A Ball Of Blue Flame

English: 42, The Answer to the Ultimate Questi...

I didn’t speak before now about my last exam. The thing is, I’m really not sure how I did.

It felt good. I left the exam hall exhausted, elated, as if I’d given my all.

I just wish I could be sure that my all is the all they wanted.

I have no complaints about the paper. Couldn’t really have been better from my point of view. I was able to avoid the cost analysis question I dearly wanted not to do. It wasn’t a hard one; basically it’s just a sum. The problem was those two words – “cost analysis”. I had to stay alert through a whole exam, and just looking at them makes my eyelids droop.

The systems theory question on the other hand was all too exciting. Yes, seriously. It involved concepts that have interested me for a long time. Visualising the world not as discrete objects but in terms of interacting systems, flows of activity and information. Emergent phenomena – how all the complexity and wonder of life arises out of apparently simple chemistry, or indeed solid matter out of ephemeral probability. The danger with this was that I could easily blow the entire two and a half hours if I got hooked on a wild-eyed Idea.

So I began with the case study question, which retrod a lot of ground we’d covered in our projects. This made it easier, but had the downside that my head was preloaded with too many things I could say. And I think I said too many of them, because I spent over an hour on that one.

Thankfully, next was what’s known as a decision table. These distil a complex decision-making process into a simple table you can look up. You might – as in the example – be a college book shop trying to decide whether to keep some old titles in stock or return them to the publisher. There are a bunch of factors involved, how do you decide? Well here the table shows that if, for example, an edition is no longer current. but has been requested by staff, then the correct response is to keep it. Simplicissimo.

Condition USER RULES
1 2 3 4 5 6 7 8 9 10
Edition Is Still Current N N N Y Y Y Y Y Y Y
Old Edition Requested By Academic Staff N N Y
Any Copies Sold In Last 3 Months N N Y Y Y Y Y
More Than 15% Of Stock Sold In Last 3 Months N N Y Y Y
More Than 20% Of Stock Sold By Mid-Semester Y N N
Sales Manager Believes Book Will Still Sell N Y N Y N Y N Y
Action
Return Remaining Stock X X X
Consider Returning 75% of Remaining Stock X
Keep Remaining Stock X X X X X X

Why is the table so small? Having six conditions, each with two possible values – Yes and No – you’d think it would need (2x2x2x2x2x2=) 64 columns instead of 10. The trick is that some conditions make others redundant. Look at what happens if the Sales Manager decides a book will still sell. Their word goes, making all other considerations moot. By examining the logic in this way you can reduce the table to its essentials.

The problem then is making sure you’ve done it right. Do the rules really cover all possible situations? Could two different, contradictory actions be invoked by the same set of conditions? That latter is particularly significant because tables like these form the basis of computer programs, and when a computer is stuck between two conflicting responses it explodes.

Possibly.

Examining a table for logical consistency sounds scary, but when you boil it down it’s a puzzle not unlike a Sudoku. Having practised, I’d got the knack of solving them visually. Well, simple ones… That saved time which by now I badly needed. I’d left myself barely more than half an hour for all the theory. Things were now officially intense.

So I don’t recall clearly what I wrote… I do know though that somehow I got stuck on aspects of systems theory that bug me. Couldn’t I write a happy answer about the many aspects that I think are cool and interesting? No, apparently I can’t do that.

Really it was one particular lecture slide I was hung up on. This had compared science to the systems approach, contrasting them as analytical versus holistic, qualitative versus quantitative, so on. In other words presenting the systems approach as a counterbalance, even an alternative, to science. That struck me as just wrong; overshooting the holistic and heading into homoeopathic country. Or “needlessly messianic”, as I described it. (Which incidentally was the second entirely pointless Hitch Hikers Guide to the Galaxy reference I found myself slipping into these exams.)

In particular it described science as “reductionist”, which to me is to misunderstand it completely. Sure, science takes things apart and examines the components. But it doesn’t do that to understand the components; rather the objective is to see how they all work together – as a system. As a whole.

Holism is right there in science. To claim otherwise is to traduce humanity’s most important philosophical tool for one’s own obscure – or obscurantist – motives.

OK I didn’t say that last sentence, thank God. I was having a bit of a head rush but I still knew better than to condemn the subject I was being examined in as an evil conspiracy. I’m not doing English lit any more. And I don’t think that of course. What I hope I managed to convey is that I find systems theory attractive, but at the same time worry that this very attractiveness may make it dangerous. Is it a useful way of looking at the world, or a friend to fuzzy thinking? Well, I’m not sure – but I want it to be useful.

Maybe my suspicions were refreshing, maybe I’ll be marked down for insufficient imbibing of the Kool-Aid. In short, yet again I am certain that I either (a) did a really good exam or (b) plunged off the cliff in a ball of blue flame. One or the other.

At least it’s not dull.

All Systems Are Gone

Not Real Organisation Chart

Done. Just submitted my first ever systems analysis of a real company. It’s an assignment, I think it went OK. We (a team of three) freely admit we could have used more information than we had access to, but I reckon we probably did reach useful conclusions about the dangers this little software company faces – and what they might do about them.

Think it’s a good team. Funny reading the report afterwards; even edited together you can clearly see the difference in our styles. The others did things like bringing in detail and applying theory. My part is, well, narrative. I’m writing stories. Which is a little weird, but maybe it works. You need all of that in a report. It just maybe needs to be a bit more… blended. The sudden gear-changes from academic to emotive prose are probably more fun than they really ought to be.

Just one question remains. Why am I doing systems analysis again?

Mathematical Cabbage

Math - It's what's for dinner
Math – It’s what’s for dinner

It’s not every day you taste a new vegetable. Especially not one that defies the laws of space and mathematics. But yesterday I found just that at our local organic farm, Green Earth.

They have some exotic stuff there from time to time, even new potatoes that taste like – and I know this is hard to believe – new potatoes, but I was taken aback to see that they had fractal florets, chaotic kale, or to give it a name people actually call it, romanesco broccoli.

Fractals are a phenomenon of nature of course, and you come across them in things from fern fronds to snail shells. But you rarely see them so clearly in three dimensions. Or I should say, more than three. Imagine a wiggly line drawn on paper. It’s an idealised line, so it has only one dimension – length without width. Now we zoom in. Normally when you do that, the section of line you focus on will look straighter than the whole wiggle because you’ll see fewer twists and turns, or even none. But our line is strange. We find that when magnified it still looks every bit as wiggly as it did on the larger scale. It has wiggles within wiggles, smaller-scale twists and turns in between the big ones. This is called self-similarity, and it too is a natural phenomenon. A coastline is still wiggly whether you see it from space or look at where the water meets the sand through a magnifying glass.

If the line is more wiggly than it looked from a distance, that means that it’s also longer than it looked. So if you could somehow keep looking closer and closer forever, you’d find it was always longer. Isn’t that a bit weird? It’s just a line on a finite, two-dimensional sheet of paper, yet somehow it’s infinitely long. That leads to the idea that shapes like this wiggly line, similar on all scales, must somehow be more than one-dimensional – though still less than two. It’s one-and-a-bit-dimensional. Fractionally dimensional. Fractal.

Just as there are wiggly lines that are a bit more than one-dimensional, there are flat patterns that exist in more than two. And there are solid objects – like the romanesco in my hands – that occupy more than three. Of course it doesn’t really extend into some invisible extra space.  The fraction of a dimension is just a clever way of quantifying the self-similarity. Yet looking at it, I feel like I’m wearing 4D classes¹. The symmetrical complexity is fascinating and beautiful. Its spires are made up of spirals made up of spires, spiralling into spire upon spiral spire. Whorls within whorls. Amen.

And gently steamed for about fifteen minutes, mathematics is delicious. Especially organic mathematics.

  1. One red lens, one blue lens, one green lens.

An easy intro to fractals.

Leaving Us Confused

Histogram of sepal widths for Iris versicolor ...
This distribution of people who nod as if they know what graphs like this actually mean

Today is the day that bad decisions are made.

For it is the day that the results of the School Leaving Certificate Examination (the “Leaving”) come out. Today the students make bad decisions by getting drunk while still mostly underage. And politicians, by making promises.

Ten percent of students failed maths at ordinary level. In a knowledge-based economy that is simply not good enough, etc. Something must be done. Teachers must be fired, students must be fired, schools should be closed, opened or set fire to. Lessons must be made harder, exams easier, students must work more and take more time to rest. Draw your own headless chickens.

But… Isn’t the whole point of exams that some people fail them?

I don’t really think that ninety percent is so terrible a pass rate for an exam that, you know, is actually testing something. And not merely basic numeracy; the Leaving Cert ordinary-level paper is essentially a qualification to enter university, as almost all courses require it. So are we really in trouble if only ninety per cent of the population qualify for third level education? Less than sixty percent actually avail of it.

Could it be that the reason the public panic over standards in mathematics is that they don’t understand some basic mathematics? Because if they don’t… Wait.