Aire Do Gach Luingearachd. . .

Diciadain sa chaidh dh’fhàg sinn an clas tràth airson a dhol gu taisbeanadh mu Ro-aithris na Luingeis aig a’ Chrichton, le còrr is ceud neach. Tha an neach-labhairt, Charlie Connelly, air a bhith dèidheil air a’ chraoladh o chionn fhada, mar a tha gu follaiseach air mòran dhaoine eile. Bidh seòladairean agus iasgairean ga chleachdadh gu mòr ach tha a’ mhòr-chuid de luchd-èisteachd nan leabaidh agus tha e gan socrachadh agus gan cuideachadh a’ cadal. Gu neònach, tha e math airson seo a chluinntinn gu bheil uisge trom agus gaothan a-muigh air a’ mhuir, agus tha e dha-rìribh! Tha e ag obair dhòmhsa.

Bha Mgr Connelly glè mhath air gun a bhith sgìth ach chan eil mise agus mar sin cha bhith mi a’ bruidhinn airson ùine mhòr. Thòisich an t-Àrd-mharaiche Fitzroy, caiptean a’ Bheagle, air ro-aithris na sìde airson shoithichean san naoidheamh linn deug agus b’ e còd Morse agus teileagrafaireachd a’ chiad ro-aithris luingeis. Chaidh an cleachdadh an toiseach air an rèidio ann an 1924 agus bha iad cho cudromach is gun do rinn iad an ro-aithris fhathast nuair a bhàsaich an Rìgh agus dhùin an rèidio airson caoidh.

Bha Connelly airson tadhal air tìr anns a h-uile sgìre mara far an robh tìr. Chan eil fhios agam an do shoirbhich leis leotha uile, ach chaidh e gu eilean Danmhairgeach ann am Bàgh na Gearmailt far an robh ionad bhùthan an rud as inntinniche. Air Utsire bha sgioba ball-coise glè shoirbheachail a bha an urra ri an luchd-dùbhlain a bhith tinn mara nuair a chluicheadh ​​iad nan aghaidh. Tha iad a-nis air an toirt gu bhith a’ cluich air tìr-mòr Nirribhidh agus chan eil iad air geama a bhuannachadh bhon uair sin. Thadhail e cuideachd air Sealand, ann an Linne na Tamais, a tha na àrd-ùrlar a tha ag ràdh gur e dùthaich neo-eisimeileach fhèin a th’ ann. Is dòcha gun deach e gu Lundy cuideachd, far a bheil càl ro-eachdraidheil. Cha b’ urrainn dha faighinn gu Rockall. Tha Rockall trì cheud cilemeatair bho Shòaigh anns na h-Eileanan Siar agus bha e na phàirt de Siorrachd Inbhir Nis. Tha e còig ceud seasgad seachd cilemeatair bho Inbhir Nis, agus tha sin na shlighe fhada ri thighinn gus na bionaichean fhalamhachadh. Chuir an t-Arm dithis shaighdear agus bogsa geàrd air airson beagan mhionaidean. Tha Èirinn ag ràdh gur ann leotha a tha e, agus tha Innis Tìle agus na h-Eileanan Fàro ga iarraidh.

Is e ‘Sailing By’ le Ronald Binge an ceòl airson an Shipping Forecast agus chaidh a sgrìobhadh airson bailiùnaichean èadhair theth.

Mu dheireadh, chleachd an nobhail agam ‘Unspeakable’ na sgìrean mara Shipping Forecast mar shiorrachdan, ach is e sin sgeulachd eile gu litireil.

Ar Dinnear

Airson iomadh bliadhna a-nis, tha mi air biadh sònraichte ullachadh aon uair san t-seachdain. Roimhe seo, bhiodh biadh sònraichte agam airson gach latha den t-seachdain, ach dh’fhàs mo theaghlach gu math sgìth dheth sin, agus mar sin is e am biadh seo an aon bhiadh a bhios mi fhathast a’ dèanamh gach seachdain. Tha bhidio YouTube mu dheidhinn air aon de na seanalan agam. Is e seo am biadh a thuit mi air an làr mus tàinig mi gu clas Gàidhlig beagan mhìosan air ais, agus mar sin bha mi fadalach airson an leasain sin.

Tha mi a’ smaoineachadh gu bheil e cudromach do theaghlach biadh ithe còmhla, agus na h-aon bhiadhan ithe gu cunbhalach gus ar cumail ceangailte. Is toil leam cuideachd biadh a dhèanamh a tha mo theaghlach dèidheil air. Air Diardaoin, is urrainn dhomh tilleadh agus am biadh seo ithe agus chan fheum mi a theasachadh, oir is e salad a th’ ann. Nuair a rinn mi e air Dihaoine ann an Sasainn, rinn e nas fhasa a dhol gu cafaidh Street Pastors far an robh mi a’ cuideachadh. Is urrainn dhomh cuideachd dèanamh cinnteach gum faigh ar mac, a tha a’ fuireach còmhla rinn, biadh fallain an-asgaidh aon latha san t-seachdain ma nì mi seo. Rinn mi e gu cunbhalach airson lòn eaglaise cuideachd, le biadh eile.

Tàthchuid: sligan pasta làn-ghràin, sùgh liomaidan uaine, basail, sabhs soy, ola ollaidh, ollaidhean, pònairean dubha air am bogadh agus air am bruich gu math, ceithir-deug duilleagan basail, piopairean, aon chucumar, tomatoan agus tofu no càise buabhall uisge. Chan eil ar mac ag ithe tofu, agus mar sin gheibh e am càise buabhall uisge na àite. Chan eil sinn ag ithe a’ chàise.

1. Bruich am sligan ann an uisge airson deich mionaidean.
2. Fhad ‘s a tha am sligan a’ goil, gearraich na tomatoan agus an cucumar agus cuir iad ann am bobhla.
3. Drèanaich agus cuir na h-ollaidhean agus na pònairean dubha ris.
4. Reub ceithir-deug duilleagan basil airson gach bobhla agus cuir iad ann am bobhlaichean.
5. Dòirt an ola a-steach do bhobhla.
6. Gearr agus brùth na liomaidean uaine a-steach don bhobhla.
7. Cuir an sabhs soy ris a’ bhobhla.
8. Cuir na piobair ris agus measgaich an leaghan gu math le forc.
9. Cuir eagal aig sligan, drèanaich agus cuir ann am bobhlaichean.
10. Dòirt an dreasa a-steach do na bobhlaichean, measgaich gu mionaideach agus fritheil.

Beagan rudan. ’S e liomaidean uaine toradh as searbhaiche agus tha iad nas saoire na liomaidean, agus mar sin ’s fheàrr an cleachdadh. Tha basil math ach tha e làn alùmanaim, agus mar sin is dòcha nach eil e sàbhailte. Tha na beathachadh a’ toirt a-steach pròtain, bhiotamain C, bhiotamain B, searbhag folic, flavonoids, carotenoids, sinc agus feadhainn eile.

Mìosachan Reul-eòlais

Tha neach-dèiligidh agam a tha an-dràsta ag iarraidh orm mìosachan reul-eòlais a dhèanamh dha. Is e seo an dàrna turas a rinn mi rudeigin mar seo. O chionn grunn bhliadhnaichean, rinn mi mìosachan planaid dhearg airson bliadhna a’ phlanaid dhearg 214 bliadhna às deidh dha Galileo fhaicinn an toiseach tro teileasgop. Bha sin gu math cumanta ach leis gun do dh’innis a’ chompanaidh clò-bhualaidh breug mu chaitheamh inc aon de na clò-bhualadairean a chleachd mi air a shon, bha e ro dhaor a dhèanamh. Dh’fhàs mi feargach agus thilg mi am clò-bhualadair dhan ionad-reic. B’ àbhaist dhomh a bhith nam dhuine gu math feargach. Chan e sin an duine a th’ annam tuilleadh. Na bi gam bhreithneachadh a rèir na b’ àbhaist dhomh a bhith.

Tha ùidh mhòr aig mo neach-dèiligidh ann an tachartasan anns na speuran leithid cuin a tha a’ ghealach a’ coimhead nas motha no nas lugha na an àbhaist, cuin a tha a’ ghealach eadar sinn agus a’ Ghrian no nar sgàil agus dàrna gealach ann am mìos, agus mar sin thairg mi mìosachan a dhèanamh dha a dh’innseadh dha cuin a thachradh iad sin. Bha e glè thoilichte leis an seo, agus mar sin nì mi sin, le bhith ag innse do einnsean reusanta mar a nì thu e oir is e seo an dòigh as sìmplidh air a dhèanamh.

Ciamar a nì thu e, is e sin ceist eile. Ged a tha beagan eòlais agam, tha e duilich suidheachadh na gealaich agus nam planaidean obrachadh a-mach. Bidh e airson faighinn a-mach cuin a tha a’ ghealach a’ coimhead as motha, cuin a tha i a’ coimhead as lugha, ìrean agus cuin a tha a’ ghealach, a’ ghrian agus an Talamh ann an loidhne dhìreach. Tha iad sin gu math furasta. Ach feumaidh mi cuideachd obrachadh a-mach cuin a tha coltas planaidean a’ dol air ais, cuin a tha trì ann an loidhne dhìreach eadarainn, cuin a tha iad a’ coimhead as fhaide bhon Ghrian, na gluasadan agus na h-ìrean aca, agus innse dha càite a bheil iad. Tha cuid dhiubh sin furasta cuideachd, ach chan eil siostam na grèine rèidh, chan eil na orbitan nan cearcallan agus chan eil na h-àiteachan far a bheil iad as fhaisge air agus as fhaide bhon Ghrian san aon taobh. Feumaidh mi co-dhùnadh cuin a thòisicheas mi. Is dòcha gur e deagh cheann-latha a th’ ann am Bliadhna Ùr 4713 RC, ach chan eil fios agam càite an robh iad an uairsin, agus mar sin an àite sin coimheadaidh mi airson àiteachan agus gluasadan o chionn ghoirid nan cùrsaichean aca agus obraichidh mi a-mach iad às an sin. Feumaidh mi an uairsin na suidheachaidhean a chithear bhon Ghrèin a thionndadh gu na suidheachaidhean a chithear bhon Talamh, obrachadh a-mach dè cho fada ’s a bheir e air solas faighinn bho na nithean thugainn an seo agus mar a tha an àile gan dèanamh coltach ri bhith ann an diofar àiteachan.

Chan eil fhios agam dè a chanas mi ris na planaidean anns a’ Ghàidhealtachd. Is e an dàrna fear gu soilleir Reul na Maidne agus Reul na Feasgair. Dh’ fhaodadh an ceathramh fear a bhith air ainmeachadh mar rudeigin coltach ri bàrr sleagha Chù Chulainn, ach is e ainm Èireannach a tha seo agus tha e cuideachd air a chleachdadh airson reultan-reubadh. Tha mi airson barrachd fhaighinn a-mach mu bhith a’ coimhead rionnagan anns a’ Ghàidhealtachd.

Is dòcha nach eil fios aig mo neach-dèiligidh gu bheil na tha dha-rìribh a’ tachairt anns na speuran gu math eadar-dhealaichte bhon rud a thathar ag ràdh a thachras a rèir reul-eòlas, ach feumaidh mi a bhith onarach, agus mìnichidh mi rudan mar a tha iad dha-rìribh.

Feamainn

Tha na costaichean timcheall na-h-Alba nas fada na na costaichean timcheall na Sìna, mar sin tha e mòran feamainn. Tha e trì fineachan feamainn: dhearg aig an cas na tràigh, dhonn air an meadhan agus h-uainne air an ceann.

Dhearg

Dhonn

Uainne

Tha e cuideachd feamainn ghorm ach chan eil an duine i ith. Tha an feamainn an biadh blasta, slàn agus an-asgaidh. Tha feamainn dhearg agus uainne lusan ach chan eil an feamainn dhonn lusan.

Tha cho mòran mathas ann an feamainn. Tha e air uairibh tuilleadh ‘s a’ chòir. Tha e ola iasg innte.

Nis their mi dhà rhiaghailt còcaireachd airson feamainn:

Tàthchuidean: duileasg, buntata, creamh, piopar dearg, sìolan sgeallan, ola, balgan-buachair, uinnean, piopar tiolaidh no cantarnaid.

Goil an buntata, glan agus geàrr. Teasaich ola agus cuir ri na sìol agus buntata. Fraidhig gus buidhe agus thoir air falbh. Blàthaich an ola agus fraidhig còig mionaidean na tàthchuidean eile ach a-mhàin duileasg. Cuir ri an duileasg agus buntata. Gluais deug mionaidean agus frithealadh.

(Ma dh’iarras tu, bheir mi air falbh an dealbh seo.)

Bara lawr. Aran slòcan. Tha e dà fheamainn airson an biodh seo: glasog agus slòcan. Goil an feamainn gus bloinigean-gàrraidh, rol ann na coirce agus fraidhig ann geir bagùn no ola trom, ith airson bracaist.

Mu dheireach, is dòcha gun ith sibh feamainn oir tha an cairgean ann an reòiteag, “blancmange“, ceitseap no stuth-fhiaclan, agus mòran eile.

I Just Wanted To Know The Word For “Centre”!

Gàidhlig is, as you know, a language I find phenomenally hard. I’ve said in the past that the best way of learning it is to know it already. It’s a bit like when you stop and ask for directions to somewhere and the reply is “Oh, I wouldn’t start from here if I were you”. Nonetheless it’s got to be done.

The above picture is of the Burns Centre in Dumfries. The obvious joke will not be made here as Doonhamers are thoroughly sick of it and have heard it a thousand times. It occurred to me the other day though, that although I know the Welsh words for “centre”, owing to almost getting a job at the Canolfan y Dechnoleg Amgen in Wales – they’re actually “canol” and “canolfan” and not speaking Welsh I have no idea what “-fan” does – I had no idea at all what the Gàidhlig word was. I do know the word for “middle” – meadhan – but “middle” is not “centre”. I’m also aware that the word in English is used figuratively as well as literally, which is also a usage of “canolfan” in Welsh, but wasn’t cognisant of such a usage or otherwise in Gàidhlig.

Well, it turns out, unsurprisingly, that it isn’t that simple, although the reasons it isn’t aren’t quite linguistic. It starts out fairly straightforwardly. The Robert Burns Centre is probably called something like An Ionad Raibeart Burns, assuming “Raibeart Burns” doesn’t need to be put into the genitive, and it’s even true that “ionad” means “centre” in figurative and literal terms, as well as meaning “location” and “situation”, although I’m still confused as to how it’s pronounced the way it is because there’s clearly a rule about whether the I or the O is pronounced, so I initially thought it was “yonnat” but apparently it’s “innet” (I’m not bothering with IPA at the moment because I’m on the wrong device for it and in any case it’s been said that the IPA is inadequate for transcribing this language, and there’s a whole other conversation to be had about that). So you might think you’ve got it sorted and everything’s very very good, but actually it isn’t, at least from about 2008 CE onward, because at that point someone did something subversive.

Technical language is often perceived as a barrier to understanding which maintains an in-group and an out-group. This is certainly sometimes true, but at other times not using it makes it almost impossible to talk about something. Cults, sorry, new religious movements, often seem to use language this way in order to exclude outsiders from understanding what they’re talking about and also often to make it seem to their followers that they know what they’re on about. When this isn’t done, which notably occurs in botany with the words “nut” and “berry”, people often object because it leads to bananas being called berries and peanuts not being nuts. In fact hardly anything is a nut. To hide this quandary away, scientists and mathematicians often draw on Greek or Latin as a kind of nice neat cover for the messy box of what to call things. Hebrew and Sanskrit are also sometimes used. In fact, Sanskrit is often formally used to refer to phenomena in Gàidhlig. Rather refreshingly, “ionad” is used thus, presumably as part of some kind of statement against the Latinisation or Hellenisation of technical terms.

Understanding this usage is possibly one of the steepest learning curves I’ve ever encountered. This is how it’s described when you type something related into Google:

As a Grothendieck topos is a categorified locale, so an ionad is a categorified topological space. While the opens are primary in topoi and locales, the points are primary in ionads and topological spaces.

Clear? Didn’t think so. It isn’t even as straightforward as being about topology or group theory. It sounds like a concept related to topological space but that’s only tangentially true, because apparently this is category theory. The idea seems to be to take various branches of maths and generalise the concepts and processes which exist and occur within them. It feels like a theory of everything but it isn’t. It’s kind of metamathematics although I’d prefer to reserve that idea for something like number theory. It involves three types of thing, one made up of the other two. Categories, made of objects and morphisms. To my rather naive brain, this sounds a bit like group theory and a bit like topology, and probably a bit like linear algebra if I knew what that was, which I don’t, so I’m going to wrestle with this here and try to understand it.

My first thought was the Canterbury Cross, which was used as the emblem for my secondary school and looks like this:

Back when I’d just started at that school, we were supposed to make an ashtray, because in those days tobacco smoking lacked the stigma it has now been allowed to acquire. This involved taking a square sheet of aluminium and clipping the corners inward to make a shape somewhat like this, then folding them inward. Being dyspraxic, my attempt to do this was catastrophic. I was shockingly bad at practical subjects, or rather the ones I was actually allowed to do, which is again another story. On one occasion I was simply sawing a piece of perspex into the right shape and it literally exploded very loudly in a puff of acrid smoke, to which my plastic teacher’s response was to ask, wearily, “What have you done now?”. I could go into the gender politics of all this but anyway, we’re talking about the Canterbury Cross. My initial attempt at understanding a ionad is that it’s like the middle portion of this cross in that you can trace a line from it to each of the arms, but not from one arm to another. This is not quite what I mean of course, because it never is, but there seems to be a sense in which this is true. It is in fact dead easy to draw a line from one arm to another, but it still seems to be connected in such a way that the others aren’t. This is probably not it though.

Category theory is apparently difficult because it’s an abstraction of an abstraction. Group theory and topology are already quite abstract, though still applicable quite easily. Category theory takes it a step further. I’m going to have another go.

Maths generally consists of objects and operations on those objects. 2+2=4. Addition is the operation there and the numbers are the objects. Likewise, the top slice of a Rubik’s cube can be turned clockwise through a right angle and then turned back, and there are twelve possible sets of arrangements of a Rubik’s cube which it’s impossible to reach from any of the other sets. These operations of turning are within these sets of arrangements and this is a typical application of group theory. The sets of arrangements are the objects. I’m currently trying to imagine a species of intelligent extraterrestrials who grasp group theory intuitively but can’t count, because they have five sexes. More on that another time. Anyway, geometry has this too. A shape can be reflected, magnified, rotated and so on. In each of these cases and many others, there are the operations and the elements. Category theory summarises branches of mathematics by turning them into a series of items joined together in various ways by arrows, so it aims to do to maths what maths aims to do to the world, and it does it with things like this:

Presumably, and this is just me, if you can find two branches of maths which can be summarised using the same diagrams, they’re really the same branch and if there’s another diagram which is known from one branch but not another all of whose other diagrams are the same, it’s worth looking into whatever’s represented by that extra diagram as it might well work in the other branch.

I seem to have gone rather far from the Canterbury Cross here and that might well be due to there being no connection between the two topics. In fact I think there’s bound to be a connection because of the nature of the shape, but it might not be what I think it is. For instance, you can take a Canterbury Cross and flip it horizontally, vertically or diagonally without changing the shape, and you can also reflect it, so there are clearly symmetry groups which can be applied to it which can’t to, for example, the conventional long cross used as a symbol of the Christian faith, so things can be done to this which are relevant to group theory. So it is relevant, but the thing is that you could do the same kind of thing with a Star of David, though different in detail because that shape can also be rotated to fit into itself in various ways which a Canterbury Cross can’t, and all that stuff you could represent very generally in a Category Theory diagram but there’s nothing special. So it seems I haven’t got anywhere near understanding what an ionad actually is, except that it’s something to do with Category Theory.

So, my next guess then, which might well be wrong for all I know, is that Grothendieck Topology is a way of looking at those diagrams which compares them so that one can generalise from them and make useful advances by comparing different mathematical fields. Is it that? I don’t know! And I seem to have to work out what that is in order to work out what ionad actually means in that sense.

So I seem to have arrived in some sort of state of conceptual splodge and confusion. It almost feels like I can’t bridge the gap between incomprehension and the holy grail that is the concept of “ionad”. I feel the same way about calculus, which in one of the two cases I consider to be the idea of being able to tell which way a wiggly line will go next and wonder vaguely whether astrologers use it to locate planets or whether they just use ephemerides, and that’s as far as I can get. With calculus, by the way, I’m aware of there being two mutually inverse types. With category theory, who knows? How do you get to the point where you can confidently say you can understand something? How do you know you haven’t got it completely wrong? Well, usually I suppose you can test it in the real world, so if I wire a three-pin plug wrongly I will briefly know when the electric shock throws me across the room and kills me, and if I make a (vegan) soufflé wrongly I will become aware of that when it collapses as soon as I take it out of the oven, but in this case, how will I know when I’ve got it wrong? It seems too abstract to test. I want to savour this state of personal bafflement and adumbrate its characteristics.

(Can you even make vegan soufflés?)

So to survey my mathematical knowledge, I can manage the following:

• I scraped an O-level in maths. This probably doesn’t indicate much about how well I understand it though, because I’m fluent in French even though I failed the O-level but not in Spanish even though I have a B at GCSE.
• At first degree level, I’ve studied statistics to the extent that I can see through deceptive practices which purport to employ it, use it in my own quantitative research and assess the quality of other quantitative research. However, stats is arguably not maths.
• Also at first degree level, I’m very confident in the use of formal logic and have extended my knowledge beyond the mere understanding of sequents, truth-tables and well-formed formulae, and I also have a firm grasp of the foundations of mathematics, which extends into number theory.
• I’ve pratted about a bit with stuff like fractals, non-Euclidean geometry and things which take my fancy on the lower levels of the kind of fun maths which crops up in the likes of Martin Gardner’s and Douglas Hofstadter’s writing.
• Not sure if it’s maths but I’m kind of okay at coding provided OOP isn’t involved and it follows an imperative paradigm.

I’m also not scared of maths. I’m not wonderfully good at it but in the same way as someone who feels almost alien to me might enjoy a kick-about with a football of a Saturday afternoon as opposed to playing in the FA Cup, I dabble a little bit. For instance, I’m motivated to find a non-iterative algorithm for calculating square roots although I haven’t got round to it yet. I also find it incomprehensible how people can say that they’ve never applied most of the maths they learnt at school and wonder how hard their lives must be as a result, unless they don’t realise they’re applying it. Last night I used E=mc² and 4πr² along with a bit of trig to work out how much energy our solar panels are likely to get from the Sun today, and to me that seems useful although somewhat inaccurate owing to the fact that the planet inconveniently has an atmosphere, furthermore with clouds in it, and that really is not that hard although it takes quite a long time if you don’t use a calculator, and where’s the fun in that? I suppose that has the same role in my life as football does in someone else’s. But I still can’t understand this. I also wish I knew how close I was getting.

Let’s have another go.

There are these things called topoi, and other things called pre-sheaves and sheaves, and they relate to this situation. Topoi appear to be places set up to do particular kinds of maths comfortably. Is that what they are? Well, I just asked an AI and it may have been trying to please me because that’s what they do, but it agreed that that’s what a topos is. It also started talking about sheaves, so yikes.

Okay, so what’s a sheaf and why are there pre-sheaves? My initial thought here is that we have conceptual ring binders, we’re wandering all over a large warehouse covered in mathematical papers from all sorts of fields, and we’re collecting them together in the ring binders according to what category (there’s that word again) they’re in, and that the pre-sheaves are the empty binders and the sheaves are the full binders. Is that it? Plug that metaphor into an AI and see what it says. . .

Right, done that with two different AI chatbots and I’m wary that they may be eager to please, but both of them said that I wasn’t too far off although open sets are involved. I think of open sets as akin to the Bedeutungen of family resemblance definitions as opposed to those of definitions based solely on necessary and sufficient conditions, and to be honest I think I’m right about that. I could be confidently incorrect of course. And once again, leaving the sycophancy problem aside, although I’m not completely correct, I’m not one hundred percent wrong either. There also seems to be something about them sharing a corner.

As I’ve said, there was this guy called Alexander Grothendieck who was unlucky enough to be born in Germany in 1928. After a traumatic childhood, he became a mathematician, some say the most important of the twentieth century CE. At some point he actually left mathematical academia and became a political activist and a religious recluse, and he gave lectures in Vietnam while being bombed. I know very little about him but I wonder, given that limited information, whether his life indicates the potential role of maths in people’s lives as a source of inner peace, and also the affinity between mathematical beauty and the spiritual realm. I am actually trying to do that right now in writing this. I’m trying to escape, and I hope to provide others a temporary respite, from the vexing nature of current political developments. All that said, I also wonder if it is in fact germane to the current situation in some way. For instance, while I’m writing this I’m not worrying about Gaza, the rise of global fascism or the toilet problem. It may however be the source of a potential argument against the supreme court ruling on “single sex” spaces, but it doesn’t have to be to serve a therapeutic purpose.

And I’ll carry on. I’d say that Grothendieck was responsible for innumerably many mathematical ideas except that because he was a mathematician one must pick one’s words carefully and note that in fact the cardinality of his ideas is not the same as the power of the continuum and that, depending on how you count ideas, he probably had a finite number of them. On the other hand, it might depend on what counts, so to speak, as an idea. In any case, one of the many things he came up with is the aforementioned Grothendieck Topology. I’m abandoning this for now due to sheer bafflement and lack of mental energy.

Here’s a thought. England’s surface southeast of the Tees-Exe Line and the English coastline from the Tees to the Exe are very different in character to Scotland’s surface and coastline. Is it possible that the concept of the ionad is more useful or applicable to either of those aspects of Scotland than the part of England mentioned, and of course I’d like that because the concept itself is from Gàidhlig, or rather Q-Celtic. The big difference between the two coastlines, to start with, is that Scotland is more fractal than lowland England, and actually any of England but it’s more striking defined thus. Something similar also applies to mainland Scotland combined with its islands, to Scotland with the lochs and sea lochs and by extension to Scotland including the mountains. And this has practical applications: it’s harder to get around here than it is in lowland England and you get situations where Mull of Kintyre is seventy kilometres from Kilmarnock as the crow flies but 272 kilometres by road, mainly due to Loch Fyne. Here there could be steep slopes, lochs in the way and a very fractal coastline, or islands at varying distances from each other which may even exist intermittently according to the tide. Southeast England is much smoother and less complicated on the whole. At the same time it’s worth remembering that an ionad is a concept found in an abstraction of abstractions which may therefore still not apply very well to the physical geography of Scotland.

Except that I think it does. There are several aspects to this place resulting from its geology, which has consequences for its terrain, coastline, transport network, biomes, other aspects of ecology, dialects and presumably other cultural aspects. For instance, here’s the Scottish rail network:

. . .and this is the Central Belt’s rail network, found in the rectangle within the other map:

Due to the population distribution and engineering difficulties, the complexity of the rail network is the opposite of the complexity of Scottish terrain. It seems feasible that some kind of table of ratios between the fractal dimension of the surface in a particular area and the number of train stations or connections could be constructed, and there might also be some mileage, so to speak, in working out how long it takes to get between two places by rail, and then comparing it to how long it takes by road and separating that into walking, cycling, driving and taking the bus, or for that matter a ferry or plane. In fact all this analysis could reveal things about transport policy and decisions made by the Westminster or Scottish governments on these matters. Considering the fractal nature of the terrain and coastline together with the topology of various transport networks suggests also that it would be useful to find some way of unifying these two different mathematical ways of considering the country.

It goes beyond that too. The Gàidhlig language is, at least from the outside, characterised by remarkable variations in accent. Moreover, the distribution, both today and historically, of different dialects and languages in Scotland is likely to be connected to the terrain and accessibility of different parts of the country. In England, at least historically, there has been notable variation in accent in Lancashire in particular, and it seems that similar variation occurs in the Gàidhealtachd, to the extent that if your Gàidhlig is poor people might just perceive you as being from a different island rather than just not very good at it. This is because of the divisions caused by multiple islands and glens separated by peaks, a similar situation as obtains in New Guinea, and interestingly also in the sea around New Guinea, causing respectively great linguistic and biological diversity. It’s been said that Scotland is able to masquerade as all sorts of other countries, such as Norway, the Caribbean and maybe Austria. All of this variation is linked to the terrain, and I’m sure could be usefully modelled mathematically. I’d also be very surprised if this was irrelevant to ecology and biomes.

Therefore, there are several different fields of maths which could be used to capture and express the complexity of this country in various useful ways. For instance, anyone who’s played Britannia will be aware that it usually takes ages for the Picts to disappear, something reflected in real world history, and this is I guess because they were hunkered down in remote areas which couldn’t be easily accessed by other peoples, and maybe the living was also so hard there that they didn’t bother. This hypothesis could, I think, be tested using some kind of mathematical approach. There is also a very small tree line in the Cairngorms and there seem to have been glaciers there, again in a small area, until something like the seventeenth century. It took longer for wolves to become extinct here than it did in England. There are all sorts of things like this which result from the distinctive characteristics of the northwestern part of Great Britain and its associated smaller islands which can be modelled mathematically in different ways, and they’re practically very important. The logistics of moving things or oneself around the country, for example, or of understanding the locals in different places, are connected to this.

Here, then, are various mathematical ways of approaching the question of Scotland.

Firstly, the inverse correlation between rail network complexity and terrain complexity lends itself to graph theory, operations research and algebraic topology. In the last, islands and mountains constitute holes. The problem of finding the most efficient routes between places belongs to operations research. So with this there’s:

• Graph theory
• Algebraic topology (I hold my hands up here to say I only have a vague grasp of what this is).
• Operations research (which was actually my dad’s job).

Secondly, the isogloss patterns in Gàidhlig accent variation could involve:

• Graph theory again, regarding communities as nodes and communication links as edges of various weights.
• Topological spaces, where dialect regions are open sets with isoglosses as boundaries between them.
• Sheaf theory, apparently. Goodness knows how. I haven’t got to the point where I understand this much except to imagine lots of people wandering around with ring binders in a warehouse with scattered random maths papers all over the floor. I’m getting there.

Thirdly (this is stylistically frowned upon isn’t it?), biome variation:

• Cellular automata of all things! The idea that in a particular area, there may be more or fewer resources required by particular species which determines whether they flourish or something else does, or perhaps something else flourishes on the corpses of what didn’t flourish.
• Statistics: picks up the patterns of biomes. In particular I strongly suspect that there’s more biodiversity at boundaries between biomes than deep within large homogenous biomes, and Scotland of all places has those boundaries in spades, and I’d like to look into that.

Fourthly, climate:

• Fluid dynamics (some of these things are just words to me, but not this one).
• Differential equations (these definitely are).

Fifthly, the legendary fractal nature of the coastline:

• Fractal geometry (who’d’ve thought?).
• Chaos theory.
• Something called Measure Theory.

The power law regarding the size of lochs, islands and their distribution:

• This is again fractal geometry, as it’s essentially a vertical version of the coastline issue.
• Statistical distribution along the lines of Zipf’s Law and, I’m guessing, the log-normal distribution, alias the 80:20 rule.
• The phenomenon of clustering in random and pseudorandom distributions, manifested here on a plane.

In this case, deviations from these tendencies are themselves interesting. For instance, it might turn out that the areas of lochs are not distributed in such a way that the majority of them constitute together less than half of the water area in Scotland. For a start, nine-tenths of British fresh water is in Loch Ness.

The fields which come up repeatedly here are fractal geometry, topology and actually measure theory, which I mainly left out because I don’t know what it is. It seems that it arose out of the Banach-Tarski paradox, which includes such oddities as being able to dissemble a single ball and then build two balls of the same size as the first one out of a finite number of components, or taking a ball bearing apart mathematically and reassembling it into an object the size of the Earth. Clearly these things can’t actually be done, but they seem to be intuitively feasible when you look at the details, because spheres and balls are each infinitely large sets, and you can take an infinite number of items out of an infinite set and still be left with an infinitely large set. Measure theory tries to resolve this problem by providing a way to decide exactly how big sets are. I can’t take this any further.

So, there are these three areas of maths along with certain others which come up at least a couple of times: measure theory, topology and fractal geometry. Just in passing, Scotland is not unique in this respect because there are other countries and regions in the world to which these same features apply. These include the aforementioned Papua New Guinea, the South Island of Aotearoa/New Zealand, Japan (maybe Hokkaido even more than the whole of Japan), Switzerland, Norway and of course Nova Scotia. Not all of these have the full set, and it should also be borne in mind that there are also “anti-Scotlands”, including the Netherlands, countries which include bits of the Sahara Desert, most of Antarctica and Kansas. I’d also be very interested to know how North Carolina fits in. It isn’t either that these countries and regions are boring or even that the same mathematical fields don’t apply to them, but what doesn’t happen is that the fields in question apply usefully or interestingly to them. In British terms, the opposite of Scotland in these respects is probably East Anglia. Hence this comparison has already become meaningful and productive and hasn’t just been a waste of time. Also, seriously, no disrespect to the places which are “boring” in this respect, and in fact for all I know there are different aspects of those countries to which exactly the same mathematical fields could become relevant, such as the distribution of sizes of grains of sand in the Sahara.

All of these fields include concepts of dimension, open sets, functions and spaces. The concepts of sheaves and ionadan also come up, so at long last I might finally be able to declare myself ready to understand what “ionad” actually means.

An ionad, which is actually taken from the Irish sense of the word rather than the Gàidhlig but the word is the same barring accent and pronunciation, means “place” or “locale”. In that way it’s a little similar to the concept of locus in geometry, and it aims to mix topology and category theory in such a way as to allow one to reason spatially in a point-free and structured manner. An ionad is like a topological space whose open sets are the starting block and points can be derived from those open sets. If topology, category theory and sheaf theory are each thought of as circles in a Venn diagram, like red, green and blue in additive colour or cyan, magenta and yellow in subtractive colour, an ionad is the bit in the middle which is white in the former case and the infamous “brown splodge” in the latter. Of course I’m nowhere near understanding sheaf theory at this point and still have the Filofax people wandering all over the explosion in the maths warehouse in my head, but I’m closer. But apparently an ionad is useful in the following ways (and others):

• It explains how different parts of Scotrail interact without assuming the points are primary, so presumably it could work as a way of explaining train delays and replacement bus services.
• It helps to describe when native speakers of Gàidhlig are likely to perceive each other as speaking with different accents and when they’re likely to hear them as familiar, even when there are some differences in those accents.
• It enables you to model what happens on the borders of two biomes such as peatland and Caledonian rain forest rather than having to think of the border as merely a line between two more easily understood biomes. There, it allows smooth models rather than sudden jumps.
• You can spot scaling rules about the coastline of Scotland and understand its geometry without having to think of it as a series of straight lines or curves.
• It does the same thing with the size distribution of lochs, which is hardly surprising considering the Scottish terrain is just a plane-based version of the line which is the coastline.

The idea over all of this is that you don’t start with the points but with open ideas about what categories might be needed, so you might think in terms of Highland and coastal towns, towns with active train stations and the Gàidhealtachd.

So to finish, whereas I still don’t really have a confident understanding of what an ionad is, I do very much feel that as a mathematical concept it seems to be particularly apt as applied to Scotland, and generally have a feeling that it’s like when oil floats on water or an air bubble rises through a burn, but paying attention to the boundary between them and the skin of the bubble in their own right and as primary. That, I think, is what an ionad is!

And I’m perfectly happy for someone to come along and explain why I’m completely wrong.

Crotchety Old Grandpa Of A Language

I’ve blogged about Gàidhlig on here before, but I’m guessing also that there are entire blogs on the language, so I think it’s okay for me to talk about it again. Though I don’t recall exactly what I said in that post, it amounts to the highly idiosyncratic nature of the surviving Celtic languages, which is unfair because back in the day they were very similar to Latin, even uncannily so. But something happened to the languages the Celts spoke once they reached these isles, and oddly it happened to both lots. The Celtic languages spoken in what Gàidhlig calls Na Eileanan Bhreatainn didn’t stem from a single language or even two closely related languages, but from two languages which had already been evolving apart from each other for many centuries, so the peculiarities of the six surviving or revived languages are quite mysterious. But I’ll come back to that in a bit.

I think I first started to try to learn the language in 1978 CE. I know it was quite some time before studying O-levels was an imminent prospect, so it can’t have been after 1981. I remember this because the library book I was using had school exam past papers at the back and I found this quite intimidating and expected never to get any qualifications at the time. The actual book I didn’t find at all daunting though. This contrasts with my almost simultaneous attempt to learn Russian where for some reason I got stuck on a single world, «идёт», which was enough to make me give up (apparently it means “is coming” according to Google Translate). However, since the book was due back after a few weeks and I didn’t renew it, I only got a few lessons in.

Welsh television was somewhat widely available in the ’70s, so if I’d tried to learn that it would’ve been easier to expose myself to the spoken world, and to a limited extent I did in fact do this, but as far as I know there was absolutely no Gàidhlig television or radio in England. In Kent, it was easier to pick up Dutch television than Scottish, so it was a bit of a struggle to learn it. There was a TV series called ‘Can Seo’ whose books were available, but I don’t think it was available on the telly in Kent. Over that time, it didn’t seem difficult, although it was unusual. I tried a few more times in the ’80s and was really put off when I read Anthony Burgess’s description of the Welsh language and realised that the initial letters of words changed rather than just the endings. This is actually not unusual outside Indo-European languages – Bantu languages such as Swahili do it for example – but at the time it considerably freaked me out and discouraged me because it meant that if I didn’t know a word, I couldn’t necessarily just look it up in the dictionary because it often wouldn’t be there. The answer, of course, is to learn the changes, but you have to do that even before you get to look it up, so it immediately becomes a slog.

The Q-Celtic languages – okay, I’ll explain that in a bit but I mean Irish, Gàidhlig and Manx, also known as the Goidelic – have the added issue of spelling. Welsh is, despite what English people say, very phonetic and actually somewhat similar to Old English in its orthography. Irish and Gàidhlig are decidedly not, for various reasons, and Manx has a different problem because it’s been squozen into English spelling without actually having English-like pronunciation, with the result that although it looks to an English reader like a breath of fresh air, what you see on the page doesn’t actually correspond that closely to what you hear. I always say that they should be written in Cyrillic, because that script also has to deal with languages whose letters are doubled as broad and slender a lot of the time and does so by using extra vowel letters and the soft and hard signs, sometimes, as with Serbian, introducing extra letters. I actually suspect the intimidating-looking spelling is a factor in it not spreading more widely. That said, according to our teacher yesterday the number of speakers in Dumfries & Galloway, or should I say Dùn Phrìs is Gall-Ghaidhealaibh, has doubled in the last decade, and there are moves to use the Gàidhlig version of “Welcome to Dumfries & Galloway” on the signs into the region.

It isn’t just that either. It’s been said that of all the Indo-European languages, the Celtic branch has deviated furthest from its roots. Were it not for the fact that most of the vocabulary has been inherited relatively cleanly from its ancestors, nobody would guess that they were even in the same family. I was rather surprised to hear from an actual Scot a few months ago that she’d heard that it was close to Sanskrit! The existence of a phenomenon known as sandhi does link them, to be sure, but this is not unique to the two by any means. It’s also been said that the unit of the Gàidhlig language is not the word but the sentence, and I basically agree with that. I’ll illustrate the issue with a phrase we learnt yesterday: Tha mi air m’obair a leigeil dhiom. This means “I’m retired”. However, literally it means “Am I my work a-laying aside from me”, and switching the syntax from the VSO of Celtic, “I am laying aside my work from me”. There is another way of saying it – tha mi retireadh – “I am retired” – but where’s the fun in that? This does, however, illustrate one of the weirdnesses of the language: it’s entirely possible to use it as if it were a more conventional European language and literally say “I am retired”, but on the whole, it just isn’t done! It’s all circumlocutory. I used to find this exasperating, but no longer.

So, more personally and experientially, the class is good. Despite the fact that I started to learn forty-six years ago, most of the other students are ahead of me even though some of them have only been doing it a few weeks. The teacher is great, although she sounds like a Geordie. I don’t know if this is because she’s from the Borders and they sound like that over there. There are other Sassanaich in the class than Sarada and I, thankfully, although unsurprisingly most are Scots. Lessons are an hour long, and as Sarada noted, this is quite long enough. Some of what one hears in Scottish and even more so in Hibernian English reflects Celtic idioms, so for example I’d expect to hear “the hair on her” rather than “her hair” around here and likewise in Gàidhlig “a’ ghruag oirre” – “the hair on her”. This is one of the things that spares the Scots language itself from just being another Germanic language like Frisian or Danish – it has both Celtic borrowings and idiomatic influences. It doesn’t have the breeziness, and therefore the boredom, of learning most other European languages because it is so very different. More different in many ways, in fact, even than Finnish, which isn’t even Indo-European but at least has the decency to behave as if it is. The highly idiosyncratic nature of expression does in fact tend to infect the way I express myself in English and it actually seems to mess with your head to some extent, making fluency in English harder.

Although the teacher suggested to me that I go up to the next level, me having told her that I’d been studying it since 1978 and knew fifteen languages (not that well though, in either case) and her having heard me speak, I am seriously not ready to do so. As I put it to her, the principles are clear in my head but the practice is another matter entirely. Maybe at some point it’ll happen.

To come back to the points I mentioned earlier, there’s an hypothesis out there called “Italo-Celtic” which is about the idea that Celtic and Italic, nowadays Romance as the others became extinct during the Roman period although they did influence some dialects of Italian, stem more recently from the same language than the rest of Indo-European, or alternatively that they were spoken in close proximity to and influenced each other. I personally honestly suspect the former. The Italic and Celtic languages really were spoken in adjacent areas, the former on the Italian peninsula and the latter somewhat further North in today’s Austria, and this gives Gàidhlig the redeeming feature of having numerous cognates with Latin which really helps. For instance, “feasgar” means “afternoon/evening” and clearly corresponds to the Latin vesper, and “fear” – man – similarly reflects “vir”, and in fact also the English “were” as in “werewolf” – “man-wolf”. “Obair” is very clearly linked to opus, but calls to mind the later plural become singular opera, and I imagine this is because in some positions S becomes R but I’m just guessing. Therefore it does help and I’m not completely at sea.

Just to compare the numbers from one to ten in Proto-Celtic and Proto-Italic:

Italic	Celtic
oinos	oinos
duos	dwau
tres	tris
kwettuor	kwettwares
kwenkwe	kwenkwe
seks	swekhs
septem	sekhtam
okto	okhtu
nowem	nawan
dekem	dekam

If this pattern is repeated across the two proto-languages, it seems to me that they were basically two dialects of the same language, and the same definitely does not apply to the other big groups of European languages such as Germanic and Balto-Slavic compared to Italo-Celtic.

There’s also the division between Q- and P-Celtic, which also occurs in Italic but only Q-Italic languages have survived. Romanian does use P sometimes but this is a later development. Celtic is distinctive in having lost its original /p/ sound, so any such sounds which occur in it today are later developments. Basically, the Q-Celtic languages, also known as Goidelic and now including Manx, Gàidhlig and Irish, retained the “kw” sound into historical times, so for example the Primitive Irish word for “son”, “mac” in Gàidhlig, was actually “MAQ”, i.e. “makw”, but in the P-Celtic languages, alias Brittonic languages and now including Welsh, Cornish and Breton this became a new /p/ or /b/ sound, so the Welsh word for “son” is “mab“. This is just my opinion, but I find it interesting that the same division existed in Italic, with Latin and Faliscan Q-Italic languages and Oscan and Umbrian P-Italic, and I think this really means that the Italic and Celtic languages were originally not just close but were actually in the same branch to the extent that this variation divides the entire set of languages into two halves, with the Q-Celtic languages closer to Latin and the P-Celtic closer to Oscan.

There seem to have been two incursions of Celtic speakers into these isles, one Q-Celtic and from Galicia in what became Spain, and the other P-Celtic and from transalpine Gaul, i.e. most of today’s France. The division already existed before they came over, and then the mysterious thing happened to change the languages into what they are today. I’ve talked about this before because up until recently I thought it was just me, but the odd thing is that they share features with the completely unrelated Semitic languages such as Hebrew and Arabic. In fact I even tried to use the Arabic relative Maltese as a way of helping me with Gàidhlig, but that language has gone in exactly the opposite direction and been strongly influenced by Italian, making it pointless. It was therefore quite interesting that our teacher pointed out that the phrase for “I am disabled” is “tha ciorrarm orm” – “there is a disability on me” – observing that it sounded quite Biblical. Similarly, the Gàidhlig for “humanity” or “humankind” is “an mac an duine” or “the son of man” as it were. The King James Version of the Bible is notable in being nearer to a literal translation of the Hebrew than many other or newer versions are and I’d be almost prepared to bet that many of the idioms in English inherited from the KJV are also found in Gàidhlig, not because of the influence of the Bible but due to the language’s baffling similarities with Hebrew. In fact, recently I’ve found that Arabic, which I don’t understand, is notably easier to disentangle than it used to be, possibly for this reason. As I say, I’ve covered this before but there are three schools of thought regarding this: it’s coincidence; it’s due to implicational universals (the languages may share just a couple of features which force the rest of them to be similar because otherwise they wouldn’t work or the human mind wouldn’t be able to use the languages); it’s due to an Afro-Asiatic substrate in these isles before the Celts got here which influenced the languages.

So I’ve tried to be brief, I’ve labelled various objects around the room: uinneag, doras, balla, sòfa, bòrd, sporan, telebhisean, leabhar, baidhsagal, cuisean, briosgaidhean, staidhrichean, pink for feminine, blue for masculine and alternating pink and blue letters for nouns which are either, and I’m about to watch some telebhisean Gàidhlig (that’s probably wrong), so progress will be made!

Startling Semitic-Celtic Parallels And Overinterpretation

Some time ago in the 1980s I think, I made one of my many attempts to learn Gàidhlig and noticed something rather strange. I already had some knowledge of Hebrew and Arabic from when I was younger, and it suddenly struck me that the Celtic language shared some remarkable unusual features with the other two. From what I can recall, these included verb-subject-object word order, two genders – feminine and masculine – and something I can only vaguely remember about how prepositions and pronouns work. At the time, I didn’t know what to make of it. It seemed to be more than a coincidence because three always counts to my mind as more than chance allows, but it was difficult to think of a way of how it could’ve happened. I eventually settled on a rather vague conclusion that maybe Semitic language speakers had travelled north from the Maghreb into Iberia, which Q-Celtic languages are sometimes claimed to originate, and that they then influenced the ancestor of the Irish language in some way. However, this doesn’t work particularly well as it fails to explain how Welsh and Cornish also have these features. After a while, I just put it down to coincidence and my tendency to see patterns where none exist other than the ones my mind has imposed upon them.

At this point I’m going to veer off into probability to illustrate why three things in common is my threshold for statistical significance. It’s common to plump for one in twenty as the point at which something is considered significant, and scientific experiments often use this. In recent years I’ve seen rather too many dubious-looking scientific papers which seem to go for a much lower limit and I now wonder if there has been a new development in statistical theory which justifies this, or whether it’s more to do with “publish or perish”. Anyway, probabilities multiply, so if you flip a fair coin three times and it comes up heads every time the probability of that outcome is one in two times one in two times one in two. 2³ is eight, still below the point when one decides something is significant, but the probability of something happening is not always one in two. For fair dice, you’d only need to throw a six twice for it to become significant: one in thirty-six is six squared. Taking this the other way, the mean probability for three events to multiply up to one in twenty is of course the cube root of twenty, which is just over one in 2.7. However, this reasoning is faulty because we see patterns as opposed to the absence of patterns, so given the large number of other grammatical features one could pluck out of Celtic and Semitic languages, the ones that don’t fit might be ignored and the calculation then becomes extremely complicated because one then has to consider how to delineate specific grammatical features and how to count them, then work out what the chances are that two sets of languages share three grammatical features based on this and the number of possible options. For instance, with syntax the options, assuming a largely fixed word order which doesn’t always happen, are SVO, SOV, OVS, VSO, VOS and OSV, which is one in six. However, other features are quite arbitrary. There are languages out there with more than two dozen grammatical genders, for example. It’s possible to imagine a language whose every noun has a different gender.

Another pattern which definitely is meaningful which can be plucked out of Celtic languages as they are today is the fact that they and Romance languages, more specifically Italic languages, which are Romance languages plus Latin and its closest contemporary relatives, are closer to one another than they are to other branches of the Indo-European language family. Some of these features are the result of parallel evolution. For instance, all of the surviving six Celtic languages have two grammatical genders consisting of feminine and masculine, and this is also true of all Western Romance languages (though not of Romanian, which still has neuter). Besides this, other Indo-European languages tend to use an ending like “-est” to express the superlative of adjectives, but Italic and Celtic tend to use something like “-issimum” – “best” versus “bellissimo” for example. There are a number of other similarities which may be preserved ancient features lost from the other languages, features acquired because they were neighbours or features acquired in their common ancestral language. These are, though, easy to account for because Italic and Celtic just are obviously related, were spoken near each other and so on. The idea of a parallel between Celtic and Semitic is much harder to explain, which is why it might not exist at all.

Recently, I discovered that my personal will o’ the wisp is not in fact just mine. Professional linguists have noticed this too, and there are even theories about how it might have happened and a number of other features in common. VSO and inflected prepositions are just two of several parallels. I should explain that in Gàidhlig and its relatives, prepositions vary according to who they refer to, so for example “agam” means “at me” and “agat” “at thee”. The origin of these is easy to account for, that the words have simply been run together over the millennia, but few other languages do this. Arabic and Hebrew, on the other hand, do. The languages also do things with these prepositions which other languages don’t. They express possession and obligation with them. “The hair on her” – “am falt oirre” is “her hair” and “I need/want/must have a knife” is “tha bhuam sgian” – “there is from me (a) knife”. That “(a)” indicates something else they have in common: they all have a word for “the” but none for “a”. It’s unusual for a language to have a way of expressing definiteness without indefiniteness. Interestingly, Anglo-Saxon and Old Norse, both spoken in these isles, also had a way to say “the” but not one to say “a(n)”, and this may be a clue as to how these apparent coincidences happened. Breton, however, does have an indefinite article. Likewise, all the languages repeat the pronoun at the end of a relative clause – “the chair which I sat on it” and not “the chair (which) I sat on”. There’s also the way the word for “and” is used, or rather, a word for “and”: “agus” in Gàidhlig (there’s another word, “is”) and “wa” in Arabic (“ve” in today’s Hebrew). In English, “and” is a simple coördinating conjunction like “or” and “but”, but in the other languages it can also be used as a subordinating one. It can also mean “when” or “as”. This is also unusual. “Agus”/”ve” can also be used to mean “but” or “although”, and in fact as I understand it, the Arabic “wa” is the only option to express “but”. Besides this, there’s what’s known as the construct state genitive in English descriptions of Hebrew grammar. Arabic doesn’t say “the man’s house” but “man the house”, or “taigh an duine” in Gàidhlig – “the house man”. This is in spite of the fact that the language in question has a genitive form for the noun in question. This makes approximately eight features found in Celtic and Semitic languages but only rarely in others.

And there’s more. The surviving Celtic languages are unusual among Indo-European languages in having these features, and are in general quite aberrant compared to the others. That said, there are branches of the family which have unusual features for it, such as Armenian, which has grammar more like other languages than Indo-European in that it hangs successive suffixes off the ends of words per idea as opposed to having combined ideas in each suffix (in English we have, for example, a final S for genitive (possessive) and plural and don’t need anything extra). Even so, were it not for the known history and the fact that so much Celtic vocabulary is clearly similar to that of other European languages, nobody would guess Celtic languages were Indo-European. In fact, the very features which they share with Semitic languages are the ones which make them unique in the Indo-European family.

They are also emphatically not related to each other, or at least so distantly related that there are languages native to Kenya and Tanzania which are closer to Hebrew and Arabic and a dead language spoken in present day China which is closer to Welsh (and in fact English) than they are to each other. Semitic languages are part of a family now referred to as “Afro-Asiatic”, which also includes Tamazight, a Berber language, and Ancient Egyptian, spoken five thousand years ago and still nowhere near the speech of the Kurgans at the time which are ancestral to Celtic, Germanic and the like. There are, however, a few theories about how this has happened.

One apparently anomalous circumstance which can be seen from the New Testament is that Paul wrote a letter to the Galatians. These lived in Anatolia, the Asian portion of present-day Turkey, and they spoke a Celtic language. This language was clearly in close proximity to the Semitic lingua franca of that region at the time, Aramaic, as well as various others such as Assyrian. It’s therefore been suggested that the whole of the Celtic branch was influenced by this local connection, all the way across to Ireland in the end. To me, this seems a little far-fetched, but it is true that there’s a concentration of a particular set of genes which marks the Irish, and incidentally myself, as possible wanderers from the Indo-European ancestral land who went as far as possible at the time. This may make the so-called Celts the ultimate invaders in a way and contradicts the common mystical, matriarchal and peaceful image some people seem to have of them. This migration also forms part of another theory, that farming, having been invented in the Fertile Crescent where Semitic languages were spoken, then spread culturally across Europe to these islands and took linguistic features with it. Either of these ideas being true could be expected to imply that all Celtic languages, not just the modern survivors here and in Brittany, had these features in common.

Significantly, the speakers of Celtic languages were probably the first Indo-European speakers to arrive in Great Britain and Ireland. Prior to that, clearly there were other people living here who had their own spoken but unwritten languages. It’s possible that traces of these may survive in place names. It used to be thought that the Picts spoke a non-IE language, possibly related to Basque, but this has now been refuted. The features Irish, Welsh and the rest have in common with Hebrew and Arabic are also apparently shared with Tamazight and other languages of the Maghreb, although to me that’s hearsay – I haven’t checked them out. Consequently, one rather outré theory, is that before the Celts got here the folk of Albion and the Emerald Isle spoke a Semitic language, and Celtic was influenced by this when it got here. However, there doesn’t seem to be much reason to suppose this to be so other than the connection.

Leaving those theories aside, I would bring up the issue of linguistic universals, and particularly implicational universals. Some features are common to all spoken languages. For example, every known spoken language has a vowel like /a/ as in “father” in it, every language which distinguishes questions tonally involves changing the pitch of the voice towards the end of the sentence, and every language has at least some plural pronouns. There’s a particular set of implicational universals around SOV languages which they tend to have in common, such as being exclusively suffixing, to the extent that it used to be thought that there was a so-called “Altaic” language family including Turkish and Mongolian, and some would even include Japanese and Korean in that, but they’ve turned out not to be closely related but have sometimes grown more alike through contact, but they also have many of these implicational universals, suggesting to me some kind of possible “standard” human spoken language with those grammatical features. I would tentatively suggest, and I may well be wrong, that the features Celtic and Semitic languages share are in fact similarly implicational universals. Both of them have an unusual syntax and this may lead them both down the same path.

But there’s an extra layer to this which intrigues me. There used to be a famous Hebrew teacher who introduced the subject as “Gentlemen, this is the language God spoke” (yes, this is extremely sexist but it was a long time ago), and similarly Arabic is considered a particularly sacred language almost designed by God to write the Qur’an. Hence the features mentioned are used in two very important sacred texts, and if I’m going to go all religious and mystical on you, just maybe the Celtic and Semitic languages have a special place in spiritual practices, and this is about that. But leaving that aside, it still seems to me that the most likely explanation for the things they have in common is simply that they are a particular “type” of language, just as Japanese and Turkish are, without needing to have any genetic relationship.

They’re also both really annoying!

The issue of overinterpretation will have to be held over until tomorrow, sorry.