Disappointments

There were three small disappointments yesterday. The plan didn't work, because CMCC had a lecture straight after the meeting (I didn't even get as far as asking as he mentioned it when someone asked if they'd be able to discuss something with him afterwards); we got assigned groups for the group project in Computational Statistics and I'm not too convinced my particular lot will be good to work with (though I don't really know them at all and have never spoken to them so I could easily turn out to be wrong); and worst of all, at the Environment Forum another person from my halls said he wanted to become a Sustainability Champion. At first glance, this sounds like a good thing- the more people promoting environmentally friendly living the better, one would have said. But actually I'm really not happy about it. Partly this is because of who it is- I actually met this guy, C, during the welcome party and while he was nice enough in a social setting (though I left without any desire to ever see him again, I also had no desire not to see him again), it became apparent just over the hour or so long discussion the three of us had after the meeting that he wasn't going to be good to work with- to be fair, the specific combination was not going to gel nicely and effectively. He seems pretty strong willed and insistent on doing certain things he's set his mind on- while in some ways that's a good quality (after all it's also known as determination), it unfortunately brings out a similarly strong willed opposition in me- and the strong wills make it difficult to talk through things slowly and thoroughly and listen entirely to each others' arguments before coming back with a point of one's own. For example, he has a big thing about waste disposal. So far, so good- after all it's certainly one of the areas we should be focussing on. But one thing he very firmly wants is a separate communal bin for white paper- "even if it was all the way down by the laundry, I'd be happy to go down there to throw my white paper away; I use a lot of it and-". Such were the wills that we weren't able to discuss this as calmly and methodically as I would have liked: I believe that he wanted one because he believes the pink recycling bags in the kitchen are not being sent off for recycling but just emptied in with the rest of the rubbish (though I couldn't quite get out of him whether he'd still need one if that scheme was working fine). Of course, if it's true, then that's terrible- though, as the Sustainability Champions Co-ordinator, who stayed behind after the meeting for half an hour or so, said, it could be that the council need to generate a large enough uptake before they can actually send them to be recycled. His belief, I think, was that the residence management or cleaning staff are the ones who lump it together- though if the council are not recycling it then that doesn't make a difference- but I question this. He claims to have seen it happen on more than one occasion, but I'd been talking to the manager the day before and he volunteered, though we had actually been talking about the residents' end of the chain, the information that he was planning to get another bin to store the recycling waste in or to ask the council to collect twice a week. So I think it is quite possible that what C saw was stuff from the recycling bags having to go in with the ordinary waste after the recycling storage was full for the week- bad but being remedied (hopefully). I explained this to C (what with the strong wills, I actually explained it more than once), but I wasn't suggesting that that was the end of the matter- I said we should look into it, but find out what really does happen to it before trying to implement alternatives. Again, I couldn't quite get a straight answer out of him, but he seemed to be wanting to go straight ahead without investigating first, and told us when we parted that he'd look into schemes that do white paper recycling. Of course, there's no harm finding out about that even if we do have yet to take the first step, but the way he said it gave me the impression that having found out about it he would launch, or want to launch, straight into arranging it.
On my part, I'll admit to being a bit more intractable about the planned menu for the Climate Change Awareness Week Halls Quiz, though I did manage to say that we could discuss the details of it later and that we probably could make different things (luckily the strong wills meant I hadn't quite been able to get out a statement of my reflex position earlier in the conversation, that the food should hardly change; I would have run up against a lack of logical reasons if I hadn't been interrupted and I'm glad I was). I was also too forcefull on the questions- the Sustainability Champions Co-ordinator, like CMCC when I mentioned the idea to him at Archway, thought it should be a pub quiz with a round on climate change, but I thought the whole thing should be about it. I did manage to say that I wasn't sure how the others felt (looking at them) but personally..., but then I was arguing the point with her without the others having a chance to express their views.
It's not just about the personalities though: I actually think this will mean more work not less. Which would be fine (though stressfull) if it meant more effect- but I believe it will in fact mean we get less done. Two from one was an improvement- it made decisions easier where I really wouldn't have been sure myself; we managed to come up together with an eminently presentable leaflet and introductory letter that I believe neither of us (well certainly not me anyway) could have managed apart; we've both made some effective posters with mine having the strength of presenting information clearly and attractively, and SC2's being persuasive, amusing and memorable; and there's been an extra person to try and catch the manager in. But it's been hard enough trying to find times for the two of us to meet up, and sending things to each other by email to approve; trying to find times for three and wait for two people to comment on work is going to be very hard. And when we do meet up, because of the dynamic it seems likely that (though I will try not to let it happen) we will spend more time at opposite positions trying to convince each other not to do things than actually getting stuff done. SC2 and I haven't always had the same views about things, but because neither has been really set on anything, but rather undecided and leaning one way, we've been able to put forward a few arguments and then one of us decide the other is right- and if one has a reason for not doing something that the other wants to do, we've often been able to explore the reasons for that and incorporate a change that addresses them- sometimes an entirely different third option we'd only just thought of.
Finally, I suppose I am a little resentfull of his coming late- there's no reason why he couldn't have applied at the same time as us if he'd wanted to, and we've got a good team going that he wants to effectively do away with (since it will be so different with the three of us). And he doesn't respect the fact that we've been doing this for a couple of weeks- and that we have, for example, talked to the manager and know a bit about the situation- he seems to think he is in just as good a position as us. But of course, there's nothing I can do about it, we (I? Not sure how SC2 feels) are just going to have to put up with him. And maybe draw up some kind of division of responsibilities...
Anyway, all yesterdays disappointments were building up to The Disappointment today. Today the plan worked, after a fashion- I got to go down to the Quad Cafe with CMCC after the committee meeting, and it was just the two of us, though we were joined by someone else before long. I even managed to ask the Question, in what may possibly have seemed a totally naturaly and innocent way. But I was pretty sure of the answer beforehand- when the committee moved to another room to fill in nomination forms for those standing in the Michaelmass elections after the meeting, he and the Residences Officer actually kissed once or twice (this part of the meeting was very informal, I hasten to add, and it was mostly when people were leaving). Again, conclusive in almost every case but here only very suggestive- after all, it wasn't French kissing though admittedly any sort of kissing on the lips is extremely non-standard between best friends of whatever gender. It did at least have the virtue of making the Question into something that was more likely to be asked purely in the interest of making conversation than before- I actually did it when we finally sat down at the Quad Cafe, having bumped into someone CMCC knew who was still buying sandwiches before coming to join us; thankfully there had been a long enough pause for it to sound like thinking of something to say. I said it casually (I hope) and with a smile, and it may have passed for more of a humorous comment than a genuine question- in any case, at least it had been placed in something of a grey area as far as too personal went since if he wanted to keep it private he wouldn't have kissed her at the meeting.
Of course, I wish he had turned around and said something like "No, actually, though I can see how you might have got that idea". But there is also an element of relief to this outcome- I would almost certainly not have achieved anything even if he had been single and at least this way I won't keep telling myself that nothing will happen if I'm not brave enough to take some kind of action. And maybe I won't feel the need to impress him so much either... It goes without saying that I'm going to try to re-platonicise my feelings, and stop my stomach lurching whenever I catch sight of (or think I catch sight of...) him. But I do really enjoy talking to him (or hearing him talk) and I would like to be friends if possible- so this does present somewhat of a challenge: my general method of getting over crushes involves not just forcing the train of thought onto new tracks (generally over on the other side of a mountain range) every time it stops at the object's station, but labelling the visual-and-personality-impression image over with 'Silly' (I've never quite worked out whether this has actually brought about my despising of most of the people I have had a thing for, or whether due to a very wrong first impression and subsequent resistance to reality they have in fact all been worthy of this, and I have discovered it later). This is not going to work if I'm going to be spending any amount of time with him, and what with him being co-chair of the Green Party, it is pretty certain that I will. So I am going to experiment with just trying not to think about him, and will hope that that will also cut down on my feelings when I do see him. There will be something of a test of that tomorrow (though of course that will be very early days) as it will be the Union General Meeting where he'll almost certainly speak, and so I will be able to see what it's like watching him without him being aware of my reactions (and me needing to carefully control them) as would be the case in a smaller setting.
Today, though, rather than starting the deliberate thought change I have taken the easier path of distractions. After the revelation* I was going to the library anyway, and decided to plunge back into Computational Statistics as I knew my mind would just wander with Principals and Methods and I wouldn't get anything done. As it is, my concentration wasn't perfect, but I still got pretty into it and was able to forget for quite long periods. For once, the topic as well as the computing was actually interesting- the past two weeks the data has been share prices over time which really doesn't grab me. This time, rather than data, some of the questions focussed on the logistic function: X1=r(X0)(1-X0)**. In other words, you take a number (between 0 and 1), subtract it from one, multiply that by your number, and then multiply again by another number r. You then use the answer to go round again. For example, if we decide to have r as 3, and start with X=0.25, then we get 3*0.25*0.75=0.5625, and then we do 3*0.5625*0.4375=0.7383 and so on, generating a sequence of numbers. I'd come accross this before when reading popular maths books before I came to university, and had seen the diagrams that follow, but this was the first time I'd created them for myself. One question involved writing a function to draw a diagram like this:The curve is just the function r(x)(1-x)- a plot of the value get for each x value if we carry out the process just once. Here I've used r=1. The black line meanwhile is y=x. So far so simple. The interesting bit is the red line. This could have started from anywhere, but in this diagram I've chosen a starting point of x=0.5. The mini programme I wrote, incidentally, allowed r and the starting point to be changed, so I was very easily able to generate the following pictures. Anyway, the red line goes from our starting point on the x-axis up to the curve. It then goes horizontally to the line y=x. Since it keeps the height it had when it hit the curve, the y co-ordinate when it gets to y=x is still r(x)(1-x). And of course, at y=x, the x co-ordinate equals the y co-ordinate- in other words the x co-ordinate has now changed from 0.5 to 0.5*0.5= 0.25. The line then goes back to the curve, keeping that x value, so that at the curve we have y=0.25*0.75=0.1875. It keeps travelling between the curve and y=x, and every time it moves vertically to the curve, we get a new y value y=x(1-x), and every time it moves horizontally to y=x, that y value becomes the new x value. So we are moving through the sequence as before, but this time doing it on the graph.
As you can see, the red line zig-zags between the line and the curve getting smaller and smaller and heading for the origin. You might think that that is all it would do, which would be rather boring. But actually, if we change the value of r, we can see some quite interesting things:For r=2, if we start at 0.5 again we only get one vertical line. That's because 2*0.5*0.5=0.5- we just get the same value back again every time (you can see this on the graph by the fact that the curve and y=x cross at 0.5). The same thing would have happened with r=1 if we'd started with 0; y=x doesn't cross the curve anywhere else for r=1. Going back to r=2, if we start at 0.1 instead, we get:
This time, instead of heading for the origin, the sequence heads for the place where the lines cross, at x=0.5. Now if we change r to 3, and start at 0.1 again, we get this rather different picture:This time, it's spiralling in rather than zig-zagging- though it still looks like it's heading for the place where the lines cross.
We didn't have to start at 0.1; anywhere except where the lines cross would have done:
So far, it looks like it will always home in on the place where the lines cross (where x=r(x)(1-x)). Sometimes it will spiral, sometimes it will zig-zag. Right? Wrong! Look what happens when r=3.87:Instead of heading for one point, this time the sequence moves all over the graph (all over the range of x).
So for what values of r does the function 'behave nicely' and head for one value, and for what values does it do the above? Well, this diagram- which was the task for the next question- is the one I am proudest of. Not that it is really any harder than the others, it just looks very impressive. And it is the final diagram they give whenever any book talks about the topic:Very pretty, but what does it mean? Well, along the bottom you have values of r (ignore the labels, they were a mistake I've just noticed), and up the left hand side values of x. For each r, the computer has calculated the logistic function r(x)(1-x) 1000 times (starting with x=0.5- but any value would have done) and plotted the last fifty of these values. For values of r up to 3, these last fifty x values are homing in on one number, and each of the fifty points is so close to the rest (since we are so far on in the sequence) that on the graph all fifty look like just one point, making just one line when all the r values are taken together. The fifty values is what had to be plotted in practice, but you can think of it as showing the point that the sequence is heading for at each value of r.
After r=3 though, the line splits: for these r values, instead of heading for one point, the sequence heads for two at once- one value is close to one point and the next close to the other, then the next is a little closer to the first point and the one after that a little closer to the second. It then splits again and goes between four points. As r gets closer to 4, the sequence visits more and more points. The diagram stops at 4 because after that the sequence stops heading for anything but just gets bigger and bigger (in absolute value)- because the highest value x(1-x) can have is 0.25 (when x=0.5), so that for values of r less than 4, r(x)(1-x) is between 0 and 1, but for example, if r is 5 and starting with 0.5, the first few values of the sequence are 1.25, -1.5625, -20.0195, -2104.0058,...

So that was a nice distraction. And after that I went to see a Spanish film being shown by the film society in one of the lecture theatres (one equipped with speakers (though not great speakers) as well as a data projector, and with steeply sloping tiers of seats). It was Almodovar's Women on the Verge of a Nervous Breakdown; it was originally scheduled for last Thursday and I was sorry I was going to miss it for the Maths and Stats Freshers' Dinner, but luckily they had to cancel it at the last minute and show it today instead. It took a while for them to get it started (technical difficulties, I think), but I was chatting to a nice General Course student, the conversation having started over our joint efforts to find the room, so I didn't mind. It was a really good film- very very bizarre but very funny too and with an interesting visual style. They served sangria as well, which was stronger than it seemed but quite nice. The whole thing was free for film society members, and membership was only £3 so I think I got a bargain there. I'm hoping to be able to go to more of their showings over the year but I suppose it depends what else I've got going on!

*Ok, revelation is too dramatic a word for something that was already staring me in the face. And it wasn't exactly right after either- the other person joined us and we had quite a conversation, then he left, and I was just thinking of going myself (it had been long enough not to look as though I no longer wanted to spend time in his company) when it became apparent that his girlfriend would be coming along shortly so I felt I had to stay a bit longer so as not to look like I was avoiding her. I had a bit of a chat with her (she's really nice, actually, and not in awe of him which is obviously very healthy and probably very good for him), while he was getting her a tea, and then they both left only it wasn't quite clear immediately whether one or both of them was coming back- so again I waited a bit so as not to seem to be avoiding either of them- then took a look round but they'd disappeared so I finally went.

**Obviously the notation is completely out there but it's the best I can do without LaTeX or something; ideally I'd do subscript t and t-1 in place of 1 and 0