I agree, because really all numbers are imaginary. Numbers are also wonderfully useful for describing nature, and it's amazing how what might start as a quest for completeness and elegance ends up reflecting something about the real world. Each extension on our use of numbers is an augmentation, an extended toolkit to solve different problems, but doesn't negate anything which went earlier. For example finding the roots of a polynomial often represents a problem where complex solutions aren't applicable, and "no solution" is the more meaningful result. One kind of mathematics may be bigger and more complete than another, but that doesn't make it better or more true. It just depends on what you need from it.
The other fields are attempting to describe reality. While Newtonian physics is useful, as an approximation, it's also quite clearly wrong. You can imagine a universe which follows those rules but it's not this universe, and that's why it's wrong. Mathematics doesn't care about this universe, so you can pick whatever rules you want. Imaginary numbers are not "more accurate", they don't invalidate any previous understanding. They are an imaginary concept with interesting properties. For mathematics, that's enough.
The answer to that question didn't change, what changed is how you might interpret the question.
If I asked “what are the REAL roots of x² + 2x + 2” the answer is still "none". And prior to imaginary numbers being widely used, that is how the question would have been understood.
Mathematics involves making choices about what set of rules we're working with. If you don't allow the concept of negative numbers, the equation "x+1=0" has no solution. If you give me an apple, then I have no apples, how many apples did I have before? The question describes an impossible situation, and that's a perfectly valid way to view it.
Different sets of rules can change what's possible but don't invalidate conclusions based on other sets of rules. We just need to specify what set of rules we're working with.
Another quick fix is to set up a "Note to Self" group in Signal (make a group with 2 people then remove the other member). Nice tidy way to move things around, with a history of things you moved earlier
That's hilarious. I do hope it gets evaluated at run time. That way you could have a program that works most of the time but if some rare circumstance caused it to execute commands in a sequence where the correct level of politeness was not maintained it would get the hump and crash
For me I found casual or occasional smoking could too easily become "just one more". I hated the fact that it had a grip over me but I needed a more definitive reason to quit.
What worked for me was when my sister told me she was going to have a baby. I didn't want that kid to have smoking adults in her life. Which meant I had to quit, and hopefully that would help my sister to quit as well. I don't know if my actions made any difference but she did quit. Doing it for a kid was a powerful motivator for me. When she gave me the news, I put down the phone, tossed my remaining cigarettes in the trash and left it at that. Not even one last one. I knew I had the motivation I was waiting for and that was the end of it.
I guess everybody has their own way that works for them and you just need to find what that is.
I agree that it's on a whole other level, and it poses challenging questions as to how we might live healthily with AI, to get it to do what we don't benefit from doing, while we continue to do what matters to us. To make matters worse, this is happening in a time of extensive dumbing down and out of control capitalism, where a lot of the forces at play are not interested in serving the best interests of humanity. As individuals it's up to us to find the best way to live with these pressures, and engage with this technology on our own terms.
My PC had been running like shit for a while and I was already weighing up options for replacing it, when I got the popup message from MS about Windows 10 expiring, and how my only option was to dump the PC. So I installed Linux out of pure spite. Runs like a dream now. Thanks Microsoft!
bampop @ bampop @lemmy.world Posts 0Comments 111Joined 4 mo. ago
I agree, because really all numbers are imaginary. Numbers are also wonderfully useful for describing nature, and it's amazing how what might start as a quest for completeness and elegance ends up reflecting something about the real world. Each extension on our use of numbers is an augmentation, an extended toolkit to solve different problems, but doesn't negate anything which went earlier. For example finding the roots of a polynomial often represents a problem where complex solutions aren't applicable, and "no solution" is the more meaningful result. One kind of mathematics may be bigger and more complete than another, but that doesn't make it better or more true. It just depends on what you need from it.