joigus

The story of my life when it comes to women. No, you're right, of course. It could be the victim of a cognitive bias. I'm aware of that. That's why I was appealing to a good sounding board.

Oh, I'm not very good at number theory. I would have to review some related stuff, like the Euclidean algorithm, divisibility criteria, etc, and see if some of the central ideas illuminate me. But let me try to trim the statement a little bit. Is it: Find a polynomial f(n) with 0<deg(f)<infinity, such that f(n) is prime for all n in the integers? Of course, it'd be the integers. Sorry for mentioning the rationals. Something doesn't seem right, unless you set a bound for n.

Yeah, something like that. It's the sense of urgency that troubled times potentially give the right kind of people. I'm not suggesting that a third world war is necessary, of course. Yes, that's true. This is compatible with what I say, rather than contradictory. Of your other argument I'm not so convinced, as it may well be that you need another indipendent condition to fuel the causal drive. Example: Maybe those human groups did not have the proper cultural seeds planted. Let's say at that particular time they were planting other cultural seeds.

With all due respect, Galileo, Newton and Einstein are soooo in a different league! IMO, theory became orders of magnitude harder after WWII, so it's perhaps unfair to compare him... I sometimes think of Feynman as similar to Newton (developing of a new calculus, mathematical tools of the highest order), but he didn't get lucky in formulating new laws. The closest he got (according to his own admission) is the V-A Lagrangian for weak interactions.

Ok. I suppose that makes Einstein the exception. He thrived during an uneventful spell in Bern. Didn't suffer any turmoil. Went from heaven to heaven. Take Schrödinger, or others in the 20's-30's. My argument stands. And please focus on the big picture of it. Does social/political turmoil (paradoxically and positively) influence the highest creativity?

Not GR, though.

I'm taking you up on this mentioning science by its big names... I personally can't think of any valid reason why nobody has appeared in the last 100 years to fill the shoes of the Newtons, Galileos and Einsteins of yore. Being full of admiration for such people myself, I must say I don't think there's anything supercalifragilisticexpialidocious in the appearance of certain types of individuals. Those able to solve especially challenging problems that take some highest-order, highly-conceptual sorting out. Statistically, it must just happen every so and so. More frequently so the more humans are born. So why hasn't it happened? Here's a frightening idea: Newton had to take refuge in Woolsthorpe after the Great Plague of 1665, Einstein had to take refuge in America after the Nazi persecution of Jews, and Galileo suffered persecution from the Roman Inquisition due to his non-orthodox views on astronomy. Could it be that we need more... --dare I say it?-- persecution? Of course, I'm just trying to be constructively provocative. My reflective point being that there could be something about times of great strife* that brings the best of human beings and make really top-notch ideas be born. Does any of that make sense? * In a milieu that has the proper cultural seeds planted, of course.

Exactly. The most significant critical experiments are far fewer and farther between. This gives more than enough time for people to fall into what I would call theoretical "bubbles" of (perhaps) unnecessary hidden assumptions. You could call this "theoretical daydreaming". After a while a dangerous area of misleading terrain forms. People involved embrace theoretically very promising, very interesting ideas, but with a lot of semi-digested ancillary junk that maybe shouldn't be there in the first place. Good topic. I did notice Hossenfelder's pessimism too.

That's the beauty part, right? 😬

When is an insect bite not best avoided? Thanks for the scale information. Do you happen to know the species?

Spotting obvious solutions first can sometimes be very helpful to obtain the non-obvious ones when the equation is polynomial and has degree > 4. Example: x5=x What would you do?

You mean two sevenths of a pie are different from the 2/7 of the other portion? Oh, OK, I get it. Children appear to be able to count the exact number of atoms in a portion of pie.

Oh, that's so Italian! No, com'on, those recollections I'll keep to myself. But you sent me down memory lane now.

Thanks for the very interesting historical note. I didn't know it went by the name of 'hexagonal aether'. I do remember Feynman's Lectures on Physics mentioning it along the lines of 'Maxwell conceived of an aether made up of gears' or something like that.

Friends fairly sharing pizza has always worked for me. I seem to remember some explanation with pie when I was a kid. It's possible my brain has edited my memories and it was all more formal than I care or dare to remember. Pies work because rational fractions make immediate intuitive sense, IMO. I lost my innocence when I had a teacher at university who said something like 'definitions are not to be understood; definitions are definitions!' which, let me say, I think is completely wrong. Definitions should be motivated. For this man definitions were like a thunderbolt from mathematical heaven. Marcus du Sautoy explains Egyptian, Babilonian, Indian and Chinese mathematics with beans, and peas, and eggs, and things like that, in a wonderful documentary about the history of mathematics.

Exactly. And it would share cosmological equation of state with ordinary matter. It would be another garden-variety type of matter to be detected in scattering experiments. Why bother with superconductivity if the idea doesn't even leave the ground?

Yeah, we got it. To boldly think what no one has ever thought.

One problem with this configuration is that it is anisotropic. And what keeps the spheres from collapsing due to electrostatic attraction? You need a constraint, like rigidities in mechanical problems. Or guess what... quantum mechanics. Dislocations, or kinks, or twists in this grid would not propagate equally in every direction, I think. You should also be aware that field theory does all of this much more simply and elegantly. Plus it gives the right predictions. And that people have tried for ages to build something in the way of a mechanical model, without success...

has a better chance? Yes, it seems to go in the direction of helping kids understand positive integer multiples of (-1) as sequential subtractions. It's very much in the spirit of what @John Cuthber said.

Blah. Ahem: What would make you conclude that the cosmological constant problem has been solved? What would make you conclude that the cosmological constant problem has been solved? What would make you conclude that the cosmological constant problem has been solved? What would make you conclude that the cosmological constant problem has been solved? What would make you conclude that the cosmological constant problem has been solved? What would make you conclude that the cosmological constant problem has been solved? What would make you conclude that the cosmological constant problem has been solved? As in 'I would be happy if you answered any of my concerns' (2nd conditional). From Oxford Dictionary: (my emphasis) If 1) an idea like SUSY were confirmed, and 2) the symmetry were broken slightly enough that it allowed for a small value of vacuum energy, that would make us conclude that the problem has been solved. Has it? No.

You're right about that. Those go under the name of selection rules for photon absorption/emission. The one that rings a bell to me is \( \Delta S = 0 \) for angular momentum. As magnetic dipole moment is proportional to spin angular momentum, there you go. Here's an interesting Q/A dialogue on the topic, that explains more: https://physics.stackexchange.com/questions/174719/selection-rule-delta-s-0-why-does-a-photon-not-interact-with-an-electrons-sp

1st: Find the reason for the monumental overcount in QFT Example: The exactly supersymmetric Hamiltonian gives zero for the expectation value of energy of the vacuum. 2nd: Find the reason why the actual energy is not exactly zero, but a little positive correction to that Example: Postulate a mechanism to break SUSY ever so slightly that the expectation value of vacuum energy is slightly above zero. Then solve for the values of symmetry-breaking parameters for different models. Then go to the lab. Something like that.

Relativistic conservation of momentum would be violated. It's a common exercise for students to prove. Only virtual photons can be absorbed by an electron. They must be off-shell is another way to say it. Somewhere on these forums I included a proof of the converse theorem. Namely; that a free electron cannot emit a 'proper' photon (one that satisfies Einstein's mass-shell condition). The alluded result can be found here: https://physics.stackexchange.com/questions/225522/free-electron-cant-absorb-a-photon Sorry, @Genady. I hadn't noticed you'd already answered that.

The sorriest part of this is they don't even realise how big a number 10123 actually is. There's nothing that we can see or grasp, or intuit, the counting of which is 10123 in the observable universe. You must get into combinatorics of countable things in the universe to get to (and surpass) a number like this. Even the number of photons is ridiculously small in comparison. So coldly stating that there are 10123 Helium-like things among us and nobody has ever noticed takes some gall.