palordrolap

It depends, and it’s not necessarily the same answer every time even if it’s the same player(s) playing the same scenario in the same game over and over.

This is going to be incredibly confusing for the people who spring into existence as a result of the change but have memories consistent with them never having existed. I mean, what would their memories even be?! And it would be even more confusing for their living ancestors who may find that as well as now having (grand)children they have no memory of, the ones they do have memories of suddenly no longer exist.

There are too many timeline branches from that one incursion to cover all the bases here. Does someone with my name exist (alternative sperm / egg theory)? Do they live in the same house? Do I get caught and arrested either way? How soon do I realise what’s happened?

I mean I probably realise a lot sooner than the average person because I’ve consumed a lot of sci-fi and am well aware of It’s a Wonderful Life, but it doesn’t really help.

My parents probably live in the same place. I’d go there for help if I hadn’t figured it out yet. Maybe if I had. I don’t know whether they would help for sure though.

My father might think I’m actually a descendent of one of his parents’ relatives. My mother would definitely see the resemblance. Maybe I also look like my “replacement”. That would be traumatic and confusing for all concerned though.

Imagine getting a DNA test done to prove it. That’s a long way off and/or unlikely , but it would conclusively prove I’m their kid. There’d be hospital mix-up investigations. It wouldn’t be the first time there have been twins. Now I must be a long lost fraternal twin of another person who has my name.

If they have no child of a similar age, that just raises even more questions. Did they collectively lose their minds and abandon a child at some point?

But that’s distant speculation. Maybe they tell me to get lost. Maybe I don’t go there in the first place.

If I do realise what’s happened sooner rather than later, maybe I leave my parents alone. I’d probably go to a local hospital and lurk around the cafe and shop until I get help, get my head together with a better plan, or get arrested. I need medication anyway, not that I can prove that. I assume drug names are the same.

I’d probably have to take each moment as I find it and act accordingly. As to how I’d act, that’s very hard to say until it’s actually happening.

Since there’s a reasonably strong link to calculus, and mechanics as you’ve already found, it could theoretically help in physics simulations either in a computer or on paper.

As for practical application, well, emulating physics is pretty important in a lot of computer games, or getting robots (assembly line arms, androids, automated vacuum cleaners) around the place and to do what they need without accidentally catapulting themselves into next Tuesday.

How that’s actually programmed might not involve dual numbers at all, but they’re one way of looking at how those calculations might be done.

A lot of “advanced” maths comes from asking “What if this was a thing, how would that work? Would it even work?”, so you could say there’s a deliberate sense of “fake” about it.

Dual numbers come from “What if there was another number that isn’t 0 which when multiplied by itself you get 0?”

Basic dual numbers (and complex numbers) are no harder than basic algebra, shallow end of the pool kind of stuff, but then not everyone is comfortable getting in the water in the first place, and that’s OK too.

Came here to say this, but since it’s already here, I’ll throw in a bonus mind-melting fact: ε itself has no square root in the dual numbers.

1. I have this odd, perhaps part troll, feeling that there are two, and only two, roots of the Riemann Zeta function that aren’t on the critical line, and are instead mirrors of each other at either side of it, like some weird pair of complex conjugates. Further, while I really want their real parts to be 1/4 and 3/4, the actual variance from 1/2 will be some inexplicable irrational number.

2. Multiplication order in current mathematics standards should happen the other way around when it’s in a non-commutative algebra. I think this because transfinite multiplication apparently requires the transfinite part to go before any finite part to prevent collapse of meaning. For example, we can’t write 2ω for the next transfinite ordinal because 2ω is just ω again on account of transfinite and backwards multiplication weirdness, and we have to write ω·2 or ω×2 instead like we’re back at primary school.

Ahh, Liquid Television. Thank you. The other block of odd programmes that ended up on BBC2. It’s been a long, long time, so I’m not surprised I mixed them up!

Aeon Flux (the anime TV series, not the movie)

I want to say it was aired as part of the Def II, teenage audience program slot on BBC2 in the '90s, the original UK home of Ren and Stimpy and The Fresh Prince of Bel Air, but the Wikipedia article for Def II doesn’t mention it at all.

Edit: Nope, it was Liquid Television (see reply). Some but not all of MTV’s weird programmes ended up on BBC2, sometimes even under the original parent name, like Liquid Television.

Get a 15 puzzle. Or try a digital version.

That was about my level of figuring out. One less dimension to worry about. Never could do the cube.

One such implementation is here: https://www.chiark.greenend.org.uk/~sgtatham/puzzles/js/fifteen.html