D H

From one extreme to another, We shouldn't terraform Mars no matter what, even if it's sterile. If Mars has life, we shouldn't terraform Mars, doubly so if the life is non-terrestrial in nature. Variants: If Mars has life, we should leave Mars alone. Period. If Mars has life, we should study it but only with unmanned probes that are completely and thoroughly sterilized multiple times during the fabrication process and a few more times on the way to Mars. If Mars has life, it is obviously in trouble. We should aeroform Mars (make it more suitable for Mars life). If Mars has life, limited human missions to Mars are acceptable if we take extreme cautions to ensure that we don't introduce any terrestrial life to Mars. [*]If Mars has life, we can still terraform Mars, but we should make little enclaves for those obviously dwindling remnants of Mars life. If doing so doesn't cost too much. [*]If Mars has life, we should commit xenocide. Some reading material: "Ethics of terraformation" http://library.thinkquest.org/C003763/index.php?page=terraform02 A summary article. Use this to get a flavor of the debate. From the article, "The vast majority of Mars scientists and planetary biologists belong to the 'Green' camp in that they believe that Mars should be made 'green'. They have several impressive arguments in their arsenal. ... The 'Red' camp, in the minority, is adamantly opposed to the terraformation of Mars. 'Reds' believe that humans have no right to essentially destroy the current face of Mars just for our own concerns, and that we should preserve it in its current state so that we might conduct scientific experiments and learn more about the planet." David Grinspoon, "Is Mars Ours? The logistics and ethics of colonizing the red planet", Slate, 2004. http://www.slate.com/id/2093579/ Dr. Grinspoon is the Curator of Astrobiology at the Denver Museum of Nature & Science and has served on multiple NASA and ESA interplanetary science teams. From the article, "But before we go there and set up greenhouses, dance clubs, and falafel stands, let's make sure that, in some subtle form that could be harmed by the human hubbub, life does not already exist there." Dave Brody, "Terraforming: Human Destiny or Hubris?", adAstra Online http://www.space.com/adastra/adastra_terraforming_brody-1.html Summarizes the debate between Chris McKay, astrogeophysicist at NASA Ames and Bob Zubrin, President of the Mars Society. Zubrin ranks as a high 3 on my scale. McKay, 2c. "Ethics of terraforming", redcolony.com http://www.redcolony.com/art.php?id=0107290 This article does a semi-decent job of presenting both sides given that redcolony.com is a rabidly pro-terraforming site. "Ethics of terraforming", Wikipiedia http://en.wikipedia.org/wiki/Ethics_of_terraforming Listed only because Wikipedia has an article on everything.

http://www.purplemath.com/modules/nextnumb2.htm Let me know if that answers your questions.

I agree with ajb. Finding life on Mars will tell us that life is very tenacious and might tell us that life is likely to form in star systems that are somehow pre-conditioned for life. Actually, I think life on Earth already tells us the latter. Life (primitive life) arose on Earth very soon after Earth became suitable for life. To say that life is common in the universe we will need to find signs of life in some other star system. stuff[/hr]A couple of other random thoughts 1. If we found that Mars life is based on left-handed organic molecules that would be interesting and rather telling. 2. Finding life on Mars would almost certainly put the kibosh on Mars Society's grandiose plans for colonizing/terraforming Mars. Heck, it would probably put the kibosh on NASA's long-term plans for human visitations to Mars.

Brain size isn't everything. Chimps have much better short term memory than humans. The gift of gab apparently was not free. Something happened to us 70,000 or so years ago. Tools changed very slowly until then. Art was a bunch of hand smudges until then. Tools and art suddenly began changing rapidly and became much more sophisticated. I think that "something" was language. Whether that was genetic (foxp2 or some unknown genetic marker for language; the jury is still out on foxp2 in Neanderthal) or lamarkian (language follows lamarkian evolution), I don't know and it doesn't matter. We began thinking much more abstractly than every before. Growing geometrically from 15,000 to 1 million in 60,000 years is a very strong growth rate.

The first problem is what constitutes genius. Humanity appears to have gone through a population bottleneck 70,000 years ago or so that more or less coincides with the appearance of Y-chromosomal Adam and with the explosion of Mt. Toba. Population bottlenecks are a ripe time for punctuated equilibrium events. Humanity went through the Upper Paleolithic Revolution around the time of this time. You made your speculation: I'll make mine. Something happened to our brains 70,000 years ago. The genius of archaic homo sap may well have been today's town idiot. They invented a rudimentary proto-language, the atl, some advanced stone tools, and maybe domesticated the dog. That population bottleneck represents a second problem: population level. It was not constant. It took 60,000 years after that bottleneck for the population to grow geometrically from 15,000 or so to 1 million 10,000 years ago at the onset of agriculture. Moreover, that 1 million per generation is off by a factor of about 2. People who survived infancy lived longer than 20 years. So, rather than your 9.5 million geniuses between the onset of humanity and the invention of agriculture (190,000 years / 20 years/generation * 1 million people/generation * 1 genius / 1000 people), I get about 400,000. Now comes the third problem: Those 400,000 geniuses were spread out over a 60,000 year interval. Even with most of them living in the last 10,000 years before the development of agriculture, that's far too few geniuses for any. Each was alone. Agriculture, art, pottery, bows and arrows, writing: All were invented, reinvented, and re-reinvented at different times by different peoples. There was very little communication between civilizations, so the few geniuses around had no giant shoulders on which to stand.

Since you "you'd get a double right circular cone with it's tip missing" (better: a right frustum of a right circular cone), I am going to assume that a. The planes containing the circle and the polygon are parallel. b. The line connecting the centers of the circle and polygon is perpendicular to the circle and polygon. You haven't adequately defined the shape. So, let me take a hack at defining it for you. The definition is constructive. 0. Label the vertices of your n-gon. 1. Circumscribe a regular n-gon around the circle, label these vertices, and orient this new polygon so that corresponding vertices of the original n-gon and the circumscribed n-gon "line up" (i.e., lines connecting corresponding vertices are either parallel to one another or meet at a point). Note that this new n-gon will have a radius of [math]r_n = r_1/\cos(\pi/n)[/math]. 2. Develop a function [math]f(x)[/math] with [math]f(0)=0[/math], [math]f(d)=1[/math], and [math]0<f(x)<1[/math] for all intermediate values of x. The linear mapping [math]f(x)=x/d[/math] will do nicely. 3. Construct n-gons parallel to and co-aligned with the two end n-gons along the line segment connecting the two end n-gons. These n-gons will change in size from that of the original n-gon to that of the circumscribed n-gon according to the distance [math]x[/math] between the centers of the original and intermediate n-gons: [math]r_p(x) = r_2 - f(x)\cdot(r_2-r_n)[/math]. 4. For each of these intermediate n-gons, construct a circle with radius of [math]r_c(x) = f(x)*r_1[/math] inside the intermediate n-gon. This circle will have a radius of [math]r_c(x) = f(x)*r_1[/math]. Use this circle to round the vertices of the intermediate n-gon. 6. Note that the original n-gon is not changed and the new n-gon becomes the circle. At intermediate points you will get ever more rounded polygons the closer you get to the circle. With this, you should be able to compute the perimeter of each rounded n-gon as a function of distance from the original n-gon. From there calculating the surface area or volume is simple calculus.

This paper at arXiv, http://arxiv.org/abs/astro-ph/0508591v3 is quite relevant to the topic at hand.

How would resurrecting Neanderthal be any different from the experiments performed at Auschwitz, Unit 731, Laboratory 12, Camp 22, and Tuskegee, just to name a few? The tenants of the Nuremberg Code (http://ohsr.od.nih.gov/guidelines/nuremberg.html) are 1. The voluntary consent of the human subject is absolutely essential. This means that the person involved should have legal capacity to give consent; should be so situated as to be able to exercise free power of choice, without the intervention of any element of force, fraud, deceit, duress, over-reaching, or other ulterior form of constraint or coercion; and should have sufficient knowledge and comprehension of the elements of the subject matter involved as to enable him to make an understanding and enlightened decision. This latter element requires that before the acceptance of an affirmative decision by the experimental subject there should be made known to him the nature, duration, and purpose of the experiment; the method and means by which it is to be conducted; all inconveniences and hazards reasonable to be expected; and the effects upon his health or person which may possibly come from his participation in the experiment. If Neanderthals were sapient, they deserve to be treated as humans. Item 1 of the Code cannot be followed for the simple reason that there are no Neanderthals around to give consent. The only way we can ethically resurrect Neanderthal is to pre-ordain them as animals and therefore not subject to rules against unethical human experimentation. 2. The experiment should be such as to yield fruitful results for the good of society, unprocurable by other methods or means of study, and not random and unnecessary in nature. Those have advocated resurrecting Neanderthals have done so on the grounds that they will be a tremendous zoo exhibit (post #3), that it will make humans "feel good" (post #5), or that it will show that humans arose through evolution (post #7). In short, resurrecting Neanderthals will make for a great freak show. A great freak show is random, capricious, and is not for the good of society. 4. The experiment should be so conducted as to avoid all unnecessary physical and mental suffering and injury. We would not be able to resurrect Neanderthals' society (that is lost forever). They would be alone amongst the very creatures who most likely killed them off the first time around. To rub their noses in it, I am sure we would tell the resurrected Neanderthals that we are very sorry our ancestors killed them off. While doing so might make homo sapiens sapiens feel better, I doubt it will make the resurrected homo neanderthalis feel good. 9. During the course of the experiment the human subject should be at liberty to bring the experiment to an end if he has reached the physical or mental state where continuation of the experiment seems to him to be impossible. 10. During the course of the experiment the scientist in charge must be prepared to terminate the experiment at any stage, if he has probable cause to believe, in the exercise of the good faith, superior skill and careful judgment required of him that a continuation of the experiment is likely to result in injury, disability, or death to the experimental subject. Suppose the resurrected Neanderthals find they cannot live with the knowledge that our ancestors drove their ancestors into extinction. The only way to bring the experiment to an end will be to drive Neanderthal into extinction a second time around. There is no way to ethically terminate the experiment.

I find the idea incredibly and completely repugnant. Why resurrect Neanderthal? So we can poke it, prod it, perform experiments on it, determine whether they could speak? (See http://www.slate.com/id/2205310/?GT1=38001.) I see no difference between resurrecting Neanderthals for scientific experimentation of any kind from the efforts of Drs. Josef Mengele and Taliaferro Clark. So we could put it in a zoo? (See the previous post.) Caging a creature with near-human intelligence to provide some 19th century freak show titillation is even more repugnant than poking and prodding it for pseudo scientific reasons. So we can rub our noses in our own "speciesism"? (See http://hplusbiopolitics.wordpress.com/2008/11/10/why-we-should-resurrect-neanderthal/.). This is political correctness run totally amok. So we can rub their noses in the fact that we drove them extinct 25,000 years ago or so, only to drive them to extinction again after we outlaw cloning of Neanderthals? We need to address these ethical issues before humanity starts down this road. Resurrecting Neanderthal would, in my opinion, violate several of the tenants of the Nuremberg code.

Earth logic is quite consistent with the relativistic velocity addition rules. [math]v = \frac {v_1+v_2}{1+v_1v_2/c^2}[/math] For [math]u,v\lll c[/math], the denominator is nearly equal to 1. Thus as velocities become small our Earthly logic rules ([math]v=v_1+v_2[/math]) become very close to correct. For small velocities, the simple addition rule overstates the relativistic addition rules by a factor of about [math]1+v_1v_2/c^2[/math]. Example: A pair of jet fighters flying straight toward one another, each traveling at Mach 1 (1225 km/hr) have a relative velocity of 2450 km/hr by the Galilean transform and by the Lorentz transform. The difference between the two is 3×10-9 km/hr: Immeasurably small.

Jupiter's atmosphere extends about 5,000 km above the 1 bar "surface" (~71,500 km at the equator). Assume the upper atmosphere is rotating at Jupiter's sidereal period, one rotation per 9.925 hours. At 76,500 km, this translates to 13.5 km/sec. Jupiter's upper atmosphere reaches temperatures of ~1200 kelvin. For protons (ionized hydrogen), this translates to a vrms of 5.5 km/sec. Adding this to the rotational velocity yields 19 km/sec, which is far less than 58 km/sec, Jovian escape velocity at 76,500 km.

Arguing semantics is all you are doing here. You are arguing about the meaning of words and the best way to word Newton's laws of motion. You are not backing up your arguments with mathematics or with logic. In short, semantics.

The above equation is very generic. It pertains, for example, to gravitation and the electrostatic force. Collisions are simply a manifestation of the electrostatic force. F=m*a is Newton's second law, not Newton's third law. One way of thinking about "F=m*a" is that it defines force (net force, actually) in terms of acceleration. The Coulomb force, F=ke*Q1*Q2/r2 is a good example of Newton's third law. That expression is the magnitude of the Coulomb force of charge 1 on charge 2 and the Coulomb force of charge 2 on charge 1. To get to Newton's third law, you have to go to the full vector form of the Coulomb force: [math]{\boldsymbol F}_1 = k_e\,\frac{Q_1Q_2}{r^2}{\hat{\boldsymbol r}}_{2\to 1}[/math] [math]{\boldsymbol F}_2 = k_e\,\frac{Q_1Q_2}{r^2}{\hat{\boldsymbol r}}_{1\to 2} = -{\boldsymbol F}_1[/math] Forces do come in pairs. Moreover, they come in equal-but-opposite pairs. Understand this and you will understand Newton's third law. When I get back to work tomorrow at NASA (I'm on vacation now) I will try to chase down this example. It is a terrible example of Newton's third law. The third law reaction to thrust is the rearward acceleration of the air flow by the plane's engines or propellers. The third law reaction to drag is the forward acceleration of the airflow by the plane's passive surfaces. Third law forces always act on different objects. Newton's first law defines the concepts of momentum and inertial reference frames. Newton's second law defines force in terms of behavior. Newton's third law says forces, whatever they are, come in equal but opposite pairs. There is no mention of inverse square laws. Good thing, that: You're wrong. Hooke's law is not an inverse square law and it too obeys Newton's third law. You would better serve yourself if you drop the attitude. It is impeding your ability to learn. The forces you encounter in the everyday world do come in equal but opposite pairs.

Sure. Given a system of N particles, the force [math]{\boldsymbol F}_{a,b}[/math] exerted by particle a on particle b and the force [math]{\boldsymbol F}_{b,a}[/math] exerted by particle b on particle a are related by [math]{\boldsymbol F}_{b,a} = -\,{\boldsymbol F}_{a,b}[/math] I just did (see the above equation). Forces that obey Newton's third law (e.g. most classical forces) always come in pairs. One way to look at Newton's third law is that forces represent interactions between pairs of objects that conserve momentum. Interactions between objects and the conservation laws are more fundamental (and more universal) than Newton's laws of motion.

PlayStationX, you are saying Newton's Third Law is wrong, and in doing so you are the one embarrassing yourself. your sentence does not make any sense, id say you are confused. "Yes, the rock pushes back on you with as much force as you push on it. ", - only if you are talking about some other rock that does not move when you push it. if it moves, then you obviously pushed it stronger: F(you)=m*a - F(stone)=m*a; if there was any movement, you can see from the formula that resisting force had to be less than applied force for it to happen. Suppose you push on a rock with some force. The rock will push back on you with a force that is equal in magnitude but opposite in direction to the force you exert on the rock. Whether or not the rock moves is irrelevant. This is completely wrong. You have a very basic and very common misunderstanding of Newton's Third Law. Third law force pairs always pertain to a pair of objects. Forces always come in pairs. Now you are sounding very much like a crackpot. You need to drop your condescending attitude, your arrogance, your misunderstandings, and your crackpot notions.

One name for the topic being discussed in this thread is regression analysis. An even broader term: numerical analysis. Just to give an idea of how broad this topic is, many colleges and universities offer a course called "Introduction to Numerical Analysis". It sounds like several of you are looking for some magical algorithm that takes in one bunch of data and says "This is a parabola with coefficients A, B, and C", takes in another bunch of data and says "this is an exponential growth curve with time constant tau". That truly would be a magical algorithm, and like unicorns, leprechauns, and flying spaghetti monsters, it doesn't exist. Real data do not come nice and pretty like (0,3), (1,9), (2,19), (3,33), (4,51). Something like (0,3.1), (1,8.9), (2,19.1), (3,233), (4,51.1) is much more realistic. A fourth-order polynomial will fit these five points exactly -- and will be exactly wrong. In general, given N+1 data pairs a Nth order polynomial will always yield a perfect fit. So why is this perfect fit almost always wrong? Suppose you have 1001 measurements at hand. I don't know of a single natural process that follows a 1000th order polynomial. The underlying process is more likely to be much simpler. Knowing what kind of equation one should fit to can be a bit of an art. Having an idea ahead of time (e.g., a scientific theory you are trying to verify) helps a lot. Going back to the data I made up: (0,3.1), (1,8.9), (2,19.1), (3,233), (4,51.1). That penultimate pair, (3,233) is completely out-of-line with the rest of the dataset. If you throw that data pair out, you will get four points that fit quite nicely to a parabola. Discarding outliers is a time-honored technique. Sensors sometimes give completely wrong readings. Lab technicians sometimes make mistakes. Suppose you redo the test at this point and get (3,32.9). That fits with the quadratic model. Throwing out valid data is not a good thing to do. Suppose you redo the test at the point in question and get (3,229). You do it again: (3,236). Now what? Measure at 2.9 and 3.1, that's what. Maybe you've discovered something important. If you had simply followed time-honored tradition you would missed something big. Many serendipitous discoveries happen just like that. This is one of the many reasons a magical equation finder cannot exist.

I would say "no", also. While our intelligence resulted from evolution, that which results from our intelligence is not. For one thing, evolution is a Darwinian process. Knowledge is Lamarkian.

You cannot feel gravity. Whether you are moving toward the Earth, around the Earth, away from the Earth is irrelevant. If the only force acting on you is gravity, you feel weightless.

The feeling of weightlessness is not to an astronaut falling with the curvature of the Earth. It arises from falling, period. After the Apollo vehicle performed its trans-lunar injection burn, the Apollo astronauts "fell" all the way from low Earth orbit to the Moon. The feeling of weightlessness arises whenever gravity is, for all practical purposes, the only force acting on a person.

Alternatively, you could do what I do: I set my alarm clock roughly 19 minutes ahead in a vain (and fruitless) attempt to overcome my procrastinating ways. Since my clock is already 19 minutes off, that extra one second error from ignoring leap seconds is irrelevant.

Now that the Obama transition team has seen the obvious (the obvious always being seen as being such after the fact), every president-elect from this point on will ask for and be granted a waiver to the rules regarding .gov sites. Heck, they probably won't need a waiver. By the time we have another new President, I suspect the GSA will have internal rules that require them to create a website for the incoming President. This is the 21st century, after all. I voted for McCain and I see absolutely nothing wrong and everything right with change.gov. Whether I voted for Obama or not is irrelevant. He is now my President and I want him to use every tool available to do the best job possible for our country.

First things first: Welcome to Science Forums! That would be me. As a member of the staff I should have both stated that the thread was being moved and given a rationale for doing so. In this case I did do the latter but did not do the former. Sorry for any confusion. I can be a bit brusque when confronted with absolute nonsense. The rules of science are somewhat relaxed (but not eliminated) in the speculations section. If there was an easy way (or even a not-so-easy way, just any way) to truly distinguish pseudoscience from speculations we would not allow pseudoscientific postings at this forum. The borderline between the two is not well-defined, hence pseudoscience and speculations.

Grouping everyone into sixteen, or twelve, or nine categories is just stupid. The correct number of groups is 42.

I like it! Merged post follows: Consecutive posts merged25 seconds later ... seconded!

That is an accurate conclusion. For more, google "hydrostatic equilibrium". The wikipedia article: http://en.wikipedia.org/wiki/Hydrostatic_equilibrium.