Yeah but we can't emulate a normal clock with flooding clocks, if we could, then we'd just do that for all of the clocks and bam flooding only computation is TC.
The smallest known TC waterfall setup is fully described in the Spiral Rise wiki page https://esolangs.org/wiki/Spiral_Rise I don't see an obvious way of improving that, though I am not a good waterfall programmer.
Really what we need for flooding clocks is some way to shrink them down again, but I don't see any repeatable way to do that.
Another card that is close to working is Wilhelt, the Rotcleaver but it can only make the same type of token that just died, we can distinguish between Wilhelt and Xathrid necromacer tokens, but it doesn't seem useful yet....
ACTUALLY WAIT NEVERMIND I THINK I FIXED IT! Dread Slaver! I think this saves us!
we use our existing dual typed creature's cards as the clock's key creatures, for example:
rotlung (cleric zombie)
chancellor (phyrexian angel)
phabine (cat advisor)
veyran (efreet wizard)
yarok (elemental horror)
master transmuter (human artificer)
That's enough for 6 clocks + halting clock. We lose a cardslot to give dread slaver lifelink (not sure what the best card for this would be), but that's clearly worth it.
EDIT: blehhh this fails if the opponent can start resolving arcbond triggers from other creatures... well this is still fewer cards lost for this deck than the sanctifier fix.
I think even though that looks workable, the consequences from losing every color of mana and basic land type for further comboing looks like it loses a lot of additional computation potential vs the alternative of using the sanctifier version with limited arcbond casts.
Hmm, what about Requiem angel?
It kind of looks like it makes a sort of “lazy” waterfall model, where the diagonal must be zero, as an X dying can’t make an X. (and waterclocks that are already at zero don’t trigger again)
Converting a normal waterfall program into requiem angels is a bit tricky, but looks possible.
Each clock needs three types now, A* which supports A’ and A”
The A’ angels makes an A” and the A*s, B*s, and C*s for the other clocks
The A” angels makes an A’ and the A*s, B*s, and C*s for the other clocks
With DCs set up so that the only type that is not an A’ is an A” and vice versa
This clearly behaves just like a normal water clock, just alternating between A’ and A” (edit: this is not actually clear, and is more complicated, but I think can still be made to work)
DCs make all of the * types into all of the ‘ and “ types
Each ‘ and “ type is chain DCed into all of the other ‘ and “ types except for their partner (and not the * types!). This causes loops which resolve via timestamps, thus we need the loops to be pretty carefully constructed so that A’ is not A” and vice versa. (I think we might have to also sacrifice one type per clock to be a DC timestamp gateway.) I think that forces us to make DCs to already be in a bunch of specific broken dependency loops?
Worst case in terms of types would require an intermediate type in each direction of each key type pair (to prevent B’ becoming B” through A’ being a B”)
We have like 280 types (thanks warhammer!) and that worst case still lets us make 8 full clocks (8*3+(8*2)*(8*2-1))=264 with a bunch of room left over.
Halting can be its own clock with a unique type as well, because it tripping ends computation.
Can we make the same B->C A->B C->D D->A broken loop? Yeah I think so because we have krrik as an AH and it can die by making a B.
What about lazy flooding clocks? I don’t think that gives us any more power and instead exasperates the problems with flooding clocks...
life and limb letting us get easy green mana and preventing us from letting the opponent get haste probably ruins more than it saves compared to limiting arcbonds, though being able to trigger landfall for like scute swarm or rampaging baloths could be nice.
Yeah Sephara maybe works but its a pretty different computational system because the flying tokens stick around forever so the clocks get longer and longer, and it seems difficult for such a system to be able to keep a halting clock from tripping for very long.
One thought: swapping coat of arms for sliver legion so we have to have a monotyped creature of every type we care about keeping alive?
I don't think it quite works, because we can just have a sliver legion of type A and break it with B->C A->B C->D D->A crusades like before.
It does allow for different types of flooding clock, as different clocks can have a different number of sliver legions pumping them. Even one without a boost, that always trips every tick. These don't seem super useful but this makes for strictly more versatile flooding clocks which maybe inches our way to being TC.
After running some more experiments Im pretty sure flooding waterclocks are not TC,
I think there is be a hybrid computation using both bishop of wings and necromancer/reanimator with the tokens being distinguished by sanctifier, instead of with the extra dralnu's crusade type, but that runs into the issues with sanctifier's protection.
I also looked at a bunch of other TC approaches/tarpits/methods, like a tag system, or two linked PDAs, but they mostly seem either extremely impossible to implement, or impossible to force into a non-breaking configuration.
time to figure out a new way to implement noninteractive Turing complete computations! whee! somehow! I did it once i can do it again. (though actually it looks like it never actually worked at all.....)
I'm still not completely sure this really sinks our deck like that. Maybe I'm just holding on to vain hope that somehow it can be fixed, but I want to fully understand this before giving it up for lost.
Do the effects look at each other fully before deciding if there is a dependency or not? Does some crusade in a loop have an opportunity to do nothing if it has an early timestamp? or is the C->D crusade forced to apply after the B->C crusade and A->B crusade if there's just an A in play?
Also it seems like that line can only possibly shrink the Cs by one, so we get saved by coat of arms?
I think im missing something from that explanation.
If this is all being kicked off by the C waterclock going to zero, so by definition all of the Cs and C's supported types also die. So I'm not seeing how this construction has the opportunity to not halt the halt clock whenever C zeroes?
I think Alseid of Life's Bounty could work? protection source + has lifelink. Though with scrambleverse the opponent can get mana too and sac it as well so it doesn't work...
This formulation does make setting things up a little more awkward as it is harder to target the opponent's stuff, without martyr of spores, but we don't need to do that a lot.
The main annoyance is probably chancellor of the annex, but we can still bounce it with AE/Arcbond.
Yeah a specific counterexample is not necessary, It's just a bit trickier than it looks at first glance.
The idea was that Rotlungs can be made indestructible with resolute watchdog before donating them. The watchdog also allows us to make dummy indestructible creatures of the other types to balance out any problems from having the rotlung types.
There were other tricks like additional copies of dralnu's crusade or coat of arms and doubling up on the key creatures. But those were mostly to make the mapping more efficient.
Its a bit less efficient than the necromancer version which is less efficient than bishops, but it should still work.
Edit:
new page here's the deck with the patch: (still should probably prove more rigorously that arbitrary waterfall programs are reachable)
my point before was that the second dralnu's crusade for B->C is not part of the dependency loop but depends on the result of the loop and will thus apply at the end.
The problem is if we make a long loop A->B B->C ... Z->A , then making a bunch of N in the middle will receive all of the buffs, but when we make something else like an A, the N will lose a bunch of their buffs, so they lose more than coat of arms counteracts. (depending on timestamps.)
Hmm, this does look pretty awful.
One thing to note that complicates this a little is that because Xathrid Necromancer is itself a human, any type we create that also has death triggers will always exist and be subject to dralnu's crusades the same way. Also, once the opponent decides to not trip the N clock early, they don't have that option again until the clock zeroes out the added creature. So I think creating a specific counterexample computation is at least a little nontrivial?
Though I don't see why we would need to care about the spoiler type dying, or any problem with resetting a clock like that.
One other solution would be Rotlung reanimator with martyr of spores -> resolute watchdog to keep them alive? How often do we need to bounce the opponent's things anyway?
I tried to break things with this before but couldnt, and I think the problem in your example is that if you have two dranlus making B->C then there is a way to order them so every A, every B and every C always ends up as an ABC.
and its by applying B->C C->A A->B and B->C in that order. But that does seem to cause the As to lose a toughness on net when the first B is created...
I think you may have a point though and I need to think about this. It seems to me that having a square dependency with unequal diagonals may have this problem as well.
(PS: This would be a great time for someone to prove flooding waterfall TC and we can remove dralnu's crusades entirely)
The smallest known TC waterfall setup is fully described in the Spiral Rise wiki page https://esolangs.org/wiki/Spiral_Rise I don't see an obvious way of improving that, though I am not a good waterfall programmer.
Really what we need for flooding clocks is some way to shrink them down again, but I don't see any repeatable way to do that.
Another card that is close to working is Wilhelt, the Rotcleaver but it can only make the same type of token that just died, we can distinguish between Wilhelt and Xathrid necromacer tokens, but it doesn't seem useful yet....
ACTUALLY WAIT NEVERMIND I THINK I FIXED IT!
Dread Slaver! I think this saves us!
we use our existing dual typed creature's cards as the clock's key creatures, for example:
rotlung (cleric zombie)
chancellor (phyrexian angel)
phabine (cat advisor)
veyran (efreet wizard)
yarok (elemental horror)
master transmuter (human artificer)
That's enough for 6 clocks + halting clock. We lose a cardslot to give dread slaver lifelink (not sure what the best card for this would be), but that's clearly worth it.
EDIT: blehhh this fails if the opponent can start resolving arcbond triggers from other creatures... well this is still fewer cards lost for this deck than the sanctifier fix.
It kind of looks like it makes a sort of “lazy” waterfall model, where the diagonal must be zero, as an X dying can’t make an X. (and waterclocks that are already at zero don’t trigger again)
Converting a normal waterfall program into requiem angels is a bit tricky, but looks possible.
Each clock needs three types now, A* which supports A’ and A”
The A’ angels makes an A” and the A*s, B*s, and C*s for the other clocks
The A” angels makes an A’ and the A*s, B*s, and C*s for the other clocks
With DCs set up so that the only type that is not an A’ is an A” and vice versa
This clearly behaves just like a normal water clock, just alternating between A’ and A” (edit: this is not actually clear, and is more complicated, but I think can still be made to work)
DCs make all of the * types into all of the ‘ and “ types
Each ‘ and “ type is chain DCed into all of the other ‘ and “ types except for their partner (and not the * types!). This causes loops which resolve via timestamps, thus we need the loops to be pretty carefully constructed so that A’ is not A” and vice versa. (I think we might have to also sacrifice one type per clock to be a DC timestamp gateway.) I think that forces us to make DCs to already be in a bunch of specific broken dependency loops?
Worst case in terms of types would require an intermediate type in each direction of each key type pair (to prevent B’ becoming B” through A’ being a B”)
We have like 280 types (thanks warhammer!) and that worst case still lets us make 8 full clocks (8*3+(8*2)*(8*2-1))=264 with a bunch of room left over.
Halting can be its own clock with a unique type as well, because it tripping ends computation.
Can we make the same B->C A->B C->D D->A broken loop? Yeah I think so because we have krrik as an AH and it can die by making a B.
What about lazy flooding clocks? I don’t think that gives us any more power and instead exasperates the problems with flooding clocks...
bleh, looks like a dead end.
One thought: swapping coat of arms for sliver legion so we have to have a monotyped creature of every type we care about keeping alive?
I don't think it quite works, because we can just have a sliver legion of type A and break it with B->C A->B C->D D->A crusades like before.
It does allow for different types of flooding clock, as different clocks can have a different number of sliver legions pumping them. Even one without a boost, that always trips every tick. These don't seem super useful but this makes for strictly more versatile flooding clocks which maybe inches our way to being TC.
I think there is be a hybrid computation using both bishop of wings and necromancer/reanimator with the tokens being distinguished by sanctifier, instead of with the extra dralnu's crusade type, but that runs into the issues with sanctifier's protection.
I also looked at a bunch of other TC approaches/tarpits/methods, like a tag system, or two linked PDAs, but they mostly seem either extremely impossible to implement, or impossible to force into a non-breaking configuration.
That really sucks.
time to figure out a new way to implement noninteractive Turing complete computations! whee! somehow! I did it once i can do it again. (though actually it looks like it never actually worked at all.....)
Do the effects look at each other fully before deciding if there is a dependency or not? Does some crusade in a loop have an opportunity to do nothing if it has an early timestamp? or is the C->D crusade forced to apply after the B->C crusade and A->B crusade if there's just an A in play?
Also it seems like that line can only possibly shrink the Cs by one, so we get saved by coat of arms?
I think im missing something from that explanation.
If this is all being kicked off by the C waterclock going to zero, so by definition all of the Cs and C's supported types also die. So I'm not seeing how this construction has the opportunity to not halt the halt clock whenever C zeroes?
Katilda, Dawnhart Martyr is also close but it seems difficult to make enough of the auras.
This formulation does make setting things up a little more awkward as it is harder to target the opponent's stuff, without martyr of spores, but we don't need to do that a lot.
The main annoyance is probably chancellor of the annex, but we can still bounce it with AE/Arcbond.
The idea was that Rotlungs can be made indestructible with resolute watchdog before donating them. The watchdog also allows us to make dummy indestructible creatures of the other types to balance out any problems from having the rotlung types.
There were other tricks like additional copies of dralnu's crusade or coat of arms and doubling up on the key creatures. But those were mostly to make the mapping more efficient.
Its a bit less efficient than the necromancer version which is less efficient than bishops, but it should still work.
Edit:
new page here's the deck with the patch: (still should probably prove more rigorously that arbitrary waterfall programs are reachable)
1 Coat of Arms
2 Rotlung Reanimator
3 Artificial Evolution
4 Arcbond
5 Comeuppance
6 Dralnu's Crusade
Starting a Computation
7 Opalescence
8 Wrong Turn
9 Kaervek's Spite
10 Goblin Boom Keg
11 March of the Machines
Utility
12 Vedalken Orrery
13 Metalworker
14 Twinning Glass
15 Thousand-Year Storm
16 Bloodbond March
17 Chancellor of the Annex
Foundry Stage
18 Resolute Watchdog
19 Soul Foundry
20 Phabine, Boss's Confidant
21 Cowardice
22 Mirror of Fate
23 Chromescale Drake
24 Ashnod the Uncaring
25 Ratadrabik of Urborg
26 Spellweaver Volute
27 Veyran, Voice of Duality
28 Fated Infatuation
29 Lingering Souls
30 K'rrik, Son of Yawgmoth
31 Archon of Falling Stars
32 Pious Interdiction
Helix Megastage
33 Spellweaver Helix
34 Worldfire
35 Starlight
36 Abandon the Post
37 Abandon the Post
38 Mox Ruby
39 Yarok, the Desecrated
Blue Mana Stage
40 Master Transmuter
41 Floodchaser
42 Great Furnace
43 Brutal Suppression
44 Search for Glory
45 Snow-Covered Island
46 Arboreal Grazer
47 Firebrand Ranger
48 Groundskeeper
49 Forest
White Mana Stage
50 Ruin Ghost
51 Weathered Wayfarer
52 Archaeological Dig
53 Ghitu Encampment
Start
54 Mana Crypt
55 Epic Experiment
56 Resurgent Belief
57 Omniscience
58 Infectious Inquiry
End Layers
59 Mind's Eye
60 Smoke Spirits' Aid
The main advantage of the resolute/reanimator fix over Slight/Sanctifier is that it doesn't cost a deck slot. (unless I'm missing something there?)
The problem is if we make a long loop A->B B->C ... Z->A , then making a bunch of N in the middle will receive all of the buffs, but when we make something else like an A, the N will lose a bunch of their buffs, so they lose more than coat of arms counteracts. (depending on timestamps.)
Hmm, this does look pretty awful.
One thing to note that complicates this a little is that because Xathrid Necromancer is itself a human, any type we create that also has death triggers will always exist and be subject to dralnu's crusades the same way. Also, once the opponent decides to not trip the N clock early, they don't have that option again until the clock zeroes out the added creature. So I think creating a specific counterexample computation is at least a little nontrivial?
Though I don't see why we would need to care about the spoiler type dying, or any problem with resetting a clock like that.
One other solution would be Rotlung reanimator with martyr of spores -> resolute watchdog to keep them alive? How often do we need to bounce the opponent's things anyway?
and its by applying B->C C->A A->B and B->C in that order. But that does seem to cause the As to lose a toughness on net when the first B is created...
I think you may have a point though and I need to think about this. It seems to me that having a square dependency with unequal diagonals may have this problem as well.
(PS: This would be a great time for someone to prove flooding waterfall TC and we can remove dralnu's crusades entirely)