Virginia’s Relativity

                 Virginia Woolf at age 20


Doing some research reading on Virginia Woolf for a post yesterday about her novel To the Lighthouse, I came across an article that made what seemed like a weird connection between Woolf and Albert Einstein.

Imagine this: Virginia has a conversation with poet William Butler Yeats. It is 1934. Yeats wanted to talk about her very experimental novel from 1931, The Waves. Yeats’ interpretation of it was mystical and he had visions of “the Occult.”

She wrote in her diary after the conversation that you “can’t unriddle the universe at tea,” She also noted that Yeats had said that “Neither religion or science explains the world. The occult does explain it.”

Virginia was more interested in science than the occult. She was interested in physics and astronomy. Albert Einstein’s Special and General Theories of Relativity were news in 1905 and 1915 respectively and astronomer Arthur Eddington proved (observationally) relativity in 1919, and it became something heard by (but not really understood by) the general public.

What might a novelist do with Einstein’s theory that events in time are not the same everywhere for everyone? It could certainly change how you used time as a narrative structure.  That is what is happening in To the Lighthouse and the article’s author sees the influence in her Orlando, and The Waves, which are two novels I don’t know very well.

Virginia – and others in and out of the literary world – were influenced by Einstein’s view that this is a non-linear, probably godless and probably impossible to fully understand the world and universe.

The article goes into much greater detail but what seems to at least partially have created some of the popularity of his theories in the culture was that they were just so damned counter-intuitive. They turned earlier ideas upside down.

Did Woolf read Einstein’s work? Not clear. She might have just heard it in conversation with friends like philosopher Bertrand Russell who published the ABC of Relativity in 1925. Maybe she read some of the many newspaper accounts. 

Did it get her thinking in such a way about narrative that the character Orlando in that same-named novel is a boy in Shakespeare’s time but later wakes up as a woman in the 20th century? Time in the novel is relative and it moves much more slowly for Orlando than for the rest of his/her world. That’s a paradox that Einstein suggests, though not in such an extreme fashion.

Yeats wanted her to consider that there is a world beyond this one we see. Einstein would agree, but he wouldn’t explain any of it as mystical or having to do with religion. Either would Woolf, who would have a character in Mrs. Dalloway say that “there were no Gods; no one was to blame; and so she evolved this atheist’s religion of doing good for the sake of goodness.” It’s a philosophy of simplicity and seeing the marvelous in every day.

And yet, her life ended in suicide. She finished her last novel and fell into another depression as she had before. It was the start of World War II and her London home was destroyed during the Blitz. Her diary was full of thoughts about death. Woolf was overtaken by mental illness throughout her life and was institutionalized several times and attempted suicide at least twice. Her illness may have been bipolar disorder, for which there was no effective intervention during her lifetime. On March 28, 1941, she filled her overcoat pockets with stones, walked into the River Ouse near her home and drowned. She left a suicide note, addressed to her husband:

I feel certain that I am going mad again. I feel we can’t go through another of those terrible times. And I shan’t recover this time. I begin to hear voices, and I can’t concentrate. So I am doing what seems the best thing to do… 
I can’t go on spoiling your life any longer. I don’t think two people could have been happier than we have been.  V

Einstein at Princeton

Albert Einstein
Einstein on the steps of his Princeton home. It’s a photo I have always liked because as a young person I had several pairs of those fuzzy slippers and thought Albert and I had a kind of connection. Photo: Historical Society of Princeton

I have admired Albert Einstein since I was a young teen.  I believe my early attraction was to him was because he was “the genius” of that time and because of some quotations of his I saw that I loved – and the photos of his crazy hair, riding a bicycle and sticked out his tongue that made this genius seem human. I bought a poster of him that had the quote “Imagination is more important than knowledge,” which at the time probably made me feel better about my solid “B” average in school. It was years later that I saw that famous quote in context. That sentence is followed by “For knowledge is limited to all we now know and understand, while imagination embraces the entire world, and all there ever will be to know and understand.”

When I was a student at Rutgers College, I drove to nearby Princeton, New Jersey to find the little house he had lived in at 112 Mercer Street for the last part of his life. It wasn’t a museum and there were no markers to say that he had lived there. I was once told on a walking tour of the town by the Historical Society of Princeton that Einstein and his family did not want it to become a museum. It was added to the National Register of Historic Places and designated a U.S. National Historic Landmark. I also learned that when I visited in 1971, the house was owned by his step-daughter Margot Einstein who lived there until her death in 1986.

I have always liked the town of Princeton and the University campus looks the way I had imagined as a teenager that college campuses were supposed to look. It seemed like a good place for Albert Einstein to live after he escaped Nazi Germany.

Today I read that it was on this day in 1933 that Albert Einstein officially moved to the United States to teach at Princeton University, and I discovered something disturbing about that arrival.

Einstein was visiting the United States in February 1933 and he realized that he could not return to Germany with the rise to power of the Nazis under Germany’s new chancellor, Adolf Hitler. He was a visiting professor at the California Institute of Technology in Pasadena. He and his wife Elsa were returning to Europe in March and learned that the German Reichstag had passed the Enabling Act, which transformed the government into a de facto legal dictatorship with Hitler as Chancellor. They could not go on to his apartment in Berlin.

They later learned that the apartment and their summer cottage had been raided and all his papers confiscated. When they landed in Antwerp, Belgium, Albert went to the German consulate and surrendered his passport, formally renouncing his German citizenship. They found out years later that their cottage had become a Hitler Youth camp.

Einstein's Princeton home today

Einstein received offers from all over the world, including Paris, Turkey, and Oxford University, but he decided that Princeton’s offer of a teaching position at the Institute for Advanced Study, a home, and a good salary far away from Europe was best.

What I only learned today was why he hesitated about coming to Princeton University.

The University had a covert quota system that only allowed a small percentage of the incoming class to be Jewish. The Institute’s director, Abraham Flexner, was worried that Einstein would be too directly involved in Jewish refugee causes, so he carefully controlled public appearances, including declining an invitation to meet with President Roosevelt at the White House. Eventually, Einstein found out about the missed opportunity and called Eleanor Roosevelt and arranged for a visit. There is a letter he wrote to a rabbi friend of his about the incident. The return address on the letter is “Concentration Camp, Princeton.”

That was 1933. Did the campus become more welcoming to Jews as a possible war with Germany seemed more likely?  Five years after Einstein settled on campus, incoming freshmen at Princeton University ranked Albert Einstein as the second-greatest living person. They ranked as the greatest living person Adolf Hitler.

Walking with Einstein and Gödel

I picked up the book When Einstein Walked with Gödel this past week at the library because of the title and the photo on the cover of the two mathematicians walking across a campus in Princeton, New Jersey.

I was disappointed that the entire book was not about the two of them, but is instead a collection of essay by Jim Holt. The title essay is one I really like as it deals with one of my favorite topics – our changing notions of time. It comes from a friendship between Albert Einstein and Kurt Gödel when they were both working in Princeton in the 1930s. Einstein had shaken the physical world with his work, and Gödel had shaken mathematics. They ended up taking almost daily walks to their offices at the Institute for Advanced Study.

Gödel would have looked pretty fancy (he liked white linen suits) and Einstein would have looked like the absent-minded genius that we know with his crazy hair and too-big pants.

But what really interests me in reading the essay today was the walking. Today was a very nice spring day that was warmer than it has been. I took the covers of the deck furniture and sat outside with my lunch and coffee. And I went for a walk.

I love walking and I am a firm believer in the power of walking to spark creativity and thought. (More on that tomorrow) Of course, it would be great to have the content of those walking conversations between Al and Kurt. I imagine that the conversations went beyond math and physics, though I’m sure math and science were the main themes.

I have so far only skimmed a few of the other essays in the book, but each could be a walking conversation. Did you know that the word “scientist” was only coined in 1833? It was a philosopher, William Whewell, who used it in his efforts to “professionalize” science and separate it from philosophy. Holt quotes Freeman Dyson (another person at the Institute who I actually got to meet and talk with briefly when he gave a talk at NJIT) as saying that “Science grew to a dominant position in public life, and philosophy shrank. Philosophy shrank even further when it became detached from religion and from literature.”

I certainly couldn’t keep up with Einstein and Godel on the science of time, but I would love to put in my own ideas and get some feedback from the boys.

Some of Holt’s questions that he attempts to answer in the essay are also intriguing ideas for a walking conversation. Does time exist? What is infinity? Why do mirrors reverse left and right but not up and down? And the biographical sketches of famous and not-so-famous thinkers makes me want to go on walks with them too – Emmy Noether, Alan Turing, Benoit Mandelbrot, Ada Lovelace and others.

The Pi of Rivers

I met pi in school. You probably met pi that way too. It is that number used to calculate the circumference of a circle. Pi is shown symbolically as:


Pi is the ratio of the circumference of a circle to its diameter. It is an “irrational number” which means its exact value is inherently unknowable.

Using computers, we have calculated billions of digits of pi, starting with 3.14159265358979323…   –  but no recognizable pattern emerges. So strange. The digits of pi continue to infinity. Does anyone really understand infinity?

Ancient mathematicians did not like irrationality because it didn’t work with the concept of an omniscient God.

Recently I read about another pi connection which is also strange. In 1996, the UK earth scientist Hans-Henrik Stølum published a paper announcing that pi explains the seemingly chaotic paths of rivers in a mathematically predictable pattern.

This is called a river’s sinuosity. By dividing the river’s actual meandering length by the length of the direct line drawn from source to sea.

Of course, some rivers flow pretty straight from source to mouth , so they have small meandering ratios. Some rivers wander all over the place and have high meandering ratios.

But the average meandering ratio of rivers seems to be pi. Good old 3.14.

Albert Einstein used fluid dynamics and chaos theory to show that rivers tend to bend into loops.

If a river has a curve that will generate faster currents on the outer side of the curve. Those currents will cause erosion and so a sharper bend. That will eventually make the loop tighten. I have read that then chaos will eventually cause the river to double back on itself and form a loop in the other direction.

I did some more research on this river connection and found that this claim may not be accurate.

Someone put up a website at one point to crowdsource river data. The site at seems to be dead now. People could put in the coordinates of the mouth and the source of a river, and the length of the river (from Google Maps and Wikipedia probably) to calculate the sinuosity of a river. That study looked at 258 rivers and found an average sinuosity of an un-Pi-like 1.94.

Hmmm. Maybe it is another mathematical constant, like the golden ratio (phi) which we often find in nature. That value is 1.618. Nope.

What about if you look at pi/phi? You get 1.94. Okay, that’s a strange “coincidence.”  Or something more than coincidence?

I need to be careful with all this, because I saw the film titled Pi. I saw this science fiction film when it was released in 1998. It is a difficult film to label. It is surrealist, psychological, thriller, that delves into religion, mysticism, the relationship of the universe to mathematics and number theory. It was written and directed by Darren Aronofsky in his directorial debut.

I read it as a cautionary tale. It is about a genius oddball mathematician, Max, who has been working for a decade trying to decode the numerical pattern beneath ordered chaos. The ordered chaos he studies is the stock market.

Max’s belief that there is some mathematical “code” underlying everything compares in my mind with Einstein trying to find that theory that explains it all. That quest frustrated Einstein through the end of his life.

Beware of that quest.

Ripples in Spacetime

After decades of research, in September 2015 the twin Laser Interferometer Gravitational-wave Observatory (LIGO) detectors measured ripples in the fabric of spacetime. That ripple is known as gravitational waves. They arrived at the Earth from a cataclysmic event in the distant universe. The new detectors had just been brought into operation for their first observing run when the very clear and strong signal was captured.

Back in 1916, Albert Einstein predicted the existence of gravitational waves. These miniscule ripples in the fabric of spacetime are generated by unfathomably powerful events.

In Black Hole Blues and Other Songs from Outer Space, Janna Levin says that if those ripples and other vibrations could somehow be recorded, we could observe our universe through sound. What might we hear? The hissing of the Big Bang, the songs of collapsing stars, the low rumblings of merging galaxies, the smash of two black holes collapsing into one.

Spacetime takes the concepts of time and three-dimensional space and fuses them together. In classical mechanics – think of Isaac Newton – time is separate from space. In special relativity – think of Einstein – time and space are fused together into a single 4-dimensional “manifold” called spacetime.

Can you really grasp that concept? I think I do, but ask me to explain it and I go blank.

Many things about space and time are at a scale that really is incomprehensible to most of us. Based on the observed signals, the LIGO scientists estimate that the black holes for the event they detected were about 29 and 36 times the mass of the sun. I can’t imagine that. The event took place 1.3 billion years ago. I also can’t imagine that.

For this event, about 3 times the mass of the sun was converted into gravitational waves in a fraction of a second. The peak power output would have been about 50 times that of the whole visible universe. This energy is emitted as a final strong burst of gravitational waves.

This past October, Rainer Weiss, Kip Thorne, and Barry Barish won the Nobel Prize in physics for directly detecting gravitational waves.


Knowledge and Imagination


“Imagination is more important than knowledge.” ― Albert Einstein

Knowledge versus imagination. Einstein spent the latter part of his life pursuing a “single, all encompassing theory of the universe.”  He wanted to able to describe all of nature’s forces – to explain it all. He didn’t find it.

James Taylor sings in “Secret of Life

Now the thing about time
Is that time isn’t really real.
It’s just your point of view,
How does it feel for you?
Einstein said he
Could never understand it all.
Planets spinning through space,
The smile upon your face,
Welcome to the human race.

That Einstein quote at the top of this article continues “…for knowledge is limited to all we now know and understand, while imagination embraces the entire world, and all there ever will be to know and understand.” Imagination is often the pathway to increasing knowledge.

It is interesting that astronomy experiments now might test an idea of Einstein’s that he proposed almost exactly a century ago. It has been a longstanding question of why the Universe is expanding at an accelerated rate. Calculations in a new study could help to explain whether dark energy, as required by Einstein’s theory of general relativity, or a revised theory of gravity are responsible.

Einstein wasn’t a big fan of a lot of the physics that came at the end of his life, and would probably not be a fan of string theory.

Brian Greene is a professor of mathematics and physics at Columbia University who is probably best-known to the public for his NOVA television specials. He is one of the best “explainers” of this deep science. He explains string theory and I can understand it – until he stops explaining it and I have to tell someone else what he meant. The idea of minuscule filaments of energy vibrating in eleven dimensions that make up the “fabric of space.. and create every particle and force in the universe” is not easy to understand or accept.

String theory fills in the gaps of Newtonian physics, especially regarding how gravity works, and Einstein’s Unification Theory depends on the existence of extra dimensions, which contain these filaments and some string theorists posit that there are at least eleven dimensions. For all of us used to living in four dimensions, that is tough to imagine.

James Gates is known for work on supersymmetry, supergravity, and superstring theory. When he was asked about Einstein’s statement that “imagination is more important than knowledge,” he said“For a long time in my life, imagination was the world of play. It was reading about astronauts, and monsters, and traveling in galaxies, all of that kind of stuff, invaders from outer space on earth. That was all in the world of the imagination. On the other hand, reality is all about us. And it’s constraining, and it can be painful. But the knowledge we gain is critical for our species to survive.”


Brain Greene on string theory