Puzzle At Goe On Day 212

[Muratus del Mur]

people that signed up for reward will get a nice reward if they find the right answer OR they will get a ugly penalty if they fail to do so. People that signed up without reward wont get anything if they solve it but will also not be penalised if they fail.

for reward:
Miq, Maya, April Rain, *Burns*, Handy Pockets, Ailith, Nimrodel, Zleiphneir, Darigan, yrthilian

without rewward:
Curiose, etluhcs teragram
and now anyone since i put it on the forum

There is a high chance that nobody will answer it right, in that case, i will reward the one that answers it right even if it is from the "without reward category" !


Question:
[b]imagine you have a hollow sphere and its interior surface is a mirror, what would you see if you were one single mathematical point in the center of this sphere?[/b]

Clarifications:
No, its not complete darkness, consider there is light inside the sphere so the reflexction works. The observer is indeed a mathematical point meaning no shape or size. Consider the light source to be in the center, unifrmly spread. Take into considereation light interference, you know, when two waves conbine they can cancel eachother or amplify eachother. if there is a slight difference in their frequence , as it might appear due to the spherical relfection, that could split the light into composing frequencies, "ripples" will form.

This is not a trick question. The answer needs to be well documented and based on solid argument. It is a pure optics and logic puzzle, sketches might help. Google will help for sure. There is no deadline, but once i have an answer from all participants (those for reward) , the quest will end. I will consider only ONE single answer from each so dont send twice or more times.

Good luck!

p.s. this IS md related from a logical point of view, but not an obvious one. some of you might understand what i mean , most wont.

[Muratus del Mur]

Feel free to argument your answer with materials taken from the net, only dont forget the details of what i asked. There is no person inside the center and all the things that would make a difference in such a case is the actual interference of the light causing dark and light areas.... I an giving you this clue to avoid getting copy pasted answers from some sites that tried but failed into answering this riddle before.

[Muratus del Mur]

riddle is over, please stop sending me any more answers.
I will announce the winner(s) tomorow!

[Muratus del Mur]

It seems some of you really worked hard to find an answer.
Congrats that you took my challenge even with the danger of being punished , as i put it initially.
This was a hard question because there is no answer to it Such a thing can't be tested under any circumstances and under an ideal environement , the size of the sphere, the frequency of the light, even its intensity, all would matter , and i didnt provided any of these.

It was not a trick question at all, i expected an elaborated answer to see you put your "little gray cells" at work, and some did.

For those not on the list, i read all your replies, thank you. I could point out
Kafuuka - strict and to the point
apohpys - close but presented more like an assumption without details
dst - your observations are correct for half a mirror, this one was a little more complicated
Shadowseeker - if you were on the list with those signed up with the reward risk, you would get one and the others none(or less) You covered well the missing points of the question. However there is a flaw, i dont think you would see anything in an ideal environement because to see means some of the light gets back to you and those ranbow interefernces you describe would probably not reach the observer back.
BFH Lightning - da vinci observation mirrors have little to do with this, the observer in the middle is theoretical in our case and unobservable
mcvitie - same reply as for dst
Princ Rhaegar - saying you see only yourself is very very incomplete


For those on the list:
I will not punish any of you that tried hard enough to answer, but instead I will reward all answers that provide enough insight on the matter, even if they are fundamentally wrong, it is clear you tried hard.

April Rain - elaborated
Zleiphneir - very interesting one
Ailith - its good you tried, but yes it could have been more detailed
*Burns* - so you are a size zero dot, as you admit, but you would see your eyes pupil?
Maya - like i said after, there was a light source in the setup. However its good you noticed that case too, in a perfect mirror sphere you would see nothign wothout light indeed.
Nimrodel - your answe as short and without much arguments as it is, contains very interesting information. I will think about the 6 time reflexion.
Miq - correct but very imcomplete comparing to the other answers i got. Your answer is more ideal than the problem itself.

Handy Pockets,Darigan, yrthilian
I got no answer from you please tell me where you sent it, if you did send one before this was finished.

Explenation:
i said at some point this is somehow related to md. Well md is a mirror but it is not a mirror sitting on a table, it is a mirror at your borders. A cube is one aspect of your borders, summ them all together and ..you get the thing described in the AL with the traveler story. I didnt knew the answer to this riddle, but your answers helped me understand define the question better. It was not an adhoc puzzle, it was a riddle that was torturing me for some time, and to be honest it still is.



Considering the fact there was no answer to be strikingly correct, and that i dont want to punish anyone...what would be an acceptable award for those in the list (excetp those i didnt got any replies from)?

[Darigan]

I'm sorry Mur I've been thinking over your question in my mind doing a bit of research. I wanted to send you a definitive answer though...I'm not sure if there is one. Being one mathmatical point in a closed sphere whether able to see your reflection or not if so then It would be an endless stream of numbers perhaps such as PI but not quite. If you can't see your reflection then looking into the reflective darkness would show you/ the mathmatical point as one singular number. This is all just theory of mine of course.

[Handy Pockets]

Mur

I am sorry. I worked today and I work second shift. I thought I had more time. I send my answer through your "send me message" in the member list of forum.

I realize more time has past then one day of work, I really wanted to find an answer. I re-read this topic and realize my answer was not handed in on time.

Handy Pockets

Edited August 3, 2010 by Handy Pockets

[Shadowseeker]

Ah. I actually don't feel like there is a flaw, because I did put up some rules in order for that theory to work:

b)Thus it is a closed system, because the energy won't disperse or be altered. Unlikely, but yeah.

[...], so we would "see" a colorful wave spectrum flowing forth and back.

"See", as in, we don't notice it for real, because that absorbs. But beforehand I claimed that it's a closed sys, and the energy won't disperse, alas the "seeing" won't do so either..if it would, it would break off the assumptions and turn into a problem which is unsolvable, because that is a variable which would interfere.


It's fine with no reward for me..I actually saw the Goe thing you wrote up in the mood panel in time, but I wasn't in the mood for moving there. Too much studying. Doesn't mean I wouldn't take one though.

The puzzle seemed interesting though, but still lacks in some aspects, simply because you have to make a lot of assumptions in order to get it to work. A perfect logic/physics puzzle if you ask me wouldn't need that. That's also why I hate sudokus which actually have several solutions...then its not a logic puzzle anymore that is clear.

----offtopic off---

I suggest some light rewards. This could include a variety of random CTC's..like, have a pool like at XMas, and one or two are extremely rare, the others being valuable, but more common. First coming picks a number and gets the ctc matching, and then onwards.


Some candy? Since you work on those already. (aka consumable/creating item or so, or a wish for one that isnt too crazy)

What would be the most interesting would be if you made another puzzle now though...but that's the words of a trickster and would probably earn me the wrath of many.

Edit: Just came up with something more interesting. A trip to certain places. Exploration of some unknown places perhaps?

Edited August 3, 2010 by Shadowseeker

[Totenkopf]

heh, nice brain torture
though having read the book, i think the answer Mur was hoping for was "circles" (dark and light circles caused by light interference or somesuch)

but honestly, i'm curious, now that there's no contest anymore, since i was kind of an optics "fan" in high-school, given the proposed situation, i.e. perfectly spherical (though that does not actually exist), perfectly reflective (though again that does not exist, though we do have "supermirrors" which reflect like 99.9999%) and perfectly uniform punctiform coherent light source in the center (which again does not exist IRL) and non-corporeal observer, is there anyone that thinks the light would _not_ reflect directly back towards the center (besides there being no interference whatsoever due to having a _single_ _coherent_ light source)?

Edited August 3, 2010 by Totenkopf

[Fyrd Argentus]

Mur did not see fit to reply to me so I will post.... as a PhD Physical Chemist who has taught classes in quantum mechanics at Stanford University, I don't need the internet, and can tell you the answer to this well-known, textbook problem -- no "image" at a mathematical point, but rather an electromagnetic wave function at that point in space that follows the blackbody spectrum, which is dependant only on temperature.

The only assumption here is that since he described a "hollow sphere" this must be of macroscopic scale - and that is not much of an assumption since a smaller sphere would have had atomic fine structure and not be well modeled as a continuous sphere.

Yes, radio waves can be of macroscopic scale, but you don't "see" them.

[Jubaris]

it was obvious from the start that you were not specific at all, but wanted an answer, so I made number of assumptions by some kind of default, and with assumptions that the sphere is perfect, that its surface is reasonably distanced from your existance as a dot and that you can see clearly, and that your existance in the sphere can be spoted in the reflections (dot does not have a definition so you cant disregard it) - my answer was that you would see yourself in the mirror (or replicas of your reflection, depending of the range of your eyesight), without much effort to test it o paper, random guess that the light beam you send should, in the center of the sphere, reflect directly to you.

giving incomplete question and making people respond to it (well, suggesting them to try ) is a bit pointless

Edited August 3, 2010 by Rhaegar Targaryen

[cutler121]

[quote name='Fyrd Argentus' date='03 August 2010 - 01:49 PM' timestamp='1280843379' post='65007']
Mur did not see fit to reply to me so I will post.... as a PhD Physical Chemist who has taught classes in quantum mechanics at Stanford University, I don't need the internet, and can tell you the answer to this well-known, textbook problem -- no "image" at a mathematical point, but rather an electromagnetic wave function at that point in space that follows the blackbody spectrum, which is dependant only on temperature.

The only assumption here is that since he described a "hollow sphere" this must be of macroscopic scale - and that is not much of an assumption since a smaller sphere would have had atomic fine structure and not be well modeled as a continuous sphere.

Yes, radio waves can be of macroscopic scale, but you don't "see" them.
[/quote]

Well that's not quite correct,

Actually what you are describing is the radiation solution for a perfectly reflective box with a hole through which the trapped energy escapes (and thereby you can measure the state or temperature of the radiation trapped within). For that problem, the black body solution you describe is the correct solution, but that wasn't the problem that Mur proposed. He wanted to know what "image" would appear at the center point of the sphere.

The easiest way to think about this (yes many other people have already provided the solution) is to use a test object and see what it would look like at different points in the sphere. If the object is close to a wall and you were looking at the closest point on the wall, the reflection is basically the same as looking in a flat mirror. If you looked at the furthest point in the sphere from there you would see an inverted image of your test object. That is where the interesting point of the center of the sphere comes in. Light reflected off the "near" side of the sphere is reflected normally whereas light reflected off the far side of the sphere is inverted. Now move the test object closer and closer to the center of the sphere. The reflected size of the inverted and normal images increase as you approach the origin of the sphere and become less and less sharp due to the defocusing nature of the sphere near the origin.

Obviously the point at which the inverted image changes to an upright image cannot be visualized because if there were an image there the light forming the image (I am speaking loosely to keep this short) could not continuously be transformed from the inverted to upright image in the limit that the test object approached the center of the sphere. The defocusing effect is what keeps the physically real system from exhibiting a paradoxical reflection.

So Fyrd what you described wasn't really the question that was being discussed.

Now, if the question had been about a perfectly milk radiating spherical cow, then I would have gone with your solution except I would have called it white body radiation. (I had to do something so this post wasn't completely serious, feel free to neg rep me.)

Cheers,

Cutler

[(Zl-eye-f)-nea]

I found this quite an enjoyable thought experiment, had two answers but stuck with the one I gave - both had the same reasoning.

I don't know about anyone else but if we get rewards...I want a Pony

Z

[Totenkopf]

[quote name='Fyrd Argentus' date='03 August 2010 - 04:49 PM' timestamp='1280843379' post='65007']
as a PhD Physical Chemist who has taught classes in quantum mechanics at Stanford University
[/quote]

wow, that beats hands-down my high-school fancy for optics (actually it was more of me being the only one in my highschool that year who chose optics over electro-magnetics and nuclear over atomic physics for the final high-school physics exam )

[quote]
no "image" at a mathematical point, but rather an electromagnetic wave function at that point in space that follows the blackbody spectrum, which is dependant only on temperature.
[/quote]

while I fully agree with that, a perfectly reflective inner surface and the "hollow" bit make me think "no heat absorption", at least in theory (and that's only if the observer and whatever generates the light don't absorb any heat themselves). and in that case the light should still be in the human visible spectrum regardless of how much it bounces around, so an observer [u]with human sight[/u] should be able to see "something", though with the above conditions it'd only probably see a whole lot of light coming back at it (not to mention get burned to a crisp if the light-source is strong enough and the observer actually had a body )

however we really must go into "how" the "observer" actually "sees", since it's non-corporeal - is it single-directional (like a human retina - it would need the light arriving at a certain angle to discern it, which would definitely ignore most of the light bouncing around), is it multi- or even omni-directional (does it perceive the whole sphere at once, in all directions - btw i think that's an even better thought experiment, how THAT would look like, to be in the centre of a sphere and see in 360 degrees)? is it in the human visible spectrum? and so on and so forth...

[quote name='cutler121' date='03 August 2010 - 05:43 PM' timestamp='1280846633' post='65010']

The easiest way to think about this (yes many other people have already provided the solution) is to use a test object and see what it would look like at different points in the sphere. If the object is close to a wall and you were looking at the closest point on the wall, the reflection is basically the same as looking in a flat mirror. If you looked at the furthest point in the sphere from there you would see an inverted image of your test object. That is where the interesting point of the center of the sphere comes in. Light reflected off the "near" side of the sphere is reflected normally whereas light reflected off the far side of the sphere is inverted. Now move the test object closer and closer to the center of the sphere. The reflected size of the inverted and normal images increase as you approach the origin of the sphere and become less and less sharp due to the defocusing nature of the sphere near the origin.

[/quote]

i think you're missing the point that there is no physical object inside, both the light emitter and the observer should be non-corporeal somehow, so there wouldn't be a reflection of anything to play around with

[Burns]

I hate riddles without proper answer! *pouts*

And i support Zleiphnir's thought, a pony would be cool =D


Apart from that... even a size 0 observer needs something to observe with, so yeah, i see my size 0 eyes =))

[Fyrd Argentus]

Okay Cutler, you're better at getting inside Mur's head and second guessing him than I am. + rep for the humor.

I still maintain there is no image at a point, it is a singularity. Get the picture?

Edited August 3, 2010 by Fyrd Argentus

[Kafuuka]

[quote name='Totenkopf' date='03 August 2010 - 11:33 AM' timestamp='1280828025' post='65003']
is there anyone that thinks the light would _not_ reflect directly back towards the center (besides there being no interference whatsoever due to having a _single_ _coherent_ light source)?
[/quote]
Yes. I addressed this in my answer. Photons follow the laws of conservation of energy, momentum and angular momentum. Theoretically a three body interaction consisting of two photons and the mirror, can account for photons deviating from a pure reflection, without violating the conservation of energy and momentum. For angular momentum it might be necessary to take into account four photons, but such does not matter.
The deviations should occur with a non-zero probability, which is probably monotonously decreasing in function of the absolute deviation. However I doubt it could be experimentally verified since the whole setup requires several physically impossibilities.

This supports the black body concept, since photons that deviate will never pass the center point again. Unless they experience a second deviating reflection, opposite to the first one. Until such happens these photons are lost to the cavity, or the cavity works as a black body.

[freelancer]

[quote name='Muratus del Mur' date='02 August 2010 - 11:18 PM' timestamp='1280809098' post='64989']
Considering the fact there was no answer to be strikingly correct, and that i dont want to punish anyone...what would be an acceptable award for those in the list (excetp those i didnt got any replies from)?
[/quote]

Thank You for not punishing us and even offer us rewards. Umm since no one else seems to have any idea, i think maybe some coins.. silvers or golds? and im sure we would also accept a drachorn too

lol i know... but its worth a shot, no?

edit: This is April Rain

Edited August 5, 2010 by freelancer

[Yrthilian]

Sorry Mur

I was working on the answer but i only had my Ipod on my for net access
internet is not good on it to be honest and a bit slow.
I am not finished my writings on it but if you wish i can still send it on
later just for though.

Note i am not a colladge persion or anything like that but
sometimes one does not need to be for a good answer

[Muratus del Mur]

coins then. (i ran out of poneys

i will think about how many, i think the above answers will have an influence on that