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Showing content with the highest reputation on 08/14/20 in all areas

  1. Loop through all 4,000 pages of members in the search and scrape their content with Selenium or some such lol? Might want to set a delay though could cause issues with site reliability.
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  2. I think one subtle point that is often overlooked, and can be important, is that "species" is an arbitrary distinction invented by humans for ease of categorising and cataloguing organisms. It doesn't't really correspond to anything specific in nature. For example, Darwin's finches are biologically isolated (hence regarded as different species) mainly by geographical separation. In many cases, they could interbreed if brought together. So, even though "inability to breed" is commonly thought of as the definition of species, it is only part of it. A number of different factors are used to help draw the (arbitrary) line between populations. (This obviously relates to the chicken-and-egg discussion in another thread.)
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  3. I didn't!! +1 Please elaborate or give me a reference, if you don't mind. I agree. ----------- I would like to think, and comment, and read more comments, about how all this Stokes' theorem story could have some bearing on the question of time, as integrating on the boundary of a set requires orientation, while integrating on a bulk that is not a boundary, doesn't. Same as time. I googled for the circle, as I wasn't sure. Here's what I found: My apologies, @studiot, because I've been talking all the time about exterior calculus without mentioning, explaining, or giving a proper reference: https://en.wikipedia.org/wiki/Exterior_derivative It's the technique to wrap it all up (Stokes, Green, Gauss, etc.) into one unified description. Thus, for example, Stokes' theorem (or is it Green's?) can be obtained by exterior differenciating a line element (1-form): \[d\left(v_{x}dx+v_{y}dy\right)=\] \[=v_{x,x}dx\wedge dx+v_{x,y}dy\wedge dx+v_{y,x}dx\wedge dy+v_{y,y}dy\wedge dy=\] \[=v_{x,y}dy\wedge dx+v_{y,x}dx\wedge dy=\] \[=\left(v_{y,x}-v_{x,y}\right)dx\wedge dy\] \[\int_{\partial\Gamma}\textrm{curl}\boldsymbol{v}\cdot d\boldsymbol{S}=\oint_{\Gamma}\boldsymbol{v}\cdot d\boldsymbol{l}\] It's powerful because you can do it for any dimensions, surface element, line elements, volume elements, and in general, n-surface and (n-1)-surface elements.
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  4. Quite possible, I am not sure what the convention for the notation is, on this one. I thought I have seen people use circles on both integrals...? Indeed. Did you know that the form of the GR field equations follows from this seemingly simple topological principle? Both this principle, and the generalised Stoke's theorem above, are IMHO among the most beautiful results in all of mathematics The name kind of rings a bell somewhere, but I wouldn't be intimately familiar with what he did (even though I live in Ireland). This is probably a good time to reiterate that all my maths are entirely self-taught, so there are large holes in my mathematical knowledge. I really only ever looked at those areas that are directly relevant to the areas of physics I am interested in. Gladly I'm somewhat out of my depths on this one, since I've never really studied QFT in any detail. That's a shortcoming I am intending to rectify when I have the time and inclination.
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  5. The Argument from Incredulity is especially dangerous, imo. Those who use it THINK they've asked a question, and usually expect an answer, but all they've done is stop the discussion (and thus their learning) with a non-supportive statement that can't have any meaningful replies.
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  6. I personally think any legistation laid down more than 50 year's ago, is vulnerable to deliberate misinterpretation. It was written for that moment in time and, however well intentioned or cleverly designed, every generation should revisit with the intention of an update. The modern way to eliminate gerrymandering, I think is proportional representation; although, no doubt a future (50 + years from now) Trump would have a go.
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  7. I don't think it is that simple. The duality we are referring to here is a duality between distinct types of physical theories - geometric theories of spacetime (on the bulk) on the one hand, and conformal field theories (on the boundary) on the other side. How does this relate to the FTC? Try this: \[\oint _{M} d\omega =\oint _{\partial M} \omega \] Even for this, I am struggling to make a connection to the AdS/CFT correspondence.
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  8. I wasn't going to post this before I had fin ished working on it but here is a summary. Please ask if there is anything you don't understand as it is not really beautiful enough for formal presentation. However this is not a competition so any suggestions as to the form of rho(r) is welcome. Edit I thought I posed this last night but obviously skipped the submit button. Note the correction to Martoonsky's original posting. It seems that we are all converging to a similar solution. My idea of a power series was to represent P(r) as a power series or inverse power series. This would then be multiplied through by the jr gravity term and allow easier term by term integration. The downside is that there is only one calibration point for the constants at r = R. Perhaps MigL's equation could help, I have not heard of this, cosmology/astrophysics is not my bag. +1 Have you any references MigL?
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  9. Since pressure is only dependent on the column of air above it, and ( pressure generated ) self heating, IOW we disregard any convection heating from the walls of the tube, why not just consider a gravitationally bound ball of gas ( say N2 ), the center of which is in equilibrium with pressure pushing outwards and gravity pushing inwards ? IIRC the Tolman-Oppenheimer--Volkoff equation is used for modelling star formation ( and compression of the fusible fuel on thermonuclear bombs ), and can be applied. The equation ( in spherical co-ordinates )for a static spherically symmetric star is derived by plugging in the energy momentum tensor for an ideal fluid into the Einstein field equations, along with conservation conditions. In the non-relativistic limit this reduces to simple hydrostatic equilibrium such that dP = -g(r) p(r) dr where P=pressure and p=density. I don't remember where I saw them, and perhaps someone more familiar with astronomy/astrophysics than I am might know, but I recall seeing tables, for the central pressures of various size stars, before the onset of fusion. It should not be a problem to extrapolate to a ball of nitrogen with the same radius as the Earth ( + atmosphere ).
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  10. Yeah, convection sounds like it could only do so much good if there is an actual difference in dewpoint to allow sweating to help. Just so we're clear I'm referring to dark clothing in a hypothetical circumstance where all other considerations are already addressed. (Eg. Taking public transit everywhere you go, or not going out at night except through walking trails to which motor vehicles have no physical access at all, let alone lawful physical access, etc...)
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  11. Found an interesting article on this: https://www.theguardian.com/science/2012/aug/19/most-improbable-scientific-research-abrahams Granted be curious to find out how much an impact higher levels of humidity would have.
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  12. Speciation occurred in the female parent. The egg is built after fertilization. Therefore the chicken came first. You can be superstitious but you cannot be a little bit stitious.
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  13. It sounds like yo are describing a rather extreme version of the ladder paradox: https://en.wikipedia.org/wiki/Ladder_paradox (Note that, like all "paradoxes" there is no paradox here.)
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  14. I got this wrong. There is a paradox if the ship starts in the middle of the simplified universe and accelerates, ending up sticking out both ends. It's resolved by Born rigidity https://en.wikipedia.org/wiki/Born_rigidity : If the ship started "inside" the universe and accelerated quickly enough that its 10m rest length would stick out both ends, that ship could not maintain a 10m length during that acceleration, and it would not stick out both ends. If the ship starts outside the simplified universe and is already inertial and 10m before the back of the ship enters the 1 m contracted universe, it could stick out both ends of the universe.
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  15. There's no paradox. You're talking about a finite spacetime that seems to be flat. Or basically an object with a proper length of over ten billion light years. You're calling that "the universe", which is fine as long as you avoid attaching meaning to that label, like that everything else you specify must be within that. Not everything in the (flat, toy) universe gets length contracted. Only the stuff that is moving relative to you does. The pilot isn't moving relative to the ship. If the ship is part of the universe, the universe won't be contracted to 1m, only the stuff moving relative to it. If the ship's not part of the universe, the universe can be like a 1m-thick wall traveling past the ship at near c. If you want to talk about the ship being at rest inside the flat universe, and then accelerating "instantly" to near c, then simultaneity is important if the universe is not static. It sounds like the ship is implicitly Born rigid, and clocks on parts of it would become out of sync with each other (by billions of years??). I think you would see the far edge of the approaching 'wall' appearing to age over twenty billion years in the nano seconds it takes to pass you, due to the relativity of simultaneity and relativistic Doppler shift. Actually, that idea's more complicated than I thought. Say the ship starts in the middle of a toy universe, and instantly accelerates to near c. Ignoring simultaneity, you might conclude that the universe contracts to a wall in the middle of the ship, with the ship sticking out both ends. But that's impossible because the back of the ship never travels backward. No part of the ship ever enters the "back" half of the universe. But with relativity of simultaneity, the different parts of the (Born rigid) ship travel through the front half of universe at different times... eek is that right? I think a pilot in the middle of the ship could consistently conclude, "I'm in the middle of the "universe" which is 1m wide and is smaller than my ship would be at rest (which it currently is not, it doesn't share a single inertial frame), but the back of my ship has already passed through the front edge of the universe has not yet reached the same speed as me and the universe is not yet contracted for them."??? That's confusing, I doubt I got it right. However, relativity of simultaneity does resolve this part of the paradox if you do it right. It sounds like you're referring to the spacetime as 'the universe' and others are referring to all the moving stuff in it as the universe? If all the stuff was moving, the pilot would measure it as length-contracted.
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  16. Does it? Can you point to science that confirms this?
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  17. I think you need to be careful not to confuse the cosmological horizon (i.e. the limit to how far out we can observe) with the actual size of the universe. These are not the same things. The physical universe itself does not have any borders. But this is not what physically happens - refer again to relativity of simultaneity. I would recommend a read of the link I gave earlier on the ladder paradox (if you haven’t already), it is conceptually quite similar to this scenario. But whichever way you look at it, there will of course never be a physical paradox, since you can’t construct those within the axioms of special relativity.
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  18. So I will try to answer my own question since you didn't. Google tells us that the diameter of our visible universe is 8.8 x 1026 metres. Suppose this ship flew left to right across our visible universe, what would its relative velocity be to us to compress the diameter of our universe to 1m ? IOW at what speed would it bypass us ? Applying the Lorenz contraction [math]\sqrt {\left( {1 - \frac{{{v^2}}}{{{c^2}}}} \right)} \left( {8.8*{{10}^{26}}} \right) = 1[/math] Square both sides [math]\left( {1 - \frac{{{v^2}}}{{{c^2}}}} \right)\left( {77.4*{{10}^{52}}} \right) = 1[/math] Rearrange [math]\left( {1 - \frac{{{v^2}}}{{{c^2}}}} \right) = \left( {\frac{1}{{77.4}}*{{10}^{ - 52}}} \right) = 1.3*{10^{ - 54}}[/math] Rearrange again [math]{v^2} = {c^2}\left( {1 - 1.3*{{10}^{ - 54}}} \right)[/math] Take square root both sides [math]v = \left( {\sqrt {1 - 1.3*{{10}^{ - 54}}} } \right)c[/math] Wolfram alpha cannot give me this square root the result is so close to c
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  19. Yeah. It's interesting that the Universe could have a finite volume but still be impossible to cross.
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  20. Indeed! Good point This essentially renders the entire scenario unphysical, because you can never make the total distance =1m, regardless of how close to c you get.
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  21. Have to factor in expansion as well. For distant destinations, the distance is growing at a rate faster than the ratio c.
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  22. This is not as straightforward as you might think, because the universe does not have a “length” since it doesn’t have any boundaries; it’s also not an inertial frame. At most it can have the topology of a closed manifold, in which case, if one travels long enough in one direction, one would eventually return to one’s starting position. The problem with this is that, if this is the case, then the geometry of that manifold cannot be Minkowskian, so you cannot naively apply Lorentz contraction - you’d have to find a solution to the Einstein equations which combine relativistic motion with FLRW spacetime (which probably exists, though I haven’t seen it). Note that this is necessary because you’d have the manifold curve back onto itself over a total circumference of 1m, so curvature is definitely not negligible here. It is conceivably still possible to make the total distance travelled appear to be 1m, though calculating how the ship needs to move in order to get that effect is quite nontrivial. Even if it is possible, there still wouldn’t be a paradox, because of relativity of simultaneity (which is also non-trivial here due to the background manifold not being Minkowski). This whole thing is conceptually similar (albeit more complicated due to the above considerations) to the well-known ladder paradox.
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  23. without Einstein the Physics would have taken a different route.
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