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Not all men do, and as Charon noted there’s a larger global trend occurring whereby divisions are getting more pronounced between men and women. It’s sometimes more a predictor than income level and education. In my small universe, they tend to be tech bros. The types who think Joe Rogan and Elon Musk represent the ideal (or who join sites like ours to defend incels, for example). It’s not local to Trump, but is absolutely being reinforced on social media and information bubbles. And with our insanely tight county-by-county voting within the long outdated slavery-protecting electoral college system, those tiny changes in turnout and choice at the margins matter quite a lot.

I wonder; if a poll was conducted just of men, would we see a divide in support for Trump and Harris based on parental differences? Will men who are fathers to girls be more likely to vote for Harris vs men who are either childless or only fathers to boys? As for what you said about the GOP being better at branding themselves pro economy, I wonder what it would actually take to debunk this myth for people. Great responses btw, I really appreciate you guys. I think it may have more to do with the Internet giving teeth to most points of historical contention, controversy and disagreement. While also inviting more people into the discussion than were able to in pre-internet days. The Internet is a double edged sword in that it can drastically expand the reach of any thought, message, idea, truth or falsehood. As well as the speed which it does this. A lot of people don't even realize that fax wasn't just replaced by email, it was completely and totally outperformed by email. The number of documents that started to be sent by email over fax was increased by over 1000% as the time it took to send 1 document and the time it took to send 200 were virtually the same. In summary, the Internet made every view, debate and argument much louder in our lives. Pre-internet if you wanted to hear someone discuss the differences between men and women, you had to attend a lecture, read a book, watch the right TV show or listen to the right radio show, or maybe you just discussed this stuff with friends at the pub, but you really had to go out of your way. Now you have 100s of options of where to go to discuss these things at the push of a button. The Internet has in some way become a magnifying glass or a microscope to what Jung called the collective consciousness. Everything from good and bad, best and worst, exciting and mundane, true and false, about humanity and how we think, feel and interact is now much louder.

Short answer - No, it isn’t possible or practical to make airplanes that are completely bullet-proof. But dating back to the days of WW2 several methods were used by the allied forces to try and mitigate the damage done to their warplanes by enemy fire. One was the installation of self-sealing fuel tanks in bombers and fighters to prevent a large loss of fuel, and avert the risk of high octane fuel fires when a gas tank was hit. https://en.wikipedia.org/wiki/Self-sealing_fuel_tank These self-sealing tanks made use of a double skin of rubber, one layer of which was vulcanized rubber (hardened with sulphur), and the other was natural rubber. When the tank was perforated by a bullet, leaking fuel would come into contact with the untreated layer which would swell and seal the leak. These tanks could allegedly withstand .50 rounds. Another interesting approach was that of Austrian mathematician Abraham Wald who escaped to the USA and worked for the Statistical Research Group (SRG) in New York during WW2. https://medium.com/@penguinpress/an-excerpt-from-how-not-to-be-wrong-by-jordan-ellenberg-664e708cfc3d Abraham Wald was asked to analyse the pattern of bullet holes found in heavily damaged US bombers returning from combat sorties over Europe, and to recommend where to place additional armour plating to protect the planes better without adding too much weight to them. Wald made the highly counterintuitive suggestion that the extra armour plating should be added to those areas of the planes that *didn’t* have bullet holes in them ! He did so because he realised that his SRG only got to study those planes which had actually made it back to base because they *hadn’t* been hit in any vital area of their fuselage - e.g. the engines. This is a good example of recognising and avoiding ‘Survivorship Bias’ in engineering analysis. https://en.wikipedia.org/wiki/Survivorship_bias

And with regards to women, it's probably the mess he, and his appointees to the Supreme Court, have made of the abortion issue. Not to mention his disrespect for women, in general, sometimes actually criminal.

Metabasite is a broad term for a metamorphosed basic (ie. low silica) rock. If that low silica rock was originally a basalt (as in this particular case) we can be more specific and call it a metabasalt. The terms aren't exactly synonymous, but ... A lot of these newer terms have appeared due to the modernisation of rock type systematics that the BGS has been implementing over the last couple of decades. More at BGS Rock Classification Scheme My crib sheet for metamorphics attached. Most of the outcrops in this area have been subjected to a 'greenschist' grade of metamorphism which is typically characterised by the green mineral chlorite. I'm not 100% sure that @exchemist's blue is the glaucophane blue of 'blueschist' grade, but it's possible. Classification of Metamorphic Rocks.pdf

Regarding economy, there are two factors. For whatever reasons, the GOP was better in branding themselves pro-economy, despite all the data suggesting otherwise. For Trump, the image is enhanced by his TV show, where he plays a successful businessman. The fact that folks get basic things wrong, is probably not very surprising. With regard to men, there is something worldwide going on, though the specifics vary especially on the age demographics demographics between countries. In many countries, men prefer a person that present themselves as an autocrat. Essentially, an insecure person's idea of a strong person. There is also a strong flavour of sexism among Trump voters, as studies have pointed out. Women, understandably are more likely to feel threatened by these sentiments (though apparently, racism can override these sentiments https://doi.org/10.1007/s11109-018-9468-2)

...careful not to step in a poodle...

Ok, I went back to your square, but on second thought I can't make sense of it. I thought I understood (crudely) what you were trying to do. Now I see you're dividing the square into pieces that actually overlap, so it's not a partition of the square really. It's something else. So I went to a completely analytical POV, ignoring the picture. I see no proof of convergence yet. Maybe you provided it before on some other thread, but I missed it. In purely analytical language, what you're saying is that, \[ \sum_{n,m=2}^{\infty}\frac{1}{n^{m}}=1 \] which, yes you're right can be proven, as the partial sum satisfies, \[ \sum_{n=2}^{k}\sum_{m=2}^{\infty}\frac{1}{n^{m}}=1-\frac{1}{k} \] So, yes, you're absolutely right AFAICT. But I still don't understand your square, I'm sorry. I had to interpret it purely analitically, with no pictures. PS: I tried to relate it to Riemann's zeta function, but I fell back to an infinity-infinity indeterminate, \[ \sum_{n,m=2}^{\infty}\frac{1}{n^{m}}=\sum_{m=2}^{\infty}\left(\zeta\left(m\right)-1\right) \] as I told you your method seems to indicate. The way to go is to build the partial sum Anyway... I'm a bit tired to do hard math now. That was fun.

As @MigL says, the idea of a multiverse is far from being "mainstream science". In fact it is not even science at all, but a highly questionable metaphysical idea, as it is completely untestable, having no observational consequences. I must admit I have never understood the Fermi Paradox. As Douglas Adams's character Slartibartfast observes, "In space travel, all the numbers are awful". Therefore if Einstein was right, interstellar travel is inevitably both very costly and utterly pointless. So why would intelligent aliens attempt it? One might even cite the Fermi Paradox as evidence that relativity is very likely correct!

During my vacation I learned, among other things, that Minimum Description Length (MDL) principle can be seen as a formalization of Occam's Razor in the context of statistical modelling and data analysis. Thanks @joigus for sharing this that triggered my curiosity: I had some practical experience from related areas such as data compression and communication. But I did not know much about the science that formalize and quantify intuitive but vague concepts (for instance complexity, simplicity, randomness of individual objects) and hence allows one to talk about them in a rigorous way.

I'm getting really annoyed with having to think twice when I see manipulated images now on facebook. We are the lucky ones because we have references, being pre-internet, but it's going to be impossible for youngsters growing up now to differentiate fact from fiction.