Wikipedia:Reference desk/Archives/Science/2013 October 31

= October 31 =

Testing for Pink Noise
I am aware of statistical tests for white noise in a real signal (Box-Pierce, Ljung-Box tests) and red noise (Percival test) but am unaware of any statistical tests for pink noise in a signal and cannot find any literature on this, only properties of pink noise and the generation of pink noise. Does anyone know of any? — Preceding unsigned comment added by 211.31.25.66 (talk) 07:48, 31 October 2013 (UTC)


 * Articles related to Flicker noise have detection and elimination techniques. Suppressing flicker noise below the thermal noise floor is generally the goal. Double correlated sampling and chopper stabilization are techniques to move the flicker noise below thermal noise.  detection is basically all 1/f noise is pink noise. --DHeyward (talk) 08:11, 31 October 2013 (UTC)
 * I think it's important to point out the distinction between pink noise and flicker noise, which our articles don't make clear. Pink noise is any noise with a 1/f (3 dB per octave) spectral density. Flicker noise is a type of pink noise produced in electronic devices.  The two terms aren't synonymous. Tevildo (talk) 22:14, 31 October 2013 (UTC)
 * Flicker noise does from the description seem to resemble shoot noise but where every single electron contributes and thus it looks different but have the same base? Electron9 (talk) 23:39, 31 October 2013 (UTC)
 * Shot noise has a white (frequency-independent) spectral density, not a pink (1/f) density. I'm afraid I don't understand the rest of your question. Tevildo (talk) 00:06, 1 November 2013 (UTC)


 * It is indeed important to realsise that there is a very important difference between flicker noise (also known as 1/f noise) (f for frequency) and pink noise. The Wikipedia articles on flicker noise and pink noise are all mixed up - the authors have been confused on the meaning of "1/f".
 * Flicker noise arises in vacuum tube cathodes, junctions between thin metal films, and junctions between metals and semiconductors, has a power spectrum that drops 6 db for each octave increase in frequency, and rises in proportion to the square of the DC current thru the junction. Saying that it drops 6 dB for each octave increase in frequency is of course the same as saying flicker noise voltage is proportional to 1 / frequency.  Since power is proportional to voltage squared, power drops 4:1 for each 2:1 increase in frequency.
 * Pink noise is white noise that has been filtered to produce a power spectrum that drops 3 dB (ie power halves) for each octave increase in frequency. When expresed as a voltage, pink noise halves for each 4:1 increase in frequency. Because of this, pink noise cannot be produced by a capacitor shunting a noise current source.  In analogue circuits, pink noise is produced by a complex network of capacitors and resistors that approximates an impedance proportional to (1/f)1/2, not 1/f.
 * One way to prove out pink noise is to inverse filter it (i.e., use an A = k.f1/2 filter) back to white noise in a finite bandwidth and then apply the usual tests for band limited white noise.
 * Note: Those of us old enough to have worked with vacuum tube operational amplifiers, and those of us who are old enough to have listened to the amplified Low frequency noise from the early junction transistors (eg OC71, AC125, Japanese HJ15, etc) know why popcorn noise is called popcorn noise. And we know it is random, but it sure doesn't sound like pink noise or filtered thermal noise.
 * A classic textbook that covers white, coloured, and popcorn noise is: Electrical Noise by W R Bennet, McGraw Hill 1960. An oldie but a goodie. Poporn noise discussion starts on Page 87.
 * 127.0.0.1 (talk) 00:24, 1 November 2013 (UTC)
 * Perhaps some sample sound files (.wav) would make it easier to "get" ? Electron9 (talk) 04:46, 1 November 2013 (UTC)
 * I had a quick search online for a popcorn noise sample, without success. That's not surprising, as popcorn noise has long been just about a non-problem.  It was a problem with the early (1950's) germanium junction transistors.  Some were worse than others - you could buy more than you needed and select on test the good ones.  To the best of my knowlege, no physicist has figured out a workable theory for popcorn noise yet, but manufacturers have long worked out from experience factory processing methods to all but eliminate it - at least to the degree that shot noise predominates.   When you amplify the noise from a good bipolar transistor, it sounds just like white noise (which is of thermal origin - the random movement of charge carriers).  It sounds as in "hissssssss.....".  It you filter white noise to make pink noise, by comparison it sounds more of an "ahhggrrrrrr....".  If you then band limit it to say 0 to 300 Hz, it then sounds like LP record rumble.  If you amplify the noise from the early germanium junction transistors (OC71 & the like), and band limit it to the same 0 to 300 Hz to get rid of the masking shot noise, it sounds vaguely like popcorn popping in those big display poppers movie theaters have.  It sort of comes and goes a bit like the noise of popping popcorn does.
 * Incidentally, another name for popcorn noise is burst noise. Wikipedia has a short article entitled Burst Noise, apparently written without knowlege of the popcorn / 1/f article (or was it vice versa?)
 * 120.145.135.143 (talk) 05:14, 1 November 2013 (UTC)
 * Any takers on correcting the relevant articles? ;-) Electron9 (talk) 11:28, 1 November 2013 (UTC)
 * Certainly not me. If I was to set out to correct all the errors in Wikipedia articles that come within scope of my chosen professional field, I'd be doing it full time for years - only to have some peanut revert it again. Certainly not me, not until Wikipeia institutes a system of moderators at at any rate. 120.145.135.143 (talk) 12:07, 1 November 2013 (UTC)
 * One way to deal with it is to produce a "good version". When peanut lifeforms come around and mess it up other people will find the good version in the change history. Usually the coherent content and solid sources is a sign of good a article. Electron9 (talk) 19:52, 1 November 2013 (UTC)

Agriculture and global food supply
Can you tell me what the current amount of staple foods needed for the world supply is? I want to know the amount of food produced for at least 3 staples and the total world population of those 3 staples.--131.96.121.122 (talk) 13:53, 31 October 2013 (UTC)


 * Is meat one staple, grain another staple, and fruits still another staple?


 * Also, if meat is one staple, does this mean that beef, mutton, pork, and chicken meat are all one staple?--131.96.121.122 (talk) 14:40, 31 October 2013 (UTC)
 * I think you misunderstand the concept of a staple food. There is never more than one staple in a given community with a common diet. --Trovatore (talk) 18:31, 31 October 2013 (UTC)


 * Is beef a staple food?--98.88.147.108 (talk) 05:45, 1 November 2013 (UTC)
 * Not really, according to the staple food article. Staples are primarily plants rather than animals. ←Baseball Bugs What's up, Doc? carrots→ 06:24, 1 November 2013 (UTC)
 * Thanks.--98.88.147.108 (talk) 07:08, 1 November 2013 (UTC)

Actually, having looked at the article, I think it fails to define the concept strictly enough. As I understand it, a true "staple" is a single food from which you get the overwhelming majority of your calories, say 80%, day in and day out. That's why there can never be more than one, and for most people, zero. --Trovatore (talk) 17:43, 1 November 2013 (UTC)

World Population in 50 years
What is the projected increase in world population for the next 50 years? (If you can, give me a weblink, too.)--131.96.121.122 (talk) 13:55, 31 October 2013 (UTC)


 * Population growth has a projection. OsmanRF34 (talk) 14:09, 31 October 2013 (UTC)


 * So, we're looking at a world population of 10 billion in 2063.--131.96.121.122 (talk) 14:18, 31 October 2013 (UTC)

These are the most recent United Nations World population projections: http://esa.un.org/wpp/unpp/panel_population.htm Futurist110 (talk) 05:38, 3 November 2013 (UTC)

Trousers
Cuold you please explain me how wearing two trousers (or, in general, wearing multiple layers of clothes) produce warmth?

Sorry for a stupid qestion, but I really don't know. --Roman1969 (talk) 14:44, 31 October 2013 (UTC)


 * This will trap a layer of air between the clothes, and air has a very low thermal conductivity coefficient. So, what then happens is that the same amount of heat that your body produces must still escape via your clothes, but this heat will escape from the top layer of your clothes, So at that top layer the temperature will be the same (because heat transfer depends on the temperature difference and the heat transfer between the top layer and the air will be the same). Then the hat transfer from your body to that top layer must also be the same in bith cases, but nowwith more air trapped between the top layer and your body, the tamperature difference must be larger, so the temperature at your skin will be larger. Count Iblis (talk) 14:56, 31 October 2013 (UTC)


 * An air layer is part of the answer, but two layers of the same material also cuts in half the heat transferred by conduction through the fabric, and also decreases the flow of cold wind if the fabric is porous enough to allow any air current. Edison (talk) 18:55, 31 October 2013 (UTC)


 * Layers also provide another advantage: It's important to prevent sweat from building up, which can then make you very cold and uncomfortable later. With layers, you can add or remove layers as needed, to keep comfortable.  If you had a single, thick item of clothing, you would lose this flexibility. StuRat (talk) 16:49, 31 October 2013 (UTC)


 * This is probably clear, but just in case: Clothing doesn't produce any warmth, it is only your body that produces warmth. Clothes only reduce the heat loss of the body. You can wrap a stone in as many layers as you wish and it will not warm up.86.179.30.226 (talk) 22:41, 31 October 2013 (UTC)


 * But a hot stone will cool more slowly (to really state the bleedin' obvious). Alansplodge (talk) 13:57, 1 November 2013 (UTC)


 * A hot stone wrapped in varying layers :-) . {The poster formerly known as 87.81.230.195} 84.21.130.203 (talk) 16:25, 1 November 2013 (UTC)


 * Some times that kinda stone gets hot because it is missing a particular layer... -- Jayron  32  20:04, 1 November 2013 (UTC)


 * I should add that the reason sweaty clothes are so bad is that sweat greatly increases the thermal conductivity of the material, allowing body heat to escape much more quickly. StuRat (talk) 06:11, 3 November 2013 (UTC)

RPG-29
I have a curiosity about RPG-29 rocket: in its technical description is said that it could penetrate 750 mm of RHA (Rolled homogenous armour) or 1500 mm of reinforced concrete. This sound to me very strange: the reinforced concrete has a tensile strength of 12-15 megapascal and the RHA of 1000-1200 megapascal (80 times higher). How it's possible so low difference beetwen the two penetration? Isn't maybe the data for RHA overstimed or there is any other reason? 80.116.228.89 (talk) 17:37, 31 October 2013 (UTC)


 * An RPG uses a shaped charge. The liner of the charge is compressed into a narrow jet of metal moving at speeds up to 14 km/s. At those speeds, the strength of the armor plays a minor role, it's mainly the density or weight that determines how far the charge penetrates, that's why some tanks use depleted uranium in their armor. Ssscienccce (talk) 18:26, 31 October 2013 (UTC)
 * See also composite armour, that mentions that fused silica glass had a higher stopping power than steel (not sure that can be explained by density). To defend against hollow (shaped) charges, explosive reactive armor has been developed: an explosion moves part of the armor while the jet of the shaped charge is penetrating, disrupting the shape of the jet and diminishing the penetrating depth. To defeat reactive armor, the RPG-29 and other HEAT rockets use two shaped charges, the first will trigger the explosive charge in the armor, the second strikes milliseconds later, when the armor isn't "reactive". Ssscienccce (talk) 19:13, 31 October 2013 (UTC)
 * A cheaper defence is Slat armour, a heavy grill that detonates the charge before it reaches the body of the target vehicle. It is however, equally vulnerable to the tandem-charge weapons that Ssscienccce describes above. Alansplodge (talk) 13:55, 1 November 2013 (UTC)

'Real world length contraction' moved to archives. Why?
I'm new here... wondering why discussion of my question "'Real World' Length Contraction" was deleted from the current menu and moved to the archives, while, for instance the "vomiting while pregnant" question and others remains on the up-front menu. Wherever I raise the question of a variously contracted Earth diameter, or contracted distances between stars... depending on all varieties of relativistic frames, I am either called a crank (and banned from science forums) or told that challenging mainstream length contraction is inappropriate... or the topic is hidden in the backwaters, like the archives here. Will someone here please explain why my question was brushed aside as above with no answer? Thanks — Preceding unsigned comment added by 63.155.141.178 (talk) 17:58, 31 October 2013 (UTC)

I just asked about the above but forgot the headline... and the question disappeared. — Preceding unsigned comment added by 63.155.141.178 (talk) 18:04, 31 October 2013 (UTC)
 * Because questions 5 days old are archived automatically. Ssscienccce (talk) 18:12, 31 October 2013 (UTC)


 * If there's more you feel needs to be explored, feel free to open a new question along those lines. Ideally, don't just ask the same question (unless, say, no one responded at all), but focus on what you feel was not addressed. --Trovatore (talk) 18:16, 31 October 2013 (UTC)

Thanks. The question was left hanging at the challenge of a shrinking Earth diameter, depending on the velocity and direction of relativistic frames observing it. The muon question was also left unanswered. I'll open a new question on those cases of supposed contraction specifically.


 * The point is that you come over as quite hostile. You're essentially saying "I don't believe in Special Relativity - it's impossible" - which is not asking us a question.  In fact, you're entirely wrong.  Special relativity is true - it's one of the better tested scientific theories - and much of what happens in the universe can only be explained by it being true.  People have gone so far as to measure the ticking of the clocks on actual, for real spacecraft to see if time is slowed for them - and it is.  If you own a GPS unit - you may be surprised to know that there is software inside that little box that has to compensate for both special and general relativity in calculating where you are in the world.  This stuff really isn't up for debate.


 * So we're telling you the answer - "The Truth". It's OK if you don't fully understand it - by all means, ask for clarification.  But issuing "challenges" and being generally combative is hostile to our volunteer staff, who's mission here is to tell you the truth and explain it if you don't understand.  We're not here to disprove or challenge whatever wonky ideas you may have of your own.  If you wish to dismiss all of mainstream science on this point and ignore what 100% of the respondents here are telling you, that's fine - go away and be flat out wrong someplace else.  But please don't argue with us.  We're telling you the truth as researched most carefully by hundreds of people who were all a lot smarter than any of us here!


 * Subjects like relativity and quantum theory are strongly contrary to "common sense" - but that's not because they're wrong - it's because we humans have evolved in a world where nothing much moves anywhere near to the speed of light (except light) and all of the objects we deal with routinely are bigger by far than an atom.  The "common sense" that we evolved as stone-age hunter-gatherers on the African plains is pretty much useless for explaining what goes on in realms that it did not evolve to handle...so we find it hard to get our heads around the reality of the universe at these crazy speeds and scales.  I forget who said it, but:  It's not natures' duty to be understandable by mankind.


 * Perhaps you'd do our volunteers the kindness of toning down your rhetoric - and rather than telling us that this is all wrong and impossible (which it's definitely not), confine yourself to politely requesting clarifications for the parts that you don't understand. Do that, and things will progress more smoothly.


 * SteveBaker (talk) 21:38, 31 October 2013 (UTC)


 * I didn't read all that, but you apparently missed his question, the OP asked for an explanation or the underlying mechanisms regarding length contractions. Not that hard is it? And of course, "100% of the respondents here are telling you" is not accurate (reread the thread).  --Modocc (talk) 00:17, 1 November 2013 (UTC)


 * Should we run an experiment with a plane and measure the Earth's various contractions while dog-fighting, we could build a huge database and subject it to supercomputers and produce funky maps, but that would not necessarily change how the data is processed. However, I'm a scientific realist, because our science is evolving (for instance, compare how messed up ancient land maps used to be compared with today's detailed maps) and it's going to take some effort to progress further. Like Steve said, it is OK to ask for clarification on relativity, but this isn't the appropriate place for debate (see the policy guidelines above). -Modocc (talk) 01:40, 1 November 2013 (UTC)

Contracted Earth diameter and atmosphere depth
My "real world length contraction" question was moved to the archives (after the 5 day limit, I'm told... but doesn't seem to apply to other topics), so here are the unanswered challenges from that exchange: If a relativistic frame (future ship or whatever) approaches Earth in the direction of its axis at .866c, special relativity (SR) says that it will measure the polar diameter to be about 4000 miles. Then if it turns around and approaches at the same velocity in the direction of the equatorial diameter, that will now be measured as 4000 miles, and the polar diameter will have restored to its proper length just under 8000 miles. SR insists that all frames are equally valid, so then Earth must "morph" with every possible velocity and direction from which it could (relativistically) be observed. True of false?

Muons traveling through our atmosphere have higher velocities than lab-accelerated muons, so they decay more slowly ("live longer") and therefore travel further than lab muons, so they can reach Earth's surface. SR claims that the depth/thickness of the atmosphere contracts "for those muons." But the atmosphere remains about 1000 km all around Earth at all times, not contracted by what incoming muons would "observe." Different observations can not change physical objects or distances. SR claims that it does. SR advocates now have another 5 days to reply to this challenge. — Preceding unsigned comment added by 63.155.141.178 (talk) 18:51, 31 October 2013 (UTC)


 * SR says that the squared invariant distance between two points in space-time (x,y,z,t) and (x',y',z',t') is


 * s^2 = (t-t')^2 - [(x-x')^2 + (y-y')^2 + (z-z')^2]


 * where the time and the positions are measured in the same units (so the speed of light, is set equal to 1). So, SR disputes the validity of Pythagoras' formula and it disputes that time intervals are invariant. Count Iblis (talk) 19:32, 31 October 2013 (UTC)


 * I don't see your problem here. Relativity says that sizes, masses, rate of passage of time and a bunch of other things depend on the frame of reference of the observer.   In your example, people approaching the earth from different directions and speeds would indeed see the earth as having different sizes and shapes simultaneously.  The idea that two people perceive things differently because they are moving at different speeds and directions should come as no surprise to you.


 * It's not quite a correct analogy - but consider the doppler effect for sound.


 * There is a person driving a fast car along a straight road and a person standing still at the side of the road. As he's driving along, the first guy leans on the horn and hears a sound of constant pitch as he passes the guy who's standing still.  But the guy standing on the side of the road hears a higher pitched sound as the car approaches him and a lower pitched sound as it passes him and heads off into the distance.  Ask the two people what pitch the horn had and they'll disagree.  The horn doesn't have to have two pitches simultaneously - it's just that the frame of reference for the two observers is different.  Position 100 people at different points along the road, all moving at different speeds and you'll get 100 different perceptions of the exact pitch of the car horn.


 * CAVEAT: This isn't actually a very good analogy because sound exhibits doppler differently from the way light does - but the point is that it's OK that an object can simultaneously be perceived as being many different sizes, masses, etc by different observers.


 * As I said before, you have to read (and completely understand) things like the Ladder paradox. In that example, a fast-moving 20' ladder fits into a 10' building - from the point of view of an observer standing next to the building - and the 20' ladder moves through the 5' building from the point of view of an observer riding on the ladder.  This is entirely non-contradictory - but it is confusing as all hell for people who aren't comfortable with special relativity.


 * So the answer to your first question is that the earth doesn't "morph" - it simply "is" a whole bunch of different sizes (etc) depending on the frame of reference of the observer.


 * Your description of what happens with Muons is correct. From our point of view, they are moving ungodly fast, so time for them has slowed down - so they make it through the atmosphere without decaying.   From the muons' point of view, time is ticking along normally - but the earth (and it's atmosphere) has contracted to a nearly flat circle and the atmosphere is so thin that it can make it through easily.  This is not contradictory - it's an entirely consistent story - and the outcome (that the muon makes it through the atmosphere) is perfectly correct from both viewpoints.


 * You boldly assert that "Different observations can not change physical objects or distances." - but you are quite wrong. That is exactly what does happen.  Consider the behavior of muons to be proof of that.  There have been numerous other experiments that demonstrate this kind of thing.  Special relativity is a proven fact - weird though it seems.   You really can fit a 20' ladder into a 10' building if you move it fast enough...but if you're sitting on the ladder, things seem VERY different.


 * But think back to my (technically, rather bad) car horn analogy. Different observations of the car horn did change the frequency at which the various observers heard the sound.  This is just like that (although the analogy is only perfect for lightwaves - not sound).


 * SteveBaker (talk) 21:17, 31 October 2013 (UTC)
 * If I might indulge in a bit of devil's advocacy - the statement "different observations cannot change physical objects" is correct (in this context, although we might get to the Copenhagen Interpretation soon). Different observations change the values of measured times and distances for a given (unchanging) physical object.  The object doesn't change, although its length does. Tevildo (talk) 21:23, 31 October 2013 (UTC)
 * Yes...we should perhaps think of the "rest length" of an object (like it's "rest mass") as being a constant that doesn't change, and that all practical measurements of the object are a combination of the rest-length and a scaling factor that depends on relative motion. Splitting the length into those two parts resolves the confusion.  The object's rest-length is an unchanging property of the object itself but it's modified by a factor that is observer-dependent.  However, the key point here is that this second factor isn't like an optical illusion or seeing something in a distorted mirror.  The point of the Ladder paradox is that a fast-moving object doesn't just look smaller - it will actually fit into a smaller space...from the perspective of some observers.
 * SteveBaker (talk) 21:46, 31 October 2013 (UTC)
 * I think it's resolved if you use the unchanging speed of light as the measurement. A 1 meter bar measured with a 1000nm laser is 1 million wavelengths long.  I believe it's always 1 million wavelengths long.  That fact that an observer will disagree on the wavelength of the laser, but not the speed of light or the number of wavelengths measured by the comoving laser is the invariant physical property.  --DHeyward (talk) 09:50, 1 November 2013 (UTC)


 * Your "challenge" is like saying that the rules of perspective require objects to grow and shrink. The only difference between that case and this one is that there aren't a bunch of dumb popular books telling you that perspective means that the size of objects is "relative to the observer" and that that has profound philosophical implications. Ignore the second-rate philosophy and you'll be fine -- BenRG (talk) 21:39, 31 October 2013 (UTC)
 * I like that analogy...but we have to be a little careful though. The moon seems like it would fit into a matchbox because of perspective - but we know that it's not "really" that small and that it won't fit into such a small space.  With Special Relativity, if the moon were moving so fast that it appeared to be that small, it really would fit into a matchbox. SteveBaker (talk) 21:49, 31 October 2013 (UTC)
 * Well, no, for a couple of reasons. First of all, length contraction is only in the direction of motion, so you'd need a Moon-sized matchbox in the other two directions.  Then, yes, in the matchbox's frame of reference, you could (very briefly!) have the Moon contained within the top and bottom of the matchbox, say a centimeter apart, but only because you don't agree with the Moon about simultaneity.  You'd have to let the Moon in, close the box (that might involve moving the top faster than the speed of light, but whatevs), then bask in the satisfaction that the Moon is inside the box before it obliterates the other side.  From the point of view of a lunar observer, the events happen in a different order. --Trovatore (talk) 21:55, 31 October 2013 (UTC)
 * Yeah - sorry, you're right about the contraction being only in one direction - you couldn't get the moon into a matchbox like that - but a pole that's the same diameter as the moon would...and the distinction between that and perspective is significant. SteveBaker (talk) 03:48, 1 November 2013 (UTC)
 * Only I know of no events that have been measured to have occurred in reversed order due to frame differences. Also, BenRG perspective analogy and Steve's admission objects don't "change" admits to what? Changes in perspective which means what? Apparent change, in a way similar to the way stars go flying about when I turn around. --Modocc (talk) 02:18, 1 November 2013 (UTC)
 * No! You are completely wrong. The idea that you literally can fit a 20' ladder into a 10' building by moving it fast enough (again, please read ladder paradox) means that this is a very different thing than perspective and things moving in your field of view when you move your head.  This is a completely physical dimension change. SteveBaker (talk) 03:48, 1 November 2013 (UTC)
 * No! You cannot fit a 20' ladder in a 10' room, since fit means "store within unmoving", not "pass through at close to the speed of light". μηδείς (talk) 03:56, 1 November 2013 (UTC)
 * No? Think about the implications Steve, if that were true then an electron accelerated at our labs (or something bigger in the future) could cause the Earth or our Sun (or some distant star) to be made so thin that it will fit in gigantic envelope. -Modocc (talk) 03:54, 1 November 2013 (UTC)
 * The implications have been thought of before by some very smart people. See ladder paradox. The sun very well can fit in a very wide envelope, in a certain reference frame, and only briefly. Standing in another reference frame the sun would burst out the back of the envelope and only a small portion would be inside at any one time. There is nothing about this that is either contradictory or which breaks the laws of physics - it's simply a matter a perspective, and its very very weird. Someguy1221 (talk) 04:02, 1 November 2013 (UTC)
 * More importantly, physical changes only happen with the speed of light, thus the fact that I drove instead of walked to the store yesterday does not mean our neighboring galaxies shrank a tad more during my faster trip than on the previous day even though my frame did change. -Modocc (talk) 04:18, 1 November 2013 (UTC)


 * The comment on proper length above reminds me of a question: rather than saying sqrt(x^2+y^2+z^2-c^2t^2), could we define time as an imaginary number t' = ict, so you'd have sqrt(x^2+y^2+z^2+t'^2)? Since this is obvious I imagine there's some reason against it... Wnt (talk) 03:51, 1 November 2013 (UTC)
 * That actually was a popular approach for some time; it went out of fashion somewhere in the latter half of the 20th century. The problem with it is, it's a bit too cute; it obscures the difference between a true metric and a pseudometric, which is a real difference.  If proper time were a true metric, then you couldn't have two distinct (event) points that have interval 0 between them &mdash; but you can. --Trovatore (talk) 04:16, 1 November 2013 (UTC)
 * Hmmm, can you explain this about the two event points? I see it is mentioned in metric (mathematics) but I'm totally not getting how spacetime isn't a metric (or in general, what "d" means in this context). Wnt (talk) 07:08, 1 November 2013 (UTC)
 * The metric defines a norm on the vector space and this should then satisfy all the axioms for a norm. One of the axioms is that ||x|| = 0 if and only if x = 0. Now imaginary time is used in quantum field theory, to get nicer behaved path integrals, the amplitude of a process is given as a path integral over exp(i Action of field configuration), and you can change the integrand to this to exp(- Euclidian Action of field configuration). As explained here in the "Alternative" to the WKB approximation, you see that the imaginary term becomes a real term, but the potential changes sign. So, instead of having to consider a tunneling through a potential barrier, the problem is now a particle propagating from one hil to another throug a valley, and then it is immediately clear what the dominat contribution to the path integral is. All you then have to do is to transform the asnwer back from Euclidian time to ordinary time. Count Iblis (talk) 18:40, 1 November 2013 (UTC)


 * Actually, I believe the proposition of SR is that the only invariant physical property is the speed of light is the same in all frames of reference, energy of light is inversely proportional to wavelength and energy is conserved in all frames of reference. This is the fundamental property that "distorts" lengths, time, and mass.  Say you have a laser in spaceship that is moving towards earth in your spaceship.  The wavelength in that frame is 440nm.  Couple that with the velocity of light and you can measure distance.  But another observer in a different frame measures the laser and has the same speed of light.  The kinetic energy of motion changes the wavelength of light, though, not the speed.  This is counter-intuitive to our normal experience that kinetic energy increases velocity.  Let's say the "at rest" observer measures the laser wavelength at 220nm as it moves toward him.  If you treat the wavelength of the laser as unit length dimension, how many wavelengths are the two objects apart?  If I say the distance between the two objects is 1,000,000 wavelengths because the speed of light is fixed, suddenly the measured distance changes depending on the observer relative velocity. Not only that, but if earth had the same 440nm laser pointed at the spaceship, the spaceship would see a 220nm laser.  The consequences of measuring with a fixed speed of light, conservation of energy and the energy of light being inversely proportional to wavelength, gives rise to all the relative weirdness.  --DHeyward (talk) 09:34, 1 November 2013 (UTC)


 * We actually have an article on the postulates of special relativity. As originally formed, Einstein only assumed that the laws of physics (specifically Maxwell's equations) are equally valid in all reference frames, and the speed of light is invariant between reference frames. This is why what the OP is asking for, a mechanism, cannot be provided. As you say, length contraction and all the other weird phenomena that are observable thanks to special relativity are direct consequences of these postulates, and not any complicated physical mechanisms. As that article mentions, there are also other derivations of special relativity that do not require any assumptions about light, but yield the same conclusions (in addition to concluding that the speed of light is invariant). Someguy1221 (talk) 10:09, 1 November 2013 (UTC)


 * DHeyward and Someguy are correct. In addition, with respect to proof, one also can ignore SR postulates and merely point to the results of direct measurement! So there is no "need" for the postulates in that sense. ;-) So people can be pretty stubborn about this. In addition, unwavering standards are important, thus with the invariant light-speed yardstick relativists have had a substantial degree of success with this, sort of. Consider how we go about measuring the density of gold precisely, one needs pure gold that isn't being periodically contaminated. Likewise, suppose we measure the height of students with a wooden doorframe, and the students' heights vary slightly with time. Suppose too that we don't know what the cause is, but any theorist with this data can certainly conclude that the students' heights are changing periodically simply because of the data and his maths backs him up. He has solid, rock-hard data correlating the changes to something, but he has no idea why, but claims that since his proposed model is correct thus far, it will continue to be (even though he is predicting time reversals too). That's fine, but if someone is predicting measurable time reversals, I'd tell the door frame theorist to back up and rethink the problem and their assumptions from scratch, by studying the dynamics of that door. -Modocc (talk) 14:55, 1 November 2013 (UTC)

My opening paragraphs have not been addressed. The "challenge" is that obviously Earth neither changes diameter lengths (it is a semi-solid/rigid body, and there is no physics explaining physical contraction)... nor does it "have" and infinite number of diameters at the same time as according to all possible frames measuring from all possible speeds and directions of travel. Neither does the atmosphere change in depth (etc.) as a result of the velocity of incoming muons. (See my second opening paragraph.) The philosophical basis implicit in such claims is the idealism (as per Einstein) that there is no "real world" independent of observation. This has come to be expressed in SR's dictum that "there are no preferred frames of reference"... that "all are equally valid," so Earth's diameter "depends on how you look at it," in common vernacular. Realism, on the other hand, "realizes" that the world/cosmos exists "as is" (as formed and naturally changing according to the laws of physics) independent of changes in how it (any given object or distance) might be observed (from relativistic frames in this case.) My contribution to science as a professor of the philosophy of science (retired) has been to contrast Einstein's idealism (that reality depends on observation) with realism (that the world exists and has its intrinsic properties in and of itself independent of observations/measurements.) I ask again that this issue be addressed as a clarification of whether physical objects/distances shrink as a result of various observations, and if so, by what physics. I have been prompted to sign my posts. I was repeatedly insulted as a crackpot and told that my contributions to "disambiguate" length contraction were inappropriate in the editing discussions of the LC section, so I came to the reference desk, as suggested, with this perspective. Again, please address my opening paragraphs. LCcritic (talk) 18:35, 1 November 2013 (UTC)
 * The line between physics and metaphysics has always been arbitary, but special relativity is comfortably on the scientific side. I'm afraid your statement "Earth neither changes diameter lengths... nor does it have [an] infinite number of diameters" is just wrong - it is not consistent with repeatable observations that can be performed in the real, physical world.  The Earth's measured diameter _does_ change, depending on the relative movement of the Earth and the observer.  You may deny the truth of this statement, but the Universe (and not just we humble RD editors) doesn't agree with you.  A discussion of what "true" and "the physical world" and "reality" mean are within the realms of metaphysics, and more appropriate for the Humanities desk, but, whatever the words mean, the Earth's diameter still shrinks.  Eppur si muove. Tevildo (talk) 19:04, 1 November 2013 (UTC)
 * Special relativity is physics, but it's questionable whether special relativity, per se, has an opinion on whether the Earth "really" shrinks. I'd say that's a bit outside its remit.
 * The Earth's diameter will be different in the coordinate system of an observer moving relative to the Earth, but, you know, it's just a coordinate system. You can come up with all sorts of silly coordinate systems.  The only difference is that it's a coordinate system that's especially convenient for the moving observer; it has some special properties, and these can indeed be confirmed by experiment.  But whether those properties equate to a "real" shrinkage is a matter of interpretation, not physics in the strict sense. --Trovatore (talk) 20:54, 1 November 2013 (UTC)
 * The diameter of the Earth measured by the moving observer _is_ less than the diameter measured by the stationary observer. That's physics.  Is this a "real" shrinkage?  That's metaphysics, but  only as regards the meaning of the word "real".  The diameter is smaller, whatever we say about it. Tevildo (talk) 21:08, 1 November 2013 (UTC)
 * But the "diameter" is just the difference between two coordinates in a coordinate system, and coordinate systems are essentially arbitrary. The only thing that connects the coordinate system used by the observer to the phrase "measured by the observer" is certain coherency properties that it has for that observer.  The connection between that and the question of "real shrinkage" is a bit tenuous. --Trovatore (talk) 21:16, 1 November 2013 (UTC)
 * So, is there a "real diameter", which is not the difference between two sets of coordinates? If so, how is it defined?  How can it be measured?  Assuming the Lorentz tranform does not apply to this measurement, in what sense is it a "length"?  Tevildo (talk) 21:31, 1 November 2013 (UTC)
 * I didn't say there was a "real diameter". If there is no "real diameter", then there's also no "real shrinkage", n'est-ce pas?  But what I think LCcritic is getting at is, the atoms that make up the Earth don't care about the coordinate system of some observer moving relative to them; they just keep their appointed distances from one another, in the coordinate systems convenient for them.  The sum of those distances makes up the "diameter of the Earth" in any ordinary sense, irrespective of what observers might do.
 * I think this is really kind of a good point that is being obscured in this discussion. If I speed up, does it have any effect physical effect on the Earth itself?  No, of course not, and I don't think anyone ever really said it did, which is why the point probably doesn't resonate so much with a lot of people who have already internalized SR.  They already know that; it seems like a strawman.  But we should recognize that it is a point of confusion. --Trovatore (talk) 21:41, 1 November 2013 (UTC)
 * Yes, I see your point, the presence of the moving observer doesn't affect the stationary observer's measurements, although saying that the Earth shrinks might sound as though it does. My point is that the moving observer's measurements are equally as "real" as the stationary observer's.  The cosmic ray muons mentioned earlier really do have a longer lifetime than the laboratory muons, and the atmosphere really is thinner for them - it's not an illusion or a mathematical convenience to explain an "underlying" physical reality where the lengths and times don't change.  Such a "reality" doesn't exist. Tevildo (talk) 23:09, 1 November 2013 (UTC)
 * Yes that about sums up the relativistic perspectives. Classically though, simultaneity is invariant and distances between spacial points don't change either. This classical paradigm actually has nothing to say about whether or not clock rates slow down or speed up due to acceleration, so your last point regarding an absolute time being nonexistent is inapplicable. With such critiques, one must be very careful to distinguish between reality and the model of reality. The latter merely needs to be self-consistent even if not true. -Modocc (talk) 00:38, 2 November 2013 (UTC)
 * Ironically, Galileo had a classical foundation, whereas the people he said it to whom unsuccessfully censored him were indoctrinated. Hopefully, we are a tad more civilized now, I hope, 'cause sometimes the best knowledge which is grand is hard to come by. --Modocc (talk) 20:43, 1 November 2013 (UTC)

Regarding this exchange: Tevildo: ‘So, is there a "real diameter", which is not the difference between two sets of coordinates? If so, how is it defined? How can it be measured?” Trovatore: ‘I didn't say there was a "real diameter". If there is no "real diameter", then there's also no "real shrinkage"... The proper length as measured from at rest with an object, “hands on,” measuring rod applied directly to the object will be its true physical length without any complications associated with images of the object traveling at light speed meeting an observer approaching the object and its image at near light speed. The Lorentz transformation does a good mathematical job of translating the contracted images into the true, “proper,” at rest length of the object, without measurement distortion via relativistic effects. Even thought this is a criticism of SR interpretation, it does not negate the constant speed of light. That constant does not require physical shrinkage. Yet the basic philosophy is ignored. Is Earth a “real physical object,” (independent of observation.) That question may be too philosophical for relativity idealists who implicitly philosophically (consciously or not) negate a real world independent of observation? But Earth still doesn't physically shrink, regardless of how distorted it might look from a great variety of relativistic frames. (Realism.) — Preceding unsigned comment added by LCcritic (talk • (edit) Sorry, forgot to sign. LCcritic (talk) 00:42, 2 November 2013 (UTC) contribs) 00:38, 2 November 2013 (UTC)
 * There's a very good book called "Boojums All the Way Down" by David Mermin which addresses the metaphysical implications of special relativity, and which I would recommend to anyone interested in the issue. The main disagreement that we (and received scientific opinion) have with your views is that you distinguish between the "true length of the object" (as measured by the stationary observer) and the "measurement distortion" of the moving observer.  Both lengths are equally real/valid/true in their corresponding reference frames, despite their being different.  The Earth doesn't just _look_ smaller, it _actually is_ smaller for the moving observer.  The problem is (as I see it) in the meaning of the words "smaller" and "length", rather than in physical reality.  It may be "intuitively obvious" that the length of an object is constant if the object doesn't change, but this intuition is invalidated by the experimental results, in the same way that a stationary Earth and moving Sun is obvious but invalid. Tevildo (talk) 01:12, 2 November 2013 (UTC)
 * The answer is "Yes, but you're measuring it wrong." SR is special cases.  The implications of SR and more fundamentally, "non-zero mass" frames of reference and general relativity, affect all observable phenomena because our common experience uses inappropriate measures.  Just like I can create a model that says the sun rotates around the earth in 24 hours, rather than the earth rotates around the sun in 365 days, doesn't have any implication on what the earth or sun is.   We can create earth centric frames and describe mathematically what everything looks like and indeed we do.  "The sun is directly overhead", "Sunrise is at 7:00 a.m", "London is 5 hours ahead of New York", are all terms you can relate to but in no way represent the physical nature of what is observed.  --DHeyward (talk) 11:03, 2 November 2013 (UTC)
 * Observations such as "The sun is directly overhead" are entirely valid measurements though, but there is certainly a tendency for us mere mortals to incorrectly model our measurements. The adage garbage in garbage out tends to apply to beliefs not observations (although witnesses can be unreliable). Presently, there are umpteenth interpretations of quantum mechanics and these cannot all be correct. With my doorframe experiment, the students' heights will depend on the time of year due to changes in humidity, but the students do not have different intrinsic heights because of this effect. Yet if my doorframe was a part of the royal standards two thousand years ago and the castle's witch was unaware of its varied moisture content she might have insisted that the subjects' time-dependent heights were a reality and without an alternative explanation for her observations her subjects would have likely have believed her too. Modocc (talk) 14:32, 2 November 2013 (UTC)
 * SR is nonEuclidean [pseudo-Euclidean] which means that the weirdness is inherent in the model, thus it cannot be interpreted as simply as a way of transforming images that are convenient to one's reference frame. In other words, either its postulates are valid or they are not because there exists an alternative model that is less weird . -Modocc (talk) 15:37, 2 November 2013 (UTC)
 * OK, this is the second time I've had to correct this. Please stop calling SR "non-Euclidean".  SR applies in flat spacetime, so it's as Euclidean as it gets in this context.  GR is non-Euclidean. --Trovatore (talk) 02:37, 3 November 2013 (UTC)
 * I struck that. What I was trying to say was that SR is not Galilean relativity, which will preserve the Euclidean geometry of spacial distances, such that cubes remain cubes independent of reference frame. In other words, if spacial distances are absolute, then there exists a model of that space and it's not SR. -Modocc (talk) 09:05, 3 November 2013 (UTC)


 * SR is non-Euclidean, although you could call it pseudo-Euclidean. SR uses a Minkowski space, which is not a Euclidean space, although it is a pseudo-Euclidean space, as well as a particular kind of pseudo-Riemannian manifold.  Red Act (talk) 15:22, 3 November 2013 (UTC)
 * Pseudo-Euclidean is, as I said, as Euclidean as it gets in this context. So calling it "non-Euclidean" is confusing and inappropriate. --Trovatore (talk) 19:10, 3 November 2013 (UTC)
 * The last time this came up, the leads I read seemed too vague or ambiguous, so I'll just try to be more explicit. -Modocc (talk) 16:15, 3 November 2013 (UTC)

For simplicity sake I'll let Tevildo's statement serve as an example for all cases of supposed contraction: "The Earth doesn't just _look_ smaller, it _actually is_ smaller for the moving observer." This (perhaps unconsciously) endorses idealism (There is no world independent of observation) and negates realism (The world's physical properties do not change with how you look at them.) He does not differentiate between Planet Earth as is (and as it was before observers evolved)... as it has been for billions of years (though slowly getting fatter around the equator)... and how it might look from a relativistic perspective "for a moving observer."

So it's polar diameter "IS" 4000 miles "for" my ship approaching at .866c from the axis direction (and its equatorial diameter IS 7926 miles.) Then the ship turns around and approaches at 90 degrees from the axis and, whaddaya know, now the equatorial diameter "IS" 4000 miles and the polar diameter IS 7901 miles. Please just explain that if you can, Tevildo. Please include the physics of such 'massive' planetary shrinkage, restoration/expansion and then more shrinkage in the opposite direction. Then please explain how the phrase "for a muon" makes the atmosphere shrink to way less than 1000 km (as well established by science) in front of each muon. Then please explain how the distances between stars (as naturally distributed in space) "IS" contracted by relativistic interstellar travel. Thanks. LCcritic (talk) 18:31, 2 November 2013 (UTC)
 * Lorentz transform covers the mathematics. These equations are consistent with experimental results and therefore are the basis for the theory of relativity, in the same way that F = GMm/r2 is the basis for Newton's theory of gravity.  The universe happens to behave in that way.  _Why_ it does is a metaphysical question - science (attempts to) describe _what_ the universe does, and what it does is follow the Lorentz equations.  That being said, purely in the realm of metaphysics, philosophical realism does _not_ state "the world's physical properties do not change with how you look at them" - it states that the world exists independently of observation, but only that it _exists_, not that its properties have to behave in any particular way.   Tevildo (talk) 18:52, 2 November 2013 (UTC)
 * Sounds like folks here are hung on semantics. When we refer to the "mass" of a particle, we generally mean "rest mass".  So when we speak of the "width" of a ladder, should we not imply "rest width"?  The ladder doesn't shrink - its "relativistic width" is just different. Wnt (talk) 19:12, 3 November 2013 (UTC)

Tevildo, you have totally avoided every point in my last post. If you say that the math proves length contraction (say, because it is the reciprocal of time dilation) then, for instance, a slow ticking clock on a fast moving interstellar ship is supposed (theoretically) to make the distance between stars contract. Given that the stars are distributed in space independently of how distances might be observed by fast ships, or how slowly their clocks might keep time at high velocity travel, the claim that stars move closer together "for" all such (futuristic) ships... the faster the ship, the closer the stars to each other... is very foolish and obviously false. That is the argument from realism as opposed to the idealism, which claims that there is no real, actual distribution of stars in space (or diameter of Earth) independent of how variously such distances might be seen as above.

Nor did you address the infinite variety of Earth diameters as measured from all possible frames traveling at all possible speeds and approaching from all possible directions. Again, the (perhaps unconscious) philosophical assumption is, "There is no real world (Earth) independent of observation." Your claim (often used by SR theorists) that, "These equations are consistent with experimental results" *does not address my challenge*, either in my original post or my last one. It is not "metaphysics" to "disambiguate" length contraction as above. It is, in fact, *metaphysics* to claim an infinite number of Earth diameters (in all possible directions) without a shred of *physics* to support the claim. The claim that the world changes as measurements of it change (relativistically speaking) IS metaphysics, meaning beyond physics (in the realm of idealism). Please address the points as I made them. If that is too much to ask, then please just answer the one question addressed to you above: [So it's polar diameter "IS" 4000 miles "for" my ship approaching at .866c from the axis direction (and its equatorial diameter IS 7926 miles.) Then the ship turns around and approaches at 90 degrees from the axis and, whaddaya know, now the equatorial diameter "IS" 4000 miles and the polar diameter IS 7901 miles. ** Please just explain that if you can, Tevildo.**] LCcritic (talk) 19:08, 3 November 2013 (UTC)
 * There are few responses that can be made to the argumentum ad lapidem, and I doubt if I can find one here. Your statement "the faster the ship, the closer the stars to each other is very foolish and obviously false" is a perfect example of an ad lapidem - all I can do is repeat my statement that it isn't consistent with physical reality.  If you go through the mathematics in Lorentz transform, Derivations of the Lorentz transformations, and the (IMO, rather more accessible) derivation in Mermin's book, you'll see how the equations are derived from first principles, as a general statement of how measurements in two different frames, moving with respect to each other, are related.  These equations involve the invariant velocity, c, which, by combining the Lorentz transform with Maxwell's Equations, can be demonstrated to be the speed of light.  Because, in our particular universe, c has a finite value, which we can measure, we can therefore calculate the length contraction appropriate to the two frames you mention.  Why c has that particular value may, one day, be explained by a scientific theory, but that theory has not yet been developed.  Why algebraic equations can be used to describe accurately the behaviour of the universe is a metaphysical (or sociological?) question that I can't answer.  I assume that you won't consider this to be an "explanation", unfortunately.  Perhaps someone else may be able to provide one that's acceptable to you, but I consider it unlikely. Tevildo (talk) 20:49, 3 November 2013 (UTC)

Tevildo, I have repeatedly asked this "encyclopedia reference desk" to clarify the standard SR claim that physical objects and the distances between them contract, based on different frames of reference measuring the same object or distance differently, as if it is a given that different measurements equate to different physical lengths. My primary example has been the claim of a changing shape of Earth (with all varieties of different diameters), varying drastically with different observations from relativistic frames. The alternative "explanation" given has been that it doesn't change but *IS all different shapes at the same time*, just "depending on how you look at it" with no objective measurement of the physical body Earth possible ("all frames being equally valid." (The following was deleted when I posted my reply... Here it is again:

You continue to evade the challenge, now citing "argumentum ad lapidem"... a logical fallacy that consists in dismissing a statement as absurd without giving proof of its absurdity." The burden of proof that Earth's shape changes, or that it has an infinite variety of shapes ("for" all possible observing frames) is on the theorists who make that claim. *There is no empirical evidence for length contraction.* The "length contraction" section should at least mention this fact, but the editors will not allow it. (I've tried.) Instead we have folks such as yourself (assumed to be experts) denying the absurdity of an earth changing shapes or having multiple shapes. Will someone here *please* address the specifics of my opening post and my last post to Tevildo, who refuses to answer my direct questions. LCcritic (talk) 18:31, 4 November 2013 (UTC)
 * I may regret this, but could you please state your "direct question" in one sentence without becoming abusive, so that I may attempt to answer it? I do not promise to succeed in answering it, of course, but it isn't clear to me how I have failed to answer it, as I don't know precisely what it was.  And you _have_ dismissed the theory of relativity as absurd ("very foolish and obviously false") without providing an argument to support your position.  This question will scroll off the desk in a couple of hours, so this will probably be our last exchange. Tevildo (talk) 22:22, 4 November 2013 (UTC)

SSRI/SSNRI WITHDRAWAL
Can someone please add SAVELLA (Milnacipran) withdrawals in with the other SSRI/SSNRI Withdrawal symptoms? It is a fairly new medication, though it has severe withdrawal symptoms, very similar to others you have listed on the page. I would just like others to be informed about coming off this medication.

Thank you kindly,

Laurie Hart — Preceding unsigned comment added by 2602:30A:C0CB:4D60:78B7:92FD:3CA1:56C6 (talk) 19:17, 31 October 2013 (UTC)
 * If you have a reliable source that supports the change, then be bold and add it, or make a suggestion on the article's talk page. RudolfRed (talk) 20:27, 31 October 2013 (UTC)
 * I assume you want the article SSRI discontinuation syndrome changed. Milnacipram withdrawal has been studied  but doesn't sound impressive.  A review financed by Eli Lilly and a bunch of other drug companies  says on page 8 that:


 * "A post hoc analysis of patients abruptly withdrawn from paroxetine or milnacipran as part of a double-blind comparative study showed that paroxetine produced significantly more discontinuation emergent adverse events than milnacipran. In addition, the nature of the adverse events differed between the two antidepressants, with patients withdrawn from paroxetine showing the classical symptoms of dizziness, anxiety, and sleep disturbance (insomnia and nightmares), while those withdrawn from milnacipran showed only increased anxiety. However, some discontinuation symptoms have been reported, and good clinical practice and regulatory authorities always recommend gradual discontinuation from any psychotropic drug."


 * Honestly, given the spotted history of drugs that have been claimed to lack their predecessors' side effects, I am skeptical to read a statement like this, but I have zero experience in this area and I'm in no position to dispute their statement. Wnt (talk) 03:41, 1 November 2013 (UTC)

Effect of poor Eyesight on life skill development
Can poor eyesight through childhood and adolescence cause any significant lack of life skill development, knowledge etc? Clover345 (talk) 22:25, 31 October 2013 (UTC)


 * At the very least, it would tend to limit your career options. ←Baseball Bugs What's up, Doc? carrots→ 11:22, 1 November 2013 (UTC)


 * Well, at least they will be qualified to work as an umpire. :-) StuRat (talk) 15:59, 2 November 2013 (UTC)


 * There could also be negative impacts on social development. For example, if they go out with unkempt clothes, hair, etc., since they can't see a stain, etc., this might make them less popular. StuRat (talk) 15:59, 2 November 2013 (UTC)


 * Vision problems — especially if they are undiagnosed — can have a severe effect on educational development see: Also, children who can't see well enough to play games or take part in other activities with their peers are going to miss out on social development. Richerman    (talk) 09:29, 3 November 2013 (UTC)


 * Anyone who has worn glasses in childhood has probably copped being called four eyes, which may have an adverse effect on some. If their eyes are particularly bad requiring extra thick lenses then they may receive an unusually high level of harassment. If socialising, or learning how to do so effectively is a life-skill then some children may withdraw or become anti-social because they are 'different' or made to feel different by uncaring classmates. Richermans point about undiagnosed sight problems, and the other issue of sports is a very good example. 220  of  Borg 12:22, 3 November 2013 (UTC)


 * The WP page Low vision seems to have relevant content, though it doesn't seem to discuss life-skill or social development. 220  of  Borg 12:42, 3 November 2013 (UTC)