I made a very small dent in the tsundoku on my bedside cabinet last night, and turned at last to a book by O Meien on "The New Age of Go AI". It was supposed to help me nod off, but it kept me awake. Here's a few of the reasons why.



You may recognise this position as from Game 1 of the million-dollar match between Yi Se-tol and AlphaGo in March 2016. O Meien was present there. He has a special status in the go AI world. Apart from his own interest in computers, he is probably - as a multiple title holder - the highest-ranked player to write about AI in depth.

His book dates from March 2017 and so is really about AI based on training with human games rather than self-play. That doesn't matter too much here, though it does explain why Yi played the odd "shimari" in the lower right. He wanted to achieve a position the computer hadn't seen before. This fuseki arrangement (rather than the one with Black A) had actually appeared a couple of times before, but in effect he probably achieved his objective.

But it was the triangled White 10 that fascinated O. In general, in human play White is reluctant to approach in the top right whenever Black can combine a pincer with another stone (as here). AlphaGo went with it anyway.

Lizzie/LZ (the self-play version) agrees. So there's the first interesting point - the bots trained on human games and self-play agree.

It is also of interest that LZ looks at just three moves: this White 10, B and C, all fairly close. This seems to go against human wisdom, in that White is playing close or contact plays on a side dominated by Black. As I have remarked in other threads, the Japanese pro view appears to be that the bots are aiming for early overconcentration, so the move in such areas has to be a full-frontal attack (shoulder hits are also in the armoury; even the early 3-3 invasion can be seen as inducing overconcentration, and the new outside player's replies as resisting that).

Next interesting point: these three moves are also chosen by LZ if Black makes the bigger (Dosaku) "shimari" at A. But LZ hen gives White a markedly better score! That seems to go against human intuition that A is better than the shimari of the game, which is less "connected" with the upper-right corner stone. Connection can be bad? That's what O seems to be suggesting.

First, O Meien said he approved of White 10 himself. But what he really approved of was White's strategy, which was revealed in the diagram below:



I'll leave you to look up the actual moves (effortful practice!), but the important point is the evaluation of this position. O points out that the Black stone at A is not participating in the fighting, and so he wants to be White. (It is this kind of evaluation that pros often use for counting the game BTW - they keep a debit-credit list of such bad moves in their heads, being able to pin a value on each error.)

O doesn't say specifically, but it seems this also explains why, to a bot, Black's right-side position is better than if it had used the usual shimari at B: it would be even less involved in the fighting and would actually be overconcentrated.

What we seem to come back to time and again is simply that bot play is EFFICIENT. Perhaps there really isn't much more to it than that. Overconcentration is one measure which humans seem able to get to grips with. Maybe another measure is how many of your stones participate in a fight (defined how, thohgh?), and of course if you can efficiently place stones so that they participate in more than one fight, you win the lottery.

Interesting. I have a question/comment though...



My understanding was that even then Alphago had been doing self play training after going through all those human games. Given that fact, then trying to get it in an "unfamiliar" position was actually a very dubious strategy based on a misunderstanding of how the AI worked and Yi should just have played his best rather than trying to "game" alphago.

Correct, although the seed for its self-training did make a big difference, as you can see just by comparing the play of AlphaGo and AlphaGo Zero (of course, there are other differences between the two systems besides the initial training data).


Given what people knew about AlphaGo at the time, I think that playing a barely-suboptimal move to try to get the game into new territory was perfectly reasonable. It's not like it was a multi-point mistake.

Based on what I knew at the time, I thought it was a bad strategy. I suspect/fear Lee didn't actually consult much with go bot experts despite the high stakes. I heard many other Korean pros thought he was lucky to be the chosen opponent because it was an easy million. Myungwan Kim was unusual in not thinking that.

Go is about "EFFICIENT" moves.

If you are good at evaluating your and your opponents single moves regarding efficiency you dont have to count "territory" and "potential territory" all the time.

Indeed I think I am usually better at judging early game position, like Bill has been posting with the Elf judgement threads, by tallying up the moves' goodness/badness than by counting points, e.g. https://lifein19x19.com/viewtopic.php?p=249447#p249447

Thank you for sharing O Meien's thoughts and yours. Very interesting, informative, and instructive.



The "micro-Chinese" extension was not on Elf's radar, either, in its GoGoD commentary on the game. It got 1 count'em 1 playout, compared with 31.5k playouts for Elf's top choice. Still, Elf rated it only 3½% worse than its top choice, a in the diagram, which I think is within Elf's margin of error here. It also rated only 2% worse than Elf's second and third choices, b and c.

Click Here To Show Diagram Code

[go]$$B Moves 1 to 7
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . 5 . . . . . . . . . . . . . |
$$ | . . . 2 . . . . . , . . . b . , 1 . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . 6 . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . 7 . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . c . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . 4 . . . . . , . . . . . , . . . |
$$ | . . . . . a . . . . . . . . . 3 . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

b and c may not have been on Yi's radar.



Yes. The top bots value pincers less than humans do, or did at that time. was totally off of Elf's radar (0 repeat 0 playouts). Elf's choice is the beloved underneath attachment at a.

Click Here To Show Diagram Code

[go]$$W Moves 8 to 10
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . . . . . . a . 3 . . |
$$ | . . . O . . . . . , . 2 . . 1 , X . . |
$$ | . . . . . . . . . . . . . . . . b . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . c . . . |
$$ | . . . . . . . . . . . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

It seems unlikely to me that AlphaGo looked at just those plays. Rather, one or more humans made the decision to reveal those possible plays that AlphaGo considered, based upon reasons they did not give.



I dunno about that. For one thing, b is joseki. For another, Attachment for sabaki, as the saying goes. Where do you need sabaki if not in the opponent's parlor?



I assume that sequence was the mainline variation that AlphaGo considered. Calling it a strategy is fine, but I think that it is a little too detailed for that. (Edit: Now that I think about it, I kind of like scenario. ) More important is that we should not believe that if AlphaGo played itself after that it would make those plays. The further down the variation we go, the less likely it is that AlphaGo would make the play, and the less accurate its winrate estimate. The main reason is that later plays are based upon fewer playouts. and are simply less reliable. Did the humans reveal the number of playouts for each play?



Well, I hope there is. I learned that as a 4 kyu. It helped my game, but efficiency is one of those concepts that we keep learning about.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Or efficiency gets an ever more evolved concept. Then there is no need for more than efficiency

O Meien gives one further example of how Game 1 of the above match astonished him and other pros. It was move 80, shown below. White (AG) has ignored Black's approach move in the lower left.



O gagged on this move. He said virtually no human would play it, and he called it a 'repair' move. There are times when such a solid play might be praised as a 'thick' move but O makes no reference to thickness. His headline in fact tells us that in his view this move is about bots having "different logic" from humans.

The way he explains this requires some knowledge of Japanese terminology, so let me get that out of the way for you first. English speakers have 'aji' in their toolbox. Japanese speakers have te ga aru, aji, and nerai, plus a few others such as aya and fukumi, but the first three are the ones O talks about here.

The repair move (teire) of the game is about the possible aji of Black A. Aji refers to a situation where a player may be able to cause some mischief if future circumstances develop in some as yet undefinable way.

Te ga aru refers to when "a [concrete] move exists." It is in plain sight and is obvious to both players. It is two sided in that both sides would happily play there, but it just hasn't been played yet because there has been bigger fish to fry. B is an example here. It is the elephant in the room. To extend the menagerie, aji represents ants in the pants.

But the zoological key to this position is the cat lurking in the bushes, read to pounce on the pigeon. This is encompassed by the term nerai, which usually gets lost in English because it is translated in so many ways (e.g. target, aim, objective) and in any case the verbal aspect of the noun is always lost (lurking, lying in wait, taking aim). There is a feeling of the target being hidden, or at least unsuspecting. And it is much more concrete than aji. Aji refers to a move you may be able to play. A nerai is one you can play. It is a very common term in Japanese, especially in pro talk. It differs from te ga aru in that it is one sided. The pigeon side doesn't really want to go there. It would be close to making a move like connecting on a dame point. It's the cat that wants to play there, and cats can be very patient - a good thing in go. So, in short, a nerai move is halfway between te ga aru and aji.

It is the nerai in this position that you need to find. O doesn't actually say that he missed it himself, but he was astonished enough to look it up in the AlphGo log, and was further surprised to note how much earlier AG had been looking at it (well before this position, I infer, but he doesn't actually say). Do try to find it yourself before reading on.

Before we come to that, though, let us get back to O's initial reaction, or his "logic". He reasoned that if the aji at A had worked at once, Black would have played there at once. He didn't so a move there by White wasn't urgent. A White move around B was not big enough yet and so the logical move was to preserve the "status quo ante" (presumably meaning territorial balance) by playing at White C (which is where Black played next). This he regards as a move any human pro would play. He obviously also thought to himself "Rem acu tetigisti."

But, oh no, feline AG had columba pie on the menu. It had seen that it could respond to a double approach in the lower left by taking sente (even that surprises me - you normally assume you will end up in gote if outnumbered), and so could turn to its unsuspecting target - on move 102!

If you feel in the mood for deep thought, I'll add another aspect for you: timing. When discussing the style of Honinbo Shuho, I introduced the concept of kairos, in which he excelled, and with which he probably also imbued Honinbo Shuei.

A te ga aru move such as B above is normally achieved through normal sequential play as the sizes of plays decrease. Rather like the endgame writ large. Chronos is the Greek term for sequential time. Kairos, in contrast and like nerai, is about timing opportunities out of sequence. Knowing when to strike. Which also means knowing how to set your targets up.

AG's nerai here was move 102:


.

I remember this passage of play very well from watching it live.

I was quite staggered. The line White played against the double approach is the sort of thing used as a space-filler in Japanese magazines. But contextualised by the idea that White can (apparently) give away points here. Which means it's not a corner opening at all, but a middlegame ploy.

The right-side fight is complex. For those who only knew the games against Fan Hui, the power AlphaGo showed here must have been a revelation.

Knotwilg:

Thank you John for demonstrating, yes it can. I adore the insights you provide into the different kinds of hidden potentials in the game of go, we mortals just call "aji" because of our ignorance .

Thanks again, John. Verrrry interesting.



Quote of the day:

Unlike some people we know.

In the Elf GoGoD commentaries, Elf has an interesting take on and .

Click Here To Show Diagram Code

[go]$$Wcm74 Moves 74 to 80
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . O . O . X X X . . . . |
$$ | . . . . . X . . O X . X . O . O O X . |
$$ | . . . O . . O . O X . X . . O , X . . |
$$ | . . . . . . . . O X O X . X O . . X . |
$$ | . . O . . . O X X O O X . . O . . . . |
$$ | . . . . . . 7 . . O X O . . O X . . . |
$$ | . . . . . . . . O O X O . . O X . . . |
$$ | . . . . . . . O X . X X O . . X . . . |
$$ | . . . , . . X X X X . . O . . , . . . |
$$ | . . . . . . . . . . X O . . . . . . . |
$$ | . . . . . . . . . O O X O . . . X . . |
$$ | . . . . . . . . 4 . . X O . . . . . . |
$$ | . . . . . . . . . . . X O . . . . . . |
$$ | . . . . . . . . . . . X O . . . 5 . . |
$$ | . . . O . . . . . , . X 1 . . , . . . |
$$ | . . . . . 6 . . . . . 2 3 . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

Elf has wanted White to play since , inclusive.
Things get worse for Black, in Elf's view, after . Elf indicates that it is a blunder, losing more than 10% in winrate, from 16½% down to 6%.

That consideration may also bring closer to human thinking. Did human pros, before or after the fact, think that White had an almost won game after ? If White does have a won game, a protective play to nail down the lead makes sense in human terms.

More about . To repeat O Meien's reasoning:


Well, Elf thinks that Black should indeed play at A. That being the case, it is no wonder that AlphaGo thought that was urgent. So might a human who thought that A was a Black threat. Here is Elf's mainline variation for .

Click Here To Show Diagram Code

[go]$$Bcm79 Black's threat at
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . O . O . X X X . . . . |
$$ | . . . . . X . . O X . X . O . O O X . |
$$ | . . . O . 5 O . O X . X . . O , X . . |
$$ | . . . . . . 6 . O X O X . X O . . X . |
$$ | . . O . 0 . O X X O O X . . O . . . . |
$$ | . . . . 9 7 3 1 . O X O . . O X . . . |
$$ | . . . . . 8 . 2 O O X O . . O X . . . |
$$ | . . . . . 4 . O X . X X O . . X . . . |
$$ | . . . , . . X X X X . . O . . , . . . |
$$ | . . . . . . . . . . X O . . . . . . . |
$$ | . . . . . . . . . O O X O . . . X . . |
$$ | . . . . . . . . X . . X O . . . . . . |
$$ | . . . . . . . . . . . X O . . . . . . |
$$ | . . . . . . . . . . . X O . . . O . . |
$$ | . . . O . . . . . , . X O . . , . . . |
$$ | . . . . . . . . . . . X O . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

Pulling the Black stones out carries threats both above and below. Black's stones are still weaker than White's center stones, but Black has the move.

Click Here To Show Diagram Code

[go]$$Bcm89 Black's threat, continued
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . O . O . X X X . . . . |
$$ | . . . . . X . . O X . X . O . O O X . |
$$ | . . . O . X O . O X . X . . O , X . . |
$$ | . . . . 4 . O . O X O X . X O . . X . |
$$ | . . W 3 O . O X X O O X . . O . . . . |
$$ | . . . 5 X X X X . O X O . . O X . . . |
$$ | . . . . . O . O O O X O . . O X . . . |
$$ | . . . 1 . O . O X . X X O . . X . . . |
$$ | . . . , . 2 X X X X . . O . . , . . . |
$$ | . . . . . . . . . . X O . . . . . . . |
$$ | . . . . . . . . . O O X O . . . X . . |
$$ | . . . . . . . . X . . X O . . . . . . |
$$ | . . . . . . . . . . . X O . . . . . . |
$$ | . . . . . . . . . . . X O . . . O . . |
$$ | . . . O . . . . . , . X O . . , . . . |
$$ | . . . . . . . . . . . X O . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

The keima, , is a strong play. Elf stops this variation here after because the number of playouts for subsequent plays drops below 1500. I am not qualified to judge this result, except to say that to me it looks playable for Black. Because of the threat to White's center stones, I expect that White will have to give up the stone.

Anyway, Elf likes this variation, and apparently AlphaGo did, too, or a similar variation.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Just going back to the first point about the non-joseki attachment of White 10 for a moment, that game I tewarid from Bill's Elf game 12 also had a similar idea from the great Lee Changho. https://lifein19x19.com/viewtopic.php?p=249640#p249640. The normal idea with high pincers to 3-4s is to jump out before attaching in the corner, but in that game Lee decided to attach first just like AlphaGo did against the younger Lee. I think that was also to do with making the pre-existing side extension misplaced.

As for 79 being bad, I don't think that's so hard to understand. It's inconsistent with 77 so low efficiency. At that point black faced the problem of how to deal with White's cutting stones in the centre. There are 2 main strategic choices:
1) capture them in a net.
2) develop both cut groups so they can live independently so it's not a problem if the cutting stones run.
For the lower black group one way to do 2 would be approach on the lower side and hope White backs off (is that a dream? Pincer possible) and make some eyes and territory on the lower side. Trouble is the g10 group doesn't have easy eyespace so it's harder to do plan 2 with it. So that's probably why Lee chose plan 1. When g10 gets strong it also makes pulling out the 2 stones easier.

But once he's netted the cutting stones he doesn't need the approach on the lower side to make eyes, it's just territory, and makes 77 somewhat wasted, eg if 79 was already in the board would black prefer to move 77 to some more ambitious gobble move like g7 or even d10?

Bots have taught us that answering an approach to 4-4 is less urgent than we thought, so approaching them can be bad often too if there are other urgent moves involving strength and weakness of groups elsewhere. Master Vs Jiang weijie is a particularly memorable example.
https://www.alphago-games.com/view/even ... 34/move/37

P.S I have noticed a general tendency of mine to play mistakes of type 1 when 2 is better, i.e thinking a move is honte but actually it's too slow. Also with nets you need to be aware what kikashi they leave and be wary of overconcentration. That was the a mistake Kageyama made in that position I analysed a while ago.

If we assume* pulling out the 2 stones is too much with g10 group still weak then it is only after black has defended at 77 that it is a serious threat. So it is only on one prior move namely 78 that White might have defended, and one move 79 that black might have pulled them out. I can see White wanting to play 78 as in the game to make sense of the wall built on the previous moves: by separating the black corner White ensures his wall isn't an eyeless dame stick but attacks and makes it 2 dimensional with some eye potential, breaks a lot of black territory and sets up the famous invasion for later (which wouldn't have been so effective had Lee found the right time to peep at o9).

Also just because Lee made the mistake of not pulling them out for 79, AG only plays the board assuming it is playing against an opponent as strong as itself so defended because it thought it was the best move against Black's best moves. It doesn't do the human psychology (probably) bad habit of "my opponent didn't notice this good move so I won't defend against it but greedily grab other points in the hope I can come back later" strategy. I say probably because when deployed well this probably can win you more games. Indeed a bot trained to use such strategies could probably beat a top human by say 30 instead of 20 points.

* Which Elf apparently doesn't: if it thinks White should have defended there before 78 then presumably it also thinks black should pull them out before 79 and can handle g10 weak too.

White played the nose attachment to Black's two stones in question with . Containing them was on Elf's radar for onward. Running out with them was on Elf's radar for onward. It was only after that running out became Elf's first choice for Black.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Ah, thanks Bill. So it was on Elf's policy network for a while as a move worth investigating, but with some reading rejected it. It's nice that our bot overlords agree with basic human heuristics.

Although I am only part way into O Meien's book, and I do tend to focus on language more than most because of my background, I have to say I have been struck by his use of language.

I have already mentioned his Latinism (and he also cites Hannibal's march on Rome) and the fact that, so far at least, he eschews many normal go terms such as 'thick'. Even when he does use them he has a habit (here) of making them stand out in some way. For example, he uses words like 'heavy' in quotes, as if to say, "I'm not really talking about heavy in the way you normally understand but in a special AI sense" (and that particular case is very pertinent in Game 2 we are about to look at). Similarly, when he talked about nerai he highlighted it by waxing lyrical about how there's many a slip twixt cup and lip and many far-off nerai targets are not achieved because too much goes on in-between. I think we can see from Game 1 why he had a bit of a hang-up about nerai!

Another example that struck me, which he uses more than once, is the phrase 'standard theory' 標準理論. That's perfectly clear and many Japanese wouldn't bat an eyelid at it, but he does put it in quotes and eschews the routine go word for go theory, kiri　棋理. Again it's as if he is grasping for new ways to talk about new things, which is especially difficult when those new things look just like old things. Game 2 had several such difficulties.

There were several surprises for him and other pros, but the biggest surprise was that they came in a connected passage. In Game 1 it was possible to believe that AlphaGo was just a tactical monster that saw much further ahead than humans, the nerai being a perfect example. But in Game 2, the connectedness of AG's play looked deep (and novel) strategically.



This was O's first highlight. He said the pros had been looking forward to seeing how AG would play as Black, and for the first few moves they were very happy with what they saw. But Black 13 (triangled) wiped the smiles off their faces. (For me it brought a smile because it made me think AG was chiding Yi for choosing the strangulated Chinese in Game 1, saying: "See this is how it should be done!").

It was not the idea of tenuki that astonished O. He said it's perfectly reasonable in the case when the squared stone has not been played and Black can then treat his remaining two stones in that area as light. The problem for him was that the addition of the third stone makes that group heavy (or "heavy", to be precise) and so a move at A is now required in order to relieve that heaviness. This, he says, is "standard theory".

O says that he and his fellow pros initially came to the conclusion that the Black tiger's mouth shape was indeed heavy but not really attackable just yet, and that's why AG could tenuki. The subsequent moves, however, brought in the notion that heaviness was the wrong concept. This shape is more of a foundation stone.

O does not discuss White 14, but you can almost hear his eyes pop at Black 15 (below). This got an immediate name - the sugu nozoki or 'immediate peep'. And he says it too goes against "standard theory."



But he adds that this move was quickly adopted by top pros (interesting that he specified "top" pros ) and he gives the rationale: Black's loss in forcing White to connect against the peep is trivial compared to the gain, which is that White will connect directly here, whereas later on he might respond in different ways (e.g. with a kosumi). It is therefore "good timing." O doesn't explain why White must respond with solid connection now rather than varying, but presumably you have to be a "top" pro to understand that. It seems, though, the main reason it has not been played up to now is that it lowers the temperature (shitabi ni naru).

But once again the subsequent moves can cast a new light, AG continued with a now well known and popular joseki in the lower left.



O's interpretation of this sequence is interesting. I suspect most amateurs now play it because it's fashionable, it's joseki and they know some of the lines. But O believed AG was using it strategically for sabaki (without the quotes, so nothing too special there), and the idea was for Black to settle himself here as a way of alleviating any forthcoming attack on his stones to the right (i.e. forestalling any possibility of a splitting or karami attack).

All of that was O's Highlight 1 of Game 2. As his first long section he looks at two or three highlights in each of the five AG-Yi games. Highlight 2 in Game 2 is something special: the fake shoulder hit - the shoulder hit in thin air. This is real Harry Potter stuff! Professor Albus O Dumbledore has revealed what the standard theory of wizarding tells us. What will Dobby the Elf be able to tell us, with his insights into dark secrets from Malfoy Manor?

(Emphasis mine.)

Many thanks, John. It seems as if O Meien is doing what I said we humans would do, modify old concepts and perhaps come up with some new ones. Gradus ad Parnassum. More power to him!

As for the rest of your note. Much for me to mull over over breakfast.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.