RE: [MLUG - DISCUSSION] beginner slide rule wanted

[Mike Miller <EMAIL:PROTECTED>]

On Wed, 2 Jul 2003, Jonathan King wrote:

> Now, if you fast forward to 2003, it's clear that we're not in such
> great shape anymore.  Nobody really knows much about estimation or back
> of the envelope calculation, so there are way too many people who can
> give you 8 sig figs of nonsense and not have any clue what happened.
> And then you take away their calculator, and they are toast.

Is this different than it used to be?  Sure, people like you and me can
immediately say approximately what 23704 x 3864 is, and we could do that
back when we were teenagers, but most people can't do that, and most
people couldn't do that when we were teenagers.  Psychology students can't
do that kind of computation now, and they couldn't do it 25 years ago
either.

Here's what I think - and this is a really important idea that should be
considered widely.  I'm sure you'll agree.  We need to teach kids to do
this kind of in-the-head arithmetic.  We should cut way back on the
traditional arithmetic problems and focus on approximation.  When we need
the right answer, we don't do it by hand, so why teach kids to approach
problems that way?  How do we make changes in our school systems so that
arithmetic can emphasize approximation?

For one, we should be teaching kids to add columns of numbers from left to
right, not right to left.  Same for multiplication of pairs of large
numbers.  Long division is good as it is, I guess.  What else?

How can we make this really happen?


> So every year I walk students through the Tower of Hanoi Problem with a
> small number of disks, establish that the number of moves it takes for
> the n disk problem is 2^n - 1, and then ask for people to guess how long
> the 64 disk problem takes if you can do 1 move per second.

I do it as (2^10)^6 * 2^4 which more than 16*(10^3)^6 = 1.6*10^19 seconds.
But how long is that?  There are 3600 seconds per hour and 24 hours per
day so there are about 8.6*10^5 seconds per day and about 3.7*8.6*10^7 or
3.2*10^8 seconds per year.  So that means (1.6/3.2)*10^(19-8) = 5 x 10^10
days to solve.  That is 50 billion.

> The modal guess is usually off by a factor of 50 billion or so.  I
> submit that an error anywhere near this large would never happen to
> anybody who knew how to use a slide rule.

Is that because they usually say that it will take one full year?  It
isn't an easy inside-the-head kind of problem.  I would struggle to get a
good answer and I'm pretty good at that kind of thing.


> That's not to say that I think a slide rule is the only way to learn
> about how to do stuff like this, just that it is *a* way, and it's not
> clear to me that many better ways have come down the pike since the 70s.

Well, you have to think about the basis for slide rule calculation:  It's
the sort of thing I was doing above:  Using engineering number notation
(is that what they call it) where we use things like 3.65 x 10^2 instead
of 365.  Make students do this a lot and you'll be most of the way there.

Give them a lot of multiplication problems that look like this:

1.3 x 7.2 =

8.4 x 3.9 =

Make them give only two significant digits and make them do it in their
heads.  We can teach them to do this and it will be worth it.  They can
use it in almost any occupation.  They can even use it when grocery
shopping.

Mike
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