A lost alchemical poem of Raleigh's

I dreamt that I had acquired a rare old book entitled Ralegh the Alchemiste, which quoted these lines of Sir Walter Raleigh's poetry and interpreted them as a reference to the alchemical process of nigredo ("blackening").

I hope when I die, and the Ages doe roll,
My Bodie will blacken and turne into Coale :
Then Ile looke from the Doore of my heauenly Home,
And pitie the Miner a digging my Bones.

Doesn't that almost sound as if Raleigh could have written it?

In the waking world, of course, these lines are not Raleigh's but come from the 1946 folk song "Dark as a Dungeon" by Merle Travis, later sung by Tennessee Ernie Ford, Johnny Cash, and many others. I'm partial to Jerry Garcia and David Grisman's version myself.

"Low-gravity" skimming and slow-jumping dreams revisited

This is something I posted back in 2013 on a different (now defunct) blog, with some new material appended.

⁂

Low-gravity dreams evoke "real" memories

. . . when swift Camilla scours the Plain,
Flies o’er th’unbending Corn, and skims along the Main.

— Pope, Essay on Criticism

I have had dozens of dreams in which I seem to be less than ordinarily affected by gravity. The dreams always appear to take place on earth, and other things and people in the environment behave normally; only I (and occasionally a few other people) move as if in a low-gravity environment.

These dreams take two basic forms. In the more common of the two, I am walking and find that every step sends me sailing gently into the air, several meters up, and then slowly back down. I can move almost effortlessly this way; by simply “kicking off” from the ground a few times a minute, as one might do when using a playground swing, I can keep myself moving forward in great slow bounds. In the dreams, the thought that always accompanies this is: “I’d forgotten I could do this. I should do this more often.”

In the second form of the dream, I am in a supine position about 70 cm above the ground and am moving “forward” (that is, in a caudal direction). As in the jumping dreams, I have to “kick off” with one foot occasionally to maintain my speed, though in these dreams I am reminded more of a skateboard than a playground swing. In these dreams, unlike the others, I do not rise or fall; I stay at a constant distance from the ground, and kicking off serves only to give me a burst of forward speed, not to send me sailing up into the air.

In my slow-jumping dreams, I have an exhilarating sense of freedom, and at the apex of my leaps I enjoy looking down on the scenery (generally rolling green hills, dotted with trees). In the supine-skimming dreams, though, I often feel that I am going where I am “supposed to” go, following a leader who is walking ahead of me. I never see this leader, though, because I am always looking straight up at the sky — though I am somehow simultaneously aware of the ground (usually a hard gray surface) rushing past beneath my back.

What makes these dreams unusual is that, upon waking, I am left with an unshakable conviction that they really happened. I don’t mean that I feel as if the dream itself had been real — the dream was obviously just a dream. However, I have a compelling feeling that the dream is reminding me of something I really experienced, that some long-forgotten memory from my real life has been jogged almost back into conscious recollection by the dream. I feel sure — my body feels sure — that somehow, somewhere, sometime, I really have moved that way, if only I could remember where or when. But, rack my brain how I may, I can never quite retrieve those elusive memories. I am left with an unsatisfying certainty that somehow those dreams must be about something “real,” but without being able to explain how they possibly could be.

⁂

Appendix 1: Selected comments from readers

This post attracted a slow but steady stream of comments from readers, the most recent of which was just a few months ago, more than six years after the original post. Here are some of the more interesting comments, lightly edited for spelling and such. Not only have many other people had this kind of dream, but many of them have a similar conviction that it must be somehow real.

Bruce Charlton wrote:

Assuming, for a moment, that these seem real because they are in some sense real – do they feel more like memories of the past (maybe partial or distorted) of something that really happened (e.g. reincarnation, pre-mortal existence); or yearnings for something in the future that is real but not of this world (like CS Lewis’s idea of ‘Joy’/ Sehnsucht)?

I replied:

Definitely past memories, not yearnings. The feeling is I’m sure I’ve done this before.
Since this is a recurring theme in my dreams, I suppose it could be that each dream is simply reminding me of similar past dreams, but the memories feel like memories of real, waking events.

Mary wrote:

I realize it’s three years later, but I was searching for others who might share my perception that moving in a low gravity environment felt intuitively more like reality than my reality in waking life, and found this. I always walk in dreams as if I’m hopping and gliding, more launching and gliding. I feel very fluid and natural in the dream – like moving this way was all I ever did. To add to that, when I was very young, age three or four and younger, I would spin around a pole, but remember having this fear that I was going to launch myself into the stratosphere, and I remember feeling that way often when I would play outside, particularly when it was dark. This worry became a phobia and limited my activity to some degree. I do feel like I lived in a place where low gravity existed, and try to fit that into my perception of waking life with little success. The idea does tug at me, enough to search for others. Cheers.

Cindy Schneider wrote:

Sorry, it’s another year later, but I had this dream last night and all day I’ve felt like it was really a memory and I’ve been trying to figure it out. I can “remember” feeling this glide, and looking down, seeing my feet slightly off the ground, and just knowing that if I slide my feet together and turn, I can get more distance. It’s like taking really big strides in slow motion, but your still covering distance. I remember feeling that probably not everyone can do this, and it might be a pretty cool thing I should keep doing. But it also felt totally normal. I had a hard time waking up and reconciling whether or not I was remembering something I had done or just dreaming.

Martin wrote:

Last night, was a sleepless one. I was trying to figure out how and why I was having this kind of a dream coming over and over again, back in 2013. I’d narrate to my friends, but they laughed at it. The dream is no longer coming as frequently as it was before. I don't know why, but I am always into knowing much about our lives because I feel that we still haven't done what we can easily do.

Agellius wrote:

I believe I have had the same type of “slow-jumping” dream. The thing that stands out for me about these dreams, is that I almost always eventually jump a bit too hard and find myself at a higher altitude than I intended, and in danger of falling. However I never really get hurt.

I do not, however, have the feeling you describe that the dream represents a real memory. It is amazing, though, how normal and natural the “jumping” feels in the dream. It’s obviously not anything I’ve done in real life, yet I seem to have a complete understanding of exactly how it would feel to experience it, how to control it, how much effort to put into each bound, etc.

I haven’t had the supine-skimming dream that I can recall.

Chrstphre Campbell wrote:

That is one of the most compelling things about dreams, is that while experiencing them, and simultaneously being aware that you are dreaming, everything seems "normal" or "the way it should be." 

I often have "memories" of things, sometimes recalled from dreams, and sometimes not, that I wonder if they are real memories or dream memories, and the test that I apply is: When did this happen?

If I can’t place it as happening before or after well founded memories, then I assume that, despite its extreme lucidity, it must be a dream memory that happened in some other reality.

Dreams are the real reality, This waking stuff is our experiences in a fractional reality created by the [angels] to either teach us something important, or to enslave our souls for some purpose that the angels themselves are unable or unwilling to do.

Mikee Remastered wrote:

This may seem a little ‘out there’. But that’s because it is. I have had dreams like this before too. For me I was fully aware I was dreaming, so it was a lucid dream. And whenever I jumped into the air, gravity was low and I could do these fantastic slow leaps and when I was coming down slowly I could feel the air on my face. And it felt incredibly real.

When I researched into it. Turns out a lot of scientists believe in a theory that we used to live on Mars (I said it was out there). And that we may have been left here after our planet was destroyed. Mars is a funny planet. Because it once had a fully functioning Magnetic field like Earth and huge oceans of water like Earth. These are facts now. Meaning it had a good atmosphere, water, and may even have had air just like our planet did. It could explain why millions of us have always felt lost, or not at home here, a feeling like we don’t belong on this world. It could explain why many, many people have experienced low gravity dreams. It could explain why Humans are the only living creature on Earth that are so advanced compared to other species here. It could explain, our bad backs. Yes that’s actually not a joke. The humans are the only species on Earth that are prone to getting bad backs in life, even if they look after themselves. Most end up with them. While no other creature that is native to this planet does. This is all thought to be down to our bodies originally evolving to a much lower gravity.

All life on this planet gives birth with great ease. Except for the humans. Giving birth is incredibly dangerous for the mother and the baby in Humans. Whereas all other life is able to give birth alone without the need for help. And a scientific fact, is that this is down to humans Skull structure. The head formed from a baby is largely round. Our heads take on this shape because of gravity. It is thought that if we lived in low gravity, our heads would form taller and skinnier. Birth shouldn’t be painful. Yet it is.

I replied:

Interesting ideas, Mikee, but it seems unlikely that we came from Mars. Humans, while unique in many ways, are still clearly members of Earth-based biological taxa. Our very close genetic similarity to the African apes — and, to a lesser degree, to other Earth animals — is hard to explain on the hypothesis that we are aliens. 

Bad backs and painful birthing are most likely the result of our recent transition to bipedalism, to which we have adapted only imperfectly.

Damon wrote:

I am glad I found this post. I have had recurring dreams like the rest of you.

The first is of ability to float around a few inches off the ground. This one is not the most common dream. It comes as a memory like I used to do this in middle school. I literally woke up one morning convinced that I used to be able to do this and spent the next few days trying to make it happen again. I can almost convince my body or at least the nerves in it that I am becoming weightless in an attempt to levitate off the floor. 

The second and most recurring dream I consider to be a floating one of sorts. See in these dreams I typically have to be running or jogging but with each jump I will fling myself a little higher in the air and slowly come back down until I get to a point where I am very high and scared of hitting the ground. Often times I find myself grasping at tops of trees so I don't go too high that I will fall to my death. Sometimes I do this on two feet; other times O will run on all fours. Regardless, it is exhilarating and I love having these dreams. In them I will be running from military or playing hide and seek with friends or anything but still same thing just each jump gets me higher like I have less gravity than others. Its a great dream and I wish I could do it in real life.

I wrote:

I just found this very similar description in Stephen Brook’s Oxford Book of Dreams (p. 107). Brook is quoting from Leigh Hunt’s 1820 essay “Of Dreams.”

“[T]he dreamer sometimes thinks he is flying in unknown regions, sometimes skimming only a few inches above the ground, and wondering he never did it before. He will even dream that he is dreaming about it; and yet is so fully convinced of its feasibility, and so astonished at his never having hit upon so delightful a truism, that he is resolved to practise it the moment he wakes. ‘One has only,’ says he, ‘to give a little spring with one’s foot, so and — oh! it’s the easiest and most obvious thing in the world. I’ll always skim hereafter.'”

Mudmind replied:

Wow. Skimming a few inches above the ground with a little spring with one’s foot describes my experiences well. I would just consider these ordinary waking memories, if it hadn’t been for the inconsistency with the rest of my memories and ideas of how stuff usually works. 

Another, contrasting recurring dream is that I’m running to get away from something, unlike the previous dream, where it’s a joyous, casual thing. In these dreams the running is more laborious and slow, like running in water. 

As I’m writing this I realize the two gaits might represent something I’ve learned in recent years about how I work. When following my natural interest and joy I seem to have a whole lot of ‘free’ energy and attention, but when I do stuff because I think I should, or somehow motivated by fear or obligation it often requires a lot of effort and energy. 

Its like different forms of gravity that we dance with. Maybe propelling away from stuff with fear is just less effective than gravitating towards stuff with joy, love or interest. I mean, when I think about it, it seems like much of our world is shaped by attractive forces, like gravity and love. Doesn’t love just feel like a kind of gravity, but on the emotional plane?

Renita wrote:

I dreamed like this yesterday and feel the same way. That’s why I am searching. What is the meaning of this? Glad to know I am not alone.

Luoluo wrote:

I share the same experience with you all. We may have lived our past lives in some other low gravity planet, and that kind of memories passed on to this present life.

Imran wrote:

I have same experience. I concluded that my dreams are representation of my memory and my thoughts, all of them I can explain this way. But I always wonder where from this kind of dreams, why that? I mean it is only one I cant explain by my past experience. Glad to know I am not alone

Jack Dida wrote:

Hi, there. The explanation of your dreams is really, really similar to mine. I feel special in some way but I can’t explain how I know that I am different. Who can tell me more about these low-gravity dreams? Is it my past life or still-to-come life or what?

Chinto14 wrote:

Dreamed like this last night, but with a man holding me and we were in a horizontal position slowly bouncing at the earths ground like it has a slow gravity. It feels so real, and I felt love.

Scott Robbins wrote:

I have similar dreams but in mine it is almost like I am suspended, and my feet barely touch the ground, so I can hardly get any traction for forward motion. It is a very frustrating and unsatisfying feeling, very unlike the peace and excitement of the more jumping dreams of others here. I try to run, but barely get going.

Catwoman by day wrote:

I have the same experience. I keep having dreams where I take a running start and then can fly or hover a few feet from the ground. As long as I keep up momentum, I stay in the air. And I always wake up feeling like this was a natural ability. I lay in bed trying to figure out how I did it, why I feel this way, how I can do it again…. it’s been frustrating me for years. I wish I knew what it meant. It’s the only kind of dream I ever have where I wake up believing it’s as true and real as my ability to walk. Wish it was.

Fellow Dreamer wrote:

I’ve been having dreams like these for years, practically verbatim to yours, and was so glad to find this article. In some dreams I’ll be exiting a building, then bouncing miles in the air and landing softly, then repeating, but nobody around me seems to notice or care. In others, I’ll be somewhere like a library, and casually floating off the ground to reach the higher books, then propelling myself in different directions, while again, people are not reacting to it. They don’t feel like memories, but it does feel incredibly natural and real. I wake with that sensation that I can actually do it, and my dreams are trying to remind me how. These dreams occur so much that I’ve actually stood up in real life, closed my eyes and tried to concentrate as hard as possible into making myself levitate — as absolutely absurd as that sounds, all I can say is that I’m otherwise a fairly practical person, but imagine having dreams of playing piano so fluently that it felt like you really could, so much so that you began practicing piano and found you were a natural. You wouldn’t have started if you didn’t feel so confident doing it in your dreams. That’s how these dreams make me and a lot of others feel, it seems. It’s a very strange phenomenon.

Tony J. Martin wrote:

I’ve had low gravity dreams for years. At first it started with me holding onto a kite and flying hundreds of feed into the air. Now, its more like 75% less gravity, where I can easily jump 20 feet in the air, and casually glide down while doing several spins and flips. Often jumping off of buildings, this dream has always taken place in a complex I grew up in as a teenager. I have this feeling that the low gravity has something to do with love, or passion for a skill that you should be seeking more thoroughly. Good dreaming!

Jamee Novotney wrote:

I know you posted this years ago but absolutely everything you described and how you said it is exactly what I am experiencing. I found myself trying to do the jump straight soar when walking to work today and quickly remembered,Wait! That’s only in that dream “memory”. Definitely like I have done it for real and almost like it's a habit but I don't know. I couldn't explain until I read this. It's always trees and hills and a gray like sidewalk or something. This is sooo weird. Thanks for sharing.

Mateus Vieira wrote:

I’ve had quite a lot of those. In mine I can jump super high, in a very controlled manner, and slowly with very little gravity. Sometimes I look down from way above or play around hopping from wall to wall. In my case it might have to do with depersonalization, wich causes the feeling of being bodyless. Or maybe I’m trying to look at my surroundings from a distance. These dreams feel very good though.

Jordon wrote:

Yeah ! Bounce dreams !! I’m right there with you on this one and have had very much the same experience with my dreams. For me this is usually the trigger I need to notice that I’m dreaming and become much more in control, I’m often able to overcome the gravity and fly from there as well.

Refreshing to read that someone else has had the same dream with the same feelings after this sort of dream as myself.

⁂

Appendix 2: Sylvan Muldoon's typology of flying dreams

The following is taken from Sylvan Muldoon's 1929 book The Projection of the Astral Body. Muldoon was of the opinion that many, perhaps most, flying and falling dreams were triggered by the nocturnal activities of the subtle (or, to use the lingo which has become standard but which I have always found somehow grating, "astral") body, which during sleep is often slightly (and sometimes more than slightly) out of coincidence with its physical counterpart. The "dream-body" referred to in this passage is the same as the astral body.

There are several variations of the flying dream, almost as many as there are positions for the astral body to assume and movements for it to make, as it oscillates in the air, over the physical body or on the surface of the ground. Remember, "projection dreams" are almost invariably "true action" dreams. If you could control your dreams, you could control the movements of the dream-body. Of this, more later!

One variation of the flying dream is the "swimming dream," with or without motion of the legs and arms. This always occurs while the astral body is worming along, lying in a horizontal position in the air.

Another variation is that in which the dreamer is standing upright, and is moving at great speed over the surface of the earth, or along a street, etc. One is actually doing this in the dream-body, during many such dreams, i.e. moving at the intermediate speed. [Note: Muldoon has previously discussed three different speeds at which the astral body may move.] I have awakened in this dream several times, to find myself doing this in reality in the astral. Usually this dream is pleasant.

Again there is the "giant stride" dream, in which the dreamer seems to be moving over the surface of the earth, in giant strides -- very gracefully, almost gliding alone -- ludicrously, at times. This is another true-action dream. At such a time the dreamer is moving in the air in the astral body, and although there is motion of the limbs, he is being moved by the subconscious Will. Thus, every step covers a great distance, for it is not the actual step which drives the body forward.

This is akin to the steps taken by children whirling on the play-ground apparatus --  the "giant stride" -- the body travelling some distance between each step. Did you ever see a runner shown in slow-motion pictures? I know of no better example of the "giant stride" dream than one sees there: the gliding effect, the gracefulness, the apparent lack of weight, etc. -- as if the runner were sustained by the air, each step covering a great distance.

Muldoon's "giant stride" dream is, I think, identical to what I have called "slow-jumping." Here is what the playground apparatus he mentions looked like:

It's a bit surprising that, what with all the off-the-wall theories being thrown out by commenters -- past lives and living on Mars and what not -- no one thought of "astral projection" (out-of-body experiences) as a possible explanation.

The Spanish Tetragrammaton

The Tetragrammaton ("four-letter word") is the proper name of the God of the Hebrews, spelt yod-he-waw-he, and supposed never to be pronounced. Observant Jews, when reading aloud from the Bible, replace the Tetragrammaton with "my Lord," "the Name," or some similar expression. In keeping with this custom, English Bibles generally replace it with "the Lord."

How might the Tetragrammaton be transliterated in the modern Roman alphabet? "YHWH," reflecting the hypothesized ancient Hebrew pronunciation of those letters, has become conventional, but here's another approach.

Yod, the first letter of the name, is genetically related to I and J. Because yod is the 10th letter of the Hebrew alphabet, we prefer J, the 10th letter of the Roman alphabet, as the closest equivalent. He is genetically related to E, and each is the 5th letter of its respective alphabet. Waw is genetically related to five different Roman letters: F, U, V, W, and Y. But because waw is the 6th letter of the Hebrew alphabet, our preferred equivalent is F, the 6th letter of the Roman alphabet. Thus the Tetragrammaton is rendered JEFE.

Jefe, as it happens, is a word in Spanish, meaning "chief, head, leader, boss" -- astonishingly close in meaning to the conventional substitute "Lord." But, as in English, grammar demands the use of the definite article -- el Jefe, "the Chief" -- and El happens to be another of the Hebrew names for God!

In fact, Spanish Bibles generally use el Señor for the Tetragrammaton. It's a pity that such a perfect equivalent was passed up.

Cat bitten by radioactive spider

This is Geronimo, one of my home's nine or ten resident felines. I haven't the slightest clue how he managed to get up on top of this tchotchke cabinet, which is a sheer vertical face with no protruding shelves or anything to use as stepping stones. I think he forgot how he did it, too, since I had to use a stepladder to get him back down.

Captivity and power: Man, he never had a chance

Content warning: In this post I discuss (among other things) what I consider to be an artistically very effective use of what those parents' guides would call an "f-word derivative" in a punk rock music video. If that's not the sort of thing you want to expose yourself to, skip this one.

The captivity and power of the devil

Here are some of the very natural-sounding phrases that come up if you search the Bible for the string "and power": strength and power, force and power, spirit and power, authority and power, faith and power, honour and power, dominion and power, glory and power.

And here's a line from the Book of Mormon which I've been brooding over recently.

[Men] are free to choose liberty and eternal life, through the great Mediator of all men, or to choose captivity and death, according to the captivity and power of the devil; for he seeketh that all men might be miserable like unto himself (2 Nephi 2:27; emphasis added).

Captivity and power. How does that work? Isn't captivity a lack of power?

In the past I always thought that, while the syntax may be a bit infelicitous, the meaning is clear enough. The "power of the devil" refers to the power which the devil himself possesses, while the "captivity of the devil" indicates other people's being in captivity to the devil. Only a tedious grammar pedant (something no one would ever accuse me of being!) would read it any other way.

⁂

After giving it some thought, though, I think that there are in fact good reasons, above and beyond over-literalism, for reading this passage as stating that both the devil and those who follow him are in the condition described by the seemingly oxymoronic conjunction "captivity and power."

The logic is simple enough. The devil tempts people to be evil and sinful, and is himself evil and sinful; therefore, whatever condition the devil himself is in, those who fall into his snare will tend toward that same condition. If Being Evil has given the devil great power, we can assume that people can also acquire great power by Being Evil. Likewise, if sin leads to captivity, we can assume that the devil, as the sinner par excellence, is also in a state of captivity. In other words, it doesn't make sense that the very same course of action should lead to power when pursued by the devil but only to captivity when pursued by anyone else.

⁂

Against this line of reasoning, there is the possibility that the arch-tempter is not also the arch-sinner -- that, like any reasonably competent pusher, the devil knows better than to get high on his own supply -- that he suckers people into committing sins that he himself isn't stupid enough to commit, thus bringing them into captivity while maintaining his own freedom.

There clearly has to be some truth to this. The devil can't possibly be the exemplar of every vice in the same way that God is arguably the exemplar of every virtue. A slothful devil couldn't be bothered to actually tempt people, for example, while a cowardly one would never have defied God in the first place. One of the litany of names applied to the devil in Revelation 12:9 is "the great," and I think we must concede that there is a sense in which he lives up to that title. If the devil were a mere nogoodnik, a congeries of vices, a contemptible sin-ridden fleabag of a spirit, he would be of no account, and there would be no need for us to so much as take notice of his existence. Fallen angels do not become vermin but dragons, roaring lions seeking whom they may devour.

But for all that, there is also a sense in which the devil is contemptible. As Lehi puts it in the Book of Mormon passage quoted above, "he seeketh that all men might be miserable like unto himself." I think in the end we must insist on the literal aptness of the phrase captivity and power.

⁂

To try to get a handle on this, I tried to think of other instances of "captivity and power" occurring together, and the first example that came to mind was the beast of burden. A draft ox is an immensely powerful animal, a ton and a half of pure muscle, but it nevertheless lives in captivity. Or, considering political power rather than muscular strength, we might think of a tyrant, reigning with blood and horror, hated by his people and obeyed out of fear alone. How much freedom does such a man, living under the constant threat of assassination or revolution, really have? What choice does he have to bar himself up in a virtual prison, surrounded by guards? What choice does he have but to rule with conspicuous brutality, lest any show of weakness embolden his enemies? Or, coming closer to our Satanic theme, we might consider anyone who has made a Faustian bargain of the kind reportedly offered to Jesus: "All these things will I give thee, if thou wilt fall down and worship me" (Matthew 4:9). "The captivity and power of the devil": The devil offers power, but only on condition of captivity.

What the ox, the tyrant, and the Faustian soul-seller have in common is that, while they have the ability to do things that others cannot do (power), their ability to decide which things to do (liberty) is severely curtailed. Marlowe's Faustus at first wants the devil to reveal to him the secrets of the universe -- only to find out that, sorry, that's not one of the things that sold souls are permitted to pursue. In the end, he is reduced to frittering away his Satanic powers on trifles and degradation -- playing practical jokes, trying to sleep with Helen of Troy, that kind of thing. Captivity and power.

⁂

But if the "captivity and power of the devil" simply refers to the fact that the devil offers power with strings attached, power that can only be used in certain ways and for certain ends -- well, doesn't the "liberty and eternal life" offered by God also come with restrictions? Even more restrictions than the devil's offer, in fact, since there are many more ways of being evil than of being good, just as there are many more ways of dying than of staying alive. In the same vein, Tolstoy famously observed (in words that I dare not attempt to translate, for fear of angering the ghost of Nabokov, but will paraphrase) that happy families are all alike, while each unhappy family is unhappy in its own way. The devil's disciples ought logically, then, to have considerably more elbow room than God's -- but the problem is that people don't want to die, or to live in unhappy families, so the "freedom" promised by those options is meaningless.

It may be readily observed that, judging by what economists would call "revealed preferences," most people obviously don't really want to be saints, either -- but at least it is possible to want to be a saint, to want good and nothing but good, and a great many of us at least want to want to be saints. We can imagine gradually purifying our hearts and our desires until "we have no more disposition to do evil, but to do good continually" (Mosiah 5:2). The reverse -- wanting evil and nothing but evil -- is not really possible and cannot be coherently imagined. No one, not even the devil himself, can love sin as such completely and unreservedly; all we can do is love certain aspects of sin and try not to think too much about the others. The devil's power is captivity because, in the last analysis, it is only the power to obtain what no one could ever really want.

To close with another Book of Mormon quote, Samuel the Lamanite told the wicked Nephites, "your destruction is made sure; yea, for ye have sought all the days of your lives for that which ye could not obtain" -- namely "ye have sought for happiness in doing iniquity" (Helaman 13:38). That's the bottom line. Those who follow the devil are seeking what they simply cannot, by the nature of things, ever obtain. It is in that sense that the devil is the "father of lies," and that his power -- the power he offers, and the power he himself possesses -- is really only captivity.

Applying Kevin McCall's logic to squares and other non-centered figurate numbers

Note: this post uses special terminology and notation introduced in the last post. You should read that first in order to understand what follows.

⁂

Kevin McCall's proof of the RPS theorem for reduced triangular numbers is based on the following observation:

The series of triangular numbers is generated by starting with 0, then adding 1, then adding 2, then 3, and so on through the succession of natural numbers. Due to the fact that k - n ≡ -n (mod k), one you've added numbers up to a certain point, you start doing the modular equivalent of subtracting those same numbers in reverse order, creating a palindrome.

Thus, if we consider the sequence of triangular numbers reduced modulo 10:

• 0
• +1
• +2
• +3
• +4
• +5
• +6 ≡ -4 (mod 10)
• +7 ≡ -3 (mod 10)
• +8 ≡ -2 (mod 10)
• +9 ≡ -1 (mod 10)
• +10 ≡ 0 (mod 10)
• +11 ≡ +1 (mod 10)
• +12 ≡ +2 (mod 10)
• +13 ≡ +3 (mod 10)
• +14 ≡ +4 (mod 10)
• +15 ≡ -5 (mod 10)
• +16 ≡ -4 (mod 10)
• +17 ≡ -3 (mod 10)
• +18 ≡ -2 (mod 10)
• +19 ≡ -1 (mod 10)
• +20 ≡ +0 (mod 10)
• etc.

At the end of this 20-step cycle, we are back where we started, with a number that is congruent to 0 (mod 10), and the cycle starts again.

Note that we have to go through two cycles of adding and subtracting the numbers because +5 ≡ -5 (mod 10). We count it as +5 the first time around and -5 the second time, so that it cancels out. If the modulus is odd, only one cycle is necessary.

⁂

Now let's consider the sequence of square numbers. We generate this series by starting with 0, then adding 1, then adding 3, then 5, and so on through the succession of odd natural numbers. This results in an RPS for much the same reason that the triangular series does: adding successive numbers is the modular equivalent of adding up to a certain point and then subtracting the same numbers in reverse order. Here's how it works modulo 10.

• 0
• +1
• +3
• +5
• +7 ≡ -3 (mod 10)
• +9 ≡ -1 (mod 10)
• +11 ≡ +1 (mod 10)
• +13 ≡ +3 (mod 10)
• +15 ≡ -5 (mod 10)
• +17 ≡ -3 (mod 10)
• +19 ≡ -1 (mod 10)
• etc.

As with the triangular numbers, we have to go through two cycles so that the two 5s cancel each other out. Notice that, unlike the triangular numbers, this sequence never returns to adding 0 (mod 10). That is why the triangular numbers reduced mod 10 = RPS (0136051865), while the squares are RPS (0)1496(5) -- the extra parentheses indicating that there are not two 5s in a row in the middle of the cycle, nor two 0s in a row at the end of one cycle and the beginning of the next.

⁂

Moving on to the pentagonal numbers, they are generated by starting with 0, then adding 1, then 4, then 7, then 10, and so on -- every third natural number. The pattern should be obvious by now: The sequence of n-gonal numbers is generated by starting with 0 and adding, successively, every (n - 2)th natural number, beginning with 1. Here's the generation of the pentagonal sequence modulo 10.

• 0
• +1
• +4
• +7
• +10 ≡ +0 (mod 10)
• +13 ≡ -7 (mod 10)
• +16 ≡ -4 (mod 10)
• +19 ≡ -1 (mod 10)
• +22 ≡ +2 (mod 10)
• +25 ≡ +5 (mod 10)
• +28 ≡ +8 (mod 10)
• +31 ≡ +1 (mod 10)
• +34 ≡ +4 (mod 10)
• +37 ≡ +7 (mod 10)
• +40 ≡ +0 (mod 10)
• +43 ≡ -7 (mod 10)
• +46 ≡ -4 (mod 10)
• +49 ≡ -1 (mod 10)
• +52 ≡ -8 (mod 10)
• +55 ≡ -5 (mod 10)
• +58 ≡ -2 (mod 10)
• +61 ≡ +1 (mod 10)
• etc.

The cycle here is more involved because we are adding every third natural number, which means that after we reach the -1 which cancels out the original +1, we do not go on to either - or +1 and the cycle does not yet begin anew.

⁂

Skipping hexagonal numbers for the time being, let's jump straight to what we're really interested in: the heptagonal numbers -- the only figurate numbers yet examined which do not yield an RPS when reduced modulo 10. In keeping with the pattern, the heptagonal numbers are generated by adding, successively, every 5th natural number -- yielding, modulo 10:

• 0
• +1
• +6
• +11 ≡ +1 (mod 10)
• +16 ≡ +6 (mod 10)
• +21 ≡ +1 (mod 10)
• +26 ≡ +6 (mod 10)
• +31 ≡ +1 (mod 10)
• +36 ≡ +6 (mod 10)
• etc.

As can be seen, we just continue adding 1 and 6 (or subtracting 9 and 4) forever. This gives us a repeating cycle with a period of 20 -- because 10(1 + 6) ≡ 0 (mod 10) -- but no palindrome is created because we never reach -1/+9 or -6/+4.

⁂

My tentative conclusion is that the sequence of (non-centered) n-gonal numbers reduced modulo k will always be an RPS if n - 2 and k are relatively prime. When that condition holds, adding every (n - 2)th natural number in succession will (I think) mean in hitting all possible modular values, resulting in an RPS. The triangular numbers are a special case because for that sequence n - 2 = 1, which is coprime to every integer.

Where n - 2 and k are not coprime, an RPS may result, but not necessarily. I need to think a little more about what exactly determines which such sequences are RPSs and which are not.

What species was Bitter Green?

Is the title character in the Gordon Lightfoot song "Bitter Green" (1968) a dog, a horse, or a woman?

Upon the bitter green she walked the hills above the town
Echo to her footsteps as soft as eider down

This certainly sounds like a horse. A grazing animal would naturally spend its time "upon the . . . green," and only the footsteps of a large hoofed animal would echo through the hills. A woman's footsteps might echo on pavement, but not on a green. It's hard to know what to make of the last phrase, since "footsteps as soft as eiderdown" surely means silent footsteps, the kind that don't echo. Anyway, on balance these lines support the horse theory.

Waiting for her master to kiss away her tears
Waiting through the years

"Master" normally refers to the human owner of a domestic animal, but it might be used poetically of a woman's husband or lover. Tears of sorrow, on the other hand, are shed only by human beings, but again could be ascribed poetically to other species. Waiting through the years for one's master to return is a behavior most stereotypically associated with dogs, but horses and women have also been known to do it.

Bitter Green they called her
Walking in the sun
Loving everyone that she met

"Loving everyone that she met" sounds like an animal, and specifically like a dog. Applied to a woman, the phrase is rather scandalous and also seems inconsistent with the idea of a Penelope patiently waiting for her true love to return. "Bitter Green" itself also seems like a name that would be more naturally given to an animal than to a person. A woman would be known by that rather strange nickname only if no one knew who she was or what her real name was, which is inconsistent with "loving everyone that she met."

Bitter Green they called her
Waiting in the sun
Waiting for someone to take her home

This also sounds like an animal. A woman whose husband or lover had disappeared would still have a home and would naturally wait there (perhaps by the window, wearing a face that she keeps in a jar by the door) rather than in the sun.

Some say he was a sailor who died away at sea
Some say he was a prisoner who never was set free
Lost upon the ocean he died there in the mist
Dreaming of her kiss

Horses don't kiss people, but dogs and women do.

But now the bitter green is gone, the hills have turned to rust

Is this just a seasonal change? But Bitter Green waited "through the years."

There comes a weary stranger, his tears fall in the dust
Kneeling by the churchyard in the autumn mist
Dreaming of a kiss

This strongly supports the woman theory. The most natural interpretation is that the long-awaited "master" finally returns, but too late, and kneels in tears at Bitter Green's grave. It seems unlikely that a dog or horse would have been buried in a churchyard, especially in her owner's absence. (Against this, note that this line is "dreaming of a kiss" -- not "her kiss" as in the chorus. Perhaps the wife whose grave the stranger is visiting is distinct from Bitter Green.)

⁂

Another question that arises is, why "Bitter Green"? How did that particular phrase come into Lightfoot's mind? To me it suggests the bitter greens of the Passover feast, and "waiting for someone to take her home" carries echoes of "next year in Jerusalem" -- but I think it unlikely that Lightfoot, who is not Jewish, consciously intended any such allusion.

In one of the sci-fi stories I wrote as a very young child, the astronaut protagonist had, among other items of spacefaring equipment, a "space shovel" which he used for digging on the surface of distant planets. I had no very clear idea of how a space shovel might differ from a common-or-garden shovel, but the phrase "space shovel" just sounded right, and it seemed that an astronaut ought to have one. It was not until years later that it dawned on me that "space shovel" sounded an awful lot like the then-common phrase "space shuttle," and that it was almost certainly this unconscious echo that made me think the former phrase "sounded right." I think some similar unconscious association was likely behind Gordon Lightfoot's choice of the phrase "Bitter Green."

Are all reduced sequences of figurate numbers repeating palindromes?

Time for another mathematical interlude.

⁂

Preliminaries: Terminology and notation

A palindrome is any series of elements that is the same forwards and backwards. Each palindrome thus consists of two parts, which we shall call the head and the tail. The tail consists of the same series of elements as the head, but in reverse order. For example, in the palindromic word “noon,” the string “no” is the head, and “on” is the tail. In “noon,” the head and tail are entirely separate, but in a palindrome with an odd number of elements, the end of the head will overlap with the beginning of the tail. For example, the head of the palindromic word “level” is “lev,” and the tail is “vel”; a single “v” does double duty as the last element of the head and the first element of the tail.

No special notation is required to write a simple palindrome such as “noon” or “level,” but we are concerned in this post with repeating palindromic series (RPSs). If a palindrome consists of a head followed by a tail (possibly overlapping), an RPS is a head followed by a tail, then the head again, then the tail again, and so on to infinity. In the notation we will be using here, an RPS is represented by "RPS" followed by its head enclosed in parens (round brackets), thus:

• RPS (no) = noonnoonnoonnoonnoon...

If the end of the head overlaps with the beginning of the tail, an additional open-paren is placed before the first element of the tail, thus:

• RPS (le(v) = levellevellevellevellevel...

In an RPS, unlike a simple palindrome, overlap at the other end is also possible. For example, the word “grammar” is not itself a palindrome, but “grammar” endlessly repeated is an RPS. The letter “g” is both the beginning of the head and the end of the tail. This sort of overlap is indicated by placing a close-paren after the last element of the tail, thus:

• RPS (g)ram) = grammargrammargrammar...

It is possible to have overlap at both ends, as in this example.

• RPS (v)oo(d) = voodoovoodoovoodoo...

Overlap need not be limited to a single element; it can be a series of elements, provided that series is itself a palindrome. For example, consider the RPS created by endlessly repeating the word “sestet.”

• RPS (ses)t(e) = sestetsestetsestetsestet...

I should also mention that, much like a repeating decimal, an RPS has a beginning but not an end. As with a decimal like 0.16666666..., there may be a non-repeating segment at the beginning, before the RPS proper starts. Our notation can deal with this by putting this non-repeating segment before the first paren, as in this example.

• RPS n(eve)(r) = neverevereverevereverever...

One final note about the notation: If each element in the RPS can be represented by a single character (a letter, a one-digit number, etc.), it can be written as in the examples above, without commas or spaces. If the elements of an RPS are words, multidigit numbers, etc., the elements should be separated by commas and spaces.

⁂

RPSs in the sequence of triangular numbers

Several posts on this blog have dealt with the fact that, for any modulus k, the sequence of triangular numbers reduced modulo k will be an RPS. Two different proofs of this have been given (here and here). The pattern is easiest to see when k = 10, since (in the decimal system) any number reduced modulo 10 is equal to the final digit of that number.

The first several triangular numbers are: 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666...

If we reduce that sequence modulo 10 (by replacing each number in the sequence with its final digit), we get: 0, 1, 3, 6, 0, 5, 1, 8, 6, 5, 5, 6, 8, 1, 5, 0, 6, 3, 1, 0, 0, 1, 3, 6, 0, 5, 1, 8, 6, 5, 5, 6, 8, 1, 5, 0, 6...

This reduced sequence is RPS (0136051865). Any other modulus will also yield an RPS.

⁂

Square numbers

Only some three months after proving the RPS theorem for triangular numbers did I notice that the sequence of square numbers shows a similar pattern. Below are the square numbers from 0² to 50². Start at the upper left, follow the zigzag down to the bottom, and then come back up the zigzag on the right.

Numbers in the same column have the same last digit (i.e., are congruent modulo 10). Numbers in the same row have the same last two digits (i.e., are congruent modulo 100).

Square numbers reduced modulo 10 = RPS (0)1496(5).

Square numbers reduced modulo 100 = RPS (0), 1, 4, 9, 16, 25, 36, 49, 64, 81, 0, 21, 44, 69, 96, 25, 56, 89, 24, 61, 0, 41, 84, 29, 76, (25).

I haven't checked if other moduli also yield RPSs, but, based on my experience with triangular numbers, and on the general principle that there is nothing mathematically special about powers of 10, I feel quite certain that they do.

⁂

Other non-centered figurate numbers

Pentagonal numbers: 0, 1, 5, 12, 22, 35, 51, 70, 92, 117, 145, 176, 210, 247, 287, 330, 376, 425, 477, 532, 590, 651, 715, 782, 852, 925, 1001, 1080, 1162, 1247, 1335, 1426, 1520, 1617, 1717, 1820, 1926, 2035, 2147, 2262, 2380, 2501, 2625, 2752, 2882, 3015, 3151, 3290, 3432, 3577, 3725, 3876, 4030, 4187...

Pentagonal numbers reduced modulo 10 = RPS (01522510)275607)

Hexagonal numbers: 0, 1, 6, 15, 28, 45, 66, 91, 120, 153, 190, 231, 276, 325, 378, 435, 496, 561, 630, 703, 780, 861, 946, 1035, 1128, 1225, 1326, 1431, 1540, 1653, 1770, 1891, 2016, 2145, 2278, 2415, 2556, 2701, 2850, 3003, 3160, 3321, 3486, 3655, 3828, 4005, 4186, 4371, 4560

Hexagonal numbers reduced modulo 10 = RPS (016585610(3)

Heptagonal numbers: 0, 1, 7, 18, 34, 55, 81, 112, 148, 189, 235, 286, 342, 403, 469, 540, 616, 697, 783, 874, 970, 1071, 1177, 1288, 1404, 1525, 1651, 1782, 1918, 2059, 2205, 2356, 2512, 2673, 2839, 3010, 3186, 3367, 3553, 3744, 3940, 4141, 4347, 4558, 4774, 4995, 5221, 5452, 5688

Heptagonal numbers reduced modulo 10 = 01784512895623906734 endlessly repeated -- not a palindrome!

Octagonal numbers: 0, 1, 8, 21, 40, 65, 96, 133, 176, 225, 280, 341, 408, 481, 560, 645, 736, 833, 936, 1045, 1160, 1281, 1408, 1541, 1680, 1825, 1976, 2133, 2296, 2465, 2640, 2821, 3008, 3201, 3400, 3605, 3816, 4033, 4256, 4485, 4720, 4961, 5208, 5461

Octagonal numbers reduced modulo 10 = RPS (01810)56(3)

Enneagonal numbers: 0, 1, 9, 24, 46, 75, 111, 154, 204, 261, 325, 396, 474, 559, 651, 750, 856, 969, 1089, 1216, 1350, 1491, 1639, 1794, 1956, 2125, 2301, 2484, 2674, 2871, 3075, 3286, 3504, 3729, 3961, 4200, 4446, 4699, 4959, 5226, 5500, 5781, 6069, 6364

Enneagonal numbers reduced modulo 10 = RPS (0194651441564910)69)

Decagonal numbers: 0, 1, 10, 27, 52, 85, 126, 175, 232, 297, 370, 451, 540, 637, 742, 855, 976, 1105, 1242, 1387, 1540, 1701, 1870, 2047, 2232, 2425, 2626, 2835, 3052, 3277, 3510, 3751, 4000, 4257, 4522, 4795, 5076, 5365, 5662, 5967, 6280, 6601, 6930, 7267, 7612, 7965, 8326

Decagonal numbers reduced modulo 10 = RPS (010)725(6)

This is so bizarre that I almost think I must have made some mistake, but I'm pretty sure I haven't. Inductively, it looks like virtually all non-centered figurate numbers reduce to RPSs, but the heptagonal numbers are an exception! Why? Are there other exceptions?

⁂

Centered figurate numbers

Centered triangular numbers: 1, 4, 10, 19, 31, 46, 64, 85, 109, 136, 166, 199, 235, 274, 316, 361, 409, 460, 514, 571, 631, 694, 760, 829, 901, 976, 1054, 1135, 1219, 1306, 1396, 1489, 1585, 1684, 1786, 1891, 1999, 2110, 2224, 2341, 2461, 2584, 2710, 2839, 2971, 3106, 3244, 3385, 3529

Centered triangular numbers reduced modulo 10 = RPS (1409164596)

Centered square numbers: 1, 5, 13, 25, 41, 61, 85, 113, 145, 181, 221, 265, 313, 365, 421, 481, 545, 613, 685, 761, 841, 925, 1013, 1105, 1201, 1301, 1405, 1513, 1625, 1741, 1861, 1985, 2113, 2245, 2381, 2521, 2665, 2813, 2965, 3121, 3281, 3445, 3613, 3785, 3961, 4141, 4325, 4513

Centered square numbers reduced modulo 10 = RPS (15(3)

Centered pentagonal numbers: 1, 6, 16, 31, 51, 76, 106, 141, 181, 226, 276, 331, 391, 456, 526, 601, 681, 766, 856, 951, 1051, 1156, 1266, 1381, 1501, 1626, 1756, 1891, 2031, 2176, 2326, 2481, 2641, 2806, 2976, 3151, 3331, 3516, 3706, 3901, 4101, 4306, 4516, 4731, 4951, 5176, 5406

Centered pentagonal numbers reduced modulo 10 = RPS (16)

Hex numbers: 1, 7, 19, 37, 61, 91, 127, 169, 217, 271, 331, 397, 469, 547, 631, 721, 817, 919, 1027, 1141, 1261, 1387, 1519, 1657, 1801, 1951, 2107, 2269, 2437, 2611, 2791, 2977, 3169, 3367, 3571, 3781, 3997, 4219, 4447, 4681, 4921, 5167, 5419, 5677, 5941, 6211, 6487

Hex numbers reduced modulo 10 = RPS (17(9)

Centered heptagonal numbers: 1, 8, 22, 43, 71, 106, 148, 197, 253, 316, 386, 463, 547, 638, 736, 841, 953, 1072, 1198, 1331, 1471, 1618, 1772, 1933, 2101, 2276, 2458, 2647, 2843, 3046, 3256, 3473, 3697, 3928, 4166, 4411, 4663, 4922, 5188, 5461, 5741, 6028, 6322, 6623, 6931, 7246

Centered heptagonal numbers reduced modulo 10 = RPS (1823168736)

Centered octagonal numbers (i.e., odd squares): 1, 9, 25, 49, 81, 121, 169, 225, 289, 361, 441, 529, 625, 729, 841, 961, 1089, 1225, 1369, 1521, 1681, 1849, 2025, 2209, 2401, 2601, 2809, 3025, 3249, 3481, 3721, 3969, 4225, 4489, 4761, 5041, 5329, 5625, 5929, 6241, 6561, 6889, 7225, 7569

Centered octagonal numbers reduced modulo 10 = RPS (19(5)

Centered enneagonal numbers (i.e., every third triangular number): 1, 10, 28, 55, 91, 136, 190, 253, 325, 406, 496, 595, 703, 820, 946, 1081, 1225, 1378, 1540, 1711, 1891, 2080, 2278, 2485, 2701, 2926, 3160, 3403, 3655, 3916, 4186, 4465, 4753, 5050, 5356, 5671, 5995, 6328, 6670, 7021, 7381, 7750, 8128, 8515, 8911, 9316

Centered enneagonal numbers reduced modulo 10 = RPS (1085160356)

Centered decagonal numbers: 1, 11, 31, 61, 101, 151, 211, 281, 361, 451, 551, 661, 781, 911, 1051, 1201, 1361, 1531, 1711, 1901, 2101, 2311, 2531, 2761, 3001, 3251, 3511, 3781, 4061, 4351, 4651, 4961, 5281, 5611, 5951, 6301, 6661, 7031, 7411, 7801, 8201, 8611, 9031, 9461, 9901

Centered decagonal numbers reduced modulo 10 = RPS (1)

Centered decagonal numbers reduced modulo 100 = RPS (1, 11, 31, 61, 1, 51, 11, 81, 61, 51)

Star numbers (i.e., centered dodecagonal numbers): 1, 13, 37, 73, 121, 181, 253, 337, 433, 541, 661, 793, 937, 1093, 1261, 1441, 1633, 1837, 2053, 2281, 2521, 2773, 3037, 3313, 3601, 3901, 4213, 4537, 4873, 5221, 5581, 5953, 6337, 6733, 7141, 7561, 7993, 8437, 8893, 9361, 9841, 10333, 10837

Star numbers reduced modulo 10 = RPS (13(7)

It certainly looks as if all such sequences reduce to RPSs, but the unexpected exception of the (non-centered) heptagonal numbers makes me hesitant to jump to that conclusion.

⁂

So the new mission (paging Kevin McCall!) is to come up with a general proof that almost all figurate number sequences reduce to RPSs -- a proof that makes it clear what the exceptions are and why. There's obviously a pattern here that goes beyond the triangular numbers, and it should be possible to express that pattern mathematically.

Hatelove

George Orwell's Newspeak was in many ways prophetic of modern politically correct language, but he made two important errors. First, Orwell's Newspeak used crime in compound words (crimethink, crimestop, etc.) to indicate anything that was beyond the pale, whereas Nowspeak has found hate to be more effective for that purpose. Second, Orwell defined goodsex as "sexual intercourse only for procreation" and sexcrime as "sexual intercourse for pleasure" -- implying, to put it mildly, values somewhat different from those currently endorsed by real-world totalitarianism. So, in the spirit of updating and correcting Orwell, I offer this addition to the PC lexicon:

hatelove: biologically natural relations between a man and a woman within the bounds of marriage

⁂

It's a felicitous enough coinage, I think you'll agree, capturing something of the spirit of blackwhite ("the ability to believe that black is white, to know that black is white, and to forget that one ever believed the contrary") -- but, you might ask, what is actually so hateful about hatelove?

Glad you asked.

1. Being disproportionately practiced by privileged white people, hatelove is inherently racist and elitist. Furthermore, its procreative aspect (see 3 below) means that it leads to the production of more people of the hatelovers' own race and class, something only a white supremacist would want to do. In essence, hatelove boils down to a deliberate act of genocide directed against the Other.

2. Hatelovers may use the "consenting adults" excuse to argue that their predilections are their own business, but in fact each and every hatelove relationship contributes to the cancer of toxic heteronormativity. Heteronormativity is (as Studies Have Shown) one of the leading causes of suicide, so in a way hatelove is a kind of murder.

3. Worst of all, hatelove is known to produce fetuses -- parasitic and often dangerous growths which, conveniently enough, never affect white cisgender men. This makes hatelove a form of misogynistic and transphobic violence. Moreover, each fetus thus engendered will, if (foolishly and irresponsibly) allowed to develop to maturity, go on to release as much as 30 tons of deadly carbon dioxide gas into the atmosphere, thus directly contributing to the destruction of the planet.

If that's not hate, what is?

⁂

This is, of course, satire, but we live in a world where satire dates very quickly, as it never takes long for reality to catch up with it. The SPLC already classifies pro-marriage organizations as hategroups (I recommend writing such terms as single words to emphasize their Newspeakiness), and I venture to predict that it won't be very long before we start hearing rhetoric very close to that used in this post.

Go tell that long-tongued liar

I suppose it will come as no surprise to hear that I generally find Marilyn Manson (Brian Warner) repulsive and unlistenable -- but, credit where due, his is hands down the best version of this old classic.

For comparison, here's how the same song was rendered by Elvis:

And by Johnny Cash:

Cash did a very good job with it, too -- and of course Manson is heavily dependent on his version (even including the line "John, go do my will"; I guess "Brian" just didn't have the same ring). Still, I have to admit that in this particular instance the Man in Black was outdone by the Man in Black Lipstick. Basically, people like Manson exist for the purpose of singing this kind of song.

It's natural to repeat things 2^n - 1 times.

Fifteen! Fifteen no's . . . ha ha ha!

I try to cover all the bases here.

⁂

No.

No no no.

No no no no no no no.

No no no no no no no no no no no no no no no.

No no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no.

⁂

I find that I can continue this series more-or-less indefinitely: first 1 "no," then 3, then 7, 15, 31, 63, and so on -- each number in the series being twice the previous number, plus one. For me, these are all natural numbers of times to repeat things. I just naturally stop at 2ⁿ - 1, without consciously keeping count. (In fact, I only discovered the pattern by recording myself and then going back and counting the no's.)

Try it yourself (preferably not in a public place!). Is this an idiosyncracy of my own, or have I just discovered Tychonievich's First Law of How Many Times People Repeat Things?

Thinking about prayer

A recent post by S. K. Orr (well, "recent" by my slow-thinking standards, anyway) has had the effect of eliciting some firm intuitions about prayer and getting me thinking about how best to understand them. The post is quite short and well worth reading in its entirety, but here are the essential bits.

For the past couple of years, I have daily passed a man on a bicycle on the way to work. . . . And for at least a year now, I have said a prayer for the bicyclist every time I pass him. As I near him, I lift one hand and usually whisper something like “Protect him, Father,” or “Bless him in his day, Father.” . . .

Sometimes in these quiet hours, I wonder what the bicyclist would say if he knew a stranger says a prayer for him every morning when briefly passing by. And I wonder if any stranger has ever prayed for me for no other reason than seeing me and feeling the nudge to do so. I like to think that someone, at some point, has done so. It is not for me to say whether or not I have been spared harm on a particular day because some unseen watcher lifted a hand and whispered some holy words on my behalf.

I am not a prayerful person, but this post convinced me that I need to be. Mr. Orr's daily prayers for the bicyclist are undeniably good and important; it remains only to understand why and how -- and, of course, to "go and do thou likewise."

The post touched on a lot of "problematic" issues regarding prayer and confirmed that, problematic or not, they are real and must be dealt with. Here I will lay out some of those problems, and the conclusions I have come to after dwelling on them for a few months.

⁂

God sometimes does, because he has been asked, things that he would not have done if he had not been asked.

Orr speculates that he may "have been spared harm on a particular day because some unseen watcher" prayed for him, and implies that his own prayers may have caused the bicyclist to be spared particular harms that would have befallen him otherwise -- that, despite God's goodness and his love for the bicyclist, he would not have protected him to the same degree had he not been specifically asked to do so.

I think we pretty much have to believe this. It hardly makes sense to ask God for specific things unless we believe that our asking affects the probability of those things happening -- unless we believe that we can sometimes change God's mind and persuade him to do something he would not otherwise have done.

But it seems strange that a loving God who is willing and able to help and protect us, and who "knoweth what things ye have need of before ye ask him," would make his help and protection conditional on being asked -- and asked by anybody, apparently, even a perfect stranger.

If God would help me only if I asked him to do so, that would be understandable in terms of his respecting my freedom and giving me ultimate control over my own life. One thinks of the famous line from the Apocalypse: "Behold, I stand at the door, and knock: if any man hear my voice, and open the door, I will come in to him" (Revelation 3:20) -- which presumably means that God will become active in a given person's life only if that person invites him to do so. If, on the other hand, God may also intervene in my life because someone else invited him to do so -- which is what the efficacy of petitionary prayer for a third party implies -- then it's as if he stands at the door, knocks, and waits for anyone, even a random passerby on the street, to open the door. If he doesn't need my permission to intervene in my life, why does he need anyone else's? If he is willing to come in without being invited in by the homeowner, why not without being invited by anyone at all?

(To be clear, I assume that God does often intervene without being asked, but we are here considering those cases in which petitionary prayer has made a difference -- cases in which God intervenes because he was asked and would not have done so otherwise.)

⁂

Even if we want the same things as yesterday, we still need to ask for them again today.

After hearing "Bless him this day, Father" every day for a couple of years, God surely must have figured out that Mr. Orr wants him to bless the cyclist every day, making further prayers of that sort unnecessary. But somehow, saying "Bless him this day" every day -- rather than saying "Bless him every day" once -- is the right way to do it. In most areas, repetitiveness tends to make things meaningless, but in the case of prayer -- despite the warnings against "vain repetitions" in some of the Gospels -- repetitiveness lies very close to its heart.

And just as it is right to pray for a particular day, it is right to pray for a particular person -- "Protect him, Father," not "Protect everyone who needs protecting."

⁂

God sometimes influences us to ask him for particular things.

"I wonder if any stranger has ever prayed for me for no other reason than seeing me and feeling the nudge to do so." The one doing the nudging in such a case would presumably be God himself -- which is pretty strange, if you think about it.

"Hey, that person could use some help. Why don't you ask me to help him?"

"Okay. Would you please help him?"

"Sure!"

Wouldn't that be a very strange conversation if it took place between two human beings? Why do we accept it as a normal way of interacting with God? It really makes sense only if the first person cannot act unless the second person asks him to. I hope it will be understood that no blasphemy is intended when I say that it reminds me of nothing so much as certain versions of the legend of Faust, where the devil can only do what Faust commands and is therefore always trying to persuade him to command particular things. In a Faustian context, that makes sense, but this is God we're talking about.

⁂

Prayer is expanded agency, serving as training for theosis.

It occurs to me that most of the philosophical problems associated with efficacious petitionary prayer are the same problems that are associated with ordinary human agency.

Why would God intervene in a person's life because I asked him to? If intervening is the best thing to do, God ought to do it whether I ask him to or not; if it is not the best thing to do, he ought not to do it even if asked. But we might with equal justice ask, Why would God allow me myself to intervene in anyone else's life? -- or, for that matter, to make decisions about my own life? If God knows best, why does he allow anything of importance to be decided by anyone else? Suppose I see a homeless man and, instead of asking God to bless him, I just give him a twenty. Will the effect of that gift ultimately be good or bad? Only God knows, and therefore (so the logic goes) God ought to be the one to decide, and ought accordingly either to force me to give or prevent me from doing so. But God respects our agency, or free will, and cares more about preserving that than he does about seeing to it that the Best Possible Thing is done.

In the gift of petitionary prayer, God has given us what we might think of as a sort of expanded agency, subject to "parental controls." If he granted each and every one of us unlimited magical power, so that we could literally do whatever we wanted, the result would obviously be disastrous, so he grants us direct and absolute control only over a few things -- but he also gives us the potential ability, through the medium of prayer, to "do" anything that God himself can do. We are far too ignorant, immature, and irresponsible to be given free rein with this kind of power, but we are encouraged to try out hand at it, as it were -- to ponder how we think the divine power might best be used, to put these proposals to God, and -- sometimes -- to see those proposals carried out.

By encouraging us to pray and ask him to do things, God is quite literally encouraging us to play God -- in the same sense in which little children play, and are encouraged to play, at being adults. To engage in petitionary prayer is to put oneself in God's position, decide what you think he ought to do, and then say to God, in effect, "If I were you, I'd so such-and-such." How jaw-droppingly presumptuous is that? And yet it's something God actively encourages, even commands, us to do. One thinks of the story (in Genesis 18) of Abraham, negotiating with God over the destruction of the cities of the plain: "That be far from thee to do after this manner . . . Shall not the Judge of all the earth do right?" Abraham seems to have been well aware that he was rushing in where angels fear to tread -- "Behold now, I have taken upon me to speak unto the Lord, which am but dust and ashes" -- but he proceeded nonetheless. And he was called the Friend of God.

All of this makes sense if we assume that the primary purpose of prayer -- as of everything else in this life -- is educational. And what we are being educated for is theosis, becoming Gods. That is why God expects us, through prayer, to take an interest and an active role in how the divine powers are used and even, as ridiculous as it may seem, to give him our requests and recommendations. Probably the vast majority of those recommendations will be rejected, or implemented only in part, but that's all part of the learning process. "The servant knoweth not what his lord doeth -- but I have called you friends" (John 15:15).

Keep a-movin', Dan

The woman saith unto him, Sir, give me this water, that I thirst not, neither come hither to draw.

-- John 4:15

Give me my scallop shell of quiet,
My staff of faith to walk upon,
My scrip of joy, immortal diet,
My bottle of salvation,
    My gown of glory, hope's true gage;
    And thus I'll take my pilgrimage. 

Blood must be my body's balmer;
No other balm will there be given.
Whilst my soul, like quiet palmer,
Travelleth towards the land of heaven. 

Over the silver mountains
Where spring the nectar fountains:
    There will I kiss
    The bowl of bliss,
And drink mine everlasting fill
    Upon every milken hill.
My soul will be a-dry before;
But after, it will thirst no more. 

-- Sir Walter Raleigh, The Passionate Man's Pilgrimage

Matthew's Messiah is the most "Davidic"; John's, the most "Samaritan"

As discussed elsewhere on this blog, Jews and Samaritans had different understandings of what sort of person the Messiah was supposed to be. The entire Messianic tradition of the Samaritans is derived from the 18th chapter of Deuteronomy. Their Messiah is a prophet like Moses -- the only prophet besides Moses, in fact -- who will tell us all things. The Jews, on the other hand, added to this the Messianic writings of the prophets, in which David has largely eclipsed Moses as the Messiah's most important precursor. If the Samaritan Messiah is essentially a prophet like Moses, his Jewish counterpart is primarily a king like David. The two visions are not mutually exclusive -- both peoples expected the Messiah to be both a prophet and a king -- but they represent very marked differences in emphasis.

Corresponding differences in emphasis are found in the Four Gospels. A writer with a more "Samaritan" idea of the Messiah might be expected to mention Moses more often, and to give the Samaritans themselves a more prominent role in the Gospel story. A writer whose views were more traditionally "Jewish," on the other hand, would mention David more often and speak more of kings and kingdoms.

I searched each of the Gospels for the strings "Moses," "Samari-," "David," and "king-." (Why not also "Jew" and "prophet" to contrast with "Samaritan" and "king"? Well, naturally most of Jesus' story takes place among the Jews, so of course every Gospel will mention them a lot. "Prophet" is also not useful for distinguishing between the two Messianic visions, since the Samaritans see the Messiah as being primarily a prophet, while the Jewish Messiah is based on the writings of the prophets.) Here are the results.

To control for the varying lengths of the Gospels, the numbers indicate
what percentage of verses in each Gospel contain the target string.

The pattern is clear, and confirms the impression I already had. The Fourth Gospel ("of John") emphasizes Moses and the Samaritans, while downplaying David and Jesus' role as king; Matthew shows the opposite pattern; and Mark and Luke are intermediate.

I should mention that it is already my opinion, for reasons unrelated to this issue, that the Fourth is the most trustworthy of the Gospels and that Matthew is the least so.