Thanks for the link, great read. I think I get you here; in the context of a DSL where it's impossible to travel more instructions than X, suddenly you don't have a halting problem anymore as you've artificially limited that language's ability to travel beyond a known/fixed set of states.
The second you wield a language which has constructs like Haskell, where in theory you can iterate over an infinite list of items (thinking about it even any language where for i in input_var is possible); the halting problem hits you in the face like a brick.
Its almost a chicken and the egg problem, where you can't know how long it will run for/whether it will halt without already knowing the answer, but if you knew the answer, you wouldn't need the program to find it.
Ahhh this is fantastic thank you; it _is_ hard to reconcile whether problems come with the original topic or whether they are introduced by the abstraction that we _need_ to make in order to quantify a thing/explain it to ourselves and others.
Regarding the downcast/upcast; I think it _can_ be possible to do this successfully;
> I have a glass, I throw it at a hard surface. What will happen? Well (duh) the glass will (most likely) break.
This hypothesis completely ignores nearly 100% of all relevant physics and the laws surrounding the problem; the arrangement of air molecules, the arrangement of the molecules in the glass, the physical forces governing me, it reduces the entire equation down to some really basic napkin physics.
But; does the outcome work? Has my interpretation of the universe and its physics actually predicted what will happen?
Probably a stupid example, but I think that a lossy picture of the universe can still yield a correct answer.
I can't physically run a simulation of the entire universe in my brain, as my brain is part of that same universe. Lossy representations/models are a necessity in the thinking-ham bound world in which we exist.
Thank you for your insightful answer, in reduction; "Don't fight a god, you won't win, and you'll definitely die in the process!"
The approach you describe though is brute force. I don't think (if there even is an answer to this problem) that it can be brute forced; that's where you run into the limits of hardware/computation/energy and start talking about timeframes which exceed the life of the universe.
I think brute force might be a useful tool in places to validate results, but if there _is_ an answer to this problem it's purely mathematical.
Apologies for sounding both excited and naive; these sorts of challenges make me happy in strange ways that no other thing does!
Thank you internet stranger, for introducing me to hard-maths drugs; am hooked!! \o/
I love the idea of this. So the BB problems are individual iterations of the halting problem right? To truly solve the problem one would have to come up with a program which would operate on all possible BB numbers?
This truly leads into "computation"; when we're dealing with known quantities, yes, we can "solve" the halting problem. The second you move into "we don't know the answer yet", the can of worms opens. Thank you.
This is what makes me sad about the AI age; many articles now have the same phrasing, the same analogies, the same quips, structure, the same wording; once you start to see it there's no going back.
I actually laughed quite a lot to begin with, GPT models saying things like "...might look like P, but is NP wearing a hat and a lab coat..." and "...is a haunted house disguised as a git repository..."; but alas when you've heard them a million times everywhere it really starts to bite.
Something has always nagged me about the halting problem, might be my mis-understanding of the problem space but;
- You have a piece of software
- That software does in memory compute only
- The software does not touch any peripherals, networking, or any other external source which introduce unpredictability (x)
I'm convinced that somehow this can be solved/proven whether the execution will halt or not.
(x) The second you touch any external peripherals or networking, you're effectively asking the question of "If I phone my friend, will they pick up the phone?" -> to which the only answer is, "They'll pick it up, only if they pick it up/are there". You can't answer that question without trying it.
Am I missing the point? I'm sure you can introduce other edges even in the limited model above, e.g. where a memory stick stops responding or something; but all in if you have reliable kit and don't touch anything external, why can't this be solved?
I'm not a religious person but this seems relevant to your comment;
> So I commended the enjoyment of life, because there is nothing better for a man under the sun than to eat and drink and be merry.
As someone with autism and ADHD; I have spent my life trying to understand better ways to do things, optimisations, doing things "right" or "better" or "faster", and trying to come to terms with others who don't really give a shit about any of it.
The conclusion I arrived at is that the snapshot of time I get in this form is best spent enjoying what this form has to offer, nothing more.
- My sausage'y shaped fingers can't manipulate time or gravity; but they can tickle my children and make them laugh.
- My heart can't fix anything; but it can help me to understand others suffering and guide my actions.
- My eyes can't see the whole electromagnetic spectrum; but they can appreciate a beautiful vista and fill me with wonder.
When TFA mentions that a star just ate a planet, I remember just how small and unimportant I am outside a tiny speck of the world; and rejoice that I'm not responsible for anything super important outside that little speck. \o/
Here here. 100% in agreement, people seem to have forgotten that the majority hold the bargaining power. You'll always have people who cross "strike lines", but by and large if the entire user base simply said; no, and walked; the world would definitely be a better place, in so many ways.
I don't hold France as a shining example of humanity; but by-christ if they get upset they actually take those feet, one in front of the other and fight tooth and nail against `$thing`. Even if they don't "win", they /don't go quietly/.