[HN Gopher] Feynman vs. the Abacus (1985)
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Feynman vs. the Abacus (1985)
Author : marcodiego
Score : 40 points
Date : 2021-07-23 19:52 UTC (3 hours ago)
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(TXT) w3m dump (www.ee.ryerson.ca)
| wolfi1 wrote:
| I was always wondering what method the Abacus guy used for
| calculating the cubic root
| pavpanchekha wrote:
| Suppose you have a number: x = a0 10^1 + a1
| 10^0 + a2 10^-1 + ...
|
| If you write down x * x * x, you get something like:
| x^3 = a0^3 10^3 + 3 a0^2 a1 10^2 + (3 a0 a1^2 + 3 a0^2 a2) 10^1
| + ...
|
| Now equate this term by term to your goal, which is:
| x^3 = 1 10^3 + 7 10^2 + 2 10^1 + ...
|
| From the first term, you get: 1 = a0^3
|
| So a0 = 1, giving us an answer of 10 so far. Plug that in to
| the second term and you get: 7 = 3 a1
|
| which gives a1 = 2---you always round down. The answer is 12 so
| far. We have a carry of 1, which we need to add to the next
| one. That gives us: 12 = 3 * 1 * 2^2 + 3 * 1^2
| * a2 = 12 + 3 a2
|
| Which leaves a2 = 0. So the answer is 12.0 so far.
|
| As you go further, there are more and more terms hence the
| "scaling" phenomenon you see. Every time you are solving a
| polynomial equation in one variable, where the solution is an
| integer 0 through 9; my guess is that on an abacus you do
| binary search instead of root finding. On paper this sounds
| easy, but on the abacus it sounds impossible--each of those
| adds and multiplies is its own crazy sequence of steps.
| dang wrote:
| One past thread:
|
| _Feynman vs. The Abacus_ -
| https://news.ycombinator.com/item?id=5849665 - June 2013 (33
| comments)
| smoldesu wrote:
| Low-precision mathematics saves lives.
| Koshkin wrote:
| (Allowing wider margins of error and larger tolerances means
| better reliability and stability.)
| beloch wrote:
| "The number was 1729.03. I happened to know that a cubic foot
| contains 1728 cubic inches, so the answer is a tiny bit more than
| 12."
|
| There are people lauding and panning Feynman in this thread, but
| this story illustrates a very important lesson that I've seen a
| lot of very smart people fail to learn.
|
| Whenever you're doing a calculation, _especially_ if you 're
| using a computer or calculator, make an approximate estimate of
| what the result should be. Don't just assume that whatever method
| you use will produce a correct answer.
|
| A man with an abacus (or computer) is probably going to be faster
| than someone like Feynman most of the time, but he's also going
| to make mistakes. Big ones. He might not make them frequently,
| but mistakes always happen sooner or later. The trick is to catch
| them when they do happen. That's hard to do if you have
| absolutely no sense of what the answer _should_ be. If, however,
| you start from a rough estimate using anything your brain can
| come up with, as Feynman does in his anecdote, you 're a lot less
| likely to produce a badly wrong answer without realizing it.
|
| If this contest had gone on long enough, Feynman would have been
| beaten badly in several rounds if he messed up a calculation and
| had to start over. The thing is, Feynman would know when this
| happened because the outcome wouldn't agree with his initial
| estimate. The man with the abacus would, eventually, have
| produced answers off by several orders of magnitude _without
| realizing_.
|
| Rough estimates are _important_.
| ypeterholmes wrote:
| They said "When you grow up, you won't always have an abacus in
| your pocket!" And yet here we are.
| retrac wrote:
| And if anyone saw that coming it was Feynman. This isn't quite
| prophetic for 1959 but it's close:
|
| > I don't know how to do this on a small scale in a practical
| way, but I do know that computing machines are very large; they
| fill rooms. Why can't we make them very small, make them of
| little wires, little elements - and by little, I mean little.
| For instance, the wires should be 10 or 100 atoms in diameter,
| and the circuits should be a few thousand angstroms across.
| mrtnmcc wrote:
| Quite a coincidence... Robert Noyce invented the first
| monolithic integrated circuit chip at Fairchild Semiconductor
| in 1959.
| MaxBarraclough wrote:
| The _you won 't always have a calculator_ justification was
| always a poor one, even ignoring that we all carry computers
| these days.
|
| You don't study mathematics just to improve your mental
| arithmetic. If mental arithmetic were the point, you'd just
| practice mental arithmetic for your whole mathematical
| education, rather than progressing to more advanced topics.
| r3trohack3r wrote:
| It feels like, in every one of Feynman's arithmetic stories I've
| read, he always says how lucky he was that someone used a
| specific number.
|
| At some point it stops being luck.
| paulpauper wrote:
| it's like the math equivalent of being fielded softball
| questions
| BurningFrog wrote:
| Or, when you enough special cases, you're almost always lucky
| to hit one of them.
|
| Which is another way of saying what you're saying, I think.
| umvi wrote:
| When I read his book I got the distinct impression that he
| _grooms_ anecdotes. That is, he will subtly manipulate a
| situation (or the recounting of it) in order to make a better
| story. His stories are highly entertaining as a result.
| leephillips wrote:
| A lot of us do this to some extent, don't we? I mean, I'm no
| Feynman, but I have done some things thinking, _if this works
| out, it's going to be a great story._ Sometimes there really
| is no other good reason for doing them.
| marcodiego wrote:
| "In the fields of observation chance favors only the prepared
| mind."
| mhh__ wrote:
| Murray Gell-Mann did say once that he was annoyed by Feynman's
| tendency to invent anecdotes about himself. He wasn't lucky in
| the sense that he was a brilliant scientist but he also had a
| huge ego which he needed to validate publicly.
| meowface wrote:
| I don't doubt the claim, but this story is so specific ("the
| cube root of 1729.03") that it seems plausible there may be
| at least some truth to it. And it starts off with him being
| soundly beaten in adding and multiplying, so it's not totally
| egotistical. (I get that it's still pretty egotistical, since
| the parable is that he understands the actual numbers while
| the salesman is just using a rote, mechanical process without
| fully understanding the underlying theory.)
|
| I could definitely see him totally making this up by working
| in reverse (decide to teach a lesson about mechanical vs.
| fundamental understanding, start with a tough operation, pick
| a mentally tractable number like a bit over 1728, tack on the
| simpler arithmetic contests before it to contrast and build
| tension), so I'm not saying it's a good argument for it being
| real. Just that it's tough to say one way or another.
| svachalek wrote:
| It may be annoying, but I'll grant he earned it. The world is
| full of gigantic egos with little of substance to say.
| cpp_frog wrote:
| If I remember correctly, according to Leonard Mlodinow's
| _Feynman 's Rainbow_, Gell-Mann wrote that in Feynman's
| obituary for the Physics Review. It "raised quite a few
| eyebrows".
| mjreacher wrote:
| He says the same in this interview too
| https://www.youtube.com/watch?v=rnMsgxIIQEE&t=109s
| hellbannedguy wrote:
| I like, and respect t Feynman, but feel most of his stories are
| a humble brag.
|
| I can only take so much of his writing. On a psychological
| level, I have thought about it over the years, and come up
| empty. I probally don't know enough about the man.
|
| What got me thinking about it was one of his stories about the
| kid who could tell you what's wrong with your radio with his
| hearing.
|
| I understand needing to protect your ego later in life when you
| didn't get the respect you deserved. In the stories, the trait
| started very young.
|
| And maybe I'm completely mistaken? It just might be his way
| writing that has me wondering?
| leephillips wrote:
| I get the opposite impression. The facts of many of these
| anecdotes would force you to believe that he must have
| unfathomable genius. But he honestly seems to believe that
| luck played a huge role; sometimes, the only role. I remember
| one story where someone puts a huge blueprint in front of him
| of some kind of plumbing installation of immense complexity.
| It's not working right. He feels overwhelmed, so, just to
| have something to say, he points at random at a valve and
| asks what it does. That turned out to be the key that let
| them solve the issue. He thinks this is just blind luck,
| because he had no idea what anything did in the diagram. I
| think it's more likely that his genius subconscious saw
| something.
| whoaisme wrote:
| "He thinks this is just blind luck, because he had no idea
| what anything did in the diagram. I think it's more likely
| that his genius subconscious saw something."
|
| Reading your comments gives me a better understanding of
| how cults of personalities are a thing.
| pmoriarty wrote:
| Flash Anzan at the All-Japan National Soroban Championship 2012:
| [1]
|
| Background on how students train to do this using the Soroban
| (the Japanese Abacus): [2]
|
| Another demo: [3]
|
| Two nine-year-old girls play shiritori[4] ("a Japanese word game
| in which the players are required to say a word which begins with
| the final kana of the previous word") while adding 30 three-digit
| numbers flashed in 20 seconds: [5]
|
| [1] - https://www.youtube.com/watch?v=7ktpme4xcoQ
|
| [2] - https://www.youtube.com/watch?v=Px_hvzYS3_Y
|
| [3] - https://www.youtube.com/watch?v=JawF0cv50Lk
|
| [4] - https://en.wikipedia.org/wiki/Shiritori
|
| [5] - https://www.youtube.com/watch?v=_vGMsVirYKs
| FreeRadical wrote:
| 1729 was also Ramanujan's taxi number
|
| https://mathworld.wolfram.com/Hardy-RamanujanNumber.html
| paulpauper wrote:
| it's because 12^3 differs from 1729 by just 1, making the error
| very small when using series
| klyrs wrote:
| I'll have to pull this one out next time I hear somebody
| complaining about the imperial system of measures being useless
| ithkuil wrote:
| nah, that's clearly an argument in favour of full blown
| duodecimal system.
|
| 1729 decimal is 1001 duodecimal, Every kid raised in a
| duodecimal system that had to learn how to convert into decimal
| in order to interact with us barbarians knows this fact.
| Koshkin wrote:
| I love the chaos of the imperial system. It has the taste of
| life itself.
| uwagar wrote:
| feynman is always smart in his autobiography.
| mandmandam wrote:
| If you're gonna try and convince people Feynman wasn't smart,
| try a bible group.
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