# A simple algorithm for naming all numbers in all bases that are a positive power of two, based on the Major System of mnemotechnics.

## Introduction.

The base ten counting system has a set of spoken names and rules for pronouncing them that works well, and that we take for granted. Other bases, such as binary, or base eight, or base sixteen seem inhuman, difficult, and useless mainly because they lack an analogous system of names, so that people resort to reading the numbers out like telephone numbers and then saying what base it is to allow the listener to decipher what the number means. To remedy this deficiency in my favorite bases, which are those that are powers two, I developed a unified names and pronunciation system for all base that are a positive power of two. This allows one to use any base that is a power of two, and therefore a form of binary, in a way that is analogous to how we use base ten. In other words, I have created a spoken language for these other bases, and I optimized it for ease of learning and concision.

## Concisely pronouncing powers of two both positive and negative using a set of names generated by an easily learned algorithm.

I have created a simple algorithm that allows one to deduce how to pronounce any number in any form of binary. This is so as for people to be able to try out the system with minimal investment of time.
I used a subset of the encoding system used in the well-known (in the world of mnemotechnics) Major System of mnemotechnics to link the ten numerals of base ten to ten consonants that are easily recognized and distinguished from each other. They are as follows.
0 = s
1 = t
2 = n
3 = m
4 = r
5 = l
6 = sh
7 = k
8 = f
9 = p
Unlike in the Major System, in my system vowels also encode something. For now I use only four vowels, viz i, a, u, and o, chosen for being at or near the corners of the vowel chart of phonology, and thus as far apart as possible from each other on the chart, and therefore as unlike each other as possible in sound:
normal = i, reciprocal = a, negative = u, negative reciprocal = o
Vowels are pronounced as short, i as in hit, a as in cat, u as in foot, o as in cot.
The vowels are pronounced with a final glottal stop when at the end of a syllable, for example -2⁸ = fu is pronounced like in the Cockney English (and increasingly in standard British English) pronunciation of the first syllable of “football” (which is pronounced foo’ball) ie foo’. The t sound is replaced with a glottal stop, meaning a closure of the glottis in the throat. An example from American English of a final glottal stop is in the first syllable of “uh oh”.
If confusion with existing English words, when written longhand, is a problem, a silent h could be used in front. Thus, optionally, not “pip” but “hpip” and so on for all those that are English words. This is analogous to the silent w in “two”, which serves to distinguish it in writing from “too”, and “to”. Note that in speech there is no confusion, and likewise with “one” (sounds like “won”), “four” (sounds like “for”), “six’ (sounds like “sicks”), and “eight” (sounds like “ate”). Somehow the context and tone of voice and so on disambiguate adequately between, say, “I have one” and “I have won”. Note that if the silent h is left off for any reason, there is still no danger of misreading it as a different number, so it is optional to include the silent h. In any case, it is not necessary to write numbers longhand to be understood clearly. It just looks better. Compare “I have one.” with “I have 1.”

## The table of names.

To take the third row as an example,
2² means two to the power two, i.e. two squared, which is four. Thus, the word “ni” means four.
Only the first column needs to be understood at this stage, but for completeness, here are explanations of the other three.
2^-2 means two to the power negative two, i.e. the reciprocal of four, which is a quarter. Thus, “na” means a quarter.
-2² means minus one times 2², i.e. minus four. Thus, “nu” means minus four.
-2^-2 means minus one time 2^-2, i.e. minus a quarter. Thus, “no” means minus a quarter.
Since “no” is already an English word, optionally “hno” would be used instead, later. But for now, I want to keep things simple.
Counting from one to ten in binary can be done in a variety of ways:
Base 2: 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010.
One, two, two one, four, four one, four two, four two one, eight, eight one, eight two.
Si, ti, ti si, ni, ni si, ni ti, ni ti si, mi, mi si, mi ti.
Note that there is no need to specify the base except when using Arabic numerals. Just as three score years and ten unambiguously means seventy, ni unambiguously means four, whether in base two or base four, or any other base.
Here’s the table of names (it’s infinite, so only parts of it are shown here):

## Counting higher in binary.

Counting the numbers off using the fingers of one or both hands works well to prevent me from losing count. Once I get to the end of my ten manual digits, I just start again at the beginning calling it eleven and so on. Thus, when I say, “two one,” I am holding up three fingers. When I say eight two, I am holding up ten digits. When I say ri four, I am holding up ten digits again, which confirms that I haven’t lost count, because that’s as it should be, since ri is sixteen and sixteen plus four is twenty.
One, two, two one, four, four one, four two, four two one, eight, eight one, eight two, eight two one, eight four, eight four one, eight four two, eight four two one, ri, ri one, ri two, ri two one, ri four, ri four one, ri four two, ri four two one, ri eight, ri eight one, […], ri eight four two one, li, li one, li two, […], li ri eight four two one, shi, shi one, […]
Si, ti, ti si, ni, ni si, ni ti, ni ti si, mi, mi si, mi ti, mi ti si, mi ni, mi ni si, mi ni ti, mi ni ti si, ri, ri si, ri ti, ri ti si, ri ni, ri ni si, ri ni ti, ri ni ti si, ri mi, ri mi si, […], ri mi si ti si, li, li si, li ti, […], li ri mi ni ti si, shi, shi si, […]
Base 2: 1, 10, 11, 100, 101, 110, 111, 1000, etc.

## “Binary decimals”.

Base 2: 0.011[2]
= 2^-2 + 2^-3 = na ma
Base 2: -0.00000000001
= -2^-11 = tot
Base 2: -0.00010000001
= -2^-4 + -2^-11 = ro tot

## Unconventional binary counting.

When telling the time in English, “five to twelve” is the same as “eleven fifty-five”.
Analogously ri su = 2⁴ — 2⁰ is the same as mi ni ti si = 2³ + 2² + 2¹ + 2⁰
7 = 8 -1 = mi plus su = mi su
7/8 = 1–1/8 = si plus ma = si ma
62 = 64 -2 = 2⁶ — 2¹ = shi plus tu = shi tu
63 = 64 -1 = 2⁶ — 2⁰ = shi plus su = shi su
64 1/64 = 2⁶ + 2^-6 = shi plus sha = shi sha
63 63/64 = 64–1/64 = 2⁶ — 2^-6 = shi sho

## An integrated system of counting systems based on binary, quaternary, octal, hexadecimal, and so on, being binary counting in another form, using just one set of names for all the powers of two.

One pronunciation system and regular set of names can be used for all bases that are a positive power of two.
Any base that is a power of two, such as base four, base eight, base sixteen and so on can use the same set of names. Ni is 2² = 4. Thus, in base four one might count one, two, three, one ni, one ni one, one ni two, one ni three, two ni, two ni one, two ni two, two ni three, three ni, three ni one, three ni two, three ni three, one ri, one ri one , one ri two, one ri three, one ri one ni, one ri one ni one, ….
By saying one ri one ni rather than ri ni, I am following the English “One thousand one hundred” style. In French the article is omitted: “Mille cent” (literally: “thousand hundred.” Perhaps the French would say “ri ni” while the English say “one ri one ni”. In binary there is never more than one of a power of two, so it’s not an issue with binary.
Using the shorter “French” style: One, two, three, ni, ni one, ni two, ni three, two ni, two ni one, two ni two, two ni three, three ni, three ni one, three
With English style pronunciation of numbers, one could count in base four like this:
(Imagine a subscript ‘4’ next to each number in the leftmost column. A four in square brackets means subscript four which means the number that it is subscripted to is in base 4. They are base four numbers written in Arabic numerals.)
Base 4: 1 si 2⁰
Base 4: 2 ti 2¹
Base 4: 3 ti si 2¹ + 2⁰
Base 4: 10 si ni 2⁰ * 2² = 2²
Base 4: 11 si ni si 2⁰ * 2² + 2⁰
Base 4: 12 si ni ti 2⁰ * 2² + 2¹
Base 4: 13 si ni ti si 2⁰ * 2² + 2¹ + 2⁰
Base 4: 20 ti ni 2¹ * 2²
Base 4: 21 ti ni si 2¹ * 2² + 2⁰
Base 4: 22 ti ni ti 2¹ * 2² + 2¹
Base 4: 23 ti ni ti si …and so on.
Base 4: 30 ti si ni
Base 4: 31 ti si ni si
Base 4: 32 ti si ni ti
Base 4: 33 ti si ni ti si
Base 4: 100 si ri 2¹ * 2⁴ = 2⁴
Base 4: 101 si ri si
Base 4: 102 si ri ti
Base 4: 103 si ri ti si
Base 4: 110 si ri si ni
Base 4: 111 si ri si ni si
Base 4: 1000 si shi 2¹ * 2⁶ = 2⁶

## Names for new numerals, especially of very large bases, e.g. base 64 and above.

One can create a pseudo-numeral by simply putting brackets around a number. Eg. 63 in base 64 might be (63) or ’63’ and it can be used exactly like a numeral.
Base 64: 10–1 = (63) i.e. 64–1 = 63
Base 64: 100 -10 = (63)0 i.e. 64² — 64 = 63 x 64 = 4032
One can pronounce (63)0 as “sixty-three sixty-four” or “sixty-three shi.
That seems to work well, but if completely new names are wanted for the new numerals of very large number bases, one can say that the vowel ‘e’ (pronounced as short e like in “bet”) indicates a numeral, and then (63) can be “shem”. Because, following the same pattern that links numbers to consonants, 6 = sh, and 3 = m. Then (63)0 is the same as shem shi. Note that shem doesn’t involve a power of two and the presence of the e tells you that. Note that shim (or hshim) is 2⁶³ = approximately 10³⁰.
(123456) In base 131072 ( base 2¹⁷) is tenmerlesh. Three syllables which is the same number of syllables that are in the word “seventeen”. Thus tenmerlesh timtiskin is base 131072: (123456)0 i.e.123456 x 131072, which is technically a two digit number in base 131072. Presumably no human being is going to find a base this big to be practical, but it shows that the system can handle the biggest bases with ease.
Tenmerlesh timtiskin plus one = tenmerlesh timtiskin one or tenmerlesh timtiskin si.

My favorite activity is learning new things.

## More from Matthew Christopher Bartsh

My favorite activity is learning new things.