9 rule here.

However, I will point out that any multiple of 2 reduces ultimately to 2:

2=2
11(4 dec)=2
20(6 dec)=2
22(8 dec)=11(4 dec)=2

At this point, the N-1 rule, where N is the base, is starting to become evident. This means that the 9 rule in base 10 is a result of the N-1 rule, and that makes 9 "nothing special", but we will continue on...

In base 4, we can have values 1, 2, and 3. Based on previous bases, we expect the N-1 rule to give us a 3 for every multiple of 3.

3=3
12(6 dec)=3
21(9 dec)=3
30(12 dec)=3
33(15 dec)=12(6 dec)=3
102(18 dec)=3

In base five, we expect a similar rule for 4:

4=4
13(8 dec)=4
22(12 dec)=4
31(16 dec)=4
40(20 dec)=4
44(24 dec)=13(8 dec)=4

But, just for grins, check for the 3 rule...

3
11(6 dec)=2
14(9 dec)=10(5 dec)=1
22(12 dec)=4
30(15 dec)=3
33(18 dec)=11(6 dec)=2

So... no 3 rule.

(more later about this...)