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MatPlus.Net Forum General The Retro-Strategy convention: what is the correct way to interpret it?
 
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(1) Posted by Bojan Basic [Wednesday, Jun 10, 2020 21:27]

The Retro-Strategy convention: what is the correct way to interpret it?


Suppose that we have wPd5, bPc5 and bPe5. Suppose that it can be proved that Black's last move was either c7-c5 od e7-e5 (but it is not known which one). Now, if there is a way to fulfill the problem stipulation starting with 1.dxc5 e.p. as well as another way starting with 1.dxe5 e.p., then this would be two branches of a PRA problem.

But assume that there is a way to fulfill the stipulation starting with 1.dxc5 e.p., while if White plays 1.dxe5 e.p., then the stipulation cannot be fulfilled. Is it then correct or not to say that, under the RS convention, the problem is sound (with only one solution, starting with 1.dxc5 e.p.)? Namely, as I understand the RS convention, it is based on the philosophy that, in case of mutually dependent rights, the one that is exploited first is deemed permissible. However, for some reason, the Codex talks only about the castling rights with respect to the RS convention, and says nothing about the en-passant rights.
 
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(2) Posted by Andrew Buchanan [Thursday, Jun 11, 2020 08:18]; edited by Andrew Buchanan [20-06-11]

Hi Bojan,

Thanks for your question.

The Codex today is kind of a summary of what folk have agreed: it's not a tutorial. There are various parts where I think it could be better written, but it is what it is. If you are looking for a genuine tutorial, you could try the Retro Corner, e.g. for e.p. https://www.janko.at/Retros/Glossary/EnPassant.htm. In a (large) nutshell, here's how I suggest that you view all this, starting from first principles. For your actual answer, skip to the end.

Each kind of conditional move (in orthodox chess: castling and en passant, but fairy chess offers numerous others) should have a convention which says what we can assume about the legality of this move if the history of the game is uncertain. Basically conventions are either optimistic (it's always ok to play an uncertain move, e.g. castling) or pessimistic (it's never ok to play an uncertain move, e.g. e.p.).

Critically, these conventions only apply to forward stipulations. General retros (e.g. last move, proof game) admit no conventions: everything must be proven. Retractors need no conventions, because the (unwritten) assumption is that any feasible last move can be retracted.

If there is only one conditional forward move, then we have enough information. However, there are many positions in which there are multiple possible conditional moves in the future, and there may be logical dependencies between them. How do we proceed? We need to move to a higher level of meta-convention. There are two common meta-conventions: PRA & RS, each of them built on the two basic conventions.

PRA (partial retro analysis) says that divide up the problem into different parts: each with a different subset of the conditional moves permitted. There are two constraints in defining these subsets. First the subset has to be legal, i.e. there must be a game which results in a position with exactly this subset of permitted moves ok. Secondly, no subset of can be "improved" to another set by applying one of the basic conventions.

This is actually quite a beautiful idea, but it cries out for an example. So suppose we have a position where two castlings C1 & C2 are in doubt, and we know that they cannot be both legal. So we start with 4 possible parts. {C1,C2}, {C1}, {C2}, {} where each bracket denotes the permitted moves. Constraint 1 immediately allows us to remove {C1,C2} because it's not legal. Constraint 2 allows us to remove {} because by the castling convention this could be improved to {C1} (or equivalently to {C2}. So we end up with two parts {C1} & {C2}. Both are possibly legal, and neither can be improved.

Let's have another example. Suppose we have a position (e.g. Longstaff) where castling, C, and e.p., EP, are in question, and if e.p. is not permitted, the castling cannot be permitted either. Then the 4 candidates are {C, EP}, {C}, {EP} & {}. We are told that {C} is impossible by Constraint 1. But consider now {EP}. We could improve that to {C, EP} by the castling convention, or to {} by applying the e.p. convention. Thus we can discount {EP} by Constraint 2. So we are left with two parts: {C, EP} & {}. This scales up cleanly to more complex retro structures.

And finally, the double e.p. where it's certain that the last move must have been a double hop, {} is impossible, while {EP1, EP2} is dominated by both {EP1} & {EP2}, which are the parts.

Retro-Strategy starts from a separate premise, that there is only one position. We consider all the optimistic conditional moves, bearing in mind the history of the game including the moves played in our solution so far. We can unconditionally play any of these optimistic moves, but when we do so the range of possible histories collapses to include only those in which this move could have been legal, and then we consider the next move. Pessimistic conditional moves never get to be played under RS: they only get played under the e.p. *rule* i.e. if you can prove that the last move was a double hop you can make that move.

Let's see how the two examples apply here. First the two castlings, where there are 3 possibilities {C1}, {C2} & {}. If both the castlings are by the same player, just play one, say C1. Now the history collapses so that we only consider those possible histories in which that castling definitely was legal, i.e. {C1}. In fact since a player can only castle once in the game, the legality of C2 is irrelevant. However, if C1 was by White, and C2 by Black, then when White plays C1, we enter the collapsed history of {C1} and Black cannot castle. For some reason unknown to me, this is called out as a special case in the Codex, but Mutually Dependent Rights for castling is an obvious case of the more general RS mechanism of history collapse at work, which is really what the Codex should describe.

Let's move on to the Longstaff case. E.p. must be played immediately if it's going to be played at all, but under RS we cannot play a pessimistic unsure move. So it will never be played. If we castle, then our state collapses to {C, EP}, but given that we are too late to play the EP it's kind of academic. You can see why this kind of problem is more suited to PRA.

The double e.p. is all pessimism under RS, and so neither can be played. If there are no other moves possible in the diagram, then the game hangs without ending. I find this situation pretty cool, but I can understand that some others think it's a strike against RS.

This point brings us to the question of meta-meta-conventions. How do we know whether PRA or RS should apply? In the old days, RS was the default, and PRA problems needed to be annotated in the stipulation. Werner Keym in 2008 & 2009 pushed through a change to the conventions which is shockingly badly described in the Codex. Unless you already know what it's trying to say, you haven't a chance. (Werner's magnificent tutorial at https://www.janko.at/Retros/Glossary/Castling-and-En-passant.htm is essential reading for any retro enthusiast, but in my opinion does not compensate for the very poor and discouraging construction of the Codex entry.) Basically, neither PRA nor RS need to be annotated as such. The first assumption is that the problem is PRA, but if that doesn't work out (one clean solution per part) then you assume it's RS. I tend to view this meta-meta-convention as a notational shortcut more than anything else, and it certainly has worked out well EXCEPT that if you don't know what's going on here then you haven't a chance. Werner Keym produced an excellent tutorial for this (which you can find in the Retro Corner) but if you don't know that this silent meta-meta-convention is going on, you haven't a chance of figuring it out for yourself.

This brings us (finally) to your question Bojan. Thanks for your patience. If only one of the two possible e.p. moves leads to a solution, then under RS you cannot force it. The problem is unsound. Many people, including some very creative ones, felt this was a shame, and so there is a wonderful idea called AP (for A Posteriori) which says that under RS you *can* play a pessimistic move, as long as later on in the game you or your opponent play some optimistic moves which collapse the set of possible histories such that the pessimistic move was definitely legal. There are some amazing effects which have been achieved with this wacky and unorthodox idea.

One will find problems in chess.com where an unjustified e.p. is given as the solution, because "the problem must have a solution". If this statement is given as a constraint in the problem stipulation, then the problem works, but otherwise it's just a joke. That a problem must have a solution is a requirement for soundness, not a retro premise. However in the world of jokes all things are possible.

That's an entry level intro to the orthodox conventions, meta-conventions & meta-meta-convention. I hope you can see how the conventions can easily generalize to any fairy format, if every aspect of conditionality can be classified as optimistic or pessimistic. Other issues not covered in this intro are: interaction with whose move, AP for PRA, "SPRA" and generalization to RS, touch-move protocol, dead position, 50 move rule, draw by repetition, jokes & illegal positions. Have fun and if you have any questions just ask.
 
 
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(3) Posted by Hauke Reddmann [Thursday, Jun 11, 2020 10:27]

Well, studying computer science, *I* have a question which
is rather obvious: Can the whole system be formalized to
a degree that given a position and the list of move
dependencies, a computer could solve it codex-compliant?
 
   
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(4) Posted by Andrew Buchanan [Thursday, Jun 11, 2020 13:00]; edited by Andrew Buchanan [20-06-11]

Hauke asked:
 QUOTE 
Well, studying computer science, *I* have a question which
is rather obvious: Can the whole system be formalized to
a degree that given a position and the list of move
dependencies, a computer could solve it codex-compliant?

Yes. After some basic formalization of the Laws and the Codex, if you have an ordinary forward stipulation in a position together with the list of move dependencies, a computer algorithm can determine the solution for PRA or RS, excluding AP. It would be able to determine the parts of the RA problem, solve them, determine whether it matches the PRA requirements, if necessary shift to RS and iterate forwards there, collapsing histories as required.
 
   
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(5) Posted by Bojan Basic [Friday, Jun 12, 2020 02:04]

Dear Andrew,

What a marvelous answer, thank you very much! I was aware of most of the things you wrote (the only question was when exactly we can select a "branch" by means of RV; the answer is, as you have explained, that we can appeal to RV in order to choose among "optimistic" moves, but no "pessimistic" move can be played on the grounds of RV only), but it is great to have everything summarized so nicely in one place! I also appreciate your comments about transferring these principles to fairy problems, since I in fact arrived to my question from the fairy realms (but formulated it in an orthodox manner because it was the basic principle that I was interested about, and after making that clear, applying the same principle to fairy compositions should not be a problem).

Since you were so kind and eager to help, I will make use of that and ask one more question (not directly related to the previous one, but still about the same conventions). Suppose that we have three conditional moves, say M1, M2 and M3, all of which are optimistic. Suppose that M1 is incompatible with M2, as well as that M1 is incompatible with M3, but M2 and M3 can coexist together. Is it then correct to say that we have two parts, namely {M1} & {M2, M3}, and that by PRA they form two branches, while by RS we can decide on any one of those two parts by making a respective move (which is M1 for the first part, and can be either M2 or M3 for the second part)? In other words, the question is: since the possibility {M1} "kills" two optimistic rights, while the possibility {M2,M3} "kills" only one, this still does not mean that the first possibility has "lesser right to exist" than the second one, correct?
 
   
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(6) Posted by Andrew Buchanan [Friday, Jun 12, 2020 05:29]; edited by Andrew Buchanan [20-06-12]

Dear Bojan,

Thanks for your kind words. I hope that this kind of tutorial material can find a more permanent home to help those wanting to move to retros beyond Smullyan.

 QUOTE 
Suppose that we have three conditional moves, say M1, M2 and M3, all of which are optimistic. Suppose that M1 is incompatible with M2, as well as that M1 is incompatible with M3, but M2 and M3 can coexist together. Is it then correct to say that we have two parts, namely {M1} & {M2, M3}, and that by PRA they form two branches

For PRA, you are exactly right, we have two parts {M1} & {M2,M3}. There are eight initial possibilities: {M1,M2,M3}, {M1,M2} & {M1,M3} are inconsistent, while {}, {M2} & {M3} are dominated by {M2,M3}.

However the concept of parts *only* exists for PRA. RS never divides in this way: instead you drive forward optimistically, collapsing the history by removing any possible past which is inconsistent with the optimistic moves being made.

 QUOTE 
while by RS we can decide on any one of those two parts by making a respective move (which is M1 for the first part, and can be either M2 or M3 for the second part)?

In RS our initial set of histories is [{}, {M1}, {M2}, {M3}, {M2,M3}] If someone plays M1, then the set collapses to just [{M1}], as anything else is inconsistent, and so M2 & M3 are no longer playable. On the other hand, if someone plays M2, then the set of possible histories reduces to [{M2}, {M2,M3}] M1 can now not be played, but someone is free to play M3. If they do, then the set of histories becomes just [{M2,M3}]

The concept of history collapse is a more precise way of viewing RS, rather than the vagueness of "Mutually Dependent Rights".

 QUOTE 
In other words, the question is: since the possibility {M1} "kills" two optimistic rights, while the possibility {M2,M3} "kills" only one, this still does not mean that the first possibility has "lesser right to exist" than the second one, correct?

Yes there is no comparison of this kind. Just drive forwards being optimistic, and throwing away histories that are inconsistent with what you've done.

A lot of the motivation for these problems comes from the composer setting up different dependency maps between various conditional moves. https://www.janko.at/Retros/Glossary/Castling-and-En-passant-Jun-cm.htm is a great article which showcases some classics, and shows how they interact with different kinds of forward stipulation: directmate and helpmate.

Some might compare RS with the Copenhagen interpretation of Quantum Mechanics, under which there is a notion of collapse of the wave function under observation, while PRA is more like a "multiple worlds" interpretation. That's a fun analogy: it's cool to pretend that we are doing something serious like physics.
 
   
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(7) Posted by Hauke Reddmann [Friday, Jun 12, 2020 10:44]

I was really, REALLY tempted to write a Hollywood time travel SF blockbuster from all this. (Maybe with a dash of Game of Thrones plagiarism throw in.) Then, with only about 1000 problemists to watch, I realized that the FX costs would rob me blind :-) Some dialogue from the script leaked through, though...

Outside. A dark and stormy night.
The Witch Queen: Flee into the tower, King Haukon!
The Black Bishop: HERESY! Gods forbade this sin!
You won't escape the wrath of my mighty crosier!
King Haukon (draws his legendary +1): En gardez!
You'll never take me alive!
The Witch Queen: Old Ones, forgive me! I repair
that later! CINCINNATUS!
(A $1000000 SFX happens. King Haukon is transported
to the safety of the White Tower)
The Black Bishop: Damn you to hell and back!
You won't escape the punishment for throwing spells
around en passant!
 
 
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(8) Posted by Joost de Heer [Friday, Jun 12, 2020 14:36]

 QUOTE 

That's a fun analogy: it's cool to pretend that we are doing something serious like physics.


Chess composition is further along than physics however: Reto Aschwanden and Peter Gvozdjak published a 'Grand unifying theory' composition in Strategems in 2001.
 
 
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(9) Posted by Guus Rol [Friday, Nov 27, 2020 16:18]

Quote: ... so there is a wonderful idea called AP (for A Posteriori) which says that under RS you *can* play a pessimistic move, as long as later on in the game you or your opponent play some optimistic moves which collapse the set of possible histories such that the pessimistic move was definitely legal.

AP-logic is not that simple. As soon as you play any move (pessimistic, optimistic or otherwise), it becomes part of the certain, unnegotiable history - no proof game exists without it - and nothing you do further on can change that. This type of reasoning is based on FOL (first order logic) and AP-logic does not comply with FOL. What you need is a fuzzy approach where the legality of the e.p. move is replaced with a membership of the proof game group where e.p. is legal and a simultaneous membership of the group where it is illegal. Thus, after you play e.p., the status of the e.p. move and solution are still uncertain with a preference for illegal (pessimistic e.p. default). One could describe that state as one of "suspended disbelief". However, a future event - the AP justification - might happen which adds sufficient credibility to the "legality assumption" to make it crystallize. It is sort of an election where the mailed-in ballots may overturn the expectancy from the in-person vote count. Don't feel embarrassed to request a recount (hahaha!)

From a structural viewpoint one should consider the complete phase from e.p. move through justification/game-end AS A SINGLE MACRO-MOVE, which is either legal or illegal in its entirety (playable or unplayable if you follow Andrews terminology). No one will ever expect you to rate legality/playability while the execution of a move is still underway.
 
   
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(10) Posted by Andrew Buchanan [Saturday, Nov 28, 2020 10:45]

Hi Guus - I prefer my explanation which if a little simplistic has the merit of being comprehensible
 
   
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(11) Posted by Guus Rol [Saturday, Nov 28, 2020 12:39]

Hi Andrew! I won't start a big discussion here. I might another day. I posted my comment to let you know I am around (had to be because I needed a response to my Efrosinin post) and on the odd chance there is someone here with a mathematical mind who understands the relevance of a formal definition - which I didn't complete btw! You know I am capable of producing AP-problems which will leave everyone in a state of crisis until they are handed a proper evaluation tool.
 
   
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(12) Posted by Guus Rol [Monday, Dec 7, 2020 21:41]

The common way to describe the Petrovic AP convention is as "e.p. move justified by castling move". Besides being ultra-short it is also vulnerable to misunderstandings. Consider the following diagram. Because it is a discussion point I give the stipulation a question mark.

(AP) H#2?
(= 4+4 )


When you analyze this diagram with black on move you will find that (a) if black cannot play e.p., white will never be able to castle (not just within 2 moves, never) (b) white can castle later if black has the right to play e.p. - even within the scope of the solution. So if white castles later he proves a posteriori that black must have had the right to e.p.! That is A.P. per Petrovic - or not? Btw, the solution would then be 0. .. fxg3 e.p. 1. Rd2 g2 2. 0-0-0# (not Ke2 because white must show the castling move to justify e.p.).

The answer is no, it's a fake! The confusion comes from the assumption that the A.P. type is only about a relationship between moves while it is primarily a relationship between rights! Rights are about proof games while playable moves are about conventional permissions. The intended relationship for the A.P. type Petrovic is: "If in all proof games for the diagram with a statutory castling right, there is also a right to play e.p. - then the e.p. move may be played provided it is followed by the related castling move later! Note that in the diagram given there is no such rights relationship and it is therefore fake.

Interestingly I have never seen anybody go wrong on this; apparently composers pick this up intuitively even when the descriptions and definitions are poor. The reason is probably that Petrovic is one particular AP-type and supplemented by examples one is less likely to go wrong. Recently though I have shown there are more (many more in fairy) A.P. types requiring a generic A.P. framework for type definitions. I will not provide a detailed definition here but it is clear that they all revolve around a rights relationship which justifies a move relationship.

This is still a simplification but much better than any other story on this subject!
 
   
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(13) Posted by James Malcom [Tuesday, Dec 8, 2020 01:57]

Furthermore, in your example, White still has the right to castle without Black's en passant move, which further invalidates it. As far as I know, AP only works when it seems as if White must have moved their king or rook before if the pawn in question didn't. By asserting that the pawn moved last, with ep capture, only then you can carry out castling later on.

Here is such a "correction" as your scheme would want to render.

h#2, AP
(= 4+5 )

1. fxe3ep Rf2 2 Kh1 0-0-0#
 
   
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(14) Posted by Andrew Buchanan [Tuesday, Dec 8, 2020 05:20]

@Guus, James,

Thanks very much. Concrete, concise and clear.

James: your elegant composition is gently cooked, by 1. Kh1/2 Kf1/2 2. g4 Rh5#.

It does you credit, as it demonstrates you happily compose without an engine for validation. :)

However, there is a second more brutal cook. You don't eliminate the possibility that White's last move was a single pawn move or capture, rather than the double hop.

I will reply soon to Guus' helpful post.
 
   
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(15) Posted by James Malcom [Tuesday, Dec 8, 2020 06:05]

Well, I don't compose with a computer really, :-). I set out with a basic scheme, work out some obvious tweaks, and then toss it into the engine to find whatever stupid cooks exist, and then work further until all are eliminated and/or I give up.
 
 
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(16) Posted by Bojan Basic [Tuesday, Dec 8, 2020 06:35]

 QUOTE 
Furthermore, in your example, White still has the right to castle without Black's en passant move, which further invalidates it.

This is precisely Guus's point, isn't it? Or I misunderstood something?


 QUOTE 
Interestingly I have never seen anybody go wrong on this; apparently composers pick this up intuitively even when the descriptions and definitions are poor.

Well, there is still an interepretation as in this problem: https://pdb.dieschwalbe.de/search.jsp?expression=PROBID='P0000758%27 (about which I fully agree with your comments on PDB).

And the same issue occurs with RS in some published problems, such as https://pdb.dieschwalbe.de/search.jsp?expression=PROBID='P0008506%27 or https://pdb.dieschwalbe.de/search.jsp?expression=PROBID='P0008520%27 (mentioned at the end of this topic: https://www.matplus.net/start.php?px=1607404913&app=forum&act=posts&fid=gen&tid=1361, but unfortunately the discussion there stopped exactly when the most interesting part should start :D). In my opinion, irrespectively of the convention used, it is totally deprived of any logic to declare a side mated if it is certain that the side has a defensive move (at least one)! (The fact that we do not know exactly which of several possible defensive moves is the real deal does not affect the fact that the side has a defensive move, and thus cannot be declared mated).
 
   
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(17) Posted by Guus Rol [Tuesday, Dec 8, 2020 10:24]

@Bojan_Basic. https://pdb.dieschwalbe.de/search.jsp?expression=PROBID='P0000758%27 is my ear reddening past. In the year (I think 2006) before I completed my retro-theory I placed this comment in the PDB and it is WRONG. I appreciate your support though because it is a logical story. Today I would rate it as the 2e fake story on AP! It's the biggest logical blunder in my life (I have bad memory :-)) and it's only forgivable because the correct storyline was never written.

In essence, a posteriori is about gathering evidence - like investigating for election fraud. When you find it you were a tenacious sleuth, when you fail you were stark raving mad to start the investigation in the first place (no political opinion). Judgement is reserved until the outcome is seen - and often based on that outcome. It's a dubious kind of logic but one that increasingly runs the world. There is also a positive side to AP-logic. It permits you to change your mind from what you believed before. In the common chess logic types you can never do that. Once you castled it will always be true you had castling rights in that position whereever the solution goes.

Note there is another debatable issue in this problem fundamental for all AP-types. It's not actually rational having to castle as the last step in the justification process. It would be sufficient to manifest castling right at that point in any way! For instance by manifesting that a position is not dead. Andrew did that in a different context. But it can also be done through repetitions as in this problem. In mathematics, all proofs for a conclusion are equal, why only permit one sort of proof as a justification?

I may look into the retro-volage issue later. I know this type exists but I never explored it because I found sufficient material in more orthodox retro challenges.

Thanks for the links!
 
   
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(18) Posted by Guus Rol [Tuesday, Dec 8, 2020 10:34]

@Bojan_Basic: I didn't reply to your last issue. You are obviously right because it is the fundamental of fundamental fundamentals under retro-analysis: "there must always be a proof game". Declaring mate without proof game is absolute nonsense. That's not retrograde but fairygrade.
 
   
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(19) Posted by Hauke Reddmann [Tuesday, Dec 8, 2020 11:24]

@Guus: You wrote: "Judgement is reserved until the outcome is seen - and often based on that outcome. It's a dubious kind of logic but one that increasingly runs the world."
I refrain from any political followup :-) but have you seen the "Bill and Ted" movies? With a time machine, you can enforce this logic...and other too. This would be an interesting questions of all SF-loving physicist composers here: Is there an 1:1 correspondence of time machine logics you can sell to a reader, and retro logics?
Here are a few others:
Superdeterminism: By frelling with the time line, you force exactly the history you wanted to avoid in the first place. Your free will was an illusion.
Compability: The same, but you still have free will, as long as the result is self-consistent.
Many-worlds: Inconsistencies aren't, they belong to a different timeline.
 
   
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(20) Posted by James Malcom [Tuesday, Dec 8, 2020 14:20]

Although, Hauke, many-worlds strips away free will as well.
 
   
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MatPlus.Net Forum General The Retro-Strategy convention: what is the correct way to interpret it?