Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » Education » math-teach

Topic: In "square root of -1", should we say "minus 1" or "negative 1"?
Replies: 5   Last Post: Dec 3, 2012 12:53 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
kirby urner

Posts: 1,918
Registered: 11/29/05
Re: In "square root of -1", should we say "minus 1" or "negative 1"?
Posted: Dec 1, 2012 10:39 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply
att1.html (4.4 K)

Imagine a bus system where the buses have "circular" routes, meaning in
topological terms that they have closed loops but don't just retrace their
stops along the same roads.

The +6 goes around the loop in a clockwise direction (to the right, if the
second hand at the 12, you facing it == looking down on the bus route from
further out, ala Google Earth).

The -6 goes around the loop in a counter-clockwise direction, which, from
the center of the Earth, will appear clockwise.

Student exercise: face your partner and make your hand go in a
counter-clockwise circle *for your partner* not for you.

Student exercise: Watch yourself on TV or computer, camera facing you.
Now look in the mirror. What's the difference? To make it your hand move
clockwise in the mirror, what do you have to do?

Visiting speaker: bus routing software development specialist from Metro
(a regional government we have out here in the "Far West").

The way we do it now, it's all one bus route with the idea that it turns
around and comes back along the same path, though because of one-way
streets there will be deviations.

The bus has a "where to" sticker marking the "end of the line" where it
turns around an heads back.

This is more like the track system with tracks built in pairs. In a
funicular, there's only one track but it divides in the middle to let the
cars pass.

In this other way of doing it (loopy buses), people think of bus routes as
wandering around in partially overlapping routes that close into loops,
with a + direction and a - direction, also called R and L.

Talking about handedness more, chirality, is a hallmark of STEM-informed
curricula. Dan Suttin does a good job with this in his webinar, talking
about chirality and enantiomorphs (same thing).

One might speak of taking the bus number 6 in the minus direction (rather
than "negative") but that's urban slang. "Negative" is more "couth" (the
negative of uncouth).

More likely you'd just say "take the positive 12 to the Great Fountain,
transfer to the negative 33, ride three stops, take the positive 9 two
stops to Myrtlewood Street and voila, you're there."

The linking of "positive" and "right" is neurolinguistic and I haven't
tried to break it in choosing to look at bus routes from above rather than
from below.

http://www.tripadvisor.com/Attraction_Review-g60745-d144269-Reviews-Mapparium-Boston_Massachusetts.html

We think of time as moving "forward" i.e. "in the positive direction"
whereas "going backwards in time" is into the past. We tend to associate
"positive" more with "up" and "right" than with "down" and "left". This is
in part cultural as some languages advance through time to the left i.e.
you read them right to left (Hebrew, Arabic... Farsi).

Related concepts: Do / Undo. Reversibility. Arrow of time.
Irreversibility. Function / Inverse Function.

Lets remember that in some ecosystems the positive direction is inward
towards a convergence, a centralizer (the protons at the nucleus), while
the negative is shaped around it as electronic fields, attracted but not
convergent, not symmetric.

This is different from N / S. There's "focal positive" (coming in from all
directions) and "focal negative" (radiating away in all directions). Left
and right are more lateral motions. That which has a focal point or center
also turns. The equator is more like a number line, going West and East
from 0, the Prime Meridian.

"Did they teach anything about latitude / longitude when doing coordinate
systems with ya? No? What school did you say that was?"

Kirby



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.