I'm working on this one already for a few hours. I feel that this puzzle is ideally suited to develop some consistent logical thoughts about tempi.
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| White to move |
r2qr1k1/pp2nppp/1b6/3pn2b/8/1NPBBN1P/PP3PP1/R2QR1K1 w - - 1 1
[solution]
I expect it will take me quite some time.
UPDATE Feb 7th,
1.Bxb6
What does this move do, tempowise?
- Be3 plus Re1 form a battery. So a discovered attack is executed. Two tempi for the price of one.
- The black Queen is attacked. I used to call this "with additional punch"
- So black has three tasks to fulfil: take his piece back, save his knight and save his Queen
Hence white's move is a 3 purpose move.
1. ... Nxf3+
This:
- Saves the black knight
- Takes a piece back
- Attacks the white King by an "additional punch"
Essentially it saves two of black's three problems. He has equalized the discovered attack with a 2 purpose move. His Queen is still under the attack of an additional punch. Normally, that shouldn't worry black too much. Black's own additional punch (check) forces an immediate response from white. And black has another dual purpose move in store: Qxb6 takes a piece back AND solves the threat to the Queen.
2. Qxf3
This is another dual purpose move:
- It takes the black knight
- It releases the threat against white's King
- It adds an additional punch against Bh5
I have not decided yet whether this is a 2 or 3 purpose move.
If white would have played 2. gxf3 he would have reached the same, but without the additional punch. In that case, he would have given black the opportunity to equalize the tempi with Qxb6.
2. ... Bxf3 OR 2. ... Qxb6
Either way, black continues to stay a piece behind.
As you can see, system 2 has created a nice word salad. Yet I feel that there are enough points of engagement to simplify matters by excluding the trivial matters. And I feel that system 1 might be able to distill a few salient points out of this.
Goal: to see this narrative instead of needing to calculate it.
First thought: Black has two LPDO (BBh5 and BNe5); that's already a red flag warning that something "bad" could happen. Multiple weaknesses scream “COMBINATION!” The White Queen is RELATIVELY pinned, which means the pinned WNf3 can legally move. (Whether that is a good idea or not remains to be SEEN.) The h7-square and b6-square look promising in terms of gaining tempi. There are several interesting LoAs connecting to the PoPs.
ReplyDeleteI started looking for local areas. The first local area consisted of the BNe5, BBh5, WNf3, WRe1, and WQd1. The second local area consisted of WBe3, BBb6 and BQd8. As I looked at those two areas, the position from Thursday, February 01, 2024 - The elephant in the room sprang into my mind's eye like Athena from the forehead of Zeus - fully grown and armored, ready for war. What a great way to gain a tempo! The connecting relationships (LoA) then immediately popped into sight. All that was left was to clean up the details (determine the move order) and perform Validation (Does it work?).
The art is to find the specific problems where YOUR system 2 starts to produce word salads which confuse YOUR system 2. Apparently I'm vulnerable when my Queen is under attack. Then I am adding the administration of the values of the pieces to the equation, which is enough to overload my system 2. I can't keep track of both tempi, values and material at the same time.
ReplyDeleteSo I'm looking for a few RULES, since I suspect that I don't need to keep track of everything at the same time.
ReplyDeleteThis is weird. I stay signed in to Google, but Blogger periodically will sign me out. I have to then sign back in to Blogger, even though I've signed out and back in to Google. Blogger has a separate signin process - that uses my Google account login as my Blogger login. HUH?!?
ReplyDeletePART I:
ReplyDeleteHere’s are a few of my idiosyncratic “RULES” that have proven useful to the RCCM, in no particular order:
(1) What You SEE Is All There Is (WYSIATI) – Kahneman. It doesn’t matter what you see with your two physical eyes; if you don’t “SEE” with the mind’s eye, you are effectively BLIND.
(2) Always “SEE” (along the LoA) through any and all “obstructions” to the edge (boundary) of the board. This applies to every type of piece, including Knights and Pawns. (I “know” that Queen, Rook and Bishop operate along geometrical LoA, but I also think of Knight and Pawn moves as a special kind of geometry.)
(3) Visualize a “box” (9 squares) around the King, no matter where it is on the board. This is one of the areas in which I “ignore” the formal chess rules. If the King is in a corner, 5 of the squares constituting the “box” will be off the board. If the King is on any edge of the board (but NOT in the corner), then three of the squares constituting the “box” are off the board. A special adaptation is to “SEE” the box even if the King is away from the edge. Its own pieces/pawns or my pieces/pawns can fulfill the same role as the edge of the board. You “merely” have to “SEE” that “box” in your mind’s eye. (For a long time, when I solved tactics problems in a book, I would create an explicit “box” by using a highlighter, creating explicit squares outside the board if needed.
(4) AVERAGE values of any kind (material, usually, but also positional) have NO MEANING in any SPECIFIC position. My favorite example of the in-applicability of averages is this: are you aware that the average American family has 2.3 children? Have you EVER seen a 0.3 kid???
(5) Values associated with the pieces/pawns in the abstract are pretty gross; there is no need for extreme numerical accuracy. The simple Reinfeld values [Pawn = 1; Knight = 3; Bishop = 3; Rook = 5; Queen = 9; King = 4 in endgames] are sufficient for human chess playing. I’ve seen computer calculations that are based on centi-pawns (1/100 of the value of a Pawn). That’s perfect for a mechanical beast examining millions of positions per second but NOT for humans! You CANNOT calculate that accurately in your head (where the game of chess is actually played; if you think I’m wrong, then where is blindfold chess played?). If you think I’m wrong, then tell me what value there is for human chess playing if we increase the numerical precision to 10 decimal places (easily done with a computer). Reductio ad absurdum at its finest.
PART II:
ReplyDelete(6) When investigating (I hesitate to call what I actually do as “calculating moves/variations” in the conventional sense), always keep in mind three key points:
[1] The attacking/defending pressure of each piece on any given square is always EXACTLY 1. The material value of each piece is very closely correlated to its AVERAGE mobility on an ILLEGAL board – one that has no other pieces on it, not even the kings! Material value has NO relationship to the quantity of pressure on any given square at any given time. Consequently, when “SEEing the PoPs and LoAs, the AVERAGE material values are meaningless. Ergo, work with the interactions (specifically, the LoA) and leave the “accounting task” (totaling up the material balance sheet) until AFTER you are satisfied with the line of play. After all, you’re PLAYING CHESS, not auditioning for an accounting job.
[2] Whatever moves you make only in your head CANNOT be ILLEGAL, by definition. You can violate the RULES (including the formal rules defining how to play chess) whenever it serves your purpose.
[3] General principles are heuristics based on AVERAGES. {Refer back to (3).} If you catch yourself trying to formulate or justify your choice of move based on general principles, consider that a huge DANGER sign – and immediately STOP DOING IT! Chess is played outside of the AVERAGE “box.” General principles are a crutch for beginners, but as quickly as possible we need to learn to walk and run (PLAY CHESS) without (or more correctly, in spite of) the crutches.
(7) KNOWLEDGE (“Know THAT”) is much less important than SKILL (“Know HOW”) Yes, we MUST have a certain amount and kind of knowledge (for instance, we cannot PLAY CHESS unless we know at least a majority of the formal rules). KNOWLEDGE C-A-N be LIMITING. If you find yourself mentally saying “I can’t do THAT” (because of something you remembered that you KNOW you know), consider that another “flag” and check very carefully if in fact THAT CAN be done. GM Beim gave a Russian proverb about this: “If it doesn’t work, but you really want it to work, then it must work.”
(8) Often, we ASSUME we know what an author means, without taking the time to understand what he REALLY means. Words can have myriad meanings, depending on context. We often misinterpret or miss what is INTENDED. I’ve been trying to emphasize the notion of “SEEing” in the mind’s eye by CAPITALIZING and bolding the word “SEE”. Do you “SEE” what I MEAN?!? “SEE is equivalent to “UNDERSTAND.”
That’s a quick, short set of helpful personal maxims, principles, half-baked ideas,whatever, residing in the RCCM as an implicit part of its “thinking process” (whatever THAT is). I’m sure there is much more (perhaps that I am totally unaware of) residing in the RCCM, but that’s what sprang directly into my mind’s eye for the moment and suffices for a start.
Oh, a caveat: most of what I’ve offered above can be found elsewhere. I claim no originality. Unfortunately, I cannot always remember from whom and from where I first learned something. It represents what got ground into the RCCM by voraciously reading chess (and a lot of other kinds of) books.
I’m ASSUMING (of course) that I “SEE” what you are looking for as simplified RULES. If I’m totally out of my RIGHT mind and “blind” in my mind’s eye, just point me toward my LEFT mind and I’ll try again.
The role of logic is to simplify matters. To prune unnecessary things. System 2 has only a few Short Term Memory slots, so I must be very careful to not overload it. Rules can be so designed that they simplify matters.
ReplyDeleteIn the position above, I am inclined to panic when I contemplate the move Qxf3. Placing my own queen under attack and handing over the move to my opponent.
But there are situations where you can do that. When you already attack your opponent's queen, for instance.
I play with a lot of "what ifs" in this position. What if my King stood on h1 instead og g1? What if blacks queen was on a8? What if I took on f3 with g2 instead of with my queen? And so forth. I'm trying to get the hang of the tempo battle. What does it mean when Tal says "he can only take one piece at the time" when every piece hangs, et cetera.
What is the role of the obligation to take back? What is the role of an additional punch, etc..
Update of the post in blue.
ReplyDeleteI obviously misunderstood your need "for a few RULES." What I provided MAY (or may NOT) be useful for maximizing what can be learned from the given example. My apology.
ReplyDeleteYou asked specific questions above with the stated intent being to understand the tempo battle as it relates to this specific problem. I presume that none of them are merely rhetorical. If I misunderstood, please correct me.
Your last question identifies a common paradox concerning exchanges. It appears to be limited to a specific exchange situation but it not.
What does it mean when Tal says "he can only take one piece at the time" when every piece hangs?
You know the formal chess rules for capturing/exchanging. I won’t repeat them, thereby avoiding another word salad.
We learn [KNOWLEDGE] that when a capture takes place, everything else being equal, there is an “obligation” to recapture material of (roughly) equal value. This “obligation” is NOT a formal chess rule; captures are not mandatory. It is a heuristic or general principle or “rule” (quotes indicating it is not literally a formal rule.
Think of the rationale behind the tit-for-tat exchange sequence. You take one of my pieces, I take back one of yours of equal value — tit-for-tat. When it is not possible to maintain the material balance because of tempi, then it is NOT a tit-for-tat.
When that recapture “obligation” cannot be met, we term that a sacrifice (if it was intentional) or a blunder (if it was unintentional).
Captures are limited to one per turn to move. That is a formal rule.
Tal’’s aphorism is an excellent example of “ignoring” (intentionally violating) one of the "rules" (general principles).
The aphorism implies that the pieces remaining (which have not been capture yet) are performing some Function that is sufficiently important that the loss of material (by NOT recapturing) is worth it. This refusal to “follow the rules” can have a devastating psychological impact on the opponent. Why? Because we play with the expectation that BOTH players are following the same formal rules AND the same general principles (“rules”), and it is shocking to find out that your opponent is NOT!
The importance of tempi overriding the material values lies in the fact that there may be important Functions performed by the hanging but NOT captured pieces that outweigh the loss of the piece lost on a specific turn to move. Tal realized that he could violate a “rule” in specific circumstances.
Another example (although not stated in any aphorism that I know) is Petrosian’s use of the Exchange sacrifice, especially in various Sicilian position on the c3 square. Petrosian realized that the “rule” that a Rook is more valuable material IN GENERAL than a minor piece has too many exceptions to it to be followed dogmatically.
System 2 is having fun with this position, trying to invent a method of counting tempi. So that it can say at the end "7 plus tempi versus 6 minus tempi, so I win a piece". The methods that are invented by my system 2 are usually not very practical. So I keep playing with it, asking myself non rhetorical questions.
ReplyDeleteI made a scheme with Xmind. Every move had a "current" situation and a "next" situation. Until I noticed the triviality, and realized that the next position of the the current position equals the current position of the next position. As I said, system 2 is having fun.
What I'm after, is that I learn to see what the pieces are doing. I find move 1. ... Nxf3+ very intriguing. It does 3 things: It moves the knight out of harm's way, it takes a piece, and it gives an additional punch (check). And the difference between 2. Qxf3 and 2. gxf3 is worth to learn to see too. The first with an additional punch and the second without.
After looking at the position again, I "SAW" the simplifying idea (I think). Simply count the potential pieces along the various LoA as targets. The player with the right to move first should be able to win if he can "attack" more than the opponent. It's a simple "test" to "SEE" if further (deeper) investigation is required to find the nuances involved.
ReplyDeleteNaturally there MAY be complications along the way, such as EGT (equal but greater threat) when a higher value piece is attacked or a check before the opponent can respond, desperadoes, Zwischenzugs, Zwischenschachs, and so forth.
Looking at the specific position AND "ignoring" the formal rules (including strict alternation of move turns), it appears that White has a one-move advantage [5:4]. Obviously, that's only a "quick and dirty" methods and should NOT be relied upon for a final decision as to whether to go into the sequence, but at least it focuses attention when needed on the relevant factors. It's fairly simple to work along the main sequence, "SEEing" the branching points caused by the complications.
A couple more thoughts.
ReplyDeleteTempo wrote:
“I play with a lot of "what ifs" in this position. What if my King stood on h1 instead on g1? What if blacks queen was on a8? What if I took on f3 with g2 instead of with my queen? And so forth.
This is the kind of “moving the pieces around” that GM Davies espoused.
I mentally restricted the Function concept to defensive obligations., based on Lasker’s description. As you point out, pieces can have kinds of Functions, some offensive and others defensive. In its broadest sense, it is simply WHAT IF? applied to all pieces/pawns and the relationships between them. Following the formal rules and/or the informal ”rules” (general principles) is NOT required, and in fact, can be counter-productive when the objective is to CLEARLY “SEE” what the individual pieces/pawns can DO in the specific position — whether it is the current actual situation or a “stepping stone” position in the mind’s eye.
On a CLEAR day, the mind’s eye can “SEE” forever.
Tempo wrote:
“In the position above, I am inclined to panic when I contemplate the move Qxf3. Placing my own queen under attack and handing over the move to my opponent.”
I share that fear at times. The only antidote is to remind ourselves that we simply IMAGINE what might happen IF we do certain things. NONE OF WHAT WE IMAGINE IS REAL. The fear as well as the consequences of possible moves is all in our mind.
I’ve tried to use that panicked feeling as a trigger to remind myself that it’s NOT real. [So far, sometimes the trigger works and at other times, it doesn’t.] I usually have to mentally wrench myself away from whatever I am contemplating, which is disconcerting, to say the least.
Associating a trigger with action (any action) can help. For instance, if you get a panicked feeling, stop thinking about the board and do something physical like standing up. It doesn’t matter whether you’re playing a tournament game or analyzing at home, when the feeling occurs, always do the same thing. After that trigger PLUS action becomes a habit, you will be able to use it all the time without thinking about it. As a consequence, the action will no longer break your concentration.
That’s the theory. I’m still working on practicing the habit and haven’t completely ingrained it yet.
FEN: r2r2k1/pp3ppp/8/2pq4/3b4/1P3P2/PB1Q2PP/2RR3K b - - 0 1
ReplyDelete[From lichess.org. My computer crashed, so I lost the reference information.]
[Is this a tit-for-tat position? If so, it is probably not a good example to use to “SEE” tempi.]
Surface level features:
King safety is approximately equal. Both Kings are behind a protective pawn shield and both are vulnerable to a back rank attack. Neither King is directly threatened (although the BBd4 is controlling one of the squares beside the White King). However, the Back King has limited mobility, whereas the White King is formally IMMOBILE.
Material is even.
Pawn structure is approximately equal. Black’s pawn structure is more compact, and has direct impact on the center [BPc5].
There are both White and Black batteries operating along the d-file.
The d2-square is “controlled” [1:2] by Black’s battery.
The d5-square is “controlled” [2:1] by White’s battery.
The Black pieces (BBd4, BQd5, BRd8) are slightly more actively placed than White’s pieces (WQd2, WRd1, WBb2). The remaining two Rooks (BRa1, WRc1) are approximately equally active.
The d4-square is B.A.D. [3:3]. It is an outpost (protected by the c5 Pawn) occupied by BBd4. BBd4 is RELATIVELY pinned against the Black Queen by the (WQd2, WRd1) battery. The BBd4 CAN move if that is useful.
The d1-square is B.A.D. [2:2]. The WQd2 is “skewered” to the WRd1 by the (BQd5, BRd8) battery. This is a serious threat because if a Black major piece ends up unmolested on the d1-square, it would be checkmate.
The b2-square is B.A.D. [1:1]. The WQd2 protects it, while the BBd4 attacks it. This is a defensive Function assigned to the White Queen. If theWBb2 is captured by the BBd4, there is an additional “attack” on WRc1. This resulting threat should be considered a potential gain of tempo.
The WQd2 is “protecting” the WRd1 from Black’s battery; this is a defensive Function assigned to the White Queen.
The White Queen has two defensive Functions, but CANNOT perform either and retain both. That is a key “clue.”
General principle/”rule”: The B.A.D. square with the most attackers/defenders [n:n] (where n is the number of attackers/defenders) should be the first investigate. (I’m sure Mr. Chuzhakin’s System has a Hazardous Element associated with this condition.)
Consider the interaction of pieces involving one >B.A.D. square to be a local area. There two local areas in this position: (1) the pieces/squares associated with the b2-square, and (2) the pieces/squares associated with the d1-square. The d4-square should NOT be considered by Black because Black occupies it.
Black has the right to move first which connotes the initiative.
The first “idea” is to divert the WQD2 away from the WRd1 in order to activate the Black battery against the d1-square with a potential back rank mate. 1... Bxb2 is a diversion with an additional punch (attacking the WRc1). There is a negative twist: White can “ignore” the diversion (temporarily) and capture the higher value “target” BQd5 with 2. Qxd5. In this case, Black MUST continue with 2… Rxd5. The WRd1 “magically” acquired two new Functions and is now overloaded: (1) it must capture back on the d5-square and (2) must “protect” the WRc1. It cannot perform both Functions AND recapture material. Ergo, choosing the “lesser of two evils,” 3. Rxd5 Bxc1 and Black is ahead by a piece.
Going through this analysis convinces me that scrupulously totaling up ALL the potential tempi is unnecessary, time consuming and very likely to “confuse” System 2. It is only necessary to “SEE” the critical tempi in relation to the critical points of pressure (PoP) and Functions (Fun) along the lines of attack (LoA) found using LOGIC.
The variations take care of themselves as a result of “SEEing” the logic connecting the various elements and local areas together into a coherent whole.
What would be left when you rewrite this comment and leave everything out that is even slightly remote redundant?
DeleteMaybe I should add "with hindsight".
DeleteSorry about that word salad.
ReplyDelete"SEE" the PoPs.
"SEE" the LoAs.
Connect the LoAs to the PoPs (local areas).
"SEE" the Functions.
"SEE" the start of a main variation involving one (or more) of the local areas.
1... Bxb2
Solve any "complications" while moving forward through the main variation.
1... Bxb2 2. Qxd5 Rxd5 3. Rxd5 Bxc1
Evaluate the result.
Black is a piece ahead.
Is that less redundant?
Lol. That is not what I mean. I like the word salad. Since my system 2 knows how to handle that. What I'm after is something that system 1 can work with. Do you need to know the difference in material? Not necessarily. Do you need to know about King mobility? Not necessarily. You need to SEE the back rank mates on both sides. You need to SEE that the white queen is overloaded. You need to see that Rd1 is overloaded. That kind of stuff. The ESSENCE of the combination, so to speak.
DeleteI distinguish between “see” (perception – the physical act of sight) and “SEE” (conception – the mental act of insight).
ReplyDeletePerception is always of the surface. Conception is of the essence.
“There are none so blind as those who will not see.”
Perception, based on observation using the visual system, ‘understands’ this truth about physically blind persons. That is the ‘surface’ level of this aphorism. “Of course, blind people cannot see – THAT’S OBVIOUS TO THE MOST CASUAL OBSERVER. So, what’s your point?”
Conception, based on a deeper (analogical) level than the surface level, understands this truth about people who refuse to “SEE”. “AHA! NOW I UNDERSTAND!”
System 1 is totally responsible for physical sight. It occurs instantly, without volitional control and NO logical process involving System 2.
I’m not sure there is a clean separation of responsibility for conceptual “SIGHT” between System 1 and System 2.
“You can lead a horse to water but you can’t make him drink.”
“You can point someone to a truth but you can’t make him think.”
Parallel conceptions? Only if you “SEE” the connection.
Can we “see without “SEEing”? Yes. (Think of unskilled players seeing the given position without having any conceptual knowledge of what to do.)
Can we “SEE without “seeing”? Yes. (Think of playing chess if physically blind.)
You note:
“You need to SEE the back rank mates on both sides. You need to SEE that the white queen is overloaded. You need to SEE [note the not-so-subtle change I made] that Rd1 is overloaded. That kind of stuff. The ESSENCE of the combination, so to speak.”
We must KNOW the concepts before we can develop the SKILL to SEE the concepts as the essence of a position. System 2 “trains” System 1 by learning new concepts, shining the light of focused attention on concrete occurrences of the concepts in conjunction with specific positions. After sufficient exposure through training, System 1 has the wherewithal to bring that concept up to consciousness without being commanded to do it. It “SEEs” the concept below the surface and brings it up whenever System 2 directs attention to the surface level features. The surface level features “point to” the essence.
At least that’s how I “SEE” it. What do you “SEE”?
I cannot find the post back, but long ago I posted a position where I looked at a B.A.D. (Barely Adequate Defended) piece, and only after about 5 minutes or so it dawned on me that it might be a good idea to change my attention to the defender of the BAD piece.
ReplyDeleteIf I remember well, that inspired me to think about the standard scenarios that one should know. I even invented the tree of scenarios back then. Summarizing, my system 2 had a lot of fun, with little effect on my play.
OTOH, today I look much earlier at the defender, so maybe something is sticking after all.
What am I after? The role of system 1 is to SEE the salient cues, and the role of system 2 is to guide the attention in the right direction. The right direction still sounds a lot like the standard scenarios of the past.
System 2 is able to work with short straight sequences. Often these sequences are theme based. For instance a fork, a double attack, a discovered attack, making use of an overloaded defender et cetera. The essence of the scenarios have a close relation to the tempo battle.
And the short sequences intersect with each other. That intersections are most of the time unique, meaning that only system 2 can direct the attention to them, since that cannot be automated. So we have three things:
Salient cues (the realm of system 1)
Standard scenarios (straight sequences, currently the realm of system 2, but possibly suitable to be automated by system 1)
Intersection between straight sequences (the realm of logic, system 2, not automatable)
So it looks like a good idea that after a problem is solved and the ensuing word salad is produced by system 2, that we make the distinction which elements of the solution fit into which category. That is how I SEE it.
In the broadest abstract sense:
ReplyDeleteIs it necessary for us to “SEE” the entire ‘picture’ all at once, or is it sufficient to “SEE” one salient aspect at a time, eventually arriving at an understanding of the requirements of the position (the essence)?
In short, is there an overarching framework that will enable us to “SEE” everything simultaneously, or is the potential existence of such a framework an illusion, a quest for a nonexistent Holy Grail?
We have to be exposed to myriad examples in order to (FINALLY!) have something usable that “sticks” in our memory. How many myriad angels can dance on the head of a pin? I don’t know, but apparently “myriad” means a lot more than a few.
My personal view is that it is sufficient to “SEE” one aspect of a position at a time, without concern for how it “fits” into an overall hypothetical framework. The framework of cogent aspects is discovered, one aspect at a time, not simultaneously. Some aspects DO pop into consciousness at the same time, but NOT all of the essence at once. It may be a sequential process, but (fortunately), it proceeds at the speed of neurons in a massively parallel associative system.
I don’t think child prodigies have an explicit framework through which they “SEE” all those marvelous things that we adults cannot “SEE,” BUT, I’ve also never been a child prodigy, so what do I know about that?
[I must be in a curmudgeonly mood today; this too will pass.]
"In short, is there an overarching framework that will enable us to “SEE” everything simultaneously, or is the potential existence of such a framework an illusion, a quest for a nonexistent Holy Grail?"
DeleteYes, I think I need a framework for tempo battles. No, we probably don't SEE things simultaneously.
A framework is needed for system 2, like training wheels are useful for children who want to learn how to bike. The biggest problem when I try to solve a puzzle, is that I shoot into trial and error mode. After too many puzzles that is a habit that needs to be suppressed.
In stead, I can better begin at the beginning. There are not so much possible beginnings when it comes to tactics. It begins with a B.A.D. (Barely Adequate Defended) piece, a NOT defended piece, a possible promotion, a double attack of some sort or a trap.
Once I have found the beginning it is a matter of "zoom in (system 2), zoom out (system 1)".
I realized that we have that overarching framework already: the tree of scenarios. Read the post of July 04, 2017, for instance. I never have been able to make it practical. But that was carrion. Now the vulture is transformed into an eagle, we are talking about a whole different animal.
ReplyDelete