Dramatis persona*
Helen Chick
I've always wanted a bumper sticker that said "I'm a female, LDS/Mormon, Scout leading, geocaching, piano-playing, bicycling, mathematics educator with a PhD in maths ... and I VOTE"! I think this makes me a minority group of cardinality 1!
* Since there's only one of me and "personae" is plural (I think), I've gone with dramatis persona.
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 The rain that arrived yesterday afternoon continued overnight and into the morning. I always find it a bit depressing to hear the sound of rain on the roof when I wake up the morning (not that I’d actually slept very well—the sand-fly bites were still doing their midnight itch-and-overheat-my-feet thing), because you know it’s going to put a dampener on things (pun intended … except that it probably isn’t actually a pun, it’s just the literal version of what is often used metaphorically (sorry, I’m really just explaining that to myself!)). It was time to dress up in all our best rain gear (you know, the stuff you carry because you hope that, by carrying it, you guarantee you won’t need it), and parade our wet weather fashions to all and sundry. Then, suitably attired to handle the steady downpour, we trudged off into the grey gloom. It really was one of those trudgy days, where everything is just a little more awkward than usual and, although everything is still pretty, you kind of just want to get to where you’re going. The challenge of negotiating the track with its squelchy mud sections and frequent tendency to become a creek bed added interest to the trudge, but although there is the mental exercise of picking an optimal route (and the physical exercise of actually negotiating it, and the occasional embarrassment of finding that the anticipated secure footing swallows your foot in an ankle deep concoction of mud, water, and leaf litter) there comes a point where you (I!) just say “Fergedit” and plough straight through, boot cleanliness notwithstanding.
The track continued to follow the shoreline, but rose up quite high on the slopes and was narrow and awkward in places, as it searched for a reasonable route along the contours and into and out of the gullies through which streams tumbled. Three hours after setting off (and having encountered a few less well-equipped/organised people heading the other way) we stopped for lunch, where it was nice to offload the pack. The others in our group decided to continue directly to our next overnight stop, but Sally and I decided we would like to detour along the track to Korokoro Falls, which we hoped would be spectacular as a result of all the rain. Well, we have no idea if they were or not, but the river coming from there certainly was. As you may be able to see in the last photo (and shown in the separate page of additional photos), the track to the falls actually crosses this river—with a cable to cling to, which you can just make out slung between the orange arrow on the near side, and the faintly visible orange arrow on the far side—but the amount of water made it impossible to cross. It was still a worthwhile 2km diversion, and Sally and I enjoyed the beautiful rainforest and seeing the force of the river.
The rain was easing by this stage, and had all but stopped by the time we reached Waiopaoa Hut. A NZ member of one of the other parties staying at the hut pointed out a kereru (large native pigeon) feeding in a nearby tree, and it was great to watch it for a while. I took some photos, but they didn’t turn out all that well because my zoom lens really wasn’t powerful enough. The rain seemed to have kept away quite a few hikers which meant that the hut wasn’t very full, although it was still crowded around the stove with all the boots and socks drying out in readiness for tomorrow (there are few things more unpleasant than trying to put on cold damp socks and boots in the morning (well, actually, there are probably millions of things more unpleasant, but not right at the moment you are actually doing it!)). With the smell of steaming socks as background ambience while the evening light faded we again turned to card games for entertainment. As someone who plays only rarely I had a crash course in the rules and terminology of “Rickety Kate”, but it certainly provided an opportunity for some applied probability theory!
More photos of the day’s wet wanderings are here.
 
TO BE MOVED TO JANUARY 8
 Day 2 was a leisurely day, with the 6km journey between huts completed before lunch (just how much before depended on age, fitness levels, number of stops taken, and support of the idea of “leisurely”). It was overcast for most of the day, which meant “flat” and subdued lighting conditions for photography, but the rainforest was still beautiful and some sunshine snuck through for a brief moment or two at lunchtime. Unfortunately, during the afternoon — and before the clothes I’d washed had had a chance to dry — it started to rain.
This didn’t stop some of us venturing outside, since there was a whole afternoon to enjoy. I decided to follow the track a little further over some of tomorrow’s route, in order to try taking some time exposure shots with the tripod that I nearly always carry on hikes (well … I wasn’t carrying a tent … !). The slight problem was that there weren’t as many nice little waterfalls as we’d seen earlier, and the photos were disappointing, so you aren’t seeing them. I got myself a little bamboozled on this little excursion, too: the track went inland in order to cross the stream (they’re streams in NZ, not creeks, even when they are raging rivers) before coming back out to the lake shore again, and I completely failed to identify the point at which the direction changed which left me quite disoriented. Despite being aware of this, it happened again on the return trip, and, to my embarrassment, the following day when we continued on our journey.
Some amusement was provided during the afternoon by some members of our party who had discovered some invading non-indigenous flora, and so foraged for feral potatoes. Boiled in pieces and buttered, the fruits of the hunter-gatherers’ labours made a nice appetiser for our dehydrated fare in the evening. (That’s Sally in the photo searching for decent-sized spuds. Please note that thermals under shorts are de rigeur — or, at least, widely accepted — in tramping circles!)
With the weather inclement and the light fading, the evening entertainment was card games by candlelight, until about 9pm when everyone headed for bed. I had great difficulty coping with such early nights, and it didn’t help that I’d managed to acquire a whole collection of sand-fly bites on my legs and feet that itched like mad, starting around 11pm and continuing into the early hours. I’m sure my tossing and turning kept everyone awake in the close quarters of the bunkhouse sleeping platforms!
A collection of additional day 2 photos can be found here.
 
TO BE RELOCATED TO 7 JANUARY
 One of my Uni of Melbourne work friends likes to go hiking to wonderful places with some long-time friends from her own uni student days along with other invited tag-alongs. I’ve been on one of Ann’s trips in the past, to the lighthouse at Wilson’s Promontory, but circumstances had conspired to prevent me being able to go on a couple of other trips further afield. When Ann told me that she was planning a hike in NZ in the 2012 new year, I drooled but hesitated because it was scheduled for just after I moved to Tasmania and I knew I would still be unpacking and settling in … but then I just decided to go anyway.
We all met up in Napier a day or two before the start of the walk, a party of ten — shown at right just before we set off on the actual hike — ranging in age from the youngest (me) to a 70 year old, with many of the party being fit and enthusiastic folk in their 60s (setting examples to aspire to for the future). We travelled by bus from Napier to Wairoa and then car shuttles to Lake Waikaremoana, in order to embark on one of New Zealand’s famous “Great Walks”. These walks pass through spectacular scenery, the tracks are very clearly marked and often (though not always) more carefully graded and constructed than some of the rougher back-country hikes, and not only are there huts available but they have running water, mattresses for the bunks, and sometimes even stoves for cooking (though not in this case). Since the walks are very popular (NZ’s famous Milford Track is one such walk) you have to book the huts in advance, which also allows control of visitor numbers to regulate the impact on the environment.
We set off the next day, my pack containing a food bag that felt ridiculously heavy (but then it had 5 days’ worth of food) but without the added weight of a tent (which was just as well!), with the trek beginning with a trip across the lake by water taxi (speed boat) to get to the start of the track. We were doing an anti-clockwise circuit of the lake, which meant that we would spend three days or so working our way around the lake’s edge before tackling the climb and descent of the Panekiri Range which overlooks the lake at its southern end.
After farewelling the water taxi at the drop-off point we shouldered packs* and headed along the track. This skirted the shores of the lake, although the temperate rainforest, in all its beautiful lush dense greenness, goes right down to the water’s edge for much of the trip, meaning that you spend most of the time under its shady canopy and it’s only every so often that you get a good view out over the lake. Our first day’s walk was about 8 or 9km and we arrived at the Waiharuru Hut not long after a late lunch, allowing us plenty of time to relax, cook cheesecake (my contribution to the evening meal) and enjoy the views of the lake and far range in the afternoon.
I’ve documented the day’s travel with a few photographs and extra words on a separate page, which can be found by clicking here.
 
* Me, being me, decided to carry all my gear**. The others took advantage of the water taxi service which allowed them to have all but the necessities needed on the walk transported to the next overnight stop, which could be done for all the hut stops except for the last on top of the Panekiri Range.
** I claim that this is because it has been a while since I have done an extended walk (more than two nights), and I wanted to see if I was up to carrying a full pack on a longer trip (not that it was an entirely accurate test, because I wasn’t carrying the tent or a sleepmat). I’d like to think — egotistically perhaps — that the others thought I was being considerate of their age, and using the extra load as a handicapping method to slow down my real (or imagined) youthful enthusiasm. However, I suspect the others were actually thinking that I did it because I am a stubborn idiot. They’re probably right.
TO BE RELOCATED TO 6 JANUARY AT A LATER DATE
 One of the things I did while I was in New Zealand recently was to visit the Cape Kidnappers gannet reserve, the largest mainland gannet reserve in the world with 13000 birds**. There are four colonies of the Australasian gannet or takapu in the area, including one where visitors can get very close to the birds, many of which are nurturing chicks at this time of the year.
Gannet colonies are pretty amazing. They assault the senses, with the noise and odour being especially noticeable for the first few minutes after arriving. The birds believe in high-density living, and nest very close to each other, and the chicks were in various stages of development (surprisingly they migrate from the colony before their parents, and although they don’t really have any idea where they are going, after a few years they return to their natal colony to breed). Birds are always taking off and landing from the colony, as they go in search of food which they catch by diving at high speed into the ocean. Incoming birds fly over the colony, but it sometimes takes them two or three passes to manage the landing in the right place. This means that there are plenty of birds soaring overhead … and so plenty of photo opportunities. This, coupled with the fact that the tiny fence separating visitors from the birds, means that I took a rather large number of photos (I culled nearly half, but still ended up with nearly 100***).
 All in all, it was a trip worth doing: the birds were wonderful and the coastal scenery and nearby countryside were also quite remarkable. A selection of photos (nowhere near 100  ) can be found here.
* In the famous Monty Python bookshop sketch, the obstreperous customer wants to buy “Olsen’s Standard Book of British Birds”, but he wants the expurgated version without the gannet. He doesn’t like gannets since “They’ve got long nasty beaks! And they wet their nests”. The bookshop assistant tells him he can’t expect there to be a special edition for gannet-haters, although the assistant does attempt to make such a special edition by tearing out the offending gannet page.
** It’s always hard to interpret such brags. I have visited Cape St Mary’s gannet colony, in Newfoundland, which claims to have 24000 birds (northern gannets, rather than Australasian), but most of these are on the top of a 100m tall sandstone pillar, some 15-20 metres away from the top of the sea cliffs where visitors observe them, thus making them “non-mainland” … by 15-20 metres horizontally and 100 metres vertically!
*** And I would have taken about 20 photos in Newfoundland, because that was back in the days of expensive slide film.
TO BE REDATED TO 4 JANUARY
When referring to someone else’s mental bewilderment, we tend to say “so-and-so is not all there”.
When referring to one’s own, which is more correct: “I am not all there” or “I am not all here”?
Whatever. Clearly I am not all anywhere.
 Some of you may be familiar with the so-called “Platonic solids”, which are the five “regular” solids in three-dimensions. “Regular” means that they are made up of flat shapes that are “regular” in the sense of having sides of equal length and angles that are all equal, and then these flat shapes are stuck together to make up a solid, and, in addition, every vertex (pointy corner) of the given solid always has the same number of flat shapes meeting at it.
Pictures of the five Platonic solids are shown at right: the tetrahedron (a special triangular-based pyramid where all four sides are nice equilateral triangles), the cube (six squares, the square being the quadrilateral that is regular), the octahedron (eight equilateral triangles, and there are always four of these meeting at each vertex), the dodecahedron (12 regular pentagons, with always three meeting at a vertex), and finally the icosahedron (20 equilateral triangles, and every vertex has five such triangles meeting at it). These are the only five such shapes that exist in our well-known three-dimensional space, a fact that was known to the ancient Greeks.
 If you can accept the idea of four spatial dimensions (see very brief and inadequate explanation at the end of this post) then we can ask the question “What are the equivalents of the Platonic solids in 4D?”, or, in other words, what are the 4D shapes that are made up of regular 3D solids (just as 3D shapes are made up of 2D ones).
The answer is — sort of — at right (the thing in the middle is an Australian $1 coin, which is 2.5cm/1 inch in diameter). There are 6 regular convex polytopes in four dimensions, and thanks to the generosity of my Melbourne work friends I now have a set of 3D representations of them, given to me as a farewell gift. They are amazingly beautiful and mindblowingly fun to think about. Of course, the things I have (more photos are here) are NOT actual 4D objects but 3D depictions of 4D objects. Think about what happens when you draw a cube on paper: the drawing is two-dimensional — it’s on flat paper — even though the original cube that you are trying to depict is three-dimensional. What happens in the drawing is that you “cheat” a bit and draw some of the lines at slanty angles to represent the depth or third dimension. In other words, you lose a dimension in the drawing, but it “gets away with it” by drawing some of the right angles as slanty lines. My set of polytopes does the same thing: the shapes in the photo are 3D “pictures” of real 4D objects (if we could perceive 4D), but because we’re stuck in 3D we’ve lost one of the dimensions, and some of the lines have to be represented wonkily instead of at the angles that they “really” are in four dimensions.
[Strictly speaking the shapes in the photograph itself are actually 2D representations (since the photo is flat) of the 3D shapes which I have and which were sitting on my floor for the photo, and these 3D shapes are, in turn, representations of the 4D objects which I don't have and can only vaguely imagine!! Anyone who isn't confused at this point isn't paying attention.]
Closeup photos of each of the shapes, and some accompanying explanation (of dubious lucidity) can be found here.
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Very brief discussion about 4D
“Four dimensions” just means that there are four variables involved. Most people, if they think about 4D at all (you mean people don’t?!), probably know of 4D as “space-time” (the famous “space-time continuum ” of science fiction … and reality!). This is three dimensional space and time. Space-time thus has four variables: left-right, up-down, towards-awayfrom, and time, and any “point” in space-time can be defined in terms of four coordinates: where you are (which takes three coordinates) and when you are (which is an extra coordinate). (This assumes that we all agree on points of reference for the origin point of space and the start of time!).
But these are not the only sets of four variables that we could have. 4D space also has four variables: left-right, up-down, towards-awayfrom, and an extra, fourth, direction which is at right angles to each of the first three (which we don’t experience as far as we know, but you could think of it as going off in a wonky direction, just like the slanty lines of a cube in a 2D drawing that tries to show 3D on a flat piece of paper). It takes four coordinates (w,x,y,z) to describe where something is in 4D space (just like 2D geometry has (x,y) coordinates, and 3D geometry has (x,y,z) coordinates). Now this might seem totally unrealistic to you, because we don’t perceive that fourth right angle (well, I don’t; I can’t speak for the rest of you), but there are actually plenty of real-life situations that involve multiple variables, that we might like to graph (just as we draw graphs of distance as a function of time to show how something is travelling). So, for example, heights of plants might depend on four variables: amountofwater, amountofsunlight, amountoffertiliser, and amountoftalkingtobyowner. We might even be able to get a formula to describe how all these things interact, but what we really struggle with — BECAUSE we don’t perceive the fourth dimension — is being able to draw graphs of these relationships because we can’t easily show all four (or five or six or seven …) of the variables/coordinates.
For a fun and famous book about the difficulties of making sense of “moving up” a dimension, try Flatland, by Edwin A Abbott, which describes the adventures of a square living in a flat 2D world, who suddenly starts to experience the third dimension.
 Despite — and because of — the fact that I am moving at the moment I managed to have my Christmas card designed early. The farewelling process associated with moving means that I gave out more cards than usual this year, and so this on-line version is probably not required. However, it has become a tradition (if the two previous occurrences in 2010 and 2009 can be said to establish such a habit), and so here we are again.
May you be blessed with a happy Christmas (whatever your beliefs!) and may the new year bring peace, joy, and the fulfilment of your goals. I have a bad feeling that in some of my physical cards I managed to wish people all the best for 2011, which is a nice but rather belated sentiment, and reflects the fact that it has been such a crazy year that I have no idea what year it actually is. I am looking forward to being at least partly settled in to my new abode by Christmas, and hope to have time to complete four of my Christmas traditions before then: put the Christmas tree back up (I think that in future it won’t be a permanent fixture in the loungeroom), sing through Handel’s Messiah (even if only to a recording), watch The Muppet Christmas Carol, and do the “hospital carolling gig” with TUMS.
This year’s card was created digitally using the program Illustrator. Since it is a very powerful program and I only use it once or twice a year, I still have only a feeble command of its basic operations, and I ran out of time to figure out how to do subtle things like graded shadows on the cloth. One day I’d like to master more of its possibilities, but that day is not likely to be any time soon. Expect similar clunkiness on next year’s card! At least this year I learned a bit more about “layers” so that each wise man was created separately, and then stacked according to who was in front and behind.
Finally, for those of you who are interested (and because I am an obsessive record-keeper and cross-referencer) I have an archive gallery of all my previous Christmas card designs.
Previous posts to this blog have revealed that I chose to play mixed futsal (a six-a-side variation of soccer/football, with both male and female players on the teams) in the second half of this year, run through the Uni’s sports centre and involving groups of interested people from various departments. In addition to the abundance of contusions and a thumb dislocation experienced by yours truly, our team did not perform particularly well during the 10-week second semester season. We managed a couple of draws, but finished at the bottom of the ladder and in the playoff for 9th and 10th spots, we lost. Narrowly, but we lost. We were, however, heartened by the fact that we improved as the season progressed.
Ben, our player-manager, decided that we should enter the post-semester mini-competition.
This season began spectacularly well, with a 5-0 win. (I now have to confess that the other team forfeited, as they all had an exam that day!)
We then managed a draw, followed by our first-ever legitimate win. The only down-side to this win was that Ben, who has organised the team for several years during its record-setting non-winning streak, actually missed this match.
The following week we managed another draw, and so, coming into the final week of the round-robin competition, we found ourselves at the top of the ladder. We managed to bring together most of the players who played for us during the season, which gave us plenty of substitutes to choose from (a bonus on the hot day it turned out to be).
We had a really good game, lots of great passing and fancy footwork, that belied the poor outcomes of our earlier season … and when the full-time whistle blew we had won 3-1. And Ben was there this time.
We also think the oranges at half-time helped. The other thing that may have helped is that several weeks ago I replaced Ben’s goalie’s gardening gloves with a proper set of keeper’s gloves. This made me feel much more professional!
I can now retire … or at least command a large transfer fee for any team that wants an aging, bruise-prone goalie in Hobart.
 
A herd of eloquence: When the speaker’s lyrical language grows overblown and flowery, and you start to wilt beneath the onslaught.
 Last month, 12 of 12 fell on house-auction day. This month, 12 of 12 falls on packing day.
Nightmarish as this was, I was fortunate to have the removalists doing the bulk of the packing, rather than me. If it had been left to me, it would have taken the best part of a year.
As you can see from the photo at right, one of the consequences of packing — and, in fact, of the whole house-selling process — is that my year-long Christmas tree is not on display despite it being well into December. I’m hoping I can remember which box it is in, so that it can at least have a few days of contributing to Tannenbaumic tradition in my new abode.
I am quite sure the removalists were bemused by some of the things they were packing (so was I, sometimes, but I hadn’t had time to sort things out and actually get rid of stuff). Certainly the removalists didn’t realise the significance of some of the things they didn’t pack. The pair of A3 paper box lids in the photo, for example, used to sit in the right-hand shelves of the entertainment unit beneath the TV, where they held some of my VHS movies so that I could pull the box lid out like a drawer, instead of having to shift individual video cassettes.
I have a large number of ingenious-but-odd improvisations like that … but some people just don’t “get it”.
Anyway, enough waffle. This post is already a few days late, so let’s just cut to the chase. Here’s this month’s 12 of 12 – packing day.
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