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D H

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Everything posted by D H

  1. As everyone knows, 1+1+1+... = -1/2. How to deal with diverging series is a bit challenging. The easiest answer is to say that diverging series don't have a sum. After all, failing to converge to a sum is exactly what diverging means. A more complex answer is that divergent series such as 1-1+1-1+..., 1+1+1+..., 1+2+3+4+..., 1+2+4+8+... can reasonably be given an answer by means of analytic continuation. Analytic continuation is a very powerful tool. It won't just give an answer to these seemingly nonsense sums, it gives a unique answer. With this approach, the values for these series are 1/2, -1/2, -1/12, and -1, respectively. Consider the expression [imath]\frac 1{1-x}[/imath]. This expression has a value for all x except for 1. This expression can be expressed as an infinite series, [imath]\frac 1 {1-x} = 1+x+x^2+\cdot = \sum_{n=0}^{\infty} x^n[/imath] provided that the series converges. This series has a radius of convergence of 1. What if I naively plug x=-1 into both the expression and the series? The series that results is Grandi's series, and the expression says the value should be 1/2. That's the same value as that obtained by averaging and also by the neat little trick of finding that 1-S=S. Note that all of these "tricks" yield the same value, 1/2. Maybe there's more to this than just a trick. That's just what Hardy saw in his book Divergent Series. The reason all of these tricks yield the same answer is because of some deep properties of analytic continuation.
  2. That's not necessarily true. The old wives' tale that it is possible to get sunburnt on a cloudy day has a strong basis in fact. Clouds are opaque to visible light. Much less so to UV. There are occasions where ultraviolet radiation under cloudy conditions can exceed clear sky values. Google "broken cloud effect" and "cloud enhancement of UV" for more.
  3. There are a number of variations on this theme. Roland Omnès' physism, V. I. Arnold's notion that Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap. I suspect that Arnold would have vehemently disagreed with Tegemark. Arnold most certainly decried the non-physical mathematics that was becoming vogue at the time he wrote his remarks. It's also good to note that Eugene Wigner's "unreasonable effectiveness of mathematics in the natural sciences" does not apply to all of the sciences. I. M. Gelfand's counter to Wigner's unreasonable effectiveness was that Eugene Wigner wrote a famous essay on the unreasonable effectiveness of mathematics in natural sciences. He meant physics, of course. There is only one thing which is more unreasonable than the unreasonable effectiveness of mathematics in physics, and this is the unreasonable ineffectiveness of mathematics in biology.
  4. There is no truth to those claims. So what explains all of that nonsense against it? Some ultra-religious people think relativity must be wrong because it clashes with their religion. Some racists think that relativity must be wrong because a Jewish man came up with it. Some crackpots think that "if only I disprove relativity I will be more famous than Einstein".
  5. I knew quite budding mathematicians who went into that field precisely because there was no practical application for the mathematics they planned to work on. They realized they had what it takes to major in / get a PhD in either mathematics or physics. Either way, whatever they worked on would eventually lead to better bullets, better bombs, better ways to kill people. The difference was that if they went with physics those nastier applications of their work would see fruit in their lifetime. With mathematics, they could die in peace because those nastier applications would only take place after they had died. (That, plus the fact that math (to them) was easier than physics. Physics majors tended to be homework animals. Math majors: Party animals. A corollary is that obtaining a math PhD takes two to three years less time than does obtaining a physics PhD.)
  6. False. Suppose a falling object is just shy of terminal velocity. Here mgh will yield far too high a value. It's not an either/or situation. Air resistance will always reduce impact velocity (and hence impact force) to some extent. You can safely ignore air resistance only if the impact velocity is orders of magnitude smaller than terminal velocity.
  7. Twice now you have cryptically stated that NASA is not transparent. Twice now you have been challenged. You've said *nothing*. You also cryptically said "planet interiors". That's anything but clear. I asked for a simple clarification. How, exactly, are those two words at all related to the topic at hand?
  8. I did not ask you to be obtuse. I did not ask you to wax poetic. I did not ask you to insult. I simply asked you to explain what you meant. Is it that hard? BTW, it would be nice if you answered without attempting to be poetic. This is scienceforums.net. Try to use prose. Read the opening post. It's not about primitive extremophiles, which is presumably what you were addressing with your comment about a planet's interior. The question at hand is intelligent life. Here's the intro to the opening post: So, getting back on topic, our sun is a young star, about 1/3 the age of the universe. Of all the other planets that could theoretically harbor intelligent life there certainly must be some that are significantly older than is our sun. It's not just millions of years by which other stars/planets might be ahead of us. It's billions of years. So why are we here, and where are they? That's the Fermi paradox. To me, the easiest answer is that intelligent life is extremely rare. We might never talk to them, see them, see any sign that they exist.
  9. I should have prefaced what I said about carbon with "common". Boron is anything but common. It is exceedingly rare. Hydrogen is *not* a "very good" greenhouse gas. Hydrogen is a diatomic gas. The molecules in a greenhouse gas are triatomic or more. That's neither here nor there, however. Once again, suppose one of those super-Earths / sub-Neptunes that have been found did harbor life deep inside it's atmosphere. How could we possibly know? How could that life possibly be intelligent? Here I'm using intelligent to mean able to communicate with other life and able to build devices capable of escaping their planet's atmosphere. A hydrogen atmosphere would be particularly problematic for life. If such a planet did harbor life, how could that life be anything but extremely primitive? Certainly there's no photosynthesis. Oxidizers and hydrogen don't go mix all that nicely. Disagree with what? That we ourselves wouldn't have been able to go into space if Earth gravity had been slightly higher? That's a simple fact of the limits of chemical propulsion. We're lucky that outer space is within our grasp via chemical propulsion. That Kepler's ultimate goal isn't to find terrestrial planets? Those exoplanets larger than Earth-sized are freebies. The ultimate goal, however, is to find Earth-like planets. What, exactly, are you saying about planet interiors? How, exactly, are we going to look at the interior of any planet other than our own? What, exactly, is this supposed to mean? You've spouted this nonsense multiple times before.
  10. D H

    voting

    My first thought on seeing that was ... Arbuckle Mountains! Here's a gorgeous panoramic view of Ardmore, Oklahoma which lies but 16 kilometers from the Arbuckle Mountains: Gorgeous! Here's a beautiful mountain lake in the foothills of the Arbuckle Mountains: I vote for flat.
  11. The density and temperature never get high enough in small stars to trigger the fusion reactions that result in iron. It's not even close. Fusion will never progress beyond hydrogen forming helium in stars half the size of our Sun and smaller. The density and temperature needed for helium burning does not occur in those small stars. Our Sun will eventually make the step up to helium burning once it has consumed all the hydrogen in the core. Fusion in our Sun will stop there. Each step up the ladder requires ever greater density and temperature, but each step up the ladder produces progressively less energy. It's only the very massive stars that can make the step up to burning nickel plus helium to form zinc. That final step is a star killer because it is endothermic rather than exothermic.
  12. It's not just humans. It's all of life as we know it. Admittedly that's reasoning from a sample of one, but there are good solid reasons to think that that line of reasoning is valid. Let's start with chemistry. Imagining non-carbon life is a favorite theme amongst science fiction authors. It's inevitably poorly done. Carbon is a very unique element. There's nothing quite like it. Not even close. Imagining non-water based life is another favorite sci fi theme. Water is a rather unique compound. Once again there's nothing quite like it. The analogs are near as universal a solvent as is water, and they are liquid at significantly lower temperatures. Those lower temperatures create a big problem with those water analogs. Everything proceeds at a slower pace. It took evolution more than half of the available time during which Earth will be hospitable to life to produce intelligent life. Even if those water analogs somehow are hospitable to life, the significantly slower chemistry means intelligent life has a vastly reduced chance of arising. Finally, suppose that contrary to the above lines of reasoning, there is some form of life that doesn't rely on carbon/water chemistry. What would we look for? How could we know that it was life if we were staring it straight in the face, let alone dozens of light years or more away? The answer is we couldn't. Next thing is, why a terrestrial planet? Once again, one simple reason is that we don't know how to look elsewhere. Suppose simple life exists somewhere deep within Jupiter's thick atmosphere. That life will be hidden from us for a long, long time, and that life is forever doomed to remain primitive. Another reason is that ultimately we are looking to find intelligent life or to find a place where humans might eventually go. Intelligent life here means life with which we can communicate, remotely. That hypothesized life deep within Jupiter is doomed to be primitive forever. The same would go for life on Venus. We're looking for a planet with a surface gravity that isn't much more than Earth gravity; we ourselves wouldn't have been able to go into space if Earth gravity had been slightly higher. We're looking for a planet that has a transparent atmosphere. Would we have looked to the stars if we couldn't see the stars? We're looking for a planet that is hospitable to life based on carbon, hydrogen, oxygen, and nitrogen. All of these say to look for terrestrial planets that are very close to Earth.
  13. None whatsoever. I would say it's just the opposite. Our Sun is a fairly young star. Somewhere out in the universe there surely is, or was, an intelligent species that arose before our own Sun was even born. However, ... I disagree. From my own rare Earth point of view, I would find it quite incredible if intelligent life did exist somewhere else in the Milky Way. Note well: I said rare Earth, not unique Earth. To think that we are the sole intelligent life form in the universe is, to me, a ludicrous proposition. To think that we are essentially alone in the universe is not so ludicrous. Suppose there are a million or so truly Earth-like planets in our galaxy, but suppose the odds of intelligent life arising on a truly Earth-like planet is a one in a billion chance. That means that not only are we the sole intelligent life form in our galaxy, we are most likely the sole intelligent life form in our galactic cluster. These low odds would still mean that there are hundreds of millions of other intelligent forms in the universe. It would also mean that each and every one of those civilizations is essentially alone in the universe. By essentially alone I mean that we will never communicate with one of those other intelligent life forms even though there are hundreds of millions or more of them out there. That intelligent life is extremely rare is, to me, the easiest answer to the Fermi paradox. We can't see ET and ET hasn't been here because the nearest ET is so ridiculously far away that communications and travel are impossible. You didn't say so, so I will. Those claims are pure nonsense. Locally, electromagnetic signals fall off in intensity inversely proportional to distance from the source. That alone will make any signal eventually become undetectable. Further afield there's interstellar / intergalactic dust that can obscure the source. Even further afield, there's the huge problem of the expansion of the universe. Unless an intelligent species somehow learned to harness the broadcast power of an active galactic nucleus, the redshift and consequent reduction intensity that results from expansion will hide even the most powerful of signals. Here's what SETI itself has to say on this issue (http://www.seti.org/faq#obs12): If an extraterrestrial civilization has a SETI project similar to our own, could they detect signals from Earth? In general, no. Most earthly transmissions are too weak to be found by equipment similar to ours at the distance of even the nearest star. But there are some important exceptions. High-powered radars and the Arecibo broadcast of 1974 (which lasted for only three minutes) could be detected at distances of tens to hundreds of light-years with a setup similar to our best SETI experiments. Exactly. We are doing statistic inference from a sample point of one, something that is always a bit dangerous. While I am of the personal opinion that intelligent life is extremely rare, that is just an opinion. The true answer is that we just don't know (but knowing one way or the other is a worthy pursuit).
  14. You are correct. Bogus. Concussion rates are not increasing. It's the reported concussion rate that is increasing. That concussion rates suddenly and dramatically started rising across all sports all at the same time is a ludicrous proposition. What happened is that increased scrutiny has forced coaches et al to switch to calling an ambulance in response to Johnny having had his bell instead of saying "Shake it off, Johnny. Grab some water and I'll put you back in the game in a few minutes." This increase in the reported number of concussions is a good thing, not a bad thing. It means that there is greater awareness of the problem amongst coaches, sports administrators, parents, and participants. It means that participants who suffer concussions are more likely to receive immediate and appropriate care from a trained physician, and are less likely to be sent back onto the field of play to receive yet another concussion in the same game. Those are exactly the same bogus stats you reported earlier. Look at where the authors got those numbers and where that other article got its numbers. Those authors did not perform a study. They instead relied on the exact same study, Marar M, McIlvain NM, Fields SK, Comstock RD. Epidemiology of Concussions Among United States High School Athletes in 20 Sports. Am J Sports Med 2012;40(4):747-755. Depending on what you mean by "younger," I agree completely. That is exactly what I said in the closing paragraph of post #2.
  15. This is a take home final exam. Do not offer help. Outside help almost certainly is not allowed.
  16. If this nonsense was supposed to be an argument against that global warming, nope, it didn't work. If it was an attempt to move the goal posts, that didn't work, either. If it was an attempt at humor, that too didn't work. If it was an attempt to show that you have a lousy command of the English language, yep, that worked.
  17. Not necessarily. Which meal is "dinner" depends on where you live, what you do, and how you were raised. It's not "rotting English". It's that English has never been standardized. Here's a good one: Doubt. "I have doubts about special relativity" takes on completely different meanings depending on the nationality of the speaker.
  18. City people eat lunch and dinner (or lunch and supper); the distinction between dinner and supper is either non-existent or is a matter which is more formal. A big midday meal would lead to people falling asleep at their desks. Country people eat dinner and supper. People whose workday starts at 4 or 5 AM need that big boost of energy that comes from a large midday dinner. Except Sunday dinner. That's oftentimes a midday / afternoon meal across the US.
  19. A certain segment of the US population is ignorant (intentionally so), stupid, and easily duped. This segment: White evangelical Christians. This is the group that feels most threatened by science and is most likely to reject science. They reject biology, geology, astronomy, and climatology, all because those sciences conflict with their faith. Because of their intentional ignorance and irrational beliefs, they are easily duped, and they are being duped by two key groups. One group is those industries that have a lot to lose should climate change legislation be passed. They are spending lots of money to battle this legislation. The other group is the far right conservative movement. They have lots to gain if they can create a boogeyman to be feared and voted against. They've done this with immigrants, with the word "liberal", with environmentalists, and with climate scientists. Remove those white evangelical Christians from the mix and US views on the existence and cause of global warming isn't that far removed from views elsewhere.
  20. You're right. It wasn't time dilation. You were calculating nonsense. You had a week off. Why in the world didn't you use that time constructively to read up on what the Andromeda paradox is all about?
  21. Bzzzt, wrong. You are computing time dilation, not the Lorentz transformation. Try again.
  22. Of course they had an influence. So did India and China, ancient Greece and Rome, even Babylonia and Egypt. A true history of mathematics and science goes back a long ways. It's a story of stuff learned and forgotten but then relearned or found. The scientific revolution, however, happened but once, and it started in western Europe. Not anywhere else. By the way, it's still an act in progress. Just look at the number of people who still reject key tenets of biology, geology, and astronomy.
  23. Nonsense. You wrote it, it has your biases impregnated throughout. Keep posting all you want. I'm done with this.
  24. You have to watch out for historical revisionism in wikipedia. It's quite rampant. There's no mention of pre-science in India, China, Greece, Babylonia, Mesoamerica, or Inca civilization. Pre-science, to me, is a better name for anything prior to Galileo, and that includes Copernicus. The scientific method started when pre-science started to detach itself from religion. The real origin of the scientific method is rejection of religious and mystical nonsense. That is why the scientific method didn't arise in Persia, India, Babylonia, Mesoamerica, or the Inca civilization. The Islamic Golden Age ended well before the Renaissance started. They had a two or three century head start, and they blew it. Science did not mix well with extreme Islam. The Islamic Golden Age occurred precisely when Islam was more tolerant of new ideas than it is now. It ended with the rise of Islamic mysticism, intolerance, and extremism. It's really hard to say that the scientific method arose because of Islam when it was the religion that killed those early efforts at science.
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