Sunday, November 24, 2019

Proof that a 4-by-4 grid divides a circle into 30-degree arcs

This turned out to be almost disappointingly easy to prove.


AC is equal in length to AD, since they are radii of the same circle. C is on the vertical line that bisects AD. Therefore, CD is the mirror image of AC, and the triangle ACD is equilateral. Therefore, the angle formed by AC and AD is 60 degrees, and that formed by AB and AC is 30 degrees.

Similar triangles can be made for all the other red points, showing that they are located at 30-degree intervals.

No other grids (3-by-3, 5-by-5, etc.) divide a circle evenly like this.

Another mathematical puzzle: Why does this work?

Never having bothered to acquire any halfway decent graphics software, I've been using this trick for years to draw regular hexagons, equilateral triangles, and such.

Create a 4-by-4 grid of squares and inscribe a circle in it. The lines of the squares will intersect the circle at 12 points, which appear to be equally spaced at 30-degree intervals around the circumference of the circle. You can then connect selected points to create a triangle, hexagon, or dodecagon.

(The ancient geometers used to take it as a challenge to construct various polygons using only a square and compass. I suppose the modern equivalent would be: Using only a crappy graphics program like MS Paint, construct . . . .)


I can't remember how I happened to discover this -- just one of those happy accidents, I think. I also can't be sure, absent any mathematical proof, that the points are really evenly spaced at 30-degree intervals. (If not, they are certainly close enough that the trick can still be used to create polygons that seem to the human eye to be perfectly regular.) However, I strongly suspect that they are perfectly regularly spaced, because that's just how math is.

The last mathematical proof I embarked on, regarding congruence patterns in triangular numbers (qv) was a matter of straightforward number theory, requiring only everyday algebra, which is why I was never really in any doubt as to my ability to solve it. I am much less confident of my competence in this case, though, being innocent even of basic trigonometry. (Obviously somebody invented trigonometry without having been taught it, and I'm sure I could do the same if push came to shove; the question is whether or not I want to invest so much time and thought in a problem which has elicited only my passing curiosity.)

Hint's of Bosch's Conjurer in Magician card variants


In past posts I have mentioned the possibility of a relationship, whether direct or indirect, between Hieronymus Bosch's 1502 masterpiece The Conjurer (my favorite Bosch by a mile) and the Tarot de Marseille -- particularly the Magician and Wheel of Fortune cards.

In the process of collecting various early versions of the Magician card (qv), I noticed a few hints that that influence or relationship may extend beyond the limits of the Marseille tradition. (Only a handful of fragmentary Italian decks predate The Conjurer, so direct influence is not out of the question.)

The Cary Sheet (Milan, 1550)
The magician on the Cary Sheet (a partial set of uncut and unpainted cards sometimes considered to be the "missing link" between the Italian decks and the Tarot de Marseille) wears fez-like headgear suggestive of Bosch's conjurer, as opposed to the wide-brimmed hat typical of the TdM. Bosch, the Cary Sheet, and the TdM all agree in putting two cups on the magician's table -- but on the Cary Sheet the cups are apparently inverted (narrow side up) as in the Bosch painting, while the TdM has the cups upright. The long object situated between the two cups on the Cary Sheet is hard to identify with any confidence. The TdM would lead us to expect a second knife, or a knife sheath, but it could just as easily be a magic wand of the type that appears in the same position in the Bosch painting. And if we really want to push things, doesn't that vaguely egg-shaped object in the far right corner of the table on the Cary Sheet look more than a little like Bosch's little frog?

Tarot de Paris (1650)
It's impossible to tell what's on the magician's table in the Tarot de Paris, but there are other potential links to Bosch. The general layout of the picture is similar: The magician is on the right side of the table, with spectators on the left, and a wall behind them. As in the Bosch painting, a dog hides unobtrusively in the shadow of the table. There is also a monkey, an animal which many people have mistakenly believed to be depicted in the Bosch painting, hiding in the conjurer's basket. (In fact it is an owl.) If modern art historians have made that mistake, the makers of the Tarot de Paris could easily have done the same. Again, the magician is depicted with fez-like headgear.

Mitelli's Tarocchini (Bologna, 1664)
The "magician" of Mitelli's Tarocchini would appear to represent a clean break with Tarot tradition, dispensing altogether with the conventional table-covered-with-gewgaws theme -- but don't the dog, the hoop, and the little cluster of spectators come right out of Bosch?

Minchiate al Leone (Florence, 1790)
The Minchiate al Leone has a very strange Magician card. The familiar cups and balls are notably absent -- and who are those two people standing beside the magician? It would be a strange position for spectators; are they his assistants? At any rate, the vaguely tent-like objects in the center and in the left foreground corner of the table remind me of the equally mysterious object in the center of the table in Bosch.

And the other half . . .

I'm afraid that once I've noticed the potential for a bit of wordplay, no matter how crass, I am just constitutionally incapable of resisting it. So when I somehow happened upon this:


I couldn't help noticing how readily it lent itself to this:


Tuesday, November 19, 2019

A gallery of early or otherwise historically important Magician cards

This is primarily for my own future reference, but I post it here because others may find it helpful as well. These are the highest-quality images I have been able to find for each of the cards. They are in something approximating chronological order, keeping in mind that most of the dates are estimates.

I am indebted to Andy's Playing Cards for providing innumerable leads, and to Tarot of Marseilles Heritage for many of the images of cards from that tradition. If I've missed anything important, please inform me in the comments.

(Note: The image of the Oswald Wirth card I had originally posted was incorrect. I replaced it with the correct one on November 23, 2019. The "restored" Jean Dodal card was replaced with the original on November 25, 2019.)

Visconti-Sforza (Milan, 1451)
Ercole I d'Este (Ferrara, 1473)
The Cary Sheet (Milan, 1550)
Jacques Viéville (Paris, 1650)
Jean Noblet (Paris, 1650)
Tarot de Paris (Paris, 1650)
Mitelli's Tarocchini (Bologna, 1664)

Jean Dodal (Lyon, 1710)


Pierre Madenié (Dijon, 1709)
Jean-Pierre Payen (Avignon, 1713)
François Héri (Solothurn, 1718)
Minchiate Etruria (Florence, 1725)
François Chosson (Marseille, 1736)
Jean-Baptiste Madenié (Dijon, 1739)
François Tourcaty (Marseille, 1745)
Rochus Schär (Mümlisvil, 1750)
Claude Burdel (Fribourg, 1751)
Nicolas Conver (Marseille, 1760)
Ignaz Krebs (Fribourg, 1780)
Jacques Rochias (Neuchâtel, 1782)
Grand Etteilla (Paris, 1788)
Minchiate al Leone (Florence, 1790)
Arnoux & Amphoux (Marseille, 1793)
Bernardin Suzanne (Marseille, 1839)
Oswald With (Paris, 1899)
Lequart "Arnoult 1748" (Paris, 1890)
Rider-Waite (London, 1910)

Crowley's Thoth (1938-1943, pub. 1969)

Monday, November 18, 2019

Socrates doesn't have feathers

Emanuel Schikaneder in the role of Papageno, and the Visconti-Sforza "Fool" card
Some free-association here.

I was rereading some comments on one of my posts about The Magic Flute. I had compared Prince Tamino and his feather-covered sidekick, Papageno, to Gilgamesh and Enkidu, and William Wildblood added, "They are almost like Frodo and Sam!" Rereading that, I suddenly thought, "Or Don Quixote and Sancho Panza!" -- but I refrained from posting that because, never having actually read Don Quixote, I owe to cultural osmosis whatever superficial idea I may have of the Don and his squire and thus can't really say how similar they may or may not be to the characters in the Mozart opera.

Anyway, my curiosity was piqued enough that I read a few paragraphs of the Wikipedia article on Sancho Panza, and I was intrigued to find this: "Sancho's wife is described more or less as a feminine version of Sancho, both in looks and behaviour" -- obviously calling to mind Papageno and Papagena ("But what if Sarastro had set aside for you a girl who was just like you in colouring and dress?").

Shortly after suddenly becoming (mildly) interested in that particular Cervantes character, I happened to read Oswald Wirth's short chapter on the 16th Tarot trump, "The House of God," which depicts a tower struck by lightning. Wirth ends this chapter thus:
When this arcan[um] ceases to be unfavourable, it puts one on guard against what it threatens. Salutary fears, reserve, timidity which preserves one from ill-considered risks; simplicity of mind remote from errors of learning, common sense, the wisdom of Sancho Panza.
Sancho Panza again! The context of a House of God being struck by lightning also seemed to be a link to Papageno -- who is told, inside the Temple of Isis and Osiris, "Papageno, whoever breaks silence in this place is punished by the gods with thunder and lightning."

"The wisdom of Sancho Panza" -- and did Papageno have any wisdom to offer? Suddenly I thought of an anecdote I had heard years before from a philosophy professor.

The professor, wishing to demonstrate how easily we fall for logical errors, gave his class this syllogism: "All men are mortal. Socrates is mortal. Therefore, Socrates is a man" -- and asked them if it was valid. They rose to the bait and said that it was. The professor then presented a logically equivalent syllogism: "All birds are mortal. Socrates is mortal. Therefore, Socrates is a bird" -- and asked what they thought of that. Not valid, said one of the students. The professor asked why. "Because Socrates doesn't have feathers."

Simplicity of mind remote from errors of learning.

Saturday, November 16, 2019

Notes on John 3:13-21

This passage consists of the author's commentary following the story of Nicodemus. (I have given here and here my reasons for holding the somewhat unconventional opinion that the conversation with Nicodemus ends with v. 12.)

[13] And no man hath ascended up to heaven, but he that came down from heaven, even the Son of man which is in heaven.
I believe this is the only direct reference in this Gospel to Jesus' ascension to heaven after his resurrection. The author asserts that, to date, only Jesus had thus ascended, despite such obvious counterexamples as Enoch, who "walked with God: and he was not; for God took him" (Genesis 5:24); and Elijah, who "went up in a whirlwind into heaven . . . and [was seen] no more" (2 Kings 2:11-12). One is reminded of the same author's insistence elsewhere that, despite what is written of Moses and others, "no man hath seen God at any time" (John 1:18).

If the exclusion of Elijah from the ranks of those who have ascended to heaven is puzzling, equally puzzling is the assertion that no one since Jesus has ascended to heaven, either. The Gospel was apparently written several decades after the resurrection, in which time we might expect that at least a few of the faithful followers of Jesus would have died and, as beneficiaries of the gift Jesus brought, ascended to heaven. Whatever happened to "where I am, there ye may be also" (John 14:3)?

There is, in short, no hint of salvation in this verse. The only man who ever made it to heaven was Jesus -- and that was because he had originally come from heaven in the first place. No one, at the time the Gospel was written, had ever actually graduated, as it were, from the earthly to the heavenly life.


Before any of these problems can be meaningfully addressed, we must establish what is meant by "heaven." The original Greek is unhelpfully vague -- οὐρανός covers the same semantic ground as English heaven and sky put together, and can mean anything from the atmosphere to the sidereal realm to the home of God an the angels.

The Fourth Gospel gives no details of Jesus' ascent into heaven, but the other Gospels make it clear that it involved physically leaving earth -- and I emphasize physically because Jesus was in a resurrected, flesh-and-bone, fish-and-honeycomb-eating body at the time of his ascent. I have elsewhere argued in all seriousness that this means Jesus went to outer space, presumably to an earthlike exoplanet. Wherever he went, it must be a physical place, to refer to which it will be convenient to adopt the Mormon name Kolob, and which may be thought of as the Christian analogue of Asgard or Olympus, the physical home of the Gods. To Christians who balk at such an unorthodox idea, I simply reiterate the fact that Jesus ascended to "heaven" in a body of flesh and bone.

If we think of Jesus as having ascended specifically to Kolob, it becomes obvious that there is no reason to assume people like Enoch and Elijah went there as well. "The sky" covers an awful lot of ground -- literally everywhere except the surface and interior of this planet -- and we should no more assume that two people who "ascended into heaven" went to the same place than we would assume the same of two people who "went overseas."

(In fact, let's take that "overseas" analogy and run with it. In the Narnia stories, the character equivalent to God is known as the Emperor-Beyond-the-Sea. Supposing one of the characters were to say, "No one knows what the Emperor looks like, because no one has ever been over the sea, except Aslan himself" -- it would be missing the point to object, "No one's been over the sea! What about the voyage of the Dawn Treader?" In context, "over the sea" clearly has a more specific meaning than the words themselves would suggest.)

Where did Enoch and Elijah go? Who knows? Elijah was carried away in a cyclone like Dorothy Gale and could have ended up anywhere, including somewhere else on Earth, for all we know. As for Enoch, who "was not, for God took him," it almost sounds as if he achieved Nirvana and was absorbed into God, losing his individual identity.


As for the implication that no one since Jesus had ever ascended to heaven, either, there are many possible ways to interpret this. Perhaps the meaning is simply that no one else has been to heaven and returned to tell the tale, so that Jesus is still our only reliable source of information about that place. People who passed Dante on the street used to whisper to each other, "Look, there's the man who's been to hell!" Of course it is no special distinction to have gone to hell -- but to have been there, implying a return, is another story entirely.

Or perhaps what is meant is that no one but Jesus has ever ascended to heaven on his own steam, though many (perhaps including Enoch and Elijah) have been taken there.

Or perhaps it means just what it says: That at the time the Gospel was written, not one single soul had yet successfully followed Jesus. "Narrow is the way," after all, "and few there be that find it." This is a radical interpretation with uncomfortable implications, though, since many people universally considered to be saints had already died by that time -- John the Baptist, for example, and James the son of Zebedee. Simon Peter, too, had at least died by the time the Gospel's epilogue (Chapter 21) was added, though it's possible that he was still alive when the Gospel itself was written. In the end, I don't think this interpretation is acceptable, because it undercuts what is supposed to be a message of hope. If even John the Baptist has not made it to heaven, what chance do we have?


The reference to "he that came down from heaven" invites the question later raised by "the Jews" in John 6:42: "Is not this Jesus, the son of Joseph, whose father and mother we know? how is it then that he saith, I came down from heaven?" Well, how is it that both he and the Gospel writer say that? Remember that there is nothing in the Fourth Gospel to suggest that there was anything unusual about Jesus' birth or that he was anything other than the biological son of Joseph. (Matthew provides one miracle-filled nativity story; and Luke, another, entirely different, one -- but I assume, from the near-complete lack of overlap between the two nativity stories, and from the absence of any such material in Mark and John, that these stories are pious fictions. It also seems unlikely that Jesus would have embraced the title "Son of Man" if he were in fact the only man since Adam not to be the son of a man!)

Of course, even if Jesus' physical body was a product of ordinary mammalian reproduction, his spirit still came down from the "heaven" where it had been before he was born -- but the same is true of all men; all of us come trailing clouds of glory from God, who is our home. (Such an explanation would be acceptable only to a creationist -- meaning, in this case, not an evolution skeptic but someone who believes that a new human soul is created from nothing each time a baby is conceived, Jesus being the one exception.)

Looking for some unique sense in which Jesus "came down from heaven," I can find only the report of John the Baptist: "I saw the Spirit descending from heaven like a dove, and it abode upon him. . . . And I saw, and bare record that this is the Son of God" (John 1:32, 34). The Spirit of God had descended from heaven and remained upon Jesus. That is the aspect of him which came down from heaven. It was at his baptism, not his birth, that he became the Son of God. (So we infer from the other Gospels, at any rate; the Fourth Gospel never says directly that it was on the occasion of Jesus' baptism that the dove descended.)

[14] And as Moses lifted up the serpent in the wilderness, even so must the Son of man be lifted up: [15] That whosoever believeth in him should not perish, but have eternal life.
I would assume that most Bible readers, thinking (incorrectly) these are the words of Jesus spoken to Nicodemus, would see this as referring to the crucifixion -- in which Jesus, like the brazen serpent of Numbers, was fixed to a pole and lifted up. Jesus is saying that he must be crucified in order to save those who believe in him.

While I'm sure the author did intend to allude to the cross when he chose this particular simile, the "lifting up" of the Son of Man cannot refer primarily to the crucifixion -- or the resurrection, or the ascension -- since the author is writing in his own voice after all of these things have already taken place and yet describes the lifting up of the Son of Man as something that remains to be done.

I would guess that it probably means spreading the word about Jesus, lifting him up as a prophet lifts up his prophetic "burden," raising the cross -- as a religious symbol, not an instrument of torture -- as an ensign to the nations.

In the Moses story alluded to (Numbers 21:6-9), the Israelites were attacked by venomous snakes called seraphim (singular saraph, the same word used by Isaiah with reference to certain heavenly beings; see here for details) -- supposedly sent by the Lord as a punishment for complaining about their hardships in the desert. After many had died of snakebite, those who remained were duly penitent and asked Moses to pray on their behalf that the seraphim be taken away. Instead of taking the snakes away, the Lord instructed Moses to make a saraph of brass (or bronze, or copper; Hebrew makes no distinction) and display it on a pole. Snakebite victims who looked at this brazen serpent would live.

To the story as recorded in the Torah, the Book of Mormon prophet Nephi adds that many refused to look and be healed "because of the simpleness of the way, or the easiness of it" (1 Nephi 17:41). A later Nephite prophet, Alma, repeats the same tradition: "But there were many who were so hardened that they would not look, therefore they perished. Now the reason they would not look is because they did not believe that it would heal them" (Alma 33:20). He draws from the story the moral, "do not let us be slothful because of the easiness of the way" (Alma 37:46). One is reminded of the story of Naaman in 2 Kings 5 ("If the prophet had bid thee do some great thing, wouldest thou not have done it?"). Of course it is difficult to know whether this angle on the story represents an invention of Joseph Smith's, a midrash particular to the Nephite culture, or an authentic Old World tradition of which the author of the Gospel would have been aware.

Regardless of the provenance of the Nephite version of the story, "the easiness of the way" is certainly a prominent feature even of the biblical version, and may be part of the reason the simile was chosen. In both cases, what the victim has to do to be saved is minimal: just look, just believe.

Just as the lamb to which Jesus is compared in John 1 is not a sin-offering to secure forgiveness but rather a Paschal offering to avert death (details here), it is likewise from death that the brazen serpent saved people. The Son of Man is presented as offering the same thing: not absolution, but eternal life. Jesus is first and foremost the bringer of resurrection.

If the reference is indeed to resurrection, though, the "not perish" bit needs some explanation. (While it's true that most Greek manuscripts don't actually include "not perish but" in v. 15, that doesn't really make any difference, since the phrase is incontestably there in v. 16.) Resurrection, after all, does not mean not dying, but rather returning to life after dying. Die and perish are basically synonyms in English, but apparently the Greek word which appears in these verses (and which is distinct from the usual word for "die") denotes absolute and permanent destruction. Someone who may yet rise from the grave, then, has died but cannot be said to have perished.

[16] For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life.
The most famous verse in the Bible -- and as such, perhaps, so familiar that the strangeness of what it asserts often goes unnoticed. One would naturally expect that the gift of eternal life would either (a) be given freely to everyone who wants it or (b) be given only to those deemed worthy of it, to "good people." Instead, we are told that those who believe in the Son will have everlasting life, while (by implication) those who do not believe in him will perish. I have commented before on the Fourth Gospel's puzzling insistence on belief as such -- for example, "This is the work of God, that ye believe on him whom he hath sent" (John 6:29).

Of course every teacher wants to be believed, but this generally means assenting to some particular doctrine. The Buddha, for example, wanted people to accept the validity of the Four Noble Truths and Eightfold Path -- specific propositions to assent to, a specific way of life to adopt. Prior to becoming enlightened themselves, people would have to accept these teachings on authority, because they trusted the Buddha as a person -- but that personal trust had only instrumental value; the real point was never the Buddha himself but rather the impersonal dharma which he taught.

In Jesus, these priorities seem to be reversed. The main thing Jesus taught was that people must believe in Jesus; whatever other moral or factual doctrines he may have touched on were strictly by-the-by. The "requisite" belief, then, is clearly personal trust rather than assent to any particular set of propositions. Creeds are -- or should be, anyway -- foreign to the community of Jesus' followers. This distinction is, I believe, reinforced by the frequent reference in the Fourth Gospel to believing on Jesus' name -- meaning Jesus as a person, as opposed to any doctrine of "Jesuism" he may be thought to have propounded.

In approaching the question of why this personal trust should be accorded such importance, I have found Bruce Charlton's post "The Good Shepherd" to be invaluable. It should be read in full, but I quote the essential parts below.
The Good Shepherd leads his sheep through death to Heaven. [. . .] What is led? The soul, after death. But why does it need to be led - why can't it find its own way to salvation? Because after death the soul becomes 'helpless', lacks agency - like a young child, a ghost, a sheep.
If unable to help itself, how then can the soul follow Jesus? Because - like a young child, or sheep - the dead soul still can recognise and love; and 'follow'.
Where does this happen? In the 'underworld'. Without Jesus, the disembodied, ghostly, demented dead souls wander like lost sheep - as described in pre-Christian accounts such as Hades of the Greeks, or Sheol of the Ancient Hebrews. 
But how does Jesus save the dead souls? Everybody has known Jesus as spirits in the premortal world, so everybody can recognise him in the underworld; but only those who love Jesus will want to follow him.
I find this interpretation compelling. A spirit which has integrated itself with a physical body (and in particular, with a brain) and is then ripped away from that body at death, is left maimed and demented. Both pre-Christian tradition and modern experience with "ghosts" confirm that shades in the underworld are severely cognitively impaired. The good news is that this damage may be undone in the resurrection, but first each shade, while still disembodied and demented, must hear and follow the Shepherd. Intellect, while of the utmost value in itself ("the glory of God is intelligence, or in other words, light and truth"), will not save us, simply because we won't have much of it at the moment when salvation is needed. Hence the emphasis on childlike faith -- not because God wants us to be (merely) childlike, but because we will in fact be reduced to a childlike state in Hades and yet still must have the wherewithal to follow Jesus to salvation. Simple love and simple trust, such as a child or a sheep is capable of, becomes all-important.

[17] For God sent not his Son into the world to condemn the world; but that the world through him might be saved.
While it can mean "condemn" in the right context, the basic meaning of the Greek verb here is "judge" -- or, most properly, to separate or make distinctions. This reinforces v. 16's statement that Jesus is willing to save "whosoever believeth in him," without making any attempt to separate humanity into those who are worthy of salvation and those who are not. He will conduct anyone out of the prison-house of Hades -- but of course, to get out you have to trust him enough to follow him when he opens the gate and says, "Come on, let's go."

Elsewhere in the Gospel, Jesus does refer to himself as playing the role of a judge, and those passages will be dealt with in due course, but at least as far as the resurrection is concerned, Jesus offers salvation to all without judgment.

[18] He that believeth on him is not condemned: but he that believeth not is condemned already, because he hath not believed in the name of the only begotten Son of God.
At first this reads like a contradiction of the preceding verse: Jesus didn't come to judge or condemn the world -- but people who don't believe in him are condemned! I think the key here is the phrase "condemned already." Jesus offers salvation from death freely, without judging or condemning -- but of course if you don't trust him enough to follow him, there's not much he can do; a judgment has already been made. (I should emphasize again that "follow him" here does not mean to be his disciple or to live by his teachings, but rather something closer to the literal meaning of those words.)

So, really, no one is being judged and condemned as unworthy to receive resurrection -- but still, not everyone will be resurrected, and it strikes us as "unfair" that this should be for anything other than moral reasons. Therefore, the evangelist goes on to make the case that failure to trust and follow Jesus is indicative of moral failings.

[19] And this is the condemnation, that light is come into the world, and men loved darkness rather than light, because their deeds were evil. [20] For every one that doeth evil hateth the light, neither cometh to the light, lest his deeds should be reproved. [21] But he that doeth truth cometh to the light, that his deeds may be made manifest, that they are wrought in God.
Truth as something one can do is a peculiarly Johannine turn of phrase, appearing also in the First Epistle: "If we say that we have fellowship with [God], and walk in darkness, we lie, and do not the truth" (1 John 1:6). The context is similar, too: Those who "do the truth" are drawn to the light; those who do not, prefer to walk in darkness. What is feared, I think, is not so much public exposure before others as simply being seen as one is -- by God and, worse, by oneself. Jesus brought clarity and consciousness, and is thus feared and hated by those who are in denial about themselves, who would not care to have too bright a light shined on them for fear of what they might discover. "I heard thy voice in the garden, and I was afraid, because I was naked; and I hid myself."

This is clearly meant as an explanation of why some have "not believed in the name of the only begotten Son of God" -- but notice the absence of any language relating to belief in the sense of having opinions or assenting to propositions. Instead, it is made a question of love and hate, attraction and aversion. This confirms what I have said above, that "believing on his name" has nothing to do with creeds and everything to do with personal trust, love, and willingness to follow.

If reptilian aliens are real . . .

I clicked for a random /x/ thread and got this one , from June 30, 2021. The original post just says "What would you do if they're ...