User:NorwegianBlue/refdesk/science

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[edit] North Star

Can you tell me the simplest way to identify the North Star. I do not know what to look for in order to find. Please spell it out so clear that i can follow step by step instructions on this article in order to find it. Thank you.

The way I normally find it is to locate the Big Dipper and then follow the line that is created by the two stars that make up the edge of the bowl of the dipper on the side opposite from the handle of the dipper. By following this line in the direction of the "opening" of the bowl of the dipper, they point to the North Star which is also the last star in the handle of the Little Dipper. The rest of the Little Dipper is generally harder for me to see since the stars aren't as bright in that constellation. Dismas|(talk) 05:41, 30 May 2006 (UTC)
P.S. After checking the links I supplied, I see that this is spelled out with diagrams on the page for the Big Dipper. Dismas|(talk)
But don't use the official flag of Alaska, that is shown on the big dipper page as a map! The north star is nowhere nearly as bright as the flag suggests. Use this link instead, and you will find a better map. --NorwegianBlue 19:13, 30 May 2006 (UTC)

[edit] Diamond

I know how it crystallizes but how does that relate to valence bonding of it? (no it's not homework)Any help would be appreciated. And remember, as this question may seem ridiculously simple, as I just read above: don't bite the newbies

In diamond, carbon is in the sp3-hybridised state, see orbital hybridisation for a nice image. Each nucleus sits in the middle of a tetrahedron. Thus, it is tetravalent here as elsewhere, and each carbon atom "shares an electron" with each of its four neighbours. --NorwegianBlue 09:50, 4 June 2006 (UTC)
This brings another question - a cube is related to an octahedron in Plato's system, how can a self-dual tetraedron build cubic centered crystals ? I'd appreciate any hint. --DLL 20:18, 4 June 2006 (UTC)
I'm not sure if this answers your question, DLL, but there's a picture of the 3D structure of diamond in the carbon page. --NorwegianBlue 21:53, 4 June 2006 (UTC)
OK, the distance between the center of the tetrahedron and its summits must differ from the distance between summits linked by Valence. --DLL 22:13, 5 June 2006 (UTC)

[edit] Static electricity

When you get a shock of static electricity, simply stated, the reason is presumably that your body has acquired a surplus or deficit of electrons compared to the environment. How would one go about to estimate the number of electrons that is transferred in such a shock? Does somebody have an idea of the approximate number? When walking on synthetic carpets etc., do we usually acquire a positive or negative charge? --NorwegianBlue 12:24, 21 May 2006 (UTC)

No ,when you get a shock, its because charge has passed through your body causing the muscles to contract. THe amount of current passing depends upon the voltage, the resistance of the static generator, and the body's internal reistance (which is about 700R).
As to charge build up, I would try the Faradays ice pail experiment with the victim standing in the pail. The pail needs to be insulated from earth. THe victim would not actually get a shock because current would not pass thro the body (hopefully). Then by knowing the capacitance of the pail and its final voltage after charge transfer, one can calcualte the amount of charge passed.8-)--Light current 12:36, 21 May 2006 (UTC)
There are some calculations done by Mr Static here. The answer in his case was a positive charge of about 3 x 10-8 coulombs, which is about 2 x 1011 electrons. --Heron 13:39, 21 May 2006 (UTC)
Thanks a lot, Heron, that was exactly what I was looking for. The value of 3 x 10-8 coulombs appears to be per step, the graph might suggest a charge buildup about 20 times larger. --NorwegianBlue 13:58, 21 May 2006 (UTC)

[edit] Is it possible to see clearly underwater by wearing spectacles instead of goggles?

Inspired by the preceding question, as well as this one and this one: The reason we do not see clearly underwater is that the refractive index of the cornea is almost equal to that of the surrounding water, so that we lose the refraction at the interface between air and cornea. Is it possible to correct this by wearing spectacles underwater, (i.e. with water between the lenses and the eyes)? It would be kinda nice, goggles tend to get foggy... And if it indeed is possible, what lens strength would you need? --NorwegianBlue 21:07, 23 May 2006 (UTC)

http://www.liquivision.ca/fluidgogglesfeatures.html —Keenan Pepper 21:12, 23 May 2006 (UTC)
Thanks, gotta get one of those... --NorwegianBlue 21:49, 23 May 2006 (UTC)
Thanks a trrrrrrrrrrrrrrrrrrrrrrrrrrrillion, that was the EXACT answer I was looking for 206.172.66.172 00:10, 24 May 2006 (UTC)
Or you could just get some defog for your SCUBA mask. There are commercial preparations, or you can use a dish soap solution, or your own saliva. They all work. And you can even get a prescription in your mask. --Ginkgo100 23:59, 24 May 2006 (UTC)

[edit] Balancing a bicycle

Why is it (relatively)easy to 'balance' on a moving bicycle and the same, impossible on a standing cycle?

We all know this.... i just want to know the physics behind this everyday action

How can we easily balance ourselves (stay upright) on a moving bicycle (or bike) but the same thing is impossible when a try on a stationary two-wheeler? _________________

i did some re-searching and it looks like its not entirely 'angular momentum' as in the case of a top and also not entirely the gyro effect either... http://en.wikipedia.org/wiki/Bicycle_and_motorcycle_dynamics

all the facts are here... i can almost see the answer forming but not quite there... help me out - somebody pls put this phenomenon in nice understandable sentences

Thanks a lot

Seethahere 21:21, 22 February 2007 (UTC)

Contrary to a common belief, angular momentum (the gyroscope effect) has (almost) nothing to do with it. The main point is that you have an effective means of controlling your balance when moving, but not when standing still. It works like this: suppose your bike is starting to lean over slightly to the left (i.e. your center of mass is to the left of the line between the wheels' contact points with the ground, which is the axis you would pivot around if you were to fall over). Thus you are (your center of mass is) starting to fall over towards the left. When you notice this, your learned bicycling skill makes you make a nearly unconscious correction, by turning the handle bar slightly to the left. This causes your front wheel to move to the left under you, until the line between the wheels' contact points is once again vertically under your center of mass. In other words, you have regained balance. This correction doesn't work if you are standing still, because turning the handlebar doesn't then cause the front wheel to move sideways. --mglg(talk) 21:36, 22 February 2007 (UTC)

Ok, that is one of the most complex articles ever, for something so simple. Bikes have self-stability. That means if you just hold a bike still, you can make it steer left or right by leaning it. You can ride a bike without hands, and steer just by leaning. It's a bit like a skateboard. --Zeizmic 23:27, 22 February 2007 (UTC)

Sorry I don't believe it, a well "ghostied" bicycle will go forward without a rider for a long time without falling over, which obviously has nothing to do with slight, almost unconscious steering inputs from the rider. I've ridden both bicycles and motorcycles a lot in the past and definitely there is more to it then 'corrections' made by the rider especially on a motorcycle that's going at speed, so much so in fact that when you TRY to turn the motorcycle and then release the pressure the motorbike will return on its own to travelling in a straight line. Can you source your assumption of gyroscope effects not having much to do with it? Vespine 23:48, 22 February 2007 (UTC)
http://www2.eng.cam.ac.uk/~hemh/gyrobike.htm Skittle 10:43, 23 February 2007 (UTC)

Ah, ah. No complaining, unless you made a pretext of reading that long, long, article! :) (which covers this particular turning thing somewhere..) --Zeizmic 01:01, 23 February 2007 (UTC)

Bicycle head angle, rake, and trail
Bicycle head angle, rake, and trail
The principle is correct, but there's no unconscious inputs involved - the stability comes from the bike turning itself. The horizontal "trail" (as pictured) is the key. Explaining the details of it is beyond me, but the gist of it is that when the bike starts to lean, the trail causes the wheel to steer into the turn, straightening it up and preventing the fall. It only works above a certain minimum speed, but it's why you can let go of the handlebars and not fall over. There's no special skill involved; the bike is genuinely driving itself.
Apparently a lot of time and money goes into getting the trail right, to ensure stability. I saw a really good explanation of this very recently, but I can't for the life of me remember where. If it springs to mind, I'll post the link. Spiral Wave 01:08, 23 February 2007 (UTC)
Might it have been in New Scientist, in the "The Last Word" section? I've linked to a bit of it, although I don't know how well this will work for those without a subscription. It also provides an answer for those who don't believe how little effect the gyroscopic effect has: a bike designed to cancel out all gyroscopic effects which people could ride with ease. Skittle 10:42, 23 February 2007 (UTC)
Turns out there is also a (very) brief mention of the effect in the trail article linked in the caption. I do remember that it's why bikes are built with trail. If the steering column was vertical, the result would be highly unstable. Spiral Wave 01:31, 23 February 2007 (UTC)
You can see from the diagram that if the bike is stationary - and leans to one side, there is a gravitational force acting through the frame of the bike and a ground reaction from the point where the front wheel touches the ground. This causes a rotational moment through the steering tube that causes the front wheel to try to turn 'into' the direction the bike is leaning. If you stand next to a bicycle and just lean it to one side, you can see that happening. But when you are moving rapidly, you have forward momentum and it takes a significant amount of force to cause the bike to change direction. The reaction to that force is pushing the wheel back into a straight line - so there is a net upward force countering gravity and making the bike stand up straight. It's hard to explain without a white-board and some force vector diagrams! SteveBaker 13:50, 23 February 2007 (UTC)
All of this is true, but please realize that the self-correction induced by the rake is only there to help you make roughly the right correction. The rider still does the fine tweaking to perfect the balance (and yes, this tweaking can be done either without hands, by leaning the frame so that the rake induces the front wheel to turn, or more simply by turning the handlebar by hand). The bike is NOT fully self-balanced, as you can establish by letting your rider-less bike roll down a hill by itself and seeing what happens (I don't recommend that test with an expensive bike...). --mglg(talk) 18:31, 23 February 2007 (UTC)

[edit] Distillation of ethanol, temperature

When a mixture of ethanol and water is heated and reaches the boiling point of ethanol, will the temperature stay the same (approx. 78.5°C) until all the ethanol has evaporated, or is it possible to heat such a mixture to, say 85°C, at ambient pressure? --62.16.173.45 14:34, 28 May 2007 (UTC)

The mixture will approximately stay at the same temperature until the ethanol has evaporated. It is not totally accurate, there are some effects when you go into detail. Destillation talks about the variation of the boiling point of ethanol in a solution. There is also the possibility of Superheating.
Thank you! --62.16.173.45 18:15, 28 May 2007 (UTC)
Actually, the boiling point of the mixture will change as its concentration changes, and approach the boiling point of water (100°C) as the ethanol concentration goes to zero. The boiling point of a mixture of ethanol and water has a curious dependence on concentration: Pure ethanol boils at 78.4°C; with decreasing concentration of ethanol the boiling point first decreases (!) toward a minimum of 78.15°C at 95.6% (by weight) ethanol, and thereafter increases towards 100°C at 0% ethanol. The 95.6% mixture is called an azeotrope. The evaporating gas will not be pure ethanol but a mixture of ethanol and water vapors, with the mixture depending on temperature in its own way. The vapor will in general have a higher concentration of ethanol than the liquid, which is why you can concentrate ethanol by distillation. At the azeotropic temperature, however, the vapor mixture will have the same relative concentrations of ethanol and water as the liquid. The azeotropic concentration of 95.6% ethanol is therefore the most concentrated ethanol that can be produced by direct distillation of an ethanol/water mixture (without addition of other compounds). --mglg(talk) 16:17, 29 May 2007 (UTC)
Thanks a lot! Do you have any specific info on the boiling points at various ethanol concentrations, and on the corresponding relative concentrations of ethanol and water in the vapour phase? Is there a table somewhere on the net where I can look it up? And also, although I initially restricted the question to what would happen at ambient pressure, I am also interested in learning about the dependency on pressure, if a table that includes pressure is available. --62.16.173.45 17:03, 29 May 2007 (UTC)
  • From the OP: A web search gave a partial answer to the last question. I will post a follow-up question shortly. --62.16.173.45 20:27, 29 May 2007 (UTC)

[edit] Phase diagrams for mixtures of ethanol and water.

I recently asked a question about the boiling point of a mixture of ethanol and water, and its dependency on pressure. After some googling, I realised that what I actually was asking for is a binary phase diagram for a mixture of ethanol and water. The best I could find on an image search was this one (middle panel), which is what I'm looking for, but with very low resolution in my region of interest. This exellent tutorial explains how to read the diagram.

  • Is anyone able to provide pointers to a similar diagram, with better resolution in the range 78-100°C?
  • Is all the information I need for calculating boiling points and vapour composition at various pressures in the phase diagram, or does the phase diagram itself depend on pressure? The fact that the diagram ends at 100°C for pure water suggests the latter, since water would have boiled at a higher temperature if the pressure were higher than 1 bar. If indeed several phase diagrams are needed, does anyone have information about where to find them? My region of interest for pressure is from atmospheric to approx. 1.5 bar. --62.16.173.45 20:48, 29 May 2007 (UTC)
Sorry, I don't have a table to point you to. But the following may be conceptually helpful for the pressure question: At any given temperature, a given mixture of ethanol and water has a well-defined vapor pressure (or partial pressure) of ethanol, and a different vapor pressure of water vapor. The vapor pressures are defined as the gas concentrations that the fluid would be in evaporation/condensation equilibrium with. The vapor pressures do not depend on the actual external pressure. The fluid(s) will evaporate or condense until the actual concentrations of each gas is equal to the fluid's vapor pressure for that gas (which may itself change during the process because evaporation/condensation can affect the temperature and fluid mixing ratio). At a certain temperature, the total vapor pressure will equal the ambient pressure; this temperature is the boiling point, at (or above) which evaporation can take the form of bubbling. Increases in pressure by addition of a third, more-or-less inert gas (such as air) does not in principle change the vapor pressures, just the boiling point. --mglg(talk) 21:37, 29 May 2007 (UTC)
Phase diagram
Phase diagram


Water vapour pressure
Water vapour pressure
Thanks again! Regarding the total pressure and partial pressures, I make the assumption that the only gases present are water and ethanol vapour. I made a phase diagram with better resolution based on the one I linked to. The blue curve is the boiling point of the liquid mixture, the red curve is the composition of the gas mixture. Based on the diagram, I can see that 40 vol% ethanol in water boils at appox. 81°C, and that the mixture in the gas phase then contains about 65% ethanol. This is valid, I presume, only when the sum of the partial pressures of ethanol and water vapour equals 1 bar. Is it possible to determine the corresponding data at 1.1 bar by using this diagram, or by combining it with the graph of water vapour pressure shown below? --62.16.173.45 10:08, 30 May 2007 (UTC)
Hmm. Did some calculations to check this out, using these calculators: Water vapour pressure, Ethanol vapour pressure, created by Shuzo Ohe. The vapour pressure of ethanol at 81°C is 844.8 mmHg = 1.126 bar, and that of water is 369.8 mmHg = 0.493 bar. I was wandering whether the pressures would add up to 1 bar, and see that they don't. Am I correct in thinking that the exact purpose of the phase diagram is to correct for this discrepancy? And again, is there some way of reading my phase diagram, in order to calculate boiling points for higher pressures than atmospheric? --62.16.173.45 11:33, 30 May 2007 (UTC)
The values don't add to one atmosphere because they represent the vapor pressures above pure ethanol and over pure water; the partial pressures over a mixture of water and ethanol are different from these. What you need for complete understanding is a set of curves or tables that show the partial pressures of the two gases above a mixture of ethanol and water, as a function of temperature and of the mixing ratio in the liquid. The boiling point at any given pressure is the temperature at which the two partial pressures add to the given pressure. --mglg(talk) 16:14, 31 May 2007 (UTC)
Thank you again, mglg! I think I understand it now. I'll see if the library can help me with some tables. --62.16.173.45 19:38, 31 May 2007 (UTC)

(outdent) I found a random old reference (Phys. Rev. 57, 1040–1041 (1940)) that contains partial pressure graphs for low temperatures (20-40°C). They got the data from the International Critical Tables, which might contain data for higher temperatures (more relevant for you) as well. You can find out in the online edition, but you may have to pay to use it. --mglg(talk)

Thank you for the book reference. It probably has the data I'm looking for, but the website wouldn't even let me read the index without paying! However, I'll check it out at a library workstation, they may have a subscription. -62.16.173.45 10:08, 30 May 2007 (UTC)


[edit] What is the resistance of the human body?

Italic text —Preceding unsigned comment added by 59.93.198.63 (talk) 06:08, 3 February 2008 (UTC)

It's quite variable, depending on where you measure, skin condition, fat/lean content, the connections used, and other factors I can't think of offhand. This article should be illustrative. — Lomn 06:39, 3 February 2008 (UTC)
It also depends on what you're trying to resist.--Shantavira|feed me 09:43, 3 February 2008 (UTC)
Presumably electricity (electrical resistance). —Pengo 14:22, 3 February 2008 (UTC)
Maybe Shantavira meant what type of signal? I doubt skin is an ohmic conductor. Trimethylxanthine (talk) 04:28, 4 February 2008 (UTC)
1200 Ohm was published on some obscure website.--Stone (talk) 13:02, 4 February 2008 (UTC)
That is clearly wrong. Although we're not supposed to, here's some original research. I found my ohmmeter and a box of resistors. Measuring from arm to arm, after having licked my fingers to reduce resistance at the surface, gave a reading of slightly over 100 kOhm. To verify this, I checked against various resistors, the closest being 130 kOhm. With dry skin, the resistance is considerably higher, and I was unable to get a consistent reading, but it is certainly higher than 500 kOhm. --NorwegianBlue talk 14:03, 4 February 2008 (UTC)
I had the same experience when measuring with an ohmmeter, but I think that it's lower at higher voltages (if it weren't then it would be safe to touch household power supply - you need about 50 mA to die or so I learnt). BTW, I've heard rumors that someone killed himself with a 9 V battery by inserting the contacts into the veins in his right and left hand .... Icek (talk) 02:03, 6 February 2008 (UTC)
Wow! Do you have a source? Googled it with no luck. Should qualify for a Darwin Award! --NorwegianBlue talk 09:10, 6 February 2008 (UTC)
Unfortunately not - I read it somewhere on the internet a few years ago. What is the electrical conductivity of blood and lymph? With a salinity of 0.7% it's maybe about 1 S/m (seawater's is 5 S/m according to our article, but other ions like phosphate will probably make blood's conductivity larger). If the current is 50 mA, then the conductance should be 1/180 S. If the distance between the contacts is 1.5 m, and we assume equal thickness along the conductor, its cross section should measure 83 cm2, e. g. a cylinder about 5 cm in radius. At least it looks as if it could be true. Icek (talk) 14:41, 6 February 2008 (UTC)

[edit] Dimensions in a World (includes string theory explanation)

04:47, 2 October 2007 (UTC)210.0.136.138AHow many dimensions exist in the real world? And, how does this really mean to human beings? Can a specific person exist in a separte world of different dimensions, if that exists. Is it true that Eistein has already affirmed this?04:47, 2 October 2007 (UTC)210.0.136.138Allen Chau, from Hong Kong

There are as many dimensions as we define to exist. See degrees of freedom. One might say that the number of dimensions is equal to the rank of the system matrix. Alternatively, one might choose to describe the spatial extent of an object, which would only include three dimensions. One might also choose to represent system space in terms of phase or velocity - so we could easily have six dimensions. These concepts are quite complicated, but in short summary for layman's purposes, there are as many dimensions as we feel like adding to describe the situation at hand. Most systems can be easily described with three spatial dimensions (and often time as an additional dimension). Nimur 04:53, 2 October 2007 (UTC)
I think the OP was referring only to the commonsense meaning of "Dimension" as in space and time dimensions. We can plainly see three dimensions in space, and only three. As Einstein explained, time can be thought of as a fourth, somewhat wierd dimension. This gives our world four dimensions that we can observe. No higher dimensions have ever been observed, ever. Now, if a person were to exist in an "alternate set of dimensions" he'd better damn well be in another universe in the greater multiverse, or one of the many-worlds, because if he isn't, there's pretty much nothing but speculation to explain it (er, those first two were also speculation, but they've been floating around for quite a while). Now, the only remotely close to accepted theory that allows alternate dimensions to exist in our own universe without our observing them is string theory and its variants, but absolutely nothing can occupy these unobservable dimensions (except for strings themselves, which can sort of wiggle around in them). Everything you've seen on Sci-Fi shows about a person entering an "alternate phase" or something like that, and suddenly no one can see him, is entirely bullshit. Someguy1221 05:01, 2 October 2007 (UTC)
Mathematicians and scientists often deal in higher dimensions and calculate things using them. They can be assumed to exist on a theoretical level, in the same way that the square roots of negative numbers are assumed to exist on a theoretical level. These assumptions are useful in such contexts. But whether any human mind can actually visualise or even comprehend what they mean, outside of such theoretical considerations, is a moot point. -- JackofOz 13:05, 2 October 2007 (UTC)
Why do you say that? Have you ever read Flatland? The 2 dimensional people would have had 2 dimensional physics and called time the 3rd, and told their ref desk OPs that it's nonsense to think that you can just poof out into the 3rd dimension.. which of course the sphere does in the story, baffling their scientists --frotht 18:05, 2 October 2007 (UTC)
Erm, what? Flatland is fiction, by the way. In modern physics, if a spatial dimension exists, there is utterly nothing to prevent any particle from moving through it. And so there would be some quite severe consequences. For example, chirality could not exist in three dimensional objects, which would conflict quite severely with many observations in chemistry. That's just the simplest to imagine example (in my opinion) of where the existence of a fourth spatial dimension would alter the laws of physics (er, chemistry, whatever). Now, string theory does allow wierdness like the existence of extra dimensions that are unobservable to only some observers. For example, every particle on in the universe could be bound to a "three dimensional surface" of a higher dimensional object. Thus, as if flatland were on the surface of a sphere, we would exist in a higher dimensional universe we could not observe. And this does not necessarily prohibit other objects, universes, whatever, from not being bound and limited by this three dimensional surface we are bound to. The problem is that string theory is presently unverifiable. So it is quite correct to say that there is no accepted theory in physics that would allow the existence of unobservable spatial dimensions. Someguy1221 20:08, 2 October 2007 (UTC)
You can define any point in space relative to some fixed coordinate system using three distances. This makes it a three-dimensional world. If you follow Einstein and wish to employ the mathematical convenience of talking about 'space-time' then you need to add one time measurement. This makes three or four dimensions depending on what you are trying to measure. Nimur's degrees of freedom argument is wrong because that's an argument about measuring things other than space itself. You can choose to measure space with things other than three distances - but no matter what, you always need just three numbers...so for example, you can measure every point in space using two angles and one distance ('spherical polar coordinates') or one angle and two distances ('cylindrical polar'). In space/time, you always need four numbers. The exact formulation doesn't matter - the dimensionality of space (or space/time) doesn't change depending on how you measure it.
The extra dimensions that string theory predicts are claimed to be 'very small'. Understanding what this means is tricky - we have do take it in small steps:
  • Suppose for a moment that we were observing some two-dimensional creatures - living on the surface of a flat piece of paper. In our present world view, the paper is flat and infinitely large. There is no 'up/down' dimension for them because they are 2D creatures - they only have left/right and forwards/backwards.
  • But suppose one of those two spatial dimension (let's pick the left/right dimension) was 'small' - just a 10 miles across say. The universe can't have 'edges' - it has to 'wrap around'. By this, I mean that moving in the left/right dimension for exactly 10 miles would take you all the way around that dimension and back to where you started - for a 2D creature this would be a bit strange - but for us 3D creatures watching them, it would be like they were living on the surface of an infinitely long cylinder of paper that's just one mile in diameter. They could move as far as they wanted along the length of the cylinder - but if they moved a long distance in the other direction, they'd go all around the cylinder and back to the start. Because their 2D light beams are stuck in the 2D surface, if they looked off to the left or right using a pair of decent binoculars, they'd be able to see themselves 10 miles away.
  • In a three dimensional universe like ours, if our up/down dimension was only 10 miles across then you'd be able to travel as far as you wanted left/right or forwards/backwards - but if you moved upwards by 10 miles (or downwards by the same amount), you'd be back where you started. Also, if you were out in space and looked up using a pair of binoculars, you'd be able to see your own feet, just 10 miles away. Looking left or right or forwards or backwards - and everything looks kinda normal.
  • Now - imagine that third dimension isn't 10 miles across - but just one millimeter across. We would be almost like 2D beings - almost all of our existance would be in two dimensions since nothing in the universe could be more than a millimeter in height - and moving up or down would have almost no effect on your life. That third dimension exists - but it's hardly any use at all. We would have to be almost perfectly flat creatures - it would be ALMOST a 2D world...but not quite.
  • Now imagine that instead of the up/down dimension being a millimeter across, it's much MUCH smaller than the diameter of an atom...in that case we'd have no way to know that there even was a third dimension - it would seem exactly like being in a flat, 2D world since any motion at all in the 3rd dimension would have no effect and no object could be as tall as even an atom...atoms themselves would have to be almost exactly 2D objects. We wouldn't even know that the up/down direction existed at all. It the third dimension were that small, we might as well be living in a 2D world for all that it would matter to us.
  • OK - so back to a normal 3D world. What would happen if there were a 4th dimension? Well - we can't see it, measure it...it's not in any way detectable...so we might jump to the conclusion that there isn't one. But if the 4th dimension existed but was very small (much less than the diameter of an atom) - then it could very well be there but we'd be totally unaware of it...unable to detect it. It would SEEM like we were living in a 3D world.
The string theorists claim that there are DOZENS of extra dimensions beyond the three we can normally experience - but all but the first three are so small that we can't tell that they are there - even with the most sophisticated equipment we have. I've heard these extra dimensions described as being 'rolled up'. They might very well be correct - but we have no way to know.
SteveBaker 13:16, 2 October 2007 (UTC)
Just to note: dimensions aren't like they appear in cartoons. They aren't alternative worlds somehow layered on top of ours where aliens live (though note that in the many-worlds interpretation of quantum mechanics—something entirely distinct from the idea of "dimensions" in science—there can in fact be multiple layered realities). They aren't ways to conduct psychic or supernatural phenomena. They are different ways in which geometry can be expressed in the world in which we live, basically. The dimension of time can be as mundane as noting that things change — the apple disintegrates on your table as it moves through the time dimension. Dimensions are not all that exciting, from a science fiction point of view.
Einstein's work, via Minkowskii's interpretations of it, basically reduced discussions of time and space to questions of geometry, and emphasized that time has a geometrical, spatial component to it. This is why he is often credited with introducing the idea of time as a fourth dimension, though he was not really the first person to introduce such an idea and in fact most of our understanding of "Einstein's work" in this regard is through the filter of Minkowskii, who "geometricized" Einstein in really wonderful ways. --24.147.86.187 13:50, 2 October 2007 (UTC)
I'm not sure that I'd say that extra dimensions are not exciting in a science-fiction kind of way. If there are more than three spatial dimensions and they are 'small' (per string theory) then, indeed, they aren't much fun. But if there were a fourth dimension - but something about our minds/bodies/physics meant that we somehow couldn't percieve it - then indeed there would be sci-fi possibilities. An ability to move in that fourth dimension would allow you to do some pretty incredible tricks. Escaping from a locked (3-dimensional) room might be as simple as taking a step in the 'other' dimension, walking past the room then taking a step back again into our normal world. It would be like trying to imprison a 3D person in a 2D rectangle - they'd just step out of it using the 3rd dimension. You'd be able to tie knots that would be impossible to untie...all sorts of weird stuff. A lot of people worry about what the 4th dimension would look like - but that doesn't bother me at all - we can use computer graphics to simulate exactly how a 4D world would project onto 2D retinas just as we understand how a 3D world projects onto a 2D retina. The ikkier thing to contemplate is that some of the string theorists want more than one time dimension - and that's really hard to get one's head around. We can guess what 4D space would be like to 3D beings by analogy with how 3D space would seem to 2D beings. But we only percieve 1D time - and we can't use analogies to extrapolate out to 2D time...it's a real head-spinner. SteveBaker 15:19, 2 October 2007 (UTC)
There's a very clever little story along these lines by Heinlein, called ...and He Built a Crooked House. The opening half-page alone is worth the price of the anthology you get the story in. An LA architect builds a house in the shape of a tesseract, but cut open and unfolded into three dimensions, as you might cut a 3-d cube and unfold it into a 2-d shape. Then there's an earthquake....
The story is very carefully constructed to be geometrically accurate and it's an interesting exercise to verify that. A few details, like what happened to certain walls, are sloughed over, but after all it's just a story. --Trovatore 17:34, 2 October 2007 (UTC)
As I linked above, you might too enjoy Flatland. Many people (including myself) report it being much easier to visualize and work in additional spatial dimensions after reading flatland. I disagree with 24.147 and the other guy that extra dimensions aren't like cartoons- stevebaker's got the right idea from a common sense approach, which is what I'm inclined to believe since string theory isn't really demonstrated by anything in our real world -frotht 18:10, 2 October 2007 (UTC)
Yep - I agree, I'm quite doubtful that String Theory will ever be shown to be correct. It's a shame because it's very elegant - and correct things are usually elegant! But a theory that's unfalsifiable is not acceptable - so unless there is some kind of major new breakthrough, I think we have to put string theory back on the shelf and go back to looking for something else. SteveBaker 18:34, 2 October 2007 (UTC)
Despite all this talk of "rolling up" and string theory, I stand by my original assessment - there are exactly as many dimensions as we choose to model. I have worked physics problems which are not "wacky" (String Theory), but still imply high dimensionality - for example, a triple-pendulum can be described with six or 12 dimensions (perhaps each joint has a displacement, a momentum, and an acceleration; and maybe we want to throw in a nonlinear potential such as a magnetic attraction at each joint to an external magnet). Each one of these dimensions is a physical parameter where motion, displacement, energy, and other physical quantities can "go." We might start calling the dimensions (θ1, θ2, ...), (p1, p2...) and so forth. Dimensions can interact via the governing equations, derived from fundamental physical laws. We might take care to set up dimensions which are linearly independent and orthogonal, or we might not choose to do so. The system equations would be straightforward, and the dimensions would be quite complex.
I could just as well model the system in three dimensions of an absolute fixed frame, (X, Y, Z) and time (T). These dimensions are very straightforward, but the system equations would become much nastier, since the relationships would become very highly coupled. But, I could never reduce the complexity to fewer than the total number of variables in the system to begin with.
The same can be said of String Theory and any other "magic" theory which introduces a new variable. Decoupling complex interactions into "separate" dimensions is an operation on a mathematical model and does not change the system in any way. Simple transforms are heavily detailed in linear transform. More sophisticated decouplings are the crux of a lot of modern research topics. Nimur 17:34, 2 October 2007 (UTC)
There is a big difference between using multidimensional mathematics to solve a problem and saying that this many dimensions exist in space. It's not at all the same thing. I too have used as many as 14 dimensions to solve work-related problems in computer graphics...but the world still only has 3 dimensions.
Example: Computer graphics hardware really only draws triangles. If you want to draw a quadrilateral, it is usually split into two triangles. If you have two triangles that you think may originally have made up a quadrilateral - but you really wish (for various arcane reasons) that you could have split the quad along the OTHER diagonal, then you need to check that the two triangles lie in the same plane (if they don't then they didn't come from a quad and swapping the diagonal will do weird things to the graphics). This is a simple 3D problem as you might expect. However, if the triangles have (for example) smoothly varying colours that are linearly interpolated between their vertices - then swapping the diagonal can change the look of the final quad (imagine one triangle has three red vertices and the other has two red and one green - as is, the center of the line between the two triangles is red - but if you swap the diagonal, you get an orange colour in the middle - not at all the same thing). To check that it's safe to re-split it, you also need to check for "planarity in colour space" (Red/Green/Blue space) - so now you are doing a six-dimensional check in X/Y/Z/R/G/B space. But there are other parameters of a triangle in a graphics system such as texture coordinates, surface normal, transparency and so on - and to do a proper job, you need to know that ALL of them are 'planar'. I ended up with 14 per-vertex parameters - so I had to check for planarity in 14-dimensional space!
So yeah - it's easy to end up using math in higher dimensions as a convenient way of solving real-world problems - but that doesn't tell you anything about the number of dimensions of 'space'...which is still (seemingly) three. SteveBaker 18:31, 2 October 2007 (UTC)
Note that when I said extra dimensions weren't exciting, all I meant is "the current theories of extra dimensions are not that interesting when compared with the way that the idea of extra dimensions is invoked in popular fiction." You know, dimensional gateways, portals of alien worlds, etc. That's all. Sure, sure, Flatland, but that's not what most people have in mind when they talk about "dimensions". --65.112.10.56 20:41, 2 October 2007 (UTC)
I think we're largely in agreement, SteveBaker. Whether we are doing graphics or physics or string theory, adding new variables to the mathematics does not actually change the real system's dimensionality. It's only our model that changes. Nimur 16:01, 3 October 2007 (UTC)
Yeah - largely. I believe the string theorists claim that all of their extra dimensions are real, actual spatial dimensions - but 'curled up'. So small that we can never detect them. But they need the extra dimensions to give their strings the ability to vibrate in enough different modes to fulfill all of the things that are demanded of them in the theory. Super-strings are very tiny indeed - vastly smaller than an atom - so even the very tiny extra dimensions are large enough to let them vibrate in those directions as well as the usual three. SteveBaker 02:28, 4 October 2007 (UTC)

[edit] Reason for shift in apparent solar midday at winter solstice

The sun begins to set later about 10 days before winter solstice, and the sun continues to rise later until about 10 days after solstice. In effect, this shifts the apparent solar midday later around the time of the winter solstice. Can anyone explain to me, in layman's terms, why this happens? (I have read the article Equation of time and largely failed to understand it.) Thanks. Marco polo (talk) 02:42, 31 December 2007 (UTC)

What you have to understand is that the Sun's movement in the sky that you see every day is not only caused by the Earth's rotation. Most of it is, but a small fraction is caused by the Earth moving in its orbit around the Sun. Think of a diagram of the Earth in its orbit. In one day, the Earth has moved 1/365 of the way around its orbit, or a little less than 1°, right? But that means that, over course of a day, the Sun is now in a different direction, as seen from the Earth, than it was. It's moved by about 1°. So the Earth has to rotate through almost 361°, not 360°, to bring the Sun back to the same place in the sky. (The difference between the two amounts adds up to exactly 360° per year, corresponding to the Earth making one revolution around the Sun. The time to rotate 360° is called a sidereal day and there is one more of those in a year than the ordinary or "solar" day.)
Okay, now the tricky part is that the extra amount that I called "about 1°" is not the same every day. This is because when the Earth orbits around the Sun, it does not move in an exact circle (the distance to the Sun changes by about 3,000,000 miles from nearest to farthest) and it does not move at a constant speed. So on a certain date the Earth might have to rotate by only 361.1° (say) to bring the Sun to the same place in the sky. That means that instead of 24 hours from one solar midday to the next, it takes 24 x 361.1/361 hours, and the solar midday shifts later by 24/3610 hours or about 24 seconds. On another date at another time of year, the Earth only has to rotate 360.9° from one solar midday to the next, and midday shifts back the other way against the clock. I just used 0.1° and 24 seconds as an example; I don't know what the actual maximum of the daily shift is.
These midday shifts are going on all year (except for the times when the shift happens to be zero), and the cumulative shift can get to about 15 minutes either side of the "middle". But you only notice it near the solstice because it's when the length of the day is nearly constant that you see the sunrise and sunset shifting the same way.
--Anonymous, 05:50 UTC, December 31, 2007.
Thank you: I understood that! Marco polo (talk) 15:53, 31 December 2007 (UTC)
If you were to take a picture from the same place at 12:00 noon every day (ignoring Daylight Saving Time/Summer Time), the pattern of the sun's locations would be called an analemma. That article may help give a visual interpretation of what's happening. -- Coneslayer (talk) 16:55, 31 December 2007 (UTC)

[edit] Voice

What is it that distinguishes a male voice from a female voice? Why do they sound different? Black Carrot (talk) 19:58, 3 February 2008 (UTC)

Length of vocal cord is the short answer, see Human voice. SpinningSpark 20:26, 3 February 2008 (UTC)
You might also find Castrato interesting. SpinningSpark 20:32, 3 February 2008 (UTC)

I was looking for a longer answer. Black Carrot (talk) 02:14, 4 February 2008 (UTC)

Is this l-o-n-g enough? --hydnjo talk 08:39, 4 February 2008 (UTC)
I think Black Carrots question is a good one, which deserves a far better answer than it has received so far. If it were a mere question of vocal cord length, which basically translates to frequency, it only begs several new questions:
  • Why do children that have the same vocal cord length as women sound different from women, even if they speak in a grown-up way?
  • Why does a song played fast sound like the chipmunks?
  • Why is it usually easy to distinguish an Afro-American male from an American male of European descent, even when they use exactly the same words?
I'll try my best at answering, but this is far away from my areas of expertise, so if someone who actually knows something about this comes along, I shall gratefully stand corrected for any mistakes that I might have made. This is from the top of my head.
Anatomical reasons: The vocal cords in themselves produce a reedy sound, rich in overtones, something like a square or triangular wave (not sure which). The sounds produced are shaped by the resonances of the vocal tract. These resonances have fairly equal frequencies in women and men, but vary between the different vowels we produce because we change the shape of the resonant cavity when speaking. These resonant frequencies are called formants. The first three formants are the most important ones. What distinguishes one vowel sound from another is not the ratio of the fundamental frequency to the formants, but the ratio between the formants themselves. Therefore, when a woman speaks, the ratio between the fundamental and the first formant is quite different from the ratio between the fundamental and the first formant in a male voice. When you speed up a song, the ratio between the formants is preserved, but they have the wrong frequency. Therefore, you recognize the words, but it sounds unnatural. Children have smaller heads, and lack fully developed sinuses. I would expect that this results in their formants being located at a higher frequency, but since the ratio is preserved, the vowels are easy to distinguish. This may be one of the reasons for the wonderful timbre of a boy soprano, the elevated frequency of the first formant is well above the frequency of the fundamental, making it easy to distinguish the vowels. (WARNING: WP:OR). In contrast, adult female sopranos have a problem in that their highest notes have a frequency similar to the first formant, making it difficult to distinguish vowel sounds at high frequencies.
Cultural reasons: It is my impression that women chose different words, and also intonate slightly differently. This may vary from culture to culture. The stereotype gay parody in TV shows comes to mind. I would also suspect that cultural reasons explain the relative ease in distinguishing a male Afro-American from a male American of European descent.
Disclaimer: I am not an expert in this field. The above may contain mistakes. If you know something about this, please correct the mistakes. --NorwegianBlue talk 13:14, 4 February 2008 (UTC)
My impression is that "stereotypical" gay and black speaking styles are nothing more or less than accents. --Sean 00:01, 5 February 2008 (UTC)
Agreed, and that was exactly my point - there may be male and female accents or manners of speach, which may be difficult to separate from the physical features of the male/female voice. --NorwegianBlue talk 00:44, 5 February 2008 (UTC)