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I've read somewhere that the Sahara around 800,000 years ago was a hot humid swamp-like area (no information on what it was like 1-2mil years ago), and I'm wonder if there are any biologists/anthropologists linking the emergence of human culture in N.Africa and the migration out of Africa by homo erectus to the later desertification of the region? I'm not necessarily suggesting it's true, but it seems obvious enough a connection that quite a few people would have proposed it. 173.183.68.27 (talk) 00:12, 15 November 2010 (UTC)[reply]
What is the proposed mechanism for anthropogenic desertification of an area the size of Europe? I just don't see it as likely in the slightest. I could see prolonged greenhouse effect and etc. contributing to or accelerating desertification in a desert that size, but causing it outright? I think it's well beyond the capability of human beings until very recently to do such a thing. --Mr.98 (talk) 00:21, 15 November 2010 (UTC)[reply]
Fire, really. It's a long shot I know, but an increased population of hominids with a lot of use for fire could have created large areas of grassland, holding much less moisture and disturbing the monsoon patterns coming in from the atlantic, leading to desertification. obviously positive feedback would be the active mechanism here, I don't think it would have been possible to burn that much forest. 173.183.68.27 (talk) 00:31, 15 November 2010 (UTC) -- I guess the main weakness if that forest fires don't create grassland, so there may be something else. 173.183.68.27 (talk) 00:34, 15 November 2010 (UTC) -- i guess Deforestation in New Zealand supports this somewhat. 173.183.68.27 (talk) 00:45, 15 November 2010 (UTC)[reply]
I don't place much credence in H erectus causing this change - Sahara#Climate_history talks about climate changes impacting the Sahara. FWIW you may be interested in reading about a technique used by Australian Aboriginals called Fire-stick farming which most likely did result in large scale changes to the landscape, flora & fauna (though not necessarily desertification). --jjron (talk) 14:43, 15 November 2010 (UTC)[reply]
Have you never wondered why there can be two completely different ecosystems present at the equator; the Sahara and the Amazon? It is obvious that climate change is what keeps the Sahara in its current state, and that not enough moisture is coming in to replenish the soils, but it is equally as true to say that if there were no trees in the Amazon, there would likely be a lot of desert there too; it is the existence of the rainforest that keeps the rainforest alive because it holds on to the moisture and influences the weather (lowering temperature and increasing precipitation) in the area. I will read up on the Aboriginal situation though, that might make for interesting evidence! Thanks. 173.183.68.27 (talk) 05:34, 16 November 2010 (UTC)[reply]
The Sahara isn't at the equator; the Congo is, and is rainforest like the Amazon. But, in any case, there are lots of instances of places at the same latitude with significantly different climates, so the supposed fact wouldn't be surprising if it was true. --Anonymous, 06:24 UTC, November 16, 2010.
The prevailing winds over the Sahara have a LONG fetch over land, with almost no source of water feeding them. That's why it is so dry. In the past, when landmasses were at slightly different locations, and winds blew from different directions, there may have been more sources of water upwind from the Sahara. As it stands now, the winds over the Sahara, which blow almost straight out of the east, have about a fifth of the earth's surface to blow over before getting to the Atlantic. Generally, you find deserts on the downwind side of continents, and forest upwind. There are also rain shadow effects. Its a complex thing, however, and this is a bit of a simplification. --Jayron3206:32, 16 November 2010 (UTC)[reply]
The position of the Sahara within the horse latitudes is significant; I've often seen a popular though rather simplistic cartoon of the winds circulating in bands through the upper atmosphere and coming down over drier areas - it must be on Wikipedia somewhere... Wnt (talk) 12:21, 16 November 2010 (UTC)[reply]
I heard a story a long time ago in school that a guy proved that the head is alive briefly after being beheaded, and he did this by stating that after he is beheaded he will blink a lot. I think he was beheaded by guillotine (not sure why), and sure enough he blinked a lot after his head came off. Is this story true? Does anyone know what I'm talking about or who this guy is supposed to be? ScienceApe (talk) 00:50, 15 November 2010 (UTC)[reply]
(edit conflict) The story is told of Antoine Lavoisier, who was indeed beheaded by guillotine. It's a widely told story, but appears to be apocryphal; see The Straight Dope column on the matter. I have yet to see any serious academic supporting the story. That's not to say that a person couldn't blink after his head's chopped off, just that there's no contemporary suggestion that Lavoisier did. even citing the same source, that's pretty impressive, 173 Buddy431 (talk) 01:01, 15 November 2010 (UTC)[reply]
Hm, I can't imagine that the loss of all blood pressure wouldn't lead to unconsciousness from shock at least as quickly as pilots black out from high G-forces. A few seconds, tops. Ginger Conspiracy (talk) 01:07, 17 November 2010 (UTC)[reply]
Our Decapitation article says: "Decapitation is quickly fatal to humans and most animals as brain death occurs within minutes without circulating oxygenated blood." Some eye-blinking behavior in that time seems quite possible, especially if one has made up one's mind to focus on doing that before the event. WikiDao ☯ (talk)02:16, 17 November 2010 (UTC)[reply]
I'm talking about the Lay's potato chips. They come in small bags and big bags, and I've noticed that the small bags seem to taste better than the big bags, which before I attributed to scarcity (there's less, so each chip tastes better). Obviously the solution was to perform a double-blind study ;) I set up the project as follows: my assistant put four plates on a table: 2 labelled "small" and "big" respectively, then places the same number of chips (from the correct bag) in the same arrangement on each, then shuffling the plates randomly. She then leaves with the bags. I come in, unaware of which are which, and shuffle them again. The subject then comes in and tastes chips from two of the plates, which s/he selects and guesses on a folded sheet of paper with four circles: s/he writes either s (small), b (big) or Ø (not tasted) for each circle which s/he places in a box, knowing that it is possible that both are from the same bag. My assistant then came in and recorded each selection from the slip, and I looked on the underside of the plate and recorded the correct answers. I did not see the subject's answers, nor my partner the correct answers. I repeated this about 200 times, discarding the "used" plates and chips each time. When I brought all the data together at the end I found the accuracy rate was about 79%, which to me was shocking. Now I know what happens (and got full points on my project :), my question is: what accounts for the difference? 24.92.78.167 (talk) 01:48, 15 November 2010 (UTC) PS: The plates were paper, the writing was in pencil so as not to show through, and the chips were all sour cream and onion flavor. The subject was not allowed to touch the plates except to sample the chips.[reply]
how many subjects were there? How did you explain them to rate the chips? Were they guessing which tasted better? Which they thought was crispier? or were they asked specifically to guess which bag they thought it came from? The chips are purged with nitrogen or something aren't they? Which is inert but maybe a small amount of air still remains in the bag so when the bag is bigger the amount of air is more. My dad does plant maintenance at a smallgoods factory and he says their vac equipment can be running at 85% and it's still "good enough" even tho it normally runs at 97% or something, but even at 100% it's not a perfect vacuum. I realize the nitrogen purging thing is a completely different process, but maybe similar tolerances apply. Vespine (talk) 02:57, 15 November 2010 (UTC)[reply]
(edit conflict)Cool study! Just a few ideas:
- the amount of air in the package
- there may be a significant difference in the way/time/place of packaging that accounts for the taste, though you'd have to ask Lays
Date codes as mentioned by Ariel seem the best explanation. But the explanation can simply be unattainable. Without, that is, a lot more information and a lot larger study. Maybe the potatoes vary by packing plant, and maybe one packing plant, carrying potatoes from one source, specializes in packaging large bags, or small bags. And on and on—oil—air pollution—plastic blades in one type of machine—steel blades in another type of machine. The product is uniform, but not perfectly so, and there is probably more than one factor of variability between the large bags and the small bags. Bus stop (talk) 03:14, 15 November 2010 (UTC)[reply]
I agree. There are a whole lot of volatile flavorings and oils which can spontaneously decompose or otherwise change taste even when packed in pure nitrogen, and it's not at all unreasonable to suspect the single serving bags not only sell at higher volumes, but they're more likely to get restocked at the front instead of first-in-first-out as grocers would prefer because there are going to be more of them per unit of volume to have to fiddle around with when restocking shelves. So it's likely a freshness issue. Ginger Conspiracy (talk) 07:04, 17 November 2010 (UTC)[reply]
I try to limit my chip consumption these days, but if I recall correctly, there are a fair amount of loose salts and spices on the chips. In the course of travel and with the help of gravity, I've found that some of this salt makes its way to the bottom of the bag, resulting in the chips at the bottom being saltier and, if it is your preference, "tastier." It stands to reason that this effect is amplified in bigger bags, since, in a smaller bag, you could easily grab a chip from the middle or bottom without much digging. (Or, as in your experiment, you may dump some chips onto a plate; the small bag sample, on the whole, would have the "average" chip flavor, whereas the big bag would biased toward which part of the bag the chips came from.) This is just a theory of mine, but do you (or other readers) think this could be a contributing factor? Eric (EWS23) 13:05, 17 November 2010 (UTC)[reply]
Say you left a pound of deli turkey slices in a bag at room temp for 8 hours.
Most people will tell you to toss them. But I'm guessing you want other options. Were they unopened? Because they will cut down on bacteria drastically. Are they very salty? That helps too. You can freeze them, to kill many, but not all bacteria (but freezing does nothing to existing toxins - if there are any). You can also fry or bake them. I would use your built in chemical detector - sniff them. If there is any hint of bad smell toss them, but otherwise you are probably OK. Of course most people work on the better safe than sorry system, but if they smell OK, and you are not an infant or elderly, have a normal immune system, and are not taking antacid drugs (of any type, prescription or over the counter), your risk is low. As soon as you smell them, put them in the freezer (to cool them quickly) or eat them immediately. Ariel. (talk) 05:31, 15 November 2010 (UTC)[reply]
The practices of the deli where you bought the slices will also be significant. Were the slices freshly cut on a clean machine, or had they been in a display for many hours? I agree with Ariel that I personally would take the risk unless the turkey smells bad. A hundred years ago most people would have been happy to eat such meat without question. The human stomach is good at killing bacteria, but it cannot eliminate toxins, and, just occasionally, it fails to eliminate a large intake of acid-resistant bacteria, so there will always be a small risk, even with fresh meat. Dbfirs10:11, 15 November 2010 (UTC)[reply]
The machine is probably clean, as I've eaten their meat for a couple of months without a problem. The bags were unopened. I put them in the freezer and haven't taken a look since. Imagine Reason (talk) 14:50, 15 November 2010 (UTC)[reply]
Technically this is a medical question, so we aren't supposed to answer it, but if you're really worried, just pop them in the microwave for five minutes. Only if they were infected with botulism will there be any remaining risk. People make turkey sandwiches 8 hours prior to consumption all the time. Ginger Conspiracy (talk) 07:00, 17 November 2010 (UTC)[reply]
Partial reflection when light travels from a fast medium to a slow medium
When light travels from a fast medium to a slow medium, you get refraction, do you also get partial reflection (as you do when the light travels from a slow medium to a fast medium)? 220.253.217.130 (talk) 06:30, 15 November 2010 (UTC)[reply]
Sure you do, else you wouldn't get an effect like this:
Notice how you can see the mountain in the lake? That's because the surface reflects light. The light moves faster in the air than it does in the water, so this is exactly the effect the OP is asking about.
Hello. Gravitational energy is not infinite. An object may fall for a long time, but eventually its gravitational potential will reach zero and then no more force will be exerted on it. If this was not the case, falling objects would be accelerated forever and gravity would be a perpetual motion machine.
Dark matter exerts a repulsive force on other matter which is accelerating the expansion of the universe. However, at some point this repulsive force must become zero to prevent it from becoming a perpetual motion machine. Where is that point? Leptictidium (mt) 07:46, 15 November 2010 (UTC)[reply]
You are thinking of Dark energy, not Dark matter. And the simplest answer to your question is "no one has any idea". Dark energy is just an idea, or more accurately it's a way trying to "patch" holes in observations vs. theory. No one has observed it (they have only calculated it), and there could be a wide variation in it's effect, and still match current observations. For example an idea called Big rip does actually suggest the force will become infinite. Ariel. (talk) 08:27, 15 November 2010 (UTC)[reply]
So sorry, "dark energy" then. But if it does become infinite, isn't that a violation of the second law of thermodynamics, since it generates a force perpetually? Leptictidium (mt) 08:49, 15 November 2010 (UTC)[reply]
The "limit" is probably the edge of the observable universe (from the reference frame of the hypothetical dark energy), but since this is all hypothetical, it would be very difficult to try to prove this. Perhaps, one day, we will realise that there is a much simpler explanation. Dbfirs09:28, 15 November 2010 (UTC)[reply]
You say "An object may fall for a long time, but eventually its gravitational potential will reach zero and then no more force will be exerted on it". This is incorrect. Gravitational potential energy is calculated by integrating the gravitational force with respect to radial displacement. This integration introduces an arbitrary constant of integration, which can be chosen to make the potential energy 0 at whatever point you like. Sometimes it is convenient to take gravitational p.e. as being 0 for some initial configuration; sometimes we take gravitational p.e. to be 0 for a hypothetical infinite separation. The configuration that we choose as a zero point for gravitational p.e. 0 is an arbitrary benchmark - it has no physical significance. Gandalf61 (talk) 10:24, 15 November 2010 (UTC)[reply]
Surely if I am falling towards the Earth, the point at which gravitational potential energy would become zero is the centre of the Earth, no? Leptictidium (mt) 10:30, 15 November 2010 (UTC)[reply]
You can choose to make the gravitational p.e. zero at the centre of the Earth if you want to. Or you can choose it to be zero at the surface of the Earth, or wherever you like. It is arbitrary. The physically meaningful quantity is the gravitational force, which is the gradient of the potential, and so is unchanged by adding or subtracting a constant from the potential. Gandalf61 (talk) 11:13, 15 November 2010 (UTC)[reply]
As (not) explained in gravitational potential energy, but implicit in the formulae given and the statement about separating all bodies to infinity, there actually is a logical zero point for gravitational energy, which is when an object is separated from all other masses by infinite distance. It is (theoretically) possible then to calculate the potential energy as a negative number that is the sum of all the negative gravitational potential energies from all masses. Though in practice distant, little-known astronomical masses tend to be neglected, and often an arbitrary zero is chosen. But I don't think anyone chooses a zero at the center of the Earth, since nothing can fall to there. Wnt (talk) 11:25, 15 November 2010 (UTC)[reply]
There is no logical reason why Leptictidium cannot choose zero of potential energy to be at the centre of the earth. It is a perfectly reasonable treatment for the gravitational potential of a single body and avoids negatives, though I agree that physicists normally take zero at infinity. Dbfirs14:00, 15 November 2010 (UTC)[reply]
Yes but it has no special meaning on a cosmological scale. Even if a object is at the centre of earth it can fall to lower gravitational potential by falling in to the centre of the sun or the galaxy. The only choice of zero point that has no negative potential energy is when all mass in the universe is collapsed in to a singularity in a black hole. I do not know if such a reference point is meaningful given all the complexities with infinity and time dilations. --Gr8xoz (talk) 15:00, 15 November 2010 (UTC)[reply]
I did say "of a single body", and I know the standard treatment is to take zero at an imaginary point somewhere on the other side of the universe, but the OP was just making a simple analogy and it made perfect sense to me. Dbfirs23:03, 15 November 2010 (UTC)[reply]
Assume for simplicity that there is a point mass M all alone in the Universe, alone, that is, except for a small test particle of mass m at infinite distance from M. m has kinetic energy K = 0 at this point, and we choose the zero of potential T = 0 at this point, too. Next, m falls towards M, hence its kinetic energy K increases. At the same time, because it falls into the potential well, its potential energy T decreases. Conservation of energy requires that the motion is such that the total energy K+T remains constant (energy restricts motion), namely K+T=0. In fact, since M is assumed to be a point mass, the kinetic energy of m increases without bound - I guess that's what you mean by "gravity would be a perpetual motion machine". But that's not true, because as K increases, T continues to decrease, also with out bound, to minus infinity. Although both K and T become infinite, their sum always remains zero. Your mistake is in looking at kinetic energy alone, whereas you have to think of total energy, then there's no problem. Of course, in reality there are no point masses (except maybe black hole singularities but those cause extra problems), and therefore you cannot get anywhere infinite kinetic energy. Dark energy is a different story again which cannot be satisfactorily treated with classical mechanics. --Wrongfilter (talk) 17:31, 15 November 2010 (UTC)[reply]
Well if the potential energy converted into kinetic energy reaches the rest mass of the falling item, I believe you will reach an event horizon. Past this barrier it will not be possible to extract any more energy. Graeme Bartlett (talk) 19:30, 15 November 2010 (UTC)[reply]
I'm not sure I know the answer to this question, but I'll try my best. First of all, at issue is not whether the dark energy is "there" in some abstract sense, but whether you can build an engine that exploits the force to produce an unbounded amount of work. I think I can rule out that possibility. In the distant future, the expansion is well approximated by de Sitter space. Any particular person can be causally influenced by only a part of the de Sitter space, and that part can be covered with static coordinates that resemble a "black hole turned inside out"—in other words, a spherical region with an event horizon at the edge. The event horizon attracts objects in the interior like a black hole would; that's how the dark energy force shows up in this model. At this point it's clear that you can attach a potential energy to every point in the spherical region to make the dark force conservative. To put it another way, there's a limit to how far you can allow two masses to be pushed apart while still extracting energy from the pushing. Beyond that point, the repulsive force itself prevents you from ever receiving any energy from the motion of the masses, because the energy is also pushed away too fast for it to get to you. That shows up in this model as one or both masses crossing the event horizon.
A slightly different question is whether the dark energy itself could somehow be harvested. The nature of the dark energy is totally unknown (it may not even be there) and there's no reason to think that it can be gathered, but even if it can, the amount you can gather would be limited by the radius of the spherical region, I think.
The nature of energy conservation in general relativity is complicated and unclear. I think your question in its most general form may actually be unsolved. -- BenRG (talk) 19:41, 15 November 2010 (UTC)[reply]
There are at least a handful of viable explanations for the accelerating expansion of the universe and would thus characterize dark energy. Some of them are more parsimonious than others, but all of them are presently out of reach of observational evidence and experiment. I like to think that the universe is merely hyperbolic instead of flat, or that there are sources of mass from regions other than the big bang's, perhaps other big bangs, exerting a normal gravitational pull. Ginger Conspiracy (talk) 01:01, 17 November 2010 (UTC)[reply]
I'm sure my animals aren't unique in that they like to burrow under the sheets of my bed for the warmth. (It's mostly the cats but also one of the dogs) I've often wondered though, can the animal suffocate and if it can, how will it go? Will it simply fall asleep and never wake up? Or will the, completely healthy, animal's brain realize that it's not getting enough oxygen and make the animal want to escape, meow, whimper, etc? I realize that there are unknown quantities here and those are namely the amount of fabric on top of the animal and whether there is a tunnel to fresh air left from where they burrowed. I suppose that the answer to "can it" will be yes given enough sheets and blankets, so for now let's just assume that there is a sheet, a quilt, and another blanket.
Note: I'm not seeking medical/veterinary advice. I'm just inquiring as to the physiological response of a cat or dog and the possibility of an unfortunate event. I do not plan on testing this out on any animals, unless by "test" you think I mean continuing to let my animals sleep under the covers whenever they like. All my animals are of reasonably good health considering their ages and are seen by a vet on a regular basis. Dismas|(talk)09:21, 15 November 2010 (UTC)[reply]
Humans - who are a not dissimilar animal - don't commonly suffocate if, as frequently occurs, they are covered by the bedclothes as described. Why then would cats or dogs? FWIW I have on occasion shared a bed with a cat, who indeed liked to get under the bedclothes, and no deleterious outcomes ensued. Without being able to think of any appropriate references, I would have expected that, like you or I, a cat or dog would sense whether it was in an over-stuffy situation even in sleep, and wake up and/or move to improve matters. 87.81.230.195 (talk) 09:54, 15 November 2010 (UTC)[reply]
If I cover face with all that, it becomes incredibly hot and stuffy in a short time. I've seen cats and dogs spend much more time that way. Additionally, while we're all animals of one sort or another, dogs and cats handle heat differently than we do. Dismas|(talk)10:48, 15 November 2010 (UTC)[reply]
I have never heard of an animal suffocating like that. Aso, when I was a kid, back in the days when winters were cold in the UK and when the house had a single coal fire in the living room, I remember frequently sleeping completely under the covers. The room temperature was probably a little above freezing, there would oftem be ice inside the windows in the morning. -- Q Chris (talk) 12:35, 15 November 2010 (UTC)[reply]
[3] specifically mentions blankets and duvets as a risk for infants. It also confirms what I had suspected, the risk is more their limited mobility and ability to move these objects or otherwise clear obstructions. Notably I can't find any mention of cats suffocating in sheets or whatever but do find plenty of mention of the behaviour, I myself let the cat sleep under the duvet on occasion. Nil Einne (talk) 14:43, 15 November 2010 (UTC)[reply]
All mammals will wake and become agitated from carbon dioxide buildup in the lungs when they are suffocating, which starts as a feeling of stuffyness and becomes searing pain if ventilation isn't available. Ginger Conspiracy (talk) 00:54, 17 November 2010 (UTC)[reply]
(ec)87, are you using "bedclothes" to refer to sheets and blankets? I've never heard it used that way (though it sounds quaintly appropriate to me); everything else being equal, I would assume you're talking about pyjamas/nightgowns - and having animals stuck in there would probably lead to very little sleep at all... 64.235.97.146 (talk) 14:27, 15 November 2010 (UTC)[reply]
I concur. I suppose they can be thought of as clothing the bed rather than the person. The OED gives a definition from c1440 ". . . Bedclothe, or a rayment for a bed." 87.81.230.195 (talk) 21:19, 15 November 2010 (UTC)[reply]
(Partly OR) There are many references[4][5] about cat problems with breathing, such as after a frantic mouse chase, and it is distressing when this happens to one's own pet. OTOH a cat seems to deliberately to obscure airflow to its nose when sleeping e.g. by curling its tail over the nose as well as burrowing under bedclothes as the OP describes. A cat with a fur coat in a warm place can reduce its metabolic rate e.g. to take a cat nap, where it needs little oxygen. Our article Cat#Physiology notes the range of breathing rate 16-40 breaths per minute of a cat, which is wider than that of a human, typically 12-20 breaths per minute. The OP's question would be answered by an experiment on a sleeping and trusting pet that I am not prepared to do either. Cuddlyable3 (talk) 16:30, 15 November 2010 (UTC)[reply]
Under what conditions does hydrogen sulfide exist in the liquid phase, simultaneously as sulfur is in the gas phase? Are there more than one molecular structure for sulfur in this phase combination, maybe diatomic surfur? What does liquified hydrogen sulfide look like? How good a solvent does it make? Compare the solubility of sodium sulfanide in liquid hydrogen sulfide, to that of sodium hydroxide in water. Does it autodissociate like water? Plasmic Physics (talk) 14:14, 15 November 2010 (UTC)[reply]
As it is similar to water the structure in liquid phase is similar. The exact rection mechanism leading to polysulfide is no longer in my active memory, I thought you need basic conditions.(look at doi:10.1021/je60044a022 As it is similar to water the structure in liquid phase is similar and should look like cold water. the solubility depends on the polarsability of the solvent molecule and the hydrogen bond strength, have some time to calculate this. The auto dissociation should be to be calculated by the pKas of water and hydrogen sulfide.--Stone (talk) 21:46, 16 November 2010 (UTC)[reply]
The first row elements (N and O) can build up double and triple bonds which is highly unlikely for later rows, this makes them very incomparable.--Stone (talk) 22:21, 16 November 2010 (UTC)[reply]
Do you mean incompatible with everything or just first row non-metals? Oh, by the way, I didn't mean an exact molecular analogue to nitrogen. Tricyclo[1.1.0.02,4]tetraphosphane is an acceptable structure, I did not explicitly mean DiphosphorusPlasmic Physics (talk) 01:02, 17 November 2010 (UTC)[reply]
I was just reading yet another story about potential correlations between cell phone frequency EM radiation and brain tumors. I don't really want to debate the pros and cons of the argument here — I'm just referencing it for the context, and want to, for the sake of argument here, assume that the correlations are valid.
Most of these articles seem to imply that holding the phone an inch away or so negates the problem, or at least lessens it.
My science question: why would this be the case? Can an inch (or less) of air actually deflect enough of the EM radiation in question to make a difference? If so, shouldn't there be some relatively easy way to build shielding into the casing that would scatter the EM radiation away from the earpiece? --Mr.98 (talk) 17:48, 15 November 2010 (UTC)[reply]
If you want an example of this, test an induction-based recharger. I have one for my watch. If it sits on the recharger, it blinks, so I know it is recharging. If it is about 1/4" off the charger, it blinks. If it is 1" off the recharger, it doesn't blink anymore. At about 1/2", it is flaky. Sometimes it blinks, sometimes it doesn't. All that is between the electromagnetic source (the charger) and the watch (which is designed to absorb and make use of the energy) is air. -- kainaw™18:00, 15 November 2010 (UTC)[reply]
Forgot to answer the other questions... Can cell phones be shielded so they don't emit electromagnetic waves? Yes - easily. But, they won't work anymore. The main function of a cell phone is to send/receive EM energy. Can a simple device be made to keep the phone an inch away from your head? Yes. About 10 years ago, I saw a guy on TV telling you that you need to cut 1" off a toilet paper tube and tape it to your phone to keep it 1" away from your head. -- kainaw™18:03, 15 November 2010 (UTC)[reply]
Let me clarify, because I think it's not clear what I'm suggesting, or something. (Obviously I know that the phone needs to be emitting to be functional. Obviously I know you can build in some kind of physical means of keeping the phone an appropriate distance.)
Below is a crude but hopefully amusing ASCII diagram of someone holding a banana-shaped phone which is sending out microwave radiation in an approximately spherical pattern, zapping our poor fellow's brains with said EM radiation. (I have placed the phone some distance from the head, but that is just to illustrate the radiation direction. Imagine it is right next to the head.)
ooo . . .
o o . . .
0 x x 0 . . .
| u |...\\....
| P |...||....
\___/ .// .
/ \ . pO .
| | || .
Here is another similarly crude diagram where some sort of barrier has been put on the face-side of the phone which reflects the EM radiation off of it. The result is that only a small part of the overall EM sphere is reflected or scattered away from the head:
ooo . .
o o . .
0 . . 0 . .
| u | \\\....
| U | |||....
\___/ /// .
/ \ pO .
| | || .
It seems to me that this would be relatively trivial and only have a marginal effect on phone quality? (It would be, I presume, a directional effect, so the direction you were facing might change your reception.) Is this a ridiculous notion?
And while I am not a scientist, it strikes me that the induction charger might not be exactly analogous, since it involves a different part of the spectrum and different intensity? --Mr.98 (talk) 21:17, 15 November 2010 (UTC)[reply]
I know some things about science, I can confidently tell you that energy of the EMR used by cellphones do not meet the required threshold to cause you to develop cancer. It is simply a urban myth reslting from a poorly conducted experiment. Plasmic Physics (talk) 22:00, 15 November 2010 (UTC)[reply]
I'm not asking you for an assessment of the threat, as I made clear in the first paragraph of my question. I really do wish people would actually read the question before trying to answer it. This seems to be a real epidemic on here lately. --Mr.98 (talk) 23:54, 15 November 2010 (UTC)[reply]
There is no need for such a contraption as what you're proposing, is what I was trying to say. The air does not absorb the EMR, if it did, then the signal can not travel long distances. The cellphone emits a spherical wavefront, the energy of a wavefront is almost constant at any radius however, the energy is spread over a larger surface when the radius is large. This is propotional to luminous flux. Moving the cell phone away from the ear, increases the radius and consequently decreases the luminous flux. Luminous flux affects rate of possible DNA mutations per unit time. The frequency of EMR affects how DNA reacts. Plasmic Physics (talk) 00:23, 16 November 2010 (UTC)[reply]
Again, I don't really care about your off-the-cuff, undergraduate-physics assessment of the hazard. That's an issue I don't actually think you know enough to answer about. --Mr.98 (talk) 14:09, 16 November 2010 (UTC)[reply]
Why would it only have a marginal effect on quality?!? Going by your illustration, You've just completely cut out reception of all cell-towers to your left! Worse is if you make a call facing one way, and then turn to face the other way you'd lose your connection and the phone would probably not have time to make a new connection so the call would just drop.
Looking at your illustration again, perhaps you think that the waves bounce off your skull? They don't. They go straight through. Phones just wouldn't be usable otherwise. APL (talk) 22:11, 15 November 2010 (UTC)[reply]
I don't think the bounce off the skull, no. If you conceptualize the radiating frequencies as a sphere coming out of the phone, I think you'd need a wedge of about 25%-30% removed to avoid going through the human skull, based on some rough approximations on my part. Which probably would have an appreciable effect, if you are in an area with only a few cell towers. But I assume that most urban areas are pretty well saturated by towers at this point (at least where I live, it seems like every large building has one). So the worst effect would be that sometimes you'd have to turn to find a better signal? That doesn't seem like the worst outcome to me, if there is actually a long-term risk otherwise.
But if that's the case, why does adding the inch of air between your head and the phone matter? What's the inch get you? To return to one of my original questions, why would it be any safer to hold the phone an inch from your head? --Mr.98 (talk) 00:10, 16 November 2010 (UTC)[reply]
I think most mobile phones already have a directional antenna that mostly radiates away from the head, this gives best signal quality since almost no radiation passes through the head, some are reflected and the most are absorbed.
File:Cellphone head sar 1.pngCalculated specific absorbed radiation (SAR) distribution in an anatomical model of head next to a 125 mW dipole antenna. Peak SAR is 9.5 W/kg averaged over a 1 mg cube. (USAF/AFRL). Note the concentration to the surface, most of the radiation only penetrate a few cm.
I have not heard the recommendation to hold the cellphone a inch from the head. I think it is reasonable to assume that any health effect decrease faster than linearly so it is better to spread the exposure over larger area if the effect exists at all. I also think the recommendation can have to do with the near field of the phone, this can afect both reception and health effects. --Gr8xoz (talk) 02:04, 16 November 2010 (UTC)[reply]
OK, this I get. It's not the air, it's the distance from the point source, so that the amount of EM radiation is more diffusely distributed. That is useful to know and I see where I was confused about the nature of the alleged threat — thanks! --Mr.98 (talk) 15:21, 16 November 2010 (UTC)[reply]
Gr8xoz actually has a relevant point. If holding the phone 1 inch from the head improves reception then this is a good thing if you are concerned about the level of the radiation for whatever reason since this will generally be reduced (as the phone adjusts the signal strength based on the reception). This BTW is a common concern with things that allege to reduce radiation to the body, by screwing with the signal they may just make the signal stronger. Of course if by holding your phone 1 inch away your call lasts longer because you can't hear each other properly this may also negate any purported beneficial effect. Also while I'm less sure of this, I presume if you're using packet switched calling, more noise may mean more transmission may mean more radiation. Nil Einne (talk) 08:50, 16 November 2010 (UTC)[reply]
The industrial solvents which leach out of typical consumer electronics in response to heat and perspiration are far more carcinogenic than any radio frequency electromagnetic radiation. Ginger Conspiracy (talk) 06:55, 17 November 2010 (UTC)[reply]
On the case of shielding, the wavelength of mobile phone RF is from 10 to 30cm. A shield needs to be considerably larger than the wavelength to block otherwise the theory of diffraction applies and the waves move around your little shield. You can try for a cardioid radiation pattern, with a null towards the head, but as mentioned that will cause dropouts in one direction. A tinfoil hat may be needed. Graeme Bartlett (talk) 09:40, 17 November 2010 (UTC)[reply]
As a high school teacher where students are not supposed have phones visible in class, a common storage location used by female students is in their bra. If they can cause brain tumours, what about breast cancer? HiLo48 (talk) 18:09, 15 November 2010 (UTC)[reply]
I would not summarize the current state of medical opinion on mobile-phone effects so bluntly. There is an enormous body of research on mobile phone health effects, and it is hard to say there is a strong consensus opinion. Our article, Mobile phone radiation and health, summarizes the state of knowledge pretty thoroughly. A few things we do know for sure: the frequency that cell-phones operate at can cause radiological harm. The intensity at which cell-phones operate at might be safe. Numerous studies exist, varying in their level of certainty and scholarly merit; the results variously confirm or refute the idea that mobile phones have increased cancer (and specifically, tumor and glioma) incidence. Nimur (talk) 18:59, 15 November 2010 (UTC)[reply]
I know that we don't yet have scientific certainty on whether cell phones can cause cancer. My question was a hypothetical. Ifthey can cause brain tumours, what about breast cancer? These girls have them close to their breasts for longer periods than normal users would have them close to their heads. HiLo48 (talk) 21:12, 15 November 2010 (UTC)[reply]
Can you please cite A few things we do know for sure: the frequency that cell-phones operate at can cause radiological harm. Microwaves fall between radio waves and infrared and visible light on the electromagnetic spectrum, neither of which cause "radiological harm". I'm not saying the case is shut, but if there is an effect, it isn't great, that is for sure. Very few technologies are perfectly safe, look at cars, the amount of people that die because of cars is staggering, but it's a risk we accept because the benefit of road travel is so great, even if a few people die by mobile phone, I dare say most people would still accept the risk rather then give up their phone. That's not saying that if we do find "something" we shouldn't make phones safer if we can, but it does mean that if we can't find a link we should make one up to panic people into buying magical microwave blocking holograms for $30 that do nothing. Vespine (talk) 22:10, 15 November 2010 (UTC)[reply]
I would hardly panic: I personally think the risks of cancer due to mobile telephony are small. But here are some citations: first, the thermal effects section of our article - it is beyond dispute that microwave radiation can cause tissue heating. A Google scholar search on biological effects of microwave radiation turns up numerous books and papers. And here's an IEEE paper, Biological effects of radiofrequency/microwave radiation, that essentially summarizes 50 years of research, establishing "safe" power exposure thresholds. I'm of the impression that even at full transmit power, the radio-intensities in mobile telephones are below the threshold of "significant" risk, but I would be reluctant to call it "zero" risk. Nimur (talk) 01:00, 16 November 2010 (UTC)[reply]
See the article above or the article I posted in the topic above this one. There is still a lot of scientific uncertainty on the question. The NY Times article cites a number of cases where EM radiation in the frequencies in question did create detectable abnormalities in rats. It's unclear what the epidemiological connection is or whether we can detect one at this point. It's unclear what the long-term risk is, which makes it impossible to make a good cost-benefit decision. Nobody is suggesting that a cell phone will give you cancer tomorrow — the suggestion is that after a few decades of heavy use like we've been doing since the late 1990s, there could be a huge uptick in things. It seems to me like a reasonable thing to wonder about, and to be cautious about, given the volume of people we're talking about here. Automobiles are not a great comparison — people were willing to adopt reasonable measures (which cost time and convenience) for safety (e.g. seat belts). --Mr.98 (talk) 23:47, 15 November 2010 (UTC)[reply]
It strikes me that it would matter whether or not the phone's EM radiation was constant when the phone was in "standby" (not talking) mode, among other things. I think the short answer is "nobody is really sure." Breasts and brains are different types of tissue, for one thing, and would presumably respond differently. It's not clear that causing one kind of cancer would necessarily imply that the other kind would be caused the same way, is what I'm saying. --Mr.98 (talk) 21:22, 15 November 2010 (UTC)[reply]
In any case, phones transmit almost not at all when they're sitting there unused. However, I suppose in this day of wireless headsets, you might have a phone in your bra that was making a call. APL (talk) 22:22, 15 November 2010 (UTC)[reply]
Don't phones do some sort of connection every so often? I know someone who leaves a (GSM) mobile near their speakers/amp all the time (connected to their computer) so you do hear it connecting every so often when not doing anything (even receiving SMS or whatever). I don't know how this power level compares to when it's making a calls or internet connection but it's obviously higher then the normal baseline. It doesn't last extremely long but then again for typical teens in many countries most of their usage may be sending and receiving SMSes anyway although in some I would guess mobile internet usage is increasing. If I were the parent of a teen, I'd be more worried about them getting some sort of RSI or other problem from SMSing too much or perhaps going deaf from listening to loud music then I would breast cancer from storing their phone in their bra. Somewhat OT but some people store their phones in a pouch around their waist, while not as close this is usually fairly near the testicles for males and I know people who don't like it for that reason. Many store their mobiles in their pocket which although further isn't that far. (From a search, the heat from laptops seems to be a more common concern however.) Nil Einne (talk) 08:32, 16 November 2010 (UTC)[reply]
Yes, they do register with the nearby cell towers periodically so the network knows when to do a hand-off, where to send ring signals, so authorities can track your position if you're accused of a crime, etc. Ginger Conspiracy (talk) 06:54, 17 November 2010 (UTC)[reply]
The industrial solvents which leach out of typical consumer electronics in response to heat and perspiration are far more carcinogenic than any radio frequency electromagnetic radiation. Ginger Conspiracy (talk) 06:54, 17 November 2010 (UTC)[reply]
Any cancer risk from cell phones is elevated in adolescents. Other studies show a direct correlation between exposure to mobile phone radiation and reduction in male spermatozoon function. ~AH1(TCU)03:41, 18 November 2010 (UTC)[reply]
I often come across the claim that humans evolved to have smaller pelvises because bipedalism wouldn't be practical otherwise...with the price that childbirth becomes much riskier. But this seems hard to reconcile with the obvious fact that a lot more women appear to have difficulty giving birth than have difficulty simply walking upright...so how to justify the claim that they both exert comparable amounts of evolutionary pressure (or at least did before the advent of modern medicine and medicalized childbirth?) 129.2.129.161 (talk) 18:25, 15 November 2010 (UTC)Nightvid[reply]
Bipedalism#Humans discusses speculation as to why we have evolved to be bipeds; it says there are at least 12 theories about this, so it's going to be a little difficult to pick a single answer to your question about evolutionary pressure. Interestingly we have a whole article on Human skeletal changes due to bipedalism which does not mention the pelvis. (It does mention the hip.) Comet Tuttle (talk) 19:16, 15 November 2010 (UTC)[reply]
You've missed that childbirth would not be such a problem if babies did not have such large heads. The question is, when did we start to get such large heads that this caused a problem? Most speculation I've seen places that after the rise of bipedalism. The evolutionary arms race then comes between the baby, 'wanting' to be born with as large a head as possible, and the mother, who needs to survive the process well enough to raise the child. This is speculated as the reason why human babies are born so helpless, effectively premature even at full term, so that they can continue to grow their enormous heads outside the mother, after having made it through the pelvis. 86.164.144.120 (talk) 20:22, 15 November 2010 (UTC)[reply]
It's well accepted that Sugar damages your teeth especially in large quantities, but is Aspartame (specifically from diet sodas) as bad, the same, or worse then sugar on teeth? Are there any studies that address this? Thanks! Chris M. (talk) 19:15, 15 November 2010 (UTC)[reply]
From this link, 'The American Dental Association has noted it "welcomes the development and FDA approval of new artificial sweeteners that are shown to be safe and non-contributory to tooth decay. . . . Aspartame is an FDA-approved, safe sweetening agent and flavor enhancer that can be substituted for sugar in the diet."' That doesn't explicitly say apartame is non-contributory to tooth decay though. Franamax (talk) 20:53, 15 November 2010 (UTC)[reply]
Here is a 2001 American Dental Association review which says "Non-nutritive sweeteners found in diet soft drinks may not be directly cariogenic because tooth decay producing bacteria cannot ferment aspartame...". Here is the ADA mentioning "...non-cavity causing sweeteners such as aspartame...". Still haven't found a specific study though. Franamax (talk) 21:04, 15 November 2010 (UTC)[reply]
Think about how sugar damages teeth. Bacteria ferment it to some sort of acid, generally by oxidising the carbon backbone until a carboxylic acid group appears. How are bacteria going to ferment aspartame? It is a peptide yes but the COOH groups are esterified. John Riemann Soong (talk) 23:47, 15 November 2010 (UTC)[reply]
Not to mention that the amount of aspartame needed to get a level of sweetness is much less than an equivalent amount of sugar. There's so little aspartame in most foods that the effect on teeth is really a moot point anyway. Keep in mind, though, that something like Diet cola generally still has Phosphoric acid, which will still attack teeth. Buddy431 (talk) 03:45, 16 November 2010 (UTC)[reply]
A conspiracy theory that doesn't hold up. If there were any truth to this the powerful sugar industry, which in America has kept trade restrictions alive and well, would be all over it. Imagine Reason (talk) 23:20, 16 November 2010 (UTC)[reply]
Compared to other cars, the Nissan GTR is heavier and less powerful but still is incredibly fast. I've compared it with more powerful cars that also have AWD. I've also compared it with lighter more powerful cars. All of this combined with the low price does not make sense to me. If anyone can help, I would appreciate it. 158.135.169.37 (talk) 19:44, 15 November 2010 (UTC)[reply]
Well, obviously how a car performs in a race isn't just about power and weight, otherwise, the winner of every race could be predicted by just plugging in figures into a simple formula, which is obviously not the case. If you are interested you should probably start by reading the article Nissan Skyline GT-R, It has a lot of information about the car's performance features.Vespine (talk) 21:47, 15 November 2010 (UTC)[reply]
In particular, "tests showed the car had a factory power output of closer to 330 PS (325 hp) at the flywheel. The lower published figure was Nissan's response to the need to abide by a gentleman's agreement between the Japanese auto manufacturers not to release a car to the public exceeding 280 PS (276 hp) of power output," refers to an engine which can easily be adjusted to put out 450-500 horsepower. That and the fact that the GTR body has since the 1990s been far more about aerodynamics than design styling like most of the cars in its class. Ginger Conspiracy (talk) 06:48, 17 November 2010 (UTC)[reply]
You haven't defined "incredibly fast", so it's hard to pin anything down. For stoplight-to-next-stoplight fast, torque will be most important, and the gear ratio will count too. For a highway car, the ratio of the highest gear will decide how fast it can go, in combination with the horsepower. For getting around a road course or rally stage, handling becomes important (steering, brakes). For oval or sprint track racing, you optimize straight-line acceleration, slowing into a corner, and accelerating out of a corner. To keep a "fast" car cheap, match the gear ratios to the torque curve of the motor so it appears fast, then minimize everything else. Take out the standard ABS, rear wiper, comfortable seats, use a smaller HVAC system, allow only 2GB of storage in the MP3 player (if you've gotten to that stage, you're pretty desperate to cut weight and cost :). Automobiles actually made for sale are a whole package, so you have to evaluate all their costs and benefits. You didn't mention fuel costs or insurance rates at all, and those can have a huge impact on just how "incredible" you think a car is once you are the one actually operating it. Franamax (talk) 07:26, 16 November 2010 (UTC)[reply]
In terms of the 'cost' part of the question, some of that comes down to expectations, 'street cred', showoff factor, market psychology, or whatever you may like to call it. In short Nissan is chiefly recognised as a manufacturer of relatively bland, low cost, mass market cars. So even if they produce a killer car like the GTR, they can't expect to get the sort of coin for it that the exclusive marques like Ferrari, Lamborghini, Porsche etc can ask. Why would anyone pay that money for a shopping trolley brand when they could be driving one of the world's exclusive cars, even if the Nissan is faster, more powerful, better optioned, more reliable, or whatever else it may be? Like it or not, you do pay for the badge. --jjron (talk) 12:30, 16 November 2010 (UTC)[reply]
The following discussion is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.
hi, i am using roaccutane treatment since 4 months. however, after i read in the article in this site that it makes back ache, a question crossed my mind: is it dangerous to continue with this treatment if there is a disc problem even if it is not a serious problem? because i used to have back ache before i started roaccutane. i am looking forward to get your reply even if it is medical question because it will help alot. thanks
The reply is that you have to consult your doctor. Please do not trust random strangers over the Internet with important medical questions; your health may be damaged if you follow bad medical advice, even if it's given with good intentions. Comet Tuttle (talk) 20:58, 15 November 2010 (UTC)[reply]
The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.
If a distance unit like a meter is used to measure length in 3-dimensions and a unit like a second is used to measure a length in time, which some indicate is the 4th dimension, is there a conversion equation that states the measurement of time in that of distance? For instance, X seconds = a * Y meters. -- Sjschen (talk) 21:58, 15 November 2010 (UTC)[reply]
I'm not entirely sure what you're asking, but it sounds like it has to do with special relativity. At velocities approaching the speed of light, a coordinate or vector of time has to be descibed in terms of space. As in, for this spatial coordinate or vector, time is such. One should be carefull when discussing dimentions, space and time maybe dimensions, but they are different kinds of dimentions. The are, up to date, twelve spatial dimentions, and two temporal dimenstions. Plasmic Physics (talk) 22:19, 15 November 2010 (UTC)[reply]
Only four are accepted in Special relativity where the "conversions" are really rotations in 4-D space-time. Different proposed theories predict different numbers of possible dimensions, but only the four of special relativity have actually been "discovered". Most of the other "predicted dimensions" are too small to measure. Dbfirs22:31, 15 November 2010 (UTC)[reply]
I'm just curious because if one can use meter to measure the the "first 3" dimensions I'm wondering if one can use the same unit to measure the "4th" dimension, given some imaginary alien that lives in these 4 dimensions just like we do our 3. It certainly would be fun (albeit nerdy) to say that the laundry will be done in some X meters instead of minutes. -- Sjschen (talk) 23:51, 15 November 2010 (UTC)[reply]
You're confusing spatial dimensions for temporal dimensions, there is a hypothetical fourth spatial dimension which is defined in terms of meters. Time is not the fourth spatial dimension, it is the first temporal dimension, it is the fourth perceptable dimension. Everything lives in these four dimentions. Plasmic Physics (talk) 01:29, 16 November 2010 (UTC)[reply]
Us earthlings do it the other way round! We define our metre to be 1⁄299,792,458 of a light-second! We do it that way simply because we can measure time far more precisely than we can measure length: so it makes sense in practical terms to define the unit of length in terms of the unit of time, rather than the other way round. But, logically speaking, there's nothing to stop me saying that it takes my washing maschine about 8 light-micrometres to do a load of laundry ;) Physchim62(talk)00:48, 16 November 2010 (UTC)[reply]
Ah yes, sorry, I gave the wrong result. 8 light-micrometres is about how long I spend each day wondering how I always seem to have clean laundry. My partner tells me that the washing machine takes about 720 light-gigametres to do a load, and has suggested I measure this value more precisely myself ;) Physchim62(talk)01:37, 16 November 2010 (UTC)[reply]
You can choose to use a system of natural units in which the speed of light is 1 by definition, in which case time can be measured in meters (not "light-meters"), just like spatial distance. Instead of thinking of "space" and "time" as two "different kinds of dimensions", it works fine (better even, when doing general relativity) to think of spacetime as being a 4-dimensional manifold in which "space" and "time" dimensions are not distinguished, except for there being a metric tensor that introduces a local directionality to spacetime. Red Act (talk) 03:39, 16 November 2010 (UTC)[reply]
The OP is asking for the distinction between tropospheric ozone and stratospheric ozone. The mechanisms for creating the two are very different, and the two sources of ozone do not mix. Stratospheric ozone is generally created from the action of ultraviolet light on oxygen in the stratosphere. This ozone in the stratosphere then absorbs more UV light, and prevents that UV light from reaching the troposphere. Within the troposphere, most of the ozone is anthropogenic (human made); it is generally created in car exhaust. Tropospheric ozone is a serious polutant, as an eye and lung irritant. There would always be trace amounts of tropospheric ozone, due to lightning, but its concentration would be much less without humans. Paradoxically, human activity also tends to decrease the availibility of stratospheric ozone. So the next effect of human life seems to be to remove ozone from the stratosphere, where it can effectively block UV radiation, to the troposphere, where it aggrivates asthma and allergies. --Jayron3204:24, 16 November 2010 (UTC)[reply]
"it is generally created in car exhaust" kind of, but actually its formed when NO2 is broken down by sunlight and reacts with oxygen. We do have a specific article on tropospheric ozone by the way. I might be wrong here, but I can't think of any natural processes that produce NO2. Whilst there would be a very very tiny amount of tropospheric ozone naturally, our actions definitely significantly increase it. Ah yes, a source, this bascially backs up what I said, but unsurprisingly confirms I was wrong, tiny amounts will be formed due to plant VOC emissions. A google scholar search for "tropospheric ozone natural" brings up papers which you might find interesting. One thing they discuss which our article neglects (been meaning to sort it out) is that tropospheric ozone damages plants as well (thankfully all that CO2 we're producing goes some way to negate the effect. SmartSE (talk) 15:20, 16 November 2010 (UTC)[reply]
Lightning also produces ozone (and this occurs in the troposphere), but the quantities are small compared to the other sources discussed above. In any case, lightning is rarely anthropogenic. Nimur (talk) 17:13, 16 November 2010 (UTC)[reply]
I'm not sure whether any significant concentrations of tropospheric ozone exist naturally, but without anthropogenic emissions there would be no atmospheric halocarbons. ~AH1(TCU)03:35, 18 November 2010 (UTC)[reply]
At what point is change noticeable to the human eye? As if I where to add one granule of sand to a heap, at what point would any person recognize change? 66.229.227.191 (talk) 23:29, 15 November 2010 (UTC)[reply]
Your question is not very clear, are you asking if there is a paradox because some changes are too small to perceive with the naked eye? I don't see any paradox. Vespine (talk) 00:19, 16 November 2010 (UTC)[reply]
I guess in the title I was inplying that it is somewhat a paradox, as I was hoping to find a mathematical solution to the Sorites Paradox. But that wasn't apart of the question, I just want to know at what size does change become perceivable? 66.229.227.191 (talk) 00:25, 16 November 2010 (UTC)[reply]
It's not a mathematical solution, per se, but a question about human psychology/physiology. There probably isn't one answer in most cases, but a spectrum of likelihood where people will say it falls on one side or the other. (This is the "group consensus" mentioned in the article, which is probably the most "scientific" way to study the question, though it will aid the philosophers none.) On some issues, though, there are physiological reasons that we detect certain things as being discrete changes. Color, for example: show people a rainbow spectrum of chips with very slight differences between each color, and ask people to point to "red", and they'll all pick the same chip, more or less. This is because it correlates with the firings of the nerves in our eyes, or something like that ("red" is when one cone triggers at the maximum, and a rod at its minimum, or something like that... it's been awhile since I took psych). --Mr.98 (talk) 00:47, 16 November 2010 (UTC)[reply]
Wow, I'd never heard of the Sorites paradox until I read this question, and yet I have a paper in submission at the moment which discusses a very similar problem in metrology... It's amazing what you can learn at the WP Reference Desk! Anyway, the paper hasn't passed the reviewers yet, so let's hope they don't ask me to discuss Greek philosophy on top of everything else ;)
To translate my proposition into the language of the Sorites paradox, I say that a heap is no longer a heap if you can tell the difference on removing a single grain. A bit like saying you're rich if you don't have to worry about your bank balance! In more formal terms, "tell the difference" is related to the measurement uncertainty of whatever method you are using to measure your heap: nowadays, that doesn't just have to be human vision. So, if we define the quantity n as the "size" of the heap (by whatever method of measurement), and the quantity N as the number of grains, the heap remains a heap if the quantity 1/N can be treated as a differential dn/n under the conditions of measurement, the quantity 1/N being the fractional change in the number of grains when N changes by one grain. You can treat 1/N as a differential if the discontinuity in the measurement result when the number of grains changes by one grain is, or would be, significant compared to the uncertainty of the measurement result, discounting the contribution to the uncertainty from any correction for systematic measurement error.
The problem with the paradox is one of human perception and linguistics, not reality. We make the distinction between grains of sand and a heap, not nature. I don't consider it much of a paradox, myself. A term like "heap" has no real scientific meaning, which is why we use precise terms for masses of thing (e.g. a kilogram) for things that have to have real answers. I have heard philosophers banter on about "baldness" in the same way — when do someone become "bald"? What's the hair that does it? It's just navel gazing in my opinion. --Mr.98 (talk) 14:04, 16 November 2010 (UTC)[reply]
My solution would be to define the heap only in the limit of N to infinity (and making the grain size scale inversely with N so that the total volume remains constant in the N to infinity limit). If N is not strictly infinitely large, you only have an approximate heap that gets worse the smaller N becomes.
In statistical mechanics a similar problems arises in the theory of phase transitions. Given some amount of matter, you want to be able to say that it is in one phase or another phase (like liquid or gas). But it turns out that for finite amount of substance, phases are not defined. Obviously, if you have only a few molecules, you can't tell which phase the substance is in, so the situation is analogous here. Strictly speaking, you need to take the limit of an infinite amount of substance (the so-called thermodynamic limit). What happens mathematically, is that the partition function is an analytic function of the temperature for any finite number of particles, but in the limit of an infinite number of particles, a singularity can develop which then defines the phase transition.
The point is then that a Taylor expansion at a point in one phase won't converge into the regime of the other phase. So, an extrapolation based on accurate measurements of the properties of the system in one phase to predict the behavior in the other phase will fail. As long as accurate extrapolation gives the correct result (in the limit of infinite accuracy), you can say that the system is qualitatively the same and thus in the same phase. Strictly speaking, you need an infinite amount of particles for the distinction between phases to arise. Count Iblis (talk) 04:36, 16 November 2010 (UTC)[reply]
In psychology, this concept is called a just-noticeable difference or JND, and has been studied very intensively as part of psychophysics. The principle result is that a JND is generally a constant proportion of the perceived magnitude of a quantity, however the size of that proportion varies according to the nature of the stimulus. This rule is known as the Weber-Fechner law. Looie496 (talk) 17:52, 16 November 2010 (UTC)[reply]
There's already an equation? So I spent all of last night trying to create an equation myself was useless... this actually happens to me quite often... they should make a rule to do more research before trying to solve something that's already been solved :/ 66.229.227.191 (talk) 20:31, 16 November 2010 (UTC)[reply]
A jaded grad student once told me "spending merely a few weeks in lab can easily avoid the necessity for doing a 5-minute literature search." DMacks (talk) 20:54, 16 November 2010 (UTC)[reply]
It wasn't useless: your brain is now slightly different than it would have been if you hadn't tried to solve the problem yourself, presumably for the better. You have shaped yourself slightly. 86.163.213.68 (talk) 00:09, 17 November 2010 (UTC)[reply]
In scientific experiments there is an essentially arbitrary criterion that if statistical tests find that a difference of the size observed would be found 5% of the time just by random chance, that this is significant. I don't know if people decide by eye that one pile of sand is larger than another pile of sand on the same basis (that there is a small risk that they would imagine a difference of the same degree between two equal piles), but it is possible. Wnt (talk) 02:02, 17 November 2010 (UTC)[reply]
There is a mathematical reason that scientists use 95% as a level of significance. If your chains of inferences take place at the 95% confidence level, the likelihood that you will be mislead by random chance is vanishingly small. But at the 90% confidence level, chains of inference can mislead you by random chance fairly often. I have a more concrete quantification in my library; I'll look for it, but for five inferences with random interdependencies the difference is something like 0.001% vs 3% if I remember correctly. Ginger Conspiracy (talk) 06:33, 17 November 2010 (UTC)[reply]
