The QUESTION IS --
We live in a 3-dimensional world: depending on your viewpoint,
objects have length, breadth, and thickness or height, width, and depth.
Mirrors, film, TV, and computer screens show us only a 2-dimensional world:
with images having only height and width, but withOUT depth.
So, then ...
Q. Why then when you look in a single plane mirror is the image reversed
only right-for-left and not also top-for-bottom?
Responses will NOT be graded, (although good penmanship helps),
but the more interesting ones will likely be posted somewhere.
Brevity counts. Avoid discussions of transcendentalism, relativity,
time travel, and quantum physics.
__ AS FOR THE REAL ANSWER well, as June Allyson would say,
"that DEPENDS" on your perspective and point of view.
Actually, the image is NOT reversed right-for-left,
the observer's feet are still toward the ground
the observer's head is still toward the sky
the observer's right shoulder is still toward the wall (or whatever)
the observer's left shoulder is still toward the door (or whatever)
The directions of ...
toward the ground, toward the sky, toward the mountain, toward the sea,
toward the wall, toward the door are all real, tangible, and demonstrative.
The directions or rather concepts of left and right are relative and UNreal.
The L-R reversal only "appears" to happen -- sort of by illusion or mis-perception;
what actually has happened by use of the mirror is a front-back reversal
along the axis at right angles to the face of the mirror.
If you stand facing north on a large flat compass dial in front of a full-length mirror, and
if you define "right" as the direction in which you turn from north to face east, and
if you wave your "right" hand, then the image's "right" hand waves back.
When facing a "normal" person, then their left is directly opposite your right, but
when facing a "reflected" or front-back "inverted" or "reversed" person,
then assumption is made that the same relationship is in effect.
Actually, the image is NOT reversed right-for-left,
but rather it is this INCORRECT ASSUMPTION that leads the observer to that conclusion.
The following is extracted from the first few URLs listed below ...
"Mirrors invert front to back, not left to right.
The popular misconception of the inversion is caused by the fact that a
person when looking at another person expects him/her to face her/him,
so with the left-hand side to the right.
When facing oneself (in the mirror) one sees an 'uninverted' person."
"The simple and complete answer to the mirror problem is that the mirror
doesn't mysteriously reverse left and right (or up and down).
We reverse left and right on almost everything we see face to face,
by spinning it or ourselves round the vertical axis.
That's where the mysterious difference between up-down and left-right comes in."
see LOTS MORE at ...
http://www.redrice.com/ci/mirrorProblem.html
http://math.ucr.edu/home/baez/physics/General/mirrors.html ***
http://hermes.physics.adelaide.edu.au/~dkoks/Faq/General/mirrors.html
http://www.hants.gov.uk/hantsweb/stoat/mirrors/answer.html
http://www.howstuffworks.com/question415.htm
http://www.physics.purdue.edu/demo/7A/left_to_right_reversal.html
http://www.glenbrook.k12.il.us/gbssci/phys/Class/refln/u13l2b.html
http://www.cogsci.ecs.soton.ac.uk/cgi/psyc/ptopic?topic=mirror-reversal
http://jcbmac.chem.brown.edu/scissorsHtml/geometrical/symmetry/mirror.html
http://psycprints.ecs.soton.ac.uk/archive/00000161/
http://www.mathpages.com/home/kmath142.htm
http://www.mathpages.com/home/kmath354.htm
http://www.mathpages.com/home/kmath441.htm
Further Reading:
The Left Hand of the Electron, by Isaac Asimov, contains a very readable discussion of
handedness and mirrors in physics.
http://www.fortunecity.com/emachines/e11/86/l-hand10.html
http://www.amazon.com/exec/obidos/search-handle-form/002-4497246-3019234
http://www.amazon.com/exec/obidos/tg/detail/-/0385043457/002-4497246-3019234?vi=glance
The Ambidextrous Universe, by Martin Gardener is another book that covers this subject.
http://www.amazon.com/exec/obidos/ASIN/068415790X/csicop/002-4497246-3019234
The Feynman Lectures Volume 1 contains a chapter on Symmetry in Physical Laws,
that deals with what we mean by left and right, and how we might go about
instructing a Martian on these concepts.
This is the same guy that's the subject of the tome ...
"Surely You're Joking, Mr. Feynman!": Adventures of a Curious Character
http://www.amazon.com/exec/obidos/search-handle-form/002-4497246-3019234
The responses follow with some snide comments marked in brackets [ ] by HTH.
__ from T_H...
Optical gravity?
(A little humor).
[ yep that's a little alright ]
__ from DAM...
"Any image that we "see" is displayed upside down on the back of the eye.
So, when the mirror displays it upside down, we "see" it right side up at the
back of the eye.
Our brain, corrects the images we "see" to right side-up when necessary,
since we know people can't stand on their heads.
In looking into a mirror, this brain transformation is not required."
[ yeah sure ;-) ]
___ from RMM...
From my old sysprog days, let me use a quote that always worked for me:
"cause thats the way it works" ....
[ yep: working as coded ]
___ from AFZ...
It doesn't. We interpret the image as reversed.
[ short and to the point ]
___ from R_A...
Reflected light travels in the direct beam as deflected.
[ real management talent here; must have an MBA ;-) ]
___ from R_A..(rebuttal)..
No, obviously someone with too much time to avoid being curious. Now is
someone going to give us the correct answer. Something like "... a single
plane mirror reflects the reversed image only with reference to an
intervening axis or horizontal plane."
[ That's more complex than the question; maybe this is getting to be non-Euclidian ]
___ from RCC...
The image is not reversed, It is a real time reflection.
[ and so the point is .?. ]
___ from CPA...
When I look into a single plain mirror my image is not reversed, right arm is on the right,etc.
___ from JAT...
I think Ive heard this one before : our minds somehow flip the image because
it is too incongruous, while a mere "mirror image" reversal looks more
natural. I think I also read somewhere that if you look through an
old-fashioned camera long enough, that image will seem so normal that it
will eventually right itself.
[ OH: so that's why Ansel Adams, Alfred Stieglitz, George Ellery Hale,
and Edwin Hubble were so good at their work ]
___ from BON...
I think I know the reason--but there ain't no way I can explain it, if that
makes any sense. (It has to do with the vortex, and the cross-over image. I
have the same situation on the "peep-hole" in my front door. You can see
what's outside--but to the human eye, the image that you see is reversed.)
___ from JJS...
Everybody knows that mirrors are just gateways to another (virtually
identical) dimension. The only visible difference is that the two dimensions
are vertical (left to right) opposites of one another. We are merely
observing our counterpart in the other dimension doing the exact the same
things that we are, at the exact same times - - AND they are observing us in
exactly the same way. Remember this the next time you get out of the shower.
The glass on mirrors is the only mechanism that prevents the two dimensions
from interacting. It is well known that any interaction of the two worlds
would produce disastrous results, which has been verified (by accident) many
times over the years whenever a mirror gets broken and the two are allowed
to ever-so-briefly interact. Hence the adage It is bad luck to break a
mirror!
As for your question as to why the inhabitants of this other dimension are
not also up-side-down as well as vertically opposite - - WELL - -That is
just plain silly!!!
[ Rod Serling would be oh so proud ]
___ from DWK...
Ah yes, reminds me of high school and the 2" diameter and about 12" long round tube
full of clear liquid, and a short sentence with 1 " letters an inch or two
behind it, and only some of the letters were upside down/reversed.
Embarrassed to say how long it took me to figure that one out!
___ from NSF...
In dealing with a mirror, the left side of your face is opposite
its image, the right side of your face is opposite its
image, your left foot is opposite its image, your
right foot is opposite its image. Nothing is reversed.
Rather, another person facing you sees you from a
reversed perspective relative to the "view from you".
Question: If an alien being appeared before
you and wanted to know the meaning of left & right,
how would you respond? I think it's a subjective thing
we were taught as children, and has little meaning in
objective terms. As a result, your query about the
mirror reduces to a subjective impression.
[ suscinct and to the point --
Right is the direction that you turn from viewing Polaris to viewing the rising Sun.
Left is the side of the body with the descending colon. ]
___ from JRJ...
I'm sorry but, anyone that would ask a question like that couldn't
possibly understand the answer.
[ best cop-out ]
___ from R_R...
Does it have to do with your frame of refrence? And isn't it just
(directly) reflected light? When you look at a mirror, instead of
looking at the object "straight on" aren't you looking at it
'backwards" (not upside down)?
[ so why is it 'backwards" on only one axis? ]
___ from EEK...
Why does a mirror interchange left and right while not inversing top and
bottom?
For this discussion, imagine a two-by-two array of squares drawn in an
arbitrary X-Y plane, their sides parallel to the axes, and the center of the
array located at the intersection of the X and Y-axes. Imagine that the
squares are numbered 1, 2, 3, and 4, starting with the positive-X,
positive-Y quadrant, going clockwise, as viewed from the positive Z-axis.
Now envision four "point" sources of light on the array, one per square,
located at the corners of the array. That is, on each square, on the corner
opposite the intersection of the X and Y-axes.
Now assume that there is an observer, "A", who is looking directly at the
array from a point on the positive Z-axis. Hopefully, one can envision the
space enclosed by the rays and the array as looking like a four-sided
pyramid where the outline of the array forms the pyramid's base and the
observer is at its apex.
With this depiction, hopefully you will agree that "A" sees Square 1 at his
top right, Square 2 at his bottom right, Square 3 at his bottom left, and
Square 4 at his top left.
Now suppose there were another observer, "B", also located on the Z-axis,
but on the negative side of the X-Y plane. "B's" view of the array also
could be imagined as being a similar four-sided pyramid, but "B" would be
looking at the obverse side of the array.
Here goes an explanation?
With this model, "B" sees Square 1 at his top left, Square 2 at his bottom
left, Square 3 at his bottom right, and Square 4 at his top right. Thus,
one could say that "B" is looking at a mirror image of what "A" sees, albeit
is merely the other side of the array that "A" sees.
Assuming this has made sense to this point, now envision the insertion of a
two-way mirror mid-way between "B" and the array, with "B" on the see-thru
side. Now, envision a third observer, "C", located at the center of the
array, looking at the reflection of the array in the just inserted mirror.
Using the pyramid notion, "C's" pyramid would look exactly like "B's", but
folded in half along the Z-axis.
What "C" sees is exactly the same image that "B" sees. In fact, one could
say that both "B" and "C" see the very same light rays, and in the very same
arrangement. That is, a "mirror" image of what "A" sees. Note that left
and right are reversed for both "B" and "C", while top and bottom are
untouched.
One could validate this description by drawing straight lines between the
light sources and the various observer locations.
For the purposes of this discussion, assume:
· "Point" sources of light radiate rays from an infinitesimal source.
· Observers, from any vantage point, only see one ray from each
"point" source of light.
· Light rays travel in straight lines and we only see those rays
pointed directly at us
· The two-way mirror does not distort what "B" sees
· The angle of reflection equals the angle of incidence at the two-way
mirror
· "A", "B", and "C" agree on the direction of "up"
Here is a sketch (hopefully, email gives it justice)
+y
|
4 |
|\ | |\
| \| | \
| \ 1 | \
+z- - A - - - - - - - - -| C | - - - - - - - - - - - -|- -| - - - - - -- - - - - B
3\ | \ |
\ |\ \ |
\| \ \|
/ 2 \ \
Array/ \ \Two-way Mirror
+x
[ and the leg bone is connected to the thigh bone ... ]
[ brevity was NOT one of the STRONG points of this discussion ]
___ from EEK... [ again, after I took exception to his use of the word "Obverse"
(which Webster defines as the opposite of "Reverse") and to his avoidance of the question ]
I've been looking for an "ah ha" and the closest I can come is the notion of
"obverse". Maybe I am using the word incorrectly, but this is what I am
thinking when I say "obverse": the view from the other side.
For example, looking at a stencil from the "right" side and looking at it
from the "obverse" side. From one side, letters and numbers look "correct".
From the "obverse" side, one would see a "mirror" image of the cutouts.
Using my previous model, let us suppose "A" is looking at the "right" side
of the array. "B" sees the "obverse" of what "A" sees and "C" sees the
"obverse" of what "B" sees. (In considering your remarks, I have concluded
that I made a major mistake when I said "C" sees exactly what "B" sees. "C"
sees what looks like that which "A" sees, and the obverse of what "B" sees.)
Assuming that you agree that "B" sees the "obverse" of what "A" sees, I will
take a crack at illustrating that "C" sees the "obverse" of what "B" sees.
Let us suppose that we replace the two-way mirror with a correctly sized
real object. That is, replace the two-way with an appropriately sized array
with characteristics similar to the original array. Then, I believe you
will agree that "C" sees the "obverse" of what "B" sees.
Now, the question is: is the replacement of the two-way mirror with a real
object a fair substitution? Why is it that we can substitute a real object
for the two-way? The answer is: for any given light ray, the ray perceived
by the observers follows exactly the same path as the ray being replaced.
That is, for "B", the single ray that he perceives from the substitute
source exactly coincides with the original because the substitute source is
located exactly where the original ray strikes the two-way. (Given a
straight line between two points, a line drawn from any point on the line to
one of its end points will coincide with the original line.) Similarly, the
single ray that "C" perceives from the substitute coincides with the
reflection of the original ray for basically the same reason.
Given that the above is accepted, why are left and right reversed in a
mirrored reflection while top and bottom are not? I think you will not like
this explanation, but it is the behavior of obverse views.
[ Especially in a field of vebose optical gravity;
Gotta give this guy credit for wordiness.
HOWEVER, it's quite in quadrature to the question,
and thus contributes naught along the axis toward the answer.
OBVIOUS MANAGEMENT TALENT!! ]
//////////////////////
== Walking Paths ==
Top
The QUESTION IS --
Describe ALL the place(S) on the Earth's surface where you can follow each of the three(3) paths described below and be back at the starting point ...
A. 1 mile south, 1 mile east, 1 mile north
B. 1 mile south, 6 miles east, 1 mile north
C. 1 mile south, 8 miles east, 1 mile north
There are two set of answers possibly applicable to the cases mentioned ...
J. The North pole
K. All of those points which are 1 mile north
of a line of latitude near the poleS which is N-miles long
or an integral sub-multiple (1/1, 1/2, 1/3, 1/4, ...) of that length.
For A, J is true;
K is true; there are NO such lines of Latitude near the North pole,
but many (an infinite number) near the South pole.
For B, J is true;
K is true; there are NO such lines of Latitude near the North pole,
but many (an infinite number) near the South pole.
For C, J is true;
K is true; there is ONE such line of Latitude near the North pole,
and many (an infinite number) near the South pole.
The responses follow with some snide comments marked in brackets [ ] by HTH.
___ from N_C...
My answer to the question is
"The North Pole".
[ less that 1% correct ]
___ from JJS...
Only one place on earth - the North Pole...
[ less that 1% correct ]
___ from G_M...
North and South Poles.
[ less that 1% correct; and 50% INcorrect - So.Pole is NOT one of the spots ]
___ from DWK...
North Pole?
[ less that 1% correct ]
//////////////////////
== Hairy People ==
Top
The QUESTION IS --
If there are more people in Bigville than there are hairs on the head of the hairiest person,
then are there at least two of them with the EXACT same number of hairs on their head?
Yes or No, and why?
The answer is YES.
If the answer were "no" -- meaning that NO two people shared the same count,
then there would have to be a separate, distinct, unique hair-count number
for everybody.
But since there are more people than the largest hair-count number,
therefore there are at least two people sharing the same number,
because by definition there are not enough numbers available to assign a different
one to everybody.
To demonstrate, let's take as a general case there are 9 people
and the hairiest person has 7 hairs.
Then the assignment could look like ...
Person number : 1 2 3 4 5 6 7 8 9
Number of hairs: 1 2 3 4 5 6 7 7 7
or : 1 2 2 3 3 4 5 6 7
but clearly, simply on an allotment basis,
the same number of hairs must be assigned to more than one person. QED
The responses follow with some snide comments marked in brackets [ ] by HTH.
___ from S_H...
No, because the number of people, Np, will be greater than the maximum
number of hairs, Nmh, on the hariest head. Thus Np > Nmh. If we assume
that there is only one person in BigVille, and that person is bald, then Np
= 1 > Nmh =0. This trivial case proves that the statement is false in
general.
[ this may be in the degenerate case of 0 and 1, but NOT in Bigville;
there's one exception in every crowd. ]
___ from B_O'N...
Based on the information given, I would say the answer is: Not Necessarily.
There's nothing in the clue to indicate that there is a finite number of
people in Bigville. Thus, there may or may not be two or more individuals
with the exact same number of hairs on their dumb-#$% heads.
[ INcorrect. Even as we crowd Bigville with more and more people approaching infinity,
then it makes the answer more and more "YES", because if there ARE more people
than there are hair-counts to go around on a non-duplicative basis,
then some two people are sharing a duplicate count. ]
___ from DWK...
Yes, it is statistically likely.
Been too long since statistics class to give you a discourse on why.
They always talked in class about the possibility of the coin landing on its
edge too...
[ Correct answer, but it's NOT a matter of chance or stats, rather it's a fer-sure ]
//////////////////////
== Two Trains ==
Top
The QUESTION IS --
Trains A and B leave their respective stations 100 miles apart at 12:00noon;
they are both travelling at 50 mph on a single track toward each other.
At the same time an eagle leaves a spot midway between the two stations travelling at
200 mph; first it flies to meet train A and then to meet B and then
back and forth between the two trains until the trains meet.
Q. How far will the eagle have flown?
In one hour each train will travel 50 miles and they will have met.
This process goes on for one hour.
In that one hour the eagle will fly 200 miles.
//////////////////////
Keep Wondering, Questioning, and Pondering; That's What Life's All About.
On_Other_Stuff