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Jul 29, 2001, 4:23:59 AM7/29/01

to

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.

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

Jul 29, 2001, 4:48:10 AM7/29/01

to

rsn...@swbellnospam.net writes:

>

> Does anyone else have examples of SF gettin' jiggy wit' mathematics?

>

> 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

Jul 29, 2001, 10:15:32 AM7/29/01

to

Nathan Raye wrote:

>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.

Jul 29, 2001, 11:44:06 AM7/29/01

to

rsn...@swbellnospam.net wrote:

>

> 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.

>

> 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

Jul 29, 2001, 3:50:01 PM7/29/01

to

<rsn...@swbellnospam.net> wrote:

> 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

Jul 29, 2001, 7:56:08 PM7/29/01

to

rsn...@swbellnospam.net wrote:

: 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.

: 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

Jul 30, 2001, 7:11:42 AM7/30/01

to

On Sun, 29 Jul 2001 02:23:59 -0600, rsn...@swbellnospam.net wrote:

>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.

Jul 30, 2001, 7:18:23 AM7/30/01

to

On Sun, 29 Jul 2001 02:23:59 -0600, rsn...@swbellnospam.net wrote:

>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

Jul 30, 2001, 11:12:53 AM7/30/01

to

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.

>

>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

Jul 30, 2001, 11:58:08 AM7/30/01

to

In article <Xns90EEAEE1EA9...@194.19.1.61>, crs...@tin.it (Cristiano Sadun) wrote:

>

>>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.

>

>

>>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

Jul 30, 2001, 12:03:21 PM7/30/01

to

On Sun, 29 Jul 2001 02:23:59 -0600, rsn...@swbellnospam.net wrote:

>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.

Jul 30, 2001, 1:46:35 PM7/30/01

to

crs...@tin.it (Cristiano Sadun) wrote in

<Xns90EEAEE1EA9...@194.19.1.61>:

<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

Jul 30, 2001, 1:44:56 PM7/30/01

to

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?

Jul 30, 2001, 2:47:51 PM7/30/01

to

m.e...@nospam.hotmail.com (Martin Elzen) writes:

> 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.

Jul 30, 2001, 2:47:33 PM7/30/01

to

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.

Jul 30, 2001, 3:31:17 PM7/30/01

to

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 ]

Jul 30, 2001, 2:20:33 PM7/30/01

to

ger...@indigo.ie (Gerry Quinn) wrote:

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

Jul 30, 2001, 4:12:54 PM7/30/01

to

rsn...@swbellnospam.net wrote in message news:<3B63C81E...@swbell.net>...

>

> 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

Jul 30, 2001, 4:33:41 PM7/30/01

to

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.

>

> 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

Jul 30, 2001, 5:31:03 PM7/30/01

to

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.

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

Jul 30, 2001, 5:31:34 PM7/30/01

to

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.

"Convergent Series"

Jeffs

Jul 30, 2001, 5:32:36 PM7/30/01

to

Cristiano Sadun <crs...@tin.it> wrote:

: 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

Jul 30, 2001, 5:53:28 PM7/30/01

to

Matt Ruff <Storyt...@worldnet.att.net> wrote in message news:<3B642E86...@worldnet.att.net>...

> 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.

> 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

Jul 30, 2001, 5:39:26 PM7/30/01

to

In article <3B63C81E...@swbell.net>, rsn...@swbellnospam.net

writesI can't believe it! It's been more than 24 hours and nobodies mentioned

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)

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)

Jul 30, 2001, 5:41:04 PM7/30/01

to

In article <GHALM...@world.std.com>, Paul Ciszek <pciszek@antiabusewor

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.

>

>The demon story was "convergent series". _Limits_ was a short story

>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.

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.

Jul 30, 2001, 6:51:40 PM7/30/01

to

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.

Jul 30, 2001, 6:56:48 PM7/30/01

to

jerry_f...@yahoo.com (Jerry Friedman) writes:

>Matt Ruff <Storyt...@worldnet.att.net> wrote in message news:<3B642E86...@worldnet.att.net>...

>>

>Matt Ruff <Storyt...@worldnet.att.net> wrote in message news:<3B642E86...@worldnet.att.net>...

>>

>> 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.

>> 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?

Jul 30, 2001, 5:06:02 PM7/30/01

to

Bitstring <868zh6q...@amonduul.ecn.ou.edu>, from the wonderful

person rmtodd <rmt...@amonduul.ecn.ou.edu> said

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

Jul 30, 2001, 5:09:02 PM7/30/01

to

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?

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>.).

Jul 30, 2001, 8:23:40 PM7/30/01

to

In article <9k4ods$8...@gap.cco.caltech.edu>,

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.

>

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.

>

>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.)

>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

Jul 30, 2001, 10:59:41 PM7/30/01

to

"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_

Jul 30, 2001, 11:34:17 PM7/30/01

to

"Geoffrey A. Landis" <geoffre...@sff.net> wrote in message news:<3B65C4A4...@sff.net>...

> 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.

> 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

Jul 30, 2001, 11:41:05 PM7/30/01

to

On Mon, 30 Jul 2001 15:58:08 GMT, ger...@indigo.ie (Gerry Quinn)

wrote:

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)

Jul 30, 2001, 11:55:47 PM7/30/01

to

>Niven wrote a short story using an infinite series against a demon

>...

>...

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)

Jul 30, 2001, 11:59:43 PM7/30/01

to

In article <Xns90EEAEE1EA9...@194.19.1.61>,

Cristiano Sadun <crs...@tin.it> wrote:

>They eventually manage to do it using (if my memory

>doenst fail) building a pendulum with themselves.

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.

Jul 31, 2001, 2:57:26 AM7/31/01

to

"-- And He Built a Crooked House" by Robert A. Heinlein. The architect

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.

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

Jul 31, 2001, 3:06:05 AM7/31/01

to

G...@quik.freeuk.com (GSV Three Minds in a Can) wrote in

<PhzcJ5lu...@quik.freeuk.net>:

<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!

Jul 31, 2001, 3:15:54 AM7/31/01

to

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.

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

--

Jul 31, 2001, 5:35:51 AM7/31/01

to

In article <3B63C81E...@swbell.net>, <rsn...@swbellnospam.net> wrote:

>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.

>

>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 an odd scene in one of Delany's Fall of the Towers novels>

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

Jul 31, 2001, 6:48:59 AM7/31/01

to

In article <qGj97JAO...@smokering.freeserve.co.uk>, "Steve Charlton"

<st...@nospam.freeserve.co.uk> wrote:

<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

Jul 31, 2001, 7:13:14 AM7/31/01

to

In article <90EFE54Ddgemp...@cnews.newsguy.com>,

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.

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.)

Jul 31, 2001, 7:15:39 AM7/31/01

to

In article <9k5aff$qk0$2...@news.jump.net>,

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.

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.

Jul 31, 2001, 7:32:33 AM7/31/01

to

ten...@alumnae.caltech.edu (Ross TenEyck) writes:

> 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.)

> 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]

Jul 31, 2001, 7:33:36 AM7/31/01

to

m.e...@nospam.hotmail.com (Martin Elzen) writes:

> 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.

> 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_

Jul 31, 2001, 7:37:04 AM7/31/01

to

GSV Three Minds in a Can <G...@quik.freeuk.com> writes:

> Did the Romans =have= abacuses/(abaci?)??

> Did the Romans =have= abacuses/(abaci?)??

_Abacus_ *is* a Latin word...

Jul 31, 2001, 2:32:25 AM7/31/01

to

In article <PhzcJ5lu...@quik.freeuk.net>, GSV Three Minds in a Can

<G...@quik.freeuk.com> writes

<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.

Jul 31, 2001, 8:43:11 AM7/31/01

to

David Empey wrote:

>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.

Jul 31, 2001, 5:59:51 AM7/31/01

to

"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

Jul 31, 2001, 9:56:13 AM7/31/01

to

GSV Three Minds in a Can <G...@quik.freeuk.com> wrote in message news:<chGYZ4k6...@quik.freeuk.net>...

>(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

Jul 31, 2001, 10:02:02 AM7/31/01