History of the Argam numeral set

## 1980s

The “proto-argam” numeral set, phases of piecewise development. The notion began between 1981 and 1983. The argam numerals started out as a least change system that accreted piecewise definitions in several stages before adopting a multiplicative approach. Originally, the proto-argam was a duodecimal solution, adding two transdecimal numerals in the early 1980s (during middle school). The transdecimals were lifted from a constructed language alphabet

* The digit ten resembling “1|” which was the letter “A”, and was named “desen”, pronounced as /DESS-ehn/, in resonance with the English pronunciation of Latin “decem” evident in “decimal”, “December”. This was found to be confusing, so the numeral was changed. De Vlieger wanted the numeral to resonate with the Hindu Arabic range, so a “2” was rotated 180° (), since ten is even, and the resultant numeral resembles sort of a backward 5. The numeral conveyed notions of the prime divisors of ten, so it has stood as a rational solution for digit-ten.
* The digit eleven resembled a backward seven () with a convex downward stroke, the letter “B” in the conlang, and was named “dalen”, pronounced as /DAH-lehn/, alliterating with the name for digit ten and picking up some sense of the English word “eleven”, made a bit more concise. De Vlieger was satisfied with the numberform as it harkened the form of another large prime numeral “7”. Since the early 1980s, only the names have changed to dess and ell. Soon after in the early 1980s, De Vlieger expanded the numeral set to cover hexadecimal. Base sixteen appealed to De Vlieger before duodecimal, in 1981, having seen it in an Apple ][ + Basic programming manual. De Vlieger accepted the alphabetic transdecimals until shortly after producing the duodecimal proto-argam transdecimals.
* By 1983, De Vlieger had proto-argam covering digits twelve through fifteen. Initially the twelve had the form similar to “λ”, called “ceren”, pronounced as /SEHR-ehn/, but this was lost to a form similar to “C” with the same name in 1985. The ceren as a C was not satisfactory, and evolved to a form similar to a “γ” written on the baseline with a wider bowl resembling a “6” with the involuted curve allowed to remerge on the left similar to the rightward-leaning riser, making a symmetrical numeral now called “zen” ().
* The next three numerals, digits thirteen through fifteen, modified the Hindu Arabic numerals {6, 3, 9} by reflecting them on a vertical plane to resemble the alphabetic transdecimals {d, e, f} (, , ). These had the names “thisen”, “erin”, and “leqis” in 1985. These forms have survived as originally conceived. The digit-thirteen bears the name “thise”, but the digits fourteen and fifteen have the names “zeff”, weathering from “diseff”, and “trick”, weathering from “trikin” respectively.
* In 1986, the numerals for digits 16 through 20 were produced. These numerals extended the notion of modifying the extrapolated alphabetic convention, “g” for 16, “h” for 17, etc. The digit-sixteen as “g” brought the letter above the baseline to stand as a numeral, simplifying the descender so that it resembles a “ρ” on the baseline (). It was named “ract”, a truncated word “tesseract”, but this was abandoned and is now called “tess”.
* Digit seventeen is a modified letter “h” with a concave right leg (), and has had many names that depended on a prime-naming convention. The name it now possesses, “zote”, derives from the Italian name for nitrogen, with an atomic number

# Z
7

{\displaystyle Z=7}

. The naming convention that emerged in 2006 was using the chemical name with atomic number

# Z
Π

{\displaystyle Z=\Pi}

, the prime counting function for the prime p (this convention later applied to numberforms for primes

p
>
83

{\displaystyle p>83}

).
* Digit eighteen is a digit twelve (“zen”) rotated 180° (), weakly resembling the letter “I” in loose cursive. The numberform is satisfactory because eighteen is twice nine, so the rationale that suited “zen” as twice-six also suits “dinove” (weathering to “dine”) as twice-nine.
* Digit nineteen took cues from the angular numberforms of “7” and “ell”, being a “7” with a horizontal middle stroke whose left endpoint is connected by a vertical stroke to the left endpoint of the top horizontal of the “seven” (). This numberform did have an association with both

19
≡
9

(
mod
10
)

{\displaystyle 19\equiv9\, (\text{mod }10)}

 and

19
≡
7

(
mod
12
)

{\displaystyle 19\equiv7\, (\text{mod }12)}

. Digit nineteen is called “ax”, a briefer version of the name of element

# Z
8

{\displaystyle Z=8}

, oxygen.
* Digit twenty weakly resembles a horizontally-flipped “k”, it is actually a “dess” with its bottom bowl brought up and over the top horizontal (). The extant English word “score” serves as its name.

This set constitutes the proto-argam numeral set, defined piecewise between 1981 and 1987.

## Extension to Trigesimal

The aborted additive expansion of the proto-argam set. De Vlieger extended the set in 1991 using additive definitions mounted on a numeral base of the first twenty of these twenty-one numerals. The number bases 12, 16, and 20 served as expansion levels for the proto-argam; ultimately 60 was the “holy grail”. I produced a sixty numeral proto-argam using several additive methods, and re-evaluating digits {17, 18, 19} at times. One method of doubling the twenty unit-figures was to stroke through the center of some numbers, others that didn’t lend themselves to this treatment had a small tight circle drawn under or incorporated into a descender. The numeral “cadex” or “dex” for digit-24 remains a “zen” with a stroke through the vertex (), and is the only numberform to have survived from this early August 1991 study. Two appended vigesimal-figures was used to arrive at base sixty, but wasn’t satisfied with defining the digits of sixty with an implied “sub-base” of twenty (i.e., a vigesimal-coded sexagesimal). Some of the range between digits 21 and 29 were allowed to weather, or new numberforms were innovated, so that a numeral base of thirty forms is available. De Vlieger innovated a form for digit-28 () that simply echoed one of the arcs of the numeral “zeff” (digit-14, ), which resembles a horizontally-reversed “3”. This still stands as the numeral “caven”, the only survivor (along with digit-24) of this expansion. De Vlieger was more satisfied with a trigesimal-coded sexagesimal.

## Argam Arimaxa and the Multiplicative Definition

The argam arimaxa and the multiplicative expansion reform of 2006-2008. In the autumn of 1991, De Vlieger produced the first version of the argam-arimaxa, a set of sixty piecewise-defined numerals. Formerly additively-defined numerals like digit-36 took on a multiplicative definition. Before autumn 1991, digit-36 was constructed using a thirty-figure and the unit figure “h”, so that it appeared like, say, a “6” with a cedilla (¸) attached to the bottom (). Coincidentally, digit-36 has a lot to do with 6 multiplicatively, and less to do with thirty. The new numeral for the square of 6 was at the same time two numerals “6” attached at their upper right points, and a “dine” (digit-18) with the evenness-figure (°) attached to its lower right. The numeral took on the name “exent”, the -ent suffix signifying it is a perfect square. Digit-25 is a “5” rotated 180°; its name started out as “kinent” but was changed to “quint” as it is briefer and still conveys its fivefoldness. Digit-49 had a form that was arbitrary and slightly modified so that it is a combination of two numerals “7”, one written upside-down atop the other, though now the numeral doesn’t much resemble seven, with the name “effent”. Digit-42 is a combination of the numerals “6” and “7”, named “exeff”. Digit-thirty is likewise a combination of “5” and “6”, named “kinex” or “kex”. Digit-32 began as a “5” reflected across a horizontal axis so it resembles a sort of “2”.  Over time this smoothed into a related but different shape. Initially it had the name “cadoct” but a new name was generated in 2007 that reflects the original notion behind the number form:

# 32

2
5

{\displaystyle 32=2^5}

; the name became “twive”, which is more concise. (The later digit-64 retains its name “octent” but might be called “twex”.) This set closely resembles the current argam-sexagesimal. The set grew in 1992 and 1993 to one hundred piecewise-defined numerals, which I reformed between November 2004 and mid 2006. Many of the upper forty numerals were discarded and redefined in Dallas in November 2004. This is when the multiplicative definition really kicked in. The sequences {17, 34, 51, 68, 85, 102, 119, etc.}, {19, 38, 57, 76, 95, 114, etc.} were redefined, like Haussmann’s renovation of Paris (i.e., the blazing of boulevards through the urban fabric of tight streets) replacing the earlier numerals for integers in those sequences. The multiples of these primes attempted to use “radicals”, i.e., figures for three, four, five, etc. to modify the numerals “zote” and “ax”. Most of the higher range of the argam-kinoctove (the argam of 360 contiguous numerals) use the multiplicative method to define numerals.

## Argam today

### Bringing the Argam beyond 120

The rykami-argam, s7836, De Vlieger's “Sketchbook of Numbers”, studied the expansion of the argam beyond 120. Three techniques served to help produce new argam. First, the chemical elements were marshalled into inspiring new prime numerals to around 500. An “infinite multiplication table” served to generate small multiples of the lower range of integers (s7836a11, s5231a92). A game I played on flights between St. Louis and Ithaca, NY that basically generated sexagesimal-regular numbers served to produce highly-composite numerals, eventually evolving into the PDF sexagesimal factor study.

### Attempts in extending the numeral set

Years after De Vlieger uploaded the Sketchbook of Numerals, people who have seen and have been fascinated by the work has made attempts on extending the numeral set, with the next superior highly composite number, 2,520, as a common goal.

A closed FANDOM wiki, the "EX515 Wiki", has produced Argam up to approximately 1,200 numerals, which was considered "semi-canonical" by De Vlieger on a discussion post on DozensOnline.

The Paul Marciano Wiki produced (semi-canonical) argam up to Digit-3200, excluding primes

≥
653

{\displaystyle \geq653}

 and their multiples. Ismarragam up to digit-6,200 could be found, although many are incorrect.

In June 2021, the typeface "Vinci Argam Mono" was extended to 480 numerals.

The Valerian Argam-Sevoctovess typeface has been completed on September 8, 2021. Additive radicals, inspired by those in Argam-Arimaxa, has been developed to extend the numeral range up to 55,440.

## Summary

The argam transdecimal numeral set began with digit-ten in the 1980s as a multiplicative concept, based on the prime decomposition of the digit. It took me more than twenty years to determine how to extrapolate those middle-school notions to cover more than 360 transdecimal numerals! The middle phases of the expansion of the argam numeral set as proto-argam went through several conceptual episodes before the multiplicative reform of 2004-2006. This recounts generally how the argam numeral set evolved.

## Evolution of each numeral

Below shows the evolution of each of the first 120 argam (Numerals 1-120 share the same canonical form in both Icarine and Valerian forms). Numerals in purple are alternates.

Pages about Argam numerals

## References

1. ↑ [www.vincico.com/arqam/digits/argam-ajamyse.html Argam Ajamyse], Transdecimal Observatory
2. ↑ Gallery of Numbers (3100-3199), Paul Marciano Wiki