Personal Blogs

Tishy and I went to my mother and fathers' today. Gardening was the plan.

We arrived, were ushered into the back-room, where sitting on the floor was something that, at first-glance looked like a product of my dad's mind. But when I got up close and had a good look at the thing, was clearly something that came out of my mum's mind.

It was an odd thing: some half-painted, badly-distressed, wood cut into recto-linear chunks and fitted together as a rectanglular jigsaw where nothing matched and there were no symmetries.

My dad had clearly had a hand in it somewhere—the chunks had the severely defined edges that you only get from someone who knows how to deal with wood. One of the cuts went against the grain and was still sharp.

I hunkered down to have a good look. There were places where decisions about the final outcome had yet to be made, but I saw where it was heading. There was a heap of proto-kindling lying on the floor next to the thing.

"Where did you get the wood?", I asked.

I should explain that. I'm not madly daft about wood, but I grew up with my dad as a parent, a parent who is positively mental about the stuff. I know enough about wood.

And I was bloody sure that what I was looking at wasn't something that he'd keep. It was re-pink-painted pine, and not a good pine either.

"We went to a salvage yard". We listened to her story about that.

Then we did the gardening and had a nice bottle of M & S Rosie. Tish and my Dad share something that my mum and I don't understand, so while they were off doing that we chatted.

Mum and I share something too, so as we talked  I started messing around with the work. Without moving anything that was already there, I introduced symmetries.

Mum is just out of four weeks of radio, I can see that she's knackered, I've been worried that she'd lose the will to live.

Taking a crappy old bit of wood and attempting to make art out of it assures me that her mind is in the right place.

I know that as she waved us off she was going to undo my changes as soon as we were out of sight.

I could kick myself for being so lax.

Danny poked me in the arm with a firm finger, "he's not OK", he pointed over my shoulder, we were at the back-gate having a fag. I turned and saw the wee boy eating his lunch in the bike shelter.

It was bloody obvious that we had a problem. No twelve year old should look so bleak and isolated.

"Have you seen anyone have a go at him?"

"No".

There is a process to go through. I flagged up the problem with guidance and explained to Danny what he should do when this happens again to some other poor sod, as it will.

I work in a good school, people care, I go through the motions because I know that it will make the right wheels turn ... still. Sometime you need to be creative.

Danny and I were having another fag.

"We're going to watch him?", I asked, twat that I am.

"What do you think?".

"We need to watch him."

The wee boy doesn't know it, and hopefully never will, but he has two, rather scary, old men watching over him.

See, that's the sod of the world: your fond imagining of what you think is going on isn't.

I'm lucky, I suppose, that in the normal run of things, it never occurs to me that people notice either me or my doings. In my head I'm almost invisible to others.

Today the school-nurse swaned up to my tank and asked, "neil, are you OK?"

"Yes, why?"

"As you came up the stairs you looked...", here she paused and made a gesture of a sweeping nature, "so desolute".

I was thinking about something else, what worries me is that she may be half-right about me.

I saw the Scottish Higher maths paper today. Odd thing I thought, then I thought about me and normal and had a rethink.

It certainly wasn't, the type, of question paper, that I sat nearly forty years ago—I know that because there were two questions involving the equation of a circle; something that we never studied in yore days.

There were a couple graphing questions that gave me a bit of angst at first glance—draw the graph of a derivative. But I wasn't doing the exam, so I had no panic, I got there.

I didn't work through all of the problems, but I did difficulty-rate them all.

Question seven seemed hard. It wasn't—it just poked into a blindness that I have: logs. For some reason I always need to work out how logs work when they dance onto my stage.

Perhaps more interesting was a question which I shrugged off—we were given a circle and a line which intersected, we were given their equations.

Next question we were asked to find another circle that shared that line as a chord, a reflection of the original circle through the chord.

I could see lots of ways of how to do this, [all rather reliant on the fact that we had a nice way to put things into the standard form, which I didn't check] but introspecting my way[s] I couldn't see anything fast. There must be a quick way to do this, otherwise they wouldn't have asked. Why can't I see it?

What I did like is that we didn't have that solid-battery [applied maths] of differentiation/integration questions that I faced.

Yes, I'm a pure maths man, but I thought that today's paper was a better test of maths ability than the exam that I sat of yore.

[There's a post to be had as to why I can do higher level maths, and yet I'm almost hopeless in some major areas of the subject.]

I always suspect a plumber who carries a bag full of hammers. I'm hopeful that our future geeks won't just know calcuus.

It was all going so well, I felt like I was in the groove, study-wise, [what Maxy calls the flex]. And then it all stalled. This weekend I've done nothing.

It all stalled at exactly the same place that it did on the last block—as soon as I had to start messing around with tiling cards and overlays. There's something about sliding sheets of acetate that I just don't enjoy. Probably because I'm hopelesser at it than your average five year old.

In front of me I have a huge brown-envelope [the Geometry envelope] filled with the damn things. I lift things for a living, but such is the envelope's weight that I only move it with due care for my back.

I have a tutorial next weekend, so I have a week to complete the unit. I'm not sanguine. I could just shut-up and stop parading my ignorance during tutorials? Still, me as a black affront in the stupidity stakes hurts nobody, and may be a duty for me.

Enough of this navel-gazing neil, do some work!

"You do realize that about twenty years ago we started staying in together", my wife said.

We don't, as a couple, pay too much attention to dates, [neither of us can remember when we got married] so this threw me a bit; she was being cheeky. I agreed; ie pretended to remember, then she took it too far, "so where are my flowers? You forget everything!" I flipped...

"I remember the first time I saw you, in that hotel that no longer exists. You were wearing a black shift dress, one of your dad's white cotton shirts buttoned all the way up, pink shin length socks folded down over your brown leather pixie boots. Your hair was straight and back combed. Your make-up was much the same as it is tonight except that your eye-shadow was bronze-brown and your lipstick was an off-scarlet..."

"It was the 13th of November, I'd been playing chess in Aberdeen, I was reading a book about the Sveshnikov...in fact, to this day, I can't see that opening without thinking of you..."

"What ear-rings was I wearing?" Trick question [she had a single black stud in her right ear].

"Do you remember what I was wearing?", I asked. Of course she didn't.

My life is a catalogue of regrets, but every time I think about how it might have been better I run into a huge problem—I might not have met my Tish. I'd put up with a much-much-much worse life if you threatened to take her away from me. It's more than that: there isn't a thing in the universe that you could give me that fills a Tish shaped hole. Love is a sodding nuisance but it's good that it's there.

Still, she should have remembered that I was wearing a Hawian shirt...it was bright yellow and featured pineapples

I helped a teacher rearrange her classroom today. After we'd finished we both agreed that there seemed to be more space. I pointed out that there couldn't actually be any more space, we hadn't taken anything out [and we didn't do anything 3-D]. But there was more space.

I went away for a wee ponder. The main change was that instead of ten blocks of three desks there was one big block in the shape of a square W.

Ah, borders and faces!

The original arrangement had eleven faces and ten borders. The new arrangement had only one border and two faces. Does this matter? Yes, I think that it does.

For example you want to paint a room, what do you do with the furniture? You shove it all together into the centre of the room don't you? You reduce it to a single border of the shortest possible length and the faces to two.

You don't get any more floor area but you get better connected space [not a proper term].

There's something topological about this...

I sit here, at the end of my holidays, amidst the detritus of papers/books/ashtrays/empty containers of the things that affect my mind/pencils and wonder where I am. That would be maths wondering.

I have, just over, four units left to do before June; I have two half-semi-fair-copy half TMAs done; I seem to be caught-up. So why the angst?

Because I've been here before.

As you delve deeper into maths you begin to find that you can't hide from your mind much, you get to know what you're good at, what you suck at, where you are lost. Why is this so?

• Everything that you do has to be supported by proof.
• You are constantly having to jump from the visual to the abstract.
• You need to put together results that don't appear to be related.

Anyway, bollocks as the above may be, I see that I'm approaching areas where, although I don't absolutely suck, I'm going to have problems.

I have a slight wiggle-space, should I go back to the basics of group theory? The answer is yes, the question is will I?

[This is a mid-think post about something that I will, maybe, write a more reasoned post about in my nonsense.]

For one reason or another I needed to look back through my blog posts—crivens, I have written loads of loads of nonsense, haven't I?

Anyway, I got interested in what I was doing/feeling this time last year—much the same is the answer. Is this a good thing?

Maybe, but in one sense very not—I can see that I'm falling [have already fallen?] into the same study-trap that I was in then: I'm not pushing myself hard enough.

For example, last night I was working my way through a group theory proof, I could see, in a general sense, what was going on. But I was skipping over details, you can't do that! Not when you're learning anyway. I wouldn't do this if I was reading code—then I would need to see what every line did.

The time has come when I either, need to get serious about maths, or decide that these maths is just a hurdle that I have to jump over in whatever way that I can.

If I decide the former [which I will] then I need to buckle down and start making this stuff mine. By which I mean that I need to be able pull together what I know in an organized fashion. At the moment there's too much, "oh, yeh I knew that" when I read the answer and not enough, "how do I get from there to there? What things do I know?"

I'm not explaining myself well here. That's the problem, I've worked on quotient groups for nearly three years now, could I explain them [and why they were important] to my wife? [She wouldn't let me.] Can I explain them to myself?

For the topology course I don't have the same problems, although I can see the problems approaching. [I just tried to explain something that I thought that I knew in the forums, fortunately I realized my error in time].

If you can't explain then you don't know.

Such a pest—everything that you know about them has to be proved. And the proofs tell you that everything that you know about them is true.

So waste of time? Not exactly, you need to be sure about these things. Obvious isn't always true when in comes to maths, or anything.

The proofs that you use for integers are pointers to the proofs that you will need to use where things aren't so obvious. That's what maths is all about—making sure that the bloody obvious is true or that you can prove the utterly unlikely and all points between. Or saying that the obvious is terribly wrong.

This is what I hate/love about maths—you can't hide from the truth. You can try, but some git will pull you up. And you are the first judge of whatever crap you're selling.

Well, I did, after all that's why Évariste invented all the groupy stuff for isn't it. What really shocked me was the whence where it came to the fore.

We were working our [my, me, singular] way through some sedate colouring problems when, and this is always a flag when it comes to maths, we began to develop a new notation. Suddenly there it was—a group action on a set of colourings can be modelled using a polynomial.

So now I have yet another hero... Polya

Every so often people ask me if maths is hard. To which I say that it isn't. If you've done the hard work.