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The New-Old Numerals or Why this sucks

Well, it does suck.  To begin with, calling it the 'new numbers' is something of a contradiction, because although they haven't been in colloquial use for a long long time, they are actually very old numbers.

It works this way:

1. Q-Celtic inherits a decimal system (based on 10s) from Indo-European

2. This develops into a vigesimal (based on 20s) system from the old "outdated" decimal system.  This is because Old Irish educators decided it was too difficult for children to learn maths in a decimal system. Swipe at the people who came up with this nonsense about vigesimal number systems being too unwieldy for maths intended.

3. This system is then in use for a long time until "modern educators" get their hands on Irish and Gaelic and change it all back

... Talking nonsense, are we?  Let's take an excerpt from a Basque textbook then, a people who is lightyears ahead of Gaelic in terms of language planning.  We find equations which read hirurehun ta larogeita hamabi zati berrogeita bederatzi berdin zortzi, literally "three hundred and four-twenty-and ten-two divide two-twenty-and nine equal eight".

Incidentally, the Basques do calculus with these numbers and no children have been diagnosed with cortical meltdown yet ...

For those who are curious the Old Irish numbers were as follows (modern forms in green - interestingly, they are derived from the old genitive forms):

Which one to use?  Up to you, but you'll have to learn both anyway.  Children in GME learn only the new-old system, but you will come across the traditional system all over and many older speakers don't know the new-old system ... so at least for the time being we're stuck with TWO of them <sigh>.  Almost as efficient as Great Comrade Mao Zedongs spelling reform.  Don't ask.

On the other hand, having the two systems side by side has its uses too.  In the traditional way talking about decades is slightly cumbersome, at least with certain numbers e.g. the thirties as na deich ar fhicheadan is just weird - but the new old numbers work excellently here:

We recommend you learn the old system and use it and simply be aware of the new-old system, perhaps just using the above terms for decades in the new-old system.  And pay attention who you are talking to - children from GME often mistake trì fichead for trithead!

Another reason this sucks is that it does not only force learners to learn TWO number systems, but the new-old system isn't that straightforward either as they may think.  Although in counting the general approach is to say the number and then the object being counted e.g. ochdad is a seachd guib '87 beaks' there seems to be a certain amount of confusion even amongst the propagators of the new old systems about this.  Apparently you have a choice of saying either ochdad gob is a seachd or ochdad is a seachd guib, except when doing calculations when you are supposed to put it at the end always ... confused?  You're not on your own then ... at least the traditional system is consistent.

As you will have noticed, the traditional way of counting gets (relatively) straightforward after 40.  So we are going to give you the new-old numbers only up to 50 plus the full tens and a few higher numbers.

1. The new-old numbers themselves aside, the main difference between the systems is that while the traditional system looses the ar fhichead bit after 40, the new-old system gets rid of this altogether and simply uses decimal + a h-aon, a dhà ...

2. No, hundred has not been changed to ceudad - although there is a word ceudad, but this means 'percent' in Gaelic e.g. 40% = dàichead sa cheudad.

3. In this system, all full tens are followed by the singular forms of the nouns.

4. Aon, dà and the ordinal numbers behave like in the traditional system so we haven't explained all over agin.

So, how do you deal with higher numbers in this system? 

Footnote or ten ...

1. The comma is only "notional" that is, it's a "speech break" you put in when saying the number.  You don't actually write it when spelling out numbers - we just put them in here to demonstrate where the breaks would be.

2. The numbers 2-6 lenite ceud, so you get dà cheud, trì cheud, ceithir cheud, cóig cheud and sia cheud.  This is NOT completely arbitrary but the last remining vestiges of something Gaelic lost.  Traditionally (well, several hundred years back in Gaelic terms), the number 1-6 lenite while the numbers 7-10 nasalize.  Meaning?  Well, seeing Irish still does this, let's have a look at how you count boats in Irish: bád, dhá bhád, trí bhád, ceithre bhád, cúig bhád, sé bhád, seacht mbád, ocht mbád, naoi mbád, deich mbád.  Cool, isn't it?  Gaelic stopped doing this a long time ago - except with the word ceud for whatever reason.

3. Between 1001 and 9999, you can employ "splitting" into hundreds as you would with a year, e.g. 1267 as dà cheud dheag, trì fichead is a seachd.

4. As mentioned above, there is the possibility to express numbers up to 200 in twenties e.g. 136 as ceud, sia deug ar fhichead or sia fichead is a sia deug.  So 136 ice-creams would be sia fichead reòiteag is a deich.

5. Leth refers to a half of the previous largest round 100, 1.000, 10.000 etc unit.  This gives a value of 50, 500, 5.000 etc.  These are then combined to give 150, 1.500, 15.000 etc.  Enter the "illogical" step.  You might imagine that trì cheud gu leth equals 450.  Wrong.  It equals 350.  This principles applies at each level (100, 1.000, 10.000 etc).  You can then add the numbers 1-9 to these expressions, but once you hit the next full 10, you have to revert to the "normal" way of counting, e.g. dà mhìle gu leth, dà mhìle gu leth is a h-aon, dà mhìle gu leth is a dhà ... dà mhìle gu leth is a naoi, dà mhìle is trì fichead.  Leth cheud, leth mhìle etc work the same way.  Alternatively you can just stick to the "normal" numbers.

6. And last but not least, there is a tendency to stick the thing being counted at the very end with large numbers, especially with monetary units, so ¥51.655 would be dàichead mìle, sia ceud, trì fichead is a cóig Yen rather than dàichead mìle, sia ceud, trì fichead Yen is a cóig.