# Wikipedia:Reference desk/Archives/Science/2009 November 28

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# November 28

## Time dilation and multiplayer games

Would it be even theoretically possible for a multiplayer game to accurately model time dilation for one player relative to another? 24.235.164.10 (talk) 06:10, 28 November 2009 (UTC)

78.139.5.39 (talk) 07:36, 28 November 2009 (UTC)On the page "Speed of Light" I am reading the following sentence: "In models of the expanding universe, the farther things are from Earth, the faster they move away from us". It seems to mean the we are, after all, living in a geocentric universe, right? And it seems to me that this kind of sentence appears everywhere (not only on this particular page), when we talk about the expansion of the universe. How about directions?

For a real time game I think the answer is no in the general case. For example if the players are supposed to be able to interact in real time and then one of them goes away quickly and comes back (as in the twin paradox), their times will be out of whack with each other and they won't be able to interact in real time with each other properly. One work around would be for the game to slow down when you start moving quickly relative to some reference frame, but then you really lose the magic of relativity. For a turn based game you could for example give out extra turns or bonus movement or whatever.
It's pretty unfortunate. I would love to see a multiplayer space shooter or something like that which models special relativity. Rckrone (talk) 08:00, 28 November 2009 (UTC)
No, that statement does not imply that we live in a geocentric universe. No matter where you are in the universe, the farther things are from you, the faster they move away from you (on cosmological scales). Picture a bunch of dots drawn on a balloon that's getting steadily inflated. Pick one of the dots. The other dots are moving away from the chosen dot, and the farther a dot is from the chosen dot, the faster it moves away from the chosen dot. But the same thing is true no matter which dot you choose to take the perspective of. Red Act (talk) 09:11, 28 November 2009 (UTC)
I wonder if this question would be better addressed on the computer desk. I should first clarify my understanding of special relativity and time dilation is limited, in fact I wasn't sure whether to post at all but decided to post based on above posts. While not time dilation, some FPS games have allowed one (or multiple) players to have some sort of powerup (skill/weapon) which works in multiplayer, that is able to 'slow down' time or allows the player to go 'faster' then 'normal' time. This allows them to travel at faster then normal speed (I think) while making other players slower then normal (I think), so the players using the powerup appear to be going very fast relative to the other players. I'm not sure of the precise difference, it obviously isn't 10x, I think it's closer to 2x. For example, F.E.A.R.#Multiplayer [1] (technically in the game story the player is going 'faster' then 'normal' time) & TimeShift#Gameplay [2] (if I understand it correctly, technically in the game story time is slowed down and the player is going at normal speed) & also I think some Source (engine) mods. I presume a similar thing could be used for some aspects of time dilation, e.g. one player at relative rest and the other moving close to the speed of light. Nil Einne (talk) 09:49, 28 November 2009 (UTC)
Don't forget time dilation is symmetric - every player would have to see time passing more slowly for every other player that was moving at a constant velocity relative to them. Then you would need general relativistic corrections for players and objects that were accelerating relatve to one another. Very difficult to achieve in a real-time MPG, I would think. Gandalf61 (talk) 10:33, 28 November 2009 (UTC)
I admit, this is one thing that confused me after reading the article and hence my reluctance to post. Perhaps I should make a seperate topic but it seems this is relevant to understanding the question and answers... Let's say the typical space flight example, someone takes a ship from earth at close to the speed of light and goes somewhere and later come back. For them it's been 50 years, but a billion years has passed on earth and as it turns out it survived but cats are now the dominant species. I can understand how to the point of the people and cats on earth, it seems that time is passing very slowly on the space ship. I'm confused how it seems to the person on the space ship that time is passing slowly on earth since it seems to me if they are observing all their loves ones dying in a minute and then cats taking over in a few days, time is passing rather fast on earth? (I understand how the observation would get complicated since it will take longer and longer for the information to reach them as they are going away and shorter and shorter as they are coming back but although I haven't completedly thought that part true as with a number of areas of special and general relativity it confuses me no end and I can't see any way it would 'work'.) Nevermind found this is actually dealt with in Twin paradox linked above (sorry neglected to read it earlier) Nil Einne (talk) 12:08, 28 November 2009 (UTC)
Yes, that is, indeed, the Twin paradox. A lot of people talk about the Twin paradox and forget to mention in what way it is apparently paradoxical. Twins ending up different ages is not a paradox, it is just weird. It really annoys me when people claim that that is the Twins Paradox - it isn't, it's just time dilation. Twins both thinking the other twin is older than them is a paradox (which is resolved, of course, by one of the twins not being in an inertial frame the whole time). </rant> --Tango (talk) 12:20, 28 November 2009 (UTC)
This is a tangent, but there's a good depiction of time dilation effects in The Forever War. Fences&Windows 17:26, 28 November 2009 (UTC)
There is a simulator of relativistic effects: http://realtimerelativity.org/. It's single player though. Fences&Windows 18:35, 28 November 2009 (UTC)
Well - yes and no. Obviously if two players of the game are identical twins in the real world - and also in the game - then one of them climbs into a spaceship in-game - and shoots off at a large fraction of the speed of light - then returns home, in the game world, we can loudly assert that the two twins now have different ages - even though they don't in the real world. We could handle that merely by drawing their avatars looking appropriately ancient and youthful. But the problem is that the experience of that happening in the real world would not be reasonable. The twin who is older in-game would have spend his/her time being involved in many more adventures, racking up more 'stuff' (gold, weapons, abilities, etc) than the more youthful twin. But the only way to handle that in-game would be to somehow prevent the younger twin from playing so quickly - or somehow cram more experiences into the in-game experience of the older one. If they each encounter one deep-space battle per day of real-world time, then they'd both end up with the same amount of experience in-game - and that would be wrong. Speeding up the rate at which battles happen for the older twin might make the game unplayable - reducing the number of battles the younger twin would encounter would make the game terminally boring. So it's possible - but it would make for a crappy game, so it's very unlikely anyone will do that in the fully 'general' case. We could of course do it easily if all of the players are travelling around in the same giant spaceship at the same speed. I suppose we could also do it if the maximum speed of spacecraft was limited sufficiently to make the time distortion not too destructive to gameplay. Of course if we did that - and somehow made it work - then the game experience would be more intense for the people who stay home and don't fly off at high fractions of the speed of light - and more boring for those who do. That's not the kind of game mechanic that's going to be hugely attractive to developers because it would tend to be a dis-incentive for high speed travel - which would be the one thing that would make the game seem interesting! SteveBaker (talk) 18:58, 28 November 2009 (UTC)
The problem with the slower end of relativistic travel is that is it completely useless. It's too slow to be useful for interstellar travel and unnecessarily fast for travel within a solar system (Earth to Saturn in 2 hours rather than 20 just isn't worth all the difficulties). You can add in incentives to travel fairly easily, though - quests that require travel, interstellar trade, different difficulty levels in different places, etc.. --Tango (talk) 19:08, 28 November 2009 (UTC)
You can't correctly model the twin effect, but you can model redshift and blueshift without the twin effect. It could look a lot like a relativistic world, with redshifted clocks appearing to run slower and blueshifted clocks appearing to run faster (along with everything else on board the ships, including actions by the players), but when two ships separated and met up again, the occupants would always have had the same amount of play time in between. This would require a lot of buffering of old game state, but it is possible. -- BenRG (talk) 08:02, 29 November 2009 (UTC)
Buffering old game state is useless - MMO games are interactive. You can't interact with actions performed by other players hours or even minutes ago. They have to be playing right now. The only way you stand a chance of doing this is defining one single frame of reference for the game server and force the players to experience speeded up or slowed down game time - that's not going to feel realistic though. SteveBaker (talk) 18:43, 29 November 2009 (UTC)
If this could be done, the person who would have done it is Greg Egan. He is a well known Science Fiction writer but also a competent programmer by trade. He takes great pride in ensuring that everything in his novels are scientifically absolutely accurate and doable (or at least, do not contradict any known scientific principle). In one book, there is a mention of a game of quantum football where the players move the ball, not by kicking it, but by adjusting the quantum wave function around the ball by running around the pitch. This game was incidental, not even central to the plot, so I was quite stunned when I found Egans website years later and right there was a Java applet playable version of the game online following all the rules of real quantum mechanics. If anyone has a good strategy for this game by the way, please let me know, I am completely baffled (I have scored goals, but only by complete random flukes). Sadly, although there are many articles on time dilation on his website, there is no multiplayer game. SpinningSpark 12:11, 29 November 2009 (UTC)
I found a puzzle site that argues that such a game is impossible, because "In a multiplayer game, there's no way to guarantee that players won't talk to each other in the "real world," and that would constitute information traveling faster than the speed of light in the game world, because players could use real world knowledge to make in game decisions.":[3]. There's also a similar discussion on Reddit about this very issue froma month ago:[4] Here's a discussion of how to implement real-time slow motion for a player in a multiplayer game, which is essentially the same problem (it amusingly descends into flaming):[5] They mention that there is a multiplayer game in which time effects are used: TimeShift. Fences&Windows 14:36, 29 November 2009 (UTC)
The possibility of cheating by going "real world" is a bit of a red herring, you can find cheats in the real world for any game. The main question is, can it be done in the game world. As mentioned above, any game implementation will require buffering. To my mind, this will require the "dilated" player(s) to go offline for a period, which is obviously going to detract from the gameplay. For example, take the twins paradox scenario as an example. The twin that went on the journey and then came back to earth will see the earth timeline strongly dilated, the twin that stayed on earth is now much older. At the point the travelling twin decides to return to earth (actually arrives) the gameplay must require that player to go offline and wait out the game. S/he will not be allowed to return and re-enter the game until enough game time has passed on earth so that s/he can appear at the logically correct time. SpinningSpark 15:47, 29 November 2009 (UTC)
If you were determined to prevent out-game communication in an MMO, you could pretty much do that - carefully anonymizing the players in-game, arranging that in-game communication was carefully stripped of personal information and preventing people with similar IP addresses from playing on the same server. SteveBaker (talk) 18:16, 29 November 2009 (UTC)
Cheating aside, if you don't mind forcing players to wait while others catch up then it's easy enough to make this work. Each player has a 4-D location in the game's spacetime at any given real-world time, and they move through game spacetime at a rate of one game-proper-second per real-second while playing. You just have to maintain the constraint that all players are spacelike separated from each other. If a player is about to enter another's future light cone, you suspend that player's game for a while. It's as simple as that. I don't think it would be much fun, though, except as a novelty. It's annoying when a streaming video freezes midway through and says "buffering", and this is pretty much the same thing. -- BenRG (talk) 20:05, 29 November 2009 (UTC)
What about a change in the perception of time, which can occur under certain circumstances and states of mind? ~AH1(TCU) 01:50, 2 December 2009 (UTC)

## Betelgeuse

Did anyone glance Betelgeuse last night from the UK? It seemed unusually bright and particularly red, especially compared to the other stars. I know it's a red supergiant, but the colouration seemed particularly noticeable last night. For what it's worth, I was observing at about 2215 from Oxford. Brammers (talk) 09:56, 28 November 2009 (UTC)

It is a variable star, so it is possible it was genuinely brighter than usual (which would make the colour more obvious due to the way the human eye works). It is also possible it was some kind of optical illusion. I'm not sure where to look to find details of its brightness at given times, so I can't determine which possibility is correct. --Tango (talk) 10:23, 28 November 2009 (UTC)
Well Betelgeuse is most likely a supernova already, and it's light might reach us pretty soon. Pretty soon means anywhere within a few centuries, so there are chances that we might see it ourselfs. --131.188.3.21 (talk) 14:22, 28 November 2009 (UTC)
a) To avoid unnecessarily convoluted language we usually use the present tense to refer to events for which the light is currently reaching us, b) I think "most likely" is overstating the probability. It is certainly possible, but far from certain. Our article says it "may" go supernova (by which it means the light from the supernova will reach us) in the next 1000 years and it is 640 light years away, so that is a long way short of it being "most likely" to have already happened. --Tango (talk) 15:18, 28 November 2009 (UTC)
Pardon me for not being clear enough. Assuming a symmetrical probability distribution for the event happening here (I mean, light reaching us) in the next 1000 years places the probability of it already been happened there above 0.5 in case of it being farther than 500 light years away. Of course, this might be just a wild speculation. Betelgeuse shrinking 15% in the last few decades and accelerating, however, shifts (at least I think) the mean of the probability distribution to a closer time point. —Preceding unsigned comment added by 131.188.3.20 (talk) 16:16, 28 November 2009 (UTC)
"May happen" is very different to "will happen". --Tango (talk) 17:42, 28 November 2009 (UTC)
Ok, then mentally replace "most likely" with "above 50% chance" and "will happen" with ... erm.. where did I wrote this? --131.188.3.20 (talk) 17:49, 28 November 2009 (UTC)
I think Tango means that since the SN only may happen during the next 1000 years, we can't say that the probability of it happening within 640 is > 0.5. Assuming a uniform distribution: P(t<640) = 0.64P(t<1000) < 0.64, but we have no lower bound on P(t<640) since all we know is that P(t<1000) is greater than 0. Olaf Davis (talk) 21:01, 28 November 2009 (UTC)
Why are we whispering? LOL --Tristan. Crap, I've got to work on my paper! —Preceding unsigned comment added by 76.235.111.185 (talk) 23:20, 28 November 2009 (UTC)

Thanks for the answers guys :) I never realised variables could be so variable! Brammers (talk) 17:15, 1 December 2009 (UTC)

Yes, but Betelgeuse has apparently shrunk about 15% in diameter in the past 15 years, so the supernova process may be underway from our viewpoint. There are known unknowns and unknown unknowns. ~AH1(TCU) 01:49, 2 December 2009 (UTC)

## Military Equipment

Greetings! How do you call this piece of equipment carried by the soldier in front? Thanx! Grey Geezer Grey Geezer 10:02, 28 November 2009 (UTC) —Preceding unsigned comment added by Grey Geezer (talkcontribs)

It's an M224 mortar without the support or base - BTW not sure this shouldn't have been on the miscellaneous desk. Mikenorton (talk) 11:28, 28 November 2009 (UTC)
Thank you for the answer! (I followed "engineering and technology"). 62.241.104.212 (talk) 01:04, 29 November 2009 (UTC)

## Isomorph only in Developmental Biology?

I've posted this as a query on the Talk page for Isomorph. I'd appreciate a confirmation and/or explanation of whether this word can serve as a noun for non-living structures whose substance is unchanged when its shape is altered. Context: a descriptor of the Tower of Hanoi puzzle. -- Deborahjay (talk) 14:23, 28 November 2009 (UTC)

Whether or not "isomorph" is a valid word in English in different fields is a question better put to the language desk. Wikipedia articles should not be, or have added to them, dictionary definitions. Wiktionary is the project that likes that stuff. Isomorphism has a meaning in mathematics and a number of other fields, see Isomorphism (disambiguation). Alternative meanings of the term "isomorph" should be explained in the appropriate article, if there is one, and the isomorph article left as isomorph (biology). For the Tower of Hanoi example, I would think that the relevant article would be group isomorphism. SpinningSpark 17:10, 28 November 2009 (UTC)

## Are there people with two anuses?

I just watched this porno and the girl in it appeared to have two anuses. Upon Googling, there does seem to be something called 'duplication of the anus' and it's and established medical phenomenon. Why then is there no information about this in Wikipedia?--Damriteido (talk) 14:49, 28 November 2009 (UTC)

You've answered your own question (per the heading) by searching on Google and finding it an established medical phenomenon. As Wikipedia content is written by people with reliable information and citable sources, go right ahead and add it to the Human anus article, possibly right after "birth defects." If you're not sure how to edit directly, start by adding this information (as you did here) with your sources in a New Section on the Talk:Human anus page and follow the responses. -- Deborahjay (talk) 15:05, 28 November 2009 (UTC)
We get these kinds of questions fairly often - and in every case (so far) we've established that what you see is just a movie-special-effect - generally latex and makeup. So, no - do not add it to any Wikipedia articles - Porn movies do not constitute a reliable source! SteveBaker (talk) 18:40, 28 November 2009 (UTC)
Well the porn movie is obviously bullshit but the medical condition does really exist [6] [7] [8] [9] [10] et al (had planned to offer Bing result but it wasn't particularly useful). I'm not convinced this belongs in the human anus article though. There are many very rare medical conditions which likely don't belong on such central articles (perhaps they belong on some other article). And yes, per the sources "congenital double anus are very rare" & "Anal canal duplication (ACD) is the most distal and the least frequent digestive duplication" it is very rare. That's probably also one of the reasons no one has written about it yet. Incidentally, don't expect it to be anything like the porn movie. Nil Einne (talk) 20:56, 28 November 2009 (UTC)
Some learners of Italian (or Spanish) seem to report such things, though. Italian makes a clear distinction between single and double consonants. If you want to say you're twenty-seven years old, say clearly ho ventisette anni and definitely not ho ventisette ani. It's important.
When I studied in Italy, there was an intensive language course for a couple of months prior to the school year, and one day we had an exercise where one student role-played someone ordering in a restaurant. She ordered pene con pomodoro. --Trovatore (talk) 18:53, 28 November 2009 (UTC)

## How exactly would FTL violate causality?

I think I know quite well most of realtivity, but there is still one part which I can't figure out completely. Let us try a Reductio ad absurdum method: Supposed we had a small spaceship capable of faster than light travel, how would it be possible to send matter, or at least information to the past? What would be an example of an exact scenario which would lead to this? --131.188.3.21 (talk) 15:29, 28 November 2009 (UTC)

See Tachyonic antitelephone#Sending signals into one's own past. Red Act (talk) 16:29, 28 November 2009 (UTC)
Even more thorough than our article is the source our article cites: The Tachyonic Antitelephone, published in Physical Review (1970) by the American Physical Society (a decidedly reliable source on such matters). The conclusion is that experimental study of faster-than-light phenomena will yield negative results or result in contradiction. Nimur (talk) 22:09, 28 November 2009 (UTC)
Sending a message at superluminal speed from O via A to B into the past. Both observers consider the temporal order of the pairs of events O and A as well as A and B different.
There seem to be problems with the math in that article. v > 2*a / (1+a^2) Here "a" is dimensionless while "v" is in meters/second. However, thank for the direction where I can do more searching. --131.188.3.20 (talk) 14:39, 29 November 2009 (UTC)
See also the diagram here, which shows it quite vividly. "Therefore an object moving faster than light, say from O to A in the adjoining diagram, would imply that, for any observer watching the object moving from O to A, there can be found another observer (moving at less than the speed of light with respect to the first) for whom the object moves from A to O. The question of which observer is right has no unique answer, and therefore makes no physical sense. Any such moving object or signal would violate the principle of causality." --Mr.98 (talk) 00:07, 29 November 2009 (UTC)
Implicit in these kinds of explanations is the idea that the thing that happens at the earlier coordinate time is the cause. I don't understand why anyone would assume that; there's no physical justification for it. I'd assume that the thing that happened at the earlier cosmological time would be the cause, since the low entropy of the big bang is supposed to be the reason for the second law of thermodynamics, which defines the arrow of time. Using cosmological time avoids the logical incoherence of using coordinate time. But it has its own problem, namely that there are spacelike geodesics that reverse direction in cosmological time. The Phys. Rev. D paper seems like a waste of space to me. It spends pages on an obvious contradiction that should have been a one-sentence footnote, and it never talks about the nature of causality, which is the essence of this question and is still very poorly understood 40 years later. -- BenRG (talk) 07:45, 29 November 2009 (UTC)

## Optimum positioning of bookshelf brackets?

I'm putting up some bookshelves. These consist of brackets which support chipboard or contiboard 'planks'. The brackets can be positioned anywhere. In my experience the heavily loaded chipboard shelves tend to sag over time. Where would be the optimum place to position the two brackets to minimize the amount of sagging? If, for example, the brackets were placed right at the ends of the shelves, then it would sag in the middle. Moving the brackets in a quarter of the shelves length, so that there was half the length of the shelf between them, would be better: the ends of the shelves would be cantilevered, and nowhere on the shelf would be more than a quarter of its length from the brackets. But the two quarters of the shelf between the brackets would get some support in the middle from each other - so the brackets could be moved further apart. Has anyone ever calculated the optimum place to position two brackets under a bookshelf? 92.27.169.45 (talk) 17:28, 28 November 2009 (UTC)

That would depend on the material (of the plank), one would have thought. Whether they've worked it out for some things, I don't know. - Jarry1250 [Humorous? Discuss.] 17:34, 28 November 2009 (UTC)

I do not think the material the plank was made of would affect the optimum position, although it would affect the amount of sag seen. That suggests that a spline of cardboard could be used as a test material. 92.27.169.45 (talk) 17:45, 28 November 2009 (UTC)

Are you assuming an equal weight of books on each part of the shelf? --Phil Holmes (talk) 17:38, 28 November 2009 (UTC)

Yes. 92.27.169.45 (talk) 17:42, 28 November 2009 (UTC)

With equal weight all along the shelf I think it would bend according to the cube of the length from a support, square for the length and another bit for the weight of the length. Thinking of the bit in the middle as being rather like four ends stuck together my guess would be you want the middle bit to be 2 times the cube root of 2 long compared to 1 for each end. So about 2:5:2 for the lengths. You really need somebody who has done this sort of thing rather somebody who sticks their finger in the air, an engineering student for instance would I'm sure be able to do it no problem. Dmcq (talk) 18:09, 28 November 2009 (UTC)
If I was just sticking up a bookshelf I believe I would have put the brackets further apart than what I've calculated there. So it'll be interesting to see if my unthinking part is being cleverer or not :) Dmcq (talk) 18:21, 28 November 2009 (UTC)
There are three different failure modes to consider:
1. A bracket pulling off of the wall or snapping or something because the load is too great.
2. The plank snapping because the load is too great.
3. An unbalanced weight on one extreme end of the plank causing the opposite end of the plank to flip upwards.
The last one is a bit tricky - if the plank is just resting on the brackets, that's a different situation than if the plank is screwed to the brackets.
For the first failure mode - it actually doesn't matter how the brackets are situated - so long as everything is symmetrical. Each bracket supports half of the weight and it doesn't matter whether they are closer to the center or out at the ends because symmetry guarantees that they are each bearing the same weight.
For the second failure mode. If you positioned the brackets right out at the ends - or both at the center(!) then the center of the plank is what will break. But if you place the brackets at the 25% and 75% positions (as you suggest) then the force on the center of the plank is zero - a perfectly evenly overloaded plank would theoretically break in two places - right over the brackets. That's better because you've halved the amount of leverage and effectively doubled the strength of the thing. It seems to me that moving the brackets either closer or further from that position increases the leverage.
For the third case - there is no problem when the shelf is perfectly evenly loaded - but if it's asymmetrically loaded then there are two cases to consider:
• If the shelf is just layed onto the brackets without being fixed down then if (say) the brackets are at the 25%/75% position and you put a heavy book on one end of the plank - then the opposite end might flip up. The fix for that is to put the brackets as far apart as possible.
• If the shelf is fixed down onto the brackets then when there is a heavy weight on one end of the plank - the bracket at the opposite end is helping to hold the plank down and stopping it from flipping. But still, the best case is when the brackets are at the extreme ends.
So there is a trade between the risk of an asymmetric flip (best minimised by putting the supports at the ends) and the risk of a plank snap (best minimised when the brackets are closer to the center...maybe 25%/75%). This is a contradictory requirement - so we know that the optimum position depends at least in part on the firmness with which the plank is attached to the brackets and the weight of the plank itself - contrasted with the strength of the material from which the plank is made. It follows that we can't answer the question of optimum positioning until we know something about the strength-to-weight ratio of the plank. A light-but-strong plank is unlikely to break but more prone to flipping under asymmetric loads - so the brackets need to be further apart. A heavy-but-weak plank would be more prone to breaking than flipping - so the brackets need to be closer together.
Hence we can't come up with a definitive answer without resorting to some ugly questions of material science!
SteveBaker (talk) 18:24, 28 November 2009 (UTC)
You have to be a bit careful with the first case — the position of the brackets can matter because the shelf (as analyzed below) can deform when loaded. (And there are static and dynamic loads; consider the effect of dropping a CRC Handbook or the like from even a short distance up.) In the simplest case, deflection of the beam applies a torque to the mounting brackets. There can be additional, interesting forces if the shelf is fairly deep and the front-to-back loads are uneven. TenOfAllTrades(talk) 02:11, 29 November 2009 (UTC)

Thanks, but the risk of failure does not concern me here - the problem is whetre to position the two brackets to get the least deformation in the plank/beam. 92.27.169.45 (talk) 21:32, 28 November 2009 (UTC)

Here is a very "theoretical" solution. Assuming a uniform load, ignoring the other modes of failure, and assuming the shelf only deforms elastically, then we can apply the Euler–Bernoulli beam equation. Solving this for a uniform beam with a uniform load tells us that the deflection u(x) must be a quartic in x. Boundary conditions are that u = 0 and du/dx = 0 at each of the supports. If the supports are at a and -a then
${\displaystyle u(x)=k(x^{4}-2a^{2}x^{2}+a^{4})}$
Deflection at centre of shelf is ka4. If optimum configuration is such that deflection at each end is equal to deflection at centre then
${\displaystyle k(x^{4}-2a^{2}x^{2}+a^{4})=ka^{4}}$
${\displaystyle \Rightarrow x={\sqrt {2}}a}$
So length of beam is ${\displaystyle 2{\sqrt {2}}a}$, and distance between supports is ${\displaystyle 1/{\sqrt {2}}}$ of the length of the shelf. Gandalf61 (talk) 18:37, 28 November 2009 (UTC)
Is du/dx = 0 at the supports a reasonable model of a board simply resting on top of a bracket? Intuitively it feels like you'd be likely to get non-zero slope at the brackets. Olaf Davis (talk) 20:55, 28 November 2009 (UTC)
I hadn't considered that in my version either. I think you're right, the bracket would not hold against the small twist even if it was screwed on. Plus this solution doesn't consider the condition between the brackets and the ends which because it is considered fixed at the brackets should be modelled by another equation. I guess you mean the bracket should be considered as a pin in the terminology of the article. Must go and get some paper and work yet another version out. Dmcq (talk) 09:08, 29 November 2009 (UTC)

Does that mean that the supports ought to be 15% of the length of the shelf in from the end? I'd like the average absolute deflection to be as little as possible. 92.27.169.45 (talk) 21:32, 28 November 2009 (UTC)

Yes, to the nearest %. However practically my experience with making wooden bench seating is that it matters a lot exactly whether the supports are screwed into the shelf (there is a screw hole in the underside of many of them) and how rigid the supports are anchored. --BozMo talk 21:56, 28 November 2009 (UTC)
Particularly make sure the brackets are anchored into the wall at a stud, and not just into drywall. Here's a tutorial; if you don't know how to find wall studs, you can buy an electronic stud finder tool which helps detect them. Nimur (talk) 00:41, 29 November 2009 (UTC)

We usually have plastered brick walls where I live. 89.240.199.137 (talk) 15:19, 29 November 2009 (UTC)

Henry Petroski's The Book on the Bookshelf. New York: Alfred A. Knopf. 1999. ISBN 0-375-40649-2. may be of interest to the OP.John Z (talk) 08:27, 29 November 2009 (UTC)

What about where you've got three supports rather than just two? 89.240.199.137 (talk) 15:20, 29 November 2009 (UTC)

Unless you get them vertically positioned very carefully, that could be worse than two. If the middle one is a tiny bit high, then might be supporting most of the weight just on that one. Or even worse, or having the torque of an entire half (one side of the middle one) against similar torque of the other, trying to break the board across this pivot point. I can't find a ref at the moment, but I remember reading something about Roman or Greek engineers learning to use two-point support when storing their stone columns horizontally. DMacks (talk) 15:47, 29 November 2009 (UTC)

I think you are missing the point. I am not concerned with the brackets breaking off, which you and someone else who wrote a long piece above seem to be, but with the chipboard shelf sagging after a few months under a heavy load. Where I live most houses have solid brick walls, perhaps you are thinking of the problems that may arise with the US style of house construction. 78.147.183.186 (talk) 21:56, 29 November 2009 (UTC)

An alternative approach (which I have used) is to put the brackets almost at the end of the shelves, but to screw some pieces of wood to the underside of the shelves to male them more rigid - I use 2"x2" wood, long enough to be just shorter than the distance between the supports. --Phil Holmes (talk) 15:41, 29 November 2009 (UTC)
I found a site [11] which looks like the bookshelf with pins supporting. Equating the deflection at the ends and at the middle with x being the overhang compared to 1 between the supports I got an equation 48x^4+96x^3+24x^2-16x-5=0 which using the Mathematica site gave me a solution of x=0.403. So that says the lengths should be as 2:5:2. Which is practically exactly my last solution even though then I considered the bookcase fixed at the brackets. Since that's in between the two otehr solutions given I claim the consensus position :-) (I must admit just putting a piece of wood underneath would work but it's so so, well practical. Words fail me) Dmcq (talk) 23:01, 29 November 2009 (UTC)

Thanks again. I've realised that I will be using three supports, rather than two. What is the optimim positioning for them please? One of them will be in the middle. And the previous calculation was that the brackets should be 15% in from the end (as far as I understand), the more recent calculation is that they should be 20% in from the ends. So is it 15% or 20%?78.146.171.75 (talk) 12:25, 30 November 2009 (UTC)

Since SteveBaker said 25% and Olaf Davis said about 15% and I said about 22% that's why I was claiming the middle ground. But anyway I'm right - you don't expect somedbody here to admit they're wrong do you? ;-) As to the 3 supports I'd guess positioning 2:5:5:2 would be good though the end should probably be slightly further out I think, which would make the outer supports 2/14 = 14% from the ends. Though as Phil Holmes says putting a bit at right angles underneath will solve the sagging problem whether you have two brackets or three. Dmcq (talk) 15:49, 30 November 2009 (UTC)

## Disease question

Is there a name for the phenomenon where one is sick, and lights seem dimmmer? P.S.:No medical advice, I am writing a paper for my first-year medicine course. --Tristan —Preceding unsigned comment added by 76.235.111.185 (talk) 23:17, 28 November 2009 (UTC)

Hypoesthesia? See also photosensitivity and light sensitivity, and photophobia (which is sort of an opposite effect). Nimur (talk) 00:33, 29 November 2009 (UTC)

I mean, in an objective sense it sounds like you're talking about Miosis, but that is something physical that happens to the eye, so may just be one cause of the symptom you are describing. The article might be a good jumping off place for you though. --Shaggorama (talk) 08:23, 29 November 2009 (UTC)