

Feynman vs. The Abacus - js2
http://www.ee.ryerson.ca/~elf/abacus/feynman.html

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drostie
There's actually a really sneaky moment in here which is not totally revealed.
Feynman says that he first works out 12, then 12.002, then the man with the
abacus says "12.01!". He asks for more digits.

What is sneaky here is that 12.002 is a very rough approximation that Feynman
is making before doing a long division. He has the formula of

    
    
        12 * (1 + 1.03/1728)^(1/3)
        ~= 12 * (1 + (1/3) * 1.03/1728)
    

But he simply hasn't had the time to do the long division yet and has just
approximated 1.03 / 1728 by 1/2000\. At this point he has the formula, and
quite possibly even knows that the error goes like - 12 x^2 / 9 which would be
something like one part in a million, but he wants to do his long division to
get the extra decimals to show off.

There's actually a slightly more slick way to get to this where you start from
12 and compute:

    
    
        (2/3) * guess + (1/3) * number / guess^2.
    

The 1/3 and 2/3 are chosen to minimize the error, and you wouldn't know this
if you've never worked it out. (I only worked it out because I would
occasionally be stuck without a calculator on exam problems.)

It works really well on these sorts of problems; you compute 1729.03 / 144 and
aside from the leading 12 you get:

    
    
        0.0071527777...
    

You divide this fraction by 3 to get:

    
    
        0.002384259259...
    

which is precisely as far as Feynman got, but the reasoning is much quicker.
If he'd been even faster with this he might have been able to apply guess =
12.002 to get another couple of decimals in the same time.

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GuiA
Slightly offtopic: The abacus is a fascinating tool; often considered an early
prototype for tangible interfaces.

"Among other historical inspirations, we suggested the abacus as a compelling
prototypical example. In particular, it is key to note that when viewed from
the perspective of human- computer interaction (HCI), the abacus is not an
“input device.” The abacus makes no distinction between “input” and “output.”
Instead, the abacus beads, rods, and frame serve as manipulable physical
representations of numerical values and operations. Simultaneously, these
component artifacts also serve as physical controls for directly manipulating
their underlying associations."

(Brygg Ullmer, PhD thesis, MIT media lab)

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gmu3
I think Nicholas Carr made an interesting distinction in The Shallows about
the usefulness of tools in the context of short and long-term memory
(interesting even if I feel ambivalent about it):

"In freeing us from the work of remembering, it’s said, the Web allows us to
devote more time to creative thought. But the parallel is flawed. The pocket
calculator relieved the pressure on our working memory, letting us deploy that
critical short-term store for more abstract reasoning. As the experience of
math students has shown, the calculator made it easier for the brain to
transfer ideas from working memory to long-term memory and encode them in the
conceptual schemas that are so important to building knowledge. The Web has a
very different effect. It places more pressure on our working memory, not only
diverting resources from our higher reasoning faculties but obstructing the
consolidation of long-term memories and the development of schemas. The
calculator, a powerful but highly specialized tool, turned out to be an aid to
memory. The Web is a technology of forgetfulness."

~~~
zwischenzug
That's a great quote, and articulates something that's been bothering me about
the web and why I've increasingly withdrawn from it. I find the web is a great
tool for fishing for stimulus to further thought, but at some point I need to
get away from it to develop skills in a way that feels slower, but is actually
deeper.

To use an office metaphor: it's a great water cooler, but you can't write your
report at the water cooler.

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stcredzero
_> I realized something: he doesn't know numbers. With the abacus, you don't
have to memorize a lot of arithmetic combinations; all you have to do is to
learn to push the little beads up and down. You don't have to memorize 9+7=16;
you just know that when you add 9, you push a ten's bead up and pull a one's
bead down. So we're slower at basic arithmetic, but we know numbers._

A cautionary tale about tools.

~~~
MrMan
Maybe one of "them" could post here offering some opinions about ways in which
learning the abacus enhances or extends "their" thought processes in useful
ways. Or are "they" too limited by their rote learning? Or are we safe in our
comforting knowledge that we have nothing to learn from "them?"

~~~
stcredzero
I was thinking about dynamic languages and IDEs. And before you rush to any
other conclusions, I've written a big part of one of the latter.

------
Kliment
This is from the book Surely You're Joking, Mr. Feynman, available at
[http://www.chem.fsu.edu/chemlab/isc3523c/feyn_surely.pdf](http://www.chem.fsu.edu/chemlab/isc3523c/feyn_surely.pdf)
Plenty of other similar stories in there too.

~~~
packetslave
I'm fairly sure SYJMF is a copyrighted work and this is an illegal (probably
OCRed) copy. I'd be happy to be proven wrong, however.

~~~
sillysaurus
Feynman would have wanted his stories shared, not hoarded. We live in an
insane time when sharing the stories of a dead man could be considered an
illegal act.

~~~
packetslave
I'm pretty sure that's not how copyright works.

~~~
sethrin
I'm pretty sure copyright doesn't work.

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msvan
This must be the best argument ever put forward against using the metric
system.

~~~
tspiteri
How? I can see no way this argument can be used against the metric system.

The abacus method is a fundamentally different way of doing arithmetic, that's
why the abacus guy didn't know numbers. But metric and non-metric are
fundamentally similar, only metric is much easier, gets out of the way, and
lets you think about the quantities instead of thinking about factors.

~~~
msvan
That was sarcasm. I was surprised that he knew those factoids about feet and
inches, which eventually gave him an edge in the competition. He won because
of them. And that was the only benefit he ever got out of not using the metric
system.

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Quai
Same story, in a bit different setting, and its a video!

[http://www.youtube.com/watch?v=Ofb0BlBVOGE](http://www.youtube.com/watch?v=Ofb0BlBVOGE)

~~~
Quai
I saw the video a few months ago, and it didnt make any sense to me. I didnt
imagen Feynman as a guy that would go up to a stranger just to show off his
math skills. The linked story makes much more sense!

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kahirsch
[http://en.wikipedia.org/wiki/1729_(number)](http://en.wikipedia.org/wiki/1729_\(number\))

~~~
marcosdumay
If I make an article about 224 with the only property that it's the lowest
natural number currently lacking an wikipedia article, will it get deleted or
will it stay wrong?

~~~
fduran
I read somewhere (perhaps a Martin Gardner's article) saying that numbers
couldn't be classified as "extraordinary" (having interesting properties) and
"normal" because then the first normal number could be deemed extraordinary.

------
js2
I was reminded of this story while trying to explain to my 12 year old (again)
the importance of knowing numbers and ways to play with them in your head. I
was glad to find the story online, and I'm happy HN found it interesting
enough to make the front page.

As elsewhere mentioned in the comments, if you enjoy this story you'll
probably enjoy reading all of Surely You're Joking, Mr Feynman.

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Pitarou
This is a story about using the wrong tool for the job.

The Japanese abacus is a powerful tool for addition and subtraction. As
Feynman said, a skilled user can add faster than you write the numbers down.
Even today, its excellent user interface still puts it ahead of a typical
pocket calculator. But for cube roots ... it sucks.

I wonder how Feynman would have fared against a slide-rule salesman?

~~~
Stratoscope
> I wonder how Feynman would have fared against a slide-rule salesman?

"More digits! More digits!"

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nhebb
This was the one scene from the movie Infinity [1] that I really didn't like.
Instead of a restaurant in Brazil, the script had Feynman challenging a
shopkeeper. Unfortunately, the way is was done made him come off as arrogant
and obnoxious in that scene. Other than that, though, it was a decent flick.

[1]
[http://www.imdb.com/title/tt0116635/](http://www.imdb.com/title/tt0116635/)

~~~
yawaramin
Thank you for mentioning the movie. I'm a big Feynman fan.

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altrego99
I found it difficult to approximate 1/(3*144).

