Sunday, February 04, 2007

A Tricky Question

Updated 05/02/06: See below.

Imagine you are standing in front of a mirror, facing it. Raise your left hand. Raise your right hand. Look at your reflection. When you raise your left hand your reflection raises what appears to be his right hand. But when you tilt your head up, your reflection does too, and does not appear to tilt his/her head down. Why is it that the mirror appears to reverse left and right, but not up and down?
This is allegedly one of the questions from actual interviews conducted by Microsoft. Some of the questions in that page are simply assessments of creativity and out-of-the-box thinking, and that means there are no "right" or "wrong" answers, but only "good" or "mediocre" answers. However, this question is different, and it really stumped me throughout. We all know that a mirror image inverses the left-right direction of an object, but why does it do so on the left-right axis selectively, without affecting the up-down and the forward-backward axis? This is not a "fancy" mind twister, it's in fact one of nature's peculiarity that stares at us all the time.

It took me several "day-dreaming sessions" to figure out a rigorous answer for that. All of a sudden I felt lucky for not pursuing careers that require tremendous ingenuity and creativity. Somehow I think that I have become blunter and slower in mental capacity as I grew up. Does the brain grow old? It might have been so in my case. Sometimes I even blame the medical course for "dumbing and numbing minds", but that was not exactly a good excuse.

Anyway due to time constraint I will just leave the post here and let any interested minds spend a few minutes in that question. I am interested to hear great and elegant answers from anyone. I will post my answer when I am free (if anyone is interested), but it might be a week or two from now, considering that I will fly back to Melbourne this Thursday and prepare for the new semester on next Monday. If you aren't interested in this particular question, the page I mentioned above contain many more questions that could keep you busy for weeks. So I invite everyone to spend some time twisting our brains to keep them sharp and shiny! :)

Update: I haven't had time to put up my own answer in my own words. However, when I was googling randomly I came across one of the explanations for the question. To be frank that explanation was too wordy to my liking so I didn't really finish it. But from what I got at a glance, it seemed like a great explanation. Have a look at some other Q&A inside too. Remember this question? "On Earth, from where can you walk one mile south, one mile east and one mile north and return to the starting point" The answer is surprising.


Ka Lip; said...

The first things that springs to mind is the arrangement of our eyes... but I'm not physics graduate *shrugs* can't really think of any other reason..

Anonymous said...

Erm... what i think is...

We have 3 dimensions mah, X Y and Z. Let's say X and Y is left right and up down respectively for us, Z is forward and back for us. When we look into a mirror, because X and Y is parallel to the mirror surface, so it is same whether in the mirror world or real world. But the Z dimension is like poking into the mirror (when we walk forward, our mirror image walk towards us also), so Z dimension is opposite to what we seeing.. so in the X Y Z dimension system, mirror world and real world has 1 dimensional difference. But then we always assume that front is front, back is back, up is up, down is down ( because we are standing straight facing the mirror), so we just ourselves see the dimensional difference in the X dimension, which is our left right... oh my god... i not sure about it also//

ShouFarn said...

Heh, exactly my answer. It would be: because light travels in a straight line, so your right hand will be reflected in the mirror as your right hand, and your left hand will also be reflected in the mirror as your left hand, just that it only shows whichever side you show it, which in this case is your "front" side.

The mirror has now reconstructed your image from the light bouncing off you. But the mirror is two dimensional, saying that the image is raising "his/her left hand" has no meaning at all because there is no "his/her left hand", merely your right hand's image.

This question is to trick us because we normally take for granted that things are 3D. Thats my take on it anyway.

day-dreamer said...

Is it because a human's face is usually symmetrical left-right instead of up-down? If you get what I mean... sorry, dunno how to put it using the right words. :D

I also dunno what I am talking about... hehe.

ShouFarn said...
This comment has been removed by the author.