Adam Davidson on Immigration

Illustration by Andrew Rae, source New York Times

Adam Davidson has a very nice New York Times Magazine article, "Debunking the Myth of the Job-Stealing Immigrant", in favor of "radically open borders."

Here's how a top professional journalist and writer puts together the central argument, so much more cleanly than I can do it:

So why don’t we open up?

The chief logical mistake we make is something called the Lump of Labor Fallacy: the erroneous notion that there is only so much work to be done and that no one can get a job without taking one from someone else. It’s an understandable assumption. After all, with other types of market transactions, when the supply goes up, the price falls. If there were suddenly a whole lot more oranges, we’d expect the price of oranges to fall or the number of oranges that went uneaten to surge.

But immigrants aren’t oranges. It might seem intuitive that when there is an increase in the supply of workers, the ones who were here already will make less money or lose their jobs. Immigrants don’t just increase the supply of labor, though; they simultaneously increase demand for it, using the wages they earn to rent apartments, eat food, get haircuts, buy cellphones. That means there are more jobs building apartments, selling food, giving haircuts and dispatching the trucks that move those phones. Immigrants increase the size of the overall population, which means they increase the size of the economy. Logically, if immigrants were “stealing” jobs, so would every young person leaving school and entering the job market; countries should become poorer as they get larger. In reality, of course, the opposite happens.

Most anti-immigration arguments I hear are variations on the Lump of Labor Fallacy. That immigrant has a job. If he didn’t have that job, somebody else, somebody born here, would have it. This argument is wrong, or at least wildly oversimplified. But it feels so correct, so logical. And it’s not just people like my grandfather making that argument. Our government policy is rooted in it.

The single greatest bit of evidence disproving the Lump of Labor idea comes from research about the Mariel boatlift, a mass migration in 1980 that brought more than 125,000 Cubans to the United States. According to David Card, an economist at the University of California, Berkeley, roughly 45,000 of them were of working age and moved to Miami; in four months, the city’s labor supply increased by 7 percent. Card found that for people already working in Miami, this sudden influx had no measurable impact on wages or employment. His paper was the most important of a series of revolutionary studies that transformed how economists think about immigration. Before, standard economic models held that immigrants cause long-term benefits, but at the cost of short-term pain in the form of lower wages and greater unemployment for natives. But most economists now believe that Card’s findings were correct: Immigrants bring long-term benefits at no measurable short-term cost.

Needless to say the "lump of labor" fallacy pervades politics, policy, and popular discussion on more than immigration. But Adam doesn't bother with the 100 other fallacies.

A beautiful stylistic choice: Adam's antagonist is ... his grandfather. That lets Adam have an anonymous, sympathetic antagonist, who is slowly changing his mind in Adam's favor. Adam doesn't have to pick on a particular individual or set of individuals with complex opinions; he doesn't resort to the horrible vague antagonist, "some think;" and he avoids the usual partisan politics and vilification of so much political blogging and editorial writing.

Students: notice concrete not abstract words. "Using the wages they earn to rent apartments, eat food, get haircuts, buy cellphones."  Not "Using earned income to demand goods and services."

From the Next State: Galileo and Sir Isaac Newton

Among the descriptions of transcendental communication in William Usborne Moore's "record of investigation into spiritistic phenomena" Glimpses of the Next State (1911) are seances when communicators from the ascended realm announced themselves as Galileo (1564-1642) and Sir Isaac Newton (1642-1727). 

In the early 20th Century, disembodied voices were heard at seances or 'sittings' conducted by Spiritualist mediums known as 'trumpet mediums' (or 'independent voice'/'direct voice' mediums) as the voices manifesting in their presence were heard to emanate from horn-like devices called a 'trumpet.'  Two mediums residing in Detroit, Michigan were Mr. A. W. Kaiser, thirty-three-years-old, and Mrs. Henrietta 'Etta' Wriedt, whom Moore described as "forty nine years of age, a slightly built, delicate woman, much subject to bronchitis and neuritis" yet "in her prime as a psychic."  Moore reported instances when the Direct Voice phenomena occurred without trumpets during sittings, as in the case of Leslie Flint later in the century.

Hearing historically famous names speak at a seance became a matter of contemplation for Moore, who first heard 'Sir Isaac Newton' at a seance conducted by Kaiser.  Another sitter during the occasion was an acquaintance of Moore named Henry Clay Hodges, whom Moore described as "the veteran spiritualist" and "editor of The Stellar Ray, also Two Thousand Years of Celestial Life (by "Clytina") and Science and Key of Life (by Alvidas)."  The following is from Moore's description of a seance on February 4, 1909 (12 noon to 1 p.m.).  The transcripts are obviously imperfect as tape recorders were not yet commonly used by the public.

The important features in the sitting were the visits of spirits purporting to be Sir Isaac Newton and Dr. Richard Hodgson.  The former assumed an old, feeble voice.  He said to me: "Sir Isaac Newton; I am pleased to be able to come.  Since I passed over I have been studying the laws of gravitation, light, and colours; and I desire to impart this knowledge to the world I have left.  It could be done if the proper circle could be arranged and conditions were good, in the same way as was done when the spirit who has just been here [Clytina] communicated her messages to your friend.  The forces are becoming used up, and I cannot stop long now.  Good-bye."

Q.: "One moment, Sir Isaac.  Can you tell me, in a few words, what is gravitation?"

A.: "Gravitation is a force generated by the rotation of the globes through ether."

Q.: "May I take it that it would be covered by the term 'electro-motive force,' and that the ether is, so to speak, the armature?"

A.: "That would cover the matter very nearly.  Good-bye."

Moore commented about this incident:

(I cannot, of course, assert that my visitor was Sir Isaac Newton; in fact, it appears, on the face of it, extremely improbable; but I can that the psychic was incapable of inventing this novel theory of gravitation.  I had heard of it from one man in England, who is now working upon this hypothesis.  As far as I know, no American has initiated any theory of the kind, and only one man in this country.  This man is sanguine of success, but, as yet, has not yet published a single line regarding the matter; with the exception of his immediate family, I question if there are ten people who are aware of the nature of his studies.  Personally, I do not see how he can be correct, for scientists have informed us over and over again that the ether of space is frictionless.  If it were not so, it would appear certain that the globes would soon cease to rotate.)

It was, no doubt, to the presence of Mr. Hodges that the visit of the spirit purporting to be Sir Isaac Newton was due.  He has been engaged for years attempting to wrest the secrets of nature from the Greeks of past ages, through the mediumship of Mr. Cole.

After Sir Isaac left, a voice came through the trumpet, "Doctor Richard Hodgson."  I said: "I am delighted to see you; I have often wished to do so."  A.: "Yes, I have tried to impress you on three occasions."

During Moore's third trip to the United States with the purpose of investigating phenomena associated with Spiritualism (or 'spiritism'), he stayed with Mrs. Wriedt and her husband as a guest for twenty days, occupying a room near the seance room.  On Sunday, January 15, 1911 from 2 to 4:15 pm Moore and Dr. John, a physician from Ontario, engaged in what Moore called "a good séance" with Mrs. Wriedt.  Galileo was the eighth speaker to be heard.  Here is Moore's description of the conversation.

Galileo now announced himself plainly, and spoke loudly through the trumpet in English.  He said: "I invented the telescope, and was persecuted for my beliefs."  He spoke bitterly of his persecution, and declared: "They burnt me at the stake."  I said: "Oh, come, not quite so bad as that."  He replied: "Well, they wanted to."  He mentioned Marconi, and said: "He is not making perfect one thing at one time, but is branching off into experiments."  (I have no idea to what he was alluding.)

Q.: "The fact that the world is round was well known, was it not, to Plato, Pythagoras, and Hypatia?"

A.: "Plato knew it, but was afraid to speak out.  We do not know Hypatia by that name; we call her . . . . . ."(Name blurred; I could not catch it.)

Q.: "I mean Theon's daughter."

A.: "Yes, I know; Theon's daughter."

Q.: (by Dr. John): "How did you get the idea that the earth moved round the sun?" 

(Galileo then went into a long description of a vision he had in his room, the language he heard during the vision, and a scroll that was exhibited for him to read.  In doing this he used both Greek and Latin.  I was unable to follow, and I do not think Dr. John was more fortunate, for he spoke quickly and not very concisely.)

Q.: "Is Mars inhabited?"

A.: "Mars is inhabited, and will some day come into contact with the earth by means of electricity."

Q.: "Do the etheric waves in wireless telegraphy pass over or through the earth, mountains, and seas?"

A.: "Over.  They are met above by a layer of etheric resistance, and deflected down again."  (This is the best interpretation I can give of what he said.)

Q.: "Is there a planet beyond Neptune?"

A.: "No."

Galileo was followed by Iola's father, with whom I had a talk about family matters, very convincing as to identity, but of no interest to the public.

On January 24, 1911 with medium Mr. A. W. Kaiser there was interaction with 'Sir Isaac Newton.'  Moore wrote:

I repeated our conversation of February 4, 1909, which he confirmed.  I said: "We are always in a difficulty about personations."  He replied: "There are such things as personations, but they never come to earnest minded investigators."

Q.: Do you know if the 'Cleopatra' and 'Hypatia' who come to me are personators or not?"

A.: I cannot tell unless I investigate; but, as they come to you, I cannot believe they are."

Q.: Is there a planet beyond Neptune?"

A.: "There is; and astronomers on your side are, I believe, now looking for it."

Q.: "Galileo came to me the other day, and said there was not.  Do the etheric waves in wireless telegraphy pass through or over the earth and mountains?"

A.: "As ether is everywhere, they pass through everything; the vibrations of etheric waves for wireless telegraphy are analogous to X-rays, which, as you know, can pass through solid obstacles.  There are differences of opinion on our side, as on yours.  Many men of science are working away here, and making experiments on the earth plane.  They impress mortals."

Q.: "There is a friend of mine in England, living in Wiltshire, who has worked long on the gravitation theory you gave me last time we met."

A.: "Yes, I know; I impressed him."

Q.: I mean Admiral F."

A.: "Yes.  I have been working long here on gravitation and anti-gravitation."

Q.: "I doubt if my friend realizes he is being impressed."

A.: "Perhaps not; but that does not matter to us as long as the impression is effectual."

Then other communicators were heard, including Kaiser's 'control' Dr. Jenkins, who is quoted: "We are trying to make conditions perfect for the Jonson [medium] materialisations . . ."  At a seance the following day, Moore asked Dr, Jenkins about personating spirits —

He said: "They do not come to earnest-minded investigators.  Your development here will lift you speedily in our life."  He hoped to bring Sir Isaac Newton tomorrow.

On January 26, Moore was the only sitter with Kaiser when Sir Isaac Newton was again heard.

Then [was heard] Sir Isaac Newton.  I asked him to be so good as to tell me what he had meant on a former visit about anti-gravitation.  He replied: "We are investigating the forces which can be generated to oppose gravity.  There are such forces.  For instance, supposing you get a musical note of equal vibrations to those of gravity, you have a force sufficient to oppose gravity.  If you get a musical note the vibrations of which exceed those of gravity, you have a force anti-gravitational."  At my request he repeated the words "musical note" twice.

He continued: "Construct a bell and strike it.  The 'sound' vibrations from the bell meet the normal sound vibrations and overcome them.  I am impressing your friend on this subject."

(I wrote my notes in the next room immediately the sitting was over, and I conclude that both Kaiser and I were to some extent impressed still by the spirit we had heard talking so clearly a few minutes before.  I am sure that I took in accurately the words of the message.  Kaiser agreed.  We thought he might mean: "There are musical vibrations which, when set in motion, enable objects near to overcome the force of gravity."  But I cannot offer any explanation.  I affirm that the words I have repeated were used, and there I must leave it.)

The final quoted comment—answering Moore's question "Am I right in supposing that psychic demonstrations are performed more easily in this neighborhood, around the great lakes of America, than elsewhere?"—is "Yes; this is on account of the electrical conditions."  A following statement from Dr. Jenkins may help clarify the meaning:

"We shall do little this morning, as we are collecting spiritual forces to help you in your investigation in the near future.  I will visit you in England; the whole spiritual world will assist you in your work, I know, and will help the beautiful spirit who attends you.  Good-bye."

On the next day (January 27), during a seance when Moore was alone with Mrs. Wriedt, the conversations with Galileo and Newton were mentioned.  The interlude began with Mrs. Wriedt stating, "I see the name of Stone."  Then a voice was heard: "My name is Stone."  The comments were made, "I only know of one 'Stone.  He was Astronomer Royal at the Cape of Good Hope."  The voice then is quoted:

"I am he, and I am very glad to be here this morning.  I thought I would come on the strength of our old acquaintance.  Mr. Gladstone [another communicator] told me of you; he is much interested in these phenomena."

Q.: "Is G. right in supposing there are stars [of the first magnitude] which have no parallax?"

A.: "He is."

Q.: "I have lately spoken with Sir Isaac Newton, and he said that gravitation could be opposed by the vibrations of a musical note . . . . . .

A.: "Ha!  Ha!  Newton would find that pretty hard to explain himself."

Q.: "Is there a planet beyond Neptune?"

A.: "Yes, but it is uninhabited."

(I mentioned Galileo, and Stone said: "Ah, he is a well-known spirit here.")

Q.: "Do you know anything of Mars?"

A.: "Mars will some day be connected with the earth by electricity.  The inhabitants are small, short and dark; they have organisms to withstand the rarefied atmosphere and intense heat.  I am still working on astronomical problems.  Good-bye."

On February 14, Moore was again sitting alone with Mrs. Wriedt and asked her guide 'Dr. Sharp': "Why should a distinguished historical character such as Galileo come to me?"  Dr. Sharp addressed one of Moore's recurring concerns about seance room communicators possibly impersonating famous figures and is quoted: "No personations could come to you.  If Galileo felt he could help those that come after him in the same work, he would do so."

In The Voices (1913), the book that is the sequel to Glimpses of the Next State, seance descriptions are presented by Moore and other book contributors about Direct Voice séances with Mrs. Wriedt.  Moore's friend Colonel E. R. Johnson mentioned that during a 1913 seance he asked many questions of communicating friends and relatives.  The reported facts from them included commentary about planets: "The sphere called 'Mercury' is a very hot place, and we do not speak of it . . . Mars (the planet) is inhabited by a short, dark people, resembling the people here.  They have no houses, only huts."

After reading these various passages about Mars from Moore's books, I conducted an Internet search for some of the pertinent key words.  Some of the details in NASA images that I found do, in fact, lead the observer to consider the possibility of life on Mars (rather than life existing in another dimension or 'sphere').  The following photographic images provide examples.  (Perhaps I should mention my general lack of confidence in NASA data being unaltered and unredacted.  After all, the organization is a government agency/hierarchy.  This makes simple honesty among staff members a matter dependent upon protocol with people in leadership positions who are susceptible to assuming cover-ups and disinformation to be aspects of 'status quo' regulation.  Such tactics would encompass photograph alterations.)



This is a brightness-enhanced version of a NASA photo.  Source: abovetopsecret.com
NASA original photo: "Spirit :: Panoramic Camera :: Sol 728" 



Source: UFO Sightings Hotspot Blog (anonymous blogger)
(left) NASA original photo:
http://photojournal.jpl.nasa.gov/jpeg/PIA10214.jpg (detail is found in lower left of source photo)
(right) NASA original photo: http://mars.jpl.nasa.gov/msl-raw-images/msss/00569/mcam/0569ML2307004000E1_DXXX.jpg

 

 

Galileo is among the renowned names found in transcripts of discourses obtained by table-tapping seances where Victor Hugo was a participant. between 1853 and 1855.   The two Galileo discourses are among the numerous English translations presented in Victor Hugo's Conversations with the Spirit World: A Literary Genius's Hidden Life (2008) by John Chambers.  The first discourse was communicated on Sunday, December 10, 1854, beginning at 9 p.m.  The source is Oeuvres Complètes of Victor Hugo, volume 9, 1450-51.  Chambers reminded: "Galileo Galilei was the Italian scientist (then called a 'natural philosopher') who formulated the basic laws of falling bodies, which he verified by careful measurements.  Galileo constructed a telescope to study lunar craters and discovered four moons revolving around Jupiter.  Espousing the Copernican cause, he spent the last nine years of his life under house arrest for refusing to tell the Inquisition that the earth did not move."  After the name of Galileo was presented to those seated around the table, the statement given was:

I've come to respond to Victor Hugo's objection about the scientific inexactitude of the cosmology of the tables.  Let him formulate that objection.

Hugo is quoted as having asked about the names of the actual constellations, not as seen from Earth but what were the real constellations from a celestial language?  Here are some excerpts from the discourse answering Hugo's question.

My answer is in two parts.  Firstly: if the table had to speak celestial language, not human language, you wouldn't understand a word.  In celestial language, man is not called man, nor beast beast, nor plant plant, nor pebble pebble, nor earth earth, nor air air, nor water water, nor fire fire.  Heaven is not called heaven, star is not called star, constellation is not called constellation and God is not called God.

God speaking is God language, God language is God mouth, God mouth is God body, God body is God man, God man is God beast, God beast is God plant, God plant is God pebble.  Can you imagine it?  God pebble!  He who is not even God star!

Angels are not Professors of Divine Language, substitute lecturers in the Faculty of Infinity . . .

No; everything is nameless, everything is sunlight and unknowing, everything is sunbeam and mask, everything is sun and roving. 

The dictionary of infinity is filled with the punctuation of stars, and what would you say, puny man, if, to speak to you in the language that you want, this little table, instead of syllables, words and sentences, suddenly hurled millions of stars in your ear, launched Jupiter, Aldebaran, and Saturn in your face, and spread out on your page the immense ink blot of the starry night while scribbling down corrections with furious comets?

Chambers reported that the Galileo communicator promised to return on Sunday, one week later.  On that night (December 17), the sitting began at 9:45 p.m.  "Galileo announced his presence.  Hugo asked him if he would complete his answer of last time by explaining the nature of the real constellations as distinct from the unreal constellations fabricated by mankind."  The reply is translated to English as —

That is your other mistake.  Listen: I've talked about how the tables are forced to use your language to make themselves understood by you.  Now, your language is merely a set of conventions; your language is a smoke screen issuing from your mouth and covering the stars over with clouds.

Does that mean you humans are wrong about everything?  No!  In feeling out the heavens, your hands sometimes touch the radiant knobs of the doorways of the divine.

Here are further excerpts from the discourse.

You say to me: I want the real heaven and not an imaginary heaven; I want the real firmament, real constellations, real suns; I want the total immensity of God, without a break, without a gap; I want the abyss without emptiness; bring me infinity; bring me mystery; I demand a map to Jesus's tomb, the itinerary of the resurrection; may they show me the incommensurable, sound the unsoundable out for me, open the seals of heaven for me.  I want to go through the promises of the stars with a search warrant.  Human constellations, let's see your papers.  Big Dipper, identify yourself.  Capricorn, you're lying.  Aquarius, you're lying; you're a suspicious character.  Firmament, you're under suspicion, I want to search your pockets, no more subterfuges.  Lock all the doors; let no star escape!  Handcuff God; I've got to question Him!  And now, dark night, come before the court.  And now, radiant day, answer.  And now, accused suns, rise in your seats.  I am president of the nighttime court of the assizes; I have a jury of ghosts; I declare the court to be in session.  Silence in the gallery of the stars!

Let the witness Galileo enter!

I, Galileo, declare that I don't know the contents of infinity; I don't know where it begins and where it ends; I don't know what comes before, after, in the middle, to the right, to the left, east, west, south or north of infinity; I don't know its inside or outside; I see heavenly bodies, heavenly bodies, heavenly bodies; I see stars, stars, stars; I see constellations, constellations, constellations; I see sunbeams mixed with cloud-bedecked splendors and great blazings-forth of flame, bedazzlement lost in contemplation, contemplation plunged into bedazzlement; I'm caught up in the prodigious turning of the golden-hubbed wheel of heaven.  Where is it going?  I have no idea.

Victor Hugo was not satisfied with the response.  The following day, Hugo, his wife, and their son Charles requested the communicators to be more specific.  Then, as Chambers wrote: "Not Galileo, but the Shadow of the Sepulcher, made his presence known."  A new discourse commenced —

I've come to bring you, not one of the keys to heaven, which must remain closed to human science, but one of the keys to God the whole power of whom is to fling open the gates of the loftiest progress to which the human spirit is capable . . . .

 

A New Structure for U. S. Federal Debt

A new paper by that title, here.

I propose a new structure for U. S. Federal debt. All debt should be perpetual, paying coupons forever with no principal payment. The debt should be composed of the following:

1. Fixed-value, floating-rate debt: Short-term debt has a fixed value of $1.00, and pays a floating rate. It is electronically transferable, and sold in arbitrary denominations. Such debt looks to an investor like a money-market fund, or reserves at the Fed. 
2. Nominal perpetuities: This debt pays a coupon of $1 per bond, forever. 
3. Indexed perpetuities: This debt pays a coupon of $1 times the current consumer price index (CPI).
4. Tax free: Debt should be sold in a version that is free of all income, estate, capital gains, and other taxes. Ideally, all debt should be tax free. 
5. Variable coupon: Some if not all long-term debt should allow the government to vary the coupon rate without triggering legal default. 
6. Swaps: The Treasury should manage the maturity structure of the debt, and the interest rate and inflation exposure of the Federal budget, by transacting in simple swaps among these securities.

Of these, I think the first is the most important. Think of it as Treasury Electronic Money, or reserves for all. Why?

Economists have long dreamed of interest-paying money. It fulfills Milton Friedman’s (1969) optimal quantity of money without deflation. Paper money is free to produce, so the economy should be satiated in liquidity...

Our economy invented inside interest-paying electronic money in the form of money market funds, overnight repurchase agreements, and short-term commercial paper, and found it useful. But that money failed, suffering a run in the 2008 financial crisis. Treasury-provided interest-paying electronic money is immune from conventional runs. Money market funds 100% backed by fixed-value Treasury debt cannot suffer a run...

By analogy, in the 19th century, the Treasury provided coins. Banks issued notes. Notes were convenient, being a lot lighter than coins. But there were repeated runs and crises involving bank notes. The U.S. government issued paper money, which might inflate, but cannot suffer conventional default or a run. That money eventually drove out private banknotes, and that source of financial crises was permanently ended. (Crises involving demand deposits did not end, but here the U.S. tried a different policy response, deposit insurance and risk regulation. It has not worked as well.)

In the 21st century, the Treasury has exactly the same natural monopoly in providing default-free and run-free electronically-transferable interest-paying money to private parties. It should do so.

If the Treasury offers what are essentially interest-paying reserves, then we don't have to argue about the size of the Fed's balance sheet, ON RRP, etc.

Nominal perpetuities are a nice way to condense the hundreds of outstanding issues into one, which should increase their liquidity a good deal.

Indexed perpetuities are a cleaner way to implement today's tips.

The tax free analysis is maybe the most interesting. I put together a little tax clientele model with some interesting results. No, issuing tax free debt is not a present to rich people. By attracting the high tax clientele back to Treasury debt, we should see lower net (after tax) interest costs to the Treasury.

I have a nice implementation of Treasury swaps too, that might open them up a lot.

Comments welcome. It's a bit long because it responds to a previous round of comments, so if you're bubbling over with what's wrong with the proposals, do check that I haven't already answered your comment.

Jumps and diffusions

I learned an interesting continuous time trick recently. The context is a note, "The fragile benefits of endowment destruction" that I wrote with John Campbell, about how to extend our habit model to jumps in consumption. The point here is more interesting than that particular context.

Suppose one time series \(x\), which follows a diffusion, drives another \(y\). In the simplest example, \[dx_t = \sigma dz_t \] \[ dy_t = y_t dx_t. \] In our example, the second equation describes how habits \(y\) respond to consumption \(x\). The same kind of structure might describe how invested wealth \(y\) responds to asset prices \(x\), or how option prices \(y\) respond to stock prices \(x\).

Now, suppose we want to extend the model to handle jumps in \(x\), \[dx_t = \sigma dz_t + dJ_t.\] What do we do about the second equation? \(y_t\) now can jump too. On the right hand side of the second equation, should we use the left limit, the right limit, or something in between?

The usual answer is to use the left limit. We generalize the model to jumps this way: \[dx_t = \sigma dz_t+ dJ_t \] \[ dy_t = y_{t_-} dx_t = y_{t_-} \sigma dz_t + y_{t_-}dJ_t \] where \(y_{t_{-}}\) denotes the left limit.

That approach has some weird properties however. Suppose \(y_{t_-}=1\), and \(dJ_t=1\). Then \(y_t\) jumps to \(y_t=2\). But suppose there are two jumps of size 1/2, one at time \(t\) and one at time \(t+\varepsilon\). Now \(y\) jumps up to 1.5 after the first jump, and then jumps another \(1.5 \times 0.5 = 0.75\), ending up at \(y_{t+\varepsilon} =2.25\). Two half jumps have a different response than one full jump.

Suppose instead we extend the original model to jumps by taking the jump limit of a continuous process. Imagine that we observe realizations of \(\{dz_t\}\) that get closer and closer to a jump in \(dx_t\), and let's find what happens to \(y_t\). The general solution to the first set of equations is \[ y_{t+\Delta} = y_t e^{(x_{t+\Delta}-x_t - \frac{1}{2}\sigma^2\Delta)}\] so, in the limit \(\Delta \rightarrow 0\) that \(x_t\) takes a jump of size \(dJ_t\), the jump-limit of a continuous movement is \[ dy_{t} \equiv y_t -y_{t_-} = y_{t_-}(e^{dx_{t}}-1) = y_{t_-}\sigma dz_t + y_{t_-}e^{dJ_t}\] rather than \[ dy_t = y_{t_-} dx_t = y_{t_-} \sigma dz_t + y_{t_-}dJ_t \] So, the left-limit method produced a response to a jump that was different from the response to a continuous process arbitrarily close to a jump. For example, the left-limit approach can produce a negative \(y_t\), but this method, like the diffusion process, cannot fall below zero. This method also produces a response to two half jumps that is the same as the response to a full jump.

As you can see, the difference is whether the state variable \(y_t\) gets to change during the jump. In the left-limit approach, the same \(y_{t_-}\) gets applied to the whole jump. In the continuous-limit version, \(y_t\) implicitly gets to move while the jump in \(x_t\) is moving.

A nonlinear function of a jump is a little novel, but there's nothing wrong with it, and it exists in the continuous time literature. We don't see it that often, because when you're only studying one series it's easier to just change the distribution of the jump process instead. This question occurs when you can see both series x and y and you want to model the relationship between them.

Which is right?

Which extension to jumps is correct? Both are mathematically correct. There is nothing wrong with writing down a model in which the response to a jump is different from the response to continuous movements arbitrarily close to jumps. The answer depends on the economic situation.

For example, consider models with bankruptcy constraints. Agents who can continuously adjust their investments may always avoid bankruptcy in a diffusion setting. If we extend such a model to jumps with the continuous limit approach, implicitly preserving the investor's ability to trade as fast as asset prices change even in the jump limit, we will preserve bankruptcy avoidance in face of a jump in prices. However, if we model portfolio adjustment to jumps with the left-limit generalization, agents may be forced in to bankruptcy for price jumps.

Sometimes, one introduces jumps precisely to model a situation in which prices can move faster than agents can adjust their portfolios, so agents may be forced to bankruptcy. Then the left-limit generalization is correct. But if one wants to extend a model to jumps for other reasons, while avoiding bankruptcy, negative consumption, negative marginal utility (consumption below zero or below habits), violations of budget constraints, feasibility conditions, borrowing constraints, and so forth, then one should choose a generalization in which the jump gives the same result as the continuous limit.

Similarly, when extending option pricing models to jumps, one may want to model the jump in such a way that investors cannot adjust portfolios fast enough. Then the left-limit extension is appropriate, and investors must hold the jump risk. But one may wish to accommodate jumps in asset prices to better fit asset price dynamics while maintaining investor's ability to dynamically hedge. Then the nonlinear extension is appropriate, maintaining the equivalence between jumps and the limiting diffusion.

A little more general treatment

A little more generally, suppose \[ dx_t = g dt + \sigma dz_t \] \[dy_t = \mu(y_t) dt + \lambda(y_t)dx_t.\] We want to add \(dJ_t\) to the first equation. The left-limit approach is \[dy_t = \mu(y_{t_-}) dt + \lambda(y_{t_-})dx_t \] If there is a jump \(dJ_t\), \(y\) moves by an amount \[\frac{1}{\lambda(y_{t_-})}dy_t \equiv \frac{1}{\lambda(y_{t_-})}(y_t - y_{t_-}) = dx_t .\] The limit of a continuous movement solves the differential equation \[\int_{y_{t_-}}^{y_t} \frac{1}{\lambda(\xi)}d\xi = dx_t\] Again, you see the crucial difference, whether the state variable gets to move "during" the jump. We can write this as a differential, by writing the solution to this last differential equation as \[y_t-y_{t_-}=f(x_t-x_{t_-};y_{t_-})\] and then \[dy_t = \mu(y_{t_-}) dt + f(dx_t;y_{t_-})=\mu(y_{t_-}) dt + \lambda(y_{t_-})\sigma dz_t+f(dJ_t;y_{t_-})\]

So, you don't have to extend the model to jumps with the left-limit approach, and you don't have to swallow the idea that a jump has a different response than an arbitrarily close continuous-sample-path movement. The last equation shows you how to modify the model to include jumps in a way that preserves the property that the jump has the same effect as its continuous limit.

The point

Why a blog post on this? I asked a few continuous-time gurus, and none of them had seen this issue before. If someone knows where this has all been worked out with proper is dotted and ts crossed, I would like to know and cite it properly. (I would think the literature on option pricing with jumps had done it, but I couldn't find a reference.) Or perhaps it hasn't been done and someone wants to do it. I'm not good enough at the technical aspects of continuous time to write this with the right precision and generality.

And it's a cool trick that may be useful to someone outside of the narrow context that we had for it.

Update: 

Perhaps the right application is stock prices and option prices. When stock prices jump, someone must have studied the case that option prices move by the same amount the Black-Scholes formula gives for the same size stock price movement. Does anyone have a citation to that case?

Hospital Supply

In my view, health care supply restrictions are more important than the insurance or demand features that dominate public discussion. If you are spending your own money, yes, you shop for a good deal. But spending your own money in the face of restricted supply is like hailing a cab to LaGuardia at 5 o'clock on a rainy pre-Uber Friday afternoon. We need to free up innovative, disruptive health-care supply. Let the Southwest Airlines, Walmarts, Amazons and Apples in.

But where are the supply restrictions? Alas it's not as simple as the NY taxi commission. Supply restrictions are spread all over Federal, state and local law and regulation, and usually hidden.

So, I was interested to discover an interesting supply restriction in this editorial in the Wall Street Journal last week.

Last year the Daughters of Charity Health System sought to sell its six insolvent hospitals in California to Prime for $843 million including debt and pension liabilities. State law requires the AG [California Attorney General Kamala Harris] to approve nonprofit hospital acquisitions. Ms. Harris attached several poison pills at the urging of the SEIU [Service Employees International Union], which forced Prime last week to withdraw its offer.

State law requires the AG [Attorney General] to approve nonprofit hospital acquisitions. How could this go wrong?

Since 2010 operating losses at Daughters hospitals have tripled to $146 million. High pay scales, inflexible work rules and rich pension benefits have swelled labor costs to 74% of revenues compared to the nationwide average of 58% at nonprofit systems.... 

... Of six bidders, only Prime agreed to assume the $300 million liability for worker pensions. Prime also scored high on 10 of Daughters’s 11 bidding criteria including financial wherewithal and historical service quality. 

Prime’s problem was the SEIU’s  opposition owing to the company’s rejection of a so-called neutrality agreement, which would facilitate unionization at all of its hospitals. Only four of Prime’s 15 hospitals in California are unionized. Since 2009 the SEIU has run a public campaign against Prime, leveling accusations of Medicare fraud and unchecked sepsis. 

Ms. Harris has taken up the union cause. In 2011 the AG vetoed Prime’s acquisition of the bankrupt Victor Valley Community Hospital as “not in the public interest” though a report produced for her own office concluded that Prime’s “capital investment over the next five years should lead to substantial improvement to facilities, infrastructure, and certain services at the Hospital.”

Now you may say, how nice. The Attorney General is stalwartly backing the union cause, trying to raise wages and employment for struggling "middle class" Americans. Except, it's the same people who pay the higher health-care costs and suffer worse service.

Regulation from the top is supposed to "bend down the cost curve" in medicine. But true cost reductions, efficiency improvements,  and quality improvements are painful. Ask United's pilots union, Walmart's competitors, or Kodak's employees.

The tone of the Journal's editorial suggests a morality play. I think not. I can't imagine any regulator, attorney general, HHS secretary, or politician, given the power to approve or disapprove hospital acquisitions, doing so in a way that truly lowers costs and improves quality following the only path we know that actually works, allowing disruptive competition. You only cut costs by, well, cutting costs. And disruptive competitors only enter if they have the right to do so, not the discretionary approval of any politician or political appointee.

Update in response to comments: "After the ACA" has a long list of supply impediments. I'm trying to learn about additional ones.

The Bangs Sisters

In the seventh chapter of Glimpses of the Next State (1911), Vice-Admiral W. Usborne Moore described witnessing in Chicago the "precipitation" of letters and paintings in the presence of the Bangs Sisters.  He had received a testimonial letter about their astonishing mediumship from "a gentleman of considerable position and influence in Canada"; however, others made assumptions about them due to disbelief.  Moore wrote:

On the way up from New York I had heard a great deal of evil about the Bangs Sisters; and I had also seen five of the pictures done, as their owners told me, in their presence, within three feet of them, by invisible agency, and through the mediumship of these women, whose only participation in the production was that they held the canvases.  I wished to make a thorough test of both letters and pictures.

This is an example of a portrait 'precipitated' in the presence of the Spiritualist mediums known as the Bangs Sisters. 

The Bangs Sisters: May (born 1853) and Elizabeth ('Lizzie' 1859-1922)

 

 

During his first sitting on January 17, 1909, May Bangs used two slates, between which Moore placed a sealed letter he had brought.   The letter was written to his guide Iola and enclosed with it were four blank sheets of paper from his hotel for a reply.  Other items used during the session were rubber bands, a small pot of ink and a piece of 'bristol-board.'  At May's instruction, he wrote the name to whom the letter was addressed on a piece of paper and put it on top of the slates without May being able to see what he wrote.  May then began to see clairvoyantly and described the form of a young lady whom he recognized as his guide Iola accompanied by four other people whom Moore surmised to be family members. 

May then recited the exact questions from the letter and said "Is this the name?" while handing him, from the pad she held, a slip of paper that had written on it "the Christian and surname of Iola when in earth life."  After forty-five minutes, three taps heard from the slates indicated that the reply was finished.  "I took off the bristol-board and found my piece of paper gone.  When I opened the slates I found the paper inside by the letter.  The latter was slit open from the top, and four pages of reply were found inside . . . The letter of reply contained private messages which I am unable to make public.  It was signed correctly, and answered nearly all my questions."

On the following day, he asked for a picture (painting) to be precipitated of his guide "as she is now in spirit life."  He observed and described the preparations for the session that occurred between 11am and 12:30pm.  "Two thin canvases stretched on wooden frames and covered with thin paper were placed face to face and held up in the window.  The blind was drawn to the top of the canvases, and curtains were hung up in my presence on either side."  He noted that the light coming through the two semi-transparent canvases was sufficient for taking notes and seeing everything that occurred. 

May Bangs sat on my right side, facing me, and pinching together with her right hand one side of the canvases; Lizzie Bangs on my left side facing me, and pinching together the other side of the canvases with her left hand.  I faced the middle of the canvas, my nose being between two feet and two feet six inches from them.  We had to wait some time.  After a few minutes the canvas assumed various hues, rosy, blue and brown; it would become dark and light independently of the sun being clouded or not.

Dim outlines of faces occasionally appeared in different parts of the canvas.

For around five minutes, Moore took May’s place when she went to get something for her sister’s cold.  His report continued —

We had been sitting forty minutes when the right and left edges of the canvas began to darken, and the face and bust suddenly appeared.  It was finished in thirty-five minutes—i.e., one hour and fifteen minutes from the time we first sat down.  On separating the two canvases, it was found that the picture was on the further side of the one nearest to me, and the material was quite damp; the other canvas, which had been pressing against it all the time, was unsoiled.  The stuff comes off on the finger, a smutty, oily substance.

Iola

He made an appointment for another painting of Iola to be precipitated.

We now wanted to find out which one of the other photographs in my possession it was the wish of my guide I should bring on the 20th, the day appointed for my next picture.  Without the psychics seeing them, I laid out five under the cover of a card, face downwards.  May Bangs said: "Not the little one" (there was one taken at a very early age).  "The one nearest to me is a profile picture."  (Correct.)  "She rather objects to the old-fashioned style of the hair, but selects that as she sees you like it best."  (Correct.)

 

Moore reported unexpected occurrences during the precipitation of the second portrait.

 

. . . I was looking through the back of the picture, and it was forming on the further side of that one of the two canvases nearer to me; consequently had it gone on as it was and been finished, it would now (when framed) be profile left.  When the portrait was nearly finished the two canvases were lowered towards me on the table (the mediums being impressed, apparently, to do this).  A telegraphic message came by taps to May Bangs, who said: "She wants this picture for your wife specially, as well as for you.  She thinks that your wife would prefer to see her in the pose to which she is accustomed."  Up went the canvases again to the window, and I found that the whole picture was changed round . . .

 

In a few minutes the portrait was completed, May Bangs remarking: "She says she cannot put in the hand."

 

As a matter of fact, in this photo there is a hand (the left) supporting the cheek on its left side.  This was omitted in the coloured picture.

 

. . . the picture is by no means a slavish copy of the photograph.  It's pose is more upright, the face spirituelle, and the dress not exactly the same.  There is a firmness, a decision, and an appearance of calm and contented happiness in the face which is absent in the carte-de-visite.  It is a work of art.  I can only say this of one other picture in my collection.  They are all interesting, and each has its peculiar test value; but some of the dresses are stiff, and there are many anatomical deficiencies.  This one, however, is without a flaw, and there is just sufficient difference between it and the photograph to show distinctly to the most casual observer that one is not a professional copy of the other.

Moore was prepared to accept seeing with his own eyes the precipitation of the portraits because of his previous research of Spiritualism that included diverse seance room interactions with relatives and acquaintances who'd made the transition to another phase of life as well as with North American Indians and occasionally famous historical figures: buccaneer Sir Henry Morgan, scientists Sir Isaac Newton and Galileo, and Egyptian queen Cleopatra.  During his investigation of the Bang Sisters' mediumship in 1909 and 1911, Moore at times implemented precautionary measures to ensure results would be unquestionably genuine spirit manifestations.  These precautions included using his own chemical ink, slates and marked paper.

On January 19, 1909, Moore prepared some further questions for his guide and sat with May Bangs.  He mentioned the medium writing on her pad what he presumed she was seeing in 'the astral light' — "May Bangs read out to me the questions in my letter . . . They were all correct in sense, thought not in actual phrasing; and the curious thing was that she read them out in precisely the proper consecutive order . . ."  He again received a phenomenal reply with the envelope upon retrieving it from the slates.

My dear -----,

I am with you once again and, as ever, delighted to manifest my presence in ever so slight a manner.  Now . . . . . . you are trying me again—trying my memory of earthly things, places, and persons and how I do wish I could tear asunder the little barrier preventing me from giving free and full expression, but do you know . . . . . . in all these matters my memory is perfectly clear when I stand free and unhampered in the spiritual atmosphere but somehow when I return into earth's atmosphere, so many things become hazy and incomplete; in other words, it is not designed that mortals shall know it all.  If it were so research would be of the past, and spiritual matters of earth be at a standstill.  These little indifficencies (sic) lead the mind to further inquiry, and little by little the returns bringing reassurance is given.

I am not familiar with all the laws governing spirit return in outward demonstration.  I am constantly learning and in time know I shall bring the beautiful truth into your own home.  I am trying and shall continue to try for the desirable conditions, for I feel coming to you, and . . . . . . alone I would find that condition of thought that heretofore has been missing, and thereby give free and full evidence of identity you so much desire.  The law of evolution is carrying us onward and upward in spiritual truth just as fast as mortal mind is capable of accepting and understanding in its true light; and if at times we fail to give you all that your mind requires do not doubt, but know, that time will reward you.  It surely will, and right here I want to say that our beautiful "Cleopatra," who was such a wonderful intelligence here on earth, and in her many years of life and study in the higher advanced spheres in spirit life, is more capable of guiding you in these scientific problems than those who have been in spirit life in times of the past century, and to help you to solve and furnish the missing link for the world of science.  This has never been given, because science in the material world has not yet reached an understanding of the elements and laws even of their own atmosphere.  They acknowledge the existence of Electricity, its results and effect under certain conditions reached through long study and experimenting, but they cannot produce it independent in substance.  It is the propelling power of all life, all action, and the time will come when your people of science will understand it better, and so there are other elements in the very atmosphere about you that spirits must understand and utilise to bring about the results.  It is because of your ignorance of these elements and lack of knowledge of the average spirits, myself included, coming in contact with these laws that form the barrier of expression.

As before stated, in my own domain, all that you seek to know of me this morning is as clear as the noonday sun, but my great anxiety to have powers to give it, as also your anxiety to receive, for the time bars me in expression.

There are many subjects of your letter I would like to take in full explanation fully, but I fear I cannot in this one meeting, so I shall only refer to them briefly, for all come under the same law.

That I am with you in every move you make, travelling from your own location to that of your home in England, you need not doubt.  I do not take record of the intervening space of action but rush on straight, glide through space, as it were, in the twinkling of an eye.  I do not know all that transpires in your daily life as to material things, but make recognition of them on the whole, and particularly of your success and happiness for this is ever uppermost in mind.

. . . . . . I will go to . . . . . . and prepare her mind, so that she will overcome that timidity of spiritual matters, for I am desirous coming to her as I have to you, and believe, yes know, with her willingness and your combined efforts some wonderful demonstration may be received in the home proving this great truth.

I have been impressing the psychic how to answer some of your inquiries, for I cannot refer to all in writing.  I now feel the forces waning, and must soon close.

The little impressions forming on one of the photographs is my effort, and I hope to conclude my efforts with some manifestation conclusive and interesting to you. . . . . . . Adieu.  (Signed by the earth name of Iola.)

The handwriting is the same as that in the previous letter, and has no resemblance to that of Iola when she was in earth life.  All the hand writing of replies to letters through the mediumship of the Bangs Sisters has the same characteristics, as if written or precipitated by one amanuensis.  It seems probably that the spirit dictates to a "writing guide," whose idiosyncrasies creep in.  There are Americanisms in the above letter which certainly did not emanate from my guide.  I consider that the general tone of the letter is much in advance of the mind of the psychic in the room.  The pages were numbered by the writer, and the sequence of the writing was as follows: Page 5 was found at the back of Page 4, page 6 at the back of page 3, page 7 at the back of page 2.

Another precipitated letter was received from Sir 'A. G.' with whom Moore had conversed during a Direct Voice seance with Mrs. Wriedt in Detroit earlier in the month.  Moore wrote that Sir A. G. during his lifetime had held the position of English Consul-General in Cuba during the Spanish-American war.  On January 21, Moore sat with May Bangs for a reply to a letter he had written that afternoon to Cleopatra.

My letter contained a request that Cleopatra would cause her portrait to be precipitated at 10:30 on the following morning, and began in this way: "Will you precipitate your portrait on the canvas to-morrow at 10:30, and will you add such words or signs as will be recognized by an experienced student of Egyptian history?"

The following are extracts from the reply:—

My good friend of earth.  You have been told that I have come into your life for particular purposes, and it is true.  A long, long time I have been on the spirit side of life.  Ages it is as you calculate time, and during that period I have passed into realms far remote from earth.  All that was near and dear to me of your sphere have long, long since joined me, and also advanced through numberless spheres.  Truth is ever uppermost in the soul's ambition, and the time has come when mortals shall come further into the light.  There are many mysteries that only spirits of long time, experience, and study can impart to those of your sphere with any degree of understanding and practical application.  So it is that I have come into your life to aid in this very desirable work and I have chosen you as my subject through whom to work.  I know of your earnest desire to fathom for yourself and the world this great momentous question.  And I am bringing to you these different phenomena in evidence of my presence in introduction of my identity.  I am very desirous . . . . . . . . . . . . you my portrait through this influence and the good artist that is also high and proficient in his art knowledge that you may know me better.  And so from that chain or harmony and receptivity that will ensure the highest spiritual good.  In brief, I desire to come to you through your own psychic power and receptivity that is gradually unfolding as you continue in your research.

I promise to come to you in likeness, dress, and all the characteristic emblems true to my native land of earth here that I am sure will be recognized by experienced students in Egyptian history . . . . . . As you open the way, for the present all these wonderful experiences are for you alone.  They will bring the truth and light in such a way that shall demonstrate to others, and make . . . . . . thought.

Yes, people of different spheres live together in spirit life.  This truth I will explain to you again when better conditions and space affords opportunity.  It is always most wise to anyone (?) in the morning hour for spirit phenomena when the life current is at high tide, as it were.

. . . . . . As you gain spiritual knowledge here so do you prepare yourself spiritually for a higher understanding in the life to come.  Your chances for advancement are good in the life to come.

My good friend, I have not come to you at best this evening.  I shall therefore ask another opportunity at your pleasure and convenience.  In guidance, Cleopatra

Of course I am not in a position to assert that the Cleopatra of history wrote this letter.  I cannot possibly tell whether it was a personation or not; I have no means of doing so.  The immediate interest in the letter does not, in this case, lie in the identity of the writer, but in the nature of the ink with which it was written.  The writing is not dissimilar to that in the reply from Sir A. G.  It seems highly probable that all the letters are written, or precipitated, by the same spirit, a "writing guide" of the psychic, whom the individuals on the other side use as we do a typist. 

Moore witnessed the precipitation of the portrait of Cleopatra and wrote that the picture while in progress could be seen clearly through the back of the canvas.

Afterwards, but not while I was looking at it, the colours deepened a little, flowers were added to the embroidery of the dress, a ring was put on the finger of the left hand, and the picture acquired a general appearance of greater richness and finish.

 

. . . it is undoubtedly a representation of an Egyptian Queen, and, considering the way in which it was done, a fine example of spirit power.

Cleopatra

On January 22, the pages of the letter were blank when retrieved from the slates; however, while waiting "a bouquet of pink carnations and sweet-smelling narcissi fell from above with considerable force on to the card [a white card covered both slates and ink].  This was in full gas-light."

The messages from Iola through different mediums resulted with an occasion when Moore noticed a change of perspective.  Sitting with May Bangs on March 2, he asked for Iola to reply for her "asking me to sit for a picture of Hypatia after [previously] doing all she could at Rochester to prevent me from getting it."  Moore presented extracts from the response —

Regarding the messages at Rochester in regard to Hypatia's portrait, I will simply say I was influenced in my communications by Prof. H-----.  You understand . . . . . . and when I was free and independent I communicated direct.  I am delighted that you followed my wish.  I should indeed have been disappointed had you returned to England without it.  It was simply a case of one spirit trying to dominate over another.  These experiences you must not give to the world now; the time will come when all those undeveloped communications will occur . . . . . . Thos. J. Hudson is entirely responsible for the message given—but let it pass . . . . . .

Two days later, Moore sought more information from Hudson about the turn of events and the response included the statement:

In my recent communications advising you not to have Hypatia's portrait I was somewhat persuaded by other intelligences as the spirit Iola was persuaded by my advice; but since I have had the pleasure of coming to you here and witnessing the wonderful power and work, and have learned all the good that has been planned, I am delighted that changes have been made, and you have the portrait.

Moore reported:

Across the second half of the last page there is a postscript, in blue pencil mirror-writing, in a different hand to the body of the letter, and also to the script through Mrs. Georgia, which runs as follows:—

These questions [Hudson's queries in mirror-writing given through Mrs. Georgia at Rochester] will be answered through the psychic power of the medium through whose hand the questions were written; both the mediums and guides now understand.

On the outside of the letter was written:— "My good friend,—Kindly retain the writing for yourself, for reasons I have within explained.—Thos. Jay. Hudson."  The handwriting of this afterthought appears to be the same as that in the body of the letter.

Moore described receiving a precipitated letter from F. W. H. Myers on March 2.  A psychical researcher during his earth life, Myers had previously communicated with Moore through Mrs. Georgia's automatic mirror writing.  Moore reported in Glimpses of the Next State about the transcendental contact of Myers to him via letter.  Here is the beginning and concluding portions of the letter and Moore's comments.

On March 2, I wrote a letter in my hotel to Mr. F. W. H. Myers, reminding him of his promise made at Rochester to endeavour to reply to a letter from me at the Bangs Sisters', at Chicago, and asking him to identify himself as far as he could for the benefit of his friends in England.  The following was the reply found in the closed letter between the slates:—

My Good Friend and Co-worker.

I greet you this evening and am very pleased to come to you.  It is very kind of you to give opportunity of all this grand phenomena proving continued life after so-called death.  It is indeed unfortunate that spirit is somewhat limited in power of expression especially so when called upon to relate or recall some special event or circumstances occurring when in the earth form; this my good friend is due to the fact that the spirit is over-anxious to manifest in a way the mind suggests, the knowledge of which is perfectly clear to the spirit when in its free atmosphere—but when returning to manifest to mortals the atmosphere and all the conditions pertaining or surrounding to this life is so dense and clouded, that for the time being memory of these matters are renewed only as you make reference to them; thus again the Science of Spirit communicating with mortals is so intricate that it is quite difficult to master this alone, without entering into other branches; or is it designed by the Great overwhelming power, that Intelligence men call God, that mortals should be able to penetrate all pertaining to this or higher life?

 

. . . and little things like these manifestations do and will confound the mighty.  Give my very best wishes to our great brother and co-worker, Sir ------, also Sir ------ ------.  I am with them heart and hand in this great cause and though they have been able to reach the point where they can determine this question for the world greater achievements are being made right away, until in a very short time sufficient evidence will be given that may be able to give to the world a clear solution that shall occasion mortals to accept it in great majority as a truth, absolutely fixed truths.

I urge you to continue in your research my friends, I find since entering this great world of worlds that I knew but little, nay nothing, in comparison with that which is to be known.  I am still deeply interested in research and shall give you matters of interest from time to time, for our sensitives are growing more sensitive each day and this is the element required to give freedom of expression that brings evidence of identity.

Yours ever in the cause of all truth and light,

F. W. H. Myers

The letter offered philosophical commentary rather than any simple factual and "evidential" confirmatory evidence about the identity of Myers.  At times differentiating transcendental communication as evidential or philosophical, Moore occasionally worried about the potentiality of 'personating spirits' yet his perspective was influenced by misunderstood incidents involving Florence Cook and Frederick Foster Craddock.

The portion of the F. W. H. Myers letter omitted above is presented with the following excerpt.  Negative and pessimistic thoughts are expressed in this passage.  This portion of the letter shows that individual attitudes and perceptions can continue in the next state of life, showing variations in philosophy among transcendental communicators.  The reflection had just been given considering mortals being "able to penetrate all pertaining to this or higher life?"

Were it so, the people of Earth would become very dissatisfied with life, and more often tap (?) the time of their stay short, or, in other words, undo the set laws of nature.  Conviction is individual.  Science in the material world can never reach a point of understanding to explain these things; it is utterly useless, but each member can receive and become satisfied to his or her own understanding: this is all.  However the law of evolution is carrying you onward and upward until you all feel a close correspondence in your own soul to the Great One's Soul . . .

 
The Bangs Sisters were controversial figures among people not personally acquainted with them and their work.  Moore commented:
 

The manifestations which appear through their mediumship are of such a startling nature as to render it in the highest degree improbable that anyone, however experienced he may be as an investigator, can credit the accounts of what takes place, unless he has actually seen the various phenomena that occur.

Author Hereward Carrington accused the Bangs Sisters of fraud.  He claimed to have consulted them in an article of a 1910 issue of Annals of Psychical Science.  In Appendix C of Glimpses of the Next State "Mr. Hereward Carrington and Fraud," Moore responded to the article.  He reported that Dr. Isaac K. Funk had hired Hereward Carrington to visit Chicago, "requesting him to see the Bangs Sisters and to report to him the phenomena that he received in their presence."  Moore commented that Carrington's diagram of the room used for the sitting was incorrect, suggesting that "he has never been inside the house at all."  Moore included in this chapter Carrington's May 13, 1911 letter published in Light about the Bangs Sisters.  In one of two letters by Moore responding to Carrington's letter, Moore offered what he had learned about Carrington's claims from the sisters themselves: "The Bangs Sisters deny that he did [enter their house].  Lizzie assured me most positively that she would have recognized him, and that they had never sat for him at any time."  Moore responded to Carrington's claim that he had purchased a blank canvas from the sisters: "I understand that the Bangs Sisters did not sell him any canvas.  Let him produce their receipt for the money he paid for it!"

Carrington gave his version of a visit to the Bangs Sisters in his autobiography Personal Experiences In Spiritualism (1913).  He wrote: "I gave my name as Herald Thompson, and my mother the name of Jane Thompson.  I knew that, had I given my own name, I should have obtained nothing, and would probably have been refused a sitting."  He published a transcript of "the message which I received" -- a letter addressed to "Dearly Beloved Son Harold" and signed by "Jane Thompson."

A 1905 article from the Lily Dale newspaper The Sunflower shows the Bangs Sisters' perspective of their interaction with Dr. Funk.  The article is one of the period accounts presented in Ron Nagy's book Precipitated Spirit Paintings (2006).

"Dr. Funk himself is satisfied," said Miss Minnie Bangs.  "Here is the beautiful dictionary he sent us for Christmas, and here are the letters he wrote us before we sent the framed pictures to him.  These do not look as if he discredited us, do they?"

Here are transcripts of the letters from Dr. Funk.

New York, December 22, 1904

I sent you a check covering the balance of the two pictures, including frames, which were completed.  As soon as the package comes with the third picture in it I will send you the check for that.  I trust that your artists friends were able to get that picture also correct.  The one of the old lady whom I called mother Jeannette Thompson seemed to be a perfect one.  I hope it will please my wife when it arrives.  After their arrival I will have several of my friends see them, including Professor Hyslop, and I hope that we may be able to see you both in New York City, and have experiments made that will bring to the knowledge of the public, in a scientific way, the marvels which you seem so able to perform.

—I. K. Funk

New York, Dec. 28, 1904

The consignment of pictures came duly on hand on Monday, Christmas Day, just in time to serve my purpose.  They are certainly good reproductions, as far as my memory enables me to judge.

—I. K. Funk

 

In Precipitated Spirit Paintings, Lily Dale museum curator identifies similarities between the phenomenal paintings associated with Spiritualist mediums the Bangs Sisters and the Campbell Brothers.  Nagy reported: "In all cases the portraits appeared without eyelashes.  The eyes have a depth and vitality that I have never before seen or experienced, in a painting."  In the Foreword to Nagy's book, Raymond Buckland commented about the precipitated portraits: "To see the photographic-like quality of these works, done before the advent of color photography (the first commercial color film was not available until 1907), is unbelievable.  Yet a relatively large number were produced.  Most are still extant, in such Spiritualist communities as Lily Dale, New York, and Camp Chesterfield, Indiana."

Samples of the precipitated paintings associated with the mediumship of the Bangs Sisters can now be viewed on the Internet via a key word search of their name.  Here are links to three Camp Chesterfield pages of precipitated paintings created in the presence of Lizzie and May Bangs: Page One, Page Two, Page Three.  Two of these paintings are shown below.

A previous blog article about phenomenal artwork is Three Accounts of 'Precipitated' Portraits (from Old Diary Leaves). 

A Camp Chesterfield art gallery/museum holds the precipitated painting that has been entitled "The Spirit World" showing people in a canoe crossing a river toward a castle in a sphere of the ascended realm of human existence. 

Queen Victoria