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02:01:16 <esowiki> [[User talk:Ais523]] https://esolangs.org/w/index.php?diff=70121&oldid=70113 * Ais523 * (+591) /* The Waterfall Model UTM */ I don't know the minimum, but it's a lot less than 124
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03:00:49 <ais523> re the M:tG Turing machine: if all you want is a TWM problem that the judges won't be able to work out the resolution of, I recommend quadratic residuosity
03:00:56 <ais523> which should be pretty easy to implement in TWM
03:01:18 <ais523> I posted https://crypto.stackexchange.com/questions/70743/what-makes-the-quadratic-residuosity-problem-hard as a setup for encoding QRosity into TWM, hopefully in a program that's small enough to memorise
03:01:47 <ais523> (the issue being that we need to find an example program for which there's no known way to discover whether it halts or not in a viable length of time)
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03:11:10 <ais523> MTGBusyBeaver: I'm going to bed now but I'll try to get online tomorrow, the idea of combining a universal computer and a no-infinite-loops deck hadn't occured to me at all but is the sort of ridiculousness I approve of
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03:50:56 <Hooloovo0> I think some of the more simple ones I've seen in other ]]
03:51:18 <Hooloovo0> err other simple systems are a twin prime checker and a collatz relative in CGOL
03:51:34 <Hooloovo0> but those are still pretty complicated, and aided by the 2d nature of the CA
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04:52:47 <MTGBusyBeaver> Thanks ais523, unsolved problems arent actually very good, as either it is proved false in which case the machine never halts, or there is a counter example probably at less than 10^^^10, which is a score we can already beat.
04:53:26 <MTGBusyBeaver> So we want to implement the biggest busy beaver machine possible
04:55:20 <MTGBusyBeaver> But that is limited by the namespace, so we really get the improvement via a UTM.
04:58:13 <MTGBusyBeaver> How does a waterfall UTM work? We can get oodles of googles as the variables in a waterfall program, what sort of ratio are we getting for the inputs to the size of machine simulated?
05:02:26 <MTGBusyBeaver> Not to mention that we can iterate the UTM to get BB(BB(....BB(X)...))
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08:17:04 <b_jonas> (also I find it ridiculous when an ultrafinitist argues that 10**400 might not exist, but if you talk about BB(BB(X)) I might have some more sympathy to their side)
08:20:39 <b_jonas> what you can get is BB(X) for a large X, just by putting O(X) (or maybe O(2)**X) tokens somewhere into the waterfall program, so you can't just compute BB(100), which is already ridiculous, but BB(10**(10**100))
08:25:41 <b_jonas> heck, you very likely can't even get BB(100), you can only pick a long-running program that you can prove will finish
08:25:51 <b_jonas> and that won't run for anything close to BB(100) turns
08:26:11 <b_jonas> though it can run longer than most of the other M:tG loop constructions
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09:40:26 <tromp> int-e: your unsatisfiability proof is correct, except that the center using all 3 colors can only be concluded in the 6th diagram
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13:32:36 <ais523> b_jonas: I think MTGBusyBeaver's point is that you can create an M:tG deck that's capable of simulating all The Waterfall Model programs below a specific size, but can't get any output from the simulations unless they halt
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13:33:23 <ais523> the question is now "how much damage can this deck do turn 1?", which is a busy beaver problem, as it'll depend on which program produces the largest output
13:34:28 <ais523> it doesn't require you to find some specific program (although it's helpful to show that you can at least construct a UTM, because that gives you a bound on how fast the busy beaver function grows in this context)
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14:49:59 <ais523> MTGBusyBeaver: fwiw, I'm concerned about the use of Arcbond in the construction; what's to prevent a player setting up an infinitely looping machine without protecting the opponent from Arcbond, and doing infinite damage that way?
14:50:16 <ais523> or does the fact that the opponent loses at 0 life count as stopping the loop, and thus it isn't infinite damage unless you do it all at once?
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15:11:02 <MTGBusyBeaver> as for iterating the BB function, why is that not something we can do? The BB machine outputs a lot of some resource, then we use that resource to build an even bigger TM and use a more finite resource to trigger the run.
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15:13:21 <int-e> The busy beaver function is uncomputable.
15:15:14 <int-e> But it's a function, so it's not just a single number.
15:17:40 <MTGBusyBeaver> BB(X) is the busy beaver number of a turing machine of size X, taking the integers to the integers, so BB(BB(X)) is a well formed statement, even though we will never be able to evaluate it
15:17:42 <int-e> There's a conceptual gap here somewhere. For example, we can create a Turing machine, that, given n, outputs a sequence lower bounds for the busy beaver function, such that the last value output is the value of the busy beaver function itself.
15:20:37 <int-e> I don't get how you intend to accomplish that iteration.
15:22:34 <MTGBusyBeaver> Because the MTG:TM incidentially outputs lets say life for us. and the size of the TM we can make is limited by our life, and running the TM takes something else eg: red mana.
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15:24:00 <MTGBusyBeaver> so say we start with a combo that makes X life and 5 red, then use our TM to turn 1 red into BB(X)
15:24:42 <MTGBusyBeaver> then we can spend another red after the BB machine halts to run BB(BB(X))
15:25:01 <int-e> There is no TM that computes BB(X), given X.
15:26:35 <int-e> Yes (more or less). But *you* have to know what that machine is when setting up the computation.
15:26:56 <int-e> And when you iterate, *you* have to come up with the TM of size BB(X) that outputs BB(BB(X))?
15:29:25 <MTGBusyBeaver> No we don't, knowing the machine exists is enough to define it.
15:30:27 <int-e> I'm missing something about the intention here.
15:30:54 <int-e> I thought you wanted to leave the game in a state where there are no choices left, and leave it to the arbiter to run it to its conclusion.
15:31:45 <int-e> Are you doing something like assuming best play by both players?
15:32:28 <int-e> (I suppose that would bring you into ATM territory where you can play such tricks indeed.)
15:32:41 <int-e> (But again, all the burden of finding the machines would be on the players.)
15:33:09 <MTGBusyBeaver> a little stronger than that. Our opponent knows what we are trying and is trying to either minimze the total damage or disqualify the deck by allowing it to go infinite.
15:35:23 <MTGBusyBeaver> single card draw is a Demonic Tutor in disguise: you can assume that the order of your deck is exactly what you want it to be. This veers pretty heavily into magical christmasland, but if we didn’t do it this way you’d have to figure out the average amount of damage a deck could deal, which is probably impossible.
15:35:24 <MTGBusyBeaver> with a deck of 60 wastes. However, they are still playing to stop you: if you give your opponent a choice, they will pick whichever one is worse for you. The only exception is that they won’t concede the game. This is a sadistic goldfish that wants to make you play it out.
15:35:24 <MTGBusyBeaver> of the time, so we define it like this: when you make your deck, I pick a finite number, say, a million, or Graham’s Number, or four. If, no matter what number I pick, there’s a line your deck can take that will deal at least that much damage, your deck goes infinite and is disqualified.
15:35:25 <MTGBusyBeaver> magic apply: if I put 80,000,000 copies of Shock on the stack and target my opponent with each one, they’ll die on the tenth one, and I’ll have dealt only 20 damage. In practice, that means you’re either winning with a giant X-spell or by attacking with a lot of very big creatures.
15:37:45 <cpressey> "Do the most damage possible in MtG" reminds me a lot of "Name the Biggest Number": https://www.scottaaronson.com/writings/bignumbers.html
15:38:20 <int-e> cpressey: I'll be generous and let you go first.
15:38:36 <int-e> (That's how it works, doesn't it?)
15:38:57 <tromp> int-e: did you say you had a less-than in 58 bits with coroutines?
15:40:50 <tromp> i was able to reproduce that:)
15:41:14 <tromp> much more straightforward than your div and even your min
15:41:33 <int-e> tromp: I thought that if you take 'min' as the blueprint you should be able to find the comparisons :)
15:41:35 <tromp> i see now what you mean by div (m+1) being ewsier
15:41:38 <cpressey> You can work on BB(10) and you can have a working theory for what BB(10) might be but you'll never know if it actually is BB(10). Similarly, you could work on BB(BB(10)) but you have to revise your theory about BB(BB(10)) every time you revise your theory about BB(10).
15:42:12 <tromp> still surprising that you can do div m with only an additional appllication to id
15:42:16 <int-e> tromp: It has occurred to me that maybe a divisibility test would be a tad shorter than the modulo operation.
15:43:08 <int-e> (I haven't put that one to the test though, yet.)
15:45:05 <MTGBusyBeaver> that's not a problem? We are basically playing that name the biggest number game, We can get a bit beyond Ackermann numbers in standard.
15:48:09 <tromp> int-e: did you also try a less-than-or-equal ?
15:48:22 <int-e> tromp: it's the same?
15:48:31 <int-e> tromp: I mean, swap the arguments and true and false
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16:00:54 <int-e> MTGBusyBeaver: Which is fine. Basically you're looking for busy beavers, where the model of computation of M:tG. You can define a busy beaver function for that, say in terms of the deck size.
16:01:06 <int-e> MTGBusyBeaver: But none of that lets you iterate the busy beaver function itself.
16:01:14 <int-e> Because it's uncomputable.
16:01:54 <MTGBusyBeaver> only this week we worked out a turing machine setup that works in the rules,
16:02:36 <MTGBusyBeaver> and can set it up to be repeatable some finite number of times
16:03:16 <Taneb> There's no Turing machine that computes BB(x)
16:04:33 <MTGBusyBeaver> No, but there is some turing machine of size x that outputs BB(x)
16:05:04 <Taneb> There's certainly one that takes that many cycles to halt
16:05:37 <Taneb> Or well, writes that number of 1s on the tape
16:06:04 <int-e> Maybe "there's a line in your deck" is not precise enough.
16:06:05 <Taneb> You can't then take that number and emit BB(BB(x)) without knowing the answer beforehand
16:06:20 <int-e> What does that mean, exactly?
16:06:31 <Taneb> At which point, why not just do that directly? Why not go straight to BB(BB(x)) + 1?
16:06:41 <int-e> (Who gets to make the choices for that line of play?)
16:07:00 <int-e> Yeah then you have no alternation.
16:07:13 <int-e> So no way of iterating the busy beaver function at all, not even theoretically.
16:07:40 <tromp> int-e: please add div test term to the repo if it offers nontrivial improvement over mod size
16:07:53 <int-e> Because the opponent will just pick a non-terminating TM instead.
16:08:07 <tromp> shld be called divides.lam i guess
16:08:30 <int-e> MTGBusyBeaver: "non-terminating" was for "something that does infinite damage".
16:08:38 <int-e> or unbounded, which is the same.
16:08:59 <MTGBusyBeaver> but the only way to do damage is by attacking with all the giant creatures the TM makes
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16:11:36 <int-e> Hmm. I see, I'm wrong about needing alternation.
16:12:09 <int-e> Plain non-determinism is enough, and you get that.
16:13:08 <MTGBusyBeaver> we need the TM to be deterministic, or we can just loop for an arbitrary amount of time and then halt
16:13:44 <int-e> The non-determinism is in the choices the player can make in setting up that TM.
16:16:30 <MTGBusyBeaver> The working TM implementation of the Waterfall Model is here: https://www.mtgsalvation.com/forums/magic-fundamentals/magic-general/615089-most-turn-1-damage-in-a-deck-with-no-infinite?comment=2434
16:17:58 <int-e> So we have: NTM A(n): guess TM B of size n; run B to completion; return number of steps taken, and a computational model that discards all non-terminating runs and picks the maximum value produced by the others.
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16:21:12 <cpressey> "a computational model that discards all non-terminating runs"
16:21:54 <MTGBusyBeaver> a run that never terminates does no damage and scores zero
16:22:33 <cpressey> How do you propose to test a run to see if it will never terminate
16:23:25 <imode> very carefully. ;)
16:24:22 <MTGBusyBeaver> we don't need to every actually construct the busy beaver machines, just know that they are bounded by BB(n)
16:24:22 <int-e> cpressey: You don't.
16:24:47 <int-e> cpressey: It's a perfectly fine definition, just not computable.
16:25:21 <int-e> MTGBusyBeaver: Obviously to actually deal that amount of money you still have to fine the busy beavers.
16:26:39 <imode> didn't know you bet on MTG int-e. :P
16:26:57 <MTGBusyBeaver> well we just want to set bounds for the damage, highest lowest bound with an upper bound wins
16:27:00 <int-e> imode: I don't. But I imagine it would be as good a way of losing money as all the others.
16:28:06 <imode> high-stakes MTG tournaments lmao.
16:32:43 <cpressey> int-e: Did you notice you didn't stop at "money", you also said "fine" for "find"?
16:34:00 <cpressey> Image of a parking patroller tucking a ticket under the wipers on a Turing machine.
16:34:49 <fizzie> int-e's all about the money, all about the dum dum da da dum dum.
16:35:16 <int-e> cpressey: No I had not noticed that.
16:35:30 <int-e> cpressey: That's a plausible typo though, at least.
16:36:39 <cpressey> I'm a little unclear on whether just having a (perfectly fine) definition is sufficient for MtG, or if you have to actually, you know, be able to compute it, in order to take your turn.
16:37:24 <int-e> cpressey: I think it works just as MTGBusyBeaver claims... you don't need to know what the upper bound is, just that it exists.
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16:39:06 <int-e> cpressey: And the trick is, non-termination doesn't kill you; it's only the things that do terminate that eventually deal you any damage.
16:39:48 <MTGBusyBeaver> We'd like to be a little less handwavey and at least explicitly construct/explain/justify the UTM in the Waterfall method
16:40:26 <int-e> cpressey: It's a really funny situation where given a candidate for an upper bound you'll (probably) never be able to tell whether it's big enough already :)
16:40:30 <cpressey> So "In principle there's a TM that deals a huge amount of damage because it computes BB(...(BB(10)...), but I don't know exactly what that TM is" is sufficient?
16:41:07 <int-e> cpressey: No, it's an NTM that computes that thing, and we do know what that NTM is.
16:41:20 <int-e> But we can't run NTMs in practice.
16:42:32 <int-e> cpressey: Somewhere, internally, that NTM *guesses* the actual TM.
16:43:09 <MTGBusyBeaver> There are only finitely many possible TMs of a given size
16:43:12 <int-e> Or TMs, plural. One that computes BB(10), one that computes BB(BB(10)), and so on.
16:43:35 <cpressey> "An NTM guesses a TM" is roughly the same as "In principle there's a TM", what I said
16:44:25 <int-e> But also kind of missing the point; for any natural number n, there's a TM that computes n.
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16:45:12 <int-e> But I didn't mention the size constraint either, so I'm not sure what my objection is.
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17:00:31 <arseniiv> <MTGBusyBeaver> we are the NTM => I would doubt that
17:01:31 <int-e> many-world quantum physics gets somewhat close
17:01:43 <int-e> but even that has a hard time collecting results
17:08:58 <ais523> I guess the idea with this Magic construction is that it lets you calculate any number a UTM can calculate
17:09:04 <ais523> up to a certain size n
17:09:21 <ais523> so we know that it's capable of calculating BB(n) and no higher number, but we don't know what input you have to give it to produce that
17:09:59 <ais523> there doesn't seem to be a conceputal issue with iterating that: you could perhaps modify it so that it's capable of calculating a range of numbers of which the highest is BB(BB(n)), given the appropriate input
17:10:02 <ais523> but not be able to determine what that input is
17:10:21 <ais523> the reason this works is that what we have is, conceptually, an interpreter that refuses to run non-halting programs
17:11:09 <ais523> I really should create a universal interpreter for some TC language in TWM some day, even if it's far from optimal
17:11:14 <ais523> just to get a baseline
17:11:26 <ais523> on how many waterclocks you need
17:11:33 <ais523> I keep on getting sidetracked trying to optimise it
17:11:51 <MTGBusyBeaver> yeah, even if it is inefficient as long as it works with 124 waterclocks
17:12:41 <ais523> well, the limit's a little less than 124 because you need a few creature types to set it up, right? Cat in particular is unusable
17:12:57 <ais523> but much less than 124 seems definitely viable
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17:14:49 <MTGBusyBeaver> but we get to use everything else as we can make the setup creatures lose their types (and avoid arcbond damage) with One with the stars
17:14:52 <ais523> I personally count halt states, although not everybody does
17:15:20 <ais523> that's a fun card, and one I came up with myself when brainstorming custom cards (although my version of it was white)
17:16:48 <ais523> `card-by-name One With the Stars
17:17:03 <ais523> oh right, I need to persuade someone to add Theros Beyond Death to that thing
17:17:08 <ais523> `card-by-name Hungry Lynx
17:17:09 <HackEso> Hungry Lynx \ 1G \ Creature -- Cat \ 2/2 \ Cats you control have protection from Rats. (They can't be blocked, targeted, or dealt damage by Rats.) \ At the beginning of your end step, target opponent creates a 1/1 black Rat creature token with deathtouch. \ Whenever a Rat dies, put a +1/+1 counter on each Cat you control. \ C17-R
17:17:13 <MTGBusyBeaver> Enchanted permanent is an enchantment and loses all other card types. (It still has its abilities, but it’s no longer a creature.)
17:17:25 <ais523> I was mostly just trying to show it off
17:18:05 <ais523> b_jonas: can you update HackEso's M:tG database to include the latest cards? given the current topic of discussion it may well be relevant
17:18:41 <ais523> backquote, not apostrophe
17:18:51 <ais523> and yes, that was an interesting idea for the construction
17:18:53 <HackEso> Coat of Arms \ 5 \ Artifact \ Each creature gets +1/+1 for each other creature on the battlefield that shares at least one creature type with it. (For example, if two Goblin Warriors and a Goblin Shaman are on the battlefield, each gets +2/+2.) \ EX-R, 7E-R, 8ED-R, 9ED-R, 10E-R, M10-R, DDS-R, H09-R
17:19:06 <ais523> my main aim was to hit the whole thing into a sideboard, so I wanted to do it with as few cards as possible
17:19:22 <ais523> but single-purpose cards are much better for what you're doing
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17:21:54 <ais523> but Coat of Arms is an artifact, so it might be hard to wish it out of the sideboard
17:24:50 <ais523> right, but the point is that you'd need extra cards in maindeck for sideboard
17:24:54 <ais523> yes, I think it's out of date
17:26:28 <ais523> Omni-tell naturally runs multiple Cunning Wish and Burning Wish, which is one of the things that made it such a good shell to set the UTM up
17:26:41 <ais523> like, the whole point was to make a UTM that was tournament-competitive
17:27:19 <MTGBusyBeaver> well wish for Mastermind's acquisition for the rest of the SB
17:28:53 <MTGBusyBeaver> though the sb doesnt have enough slots to ensure your opponent can't interact also.
17:37:24 <ais523> would the presence of Doubling Season mess up an attempt to use the UTM?
17:37:58 <ais523> e.g. by, if it were still on the battlefield at that point, producing too many triggers that could be stacked in awkward ways to introduce player-choosable nondeterminism?
17:40:03 <MTGBusyBeaver> the order the tokens etb doesn't change the operation of TM
17:40:13 <ais523> even if there are too many of them?
17:41:55 <MTGBusyBeaver> if there are more than expected, there will be some other operation we are doing, but it doesnt give us extra choices
17:42:05 <ais523> right, in that case it's fine
17:42:14 <ais523> (assuming we have a way to get rid of the Doubling Seasons, and I suspect we do)
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17:45:22 <ais523> on a related note, I was trying to prove Android: Netrunner TC a while back, but I don't think it is
17:45:29 <ais523> it has the opposite problem to Yu-Gi-Oh
17:45:45 <ais523> in Yu-Gi-Oh, there are ways to store data but you can't store a program, there just isn't enough room on the playmat
17:46:23 <ais523> in Android: Netrunner, storing a program is trivial (subroutines are a game mechanic!), but although you have a few places to write data, reading it back is incredibly difficult, and I don't think you can get sufficiently many variables that you can read
17:49:07 <ais523> another issue is that the game designers are paranoid about infinite combos of any sort, although I did manage to construct a nontrivial mandatory infinite loop
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18:08:05 <ais523> (it involved Always Be Running on the runner side, and two copies of Off the Grid, Whirlpool, Hourglass, and Mirāju on the Corp side, plus one unplayable card in hand; every turn, the runner is forced to run a specific central, is banned from jacking out, loses all their clicks, then puts the corp card from their hand back into their deck)
18:08:22 <ais523> (and on the corp turn they can't do anything but click for credits, assuming their deck is empty)
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19:00:53 <int-e> tromp: pushed (non-)divisibility
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19:04:20 <int-e> tromp: (non-divisibility is shorter because of the accident that m false = false for Church numerals m > 0).
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20:21:38 <b_jonas> MTGBusyBeaver, ais523, int-e: I'll review this conversation about M:tG later, but not this evening. I was busy with some urgent real life stuff.
20:23:05 <b_jonas> ais523: sorry, I can't update the database. so far my copies of Oracle were either a straight copy of Yawgatog's database, or mined from the previous iteration of the Oracle website. now I'll have to download the data from the new Oracle site, which I started once but it got complicated so I suspended it indefinitely, or download Scryfall's more accurate database.
20:23:10 <b_jonas> ideally both and compare them.
20:26:16 <b_jonas> for now I just want to mention that Lifespark Spellbomb; Utopia Sprawl; Freed from the Real is a simple infinite green mana combo that doesn't also let you deal unlimited damage by attacking with a small creature each turn, so that plus Disintegrate lets you deal an unlimited amount of damage only once
20:33:07 <MTGBusyBeaver> yeah, that combo would disqualify the deck as it is not bounded.
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21:02:47 <esowiki> [[Iflang]] https://esolangs.org/w/index.php?diff=70154&oldid=70118 * Hanzlu * (-1431) Blanked the page
21:03:34 <esowiki> [[Iflang]] https://esolangs.org/w/index.php?diff=70155&oldid=70154 * Hanzlu * (+1431) Undo revision 70154 by [[Special:Contributions/Hanzlu|Hanzlu]] ([[User talk:Hanzlu|talk]])
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