B. Lukács

President, Matter Evolution Subcommittee of the Geonomy Committee of HAS

lukacs@rmki.kfki.hu

CRIP, H-1525 Bp. 114. Pf. 49., Budapest, Hungary

What would have happened if proto-Magyars had stopped at Base 7 in number theory (as they were at cca. 2500 years ago), and then developed positional numeric writing?

Aristotle, greatest scientist of the ancients and encyclopaedic mind, wrote a book Problems (Problemata), not duely appreciated by most historians of Science (because this book really contains Problems, so cannot give final explanations). It is really interesting, however, for a researcher to see how and in what the great Stagirite looked for explanations at the edge of the science of his age.

The book is organised into smaller, semi-independent parts which he called "books", but for us they are rather Chapters; the XVth is "Problems Connected with Mathematical Theory", and its Paragraph 3 (with Bekker numbers 910b-911a) exposes a Problem "Why do all men, barbarians and Greeks alike, count up to 10, and not up to any other number, saying for example, 2, 3, 4, 5 and then repeating them, one-five, two-five, just as they say eleven, twelve?"

Now, the Anglophone reader may be confused here, because it is difficult to see what structure is common in "one-five" and "eleven". (I use Barnes' translation [1], but this is not a matter of translation, but matter of English.) But observe that 13 is "thirteen" in English, in which we can recognise "three-ten". It is "trinadcat'", i.e. "three on ten" in Russian, and "tizenhárom"="tízen három"="3 on 10" in Magyar ("Hungarian"; note that Magyar is a language and Hungary is a country, but really Magyar is the biggest language in Hungary). And this was the way also in Aristotle's Greek.

Aristotle's question is really: "Why all men do so?". He knows only one exception: "One race among the Thracians alone of all men count in fours...". And why? The Stagirite, neighbour of Thracians, of course, answer: "...because their memory, like that of children, cannot extend farther...". Otherwise, for the "Why?" he tries with a variety of explanation. E.g. that 10=1+2+3+4, or that we have 10 fingers Now we more or less believe in the finger explanation.

After 2300 years of scientific evolution everybody in Thrace counts in 10's. Our proverbial mathematical simpletons are reported from far peripheries of our bigger World. But was Aristotle really right for the Known World in 323 BC?

There was half an exception which he should have known. In Mesopotamia the cuneiform number writing (not the words!) was positional sexagesimal. Of course they did not apply 60 different numbers, from 1 to 59 they wrote the numbers by combinations of horizontal and vertical wedges, but for 60 they used again the number 1, but on one place shifted.

Let us compare 4 systems of number writing: Roman, Greek, cuneiform and Arabic, on the number 729:

Roman: 729=DCCXXIX (that is: 500+100+100+10+10+(10-1)

Greek: 729=y k q (that is: 700+20+9)

Cuneiform: 729=12;9 (that is: 12*60¹+9*60⁰)

Arabic: 729=729 (that is: 7*10²+2*10¹+9*10⁰).

Clearly the Roman system is the least sophisticated; it is even not strictly decimal, having separate signs for 5=V, 50=L and 500=D. Oldest Mesopotamian was something similar, having separate signs for 1, 10, 60 (!), 600 (!). Some experts guess that the origin of the Roman V is a hand, VI is a hand plus one more finger, IV is a hand with one finger minus, and X is ><, i.e. both hands. Remember this.

The Greek system is fully decimal, indeed, having separate signs for 1 to 9, for 10 to 90, and for 100 to 900. The Greek counted the hundreds, then added the tens, then the units and added up. It can more or less be mirror translated to English y k q as {seven hundred} {two-ten=twenty} {nine}. This idea is simplified by the positional Arabic system: you use the same symbols for units, tens, hundreds, thousands, myriads &c., only more and more leftwards.

During Classical Greek times, however, there was a small "race of Scythians" (paraphrasing the great Stagirite) which, for a while counted in sixes, and, what is more, for a while in sevens. My linguistic community is one of the descendants.

In a true decimal culture decimal grouping pervades everything. Twentieth century continental Europe is a fair example. Length unit was the meter; divided into decimeters, centimeters and millimeters and grouped into kilometers. Kilograms were divided into grams, liters into deciliters and centiliters. And monetary units changed into hundred smaller units: franks into centimes and liras into centesimos. Even the medieval group measure "dozen" was going out of fashion. Libraries used decimal classifications for topics. Practically the only important area not with decimal groups remained the military; however note the Turkish way. Onbası, yüzbası and binbası may be the equivalents of British corporal, captain and major, respectively, but literally they mean ten's head, hundred's head and thousand's head, preserving old nomadic Turkish organisation principles. (The Hungarian words for some military ranks are similar. "Százados" is considered the equivalent of (army) captain, but the word indicated originally that he had a "század", cca. száz i.e. hundred warriors. And so on. Hungarian military organisation went according to Turkish ways because i) Magyars were under heavy Turkish influence some 2 millenia ago; and ii) the name Hungary comes from the Onogurs living in Hungary in the VIIIth century; On Ogur of course means ten tribe, no plural after numerals in reasonable languages.)

While Englishmen used nondecimal monetary and measuring systems until the 1970's dividing a shilling into 12 pence, a yard into 3 feet and so on, the English language is quite decimal. This means two things. First, the groups are tens and powers of tens, not dozens, fives or sixes. Indeed, when an Englishman tells a number, he uses the higher units ten, hundred, thousand, &c., and "twenty" is clearly a modified "two-tens". But there is another criterion too: that the number names from 1 to 9 are all different, independent and individual names, and then 10 again is and it is Base (or, in a positional language, perhaps 10 can be called Big Unit, or Big One, but that is unusual; however see Sumerian texts where, sometimes, 60 is Big One).

And indeed, if we go over English numerals from 1 to 10, all of them seem to be individual, independent and single words; and it is so for all Indo-European languages known for me, except maybe, but just maybe, for "9" in Slavic and Baltic, see Appendix A.

This seems rather natural for an Indo-European, anyway, primitive men count on fingers, and we all have 10 fingers, have we not? Then I lead you out of Indo-Europe.

Recently Indo-European languages dominate Europe. But the biggest minority group is still Uralic. Note that before 4200 BC Indo-Europeans were exotic Easterners of the steppe, eating raw horsemeat on horseback; the civilised West and Central Europe saw Uralians on the North and Basks on the South. Sic transit gloria mundi, but still some people speak Basque, and especially my first language is Uralic, quite unnatural for the Indo-Europeans.

Indo-European languages are really near to each other, reflecting the fact that they diverged lately, because they are the newcomers. Instead of detailed analysis see only the number "3". It is "three" in English, "tri" in Russian (and in a lot of other Slavic languages), and also "tri" in Sanskrit.

The Uralic languages are more diverse, because they diverged earlier. The terminology is highly artificial, and partially misleading. I will here vastly simplify the picture, using single languages for whole subfamilies. So: the first forking is into Samoyeds vs. "Finno-Ugrians". The biggest Samoyed nation now is Nenec, reindeer half-nomads in Northeastern Europe, some 25,000 people.

Now, the "Finno-Ugrian" forked into "Finnish" and "Ugrian". If the Indo-European reader believes that he (I definitely refuse to write he/she or heesh; if you do not like genders, simply do not use them; Uralic has no genders and still can be spoken) knows what is a Finnish but does not know what is a Ugrian, he is almost right. The biggest member of the "Finnish" branch is Finnish, the majority language of Finland, and all members can be loosely called Finnish, being really near to it; excepting Lapponian. However, the name of the "Ugrian" branch is rather a joke.

Nobody ever called in this group his language to anything even resembling "Ugrian". The group consists of 3 languages, and we practically do not know any extinct member (except a half). The languages are as follows:

Danube subgroup:

Magyar ("Hungarian"), 15 million

Ob subgroup

Man'shi ("Vogul"), 6 thousand

Khanti ("Ost'ak"), 20 thousand

If you look at world maps, and look for the rivers Danube and Ob, the geographic distribution of the "Ugric" group is rather strange, but there are migrations behind that, we know fairly the details, with some cemeteries and such, and it seems that there was a common "Ugric" language about cca. 500 BC. Since the Magyar "magy" and the Man'shi "man'" both mean simply "human", the original name of the common language surely was something cca. "Man'c'", i.e. "human language". But came the XIXth century international science. They knew some pieces of information: that some Russians sometime spoke about "Yugria" somewhere in the Ural Mountain or just east of them (see Appendix B); that proto-Russian monks wrote "vengers" or "ougors" when they meant the migrating Magyars; that Germans called the Magyars "ungarisch"; and that Vth century BC Herodotus writes about the Iyrka tribe on the East which hunts on horseback. (All these points are "not exactly true".) Hence somebody reconstructed a never existent "Ugria" and named the sister group of "Finnish" "Ugrian" or "Ugric".

OK, we cannot help this otherwise than using the symbols F and U for the misleading "Finnish" and "Ugric"; and FU for the age when already Samoyeds were asundered but "Finnish" and "Ugric" speakers still were together. The 3 "Ugric" languages are clearly close relatives, Magyar is the sister group of the Ob languages, and the two Ob languages are really near each other, on the verge of mutual understanding.

Hungarian linguistics knows a lot about Uralic, FU and U languages, and I use these knowledges. Only, linguists are not mathematicians. I cite here a university textbook about the counting system of FU (maybe U) [2] as follows. "Their counting shows the advanced knowledge of decimal system; however decimal was not the original system: earlier they counted in seximal or septimal system; tíz [for 10] is already different from the Ugric words, but the húsz [that is: 20]... [can be found in some FU]". True: but what is exactly a counting system? See Aristotle [1].

After so long an explanation see the words for numbers. Sölkup is a Southern Samoyed language, with more familiar phonology for Indo-Europeans than Nenec.

I could not use the official Man'shi orthography here, because it is Cyrillic-based but with special letters, signs &c, so I use Magyar orthography; incidentally then similarities are more apparent. In Magyar orthography Man'shi=Manysi. Sölkup characters would also be hard, and even the structures of the orthographies of the two Latin-lettered languages differ. Life is not easy for evolutionists; if you are curious, go to Appendix C. However we know, how to pronunciate all these numbers; you may believe me. Magyar is phonetic.

Now, in Sölkup the only number whose name is similar to the other 3 Uralic language is "1". As for the other 3 even an Indo-German speaker can see really the similarities until 7. Also, from 1 to 6 the words are really FU. The word for 7 seems Indo-European; Magyars guess that from a Northern Iranian horseman language; and some Indo-European linguists believe that the Indo-German word came from Semitic, so it is not unheard of to borrow 7. However, what about 8, 9 and 10?

There Magyar & Man'shi obviously differ from Finnish. OK, in early times only smaller numbers were in use (see Aristotle about the loose memory of some Thracians). The Finnish and "Ugric" branches diverged not long after the acquisition of the notion of "7". And what was the last common numeric notion in the "Ugric" group?

I try to give an answer. But the situation is not simple, so first I take another approach.

Let us follow Aristotle. Uralic people in Classical Antiquity were not so childish as some Thracians, so they could remember some simple numbers above 4, however they were not on the level of Pythagoras in number theory.

Say, about 1000 BC they counted until 6. (Until 6 the words are similar in FU.) Can you count "up to 6"? No problem. Then I should call, according to the Stagirite, 7 as "one-six" or "one-on-six"; in Magyar I would tell "hatonegy", and the term does not even sound strange. Also, in a positional "Arabic" system there is no problem; using Bold Italic for the hypothetical system,

5 = 5

6 = 10

7 = 11

12 = 20

36 = 100

and so on

However historically people did not start with positional systems, but rather with something "Roman". OK, let us introduce the symbols W=6, Y=6*6 ("Big Six"), and then

5 = IW

6 = W

7 = WI

12 = WW

36 = Y

But whose symbol is W?

Roman V is maybe "one full hand". A hand resembles a V, and V means 5, the number of fingers on a hand. Really, if you went hunting wild geese, have caught 3, and want to show this from afar, you show 3 fingers. If you caught 5, you show up one open hand. If you have caught 6, you show up an open hand, and the thumb of the other. But how do you show the base number 6?

Anything is the solution of this mystery, because our "extended Roman" runic system is workable, we may jump. Proto-"Ugrians" learnt the advanced word "szat" for the big number 7 from an advanced Iranian tribe. And then what?

I am not satirical. Northern Iranians were indeed advanced in that time; the words for "cow", which is "tehén" in Magyar and "dhena" in Old Iranian, and for some metals as e.g. "gold" which is "arany" in Magyar and "zaranya" in Avestan came thence and their Iranian origins are still transparent in Magyar. And Hungarian linguists seem to be sure that Old Iranian "sapta", the "7", came into the Common Ugric, so into the common ancestor of Magyar, Man'shi & Khanti. (Tokharians may confuse a bit. Bat "szat" indicates a satem language. It is another matter about "10".) Life would be boring without gold, cows or cow-milk.

However there would have been no problem not to borrow "sapta" at all for "7", unless we wanted to use "7" as Base. Even if somebody needs an expression for "7", he can call it "6+1", so "hatonegy" in Magyar, "akwhujphót" in Man'shi or "ukkir kel' muktit" in Sölkup; all of them are of type "one on six". No absolute need to borrow a single word for "7". On the other hand, in the time when "sapta" was imported for "7", then no words were imported for "8", "9" and "10".

One can be sure in this. In the 4 Uralic languages shown the words for "10" are not similar to each other at all, and they are not Indo-Germanic (except, maybe, but only maybe, Magyar "tíz"). Recently there are single words for "10", but this is an independent development/borrowing for each language. And "8" and "9" are obviously late compound terms. In Sölkup & Finnish it is clearly "two minus ten" and "one minus ten"; in Sölkup this is a literal translation because chänk = chänki-qo = "lacks sg", so "shitti chäng köt" is literally "[the number] lacking (chäng) 2 (shitti) to 10". In Magyar & Man'shi the structure has been obscured but still "8", "nyolc" = "nyollow" is the same. (In Man'shi "nyol" is "nose", but I do not see how nose can come into "8"; in Magyar the "c" in "nyolc=8" can be found in "harminc=30", where "harmi=három=3", and in "nyollow" "low"=10, so the words for "8" in both languages contain the same something "nyol" + something for "10", and the composition was just being solidified when Magyars and Man'shis asundered; for "9" only the idea of composition is common.) You see, I can prove that "9" is "10-1" in Sölkup & Finnish and cannot do this in my first language. It seems that the construction is older in Magyar & Man'shi.

But then there was a period in the common ancestor of Magyar, Man'shi & Khanti, say about 500 BC, when the highest simple numeral was "7". Was then 7 the Base? It should have been.

The next step was already to close up to Europe: all Uralic sooner or later borrowed "10" from somewhere, formed "8" and "9" in clumsy ways and then arrived at the common European base 10. So in the history of Magyar mathematics we can reconstruct 3 grades: Base 6 until, say, 1000 BC, Base 7 around 500 BC and Base 10, say, from 100 BC. Only 2 points remain (but they are the most exotic ones): how to materially count in Base 6, and what is the mathematics in Base 7? (And I am going to give an evidence that 7 really was the base for a while.)

On the example of Roman numbers I gave a reasoning that materially it is natural to count by fives (or of course, by tens) but not so by sixes. One hand is 5 fingers. You then can show naturally and easily 1, 2, 3, 4 and finally 5. But with one hand you cannot show naturally and easily 6; and with two hands it is not natural to stop at 6 (or 7). And still, simple Uralic numbers do not go beyond 6.

Of course, if you want merely show 6, it can be done; e.g. you can show your open hand for "5" (5 fingers) and a closed fist for "6". But then still you cannot count on your fingers.

Excepting exceptional members of the community having 6 fingers per hands. The Magyars until 1000 AD, the Man'shis and Khantis until the XXth century had shamanistic religions; and originally the shaman was the intellectual expert of the tribe. And the shaman must have had extra bones. Extra tooth is good; but extra finger is the best. In Russian museums lots of shaman costumes can be found, frequently with gloves for six, even seven fingers [3]. While 7 fingers on one hand is clearly mere boasting, 6 fingers on at least one hand of a shaman is rather a rule; if somebody is born with 6 fingers, he will be the apprentice of the shaman while young. Maybe the Laurence-Moon-Biedl syndrome is behind [4]. While in the typical case this syndrome produces obesity + polydactily + mental defects + retinal problems, in close kins often only the obesity and the polydactily seem to appear. Now, observe that the able shaman can very easily fall into trance, which, no doubt, would be classified by a physician as some neural/mental disorder. So, indeed, polydactily is a real indicator for shamanistic ability; who knows how good?

If the theoretic expert of the tribe had 6 fingers, he could naturally count on his fingers in Base 6, and common members of the tribe accepted the results or emulated the method with pebbles, twigs, closed fists &c.

Hungarian science has the necessary data. Unfortunately until now no Hungarian historian of mathematics was interested in the stage of Base 6. In pure mathematical sense, of course, this counting is trivial.

I asked in Chapter 5: whose symbol is W=6? The answer is then: W symbolizes the polydactilic hand of the spiritual leaders of the steppe tribes.

While in Chapter 5 I listed serious arguments for reconstructing the stage of Base 7, these arguments were indirect. The direct argument was silently in the Table of Chapter 3, and this is the proper place to make it explicit.

In Man'shi "7" is "szát", while in Magyar "hét", and these words come from the same Ugric word which was "szat". Magyar and Man'shi numerals remained so similar that in "2", Magyar "kettô" and Man'shi "kitigh" even the dual ending is the same; the Magyar "-ô" is the regular descendant of an "-egh". Now, Magyar "száz"="100" also comes from the ancestor of Manshi "szát", in the meaning "100". As the table shows, in Man'shi "szát" is both "7" and "100"; if unequivocality is needed, "100" is "jänigh szát", so, literally, "big seven".

Now, obviously "100" is not a bigger "7". It would, however, be a bigger "10", being 10². Or, "49" could be called a "big 7". In recent Man'shi the system is already mixed up; still, as a linguistic fossil, keeps the memory of times when "szát" was Base. But "szát", the Iranian loanword, originally could not have been "10", only "7".

Now, imagine an Alternative History, when Magyar mathematical geniuses (as Johnny von Neumann & Paul Erdôs) come earlier, and Hungary develops positional Base 7 numerology. While, of course, any base is equivalent with any other, an odd base can cause surprising effects. This, together with the Magyar language, would have been an almost unsurmountable barrier for Indo-Europeans.

The difficulties of an odd base were first recognised by L. Ron Hubbard [5], who imagined a tyrant species of the Galaxy preserving the clumsy Base 11 system in order to keep their discoveries secret. Unfortunately some consequences of the odd base seemed so "unnatural" that Hubbard did not elaborate the problems. Now I work out some of them for Base 7, to remember our historical past. I still do not know what was the advantage of Base 7, but it must have had some. The disadvantage, in contrast, is really not great, but for any case, surprising.

A Base 7 system can use "Greek type" numbers or a positional, so "Arab type" system. The first is simply to use letters for numbers, for simplicity I will use Greek letters, and then

1 = a

2 = b

…

6 = z

7 = h

2*7 = q

...

6*7 = m

7*7 (the Big Seven) = n

...

up to 6*7³ = y

The second system is simply 1, 2, 3, 4, 5, 6, 10, 11, 12, 13, 14, 15, 16, 20 &c.

The most important dichotomy of integer numbers, elaborated by Pythagoras himself is even vs. odd. In Greek number writing as well as in any positional system with even base the last digit shows if the whole number is even or odd. With Base 7 it is not so.

In "Greek type" writing e a is even (that is our 8), but k a is odd (our 29). In "Arabic type" writing e a is 11, k a is 41.

Now let us see the divisibility rules for Arabic type numbers up to divisor 7. (In Bold Italic the same rules for Base 10.)

Divisibility with 2 is the even/odd dichotomy; even is a number which is divisible with 2. A number can be divided by 2 if it ends on an even number, so on 0, 2, 4, 6 or 8. A number can be divided with 2 if the sum of its digits is divisible with 2.

A number is divisible with 3 if the sum of its digits is divisible with 3. A number is divisible with 3 if the sum of its digits is divisible with 3.

A number is divisible with 4 if the number given by the last 2 digits is divisible with 4. Each such even number is divisible with 4 whose half is even.

A number is divisible with 5 if its last digit is divisible with 5 (so is 0 or 5). No simple rule.

A number can be divided with 6 if it is divisible with 3 and is even. A number can be divided with 6 if the sum of its digits is divisible with 6.

No simple rule for divisibility with 7. A number is divisible with 10 (i.e. 7 in Base 10) is it ends with 0.

As it can be seen, the only difficulty is that now divisibility with 2 involves an analysis of similar to that of 3. Divisor 5 takes the role of exotic divisor 7 in Base 10; and divisor 6 takes the role of divisor 9 in Base 10.

Otherwise, being the base a prime, equipartitions will be more complicated. Take the example of money in Base 10. The usual way is to use 2 denominators, the bigger containing 10*10 0f the smaller (dollars and cents, for example.) Take a "round" price in the bigger unit; then it can be equally distributed between 2, 4, 5, 10, 20, 25, 50 or 100 consumers. In Base 7 the only such possibility is 10 (=7) or 100 (=49). But do not forget that even our present Base 10=2*5 is rather deficient; Base 2*6=12 would be much better. Maybe this was the reason that England maintained the 1 shilling = 12 pence rate until the 1970's. And maybe this preserves the "anomalous" English forms 11 = eleven, 12 = twelve instead of oneteen and twoteen, the very anomalies hindering convincing English translation of Problems 15.3 of Aristotle.

We were surely lagging behind the Indo-Europeans in the use of big numbers. But maybe not extraordinariky so. I told that Slavic "9" seems to be not IE (and maybe connected with "10"). Now let me cite an interesting hypothesis [6] suggesting that "new~nine", "neun~neu", "neuf~neuf" are not accidentally similar, but IE successor languages still remember that sometimes "9" was the brand new number. I do not know if this is true or not; but surely, the successors of IE *neun cannot be found in Slavic languages, and also not in Baltic ones, except Old Prussian (newints) [7]. Now, for geographic and historic reasons Old Prussian was under strong German influence.

We have close relatives, still not fully assimilated to Indo-European civilisation, and we do not deny it.

Remember that Latin is kentum language while Slovakian is satem, so a k<->s correspondence is expected; that is behind the difference in "4", otherwise the etymologies are transparent. Excepting "9". And "devät'" and "desat'" are rather similar. Note that in Russian another similarity exists between "7" & "8" ("sem'" vs. "vosem'"), but not in Slovakian.

The Northern Russian city-state Novgorod had some affairs with some "Yugors" since XIIIth century. These Yugors lived in both sides of the Ural Mountain and are believed to have been the ancestors of Man'shis and Khantis. When Moscow ate up Novgorod, Yugor affairs went to Grand Duke John III and to his inheritors. From that time we hear about Yugra about the confluence of Rivers Ob & Sosva, to the south, along the Ob, about Obdor (Salehard) and Koda, and in the basin of River Tabda about the Duchy of Pelim. Yugra and Pelim was dominantly Man'shi, Koda and, perhaps, Obdor predominantly Khanti. Since Kodan history is best documented at the present state of art, I give here the list of Kodan rulers. Anyways, it is a document of the history of the second biggest Ugric nation, so I should pay attention to our little brothers.

I use Hungarian official orthography manufactured for the biggest Ugric language.

For more details see e.g. [8]. No doubt, in 1484 Moldan was the ruler of the second biggest and strongest Ugric nation (the first was Matthias I of Hungary, but only cca. half of Matthias's subjects were Ugric); Moldan had a lot of underdukes. In 1609 Duchess Anna tried to form an all-Ob-Ugor coalition against Russia (weakened in the Polish-Russian War), with the Obdor and Sosva Khantis and with the Konda Man'shis. And in 1628 the population counting finds 496 men in Koda (although we have good reasons to believe that some of them were minors).

From 1771 we have a detailed statistics for the Man'shi and Khanti population: 4834 Man'shis and 9551 Khantis. As for the Danube Ugors, Magyars were more by almost 3 orders of magnitudes, but, being Hungary multilingual, and the Hungarian government in Vienna too Austrophile, the numbers are not too reliable [9].

Finnish orthography generally follows Western patterns. Consonants are few; single vowels are to be read as German ones, double ones are long. Hungarian, however, shows vowel lenghts by priming (here for the long counterparts of ö and ü I use ô and û for Internet compatibility), and a lot of consonants are not as seem to be. The letter "y" is for softening (as in Kenya and canyon), but "gy" is really the soft "d" (an analogy is Japanese). The letter "s" stands for sh, and "sz" stands for s. Another digraph is, e.g., "cs" for ch. Vowel "a" is labial.

For Man'shi here I use Magyar orthography ("gh" is the voiced velar fricative, voiced counterpart of Scottish "ch" in "Loch", and "w" is bilabial). For Sölkup I used an arbitrary but English-like transcription from linguistic texts.

The Uralic homeland (before 4000 BC) was a Northern, broad area, probably from Western Asia to Northern Norway; the population maybe was the Eastern Maglemose race. Surely they were reindeer half-nomads; maybe Samoyed keeps most of original life and area (plus Lapps); see Ref. [10] which is also good for Sölkup texts. Ancestors of Finns had lived roughly at the same latitude as now, but much Eastwars in present European Central Russia; but then, with Estonians, Livs and a lot of small tribes they trekked to the West. Maris, Mordvins and Komis maybe did not move too much.

The U group had more complicated history. We can reconstruct the original position in Westernmost Asia, maybe even astride the Ural Mountains. But among them, these 3.5 language groups (see in due course) had the following positions. North: Man'shi. Northeast: Khanti. Southwest: Magyar. South: Manchar.

For Man'shi see Ref. [11]. Surely Man'shi and Khanti were always Northward from Magyars; domesticated animals were unfamiliar for them, except reindeers (if one can tell domestivated and wild reindeer apart), and horse. Horse terminology is U words, common within Ugric, and not shared with anybody else, including Turks. (To be sure, Sinor [12] suggests an Altaic origin for the U horse name (ló, luw, law) through the word "ulagh", which is now a Turkish-Mongolian Kulturwort, meaning posthorse.) For any case, the word is not FU, but U. Now Ob Ugors do not have horses, except for high religious acts.

Note that the Ugor linguistics reconstructed the Ugor form of the name as *Man'c'e, and regular derivatives now can be found in all 3 successor languages [13], but the present meanings are rather interesting:

1) In Magyar the name of the language/nation.

2) In Man'shi the common name of Man'shis & Khantis (but not the Magyars!).

3) In Khanti the name of one phatria of the Khantis.

Shared characteristics seem to be more between Magyar and Man'shi than between Magyar and Khanti. Also, we know from the end of XVth c. that the Westernmost Ob Ugor group, the Duchy of Pelim, was Man'shi. We also know that Magyar (U) shares some phonologic features with the Permians (F).

Then Magyars met some Turks at the upper Ural River. There are a very few Turkish loanwords which can be found in Magyar and in at least one other U language; the most famous is the word for "swan". This helps to date the dissolution of U unity. Then Magyars became involved in the Great Migration (if not sooner, in 463 for any case), and travelled as far and fast as it was possible on the Eurasian grassland.

Now comes a hypothesis; it cannot be directly checked anymore. We do know, and always knew, that Magyars divided into two groups just before the last leg of westward migration, somewhere at the Don, in the beginning of IXth century. The Bols'she Tigani cemetery of Khalikova may belong to the Eastern Magyars [14]. They trekked somewhere to the Kama and Volga Rivers, and in the first quarter of XIIIth century were contacted by Brother Julian from Hungary. Then the campaigns of Gengis, Djochi and Batu displaced a lot of peoples of the steppe.

Still at the end of the XIIIth century the slave market of the Genoan port at Crimea, Caffa, registrates some slaves whom the Tartars sold there, and a few have a strange nationality. A small percentage of sales were evaluated by modern historians, and a subsample of 66 sales seems homogeneous enough [15] from the years 1289-90. Now, 2 groups cannot be identified with existing nations/tribes: Cevian (2) and Maniar (5). Tardy has strong arguments [15] that "Maniars" in the contemporary Genoese orthography should have been pronunciated as "Mangiars" or such, and there are the Eastern Magyars behind this name. Let we believe it.

Then in Eastern Magyar etnonym the "-n'-" of "Man'shi" had remained. But one characteristics present Magyar shares with Permian Finns (F) but not with Man'shi (U) is that a (nasal+unvoiced) group has the tendency to evolve into (voiced); the classical example in the (Permian, Magyar, Man'shi) triad is "dog", which is "eb" in Magyar, but "ämp" in Man'shi. The fate if U -n'c'- is a textbook example in U linguistics. E.g. the word *an'c'ar (tusk) went to Magyar "agyar", Man'shi "änyser" and Permian "vazher", while keepig its meaning [16].

Now, there are a very few Magyar words retaining the nasal (to be sure, already before a voiced consonant); for example the twin "dob" and "domb", the first now "drum" and the second "small hill, mound". The usual explanation is the existence of one idiom where the nasal voiced the next consonant, but did not have been used up. Since the process always leads to the vanishing of the nasal in Permian, and does not go at all in Man'shi, we may hypothesize that it had a W-E gradient, so may have been weakest in Easternmost Magyar groups.

But we see just this in Caffa. We expect the common name of Magyar and Man'shi to change into something Man'char or Mangiar in Easternmost Magyar, and this us recorded for Magyars remaining East in Caffa. This is the reason that I guess Man'chars/Man'zhars/Mangiars originally just south of Man'shis.

We saw that in Man'shi "szát" means both "7" and "100" (and the second is the Big 7). Now, Hungarian linguists do not doubt that both Magyar "7" and Magyar "100" comes from U "szat", but in both cases there are some anomalies in the evolution.

In Magyar "7"="hét", and one would expect "ét". Then the expert tells [16] that the form "hét" is secondary, under the analogic influence of "6"="hat". Let it be.

But the Magyar "100" is "száz". The books give a lot of FU related words, starting everywhere with some "s-", which is the Magyar "sz-". It seems that the initial consonant more or less changed regularly when the same word meant "7" (e.g. in Khanti "tapet"), but remained unchanged when it did "100".

Maybe "100" was too strange. My guess is that the word got the "Big Unit" meaning only after some time, and then the phonetic changes were already over. Everybody may believe what he likes.

[1] The Complete Works of Aristotle, ed. by J. Barnes, Princeton University Press, Princeton, 1995

[2] Bárczy G.: A magyar szókincs eredete. Tankönyvkiadó, Budapest, 1951.

[3] Diószegi V.: Etnographia LXXI, 456 (1960)

[4] Fraser Roberts J. A.: An Introduction to Medical Genetics. Oxford University Press, London, 1967

[5] Hubbard L Ron: Battlefield Earth, 1982

[6] Mallory J. P. & Adams D. Q.: Encyclopedia of Indo-European Culture. Fitzroy Dearborn Publ., London/Chicago, 1997

[7] Brugmann K.: Kurze vergleichende Grammatik der indogermanischen Sprachen. Trübner, Strassburg, 1904.

[8] Bahrushin S. V.: Ostyackie i vogulskie knazhestva v. XVI-XVII. vv. In: Bahrushin S. V.: Nauchnie trudi, Vol. III., Izdatel'stvo Akademii Nauk SSSR, Moscow, 1955, p. 86

[9] A counting happened in the time of Emperor Joseph II, who was not crowned as King of Hungary. His administrative innovations, including land survey and census, were obstructed by the Hungarian nobility as methods of tyranny (correctly in part), and some county legislatures ordered to burn the papers at gallows (in some counties this order was executed at the death of the Emperor who indeed had no right to administrate Hungary). In turn, Imperial administration was angry with Hungarians and tried to classify as many people Imperial German as possible or impossible. However no survey has happened for first language. You can guess in that time (c. 1784) some 40-45 % of Hungary speaking Magyar as first language which then means cca. 4 million. The official language of Hungary, of course, was Latin.

[10] Hajdú P.: Chrestomathia Samoiedica. Tankönyvkiadó, Budapest, 1968.

[11] Kálmán B: Chrestomathia Vogulica. Tankönyvkiadó, Budapest, 1976.

[12] Sinor D.: Centr. Asiatic J. 10, 307 (1965)

[13] Gulya J.: in Magyar Őstörténeti Tanulmányok (eds. Bartha A. & al.), Akadémiai, Budapest, 1977., p. 115.

[15] Tardy L.: A tatárországi rabszolgakereskedelem és a magyarok a XIII-XIV. században. Akadémiai, Budapest, and citations therein

[16] Hajdú P.: Bevezetés az uráli nyelvtudományba. Tankönyvkiadó, Budapest, 1966.

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