64 Reasons
The number 64 has always had broad significance for me. I remember that when I was four and learning how to play chess from my grandfather, I counted the squares on the chessboard and always came up with a total of 64. To four-year-old me, the fact that such a large number of squares always came to 64, and that the board was always eight squares across and eight squares deep, was a minor miracle.
When I later became a qualified computing teacher, I had already learnt the importance of 64 as 2 to the sixth power. Take a '2' and double it, and on the fifth doubling, you have a 64. Nowadays, and probably for a very small window in the years ahead, the term '64-bit computing' is in vogue. Moore's Law seems to predict that computing power will increase exponentially along those lines, but there are all kinds of caveats which make this less of a law and more of a benchmark to be exceeded.
But I do remember the days of computers with only 1 kilobyte of RAM, and that allows me to see things with some sort of less excitable perspective. Computing power does indeed double all the time, but the human capacity for intelligence or stupidity (the other side of the coin) does not. We remain stuck at the high watermark of complexity and the low watermark of linearity. Linear thinking does not come naturally to humans unless the situation is rigidly constrained.
The other thing I always remember when pondering cognitive development in students is the way my parents educated me. Whenever I asked for something or said something, I was first mostly cautiously encouraged (well, sometimes discouraged and sometimes enthusiastically encouraged) and then challenged to provide reasons. 'Ten good reasons' became something I realised I would have to prepare in advance before attempting certain things.
I also learnt the repetition or deviation (and sometimes hesitation) were bad things. You tried very hard to speak at length for a few minutes, coherently and in a deliberately ordered manner, on a relevant topic for discussion. It wasn't till later that Dad introduced me to the late Kenneth Williams (and others) and Just A Minute, and I learnt why.
It's not easy to come up with 64 reasons for anything. But I've found that a good reason can be split into 64 bits. At this moment, I'm thinking of chessboards and multi-dimensional strategic games. I'm also thankful for the 64 questionnaires I received in a very short fortnight or so. They are bits of a big and messy puzzle which looks like it will be 100k words long.
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Oh yes. I have realised one thing for sure. The Age of Complacency concept applies in some pretty obvious ways to the education sector. And the fallout, while being harder to quantify, will be more severe.
When I later became a qualified computing teacher, I had already learnt the importance of 64 as 2 to the sixth power. Take a '2' and double it, and on the fifth doubling, you have a 64. Nowadays, and probably for a very small window in the years ahead, the term '64-bit computing' is in vogue. Moore's Law seems to predict that computing power will increase exponentially along those lines, but there are all kinds of caveats which make this less of a law and more of a benchmark to be exceeded.
But I do remember the days of computers with only 1 kilobyte of RAM, and that allows me to see things with some sort of less excitable perspective. Computing power does indeed double all the time, but the human capacity for intelligence or stupidity (the other side of the coin) does not. We remain stuck at the high watermark of complexity and the low watermark of linearity. Linear thinking does not come naturally to humans unless the situation is rigidly constrained.
The other thing I always remember when pondering cognitive development in students is the way my parents educated me. Whenever I asked for something or said something, I was first mostly cautiously encouraged (well, sometimes discouraged and sometimes enthusiastically encouraged) and then challenged to provide reasons. 'Ten good reasons' became something I realised I would have to prepare in advance before attempting certain things.
I also learnt the repetition or deviation (and sometimes hesitation) were bad things. You tried very hard to speak at length for a few minutes, coherently and in a deliberately ordered manner, on a relevant topic for discussion. It wasn't till later that Dad introduced me to the late Kenneth Williams (and others) and Just A Minute, and I learnt why.
It's not easy to come up with 64 reasons for anything. But I've found that a good reason can be split into 64 bits. At this moment, I'm thinking of chessboards and multi-dimensional strategic games. I'm also thankful for the 64 questionnaires I received in a very short fortnight or so. They are bits of a big and messy puzzle which looks like it will be 100k words long.
=====
Oh yes. I have realised one thing for sure. The Age of Complacency concept applies in some pretty obvious ways to the education sector. And the fallout, while being harder to quantify, will be more severe.
Labels: Cognition, Computing, Education, Intelligence, Kenneth Williams
etched with acid at 3:49:00 pm
2 Comments:
"To four-year-old me, the fact that such a large number of squares always came to 64, and that the board was always eight squares across and eight squares deep, was a minor miracle."
You remind me about the Hierophant's post about the Piraha ...
As a personal view, I just happen to think the reason why the Piraha lack words for a lot of colours that other languages would have words for, and the reason why the Piraha have such a simple number system is that after a certain point even as an adult, I'm sure you couldn't look at a heap and distinguish between n+1 and n-1 units -- and that n may be as low as 7 (when you take a quick glance).
Four-year-olds are in fact already quite linguistically sophisticated (i.e. they can be said to be speaking a full-fledged langauge) but even someone as bright as you found the idea of numerical constancy for large numbers a "minor miracle".
So it's really not that hard to see why a hunter-gatherer society who for hundreds of years may not have had reason to develop any sort of mathematics would not be able to distinguish between the number 6 or 7, and I suspect once you pass your formative years without math foundations it might be really difficult to pick math up later in life (critical window?)
I think that we invent vocabulary as it becomes necessary to us. If you live in a badly lit or visually indifferent place, 'light(ish)' and 'dark(ish)' or the equivalents are all you need for colours. If exact numbers don't matter, they won't matter.
However, if it becomes necessary (which is a different threshold for each person and in each set of circumstances that person is in), new vocabulary will be constructed for practical reasons. 'Whatchamacallit' and 'thingummy' or other placeholders are not exact enough at some thresholds.
Take for example the document found here. It shows that some people by circumstance of birth will have develop colour deficiency based on their environment. How do you think it will affect their language and culture?
The colour deficiency in this case is seasonal. This means that birth month will affect the individual's perception of the world. We accept that 'red' is warm and 'blue' is cool – but what if the individual perceives little difference between the two? Then the individual will have a different temperament and vocabulary from his peers.
Now extend the idea to different cultures from different places...
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