Showing posts with label Time. Show all posts
Showing posts with label Time. Show all posts

Wednesday, March 22, 2023

Sync: Ne(m)o and Morpheus

Today an obscure song from 30 years ago, one I haven't listened to or thought of in ages, came to mind. In order to establish that its coming to mind had nothing to do with my recent posts about The Matrix, I will have to describe my train of thought in some detail.

First of all, few days ago, I happened to be looking through my old sync log from 2016-17. One of the notes I read was this one:

2016 Mar 3 (Thu) – I read a few pages (pp. 87-89) of Ray Bradbury’s Dandelion Wine in [a cafe called] FM Station. They were playing the Lukas Graham song “7 Years,” which I had never heard before. It begins:

Once I was seven years old, my mama told me
Go make yourself some friends or you'll be lonely.
Once I was seven years old.

It then goes through various other ages: once I was 11, 20; soon I’ll be 30, 60. It ends by repeating the opening lines quoted above.

While listening to this, I was reading pp. 88-87 [sic] of Dandelion Wine. The children are discussing how Colonel Freeleigh is a “Time Machine” because he can remember so many of his past experiences.

‘Maybe old people were never children, like we claim with Mrs. Bentley, but, big or little, some of them were standing around at Appomattox the summer of 1865.’

Tom and Doug discuss what Doug calls “far-traveling” – meaning going back in time through memory.

“Far-traveling. You make that up?”

“Maybe yes and maybe no.”

“Far-traveling,” whispered Tom.

“Only one thing I’m sure of,” said Douglas, closing his eyes. “It sure sounds lonely.”

Thus the chapter ends.

A bit earlier in the book, on pp. 72-73, old Mrs. Bentley insists that she was once a little girl, but the children refuse to believe it. She shows them a photo to prove that she was 7 years old once.

In triumph she flashed her trump card, a postal picture of herself when she was seven years old…

“Who’s this little girl?” asked Jane.

“It’s me!”

The two girls held onto it.

“But it doesn’t look like you,” said Jane simply. “Anybody could get a picture like this, somewhere.”

They looked at her for a long moment.

“Any more pictures, Mrs. Bentley?” asked Alice. “Of you, later? You got a picture of you at fifteen, and one at twenty, and one at forty and fifty?”

The girls chortled.

“I don’t have to show you anything!” said Mrs. Bentley.

“Then we don’t have to believe you,” replied Jane.

“But this picture proves I was young!”

“That’s some other little girl, like us. You borrowed it.”

Like the song, this focuses on the fact that one was younger in the past – with a specific focus on “seven years old.” Both also emphasize loneliness.

That was several days ago. Today I was doing some mindless paperwork and humming to myself and discovered that what I was humming was the 1967 Monkees song "Look Out (Here Comes Tomorrow)," with the repeated line, "Oh, how I wish tomorrow would never come." It occurred to me that this was similar to Bob Dylan's line "The present now will later be past," in that both highlighted the need for a Dunnean model in order to make sense of the passage of time. If there is only one dimension of time, then the past never was -- and the future never will be -- the present. Tomorrow will never come, and Mrs. Bentley never was seven years old.

This made me think of the sync notes quoted above, and I tried to remember the term the children in Dandelion Wine had used for revisiting the past through memory -- "long-journeying"? I see now that it was actually "far-traveling," but "long-journeying" is what came to mind and what made me think of the 1993 Moxy Früvous song "Morphée," which begins with the words "Longue journée." It's all in French, a language of which I am relatively ignorant, and I never was very clear on most of the lyrics. I tried to sing it to myself but had to lapse into humming and dum-de-dumming for most of it. All I could remember was "Longue journée . . . chez Morphée . . . ce doux piège . . . et je fuis, je fuis . . . je rêne
Nemo en exil sur mes rêves fragiles" -- which I figured meant "Long journey . . . at Morpheus's place . . . something-something . . . and I went, I went . . . I reign, Nemo in exile, over my fragile dreams." Translating je fuis as "I went" was just a guess (wrong, it turns out), based on Spanish, and I hadn't the slightest idea what ce doux piège might mean, though it was one of the lines I remembered most clearly.

Then I thought: Morpheus! Nemo! I've just been posting about Morpheus and Neo -- and "Morphée" was released six years before The Matrix. Morpheus is the god of dreams, of course, but why "Nemo"? Is it a reference to those trippy old Little Nemo in Slumberland comics?


Sure enough, the very first panel of the very first Little Nemo strip (1905) mentions "His Majesty, Morpheus of Slumberland."


And what does ce doux piège mean? It turns out it means "this sweet trap." Here's the French Wikipedia article on the Venus flytrap:


Here are the complete lyrics of "Morphée":

Longue journée
Qui s'achève dans une chambre foncée
J'entends au loin les sirènes
Qui comme une vague me tirent, m'amènent
Chez Morphée
Émerveillé
Ce doux piège
Ou les gammes en délire s'arpègent
M'emportent si loin des villes
Et je fuis,
je fuis les escadrilles du privilège
Beau sortilège
On solde les vieux pays au marché des gorilles
Caché dans les bras de Morphée je rêne
Nemo en exil
Sur mes rêves fragiles

And here, since no real translation seems to be available and I can't be bothered to do it myself (at least not now; I probably will do later), is the Google Translate version:

Long day
That ends in a dark room
I hear the sirens in the distance
Which like a wave pulls me, brings me
To Morpheus
Amazed
This sweet trap
Where delirious scales arpeggio
Take me so far from the cities
And I run away
I flee the squadrons of privilege
beautiful spell
We sell the old countries at the gorilla market (???)
Hidden in the arms of Morpheus I reign
Nemo in exile
On my fragile dreams

That's "scales" as in do-re-mi, incidentally.

Tuesday, February 21, 2023

Tintin T. rex, Timey-wimey T. rex, . . . collect them all!

Belgian comic-book character Tintin is called 丁丁 in Chinese.


Tin is not a possible syllable in Chinese, and Ting sounds like a girl's name, so the best they could do was Ding-ding. You know, like a bell. A tin bell. Like a tinker would make.

The character 丁 is the fourth Celestial Stem, and as such is used to translate the letter D when used in an ordinal sense -- that is, when A, B, C, and D are used in the sense of "one, two, three, four," as in an outline or on a multiple-choice test. For example, Serie D football is rendered 丁級 in Chinese. So if you wanted to go Backstroke of the West on poor Tintin and translate his Chinese translation back into English, he'd be called DD.

The largest pharmacy in my town is named after Tintin.


Notice how the sign has a T followed by the Rx pharmacy symbol: T. rex. I'm not sure what the T is there for, unless it stands for Tintin. (Years ago, this pharmacy had the English name Tintin on its sign in addition to the Chinese, but it was taken off a long time ago.) Note that we've already connected the T. rex with the Tin Lizzie (Zeus lizard).


Comments are not searchable, so I haven't had the patience to track them down, but some time ago there was a comment by Bruce Charlton on this blog which dismissed unusual conceptions of time with a phrase like wibbledy-wobbledy timey-wimey stuff. Something like that; I'm sure timey-wimey was in there. I believe it's the standard term in Britbongistan.


More recently, WanderingGondola left a comment that also referred to timey-wimey stuff. I think it was about a 4chan comment that had been posted earlier than the post it was replying to, "implying that some timey-wimey stuff is going on." Either she was humorously referencing Bruce's earlier comment, or else Australian English is much more British than I've been led to believe!

(If any of my indefatigable readers can track down either of the timey-wimey comments, do post the link in the comments.)

Today, I spotted this at my school:


That's a T. rex-like dinosaur paired with the word little, so it counts as a mini T. rex. (It's a weird picture, too. Is that a floating bowling ball? And why is it raining Christmas trees?) As for the other word, it looks a bit timey-wimey, doesn't it, old chap?


Possibly relevant: the uail, the wolcano, and the other bric-a-brac of the Right.


Update: My readers have informed me that timey-wimey is a Dr. Who reference, which explains my ignorance. I never did much like medical dramas.

Sunday, February 12, 2023

DD, hourglass, lemniscate, gate, time

Found this on /x/ today. It looks like a slide from a PowerPoint presentation, but only one slide was posted: the one numbered 8.


We've connected the hourglass with the lemniscate or figure-eight, and the lemniscate with two letter Ds. Here we have an hourglass in the shape of two letter Ds, and a figure-eight next to it. The lemniscate has been connected with the door as a portal to another time. Here we see how the neck of the hourglass functions as a gate or door, and passing through that gate are tiny clocks, each apparently representing one Planck time.

An hourglass resembles a figure-eight, but the lemniscate of infinity is a lazy eight. If you turned an hourglass on its side, wouldn't that represent stopping the flow of time?

Notice also the geometric relationship between the DD-hourglass and 101.


The /x/ post has the subject line "Quantum Spacetime is the Holy Grail," and the text of the post is as follows:

The Grail isn't anything you might have heard it is except for perhaps the generative principle of nature itself. We are all within the grail. This is how God comes to know us. We are like fish in a great ocean, bound to our school. When the question is asked the realm is restored.

The first reply (not clear if it's the OP or someone else) adds:

Time is the chalice that holds within it Space.
Space is the great wine dark Ocean of Life
Space is Fortified by Life.
Drink well and be drunken of! This is the final commandment!

Time as a grail or chalice fits with my thoughts on the Temperance card as (among other things) a symbol of the passage of time.

"Drink well and be drunken of," in connection with "quantum spacetime," brings to mind these lines from The Hitchhiker's Guide to the Galaxy.

"You’d better be prepared for the jump into hyperspace. It’s unpleasantly like being drunk."

"What’s so unpleasant about being drunk?"

"You ask a glass of water."

"Drink well and be drunken of! This is the final commandment!" -- this sounds so exactly like Aleister Crowley that I was certain it was him and tried to search out which of his books it came from. But apparently it's not the Beast himself at all, just a pitch-perfect pastiche by this anon.

Note added: I found the source of the image in the /x/ post. It's from page 88 of a Scientific American magazine.

Wednesday, August 31, 2022

Review of Jonathan W. Tooker's Time Travel Interpretation of the Bible

I recently read Jonathan W. Tooker's 2001 book The Time Travel Interpretation of the Bible, which is available as a free pdf at the link. I do not in the end find it at all convincing, but it certainly was a stimulating thought experiment.

God as the time traveler with the last word

Tooker begins with the assumption that at some time in the future time-travel technology will be developed, at which point a variety of people with a variety of motives will go back into the past to attempt to rewrite history, with changes undoing and overwriting other changes again and again indefinitely. Therefore,

The real course of immutable history which we all share, then, must be the limit of an infinite number of changes. The history that we all share is the final word once all the time travel work has been done. Since there will always have been a finite number of human generations following the construction of the first time machine, and since the men of each generation will work only a finite number of shifts [as time travelers] during their lives, humans will never be able to write the last of an infinite number of changes. If the last word cannot be had by any mortal, then it must be had by some supernatural entity. . . . Here, we seat God on the throne of his eternal glory at timelike infinity [in Minkowski space], the end of time, a place that no mortal can ever reach.

It is not spelled out why no time-traveling mortal can ever reach timelike infinity, especially since time travel is generally conceptualized as "teleporting" from one time to another without any need to pass through the interval (finite or infinite) between them. Anyway, it is assumed that no one can. But them, confusingly, Tooker goes on to posit that the God of Abraham is actually a flesh-and-blood man from the future, possibly even the inventor of the first time machine. How then did he reach timelike infinity, which ex hypothesi no man can do? Tooker attempts to deal with this by invoking his version of the Trinity:

In the preceding sections, we have made the point to put God in the seat at timelike infinity but now we will seat the Holy Spirit there to assign God as a human man. Jesus is God as a younger man before he completes the mission of the Messiah. God is Jesus as an older man after the harvest has come and he has affected the final defeat of Satan . . . .

Note that this does not mean that the man born as Jesus grew up to be God. Rather, God is assumed to be born in the post-Einsteinian future (since he must have access to a time machine), and Jesus is one of this future man's relatively early ("as a younger man") ventures back into the past. Jesus as such is assumed not to have been born at all (as hinted at in some of the Gospels; like me, Tooker gives priority to the Fourth Gospel, but does so because it says nothing about the birth of Jesus).

Among all the changes enacted by all the [time-traveling] agents, after all the generations of mankind have come and gone, whose intention for what history ought to have been will dominate at infinity? We propose that the intentions of the man God are those which survive until the end. For this reason, the Holy Spirit is called by God's name. When all was said and done, it was his intention which survived to infinity. As the winner of the time travel war, God is the greatest and winningest warrior of all time. This is the nature of the trinity: God as a younger man fighting for victory, God himself having attained absolute dominion, and God's intention: three parts of a whole.

As best I can make out, this means that God is not enthroned at timelike infinity, and that the "Holy Spirit" that is said to be enthroned there is only a figure of speech -- not an explanation of why God has the last word in the editing of the past, but a metaphorical way of expressing the fact that he does have the last word.

Why, then, does God have the last word? This is a rather important question since, in Tooker's model, having the last word is what makes God God. The answer seems to be simply that God is good, that evil inherently leads to destruction, and that therefore only God's intention leads to eternal life.

If there comes a day when the last human dies, then life will not have been eternal. . . . Beyond that day, there would never again be someone using a time machine. Some human would have had the last word about what history was. There would be no future generations through which God's intention might propagate all the way to infinity. To the contrary, if extinction never comes, then the limit at infinity which we have associated with the Spirit of God is generated . . . . The Sovereign Lord is separated from false gods [i.e., rival human time travelers] because the timeline passing through God's ultimate victory in his Messianic mission is the only timeline that does not lead to extinction. . . . The road that leads to death is broad but the road that leads to life is narrow. All futures apart from God are doomed.

No real metaphysical reason is given for this. God is just some guy, and his way just happens to be the only way to "eternal life" -- meaning, apparently, the temporally infinite continuation of the human species and time-travel technology, not personal immortality. (Personal immortality apparently consists in being taken out of the time stream altogether, into the "elsewhere" regions of Minkowski space.) I don't know why we would assume there would be exactly one way to attain this; many ways or no way seems more likely. Actually, I'm not  clear on how "a day when the last human dies" could even be an issue in a world with time travel, since pre-extinction human could travel into the post-extinction future and restart the species. Nor do I know why we need to assume that our species does in fact survive indefinitely, approaching a limit at timelike infinity, rather than some human having the last word. None of this is clear to me, and I don't think the problem is entirely my own.

Anyway, this is the model you have to entertain in order to proceed with the rest of Tooker's thesis.

The water/earth/heaven metaphor, and miracles

Tooker proposes that in the Bible, "water" is often used as a metaphor for the past; "earth," for the present; and "heaven," for the future -- with God being the "Most High" because he (or, rather his intentions, reified as the Holy Spirit) is located in the "highest heaven," which is timelike infinity. When Satan is cast down from heaven to earth, for instance, this is taken to mean that his time-travel privileges are revoked and he is confined to his own "present." (Satan, too, is a time-traveling mortal man, as we shall see below.)

Tooker is generally reluctant to countenance any sort of "magic" or miracles beyond those that involve manipulating time through a technology to be developed in the future. Events such as the Flood of Noah and the parting of the Red Sea are reconceptualized on the assumption that "water" and "dry land" are references to the time stream. Since it is obviously impossible for the whole earth to be submerged under physical water, the Flood is understood to be God undoing his creation by going back in time and altering the past that led to it, and the ark is some sort of temporal "bubble" (whatever that would be) which is unaffected by this. It is within this framework that Tooker understands God's promise after the Flood:

I will not again . . . smite any more every thing living, as I have done. While the earth remaineth, seedtime and harvest, and cold and heat, and summer and winter, and day and night shall not cease (Gen. 8:21-22).

As Tooker points out, a flood of water has nothing to do with the progression of summer and winter, day and night -- but meddling with the fabric of spacetime does. God is promising never again to play fast and loose with the timeline to the extent that he did in this metaphorical "flood."

Smaller scale temporal editing is still permitted, though, and the passage through the Red Sea on "dry ground" (another temporal bubble) is understood in this way. God's "jamming" the Egyptians' chariot wheels (as many translations give Ex. 14:25) is also understood to be a temporal effect.

Although no water metaphor is used, the extension of Hezekiah's life (Isa. 38) is understood as a small-scale manipulation of time. Time is rewound a bit, which is why the shadow on the sundial goes back 10 degrees, so that Hezekiah can be placed on a timeline in which he lives 15 years longer than he would otherwise have done. Apparently a minor adjustment like this is not considered to be a violation of the promise to Noah since it is not enough to disrupt the cycle of day and night or the seasons.

Israel as Satan

I have noted before some of the similarities between the biblical figure Jacob, a.k.a. Israel, and the serpent of Eden. Jacob means "he seizes the heel," a name he was given because "he took his brother by the heel in the womb" (Hos. 12:3). To the serpent, God says, "Thou shalt bruise his heel” (Gen. 3:15). The serpent deceives Adam, and Jacob deceives Edom (basically the same name in Hebrew). Jacob is even described as being physically serpent-like -- a smooth-skinned man in contrast to his hairy brother -- and the account of his life in Genesis is just one deception after another. Even the name God gives him, Israel, means "he contends with God."

Why, then is Israel God's chosen? Tooker makes the rather shocking proposal that Israel is literally Satan. Satan, like God, is a time-traveling human being, and the specific human being he is, is Jacob the son of Isaac. But Israel and his descendants are nevertheless "chosen" for special protection because they are the ancestors of the man God himself, and he cannot therefore destroy them without destroying both himself and the one true timeline that leads humanity all the way to timelike infinity. Although a large part of the Bible consists of diatribes against the wicked Israelites, God is forced to continue protecting and helping them. This is the meaning of the parable of the wheat and the tares (Matt. 13): the tares (Israelites) cannot be destroyed yet without destroying the wheat (future Messiah, who becomes "God") with them. Once the Messiah has been born, though, the long-awaited time for burning up the tares will have arrived. Yes, I realize that this is, like, super anti-Semitic.

According to Tooker, Israel is explicitly identified as Satan in the Bible, but you'll only pick up on it if you compare two different verses. We are told that "Satan stood up against Israel, and provoked David to number Israel" (2 Chron 21:1). But we are also told, "And again the anger of the Lord was kindled against Israel, and he moved David against them to say, Go, number Israel and Judah" (2 Sam. 24:1). Tooker maintains that the "he" in 2 Samuel cannot refer to the Lord, since 2 Chronicles says Satan moved David to number Israel, and that therefore the only possible antecedent is "Israel." Tooker's reading is, "And the anger of the Lord was kindled against Israel [the person, Jacob], and he [Israel/Jacob] moved David against them [Israel, the nation]."  Compare that with Chronicles, and you find that Israel must Satan, because that's who moved David to number the people. I think it's a ridiculous reading, which relies on the same noun being the antecedent of both "he" and "them," but that's all he's got.

Surprisingly, despite saying he prioritizes the Gospel of John, and despite his belief that "children of Israel" is literally synonymous with "children of Satan," Tooker does not mention the episode in John 8 where Jesus calls the Jews children of the devil while at the same time conceding that they are also children of Abraham. Those who do not interpret the whole thing metaphorically tend to arrive at some version of the Fake Jew Thesis -- that the "Jews" of Jesus' time were not really Israelites at all but Edomite conversos or some such. Tooker's interpretation would be that they were children of the devil precisely because they were Israelites -- and that Jesus himself was just as much a (genealogical if not spiritual) child of the devil as they were. Both Jesus and the Pharisees were descendants both of the righteous Abraham and of Satan himself, though they varied as to which of these ancestors they took after.

All Jews are children of Satan. Jesus was a Jew. Jesus is God. It's not often that you find one person asserting all three of those things! It's hard to reconcile with the wheat and tares model -- where once the Living God has been born, all the "tares" (Israelites) will be destroyed -- all the other tares, I should say -- because it seems that in Tooker's understanding God himself is not really wheat (the product of a different seed) but rather one of the tares, one that happened to turn out good, atavistically taking after Abraham more than Jacob. If the fruit of the family tree of Israel is God himself, on what grounds can we call it a bad tree that must at some later date be hewn down and cast into the fire? "Either make the tree good, and his fruit good; or else make the tree corrupt, and his fruit corrupt: for the tree is known by his fruit" (Matt. 12:33).

Coming back to the man Jacob himself, how did someone born in the Bronze Age, long before time travel technology, end up becoming the time-traveling devil? Tooker suggests that the incident of Jacob's Ladder refers to a chance encounter with time travelers and their technology (angels are generally seen as time-traveling agents from the future), and that Jacob thus got access to this technology and decided to use it to rewrite history so that he, not God, would be the last man standing at timelike infinity (not understanding that this was impossible because, well, reasons). Satan is supposed to have made many attempts to kill God or God's ancestors (the "false gods," Satan-affiliated time travelers, demanded child sacrifice because they wanted to eliminate certain bloodlines), and the crucifixion of Jesus is one such attempt that succeeded -- at least until it was undone by more time-travel shenanigans, resulting in the Resurrection.

The command to sacrifice Isaac is presented as a similar attempt by God himself, to erase the devil from history by having his father killed. When God realizes (remember he is just a man from the future, not omniscient) that he would be grandfather-paradoxing himself, he sends another agent back to the past to stop Abraham from going through with it. 

Jacob's wresting match with God is interpreted as another aborted attempt to stop Jacob from becoming Satan. The "wrestling" is assumed not to have been literal grappling but a "time fight," a struggle for mastery over the timeline. In the end, God perceives that despite everything, allowing Jacob to proceed is preferable to the alternative, and he lets him win.

Ultimately, though, God and his agent Michael win the "war in heaven" (that is, in the future), and Satan is cast down to "earth" (that is, to his own time in the Bronze Age, no more to wander through the spacetime manifold for the ruin of souls).

Oh, and you need to keep the Law of Moses

We have seen that in Tooker's model, God is just some dude from the future and is not Good in any transcendent sense. (He rejects "God is love" as a "dehumanizing proverb," preferring Moses' definition: "The Lord is a man of war; the Lord is his name.") God's way is the right way for essentially Darwinian reasons -- because, as it happens, it is the only way that takes the inclusive fitness of the human species all the way to timelike infinity. And Satan is not an imp on your shoulder egging you on to succumb to vice; he's a dude from the past trying to kill the dude from the future. Whether you yourself are sinful or virtuous, whether you inwardly align yourself with God or the devil, doesn't ultimately seem to make much difference in this war, the outcome of which has already been determined by the ineluctable fate that decrees that straight is the way that leadeth to life.

With that as the metaphysical background, it is odd to find that Tooker's book ends with a little diatribe against "Paulism," and particularly against Paul's teaching that the Law of Moses has been superseded. Pork remains absolutely forbidden, Tooker insists, and circumcision absolutely required -- for what exactly? Because, as the butterfly effect would have it, some critical mass of humans must do those things or else the species is doomed to extinction? But we know that future history has already been written -- and rewritten for the final time -- and that the species does not go extinct. As for personal immortality and the afterlife, Tooker barely mentions it, contenting himself with a passing reference to the possibility of "going to heaven" by being shunted off the timeline into the Minkowskian "elsewhere," and leaving us to guess whether or not going there has anything to do with not eating pork.

The whole "Paul is bad because we have to keep the Law of Moses" thing almost seems like a separate theological hobby-horse, left over from before the Time Travel Interpretation had been formulated, and included here as a sort of palimpsestic holdover.

Assessment

Tooker's thesis is undeniably fun to entertain. It's fascinating to revisit all the familiar Bible stories from this entirely different perspective and see how everything might be reinterpreted in its light. In the end, though, it fails in some very important ways. Here, aside from the specific problems detailed above, are its main flaws.

First, though perhaps not foremost, it bases everything on "time travel" without coming up with any rigorous theory of the same. The idea of time travel cannot even be coherently formulated as a hypothesis in the four-dimensional world of Einstein and Minkowski, and naive attempts to do so -- the H. G. Wells style thinking that if time is just another dimension, we should in theory be able to travel in it -- are ill-conceived. To travel from Point A to Point B means to be at Point A at one point in time and at Point B at some later point in time. For example, if I was in Chicago Heights at 2:00 and Buffalo Grove at 3:00, I traveled from Chicago Heights to Buffalo Grove. "Time travel" would mean that Points A and B are not places but times, though -- leading either to tautology ("I was at 2:00 at 2:00 and at 3:00 at 3:00") or to contradiction ("I was at 2:00 at 2:00 and at 12:00 at 3:00"). I don't see any way to think at all clearly about the possibilities of "time travel" except from an explicitly Dunnean standpoint, where dimensions of meta-time are recognized. Wells unconsciously smuggles in Dunnean assumptions.

More importantly, the whole model is too "cosmic," and not personal enough, to really serve as a religion. God and Satan had a time war, and God won -- which is good, because it means the human race will survive to timelike infinity. This has all in some ill-defined sense "already" been done, and that's why all those things in the Bible happened. Fine. Now what? How does this relate to me as an individual and how I should live and what gives my life meaning? If God's ultimate victory is what really matters, then nothing I do really matters, since nothing I can do can affect that. (If it did, God would just go back in time and undo what I had done.) As for my own personal destiny, Tooker barely touches on it, except to mention in passing that it would be technically possible to "go to heaven" in the "elsewhere" regions of Minkowski space. Will God come back and manipulate spacetime to do that for me if he wins in the end? Is that why it matters? "I don't know, just remember to get circumcised and lay off the pork."

Overall, Tooker's "theology" reads like some history lesson (about things in some sense "already done") about how the good guys defeated the bad guys and made the world safe for democracy or something. Yes, very inspiring, three cheers for the flag and all that -- but if that's your answer to the Bible, are you really sure you've understood the question?

Monday, March 14, 2022

The Sempiternal Count recites ALL the digits of pi!

It begins . . .

1. Introduction

For a kids' show, Sesame Street occasionally delved into some pretty deep subject matter. I'm sure you remember the 1983 episode where Big Bird visits the ancient Egyptian afterlife and defies Osiris to secure justice for the damned soul of a 4,000-year-old Egyptian prince.

Damned Prince Sahu, his demon visitant, and the great god Osiris are far from being the only ancient eldritch characters to appear on the show, though. It's a little known fact that the "Count" character is based on a mysterious but very real immortal entity known as the Sempiternal Count. This strange being, as his title denotes, exists within the time-stream like us mortals -- he is not atemporally "eternal" as some suppose God to be eternal -- and yet he has always existed and always will. (Hence his portrayal as a deathless "vampire.") And just as you've seen on Sesame Street, he really does spend the bulk of his time shouting out numbers and laughing.

The Count recently agreed to take some time out of his busy schedule to discuss this unusual pastime of his. Below is a transcript of our interview, lightly edited for clarity and to remove most of the ha-ha-ha-ing.


2. Transcript

SC: Two! Six! Four! One! Ha ha ha . . .

WJT: If I may interrupt, my -- uh, is it "Lord Courtesy"? Forgive me for being a bit unclear on how to address a Count in English. I understand that you -- that Your Lordship -- enjoys a rank corresponding to that of an Earl, isn't that right?

SC: One! One false assumption! Ha ha ha . . . . As you would have realized had you thought about it, one can hardly claim noble birth who never experienced any sort of birth at all. I've always existed, which is why they call me Sempiternal. And do you know why they call me the Count?

WJT: Don't tell me it's really because you love to count things! I'd always assumed that that was --

SC: A gross oversimplification to make an ancient eldritch entity more comprehensible to the Sesame Street audience? Just so. There are only so many things around, you understand, and one has so much time to fill! No, I've hit upon a truly inexhaustible hobby, one that will keep me busy forever, and which is never boring because it is never repetitive. Surely you must have noticed that the numbers you caught me chuckling over when you came in were not in the sequence one normally uses for counting?

WJT: I was going to ask you about that.

SC: Digits of pi! I started back in the year 1742, and I've recited nearly nine billion of them so far.

WJT: Nine billion and counting! Just how many digits of pi do you intend to recite?

SC: All of them. After all, I have all the time in the world.

WJT: All of them? But pi has an infinite number of digits. If you recite them one by one, advancing one finite step at a time, you'll never reach an infinite number, even if you keep at it forever. You'll never reach the end.

SC: Two! Two false assumptions! Ha ha ha . . . . Suppose you told me you were going to recite all the months of the year, and I told you it was impossible because no matter how well you did it, you would never reach "Febtober." What would you say to that?

WJT: I suppose I would say that, since "Febtober" is not one of the months of the year, reciting all of them without ever reaching it is not only possible but to be expected.

SC: Now consider your implication that it is impossible for me to recite all the digits of pi because, no matter how many digits I recite, I will never reach the last one. But there is no "last digit" in pi any more than there is a "Febtober" in the year, so my failure to reach it is no failure at all and is in no way inconsistent with my reciting each and every one of the digits that are in pi.

WJT: Okay, maybe I worded that poorly. What I mean is that you can never recite all the digits of pi, because there are an infinite number of them, and you go through them one by one. No matter how many times you add one (or any other finite quantity), you can never reach infinity.

SC: But I don't have to reach infinity. There is no "infinitieth digit" of pi any more than there is a "last digit." I only have to recite the digits that are in pi. I don't have to reach "Febtober."

WJT: Poor wording again. I don't literally mean an "infinitieth digit." I just mean that because there are infinitely many digits, you can't recite them all.

SC: Because, although I have unlimited time, I have to recite them one by one?

WJT: Right. No process of adding up finite quantities can ever reach --

SC: Reach what? And remember that you can't say "infinity" or "the end." If I recite one digit after another a thousand times, I reach the thousandth digit. If I do it a quintillion times, I reach the quintillionth digit. Which of the digits of pi can I not reach by this process?

WJT: Well, for every digit of pi, it is true that it has a finite ordinality and thus can be reached by the iterative process of reciting consecutive digits. So you can reach each of the digits of pi -- but you can still never reach all of them.

SC: But what do you mean by that distinction? Do you mean that there may be two digits of pi such that reaching one of them by my method is inconsistent with reaching the other -- so that, while reaching either is possible, reaching both is not?

WJT: No.

SC: Or are you imagining some particular digit called "all the digits of pi" -- a close cousin to "the last digit," "the infinitieth digit," and the month of Febtober -- and saying that I cannot reach it?

WJT: No, not that, either.

SC: Let me help you. What you are saying is that, although I will recite each and every digit of pi -- that is, for every digit of pi it is true that I will eventually recite it -- I will never have recited them all. There will never come a time when I can say that my project is complete and that I have recited all the digits of pi.

WJT: Yes, that's just what I've been trying to say.

SC: Well then our disagreement is merely verbal. I never said that I will have recited all the digits of pi; I only said that I will. If that seems slightly paradoxical, such is the nature of sempiternity.

WJT: Okay, I guess we can agree that --

SC: But --

WJT: Yes?

SC: But suppose I told you that, as it happens, I have recited all the digits of pi. This task that can never be finished -- I have finished it. That's what I was doing for all those numberless eons before 1742.

WJT: But we've just agreed that that's impossible!

SC: Three! Three false assumptions! Ha ha ha . . . . We've only agreed that it is impossible, not that it always has been.

WJT: No, it is, was, and always will be impossible. No one -- past, present, or future -- can ever have recited all the digits of pi because there is no end to them.

SC: There is no end to them, quite right. But there is a beginning, isn't there? The first digit is three, the second is four, and so on.

WJT: But we're talking about finishing, not beginning. I don't see the relevance of --

SC: I recited them backwards.

WJT: You mean you started with the --

SC: No, that's just my point: I never started. I had always been reciting digits of pi in reverse order. At 10:17 a.m. on April 14, 1742, I recited the first digit of pi. Just before that, I had recited the second; before that, the third; and so on all the way back. I had always been doing it, for mahakalpas without number, until one day I finally finished.

WJT: But how could you have finished a finite time ago, if you began infinitely long ago and advanced step by finite step?

SC: I didn't begin infinitely long ago because I didn't begin at all. I have recited an infinite number of digits of pi, but each and every one of them was recited at a particular time only finitely antecedent to 10:17 a.m. on April 14, 1742. We have already discussed all this. Just reverse past and future and apply the same logic.


3. Commentary

3.1. Bidirectional sempiternity

A typical definition of sempiternity, as a technical term in philosophy, is "existence within time but infinitely into the future, as opposed to eternity, understood as existence outside time." That is to say, sempiternity is like a geometric ray, or like the ordered set of all natural numbers -- or like the decimal expression of pi. It has a single endpoint and extends infinitely in one direction only. The Count, on the other hand, is what we might call bidirectionally sempiternal, like a geometric line, the ordered set of all integers, or the decimal expression of pi preceded by its mirror image.

I think many more people are willing to countenance future-only sempiternity than the bidirectional variety. This ultimately comes down to a very fundamental assumption about time -- namely, that the past actually exists but the future does not. A sempiternal future, these people would say, is boundless but not actually infinite. No matter how long one goes on living, one will always have lived for a finite number of years. The future is only potentially infinite, in the sense that that finite number will go on increasing indefinitely. Past sempiternity, on the other hand, is taken as meaning that an infinite amount of time has already elapsed, making it an actual infinity.

There is really no arguing with primary metaphysical assumptions, so I can only state that I do not share this one. Either only the present is actual ("presentism," as defended by Edward Feser here vis-a-vis Kalām), or the whole timeline is actual ("eternalism," which is what I believe due to the relativity of simultaneity and the fact of precognition). And either way, as I have tried to argue in recent posts, there is no question of an infinite amount of time elapsing because no point on the timeline is infinitely distant from any other.

3.2. A project which is neither completable nor hopeless

One of the things that used to bother me as a Christian youth was the idea that one day everything would be finished, every goal accomplished, and then -- an eternity of stasis and boredom? I used to think of John Lennon's infamous line, "Imagine there's no heaven . . . above us, only the sky," and reinterpret it -- thinking of "heaven" as a state of eternal rest after all has been accomplished, and Lennon as proposing that there is no such final state, only infinite potential. In Mormonism, this conception of heaven as an eternal sabbath -- when one has become "a pillar in the temple . . . to go no more out" (Rev. 3:12) -- coexists uneasily with the concept of "eternal progression." I was very much a proponent of the latter, finding the former unbearable.

But what's the alternative? Working forever to reach a goal that can never be attained? This is another sort of hell, that of Sisyphus. Still, suppose Sisyphus finally succeeded in getting his boulder into a permanently stable position at the top of the hill. Then what?


This sort of thing really used to bother me a lot, which I suppose made it emotionally easier for me to transition to atheism, since eternal extinction seemed no more futile or meaningless than any of the alternatives. Why want eternal life if it meant either chasing unreachable goals forever, or else reaching all possible goals and damning oneself to an eternity of boredom? All is vanity and vexation of spirit. As They Might Be Giants put it,

Now it's over, I'm dead, and I haven't done anything that I want --
Or I'm still alive, and there's nothing I want to do

Though the Sempiternal Count's specific pastime of reciting digits of pi would be mind-numbingly boring for us humans, it does provide a model for a tolerable eternity. Each goal is reachable, so one's efforts are not in vain; and yet there will never be a time when all the goals have already been reached.

3.3. Something new can happen, even after a sempiternity


If something has never ever happened through all the countless kalpas of our existence, shouldn't it be pretty obvious by now that it's never going to happen? Thus the thesis that we have always existed would seem to lead to despair.

But the example of the Sempiternal Count shows that this reasoning is not valid. The Count had always been reciting pi backwards without ever finishing -- until one day he did finish, and moved on to the next thing. So the thesis that we have always existed is not after all incompatible with the doctrine that "it doth not yet appear what we shall be" (1 Jn. 3:2).


Note: I've been working on this post for a week or so. It's by pure coincidence that I finally finished it on Pi Day.

Thursday, March 3, 2022

No two points on an infinite line are infinitely distant

I mentioned this in passing in "What if there was no beginning?" in connection with the Kalām Paradox. but I think it deserves a post of its own.

The Kalām Paradox, for those who came in late, asserts that nothing temporal can have always existed. If it had, it would be infinitely old, meaning that an infinite amount of time must already have elapsed. However, it is impossible for an infinite amount of time to elapse, because time elapses one finite step at a time, and adding up finite quantities can never yield an infinite quantity.

First, I should make it explicit what sort of infinity we're talking about here. We're not talking about Zeno's paradoxes which find an uncountable infinity within countably finite quantities. In the racecourse paradox, for example, it is supposed to be impossible to run a mile, because first you have to run half a mile; and before you can run half a mile, you have to run a quarter of a mile; and so on -- an infinite number of tasks. A number-theoretical way of expressing this is that between any two integers there are (uncountably) infinitely many real numbers. To apply Zeno's spatial paradox to time, we could say it is impossible for anyone or anything to be a year old -- because before a year can elapse, 6 months have to elapse; before 6 months, 3 months; and so on -- a sum of infinitely many finite quantities, which must therefore add up to infinity. This is not the Kalām argument, which takes it for granted that things can have a finite age.

I will not bother to address Zeno-type paradoxes because no one is in any danger of believing them. The Johnsonian "I refute it thus!" is sufficient. It's very obvious that fleet-footed warriors can catch tortoises, and that it is in fact possible to run a mile. These are matters of everyday observation, as the subject matter of Kalām -- the question of whether the universe had a beginning -- cannot be.

When the Kalām Paradox denies that the past can be infinite, it is referring to countable infinity, of which the paradigm case is not the real numbers but the integers. (To be sure, time may also be infinitely divisible and thus uncountably infinite, but that is a separate question.) The image we want to keep in mind, then, is the integer number line.


I propose that linear time is like this number line. The origin (zero) corresponds to the present, the negative integers to points in the past, and the positive integers to points in the future. Let's say that -1 on the number line means "one year ago," 1 means "one year hence," and so on. (There are of course many -- possibly infinitely many -- intermediate points in time between each of these points, just as there are infinitely many real numbers between one integer and the next, but that is not germane to Kalām. We take it for granted that Zeno is wrong and that countably-finite intervals of time can and do elapse.)

The integer number line is countably infinite -- meaning not that it is infinitely divisible but that it is infinitely long. There is no "first" or "last" integer. This does not mean that there is a first integer, -∞, which is infinitely distant from the origin; there is no such integer as -∞; there is no first (or last) integer. Every integer is finite (meaning finitely distant from the origin), and therefore the difference between any two integers is also finite.

Applied to time, this means that there was no first moment of time, no absolute beginning -- not that the beginning was "infinity years ago" (-∞), but that there was no beginning.

Now according to the Kalām Paradox, this means that an infinite amount of time must already have elapsed to get to the present. This is impossible, and yet we manifestly have reached the present; therefore, there was a beginning.

The question to ask is: An infinite amount of time must have elapsed from what point to the present? If the answer is "from the beginning," the argument fails, because the claim it is trying to disprove is that there was no beginning, just as there is no first integer. If the answer is "not from the beginning, since there is none, but from any arbitrary point infinitely distant from the present," the argument also fails, because there is no such point, just as there is no such thing as an infinite integer (infinitely distant from the origin). The only answer left, then, is "a point finitely distant from the present," and then there is no more paradox.

If there was no beginning, then we can say that, for any finite number n, n years have already elapsed. This is true no matter how arbitrarily big n is, which is the sense in which the past is infinite. But it does not mean that an infinite number of years have already elapsed. Therefore, this presupposition of the Kalām Paradox conclusively fails.

I am open to corrections from readers more mathematically gifted than myself, but I have to say I'm pretty darn sure I'm right about this.

Monday, February 28, 2022

What if there was no beginning?

If you could hie to Kolob in the twinkling of an eye
And then continue onward with that same speed to fly,
Do you think that you could ever, through all eternity,
Find out the generation where Gods began to be?

Or see the grand beginning, where space did not extend?
Or view the last creation, where Gods and matter end?
Methinks the Spirit whispers, "No man has found 'pure space,'
Nor seen the outside curtains, where nothing has a place."
-- W. W. Phelps

When did that thinking thing begin to be? If it did never begin to be, then have you always been a thinking thing from eternity; the absurdity whereof I need not confute, till I meet with one who is so void of understanding as to own it.
-- John Locke

In comments to my recent post "Why does God exist?" Bruce Charlton and Francis Berger have both expressed the opinion that beings of some sort have always existed -- not atemporally like Allah, but temporally, with their existence extending back over an infinite expanse of time. Bruce Charlton wrote:

I find it very strange that (apparently) some people find it inconceivable that there should be infinite 'time' in the past leading up to now. I find the opposite impossible to imagine - i.e. that there was ever a beginning before which there was nothing.

I think I have always been like this, since I was a child. Even when I accepted the recent (and constantly changing) scientific theories about the Big Bang as a certain truth, at the back of my mind I always wondered what happened before it - and assumed some kind of eternally expanding and contracting and re-exploding cyclical universe.

The infinite temporal existence of beings -- including God, man, and even the physical elements -- is also the Mormon position, expressed by Joseph Smith in the King Follett Sermon (part 1 part 2), and was my own position until fairly recently. I therefore thought I ought to devote a post to reasons for not believing it. Before doing so, let me state again my meta position that theologies are akin to map projections -- in order to get some things right, you have to omit or distort others; and which projection is "best" depends on what you most care about getting right.


1. Infinite elapsed time

As discussed in my earlier post, the Kalām Cosmological Argument assumes that there can be only two kinds of beings: (1) beings that began to exist a finite amount of time ago; and (2) beings that are atemporal, or "exist outside of time." Everything we know, including the physical universe itself, belongs to the first category; it is therefore necessary to explain their existence by positing a being of the second type, and this is Allah.

The reason given for rejecting a third category -- beings that are temporal but never began to exist -- is that for those beings an infinite amount of time must already have elapsed. They must already be "infinity years old." However, it is impossible for anything to ever be "infinity years old," because time elapses finite step by finite step, and infinity can never be reached by adding up finite quantities.

With the caveat that it is notoriously difficult to think clearly about infinity, I think this argument is in error. It conflates "never began" with "began an infinitely long time ago." Consider by way of analogy the number line of integers. It is infinite, but it would be sloppy thinking to say it extends "from negative infinity, through zero, to positive infinity." There is no such number as "infinity" (negative or positive) on the number line. Of all the infinitely many integers on the line, not a single one of them is infinitely distant from zero.

The present moment corresponds to zero, the past to the negative integers, and the future to the positive ones. If I say that my existence (in one form or another) is infinite in both directions, in precisely the same way that the number line is infinite, does that make me "infinity years old"? No. The Kalām Argument assumes that an infinite amount of time must have elapsed from "the beginning" to the present -- missing the point that there was no beginning. A billion years ago, I existed; and a billion years have elapsed since then. A quadrillion years ago, I existed; and a quadrillion years have elapsed since then. The "infinity" lies in the fact that the statement will be true for absolutely any number I choose, no matter how astronomically large it may be; but every number, without exception, will be a finite distance from the present, and only a finite time will have elapsed since then. Just as you can get from any point on the infinite number line to any other by adding or subtracting a finite quantity, so any distance on the infinite timeline can be traversed without an infinite amount of time elapsing.

So I reject this argument against infinite temporal existence.


2. Unrealized potential

Central to Christianity is the idea that we have the potential to become like God, but that at present we are obviously very, very far from having realized that potential.

How long will it take us to realize our divine potential? A billion years? But we have already existed for a billion billion billion years (or whatever other arbitrarily large number you choose) without realizing that potential. If something has never ever happened through all the countless kalpas of our existence, shouldn't it be pretty obvious by now that it's never going to happen? Thus the thesis that we have always existed would seem to lead to despair.


3. Meaninglessness

If we have always existed, and our existence is not "necessary," then it seems to follow that we exist for absolutely no reason. Our existence has no inherent meaning or purpose but is just a brute fact, no less an "accident" then if we had originated when lightning randomly struck the primordial ooze.

I'm actually okay with this -- I spent a decade of hard atheism getting used to the idea -- but most Christians are obviously not. It is extremely common to hear that atheism makes life meaningless because it means you're an accident and exist for no inherent purpose. No, atheism makes life meaningless because it means you die, not because it means you were born. Meaning and purpose in life come only from our choices, not from the circumstances of our coming into existence.

Still, though, there's something deeply unsatisfying in the idea that existence is irreducibly "random," that we all just happen to exist for no reason at all.


4. Agency is necessary anyway

The "no beginning" scenario would be most appealing to a determinist, who maintains that the state of the universe at any given point in time is determined by its state at the point immediately previous. An infinite past with no beginning would seem to be required by this "all dominoes and no fingers" theory.

If we accept agency, though, then some causal chains at least do not extend back infinitely into the past but terminate in a free choice, an uncaused cause -- and our metaphysics must accommodate that. Since we have this experience of things having a real beginning, and no experience of things having existed forever, it seems reasonable to assume, unless there is some strong reason to assume otherwise, that all things had a beginning, and that that beginning was a free act.

Tuesday, February 2, 2021

Found poetry

I think this guy all of a sudden
could see time.
He can actually look into space and see
his movements from yesterday
and tomorrow.

When he tries to drink his coffee,
he picks up the one
from a couple of hours ago.

When he moves, time is shifted
in spontaneous ways so that there is no way to tell
the actual time.

His body and clothes are also
shifted throughout time, so his face
and pajamas are different when
he gets out of bed.

(source)

Friday, October 11, 2019

The need for a new concept of time

The idea that time is just what it appears to be -- that everything just comes and then goes, like a sparrow flying through a mead-hall -- that the past is lost and gone forever, dreadful sorry, Clementine -- is unacceptable. In such a world, everything dies. "Immortality" does not solve this problem, any more than the continued existence of the modern city of Rome can change the fact that ancient Rome is gone forever.

But the alternative -- that time is an illusion, that nothing changes -- that God and the universe as God sees it are simply an eternally static four-dimensional object -- is also unacceptable. In such a world, nothing really lives, for life is an inherently temporal thing. Stasis is not and never can be compatible with life.

What is temporal is temporary, and what is atemporal is lifeless. But Jesus promised eternal life -- really eternal, and really life -- and taking his message seriously means trying to understand what that means.

This is the problem that has been occupying most of my time recently.

Monday, May 6, 2019

Changing the future and changing the past

In a recent post, Bruce Charlton asks "Can the past be changed?" -- and answers, "Obviously not," going on to pronounce the contrary opinion "demonic." Since I have been guilty of entertaining a version of this doctrine from the pit of hell (see this post), I thought I would revisit the idea.

*

The first matter of business is to establish exactly what is meant by change. As a simple example of a change, consider my marital status, which changed in the latter part of 2010. Prior to that date, I was not married; after that date, I was and am. That's what change means: that a given proposition ("William James Tychonievich is married") is/was/will be true at some points in time and false at others.

We can represent this change graphically by means of a colored line. The dimension represented by the line is "time," with the past to the left and the future to the right, and the color of any given point on the line represents my marital status at that point in time (blue for single, gold for married). Below is a portion of such a timeline, covering the years from 2009 to 2020.

Fig. 1

We want to consider the idea of changing the future and the past, so this timeline is inadequate, giving no indication of which points on the line are past and which are future. We need to add something to indicate that the present moment is -- well, of course it's a moving target, changing even as I type this sentence, but this is a pretty low-resolution timeline, so "about a third of the way through 2019" will be good enough for our purposes. (If you should happen to be reading this post at a significantly later date, please be so good as to proceed on the counterfactual-to-you assumption that the present moment is indeed in that general vicinity.) Let us modify our timeline by reserving the bright colors used in Fig. 1 for past points in time and representing future points by paler versions of the same colors, like so:

Fig. 2

There are now two points on the timeline where the color changes. The point where it changes from blue to gold represents the event of my marriage. To the left of that point, I was single; to the right, I was, am, and will be married. The point where the line changes from bright to pale represents the present moment. Everything to the left of that point is past, and everything to the right of it is future.

Now, we have already established that my marriage in 2010 constitutes an example of a change, and our timeline above locates that change to the left of the present moment -- that is, in the past. Is this, then, what we mean by "changing the past? Obviously not -- but why not, and what do we mean?

Well, the natural answer is something like this: The change in question occurred in 2010 -- which means that at that time, 2010 was not in the past but was the present year. If what happened in 2010 were to change now, that would be what we mean by "changing the past." But this introduces a distinction between 2010-in-2010 and 2010-now which cannot be represented on a one-dimensional timeline. Such time designations require two coordinates -- (2010, 2010), (2010, 2019) -- which means our simple timeline must be expanded into a two-dimensional "timeplane" of the type pioneered by J. W. Dunne and discussed in my post "The present now will later be past."

The title of that post, taken from the Bob Dylan Song "The Times They Are a-Changin'," was chosen because, while it seems very obviously true, it implicitly assumes a two-dimensional model of time. A simple timeline, like Fig. 2 above, can represent past, present, and future, but not the idea that "the present now will later be past." The very phrase "will later be past" describes the same state of affairs as being future in one sense and past in another -- which requires a rectangular coordinate system comprising two perpendicular timelines.

Fig. 3

Now I know from experience -- my own included -- that this is point at which readers' eyes start to glaze over, but I'm afraid there's just no avoiding these diagrams. I can only ask for the reader's patience and do my best to explain. The color of each point on the timeplane in Fig. 3 represents a proposition regarding my marital status: The hue represents the content of the proposition (blue for single, gold for married), and the tint represents its tense (pure colors for past, light colors for future). Each point is located in two different temporal dimensions: The x-axis ("object time") represents the time the proposition refers to, and the y-axis ("meta-time") represent the time at which the proposition is true.

I've marked two (arbitrarily selected) regions on the plane "A" and "B," respectively, in order to use them as examples. They represent the following meta-propositions:
A: In 2010, the proposition "WJT will be married in 2012" was true.
B: In 2014, the proposition "WJT was married in 2012" was true. 
For completeness, we really ought to indicate the tense of the meta-proposition as well. Fig. 4, below, is so modified as to express this. Solid colors (such as were used in Fig. 3) represent meta-past, and stippling represents meta-future.

Fig. 4

The region marked "C" in Fig. 4 represents the following meta-proposition:
In 2020, the proposition "WJT was married in 2011" will be true.
The "was" in the object proposition is indicated by the use of a pure color as opposed to a tint, and the "will be" of the meta-proposition is indicated by stippling.

The red dot in Fig. 4 marks the place where the true present may be found. (Or at least, this was true when I wrote it, about a third of the way through the year 2019.) When we say, "2019 is the present year," the word "present" corresponds to the diagonal line separating pure colors from tints, and the present-tense verb "is" corresponds to the horizontal line separating solid colors from stippling. The intersection of those two lines, marked with the red dot, is "the present now." Dylan's statement that "the present now will later be past" means that if we start at the red dot ("the present now") and move vertically down into the stippled region ("will later be"), we find a pure color ("past") rather than a tint.

Take a minute to digest that. I want to be sure the meaning of these timeplane diagrams is clear before proceeding.

Now look back at the region marked "A" in Fig. 3 and the meta-proposition to which it corresponds: "In 2010, the proposition 'WJT will be married in 2012' was [already] true." And consider this: If I were to extend my timeplane diagram to cover a wider range of past times, there would be a region on that diagram corresponding to the meta-proposition "In 4000 BC, the proposition 'WJT will be married in 2012' was already true." This is fatalism, of the unassailable variety spelled out by Richard Taylor (whose argument I discuss here) -- unassailable because it does not depend on the doctrine of causal determinism. From the mere assumption that all possible statements about the future are (already) either true or false, and that their truth-value cannot change, it follows that all is fated, that whatever happens is inevitable.

 To escape Taylorian fatalism, it is necessary to believe that we can change the future -- an idea which is common enough in naive discourse, and which our two-dimensional timeplane allows us to model. Let us modify our diagram, then. Instead of assuming (as Fig. 4 does) that my getting married in late 2010 is something that was always going to happen, something that was already written in the book of fate hundreds of years before my birth, or as far back as you care to imagine -- instead of assuming that, let's assume instead that I wasn't going to get married on that date, not until I actually made the decision to do so. Let's assume that my decision, rather than being just another step in the inevitable unfolding of fate, actually decided something, literally changed the future. And let's further assume (as seems reasonable) that this future-altering decision was made some months before the actual event of the marriage.

Fig. 5

The black dot on the timeplane in Fig. 5 represents the moment I exercised my agency and made the fateful decision (which, I need hardly mention, is entirely different from a fated decision, the latter being a contradiction in terms and no decision at all).

The diagonal line that passes through the black and red dots, and divides the pure colors on the left from the tints on the right, represents the timeline of my life as I experience it, as a succession of object-time "presents." The horizontal line that passes through the red dot, and divides the solid colors from the stippling, represents the meta-time present. (The object-time present is a point; the meta-time present is a line.) The intersection of these two lines divides the plane into four quadrants, representing (clockwise from the upper left), what had happened (solid pure colors), what was going to happen (solid tints), what will be going to happen (stippled tints), and what will have happened (stippled pure colors).

*

The diagonal line -- my life as I experience it -- is exactly the same in Fig. 4 (where the future is fated) and in Fig. 5 (where it can change). It would appear, then, that there can be no empirical evidence for the one model or the other, no possible experience that would be more consistent with the one than with the other. Choosing one over the other would be a metaphysical assumption, not a conclusion from evidence.

However, that may not be entirely true. There is considerable evidence (see J. W. Dunne's Experiment with Time for starters) that, while the attention is generally confined to the point-present represented by the red dot, it can sometimes extend to other regions of the linear meta-time present, especially during dreams or similar states of relaxed or diffuse attention. In such states, we have access to the object-time future (precognition) and past (retrocognition) -- at least as they exist at the meta-time present. Under Taylorian fatalism (as diagrammed in Fig. 4), the content of object time does not vary across meta-time; the only meta-time change is that of tense (as the future becomes the past), so whatever future events are perceived through genuine Dunnean precognition will infallibly come to pass when the future times in question become present. There would be no possibility of seeing the future and then changing your behavior as a result of what you see, with the result that the foreseen event is averted. This is precisely what fatalism -- of the sort seen in the Greek myths, for example -- means. Cassandra's prophetic warnings are ignored and have no power to prevent the events they foretell. The prophecies regarding Oedipus are not ignored, but the very attempt to thwart them leads to their fulfillment. Either way, fate ineluctably plays out.

In the model where the future can be changed (as diagrammed in Fig. 5), even true precognitions need not necessarily come true. For example, look back at Fig. 5 and imagine that in 2009 (in both object time and meta-time -- that is, at a point on the diagonal line) I had a precognitive vision of 2011. Since such a vision would be of object-time 2011 at meta-time 2009, I would see myself as still single at that date. However, by the time object-time 2011 becomes the meta-time present, it will already have changed, so that the 2011 I experience will be different from the 2011 I foresaw. Nonetheless, what I foresaw was true. (If that seems like a contradiction, consider this analogy. I turn on the TV to the weather channel and discover that it is sunny in Taipei. I then get in my car, drive to Taipei, and upon my arrival find that it is raining. But what I saw on TV was true.) Instances of true precognition that do not come true would be evidence that the future can be changed.

The problem, of course, is that, if a vision or premonition does not come true, there would seem to be no grounds for considering it genuinely precognitive. For example, once in my late teens, at a time when I had no plans to go overseas, I had a very vivid and detailed dream in which I was about 30 and living in Vietnam. I'm 40 now and have never set foot in that particular country. It's possible that my Vietnam dream was genuinely precognitive, revealing what was (at that time) going to happen in the future, but that the future it foretold has since changed because of choices I or others have made. It could also be considered a garbled precognition of what in fact came to pass. (I do live in Asia and have for most of my adult life.) But there's no good reason to believe that, and the simplest explanation is that it was just a dream and not precognitive at all. Certainly such a dream cannot constitute evidence that the future can be changed. Is such evidence possible?

Consider the premise of the Final Destination series of horror movies. The protagonist has a sudden vision of a series of events leading up to all his friends dying horribly in a freak accident. When the foreseen events begin to play out in real life, he panics and manages to prevent his friends from getting on the doomed plane or roller coaster or whatever. Then the freak accident occurs as foreseen, except that his friends are not among those killed by it. Later they all go on to die horribly anyway, in different freak accidents, because "you can't cheat death," but that's not germane to my point here, which is that the originally premonition is clearly a true one even though it does not come to pass exactly as foreseen. When people act on a precognitive warning so that the foreseen event does not happen, but subsequent events make it abundantly clear that it would have happened had they not taken action, that is evidence that the future can be changed.

Such evidence in fact exists. The literature on precognition is full of Final Destination type stories (minus the post-accident bit where everyone dies horribly anyway). Someone has a premonition of being in a plane crash, they cancel their tickets, and then the flight they would have been on crashes. That kind of thing.

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What about changing the past? Well, it's a bizarre idea, so our illustrative example will be a little bizarre as well. I must ask the reader to suspend disbelief, ignoring for the moment the question of whether or not such things can really happen. Our question is what it would mean for the past to change, and, supposing it did change, whether there could be any empirical evidence of that change.

Suppose that "originally" I chose not to get married in 2010. Years later, in 2015, I looked back on that choice with regret and said to myself, "I wish I'd married that girl when I had the chance!" A passing genie happened to hear my remark and granted the wish. From that moment, it suddenly became true that I had gotten married in 2010. We can represent this hypothetical story graphically as below, in Fig. 6.

Fig. 6
The black dot on the plane in Fig. 6 indicates the moment at which my wish was granted. Notice that, when the past changes, the present and future change as well, since chains of cause-and-effect run horizontally from left to right across the diagram (i.e., causation is an object-time phenomenon).

Remember that the diagonal line dividing the pure colors from the tints represents my life as I actually experience it, as a succession of presents -- and notice that in the world depicted by Fig. 6, I never actually experience my own wedding or the first several years of my married life. I go directly from being a bachelor to having been married for nearly five years! Surely such an obvious discontinuity in my experience could not possibly go unnoticed, and surely the fact that people's lives don't include such discontinuities is evidence that the past cannot change -- right?

Well, not exactly. Remember that causation is an object-time phenomenon. When object-time 2010 changed in meta-time 2015, all subsequent points in object time also changed as a result of the causal effects of that 2010 wedding. For example, if photos were taken at the wedding, those photos will (after the granting of my wish) still be there in 2015 and after. But if the creation of photos is one of the effects of the wedding, the creation of memories in the minds of the participants is another. If my memories of the past are understood to be effects of those past events in the ordinary sense of that word (i.e., one of the effects of a given past event is an alteration in the state of my brain, which alteration persists through time and constitutes my memory of that event), then my memories at any given point in my life will be of what preceded that point horizontally (i.e., in object time), not diagonally along the line of my actual experience. If the past cannot be changed, the difference is immaterial, since the content of the horizontal and diagonal pasts will be identical. If it can be changed, then as soon as the change has happened, the content of my "original" past is inaccessible to me. When, at the moment marked with the black dot, I suddenly transform from a bachelor into someone who has been married for five years, my memories change as well. I would have no memory of ever having chosen not to get married in 2010, nor of regretting my choice and having my wish granted by a genie. My memory would tell me that I had "always" gotten married in 2010, and all observable effects in the present would also be consistent with that. No evidence that the past had changed would be possible.

What about retrocognition -- "paranormal" direct access to the past, corresponding to precognition and different from ordinary memory? Would that give us access to the "original" past, before it had changed? No, because like precognition, it represents an expansion of attention from the point-present to the linear present of meta-time (represented in the figures by the horizontal line passing through the red dot).

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I had originally planned to discuss the so-called "Mandela Effect" -- the phenomenon of memories that don't match documented history (such as many people's memories of Nelson Mandela having died in prison, or of the Berenstain bears being called the Berenstein Bears) -- as possibly representing memories of the past before it was changed, but our two-dimensional time model has no way of accounting for such "memories" (except to say that they are simply errors). That will require us to venture into the even-more-confusing domain of meta-meta-time -- and, this post already being quite long enough, I think I will reserve that discussion (and a discussion of the moral significance of changeable vs. unchangeable pasts, as raised by Bruce Charlton) for the sequel.

Ace of Hearts

On the A page of Animalia , an Ace of Hearts is near a picture of a running man whom I interpreted as a reference to Arnold Schwarzenegger....