joigus

Neither. But I've been known to say dumb things from time to time, and not to see things that are obvious to others too. It's bound to happen for everybody.

I'm more and more rusty on these things with every passing month, but doesn't the latter require S to be a closed set to be true? At the very least it requires a topology, if I remember correctly. Open subsets don't necessarily have minimal elements. I remember I still have a quiz/riddle on divisibility that you posed months ago pending. I'm sorry about that. Maybe you published the solution?

Knowledge is knowing that tomato is a fruit. Wisdom is knowing not to put it in a fruit salad. Philosophy is wondering whether that makes ketchup a smoothie. Common sense is knowing that ketchup isn't a smoothie. Your statement is neither knowledge, nor wisdom, nor philosophy; and least of all, common sense. Science is made of all of them, plus knowing when to drop one when the rest can do without.

Ancient traditions die hard. Peoples' identities die hard. So let me make your phrase a tad more nuanced: By around the 10th century the majority of Persians would be subject to the Muslim rule. Not "be Muslims". That I would agree with. If the local authority forces you to proclaim yourself a toad, under penalty of death, you will enthusiastically trill in response. But that doesn't mean you're a toad. There is a reason why modern Persians haven't forgotten they were once Zoroastrian, even after Alexander the Great burned their sacred book. They still hold a fire, they swear it was never put out, in honour of Ahura Mazda. There is a reason why modern-day Persians who don't necessarily believe in Ahura Mazda, deem it worth laying down their lives on behalf of their identity, quite independent from Islam. Which to me implies not all of these 10th-century Persians were actually that Muslim. Similar things happen in other parts of the world. It doesn't mean "I believe in my gods of old". It means: "You can stick your god wherever it fits in your anatomy".

For them (the Islamic regime) it's not about nuking the US. They know that's out of their reach by a loooong shot. They will not nuke Vanuatu either. The way they attack the US, and South America, and European countries, is by infiltrating different kinds of low-to-medium-level operatives (demonstrators, activists, terrorists, etc) and create havoc. "Strike terror in the hearts of the unbelievers", if my memory serves. They will do as much harm leading to destabilising the world order as they can: Israel, UAE, international trade routes, etc, with missiles and drones. Getting ordinary people to shit their pants in terror wherever their missiles and drones don't reach. See? This is the kind of ambiguous statements I honestly can't get past. Which Iranians? The minority in power since 1979, or the huge majority of Iranians whose culture is actually alien to Islam and had this parasitic culture imposed on them nearly 50 years ago? Looks like Ezra Klein is being deliberately disingenuous here. Let's rather talk about what the ordinary Iranians would want, and not what a clique of religious fundamentalists and the hitmen in their payroll would have it be.

Therefore you admit that article 5 of the Constitution of Iran refers to a historical event still to come. Now I ask you, what historical event is this, and why is it so central to Twelver theology? Literally, (from fis.iran.org). "May God hasten his reappearance" strikes me as calling for "speeding up the coming of the last Imam", which is what I said. As I do not read Arabic, nor Farsi, I cannot be sure this version is 100% free of bias, and I've had to rely on this English translation. About article 13: Allow me as well to point out that, "God does not forbid you to deal kindly and justly with those who have not fought against you because of your religion and who have not expelled you from your homes" implies that you can kill anyone whom you consider not to have fought against you. It's only that it is not forbidden not to kill them, not to rape them, or not to inject air in their veins, so they find a slow, painful death (as they have massively done recently). It's just not forbidden. You seem not to be that familiar with fard ayn and fard kifayah. (If others kill them and torture them, you don't have to). Fard ayn is praying five times a day: Nobody can do it for you. IOW: You must do it. Killing infidels, on the other hand, is another matter. That's fard kifayah. Somebody can do it for you. You don't have to kill an infidel today. Relax. That's what caliphates are for. In dealing with Islamic law, it is of the utmost importance that you can read between the lines, otherwise, they're gonna get you with taqiyya. Here: "Islamic justice and equity" = anything that Islamic law (Sharia) considers justice and equity, ie, treating politheists and atheists as scum that doesn't deserve to live, and monotheists as scum that only deserves to live under the Jizya. And be fair and just with all believers. One word can completely change the meaning of a paragraph. Religions, all religions, are a cancer of society. Some are more lethal than others though. All of them should, at the very least, be neutralised. I'm from a country that suffered 781 year of Islamic invasion. Sorry. We have (at least some of us do) a sixth sense to detect their BS. I didn't know this. Thank you.

From recent demonstrations and the savage repression by the regime, leading to more than 30,000 dead, I guess not. I already did. Please read my comment so I can correct any possible mistakes I made. I'm not an expert on the Iranian Constitution. What's more of an unknown is how much power of global annihilation they've been holding and advancing for all these years, hidden from view, knowing as we do they are committed to putting an end to this world. This is certainly my feel. What makes Trump tick is obviously basically money and power. He's only probably found it useful to spice up his political ammo with Christian fundamentalism. In this case of the Evangelist kind. I don't think he's a fundamentalist of anything.

Here: The lack of balance in the analysis. Also in answer to, On the one hand (worryingly, I admit) we have relevant people willing to portray what should be --and IMO essentially is-- a geopolitical/geostrategic affair, however ill-conducted, ill-motivated, etc as an eminently religiously motivated course of events. On the other hand (IRI) we have an echelon of highly influential, be-all-end-all fanatics, religious zealots of the coming of the end. So much so that they included it in their Constitution. Every waking hour they devote to speeding up the coming of the last Imam and are longing for Christ to come back to Earth, and "kill the swine", and "break the cross", and "abolish the Yizya", which, as you can imagine if you know anything about Islamic theology, implies either convert to Islam or die. The latter is not something they (here and there) utter, mutter or confide to others. They've written it in their law, they proclaim it. They accept nothing but it. It's the main reason for their existence. It is arguably fortunate that Sunnis (the mayority) are not in such a hurry to kill us all. The leaders of Iran have been for a while.

Shia Islam, in its Twelver version, demands (as is made explicit in the Constitution of Iran itself, article 5 --> ref. to art. 107 calling for the upcoming of the Mahdi) the coming of the End of Times (as implied by the reappearance of the Madhi), and clearly commends it as a desirable state of affairs. This is un undeniable principle of the Iranian Constitution. The ayatollahs and their acolytes long for the coming of the end of the world, as Christopher Hitchens so eloquently reminded everyone who would read/listen on several occasions. The fact that you are denouncing here to me sounds as the shadow of a shadow of a similar intent from members of the US military, although from a Christian viewpoint, and it strikes me as profoundly unbalanced in its scope, never mind some groups or subgroups of such institution being in synch with such delusional thoughts. "According to a report" and according to complaints made to "a watchdog group", and all of this reflected by "a certain paper", to me, is not enough. IMHO, the situation is bad enough as it is, without anybody trying to make it look like what's going on is another crusade from the Christians against the Muslims. Something it is not. This is playing with fire ideologically. It will take me one week at least to get up to speed with any answers on this thread, so please bear with me. I don't generally participate in these topics, but in this case accuracy is of paramount importance.

Oh, he does many, and always fills them with something of his own. There's a wonderful Rick Beato interview too. Here it is:

It rings a bell:

Exactly. To remove ambiguity, some people call these wave-like things "travelling solutions" or solitons when they do not obey the D'Alembert equation but, rather, some kind of non-linear equation. Very famous example: https://en.wikipedia.org/wiki/Korteweg%E2%80%93De_Vries_equation The Korteweg-De Vries equation is to do with modelling shallow waves, which are non-linear. If you do the substitution that @KJW suggests f(x-ct)=F(s) with s=x-ct, you will end up with a non-linear differential equation. Of course, as @sethoflagos says, in the case of D'Alembert (aka wave equation) we have backward-in-time propagation as well as FIT. John Scott Russell first noticed these travelling perturbations on the surface of a shallow canal in Scotland. He followed the solitary waves for a considerable distance while riding his horse (or so the story goes). He had the intuition that these things could not obey the D'Alembert eq., just because such equation is dispersive, contrary to what solitons seemed to do. Today we know many other: The sine-Gordon eq., the non-linear Schrödinger equation, etc. I hope this addition is useful.

Yes, but according to this definition, your unit of charge is \( .6\times10^{-19} \) Coulombs, or 1 Fr (or statC), so any ion could be nothing but an integer number of this elementary charge. There's nothing special about the Coulomb, or the Franklin, or the Heaviside-Lorentz unit of charge. There is however, something very special about the elementary charge of the electron or the positron. You could say the charge of an elementary ion is one. As to \( N_A \), as you well know, it's not a fundamental unit of "number of elementary things" that plays any central role in the laws of Nature. It's been fixed to that value only because you can translate, by means of molecular numbers, numbers of entities into numbers of grams. Had the mass of the proton been around \( 10^{-70} \) of our preferred units of mass, I'm in no doubt Avogadro's number would have been named (perhaps) Arline's number and defined to be in the ballpark of \( 10^{70} \).

Ok. Let me rephrase it this way, which may be more honest-to-goodness: You can define units of charge in terms of mass, length, and time, without ever appealing to any "properties of the vacuum". Once you learn about magnetism, you end up realising why space-time had been involved from the very beginning. F has the mole involved in it ( \( F=N_{A}e \) ). And Avogadro's number has the value it has only because grams are grams, and the mass of a proton in grams, once stripped of its units, is roughly an inverse amount of Avogadro's number.

But I didn't mention the Coulomb. I mentioned the Franklin (Fr, AKA statCoulomb or statC). Many, many people wrongly believe the so-called electric permitivity of the vacuum \[ \varepsilon_{0} \] to be an actual physical property. It's rather a part of the definition of electrostatic charge. I'm sorry that I'm not familiar with Faraday's (independent?) convention. But it sounds to me very much like it is made to depend on current rather than on electrostatic charge. Fair enough. This of course is always possible. Don't forget Maxwell's equations contain the term \( \mu_{0}j \) with \( \mu_{0} \) being the magnetic permeability of the vacuum. One could define the "permitivity of the vacuum" to be anything one wants. And then the "magnetic part of the overall EM machinery" react to varying electric fields with much more "inertia" (bigger \( \mu_{0} \) ). Every game you want to play with E and M definitions is OK as long as, \[ \varepsilon_{0} \mu_{0} = \varepsilon_{0}\mu_{0}=\frac{1}{c^{2}}\] It's not the first time that the French have made other people disagree. 😅 In matters of units, and just this once if you will, we should all have stuck with British units (Heaviside's). Much more sensible.

Gladly. We do need to step back a bit to before quantum mechanics was invented. The reason is once you introduce Planck's constant, electric charge becomes dimensionless, as you know very well and I've read you talk about in these forums several times. Before one knows anything about quantum mechanics, one can use Coulomb's law to define units of charge by, \[ F=\frac{q²}{r²} \] where electric charge is expressed in statCoulombs or, Franklins. Also, \[ F=\frac{1}{4\pi}\frac{q²}{r²} \] In Heaviside-Lorentz units. As dimensions of force are, \[ [F]=MLT^{-2} \] \[ \left[Q\right]^{2}=MLT^{-2}L^{2} \] and therefore, \[ \left[Q\right]=M^{1/2}L^{3/2}T^{-1} \] Now, the question is, does this have any significance at all by way of the physical laws? Let me state clearly: I'm totally clueless about this. The closest one can get to this purely dimensional fact having any significance at all is what I mentioned about the KG and Dirac equations. As, once we introduce Planck's constant, electric charge becomes dimensionless, that means mass can be made dimensionless too and, at least in principle, a function of charge and perhaps other (dimensionless) quantum numbers. Or maybe just as an artifice. As I've remarked over and over to other people in countless discussions, there is the possibility that physics units might be ultimately be overdetermined. Why not? Edit: I've removed one comment as it's just too speculative and not really necessary. I striked it through to keep it visible.

CGS with rationalised units for charge (Heaviside-Lorentz) are my favourite. I once won a bet that you could reduce units of charge to mass-length-time units (something which should be obvious) against a student of electronics. The MKS system introduces the crazy fiction that units of charge are (for some mysterious reason) independent of mass, length, and time. They aren't. IMO, there are foggy hints of this in the Klein-Gordon equation and the Dirac equation. (statCoulombs are proportional to the square root of grams). The KG equation is the square of the Dirac equation. And in the KG eq. mass occurs naturally, while in the Dirac eq. it has to be forced into it. I'm still waiting for that person to pay me.

"A very faint amount of light" is described as relatively few photons, rather than one photon. Intensity is related to the number of photons as well as energy of each photon. Photons in the double-slit experiment are not "pointed at" one slit or the other; they are just let go off in every direction or a range of directions. Some of them hit the screen, others go through. For those that go through, it's really not possible to say "they go through this or that slit". When photons interact with matter, I'm not sure it makes much sense to speak of this or that individual photon anymore. It is actually an essential part of the Young experiment that photons not be very high-energy, otherwise difraction would be harder to notice. Lower-energy photons diffract better, and therefore are not "being pointed" at all. High-photons point better than low-energy ones. But this has nothing to do with the faintness of the beam. A spherical wave does have momentum, only it is not precisely determined. It has a lot of dispersion. You could say the photon is an observable of that spherical wave. These "waves" do not have a little thing inside that you can picture as the individual photon going certain way. Much of it is making peace with the fact that you cannot say what you want to say, as, eg, it doesn't make sense to say that the electron has a smile.

Homeric! 🤣 I understand your concern. But you can always cut the bread twofold or threefold to suit your caloric needs. Anyway, in my defence, I burn a lot of calories cycling every week.

Right! I correct my humble contribution to less than a minute microwaving. The whole thing should take about a minute, or little over a minute. And packed with essential nutrients.

I'm surprised by this, as ever since 1918, we know energy to be a derived quantity, not a defined one, and it's based on the Lagrangian. If the dynamical system is amenable to a Lagrangian formulation, and if that Lagrangian does not explicitly depend on time, then there is an energy, and the different expressions can be obtained with a precise recipe. So it's been a while since we know all these "mainstream definitions" are nothing but the corollaries of a master theorem.

Focaccia with a bed of tomato sauce, scraps of sliced black olive and tuna, mozzarella, oregano or basil. A minute to melt the cheese in the mw oven. You can use other kinds of bread, but focaccia is best. Very similar to the coca valenciana = the Spanish version of a pizza. Very substantial. Nice thread. I'm hungry!

I think @TheVat was referring to repetition of your principle of insisting on understanding the underlying concepts. I favour the use of repetition too, to hammer home some particular ideas, or even just sequences of words (like the title of an influential work, name of the author, dates etc) that's central to the development of the topic. The reason I say this is because all of us also have this automaton inside of us, the hippocampus, that does things for us without us ever thinking about them. In fact, I favour a two-pronged system: 1) Synthesising the main ideas ("filtering", as the Vat was saying --> writing an outline of the topic at hand, which requires understanding) and 2) Automation of some items (memorising names, dates, difficult-to-spell-and-remember new words. The use of AI (or AGI) should come later, and should be presented from the start as a dialogue. With questions such as, "how do you know what the machine told you is actually correct?" etc.

Agreed. And a safe rule of thumb might be that it only works efficiently in simulating when it follows well-trodden paths, which would make it suitable for education if used properly. I know exactly what you mean. I remember being taught to use tables of logarithms... yuck! Some contact with these old tools might be interesting. Knowing what they are and how the craft got underway. But dwelling on such thechniques is a bit like insisting on learning to cook by using bifaces and grinding stones. Getting intuitions for what numbers are is what's important, but when you learn about p-adic numbers, just to take one example, you realise numbers are not the sequences of digits yout teachers taught you about, but something much more abstract.

Let me concentrate on this point, because somehow it's the closest to my heart. An important aspect of scientific endeavour consists of (or at least implies) interacting with other minds. I think putting AI to good use would entail facing the student with interacting with other working minds. It is conceivable (and very understandable) that educators need to develop the necessary criteria to extract pedagogical benefits from this. IOW: I want to see your interaction with the automaton mind. A. N. Whitehead (as reflected in my signature) once wrote: "Civilisation advances by extending the number of important operations which we can perform without thinking about them". This goes to show that the problem in a general context is not new. The question we face now is a new one: What about the important operation being thinking itself? Can we perform thinking without thinking about thinking? I think we can't. We must think about this new machine thinking, and refine the criteria. That's all. And nobody says it's easy.