Friday, June 08, 2007

Maths and internal narratives - a random thought

I'm sitting at work, doing a bit of maths (something I'm not used to, although I should be), and it occurs to me how the process of doing maths has a very strong, single narrative: A plus B equals C, multiply it by this, divide it by that, integrate it, add a constant, etc., etc... concentrating on one single thing the whole time. And I'm reminded of a story which I've blogged previously (sorry, I'm doing this via email so can't manage links) of a kid in a young offender's institute who was freaked out by discovering he actually had an internal narrative... and I'm wondering this: modern society is very good at chopping up and scattering our attention over wide areas. You could argure that a lot of marketing is aimed at doing exactly this, in order to prevent us from thinking rationally and logically about things and promoting an emotional response (so much easier to manipulate, my dear). So, are we shooting ourselves in the foot? Are we creating an underclass which will never be able to conceive a logical train of thought, because the concept of the single internal narrative is completely alien to them? There have certainly been times in my life when I've struggled to focus on one thing and my attention has been scattered. Are there people for whom life is always like that? Does modern society promote such a state? Personally, I suspect so.


17 comments:

Andrew C said...

Yes - (we are shooting ourselves in the foot) - I think it's being encouraged - schools, TV, laws all seem to be dumbing down - discouraging people from putting any thought into their lives - It's much easier to deal with people who aren't causing a fuss, and don't expect better, and that's just how the governments seem to like it.

their competitor said...

It's not a matter of content being dumbed down. It is a matter of catering to the largest available pool, which was never interested in much of anything else, and is unlikely to ever be interested in anything else. And the "thinking man's" angst regarding this inevitable process is as new as the Greek philosophers, or maybe even the tale of the flood.

Wag The Baker said...

We definitely get a lot more visual and auditory stimuli than we did 100 years ago, but we are also a lot better at filtering it. To me the cost seems to be more in our ability to notice detail and less about our ability to concentrate when we want to.

Matt F said...

I guess you're right - there's nothing new in this. But it still strikes me as a bad thing that so many people are screaming for our attention, and yet want it for so little time. We tell each other stories all the time, but why do those stories have to be so short?

Paul ◘ said...

I was trying to describe the internal dialog to a collegue tonight. We were comparing our learning approaches, study skills, and accomplishments in statistics. We agree, there comes a point where one must yield to the depth of study material and allow oneself to become "stuck" on a concept, to refuse further reading and to revisit the concept until it makes sense; or, it never will make sense. You might say that, until you have an internal dialog that incorporates a concept the concept may as well not exist to you.

Our school system (where about half of students fail the standardized objective reading test, scoring less than grade level) cannot possibly teach soul searching: it is too busy trying to teach how to understand multiple choice questions.

XXXX YYYY said...

I can't remember a time when I didn't have an internal dialog. I do remember not being able to visualize, though. I was 8 or 9 and the class was discussing it. I thought they were crazy. Closing your eyes and seeing something that isn't there?

Paul ◘ said...

I don't get the point of that. Guided imagery, on the other hand, has been shown to be effective at combating boredom. Citation < click >. Also mentioned on page 118 are "Concept maps, venn diagrams and flow-charts for example assist students to make connections, notice distinctions and see relationships."

john smith said...

I challenge your childhood position as false, Steve. You would have been unable to form an expectation, if it were true. No anticipation of gifts, etc.

XXXX YYYY said...

I was perfectly capable of thinking about things. I just couldn't "see" them in my mind.

I can visualize now, though. Still, the two processes are distinct for me. Is that not true for other people?

Makes me wonder about this kid with the "voice" in his head. Perfectly capable of thinking but without an internal narrative. For a lot of people, the two are the same thing. For him, they're separate processes.

Matt Worldgineer said...

[tc] Is it time to give up on democracy then? Yes, the intellectual class has always been quite small compared to the population as a whole, but when democracy came along society tried to change that. Public schools didn't exist in large societies before democracy, and the entire point was to expand the intellectual class to encompass most of the population. Of course, this was required in order to make intelligent voting decisions, and not just be led by the most emotive leaders.

So, has this great experiment succeeded? Or have we fallen back into our old patterns as far as intellect, with our education systems ending up more to make productive workers than thoughtful citizens?

their competitor said...

Well, I think it's at best naive to wring our hands over the masses being manipulated into watching soaps or arm wrestling contests. The reality is that people tend to be pretty good at figuring out what they're interested in.

At some level, it seems that intellectuals view the results to date as a failure because the majority is not tuning in Bill Moyers or Masterpiece Theatre, but rather watches Idol or logs on to the Internet to find out what's the latest with Paris Hilton. But it is foolish, it seems, to have ever expected anything else.

The debates of the founders, people like Jefferson, Hamilton, where decided in large ways by extremely prejudicial press, and were played out in front of a largely ignorant populace.

So as always :) my take is that things get better over time, though of course we want to keep working on improving them.

Matt Worldgineer said...

//is unlikely to ever be interested in anything else.// //things get better over time//
So which is it? Is there hope for democracy to ever work the way it was intended, or are we forever doomed to have people vote to cut gas taxes because it costs too much to drive their SUVs to the monster truck rally?

their competitor said...

These statements are not in conflict. It only seems a conflict because after they are not voting the way you'd like them to vote. Or did you think the goal was to have them vote like you? :)

What's the point of democracy if an intelligent, considered opinion is the one you have? No need for votes at all, then?

john smith said...

Don't try to pretend you don't Arthur. That statement is a disingenuous insult to intelligence.

their competitor said...

Hector, of course we'd all like to be on the right side of the debate. I for instance, can't understand why we can't privatize social security, and instead cater to fears of old people on bread lines. Both sides of any issue have these kinds of thoughts all the time.

But it's good to remember that typically, the reason the legislation you want doesn't pass is NOT that the uneducated masses vote against it. It's that the educated opposition does its damnest to make sure it doesn't pass. And that's how it's supposed to be.

Tom Kimber said...

I know what you mean Steve - visualisation is something separate from thinking, just as internal narrative is. It's just a different technique. I'd hear someone telling me to visualise some thing, and I'd think "Yeah-yeah" having appreciated that I knew what they were talking about (the thing) - but actually "seeing" it is something that I'll only do if I really concentrate - it is quite relaxing, to imagine an object, turn it round in your mind and actually look at it - If people do that all the time naturally, then I'd be surprised - because it's quite an effort for me.

I do hold models in my head (maps are a good example) that I might navigate by traversing them in my head, but I wouldn't describe it as visualisation - I don't see anything, it's a spacial inter-relation thing, and I'd just as well do it with my eyes open than closed.

I've just thought of an orange, turning it round so you see the little green sprouty thing at one 'end' - it does come naturally - I've got my eyes open as I think about it, but I suppose you could call it visualisation. It would be different though (i.e. much harder) if I were to close my eyes and concentrate on actually "seeing" the same orange.

Paul ◘ said...

These last couple posts remind me how difficult it was to watch the GOP and Dems "separate but equal" debates among the current batch of candidates for president.

There are a number of reasons why legislators do poorly in bids for president, but high on the list is that the politics of representative voting is all wrong for executive decision making. The fact that "we all voted wrong" for different reasons is not, I suggest warily, too comforting for me.