joigus

That's what I'm worried about. You proved some of its consequences if P=NP is true. IOW, it only means P=NP cannot be disproved --within your logical frame-- by reductio ad absurdum. But nothing else. That's called "begging the question." I'm not at the level of @Ghideon in these matters, I'm just telling you that you should be aware of this possible flaw. If you're aiming for the stars, you should point at them. I take it that your saying, was a joke. You may be on to something interesting after all. Even if it's not a proof of P=NP. I'll take a back sit and try to learn something.

Now, that's a very good question. And the kind of discussion that I wanted to entice here.

Seems like it was yesterday. Promise of jobs for physicists, a new era of almost limitless energy, and what not. The goose that laid the golden eggs died without a bang, and after months-long whimpers. And the world never recovered from it. Or did it? We lost a lot of our former innocence anyway. I did. Very interesting Nature article on it: Lessons from cold fusion, 30 years on https://www.nature.com/articles/d41586-019-01673-x Reflections welcome. Sorry that the topic is a bit old. It's not the anniversary that I'm interested in.

(My emphasis.) Curvature can be a 4-rank tensor (Riemann curvature tensor), a 2-rank tensor (Ricci curvature tensor), or a 0-rank tensor (curvature scalar). Watch out for 1-rank curvature tensors (vector fields); they're mean!! You took the words right out of my keyboard!

Sorry, next to total ignorant here. The Millennium Prize is on proving P=NP. I assume that's what you're aiming for: (My emphasis.) Isn't assuming P=NP kind of begging the question?

Now I understand! Those are cycling glasses, by the way.

I think that's because \( 1-1=0 \).

Rather: \[ \textrm{int}C\neq\textrm{Ø}\Rightarrow\textrm{if }x\in C\Rightarrow B_{\epsilon}\left(x\right)\subseteq C\Rightarrow\mu\left(C\right)\geq\mu\left(B_{\epsilon}\left(x\right)\right)>0 \]

This is the part I do not understand: And this is the part I do understand:

Deterring doesn't work 100% of the time. But it does in many cases. We need @Eise here. Wittgenstein or not.

Is it Lebesgue day today?

For the first one I would try the inverse direction; something like (as @mathematicsuggests), intC≠Ø⇒μ(C)≥0 Think open balls. I see you already have good help, so I'll leave it at that. Cheers.

Testing more stuff. \[ f\left(x\right)=\begin{cases} 1, & x\in\mathbb{Q}\\ -1, & x\in\mathbb{R}-\mathbb{Q} \end{cases} \] Testing more stuff. \[ \textrm{int}C\neq\textrm{Ø}\Rightarrow\textrm{if }x\in C\Rightarrow\in B_{\epsilon}\left(x\right)\subseteq C\Rightarrow\mu\left(C\right)\geq\mu\left(B_{\epsilon}\left(x\right)\right)>0 \]

Not hours; minutes. But many. Why? For all crackpots out there: https://www.gapingvoidart.com/

I think you have a point, @Sensei. I think what you're saying is "it's safer to interpolate a curve with three points than interpolating it with 2". Nobody would expect the results with anti-muons to be any different, though, because the standard model is CPT invariant. If anti-muons gave a disparate result... Now that would be a surprise! What I don't know is how difficult the experiments with taus would be. I'm guessing a lot more difficult, due to masses and lifetimes.

I'm more inclined to assess this as incontrovertible evidence of new physics beyond the standard model. But I'm reluctant to salute it as incontrovertible evidence of a "fifth force" just yet. For a fifth force to be there beyond any doubt, there would have to be evidence of new decay modes revealing brand-new gauge bosons, with new quantum numbers. But it is true that it's very difficult to conceive of a different gyromagnetic ratio of higher-generation leptons without anything dynamical being involved. The calculation of g-2 involves radiative corrections, essentially sums on all the gauge bosons "virtually flying around", and it's a dimensionless factor. If the gauge bosons are the same for different families, I see no reason why the gyromagnetic ratio should differ unless there are new radiative modes involved.

Yes, but that's not the point about matter-antimatter asymmetry. Call them what we may, the thing is there are considerably more electrons than their counterparts, and protons that their counterparts, and so on. There is an unbalance to one side, so to speak.

Beautifully put.

You need a mechanism that smooths out the universe to the presently known value, and does it at superluminal rates without violating causality in a local way. The way to do that is an expansion factor in cosmology consistent with GR. That's what inflationary models do. The fact that monopoles are swept out of sight is a bonus of inflationary models, rather than a robust argument, I think. The point being immediate generalisations of the standard model of particles physics (grand unification theories, aka GUTs) do predict these very heavy particles. So we can still pursue them (GUTs) while contemplating an explanation of why they (monopoles) aren't anywhere to be found. You need to study what the present models do in order to propose a wannabe cosmological model with any chance of being seriously considered. I hope that was helpful. I don't think a BEC will do the job, honest.

The rationale for the current inflationary model --as envisioned by Alan Guth, and developed by others--, is the need to explain certain observational facts: 1) The universe is large-scale homogeneous (this conflicts with causality: how did causally-separated regions equilibrate?) 2) The universe is extremely flat (why is it so stretched-out?) 3) Absence of heavy particles predicted by GUTs (monopoles) Your model should address these questions.

Apparently there will be a period of radio silence...

That's like saying that insects are many times stronger than ants. Humans are primates.

Indeed. That's in the other half of what I intended, really. They are no saints; they are no villains. They're neither.

Typically-prey animals are no saints. A male buffalo in heat will have no problem trampling to death a calf of his own species. Male herbivores sometimes kill each other when they're fighting for females. Many herbivores are highly territorial, and become very aggressive towards anything trespassing what they consider their territory. What's this nonsense about animal ethics? Let alone good (prey) vs evil (predators)... Rodents are known to eat their young in times of environmental stress. Animals in the wild and under high pressure to survive cannot afford the least last protein to go to waste. Nature can turn a cuddly rabbit into a frenzied cannibal eating its own kind. And back to OP. Cannibalism has never been a common practice among modern humans, for all I know. When it's been practiced, it's been mainly due to famines, or to ritualistic behaviour in ancient societies. The picture of a human looking at another and thinking "mmmm yummy!" is a caricature of a much more elaborate, complex, and relatively rare phenomenon.

Loved your video, but here's where we disagree. I think there are mathematical patterns even in the cultural world. Wherever or whenever we don't understand them, I think it's because the pattern has not been discerned as yet. In that sense, I'm Platonic perhaps. I think mathematics underlies everything.