

I love the idea (and it’s definitely true) that there are irrational numbers which, when written in a suitable base, contain the sequence of characters, “This number is provably normal” and are simultaneously not normal.
I love the idea (and it’s definitely true) that there are irrational numbers which, when written in a suitable base, contain the sequence of characters, “This number is provably normal” and are simultaneously not normal.
In 2003 (or thereabouts) I was a paying user of an Apple music product. They deliberately broke the way that I used their product, then once someone found a workaround, they broke that, too.
I tried to be their customer, and they kicked me out for not using Windows or MacOS. Now I’m emotionally invested in not giving them any money, ever.
I’d describe it as sort of 3 layers. The first is practical/everyday things, which are mostly much nicer than being alone, but require attentiveness and communication (learn what your SO doesn’t like doing, and do it. Learn what things are work together projects, and what things are stay out of my way type things for each of you, probably other aspects too) - but once you know how to take care of each other, almost everything is less work, takes less time, and costs less money. Cooking, laundry, cleaning, gardening, repairing things, painting the house are all improved. Decorating and having guests over are harder, at least for me. You have to not fall into the trap of taking the things they do for granted, even when those things are routine.
The second layer I’d describe is lust/romance, which is sort of easier, except that you must avoid letting things coast too long. You have to dedicate time and effort to discovering new things about each other, and new things you enjoy together. You should still be dating, no matter how long it’s been, and ideally you should both be planning things most of the time. In my relationship, this is usually 1-2 things per month, each.
The final layer is the emotional/support layer. Almost any time, my wife can seek comfort and support from me in a variety of ways for all kinds of things, and I get the same from her. All the big problems in life are easier when you can share them, so here the benefits are huge. This is the only thing I got basically none of from having roommates or a best friend, or dating. For my situation, there’s basically no downside to this.
Inflation is wild. Just a few decades ago, you could get this kind of thing for just an arm and a leg.
Last time I tried freecad, the geometry solver was incorrect, so it would sometimes create two (or more) shapes from a fully constrained part. Since learning about openSCAD, I’ve seen no reason to give it another try.
I once had a dream where I played a game like warcraft 2, but with mythical animals. Basically age of mythology, with better controls, and a darker aesthetic. I still wish that existed, so I could play it.
Which industry do you work in?