> What we tend to forget is that even with the catastrophic effects of climate change, the Earth is still vastly more inhabitable than other planets in the solar system.
Speak for yourself. I have never forgotten that Earth is more inhabitable than Mars or Jupiter
> Canada has a similar opioid epidemic but a different supply chain, largely skipping over Mexico. Because Canada saw similar falls in fentanyl strength, the researchers hypothesise that the supply shock was caused by something changing in China.
Yeah and (1) the codegen produces massive headers that slow compilation of anything that touches them (2) the generated classes are really awkward to use. Not a big fan of the experience of protobuffer generated code in a large C++ code base.
It's lead to a huge layer of adapters and native c++ classes equivalent to the protobuffers classes to try and mitigate these issues.
> In a real-indexed vector, that notion doesn't apply. It's "infinity plus one" all the way down: whatever real value you pick to start with, x, there's no delta small enough to add to it such that there's no number between x and x+d.
Just to clarify, uncountability isn't necessary for this. It's true for the rational numbers too, which are countable.
Yes. Indexes in infinite sets are counterintuitive, and real numbers even more so.
The famous counterexample to all of this sort of thinking is Hilbert’s hotel, which I’m sure you know but want to point it out for people who haven’t seen it before because it’s pretty mind-blowing when you first encounter it.
Say you have a hotel with an infinite number of rooms numbered 1,2,3,… and so on and they are all occupied. A guest arrives- how do you accommodate them? Well you ask the person in room one to move to room 2, the person in room 2 to move to room 3, and in general the person in room n to move to room n+1. So every existing guest has a room and room 1 is now free for your new guest.
Ok but what if an infinite number of prospective guests arrive all at once and every room in your hotel is full. How do you accommodate them? Still no problem. You ask the guest in room 1 to move to room 2, the one in room 2 to move to room 4, and in general the guest in room n to move to room 2n. Now all your existing guests still have a room but you have freed up an infinite number of (odd-numbered) rooms for your infinite number of new guests to move into.
These are all countable infinities, and Cantor showed that if the number of rooms in your infinitely-roomed hotel is ℵ_0, then the number of real numbers is 2^ℵ_0, which is obviously quite a lot more.
I would recommend spending that "couple thousand" for quote(s). It's a second opinion from someone who hopefully has high volume in your local market. And your downside could be the entire system plus remediation, fines, etc.
To be clear, I'm not opposed to experimenting, but I wouldn't rely on this. Appreciate your comment for the discussion.
No I'm not relying on it in the sense of going out and running the entire project through it, but as an accurate screener for whether it's worth doing, there's nothing comparable available.
We’re supposedly talking about 4 major crime families, it wouldn’t be one McDonalds it would be dozens and dozens. And all legal.
Nothing about this story makes sense other other than as yet another headline to try to get people talking about something other than Epstein.
Did illegal gambling take place? I’m sure. Were 4 different crime families investing significant resources to take home barely $1m/year? I’m extremely skeptical and given this is coming from Kash “I always look like I just did a line of coke” Patel, I’d say it’s more likely than not we’re getting incomplete, if not bad information
Interesting! On the guitar when alternate tunings are used, the pitches are written as they sound.
I wonder if maybe the difference is due to the fact that alternate fingerings are very common for guitar (because of having more strings spaced closer together). So notating pitches assuming a specific fingering doesn't make sense.
Plus I don't think the mapping from the staff to muscle memory for guitar is nearly as strong because we have frets.
12 pizzas. Let’s say large. That’s 12 slices each? Average person eats let’s say 3 slices (some won’t eat, some have one, some have four, some, like me, have brains that are perpetually stuck on Grad School and will embezzle slices until there’s no leftovers). So 144 slices could do maybe 48 (let’s say 50 people). So that’s give or take $4 per person.
That’s one of those “a travel booking error worth of money brings a subjective amount of joy, and the only wrong move would be to stop unless the team wants it to stop” things.
Which is absolutely ripe for some Director of Couch Spelunking to earn their Golden Monocle award for making the spreadsheet show brackets around budgets and win a trip to Boise.
Speak for yourself. I have never forgotten that Earth is more inhabitable than Mars or Jupiter