You know the problem with the world
today? I'll tell you what the problem is.
It's kids today.

The problem is that kids start using
calculators quite early in school. This
has
two adverse consequences. First, they
fail
to develop an intimate acquaintance with
numbers - the sort
of thing that tells you
that 81 is divisible by three, or that
fifteen
fifteens are 225, or that two eighteens
are
thirty-six.

Second, and worse, they fail to develop
an
understanding of magnitude. If they
multiply 0.17 by 207, they don't have any
intuitive expectation of whether the
answer will be about 3.5, about 35 or
about 350. This is a severe handicap
because, even when using a calculator,
it's
easier to drop a zero or misplace a
decimal than it is to mis-enter or mis-
read
a digit, and the results are
magnitudinally
catastrophic.

I'll tell you what the world needs. What
the world needs is the MaxCo Pointless
Calculator.

The Pointless Calculator has no
trignometric functions. Nor does it do
natural logarithms, square roots or
anything else aside from basic
arithmetic.

It does, however, have one thing that no
other calculator has: a missing decimal
point. Neither the keypad nor the display
includes the decimal point.

You want to multiply 1.7 by 207? OK,
just
do 17 x 207 and get 3519 as your
answer.
It's up to you to figure that this means
35.19, and not 3.519 or 351.9. You
need to know 22 divided by 3? You get a
7 and then as many 3's as the display will
hold. Leading and
trailing zeros are dropped, so an
answer of 137 could be 0.0137 or
137000. Go figure.

Addition and subtraction are a bit trickier
(17.6 minus 4.25, for instance), but it's
up
to you to figure that out too: just do
1760
minus 425 to get 1335, then think about
it
to realize this means 13.35.

Instead of starting to use calculators
after
only minimal experience with hand-to-
hand arithmetic, children would progress
on to the Pointless Calculator, and would
have to stick with it until they started to
need trigonometric functions and other
things that won't work without the
decimal
point.

I'm not surprised to find a book about
*collecting* pocket calculators. What
beggars belief is that someone found it
necessary to write a book on *how* to
collect them. I mean, (1) get calculator
(2)
repeat. Worms fail me.

[EDIT] Ah. I see from the link that it's
actually a "Collector's Guide to Pocket
Calculators." Obviously aimed, though,
at the single collector.

But I never grew up with calculators - I only had one in my last year of school (a nice vacuum-flourescent display Casio with the basic four functions). So I've done maths at school the manual way, for the most part. There's absolutely nothing about 81 that suggests that it is divisible by three. It might be, it might not - who knows. I'd have to try it and find out. The number itself, the shape, the size the position, doesn't offer any clue. Exactly the same with fifteen fifteens - they may fit nicely into 225, or they might not. Who can possibly tell just by looking at it? The number itself doesn't carry that information on it. I don't have that information. I'd have to go and get it.

I still remember seeing one of the first pocket calculators in my maths class. the lesson stopped so that everyone could play with it. I think the battery lasted nearly a whole hour.

//There's absolutely nothing about 81 that suggests that it is divisible by three.\\

Yes there is, it only nine(three threes) away from 90.

8+1=9 divisible by three.

72, 7+2=9 divisible by 3

as is 36 and 27. also 18.

39 is three threes away from 30 and 3+9=12=3 times 4.

42, 4+2=6 divisible by 3.

(by divisible I mean that it can be divided by, is that the right word?)

Anyway, when you learn litle tricks like this you can greatly improve your guessing skills. Guessing the outcome of sums becomes second nature and some people can do this to an astonishing level.

All people who are extremely good at doing sums in their heads do not really calculate at all. They make a guess first and then fine tune it to the exact answer with tricks like this.

I am not particuraly good at it myself, but being a bartender I can calculate the price of an order like: 3 beers, one coke, two white wines and a mars bar, quicker then the cash register. (it's 11,30 euro's).

I can do this partly because I know by hart the cost of multiple drinks so I can make a guess and partly because I use little tricks.

Now my grandfather, he could do any sum that I put to the pocket calculator quicker than I could type it in. By the time I was ready to press =, he told me the answer to sums like: 235 times 567, or 5874 divided by 456. He did not calculate the sums step by step but he just sort of knew the answer straight away.

Also compare the chinese practice of counting with a sort of rack with beads on (don't know the proper name) that shift from left to right and have different colours. People who are good at this can do summs into the millions and billions much faster than we can with a pocket calculator.

I bun this idea for two reasons, the sentiment and the title, even though you use points where we use comma's and vice versa.

Oh, and what [UnaBubba] said to. (also I would like an option to always say what [UnaBubba] said unless I don't agree.)

On estimation skills: imagine you have a thousand steel balls with a diameter of one millimeter, how much would they weigh?

I don't know exactly but people tend to say a kilo or ten kilo's or something like that.

Now take ten of those balls and lay them in a straight line, you get a line of a centimeter. Put nine more lines beside it and you have a square centimeter with a hundred balls. Put nine more square centimeters on top of that and you have a cubic centimeter of one thousand balls. About as big as your finger tip. Can't weigh more than a couple of grams right?

-refrains from further annotation with difficulty-

4.11 grams (assuming 7850kg/m3 for steel).
(Yes, I'm a geek and I had to use a calculator; and no, I wouldn't have guessed anything close to that small.)

Fantastic. Now just take everything you said about kids not having any intuitive understanding of mathematics, physics, etc, and apply it to university graduate engineers. Scary, no?

Well I assure you it is the case, for a large number. Having come out of uni a few years ago I was appalled at the skillset some of my fellows had. I mean, give 'em the right equation, or proof, or whatever, or a computer FEM programme (note spelling - :) and they'll be technically excellent. It's like rote learning on a massive scale.

But on many occasions I was wittness to some astounding, <and rather terrifying, if you think about it) examples of obliviousness. For examples, our tute group was given some menial computer-modelling tasks, like what is the failure load of beam x, or max rpm of conrod/piston system y, etc. These children can whip up the 3d model in minutes, apply loads and constraints, mesh, and hit the go button quicker than you'd beleive.

Then blithely hand in a report that says max rpm for a formula 1 engine is 10 million Rpm or some other such nonsense - because they'd put the wrong loads on, or meshed badly, not thought through their constraints, etc. There is no logic clause in their instinct that says "hold on, that's not right". Mere weeks later these kids were unleashed into an unprepared society.

Now it's not their fault, it's the system - clever kids being taught not to think. I beleive tools, if not the same as, but certainly along the same vein as the one above would help enormously.

81 divisible by 3? Useless trivia in the real world, unless you happen to be a shop keeper stacking 81 products 3 high.

In my experience, 81/3 just isn't going to come up much more frequently than 80.9343 / 3.1417. You might start off with round numbers, but mix a bit of metric with imperial, have to use diagonal lengths or curves, move out of 2D, etc... and you are immediately thrown back to doing long division or using a calculator.

Granted, the 2^n series is useful for computing, division by 12 is useful for building and division by 14 good for cooking but none of those are division by three...

I'd hope someone in a technical field would instinctively know that 81 was divisible by three. Or at least work it out in <3 seconds. I get your point with the pi-times-table, but I know a 2m dia pipe has a circumfrence of 6-and-a-bit metres. I've seen a workshop engineer have to fetch his calculator to work out that a 6m sheet of steel won't go all the way around.

Hey, I'm all for not remembering useless information. Rote learning is dangerous, and I keep any impiortant data/equations in a book, lest I misremember. But simple is simple. If you don't work with numbers daily, fine, no probs. But I get worried when I see teachers counting off numbers on their fingers, and misspelling simple words. It's good to have a feel for things, if only so your bullshitometer is working.

Isn't a calculator with no decimal point a Slide Rule?

Also, knowing 81 is divisible by 3 is nothing - the Indian mathematician Srinivasa Ramanujan had an intimate knowledge of the properties of a vast number of numbers - as in the famous anecdote told by the British mathematician G. H. Hardy: "I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways." (see link)

//The problem is that...//
We know... *everybody* knows, but with a calculator they can get through school faster and after that it's (nominally) *their* problem... Sad.

//imagine you have a thousand steel balls...//
answer: weight of a steel sphere with a 1cm diameter: it's a word "trick"; when you hear the phrase "steel ball" do you think of something that's in the order of a 1 mm dia?

//counting with a sort of rack with beads on//
abacus - I keep meaning to pick one up to see if I can get faster on one of those than on an adding machine.

[-]'d though, I think you should just take them away. There's no reason a gradeschool student needs a calculator.

Perhaps one could have a calculator which could do some arithmetic, but anything above "4" it represented merely as "A Suffusion of Yellow". You could still use it to do arithmetic, but you'd need to remember how many tens you shifted it by.

Wow - turn your back for a few hours
and the annotations pile up. All seem
to be valid - I'm just saying that
inability to estimate magnitude (and
consequent tendency to make
spectacular errors to several significant
digits) is too common, and commoner
now that people have less hand-to-
hand experience with numbers.

And Hippo, yes, a pointless calculator is
a slide rule. See "Digital slide rule" for
details....

//81 divisible by 3? Useless trivia // Not
at all. Familiarity with numbers (including
magnitude) is like being able to play the
piano: it's different from knowing where to
look up the fact that middle D is two
semitones above middle C. To take
another analogy, I can follow a flight
manual for a 747, but you wouldn't want
to fly with MaxAir.

If you want to improve kids' basic mental arithmetic, put dartboards in all classrooms. Once they get hooked on the game, they'll be adding up triple 17, double 12 and 15, and subtracting it from the 166 they were on before to figure out what 'out' they're now on in no time.

When the first calculators started showing up in school, my math instructor made a requirement for anyone who wanted to use one in class: doing a page of 72 addition or multiplication problems in 60 seconds, with no errors.

At first try, we all thought he was crazy. Nobody could do that. But we gradually learned the tricks - start right, work left, alternate directions across the page, eyes two problems ahead of pencil, etc. - in a little under a month every single person in that class was able to do it. That even included some who... well, some from whom you'd expect less.

Some of the kids stopped pestering their parents for calculators, since there wasn't anything the calculators could do that they couldn't. Others <grin> decided that a four-function wasn't going to be of any help, and we needed the top-of-the-line scientifics.

(Couple of years later, that teacher got canned for "making unreasonable demands of his students". Subsequent teachers, while more popular, didn't get better results.)

Geography teachers, individually and collectively, have widely expressed sadistic character traits, and uncanny accuracy when throwing blackboard erasers; most of them are florid psychopaths who were found to be far too violent, aggressive and unstable for the Royal Marines, the Police service or professional Rugby, and so were channelled into Geography teaching as a sort of covert care-in-the-community, where their behaviour will not be considered unusual. Placed in an environment with no practical limits on their eccentricities of behavior, they rapidly degenerate into power-crazed, megalomaniac bullies, gaining malicious glee from the pointless torture of students who have the misfortune to be cast into their evil clutches by a brutal and uncaring society.

Yes he does. In darts, you're "on an out" or "on a finish" if you can finish in your next turn at the board (i.e. with your next three throws). Highest possible out is 170 (triple 20, triple 20, bull), then 167 (triple 20, triple 19, bull), but as Jinbish mentions, it's not possible to finish from 166 in three darts.

On the other hand, the player I mentioned, if he's any good at mental arithmetic, will know he's now left on 76 after the three throws he just had, leaving him various possible options next turn, e.g. 20, 20, double 18 or triple 20, double 8.