Bad drawings but wonderful prose

It’s not all that long since I last (and indeed first) referred to the Math With Bad Drawings blog within these pages.

However, a post that appeared there the other day is such a peach of a short story that I couldn’t refrain from bringing it to your attention.  It is, as befits the nature of that blog, quite mathematical in character (and, more specifically, about differential calculus – though it doesn’t really go into the gory details) so if that sort of thing scares you too much, feel free to run away and hide behind the sofa until my next post (which almost certainly will be about something completely different).

Assuming you’re still here, the story is called The Differentiation: A Survivor’s Tale and is, uniquely among all the mathematical fiction I have ever read (which is a fair amount, over the years), told from the perspective of the exponential function.  The whole thing is firmly based on the behaviour of different classes of functions under the operation of differentiation and I suspect it would be fairly incomprehensible to anyone without a reasonable grounding in calculus, though it could be quite a useful way of helping to remember the general principles, without getting bogged down in the technical details, for somebody who is just learning the subject.  Given the pedagogical nature of the blog as a whole, I suspect that may have been at least partially the author’s intent.

The story also has a nice twist in the tail that makes it almost work as a social commentary on something or other (though I can’t say more without spoiling the punchline for anyone with sufficient mathematical background to follow the story in the first place).

Perhaps the best categorisation of it is as a mathematical horror story, which is one of the ways it’s been tagged on the original blog.  That works on at least two levels as for the mathematically inclined it is quite a chilling tale and for anyone else the very fact that it is mathematical is probably sufficient to induce a cold sweat.

Anyway, I should probably refrain from further analysis and let the story speak for itself, to those who have ears to hear.

(And, yes, there was a stealth pun in that last sentence, since differential calculus is one of the major subdivisions of the branch of mathematics known as real analysis.)

Doing Saturday

Since my visit to Catalonia last August, I have been working quite a bit, if not entirely steadily, on my Spanish, and also having a go at learning some Catalan.

I will shortly be going out there again for another visit, so it will be a good opportunity to assess how much I’ve learned in the past 14 months.  My feeling is that it will turn out to be quite a lot, though there’s still much more to learn of both languages.

When I first started trying to learn Spanish, just over 20 years ago, it was from a book entitled (rather optimistically) Spanish in Three Months.  Suffice it to say that it took me somewhat more than 3 months to get through the book – in fact, I didn’t get round to systematically working through all the chapters until some time after my last visit to Spain.  I don’t suppose many people would buy a book called Spanish in Twenty Years and, to be fair, I don’t think the author or publishers can be blamed for the amount of time it took me to finish the book.  In fact, I’ve used quite a few different resources in my quest to learn Spanish and in many respects this book is probably one of my favourites (though I think that any study of something as complex as a language really needs to make use of multiple sources of information).

After getting back from Catalonia last year, I initially decided that I would concentrate on improving my Spanish for several months, if not years, before taking more than a cursory look at Catalan, but I quickly acquired several Catalan books so that I’d be prepared when the time came.  One of these was Catalan in Three Months, a sister to my first Spanish book.  Several times over the last year I have dipped into this book but about a month ago I decided to systematically work through it (tackling the exercises and writing down vocabulary, etc.) and this time I was able to reach the end within about a fortnight.  Admittedly, it’s a slightly shorter book than the other one (or at least breaks its material into fewer chapters) and I was going at a slightly too fast pace in order to get a broad overview of the language, so I haven’t fully assimilated a lot of the grammar or vocabulary (though the same can be said of Spanish, which I’ve been working at for a lot longer).

The fact that I already knew a reasonable amount of Spanish also helped me to work through the Catalan book much more quickly as, while there are many significant differences between the two languages, there is also a lot of overlap so I had a big headstart in terms of getting to grips with the basic nuts and bolts of the language.  Having a reasonable, if rather rusty, command of French helped quite a bit too, since Catalan falls somewhere between French and Spanish linguistically as well as geographically.

As I was approaching the end of Catalan in Three Months, I had a look round to see what other Catalan resources were available and I came across one in the Dummies series of books that I’ve previously found useful for getting a handle on things ranging from knitting to quantum mechanics.  The twist here was that the book was written in Spanish, and there doesn’t seem to be an English version available.  Still, I reasoned that this might be quite a good way of consolidating my grasp on Spanish as well as learning a bit more Catalan (and, significantly, some more about the culture, which was rather lacking in the other book), so I purchased myself an e-book version of Catalán Para Dummies and have gradually been working my way through it.

Amongst the things I’ve learned from studying this book are the following two gems that I wanted to make a note of:

Firstly, the Catalan word for a pestle (as in pestle & mortar) is, apparently, la mà de morter, which means “the hand of the mortar”.  Apart from being quite poetic, I find this useful because I’ve always had trouble remembering which one is the pestle and which one is the mortar.  Somehow I find the idea of thinking of the pestle as the hand of the mortar seems to make it easier to remember that it is the one shaped roughly like a small club (or perhaps an arm with a fist on the end of it), while the mortar is the bowl shaped bit.  Incidentally, I gather that the Spanish is similar (el mortero for mortar and la mano for pestle, although both Spanish and Catalan seem to have at least one other word – el pilón / el piló respectively – for the latter).

Secondly, there is a lovely Catalan idiom – fer dissabte (literally, “to make/do Saturday”) – which essentially refers to pottering round the house, doing cleaning and such other tasks as are often done on Saturdays but may equally be done at other times when you’re at home rather than out at work.  Another source I found (also in Spanish – I’ve not yet managed to track down any in English) to explain this phrase seems to suggest that it’s more about an intensive cleaning session rather than pottering around.  In either case, it’s based around the home and not necessarily confined to Saturday.  A literal translation into Spanish would be hacer sábado but this would, apparently, make as much sense as “to do Saturday” in English, so it is a Catalan-only idiom (but it joins the likes of the German word ausschlafen – literally “to sleep out” but meaning to sleep until you wake up naturally, rather than using an alarm – on my list of words or phrases that we really ought to adopt into English).

A gift from Wales to the World

One of several blogs I keep an eye on is the aptly-named Math With Bad Drawings (though, actually, I think the drawings do have a certain charm and they are in any case done with pedagogical rather than aesthetic intent).  This blog is by an American mathematician (hence the mis-spelling of maths :) ) and consists of illustrated essays on a variety of mathematical topics.

I was recently flicking back through the archives of this blog and came across an interesting post that I didn’t notice when it first appeared, last December, even though I was following the blog by then (I guess it was pretty close to Christmas, which is generally a pretty busy time when it’s easy to skip over blog posts). It is a post that describes itself as a brief biography of the equals sign (=).

You may be thinking that this isn’t the most enthralling of subjects and, although a mathematician myself (with a fairly keen interest in mathematical notation and history to boot), I’d be inclined to agree with you.  However, here’s the exciting thing I learned from the post: the equals sign was invented in Wales (*).

The article doesn’t actually contain all that much information about the early history of the sign, though it has some fascinating stuff about its meaning and usage, as well as related symbols like > and <.  There was just enough detail to enable me to hit Wikipedia and do a quick Google search for other sites to cross-check the facts (not very extensive research, I know, but probably sufficient to establish that Ben, the author of the MWBD blog, wasn’t just making it up).

Apparently the first recorded use of the equals sign was in a book called The Whetstone of Witte, by Welsh mathematician Robert Recorde, published in 1557.  It is believed that Recorde invented this sign; before this, people used to just write “is equal to” (or words to that effect) when they wanted to indicate equality, so the sign was definitely a very convenient shorthand.

The same book is also credited with introducing the plus (+) and minus (-) signs to the English speaking world, though they (unlike =) were already known in other parts of the world so presumably Recorde became acquainted with them through perusing literature in other languages, or perhaps corresponding with other mathematicians, rather than re-inventing them independently.  In any case, the book definitely had a significant impact on the development of mathematical notation – and the importance of having good notation for being able to develop mathematical ideas should not be underestimated.

(*) Actually, my statement that “the equals sign was invented in Wales” is probably not quite accurate (the original article phrases it as “the equals sign was born in Wales”, which is little better).  Robert Recorde was indeed Welsh (born in Tenby, Pembrokeshire) but he seems to have spent most of his adult life in Oxford, Cambridge and London (where he was a physician as well as a mathematician) so it’s more likely that the equals sign was born/invented in one of those places.  Still, I think it’s fair to credit it as a Welsh invention.


How far will they go?

If I had to list my favourite films, it’s almost certain that there would be several Coen Brothers offerings on the list.  For sure, both O Brother, Where Art Thou? and Fargo would appear very near the top of the list.

I discovered today that a spinoff TV series to Fargo has been made, sharing its name, Minnesota setting and more-or-less  black comedy crime drama style.

The first season was made, or at least broadcast last year, and was set about 8 years earlier (which puts it about 20 years after the film, which was released in 1996 but apparently set in 1987).  I gather there’s a small amount of overlap, including a scene where some of the characters from the series find the money that was hidden at the end of the film,  and probably quite a few references (also to the rest of the Coen Brothers’ oeuvre), but no direct cross-over between cast or characters.

The second season is due to be released next month (in the States) and will be set back in 1979.  Again, there’s due to be little direct cross-over with either the film or the first season but there will be some links.

Apparently several more seasons are planned and each one is due to be essentially self-contained, with its own time period, storyline and cast but some links to the other seasons and the film.  The Coen Brothers are, with several other people, executive producers for the show (at least for season 1) but don’t appear to have been directly involved in writing or directing it.

I haven’t yet seen the series, though I’m sure that’s only a matter of time.  I have mixed feelings about the idea but I’ll reserve judgement until I’ve actually seen it.


So much for a quiet summer

August is usually one of the quieter months for me, as most of my regular activities take a summer break.  I love this opportunity to live life at a slightly more relaxed pace for a few weeks, especially as September (along with December) tends to be one of the busiest months.

This year, however, my August seems to be quite busy, especially in contrast to the last couple of months.  In particular, I have quite a few gigs – almost as many, in fact, as I’ve had so far this year.

On average, I probably have about two gigs a month, and that pretty much amounts to some months with no gigs at all and some with 3 or 4, but rarely more than 5.  This month I have a grand total of 9 gigs, with two (or three, depending how you count) different bands.

The August gigging calendar started last Saturday, playing bass (or tuba, as it’s known outside the brass band context) with the Menai Bridge Brass Band at the National Eisteddfod (a Welsh cultural phenomenon that you can google for yourself if you don’t already know about it).  This was a competition, with 5 bands competing in our section.  We came 3rd but, more importantly, we felt that we put in a very good performance.   The first two pieces (out of our programme of 5) were televised on S4C; we start about 39 minutes into the programme and the clip should be available to view until about the end of August.  I found it particularly interesting to watch that clip, as the pieces sound completely different when heard from outside the band than when you’re hearing them from in the middle of the action.

My second gig was on Sunday evening with the Rice Hooligan Orchestra – my “demented Western Swing” trio, with whom I play upright bass (we don’t currently have a website).  We were playing for a hog roast at the Marram Grass café in Newborough, one of our favourite venues and the site of most of our recent gigs.  We’ll be back there on Sunday 30th August (probably from about 7pm) so if you happen to be in the area you may like to drop in and see us; I’m not sure how much it costs to participate in the hog roast (as performers, we get it for free) but it’s excellent food to go with, hopefully, pretty good music.

This coming Saturday will be my busiest day musically, as I have two separate gigs.  In the morning I’ll be playing trombone with the Menai Bridge Intermediate Brass Band at an event in Pentraeth (I think it’s their village fair) and then in the afternoon I’ll be heading off to the Conwy valley to play for a wedding party with the Rice Hooligan Orchestra.  On Sunday afternoon, I’ll be out with the Menai Bridge Intermediate Band again, this time at a First World War memorial concert in Menai Bridge.

The rest of the month’s gigs are all with the Rice Hooligan Orchestra.  One of them is, like this Saturday’s wedding, a private party (towards the end of the month).  The others are both public gigs – one is at Y Fricsan in Cwm-y-Glo (near Llanberis) on Friday 14th and the other is at The George in Bethesda on Saturday 15th.  I’m not yet sure of the exact details of either gig but if you’re up for coming along to one of them, give me a shout and I’ll try to find out for you.

I’m anticipating that September will be a fairly busy month, as usual.  On the gig front, though, it’s likely to be considerably quieter than August; so far I don’t have any gigs lined up for September and I certainly don’t expect to get anywhere near 9 of them!

Recursive poetry

I’ve mentioned a couple of times in previous blog posts that I rather like the xkcd webcomic, which describes itself as being “a webcomic of romance, sarcasm, math and language”.

It’s a daily comic which I follow on my blog reader and I more or less enjoy every instalment. Some stand out more than others, for various reasons, and today’s was one of these:

Ozymandias (xkcd)

There are two things I particularly like about this.

Firstly, I’ve always been fascinated by recursion, which is the basic idea on display here.

Secondly, Ozymandias (by Percy Shelley) is one of my favourite poems and is also the only thing I studied for A-Level English. That was because, when I did my A-Levels I had hoped to do English as one of them and got as far as attending one lesson (in which we read and analysed this poem). Unfortunately a timetable change meant that English clashed with chemistry and since at the time I was intending to go on and study chemistry at university, that meant I had to drop English. Unlike some other choices I’ve made, I’ve never considered that I may have made the wrong decision on this one, but I do still feel it was a bit of a shame that I didn’t get to pursue my formal studies of English a bit further. Of course, that hasn’t stopped me retaining an interest in literature (and especially poetry) over the years.

Old Soldiers

I had a bit of a rude awakening today, when I came across an article on the Guardian news blog about the Warhammer battle game.

This was a game that I used to rather enjoy playing in my youth and it was a bit of a shock when the article pointed out that the game is now 32 years old.  Admittedly it shouldn’t have been too much a shock since I’m well aware that I’m several years older than that and I am mathematically literate.  Somehow, though, the realisation of how long it is since Warhammer came out made me feel somewhat older than reminiscing to the (younger) friends with whom I was watchingsome of the Star Wars movies last weekend about how I saw The Empire Strikes Back when it was first out in the cinema, even though that was several years earlier.

As I recall, my brother got a copy of the first edition Warhammer rules fairly shortly after they first came out (and when, of course, they were not “first edition” but just “Warhammer”) and it wasn’t too long before we had our first battles.  We later got a copy of the 2nd edition, as well as Warhammer 40,000 (the futuristic, sci-fi version, which was my fairly firm favourite), and played these from time to time over the next decade or so.

In fact, we were generally more into roleplaying games (including the Warhammer spin-off, Warhammer Fantasy Roleplay, which was our main RPG for a while before being supplanted in our affections by Shadowrun and various other games) but it was always nice to be able to have a bit of a tabletop battle for a change, even if we were limited to fairly small armies.  That limitation, incidentally, was more due to our available playing space (growing up in a fairly small terraced house) than the size of our miniature figure collection, which was fairly extensive (and provided an early boost to my interest in painting – though in later years I’ve tended to paint pictures, when I get round to painting at all, rather than figures).

It’s been quite a few years since I’ve played Warhammer, or indeed any other tabletop battle game (I did have a few games of a Napoleonic battle game called Shako with a friend about 10 years ago, and I’ve a vague feeling we may have played a little bit of Warhammer then too) and I don’t particularly have any great desire to go back to it.  I’d be much more interested in getting back into playing real RPGs – I still play occasional CRPGs (i.e. Computer RolePlaying Games) but it’s really not the same.

Nevertheless, Warhammer and other wargames did definitely have an important if not particularly large role in my early life and are a part of that rich tapestry of experiences that make me who I am.

And I’m probably not the only one to ever consider how the real world might be a much nicer place if, when opposing groups had a territorial dispute or some other such cause for conflict, they got together round a large table with a bunch of miniature figures, a bag of dice and a tape measure and settled their differences that way without having to tear up the lives of thousands or millions of real people.