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Two weeks is more accurate. Because of libration (a wobbling motion) of the moon we can, over time, see about 59% of the lunar surface. Ice is confirmed in craters at the lunar south pole. The presence of this water is the primary reason this is targeted for visits and base contruction in NASA's Artemis human landing program.

There is no constantly dark or light side

This claim is not meaningless it is just plain wrong and arises from a basic misunderstanding of celestial navigation with a sextant, where the term 'arc of the sun or arc of other celestial body arises' It is not the altitude (which is the arc measured in degrees) but the plane from which is it is reckoned that changes with altitude and with altitude and other factors which have to be corrected for. This plane is called the true horizon and is not directly available to the observer so various 'observable horizons' are employed - marine navigators use the water horizon, aerial navigators use an 'artificial horizon' (yes aircraft still carry sextants for emergency navigation when the more modern electronic systems are broken). Clearly these calculations are correct since navigators do arrive at their destinations using them. The calculations and sight corrections can be quite complicated, here is a simple explanation. https://knowledgeofsea.com/correction-to-sextant-altitudes/

Since that is merely a disguised form of your (4), all you are saying is that a tensor that is antisymmetric is antisymmetric. Taking six equations to get to a tautology seems excessive, but isn't wrong. (7) still does not follow from (6). I already gave an example of a non-zero Riemann tensor that satisfies (6). All you've done is shown that a zero tensor is not inconsistent with some of the properties of the Riemann. I have no idea which comment you are referring to.

Haven't seen this type of behavior since ( video clips of ) the late 60s. Seems violent protest is the new normal for American society. This past year has seen an insurrection on the elected Government of the Country, as well as a Summer of violent protests against authority/Judicial system, while cities were taken over, and held, by unlawful protesters. D Trump just lit the fuse ( or recognized the flaw ), it can't all be blamed on him; this is uncharacteristic behavior for the American people, on both sides of the political spectrum. Does the end justify the means now? Is violence and destruction warranted when you think your cause is just ? Whatever happened to reasoning and discourse ? Has it been replaced by emotional response ? You guys better tone it down, before you actually tear your country apart ( remember 1861 ? )

Anyone wish to own up ? https://www.bbc.co.uk/news/business-55738540

@MigL Hope you don't mind, but I'm gonna take our PM exchange into the thread here (keeping your point unquoted, will share my reply here instead). We're still talking passed each other. While I said I can understand the underlying motivations, I have NOT made excuses for violence perpetrated in the name of BLM. There is violence happening as part of the movement. I don't agree with it. I'm not making excuses for it. I'm not pretending it doesn't exist. My primary point has been that the violence is the extreme outlier in BLM. It's marginal. It's super rare. It's uncommon. It's been inflated as a rightwing talking point. There has been violence. Some of it came from BLM protestors unprovoked. Some was provoked by police being too heavy handed and hitting peaceful protestors with clubs and firing tear gas into the faces of unarmed grandmothers. Some of it was rightwing extremists engaged in false flag operations. My primary point has been that it's a mistake to focus so much energy there... another example of of our white privilege. In these threads, people keep saying "it's horrible that another innocent black man was killed by another cop in another city, but destroying property has to stop." Yeah, okay... but try saying instead, "It's horrible that property is being destroyed, but these continued killings of innocent black men by police has to stop." See the difference? The pushback is saying you're prioritizing the wrong part... not that the violence is acceptable because it was done by "my team." Focusing so much on the tiny amounts of violence happening at the extreme margins of the movement distracts us from dealing with the issues motivating the movement itself. I'm not making excuses for the violence. I'm saying it's so rare that bringing up so often suggests an agenda, whether you're conscious of it or not. Please stop saying I support the violence. Please stop suggesting I'm making excuses for it. I'm simply not.

If I may comment on just this bit, our moon is tidal locked meaning that one side of the moon always faces Earth and the other side always faces away from Earth. Both sides do receive sun exposure amid this locked rotation. The "dark side" of our moon is not a reference to its level of luminosity but rather to its unobservable position relative Earth.

There has been scientific agreement that the Earth is spherical for over two thousand years. Interestingly I just found this in the Wiki: https://en.wikipedia.org/wiki/Modern_flat_Earth_beliefs#_International_Flat_Earth_Research_Society "Flat Earth Society of Canada was established on 8 November 1970 by philosopher Leo Ferrari, writer Raymond Fraser and poet Alden Nowlan;[33] and was active until 1984.[34] Its archives are held at the University of New Brunswick.[35]" (I was in New Brunswick in the class I mentioned) "Ferrari was interviewed as an "expert" in the 1990 flat Earth mockumentary In Search of the Edge by Pancake Productions (a reference to the expression "as flat as a pancake").[39] In the accompanying study guide, Ferrari is outed as a "globularist," a nonce word for someone who believes the Earth is spherical.[40] The real intent of the film, which was part-funded by the Ontario Arts Council and National Film Board of Canada,[39] was to promote schoolchildren's critical thinking and media literacy by "[attempting] to prove in convincing fashion, something everyone knew to be false."[41]" So that's my New Brunswick/Canadian take on it.

That's really interesting, because there is no evidence in history, that anyone thought the earth was flat; it's a modern phenomena.

I've mentioned this before in another Flat Earther thread, but in Junior High in the early seventies I had a history prof that was a "flat earther". He never admitted he didn't believe it, but seemed to be using it as a teaching tool to be skeptical about accepted facts. The class had fun with it. The reason he gave that a boat disappeared over the horizon was that the light was affected by gravity so the hull of the ship disappeared first then superstructure due to distance. We came up with our own reasons that "proved" the Earth was flat and argued both sides. I'm not sure why anyone takes them seriously outside of the entertainment value.

Debating with a flat earther is probably a waste of time. However, if you are going to persist, ask them to email someone in each to the Earth's two hemispheres and take a picture of the moon and send it to them. One of the pictures will be the "wrong" way up. That can't happen unless they have different ideas of which way is "up" and that requires a non-flat Earth That's very simple, it doesn't need complicated kit and he gets to choose who the Southerner and Northerner are, so he can claim that someone is lying. Another is to ask them to explain the flight times between distant cities. For example, Greenland, India, South Africa and Egypt. That takes a bit more maths.

Thanks, glad I asked, shame I don't know any, sound's like it might be quite a laugh. 😆 Off the top of my head, you could mention the test track of one of the German car maker's, it's so long and level you can't see the end, until you climb up an ordinary step ladder.

This doesn’t make any sense. The apparent motion of the sun through the sky in the course of a day is due to Earth’s rotation, not due to relative motion between Sun and Earth. So the Sun-Earth distance does not come into this at all. The issue of course is that Flat Earth rejects the notion of a rotating planet, so pointing this out will just result in hand-waving dismissal. My advice: don’t bother. I’ve been there too, and all it ever resulted in was unnecessary grief. That particular community rejects not only basic scientific observations (such as gravity e.g.), but even the very scientific method itself; there simply isn’t any common ground to base a meaningful debate on.

Let’s look very briefly at what the symmetries of Riemann actually constrain. We have two sets of symmetries - first, those that are present even in the absence of a metric: \[R{^\alpha}{_{\beta \gamma \delta}}=R{^\alpha}{_{\beta [\gamma \delta]}}\] \[R{^\alpha}{_{[\beta \gamma \delta]}=0}\] \[R{^\alpha}{_{\beta [\gamma \delta ||\mu]}}=0\] Second, we have metric-induced symmetries: \[R_{\alpha \beta \gamma \delta}=R_{[\alpha \beta]\gamma \delta}\] \[R_{\alpha \beta \gamma \delta}=R_{\gamma \delta \alpha \beta}\] \[R_{[\alpha \beta \gamma \delta]}=0\] What this means: in dimension n, every index pair can take on n(n-1)/2 independent values (due to their anti-symmetry), which initially leaves us with a symmetric matrix with \[\frac{1}{2}\left(\frac{n( n-1)}{2}\right)\left(\frac{n( n-1)}{2} +1\right) =\frac{n( n-1)\left( n^{2} -n+2\right)}{8}\] independent components. The Bianchi identities (last relation in non-metric symmetries above) constrain a further n!/(n-4)!/4! components. This finally leaves us with \[c_{n} =\frac{n^{2}\left( n^{2} -1\right)}{12}\] functionally independent components of the Riemann tensor. In n=4 dimensions, this evaluates to 20. So on a spacetime manifold with 4 dimensions, the symmetries of Riemann leave 20 tensor components unconstrained and functionally independent, meaning those components are not identically zero in the general case. Hopefully this clears things up, since it is trivially obvious that geodesic deviation does in fact exist in the real world (contrary to the OP’s claim), just like the theory says it does.

Indeed not. The cosmological model we are using (the Lambda-CDM model) is, at large scales, based on homogeneity and isotropy.

Edit: I started typing some thoughts, but I am wondering what your thoughts are, first.

Not worth it. You're trying to use reason on a person who thinks NASA (and ESA and Roscosmos and JAXA and CSNA and ISRO) are hiding the truth about the universe. Their confirmation bias would only be triggered by any scientific explanation. There's SO much fundamental misunderstanding going on with a flat Earther it would take complete reeducation to get through. Anyone who believes the Earth is flat doesn't understand gravity, or how stars and planets form.

No, and there must admittedly be some nuance involved here. Despite my strong pushback against MigL, I acknowledge my previous several posts inaccurately imply a black and white binary state on this issue of violence. Instead, it's a fine line. Apologies in advance for the long post... I'll work to tighten up my thoughts on this as we proceed... Protests against unfairness in the system should be peaceful. Calling attention to asymmetries in policing and imprisonment and economic inequity itself should nearly always be peaceful, and exceptions rare. I don't support destruction of private property or harm to individuals and neighbors. We gain allies in the fight on principle when we express ourselves peacefully and on the merits, and we lose allies when pockets of violence arise and absorb all of the attention. The violent actions of the tiny few outliers wind up overshadowing the actions of the great many. The most important messages of the cause are lost amid the shade cast by the bright light of fires in our streets and violence in our cities. We keep seeing here even at SFN as we spend page upon page upon page talking about the 4 people who set a fire in Portland or Seattle instead of the 4 Million people who did not and who were calling attention to their just cause. Simply: I'm against violence for reasons of principle, morality, AND strategy. When we see violence in things like the George Floyd protests, it tends to be conducted against innocent targets... against private property and personal businesses which have nothing whatsoever to do with the cause or the systemic issues at play. It harms those who are not involved and does nothing to improve the situation. It's not focused in a way that will drive the change we seek. It simply creates easy enemies and caricatures for simplistic attack by "the other side." This is also why we saw so many false flag operations with police and rightwing nationalists pretending to be BLM setting fires and breaking windows... so many ridiculous fear-stoking claims about the millions of antifa... they knew it would deteriorate support for the cause and distract/derail us from the more important conversation. They were right, and that's exactly what happened. Even here... Everyone should welcome protest that drives change and pushes for police accountability, but that protest should NOT involve setting cars on fire in peoples driveways or breaking the windows at the local gas station or Target supercenter. I can empathize with the anger felt by those doing these things, but I don't condone their actions. Both can be true at once, and this is the point I've been trying (and failing) to convey here throughout. Likewise... Protests against government should also be peaceful whenever possible. I don't support storming the halls of our congress with zip ties, tazers, and shouts that we should hang elected officials in the gallows just erected 100 feet away on the capitol lawn. By all means, express your protest peacefully... make the case about election fraud, and do so with evidence. Gain the hearts and minds of those who disagree with you... make your case in court... but don't engage in vigilantism or mob "justice" like a bunch of rabid dogs. You asked me about American Revolution, and I will say peaceful attempts WERE made... for decades. Even the Declaration of Independence itself was peaceful. It was only after the King sent troops in response to it that the peace was broken. One can argue that was a similar insurrection and that we'd not have a country without it. That's fair. There surely are times when violence is in order once all other peaceful options are exhausted. Peaceful options had not, however, been exhausted with BLM. The peaceful approaches were the overwhelmingly majority. The violence was marginal at best and is being exaggerated... That's the point. What constitutes an appropriate response is also contingent on how the government responds to said peaceful protest. If the defenders of an unjust government use violence to suppress peaceful protest or to imprison those with whom they disagree (like the thousands of Navalny supporters Putin just arrested in Russia this weekend, for example), then perhaps violence is needed, but it still IMO must be tied to an underlying cause which is itself just and fair and which cannot be more successfully addressed by other means. When the government seeks to suppress peaceful protestors, that is perhaps when it is time to look to the words of founders like Thomas Paine who said, "when struggling to defend rights against tyranny, it is the violence which is done and threatened to our persons which conscientiously qualifies the use of arms." ... but not before. At the end of the day, what we consider violent and acceptable is subjective. I don't advocate or support it in the vast majority of cases. There will be exceptions, though. For me, BLM was NOT one of those exceptions. I felt peaceful protest was used 99.9% of the time, and that the movement would have been better received and more effective had that 0.01% not occurred. These threads at SFN are evidence enough of this... Look at how people perceive it. Look at how I'm being misinterpreted as supporting violence because I agree with their cause. Look at how far away we all are from discussing the actual issues which needs to be addressed. For these and other reasons, I don't support violence, even though across the vast chapters in the book of history I'm sure we can find a handful of exceptions that we agree seem to warrant it. tl;dr: Civic resistance is sometimes justified, and that those who oppose injustice and tyranny are sometimes permitted violence in self-defense. To be clear, this isn’t the same as suggesting that protesters ought to resort to arms. Nor do I, and I appreciate you calling me out on it.

So in this viewpoint, there is no preferred (spatial) direction for any of the forces at play here. I was going to proceed to my follow-up question of what happens (to us) when there's no preferred direction for gravitational forces. But I'm now getting the feeling that you've already answered that. In that it's not about 'us' - it's about how mass acts on spacetime. And we're just little specks riding on that ebb and flow. Humbling thought. Thank you once again, Markus.

Oh, but that's not because it's much worse than I pointed out. It's because it's bound to get worse if you make a notational blunder of that magnitude. If you want to discuss anything in terms of a 2-index tensor being diagonal in a certain point --o perhaps everywhere?, the OP didn't tell us--, you could arrange to distinguish this by using Latin capital letters, e.g., \[A^{BB}=\frac{\partial x^{B}}{\partial\bar{x}^{\mu}}\frac{\partial x^{B}}{\partial\bar{x}^{\nu}}\bar{A}^{\mu\nu}\] Meaning, \[A^{00}=\frac{\partial x^{0}}{\partial\bar{x}^{\mu}}\frac{\partial x^{0}}{\partial\bar{x}^{\nu}}\bar{A}^{\mu\nu}\] \[A^{11}=\frac{\partial x^{1}}{\partial\bar{x}^{\mu}}\frac{\partial x^{1}}{\partial\bar{x}^{\nu}}\bar{A}^{\mu\nu}\] etc. So it can be done, but not the way the OP is doing it. Not that it's very useful to consider tensors as objects that are or aren't diagonal in any invariant geometrical sense, as they are objects referred to two different bases. Absolutely. When I'm doing maths and I get to such surprising results as "the whole of tensor algebra/calculus is bonkers, because all tensors are null" --or something like that, I'm not completely sure if that's the point--, I try to retrace my steps and, sure enough, I can spot a silly mistake. The last thing that would cross my mind is to highlight the "result" and announce to the world, "hey, I've found an enigma".

Again, this essentially comes down to the difference between topology and geometry. When we say the universe is spatially infinite, what we actually mean by this are three things: 1. Spacetime has no boundary 2. For any arbitrary pair of (spatial) points {A,B}, there exists another pair of points {C,D} the spatial separation of which is greater than that of {A,B}. 3. Spacetime is singly connected Herein, (2) actually implies (1), but I’m listing them separately for added clarity. These three conditions are true at all times t>0, including immediately after the BB, and at the present time; so this does not change, and it - roughly - represents an aspect of the global topology of the universe. On the other hand, when we say that the universe was singular at the BB, what we mean is that as t -> 0, the separation between any pair of arbitrarily chosen spatial points will tend towards zero; and it means that no geodesics can be extended beyond the hyperslice t=0, without them extending into the future again (so this is a bit like a “pole” in spacetime). It does not really mean - at the danger of straying into the disciplines of metaphysics and philosophy here - that only a single point existed; the spacetime manifold was already there in some sense, but there was no notion of “separation between events” yet. So it’s the geometry that was singular, but not necessarily the topology. Of course, this is the purely classical picture, it does not account for any quantum effects (which will likely change the story quite radically).

Keeping with the Star Trek theme: And it wouldn't be complete without an A Weekend at Bernie's reference:

I have lived at subsistence level for extended periods of time with various cultural groups. Its quite possible in smaller groups to live pretty autonomously with little conflict and no clear authority figure. Women would often carry hunting tools foraging with children. Opportunity doesn't care if you are a designated hunter. Children may may be 1st priority, and abilities hampered by pregancy, But the skills can be learned pre-child bearing to take advantage and some enjoy the hunt enough, or have the skills to relegate child care. None of these groups were Nomadic, and I under stand there are a lot of cultural differences. But my point is necessity is a great leveler.

Except, if we did, it wouldn't be.