Chebucto Regional Softball Club

@futurebird @GezThePez I can confirm that this was something that confused young teenaged me. Not so much the transition but the fact that there wasn't a transition. It wasn't until I learned about affine transforms (a tiny bit at A level, most at university) that I realised that it even was possible to take something from one form of expression and mechanically translate it to the other.

This is often also a special case of the distinction between imperative and declarative programming.

You wrote both of these as imperative, but, from your original example, the goto is unusual. The way that this is normally written (when introducing children to it) is declaring that a line exists which is drawn for all rho where sin(rho) = cos(rho), whereas the second form is explicitly imperative (you're giving commands to a turtle). I wouldn't normally write the first form with goto, I'd write it just setting pixels.

Your third example is also interesting because it's very much a declarative form: a circle is defined as all points that are equidistant in a 2D plane from a defined point. And realising that lets you derive your first form because the first form is 'just' the definition of all possible triangles where the hypotenuse length is a constant. But all of these are forms that provide continuous functions that specify the locations of all of the points on a line, whereas the turtle one is a set of instructions.

You can turn the declarative forms into equivalent imperative forms (as you did) by saying 'for each point in some discretised form, draw a line segment or pixel that approximates it'. But transforming it to the imperative form for the turtle is much harder because the quantisation becomes more explicit.

And this might be why I haven't done computer graphics since I finished my PhD.

@futurebird @CptSuperlative @emilymbender Summarisation is the one I’d be most nervous about because creating a summary is hard: it requires understanding the content and knowing which parts are relevant in a given context, which is why LLMs tend to be awful at it. They don’t understand the content, which is how you get news summaries that get the subject and object the wrong way around in a murder. They don’t know what is important, which is how you get email summaries that contain a scam message and strip all of the markers that would make it obvious that the message is a scam.

If you’re going to read all of them and are just picking an order, that’s probably fine. The worst that a bad summary can do is make you read them in the wrong order and that’s not really a problem.

@futurebird Unless the star moved really fast, probably not much. About the only thing in our development that comes to mind is that you may not have a stable equivalent of the North Star, so navigation would be harder (but you'd need a fairly large relative speed for that to really be the case). As long as you had an iron core, magnetic navigation would still work, you just might explore the world a bit more slowly (without an iron core, being cooked by radiation would be an issue).

Newtonian mechanics came from things in the solar system, rather than beyond. Having a large gas giant that cleaned up the solar system (so there's just one other planet left) would be more of a problem than a rogue star.

General relativity was first demonstrated with gravitational lensing during an eclipse, but that wouldn't be affected (though we are very lucky in our moon for this and various other reasons). But it was later demonstrated by GPS satellites, so even if you missed the eclipses then you'd get a later chance (fun fact: original GPS satellites had a backup mode in case Einstein was wrong).

The question that bothers me is whether the opposite of this. In China, science effectively stalled for hundreds of years because they didn't invent glass, which was a prerequisite for most of chemistry. Perhaps there's something that's really obvious to people on a rogue star that's the equivalent of glass for us and is the thing that you need to unlock an entire field of science that we simply are not aware that we miss. For example, a simple way of synthesising bosons would enable trivial low-radiation nuclear power, but we have no idea how to do it. Maybe if you observe the galaxy from a different vantage point, it takes you down a path where you discover that it's easy.

@apophis @futurebird I don’t know if it’s ever evolved for insects, but some jellyfish have this kind of cyclic regeneration thing. All of the parts have evolved separately, so I don’t see a reason why the combination couldn’t, in theory.

I suspect it would be unlikely because, normally, evolution selects against immortality. If a species is immortal, it either creates more offspring and competes with the, for resources and goes extinct, or it stops producing offspring (or produces them at a rate that accounts for accidental deaths only) and therefore stops being subject to mutations and so can’t evolve to adapt to changing circumstances.

That said, if it’s a metamorphosis style transformation rather than a simple moulting, there is scope for transcription errors there and so possibly it would continue to evolve.

@futurebird I mostly stopped about ten years ago. Poor treatment if workers was the main reason at the time but I found that they were rarely the cheapest option even then and it's got worse. I sometimes use them to find the thing that I'll buy elsewhere.

For books, they're usually the most expensive option now.