Disclaimer: I liberally added fonts and images from online. No copyright infringement intended.

I often wondered if it is possible to create glyphs (pictorial representation) of all combination of telephone numbers that can be decoded at glance. Unless the number consists of familiar patterns, form, sequence it becomes frustratingly difficult to commit them to memory driving at 65mph on freeway.

First let us introduce the glyphs for base (0,1,2….9): Following reveals the whole spectrum of numbers with a specific BASE (in this case 2):

Of course the various types of niche or arches represents different form relative to “BASE 2”.  If the same arches appear at the upper-right or left corner (depending upon pattern) then it will denote different numbers per BASE.

These are all very arbitrary; so we can use any general form for any specific arch.  We shall use the special case of Magritte’s man for the sequence which are all of the same digit.

Let’s us now consider different variations of a 3-digit number.

It can be increasing. Such as 123
Or decreasing: 321
If neither, then we can have a palindrome like 323.
Form of 323 reversed can be 232. Call it reverse or obverse palindrome.
We may have all same 333.
We can also have a double double unit such as 662. Reversing it gives 266.

Enough rambling; let’s play with some random 3-digit numbers. Using some random random generator from internet I get a list whose general form I have verbally described:
206 = Turns out we do not have a convention yet. But a guiding factor is 0 which splits a 26. Now this 26 can be thought of as 13×2. What does 13 do? Well it’s is 1 less of 14, or sub-base minus 1 of 714, my city area code. Note: We will try to think backwards to this CODE of 714. Since we are yearning to be as intuitive as possible, feel free to derive it to a pattern based on your area code.
312 = Again, it has not been defined yet. But to me a pattern that may strike out is that it is a increasing sequence which has been shifted to the right.
422 = This one we have in the bag. It is a unit double double form.
534 = This is an increasing sequence shifted to the right.
653 = It is decreasing sequence.
305 = This has the same form as 206.
844 = Unit double double pattern.
304 = It is 1 minus 305.
852 = Decreasing pattern.
968 = This one is a weird one. We will return to it later.

Okay, so how do we generalize to an algorithm given any sequence of 3-digit number?

Well, let’s see. Right now, word count is 490. This can be thought of as 7 squared zero, giving us 7 for the first digit of my area code 714. But how to verbally pin it down forward?

STEP 1: UNIT(BASE)
STEP 2: SQR(R)

which roughly translates as take the unit of BASE which I am redefining to be 714. Note, previously we talked of a different base. So, take the unit of BASE and SQUARE the R(esultant), then adding a zero to the end result.

How to represent 094? Simple. Call the first algorithm BUTTERFLY. And then use the function REVERSE.
Or REV(BUTTERFLY).

Things are quickly getting muddy. So let us back-out a second, and get a random 7-digit number. Certain plumber in a certain state has a number 439-3407.

What pattern seems to jump out (bearing well in mind it may vary individually?). It can be grouped to: 4,39,34,07 because the 3-digit sequence has no basic pattern.

Although it is of different state, I will affix it to my area code. Then we will create an algorithm. First , it’s time for some terminologies. If we take the CODE 714 and call it BASE, then there are components called UNIT or 7. DBLUNIT or 14. Singleton or 1. SUBUNIT or 4. SUBBASE or 71.

To unleash an inner Bhaskara, here is the algorithm. Extracting SUBUNIT, subtract 1 to get and putting it at the end, then reverse it around 9 ending it in add-1 of it and sub-2 of it.

Quite a mouthful. To formulate it in steps:

STEP 1: SUBUNIT(BASE)
STEP 2: SUBUNIT(BASE),SUBUNIT(BASE)-1
STEP 3: WRAPAROUND(SQUARE(2,2), {here (2,2) denotes step 2, position 2]

So far we have BASE or 714 and then SUBUNIT of 714 is 4. Then we write it as it is comma “as it is” minus 1. Or 4,3.

“Wrapping it around” 9 gives us: 43,9,34 where 9 is actually square of step 2, position 2.

A caveat: the grouping has changed now: It is (43)(9)(34). We definite 9+1 as 0m where 9-2 obviously gives us 7.

Where does the picture fit in? We are getting there. Since it is a BASE 4 game, we can use the glyph of 4 with the various arches representing different forms or patterns.

Before it gets further confusing, let’s harken back to the medieval lady with arches. So there are 24 different patterns for the number 2 as the SEED VALUE. Furthermore, we decide that putting the arches to the left side will give different values. So 48 different patterns.

Difficult part is memorizing all the 24 different patterns. Then one can mix and match and generate any number. Theoretically speaking of course.

For 7-digit number sequence there are 10 million permutations.  But we only have 48 different forms for each number and there are 10 of them giving us 480.  This barely scratches the surface.

Is there a taxonomy of forms of 7-digit phone numbers? Can we at least force a pattern? The thing is each glyphs by themselves represent all of the same digits. So the Egyptian scribe, if written by itself, gives us 111-1111.

Adding the thinly bordered ogee arch of the first character in the spectrum gives us a random pattern of an algorithm.  Basically what it’s saying is take BASE-1 and perform a familiar operation. And when it’s on the left, it will perform a reverse operation.

Admittedly of course, the ornamental arch may not be quickly grasped driving at 65mph highway; but, due to the visual nature it will stick to memory more easily.

Another possible representation can be using the skeletal form of the following: Bubbling in the nodes will give either number. Open or closed. And shading in segment will give a sequence.  Do visual tangrams exist for all permutations of 7-digit number? How about 123-4567? May be an acyclic graph for 1/2?

We have reached a cul-de-sac. Introducing a new glyph, hopefully will help resolve the missing pieces of number forms. 