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Towards An Ideal Numeral System

Jamie Stroud

Table of contents


America uses a combination of numeral systems, primarily base-10 (decimal) and base-12 (duodecimal). It'd be simpler to use a single numeral system. Furthermore, I'll demonstrate in this article that base-8 (octal) is the ideal numeral system. For clarity's sake, when I use numbers in this article they'll be in decimal, unless otherwise noted, so as not to cause confusion.

Different Numeral Systems In Common Usage

Evidence For Octal

There's no evidence to suggest that decimal offers anything of particularly special use, nor does nature seem to be especially fond of decimal apart from humans having 10 fingers (including thumbs). Duodecimal is said by many to be especially useful since it can be divided by both 2 and 3 without involving fractions, and this is something neither decimal nor octal is capable of. However, why should 3 be thought to be so special, so important, to be divided by without involving fractions? The world is more likely to function by pairs and repeating phenomena (e.g. particles/antiparticles, attraction/repulsion, diecious species, any properties with polar opposites, fractals, etcetera), and so in the end it's more important to work well with pairs and repeating phenomena. With all that being said, I'll note how nature and society seems most inclined towards and would make the most use of octal over all other numeral systems.

jason padgett planck lattice


Many people have a difficult time understanding what it means to use a different numeral system and/or how to process numbers in a different numeral system. I'll explain how numeral systems work for clarity's sake.

Numeral systems are based on multiples of 10, with different numeral systems having different number values/quantities for "10". After 10, the cycle essentially repeats. Notice how similar "teen" and "ty" sound to "ten". You can tell they're a modification of "ten" based on how they function. For example, look at "forty", it's the fourth multiple of 10. 4 x 10 = for (FOUR) x ty (TEN). You can notice this for almost all numbers, twen(ty)one (Two x Ten + One), twen(ty)two (Two x Ten + Two), etcetera.

Eleven through nineteen (11-19) is somewhat of a special case from the rest of the numbers in English. This is because they essentially function backwards from the rest of the numbers in regards to how they're named. For example, fourteen could hypothetically be teenfour or tyfour and it'd be more logical. Most languages do this actually, and so English's way of naming numbers is more complicated than most.

With all that being explained, an octal numeral system would function something like this:

*Saying one-hundred is redundant. In octal, you wouldn't say one-eight (10), one-eight-one (11), one-eight-two (12), etcetera. Or in decimal, you wouldn't say one-ten (10), one-eleven (11), one-twelve (12), etcetera.

*Zero and seven are awkward in that they're 2 syllables while the rest of the single digits are one syllable. For example, they could be called "zee" and "ven", respectively.

*In practice, people use numeral systems with the end of the base number functioning as the end of a sequence, but logically the end of a base number actually functions as the beginning of a new sequence or new "row".

To exemplify how people generally use numbers
0 1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20  
21 22 23 24 25 26 27 28 29 30  

To exemplify how logic uses numbers
0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29

As you can see, the last digit of each respective number always lines up in the latter example whereas they're one off in the former example. This has implications when it comes to creating symmetrical arrays.

In Closing

If social network companies like Facebook and Twitter implemented codes to automatically put octal numbers in parenthesis whenever someone posts with decimal numbers, it'll get people used to seeing the numbers of that numeral system. Through repetition of frequently seeing octal numbers next to decimal numbers, they'll be able to more easily adapt to it. To avoid confusion for those who want to progress quickly to octal but don't want to cause confusion or risk misinterpretation by others, the clarification can be put in parenthesis. For example, 100 in octal could be written as 100 (oct), whereas 100 in decimal could be written as 100 (dec).


Regular Time Octal Time
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