Pure Maths

I suppose that this is now getting serious—out of my comfort zone. Good.

Or, an impure boy’s continuing journey towards purity.


getting to know you M208

It always ends up thus—me squatted on the floor messing around with cut-out bits of paper. Yup, Group Theory and Symmetry. This time it’s a wee bit worse as we were supplied with, what’s the word, nets for some Platonic solids. You know the sort of thing, don’t you? So glue, knife, cutting mat and multitudinous uses of the word ‘bugger’ will feature here, at casa anderson, soon.

After no thought I decided to just tackle this course as I always do—a fast, shallow, reconnoitre of the terrain. So I’m already getting into the Group Theory. Hence the bits of paper—we always start with symmetry when it comes to Group Theory. But…

the introductory block

Was interesting. Mostly it was about stuff that we covered during MS221, there was new material. Enough new material to be getting along with, enough to get my brain re-engaged with maths. Rather too much re-engaged—with the fervour of the learner I began posting tosh [that would be a different type of tosh] on my computer course-forum. Enough to make my mornings slightly more hellish.

I keep a book, usually of an improving nature, by my bed at all times, so that when I wake I can, immediately, read it, rather than think about all of the wrong things that I’ve done yesterday. Until after my breakfast.

Still, I suppose that I should appraise you of what’s involved. The books are labeled thus:

  • Real functions and graphs
  • Mathematical Language
  • Number systems

None of which precisely describe what’s ‘in the tin’. Let’s take Number systems:

  • Real Numbers–ok
  • Complex Numbers–ok
  • Modular arithmetic–well…I suppose so
  • Equivalence relarions–fuck off

Then what do I know? The best thing about learning stuff is that you become aware of your ignorance. I shall always be stupid and I glory in that. But I’ll retain still the right to nit-pick at you.

Karma—snow is falling. Heavy snow.


ratcheting it back up again

Over the past couple of days I’ve been trying to get myself back into the maths-groove. Shockingly I’ve allowed my maths-brain to atrophy rather badly, I haven’t done any maths since October, and it shows. Worse, perhaps, is that my hands seem to have forgotten their business.

Mathematics, like mechanics, or programming, or writing, isn’t something that you can learn just by reading about it—you have to do it. And when you do some thinking-things your hands learn alongside you. You’ll then rely on them to ignite the mind—you sharpen the pencil, you shuffle the paper, you moisten the throat, you apply pencil to paper and the mind kicks in—the hands have started their moves.

Well in my perfect world perhaps. Still I’m a firm believer in the value of externals when learning. By which I mean the props that we use to support our learning. For me, for maths, this is mostly a pencil and a lot of paper—to teach my hands. Others use other tools—visit the OU blogs and you’ll find a hundred variations on a hundred techniques. But not everybody can use tools—how does Steven Hawking study? [If he has to.]

Well, maybe he doesn’t use tools/props now, but I’m willing to bet that he did. Perhaps he now uses ‘mental’ tools, tools that us, mere mortals, are unaware of. As we grow, the plastic bucket-and-spade that we, once, took to the seaside may no longer suffice; the sharper, bigger tools that were once denied us may be what we now need.

David Bronstein, the nearly world chess champion famously used to analyse using the display board, that’s because he was one of the best chess players ever, not a good reason for us to do the same. And in this case I know he didn’t start off this way—you have to get very-very good at chess before people care to start following you on a display board. This couldn’t have been his teenage behaviour.

One of the great moments of my life was playing a chess-congress in Livingstone in the early nineties. Such things are such things—things you do to play chess. But when Dad and I arrived there was a buzz—Bronstein was here, we were in the same room as a ‘Great’. He was a truly gracious man who spent many hours going through others’ games. Personally I didn’t learn anything—Reimann drops into your maths club? Talk well-over my head.

So we must always be looking at our toolbox—proverbially if all you have is a hammer… Perhaps it’s time to be looking at mine?



After journey worthy of a Homeric ode the books arrived. So, now that I’ve got them, what do I think?

Yesterday we were entertaining the in-laws so I didn’t have a chance for an in-depth perusal—all I can really say is that there seemed to be a lot of them—I strained my back lifting the box. [There were videos and audios too, but I, almost, never use these so we’ll ignore them.] The one thing that I did notice was that there seem to be two blocks devoted to group theory, good. Nay, great.

I like group theory [my maths hero is Galois] but I only ever managed to get so far with it—at heart I’m lazy. No, that isn’t quite right, but without some kind of outside pressure I can’t/won’t/don’t focus. I get distracted, I wander off.

One of the hardest things in this life of ours is to be honest about ourselves. Indeed should I live to be a hundred I’ll still find myself telling myself lies about myself. But I am beginning to become honest about the way that I learn—the OU does that to you. [Take this beautiful piece of honesty—one of the most thought-provoking things that I’ve read in a long while.] I now know that I have to trick myself into learning. Think about that. Bit odd isn’t it? Trick yourself! Can you imagine what it’s like to live inside my head?

But then we are all odd in our own unique way. One of the great joys of this online-learning life of ours is that we get opportunities to inspect the oddnessess of others.

I’m chaotic, others are different and they fascinate me. Let’s take, for example, Chris and Nilo, they’re both have distinct styles of learning and I’m a wee bit in awe of both.

For the sake of a point I’m going to eschew subtlety here—but you’re grown-ups, you can ignore my abstraction of truth and make up your own minds.

For Chris it’s the book. I have a collection of ‘old’ maths books but for me they’re never the starting point—they’re merely a source of exercises. I couldn’t take a maths book and work my way through it. Chris seems to do this without effort.

For Nilo it’s the tools. [This is a gross calumny, Nilo is one of the most probing (that’s not quite right—universal?) mathematicians that I know of, but point!] He submits PDFs for his TMAs. That’s dedication. He watches videos, he has maths applications, he approaches maths from every angle that he can. I can barely bring myself to use Wikipedia.

They’re different for me, I’d like to be like them—but I’m not. But we all share the same fountain of joy: maths.

That’s the lovely thing.


the books came…then…went

They almost got here—so close…but so far.

Those of you who follow this tosh will, at this point, be expecting an acerbic rant about the incompetence of delivery drivers—not going to happen. Why not? Well because this ‘OU journey of mine’ has made me a better person. Actually not so, but I have learnt some things.

My house was built after the other houses in my street and is numbered strangely. What, I think, happened was that the driver had lost the ability to see my house. He’d made an assumption about the way the road was numbered, one that was normally reasonable, it was just that it was wrong in this particular case. At which point, to his mind, my house didn’t exist; because it wasn’t where it should be. This happens to me all the time—I create a mental-picture out of who’s frame I cannot break.

I started this ‘OU journey of mine’ with the intention of learning how to, properly, do what I did for fun—computing; to be able to understand what other people said/wrote about said subject and to stretch my flabby mind. The mind has been stretched—I just hadn’t noticed how far. Most of that progress has been down to the rigour imposed upon me by mathematics.

One might think that creating programmes/applications would impose the same discipline—doesn’t. You can write arse-code that works, all-too easily, alas.

During one of my early maths tutorials someone asked a rather searching question [although I didn’t realize the searching nature of it at the time] of the tutor. I was surprised at what happened, his face went blank for about sixty seconds before he gave an answer. I now see that he wasn’t searching for an answer—he was searching for a way to explain it to us! He saw what we didn’t—we weren’t ready for the real answer. That’s how I want to be.

I may never get there, for now the road itself is enough. There have been a couple of times this year where I gave a considered response where once there would have been flim-flam bullshit. I’m prouder of that than of anything else I’ve done this year. More of those moments are more important than the letters that I might get after my name. I suspect that it will be easier to get a degree than to be who I want to be.

Kay [in system] would say ad astra, but for me it’s always going to be per ardua. To tell the truth I’m looking forward to the per ardua.

Hello M208!