The way we count out loud in other bases is wrong. Here’s an okay way to do it.
Base ten is the only base in which we count out loud in a way that is even close to okay. Out loud nondenary (non-base-ten) counting makes us all sound like false beginners who can read out the letters of a word in the target language, and even understand the meaning of the word, but can’t pronounce the word or recognize it when spoken by a native speaker. A lamentable situation.
There is only one exception to this, which is base twelve, but base twelve rarely used by anyone not connected with the Dozenal Society of America (formerly called the Duodecimal Society of America). But congratulations to them for all their good work. https://en.wikipedia.org/wiki/Duodecimal#Notations_and_pronunciations
Binary, octal, hexadecimal, and base six are often seen and used in a written form, including in the math classroom, but the non-base-ten numbers are pronounced like we say a telephone number in base ten, a mere string of numerals. The reason seems to be the lack of a well-known system of names for any of these bases. Dozenal/ duodecimal/base twelve does have a set of names for the first few powers of twelve and this is why you can pronounce it in an okay way, better than we can pronounce base ten perhaps. Again, well done to them. Too bad they ignored all the other bases.
To remedy the absence of good ways to count out loud in any base except base ten and base twelve, I have created some pronunciation systems.
I count in binary like this: one, two, two one, four, four one, four two, four two one, mi, mi one, mi two one, … mi four two one, ri, ri one, ri two, … and so on. Or, when I want to shun base ten names entirely: si, ti, ti si, ni, ni si, ni ti, ni ti si, mi, mi si, mi ti, mi ti si, …mi ni ti si, ri, ri si, ri ti, … and so on. The names are generated by an algorithm that is easy to memorize, so you don’t need to memorize a lot of names. To learn more about this, see my for beginners article:https://bartshmatthew.medium.com/how-a-math-teacher-should-pronounce-a-binary-number-1c41773df52f?source=your_stories_page-------------------------------------
I count in octal like this: one, two, three, four, five, six, seven, one mi, one mi one, one mi two, one mi three, …, one mi seven, two mi, two mi one, two mi two, …seven mi six, seven mi seven, shi, shi one, shi two, shi three, … and so on. Note how mi is reused from binary, as is shi, being 2³ and 2⁶, respectively. To learn more see this for beginners article:https://bartshmatthew.medium.com/how-octal-numbers-should-be-pronounced-by-math-teachers-72ddb42e8e03?source=your_stories_page-------------------------------------
I have an all-purpose pronunciation system for all bases that are not a power of two, four example base three: one, two, one ta, one ta one, one ta two, two ta, two ta one, two ta two, one na, one na one, one na two, two na, two na one, two na two, two na one ta, two na one ta one…
Ta means the radix to the power of one, na means the radix to the power of two.
Thus in base five I would count: one, two, three, four, one ta, one ta one, one ta two, one ta three, one ta four, two ta, two ta one, two ta two…
Bases that have a system of names now have an alternate system of names.
I could count in base ten: one, two,…nine, one ta, one ta one,.. one ta nine, two ta, two ta one, … nine ta nine, one na, one na one, … nine na nine ta nine, one ma, one ma one… and so on.
Unlike with binary and octal and every other base that (has a radix that) is a power of two, with my base three, base five, and base ten pronunciation systems, the base (and hence the radix) must be specified for a number to be specified unambiguously, because in base three ‘na’ is 3² while in base five ‘na’ is 5², and in base ten ‘na’ is 10² (ten squared i.e. ninety-nine plus one, the number of years in a century).
In binary and octal and every other base that is a power of two, mi = 2³ = 8 = eight = the number of arms an octopus has.
As things are, as explained in detail in the article about pronouncing binary linked to above, only base twelve gets a fair shake when being compared to base ten. All the rest, for lack of an okay pronunciation system that is easy to learn, are pronounced like telephone numbers, which puts them at a huge disadvantage.
How about teaching binary or hexadecimal as a living, spoken language. Even the the least academic or mathematical of us can still count out loud in base ten, even if unable to write it.
It seems to me that the way we learn about nondenary (non base ten) counting and consequently think about it is much like studying the grammar of a foreign language while remaining unable to get past ‘Hello’ with a native speaker. These students are known as false beginners, because they seem like beginners at the target language, whereas they have in fact studied it for many years and may be able to read and write it and to some extent understand it when spoken slowly especially when the speaker is not a native speaker.
Maybe those who have “mastered” binary and/or hexadecimal are in some sense false beginners, unable to hear ‘four two’ as binary 110 (110two).
How about ‘multinumeracy’, to coin a term, meaning *speaking* more than one number base? At present, the only multinumerates are those fluent in both base ten and base twelve.
All bases, except for base ten and base twelve, are in some sense thought of, and experienced as ‘dead’, like Latin and Greek. Perhaps silent or mute would be a better way of putting it. Let’s give them a voice.
Let’s bring them to life.
Tau Day is on June 28th (6–28) because Pi Day is on March 14th (3–14).
The idea of speaking and writing mathematical formulas in a new way has a lot in common with the idea of speaking and thinking in a new way when doing nondenary counting.
Tau may be more important, but spoken nondenaries could be introduced without as much inconvenience. All I am saying, is let’s pronounce telephone number like numbers in binary in the present way, but counting and calculating numbers in a new way that is analogous to how we do that in base ten. Nothing needs to be phased out or even pushed into second place. The two ways of pronouncing will coexist, as they do in base ten.
How about a Living/Spoken Binary Day on April the Second (4–2)? And/or a Living/Spoken Octal Day on August the Fourth (8–4)? And/or a Living/Spoken Nondenary Day (not sure what date of the year that might be on)?