joigus

... for visible light.

Exactly as @exchemist says. It's not that if you shoot very energetic photons against hydrogen atoms the photoelectric effect doesn't go on. It does. But the clever trick is to use a metal, because there you can show that no matter how many photons you shoot against the metal, they won't free electrons from the metal unless they have the required frequency (energy = h x frequency). They would just be absorbed by the continuum spectrum (available energies) of the metal. And that threshold energy is nicely shown in a metal because there is a sharp gap of energy that the electrons have to surmount if the are to be kicked off from the metal. So the metal: 1) Completely absorbs any photons below the threshold kick-off energy 2) Emits electrons when the frequency surpasses that threshold energy They act like a very efficient switch for the photoelectric effect.

The result of the integral doesn't depend on which approximation you use. The second one is called the lower Riemann sum. There is another one with starts with what you would call \(f\left(x_{0}+\triangle x\right)\) instead of \(f\left(x_{0}\right)\), and ends with \(f\left(x_{1}\right)\) instead of \(f\left(x_{1}-\triangle x\right)\) It's called the upper Riemann sum. Your expression differs only in a second-order term in \(\triangle x\). You only see a big difference because your \(\triangle x\) is enormous in the image. You can actually do an even better fit by taking a polygonal approach to the curve (for the same step \(\triangle x\).) https://www.geogebra.org/t/upper-and-lower-sum?lang=en Sorry. This is the applet that I meant to show you. You must play with the n=10. Take it up to n=24, for example, and you'll see what I mean. https://www.geogebra.org/m/SNS8SYSg

I think you're only too obviously an LTP. And I'm too busy to play LT now. I'm expecting a visit from HWL.

You mean in the literal sense? We can play this game forever.

Sorry, what's the NT?

LOL. Good try. I think it's a "me, me, me, me" kind of God. There goes nearly half the commandments.

He actually is lenient enough to forego on the plain fact that the first four are just about "I'm a superstar" on the part of God. No morality there: 1. I am the supreme Lord 2. You will put me above all else 3. Don't even think about using any representation of me 4. Dedicate one day out of every seven days only to me Dawkins and others insist on this over and over. To what effect in society, I don't know. But certainly the word "atheist", which etymologically is just "non theist" has come to represent an insult to many people, in a very similar way as the word "myth" has come to hold a derogatory value in many people's minds, when it just means: Maybe it's because of the way in which some people use these words, or because of what people sometimes read into them. Or in some cases, a combination of both. I watched the Dawkins-Pell debate years ago, and I was appalled. The more stupid and ignorant his talk was, the more applause did he get. We evolved from Neandertals? Evolution is random? The universe before the big bang was a mixture of particles with perhaps a vacuum with electromagnetic forces? Appalling ignorance to the delight of his cheerleaders. Did he actually read Krauss' book, or any other science book for that matter? I agree. There are religious trends in all traditions that are more reconcilable with science than faith-based religion. Observation of the world and the self, humbleness, practice, conscious curtailing of your insatiable "needs" whenever you observe they're not so badly "needed".

There is very little I can recall you as not being aware of --if anything at all. I just want this post to be as much (and as longer) alive as possible, because it interests me very much. In fact, it's inspired me to think of opening another, related, post. I'm working on it.

Yes, I'm aware of this. This is the reason behind "maybe" when I said "maybe crystals..." I find this hypothesis --perhaps in combination with the RNA world idea-- very promising: https://en.wikipedia.org/wiki/Robert_Hazen#Origins_of_life This guy et al. did a re-run of the Miller-Urey experiment, but they added minerals, and found interesting results: Pyruvate and oxaloacetate are important intermediates in cellular respiration, so I guess they were trying to look for a primitive version of it in a convenient "chemical cauldron". Documentary (Life's Rocky Start): https://www.youtube.com/watch?v=zA4w0b2WRvo Things like tardigrades and other resilient organisms I tend to see as shedding light on amazing phenomena as: How is it possible that multicellular organisms endured episodes as Snowball Earth, and the like? Kind of like a second-order mechanism providing plausible explanation of life taking hold in spite of these cataclysmic episodes.

I'm not sure that tardigrades and panspermia are the key that unlocks this mystery. Resilience and "latency" suggest to me as mechanisms to make life more secure and widespread once it's started out and got a secure grip. Abiogenesis, I think, must be the key. Abundant water, energetic processes, chemical pumps in the way of volcanoes, RNA/amino acids worlds, maybe crystals as scaffolds for building of macromolecules, physico-chemistry of lipid membranes... These's a reason why ideas like these are suggested over and over. Speaking from sheer intuition, I think variants of abiogenesis are the way to go, and panspermia is peripheral. To me, panspermia is just pushing the problem somewhere else, but I'd be very interested to learn from other members' opinions.

Interesting... I know there are practised workarounds, or attempts at them. Here's the article that I found in The Guardian: https://www.theguardian.com/technology/2006/aug/31/guardianweeklytechnologysection2 This is about an Irish company that claimed, back in 2006, to have a magnet-driven machine that would generate more energy than is put into it. They said they would get around the restriction on patenting their invention by splitting it into components and patenting those. How successful they were I don't know. At patenting it; at making it work, I'm sure they weren't.

As I don't disagree in the least with what @exchemist and @MigL have said, I will just add a lateral argument. Patent offices do not accept claims for perpetual motion machines. And I suggest you google for this question and learn why. This is an excerpt from an article on The Guardian from 2006: By the way, nuclear reactors are no exception to the law of conservation of energy; it's just that the energy is the potential energy stored in mass, so it's "hidden". The ultimate reason why the neutrino was discovered as early as it was is that people knew some particle must be there "stealing" the energy missing from the reaction. Even though that particle didn't interact with anything known at the time. And sure enough, there it was. That's how sure we are energy is conserved.

No sex implied. It was a joke-quiz. Both the joke and the quiz are pretty lame. It's easy if you google. The thing is whether you can retrieve it from your long-term memory without looking at the real logo.

Which one is the right cathode-anode polarity?

While watching BBC reels on different topics, I noticed that many peculiar phenomena are associated to Siberia that all seem to bear a common relationship. It drew my attention that many of these seem to be related to permafrost thawing. Siberia's exploding craters: https://www.bbc.com/reel/video/p097w5p3/the-mystery-of-siberia-s-exploding-craters Batagaika crater: https://www.bbc.com/reel/playlist/ultimate-world?vpid=p08lmh55 Thermokarsts in Siberia: https://www.bbc.com/reel/playlist/ultimate-world?vpid=p08rswth The Gates of Hell https://www.bbc.com/reel/video/p08vxl52/how-the-soviets-accidentally-discovered-the-gates-of-hell- The Batagaika crater and the Gates of Hell are partly human-made, but the idea that seems to permeate here is that thawing of permafrost is revealing some kind of instability. In some cases it seems purely mechanical, but in others, maybe due to release of chemically-active organic compounds... Could that be the case? Whether these are symptoms of climate change, or totally unrelated problems, I don't know. But I would like to know. Any similar phenomena in countries with extensive permafrost? I'm thinking Canada. Maybe the Gates of Hell is the odd one out.

Thou shalt not bear false hypothesis?

Same reason why you shouldn't be concerned about how much Oganesson your convenience food has.

Just one tiny pet peeve of mine. Love & Bananas a tad over the top on the sentimental side. But that's just me.

Thanks for the tips. Love & Bananas is very moving and awareness-raising--I'll watch the other ones ASAP--. Very recently I had a sour argument on animals and compassion on social networks much less informed on average than this one. My point was that compassion does belong in the animal world, especially for humans, cetaceans, and elephants, all of which have special neurons devoted to feelings of justice and compassion apparently --Von Economo neurons--. This is in no detriment to the fact that wild life is cruel most times, even between elephants, particularly male African elephants, that sometimes fight to the death. I also had very rough treatment in the past from people who defend bullfighting in Spain and southern France. You wouldn't believe how contorted and ridiculous some of the arguments from people who defend the human right to exploit animals sometimes become. A documentary in a similar vein than the ones you've pointed to is this:

Because ancient Romans didn't quite know where the hell they were? LOL

In mathematics I know of two ways in which you can define something that merits the name and notion of space. One is that based on a metric. A metric allows you to define a distance, and from there a notion of open sets. This is called a metric space, which is the one @ahmet is talking about. Also in mathematics, you have the notion of a topological space. You give structure to this entity without even having a concept of distance, but only the notion of inclusion, intersection, etc. upon which you define the notion of base of open sets. I remember this definition, but I must confess I have no use for it, or know how to handle it efficiently. As to physics, I don't have a complete answer for you, but I think it is worth noting that some physicists today are wondering whether space is an emergent property, or epi-phenomenon; that quantum fields perhaps (the stuff), are the really basic concept, and space & time are some kind of derived property. That quantum fields somehow "generate" extension, would be a way to put it. I think Einstein had a very similar notion, and that he thought that space-time is derived from relationships between matter and radiation, which are the actual be-all, end-all of all that we perceive. But maybe I misunderstood. I think it's entirely possible that conscience produces some constriction that doesn't allow us to perceive the ultimate nature of space-time and their contents as they are, and we are cursed by our very own nature of physical systems that project the world around them in the way of a 3+1-dimensional map, but the real business of what's going on is hidden safely beyond what we perceive and, perhaps (I hope not), what we can perceive, as J. B. S. Haldane put it:

And I won't swallow it. It's a non-starter, rather than a tough pill to swallow. Exactly as @Ghideon says, that would imply that empty space has special places and special directions, and all the edifice of physics would be knocked down. Either that, or the Lagrangian formalism goes out the window; and the Lagrangian formalism works for all of physics: Classical mechanics, classical field theory, quantum mechanics, quantum field theory. I'd rather give up quantum mechanics or general relativity than conservation of momentum. And it's passed all experimental tests.

I'm glad @John Cuthber and @swansont took this thread in the right direction after my faltering start. Very interesting link from @studiot too. I agree it's all in the symmetry. You would have to have, e.g., non-spherical fluctuations in charge, to have any radiation at all.

There is a correspondence, but it's nothing very deep, I must warn you. GR is very ambiguous as to what is energy in the sense that there are different energy "components" and all can even be arranged to add up to zero. You can call the Einstein field tensor "geometric energy-momentum tensor" if you wish... Because the Schwarzschild radius depends on what kind of energy you consider as contained within your volume, you can add up all the terms (matter, radiation, dark matter, and vacuum energy) and your recalculated radius would coincide with the radius of the observable universe. Any horizon is characterised by the receding velocity being v=c, so it's more a dimensional question than anything else. Now, physicists do distinguish vacuum energy from all the rest because conceptually it's very different, thereby the mismatch. I hope that was helpful/clear. Maybe later I have more time to elaborate further. Dark energy is everywhere, and is constant. The value of the density is very low, but it fills even the largest intergalactic voids, so it contributes a lot in terms of cosmic parameters, very significantly affecting the receding velocity when you reach the cosmic horizon. In fact, it is thought to be the dominant effect at this point in the history of the universe.