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're 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 This develops into a vigesimal system (based on 20s) from the old, "outdated" decimal system.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 vigesimal system was in use for a long time until "modern educators" got their hands on Irish and Gaelic and changed it all back.

...Talking nonsense, are we? Well, let's take an excerpt from a Basque textbook from a land where where language planning is lightyears ahead of Gaelic. 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. The modern forms are in green, and interestingly, they're derived from the old genitive forms:

10	20	30	40	50
deich	fiche (gen. fichet)	tricho (gen. trichot)	cethorcho (gen. cethorchat)	coíca (gen. coícat)
deich	fichead	trithead	ceathrad	caogad
60	70	80	90	100
sesca (gen. sescot)	sechtmogo (gen. sechtmogat)	ochtmoga (gen. ochtmugat)	nócha (gen. nóchat)	cét (gen. céit)
seasgad	seachdad	ochdad	naochad	ceud

Choices, choices

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'll 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 Zedong's 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:

na ficheadan	na tritheadan	na ceathradan	na caogadan
the twenties	the thirties	the fourties	the fifties
na seasgadan	na seachdadan	na h-ochdadan	na naochadan
the sixties	the seventies	the eighties	the nineties

I recommend you learn the old system and use it. 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!

Other reasons this sucks is that it not only forces learners to learn two number systems and the new-old system is not as straightforward as some may think. Although, the general approach in counting is to say the number and then the object being counted, for example, ochdad is a seachd guib 87 beaks. However, there seems to be a certain amount of confusion about this, even amongst the propagators of the new old system. Apparently, you have a choice of saying ochdad gob is a seachd or ochdad is a seachd guib - except when doing calculations when you're always supposed to put the noun being counted at the end. Confused? You're not on your own then. At least the traditional system is consistent.