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The Fermi paradox articles call this the 'great filter', some test that a technological species must pass in order to not get filtered out. It does not look well for humans. Problem is, our current civilization depends on technological continuity to maintain itself. War is one way that ends, but so is the simple exhaustion of non-renewable resources. Once gone, that's it. We cannot advance again and the species reverts to just an animal with an expensive brain that might be more of a hindrance than a help. One has to eat an awful lot of food that other animals don't need, in order to feed the expensive toy. Despite the frequent depiction in fiction ('Aliens' come to mind), nuclear reactors cannot explode. At worst they melt down, arguably a worse fate than a bomb, but not one that is quite as fun to depict on the big screen. The species needs to act for the benefit of the species instead of the individual. I know of almost nobody capable of that. Our core moral code even forbids it. We're quite doomed to fail the Fermi test. I notice that several people might point out the problem (as I am doing here), but nobody posits a solution (including me).

OceanBreeze, there is one way it can creep into the mathematical mix physics wise. The following is a rehash of another post of mine here. Nina Byers goes into Emmy Noether and her contribution to the conceptual structures of the mathematics in modern physics in detail in her paper "E. Noether s Discovery of the Deep Connection Between Symmetries and Conservation Laws" in 1998. https://arxiv.org/abs/physics/9807044v2 https://en.wikipedia.org/wiki/Emmy_Noether At a conceptual structural level improper integrals in physics can be piecewise continuous integrals, with limits from +infinity to -infinity, that converge. Refer H.J. Keisler, p367, Definition to p369, examples 7, 8, and 9. If they are continuous and don't converge then they are indefinite integrals which are entirely different. Refer H.J. Keisler, p370, example 10, diagram 6.7.10 "It is tempting to argue that the positive area to the right of the origin and the negative area to the left exactly cancel each other out so that the improper integral is zero. But this leads to a paradox... So we do not give the integral ... the value 0, instead leave it undefined." That doesn't mean that indefinite integrals don't play a part in our physics as an indefinite integral that cycles between +infinity and -infinity at its limits, as a sub function of a higher level function, is a valid proper use of indefinite integrals as definite integrals by change of variables. Refer H.J. Keisler, p224-5, Definition and example 8, diagram 4.4.6 second equation with u and substitute infinite limits. "We do not know how to find the indefinite integrals in this example. Nevertheless the answer is 0 because on changing variables both limits of integration become the same." Reference H.J.Keisler "Elementary Calculus an Infinitessimal Approach"

If I can find it, or recreate it again, I will post it. If I remember correctly, it was a silly divide-by-zero error, as many infinite results are. What made it interesting was all the calculus involved; both their original calculation and my rebuttal. I am a bit rusty now so it might be a good refresher to review it. Thanks for the info on that other site; sounds like a visit is in order. I'm always glad to see you spending time here and helping to keep us on the straight and narrow.

That's really cool. I am hardly qualified to comment, but when has that stopped me? Whacked hard enough to drive the ore down a km, but soft enough to not splatter the stuff all over. Hard sell, that one. The fission takes place on Mars but not the asteroid pre-impact. Seems unlikely since the concentration should be higher before impact. But the ore sits there for a super long time until water does something to what, pull it together? Water does do stuff like that, so maybe. Now it needs to be a bomb, which apparently is triggered by critical mass, and the subsequent boiling off of water. That's not going to happen in a short time since the water has nowhere to go quickly. Geyser maybe, with the overall pressure holding in the rest. Without the water, it goes all bomb on us, much slower than our weapons, but far more pressure keeping it there while it goes on. Eventually the pressure breaks the surface and you get this crater, a lot like Mt St Helens depressurizing in 1980. Where is that? How much does Martian weather erase craters like that? All they have is wind driven dust. So what, it fills in? Look for a deep sand hole? Just vocalizing my naive thoughts. I admit none of it seems to kill the idea. My strongest skepticism is at the top, before all the alchemy takes place. Since we're going off topic (sort of), it turns out they recently found the world's oldest fossilized forest, right by me (bicycle ride away), one old enough to push back the date of the earliest real trees. What they mostly have is a cluster of root systems, really big ones, like with a 15 meter footprint.

Only because it is impossible to know anything at all, like say that the apple is indeed there before you. Such knowledge is a product of induction, not deduction. Similarly, if the universe is finite, there is NO possible way for us to know that either, so your conclusion that mathematics showing the former to be more probable is an indication of a mathematical error, is an unfounded conclusion. There can very much be evidence of infinity, but it isn't a proof, and your comment seems to only deny such a proof, something with which I agree. Is space discreet, where there are two adjacent locations halfway between which there isn't another location? If so, all sorts of funny conclusions can be drawn, perhaps like a preferred reference frame (invalidating all of relativity). If not, there's an infinity for you. Is that infinity observed? I don't think that counts, so no. Is it real? Not if being real is defined as being directly observed by a human. The universe might have an edge a mere 6 GLR away. No light that reaches any human has ever been more than that proper distance away. Clearly the concept of 'visible universe' uses a different notion of what is visible than that 6 GLY limit. For instance, a perfect simulation of everything we see need only process that 6 GLY radius. Anything that happens outside it cannot affect what any human can measure. This line of thinking goes down the rabbit hole of direct vs indirect observation. One concludes the apple is there via induction, not by directly observing the apple, which hasn't a clear way to do. I would have liked to have seen that infinite energy error. I love finding errors in papers making outlandish claims like the one you mention seems to. For entertainment, go to conspiracyoflight.com and find all the proofs that relativity is wrong. Find the flaw in each one. Doesn't take long, but nobody on the site every corrects any of them. Not the purpose of the site, similar to truth being the purpose of any site with the characters 'truth' being part of the website name. George Orwell saw it coming with his ministry of truth. We can say it, but it is trivially falsified. A torrid universe is flat everywhere, and yet has finite volume. One of the oldest examples is the universe of the Asteroids video game (only two dimensions of space, not three). We seem to be digressing. I mostly came into this to point out all the pop-science notions being asserted in this topic, and none of those seem to come from you.

I am stating as a fact, IF the universe is infinite, there is NO possible way for us to know that. We would have to be able to observe infinity, which is impossible by definition. We can say, and some do say, if the universe is flat everywhere, it must be infinite. Tell me how could we know the universe is flat everywhere? Again, we would need to confirm this by observing an infinity; an impossibility. I have no problem at all with mathematical infinities, but if the calculation is about something real, an infinite result is nonsense! Nothing real can be ever shown to be infinite. A calculation for infinite energy, (which I have seen made) is one such example. The calculation was made by two mathematicians with advanced degrees and they insisted it was correct. I found the error and showed them how ridiculous their calculation was. Infinite energy! More energy than in an infinite amount of universes in an infinite time and they believed it because of a math mistake!

No, the galaxaies are not "expanding." Galaxies are "moving away" from us. That Doppler effect is Slipher's observation. And yes they move away faster if they are farther away. The basis for the math of distances is the inverse square law to the brightness of light. So, we get non linear, progressively larger distances, or accelerated motion away from earth. The motion is uniform and universal. Hubbell concluded based on those findings that spacetime is expanding. Since this observed motion is based on inverse square law of distances, math can include a cosmological constant Lambda to explain it, and that is consistent with Einstein's tensor equation. An alternative view is that there exists dark energy which is responsible for the motion of galaxies which Slipher observed, away from the Earth. This would delete the Lambda cosmological constant, and would introduce some other "dark energy" matrices in the formula. Spacetime then would not be stretching (expanding). However, no one observed any matter or energy in the universe that is responsible for uniform and universal motion away from anything. So this hypothesis about dark energy is inconsistent with observation. Even though acceleration and gravity are indistinguishable in Relativity under Einstein's tensor equations. In there lies the problem, there is something within spacetime that distinguishes some accelerations from curvature (gravity). Hence, Lambda factor for spacetime itself, separate from G factor which is the curvature (gravity).

Whenever I mention the "universe" I am referring to the only universe we know about, the observable universe. Everything I say about flatness, expansion or whatever, it is only about locally, as talking about a "global" universe is not falsifiable and therefore not scientific. The universe that we observe is flat, meaning it has Euclidean geometry. We also observe this universe is expanding and the expansion is accelerating. Flatness has only to do with local geometry and it says nothing about the topology. I am not flat, and my house is not flat! The topology is 3D and as far as we know the observable universe is a sphere roughly 50 billion light years in radius. Also, a flat geometry doesn't imply the universe is infinite in extent. A piece of A4 paper has flat geometry but it has dimensions of 210 x 297 mm. All of the above is just for clarification. There is too much confusion about what a flat geometry means and what the difference is between local geometry and topology. I know everyone will not agree with what I wrote, but I believe it is correct, while inviting discussion.

Therefore the visible universe, which we cannot see beyond in any empirical way, is a spherical boundary for our physical universal models that may actually be more accurately a cubic model, but we can never test it. This might explain why the ratio of All matter (dark and Visible) over Visible matter equals 2*pi +/- 1.1% using both the WMAP and PLANCK ΛCDM percentage density figures. And also why twice the ratio of Everything (Dark energy and Matter) divided by Visible matter equals 2*pi squared +/-3%. Please note that the overdensity constant Δ c as used in Virial mass, is 100 for ΛCDM but 200 (double) for your stock standard galaxy and a sphere in a cube occupies around 54% of the total volume. Dark energy and Dark matter are mere phantoms of our restricted universal viewpoint and the limitations of our scientific process. https://en.wikipedia.org/wiki/Virial_mass#Virial_radius

Hello AnonymousLearner and welcome to our forum. I appreciate that you love engineering and you also have a curious mind. Unfortunately, the experiment you propose to try is doomed to fail for at least two reasons that I can think of: 1) Liquid water cannot exist in a vacuum. It would immediately boil and change state into water vapor. 2) Lack of oxygen would lower the reactivity of the magnesium to the point where it becomes inert; it would not react with the water even if liquid water could exist in the vacuum. 3) A third, but possibly redundant, reason this experiment cannot work is the water vapor left in the vacuum chamber would be very cold and magnesium only reacts with hot water. Don’t let this setback discourage you from thinking up other ideas. My only suggestion is that you do some research to see if your ideas have any chance of working.

How do we know that this idea is correct? In the first message about the CMBR it is stated: https://en.wikipedia.org/wiki/Cosmic_microwave_background The cosmic microwave background (CMB, CMBR), or relic radiation, is microwave radiation that fills all space in the observable universe. It is also stated: Quickly after the recombination epoch, the rapid expansion of the universe caused the plasma to cool down and these fluctuations are "frozen into" the CMB maps we observe today. However, Photons cross the space at the speed of light https://en.wikipedia.org/wiki/Photon Photons are massless particles that can move no faster than the speed of light measured in vacuum. The photon belongs to the class of boson particles. The modern photon concept originated during the first two decades of the 20th century with the work of Albert Einstein, who built upon the research of Max Planck. Therefore, don't you agree that it is a severe mistake to compare the photons to some sort of a frozen dust that fills the space? Theoretically, if the observable universe was fully curvature, we could claim that photons orbit in some sort of cycles in this limited universe size and therefore, they would "stay" in the curvature universe for billions or even trillions of years However, this is not the case as the observable universe is flat without any curvature. It is very clear that any photon which had been created at any time in the past (at any era) must continue its motion to the infinity. How can we even consider a possibility that photons from specific date (the surface of last scattering) would be so lucky to be frozen and fill all the open space. Any idea how to freeze photons in space? If it is feasible, why other photons from the universe history / Era can't also fill the space of the observable universe? Do, you think Albert Einstein would confirm this idea of frozen photons in space?

Penrose diagrams contains dots which are then said to occur after an infinity of time. Drawing these dots at finite distance is misleading since it suggests we can actually reach infinite time - we can't.

That question is not unanswered. The word "curvature" means acceleration. It is proven that the universe is "accelerating," so there is indeed positive "curvature." In theory there are 3 options, but in real world only one of those three is observed, positive curvature.