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#31
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Missing sial, iron, and nickel explains Fermi paradox
In the discussion of simulation I have just produced a blog that might
be of some interest. http://ipsim.blogspot.com On the question of extraterrestrial life, the general opinion, which does have some plausibility, is that life is common, but intelligent life rare. We don't in fact know. We can at this stage make deductions. What is known, apart from the limits we have placed on an intelligent ET, is that planetary formation is common. The planets discovered so far are by and large giants, but that is because it is all we can observe. There is also one other interesting fact. All the stars, some of which are similar to the Sun, which have giant flares all have a giant planet close to them. Hence radio emmissions from stars are governed, to an extent, by giant planets. You are right about the statistics. I have just worked this out. If intelligent life evolves according to e^(-ax^2). The differential of that is -2axe^(-ax^2) Hence if we live at time x and we assume a to be 2/500million years. If there are a billion civilizations this puts x at a value of about 10 deviations from the mean. This gives a time of about 1/10SD for evolution of the next intelligent species. It would seem from such things as Cretaceous/Tertiary that we have a Gaussian.A Gaussian is the result of a lot of separate events. Gauss in fact originally worked it out on this basis. However my point that if you are waiting 50 million years for something to happen, it could happen next year. That is what I was stressing. We can put an existential risk probability on this. It is very roughly the same time as Cretaceous/Tertiary! Hence ET is rather less dangerous than large asteroids. Certainly asteroids are more dangerous as the smaller ones can still do a lot of damage. We know from orbits that C/T will not be until at least 2020. - Ian Parker |
#32
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Missing sial, iron, and nickel explains Fermi paradox
In article m,
Ian Parker wrote: I believe that within 50 years, we'll have mind uploading. (Ray Kurzweil puts it at more like 20 years, but I am a pessimist.) If you and I are both right, then those "unmanned" probes may well have people on board, albeit in digital form. That is an interesting thought. I have a philosophical point here. Suppose we split our brains. One bit went to Alpha Centuri. The other bit went around here on Earth. Could you put those two memories together? Could two separate memories be knitted together? That's a technological question, not a philosophical one. Such merging of separate memories is a common feature in science fiction, but I'm more skeptical about it than about uploading itself. The brain isn't built the way an intelligent designer would design it; it's a messy system, with information about events spread out and mixed together with information about all other events. So recombining someone who has been duplicated, and then had significant differences in experience, is going to be very hard. Probably not impossible, I guess, but definitely in the "nontrivial" category. We could of course simply back ourselves up when we were about to do anything dangerous. Yes, that one IS trivial. I don't agree. VN machines are certainly possible, but I hope they're a long way off, and carefully regulated. If ever there was a technology ripe for disaster, that's it. I see very little benefit to justify the risk. Are you thinking about the risk that VN machines will evolve, or that they will be deliberately misused. Both. In terms of evolution, a Reed Soloman code will prevent evolution in that it will be inpossible for the VN genome to change. No, it can only make it very unlikely -- and even that, only if done exactly right. Any flaws in the implementation will make it easier (just as with any cryptographic scheme). Interesting that you're willing to seriously consider the possibility that two civilizations would arrive at virtually the same instant, but when it comes to breaking a checksum, this you refer to as "impossible." BTW - I believe we will get VN machines a long time before brain downloading. It's "uploading" please, not downloading. And I'll take that bet. Best, - Joe -- "Polywell" fusion -- an approach to nuclear fusion that might actually work. Learn more and discuss via: http://www.strout.net/info/science/polywell/ |
#33
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Missing sial, iron, and nickel explains Fermi paradox
Ian Parker wrote: On 1 Aug, 03:41, Einar wrote: Ian Parker wrote: On 31 Jul, 13:37, Einar wrote: It?s quite possible to imagine, say for every 10 species that happen in the Galaxy at least 9 linger indefinitelly at a preindustrial state of development. Maybe, but I really doubt it. Once you have cultural evolution outstripping genetic evolution, I think things are going to proceed rapidly and inevitably pretty much as they have for us. Memes evolve just like genes, only much faster. The scientific method is a powerful one because it works (it produces useful results), which is why it has caught on pretty much universally here (right-wing nut jobs aside), and it would do the same in any alien culture too. That will ultimately lead to labor-saving devices, more intensive energy use, etc. The idea of an "industrial revolution" is again an oversimplification of history. In reality, it was much more continuous like that, a long stream of ideas and inventions feeding upon one another, each step enabling the next steps. It's been an exponential curve, pretty much any way you measure it, which produces the illusion of little progress when you're living through it, but extremely rapid progress when you look back (or forward) on it. I think it was very important the idea that christianity invented that of the separation of the realms, i.e. that there were activities that were nonreligious. The ancient world lacked this distinction, hence religious activities and ideas permeated all types of activity. In the hierarchy of gods there was a god for every realm of activity. This appears to be the single largest difference between christianity and islam, in islam all activities belong to god. While the church may have been selfishly reserving religious activities for itself solelly, in order to maximize its own power, this created more opportunities for thought, speculation about things, free of religious thinking. This is why I think itīs no coincidence that scientific thought was gradually able to develope within the christian countries. However, that does not yet necessarilly give an explanation for the industrial revolution. The ancient Greegs knew about steampower, yet did not develope it. Same about the Chinese, not enough is known about wether that was the case in India. The Roman civilization inherited all the knowledge og the Greegs, and was much richer to boot. But while it appears that development of industry would have been possible, it didnīt happen. There has been a great deal of discussion about why the industrial revolution took place. I think that theoretical knowledge had more effect than people suppose. James Watt was at Glasgow university and he had to get a Newcoman engine working. He found that the engine was very inefficient. What happenned was that when water was poured onto the cylinders the water boiled at a lower lemperature because of the change in pressure. He went to see Joseph Black at Edinbourgh who told him about this. Watt then designed an egnine with valves where the steam pressure, and hence water temperature was kept up. So knowledge of thermodynamics may have been more inportant than is generally realized. Christian civilization did indeed have this spirit of enquiry and managed to acquire considerable theoretical knowledge. I think you are probably right there. Britain was successfuul because she had a mercantile economy. Other countries went in much more for state control, particularly overseas. People have been exploring it why this happened in Britain in the end. What was so special about Britain that impetus eventually developed to create a practical steam engine? In the ancient cases of models of steam powered experiments, there was clearly allways lacking reliable and efficient means of transforming the energy in the steam into logomotive power. It was the invention of the moving piston which was the big break. That took decates to be developed. In Britain uses were found for the extremelly inefficient early tipes of piston arrangement, i.e. to pump water from coalmines. By that time Britain no longer had enough forests to fuel those engines, so only in the very immediate viscinity of coal mines were they at all practical. Over time the engines were improved, and around the beginning of the 19th. century the steam engine became practical for other applications. Britain also was by that time a world power, able to import and export to allmost everywhere. So circumstances appear in many respects to have been very advantagous in Britain, more so than anywhere ellse and also more so than at any time before. Sounds bit chancy to me. - Ian Parker Preciselly why industrial revolution happened may never be fully answered. However, I read your other posts and noticed you are hoaping mind can be copied. Personally I find it unlikelly ever to be possible. Mind you, sure they are learning a real lot, but a large aspect of the problem, even though a way might be found to record thoughts being made as they are made, is that real lot of the information stored in the brain is not thought about with regularity. There are lots of memories, things you donīt often think about, and in addition things that are there that you think you have forgotten but which can be triggerd into remembrance by a chance event. All of these things, memories that you are avare of having, and those you are not avare of having, are part of what make you who you are, part of what has made you who you are. Therefore, in order for a record to be the very same personality it will have to contain it all, ellse it will not be the same. Agreed, but it might surprise you to hear me say it! I think what we need is some clarification of what I am saying and not saying. Kurzweil is talking about a complete silicon brain and life in a complete simulation. This will become possible in the fullness of time although it is not an objective I have talked about very much. It is a far furure objective. Kurzweil is one of these people who you would like to do a PhD with. He is chalenging, but you would not want to live at his pace for ever. No I think we can divide AI into the following categories. 1) Complete Kurzweil simulation. 2) Complete motor simulation. 3) Turing, including high order debating skill. 4) Interstellar AI requirements. I have discussed "1". I agree with you completely. I do not know why "2" is even discussed. Well failed astronauts don't want to face the truth. If you have a dynamical system and the laws of Physics it is predicatable. If we know the effects of motor stimulation we can make an optimal path, quite simply in the majority of cases. "3" Turing. This is interesting. I feel before we go any further we ought to know a little bit about how chatterboxes work. Eliza was brought forward as a psycotherapist. All she did was remember the inputs thast the user had made and select the most appropirate response from a database. Remember Eliza has no reasoning ability of her own, neither does any chatterbox. If I am debating with you there are a limited number of appropiate responses to the subject. If I have a large database I can cover those responses. So in fact Turing = Bueno espagnol. For both we need essentially the same thing, an accurate vector describing context. If you have been reading my previous postings you will see that I have given AI a role in combating terrorism and also in "hearts and minds". We need to find people who have joined, or are about to join jihadic groups and engage them in dialogue. This, as I have said, will require a large database, not a high order of reasoning ability. Similarly we can form Erdos type graphs. Again if we have a database, that database is capable of finding all the relationships it can understand. In the Middle East the greatest problem is getting high quality information though uncensored. This is why I advocate the conformal array. I have now thought of a design which is attractive in that it cal be scaled up and a large number of conformal arrays added. I have also thought of a low emission - could not be seen by detector vans version which would be based on doing superhet on a shielded chip, and setting a high frequency by means of a set of lower frequencies. The setting of a frequency would be based on prime number theory. I will tell you my thoughts later. What is required for an interstellar trip. First of all it is in the far future, or possibly not that far in geological terms. A probe wil need to operate autonomously. If our large telescope tells us there is a possibility of intelligent life it will need to have language learing ability. The Hittite language was decoded with one phrase. :- "Now you can eat bread and drink water". There is a method of doing this. - Ian Parker Mind you, if they ever do perfect a nondestructive method of recording a personality, especially if done within my lifetime, I wouldnīt mind hedging my options and create a copy of myself. Who knows, perhaps then one would excist among the living and among the dead presuming ther is such a thing an exchistence beyond death. An alternative might be if means of talking independent of distance were discovered, perhaps quantum entanglement can lead to that outcome. In such a case the ship might be in constant realtime contact with home at all times. Cheers, Einar |
#34
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Missing sial, iron, and nickel explains Fermi paradox
In article . com,
Einar wrote: Mind you, if they ever do perfect a nondestructive method of recording a personality, especially if done within my lifetime, I wouldnīt mind hedging my options and create a copy of myself. Who knows, perhaps then one would excist among the living and among the dead presuming ther is such a thing an exchistence beyond death. I doubt nondestructive scanning at the resolution needed will ever be possible, but here's a way to achieve the same thing, at least with a bit of luck: put off the uploading until your biological body has already failed. At that point, you have nothing to lose. Note that you can arrange for this possibility even before uploading is developed, by having yourself frozen upon your death (a practice known as cryonics). Once frozen, your condition is stable, and there's a chance that you can be uploaded and revived at some point in the future. An alternative might be if means of talking independent of distance were discovered, perhaps quantum entanglement can lead to that outcome. In such a case the ship might be in constant realtime contact with home at all times. As I understand it, there are pretty strong theoretical grounds to hold that such FTL communication is impossible. Or at least, if it is possible, then it can be used for a number of other seemingly-impossible things, like sending information back in time. Best, - Joe -- "Polywell" fusion -- an approach to nuclear fusion that might actually work. Learn more and discuss via: http://www.strout.net/info/science/polywell/ |
#35
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Missing sial, iron, and nickel explains Fermi paradox
Ian Parker wrote: On 31 Jul, 20:25, Joe Strout wrote: In article .com, Ian Parker wrote: No, I think it will be nornal. Probably if we are the first civilzation the gap will be of the order of a million years, or at least 100,000. However you can't be absolutely sure. You can be very extremely darn close to sure. In a normal distribution, the spacing between the outliers is quite large (as compared to those near the mean, which of course is rather small). What "large" means depends on the standard deviation, but in the case of time-to-civilization, any reasonable model will result in a standard deviation of hundreds of millions of years, if not billions. In that case, the spacing between the two most extreme outliers at one end of the distribution being a mere 100 KY is quite unlikely. Millions or billions is more likely. The model I was thinking about at the back of my mind was the radioactive atom. It is not impossible that there could be another civilization close to ours. Unlikely perhaps, but just possible. Right. Not sure what radioactive atoms have to do with it, but of course we can only speak of probabilities. The probability you bring up here is very, very small. In my discussions on ET I have sought to eliminate the impossible. NOT the improbable. Well, great, but that doesn't help much. It's not impossible that we're all just figments of the God computer's imagination, which will be shut off next week. It's not impossible that the our solar system is inside a vast shell 1 LY across, built by aliens, which serves as a giant 3D display, and eventually the Pioneer and Voyager probes are going to go splat against it. It's not impossible that there is some way we can't yet fathom for advanced races to leave the universe of their birth and get an entire universe to themselves, thus explaining the apparent emptiness we see. But, most of those we can't even assign probabilities too. This one we can, and it works out to a very small number. (No, I don't have a number handy; it's been a while since I actually did the math.) Why focus on such an unlikely situation, when there are far more likely ones that fit the observations just as well? (Namely, that we're the first, and our closest competitors are millions of years ahead or behind us.) I am saying that with a large number competition is more intense and there might be one near us. We of course don't know. For all we know Earth could be rare. It really doesn't matter how many there are; competition won't be more intense in any case, since all that matters is the first couple of outliers. If there are many participants, then the outliers will be more extreme, and thus more spread out. If there are few (i.e. life is rare), then the outliers won't be as extreme, but they'll still be spread out. I feel I'm explaining this poorly... where's a statistician when you need one? I will agree that an ET at our level is improbable but not impossible. Indeed. I believe that well within 50 years we will have a full space capable Von Neumann machine. An interstellar probe may well be closer than we imagine. Unmanned of course. Perhaps. I believe that within 50 years, we'll have mind uploading. (Ray Kurzweil puts it at more like 20 years, but I am a pessimist.) If you and I are both right, then those "unmanned" probes may well have people on board, albeit in digital form. That is an interesting thought. I have a philosophical point here. Suppose we split our brains. One bit went to Alpha Centuri. The other bit went around here on Earth. Could you put those two memories together? Could two separate memories be knitted together? We could of course simply back ourselves up when we were about to do anything dangerous. A civilization a million years in advance of us, I repeat, is an impossiblility. We would know about it. Unless they are intentionally hiding from us. In that case, I have no doubt that they could do so successfully, and our crude efforts to detect them would be futile. But I tend to feel that this is unlikely. More likely, there's simply nobody out there, and won't be anyone else for millions of years. When those late-comers finally arise, they'll awaken to a galaxy long since settled by us and our descendants. Agreed. What I have in mind for the medium future is in fact the large fragmented telescope. Justification - Finding out for sure. I think Einar is right. If we do not advance it we do not have curiosity we are indeed doomed. This is not to say that manned space flight is the best strategy, or that we need to think of colonies in the solar system in the medium term. In the medium term, and possibly even the short term, we need to think about improving automation techniques with an eventual VN aspiration. I don't agree. VN machines are certainly possible, but I hope they're a long way off, and carefully regulated. If ever there was a technology ripe for disaster, that's it. I see very little benefit to justify the risk. Are you thinking about the risk that VN machines will evolve, or that they will be deliberately misused. In terms of evolution, a Reed Soloman code will prevent evolution in that it will be inpossible for the VN genome to change. In terms of misuse, that would depend to a large degree on what the current political situation was. If you had cognitive AI you could build in Asimovs laws of robotics and put thise laws as a deeply encrypted part of the genome. It would not be infallible as once the knowledge of how to build a VN machine became known one would not be dependent on one machine. I think I will agree though. We would need a world that was on the whole peaceful. BTW - I believe we will get VN machines a long time before brain downloading. In fact I would probably give that 20 years. What you basically need for VN is a flatpack assembler. It is downhill after that. - Ian Parker Hmm, if a way might be found to make those split brains operate like a one. I have a different dream, namelly communication independent of distance, taking no time. Maybe, quantum computers could operate in this fashion, i.e. components being separated by lightyears, communicating through quantum entanglement. Cheers, Einar |
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Missing sial, iron, and nickel explains Fermi paradox
Joe Strout wrote: In article . com, Einar wrote: Mind you, if they ever do perfect a nondestructive method of recording a personality, especially if done within my lifetime, I wouldnīt mind hedging my options and create a copy of myself. Who knows, perhaps then one would excist among the living and among the dead presuming ther is such a thing an exchistence beyond death. I doubt nondestructive scanning at the resolution needed will ever be possible, but here's a way to achieve the same thing, at least with a bit of luck: put off the uploading until your biological body has already failed. At that point, you have nothing to lose. Note that you can arrange for this possibility even before uploading is developed, by having yourself frozen upon your death (a practice known as cryonics). Once frozen, your condition is stable, and there's a chance that you can be uploaded and revived at some point in the future. An alternative might be if means of talking independent of distance were discovered, perhaps quantum entanglement can lead to that outcome. In such a case the ship might be in constant realtime contact with home at all times. As I understand it, there are pretty strong theoretical grounds to hold that such FTL communication is impossible. Or at least, if it is possible, then it can be used for a number of other seemingly-impossible things, like sending information back in time. Best, - Joe -- "Polywell" fusion -- an approach to nuclear fusion that might actually work. Learn more and discuss via: http://www.strout.net/info/science/polywell/ If one can be frosen without harming whatīs to be recorded. Cheers, Einar |
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Missing sial, iron, and nickel explains Fermi paradox
Somehow I am missing the connection to the paradox. It appears to lie solely in
the assumption that if there is no moon event the planet will be all ocean. That does not compute unless we can explain the disappearance of the moon of Venus. If Venus had had the same amount of water as earth, and there is little way to explain a significantly different amount, there should be enough water vapor in its atmosphere to 9000psi (600 At.) of pressure on the surface. But last I heard there is negligible water in the atmosphere and clearly no such pressure. We have no idea if there is a minimum amount of ocean needed to approximate an ecology like our own however it appears reasonable that all else being equal the amount of rainfall is proportional to the evaporative surface of the oceans. It also follows as a reasonable assumption (but which cannot be supported in the least, that the more life the faster evolution but we are not in a rush so a few extra billion years does not matter. However surface area only would be a factor in rainfall. Depth would not be. So without a moon and nothing lost there is nothing prohibiting large and shallow seas. The South China Sea with a depth averaging over a few hundred feet has all the characteristics of any other ocean save it is warming at all depths. This would speed evolution among the cold bloods. Tectonic forces would still raise mountains and and volcanoes broad expanses like the Deccan Plains. As long as the planet is large enough there is no reason to suggest plates would not form and move. The only different would be the longevity of the created land above the surface. Given Earth we find old and new mountains in proximity such as in the US so we can expect there would always be dry land. So maybe a world with shallow seas needs also have greater tectonic activity requiring a somewhat more massive planet and the world average being more like Japan. So maybe the funny thing about ET is if the ground shakes he curls into a ball. Am I missing something? -- An entire cool summer is trumped by a warm day in January if you are a global melter. -- The Iron Webmaster, 3836 nizkor http://www.giwersworld.org/nizkook/nizkook.phtml Mission Accomplished http://www.giwersworld.org/opinion/mission.phtml a12 |
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Missing sial, iron, and nickel explains Fermi paradox
Matt Giwer wrote: Somehow I am missing the connection to the paradox. It appears to lie solely in the assumption that if there is no moon event the planet will be all ocean. That does not compute unless we can explain the disappearance of the moon of Venus. If Venus had had the same amount of water as earth, and there is little way to explain a significantly different amount, there should be enough water vapor in its atmosphere to 9000psi (600 At.) of pressure on the surface. But last I heard there is negligible water in the atmosphere and clearly no such pressure. We have no idea if there is a minimum amount of ocean needed to approximate an ecology like our own however it appears reasonable that all else being equal the amount of rainfall is proportional to the evaporative surface of the oceans. It also follows as a reasonable assumption (but which cannot be supported in the least, that the more life the faster evolution but we are not in a rush so a few extra billion years does not matter. However surface area only would be a factor in rainfall. Depth would not be. So without a moon and nothing lost there is nothing prohibiting large and shallow seas. The South China Sea with a depth averaging over a few hundred feet has all the characteristics of any other ocean save it is warming at all depths. This would speed evolution among the cold bloods. Tectonic forces would still raise mountains and and volcanoes broad expanses like the Deccan Plains. As long as the planet is large enough there is no reason to suggest plates would not form and move. The only different would be the longevity of the created land above the surface. Given Earth we find old and new mountains in proximity such as in the US so we can expect there would always be dry land. So maybe a world with shallow seas needs also have greater tectonic activity requiring a somewhat more massive planet and the world average being more like Japan. So maybe the funny thing about ET is if the ground shakes he curls into a ball. Am I missing something? -- An entire cool summer is trumped by a warm day in January if you are a global melter. -- The Iron Webmaster, 3836 nizkor http://www.giwersworld.org/nizkook/nizkook.phtml Mission Accomplished http://www.giwersworld.org/opinion/mission.phtml a12 Venus has no plate tectonics. However, it might if it had oceans. I think itīs believed Venus' oceans evaporated, once the Sun warmed up, and that the water left the planet altogether being blown away into space. What remains is possibly the most hostile to life plase in the solar system. Einar |
#39
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Missing sial, iron, and nickel explains Fermi paradox
In article ,
Matt Giwer wrote: Somehow I am missing the connection to the paradox. It appears to lie solely in the assumption that if there is no moon event the planet will be all ocean. That does not compute unless we can explain the disappearance of the moon of Venus. We can; Venus is too hot to have liquid water. But the case for the Moon being responsible for continents is made pretty convincingly in the book Rare Earth. IIRC, it basically goes like this: without the impact event that blasted much of the Earth's crust into orbit (forming the Moon), our crust would be too thick to support plate tectonics (just like Venus, I think). So they would end up a very uniform thickness, and the only mountains that would form would be from volcanoes, and these would quickly be eroded back down, leaving a uniform planet-spanning ocean. It's only because our crust is so thin that we can have tectonics and enough variation to produce continents and oceans. Hm. I'm not explaining this very well, but check out the book, it spends a chapter or two on this topic. Best, - Joe -- "Polywell" fusion -- an approach to nuclear fusion that might actually work. Learn more and discuss via: http://www.strout.net/info/science/polywell/ |
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Missing sial, iron, and nickel explains Fermi paradox
On Aug 2, 5:00 am, Einar wrote:
Matt Giwer wrote: Somehow I am missing the connection to the paradox. It appears to lie solely in the assumption that if there is no moon event the planet will be all ocean. That does not compute unless we can explain the disappearance of the moon of Venus. If Venus had had the same amount of water as earth, and there is little way to explain a significantly different amount, there should be enough water vapor in its atmosphere to 9000psi (600 At.) of pressure on the surface. But last I heard there is negligible water in the atmosphere and clearly no such pressure. We have no idea if there is a minimum amount of ocean needed to approximate an ecology like our own however it appears reasonable that all else being equal the amount of rainfall is proportional to the evaporative surface of the oceans. It also follows as a reasonable assumption (but which cannot be supported in the least, that the more life the faster evolution but we are not in a rush so a few extra billion years does not matter. However surface area only would be a factor in rainfall. Depth would not be. So without a moon and nothing lost there is nothing prohibiting large and shallow seas. The South China Sea with a depth averaging over a few hundred feet has all the characteristics of any other ocean save it is warming at all depths.. This would speed evolution among the cold bloods. Tectonic forces would still raise mountains and and volcanoes broad expanses like the Deccan Plains. As long as the planet is large enough there is no reason to suggest plates would not form and move. The only different would be the longevity of the created land above the surface. Given Earth we find old and new mountains in proximity such as in the US so we can expect there would always be dry land. So maybe a world with shallow seas needs also have greater tectonic activity requiring a somewhat more massive planet and the world average being more like Japan. So maybe the funny thing about ET is if the ground shakes he curls into a ball. Am I missing something? -- An entire cool summer is trumped by a warm day in January if you are a global melter. -- The Iron Webmaster, 3836 nizkorhttp://www.giwersworld.org/nizkook/nizkook.phtml Mission Accomplishedhttp://www.giwersworld.org/opinion/mission.phtmla12 Venus has no plate tectonics. However, it might if it had oceans. Or, if it had a nearby moon the size and mass of our moon, as most research based upon the regular laws of physics and planetology have to agree that a terrain as Venus has need a nearby moon or perhaps some other binary considerations. I think itīs believed Venus' oceans evaporated, once the Sun warmed up, and that the water left the planet altogether being blown away into space. What remains is possibly the most hostile to life plase in the solar system. Venus is a relatively newish planet to our solar system, as it losing roughly 256 times as much of its core energy as Earth. However, due to it's slow rotation, there's simply not enough solar tidal forces to cause the internal heat of Venus. Go figure otherwise. - Brad Guth |
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