Vaclav Blazhek - "Numerals in Arctic Languages" - Yukaghir, Chikchi-Kamchatkan, Eskimo-Aleut

4 = 3+1 = 2*2, 5 = hand, 6 = 5+1 = 3*3, 7 = 5+2 = 8-1, 8 = 5+3 = 2*4, 9 = 5+4 = 10-1, 10 = 5+5 = top

A lot of variation. Is this variation a result of not doing very much counting with those numbers?

I don't have Vaclav Blazhek's book with me, sad to say, but I've found this:

Uralic numerals: is the evolution of numeral system reconstructable? (reading new Václav Blažek’s book on numerals in Eurasia)
"As it can be seen, most of these Blažek’s Proto-Uralic recontructions are too optimistic if not to say simply bad."

Author Vladimir Napolskikh has his own reconstruction. UYu = Uralic-Yukaghir, U = Uralic, FU = Finno-Ugric (Finnish, Hungarian, etc.), FP = Finno-Permic (Finnish), Ugr = Ugric (Hungarian), Sam = Samoyedic

UYu 1, U 1: (?), FU 1 *üke, Sam *o-

UYu 2: *ket > U *kekta > FU 2 *kektâ, Sam 2 *kitâ

FU 3 *kolme, Sam 3 *näkar

FU 4 *neljä (<? Drav •nâl), Sam 4 *tetta (< Turkic (Bulg. 3) *tüät)

U 5 *witte > FU 5 *witte, Sam 10 *wüt ... ? Sam *sampa- "hand" > Sam 5 *sampalanka

U *kutte "back" > FU 6 *kutte ... Sam *maka "back" > Sam 6 *maktat

Balt 7 *setem > FP 7 *seccem ... II 7 *sapta > Ugr 7 *Säpt, Sam 7 *sejtwa

8 "without 2"

9 "without 1"

UYu *kümen- "number, many" > FU 10 *kümene (Sam 10 ~ FU 5)

U *kojese "human" > FU 20 *kuse ... Sam "two-ten"

II 100 *sata > FU 100 *sata ... Turkic (Bulg.) 100 *jür > Sam 100 *jür

Then basic numerals and counting:

UYu: (1), 2, many ... 1, 2, 2+1, 2+2, ...

U: (1), 2, 5, 20 ... 1, 2, 2+1, 2+2, 5, 5+1,... 2*5,... 2*5+5, ... 20, ...

FU, Sam: 1, 10, 100 ... 1, 2, 3, 4, 5, 6, 7, 10-2, 10-1, 10, ...100, ...

Then some similar systems:

Aghu (Trans-New-Guinean): 1 = fasike, 2 = okuomu, 3 = okuomasike, 4 = "little finger", 5 = "palm", 6 = 5+1, 7 = 5+2, 10 = 2*5

Jawony (Pama-Nyungan): 1 = antirin, 2 = tatkurang, 3 = 2+1, 4 = 2+2, 5 = 2+2+1

San (Khoisan): 1 = /wi, 2 = /am, 3 = ng/ona, 4 = 2 of 2, 5 = hand

Eskimo: 1 - 4 = (various), 5 = "hand", 7 = +2, 8 = +3, 10 = "upper side", 11 = 10+1, 15 = "in front of", 16 = 15+1, 19 = 20 not, 20 = "human"

Haida (Na-Dene): 1 = sgoâ'nsin, 2 = stiñ, 3 = lgu'nul, 4 = 2*2, 5 = lê'il, 6 = 3*2, ..., 10 = 5*2

Yukaghir (Kolyma): 1 = irkiei, 2 = ataxloi, 3 = yaloi, 4 = 3+1, 5 = "hand", 6 = 2*3, 7 = 2 above, 8 = 2*4, 9 = 10 without 1, 10 = kunel

Sumerian (counting of days): 1 = be, 2 = 1+1, 3 = PESH <? "next", 4 = 3+1, 5 = 3+1+1, 6 = 3+3, 7 = 3+3+1, ...

Sumerian (usual): 1 = ash, 2 = dish, 3 = min, 4 = esh, 5 = i, 6 = 5+1, 7 = 5+2, 8 = 5+3, 9 = 5+4, 10 u = < "many", 20 = 2*10

Notice a lot of base-5 counting and double smaller numbers, like Japanese 2 ~ 1, 6 ~ 3, 8 ~ 4, Indo-European 5 ?= "hand", 8 ?= 2*4, 10 ?= "2 hands", 100 ?= big 10, 1000 = big 100 or big hand, Proto-Berber 6 = 5+1, 7 = 5+2, 8 = 5+3, 9 = 10-1

We start out counting from 1 to 2, then adding 3, then adding 4, then adding "hand" or "palm": 5. We next do arithmetic to go up to the base for larger numbers: 10 or 20 or 60. We may then coin special words for powers of the bases, but other than that, it's all arithmetic.

Nearly every such number base is 10; the exceptions are Mayan (20) and Sumerian (60):

Maya numerals and

Sumerian language
Here are the families with native words for 100 as far as I can determine: Indo-European, Turkic, Mongolian, North Caucasian (several), Sino-Tibetan, Tai family, Mon-Khmer, Austronesian, Dravidian, Semitic, Egyptian

With native words for 1000: Indo-European, (Turkic, Mongolian: one borrowed from the other), some North Caucasian?, Sino-Tibetan, Tai family, Malayo-Polynesian, Semitic, Egyptian

I say "native", because borrowing of words for numbers is common for relatively high numbers, and "relatively high" can be as low as 6 in some cases (Indo-European, Swahili).

There are even some langs with special words for 10,000: Greek murioi (> "myriad"), Chinese wàn, Egyptian djeba, Sanskrit ayúta