Wikipedia:Reference desk/Archives/Science/2012 October 29

= October 29 =

The Philippines and total plastic bag bans
Among Asian countries, does the Philippines have a relatively high number of cities/towns that totally ban plastic bans? I know that Bangladesh is the world's first jurisdiction to ban all plastic bags, and some countries such as China and Taiwan either ban thin plastic bags or tax their use. However, in the Philippines, one province, as well as several cities and towns, even major ones, have totally banned their use. Among Asian countries, is the Philippines a pioneer in this regard? While there are several other cities across Asia that have banned plastic bags, they appear to be few and far between, with each country only having maybe a handful of places with total bans. The Philippines, on the other hand, has several jurisdictions which ban all bags, even those that are not single-use or recyclable. Most bans around around the world only ban single-use or thin bags, recyclable or biodegradable bags are usually excluded. And many jurisdictions merely tax their use, rather than totally ban them, like Taiwan. So again, is the Philippines among the countries leading the way among Asian countries in total plastic bag bans, or is the Philippines only playing catch-up among Asian countries? Total bans don't seem to be that common in countries like Japan, Vietnam, Malaysia, Thailand or Indonesia, although bags are taxed in some places in the aforementioned countries, and China has a ban on thin bags but does not totally ban all plastic bags. Narutolovehinata5 tccsdnew 02:23, 29 October 2012 (UTC)
 * Click here. They (talk) 02:46, 29 October 2012 (UTC)

Where did the first life on Earth originate?
--168.7.239.26 (talk) 06:49, 29 October 2012 (UTC)


 * Pangaea.--Shantavira|feed me 08:29, 29 October 2012 (UTC)


 * The Pangea answer is just wrong. Pangea ony formed about 300 million years ago. Life has been around much longer than that. 209.131.76.183 (talk) 12:35, 29 October 2012 (UTC)


 * In shallow water - see Stromatolite. Roger (talk) 08:33, 29 October 2012 (UTC)


 * Or perhaps in deep water - see hydrothermal vent. And there are other theories, see abiogenesis. Nobody really knows for sure. 88.112.36.91 (talk) 09:53, 29 October 2012 (UTC)


 * Agreed - this is one of the great unanswered questions. Also note that when we look at early life, we may not agree on the definition!  For example, some corroding sheets of metal in water orcan have rotten patches that grow and even reproduce themselves, and crystallization may spread out once a single nucleation event starts the process, but are they alive?  The origins of life might be nothing more impressive than that. Wnt (talk) 17:20, 29 October 2012 (UTC)


 * The most useful way to make it a well-defined question is to identify the origin of life with the origin of cells, which are structures surrounded by a barrier that controls the exchange of chemicals between the interior and the exterior. Looie496 (talk) 17:29, 29 October 2012 (UTC)


 * Looie is correct, and see The Origins of Order: Self-Organization and Selection in Evolution by Stuart A. Kauffman. My personal suspicion is there must have been some cyclical influence driving the metabolism externally, which hints at a shallow origin subject to sunlight--but that's likely just to be my lack of imagination speaking. Those of us who are old enough remember when it was universally believed that the reason for the extinction of the dinosaurs would never be found, and an asteroid strike wasn't even at the level of a fringe theory. μηδείς (talk) 19:09, 29 October 2012 (UTC)


 * We basically understand how prebiotic molecules such as peptides can be generated from scratch. What we need to figure out is how those molecules can accumulate to a density at which cross-catalysis comes into play to a major degree.  Once we have that, the rest of the story should follow. Looie496 (talk) 21:54, 29 October 2012 (UTC)


 * I have an idiosyncratic notion that RNA life existed before cells, maintaining "protein" resources as heavily modified branched side-chains. (See the biosynthesis of histidine from PRPP; ribose can be converted to the backbone of an amino acid)  Such life would have had very weak differentiation between individuals. Wnt (talk) 03:10, 30 October 2012 (UTC)


 * Maybe elsewhere. Read about exogenesis in the panspermia article. They (talk) 07:05, 30 October 2012 (UTC)


 * I think the first life originated in water bodies. But how first life originated on earth, by some chemical reactions or by the means of reproduction. The latter seems to be wrong. Sunny Singh (DAV) (talk) 11:00, 30 October 2012 (UTC)


 * It has to have been in water - that's one of the few things that we do know. Also, I don't know why so many people are talking about their (self-described) "personal ideas" - it's a scientific question, and when you reply to somebody who's asked that question, your answer should involve the scientific data! Arc de Ciel (talk) 05:20, 31 October 2012 (UTC)

See here. Count Iblis (talk) 01:21, 31 October 2012 (UTC)

how to know the lifting/gripping power of rubberized magnet sheets?
I want to make a bit of wall art, and will need rubberized sheet magnets. They will be vertically oriented ("facing" the wall) and gripping a sheet of steel. I will cut them into squares and attach them to the bases of a variety of objects. While I can easily estimate the weight range for the objects I would like to "stick" to the wall, I am having no luck figuring out how much "lift/grip" a rubbering sheet magnet might have? I assume it is a function of area. I also assume it is a function of thickness since these sheets are readily available in 0.5mm and 1mm thickness, if not others as well. Ideally I'd like to have an accurate understanding of the lifting power before I make my purchase so as to better calculate the total area required... Thank you. The Masked Booby (talk) 09:33, 29 October 2012 (UTC)


 * I suspect that this will vary from one manufacturer to another, and how well they stick will depend not just on the sheets themselves but also on the surface to which they will be attached. (Magnetic attraction falls off with the cube of distance, so it takes a very thin coating on a surface to make magnets a lot less sticky.  Think about how few sheets of paper your average fridge magnet can hold up before losing their grip.)  As well, the carrying capacity will depend on how the weight is arranged&mdash; if you have three-dimensional objects cantilevered out from the wall, you're going to see a tendency for the added leverage to 'peel' the sheets loose.
 * Your best bet is probably to purchase/aquire/beg/borrow a sample sheet and conduct some tests with it before placing a large order. If you find that the sheets don't meet your needs, depending on what you're hoping to do you may find it more effective to glue tiny rare-earth magnets to the bases of your objects.  They're very sticky, and you can buy them by the dozens or hundreds from online retailers.  TenOfAllTrades(talk) 13:28, 29 October 2012 (UTC)


 * You have to worry not just about "pulling off", which is a simple calculation of magnetic-attraction (although requires knowing some specific values about the magnets and distance) as TenOfAllTrades mentions, but also sliding down, which is affected by friction and other geometric details. If I hang a bunch of papers on my fridge door, "the magnet still holds to the door", but the "magnet and papers it's holding" all slide down to the floor. DMacks (talk) 13:54, 29 October 2012 (UTC)


 * Yes, that's exactly what I was going to mention. If you have uneven magnetic attraction and/or coefficient of friction over the surface, you can also have the object unintentionally rotate, so it won't stay "upright".  Since rubberized magnets are to be used, this hopefully will increase the coefficient of friction well beyond what you would get with the magnet(s) directly sliding on the steel sheets.  However, the rubber layer should be thin, as it also increases the distance between the magnet(s) and steel.  And, if rotation is a problem, then you should put the stronger magnets near the top. StuRat (talk) 18:58, 29 October 2012 (UTC)

Would simulation lead to an optimal solution for Circle packing in a square?
Each square in the article looks exactly like as if the circles got there by gravity or squeezing, the same for the spheres in Sphere packing. If you'd simulate indefinite slippery and sturdy, circles or spheres, offsetting a tiny bit the ones that are exactly balancing on top of each other a little (or shake), and then start squeezing them till, for instance, the box can't get any smaller without breaking spheres, would it be possible to prove that the end result would have to be packed most efficient for simple containers like a box?

If the spheres are not all the same size, but you had for instance 100 big spheres en 1000 small spheres, shaking in reality tends to move the big ones up. Does that mean that this natural dividing the big and smaller ones does not lead to the best possible solution, where there is more "air" than an optimal solution would have? Or is this dividing due to friction which would not happen if there was none? Joepnl (talk) 18:37, 29 October 2012 (UTC)


 * Not a direct answer, but placing the largest object first and then adding the rest, in decreasing order of sizes, often produces the optimal solution. StuRat (talk) 19:03, 29 October 2012 (UTC)


 * Several years ago, I went to a physics colloquium on experimental and computational modeling of on the stability of heaps of granular materials. Fascinating topic.  (And yes, we have an article: Granular material - this topic is widely studied by material scientists, civil engineers, geologists, pure physicists, and experts from other disciplines).  Joepnl, it's not common for physicists to "prove" anything - that's sort of reserved for a more pure form of mathematics - but there's certainly a lot that can be known - through simulation, experiment, and pure analysis - on this topic.  Nimur (talk) 19:09, 29 October 2012 (UTC)


 * Squeezing or shaking the circles is a hill climbing algorithm. It reminds me of using soap bubbles to find Steiner trees. It's only guaranteed to find the global optimum solution if it's also the only local optimum, which it tends not to be in interesting problems. -- BenRG (talk) 20:49, 29 October 2012 (UTC)


 * Wouldn't that depend on how hard you shake it ? If shaken enough so all the circles go back out of the square, you get another shot at global optimization with each shake.  Of course, you'd then need to evaluate each for the best packing, as it would otherwise be destroyed with the next shake. StuRat (talk) 21:01, 29 October 2012 (UTC)
 * StuRat, you've described something that sounds similar to simulated annealing; the intermediate stages of an annealing algorithm can use a hill-climbing algorithm to calculate the next iteration, adding the critically different step of "shaking up" at various points during the climb. Proper implementations will parameterize "how much to shake" to escape from local minima in a way that is problem-dependent.  Formal descriptions of these algorithms use a little more precise mathematical language to capture the nuance, but you've described the gist of it.  Nimur (talk) 21:53, 29 October 2012 (UTC)


 * There seems to be a series of numbers which have non-unique solutions for sphere packing in a square (not counting flipping/rotation): 7, 14, 19 it looks like from the pictures. Is there any rhyme or reason to this series?  What is its mathematical significance? Wnt (talk) 23:47, 29 October 2012 (UTC)
 * There is a list here, with column "loose". It differs a bit though (7,11,13,14,17,20,...) but it will take some time to download the actual pictures to see what's different. Joepnl (talk) 00:41, 30 October 2012 (UTC)
 * Hmmmm, I ran this by the spreadsheet - the exact solutions start off common for the first 20, then get rare, then become increasingly common and predominate after 1000. Since the series isn't necessarily the best series, I don't know if this is artefactual - I think after 1200 or so it is.  Before then, the values form a sort of irregular scalloped curve on a log graph. Wnt (talk) 02:41, 30 October 2012 (UTC)
 * May be you could use your analysis to find the non-optimal solutions? Joepnl (talk) 23:40, 30 October 2012 (UTC)
 * @Nimur, it's ok a if a mathematician borrows some ideas from physics to create a solid proof I think. I can imagine something like "we start with situation X (circle here, circle there), and now I'll prove that this is not optimal yet as long as a circle can still move according to these formulas (which happen to be gravity, etc) leading to X' -this might be the easy part-, and also that if the circles cannot move any further we must have reached the optimum (this might be a bit trickier :))".
 * @BenRG, I was thinking of this problem to be just one hill to climb without a local maximum. Not that I have much real life experience with this, but if I'd throw (slippery!) balls in a container it feels that the balls can't get into a situation where it needs a big shake for an optimal solution, just a small (almost 0) one for the corner case of balls on the exact top of each other. For instance, I can't find an example of circles that would stop moving in a sub-optimal solution and, vice versa, in all examples in Circle packing in a square I can't see a circle that would move if subjected to gravity (apart from 7, 14 and 19 mentioned by Wnt, where at least one circle has some space to move around without changing the size of the box). Joepnl (talk) 00:31, 30 October 2012 (UTC)
 * Mmm I guess I'm totally wrong. The example with 4 circles looks pretty hard to reach after adding the 3rd circle using just gravity. This would need a big shake. (Or possibly the walls getting wider instead of a binary search starting with a full square each time)Joepnl (talk) 00:52, 30 October 2012 (UTC)
 * Even if the problem has no local maxima the tought part is proving it mathematically. Simulation will probably give very good results, but you can't call it the best unless you can mathematically reason that it is impossible to do better. 209.131.76.183 (talk) 12:29, 30 October 2012 (UTC)

What does work is to use Monte Carlo simulations of the 2 dimensional hard sphere gas. You can extract information about the equation of state from that and then you can combine this with the Mayer expansion. The Mayer expansion yields the equation of state as a series expansion in powers of the density, so it's only valid for low densities, but you can resum such an expansion. Here you make assumptions about the asymptotic behavior of the high order expansion coefficients, which you can try to extract from the Monte Carlo simulation. You can then use that resummed equation of state to find the critical density at which the pressure goes to infinity. Count Iblis (talk) 17:01, 30 October 2012 (UTC)
 * Isn't Monte Carlo almost by definition a method which doesn't guarantee an optimal solution? Joepnl (talk) 23:40, 30 October 2012 (UTC)
 * Yes, that's why you need to use this method in an indirect way. So, there exists some maximum density rho_m corresponding to optimal packing; the pressure as a function of the density will then have a singularity at rho = rho_m. By studing the system at low densities, far away from rho_m, you can still get information about rho_m. Count Iblis (talk) 00:54, 31 October 2012 (UTC)