Peter Gold wrote:

> If legible cursive writing was the sole measurement of ability, I'd
> be in the same boat as many doctors - floating off to oblivion.

Me too - it takes me longer to read my shopping list than to get my 
groceries... ;-)

> However, I'd qualify Marcus' comment about using one's phone for
> complex calculations. If you don't have the knowledge to derive a
> statement of a need for calculating a solution by using observation,
> experience, and analytic thinking, and lack the knowledge to present
> the problem statement to the calculating device, then, unless the
> device itself has the intelligence to do it for you, and is willing
> to do it (think "I'm sorry, Dave, I can't do that") it's whether it's
> the original calculus (stones used as counters), abaci, or iPhones,
> it's useless.

Yes, I agree with that, and I suspect that Dan may as well. (Dan, I hope 
I don't misrepresent your opinion in this post - I mean "Dan" 
metaphorically rather than personally.) The thing that's changing is 
that the internet is providing those devices, so we're able to get 
correct answers without really understanding what the question was.

Take a mortgage calculator - you can pick a mortgage product, plug in 
the amount that you want to borrow and it will tell you what your 
monthly payments would be. It knows that the product you chose attracts 
an initiation fee and that for the amount that you wish to borrow, the 
bank will give you the mortgage for 25 points less than the standard 
interest rate. At a deeper level, it knows that the repayments are based 
on the assumption that the fee will be paid out of the amount borrowed, 
and numerous other details. I don't know about anyone else, but I don't 
want to know those things - I want to know if I'm in the ballpark.

Dan might question the accuracy of the calculator and the inability to 
cross-check it (especially if he was a Floridian voter... :-) and I 
would agree with him. The average person will lose the ability to do 
these calculations, but in order to create the calculator, someone will 
always have to understand how to do them. The same applies for writing, 
I suspect - most of us will be able to muddle along, but specialist 
writers will always be required.

This does leave us with a gap in our knowledge - we have no choice but 
to trust the calculator because we couldn't figure it out if we wanted 
to. I'm less concerned due to a combination of factors - I don't really 
care in the first place, I'm fairly certain that given the vagaries of 
the bank's policy I wouldn't be able to figure it out anyway and 
finally, I *want* the bank to tell me how much it will be. I can put 
much more faith in an answer that they provided than one that I worked 
out for myself.

> My mother's criticism of the multiplication table matrix printed on
> the back cover of my grade-school composition books was, "You'll
> never learn to multiply by yourself, if you can just look it up!"

Multiplication is an interesting case of abstraction in itself. 
Mathematicians (which I am *not*) regard multiplication to be shorthand 
for addition, but we don't teach that to kids. The question 5x6 can also 
be posed as 5+5+5+5+5+5, but the multiplication version is less verbose, 
so we pretend that they're different operations in order to make it less 
confusing. Well, that and the fact that the addition table matrix would 
have required a substantially bigger back cover...

> One of the sequences bore out the premise that even young kids can 
> figure a lot of this (learning to use the computers to write, look for 
> information and learning to use it) out for themselves, and help others 
> to do it.

It's hard to even imagine the next couple of generations of computer 
users. I'll get out of computers before then - it'll hurt my brain way 
too much trying to keep up with a grade 6 programming class...


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