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137When Douglas Adams wrote The Hitchhiker’s Guide to the Galaxy, he wrote that “The answer to the ultimate question of life, the universe and everything is 42.”  He was joking, but I wonder if the answer really might be 137.

Take a look at one thing about 137 in mathematics: Using two radii to divide a circle according to the golden ratio yields sectors of approximately 137° (the golden angle) and 222°.

In physics, 137 is the approximate denominator of fine-structure constant. Being a dimensionless physical constant, it is approximately 1/137 and has the same numerical value in all systems of units.

Physicists have postulated for more than a hundred years that 137 might be at the center of a grand unified theory, relating theories of electromagnetism, quantum mechanics and, especially, gravity. It’s the DNA of an atom.

As the inverse of the fine-structure constant, it is related to the probability that an electron will emit or absorb a photon (Feynman’s conjecture).

Some physicists has suggested that if the number that unified the relationship between all these concepts turned out to be 1 or 3 or a multiple of pi, that would make more “sense.” But why 137?

Leon Lederman thought that because the number 137 “shows up naked all over the place,” that means that scientists on any planet in the universe using whatever units they have for charge or speed, and whatever their version of Planck’s constant may be, will all come up with 137, because it is a pure number.

But it shows up frequently outside of math and physics.

In mysticism, the Hebrew word קבלה (Kabbalah) has a Gematria (numerical value) of 137.  It describes the “corresponding loops” which clasped together enjoin the two sections of the Tabernacle’s ceiling. These loops divided the Holy Place and the Holy of Holies – the physical dimension and the spiritual dimension – and at the boundary line of the physical world, the number 137 emerges.

Moses’ Tabernacle, the earthly dwelling place of God, was 13.7 meters long. NASA’s Wilkinson Microwave Anisotropy Probe (WMAP) has taken the best measurement of the age of the Universe to date. and ”scientists now have the best estimate yet on the age of the Universe: 13.7 billion years.”

Some people have therefore connected the science, math and mysticism. 137 refers to electrons and the odds of an electron absorbing a single photon, so in simple Kabbalah language, 137 is about Vessel and Light. It is about the physical body of man (Vessel) and our ability to ignite the Light in the soul.

One of the important physicists of the 20th century, Richard Feynman, wrote about the number 137:

“It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it. It’s one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man. You might say the ‘hand of God’ wrote that number, and ‘we don’t know how He pushed his pencil.”

According to the Bible, Abraham died at age 175, but when he was commanded by God to offer his son up as a sacrifice, he was 137. According to the Torah, Moses’ father lived to 137, so did Ishmael and Levi.

Physicist Leon M. Lederman numbered his home near Fermilab 137.  He tried to unite the Ancient Greeks’ earliest scientific observations, Einstein, and the Higgs boson, which is nicknamed the God Particle.

“One hundred thirty-seven is the inverse of something called the fine-structure constant. …The most remarkable thing about this remarkable number is that it is dimension-free. …Werner Heisenberg once proclaimed that all the quandaries of quantum mechanics would shrivel up when 137 was finally explained.” ― Leon M. Lederman, The God Particle: If the Universe Is the Answer, What Is the Question?

Wolfgang Pauli, a pioneer of quantum physics, died in a hospital room numbered 137, a coincidence that disturbed him.

Physicist Pauli and psychoanalyst Carl Jung were both obsessed with the power of certain numbers, including 137. They were fascinated by the atom’s fine-structure constant and its Kabbalistic significance. They formed an unlikely friendship and began a mystical quest that led them through medieval alchemy, dream interpretation, and the Chinese Book of Changes.

They were two people who believed 137 was at the intersection of modern science with the occult, and that it was a mystical number with a meaning beyond physics.

In 137: Jung, Pauli, and the Pursuit of a Scientific Obsession by Arthur I. Miller, it is reported that Pauli once said that if the Lord allowed him to ask anything he wanted, his first question would be “Why 1/137?”

Is there a primal number at the root of the universe
that everything in the world hinges on?


Despite the persistent ticking of clocks and our almost constant attention to time, quantum physics says it doesn’t even exist. Theoretical physicist  Carlo Rovelli writes that “There is no time variable in the fundamental equations that describe the world.” At the quantum level, durations are so short that they can’t be divided and there is no such thing as time.

And yet, he has spent most of his life studying time.

Rovelli’s book, The Order of Time, is about the way we experience the passage of time.

One of his premises is that chronology and continuity are stories we tell ourselves. We need these stories to make sense of our existence.

He asks tough – or maybe crazy – questions, such as “Why do we remember the past and not the future?”

These are questions for physicists and philosophers, but not ones most of us consider as we move through a time story from past to future that we think is uniform and universal.

His view is hard to grasp. His universe is made up of countless events. Things that happen and even physical “things” are in a continual state of transformation. No space nor time—only processes that transform physical quantities from one to another.

Time is our measure of change.

Rovelli’s short collection of essays, Seven Brief Lessons on Physics, was a bestseller and one of the fastest-selling science books ever.

If all this seems out there, remember that Einstein said that our clock time is an illusion. Time zones – a 20th Century invention – was a business decision, not a fact of the universe. Einstein said that time passes at different rates from place to place. It passes faster at the top of a mountain than at sea level. Perhaps imperceptibly to us, a clock on the floor will move ever so slightly slower than a clock on top of the fireplace mantle.

Time’s passage is a mental process, a story we tell ourselves in the present tense. It’s your own story. It’s our collective story.

But I have trouble accepting all this when explanations keep saying things like “Time runs slower wherever gravity is strongest, and this is because gravity warps or curves spacetime.”  I guess Rovelli has to use the term “time” to explain that there is no time in the way that atheists need to talk about god in order to explain why there is no God.

Benedict Cumberbatch reading the opening of The Order of Time

“I stop and do nothing. Nothing happens. I am thinking about nothing. I listen to the passing of time. This is time, familiar and intimate. We are taken by it.
The rush of seconds, hours, years that hurls us towards life then drags us towards nothingness …
We inhabit time as fish live in water. Our being is being in time.
Its solemn music nurtures us, opens the world to us, troubles us, frightens and lulls us.
The universe unfolds into the future, dragged by time, and exists according to the order of time.”

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.



Antimatter canister from ‘Angels and Demons’

The Writers Almanac got me thinking this week about antimatter and the positron. If that seems a strange topic for a writing site, then you need to consider all of the fictional uses of antimatter in literature and popular entertainment.

Science fiction writers like Robert Heinlein, Isaac Asimov and Philip K. Dick are a few of the many who have played around with this scientific discovery. The British television series Doctor Who used it for a propulsion system. That sentient android, Data, from Star Trek: The Next Generation has a positronic brain that gives him powerful computational capabilities. In Dan Brown’s Angels and Demons, the Illuminati try to destroy Vatican City using the explosive power of a canister of pure antimatter.

In physics, the idea that there may exist particles and matter that are exact opposites of the matter that surrounds us goes back to the late 19th century. It is difficult to grasp the idea that there are mirror-image anti-atoms for all our known atoms. take that idea bigger and there would be whole anti-solar systems.

And what if in those solar systems the matter and antimatter might meet? They would annihilate one another.

In 1932, American physicist Carl Anderson discovered the first physical evidence that antimatter was more than just an idea. Anderson was photographing and tracking the passage of cosmic rays through a cloud chamber, a cylindrical container filled with dense water vapor, lit from the outside, and built with a viewing window for observers. When individual particles passed through the sides of the container and into the saturated air, they would leave spiderweb tracks of condensation, like the vapor trails of miniscule airplanes, each type of particle forming a uniquely shaped trail. Anderson noticed a curious pattern — a trail like that of an electron, with an exactly identical, but opposite curve — an electron’s mirror image and evidence of an anti-electron.

He took a now famous photograph of the event and in it a particle is seen approaching the metal plate , and when it hits the plate, it loses energy but continues to curve in the direction appropriate for a positively charged electron. He later called it a positron.

He had discovered antimatter. The discovery earned him a Nobel Prize in Physics in 1936 (at the age of 31 he was the youngest person to be so honored).

Antiprotons were discovered in 1955, and the antineutron was discovered the following year. In 1985, scientists created the first anti-atoms. And other antiparticles, such as antiprotons and antineutrons, have been discovered.

These discoveries led to speculation on its practical use. In Star Trek, it forms the basis of high energy propulsion systems. So far, the amount of antimatter so far created on Earth is orders of magnitude short of what would be needed to power a spacecraft.

Back in the 1940s, biochemist and science fiction writer Isaac Asimov took up the newly discovered particle and made it the means for his fictional “positronic brain.” Made of platinum and iridium, it was his way of  imparting humanlike consciousness to the robots in his story collection I, Robot.


“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


I think it is pretty safe to assume that everyone has heard of Galileo Galilei. Not as well known is his eldest daughter.

Galileo was born on February 15, 1564, in Pisa, Italy. A mathematics professor, he made observations with implications for the future study of physics. He constructed a telescope (did not invent it) and made significant improvements to it. He supported the Copernican theory of a sun-centered solar system and so was accused twice of heresy by the Catholic church.

He had three children, but was closest to his eldest, Virginia. He saw her as much like himself in intellect, sensibility, and with an always-seeking spirit.

Virginia was born of his illicit affair with Marina Gamba of Venice. Her birth was in the summer of a new century – August 13, 1600.

That year was also when a Dominican friar, Giordano Bruno, who believed the Earth traveled around the Sun, was burned at the stake.

On her thirteenth birthday, Virginia entered a convent and remained there for the rest of her short life. She was devout but loved her father and remained in constant correspondence with him.

I learned about her when I read back in 1999 Galileo’s Daughter by Dava Sobel which used whatever surviving letters (never published in translation) between them as a major source. It is a good tale of that divide and connections between science and spiritual belief that still exists.

Virginia became Maria Celeste as a nun. We can surmise that Celeste might be a celestial nod to her father. In the convent, she was the apothecary – a kind of science of that time. She sent her father herbal treatments. She asked her father for financial help for the convent. She may have helped him prepare some manuscripts.

It is not really clear how father and daughter reconciled his heresy and her devotion. But they did. Love conquers all?

Galileo was not an atheist. He remained a Catholic and believed in the power of prayer.

Unfortunately, though letters from Maria Celeste were discovered among Galileo’s papers, his responses to her have been lost. Maria Celeste’s letters are published as Letters to fathertranslated and edited by Dava Sobel.

We remember Galileo mostly for the telescope, which he found out about in 1609. It was a Dutch gadget and initially known as a spyglass or eyeglass. It was curiosity that made faraway objects appear closer and they were being sold in Paris. Galileo saw it as a device of use in the military and promoted it as that to the Italian government.

He improved the design, as others were also doing in other countries, grinding and polishing lenses himself. The Venetian senate was so amazed and obsessed with using it to look for distant ships from bell towers of the city, they renewed his contract at the University of Padua for life, and Professor Galilei’s salary jumped to 1000 florins per year (a 500% raise from his starting pay).

That telescope cause a huge shift in the way we perceive the world we live in and the universe beyond or world.

Galileo used his improved telescope to make detailed drawings of the Moon’s phases, and he discovered 4 of Jupiter’s 67 moons (Io, Europa, Ganymede, and Callisto), though he considered them to be planets. In a 1610 letter, Galileo commented on them and said “I render infinite thanks to God for being so kind as to make me alone the first observer of marvels kept hidden in obscurity for all previous centuries.”

He reminds me of Charles Darwin in that both had a hard time with their discoveries knowing that this new knowledge would clash with existing religious beliefs. Galileo wrote a famous letter about science and religion and that conflict obviously concerned him – and his daughter, and probably some of you reading this today.

Galileo at age 42.
Galileo at age 42, when Virginia was 6, in a portrait by Domenico Robusti.

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