Sunday, February 18, 2024

Len Anderson (1944 -- 2024)

Len Anderson

LEN ANDERSON (1944 -- 2024)
Len Anderson passed away in his own bed on Mattison Lane in Santa Cruz early Tuesday morning, January 30, tended by his wife, Elke Maus.
Len earned a PhD in physics from UC Berkeley, worked in experimental high-energy physics at Berkeley and in Europe, then switched to industry where he designed sensors for paper-making machines. 

Moving to Santa Cruz in the early 90s, Len developed his talents as a poet, co-founding Poetry Santa Cruz and Hummingbird Press, organizations which sponsored poetry readings, encouraged and published the work of local poets including three books by Len himself: Affection for the Unknowable (2003), Invented by the Night (2011) and The Way Home (2019).

In 1992, Len laid down a memorable mark on the poetry scene with his clever parody of Allen Ginzberg's Howl, the infamous anthem of San Francisco's Beat Generation. Len called his work BEEP crafting it as an anthem of the "BEEP Generation", in which he caricatures the behavior of the programmers and entrepreneurs of Silicon Valley whose efforts gave birth to today's personal computers.

BEEP's opening line

A large part of Len's work deals poetically with spiritual and metaphysical themes. Like myself, Len was for a long time a practicing Roman Catholic.
Invented by the Night    p 28

And next, Len imagines for us a back-alley encounter between Science and Mysticism:
The Way Home   p 42

Modern quantum physics, consciousness and mysticism are not so easy to comprehend. These regions of experience are subtle, obscure, elusive and call out for a correspondingly subtle and sophisticated courtship. One example:
Invented by the Night   p 48
 Philosophically Len Anderson was a passionate agnostic who flirted playfully in public with the boundaries of human knowledge (as per the title of his first book Affection for the Unknowable). And in Len's books and readings he shamelessly reveals himself as a faithful lover of the Great Mystery. For his wife Elke,  his friends and community, and for fellow seekers after the Mysteries, the death of Len Anderson has left a big hole in the fabric of being.

Affection for the Unknowable   p 11

Invented by the Night   p 68



Monday, October 16, 2023

it's time to face this sex thing

August O'Connor

 it's time to face
this sex thing
It makes us men.
It makes us women.
It makes a joke
to please us
to see us smile.
It makes Beauty
to open our hearts.
It makes Love. 
            August O'Connor 

Friday, September 29, 2023

Fulton-Bennett Woodblock Prints

Kim Fulton-Bennett: Boulder Creek Library

Kim Fulton-Bennett is a man of many talents, marine biologist, science writer, composer and performer in several musical genres, primary traditional Celtic music where for several years he was half of the Dobhran ("otter" in Gaelic) duo with August O'Connor which entertained at coffee shops, festivals, weddings and private parties in the Santa Cruz area. More recently he performed with Blarney, a larger Celtic band. Inspired by his work at MBARI (Monterey Bay Aquarium Research Institute) he is currently authoring a website Seasons in the Sea which recounts the life stories month by month of conspicuous plants and animals living in and around Monterey Bay. Inspired by his contact with nature through marine bio;ogy, through hiking in the California wilderness and by surfing off the coast of Santa Cruz, Kim has been producing a series of woodblock prints some of which are now on display (Sept--Oct 2023) at the Boulder Creek branch of the Santa Cruz Library.

"I live in the redwood-covered hills behind Santa Cruz," writes Kim, "and spend my free time hiking the mountains and surfing along the wild North Coast. That's where I get the inspiration for most of my wookblock prints."

"My first woodblocks were simple designs for friends and relatives. But I soon fell in love with the magical process of carving a design into a block of wood, inking the block, and then seeing the design on a piece of paper."

"I carve my woodblocks by hand and make prints in small editions of 5 to 15 prints. Each print is signed, numbered, and dated. Because they are hand made, each print is unique."

Mt Lassen from Spirit Lake

Point Sur

Pigeon Point Lighthouse

Rockview: Moonlight

Plum Blossoms

Thursday, July 6, 2023

August O'Connor (1951 - 2023)

August O'Connor in meadow with big bodhran.

 AUGUST O'CONNOR (1951--2023)

Born in Southern California in 1951, the middle girl between two brothers, Raleigh and Greg, August O'Connor early experienced a love of animals, drama and mystery. She raised pet rats and played with snakes. And face-painted, dressed in leotard, rabbit skins, leather aviator helmet and shaking a coyote-skull rattle, she entertained her high school classmates as "Animal Woman: Protector of all speechless creatures." She starred in student plays, performed in an all-girl band and, starting as a freshman, she edited her high school's literary magazine.
After graduation, while living in Claremont, she met and married Bill O'Connor. Shortly afterwards they moved to Capitola where they attended St. John's Episcopal Church before moving to San Francisco to work at Grace Cathedral.

For eight years at the Cathedral, August O'Connor served as assistant verger, supporting Bishop Swing in ceremony, designing vestments and providing counseling, For six years she worked as chaplain at San Francisco General Hospital during the rise of the AIDS epidemic.

In recorded conversation with San Francisco social historian Lynne Gerber about her AIDS and other work, August recalled: "Lots of different lives but there is a chaplaincy thread running though it. The thread is love, I'd say, the thread is willingness to love. And to be loved, you know, because when you open your heart to someone, you might not be loved, you know." August's motto, painted on her gate post, is: "Every blessing on all beings."
August has worked in every aspect of the visual arts from large oil paintings to cartoons. In the 70s she was Art Director of Good Times, Santa Cruz's largest weekly newspaper. She designed logos for several businesses including Zoccoli's Deli and Pink Godzilla; producing signs, murals and window displays for numerous local shops. She also fashioned necklaces, earrings, bracelets, Celtic knot tattoo designs and unusual hand-hammered copper sculptures based on double spirals which she called "Buddha-mind roller coasters."
After leaving Grace Cathedral, August and her friend Nick Gardner began attending Native American sweat lodge ceremonies in Marin and Shasta counties under the direction of Karuk medicine man, Charlie "Red Hawk" Thom. When she moved back to Capitola, August mentored under medicine man Indio, eventually running her own sweat lodge events when Indio became ill. August's sweat ceremonies, carried out with Nick Gardner on the beach a few miles south of Pigeon Point lighthouse, drew a wide variety of attendees primarily from the nearby University in Santa Cruz. Also with Nick Gardner, she enjoyed many trips into the wilderness which she loved. 
In her home in Capitola, on one city lot, August put together a voluptuous Mediterranean garden crowned by an orchard of olive, apple, plum, lemon, loquat and persimmon trees. In addition to wild profusions of flowers, the garden produced food – lettuce, tomatoes, beans and potatoes as well as fruit from its trees. August's garden was a haven for bees, butterflies, bats and small mammals and had been officially certified as Wildlife Habitat #29951 by the National Wildlife Foundation.
August was a splendid chef, could create a tasty meal out of most anything. At San Francisco gatherings, she garnered admiration for her party specialty: chocolate truffles. Her turmeric toast made an unusual breakfast treat and August's mushroom omelettes were arguably the best in the known universe.
August sang and played guitar and bodhran (Irish frame drum). With flute-and-whistle player Kim Fulton-Bennett, they formed the Celtic duo Dobhran (Gaelic for "otter") which played at weddings, wineries, coffee shops and private parties and they also recorded a few instrumental CDs. Dobhran has performed at numerous Scottish and Irish festivals in Santa Cruz and Ben Lomond. A familiar presence at local Irish music sessions, August recently started a new group called Blarney with Kim, Nick Herbert and Matt Johnson, which has performed on stage, at private parties and most recently at an Irish wake in Boulder Creek.
Friends have described August's character variously as "playful dignity", as "innocent sophistication", as "kaleidoscopic life force",  as "remarkable, unique, eccentric",  and as "a tempestuous whirlwind." She herself explained "My life/is one kiss/with life."
She was hospitalized recently in Santa Cruz for a serious infection. And, on March 24, a week after St. Patrick's Day, early in the morning at age 72, this former chaplain, artist, musician, sweat lodge leader, gardener, beautiful and loving woman, August (Augie) O'Connor, passed away peacefully in her sleep.

Says Nick Herbert: "August came from a larger place and shared some of that with the rest of us."

Said one good friend: "August filled pages; she was a tome."

Added another: "August was an Irish rose."


Saturday, July 1, 2023

I Like My Hands

August playing her bodhran (Irish frame drum)

Hands, I like my hands
They do so many things
Well for me.
Hands, I like my hands
They do me well.

Feet, I like my feet
They do so many things
Well for me.
Feet, I like my feet
They do me well.

Friends, I like my friends
We do so many things
Well together.
Friends, I like my friends.
We do so well.

Lord, I love my Lord
He does so many things
Well for me.
Lord, I love my Lord
He does me well.

Life, I love Life
It's so good to be Living
And, and when I die
I'll be so glad for what
I've had.
And, and when I die
I'll be so glad.


Sunday, June 4, 2023

Deep in my Head

August O'Connor

by August O'Connor
I was deep in my head
Deep in my head
Deep in my head
When you startled me.

I was deep deep
Deep in my head
When I saw you
And you startled me.

When I saw you
And you startled me
I saw you
And you startled me.

I would like to be
Startlingly beautiful
Deep in my head
When you startled me.

I would like to be
Startlingly beautiful
I would like to be
Startlingly fair, fair, fair.

Fairer than a rose
Fairer than a perfect rose
Fairer than a dawn
Fairer than a perfect dawn.

Fair as the light
Shining from my lover's
Bright eyes

Fair as the words
Spoken from my lover's
Sweet lips

Fair as the love
Deep at the heart of everything
I would like to be
Startlingly beautiful.

I was deep, deep
Deep in my head
When I saw you
And you startled me.

Tuesday, May 16, 2023

Kauffman Flypes Rolfson into O'Connor knot

August O'Connor, Celtic knot maker


My friend and musical partner, August O'Connor, designed me a personal Celtic knot which became part of my business card plus a rubber stamp, and which she also painted on my back, my bald head and on a hat box containing my black derby hat.

O'Connor knot painted on a hat box

I recently discovered that knot theorists have classified knots according to the minimum number of their crossings and that the O'Connor knot is an example of a seven-crossing knot. According to the official knot table constructed by Dale Rolfsen there are only seven seven-crossing knots. So I naturally wondered which one of the seven Rolfsen knots corresponded to the O'Connor knot. After a simple but long and tedious calculation (presented in my previous post) I proved that the correct Rolfsen knot was 7--6.

In other words I had proved that it must be possible just by twisting and turning Rolfsen 7--6

The Rolfsen 7--6 knot

to transform it into the O'Connor seven knot. 


The O'Connor seven knot

By tying a big rope in the shape of the Rolfsen knot and trying over and over again to turn it into an O'Connor knot (which I had proved must be possible) I ended up with nothing but featureless tangles and usually was unable to even return to the original Rolfsen. Then I had to untie the rope and try again.

In short, Nick could prove it but not do it.

For reasons unknown to me, Nick's dilemma attracted the attention of prominent knot theorist Louis Kauffman who demonstrated a simple set of three moves that easily turn Rolfsen into O'Connor.

Knot theorist Louis Kauffman

 Kauffman summarized his three moves on a single sheet of paper which I reproduce here. He also hinted that he might assign this exercise to his students as a homework problem.

Kauffman's first move

The O'Connor knot might be visualized as two outspread wings positioned over a "tail". Kauffman noticed that the O'Connor "tail" already occurs in the Rolfsen knot at 2 o'clock on the standard diagram, So Kauffman's first move is to rotate the Rolfsen till the "tail" is now at the bottom at 6 o'clock.

Kauffman's second move

 For the second move we notice that the O'Connor knot's two "wings" are symmetric around the vertical axis but the Rolfsen knot is not. The Rolfsen knot has two crossings on the left-hand side (A) and zero crossings on the right (B), in the rotated sketch drawn by Kauffman.

For his second move, Kauffman then applies a twist that equalizes the number of crossings on the left and right hand sides. This twist (illustrated in the upper right corner of Kauffman's sketch) subtracts a crossing from one loop and adds it to the other. After this twist, technically called a "flype", both loops now contain the same number of crossings, and with a little bit of rearrangement, can be seen to resemble the "wings" of the O'Connor knot: Kauffman's third move.

Kauffman's third move

Kauffman's first and third move are nothing but simple reaarrangements that can be accomplished without lifting the knotted rope from the table. The real trick resides in Kauffman's second move in which he applies a simple twist (called a flype) at precisely the right position. The word "flype" is derived from a Scottish word meaning to skin or fold as in turning over the edge of a sock.

Now I know how to turn a Rolfsen into an O'Connor knot. And so do you.

With grateful appreciation for Louis Kauffman's timely aid, I offer for your enjoyment the seemingly effortless liveliness of August O'Connor's "Knotted Hare"

August O'Connor's "Knotted Hare"


Tuesday, November 15, 2022

The O'Connor Knot

August decorating a young lass with Celtic knot.


For 10 years, my musical partner in the Blarney band, August O'Connor, lived and worked at Grace Cathedral in San Francisco as a reader, artist and designer of vestments. Then, moving to Santa Cruz, she led sweat lodges for many years on the Pacific coast. But by far August's favorite church is wild nature.

August, as a talented graphic artist, worked for a time as art editor of a local newspaper. She created logos that still adorn local businesses and sweatshirts. August is particularly fascinated by Celtic knots, teaching classes on how to design them, painting Celtic knots on body parts and incorporating them into decorative objects and tattoos.

After becoming acquainted with her work, I asked August to design for me a personal Celtic knot which I have been using for many years on my business cards and as a signature/chop on documents and correspondence. I call it “Nick's Knot” but this knot is more appropriately credited to its inventor. 

Nick admiring the O'Connor Knot

The O'Connor Knot (or AOC Knot) is a Celtic-style knot with seven crossings. Knot theorists have recognized seven distinct knots with seven crossings and I have often wondered which of these seven official knots represents my personal knot, a curiosity which could be satisfied by forming a rope into an AOC Knot, then successfully deforming that rope into one of the seven classic forms. My few attempts along these lines have so far resulted only in random tangles.

Then, just a few days ago, I ran across an article by David Richeson in "Quanta”, an online science magazine, entitled “Why Mathematicians Study Knots” which informed me of a better way to match my O'Connor Knot with a knot having some official name.

I learned from this article that knots played a brief role in physics at the end of the 19th century when William Thomson (Lord Kelvin) and P. W. Tait conjectured that atoms were formed of knots (vortex rings) tied in the electromagnetic ether.

Einstein's Theory of Special Relativity banished the ether which put an end to the knotty atom hypothesis. But P. W. Tait continued to be fascinated by knots, compiling long lists of knots with various crossing numbers, studying their properties and, in effect, turning himself into the world's first Knot Theorist. (See “The Knots of Peter Guthrie Tait.”)

Paying homage to Kelvin and Tait's failed theory of atoms, Quanta magazine published a table of all knots up to seven crossings in the style of the familiar Periodic Table of the Elements. This article also showed me an easy way to match Nick's Knot -- by calculating its mathematical knot invariants and comparing them with the knot invariants of the Magnificent Seven.

List of Knots in the form of Periodic Table

So I proceeded to immerse myself in Knot Theory, mostly by watching videos on YouTube and by consulting the wonderful Atlas of Knots on the Web. Some of the knot invariants are easy to come by. The others require some simple but tedious graphing and calculation.

The first knot invariant is the Crossing Number which I already knew to be seven. The second is the Unknotting Number “u” which is the minimum number of eliminated crossings which will turn the knot into a simple loop (or “Unknot”). The third quantity is the Coloring Number “C” which is the minimum number of colors needed to color the knot segments under simple restraints.The Coloring Number, however is not an invariant. Coloring Number changes depending on how the knot is drawn, except in the case of C = 3, which is a true knot invariant, dividing all knots into two distinct classes depending on whether they are 3-colorable or not.

Incorporating these three quantities (and a fourth labeled “W”) I redrew the Quanta Knot Table including the unknown O'Connor Knot. 

What's the place of the stately O'Connor Knot?

By trial and error, and using colored markers, I was able to determine the Unknotting Number u and the Coloring Number C of the AOC Knot. Unknotting Number of AOC is 1 and Coloring Number is 4. This last result means that the O'Connor Knot does not belong to the exclusive class of 3-colorable knots, which immediately eliminates knots 7(4) and 7(7) which do happen to be 3-colorable.

The only remaining candidate knots in the Periodic Table with u =1 are the knots 7(2) and 7(6) neither of which much resemble the AOC Knot in their official presentations. So further investigation is necessary to decide which of these two will be the winner in this knotty look-alike contest.

The knot 7(5), in this representation, seems to most closely resemble the AOC Knot, but that can't work because 7(5) has the wrong Unknotting Number.

Time to go to work. I formed an oriented AOC Knot and labeled each of its 7 crossings and each of its 7 segments according to a scheme devised by Princeton math professor James Waddell Alexander in 1928. My intent was to calculate the AOC Knot's Alexander Polynomial which is for knots a unique mathematical identity card.

In addition to his mathematical fame, Professor Alexander was a notable mountaineer in both Europe and the United States. A rock formation in the Colorado Rockies bears his name —Alexander's Chimney. While at Princeton, Alexander liked to climb university buildings, and always left his office window on the top floor of Fine Hall open so that he could enter by climbing the building

i can confirm that using buildings for practice climbs is not confined to Princeton. While a graduate student at Stanford in the early Sixties, my office on the second floor of Inner Quad was adjacent to a radiator with a nylon rope attached. Physics students so inclined (not myself) would skip the stairs, toss the rope out the window and rappel directly down to campus. 

The Oriented AOC Knot awaiting Alexanderization

Alexander's genius was to discover a useful way to mathematicize the crossings and segments of a knot such that these numbers could be combined to uniquely characterize any knot no matter how complicated.

One of the features of Alexander's Way of looking at knots is that it divides all crossings into Right Crossings and Left Crossings. This division immediately gives rise to another simple knot constant — its “Writhing Number” (or simply its “Writhe”), a nomenclature I adore for its squirmy feeling.

A knot's Writhing Number “W” is defined as its number of Right-hand Crossings minus its number of Left-hand Crossings. The Writhing Number of the AOC Knot is 5 - 2 = 3.

All odd-crossing-numbered knots exist in two forms. The trefoil knot 3(1), for example, differs from its mirror image 3(1)*, a knot property called “chirality” or “handedness”. Trefoil knot 3(1) consists of three Right-hand Crossings (W = 3) while its mirror image 3(1)* is composed of three Left-hand Crossings (W = -3)

Since the handedness of a crossing does not change when the direction of its orientation arrows are reversed, it appears that handedness is a robust property of a knot diagram. When reflected in a mirror though, all RH crossing change into LH crossings and vice versa, so the Writhing Number will change sign under mirror reflection. Following this logic, the Writhing Number of the AOC Knot's mirror image would be W = -3.

Calculating the Writhing Numbers of the two candidate look-alikes we obtain W = 7 - 0 = 7 for J(2) and W = 5 - 2 = 3 for J(6). This result would seem to cinch the contest in favor of J(6) since both J(6) and the AOC Knot possess the same Writhe.

However I notice in the Atlas of Knots that the Writhing Number is not listed as one of the several parameters that distinguish one knot from its fellows. If the Writhing Number depends on how the knot is drawn then this conclusion that AOC Knot and the J(6) knot are the same might be false.The gold standard for separating one knot from another appears to be the Alexander Polynomial which can be computed from the former Crossing and Sector labeling scheme by forming the knot's Alexander Matrix, which in the case of the AOC Knot, looks like this: 

From this matrix, a simple but tedious calculation (finding the determinant of a 6x6 matrix at least half of whose entries are zero) suffices to produce the desired Alexander Polynomial. It took me about an hour to generate the first result. which agreed with neither of the AP's listed for the two candidate knots. I repeated the calculation getting a different result. Still no match. (I have never been good at doing calculations involving loads of simple arithmatic where one wrong minus sign can shipwreck the entire crew. This is the kind of mindless arithmatic for which computers were invented.) I confess that I did this stupid calculation 12 times and got 12 different answers, each time though correcting at least one error in my previous work. This task consumed three days and lots of paper.

Then on the morning of the fourth day of boring high-school level arithmatic, I fixed my final mistake. And managed to calculate my first real Alexander Polynomial!

The same Alexander Polynomial listed in the Knot Atlas for J(6).

This agreement of the two knot's Alexander Polynomials means that despite their superficial differences, the AOC Knot and the J(6) Knot are exactly the same knot. Also they are not mirror images because their Writhing Numbers are identical. (One weakness of the Alexander Polynomial is that it does not distinguish between a knot and its mirror image.)

In real life I have not yet been able to deform my AOC Knot rope into a J(6) Knot rope but my four-day pilgrimage into Knot Land has blessed me with the certainty that such a deformation is surely possible.

August continues to produce original sketches of lively animals, to hammer out odd copper orbitals and to create beautiful Celtic knots. One of my favorites is her “Love Knot” formed with 11 alternating crossings. The Knot Encyclopedia lists 367 different alternating 11-crossing knots. The Writhing Number of O'Connor's Love Knot happens to be 7 - 4 = 3, the same Writhing Number as her AOC Knot. And so we come back to where this knotty inquiry first began. 

August O'Connor's "Love Knot"

Sunday, October 30, 2022

A New Kind of Saint

November 1: All Saints Day


In this Age that couldn't be Darker
When the Lamp of Wisdom grows faint
When the Empire of Lies seems to triumph
We are needing a new kind of saint.
A saint who comes out of nowhere
From a direction you'd never expect
A saint who's tantric, organic and quantum
And politically incorrect.
A saint that performs needful miracles
More beautiful and bigger than most
Not by him but through him manifested
By the grace of a new Holy Ghost. 

Might not be a Hindu or Buddhist
Nor a Protestant, Catholic or Jew
Nor even a bright quantum physicist
Could even be me or be you.

Could even be you, my friend
When you say yes to that calling inside you.

Friday, October 14, 2022

Reality on Radio


Interview - Physicist Nick Herbert on the latest Nobel Physics Prize on Bell's Theorem, Quantum Entanglement, and Non-local Reality


Quantum physicist Nick Herbert is our special guest for the full two hours of today's show, speaking about the latest Nobel Physics Prize on Bell's Theorem, Quantum Entanglement, and Non-local Reality. He and John Clauser, one of this  year's awardees of the prestigious prize, were colleagues together in the Fundamental Fysiks Group back in the 1970's, when this line of research was being explored.

Nick makes the point that Bell's Theorem was ignored back in 1964, when it was first espoused, not because it was bad science, but because it was looking at Reality, not theory, and physicists at the time considered Reality out-of-bounds for physics research.

 So today we'll be taking a fresh look at John Bell's work, faster-than-light signaling, quantum encryption, quantum teleportation, making entangled photons, quantum computers, creating reality with our thoughts, and wondering whether consciousness is our reward for...'collapsing the wave function'?!! Enjoy!