Does anybody else out there talk to the telly while watching it?
Scully and Mulder are investigating a seemingly empty stronghold of the Secret US Government Conspiracy. They go through a door into a dark building, but leave it open behind them – as much as to say to the murderous paramilitaries that the government employs to protect these places – ‘We’re in here!’
So naturally I say ‘Close the door behind you Scully, or the goons with submachine guns will get you!’
And sure enough, in rush the gun-laden goons, shooting everywhere. But miraculously, again, they don’t manage to hit our two heros, who escape – again – but without any evidence of the murderous conspiracy – again.
Doctor Who is walking through a storeroom of mannequins and stops to examine something. Obviously, one of the mannequins is going to come to life and attack him, but he doesn’t think of that, so engrossed is he in what he is examining. So, as a mannequin comes to life and starts to sneak up on the Doctor, I helpfully call out:
‘Look behind you!’
Which he does, not soon enough to avoid being grabbed, but soon enough to wriggle out of the predator’s grasp and run away.
I can think of plenty of other examples, but not closing doors behind you and not putting your back to the wall when you’re in a dangerous place are the two ones that incite me the most.
Then there’s the one where key characters in a show, that are supposed to engage the watcher’s sympathies, make a trademark practice of buying coffee in single-use, non-recyclable cups, walk along with them chatting to each other but not drinking, and then throw the apparently full cup in a bin. Yes it might be worse if they threw it on the ground, but not by much! So I expostulate:
‘Buy a Keep-cup* Lorelei, ya environmental vandal!’
*Reusable coffee cup. Probably TM like hoovers and biros and band-aids and xeroxes.
And the one where somebody says something that they don’t realise is upsetting for another person. Like when person A says to person B, who had believed an as-yet unacknowledged romantic bond was beginning to develop between them, ‘I never thought I could have a best mate that was a girl’.
So I helpfully inform him ‘She doesn’t want to be that sort of a mate, you blind poltroon!’
Do you do that too? Perhaps only when there is nobody else around? Or do you do it regardless? Or are you one of those people that bottles up their fears, irritations and sympathies vis à vis the characters and keeps them inside?
I like talking to TV characters. It makes me feel like I have a relationship with them. A self-help guru might say I should concentrate on relationships with real people, but I think you can do both. And I don’t know any real people that are time lords or government conspiracy uncoverers. Sadly, I do know plenty of people that waste our resources and exacerbate the landfill problem by drinking coffee in non-reusable cups, but they seem immune to my hints that there is a better solution.
I have quite enjoyed watching telly recently. Perhaps it’s because the future of the world looks so black with the continuing rise of neo-fascism and the determination of governments of large, wealthy, ex-British colonies to do as little as possible to address the climate crisis (New Zealand being an honourable exception). There’s reading of course, but in my continuing attempts to get better at foreign languages, most of that is not in English, so it’s hard work. Which makes it so relaxing to just plonk on the couch for a while after work, in front of a silly, simple, comedy or drama that asks nothing of me but my attention (But NOT a reality TV show! My loathing of them is a whole ‘nother subject entirely!).
In days of yore, telly was seen by some as a brain-sapping, eye-damaging scourge. “it’ll give you square eyes!” was what my parents warned. Fortunately, I didn’t watch a great deal of telly when young, so my eyes are still approximately oval-shaped. My opthalmologist, with her specialised equipment, was able to advise me that there is a small amount of right-angling at the edges of two of my eyes, but it’s less than the average for people born in the TV era, so nothing to be concerned about.
These days it’s the internet, especially social media, that parents are worried about their children spending too much time on. Television is seen as relatively benign. Perhaps because it’s now old enough to be trusted. Or perhaps because watching telly, unlike staring at a computer screen, can be a social activity. Like in the old days of Victorian and Elizabethan theatre, we can hiss at the baddies and cheer (or warn) the goodies, lament the misfortunes, discuss what the real explanation of the mystery may be, or what the protagonist should have done when confronted with that Terrible Dilemma.
With the internet, everybody in a room can be sitting staring at their own little screen. They might as well be a million miles from the people around them. But with telly, the people in the room are watching it together, no matter how bad it is.
Is that a good thing?
Bondi Junction, October 2019
It has become apparent to me that the world needs another instalment in my series of suggestions for Adult Amusements. There have been complaints. Some are from pedants, who insist that a single monograph about standing on one leg does not constitute a series. Others, more gravely, have expressed concern about the occupational health and safety implications of people trying to balance on one leg while their mind is distracted by other things, like budgets, work-shopping and brain-storming, not to mention trying to be Pro-Active, Customer-focused, Agile, Continuously Improving and Outside the Box all at the same time.
So, belatedly, here it is. I hope that this will be considered less dangerous, being a mostly sedentary activity.
When in business meetings that do not hold us riveted with fascination, we should draw stars!
But not just any old stars. Special stars. Mathematical ones. Stars with prime numbers in them.
It is the dearest wish of every little child, after that of being a firefighter or an astronaut, to draw excellent stars in their pictures. But a wish is one thing, and its fulfilment is another. When as a child I tried to draw stars, the only technique I could think of was to draw a spiky circle. Start anywhere, and draw a perimeter that goes around an imaginary centre, that is a series of spikes. Maybe this works OK for others, but for me it typically produced a result like this (Figure 1):
It invariably goes wonky, because it’s hard to keep track of where the centre is supposed to be, and to make the points point away from that centre. Mine looks like a confused kookaburra.
When one gets a little bit older and more sophisticated, one learns – by instruction or by observation of others – the two standard techniques for drawing stars. These are the six-pointed star, which is made by drawing an upside-down triangle slightly above a right-way up one (Figure 2):
and the five-pointed Pentacle, which requires a little more coordination, but can be done without taking the pencil off the paper (which I call a ‘single pencil stroke’), by following the arrows as shown (Figure 3):
Learning to draw either of these stars is on a par with learning to ride a bike, in terms of the sense of achievement, wonder and progress. All of a sudden, one can construct an image of symmetry and elegance with the stroke of a pencil – or two strokes, in the case of the six-pointer.
I was very happy with this advance in technology for a long time, but then came the day when I hankered after drawing more bristly stars, with seven, ten or twelve points. I tried, but found I was just reverting back to the method of figure 1, and my bent stars just did not satisfy me.
One could of course take out a protractor and compass and, with a bit of preliminary calculation, measure out the exact angles needed for each point, and draw the star using that. But firstly that’s cheating, and against the Spirit of Doodling, and second it might cause others to notice that one is not paying attention to whatever the meeting is discussing.
I thought I was destined to be forever that object of public ridicule – the man with the two-star repertoire. But just as I was starting to come to terms with this being my fate, a discovery came to me in a blinding flash: instead of trying to draw spikes in a circle, I needed to generalise the methods used for the five and six-pointer. Well, to cut a long story short, I tried that, it worked, and now I can draw stars with any number of points up to about fifty.
Here is the method that generalises the way we draw five-pointed stars:
Drawing a star with a single pencil stroke
- Step 1: pick the number of points N, and draw that number of points, as evenly spaced as you can, around the perimeter of an imaginary circle. If there is a large number of points it’s best to first draw points at the 12, 3, 6 and 9 o’clock locations and then put one quarter of the remaining points into each of the four quadrants. To be precise, divide N by 4 to get a quotient Q and a remainder R. Then draw Q points in each of R quadrants of the circle, and Q-1 points in the other quadrants. Ideally, if R=2, adjacent quadrants should not contain the same number of points, but it doesn’t matter very much if that is forgotten.
- Step 2: pick a number K, greater than 1, that has no common factors with N. To make the spikiest possible star (ie with the thinnest spikes), choose K as the largest whole number less than N/2 that has no common factors with N. For instance if N=12 that number is 5. If N=13 it is 6. If N=6, 4 or 3 there is no possible K, and this method cannot be used. I’m pretty sure that, for any N greater than 6, there is at least one K for which this method will work, but I have not proved that yet.
- Step 3, choose your favourite direction in which you want to draw. Unless you are a pan-dimensional creature drawing on paper with three or more dimensions, your only possible choices are clockwise or anti-clockwise.
- Step 4 starting at any point, draw a straight line from that point to the point that is K steps away from it, hopping from point to point around the circumference in the chosen direction. We can call K the ‘side length’, since it is the length of the line that connects one point to another.
- Step 5: repeat step 4 until you get back to the starting point.
If this process is executed carefully, you will have drawn a star that has a point at every one of the points you drew in step 1. And, if you want, you can do all the actual line drawing in steps 4 and 5 without ever taking your pencil off the paper.
Here is a depiction of that process for an eleven-pointed star with side length 5:
And here is a depiction of this process for a sixteen-pointed star with side length 5:
Why do we not allow the side length K to be 1? That’s because if we do that, we just get a N-sided shape which, ignoring any irregularities in our drawing, is a regular polygon, like this, for N=12 (a ‘dodecagon’):
Now the thing about stars is that they are not convex, while regular polygons are. Using the word ‘vertex’ for a place where two edges of a shape meet, an N-pointed star has 2N vertices, of which N are points – the outermost part of a peninsula (if we imagine the shape as an island in an ocean) and the other N are the innermost part of a bay. As we go around the vertices of a star they alternate between inlet and bay. So a regular polygon is not a star because it has no bays, and that’s why K must be more than 1.
Stars with more than one pencil stroke
We observed that the above method does not work for N=6. But we know we can draw a six-pointed star, using two pencil strokes to draw two overlapping triangles. We can use the approach taken there to invent many more stars. In fact, for an N-pointed star there are M different types we can draw, where M is (N+1)/2-2, rounded down to a whole number. Each of these shapes corresponds to using a different value of K, from 2 up to the biggest whole number below N/2.
Here is how we do it:
- Step 1, for picking N and drawing the points around an imaginary circle, is the same as above.
- Step 2. We pick any K as any whole number greater than 1 and less than N/2.
- Do steps 4 and 5 from above. This will draw a shape that is either a star or a polygon. Now comes the tricky bit.
If the shape you drew has not touched all the N points around the circle, repeat the process starting on a point that has not been touched yet. I like doing this with a different colour pencil, as it helps me see the pattern and avoid getting confused.
Repeat that process, using a different colour pencil each time, until all points have been touched.
You will now have a N-pointed star, made up of a number of identical overlapping shapes, which are either all polygons or all stars.
For those that like mathsy stuff, the number of overlapping shapes – the number of pencil strokes required – will be the greatest common factor of N and K. It’s fun to try to work out why that is.
The traditional six-pointed star in figure 2 above is what you get under this method when you use N=6 and K=2. Here are a couple of others:
If we are going to draw a lot of different stars, we need names for them. We could call the star drawn with N points and side length K a ‘N-K star’, so that the pentacle is a 5-2 star and the traditional six-pointer is a 6-2 star.
If we wanted to, where N is even, we could let K be N/2. What we get then is this sort of thing:
The shape we have drawn with each pencil stroke is a single line between a point and the point directly opposite it. Strictly speaking, this too is a star, but I mostly leave it out because it’s not as interesting as the others because (1) everybody knows how to draw a star like that; (2) as any five-year old would tell us, that’s not what stars look like in pictures of things in the night; and (3) it has no inside, so we can’t colour it in all yellow (well, actually the one I drew has a tiny little inside in the middle, because it’s not perfectly symmetrical. But a more accurate drawing would have all the lines going exactly through the middle of the circle, so that there’s no inside at all).
So now you know how to do lots of great stars. You need never be bored in a meeting again. Imagine if you started drawing all the possible stars, starting at the smallest number of points and going up in side-lengths and points until the meeting finished. Leaving out the too-easy ‘thin stars’, you would draw the following stars:
5-2, 6-2, 7-2, 7-3, 8-2, 8-3, 9-2, 9-3, 9-4, 10-2, 10-3, 10-4, 11-2, 11-3, 11-4, 11-5, 12-2, and so on.
Just drawing those, given a due amount of tongue-stuck-into-side-of-mouth-concentration, should be enough to get you through at least a half hour of Death By Powerpoint.
But let’s not forget our roots. With a very few exceptions, we all started off drawing stars like Figure 1. There is a touching ingenuousness about such stars, and I think it’s good to draw them as well. Often really interesting shapes arise when we do, looking like monsters or funny animals. And one good thing about that way is that you don’t have to decide how many points it will have before you begin. You just draw spikes around a circle until you get back to the start. I’ll sign off by doing that for a star with LOTS of points (it ended up being 21), and following it up by a series of the nine different stars with the same number of points drawn by the above method.
I think that each has a certain appeal, in a different way.
Have you ever been in a meeting or other group activity that was just dragging along, keeping you teetering interminably on the edge of profound boredom? It happens to me quite often.
When children are caught in this sort of situation – such as in church or on a long car journey – they can relieve their feelings by complaining to their responsible adult ‘I’M BORED’ or ‘Are we there yet?‘
But we poor adults do not have that excellent outlet available to us. Partly because we have no responsible adult to complain to, and partly because people would judge us if we were to blurt out such phrases.
So I thought it was time that somebody came to the rescue of the wretched responsible adults that have to endure these situations. To that end, I am starting a series devoted to equipping adults with the tools to amuse themselves and stave off boredom, when caught in unexciting, unavoidable group activities.
I don’t know how long the series will be – perhaps not long at all. It is, after all, so much harder for adults to amuse themselves than it is for children, to whom everything is new and exciting (until they reach adolescence, when suddenly everything becomes old and beneath contempt).
Here, then, is my first piece of Useful Advice For Bored Adults.
Stand on one leg!
Start by lifting one foot just a little off the floor, and see how long you can keep it off. If you only lift it a tiny bit, nobody will notice, and it may not affect your balance much. You may find you can do it for ages.
Once you’ve mastered that, which might be straightaway, or might take a little while, start increasing the height to which you raise the foot. The higher it goes, the higher one’s centre of gravity is and the easier it is to overbalance.
Don’t overdo it with the high foot. If you raise your foot above your waist, people might start to look at you funny. But kudos to you if you can do that and remain balanced though. I couldn’t do it to save my life.
I recommend that, once you can sustain the foot at near knee level, you move to the next phase, which I think of as the Aboriginal pose. I think that name springs up in my mind because when I was a wee lad, for some reason the pictures we were shown of traditionally-living Australian Aborigines in the outback often showed them standing like this. I am a little nervous of calling it that in a public blog, lest anybody think it disrespectful. That is certainly not my intent. And, since the ability to sustain the pose is an admirable skill, I am hoping that it is not considered disrespectful. It certainly seems no worse, and probably much better, than saying that somebody gave a ‘Gallic shrug’, which seems a fairly accepted (if somewhat dated) turn of phrase that is by no means complementary to our French cousins.
Here’s what that pose consists of: you lift one leg and bring the foot of that leg to rest with the sole against the side of the knee of the other leg. More advanced practitioners may even rest the foot on the thigh above the knee. Rookies may content themselves with resting the foot against the upper part of the calf.
I can do this pose a bit. I find that I can rest motionless for a while like that – maybe up to twenty seconds – then I start having to make lots of little adjustments with my planted foot to try to remain in balance. These adjustments increase in frequency and amplitude until either I overbalance and have to put the foot down, or – magical relief – I re-attain a stable body position. The latter doesn’t happen very often, but when it does, it’s like winning gold at the Olympics! One looks around in triumph, just a little puzzled as to why the others in the group activity haven’t broken out in rapturous applause.
While engaged in this entertainment, I often overhear myself telling myself that not only am I staving off boredom, but I am burning calories, toning my leg muscles, getting closer to nature (really?) and building a much-needed sense of balance. This is based on a total number of scientific studies that was, at last count, approximately none. But I still feel good about it.
Plus, you get to feel like a four-year old for a while.
That’s all for now. Stay tuned for the next instalment – ‘drawing stars’.
By the way, could it be that the reason for standing on one foot in the outback is to minimise the amount of heat soaked in from the hot sand? If so, that sounds like a very sensible arrangement. But whatever the reason, I remember always thinking that traditionally-living aborigines must have a much better sense of balance than we clumsy Europeans.
Oh, and one last thing. Remember to switch feet from time to time. Otherwise you’ll end up getting all asymmetric, like Arnold Schwarzenegger on one side of your body and Woody Allen on the other.
Which would make it hard to find clothes that fit.
Bondi Junction, April 2016