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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"

I agree, an increased understanding of the property of consciousness is a possibility with brain computer interface technology.

Yes, that is a big mistake and you are the only one making that mistake. Everyone else “hopefully” understands the individual photons that comprise the CMB are moving at the speed of light, and coming at us from all directions in space. What is “frozen” is the pattern of fluctuations left on the photon field as they left the surface of last scattering. That is the familiar image we often see of the CMB: As you can see the image is not entirely homogeneous, smooth and uniform, but contains some grainy structure caused by nonuniform temperatures across the spectrum. The image we see was created at the time of last scattering, some 13+ Billion years ago. However, most of the photons which form that image were produced at a much earlier time in the evolution of the Universe. That is why some of the photons are extremely redshifted from Compton scattering. This CMB radiation appears to come from a spherical surface all around us. The radius of that “shell” is the distance each photon has traveled since it left the last scattering surface. We are able to see that image because our very sensitive radiotelescopes are looking back in time and seeing the photons as they were ~13 Billion years ago. It is not much different than when you look at a star 100 light years away from you. You are seeing an image of that star created by photons that were emitted 100 years ago that are just reaching your eyes now, traveling at the speed of light. The star is most likely not where you are seeing it now! It might even have ceased to exist in the form that you are viewing it now, but you have no way of knowing that at this moment in time. The photons in the CMB that we see today have been traveling for 13+ billion years to reach our eyes now. During that time, the universe has expanded to be ~ 1000 times larger that it was at the time of last scattering. The stretching of space also stretched the photons so they are redshifted with a redshift of ~1000. At 2.7 K, they are also about 1000 times cooler than when they left the surface of last scattering. I hope that helps clear up your confusion about “frozen” photons!

Roots? Sounds like what they did to the Brazilian Rosewood tree relatively recently- and now they're even digging those up to use. These ancient ones likely ended up with a different fate I hope anyway. But yeah it's cyclic.

Nice. I haven't studied the Paradox much but guess I should get to it. Surviving the "filter"- I can think of futures worse than not making it.

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?

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.

Neuralink's brain-computer interfaces, BCI, technology represents significant progress in the field of neurotechnology. The device's high-resolution neural interfaces allow for precise recording and stimulation of brain activity. I suspect this is only the beginning; no doubt this will lead to more and more complex brain-computer interactions. This research may even be the key to unlock our understanding of consciousness; one of the biggest mysteries of all.

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!

I disagree with the 'possible' part, but I will add that we also do not know that it isn't actually infinite, so by the same logic, it makes no sense to say that "a real infinity shouldn't be possible". I'm actually not talking about phenomena at all. I'm taking about the real universe, not our perception of it, but it seems that your definition of 'real' seems to depend on knowledge, a sort of idealistic stance. But if we take this stance, there is little difference between the abstraction that is mathematics and the abstraction that is the universe. Is time infinite? It's not like the expansion is going to stop and turn around and crunch. So we get to heat death. That happens at some finite time, after which there really isn't time anymore. No visible universe to have a volume. No observation. Not even radiation remains. I have a hard time arguing for infinite time. So it's not that the universe cannot have infinities, it is that you presume an error has been made if one is demonstrated, a sort of denial of evidence. Seems to be a strange stance to take.

We can try a old calculus trick and do an analysis as Volume approaches 0 in the density equation. we will do it for .1, .01,.001, and .0001 values for Volume. So, for D = M/V from the positive direction V = .1, M = 5.967*10^30 then D = 5.967*10^31, if V = .01, M = 5.967*10^30 then D = 5.967*10^32, if V = .001, M = 5.967*10^30, then D = 5.967*10^33, if V = .0001, M = 5.967*10^30, then D = 5.967*10^34, If V -> 0, M = 5.967*10^30, then D -> ∞+, Now let's come at it from the negative direction. which will be -.1,-.01,-.001, -.0001 values for volume. V -.1, M = 5.967*10^30 then D = - 5.967 * 10^-31 V -.01, M = 5.967*10^30 then D = - 5.967 * 10^-32 V -.001, M = 5.967*10^30 then D = - 5.967 * 10^-33 V -.001, M = 5.967*10^30 then D = - 5.967 * 10^-34 If V -> 0, M = 5.967*10^30, then D -> ∞-, Wolfram Alpha Link = https://www.wolframalpha.com/input?i=what+is+the+limit++of++D+%3D+M%2FV+as+V+goes+to+zero "If one side of a function approaches positive infinity while the other side approaches negative infinity, it means that as you get closer to a certain point on the graph from the left, the function values become increasingly large positive numbers, while approaching from the right results in increasingly large negative numbers; this indicates that the limit at that point does not exist because the function is not approaching the same value from both sides." Link = https://math.stackexchange.com/questions/23649/limit-approaches-infinity-on-one-side-and-negative-infinity-on-other-side That's how we can define this using calculus analysis techniques. "Is it continuous if limit does not exist? In other words, if the limit does not exist at a certain point, the function is not continuous at that point. Thus, the answer to the question is no: a function is not continuous if the limit does not exist." Link = https://homework.study.com/explanation/is-the-function-continuous-if-the-limit-does-not-exist.html#:~:text=In other words%2C if the,the limit does not exist. Link 2 = https://en.wikipedia.org/wiki/Limit_(mathematics) This further proves how math just breaks down at the singularity point of a black hole as the equations for basic properties aren't continuous at them.

if the universe is infinite in size, there is no possible way for us to know such a thing. It make no sense at all to speak of "real" infinities. Infinity works for us as a usable concept only. This I agree with.

Yes, as we know, the conditions required for a nuclear explosion involve a rapid, uncontrolled chain reaction in a compact mass of fissile material under high pressure. Knowing this, when a reactor is built, it is designed to prevent creating those conditions. Specifically, the reactor cores are designed so they do not build up the high pressure needed for a nuclear explosion. What is being discussed here is a hypothesis for a naturally occurring (not man made) nuclear fissile reactor on Mars. According to the source paper: The Martian Large, Natural, Paleo-Nuclear Reactor Hypothesis: “In Mare Acidalium, a large ore body of incompatible elements formed with concentrated uranium, thorium and potassium at kilometer depth, probably from an asteroidal impact. Due to the lack of plate tectonics, the ore body was not disrupted over Mars history but supported nuclear fission reactions based on a thermal mode. This process began 1billion years ago when 235U was three percent and may have been triggered by a deep intrusion of groundwater into the ore body due to loss of geothermal heat on Mars. The body was of high concentration of uranium and thorium oxides. After many millions of years in operation the paleo-reactor managed to begin breeding fuel in the form of 233U and 239Pu faster than it was burned up. Much radioactive potassium was also created by the neutron flux during this period of thermal neutron operation. At some point the ore body suffered a “prompt critical” and the water boiled out making the neutron spectrum harder and a runaway chain reaction on the 233U and 239Pu ensued. Because of the size of the ore body, and its burial at kilometer depth, the reaction was inertially confined or “tamped” so that explosive disassembly was delayed until a high degree of fission burn-up was achieved. The resulting energy release was catastrophic and resulted in an explosive disassembly of the ore body as a dust and ash cloud similar to a large asteroid impact.” It is a hypothesis only. “The occurrence of such a large natural reactor may explain some puzzling aspects of Mars data, such as the superabundance of K and Th on the surface and the large inventory of radiogenic isotopes in Mars atmosphere.” Make of this what you will, I am not convinced either way. I do find it interesting.

"density, mass of a unit volume of a material substance. The formula for density is d = M/V, where d is density, M is mass, and V is volume." Link = https://www.britannica.com/science/density I want you to see the problem I am faced which Density is defined as Density = Mass/Volume, Density = ∞. Let's say you guys are correct then Density = ∞ and Mass = 3☉, then Volume = 0, which is what special relativity says it is which is Einstein's Equation for size of space as dx' = 0 when Velocity = Speed Of Light, which Δx' *Δy' * Δz' is V' which is still 0, as 0 * 0 * 0 = 0 Wolfram Alpha Analysis Link 1 = https://www.wolframalpha.com/input?i=%3Dx(1-(V^2%2FC^2))^(1%2F2) Wolfram Alpha Analysis Link 2 = https://www.wolframalpha.com/input?i=%3Dx(1-(C^2%2FC^2))^(1%2F2) Wolfram Alpha Analysis Link 3 = https://www.wolframalpha.com/input?i=V+%3D+x+(1-(v^2%2FC^2))^(1%2F2)+*+y+(1-(v^2%2FC^2))^(1%2F2)+*+z+(1-(v^2%2FC^2))^(1%2F2) Wolfram Alpha Analysis Link 4 = https://www.wolframalpha.com/input?i=V+%3D+x+(1-(C^2%2FC^2))^(1%2F2)+*+y+(1-(C^2%2FC^2))^(1%2F2)+*+z+(1-(C^2%2FC^2))^(1%2F2) So, the equation for density reads for finite mass of 3 solar masses. ∞ = 3☉/ 0. Wolfram Alpha Analysis = https://www.wolframalpha.com/input?i=∞+%3D+(5.967*10^30)%2F+0 Sorry, I don't understand that result maybe you could clarify, WTF that means? That's with a finite value of Mass which is the size of most normal black holes which is 3 solar masses or higher. Now, with the equation for density as infinite mass at the singularity, I get for Density = Mass/Volume ∞ = ∞ / 0 Wolfram Alpha Analysis = https://www.wolframalpha.com/input?i=∞+%3D+∞+%2F+0 I'll be honest I don't really know WTF that means either but maybe you guys can tell me? So, maybe you can understand my confusion with this black hole singularity math thing my dear readers of the science forums. I think it makes more sense with Mass being infinite at the singularity point and ∞ = ∞ / 0, but I could be wrong... but actually as Halc says all this stuff is actually undefined and I agree with that assessment but was trying to make a educated guess on what it could be. The math actually starts to break down with singularities and black holes which I agree means it cannot be defined by physics and the result that I get is Infinity = Complex Infinity for both situations from wolfram alpha which is a well known computational engine for math stuff.

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).

I don't mean to pick on one person, but there seem to be plenty of mistakes. I also realize this topic is a month old. As for 'real infinities', I'm fine with them. The universe is supposedly infinite in size, which doesn't seem to contradict anything. Given that, the universe has infinite mass, but I agree that only finite mass can be contained by any finite volume. I know it is a university site, but the whole page there seems not peer reviewed and flat out wrong. It propagates the popular notion of there being a compressed point in space at the center of a black hole, which is anything but the case. Compression does not go on. Tidal forces tend to pull things apart not compress them. The center of a black hole is singular, which does not mean it's a point, it just means that physics does not describe what goes on there. A coordinate system that isn't signular at the event horizon (Kruskal–Szekeres coordinates, or a Penrose diagram) show the black hole to terminate at a space-like line at the end of time, not a place where all the mass ends up, and all of this is a description of a simple Schwarzschild black hole which by definition is eternal and has nothing falling into it. OK, the Penrose diagram doesn't necessarily show a Schwarzschild solution, but the other does. [Citation needed] Not sure what is being quoted here, but it seems to contain the same mistakes, presuming a sort of Newtonian vision where mass just gets crunched into a point in space. The bit about light (or anything) not escaping is already true at the event horizon (by definition) and is not a property specific to the 'central' singularity. The bit about the ring singularity is correct, but it's a 2D surface, not a 1D circle. It's just hard to draw all four dimensions in a 2D picture. The list doesn't mention a charged black hole, which results in a sort of fuzzy singularity that lacks a neat geometric description. Length contraction is a coordinate effect, not physical compression with proper 'pressure' and all that. I kind of do agree that matter undergoes a sort of coordinate compression as it falls to the end of a black hole. It actually gets pulled apart, but also contracted. At the end of time, it kind of just doesn't exist anymore, but that statement is an assertion of physics at a place where physical law doesn't apply, so nothing officially says that. Coordinate compression cannot contract a the dimensions of a mass down to zero. Such a frame is not a valid one. That's right, which means density (a function of space among other things) is not defined at said singularity.

sigh. At least nobody can say I didn't try to reason with you and give you a chance to drop your presumptuous assertions. Enough is enough. Thread Closed. Warning Issued Suspension being considered.

No. You will run into problems as soon as you try to represent the charge (explain it, or try to encode it into the particles). You cannot encode it into the particle by giving it a number in your mind or on paper, it must be encoded physically: by actualized numbers. You can't couple an abstract quantity to a particle: physics reads the particle, not your mind or a paper.

Charge conservation has already been explained to you: When a down quark transitions into an up quark, it involves the weak nuclear force, one of the four fundamental forces in nature. This process is mediated by the emission of a W¯ boson which is the force carrier for the weak interaction. The emission of the W¯ boson allows for charge conservation. The down quark, with a charge of -1/3, emits a W¯ boson (which has a charge of -1) and becomes an up quark (which has a charge of +2/3). The overall charge before and after the interaction remains the same. (-1/3 e). (I presume you can add -1 to + 2/3) Energy conservation is more difficult to comprehend: The mass energy of the W− boson is about 80 GeV, so it cannot possibly emerge from the nucleus as there are only a few MeV of energy available. The Heisenberg uncertainty principle says the uncertainty in the energy (ΔE) times the uncertainty in the time (Δt) is greater or equal to ћ. (ΔEΔt ≥ ћ ) Here ћ = h/2π = 1.05 × 10-34 J-s. h is of course the Planck constant (6.63 x 10-34 J-s). As you should already know, the uncertainty principle states that some pairs of physically observable parameters cannot be precisely measured simultaneously to within arbitrary accuracy. So, in accord with energy-time uncertainty, the W− boson is unstable and will quickly decay into other particles, such as a lepton (electron with charge -1) and a neutrino (charge 0). To summarize, In the beta-minus decay process: electric charge is conserved the number of quarks minus the number of antiquarks is conserved the number of leptons minus the number of antileptons is conserved flavor changing of quarks or leptons is allowed If you want a complete a derivation of the energy-time uncertainty, I suggest you do your own research first. If you do that, then and only then will I engage with you further on this subject. If you continue to make unfounded and frankly ridiculous assertions, about strange nodes on circles and Riemann spheres, this thread will be closed.

I agree with the basic idea that we need to become more sophisticated, enlightened, and compassionate to our fellow humans as we become more technologically advanced. Just as you don’t give a child a loaded gun to play with, we need to keep weapons of mass destruction out of the hands of people who harbor feelings of superstition, fear and ignorance towards others. Unfortunately, our biological and technical evolution has not eradicated those outdated religious beliefs and other human ideologies that lead to such harmful feelings towards others. I’m afraid you did muddy the waters when you wrote “there are reports that there is strong evidence of a past nuclear war on Mars of all places.” Your post would have been much better received without adding that!

At first, it might seem like there is no difference between using a wall outlet and using a power strip but there is: power strips usually have built-in surge protectors while the wall outlet more than likely has no surge protection. I am a strong believer in surge protectors as they have protected my electronics both at sea (lightening strikes) and on shore (power surges from the mains supply). In my opinion, the support agents don’t know what they are talking about since it is only laser printers that require to be on a separate circuit because they draw a lot of current which can cause problems for other equipment on the same circuit. You have an inkjet printer so it can be plugged in anywhere you like, and should be plugged into a circuit with a surge protector. However, I would not plug it into a UPS; except for the UPS bypass, which is a conditioned line with surge protection. If the support agents tell you your printer’s warranty will be invalid if you use a power strip, then go ahead and use a wall outlet (or at least tell them you are doing so). If the printer is located in your own home, nobody is going to drop in for an unannounced inspection!

Support agents for a computer inkjet printer that I own insist that I connect the printer directly to a wall socket, not through a power strip. Do the two types of connection actually differ electronically? Thanks for your help.