Wikipedia:Reference desk/Archives/Science/2007 August 17

= August 17 =

Dangerous love
Is there any evidence of a link between sexual/romantic activity and immanent physical danger in humans? Judging from books like “For Whom the Bell Tolls” there is a positive link. Are there any real world examples of, for instance, a surge in marriages during The blitz, or a surge in sexual activity in people suffering from the early stages of terminal diseases? Last question, does Wikipedia have an article on this, and if not what could it be called? Thanks! --S.dedalus 00:35, 17 August 2007 (UTC)
 * Anthony Burgess touches on this idea repeatedly in many of his novels, but I don't know if there is a formal term or even if there has been any scholarly research. DuncanHill 01:53, 17 August 2007 (UTC)


 * "A British novelist, critic, composer. . . librettist, poet, pianist, playwright, screenwriter, journalist, essayist, travel writer, broadcaster, translator, linguist and educationalist." Wow, quite a guy! --S.dedalus 02:21, 17 August 2007 (UTC)


 * I am something of a fan, and if as I seem to recall (your username is something of a giveaway) you are a Joyce fan, you may well find him of interest. He wrote a book (Here Comes Everybody - a Guide to Joyce) which I find very helpful, and clearly was a great admirer of Joyce's use of language. I think he even included Joyce as a character in a few stories, which I'll try to look out for you. DuncanHill 02:32, 17 August 2007 (UTC)


 * Of course we have the Post-World War II baby boom - caused by a huge increase in sexual activity immediately following the end of WWII - but that was from a release of imminent danger rather than the onset of it. SteveBaker 15:00, 17 August 2007 (UTC)


 * More fiction, I'm afraid, but the one lesson I learned from a childhood of watching horror movies is that if teenagers have sex in the woods, they're going to be subject to a bit of the old ultraviolence. --Sean 15:06, 17 August 2007 (UTC)

Well, it makes sense to me, at least from a male genetic perspective, to try to scatter your genes as widely as possible before your death. I wouldn’t think the same logic would hold true for a female though. This seems to be one of these phenomena that is often depicted in fiction and take for granted to be true. --S.dedalus 21:36, 17 August 2007 (UTC)

The original question was about "immanent physical danger". I think we can all agree that sexual activity comports inherent physical danger, though the danger can be reduced with prudent measures. This is not the most usual usage of immanent, a term that tends to be seen largely in theological contexts, but it does seem to fit the dictionary definition, anyway. --Trovatore 21:55, 17 August 2007 (UTC)


 * That’s true. However, I was thinking more in terms of an evolutionary or psychological phenomenon, which would be unlikely to be influenced by such considerations. So no one knows of any research that has been done on this? --S.dedalus 22:55, 17 August 2007 (UTC)


 * I think you missed my (not all that) subtle point. --Trovatore 22:57, 17 August 2007 (UTC)
 * That’s always a possibility. My understanding was that you are pointing out the danger inherent in sex. However, this would create a circular logic problem if we assume the “Dangerous love” phenomenon is true. --S.dedalus 23:52, 17 August 2007 (UTC)
 * What I was pointing out was that "immanent" is a perfectly fine word, but I do not think it means what you think it means. --Trovatore 00:03, 18 August 2007 (UTC)


 * Oh, ha ha, imminent then if you prefer. You can probably guess that spelling is not my strong suit. --S.dedalus 00:42, 18 August 2007 (UTC)


 * There's also the rickety bridge experiment. --136.186.1.191 07:31, 22 August 2007 (UTC)

Shape of the eye
I was told that prolonged wearing of glasses would cause the eye to bulge due to the eye's adaptation to the peripherial lenses. However, there is this thing I don't get. Glasses are supposed to fit your degree of near/far-sightedness, and should not require your eyes to deform to achieve focus. What's more is that (well, this I base on a speculation) if the eyes deform due to their seeking for the focus, people who are near/far-sighted and who don't wear glasses should have more or less the same problem shouldn't they?


 * Uh... I think whoever told you that is probably wrong. Sometimes people's poor vision is caused by bulging eyes, but I'm pretty sure that glasses themselves don't make the eyes bulge. --24.147.86.187 01:45, 17 August 2007 (UTC)
 * Assuming you've got the right prescription..Wearing the wrong glasses might have that effect.87.102.14.51 08:24, 17 August 2007 (UTC)
 * Sounds like an urban myth to me. Ask for some references to reputable sources. --jjron 09:50, 17 August 2007 (UTC)
 * I totally agree it's an urban myth. There is very strong evidence that, with potential side effects, contact lenses can reshape the cornea via Orthokeratology but if it were true that spectacles that could reshape the eye wouldn't we be using them to correct vision rather than permanent specs, contact lenses and laser surgery? Maybe there's more truth to the notion that wearing glasses weakens the cornea's ability to regenerate, any evidence on that? --82.12.235.69 20:29, 17 August 2007 (UTC)

Chemistry and Botany
Dear Wikipedia, —Preceding unsigned comment added by 61.95.55.2 (talk • contribs)


 * To the questioner about Chemistry & Botany who started with such charming good manners - Your question seems to have got lost - please try posting it again, thank you. DuncanHill 02:12, 17 August 2007 (UTC)

The article on Urticaria regarding treatement and cause is incomplete

I'm a victim of Utricia myself and it is a rashes from hell...very very extremely torturous.

I developed many sympthom similar to the cold/hot and other type of Urticaria. However later the actual caseu of my chronic Urticaria is actually identify by a doctor. It is due to parasite in my stomach from eating raw fish. My suffering duration was 1 year but was treated within 1 day by taking any parasite killing pill.

Hence i really hope my piece of information will be publish to share to end suffering of many in same shoes


 * Thanks for your information, but:
 * This appears to be a personal piece of information, not a question - the Reference Desk is for asking questions.
 * WIKIPEDIA DOES NOT GIVE MEDICAL ADVICE.
 * If you have referenced information from reputable sources that would support this treatment you are able to add it to the appropriate article yourself and cite the references. As is, it would be termed anecdotal evidence and would also be considered original research. So, while I'm glad you have recovered from your illness, for these reasons this would not be appropriate to be added to the article. --jjron 09:44, 17 August 2007 (UTC)

Dear 61.95.55.2, can you find a published source that describes what you experienced? In this case you may be able to update the article with your summary of the paper or book. Graeme Bartlett 02:11, 18 August 2007 (UTC)

Stroboscopic Effect again
Sorry that I couldn't get the track of discussion that day..As you have mentioned clearly that the effect is called stroboscopic effect or temporal aliasing (as steve baker said), which is only due to some tv replays or movies and also couldbe due to reflection, but I belive it's not true so...I have noticed this effect simply when the ceiling fan(for eg) rotating at high speed or a DC servo motor(with wings) speeding up\down also creates this effect in our eyes...How is this?..This is a real vision and our eye captures lively the action.Though i didn't see it under sunlight, but sure inside my physics lab light.Also what's the big difference between the daytime and nighttime's role in this?..You can give a try by looking at your cooling or exhaust fan...Thanks


 * Your lab light is strobing, at night, certain street lights (such as those in tunnels) are also strobing. This produces the effect. You should be able to move yoru finger left to right (fairly quickly) infront of your light and see several distinct impressions of the finger on your vision as you move it. Each of those impressions is due to a single strobe. If you are in natural sunlight, you don't see that effect, it will look like more of a blur. This should confirm that your light is strobing.
 * Please sign your posts with four tildes (~) Capuchin 10:18, 17 August 2007 (UTC)


 * OK - let's try again with a simpler explanation. Let's suppose your ceiling fan has four blades - set 90 degrees apart - and let's suppose you live here in the USA where the mains power is 60Hz - the voltage provided by the wall socket goes up and down 60 times a second.  The brightness of your room lights depend on that voltage so they get brighter and dimmer 60 times a second.  (Someone is going to complain that this isn't exactly true - but it's true enough for this simple explanation so we're going to ignore them!)


 * In a sense, the room goes dark and you can't see a thing - then 1/60th second later, the lights come on and you can see - then 1/60th second later it goes dark again - 1/60th second later and they are back on again. This is far too fast for you to consciously notice it - but your eyes are still seeing it.


 * Now - as for the fan: If the fan has four blades which look exactly alike, then it looks no different when it's rotated zero degrees than it does when it's rotated 90 degrees, 180 degrees or 270 degrees. It has rotational symmetry.


 * Alright - so let's suppose the fan is spinning at exactly 15 revolutions per second. That means it's turning 15x360 degrees per second - 5400 degrees per second - which means that it turns 5400/60 degrees between the time the room lights go on, then off, then back on again.  So (by an amazing coincidence brought about by my choice of numbers!) that's 90 degrees of fan rotation between the individual 60Hz flashes of light.  But remember that the fan looks exactly the same when it's rotated by 90 degrees - so whenever the light is on, you always see the fan with the blades in the exact same position.  It looks to you like it's not moving at all!  This is the crux of the thing - when the fan blades rotate by exactly 90 degrees between light flashes - it looks like it's not moving at all because the only time you have enough light to see them by - they always look like they are pointing in the exact same direction.


 * Now - in sunlight, there is no 1/60th second flashing - the sun doesn't turn on and off - you get continuous light. So now, your eyes can see the blades of the fan all the time and nothing special happens - you just see a lot of blurry fan blades.  The 'strobe' effect doesn't happen because there is nothing flashing on and off to block your vision of the times when the fan has rotated 10 degrees or 11 degrees or 12 degrees or whatever.


 * When you film the same fan blades using a television camera (which just happens to take 60 pictures per second) - you get the exact same phenomena - the fan blades move exactly 90 degrees between each TV picture - and they look as if they have stopped moving.


 * Now - it's unlikely (well, maybe not...) that the fan is really going to rotate at exactly 15 revolutions per second. Suppose it only rotates at 14.9 revolutions per second?  Well now, instead of 5400 degrees per second (or 90 degrees per flash of the room lights), it only rotates 5364 degrees per second - so between each flash of light, it turned 5364/60 degrees - or about 89 degrees between each flash of light.  Well, now - what do you see in this situation?  You don't see the fan blades in exactly the same position each flash - the fan only rotated 89 degrees between flashes.  But if the fan looks exactly the same when rotated by 90 degrees - there are two possible explanations for what you are seeing - either the fan is spinning at 89 degrees per flash - OR it's spinning backwards at 1 degree per light flash.  Sadly, our stupid brains get it wrong and guess that it's spinning very slowly backwards at 1 degree per light flash or 60 degrees per second.  This is why, as the fan spins slowly faster and faster, it seems to go faster and faster until it's turning just a little bit less than 45 degrees per flash - but when it's spinning at 46 degrees per flash, your brain starts insisting that it's going backwards at 44 degrees instead.  So you get that weird situation, where the fan seems to speed up - then abruptly reverse direction, slow down and eventually stop - then start going forwards again.


 * The effect works with anything that has some kind of symmetry that's moving just right.


 * There are lots of other complications - but that's the simplest way I can come up with to explain it. If you don't understand it now - re-read what I just wrote! SteveBaker 13:28, 17 August 2007 (UTC)


 * Once again: there are 120 flashes per second, not 60. And the phases of light and darkness are shorter yet, since you have light and darkness in each 1/120 second period. So instead of 1/60 second, you need to say something like "1/240 second later it's dark, 1/240 second later it's light again". Adjust the other details accordingly; Steve describes the general idea correctly. --Anon, August 17, edited 22:00 (UTC).


 * And read the article :) Capuchin 13:40, 17 August 2007 (UTC)

Wow that was really an useful info explained in a clear way...Thanks you two...You really have a good knowledge on science...great


 * You might be interested to know how come I know so much about this. I work in computer graphics (I used to design flight simulators - now I write computer games) - and we have the same problem with wheels of cars and blades of helicopter rotors and such.  We call it 'temporal aliasing'.  When a car with wheels that have four spokes are driving along in a computer game, they are drawn (maybe) 60 times a second - so, once again, we see the peculiar reversing of direction and so on.  This happens when the wheel rotates at one half of the angle between the spokes or faster.  So for a wheel with only four spokes, the wheel can rotate up to 44.999 degrees every 1/60th second and it looks great - but the moment it hits 45 degrees per 1/60th second, we're screwed.  Unfortunately, real car wheels often have more than four spokes - maybe a LOT more than four.  If it has 8 spokes then it'll start to misbehave at 22.5 degrees per 1/60th second.  Well, that's about 4 revolutions per second - which for a typical 24" wheel happens at a mere 17mph!  Since this looks particularly weird in the 'perfect' world of computer graphics, it's necessary to blur the wheel into a more or less uniform circular 'smoosh' well before the car gets up to 17mph!  Anyway - to make wheels and helicopter rotors and other things look good, it's essential to understand the horrible details of temporal aliasing.  SteveBaker 03:47, 19 August 2007 (UTC)

Vertical polarization
I do know that I must've looked googling for this doubts but I don't know how to pick this idea very keenly there..So I'm posting here friends...Can anybody just tell me what do they mean by "vertical Polarization" in satellite communication?..I have seen this in the TV screen of the receiver displaying satellite number and downlink freq and so along with this...Thanks in advance
 * Antenna_(radio) may be the thing to read - (I can't say I understood it myself so please do not blaim me if info is wrong)87.102.14.51 10:56, 17 August 2007 (UTC)


 * Essentially, you can think of radio waves as vibrating "in just one plane". That plane can exist at any angle, but the cool part is that if you have one radio wave vibrating in one plane (that's oriented, say, vertically, so vertically polarized), and another radio wave that's vibrating in a plane that's rotated 90 degrees (in other words, is at a right angle to the other plane, so say, oriented horizontally, so horizontally polarized), a radio antenna can sort these two signals out. The angle of the signal (and the vibration plane) is referred to as the signal's polarization. So any given frequency can be used to carry two different signals: one polarized vertically and one polarized horizontally. So your satellite company only needs half as many channels as they might otherwise need and they need to tell you that you want to receive, say, the vertically-polarized signal that's on channel 16 (as compared to the horizontally-polarized signal that's also on channel 16).


 * This technique is commonly used for microwave transmissions but it's not universal. For example, FM broadcast radio stations commonly broadcast with circular polarization or elliptical polarization; these are ways to send a signal that has both sorts of polarization simultaneously. This lets their signal be received both by dipole antennas such as are commonly used at home and by whip antennas as are commonly used by cars and portable radios.


 * Atlant 12:35, 17 August 2007 (UTC)


 * Simpler (but longer) explanation: Radio waves (and also light, microwaves, etc) can vibrate in different directions - up-and-down, side-to-side, diagonally, or all directions at once - this is called the 'polarisation' of the wave.  If you have a radio antenna that's set up to receive up-and-down vibrations ('vertical polarisation') - it won't pick up side-to-side vibrations ('horizontal polarisation') - and vice versa.  This is a rather convenient thing for satellites because it allows them to send more than one channel out on the same frequency by sending one out with vertical polarisation and a different channel with horizontal polarization.  So-called 'circular polarisation' is what you get when the signal vibrates in every possible direction at once - and these signals can be picked up by antennas set up for horizontal polarisation and those set up for vertical polarisation.  You can learn more about how this stuff works by playing with the polarisation of light using polaroid sunglasses.  Natural sunlight has circular polarisation - but when the light bounces off of a horizontal surface, the reflected light comes out with only horizontal polarisation.  Polaroid sunglasses are set up to only allow vertically polarised light to come through - so they block horizontally polarised glare - whilst allowing ordinary circularly polarised sunlight to pass through.  If you take two pairs of sunglasses and rotate the lens of one pair at right angles to the other, you notice that the two lenses block almost all of the light.  That's because the first lens only allowed vertically polarised light through - and the second only horizontal - so none of the light that made it through the first lens could pass through through the second one (well, more or less - these lenses aren't 100% perfect).   Similarly, if you wear a pair of polaroids and look at the reflection of sunlight from (say) a shiney car - you can change the brightness of the reflection by tipping your head to one side so that the glasses now allow horizontal polarised light through and block the vertically polarised light instead. SteveBaker 12:57, 17 August 2007 (UTC)
 * It's true that sunlight "vibrates" in "all directions at once", but it is not circularly polarized, which visits the directions in a predictable sequence, but rather unpolarized, which visits them randomly. (That said, what you say about polarized sunglasses is true.)  For a narrow (in terms of solid angle) pencil beam of light, I believe that sunlight is spatially coherent, but that's not the same thing either.  --Tardis 16:35, 17 August 2007 (UTC)


 * Any given geosynchronous satellite has several radio transmitters (transponders, actually) and several antennas. At any particular frequency on any particular antenna, the satellite can transmit on two polarizatons simultaneously. Most Ku-band transponders use linear polarizatoin (H and V) (Some C-band transponders use circular polarization. Circular is harder to understand but easier in some ways to implement.)  One interesting thing aboutlinear polarization: "H" and "L" are relative to the earth's axis. This means that an antenna on the equator looking at a satellite on its horizon will be "turned on its side" relative to an identical antenna that is due north of a satellite on its horizon.(this would be sited above the arctic circle.) A satellite in the middle latitudes (e.g., in Kansas) and looking at a satellite that is not due south must be tilted somewhere in bewteen. -Arch dude 13:47, 17 August 2007 (UTC)

Adherence
I was looking for some information about the non-stick frying pans and why the geckos cannot stick to teflon, but I did't find a general article about the adherence (physics), nor about the sucking pads. How does it work? Can some body give me an explanation? Thanks in advance. --Micru 11:52, 17 August 2007 (UTC)


 * The general topic article you're looking for is called adhesion, rather than adherence&mdash;but it doesn't specifically address the gecko pads. Here is an interesting article with lots of detail and pictures (warning: PDF).  This page has a shorter, press-release treatment of the mechanism.  For a detailed scientific study, see this PNAS article (free) or this Nature paper (subscription required).  Some of this information is in our articles on the gecko and on setae&mdash;the tiny hairs that let them stick to surfaces. TenOfAllTrades(talk) 14:44, 17 August 2007 (UTC)


 * Thank you for the information, it was very clarifying and interesting! I have created a disambiguation page for adherence, before it was a bit misleading. --Micru 21:15, 17 August 2007 (UTC)

clean pharmacy
how a clean pharmacy operates? —Preceding unsigned comment added by 67.188.197.242 (talk • contribs) 08:04, 17 August 2007


 * Is that even a question? Is a "clean" pharmacy something other than a well-maintained pharmacy? --  JSBillings  13:49, 17 August 2007 (UTC)


 * Cleanly, perhaps? 147.197.230.174 13:53, 17 August 2007 (UTC)


 * Maybe one that only sells legal drugs, or sells drugs only in entirely legal ways (using 'clean' in the same sense as, say, with 'clean athletes' being ones not using drugs or other banned substances)? Surely though most pharmacies would be clean in that sense? --jjron 15:14, 17 August 2007 (UTC)

Hmm, this has me wondering if there are special facilities for packaging meds for people without functioning immune systems. In such a case, it would be critical to avoid any bacterial, viral, or other contamination to the meds. In normal cases, they try to keep contamination to a minimum, but it isn't likely to kill anyone if a bacterium gets in now and then. StuRat 20:38, 18 August 2007 (UTC)

Quarks in the Universe
Has anybody calculated the estimted number of Quarks in the universe?

Would this be the largest number known to Humankind?

—Preceding unsigned comment added by 165.123.243.168 (talk • contribs) 12:48, 17 August 2007


 * In answer to the second question, no, not even close. Not even close to being close.  See our article on large numbers. —Steve Summit (talk) 12:59, 17 August 2007 (UTC)


 * It might be the largest number you could get by counting physical things - but we humans have no problem whatever imagining vastly larger numbers than the number of quarks. For example, Shannons number - which is 10120 - is said to be the number of possible games of chess. That is VASTLY bigger than the number of quarks.  (Observable_universe says that there are 1080 atoms in the observable universe - most of those atoms are hydrogen and helium - so we're probably looking at an average of no more than 10 protons, neutrons and electrons per atom - which are each made up of three quarks - so even being very generous, 1082 is the most quarks we can expect to find.  The number of possible games of chess is therefore 1038 times more than the number of quarks in the observable universe! Other sources say that there are about a googol (10100) fundamental particles in the universe - but even so - that's 100,000,000,000,000,000,000 times less than the number of possible games of chess.  But even Shannons number isn't really big - there are much more complicated games than chess!  The game of 'Go' has about 10360 possible games - so if every quark in the universe had another universe inside it and every quark in THOSE universes had another universe inside them and every quark in side THOSE ungodly number of universes had a Go board inside them - there wouldn't be enough Go boards to play every possible game.  That's a BIG number! SteveBaker 13:58, 17 August 2007 (UTC)
 * Although it doesn't affect the order-of-magnitude calculation, electrons aren't made of quarks.147.197.230.174 14:34, 17 August 2007 (UTC)
 * Oops! Sorry! I got carried away with the 'fundamental particles' thing.  My bad! SteveBaker 14:54, 17 August 2007 (UTC)
 * Depending on how you choose to define countable 'things', you could count the number of photons in the Universe. According to this site, photons (mostly the cosmic microwave background) outnumber other particles by about two billion to one.  They make the number of quarks look just pathetic. :D  If you want to stick to things with actual mass, the cosmic neutrino background contains roughly 200 particles per cubic centimeter; that works out to about an order of magnitude less than the number of microwave photons. TenOfAllTrades(talk) 14:26, 17 August 2007 (UTC)
 * It's still not enough to beat the number of games of chess - nor to come even close to the number of games of Go...and as combinatorial calculations go, those are tiny problems. The number of possible pictures you can display on a computer screen (something like 231457280!)- or the number of possible Wikipedia articles you could write using only grammatically correct English - those just dwarf the number of possible games of Go.   Once you get into combinatorial calculations, the numbers can get just insanely vast.  SteveBaker 14:54, 17 August 2007 (UTC)

SteveBaker wrote: “(something like 231457280!)” Hmmm… Do you mean: Wow! - 231457280   -  that’s a large number! or do you mean: 231457280 x (231457280 - 1) x (231457280 - 2 x (231457280 - 3) x ... ? Myles325a 23:58, 21 August 2007 (UTC)
 * It's the "Wow!" thing - sorry. (I hate that they chose '!' for factorial - anything with a factorial in it is almost always an amazingly large number - so you want to stick an exclamation after it to express surprise - and then it gets confused with the mathematical function.) SteveBaker 05:48, 22 August 2007 (UTC)


 * Indeed. And if the number of Wikipedia articles you can write is still too small a number for you, just take 10number of Wikipedia articles you can write.  Or ten to the ten to that number.  Etc.  Or see Graham's number, which is "often described as the largest number that has ever been seriously used in a mathematical proof". --Steve Summit (talk) 15:14, 17 August 2007 (UTC)
 * If you want to see large numbers, look up Ackerman's numbers. Even Ackerman(4) is insanely larger that anything mentioned above, and Ackerman(5) is incomprehensibly larger than that, ...
 * Largest finite number, please. Plenty of proofs have used various notions of infinity. Algebraist 16:30, 17 August 2007 (UTC)
 * We've all been talking about finite numbers. All of the numbers mentioned so far are huge - but definitely finite. SteveBaker 17:26, 17 August 2007 (UTC)
 * Hi. One thing: the "observable universe" in not the whole universe! Not even close. Space can travel faster than light, but matter can't. The matter beyond the "horizon" formed as space expanded; the energy from expansion collapsed and formed matter as soon as the boundary got past it. If the observable universe counted as the universe, we, or the sun, or the milky way, would be at the centre of this universe. It could be, for example, that 10120 was the number of grams in the universe. Thanks. ~ A H  1 (TCU) 22:27, 17 August 2007 (UTC)
 * Yes - of course. But by definition, we can't observe anything outside of the observable universe - so if the question relates to the entire universe then we have no answer. SteveBaker 00:35, 18 August 2007 (UTC)

Well, let’s hazard a ball-park figure. Suppose we use the Planck Constant as the unit to define our smallest times and lengths. The Planck Unit is so small you could fit more of them into an atom than you could atoms in the observable universe. The smallest time is that of a light crossing from one side to the other of a Planck Unit. Now, the largest thing we got is the diameter of the observable universe, which, let us say, is 15 billion light years across (probably less, but to be on the safe side).

Now let’s employ SteveBaker’s astonishing figure for how many possible piccies you could see on a computer screen (231457280) and extrapolate from there. Instead of a computer screen we have a screen with the diameter the 15 billion light years across. And our pixels are a single Planck unit in size. Our universe is three dimensional, not flat, so we must imagine rotating our 2 dimensional screen universe around an axis, one Planck Unit at a time. So now we have one flat screen universe multiplied by the number of Planck units it would take to stretch 14 billion light years. This is the 3 dimensional screen universe upgrade from the flat computer screen Steve Baker uses for his calculations. I don’t know how many colours Steve has figured for each computer pixel, probably millions. In the case of how many different configurations a Plank unit can take on, this is (another) area where I don’t really have much of an idea. But recently, in articles in the Scientific American to do with speculations on the nature of quantised theory of gravity, it was suggest that the Plank Unit can take on several geometrical orientations, so let’s give them 12 possible “shapes”.

Now, we can calculate the number of possible universes (as a still “picture”) as the number of different ways you could combine the digits of a number that is calculated as follows: A: Number of Planck Units in Sphere 14 billion light years in diameter X 12.

That is for a “still picture”. Of course, with Steve’s flat computer screen example, you could have a series of still pictures at, say, 100 a second, so it is relatively easy to calculate the number of such pictures you could display in an, say, an hour. (Films are shown at about 20 frames a second). Then you just have to calculate the number of possible combinations of those pictures, and you have a figure which tells you how many TV (computer screen) shows of one hour’s length can be made. About 99.9999(add about a million 9s) of these “shows” will just be colourful static with no forms at all. An unimaginably small fraction of them will be old episodes of Columbo, and some will show copies of William Shakespeare’s lost plays against a backdrop of dinosaurs and naked women. Similarly with our 3 dimensional big universe screen, we can turn the still picture into a moving one. Firstly, let’s figure that the universe is about 15 billion years old (to be on the safe side). The Plank unit of smallest time is, as noted above, the time it takes light to cross a Plank Unit of space. How many of these Plank “seconds” are there in 15 billion years. Well, take that number and multiply it by Number A, “Number of Planck Units in Sphere 14 billion in diameter X 12).

Now take this new number and calculate how many different ways you can recombine it so that every possible permutation is covered. You will then have a complete index of all imaginable universes. Not just all physically possible ones, but all logically possible ones. There will we one that is made entirely of hamburgers, and one that is just like ours except right up to this point, whereupon it all turns into chicken fat. And how large is that number. Well, it’s bigger than 42. The strange thing is a number like that could still be written in conventional notation on a small piece of paper. You can easily invent much larger numbers, but they do not refer to anything outside themselves. The number I have just described includes everything that could possibly happen plus everything that could imaginably happen in the universe. I would argue that you cannot have a number with a real referent that is larger than this. But I will leave it to someone else to express it as a whole number with an exponent.

Btw, wanna quick way you can generate numbers much larger than this? Here’s one. The operation # is defined as follows. 2# = 2 to the power of 2, 3# = 3 to the power of 3 to the power of 3, and so on. That is, 3 is raised so that there are 3 levels overall looking at the exponents. Thus 10# is 10 to the power of 10, to the power of 10, in an ascending series of exponents, until you get 10 layers. This number (10#) is far larger than the number I have just described. Now let us say G = googolplex. Look at the number G#. With 2 short definitions of G and #, you have created a number that is far larger than anything you could ever imagine. Myles325a 05:23, 23 August 2007 (UTC)

Where do all the animals go that die???
Where do all the animals go that die??? This question has been bothering me...why dont we see a bird just drop out of the sky from old age? Why dont we see squirrels all over the place that die from natural causes (road kill is easy to find). There are many more animals that have died than that are living, yet we dont find them anywhere. Where are they buried??

Anyone with insight, please fill me in. Much apprecaited...


 * Non-human animals don't bury their dead, but see decomposition for why we're still not up to our ears in corpses. As for birds dropping from the sky, it happens all the time when they've been shot.  Birds dying of natural causes are presumably holed up somewhere rather than flying, just as people dying of natural causes are generally in bed rather than running down the road.  --Sean 15:12, 17 August 2007 (UTC)
 * "birds always find a quiet place to hide" - Elton John SGGH speak! 15:19, 17 August 2007 (UTC)


 * Not all non-human animals don't bury their dead elephants bury their dead.--Fang 23 23:08, 23 August 2007 (UTC)


 * Scavengers are also a very important cause for the cleanup of dead animals (yes, I know it is part of the decomposition process). Re the old age/natural causes issue, you'll also find that not a lot of animals actually die of natural causes. Sick, injured or old animals tend to be the ones easily picked off by predators, so more often than not are effectively cleaned up before they get the chance to die of 'natural causes'. --jjron 15:24, 17 August 2007 (UTC)
 * Isn't being eaten by a predator just as much a natural cause as dying from a disease? Eran of Arcadia 19:05, 17 August 2007 (UTC)
 * If you like, but it's a different sense of "natural". When we say "die of natural causes" we usually mean old age or illness. --Anon, August 17, 22:03 (UTC).
 * Yes it is a natural cause, but in the context of this question if you die of old age as a natural cause you'll leave a carcase lying around, if you are done in by a predator, then no carcase - it gets consumed effectively immediately. --jjron 04:21, 19 August 2007 (UTC)
 * There is a colony of turkey vultures that roosts in a power transmission line tower near me. There are probably 200 birds there, each bird wieghs about 3 pounds, they must consume lots of carrion. I can imagine that as soon as an animal dies there is a race between all the bacteria, insects, and scavengers to consume the energy in the corpse.  We are repulsed by corpses but in the natural world they are an easy source of energy that other organisms can exploit. -- Diletante 15:56, 17 August 2007 (UTC)


 * Round here, the corvids and gulls take care of the dead (I often see them pecking at roadkill, etc.). I noticed that there was a (pretty much whole, aside from being partially flattened) dead cat in the road one night last year. When I got up the next morning, the crows and magpies were pecking at what was left of it - which wasn't that much. The black-backed gulls will happily swallow dead birds (up to about the size of a starling) whole. I don't know what happens to the dead gulls - I've heard the 'gulls fly out to sea to die' and 'gulls will ferociously devour their own dead as soon as they keel over' stories but I have no idea if they're true or not. I can only recall ever seeing one gull corpse. --Kurt Shaped Box 17:39, 17 August 2007 (UTC)


 * Hi. The thing is, animals rarely ever die by your definition of "natural causes". I estimate that, by your definition, 10% of animals die of natural causes. Most are eaten by predators, few survive past their first year. Some are struck by lightning, killed by hunters, die from starvation, poisoned by human-made chemicals, killed in battle, struck by a car, trapped by an earthquake, trapped in a hurricane, etc. More die from disease than of old age. In fact, the same is true for humans. The bones of vertabrate animals sometimes embed themselves in the rock and get eroded or piled upon. The amount of organic matter on Earth dosen't change much throuout time. Thanks. ~ A H  1 (TCU) 22:39, 17 August 2007 (UTC)


 * One other factor to be considered is that small animals are "disposed of" much more quickly than large ones (like humans). While a human body lying in the woods might take a year to become a skeleton and several years for the skeleton to break down to unrecognizable pieces, a squirrel might become a skeleton and pelt in a month and an unrecognizable patch of fur under the dead leaves in just a bit longer.  So, you aren't as likely to find that dead squirrel as the person. StuRat 20:33, 18 August 2007 (UTC)

Well, I've actually seen one. I was walking out of my house one day when suddenly BAM! this bird came from the heavens to land a few feet (I can only guess...10 feet?) away from me. It struggled for about 2 seconds and suddenly...you get it. I didn't know then, and went near it. It had keeled over but believe it or not, I could not make myself believe that a bird just...died in front of me. A few hours later, it was in a drain when I came back. By the way, it was a black pigeon. -- Zachary crimsonwolf  12:54, 19 August 2007 (UTC)

What caused the collapse?
(Added back by SteveBaker 15:05, 17 August 2007 (UTC) following accidental deletion from "Can you fault my logical and scientific proof for personal immortality?").

This thread makes me wonder -- what is it that causes wavefunction collapse in quantum mechanics? My (quite limited) understanding of QM is that it is "observation" or "measurement". Is that right? If so, what counts as observation? I just stumbled upon the page Consciousness causes collapse, which describes the theory that conscious observation is what causes wavefunction collapse. That sounds rather.. anthropomorphic? And anyway, do we even know what consciousness is? Can wavefunction collapse be brought about by something unconscious? Something "dead"? And a related question -- these descriptions of multiple world theories and questions of whether "you" live or die and which world "you" are in make me want to know -- what is this "you"? A couple people have mentioned how the "you" of the OP's thought experiment could lose "shells", body parts, memories, sensory stuff, etc etc... how about consciousness? How many such "shells" can you lose before there is no you left? Pfly 03:38, 17 August 2007 (UTC)


 * Well, that's the unpleasant thing. The Copenhagen interpretation says that the 'observer' plays a role and that 'observing' the event collapses the wave function.  But that's really unsatisfying - it implies something special about human observers.  What happens if a computer records the result?  Why doesn't that collapse the wave function?  Why are humans somehow special?  Yuck!  That makes an almost religious statement - I hate it.  The many-worlds interpretation avoids that.  In the Schrodinger's cat thought experiment the cat is in a dual state - alive and dead - but the scientist observing the experiment "collapses the wave function" by opening the box.  That's a deeply unsatisfying thing.  Suppose we regard the entire laboratory (including the scientist and the cat/box experiment) as a 'box'.  The scientists wife, sitting at home is going to wait until he gets home and ask him whether the cute kitty at the lab is OK or not.  From her perspective, does the wavefunction of the cat collapse when her husband open the box - or when he comes home and tells her what happened?   I would argue that the situation of the scientist before she asks is no different than the cat before he opened the box.  Until she asks that question, the scientist's wave function is in a dual state of knowing that the cat is dead and knowing that it's alive.  When she asks the question, she too is in a dual state of grieving for the dead cat or not.  The scientist no longer has a 'privilaged position' of being able to collapse the wave function.  It's only collapsed as far as he is concerned.  From his wife's perspective, it's still in that dual state.  From her perspective, you could replace the scientist with a computer that opens the box, monitors the cat's life signs and emails her the news of the cat demise - and nothing is different.  Hence, there is no difference between a computer observer and a human observer.   This is (IMHO) a serious problem for the Copenhagen interpretation.  If the scientist collapses the wave function - why doesn't the computer?  Human brains have to be special in some way - and we know that they aren't.  In the many worlds version of this, there is no problem.  The atomic event goes off - there is a fork in the universe and now we have two universes - one in which the event happened and one in which it didn't.  In both versions, the wave function has not collapsed from the point of view of either the cat or the scientist.  A short time later, in one universe, the poison gas kills the cat and in the other it does not.  From the perspective of the cat the wave function collapsed - from the perspective of the scientist, it did not.  When the scientist opens the box, (at the same time in both universes) the wave function collapses - but nothing special happens to the cat - it was already alive or dead.  From the perspective of the scientists wife, the wave function of cat and scientist has not yet collapsed.  Everything works out OK. SteveBaker 15:30, 17 August 2007 (UTC)


 * I think the idea is that anything interacting with it counts as observing it. For example, when a photon hits an electron, both of their waveforms collapse. Different interpretations have different ideas of when it collapses. In one (I forgot the name) It's essentially always collapsed. In the many worlds interpretation which Steve mentioned, it never collapses. There is some evidence about where it collapses. For example, in the double-slit experiment is done with one photon at a time, it seems to go through two slits and cancel itself out in places. This is unlikely if the waveform has collapsed before entering the slits. — Daniel 16:31, 17 August 2007 (UTC)


 * My humble interpretation is that any observation is limited in scope. If the system in question is an electron spin, and the observer is some type of two-slit machine, then the wave function collapses when the machine measures the spin via a particle count at one or the other possible targets (e.g. up-spin electrons fly left, down-spin electrons fly right).  The machine then reads out on some kind of a display (in the most simple form, the presence or absence of a hit counted on the particle detector).  However, in the larger scope, a human has not yet checked the measurement, and the system status is still undetermined.  The new quantum mechanical system is the superposition of the electron's spin AND the machine's possible readout.  The coupled system depends on the actual spin of the electron and a deterministic relationship exists between the electron and the machine readout.  However, the actual value is unknown to the outside observer; in this case, it is irrelevant whethe the electron's wave function is present or not, because the machine's ambiguity masks it... or equivalently, the machine may be deterministically coupled to an undetermined electron system.  It doesn't matter where the uncertainty lies, because the total result of the measurement is still undetermined due to ambiguity somewhere along the line.  You can continue encapsulating the "system" as far as you like - the human scientist who reads the machine is quantum mechanically undetermined between a variety of possible reactions to the measurement.  The scientist doesn't collapse into a particular response, until "measured" or "observed" by someone else.
 * The final conclusion from my interpretation is that "collapsed" or "not collapsed" is entirely dependent on who/what is observing the system. From a particular frame of reference, there must be some level of ambiguity.  Maybe this could be formalized as a "conservation of uncertainty" principle.  Nimur 17:01, 17 August 2007 (UTC)


 * Daniel, arbitrary interactions definitely do not count as measurements for the purpose of wavefunction collapse. Atoms consist of protons and electrons in constant interaction via the photon field, but you can do the double-slit experiment with them. Light travels more slowly through air than through vacuum, implying an interaction with the air, but you can do the double-slit experiment with light in air. It's even been done with large molecules like buckyballs.
 * I seem to recall that Bohr associated collapse with "an irreversible act of amplification" -- that is, the collapse happens when so much of the world comes to depend on the state of the quantum system that there's no hope of erasing the information. This precludes any chance of observing a physical wavefunction collapse as something distinct from environmental decoherence.
 * I don't think it has ever, even in the early days, been a widespread view of physicists that the wavefunction collapse as taught in undergraduate QM (a discontinuous projection) was a physical phenomenon. Bohr certainly didn't believe it was. To him it described the updating of subjective knowledge. There's an objective component to the collapse, but that's not the collapse as such. -- BenRG 19:36, 18 August 2007 (UTC)

Time-lapse of bark growing
Does anyone know where I can find a time-lapse of bark growing? I think it would look interesting, but I can't find one. — Daniel 16:41, 17 August 2007 (UTC)


 * Bark takes many years to grow (Think "tree rings"!) - I think it's unlikely you'll find such a video. SteveBaker 17:36, 17 August 2007 (UTC)


 * Some types of trees, I'm thinking especially of many species of Eucalyptus, shed their bark every year. This is a significant contribution to making areas where these trees grow to being especially prone to bushfire. It would be possible to get a timelapse of this happening; I've got one in my backyard for example that has a clear period of say three months over summer where the bark changes colour, dries out, separates from the trunk and branches, and falls off to the ground. It would actually be pretty cool to do a timelapse of it, but I don't know if or where such a video exists. --jjron 04:29, 19 August 2007 (UTC)

Polarization filter for camera
Hidy ho. Could anyone tell me what degrees of rotation are best suited for what environments/effects? I have been using this filter for close to two months, but only lately found out how it is actually used. :) Thanks in advance! 81.93.102.185 17:51, 17 August 2007 (UTC)


 * You might find our article Photographic filter useful. The angle at which you set the polarizer depends on the effect that you're trying to achieve; there are some examples in the article. TenOfAllTrades(talk) 20:09, 17 August 2007 (UTC)

Photos of earless humans
I have read that Saddam Hussein often cut off the ears of his countrymen as punishment for one "crime" or another. I need a side view of such a person (for teaching auditory neuroanatomy) and have been unable to find one on the internet. Question: Are there hearing deficits in such a person, and what are they?–138.238.10.93 17:58, 17 August 2007 (UTC)superiorolive
 * http://news.bbc.co.uk/2/hi/programmes/newsnight/4603566.stm
 * http://www.cosmeticsurgery.com/articles/archive/an~179/#a1
 * http://www.earreconstruction.co.uk/ear-reconstruction.php
 * http://www.australasianbioethics.org/Newsletters/114-2004-03-26.html#iraqi etc87.102.5.166 20:49, 17 August 2007 (UTC)
 * As for the hearing deficits - I can only guess the answer is yes.87.102.5.166 21:07, 17 August 2007 (UTC)

Thank you for this. Experimental information from the brains of other species suggests that these mutilated pinnae will cause an inability or a least a serious deficit limited to the ability to locate a sound source in the sagittal plane, while leaving unimpaired the ability to locate sound sources in the horizontal and frontal planes. --User:138.238.10.93

Vision might also be negatively affected ... if the subject wore glasses. --Sean 18:21, 18 August 2007 (UTC)

The sizes of the Large and Small Magellanic Clouds
Ok I've asked this all over Wikipedia, in the Wikipedia talk:WikiProject Astronomical objects page, the Wikipedia talk:WikiProject Astronomy/Archive 1 page, and gotten no answer, so I'm asking here. Anyway, the Large Magellanic Cloud and Small Magellanic Cloud articles are in need of some attention. Specifically, nobody seems to know how big they are. There's been several contradictory and probably erroneous figures put up (some by me), ranging from 5,000 to 35,000 LYs (for the LMC). BTW the sizes up now are most likely wrong are misinforming people. Now, in going through a few Websites I've found various estimates for the LMC, this site says 39,000 LYs, this site  says "about 30,000 LYs", this page mentions the LMC being "about 7 kiloparsecs" which is about 23,000 LYs, this NASA page  says "Spanning about 15,000 light-years or so", etc. The Celestia Astronomy programme I have says the LMC is 32,000 LYs in Diameter. As for the SMC, well this site (listed above again) says it's "3 kpc" which is about 10,000 LYs, this page  also says 10,000 LYs, while Celestia says it's about 19,000 LYs big. This page (again listed above) ambiguously says it's "under 20,000 lightyears in diameter". So, as you can see it's all quite confusing, can anyone clear things up? Does anybody know the diameters of the Magellanic Clouds? Or at-least where to get the information? I need some definitive source stating their sizes, or even just a size range, say "20,000 to 40,000 Lys" or something like that. But I can't seem to even get that, isn't there some generally accepted size in academia? And if so, does anyone know it? Thanks. --Hibernian 15:46, 24 July 2007 (UTC)


 * Well, these objects don't have hard edges that you can measure precisely - galaxies are 'fuzzy'. Do you measure the distance from the center to the utterly outermost star? If so, then the number you come up with will depend on how sensitive your telescope is because the last few individual stars out at the edges may or may not be visible depending on their brightness.  So there isn't a "true" answer - in all likelyhood the density of stars in the galaxy as a function of distance from the center follows some kind of gaussian curve and as such may truly have no definite outer limit with one or two very loosely associated stars hundreds of lightyears away from the core.  In that case, you'd have to pick some kind of metric like "98% of the stars are within XX lightyears of the center".  Sadly, I can't give you a solid answer - but this does explain why the numbers you are seeing might be quite variable depending on who you read.  If I were you I'd pick a range and say "various sources give a diameter of between 15,000[1] and 30,000[2] lightyears" and link each number to the source where you got that number.  Incidentally - are all of those numbers diameters?  Is it possible that some people are talking about the radius? SteveBaker 19:20, 17 August 2007 (UTC)

Thanks for the response. Yes I realize that galaxies have somewhat fuzzy edges, and thus it's very difficult to say what their Exact size is, but that's not what I'm after, I just need to know the generally accepted size range. For instance, we can say that the Milky Way is approximately 100,000 LY across, and we know sizes for many other galaxies. Now obviously 100,000 LY is only a general estimate, it could easily be 95,000 LY or 105,000 LY, etc. But that doesn't stop us from talking about Galaxy sizes in general terms. There are dozens of articles that state galaxy sizes, I just want to do the same for these two, but I'm running into difficulty. So what I really need at this point is to be directed to some source that is generally accepted amongst Astronomers. Does anybody know any reliable astronomy site on the net that would have the info? (Or a book?) If I can't find that, then I guess I'll have to do the next best thing and just list what the sources I can find say. --Hibernian 23:20, 17 August 2007 (UTC)




 * You are saying that the margin for error in stating the size is perhaps +/-5%. Take a look at that photo of the Large Magellanic Cloud.  Try and draw a 'boundary' line around it!  How can you possibly say where the edges of it are?!  I could pick sizes over a range of 2:1 or more.  It's a barred spiral that's been distorted by tidal gravitation from our galaxy...which makes it pretty much an irregular 'blob'!  We aren't looking at a 5% margin of doubt - I'm not in the slightest bit surprised you can't nail down any kind of exact number! SteveBaker 01:52, 18 August 2007 (UTC)


 * I'm with SteveBaker on this one. Part of a serious study of astrophysics is the major paradigm shift away from precise quantities.  This is not to say that scientific certainty is entirely out the window, but as a whole, the disciplines of cosmology and astronomy make it abundantly evident that they are not nearly as numerically accurate as other sciences.  Even the age of the universe is known only to an accuracy of a few billion years, but despite furious debate on details, it's not really important to nail that number down exactly in order to have a fundamental understanding of cosmic evolution.  Instead, these fields make a conceptual shift towards pulling bits of hard scientific truth from a very limited set of available observations with very handwavey details.  Nimur 19:09, 19 August 2007 (UTC)

Sensu?
I am databasing plant pathology slides taken in the 50s and have come across one with rust on the stem which lists the species as "Cronartium coleosporioides sensu Peridermium harknessii [currently accepted taxonomic name = Endocronartium harknessii]." Both are now placed in the family Cronartiaceae, but Peridermium is listed as Incertae sedis. I am not sure what the sensu means in this sense. I have looked at the article for sensu, and it says is "used in taxonomy to specify which circumscription a given taxon is meant, where more than one circumscription has been defined." I couldn't make heads or tails of that statement. Is the slide depicting Cronartium coleosporioides or Peridermium harknessii (Endocronartium harknessii)? If this cannot be answered what would I need to look up in order to figure it out which one it is? 128.196.125.13 19:06, 17 August 2007 (UTC) (User:Sifaka unable to log in)
 * The statement will mean that the taxonomic name has had more than one definition, and that the text after the sensu should determine which one to use. In your case where you have two different species that are not overlapping, you are correct it does not make sense, and probably is a mistake.  Is it possible that the author could not determine which of the two species the slide was sampling? Graeme Bartlett 03:42, 18 August 2007 (UTC)

Rotation of drinking-vessel as a means of controlling flow
When drinking a yard of ale, one rotates the yard in order to control the flow of beer, but how does this actually work? What forces are involved? DuncanHill 19:48, 17 August 2007 (UTC)


 * The excellent book The Flying Circus of Physics covers this: a normal tip of the glass would result in uncontrollable glug-glugs of air going up the glass and splashing precious ale outside the drinker's mouth; the rotating action swirls the liquid against the walls of the glass, creating a column of air along the central axis of the container, which allows the yard to be held at the desired angle for convenient quaffing. --Sean 20:33, 17 August 2007 (UTC)


 * Thanks, as a follow-on, is there an optimum speed of rotation, or does this vary with size and shape of the yard, or the amount of remaining beer? DuncanHill 20:35, 17 August 2007 (UTC)


 * Yes - it's something that pretty much comes with practice. I used to know a champion yard drinker (his best time was around 8 seconds!) - he had to learn each new glass because no two are ever really alike. He used a quick twist of the wrist to get the 'swirl' started - he could drink it faster (by far) than I could empty it over a sink!  It's amazing to me that the world record is 5 seconds. SteveBaker 00:31, 18 August 2007 (UTC)

force applied by moving water
Is there any equation that someone could give me even if it is a rough approximation for the force a given obeject would have exerted upon it by moving water as a function of the waterspeed. Thanks! 209.112.207.90 22:40, 17 August 2007 (UTC)


 * Are you referring to drag? -- Kainaw (what?) 22:56, 17 August 2007 (UTC)


 * The formula for fluid resistance says that the drag is proportional to the square of the speed:
 * $$F_d = C_d \times 0.5 \times \rho \times A \times V^2$$
 * Where:
 * Fd = The drag force (in Newtons)
 * Cd = Coefficient of drag (0.35 for a car for example)
 * $$\rho$$ = Density of the fluid in kg m-3.
 * A = Cross-sectional area of object at 90 degrees to the flow in m2.
 * V = Speed of fluid in m/sec.
 * SteveBaker 00:25, 18 August 2007 (UTC)


 * According to Stokes' law, the force of friction is proportional to the velocity, not to its square. It seems that the drag formula quoted by Steve and the equation of Stokes are two different limiting cases of the Navier-Stokes equations. What's the difference? (My guess: the former holds for high and the latter for low Reynolds number, corresponding to turbulent and laminar flow. Anybody knows for sure?) Simon A. 08:05, 18 August 2007 (UTC)


 * So this is why I keep old text books lying around. Anyhow, according to Physics for Scientists and Engineers, drag force is proportional to velocity for slow moving and/or small objects, while it's proportional to the square for fast moving and/or large objects.  Large/small/fast/slow depend on what specific medium you're dealing with, although apparently "airplanes, sky divers, cars, and baseballs" are large and fast enough to experience the latter while moving through air.  This text book is fairly introductory, though, and doesn't actually explain why any of this is the case.  Someguy1221 10:27, 18 August 2007 (UTC)


 * Feynmann's physics textbooks (which are IMHO, the finest undergraduate texts available) go to some lengths to explain that all of the equations for friction and drag are useful approximations - so yeah - you'll always find cases when they don't work - or they don't work perfectly. This is why we build wind-tunnels!  The worst part is that the "Coefficient of Drag" is exceedingly hard to calculate - so you pretty much end up having to guess - which means that all of your calculations are going to be very approximate no matter what.  However, if you've gotta calculate some kind of an answer - or if you need a qualitative result - then this is the right formula. SteveBaker 14:47, 18 August 2007 (UTC)


 * Although it probably won't be much better than order-of magnitude, you could consider the rate of change of momentum of the water hitting the object, which is a nice example of a derivation from first principles. (not a very accurate one, though, as already mentioned, but much simpler than "real" fluid dynamics). 80.169.64.22 17:02, 18 August 2007 (UTC)