Base Six

What is Base Six? It has something to do with math if Principal Skinner is to be believed.

http://www.snpp.com/episodes/8F17.html

The way bases work: when we talk about a number, say 1,406, we mean 1x10[sup]3[/sup] + 4x10[sup]2[/sup] + 0x10[sup]1[/sup] + 6x10[sup]0[/sup]. There are ten digits, 0 through nine, and when one counts, the progression goes 1,2,3,4,5,6,7,8,9… and then goes back to 0, and the next highest place gets increased by one. This is base ten because there are ten digits.

We humans use base ten because we have ten fingers. It’s natural for us, but really not “natural” in the mathematical sense of things. Computers use base 2, and in some way also base 16 and base 8. It could be argued that genes use base 4. But the use of base 6 is just silly because practically noone uses it for anything.

Which is why this is very funny.

This is a WAG: Skinner is tired of the old math books from the “New Math” era where - in the words of Tom Lehrer - “the important thing was to understand what you were doing, rather than to get the correct answer”. One of the ideas behind the New Math was to teach children how a number system works - so apart from our day-to-day base 10 (decimal) numbering system, the poor kids were asked to do arithmetic in base 6 , base 8 etc.

As for what constitutes a base six numbering system - it’s just a system of counting where you only use the symbols 0-5, instead of 0-9 as you’re used to. So in order to count to ten in base six, you’d go: 1, 2, 3, 4, 5, 10, 11, 12, 13, 14. Simple, eh ?

Shouldn’t the Simpsons use base 8?

There are different numbering systems that use different bases. The system we use (the decimal system) is base 10. There’s also hexadecimal (base 16) and binary (base 2), which are commonly used with computers. Octal (base 2) is also common. The different bases work like this:


binary  octal  decimal  hexadecimal
     0      0        0            0
     1      1        1            1
    10      2        2            2
    11      3        3            3
   100      4        4            4
   101      5        5            5
   110      6        6            6
   111      7        7            7
  1000     10        8            8
  1001     11        9            9
  1010     12       10            A
  1011     13       11            B
  1100     14       12            C
  1101     15       13            D
  1110     16       14            E
  1111     17       15            F
 10000     20       16           10
 10001     21       17           11
 10010     22       18           12
 10011     23       19           13
 10100     24       20           14
 10101     25       21           15
 10110     26       22           16
 10111     27       23           17
 11000     30       24           18
 11001     31       25           19
 11010     32       26           1A
 11011     33       27           1B 
 11100     34       28           1C
 11101     35       29           1D
 11110     36       30           1E
 11111     37       31           1F
100000     40       32           20

These different bases are actually useful. Also, be aware that everything in the same row is the same number, just in a different base. Binary 1010 = octal 12 = decimal 10 = hex A

Base 6 would go like this:
0, 1, 2 ,3 ,4 ,5 ,10 ,11 ,12 ,13 ,14 ,15 ,20 ,21 . . .

However, base 6 isn’t really useful, and thus it’s never used.

As a side note, in the normal decimal number 3.14159, the dot is called the decimal point. In the binary number 101.110110, the dot is called the binary point. The naming convention extends to other number bases.

:smack: I need to learn to proofread. My post should read:

Octal (base 8) is also common.

Of course, anyone who didn’t already know that should be able to guess from the name.

Hence the joke? They’re subtle.

Way off base

I think base 6 is when the sex get really kinky.

I think, considering the history books not having gone up to the end of the Korean War, Skinner’s joke was that their Math books were soooo bad, that they didn’t have a complete system…maybe…

In general, the dot is referred to as the radix point.

ARGH!! NOOOOO!

I am doing the whole binary/octal/hexadecimal thing for my Computer Science degree…I have my exam in a week…thanks for bringing it up guys! :mad: