Martin

I think you are probably joking with your picture of a solid metal measuring instrument. In case there is some touch of sincerity in the question, I will answer seriously: a piece of metal that travels near the speed of light relative Background will be melted and/or vaporized by the dopplershifted background radiation If, in sheer fantasy, by some miracle you could obtain a rigid measuring rod, 13 billion lightyears in length, with one end somehow anchored in this galaxy (so that it would move only negligibly relative background) then assuming rod inelastic--unable to stretch--the other end would necessarily be moving at near c relative background, and would melt. Solid measuring instruments above a certain size will self-destruct in the universe as we know it. Besides the quasars we have been talking about are not even that close, they are more like 20 billion, rather than 13 billion. And a 13 billion lightyear rod is already a physical impossibility. So your thought experiment does not work. Special rel would prevent you from anchoring to anything that was already out there because to do so would require accelerating the object (star, galaxy) towards us at near the speed of light.

I'm sure you will! Here's the link to cosmos calculator, to save you trouble googling it http://www.uni.edu/morgans/ajjar/Cosmology/cosmos.html If it gets cranky please tell me. When you start a session you go to the boxes over on the left margin and put in .25 for matter, .75 for cosm.const., and 74 for Hubble rate. Those are the latest values of the three key parameters. After that you can put in whatever redshift, and try a whole bunch of redshifts one after the other, if you choose. Just as a check, once you have primed it with the three parameters, if you put in redshift 8, then you should get out that the distance now is 29 billion lightyears (or 29.39 but I rounded off) and the recession "speed" or more correctly the current expansion rate of that distance, is 2.22 c. If you don't get those numbers please let us know. It's basic like knowing how to swim when you are around the pool, so I want to make sure it is working properly for you.

Cribbed directly out of Plato Symposium. Mighty fine performance! Merged post follows: Consecutive posts merged I read somewhere that evolution of 2 or more sexes also had to do with mitochondrial conflict resolution. The male is the one whose mitochondria selfdestruct. when two gametes get together you have to have some pre-arranged plan or convention to decide whose mitochondria rule. Because mito have their own genes which arent predivided so they can't take part in the choreography. So one persons mito have to win. And you don't want to waste time and energy arguing. So among our imagined slime people with five sexes A,B,C,D,E there would have to be some established rule about whose mito dominate and whose mito self-destruct. Like maybe it could be alphabetical order. A has mitochondria that survive in union with B and all the rest. B has mito that survive except when mating with A and so on. I'm not clear about this. I may have misunderstood, or the source may have been in error.

Hans, it is clearly easier to imagine inflation in a finite region. This is the picture in one of the popular inflation scenarios called Eternal Inflation. Your question is whether finiteness is logically forced, or not. Do you know the "graceful exit" problem. The idea that inflation should all stop at the same time over a huge causal-disconnected region. This is solved by programming. The "inflaton" field is imaginary, like a fairy or unicorn, so one can imagine whatever properties one wants for it. And one can imagine that the field is programmed to decay on a definite schedule. (You have seen the "slow roll" pictures of how the energy density of the "inflaton" is imagined to slowly roll down.) The inflation fantasies or, as they are called, Scenarios, have the inflation end just as the universe has been expanded by a factor of e^60. It was decided by us humans that this was the right factor for distances to expand. So now all we need to worry about is that things get off to a proper start. Inflation must begin simultaneously everywhere. Hans, I certainly agree that it is easier to imagine a simultaneous beginning if we are thinking of a finite region where everything is in causal contact. Also I personally like finiteness in cosmology. I would be pleased if it would turn out that the Planck spacecraft launched last month eventually reports a positive curvature. The whole universe, the whole of space, then is finite volume. Basically a hypersphere. That would be the conventional interpretation of such a result from Planck. But I stop short of imposing my own bias or prejudice here. I can't agree with your argument that inflation must have started in a finite region in order for it to have all begun at one time. This is intuitive, but I am not fully convinced. My problem is I'm skeptical that space with geometry as we are used to would even exist at that time. The classical model of the continuum (technically a differential manifold, something invented at Göttingen around 1850 by Bernhard Riemann and Carl Gauss) is probably not a good model for space at that time. And then what does "finite volume" mean? These are conditions like at the pit of a supermassive black hole. Extreme density and extreme geometry. Among other things, Heisenberg uncertainty, applied to the geometry itself (not just to particles) might come into the game. It could be that the quantum geometry model of Ashtekar and others is the one that is applicable. And then space is represented by a graph. What corresponds to volume is then related to the number of nodes. A very high degree of connectivity is possible in the network. This is called the quantum regime in QG, that occurs around the time of the bounce. Quantum corrections turn out to make gravity repel instead of attract, at those very high densities. Or that model might not be applicable and yet another might apply. But it is probably not the usual intuitive geometry in either case. A highly connected network can evolve into one describing ordinary 3D space with normal connectivity, or locality. This happens as a part of expansion. Only traces of abnormal connectivity may remain. Ashtekar and his group have studied both the finite and the infinite case and run computer models simulating the bounce and how the expansion we see could have begun. They may prefer the finite case (the hypersphere) but they have studied both. I don't think one can rule infinite case out. I personally don't like it. But I don't think one can logically exclude it (based on what we know and don't know at present.) There is simply too much we do not know about QG (quantum geometry/gravity). =============== To give you a taste of current research literature, here is a search using keywords "quantum cosmology" for the date > 2006. http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+DK+QUANTUM+COSMOLOGY+AND+DATE+%3E+2006&FORMAT=www&SEQUENCE=citecount%28d%29 In earlier times this list would be dominated by old names like Hawking, Hartle, Vilenkin, Steinhardt, Andrei Linde, perhaps even Veneziano. But there has been a shift of interest in the field. You hardly see those names, among the top papers. The dominant approach to quantum cosmology is now what is called Loop quantum cosmology. Based on representing the quantum state of geometry by a network labeled with quantum numbers. Ashtekar is a central figure. And nothing prevents this from changing again. It is a rapidly evolving field

Since species are the result of evo, an interesting question is how this setup of more than two sexes would have evolved. I think it may have to do with there being a fitness advantage of avoiding intermarriage or inbreeding or whatchacallit...when two close relatives mate... These slime people clone a lot. So say one colony sends out a spore and it lands somewhere and begins to grow and spread and clone, but you dont want the clones inbreeding with themselves because that's incest (leads to degenerate halfwits and such). Incest. That's the word I was trying to think of! So evo fixes it so there are N sexes. For simplicity let's picture N = 5, say, instead of N = 507---a nice small number like 5. What is the advantage? What does this arrangement do for the slime molds that makes them happier and better people? Or more evolutionary successful? This is what I want to know. Well now a colony of these people has to consist of at least two genetic distinct individuals in order for them to mate and make spores, which float off on the summer breeze. And if there were only 2 sexes then, since these slime people are sedentary and don't move around very much there is a big chance you get to copulate with your sister. We've all wanted to, right? Why does having 5 sexes (lets call them A, B, C, D, E ) make it less likely that somebody will mate with his sister? Mokele you better have a good explanation for this.

I like your question! It's a very smart question. Let me think a few minutes. The difficulty is that there is no physical process known that could cause inflation. One has to imagine an "inflaton" field which is a kind of fairytale thing. So what can one say about what is possible or not possible for a fairytale thing that has never been observed. I will think some and then try to reply.

Alan, how are you coming with the business of wrapping mind around features of the astro standard model? Have you tried using one of the online calculators to convert redshift yet? The redshift is the primary data. That is what they measure. The highest redshift observed objects are the farthest away, and they are the ones whose distance from us is increasing fastest. The highest redshift I know of being observed is that of the cosmic microwave background z = 1090. The next highest that I know of is a Gamma Ray Burst (GRB) observed in April 2009. z is around 8. One team said z = 8.2 and another team said at least 7.8. It might help you orient yourself if you simply got some practice converting a redshift like z = 8 into the standard model distance estimate. Is there any reason you want to stick with quasars? Quasars do not hold the distance record. As I recall the furthest quasar is something like z = 6.5, roughly. So the GRB I am talking about is much further away. It's up to you. Pick some redshift you like, whether of a Gamma Ray Burst or of a quasar, and convert it to distance and recession rate. Get hands-on familiarity with this. Here's a NASA report about the burst: http://www.nasa.gov/mission_pages/swift/bursts/cosmic_record.html Redshifts are your friend. They are what is actually measured, in most cases. They are nice moderate numbers, like 1.4 or 6.5. They don't have confusing units like "billion light years" or "mega parsecs" tacked on to them. Once you realize that you can always convert a redshift to a distance if you want to, then you can be much more comfortable using redshifts as a handle on distance and other things. It's the way to go. The pros found that out a long time ago. Over on campus in the astronomy building they typically are not talking about billions of lightyears, they are more apt to be talking in terms of redshift number. It's more convenient. You might convert to billions of lightyears when a TV camera is present or a reporter from some magazine is interviewing you. Redshift 1.4 means that distances increased a factor of 2.4 while the light was on its way to us. Distances more than doubled. Redshift 8 means that distances increased 9-fold. Is this helping or making it more difficult? To convert a redshift, google "cosmos calculator", prime the calculator by typing in .25 for matter, .75 for cosmo-constant, 74 for Hubble rate, and then put in your redshift like 1.4 or 8, and go.

In that case my bad! I must have confused you with some other person, whose writing style I admired (but it was poetry rather than scientific discourse). I will check back, not because I doubt what you say, but because I'm curious. I may not be able to find the post. Hmmm. I found something but I could well have misinterpreted and gotten a faulty impression! To me this is a striking image because the space (x) and time (t) axes make a kind of cross, upon which reality is affixed. I am not criticizing. I am offering praise. this is, as I see it, visionary writing infused with deep excitement and feeling. It is exactly what I imagine as proper to this particular subforum. There was another passage of yours I thought was striking and beautiful: Merged post follows: Consecutive posts mergedAnd there was what you just said: To call an assertion (evidently inspired with certainty, but not based on empirical evidence) visionary or mystical is not to dismiss it. I do not dismiss. I appreciate. And I wish to be clear about categories of human endeavor. What you are doing is not science, and does not belong in the Astro/Cosmo forum. But that doesn't mean it is bad or wrong in any way. I see it as an important human function. Call it what you want: conceptual art, spiritual philosophy, poetry, prophesy, inspired certainty, inspired utterance, the search for meaning in existence, the search for profound paradox in existence, or make up your own name. Or do not name what you do at all. As I see it, this is an essential non-science activity, to be appreciated and not under any circumstances dismissed. The flip side is that it could be characterized as portentous and adroit obfuscation. But let's not go there.

Thanks for pointing that out. So if might be fun to do the numbers, but in a very back-of-envelope fashion. Let me see if I get the same answer you have here, using google calculator. what is the number of seconds in a year? 3.15 x 10^7 I seem to recall. So we have to multiply that by G*mass of earth/(c^2*radius of earth) So what we put into google is 3.15*10^7*G*mass of earth/(c^2*radius of earth) Let's see what we get. WOW!!! Google comes back with (3.15 * (10^7) * G * mass of Earth) / ((c^2) * radius of Earth) = 0.021906788 That is about 0.022, which is what NowThat said! So now we can do the same thing for the moon. Google comes back with (3.15 * (10^7) * G * mass of the Moon) / ((c^2) * radius of the moon) = 0.000990759556 That is about 0.001 So imagine we have a master clock a long ways out from both earth and moon, moving along with the earth-moon system but effectively "at infinity". And we put two clocks carefully down in the two gravity wells. At the end of a year, the clock on earth will have lost 0.022 seconds just as NowThat says. The clock on the moon will have lost only 0.001 second. So one can guess that the answer to the question is YES. YOU DO AGE FASTER ON THE MOON. The difference is about 0.021 seconds per year. Now you noticed that I didn't even bother with the special rel effect of the moon's speed, say relative to the center of mass of the earth-moon system. That is because I think of the moon as going too slow to bother with. But I could be wrong. So I'll check it. Yeah it's OK, because the moon is only going a few millionths of the speed of light. So when you do the time dilation beta is like 0.000004, and you square it and it is like 16 trillionths. That is small even in comparison with a small number like G * mass of Earth) / ((c^2) * radius of Earth) which is on the order of a billionth. So we can forget the speed correction. You do age faster on the moon, by roughly 0.02 seconds per year. Merged post follows: Consecutive posts mergedI should thank Alan the thread-starter for getting this started. It's fun to see how it works out. there are technical details implicit in the previous like this: sqrt(1 + x)= 1 + (1/2)x - (1/8)x^2 +... and time is slowed by a factor sqrt(1 + 2*potential/c^2) = sqrt(1 - 2*Gm/(c^2 R) ) which by that series expansion is approximately 1 - Gm/(c^2 R), which is what was used in previous post. The potential is already so small that higher power terms in the series are negligible. Here m is the mass of the planet and R is the radius. One could ask why is 2Gm/(c^2 R) always less than one. It is because 2Gm/c^2 is the Schwarzschild black hole radius. R must always be larger (or else the body collapses to hole.) So dividing the Schw radius by R is always less than 1. Therefore (1 - 2*Gm/(c^2 R)) is always positive and sqrt(1 - 2*Gm/(c^2 R)) is well defined.

NowThat, thanks for that very useful bit of information! So in the case of GPS satellites, the GR gravitational potential well effect dominates the SR speed and acceleration effect. One can infer that in the case of the moon it would be even more dominant. At least I think one can infer that! Because the moon is moving much slower than the GPS satellite, so the SR kinematic effect of being on the moon would be less. And the difference in gravity between standing on moon and standing on earth is greater (what is it? One sixth gee?) than the difference in potential between earth surface and up there where the GPS are. At least I think so. Swansont please correct me if I'm missing something. This is just a quick reaction.

Reaper and Airbrush gave you about as good an answer as you can get with a question like that. If you want to think about astronomy you have to train yourself to use numbers in a consistent reliable way. Don't confuse 14 with 14 billion. Don't confuse redshift z = 6 with 6c. Don't confusion recession rate with speed. A recession rate is merely the rate that the distance is increasing, it is not the speed that something is moving. If something moves or travels in the ordinary sense then it is going somewhere, it is getting closer to something else. A galaxy is not going anywhere (except for a little trivial local motion it may have within its group). Geometry is dynamic. Distances between stationary objects change. All there is to it. That is what curved spacetime is about---Gnrl Rltvty---you heard about it. It is what causes the geometry around us to be Euclidean and what causes some largescale geometry to not be Euclidean. The Einstein equation decides how geometry acts, and whether or not distances between stationary points will increase or decrease, and what the angles of any particular triangle are going to add up to. You have no right to expect distances not to change. Once you realize that Euclid geometry is not absolute and universal there is nothing to "wrap" your mind around. Google "cosmos calculator". Put in .25 for matter, .75 for cosmo constant, 74 for Hubble rate, and 6 for the redshift. This will tell you the present distance to a quasar with redshift z = 6. And it will tell you the present recession rate. If you have a source for a quasar receding at rate 6c, I would like to see it. It is possible. But the highest redshifts of quasars I know of are around 6 or 7. That means the distance to them is increasing at a rate which is about twice the speed of light, not six times. In Dante's Inferno the people who were sloppy about numbers in their mortal lifetime are punished by wearing gasoline-soaked adult diapers which are on fire throughout Eternity. I forget which Canto this is in. Anyway Pagans and Illicit Lovers get off lightly compared with those unfortunate souls. So for heaven's sake reform your ways!

That is exciting and to me quite unexpected! Could you give us a link to source? I went to the "Science Hub" page that you have in your signature and saw that it was full of interesting news, but I didn't see the brown dwarf study. You must have it handy, so please share it with us.

Argument from incomprehension. Some points: * Infinite spatial volume is not logically equivalent to eternal. Honzik is asking do we know whether spatial volume is finite or infinite. Your talking about eternal is off topic, strictly speaking. * Current research is pushing the time horizon back before the big bang and trying to model conditions leading up to it. In effect getting rid of the supposed "singularity". That does not say anything about eternal. Just because we might pass that one barrier does not mean there will not be found another barrier. Don't jump to the conclusion of eternal just because it looks like that one barrier may be in the process of being penetrated. (And the models must be tested.) * But suppose you want to consider an eternal model, extending back in time indefinitely (I think this is pre-mature but suppose you do.) The there is in principle no problem with entropy. If a single observer, with a single measure of the entropy, is possible then the entropy can just get smaller and smaller as you go back in time. Think of the function et on the real line from -oo to +oo. It is everywhere defined and positive and increasing. No problem. Remember that the Newtonian Universe had an infinite past. And this did not bother Newton. He took that as natural. He didn't seem to think that there must be a starting line to the race. The man was not philosophically so naive. And when Boltzmann delved into the concept of entropy in the 1870s and 1880s, there was no illusion of a "big bang beginning". They were still using a Newtonian Universe, with its infinite past. Boltzmann had no problem. The past consists of finite moments each of which is a finite duration back into the past. This allows a finite positive entropy to be defined at each point in the infinite past, if you can posit an observer with a consistent definition of the state space. Boltzmann was philosophically sophisticated. Not only one of the greatest physicists of the 19th (along with Maxwell) but also he gave lectures on the Philosophy of Science at the University of Vienna. Cool guy. Also a feminist of sorts. He fought for the right of some woman to unofficially audit courses at the university, after she was denied permission (because as a woman it didn't seem to the administration to make sense for her even to sit in lecture hall ) http://en.wikipedia.org/wiki/Ludwig_Boltzmann

Astro is a mathematical science. In cosmology one makes models that you can fit data to, or compare with observations. The description of reality is not purely verbal. Southerncross' descriptions are often strikingly beautiful as poetry, but don't qualify as astronomy or cosmology. So I moved the thread here. It is the most suitable category we have, comes the closest. A special forum for "Visionary Philosophy and Poetic Mysticism" might be more appropriate but we don't have one. S+, the quality of your contributions is high. I personally enjoy, am occasionally moved, and encourage you to contribute more. I remember one time you compared Time to the cross upon which our savior was crucified---something about nails. It made an indelible impression. Your poetic meditations are almost if not quite publishable. Go for it! As far as I am concerned I wish you deep and intense inspiration. And I respect literary aptitude like yours. Just please keep it out of astro/cosmo.

There's also the possibility that the universe is simply finite. Not surrounded by anything. Having no border or boundary. That is mathematically simpler to deal with, so it is how cosmologists normally treat the positive curvature case. Although it is an appealing image, to think of our universe as a "bubble"---as in the "eternal inflation" multiverse promoted by Andrei Linde---there is neither evidence for it, nor a plausible physical model to work with. Because so exotic, not much actual research is being done. Symptomatic of this: nobody of the bubble multiverse advocates was invited to talk at Strings 2008. No talks about the "anthropic principle" as a way of selecting from the "landscape". Back in 2005 that was more popular with the researchers. Again at Strings 2009, no talks about that kind of stuff. Although enormously appealing to the imagination, the "bubble-universe" bubble seems to have burst. Largely gone out of fashion with researchers. Nevertheless some very visible people still talk about it, like Andrei Linde at Stanford. Just not much in the way of papers. The "brane clash" cosmology thing may also be on the way out. It was more popular back in 2003-2004 than it is today. Main proponents are Paul Steinhardt and Neil Hurok---neither have written much about it recently. Steinhardt's recent papers have been aimed at showing that the extra dimensions of string theory are incompatible with inflation. He seems to have come around to accepting some type of inflation (which brane clash avoided) and his "no-go" results are seen as detrimental to string. What I'm saying is at odds from the impression one could get from popular science media. I think the media still like both the clashing branes and the bubble multiverse visions very much. All I can offer as evidence for what I'm saying is rather dry facts like research publication rates and citation numbers. Maybe sometime I'll trot out the stats on this. And of course nobody is obliged to follow the lead of the research community when it changes course (but it's worth keeping an eye on what the experts are interested in all the same.) Merged post follows: Consecutive posts merged Honzik, we don't know if space is finite volume or infinite volume. You got the wrong impression about inflation. There are many inflation scenarios (none based on established physics, all need some exotic un-observed mechanism). Inflation can work with infinite volume. Doesn't require finite space or finite number of particles. Only certain specific inflation scenarios have finite space. Inflation is plausible because it solves some interesting puzzles, like the fact that the Background temperature is nearly the same over the whole sky. But even though plausible it has not been proven that it happened. There are still alternative models to explain the same puzzles. So it is not yet shown to be necessary. But with or without assuming inflation we still cannot answer if space is finite or infinite. The Planck spacecraft launched in May 2009 will help answer this. It is the first European space mission aimed at studying the microwave Background. Potentially an important advance. I have to go. Back later.

In contemporary models the big bang is not the beginning of the universe, so it is not like asking "where were you before you were born?" It is more like asking what conditions were like before the Milky Way galaxy formed. Or what was there before the solar system formed? Or what was there before life evolved? In these cases it is possible to arrive at some models that are at least in principle testable and which reconstruct the past.

This paper shows how http://arxiv.org/abs/0906.0809 It has pictures that make it easier to understand than if it was just equations.

There is a lot of interesting stuff here. Examining the evolutionary origin of consciousness and reasoning ability component by component. Instead of treating it as one big lump with a lump survival value. Examine each subsystem: what other animals share it? how could it have evolved (say in magpies, as well as humans)? how our brains are prepared to infer fallaciously in certain ways---are vulnerable---as a side-effect of some other survival fitness development. It's actually bothering me that I can't make the time to read the stuff in this thread carefully enough. An hour or two ago I was reading and then got interrupted by company. Now I'm back, but have something else that has to be done. I am remembering some research into the idea of self. which animals had evolved it. If you put a red spot on the forehead of an elephant and let it see itself in the mirror it will try to rub off the spot. It knows that it's Itself in the mirror. Almost no other animals except humans and primates will "get it" and try to rub the spot off. But it was recently found that there is a type of bird that recognizes itself in the mirror. And the birds are curious and walk around to take a look behind the mirror too, as if asking what is there and why it works. Most birds think it is somebody else they see. But this one species has a brain which is able to recognize Itself. Then the question is how did that extra brain feature and ability evolve? I really liked the Scientific American article on "agenticity" and "patternicity". Thanks. ============== EDIT: Heres a link to another forum where this was discussed and there are a lot of links to sources, and a video of a magpie trying to remove a yellow sticky from its neck that it can't see directly but can only see in the mirror. http://www.sciencechatforum.com/bulletin/viewtopic.php?f=37&t=10101 There is a PLoS journal article about this, and a link there too. It is said that only humans and 4 ape species, and Asian elephants, and bottlenose dophins, have passed this "mirror test". (not African elephants, not other kinds of dolphin, not other primates, just those specific ones.) And of course now magpies. Hundreds of animals have been tested. Most types of animal just think it is another individual, not themselves, in the mirror. So if the other guy has a spot painted on, it is no big deal. Only certain species have brains with the ability to figure out that it is them and they better scratch or wipe off the mark. So what is important here. People are studying the evolution of consciousness which means ultimately the genetic basis---certain structures in the brain that enable certain kinds of recognition, planning, tool use, picturing future situations, internalizing social interaction, concept of self, mental model of other person, personification (projection of a self onto some other thing, like an automobile or the stock market). Maybe. All these things are different. Different animal species can have a different subset of them. Maybe. They are not just learned by an amorphous general purpose brain. Maybe. They are connected, apparently, with anatomy, hardwire brain anatomy, that is genetically determined and which has evolved in various different animal species. OK, so it looks like a different approach from what has been done mostly in the past. Puzzle as to why a magpie, of all birds, would have the ability to realize that the image in the mirror was itself, and not another magpie. And why other birds would not. Like a robin will fight its own image in a shiny hubcap. Why has a magpie evolved greater sophistication than a robin, in this matter? Beautiful thread, iNow. Many many ideas are latent here.

Hi Tolmosoff, I see this as more of an individual poetic vision of the Cosmos and falling more in the line of Speculation, rather than ordinary science cosmology. That is not to say it's bad! I like your graphic imagery, of the twostroke or fourstroke combusion engine, and the Particle being the moment of highest compression, when the Spark fires. It is a beautiful metaphor that draws together many meditative and visionary strands of thought. Since it is more speculation than actual science, more verbal imagery than mathematical model that one could fit numerical data to, I will move the thread to Spec forum. Honey roasted almonds are my favorite but there is also a smoke salty tasting kind that is very good. Diamond is the highest quality, so you can be rightfully proud of being a grower for them.

Yes, within the narrow confines of how he set the problem up. I'm glad you enjoyed it too. I get a mild kick out of scenarios involving some simple algebra. Actually, if I (or my robot surrogate) were the Colonizer Captain, I would avoid type M stars because I just don't like the color! Yuck! too reddish and too much infrared compared with visible. I (and my surrogate) like cool days with bright golden sunlight. But I might use Widdekind's algebra to justify my decision to skip that star, to give an excuse to the board of directors of the Foundation that was paying me.

Reaper, thanks for pointing that out. The Gliese 581 system is a good example. Sherlock, one reason I like Widdekind's exercises is they add some zest to the astrophysics by deriving consequences for ET (or future humans and our robot surrogates) from basic formulas. In a sense it makes the formulas come alive, by putting some imagined beings into the picture. It is the kind of thing that could eventually lead someone to a creative online teaching tool or beginning astro workbook. In this case Widdy has a valid point! And it is based on some very simple algebra! Check this out. I'll repeat what Widdy is doing. The wattage of the star varies as M^4 (he gives a reference) So the habitable zone is a belt a few percent around some ideal distance D which is where the wattage hitting a square meter is ideal for water. OK? So M^4/D^2 = constant So D is proportional to M^2 by a kind of universal proportionality the same for all stars and planetary systems (just approximate but fair enough) So for starters imagine you are a colonizer evaluating prospects for settlement and you see a star with an earth-mass planet in circular orbit at the distance D from the star (or a few percent from the ideal distance D). Is this a good prospect? Well Widdy can calculate for you how much potential energy you have to sacrifice to get down to that planet. He calls that energy U, and he points out that by standard Newton it is proportional to M/D. But D is proportional to M^2! We already said. So the energy you have to blow off is proportional to M/M^2 which is 1/M. So the energy cost to the colonizer of getting down into the habitable, where he can do a flyby of the planet, is reciprocal to the mass of the star. Habitable planets of low-mass stars are more costly to visit. Because a low M means a high 1/M. ===================== This type of thing is going to carry over to pretty much any scenario you imagine. it applies not only a colonizer coming from a long distance away but also it applies to the locals who want to migrate from planet to planet within the habitable zone. The energy difference between the inner and outer boundary of the habitable is going to be a fixed percent of 1/M. So the smaller M is, the larger that will be. ===================== Basically what I see Widdekind doing is experimenting with a new kind of highschool or freshman college physics textbook, which integrates and motivates some classic basics by imagining these principles and laws applied to the job of spreading life thru the galaxy. It is not a bad idea for a pedagogical approach. And whenever you have a physics textbook example there are bound to be some simplifying assumptions. Like "other things being equal". Or like "the colonizer's main concern is the energy cost of getting down to the level of the planet in the star's gravity well." Obviously you can imagine other concerns, but in a physics problem, to illustrate something, you narrow down.

I'm in partial agreement with Vedek. The planet hunters have tended to focus on sun-like stars. Sol is type G, so they have tended to study F, G, and K. And so more planets have been found around F, G, K because they were looking more at those types of stars. But M type stars are quite numerous, and I believe planets have been found at some of them. So in the end it might turn out that there are more planets in total that are orbiting M stars. For anyone joining the discussion late, astronomers have this curious classification of stars which, going from massive hot stars down to smaller cooler stars, is the "spectral sequence" O, B, A, F, G, K, M And we were taught a mnemonic to remember the sequence: "Oh Be A Fine Girl, Kiss Me." The sequence and the quaint mnemonic go back to an earlier and more innocent time. According to Wikipedia the classification scheme was invented around 1900 by Annie Jump Cannon http://en.wikipedia.org/wiki/Annie_Jump_Cannon She is also credited with making up the mnemonic to help remember that peculiar sequence of letters.

It's a natural question to ask. Science, though, goes in small steps. I don't know any professional cosmologist who is addressing those ultimate beginning issues technically, about "nothing" or time being eternal or non-eternal. What I see them doing is focusing just on that one narrow time period 13-some billion years ago. What came before that t=0 moment? What conditions led up to the start of expansion? Broader issues necessarily get put on hold. Maybe there was a beginning of time, way way back. Maybe countless universes have branched out like the branches of a tree but the tree itself has a beginning As a rule, working cosmologists don't want to get mixed up in that kind of speculation. It is too hard to make that empirical, testable. It is hard enough to try to get a testable model of just our one big bang that we know about. I can link you to the professional research in quantum cosmology so you can see for yourself and not have to take my viewpoint. I normally only look at the after 2006 publications, but you can change the date on the search. This is the Stanford data base called Spires. Hits are ranked by the number of times the paper has been cited in other research papers. (a rough measure of importance). Don't expect to find anything readable, but you can get something out of scanning the titles (for a brief summary of contents click on a paper's "abstract"). Don't get bogged down, just skate over for a quick impression: Here are the date > 2006 papers: http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+K+QUANTUM+COSMOLOGY+AND+DATE+%3E+2006&FORMAT=www&SEQUENCE=citecount%28d%29 Here for comparison, the date < 1985 papers (back when Stephen Hawking's ideas were being actively investigated) http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+K+QUANTUM+COSMOLOGY+AND+DATE+%3C+1985&FORMAT=www&SEQUENCE=citecount%28d%29 You can see in the early bunch there is a Hawking paper in second place. Top of the list is a paper by Vilenkin, a close associate of Hawking. There has been an enormous shift in what ideas and models are considered interesting, from the before-1985 period to the after-2006 period. Remember that if you want a brief (if incomprehensible) summary of the paper you click where it says "abstract" under the title. From there you could even get the whole paper by clicking on "pdf". I'm not suggesting this, just noting the possibility. The point is that essentially none of these people are investigating eternal questions*. In the top-cited research community they are all focused intently on modeling and explaining the big bang, and also black holes but mainly the big bang. This is the immediate thing we have the leftover radiation and chemical elements from. It's got to be the focus of attention until it is understood. If they ever get to eternal questions it will have to be later. *They may speculate in words on TV interviews and in talking to journalists, but that's just popular media fluff. The mathematical model building is more focused.

There are several modern models of what was going on around that time--models that are being studied and which have to be tested by comparing observation with what they predict about presentday data. None of the modern models have time begin at t = 0. Time zero is just a good marker or reference point---the start of expansion (from a very dense state.) They all have something going on before t = 0, but there is disagreement as to what. There is a classical model that does not quite get back as far as t = 0, it breaks down. So for that classic model (based on vintage-1915 relativity) the idea of "before t = 0" is simply meaningless. It loses track of things as it approaches time zero and breaks down. So about all we can do is watch the experts in quantum cosmology (the people studying the very early moments of expansion) wrestle with the problem, which models are gaining adherents and interest among the research community, which models are losing appeal and having less research effort devoted to them. Einstein Online (link in my signature) has an essay called "Tale of Two Big Bangs" which says it very clearly. "Most cosmologists would be very surprised" if it turned out that there actually was a singularity (where time stopped) at t = 0. E-O is the pubic outreach website of one of the world's top research instutions and it's pretty up-to-date and well written, you might enjoy checking it out. It is likely less dumb-down than what is on History Channel. It is likely more clear and forthright about areas of uncertainty than commercial broadcast media can be.

Oh, sorry. You asked that earlier and I said "G is Newton's constant". You want a numerical value, and some explanation. Put this into the Google window: "G = " without the quote marks. Or just do a search for "gravitational constant." Now I'm worried, Purintjp. If you are not already familiar with Newton's grav. constant G then this little exercise of finding the critical density needed for flatness is not likely to mean much to you! that means I misjudged and over-reached. G is a universal constant that tells you the force between two things if you specify both their masses and the distance between them. But almost by miracle, even though it was discovered around 1680 by Newton it reappeared in 1915 in the Einstein equation showing how masses influence the geometry around them. In the Einstein Equation of general relativity it appears not as G but as 8 pi G. I want to let you off the hook, because I misjudged. But here is a simpler more classic vintage-1680 problem: A 100 kilogram man is standing on an asteroid whose radius is 1000 meters. The mass of the asteroid is 10 trillion kilograms, let's say, (that's 10^13 kg). What is the force pulling between them? If you type this in Google it will tell you the force in terms of the metric unit of force G (10^13 kilograms)(100 kilograms)/(1000 meters)^2 If you type this instead, it will tell you the force in a more familiar unit, "pounds of force" G (10^13 kilograms)(100 kilograms)/(1000 meters)^2 in pounds You multiply G by the two masses and then divide by the square of the distance between centers (which in this case is about 1000 meters).