Cool Uses of Mathematics in SF
rsn...@swbellnospam.net
a battle between two powerful catapults (trebuchets, if memory serves).
The antagonist makes his ballistic calculations using Roman notation
while the hero uses Arabic notation. Guess who is victorious.
Does anyone else have examples of SF gettin' jiggy wit' mathematics?
Nathan Raye
--
'Angkor Wat in Cambodia stopped being a viable alternative for a family
vacation at about the time I was in the general area riding a tank.'
- David Drake
Mark Atwood
>
> Does anyone else have examples of SF gettin' jiggy wit' mathematics?
"Luminous" by Egan, for a weird take on SF and math.
I learned kinematics when I was 13 from reading _Have Spacesuit_
--
Mark Atwood | I'm wearing black only until I find something darker.
m...@pobox.com | http://www.pobox.com/~mra
Coyu
>My favorite scene in Harry Harrison's novel _King and Emperor_ involves
>a battle between two powerful catapults (trebuchets, if memory serves).
>The antagonist makes his ballistic calculations using Roman notation
>while the hero uses Arabic notation. Guess who is victorious.
>
>Does anyone else have examples of SF gettin' jiggy wit' mathematics?
There's a scene in Gene Wolfe's _Soldier of Arete_ where troops
calculate the height of a city wall by measuring shadows and
using the law of similar triangles -- at the time the story is set,
cutting-edge mathematics. A very nice touch.
Matt Ruff
>
> My favorite scene in Harry Harrison's novel _King and
> Emperor_ involves a battle between two powerful catapults
> (trebuchets, if memory serves). The antagonist makes his
> ballistic calculations using Roman notation while the hero
> uses Arabic notation.
Wouldn't a real Roman use an abacus to make math calculations?
> Guess who is victorious.
The Stainless Steel Rat?
> Does anyone else have examples of SF gettin' jiggy wit'
> mathematics?
Neal Stephenson's "Snow Crash" and "Cryptonomicon" both have math
interludes. And Heinlein's "Time Enough For Love" has a math trick you
can use to keep West Point upperclassman happy.
-- M. Ruff
J.B. Moreno
> My favorite scene in Harry Harrison's novel _King and Emperor_ involves
> a battle between two powerful catapults (trebuchets, if memory serves).
> The antagonist makes his ballistic calculations using Roman notation
> while the hero uses Arabic notation. Guess who is victorious.
>
> Does anyone else have examples of SF gettin' jiggy wit' mathematics?
Heh. Cool idea.
--
JBM
"Your depression will be added to my own" -- Marvin of Borg
kesi...@math.ttu.edu
: My favorite scene in Harry Harrison's novel _King and Emperor_ involves
: a battle between two powerful catapults (trebuchets, if memory serves).
: The antagonist makes his ballistic calculations using Roman notation
: while the hero uses Arabic notation. Guess who is victorious.
: Does anyone else have examples of SF gettin' jiggy wit' mathematics?
_Neverness_, by David Zindell. Sort of.
==Jake
Martin Elzen
>My favorite scene in Harry Harrison's novel _King and Emperor_ involves
>a battle between two powerful catapults (trebuchets, if memory serves).
>The antagonist makes his ballistic calculations using Roman notation
>while the hero uses Arabic notation. Guess who is victorious.
>
>Does anyone else have examples of SF gettin' jiggy wit' mathematics?
L. Sprague de Camp's "Lest Darkness Fall" has a time traveller
introducing Arabic notation to help with book keeping. Niven wrote a
short story using an infinite series against a demon ... I'm not quite
sure what it was called, but "Limits" seems about right.
Frank van den Eijkhof
>Does anyone else have examples of SF gettin' jiggy wit' mathematics?
A.E. van Voght wrote a story about some alien captured (on Mars?)
long ago, with a lock based on the then-current math.
An scientist from earth was tempted by the aliens to unlock this prison
using now-current math. I must confess that I never checked the story
on correctness...
Frank
Cristiano Sadun
>My favorite scene in Harry Harrison's novel _King and Emperor_ involves
>a battle between two powerful catapults (trebuchets, if memory serves).
>The antagonist makes his ballistic calculations using Roman notation
>while the hero uses Arabic notation. Guess who is victorious.
>
>Does anyone else have examples of SF gettin' jiggy wit' mathematics?
I remember reading a very old novel by Someone :) - part of a series,
with a criminal and a police agent following him.. (Deverel and Colby of
something similar.. I read it at least ten years ago).
Well, the duo was captured into a alien parabolic mirror built
on an asteoroid and couldnt escape easily since there was no friction
on the surface. They eventually manage to do it using (if my memory
doenst fail) building a pendulum with themselves.
--
Life's something u don't get out alive..
ObjectZone - http://space.tin.it/computer/csadun
Gerry Quinn
>
>>Does anyone else have examples of SF gettin' jiggy wit' mathematics?
>
>I remember reading a very old novel by Someone :) - part of a series,
>with a criminal and a police agent following him.. (Deverel and Colby of
>something similar.. I read it at least ten years ago).
>
>Well, the duo was captured into a alien parabolic mirror built
>on an asteoroid and couldnt escape easily since there was no friction
>on the surface. They eventually manage to do it using (if my memory
>doenst fail) building a pendulum with themselves.
>
This appeared on rec.puzzles lately, and was attributed to Asimov.
- Gerry Quinn
DaveMoore
>My favorite scene in Harry Harrison's novel _King and Emperor_ involves
>a battle between two powerful catapults (trebuchets, if memory serves).
>The antagonist makes his ballistic calculations using Roman notation
>while the hero uses Arabic notation. Guess who is victorious.
>
>Does anyone else have examples of SF gettin' jiggy wit' mathematics?
>
>
>Nathan Raye
Check out _The Mathematical Magpie_, Clifton Fadiman, ed. A collection
of mathematically based short stories, many flat-out SF. Includes
works by Martin Gardner, Heinlein, Asimov, Clarke, and others.
Also see _Fantasia Mathematica._ These volumes have been around
forever, and are still in print.
--
Dave Moore == djm...@uh.edu == I speak for me.
In the wrong hands, sanity is a dangerous weapon.
David Empey
<Xns90EEAEE1EA9...@194.19.1.61>:
"The Men and the Mirror", Ross Rocklynne.
--
Dave Empey
What else could a millennia-spanning, reality-hopping,
transdimensional cult of genetically-perfect,
bloodthirsty superwomen want? --Kenneth Hite
David Empey
>My favorite scene in Harry Harrison's novel _King and Emperor_ involves
>a battle between two powerful catapults (trebuchets, if memory serves).
>The antagonist makes his ballistic calculations using Roman notation
>while the hero uses Arabic notation. Guess who is victorious.
Why didn't they use abacuses?
rmtodd
> L. Sprague de Camp's "Lest Darkness Fall" has a time traveller
> introducing Arabic notation to help with book keeping. Niven wrote a
> short story using an infinite series against a demon ... I'm not quite
> sure what it was called, but "Limits" seems about right.
Close. "Convergent Series" was the title.
rmtodd
Wise. As I recall, the math was complete bullshit, but like most van Vogt,
the story manages to be entertaining in spite of the fact that you know the
"science" is thoroughly bogus.
Captain Button
I'm pretty sure the story you mean is "Convergent Series".
--
"Gee, who'd a thunk it? Turns out alien superintelligence is
no match for our Earthly can-do spunk." - Jane Lane, "Daria"
Captain Button - [ but...@io.com ]
Ross Presser
As said elsewhere, the author was Ross Rocklynne, and the story was
called "The Men and the Mirror." It may have been misattributed to
Asimov because it appeared in a collection called _Before The Golden
Age_ (volume 2) edited and extensively commented on by Asimov.
--
Ross Presser * ross_p...@imtek.com
"Back stabbing is a sport best played by those that can't stand face
to face with their opponent." - Danny Taddei
David Tate
>
> Does anyone else have examples of SF gettin' jiggy wit' mathematics?
>
There are a number of excellent examples from the short fiction of
Greg Egan. Perhaps the most mathematically advanced is the story "The
Infinite Assassin", whose plot actually depends on the fact that
Cantor sets are nondenumerable, yet have measure zero. He also uses
some ideas from chaos theory in "Unstable Orbits in the Space of
Lies".
David Tate
Geoffrey A. Landis
>
> There are a number of excellent examples from the short fiction of
> Greg Egan. Perhaps the most mathematically advanced is the story "The
> Infinite Assassin", whose plot actually depends on the fact that
> Cantor sets are nondenumerable, yet have measure zero.
I have to say, that story always bothered me. In the ending, he maps a
set of non-zero measure onto a set of measure zero, which you can only
do if the resulting map has infinite density.
--
Geoffrey A. Landis
http://www.sff.net/people/geoffrey.landis
Jeff Suzuki
: Wouldn't a real Roman use an abacus to make math calculations?
Very likely. And in all probability, be faster than the person
using Arabic numerals.
It wasn't too long ago (like, 1950) that a skilled Japanese abacist
could out-calculate someone using an electric adding machine on a
_routine_ basis. It wasn't until pocket calculators came about in
the 1970s that the abacists began to lose.
Speaking of which: "Into the Comet" by Clarke. The crew uses
abaci to compute a course when their computers fail.
Jeffs
Jeff Suzuki
: L. Sprague de Camp's "Lest Darkness Fall" has a time traveller
: introducing Arabic notation to help with book keeping. Niven wrote a
: short story using an infinite series against a demon ... I'm not quite
: sure what it was called, but "Limits" seems about right.
"Convergent Series"
Jeffs
Jeff Suzuki
: I remember reading a very old novel by Someone :) - part of a series,
: with a criminal and a police agent following him.. (Deverel and Colby of
: something similar.. I read it at least ten years ago).
Ross Rocklynne, "The Men and the Mirror". A wonderful puzzle story.
: Well, the duo was captured into a alien parabolic mirror built
: on an asteoroid and couldnt escape easily since there was no friction
: on the surface. They eventually manage to do it using (if my memory
: doenst fail) building a pendulum with themselves.
Jeffs
Jerry Friedman
> rsn...@swbellnospam.net wrote:
...
> > Does anyone else have examples of SF gettin' jiggy wit'
> > mathematics?
>
> Neal Stephenson's "Snow Crash" and "Cryptonomicon" both have math
> interludes. And Heinlein's "Time Enough For Love" has a math trick you
> can use to keep West Point upperclassman happy.
(Annapolis, not West Point. No doubt RAH is spinning in his grave.)
If you read "The Pragmatics of Patriotism", the second half of a
speech he gave at the Naval Academy, you can see a disappointing
scene, which he records apparently faithfully, revealing that plebes
of the '70s didn't have to meet the same
time-till-graduation-calculation standards that Heinlein's generation
dod.
--
Jerry Friedman
Steve Charlton
writes
the "Cities in Flight" series by James Blish. The whole damn thing (4
books) is based on a so far undiscovered mathematical relationship
between the force of gravity and the spin of an electron. It eventually
allows simple machines (Spindizzies) to propel whole cities to the
stars.
--
Steve Charlton |Travelling in Hyperspace is a bit like
st...@gnirekoms.freeserve.co.uk |being drunk.
hint: ^^^^^^^^^ |What's wrong with that?
reverse this |You ask a glass of water!
- Douglas Adams (sadly missed)
Steve Charlton
ld.std.com> writes
>In article <3b654039...@news.nl.net>,
>Martin Elzen <m.e...@nospam.hotmail.com> wrote:
>>
>>L. Sprague de Camp's "Lest Darkness Fall" has a time traveller
>>introducing Arabic notation to help with book keeping. Niven wrote a
>>short story using an infinite series against a demon ... I'm not quite
>>sure what it was called, but "Limits" seems about right.
>
>collection, which did NOT include "Convergent Series".
"Convergent Series" the short story lent its name to "Convergent Series"
the book; a collection of (non-KS) short stories.
Ross TenEyck
I'm a little dubious. The abacus is an excellent device for
adding and subtracting integers (or numbers of fixed precision,
which as far as the abacus is concerned are integers with a
power of ten applied.)
It's usable for multiplication and division to some fixed
precision; either by doing multiplication as repeated addition
and division as repeated subtraction, or by laying out the
multiplication/division problem on mental paper and using
the abacus to handle the addition of intermediate results.
I even saw instructions on how to take a square root on an
abacus. ("Instructions" is perhaps a bit much; the procedure
amounted to: guess the square root, square your guess, compare
to the original number, adjust your guess accordingly, repeat.)
However, unlike a reasonable calculator, or even a slide rule,
it won't do trig functions, logarithms, roots and powers (except
as noted above), or many other things that one might find useful.
This is why, pre-calculators, you generally saw abaci being used
in shops and similar places, where you needed to add and subtract
lots of numbers quickly. In scientific and engineering circles,
which typically involve more multiplying and dividing, as well as
higher math functions, the instrument of choice was the slide rule.
For ballistics, I'd take the slide rule any day.
Incidentally, now that I think about it, I'm not certain the
Romans had the abacus. For one thing, the abacus strongly implies
a place-value number system, like Arabic numerals but unlike Roman
numerals.
--
================== http://www.alumni.caltech.edu/~teneyck ==================
Ross TenEyck Seattle, WA \ Light, kindled in the furnace of hydrogen;
ten...@alumni.caltech.edu \ like smoke, sunlight carries the hot-metal
Are wa yume? Soretomo maboroshi? \ tang of Creation's forge.
Ross TenEyck
>Matt Ruff <Storyt...@worldnet.att.net> wrote in message news:<3B642E86...@worldnet.att.net>...
>>
>> interludes. And Heinlein's "Time Enough For Love" has a math trick you
>> can use to keep West Point upperclassman happy.
>(Annapolis, not West Point. No doubt RAH is spinning in his grave.)
>If you read "The Pragmatics of Patriotism", the second half of a
>speech he gave at the Naval Academy, you can see a disappointing
>scene, which he records apparently faithfully, revealing that plebes
>of the '70s didn't have to meet the same
>time-till-graduation-calculation standards that Heinlein's generation
>dod.
I always wondered... did the upperclassman typically work out what
the correct answer would be before asking the question, in order
to catch plebes who just recited a random number in the right
approximate range?
GSV Three Minds in a Can
person rmtodd <rmt...@amonduul.ecn.ou.edu> said
(spoiler ahead)
The 'logic' was along the lines of the lock being a time lock coded to
the 'ultimate prime number' which was linked to the 'Eis force' (sp?)
(phooey already!) and the 'solution' was to adjust the Eis force by an
incy-weesy bit (like adding 1) after which the prime number falls into
lots of factors, one of which happens to be 'just now', so the lock
opens.
Complete hokum, but totally on par with AEvG's comprehension of science
in general - see for instance 'The Mixed Men' (wasn't AEvG also into
LRonHubb&ard stuff?).
--
GSV Three Minds in a Can
GSV Three Minds in a Can
wonderful person David Empey <dem...@cruzio.com> said
>rsn...@swbellnospam.net wrote in <3B63C81E...@swbell.net>:
>
>>My favorite scene in Harry Harrison's novel _King and Emperor_ involves
>>a battle between two powerful catapults (trebuchets, if memory serves).
>>The antagonist makes his ballistic calculations using Roman notation
>>while the hero uses Arabic notation. Guess who is victorious.
>
>Why didn't they use abacuses?
Did the Romans =have= abacuses/(abaci?)?? I know the Chinese did, from
way back, but I'm not sure that they ever made it to Rome (well, Ancient
Rome .. you know what I mean .. 8>.).
Ian A. York
Ross TenEyck <ten...@alumnae.caltech.edu> wrote:
>Jeff Suzuki <je...@bu.edu> writes:
>>Matt Ruff <Storyt...@worldnet.att.net> wrote:
>
>>: Wouldn't a real Roman use an abacus to make math calculations?
>
>>Very likely. And in all probability, be faster than the person
>>using Arabic numerals.
>
>adding and subtracting integers (or numbers of fixed precision,
>which as far as the abacus is concerned are integers with a
>power of ten applied.)
A guy with an abacus beat Richard Feynman on adding and multiplication,
tied on division, and came up a little short on a cube root (of 1729.03,
if you're interested). ("Surely You're Joking, Mr. Feynman!")
Mind you, Feynman was doing it in his head, but that's still pretty
impressive.
Ian
--
Ian York (iay...@panix.com) <http://www.panix.com/~iayork/>
"-but as he was a York, I am rather inclined to suppose him a
very respectable Man." -Jane Austen, The History of England
Chris Byler
"Convergent Series", iirc. Which is ironic - if you assume that the
time required for the demon to disappear and reappear is proportional
to the distance (he moves at the speed of light, for example), then
the time series _would_ be convergent and the demon would escape the
trap in finite time. Fortunately that doesn't happen in the story.
--
Chris Byler cby...@vt.edu
Kubera: "It occurred to me that Sam would be the number one suspect,
except for the fact that he was dead."
Sam: "I had assumed that to be sufficient defense against detection."
-- Roger Zelazny, _Lord of Light_
David Tate
> David Tate wrote:
> >
> > There are a number of excellent examples from the short fiction of
> > Greg Egan. Perhaps the most mathematically advanced is the story "The
> > Infinite Assassin", whose plot actually depends on the fact that
> > Cantor sets are nondenumerable, yet have measure zero.
>
> I have to say, that story always bothered me. In the ending, he maps a
> set of non-zero measure onto a set of measure zero, which you can only
> do if the resulting map has infinite density.
Well... you can put any set of cardinality aleph-1, like (say) a
bounded closed interval in R(n), into 1-1 correspondence with any
Cantor set extracted from (say) that piece of R(n). That's a 1-1
mapping between a set of nonzero measure and a proper subset of
measure zero. That's what's so weird about it. Yes, the Cantor set
is dense in the parent set, but it still has measure zero -- which was
the point of the climactic act of the story.
Is there something I'm missing here? Are you saying that a dense set
of zero measure would have sufficed for Our Hero's purposes?
David Tate
Richard Horton
wrote:
I believe it's "The Men and the Mirror" (or maybe "The Men in the
Mirror") by Ross Rocklynne. The Asimov attribution may result from
him having anthologized it in _Before the Golden Age_, as my vague
memory tells me he did.
--
Rich Horton | Stable Email: mailto://richard...@sff.net
Home Page: http://www.sff.net/people/richard.horton
Also visit SF Site (http://www.sfsite.com) and Tangent Online (http://www.tangentonline.com)
Timothy A. McDaniel
>...
Infinite *sequence*. "A series is an infinite sum ...". If the demon
had been caught in an infinite series, he would have gotten larger and
larger, though perhaps converging to a finite limit depending on the
exact series.
--
Tim McDaniel is tm...@jump.net; if that fail,
tm...@us.ibm.com is my work account.
"To join the Clueless Club, send a followup to this message quoting everything
up to and including this sig!" -- Jukka....@hut.fi (Jukka Korpela)
Timothy A. McDaniel
Cristiano Sadun <crs...@tin.it> wrote:
>They eventually manage to do it using (if my memory
>doenst fail) building a pendulum with themselves.
Actually, in the story, they pass a cord between them, push off so as
to spin up around the center of the cord, then release the cord at the
apex of their trajectory. One person flies over the edge of the
mirror at that point, and the other person flies off after one trip
across the mirror.
Alas! yet another story ruined by the brutal facts of Newtonian
mechanics -- in this case, conservation of angular momentum. The
"push off so as to spin up" is the "here a miracle occurs" step.
John Thomas
designs a house as a model of an unfolded hypercube. They're in
California. There's an earthquake and the building folds up _through a
fourth spatial dimension_. It looks like a plain cube on the building
lot.
There's another earthquake and the building folds into nothing. Not
rubble, but gone.
----------
There's another story, much more recent and not by Heinlein, where
someone in orbit figures when a jettisoned item will return to the
space station by using epicycles. The story was in Analog. It might be
the same story that had jokes that started "A mathematician, an
physicist, and an engineer..."
JT
David Empey
<PhzcJ5lu...@quik.freeuk.net>:
>Bitstring <90EE63F13dgem...@cnews.newsguy.com>, from the
>wonderful person David Empey <dem...@cruzio.com> said
>>rsn...@swbellnospam.net wrote in <3B63C81E...@swbell.net>:
>>
>>>My favorite scene in Harry Harrison's novel _King and Emperor_ involves
>>>a battle between two powerful catapults (trebuchets, if memory serves).
>>>The antagonist makes his ballistic calculations using Roman notation
>>>while the hero uses Arabic notation. Guess who is victorious.
>>
>>Why didn't they use abacuses?
>
>Did the Romans =have= abacuses/(abaci?)??
My memory says yes, and a Google search for abacus Romans turns
up Web pages that agree. Apparently they were counters
sliding in a grooved board.
www.m-w.com says either plural form is correct; they list
abaci first.
>I know the Chinese did, from
>way back, but I'm not sure that they ever made it to Rome (well, Ancient
>Rome .. you know what I mean .. 8>.).
One of these Web pages says the Chinese got it from the Romans!
David Empey
>
>A guy with an abacus beat Richard Feynman on adding and multiplication,
>tied on division, and came up a little short on a cube root (of 1729.03,
>if you're interested). ("Surely You're Joking, Mr. Feynman!")
Are you sure it was 1729.03? I thought it was someting like 27.03.
As I recall, Feynman started to explain to the abacus operator how he
figured out the cube root by saying "The cube root of <largest cube
less than the number in question> is <whatever it was>", at which
point the abacus operator stopped to figure it out on his abacus,
which surprised Feynman, who thought the cube root should have
been obvious. Now I can believe that Feynman would have thought
it obvious that the cube root of 27 is 3, but it seems unlikely
he'd think it obvious that the cube root of 1728 is 12.
>
>Mind you, Feynman was doing it in his head, but that's still pretty
>impressive.
>
>Ian
--
Nancy Lebovitz
>My favorite scene in Harry Harrison's novel _King and Emperor_ involves
>a battle between two powerful catapults (trebuchets, if memory serves).
>The antagonist makes his ballistic calculations using Roman notation
>while the hero uses Arabic notation. Guess who is victorious.
>
>
about sentient (?) numerical sequences in suns.
Just barely sf: Margaret Ball's _Bridge to the Sky_ has a cathedral
architect trying to get a chance to learn enough algebra to make
his work easier.
--
Nancy Lebovitz na...@netaxs.com www.nancybuttons.com
Doug Palmer
<st...@nospam.freeserve.co.uk> wrote:
> I can't believe it! It's been more than 24 hours and nobodies mentioned
> the "Cities in Flight" series by James Blish.
The bit I remember about it is that they meet some aliens and there's a
discussion about the difficulties of adapting to each other's notation.
(From memory, eg., the aliens use a 'D' symbol to indicate that something
is a constant.)
As a side thought, are there any stories about encounters with aliens
that have explored a completely different region of the space of
mathematics to humans? "Sorry, now explain this concept of 'number'
again? It looks like a sort of wierd mapping onto a Fxchil group to me,
but it makes my antennae twist just to think about it."
--
Doug Palmer do...@charvolant.org http://www.charvolant.org/~doug
Ian A. York
David Empey <dem...@cruzio.com> wrote:
>iay...@panix.com (Ian A. York) wrote in <9k4tqc$q2s$1...@news.panix.com>:
>>
>>A guy with an abacus beat Richard Feynman on adding and multiplication,
>>tied on division, and came up a little short on a cube root (of 1729.03,
>>if you're interested). ("Surely You're Joking, Mr. Feynman!")
>
>Are you sure it was 1729.03? I thought it was someting like 27.03.
"He writes down a number on some paper--any old number--and I still
remember it: 1729.03."
>As I recall, Feynman started to explain to the abacus operator how he
>figured out the cube root by saying "The cube root of <largest cube
>less than the number in question> is <whatever it was>", at which
>point the abacus operator stopped to figure it out on his abacus,
>which surprised Feynman, who thought the cube root should have
>been obvious. Now I can believe that Feynman would have thought
>it obvious that the cube root of 27 is 3, but it seems unlikely
>he'd think it obvious that the cube root of 1728 is 12.
I started to explain that it was an approximate method, and had to do
with the percentage of error. "Suppose you had given me 28. Now the
cube root of 27 is 3 ... "
He picks up his abacus: zzzzzzzzzzzzzzzzzzzzz-- "Oh yes, he says."
I think you actually remembered it much better than I did; I just looked
it up. (After spending fifteen minutes looking for the damn mis-shelved
book, and I never did find the other one.)
Ian A. York
Timothy A. McDaniel <tm...@jump.net> wrote:
>
>Alas! yet another story ruined by the brutal facts of Newtonian
>mechanics -- in this case, conservation of angular momentum. The
>"push off so as to spin up" is the "here a miracle occurs" step.
Ah. I've been feeling vaguely uneasy about that story for years, though
never clearly enough to try to work out where it lost me. Thanks.
Jens Kilian
> I even saw instructions on how to take a square root on an
> abacus. ("Instructions" is perhaps a bit much; the procedure
> amounted to: guess the square root, square your guess, compare
> to the original number, adjust your guess accordingly, repeat.)
That's essentially how a numerical square root algorithm works ;-)
I've seen a description of taking a square root by hand, similar
to long division, but couldn't make head or tail of it[1].
Jens.
[1] Part of the problem was that I read it in an old schoolbook, and apparently
the method of long division taught in German schools has changed since
the time it was printed; at least the notation was unfamiliar.
--
mailto:j...@acm.org phone:+49-7031-464-7698 (TELNET 778-7698)
http://www.bawue.de/~jjk/ fax:+49-7031-464-7351
PGP: 06 04 1C 35 7B DC 1F 26 As the air to a bird, or the sea to a fish,
0x555DA8B5 BB A2 F0 66 77 75 E1 08 so is contempt to the contemptible. [Blake]
Jens Kilian
> L. Sprague de Camp's "Lest Darkness Fall" has a time traveller
> introducing Arabic notation to help with book keeping. Niven wrote a
> short story using an infinite series against a demon ... I'm not quite
> sure what it was called, but "Limits" seems about right.
_Convergent Series_
Jens Kilian
> Did the Romans =have= abacuses/(abaci?)??
_Abacus_ *is* a Latin word...
David Allsopp
<G...@quik.freeuk.com> writes
There is only One True Reference Work on topics such as these: "The
Universal History Of Numbers" by Georges Ifrah et. al.[1] Apparently
the Romans typically used calculating tables (with sand or wax), but did
have an abacus that was just about equivalent to the classical Chinese
one. For some reason, use of counting tables survived the fall of Rome,
but abaci didn't.
Incidentally, referring to the story, no-one even in Roman times
actually calculated using Roman numerals. They used calculating tables,
which, at a pinch, you can draw in mud. There was a long apprenticeship
in learning how to use them. The thing about Arabic (really Indian, of
course) numerals and positional notation is that they make it *possible*
to calculate quickly on paper. On the other hand, doing advanced
arithmetic was high mathematics (degree-level equivalent) up to about
the Renaissance. On the gripping hand, how many people remember
(indeed, were ever taught) how to do long multiplication and long
division by hand?
[1] Drooling fanboy plug for this book. It's *awesome*, however you
want to interpret the word.
--
David Allsopp Houston, this is Tranquillity Base.
Remove SPAM to email me The Eagle has landed.
Coyu
>Are you sure it was 1729.03? I thought it was someting like 27.03.
>As I recall, Feynman started to explain to the abacus operator how he
>figured out the cube root by saying "The cube root of <largest cube
>less than the number in question> is <whatever it was>", at which
>point the abacus operator stopped to figure it out on his abacus,
>which surprised Feynman, who thought the cube root should have
>been obvious. Now I can believe that Feynman would have thought
>it obvious that the cube root of 27 is 3, but it seems unlikely
>he'd think it obvious that the cube root of 1728 is 12.
I'm no Feynman, but I know that one. 1728 is the number of cubic inches
in a cubic foot.
Robert Shaw
"Jeff Suzuki" <je...@bu.edu> wrote in message
news:9k4jmm$3cm$2...@news3.bu.edu...
> Matt Ruff <Storyt...@worldnet.att.net> wrote:
>
> : Wouldn't a real Roman use an abacus to make math calculations?
>
> Very likely. And in all probability, be faster than the person
> using Arabic numerals.
But this story is taking place in Viking England, with the
clerk using roman numerals and the vikings arabic.
Was the abacus known in England in the 800's?
--
Matter is fundamentally lazy:- It always takes the path of least effort
Matter is fundamentally stupid:- It tries every other path first.
That is the heart of physics - The rest is details.- Robert Shaw
David Tate
>(wasn't AEvG also into LRonHubb&ard stuff?).
Not that I know of, but he *was* the foremost convert to the
quintessential 1950's equivalent, General Semantics. That's where all
the "Null-A" stuff came from.
David Tate