Azure Jane Lunatic (Azz) 🌺 (![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png)
azurelunatic) wrote2004-02-06 12:55 am
azurelunatic) wrote2004-02-06 12:55 am
Weird vocabulary moment
Just ran into a worm that we'll have to watch out for with LF.
Neurolinguistic hackers (would-be) sure wig out over some bakeem* things.
I just was thinking about how to present the "When you have this stuff memorized, you will start to recognize patterns without thinking about it." I was punching numbers into the microwave, and thought about how I'd figured that the most effective way for me to heat the item for one and a half minutes was for me to input 90 seconds. How I automatically knew that thirty was half of sixty. Because I'd done that so much. Because I recognized it without thinking about it. And then I thought: Worm. Because, when we say that Little Fayoumis should always think about what he is doing, and then we tell him that it is a virtue to memorize things that have been proven so that he will not have to think about it -- what does that teach him to do? Does that teach him to not think about anything he is told to memorize? Does that teach him that when he is exposed to something a thousand times, he should turn his brain off? That the more a new idea is presented to him, the less it bears examination?
And how do we define things that should remain unchanging? Simple enough to say, "If it is established that X + Y = Z, every single time, without exception, then it is safe to memorize X + Y = Z as a fact." But, where do we draw the line to a kid who hasn't input a significant fraction of the world yet, what is solid and what is not? He's going to encounter negative numbers, and often they zonk out the minds of kids who don't live in subarctic climates. As teachers, we have the responsibility to say, "Learn this for now, but know that there are refinements that we'll introduce later, but now you can accept it, and we'll teach you where the exceptions are later. But first, figure it as if it doesn't vary."
When one's accepted that something is Always This Way, Forever And Ever Amen, one tends to ignore data that contradicts the hypothesis. Like, 2+2 = 5. Where the 2s are abstractions, that's absolutely fallacious, given something like base 10, not base ... erm ... the base where 2 + 2 = 5 is true. But for real-world situations, like if there are mice involved, 4 or 5 may morph into 25 with no warning. Granted, it takes a very closed mind to argue that two plus two equals four, when confronted with the squeaking, stinking reality of 21 baby mice and four adults in one suddenly-too-small cage. But surely there are more subtle applications, such as social rules or wierd physics moments or economics or any other science that deals with things as they are, while hemmed in by expectations of things as someone once thought that they probably were or should be.
*bakeem: from a created language, meaning odd, unusual, unique, weird.
Neurolinguistic hackers (would-be) sure wig out over some bakeem* things.
I just was thinking about how to present the "When you have this stuff memorized, you will start to recognize patterns without thinking about it." I was punching numbers into the microwave, and thought about how I'd figured that the most effective way for me to heat the item for one and a half minutes was for me to input 90 seconds. How I automatically knew that thirty was half of sixty. Because I'd done that so much. Because I recognized it without thinking about it. And then I thought: Worm. Because, when we say that Little Fayoumis should always think about what he is doing, and then we tell him that it is a virtue to memorize things that have been proven so that he will not have to think about it -- what does that teach him to do? Does that teach him to not think about anything he is told to memorize? Does that teach him that when he is exposed to something a thousand times, he should turn his brain off? That the more a new idea is presented to him, the less it bears examination?
And how do we define things that should remain unchanging? Simple enough to say, "If it is established that X + Y = Z, every single time, without exception, then it is safe to memorize X + Y = Z as a fact." But, where do we draw the line to a kid who hasn't input a significant fraction of the world yet, what is solid and what is not? He's going to encounter negative numbers, and often they zonk out the minds of kids who don't live in subarctic climates. As teachers, we have the responsibility to say, "Learn this for now, but know that there are refinements that we'll introduce later, but now you can accept it, and we'll teach you where the exceptions are later. But first, figure it as if it doesn't vary."
When one's accepted that something is Always This Way, Forever And Ever Amen, one tends to ignore data that contradicts the hypothesis. Like, 2+2 = 5. Where the 2s are abstractions, that's absolutely fallacious, given something like base 10, not base ... erm ... the base where 2 + 2 = 5 is true. But for real-world situations, like if there are mice involved, 4 or 5 may morph into 25 with no warning. Granted, it takes a very closed mind to argue that two plus two equals four, when confronted with the squeaking, stinking reality of 21 baby mice and four adults in one suddenly-too-small cage. But surely there are more subtle applications, such as social rules or wierd physics moments or economics or any other science that deals with things as they are, while hemmed in by expectations of things as someone once thought that they probably were or should be.
*bakeem: from a created language, meaning odd, unusual, unique, weird.
no subject
In base 4 however 2+2 = 10
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2 + 2 = 5 would be a diffrent number system altogether.
Sorry, feeling very math nerdy @ the moment
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We use base 10, and there are 10 digits, -
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Once we hit 9, there's no more digits, so we put a 1 in the "Tens" column, and go back to 0 in the "Ones" column. Simple stuff.
In my example before, 2+2=10 in base four, the freason is simple
The digits are
0, 1, 2, 3
so after 3, we add a 1 to the "fours" column (since it's base 4 and not 10) and reset to 0 in the one column, thus 10 (which would technically read as Four)
Binary is the same way, you have two digits, 0 & 1, and then you move to the next "column", so
0 - 0000
1 - 0001
2 - 0010
3 - 0011
4 - 0100
5 - 0101
6 - 0110
7 - 0111
8 - 1000
etc. 8 is a one in the "eights" column, and 0s in the 4 two & 1 columns.
Base 16 or Hexadecimal is also the same, adding the digits A, B, C, D, E, F to 0-9. so Ten in Hex is A. 10 in Hex is Sixteen. Two plus Two is always four, but 4 is sometimes 10 and sometimes 100 (and in base 3 it's 11)
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When I was very small, FatherSir taught us base eleven, with "cat" as the extra digit. I could count up to a hundred in base eleven more easily than I could in base ten.
Re: It could be math-ier!
By the way, I'm not sure if it's intentional but I think you stumbled upon an old math saying. "Two plus two equals five . . . for sufficiently large values of two." The are math problems where "2" isn't really "2" and always assuming that it is will get you in trouble.
BTW, using the above comment as an example you can see how you can replace "1" and "0" with "finger up" and "finger down" (respectively) to count from 0 to 31 with the fingers of one hand (or 1,023 with both). I do it all the time. Just be careful when you get to 4.
Re: It could be math-ier!
As a child I read a book which suggested that you should try counting up your grocery bills in hex and you'd be surprised how quickly you pick it up. I tried counting up my mother's, and was surprised how quickly I thought the guy that wrote the book was off his head.
Re: It could be math-ier!
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And FatherSir taught me the base-two finger trick too. There are advantages to being raised by geeks.
And yes, that math saying was the source of my 5.
no subject
One of them was 'lies to children' - where we tell children something that's actually quite untrue, because it's a 'good enough' explanation and they wouldn't understand the full explanation.
Some relevant quotes:
"The early stages of education /have/ to include a lot of lies-to-children, because early explanations have to be simple. However, we live in a complex world and lies-to-children must eventually be replaced by more complex stories if they are not to become delayed-action genuine lies."
"Lies-to-children is simply a prevalent and necessary kind of lie. Universities are very familiar with bright, qualified school-leavers who arrive and then go into shock on finding that biology or physics isn't quite what they've been taught so far. 'Yes, but you needed to understand /that/," they are told, "so tat /now/ we can tell you why it isn't exactly /true/.'"
"When you live in a complex world, you have to simplify it in order to understand it. Indeed, that's what 'understand' means. At different stages of education, different levels of simplification are appropriate. Liar-to-children is an honourable and vital profession, otherwise known as 'teacher'. But what teaching does /not/ do - although many politicians think it does, which is one of the problems - is erect a timeless edifice of 'facts'. Every so often, you have to unlearn what you thought you already knew, and replace it by something more subtle. This /process/ is what science is all about, and it never stops. It means that you shouldn't take everything /we/ say as gospel, either, for we belong to another, equally honourable profession: Liar-to-readers."
It's a good book, BTW, very well written for people who don't have backgrounds in the hard sciences, but at the same time doesn't do too much hand-waving and ignoring of the background.
The main thrust of the lies-to-children stuff is that it's important to accept their utility, but not to become hung-up on the lie. It's all about adapting and expanding as you - or the child - become able to handle another level of complexity.
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The book lists a few examples of when lies-to-children are used. The first one (where the authors go into some detail) is about rainbows. The explanation everyone knows (light refracting through raindrops like a prism doesn't actually explain what you see. It seems to make sense, but it's not the whole story.
A quick list of the other examples: "the idea that the Earth's magnetic field is like a huge bar magnet with N and S market on it, the picture of an atom as a miniature solar system, the idea that a living amoeba is a billion-year-old 'primitive' organism, the image of DNS as the blueprint for a living creature"
Some of those lies-to-children never get replaced by more complex explanations, unless you specialise in a field (or do specialised research off your own bat).
When your kids are at school, they're going to be taught this stuff - although it is good that they'll at least know from you and Mark that sometimes thing they're taught are just stages toward learning something more complex.
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My kids don't go to school, hon. Though this new one probably will have to...but Mark's kids will be home-schooled 'til they hit college, by which time they will have learned how to think for themselves. Grace is already very good at questioning things, at 9...and Christian, at 10, was *more* than capable of thinking for himself.
And those *are* the kinds of lies-to-children that I was saying that we don't use. When telling children about the light refracting thorugh raindrops, for instance, it is pretty much always stated right along with it that "this is a *simple* explanation - it's more complicated than this."
My mentioning Santa was an example of our *reasoning* for never lying to the kids.
Stop Thinking!
Enrico Fermi was famous for epynomous problems where he would
estimate, from very rough data, very close approximations of what would turn out to be the correct answer from careful measurement. One trick was to round all estimates to single significant digits. "Pi = 3, a mile is 2000 yards, a gallon of water weighs ten pounds ..." Another was that his arithmetic would never be better than his starting estimations.
"That's an acute angle, acute angle equal Pi-over-four radians; that equal .7; the sine of point seven is ALSO point seven ..."
It wasn't that he wasn't thinking but he was thinking about the situation and not the mechanics of solving it. Each of the simplifying assumptions was, technically, a lie. But they were convenient lies for the purpose. They freed up brain power for other use.
The Stop Thinking tool _CAN_ be APPLIED badly. "How long would it take me to kill every buffalo in a herd that stretches over the horizon?"
(Begin thinking) two yards per head, times about 2000 yards per mile, times 7 miles to the horizon gives a herd of 7000 buffalo if the herd was running single file ... Er, there are 3600 seconds in an hour so ... so two hours would give 7200 seconds so if I fired once per second I could only thin that herd by one file, or in ten hours by five files -- this herd is more than five buffalo wide.... I cannot complete task today. (STOP THINKING) Shoot until tired. (Fail to engage thought on days two thru buffalo extinction ...)
It is a typical human failing to approximate "any very big number" by "infinity" and causing a STOP THINKING instruction to execute in a background process. The principle advantage of scientific notation is to conceal the verybigness of certain numbers so as to allow processing to continue, (the scaling suffix to be re-attached at the conclusion.)
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