UPDATED:  See the revised version here.

Genealogy research consumes my life, albeit in fits and starts, as other projects push themselves into the forefront of my life. Lately, it has consumed every spare moment, and some not-so-spare, as I have given priority to cleaning up my database, which currently contains nearly 15,000 people. The goal is to be able to publish my database on Ancestry.com, and there are too many questionable and unsourced trees there already. If I'm going to put my data out there—and I believe I have a responsibility to do so—I want to do it as well as I can.

As I go through the process, I inevitably run into problems. The psychological process of working through them is worthy of a blog post in itself, but not now. What I will do now is begin to document here some of the work: the data, the sources, my thought processes, my conclusions. Doing so helps me think and increases my own understanding. It also gets some of the data "out there" where it may be of interest to others researching the same people. The posts will often be very long, and of little or no interest to most of my readers. Feel free to skim or skip them altogether! I post them for those random visitors who end up here through a Google search on a name of interest, because I have been helped in my own work by just such a process.To begin:

 

The Problem of David Wood

 

The Puzzle

I’m pretty happy with the line of my family tree that goes up (on my father’s side) to David Wood, born May 1, 1778 in Stow Creek Township, Cumberland County, New Jersey, died there in 1828, probably. He married, April 11, 1798, Mercia Davis, born July 15, 1777 in Cumberland County, died there December 1, 1823, daughter of Isaac and Mary Ann (David) Davis. I’m good with that.

I also have an okay line up from David’s grandfather, Jonathan Wood, who died in Cohansey, Salem County, New Jersey in 1727, and was married to Mary Ayers. This goes back to a John Wood who died at Portsmouth, Rhode Island in 1655. Details are sparse, but at least the line is there.

The problem, as is often the case, is in the middle.

I know that David Wood, Jr.’s father was David Wood, Sr., son of Jonathan and Mary (Ayers) Wood. But David Wood, Sr. had three known wives, and what details are known have few dates associated with them. I’m convinced that David Jr.’s mother was named Prudence Bowen; I haven’t found her parents, though supposedly she was the sister of David and Jonathan Bowen, of Bowentown, Cumberland County, New Jersey. Am I certain enough to put time into following the Bowen line? Probably, though not now. 

I’m not at all certain my logic will convince anyone else, but I’m equally uncertain I’ll get any better documentation. As one of my correspondents understated, "New Jersey records are very hard to find." I’ve been spoiled by working mostly with early New England ancestors. Say what you want about the Puritans, those folks knew how to keep records. And when something like engaging in illicit sex or selling liquor to Indians lands you in the court dockets, that’s a bad thing for you but a great thing for future genealogists.

 

The Sources

Vital records (birth, marriage, death), church records, wills, and probate records are wonderful genealogical resources, since they are usually contemporaneous with the events they describe.That’s not to say they’re without error, but they are generally considered reliable.New Jersey was not as good as New England at keeping these early records, but I found some.

  • Ancestry.com. New Jersey, Marriage Records, 1683-1802 [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2011, v. 22 p. 52 Prudence Bowen and Simeon Roberts, and v. 22 p. 335 Prudence Roberts and David Wood. (Original data: New Jersey State Archives. New Jersey, Published Archives Series, First Series. Trenton, New Jersey: John L Murphy Publishing Company.)
  • "New Jersey, Deaths, 1670-1988," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:Q2SZ-1FPR : 18 October 2017), Anley McWood, May 1853; citing Roadstown, Cumberland, New Jersey, United States, Division of Archives and Record Management, New Jersey Department of State, Trenton.; FHL microfilm 493,711.
  • Ancestry.com. New Jersey, Abstract of Wills, 1670-1817 [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2011, v. 9, Abstracts of Wills, pp. 50-51 Jonathan Bowen, and pp. 419-420, David Wood Sr. (Original data: New Jersey State Archives. New Jersey, Published Archives Series, First Series. Trenton, New Jersey: John L Murphy Publishing Company.)

Although published genealogies are far from primary sources, they are usually—according to my contact at the New England Historic Genealogical Society—reasonably reliable on the American side of the Atlantic Ocean, even though many fictitious across-the-pond connections abound.Therefore I’m designating these sources as credible, if not as good as primary sources.

  • Bruce W. David, The David Family Scrapbook: Genealogy of Owen David, Volume 5 (3223 Ormond Road, Cleveland Heights, Ohio: Bruce W. David, Volume 5, 1964), pp. 315-316.
  • Gilbert Cope, Genealogy of the Sharpless Family Descended from John and Jane Sharples, Settlers Near Chester, Pennsylvania, 1682: Together with some account of The English Ancestry of the Family, including the results of researches by Henry Fishwick, F.H.S., and the late Joseph Lemuel Chester, LL.D.; and a full report of the bi-centennial reunion of 1882 (Philadelphia: For the family, under the auspices of the Bicentennial committee, 1887), p. 545.
  • Dorothy Wood Ewers, Descendants of John Wood: A Mariner who died in Portsmouth, Rhode Island, in 1655 (Colorado Springs, Colorado: Ewers, 1978), pp. 54-56.

Family tree date abounds online, and its credibility is exceedingly variable.Some online trees are maintained by excellent, sometimes professional, researchers.Some contain undocumented but accurate personal memories.And there are also many, many trees that have merely copied someone else’s data that is entirely wrong—a widespread propagation of error.Unless something about the source convinces me otherwise, I consider this data suspect, but it can still be a source of ideas and hints.

  • Family tree data from Ancestry.com, FamilySearch.org, and other Internet sites.

 

The Data

From the David Family Scrapbook

David Wood Jr. was born May 1, 1778, the son of David Wood, Sr. and Elizabeth Russell. (I believe the designation of Elizabeth as his mother to be erroneous.)

From the Sharpless Genealogy

David Wood (Sr.) died about 1798, “aged over 70.” His wives and children:

  1. Lucy Lennox, no issue.
  2. Prudence, sister of David and Jonathan Bowen of Bowentown, Cumberland County, New Jersey. Children:
    1. David Jr., born May 1, 1778 in Stow Creek, Cumberland County, New Jersey; married April 11, 1798, Mercia Davis, daughter of Isaac and Mary Anna Davis.
    2. Auley McCalla
    3. Sarah
    4. Prudence
  3. Elizabeth Russell. Children:
    1. John
    2. Lucy
    3. Richard

From Descendants of John Wood

David Wood, Sr. was born 1721, died 1794 in Stow Creek, New Jersey, “over 70.” His will was written March 10, 1794, proved January 18, 1798. Two scenarios are presented for his wives and children, from different correspondents:

  1. Lucy Lennox, no children.
  2. Prudence Bowen, married 1777. Children:
    1. David
    2. Auley
    3. Sarah
    4. Prudence
  3. Elizabeth Russell, married in 1786. Children:
    1. John
    2. Lucy
    3. Elizabeth
    4. Richard

Alternatively, the following children, not assigned to mothers, and in no particular order (clearly taken from David’s will, see below):

  • Sarah
  • Prudence
  • Lucy
  • Obadiah
  • James
  • Phebe
  • Lydia
  • Aulay McAuliff (McCalfa, McCalla)
  • David
  • John

From New Jersey Marriage Records

I find nothing for a Prudence Bowen marrying a David Wood, but there are these records of marriage licenses issued:

  • Prudence Bowen of New Town and Simon Roberts of Philadelphia, June 14, 1762.
  • Prudence Roberts of Cumberland and David Wood of Salem, July 9, 1777.

It’s likely that these represent the first and second marriages of the same person, especially since that agrees with the 1777 date in Descendants of John Wood

From New Jersey Deaths, 1670-1988

Anley McWood (Auley McCalla Wood). Death, May 1853, Roadstown, Cumberland, New Jersey. Residence Stoe Creek, Cumberland, New Jersey. Male, age 69, occupation farmer. Estimated birth year 1784. Birthplace Stoe Creek, Cumberland, New Jersey. Father David Wood, mother Prudence Wood.

From New Jersey Abstract of Wills

  • Will of Jonathan Bowen, February 21, 1804. He was likely the Jonathan, brother of David of Bowentown, mentioned in Sharpless above, hence brother to David Wood’s wife Prudence. Among many other bequests, he leaves a share of his household goods to “my niece, Mary Roberts,” strengthening the notion that this Prudence was once married to Simeon Roberts.
  • Will of David Wood, Sr. of Stow Creek Township, Cumberland County, March 10, 1794. 

Wife, Elizabeth, 1/3 of personal. Son, Obadiah, £50. Daughters, Sarah, Prudence, and Lucy Wood, son, John, and if wife should be pregnant, the said child; the remainder of personal, divided between them, when of age. Son, John, to be put to a trade, when 14. To heirs of son James, 5 shillings. To heirs of daughter, Phebe, 5 shillings. To heirs of daughter Lydia, 5 shillings. Son, David, 4 acres of woodland bounded by land of David Gilman, Dorcas Bennett to John Dare’s land; also 10 acres of marsh in Stathem’s neck. Son, Aulay McCalla Wood, remainder of home plantation with buildings; also remainder of swamp at Stathem’s neck; should said sons, David or Aulay McCalla, die before of age, said property to the survivor of them. Executor—Azariah Moore, Esq. Witnesses—George Burgin, Mary More and Martha More. Proved Jan. 18, 1798.

January 10, 1798. Inventory, £221.9; made by Joel Fithian and David Gilman.

January 18, 1798. Azariah Moore, having renounced the Executorship. Adm’r—C.T.A.—Jonathan Bowen. Fellowbondsman—Benjamin Dare.

From assorted online family tree data

  • David Wood Sr. was born 1721 or 1740, died 1798, married Lucy Lennox 1760.
  • Lucy Lennox was born 1742, died 1773. Her children were Obadiah (born 1760), James (born 1760), Phebe (born 1762), Richard (born 1768).
  • Prudence Bowen was born in 1754, died in 1778, married David Wood 1774. Her children were Prudence (born 1776), Sarah S. (born 1776 or 1777 or 1779), Auley (born 1775).
  • Elizabeth Russell was born in 1755, died in 1797, married David wood in 1779. Her children were Prudence (born 1776 died 1777), Lydia (born 1778), Elizabeth (born 1779), David (born 1778), Lucy (born 1767), John (born 1780).
  • Simeon Roberts, born about 1735 in Philadelphia, died about 1766 (probate) in Philadelphia, married Prudence Bowen (born 1740 in Newton, Sussex, New Jersey) June 14, 1762 in New Jersey. Their child: John (born about 1780).

And more. The data is inconsistent and confusing as well as unreliable.

 

The Questions

So what can I make of all this?

First of all, let’s deal with the name of one of David’s sons: Auley McCalla Wood. By his death record, Auley McCalla is definitely established as the child of David and Prudence Wood.  But what kind of a name is that for a child? First of all, despite the alternate spellings given in Descendants of John Wood, Auley (or Aulay) McCalla is probably correct. The name shows up more than once in New Jersey; David Wood’s child was no doubt named after a friend, or someone his parents respected. 

The will is the most interesting document, and I’m sorry I only have an abstract to work with. Struggling with hand-written wills is hard on both the eyes and the brain, but can give insights a summary misses. Still, the abstract is something to work with.

Of the twelve children mentioned in the combined sources—David, Auley McCalla, Sarah, Prudence, John, Lucy, Richard, Elizabeth, Obadiah, James, Phebe, and Lydia—two are missing from the will. For that time period, it’s not unlikely that Richard and Elizabeth had died before the will was made, so there’s no need to assume they’re extraneous additions to the records.

That Elizabeth Russell was David’s third wife is supported by the mention of Elizabeth in his will. Next comes Obadiah. It’s not specified that he is the firstborn, but that’s customary, and as he’s bequeathed his £50 outright, he must have been at least 21 years old in 1794, unlike Sarah, Prudence, Lucy, John, David, and Auley McCalla, who are clearly not yet of age. John is something less than 14 in 1794, making him born after 1780.

The five-shilling bequests to the heirs of children James, Phebe, and Lydia are another puzzle. Why the heirs? Are James, Phebe, and Lydia older, married … and dead? Or did David just want to leave something directly to his grandchildren (sadly, unnamed)? In any case these three children seem to be married and on their own. I’m trying to be grateful to David for actually leaving a will, since many did not, instead of wanting to shake him by the shoulders and demand to know why he didn’t include surnames for most of the people he mentions.

But who are these children?

One scenario is that Obadiah, James, Phebe, and Lydia are Prudence’s children from her first marriage. It’s possible, because there were 15 years between her first and second marriages, if the dates are right. But I think it more likely that they were Lucy Lennox’s children, already grown and on their own by the time their father made his will. Of course it’s possible that Lucy simply didn’t have any children; infertility is not exclusively a modern problem. But David specifically names these children as his. On the other hand, relationship naming was more fluid in the past: When a document specifies “my brother” or “my uncle,” for example, it does not necessarily mean by these terms what we do now. 

One thing that speaks to these children being Prudence’s by her first husband is the naming patterns. It seems unusual for David to have at least two sons before giving one of them his own name. He did have an uncle Obadiah, as well as an uncle John. The sources of the names Lucy, Prudence, and Elizabeth are obvious, though if James, Phebe, Lydia, Richard, Sarah, or Auley McCalla are in his family tree, I don’t know about it. But I can’t find any information on children for Prudence and Simeon, nor for Lucy and David, to help solve the puzzle. I think it more likely these are Lucy’s children, but I may be wrong.

Wills often name children in order of their birth, but sometimes that order is within categories, such as all sons and then daughters. In this case, I would guess that Sarah, Prudence, Lucy, and John are listed from oldest to youngest; likewise James, Phebe, and Lydia; also that David is older than Auley McCalla, which we already know from their birthdates.

Figuring out birth order between one category and another is more of a problem.  Unlike most of my sources, I place Sarah and Prudence between David and Auley McCalla because of the large gap in the latter’s birthdates, although it’s possible that Prudence was born last and her mother died in childbirth..

Although it is mostly speculation on my part, here is the scenario as I imagine it. As was customary, David’s widow received 1/3 of the personal property—as I understand it, this is pretty much everything that’s not land. It was valued at £221.9, so her share would have been £74. (Or possibly £57, if Obadiah’s £50 was deducted before the division. I’m afraid I don’t know enough about legal language when it comes to wills.) That makes Obadiah’s portion a pretty large chunk of the estate, but it was not unusual back then for the firstborn son to inherit more than his siblings.

The remainder of the personal property was to be divided amongst Sarah, Prudence, Lucy, and John, probably the youngest children. This suggests that the older children may have already received gifts of goods and property and were perhaps living on their own.

David and Auley each received land. Since Auley was given the “remainder of the home plantation with buildings,” I imagine the older sons (probably Obadiah and James) had been given their shares of the land already. Why was John to be “put to a trade” (I assume apprenticed) when 14? Perhaps the land suitable for farming had already been apportioned. Maybe John didn’t want to be a farmer, and his father supported that preference, although he seems to have been too young for that to be likely.

Why were the heirs of James, Phebe, and Lydia given five shillings? Such an amount was not insignificant, but at 20 shillings to the pound, barely a drop in the estate bucket. Was it meant to be just a token for small children from Grandpa? If there were bad relations in the family and he wanted to insult them, I imagine he would have done it for even less money.

Was David Wood, Sr. really born in 1721? It seems a reasonable approximation, if it is true that he was “over 70” when he died, which was somewhere in the range 1794-1798. That makes him apparently much older than his wives, though I don't have documented birth dates for any of them. I've also seen an unsourced birth year of 1740 often suggested for David Sr. But it's not impossible that he really was that old—one of my own great-grandfathers was 59 before producing any children. Absent any compelling evidence to the contrary, I’ll stick with the earlier date, though since I think it’s a guess from the uncertain death date, I’d put it more at about 1725.

 

The Conclusions

Always being ready to scrap speculations in light of new data, this is what I now believe about David Wood, Sr.

David Wood, Sr. was born about 1725, probably in Salem County, New Jersey. (Cumberland County was formed in 1748 from the west side of Salem County.) He died between March 10, 1794 and January 18, 1798, in Stow Creek Township, Cumberland County, New Jersey. David married three times.

His first wife was Lucy Lennox, who died before 1777, and by whom he possibly had four children. These may, instead, have been the children of David’s second wife and her first husband.

  1. Obadiah
  2. James
  3. Phebe
  4. Lydia

He married, second, about July 9, 1777, Prudence Bowen, the sister of David and Jonathan Bowen of Bowentown, Cumberland County, New Jersey. She had married, first, about 14 July 1762, Simeon Roberts of Philadelphia. Obadiah, James, Phebe, and Lydia listed above may have been their children. Prudence died before 1786.

David Wood and Prudence Bowen had, probably, the following children (order uncertain):

  1. David Wood, Jr., born May 1, 1778, died in 1828. He married, April 11, 1798, Mercia Davis, born July 15, 1777 in Cumberland County, New Jersey, and died there December 1, 1823, daughter of Isaac and Mary Ann (David) Davis.
  2. Sarah S.
  3. Prudence
  4. Auley McCalla, born about 1784, died May 1853, Roadstown, Cumberland County, New Jersey. (Living in Stow Creek, Cumberland County, New Jersey.)

David married, third, in 1786, Elizabeth Russell. (This may be a married name, from a previous marriage.) Their children (order uncertain) were probably

  1. Lucy
  2. John
  3. Elizabeth, died probably before 1794
  4. Richard, died probably before 1794

 

The ancestry of David Wood, Sr. taken from Descendants of John Wood, is, in an abbreviated form, as follows:

  1. John Wood, died 1655 in Portsmouth, Rhode Island, married an unknown wife.
  2. John Wood, born 1620, died August 26, 1704 in Little Compton, Rhode Island, married Anna, surname unknown.
  3. Jonathan Wood, born August 26, 1658 in Springfield, Massachusetts, died 1715, married, by 1692, Mercy Banbury.
  4. Jonathan Wood, died 1727 in Cohansey, Salem County, New Jersey, married Mary Ayers.
  5. David Wood, Sr., as above.
Posted by sursumcorda on Saturday, October 28, 2017 at 8:21 pm | Edit
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Math, art, travel, photography. What's not to like?

For some reason, probably all of the above, this photo of "Seventeen parallel flowlines running between Flow Station 2 and Drill Site 3, Drill Site 9, Drill Site 16, Drill Site 17 and Endicott at the Prudhoe Bay Oil Field" really struck me this morning when I read David July's Mount Sutro post, The Linear Perspective Orthogonals. (The photo is from the Mount Sutro Gallery. License agreement here.)

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Posted by sursumcorda on Friday, October 27, 2017 at 6:06 am | Edit
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This is for someone who will appreciate it, even if the rest of you are covering your ears.

Posted by sursumcorda on Saturday, October 21, 2017 at 7:42 am | Edit
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I don't think of myself as a conformist. I mean, really, can you be of my generation and not like rock 'n' roll? I'm afraid I've always taken pride in being different from the general culture.

Apparently I'm slipping.

Lo and behold, my hands-down, absolute, nothing else is even close, favorite fast-food restaurant, Chick-fil-A, is the most popular fast-food restaurant in the country. Here's the state-by-state breakdown. (Click to enlarge.)

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I suppose McDonalds, which won only Alaska, North Dakota, and Washington, D.C., could argue with the methodology, since they have so many restaurants.

For the study, we looked at which chains received the most visits on average in every state based on the total number of visits to each chain divided by the number of locations in that state.

But even McDonald's can't argue with these numbers.

Chick-fil-A dominates, which isn't surprising —  the fried-chicken chain generates more revenue per restaurant than any other fast-food chain in the US.

I guess part of being independent of popular opinion means accepting the situation when other people agree with me. :)

Posted by sursumcorda on Friday, October 20, 2017 at 8:41 am | Edit
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Today's Orlando Sentinel features, on its opinion page, a wonderful article by guest columnist James O. Cunningham: What's wrong with America? 'Dear Sir, I am'. The link takes you to the front page, from which you could click to page 12—or maybe not; it's not clear to me which parts the newspaper makes available to non-subscribers. But the Sentinel also makes it possible to clip and save articles, and this one deserves wider publicity, so I've included it below. If you find the print too small, click on the image for a larger version. (H/T Porter, who grabbed my attention by mentioning the Chesterton quote.)

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Posted by sursumcorda on Tuesday, October 17, 2017 at 10:32 am | Edit
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Google frequently suggests, through my phone, articles that it thinks I might find interesting. Most of the time it's not even close: Really, I don't want to know what President Trump tweeted, any more than I wanted to hear what President Obama said on Saturday Night Live. I consider both to be inappropriate venues for a President. But recently Google was whang in the gold, with its suggestion of the video below from musician Rick Beato.

Not the whole video, actually. Mostly it's about acquiring the musical skill known as perfect (absolute) pitch, and why Beato believes it must occur during a child's first two years of life. He makes a good case, but it's a controversial point, and he apparently takes no account of recent studies demonstrating neuroplasticity in adult brains—something previously considered to be impossible. In any case, Beato himself doesn't mean adults can't develop really, really good relative pitch and get quite close to absolute pitch; after all, he has created several YouTube videos on how to do just that. But babies ... they're still something special.

The part of the video I find most intriguing is from the 6 minute point to about the 13 minute point.

One thing that surprised me, although in retrospect it should not have, is that Beato's son's acquired his ability to discern and remember pitches well before he knew any note names. But this post is not really about perfect pitch. It's also not about me feeling guilty for the opportunities lost with our children, and certainly not about making anyone else feel guilty for their own omissions. We do what we can with what we know at the time, and regrets are part of every parenthood contract. My concerns now are more general and philosophical.

What strikes me here—and it confirms what I've learned from other sources—is that our teaching habits are upside down.

Apparently, what helps babies learn is complexity. Materials with high information content. Unexpected twists and turns. So what do we do? We simplify everything for children. We give them baby talk, controlled-vocabulary books, and three-chord songs, when their brains are craving adult conversations, complex language, Bach, and jazz. Sure, they learn anyway: Babies are so desperate to learn they'll use whatever tools they can get their hands on. But despite the best of intentions, we are building cages where we should be opening doors.

Posted by sursumcorda on Sunday, October 15, 2017 at 6:23 am | Edit
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Warning: This is an unabashed Grandma-brag—but it has a generally-applicable point as well.

One of my recurrent themes here is the truth that children can do and be so much more than we usually expect of them, from toddlers to teenagers. While our thirteen-year-old grandson's accomplishment is not on a par with commanding a captured naval vessel at the age of 12, nor with captaining a trading ship at 19, I'm quite proud of him—and his parents.

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In his right hand is an oak board, similar to that from which he made the object in his left hand, which, when painted, will replace the barber-pole coat rack at a local barbershop.

When he approached the barber, who had advertised for someone to do the work, it took guts and skill to negotiate the commission, not to mention to persuade the barber that a young teen could do the job.

It was an ambitious project, and required working with some heavy-duty power tools—radial arm saw, lathe, planer, and jointer—knowing not only their operation, but proper safety equipment and procedures as well. It was a time-consuming job that required patience, persistence, and focus. That's pretty impressive at an age when many consider him too young to fly unaccompanied on a commercial airplane, to own a knife, or even to stay home alone.

He can cook full meals, too, and I don't mean just heating things up in the microwave.

Is he some sort of genius?  Of course he is, he's my grandchild!

But seriously, what distinguishes him the most from many young people is opportunity. His parents didn't just turn him loose among those dangerous tools, unprepared. He's been helping in the workshop (and the kitchen) since he was a toddler. So have his siblings. The kind of training that produces skills of this sort requires patience and persistence on the part of parents, too—and even more so, a willingness to stand up for the right of children to fly in a society determined to clip their wings.

Posted by sursumcorda on Friday, October 13, 2017 at 10:16 am | Edit
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I'm so glad that the ending of the Space Shuttle program did not mean the end of being able to watch launches from our front yard.

Posted by sursumcorda on Wednesday, October 11, 2017 at 6:58 pm | Edit
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The article may be a little heavy-going, but I know some of my readers will love it. It's not often number theory makes the headlines: Mathematicians Discover Prime Conspiracy. Maybe it's the idea of conspiracy—that always sells.

Two mathematicians have uncovered a simple, previously unnoticed property of prime numbers — those numbers that are divisible only by 1 and themselves. Prime numbers, it seems, have decided preferences about the final digits of the primes that immediately follow them.

Among the first billion prime numbers, for instance, a prime ending in 9 is almost 65 percent more likely to be followed by a prime ending in 1 than another prime ending in 9. In a paper posted online today, Kannan Soundararajan and Robert Lemke Oliver of Stanford University present both numerical and theoretical evidence that prime numbers repel other would-be primes that end in the same digit, and have varied predilections for being followed by primes ending in the other possible final digits.

The discovery is the exact opposite of what most mathematicians would have predicted... Most mathematicians would have assumed ... that a prime should have an equal chance of being followed by a prime ending in 1, 3, 7 or 9.

Soundararajan was drawn to study consecutive primes after hearing a lecture at Stanford by the mathematician Tadashi Tokieda, of the University of Cambridge, in which he mentioned a counterintuitive property of coin-tossing: If Alice tosses a coin until she sees a head followed by a tail, and Bob tosses a coin until he sees two heads in a row, then on average, Alice will require four tosses while Bob will require six tosses (try this at home!), even though head-tail and head-head have an equal chance of appearing after two coin tosses.

Soundararajan wondered if similarly strange phenomena appear in other contexts. Since he has studied the primes for decades, he turned to them — and found something even stranger than he had bargained for.

What does this mean for ordinary mortals? Who knows? It may mean nothing ... or it may lead to the next big break in cryptography. With math, anything's possible.

Posted by sursumcorda on Tuesday, October 10, 2017 at 10:04 am | Edit
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J. R. R. Tolkien said that Leaf by Niggle was the only one of his stories that wrote itself. It has long held a special place in my heart, though it has none of the majesty and glory of his Lord of the Rings books.

I hope the copyright holders will forgive me for the rather long quotation below. It is only the beginning of the story; the best part is yet to come, and I strongly urge you to find your own copy and read it all. Mine is included as part of "Tree and Leaf" in The Tolkien Reader. Apparently there is a stand-alone version, but unfortunately nothing for Kindle.

As I said, the best part, the really beautiful part, comes later in the story. But this beginning captures so perfectly the dilemmas of creative people: How to balance the demands and pleasures of "real life"with the deep-seated, sometimes almost desperate need to "work, for the night is coming" on one's own, particular calling. At least, this is my own experience, and, I'm convinced, that of Tolkien himself. Perhaps other creative people, of whom I know many among my readers, will find a resonance here.

And then go and read the Rest of the Story for encouragement.

There was once a little man called Niggle, who had a long journey to make. He did not want to go, indeed the whole idea was distasteful to him; but he could not get out of it. He knew he would have to start some time, but he did not hurry with his preparations.

Niggle was a painter. Not a very successful one, partly because he had many other things to do. Most of these things he thought were a nuisance; but he did them fairly well, when he could not get out of them: which (in his opinion) was far too often. The laws in his country were rather strict. There were other hindrances, too. For one thing, he was sometimes just idle, and did nothing at all. For another, he was kind-hearted, in a way. You know the sort of kind heart: it made him uncomfortable more often than it made him do anything; and even when he did anything, it did not prevent him from grumbling, losing his temper, and swearing (mostly to himself). All the same, it did land him in a good many odd jobs for his neighbour, Mr. Parish, a man with a lame leg. Occasionally he even helped other people from further off, if they came and asked him to. Also, now and again, he remembered his journey, and began to pack a few things in an ineffectual way: at such times he did not paint very much.

He had a number of pictures on hand; most of them were too large and ambitious for his skill. He was the sort of painter who can paint leaves better than trees. He used to spend a long time on a single leaf, trying to catch its shape, and its sheen, and the glistening of dewdrops on its edges. Yet he wanted to paint a whole tree, with all of its leaves in the same style, and all of them different.

There was one picture in particular which bothered him. It had begun with a leaf caught in the wind, and it became a tree; and the tree grew, sending out innumerable branches, and thrusting out the most fantastic roots. Strange birds came and settled on the twigs and had to be attended to. Then all round the Tree, and behind it, through the gaps in the leaves and boughs, a country began to open out; and there were glimpses of a forest marching over the land, and of mountains tipped with snow. Niggle lost interest in his other pictures; or else he took them and tacked them on to the edges of his great picture. Soon the canvas became so large that he had to get a ladder; and he ran up and down it, putting in a touch here, and rubbing out a patch there. When people came to call, he seemed polite enough, though he fiddled a little with the pencils on his desk. He listened to what they said, but underneath he was thinking all the time about his big canvas, in the tall shed that had been built for it out in his garden (on a plot where once he had grown potatoes).

He could not get rid of his kind heart. "I wish I was more strong-minded!" he sometimes said to himself, meaning that he wished other people's troubles did not make him feel uncomfortable. But for a long time he was not seriously perturbed. "At any rate, I shall get this one picture done, my real picture, before I have to go on that wretched journey," he used to say. Yet he was beginning to see that he could not put off his start indefinitely. The picture would have to stop just growing and get finished.

One day, Niggle stood a little way off from his picture and considered it with unusual attention and detachment. He could not make up his mind what he thought about it, and wished he had some friend who would tell him what to think. Actually it seemed to him wholly unsatisfactory, and yet very lovely, the only really beautiful picture in the world. What he would have liked at that moment would have been to see himself walk in, and slap him on the back, and say (with obvious sincerity): "Absolutely magnificent! I see exactly what you are getting at. Do get on with it, and don't bother about anything else! We will arrange for a public pension, so that you need not."

However, there was no public pension. And one thing he could see: it would need some concentration, some work, hard uninterrupted work, to finish the picture, even at its present size. He rolled up his sleeves, and began to concentrate. He tried for several days not to bother about other things. But there came a tremendous crop of interruptions. Things went wrong in his house; he had to go and serve on a jury in the town; a distant friend fell ill; Mr. Parish was laid up with lumbago; and visitors kept on coming. It was springtime, and they wanted a free tea in the country: Niggle lived in a pleasant little house, miles away from the town. He cursed them in his heart, but he could not deny that he had invited them himself, away back in the winter, when he had not thought it an "interruption" to visit the shops and have tea with acquaintances in the town. He tried to harden his heart; but it was not a success. There were many things that he had not the face to say no to, whether he thought them duties or not; and there were some things he was compelled to do, whatever he thought. Some of his visitors hinted that his garden was rather neglected, and that he might get a visit from an Inspector. Very few of them knew about his picture, of course; but if they had known, it would not have made much difference. I doubt if they would have thought that it mattered much. I dare say it was not really a very good picture, though it may have had some good passages. The Tree, at any rate, was curious. Quite unique in its way. So was Niggle; though he was also a very ordinary and rather silly little man.

At length Niggle's time became really precious. His acquaintances in the distant town began to remember that the little man had got to make a troublesome journey, and some began to calculate how long at the latest he could put off starting. They wondered who would take his house, and if the garden would be better kept.

The autumn came, very wet and windy. The little painter was in his shed. He was up on the ladder, trying to catch the gleam of the westering sun on the peak of a snow-mountain, which he had glimpsed just to the left of the leafy tip of one of the Tree's branches. He knew that he would have to be leaving soon: perhaps early next year. He could only just get the picture finished, and only so so, at that: there were some corners where he would not have time now to do more than hint at what he wanted.

There was a knock on the door. "Come in!" he said sharply, and climbed down the ladder. He stood on the floor twiddling his brush. It was his neighbour, Parish: his only real neighbour, all other folk lived a long way off. Still, he did not like the man very much: partly because he was so often in trouble and in need of help; and also because he did not care about painting, but was very critical about gardening. When Parish looked at Niggle's garden (which was often) he saw mostly weeds; and when he looked at Niggle's pictures (which was seldom) he saw only green and grey patches and black lines, which seemed to him nonsensical. He did not mind mentioning the weeds (a neighbourly duty), but he refrained from giving any opinion of the pictures. He thought this was very kind, and he did not realize that, even if it was kind, it was not kind enough. Help with the weeds (and perhaps praise for the pictures) would have been better.

"Well, Parish, what is it?" said Niggle.

"I oughtn't to interrupt you, I know," said Parish (without a glance at the picture). "You are very busy, I'm sure."

Niggle had meant to say something like that himself, but he had missed his chance. All he said was: "Yes."

"But I have no one else to turn to," said Parish.

"Quite so," said Niggle with a sigh: one of those sighs that are a private comment, but which are not made quite inaudible. "What can I do for you?"

"My wife has been ill for some days, and I am getting worried," said Parish. "And the wind has blown half the tiles on my roof, and water is pouring into the bedroom. I think I ought to get the doctor. And the builders, too, only they take so long to come. I was wondering if you had any wood and canvas you could spare, just to patch me up and see me through for a day or two." Now he did look at the picture.

"Dear, dear!" said Niggle. "You are unlucky. I hope it is no more than a cold that your wife has got. I'll come round presently, and help you move the patient downstairs."

"Thank you very much," said Parish, rather coolly. "But it is not a cold, it is a fever. I should not have bothered you for a cold. And my wife is in bed downstairs already. I can't get up and down with trays, not with my leg. But I see you are busy. Sorry to have troubled you. I had rather hoped you might have been able to spare the time to go for the doctor, seeing how I'm placed: and the builder too, if you really have no canvas you can spare."

"Of course," said Niggle; though other words were in his heart, which at the moment was merely soft without feeling at all kind. "I could go. I'll go, if you are really worried."

"I am worried, very worried. I wish I was not lame," said Parish.

So Niggle went. You see, it was awkward. Parish was his neighbour, and everyone else a long way off. Niggle had a bicycle, and Parish had not, and could not ride one. Parish had a lame leg, a genuine lame leg which gave him a good deal of pain: that had to be remembered, as well as his sour expression and whining voice. Of course, Niggle had a picture and barely time to finish it. But it seemed that this was a thing that Parish had to reckon with and not Niggle. Parish, however, did not reckon with pictures; and Niggle could not alter that. "Curse it!" he said to himself, as he got out his bicycle.

It was wet and windy, and daylight was waning. "No more work for me today!" thought Niggle, and all the time that he was riding, he was either swearing to himself, or imagining the strokes of his brush on the mountain, and on the spray of leaves beside it, that he had first imagined in the spring. His fingers twitched on the handlebars. Now he was out of the shed, he saw exactly the way in which to treat that shining spray which framed the distant vision of the mountain. But he had a sinking feeling in his heart, a sort of fear that he would never now get a chance to try it out.

Niggle found the doctor, and he left a note at the builder's. The office was shut, and the builder had gone home to his fireside. Niggle got soaked to the skin, and caught a chill himself. The doctor did not set out as promptly as Niggle had done. He arrived next day, which was quite convenient for him, as by that time there were two patients to deal with, in neighbouring houses. Niggle was in bed, with a high temperature, and marvellous patterns of leaves and involved branches forming in his head and on the ceiling. It did not comfort him to learn that Mrs. Parish had only had a cold, and was getting up. He turned his face to the wall and buried himself in leaves.

He remained in bed some time. The wind went on blowing. It took away a good many more of Parish's tiles, and some of Niggle's as well: his own roof began to leak. The builder did not come. Niggle did not care; not for a day or two. Then he crawled out to look for some food (Niggle had no wife). Parish did not come round: the rain had got into his leg and made it ache; and his wife was busy mopping up water, and wondering if "that Mr. Niggle" had forgotten to call at the builder's. Had she seen any chance of borrowing anything useful, she would have sent Parish round, leg or no leg; but she did not, so Niggle was left to himself.

At the end of a week or so Niggle tottered out to his shed again. He tried to climb the ladder, but it made his head giddy. He sat and looked at the picture, but there were no patterns of leaves or visions of mountains in his mind that day. He could have painted a far-off view of a sandy desert, but he had not the energy.

Next day he felt a good deal better. He climbed the ladder, and began to paint. He had just begun to get into it again, when there came a knock on the door.

"Damn!" said Niggle. But he might just as well have said "Come in!" politely, for the door opened all the same. This time a very tall man came in, a total stranger.

"This is a private studio," said Niggle. "I am busy. Go away!"

"I am an Inspector of Houses," said the man, holding up his appointment-card, so that Niggle on his ladder could see it. "Oh!" he said.

"Your neighbour's house is not satisfactory at all," said the Inspector.

"I know," said Niggle. "I took a note to the builders a long time ago, but they have never come. Then I have been ill."

"I see," said the Inspector. "But you are not ill now."

"But I'm not a builder. Parish ought to make a complaint to the Town Council, and get help from the Emergency Service."

"They are busy with worse damage than any up here," said the Inspector. "There has been a flood in the valley, and many families are homeless. You should have helped your neighbour to make temporary repairs and prevent the damage from getting more costly to mend than necessary. That is the law. There is plenty of material here: canvas, wood, waterproof paint."

"Where?" asked Niggle indignantly.

"There!" said the Inspector, pointing to the picture.

"My picture!" exclaimed Niggle.

"I dare say it is," said the Inspector. "But houses come first. That is the law."

"But I can't . . ." Niggle said no more, for at that moment another man came in. Very much like the Inspector he was, almost his double: tall, dressed all in black.

"Come along!" he said. "I am the Driver."

Niggle stumbled down from the ladder. His fever seemed to have come on again, and his head was swimming; he felt cold all over.

"Driver? Driver?" he chattered. "Driver of what?"

"You, and your carriage," said the man. "The carriage was ordered long ago. It has come at last. It's waiting. You start today on your journey, you know."

"There now!" said the Inspector. "You'll have to go; but it's a bad way to start on your journey, leaving your jobs undone. Still, we can at least make some use of this canvas now."

"Oh, dear!" said poor Niggle, beginning to weep. "And it's not, not even finished!"

"Not finished?" said the Driver. "Well, it's finished with, as far as you're concerned, at any rate. Come along!"

Niggle went, quite quietly. The Driver gave him no time to pack, saying that he ought to have done that before, and they would miss the train; so all Niggle could do was to grab a little bag in the hall. He found that it contained only a paint-box and a small book of his own sketches: neither food nor clothes. They caught the train all right. Niggle was feeling very tired and sleepy; he was hardly aware of what was going on when they bundled him into his compartment. He did not care much: he had forgotten where he was supposed to be going, or what he was going for. The train ran almost at once into a dark tunnel.

Posted by sursumcorda on Sunday, October 8, 2017 at 8:25 am | Edit
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I suppose many visionaries were also potty mouths, and I also suspect Elon Musk's new rocket dream, the BFR, owes its name as much to Roald Dahl's Big Friendly Giant (BFG) as anything. Dahl was a potty mouth, too, just not as obvious about it to his intended audience.

Be that as it may, Musk dreams big.

 

This Daily Mail article explains his plan to revolutionize earth transportation.

Musk said the vessel would both take off and land vertically, like a space rocket, and for Earth travel, will take off from floating launchpads moored outside major cities. 

It would fly most routes - New York to Tokyo, for example - in about 30 minutes, and anywhere in under an hour, and Musk says the 'cost per seat should be about the same as full fare economy in an aircraft.'

The science fiction fan in me says, "It's about time!"

The realist in me says, "I'll believe it when I see it."

The cynic in me says, "Those impressive flight time numbers fail to take into account the time it takes to get to the launchpad and through security screening, which is what really drags down today's transportation times."

Nonetheless, it seems as if the future of my beloved childhood science fiction novels is coming closer, for good and for ill.

Posted by sursumcorda on Sunday, October 1, 2017 at 9:13 am | Edit
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