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| Re: Continuation of thread |
Posted by Twakkie
on 21 Aug at 1:26PM
No, he is not correct and neither are
you.
Each line of latitude is in fact a straight line, but it
is not necessarily a geodesic. Only the equator as a line of
latitude is also a geodesic. All the other lines of latitude are
straight lines, but not geodesics.
Here are some direct
quotes from Wikipedia:
(http://en.wikipedia.org/wiki/Latitude)
"All
locations of a given latitude are collectively referred to as a line
of latitude or parallel, because they are coplanar, and all such
planes are parallel to the Equator. Lines of latitude other than the
Equator are approximately small circles on the surface of the Earth;
they are not geodesics..."
so there goes your theory of
parallelity (if there is such a word), or the lack
thereof!
(http://en.wikipedia.org/wiki/Line_of_latitude)
"A
circle of latitude or parallel is an imaginary east-west circle on
the Earth, that connects all locations with a given latitude. It is
perpendicular to all meridians."
"East" is a direction
from a point of reference. And that direction from a specific point
of reference will be along a line of latitude, as these lines are
defined as running east-west (see above).
Also from the above
we can clearly see that the lines of latitude are perpendicular to
all meridiens or lines of longitude.
This whole problem
hinges on your interpretation of what "east" is. And you have given
more than one meaning or assumption to it in your posing of the
riddle.
You first posting, and in the message I am replying
to now, you just say the person faces East and walks in a straight
line. This is ambiguous. Does this mean he is walking straight east
(i.e. along the line of latitude) or in a slightly southeasterly
direction (i.e. along the geodesic). Your interpretation is the
latter, mine the former. And my first reason, as stated before, is
that east is a direction and not a point like north and south are.
My second reason is that your path along the geodesic will
eventually intersect the equator, which also means you are not truly
moving east.
In between these two messages, you refer to a 90
degree east turn before walking on a straight line. I have showed
above that all lines of latitude are perpendicular to the meridiens,
so a 90 degree turn would also take you along a line of latitude,
and not along a geodesic. To travel along the geodesic once you
turned east would mean it is not true east, but more
southeast.
Each line of latitude is in fact also a straight
line, but not with reference to the sphere itself. Only great
circles are straight lines with reference to the sphere. Lines of
latitude are small circles with reference to a sphere, but still
give rise to straight lines.
In terms of two points,
travelling along a geodesic would be the shortest route, but this is
not what we have here. You did not give two points and ask what is
the distance between them. You gave a starting point and a
direction, and incorrectly assumed since travelling along a geodesic
is the shortest distance between two points, that your given
direction will take you along a geodesic. It does not.
It all
boils down to your interpretation of east and of a straight line, as
said before. And I think you are wrong in your interpretation and
you think I am incorrect in mine. Like I said before -
Stalemate.
I know I am correct.
If you want to get
hung up on semantics about what constitutes a "straight line" and
what is "east", then be my guest.
I can see I will not be
able to convince you otherwise, and as such it all comes down to a
matter of interpretation of the semantics of the riddle as
posed.
The problem in your answer comes in when you
extrapolate the problem to greater distances. On the equator we both
get the same answer, and we agreed on that. At other distances
(either greater or less than the equator) we differ. My assumptions
hold true for all these relative distances - yours does not. For
each distance you travel south (be it more or less than to the
equator), you get a different distance back to the north pole, but
on the equator the return distance is the same. This is where your
argument falls flat. My argument holds true for all distances and
for the equator. And this is because of your interpretation of
"east" and "straight line".
So lets agree to disagree. You
have not even slightly got me to consider your view as being
correct, and I suppose its likewise with you. Hopefully this will
give rise to some thought, if not for you, then for others also
reading this.
I am getting tired of this debate. Interesting
as it was, the time has come to close the book and move on.
I
will still respond to questions and queries in this regard, but I am
no longer going to actively trying to convince you or anyone else
that 24 miles is the incorrect answer to your riddle and that it
should be 20 miles.
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