Wikipedia:Reference desk/Archives/Science/2014 November 8

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November 8

Illacme plenipes

Is it the only animal (as of now) having the highest number of legs? — Preceding unsigned comment added by IEditEncyclopedia (talk • contribs) 05:18, 8 November 2014 (UTC)

As it says in the linked article, it has "more legs than any other creature on Earth".--Shantavira|^{feed me} 08:13, 8 November 2014 (UTC)

It's a little bit philosophical: what is a "leg"? Insect legs and human legs aren't really "the same thing", in that the insect leg is attached to a segment; we can see human somites and our legs are of course much bigger structures than that. Really, human legs are derived from fins and fins are special structures that arose in vertebrate evolution, much like tube feet are structures specific to echinoderms. All these structures are marked by Distal-less, but then again, so are jaws (which you might say are modified legs, though) and many other things. See [1] But if we allow tube feet as a sort of "leg" - which certainly would be controversial - then some echinoderms, with tube feet numbers ranging from hundreds to thousands, ought to beat the millipedes handily, or should I say footily. Wnt (talk) 09:29, 8 November 2014 (UTC)

"USE NO OIL" - why?

On the Oxygen's tank is written: "USE NO OIL", and my questions are: 1. why? 2. what can happen? 3. what is the meaning of "use no oil" (it's wide). Is it forbidden to me to touch in the Oxygen's tank while my hand has oil? I would like to get specific examples for no uses or cases that happend. THANKS 5.28.179.11 (talk) 09:27, 8 November 2014 (UTC)

Apparently spontaneous combustion. See [2], a 1919 book referring to that guideline being already well established. Many modern guides have identical advice, but I didn't see the explanation on this example: [3] It is well known to hapless astronauts and emphysema patients alike that increasing the amount of oxygen increases the risk of fire and general mayhem. I remember reading that the internet celebrity who lit his charcoal grill with liquid oxygen had to make sure not to let it soak into the briquettes, as they could become high explosive. That said... because this advice is so old, I wonder if there are known safe lubricants. (I looked up silicon grease and found one blurb saying 'safe to use' and one saying 'not safe to use', so I should defer to someone who actually knows the topic!) Wnt (talk) 09:37, 8 November 2014 (UTC)

(edit conflict) It's in reference to the fittings, piping, and other equipment that would connect to it. Those oils have a habit of being flammable, which is a pretty bad thing to have in a high-oxygen (pure and/or at high pressure) situation. Such equipment is often marked "cleaned for oxygen service", meaning they have made sure there is no residual oil from the machining/manufacturing and that pieces that are often lubricated or would contain oil for some other reason aren't. Or at least that a special grease is used that is safe for this special situation (I have no idea what their chemical composition is though). DMacks (talk) 09:44, 8 November 2014 (UTC)

As indicated above, common hydrocarbonus lubricants can under go such rapid oxidization in pure oxygen that they can spontaneous ignite - and from there, ignite metals and all that surrounds the apparatus. Fully fluorinated lubricants can be used on high pressure oxygen systems though (the fluoride atoms shield the oxidisable atoms from the oxygen atoms getting at them) the but for the average user (say using an oxyacetylene welder in a workshop) – what does he know about the chemical composition of lubricants available to him. So it is safer to declare Use No Oil. For lower pressure systems, silicone grease may be permitted in certain circumstances.--Aspro (talk) 13:01, 8 November 2014 (UTC)

Unfortunately our Oxygen clean is just a redirect to Oxygen tank. The subject is addressed briefly in the next to last paragraph, and two references are provided (one from NAVSEA, the other from NASA) that may be downloaded for more information. -- ToE 13:26, 8 November 2014 (UTC)

For an exploitation of this phenomenon in fictional form, see Isaac Asimov's murder mystery A Whiff of Death. Asimov was of course a Biochemistry researcher, familiar with such apparatus. {The poster formerly known as 87.81.230.195} 90.200.134.192 (talk) 01:10, 10 November 2014 (UTC)

LED stovetop heating elements

How does an LED stovetop heating element work? Arn't LED's suppose to be cold, and why does a stovetop LED stove work at all? How many watts does an LED stove use on high/medium/low?74.111.59.85 (talk) 15:32, 8 November 2014 (UTC)

The most likely answer is they don't work. I can't find any mention of them in any searches. Perhaps you're thinking of a cooktop which works via some other method, perhaps induction cooking, and uses LEDs for something else. Such as as indicators for the placement of pots on one of the new "freedom"/any position induction cooktops with multiple small elements (so you can place the pot or pan anywhere on the cooktop rather than in defined locations as with traditional style cooktops like [4] although that doesn't have LEDs for such purposes). Or alternatively to give fake flames like [5] [6] (people have also been doing that with fireplaces for a while although those are obviously not using induction and I'm not sure they were always using LEDs). Unless you have some further sources which demonstrate these claimed LED cooktop heating elements, I'm not sure if we can help more. Nil Einne (talk) 16:05, 8 November 2014 (UTC)

BTW, I should mention that I don't think it's accurate to say LEDs are cold. LEDs generally have a far higher luminous efficacy than incandescents or halogen lamps, meaning they produce more light for a given amount of energy. Nowadays they are often even somewhat better than fluourescents. But dealing with heat from a high powered LED is one of the big problems as it will reduce efficiency and also reduce lifespan. In relative terms the amount of heat is not much and definitely not something you'd cook with although you could burn your finger touching a high powered LED and I wouldn't call something like that 'cold'.

Of course other than probably killing it, the reason not to use LEDs would be there is no reason. The LED doesn't provide any advantage over a simple resistive heating element for a cooktop. Even if far infrared LED existed and I don't think they do, infrared is useful for some things like cooking in an oven (although these use simple resistive heating and infrared is generally only part of the heating) or room heating in some cases, examples of where you want to transfer heat over a distance to a surface. It's not really that useful for heating pots and pans on a cooktop.

Nil Einne (talk) 16:33, 8 November 2014 (UTC)

Trees shedding leaves

The Mallorn trees of Manhattan turn golden very early, and the display lasts over a month. This individual tree is in Poland.

Related: Wikipedia:Reference desk/Archives/Science/2014 September 28#Trees shedding leaves

When deciduous trees shed their leaves in the autumn, what is the sequence of species for the day on which the last leaf falls? In other words, which species is the first to become completely bare of leaves, which is the second, and so forth? At least, are there overall trends with regard to class or order or family or genus?
—Wavelength (talk) 16:59, 8 November 2014 (UTC)

Anecdotal experience is that smaller, younger trees tend to turn first. ←Baseball Bugs ^{What's up, Doc?} carrots→ 17:08, 8 November 2014 (UTC)

Leaf fall is a fairly random event which occurs due to wind and precipitation. Some trees will keep some or most of their leaves all winter, especially some oak species. Rmhermen (talk) 18:08, 8 November 2014 (UTC)

In the US coastal NE lots of dead leaves, mostly oak, don't fall until as late as the following spring, especially oak. As for changing color, the maples, ornamentals, shrubs and fruit trees like wild cherry seem to turn first, then the oaks (which are the largest) a few weeks later. This may not be helpful if you live further inland where hardwoods besides oaks are predominant. μηδείς (talk) 18:20, 8 November 2014 (UTC)

There is a lot of variation. Within species, it will depend on the local environment (understory/canopy, soil conditions, moisture, etc.), and the age of the tree. Within a given locale, timing might be loosely correlated with taxon, but around the world, plant functional type is a bigger issue, and this incorporates things such as successional status, nitrogen fixation abilities, morphology, and so on. Two trees of the same functional type but distantly related will behave more similarly than trees that are closely related by have very different functional type. Also note that in the tropics, trees are not seasonally deciduous but instead drought deciduous. In that light, the order of drop may change depending on variations between years, such that species A drops first in some years, but species B drops first in others. I concur with the anecdotes from Bugs and Medeis above. On the topic on young trees, they drop sooner in part because they also leaf out sooner, to be able to get light before the canopy_(biology) closes. The same tree will behave differently if it is in a treefall gap, compared to a closed canopy. Is this for a WP article? I can probably dig up more specific references if I know the target better. To even start on figuring out a general list of order-of-leaf-drop, we'd have to specify both a region and a forest type. SemanticMantis (talk) 19:12, 8 November 2014 (UTC)

(ec)It will depend on where you live. In the Northern hemisphere the Ash is generally one of the first to lose it's leaves [7] [8]. It also depends on the health of individual trees and how much rainfall there has been [9]. Richerman (talk) 19:16, 8 November 2014 (UTC)

SemanticMantis, no, this is not for a Wikipedia article, but just to satisfy my curiosity, although editors are still welcome to use the information to contribute to one or more Wikipedia articles, perhaps in Category:Periodic phenomena.

—Wavelength (talk) 19:46, 8 November 2014 (UTC)

Good call. The phenology page already has the category of periodic phenomena listed, but it doesn't show up in the category page for me (yet?). I also added leaf-fall, though changes will take time to propagate. SemanticMantis (talk) 20:44, 8 November 2014 (UTC)

Infinite space

If space is infinite, then does that mean that my exact clone is writing this same question on an exactly same wikipedia as this one in a different planet somewhere? — Preceding unsigned comment added by 88.115.38.169 (talk) 19:07, 8 November 2014 (UTC)

Not necessarily. One can construct an infinite list of numbers, no two of which are the same. Space being infinite doesn't require repetition, though it certainly makes it more probable. In part it depends on what you assume "infinite space" means. If you assume it means the same local physical laws and similar densities of mass and energy extending infinitely in all directions, then there are variations of that argument that would all but require that nearly everything is repeated infinitely many times. However, you can also construct theories about the universe where space is infinite but the details of physical laws and other parameters vary sufficiently that no two large scale regions are ever exactly identical. Dragons flight (talk) 19:23, 8 November 2014 (UTC)

In the generic case predicted by inflation theory, your identical copy is about $10^{10^{29}}$ meters away from you. Count Iblis (talk) 19:35, 8 November 2014 (UTC)

Of course, if there is an infinite multiverse there could be many copies of you playing out an infinite number of scenarios. However, am I right in thinking that if the big bang theory is correct, this universe must be finite as the big bang happened at a finite point in the past? Richerman (talk) 21:09, 8 November 2014 (UTC)

The Big Bang happened at specific time, but it didn't happen at a specific place. From the point of view of us living inside the universe, and from the limited region we can see, the Big Bang was an event that affected all of observable space simultaneously. It is unknown if the universe extends infinitely in space beyond the region that we can see. Common theories about the geometry of space include both infinite and finite options. Dragons flight (talk) 17:12, 9 November 2014 (UTC)

You can create an unending list of numbers that don't repeat, but once you say, and that is all there is you have made it finite. Space is unbounded, like the way the surface of the earth has no edge, while it does have a definite area. Applying the term infinite to actual physical existence may be a convenience, but it cannot be taken literally. You might want to search the archives, this topic has beaten to death an infinite number of times. μηδείς (talk) 21:51, 8 November 2014 (UTC)

Let's consider a real "unending list of numbers"...like the digits of Pi...which is infinite and never repeats and seemingly has no pattern to it. Those numbers are only globally unique. I can (in principle) find a sequence of 100 digits of pi...then look for another place within pi where those exact 100 digits occur again in the exact same order. We know for sure that such a place exists within pi because there are only 10¹⁰⁰ (a "googol") possible ways to have 100 consecutive digits - and so you're guaranteed to see duplicated strings of 100 digits, in an infinite number of places along the number, spaced roughly 100 googol digits apart. If you're a little "number animal" that lives inside pi - then even though pi itself never repeats on a macro scale, your local world of 50 digits is far from being unique...for 100% sure. So the portion of the universe that we can see must be replicated an infinite number of times through the entire infinite universe. As a being that lived far out on the edge of the identical-seeming section of one of those copies, you'd be able to see that things look a little different than they do in our copy...but no information that you'd discover about that would ever reach earth because of the speed of light limitations. So our earth and the earths in those other bubbles would never be anything other than utterly identical. SteveBaker (talk) 20:06, 10 November 2014 (UTC)

There are theories that do take infinite space literally, and theories that don't. Right now we don't know, though a globally flat universe (a very popular model) is literally infinite. See: Shape of the universe. Also, you are using the technical term "unbounded" in an inaccurate way. The surface of the Earth is bounded but has no edge. A surface is bounded if the shortest distance between any two pairs of locations within is always less than some finite number. So spheres are bounded (which in most cases is a synonym for finite), but you would have been correct if you said they have no boundary or edge. I assume that the similarity between "bounded" and "boundary" is probably the source of the confusion, but in technical uses they don't mean the same thing. Dragons flight (talk) 17:12, 9 November 2014 (UTC)

But that's just smuggling the idea of infinity in. Essentially you are saying you (they) have redefined boundedness, so that if something is unbounded, there are two points the shortest distance between which is infinity. So now I am supposed to talk of the universe, the surface of the earth, being unboundaried? You're just declaring yourself the winner by setting the terms of the debate. Any infinite model of the universe is incoherent because it means existing things exist in no relation to or definable proportion to the universe. In other words, however big the universe is, it actually isn't, because its bigger than it is. μηδείς (talk) 05:59, 11 November 2014 (UTC)

That's always been the definition of the term, nothing has been redefined. Also, it does not mean that there are two points the shortest distance between which is infinite, it means that there is no number so that for all pairs of points then distance between them is less than that. The natural numbers are unbounded, yet each is a finite distance from any other; "unbounded" does not mean "infinite distances", but "no maximal distance" - there is nothing that seems to prevent this from applying to the universe at this point.Phoenixia1177 (talk) 11:55, 11 November 2014 (UTC)

It's easy to create toy universes that are spatially infinite and mathematically well behaved, such as Conway's Life on an infinite board. It's plausible that the real world has a description of that form. -- BenRG (talk) 18:34, 9 November 2014 (UTC)

But again, if you're a glider - the 1000x1000 square grid around you will be replicated someplace else in that infinite board with another glider just like you within it. It doesn't matter whether the universe is infinite and never truly repeats - it only has to repeat on a scale that a human can detect it for there to be identical worlds with identical Steve's and BenRG's on them discussing the same exact questions. Conway's life has a "speed of light" limit, just like our universe does - so the concept of "visible universe" applies there just like it does here...and there will be lots of repeats of those places. You can argue the same way with Penrose tiles, they don't repeat over the entire universe - but there are arbitrarily large, finite areas that are precisely identical within the universe. SteveBaker (talk) 20:06, 10 November 2014 (UTC)

• We actually have pretty decent articles at infinite monkey theorem, multiverse, and block universe, with many links, references and "see also"s within. SemanticMantis (talk) 22:19, 8 November 2014 (UTC)

(...and if you like stories about the multiverse and kung-fu action, I recommend The_One_(2001_film)  :) SemanticMantis (talk) 22:22, 8 November 2014 (UTC)

The tough part here is figuring out things like cardinality of the continuum. How many universes are there - a countable infinity or an uncountable infinity? And even so, how do they map?

For example, consider an infinite set of universes containing two (2) hydrogen atoms. In the first universe, they are 1 meter apart, in the second two meters apart... up to infinity. Now there are no universes in this infinite set of universes that contain two hydrogen atoms that are one and a half meters apart, nor three hydrogen atoms. But this is a countable set of universes. I suppose you could have the hydrogen atoms arbitrary distance apart for an uncountable set of universes corresponding to the real number line... but still have none with three hydrogen atoms. So it's one thing to have infinite universes and something else to have so many freaking universes that you literally can't spare one single possibility, or half of them, or even nearly all of them. What is infinity divided by half, infinity minus one? I don't know ... infinity doesn't seem to worry about its security against thieves much. If there's a way to prove that every universe has to exist I'd be glad to hear it. hmmm, not really, come to think of it, because there are a lot of really bad universes... Wnt (talk) 22:41, 9 November 2014 (UTC)

Ignoring parallel universes...if our universe is infinite...AND fairly similar to what the see around here in terms of laws of physics and matter/energy distribution...AND if the positions, momentums and such of all particles are quantized, then if you took any random cubic parsec of it, there is only a finite number of ways that the matter and energy within that space can be distributed. That number is ungodly huge...but it's finite. So in an infinite universe, there must be infinite numbers of cubic parsecs that are utterly identical to each other at some point in time. That doesn't guarantee that there are identical copies of thecubic parsec centered on earth...but it would be AMAZINGLY unlikely that there wouldn't be an exact copy of earth...and you and me someplace out there. The question is whether the preconditions that I specify are vin fact true...and the answer to that is "we don't know". But it does seem plausible.

The glitch with the notion of an "infinite" universe, at least from the mathematical standpoint, is the implication of an infinite amount of mass and energy. It renders Conservation of energy irrelevant. ←Baseball Bugs ^{What's up, Doc?} carrots→ 06:44, 10 November 2014 (UTC)

That's not true. Conservation of energy only applies to closed systems. An infinite system can't be closed...but each individual cubic parsec (or cubic centimeter or whatever) can be measured - tracking the mass/energy passing into and out of it - and the conservation laws apply perfectly well. SteveBaker (talk) 19:41, 10 November 2014 (UTC)

Except that the evolution of such a cubic parsec is determined by random factors (e.g. nuclear decay), which means even identical regions will not stay identical over long time periods. MChesterMC (talk) 09:40, 10 November 2014 (UTC)

That's true - but if all we're concerned about is whether there is an identical earth out there right at this precise instant (which wasn't identical a picosecond ago, and won't be identical a picosecond from now)...then our OP's question is answered. Also, most of those tiny fluctuations take a while to produce noticable changes at the macroscopic level. So our parallel worlds would stay sufficiently parallel to be recognizable for a while. At first, weather changes would be noticeably different - one copy of earth gets a storm, another doesn't - some people get struck by lightning and others don't...and before you know it, the place is quite different. BUT if we have an infinite universe, then even those random factors must come out the exact same way on an infinity of identical earths...and in an infinity of others, those random factors make some very slightly different earths start to look more and more identical. Infinity is a VERY big place - where all of these things will happen. SteveBaker (talk) 19:41, 10 November 2014 (UTC)

The cubic parsec example is interesting, and sort of gets at the underlying philosophy a little better. To take a variant on it: suppose you have an infinitely large stormcloud and you want to see if you get exactly the same snowflake twice. You imagine that water has to stick to itself by certain laws, and therefore, from each snowflake there are only so many possible configurations. Yet... the assumptions about the infinite stormcloud matter. What if it is some sort of cosmic accretion disk spanning the gamut from cosmegg to Big Rip and every one of the infinite cubic parcels is at a different temperature, pressure, and/or chemical composition? Then it might be impossible to have any snowflakes in all but a countable few parcels in one infinitesimal sliver of space, and one might be unique. In the same way, our "infinite universe" might be made up of infinitely more void and cold space than warm places like Earth. We might have one 'tiny' visible universe of stars suspended above a bottomless pit of (to us) uninteresting possibilities. Wnt (talk) 16:20, 10 November 2014 (UTC)

Right - so in my description of the cubic parsec, I started out by saying that I was assuming that the hypothetically infinite universe was at least somewhat uniform. If we were indeed (for example) at the lowest entropy part of the entire infinite universe - then we could very well be unique. But other, lower entropy parsecs would still have to be identical. So while there could just maybe be no other copies of me...there could absolutely HAVE to be an infinity of other cubic parsecs that were absolutely identical...there just aren't enough possible configurations of particles and energies within a cubic parsec to allow them to all be different.

It's like trying to take 100 dice and setting them up with unique numbers showing on the top faces of all of them. Sure, you can have just one, utterly unique '6' - but of the remaining 99 dice, you need lots and lots of 1's, 2's, 3's and so on. You can only have at most 5 unique dice - and if you do that, the remaining 95 have to be all 1's or something. For us to be unique in an infinite universe, there has to be something VERY weird going on to have just one of those dice coming up '6' from natural processes alone...much more so if there are a million dice, or a trillion of them...or yet an infinite number of dice with just one '6'.

So if there are N possible configurations of a cubic parsec (N being an insanely large, but finite, number), it's plausible that M of them are unique in the infinity of space and N-M are each repeated an infinite number of times. But we'd have to be REALLY super-special for that to happen...and random quantum variations in the other M cubic parsecs would somehow have to be happening in the universe such that none of the infinite numbers of them can ever change to replicate one of those 'unique' cubic parsecs by chance alone. If the odds of it happening is non-zero, then in an infinite universe, there are an infinite number of places where it happened - so our unique parsec doesn't stay unique.

That seems possible but highly unlikely. If the universe is infinite, I'm pretty sure there is an infinite number of another Wikipedia reference desks answering this exact question right now...and an infinite number that had the discussion a thousand years ago...and another infinite number where the font is a bit nicer. SteveBaker (talk) 19:41, 10 November 2014 (UTC)

SteveBaker (talk) 19:41, 10 November 2014 (UTC)

@SteveBaker: you make a good argument, but there are still two things that nag at my mind...

• Can you rasterize an object? Per Tron, in theory, you take down the positions of all nuclei and electrons with enough accuracy that you could tell, simply from their positions, if they are bound together. Oh, yeah, and also their momenta, since otherwise it might just be a thermal collision, and to keep track of what is moving which way. But now we have tiresome Doctor Heisenberg haranguing us. Even from a "god-level perspective", can you actually get these measurements with enough accuracy that you could "scan" two people and say that they are actually similar, or is it physically impossible to have that much confidence in your measurements? Could one scan be a person and the other be an exploding soup of unconscious mishmash but they still come up as identical in your analysis?

• How many parameters are encompassed by "uniform"? If you assume a "reasonably homogenous" universe, maybe the average overall entropy is the same. But you assume also that, say, the alpha constant is the same, Planck's constant is the same, gravitational constant is the same... Question is, are you assuming uniformity only of a long list of constants, or do universes, on an infinite or multiverse scale, have an infinite number of constants and potential variations of physics that are simply not noticed by us because all of them are the same in our little region? A reasonably uniform universe might have most of them almost exactly the same but there's always something at ten, hundred, thousand standard deviations away from what it is here. Wnt (talk) 16:15, 11 November 2014 (UTC)

There are a lot of considerations here. I did say that we were assuming the laws of physics are the same everywhere - and I'm presuming that "constants" are indeed "constant" (seems reasonable!)...and I'm not talking about multiverses or extra dimensions or hyper-anything. Just our regular, boring universe - but assuming it to be infinitely large (it might be!) and more or less uniform in content...similar densities of stars and galaxies and that kind of stuff. These are not unreasonable assumptions - I'm just asking for the same approximate degree of uniformity that we see in the visible universe...so that if you teleported somewhere utterly random in the entire infinite universe - the general numbers of stars and galaxies and such would look pretty similar to what we have here. This is surely a reasonable default guess for what would be out there if the universe were infinite.

As for the "rasterize" question. Yes, certainly if we try for a PERFECT comparison between two planet-earths, we would run in to Heisenburg issues. HOWEVER: How much difference would it make if the third proton on the left of the fifth water molecule from the tip of your nose was moving 1% faster or positioned a few picometers to the right? Our macroscopic lives follow largely predictable paths despite quantum-level uncertainty - so two earths could still be sufficiently identical - even if, at the instant we compare them, there are tiny heisenburg uncertainties preventing a direct comparison.

What you're arguing about is the conditions for perfect identicality - which could easily be problematic. But what our OP is asking is whether (at the macroscopic scale) there are an infinity of Steve's typing identical answers into identical Wikipedias...and for that degree of identicality - there certainly could be an infinite number. I'd agree that 20 seconds after we do the comparison - the two Steve's we happen to be comparing are having slightly different thoughts about what they want for lunch due to quantum effects in their respective brains. But we have an infinite number of Steve's - and even if only 0.00000000000000000000000000000000000000000000000000001% of them agree that a Chicken Korma would go down really well right now - there are STILL an infinite number of them making that exact same decision. These variations cause gradual differences between worlds that seem identical right now. But infinity is...**BIG**...and there is room for an finite amount of variation and still have an infinite number of arbitrarily identical Steve's out there to whatever degree of precision you demand that identicality...even if there are also an infinite number who come back after having a Big Mac for lunch - *wishing* that they'd gone with the Chicken Korma.

SteveBaker (talk) 16:59, 11 November 2014 (UTC)

@SteveBaker: Well, it's a red flag that each "possibility", as determined by the rounded-off position of the atoms, could represent any number of different quantum states, and perhaps can't even be determined with sufficient precision except by violating laws of physics. (I'm very much not sure, but I don't think we really can determine the position of each atom to know whether it could be bound to another, without having enough looseness in the momentum that it might only be rebounding. I don't think it's just random fluctuation of water molecules we're dealing with. It's one thing to use an atomic force microscope to figure out the usual appearance of something, but something else again to do so with sufficient accuracy that you could remake a cell from the data) It underscores that the assumption that all possible configurations of atoms have some positive possibility may not be true. More to the point, our own configuration of atoms might have zero probability. (I don't know how, but somehow zero times infinity is not reliably zero) Some other configuration might come up infinitely more often, due to a potentially infinite number of underlying quantum states that all round off to the same thing. (One such possibility perhaps is "sector collapsed to a black hole"?) Infinity is such a tricky thing, every time you think you have it cornered it slips away. (Who would naively imagine that an infinite series of positive numbers could add up to less than an infinite result?) So I remain skeptical. Wnt (talk) 18:17, 11 November 2014 (UTC)

Let us re-read the original question here: "If space is infinite, then does that mean that my exact clone is writing this same question on an exactly same wikipedia as this one in a different planet somewhere?"...so we don't have to care about things that are too small to measure - or impossible to measure for Heisenburg-ish reasons. All we care about is the macro-scale similarities. Is there a clone of our OP writing this same question? There can be a VAST variation in the positions of atoms, energy quanta and all sort of other quantum-scale stuff - but unless those make our OP's clone noticeably different, we're still seeing the same person, writing the same question - and the only reasonable answer to our OP is "Yes". And actually, since there are an infinite number of such clones, you can choose amongst them to find the MOST accurate copies if you so desire - because there is still an infinity of them. Suppose you find a clone but because of the tiniest quantum-scale difference, he correctly capitalized the word "Wikipedia"...OK, not a sufficiently accurate clone to our OP...but never mind, there are still an infinity of clones who incorrectly typed a lowercase 'w' just like our OP did. No matter how close you look - right down to the precision that quantum theory allows, there can always be an infinite number of these clones. In the end, you can pick amongst the infinite number of nearly-clones to find in infinity of more exact clones. Once the differences between our Earth and the clones' Earth are literally too small/insignificant to measure - then there is no practical difference whatever - and there are STILL an infinity of those out there. SteveBaker (talk) 19:24, 11 November 2014 (UTC)

Well, my point was that the current OP may be infinitely improbable, probability zero. How is it we're considering a probability-zero event? Well, maybe those are the only ones that are selected by the anthropic principle. So far, the lack of cosmic neon signs in Hubble photos gives us some reason to suspect that worlds like this one are, at least, extremely unlikely; just how unlikely remains an open question. Wnt (talk) 21:35, 11 November 2014 (UTC)

The anthropic principle doesn't apply - each of the precise clones of Earth can use the same exact argument. The antropic principle answers the question: "If intelligent life is so incredibly unlikely - how come we exist?" - it doesn't speak to the question "Can intelligent life (or indeed, identical copies of us) exist?"

The probability of something exactly like us can't be zero, because we exist - and if it's not *precisely* zero, then no matter how small the odds, in an infinite universe, it happens an infinite number of times. I know that's counter-intuitive - but infinity is like that. The probability of there being any intelligent life may well be so small that it doesn't occur anywhere in the observable universe. The observable universe is far from infinite - hence no cosmic neon signs. But within a truly infinite universe, there must be infinite life...even though the actual instances of that are so ungodly far from each other that none can ever detect any others.

If there is an identical copy of the Earth out there - we'll never, remotely, be able to detect it...so in a sense, it really doesn't matter to us...beyond the philosophical questions such a thing would raise. SteveBaker (talk) 05:22, 12 November 2014 (UTC)

Select two random numbers x and y from the real numbers between 0 and 1. What are the odds that x = y? Zero. (digit by digit, 0.1ⁿ where n -> infinity) The odds that any successive random number after that, is equal to the first? Zero. So you had zero probability of getting that value yet you did. Wnt (talk) 06:19, 12 November 2014 (UTC)

@Wnt: What you say is true - but you're COMPLETELY missing the point. It's only only true if you need the numbers to be the same, accurate to every last decimal place...identical to an infinite number of decimal places. But if you need two numbers that are identical to only the first 4 digits, then the odds are one in 10,000. The odds of two numbers being identical to the first billion decimal places is really small - but it's not zero. The odds of two random numbers being the same is only zero if they have to match to an infinite number of digits. So - I agree that infinite precision identicality is impossible - but I'm sure you agree that finite precision identicality has a probability of greater than zero...so long as you only need a finite number of digits to match. If we allow ourselves to keep trying to find a match for an infinite number of trials - then no matter how many (finite) digits of precision we demand, we'll always find a match eventually - with a probability of 100%.

For our "identical planet" - we only need the two worlds to be identical accurate to some FINITE precision. If all of the fundamental particles are at the same positions (energies, velocities, spins, charges, etc) accurate to one part in 10¹⁰¹⁰¹⁰ - then our OP will be sitting there, typing his question on a bit-for-bit identical copy of Wikipedia. That's a LOT of accuracy for a LOT of particle - but we have an infinite number of cubic parsecs to choose from - so some of them (actually, an infinite number of them) will meet that precision criterion.

You can specify as much (finite) precision as you want in our comparison - and you'll still find an infinite number of matches to within the specified match criteria.

You can specify precisions greater than the precision it's possible (even in theory) to measure the differences - and in that case, the two worlds are indeed identical.

So, your complaint is invalid...and our OP can be confident that he has an infinite number of identical copies out there in an infinite (and roughly homogeneous) universe. SteveBaker (talk) 15:24, 12 November 2014 (UTC)

But that was my point about the rasterization: you can't even have these rasterized outputs describing all the particles in the universe. And if you could, you don't know whether some of the rasterized outputs are infinitely more likely than others, in which case the infinitely unlikely ones might be unique, occur a few times, or not at all. Wnt (talk) 18:55, 12 November 2014 (UTC)