Shadows of Higher Dimensions

During a visit to Goettingen, Germany several years ago, I visited the mathematics building, built during the height of the department, when brilliant figures like David Hilbert, Hermann Weyl, Emmy Noether and Richard Courant roamed its halls and discussed whether there could be a complete description of mathematics (a hypothesis that would be disproven by Kurt Goedel).  I noticed a marvellous display case in the department's foyer, full of incredible models of polytopes (representations of higher dimensional figures).

I recently developed a presentation about the relationship between these "shadows of higher dimensions" and unified theories of nature:

Imagining the Fifth Dimension

The history of higher dimensions is described in my book:

The Great Beyond

Labyrinths of Tile and Concrete

Our minds can craft beautiful kinds of labyrinths from a variety of distinct materials. While some of these are abstract, such as poetic verse assembled from a blend of images or musical passages derived from a mixture of folk melodies, others are more concrete. "More concrete" was certainly the motto of Henry Chapman Mercer as he constructed his labyrinthine mansion in eastern Pennsylvania almost a century ago.

Born to a wealthy family in 1856, Mercer studied law at Harvard and the University of Pennsylvania. After briefly practicing law, he decided that he was more interested in ancient artifacts and folk art, and began collecting these. He also became a master craftsman, and opened a tile works specializing in colorful, unusual designs.

In 1908, he decided to build a mansion for himself, Fonthill, which would also house at least part of his collection. To make it fireproof, and less costly, he elected to construct it from concrete. Concrete also had the advantage of malleability, so he could shape any room or hallway as his wished. Indeed, he crafted a house with passages and stairways leading in almost every direction conceivable, with manifold libraries, studies, bedrooms and so forth. Each room is at a different level, connected to at least a half-dozen others. Naturally there's a tall tower, and even separate stairs and doors for his dog Rollo. Strangely Mercer was to live in this massive castle virtually alone (except for Rollo). Apparently the one woman he proposed to thought he was way too odd!

Scattered throughout the house, and embedded directly in the concrete, are ancient tiles from Babylon and China. Other tiles include a variety of styles and periods. Alphabet tiles arranged on the walls and ceilings spell out numerous messages in Latin, German and English, characterizing the rooms and their collections. One bedroom prominently displays a gruesome tile mosaic of the story of Blackbeard's wives and their untimely deaths; which apparently further put off potential suitors.

When Mercer died in 1930, he bequeathed the house to a historical society, but willed that his housekeeper should reside there as caretaker. She lived there until her own death almost half a century later. When I was growing up I heard about this strange house where a housekeeper would let you in and show you around if it suited her that day! When she passed away, official and more conventional tours began of the house. It's a great place to get lost in a creative artist's dreams.

Emmy Noether

One of the great intellectual heroes of the 20th century was German-Jewish mathematician Emmy Noether. She was remarkable in that her accomplishments in the field of abstract algebra emerged despite considerable prejudice against her, first because of being a woman, and second because of her ethnic background. During the 1920s and early 1930s the great mathematician David Hilbert tried to secure her a professorship at the University of Goettingen, but could only obtain for her dozent (lectureship) status because of her gender. When she taught classes, he had to list himself as the official professor. Then in 1933, with the rise of the Nazi regime, an act was passed "The Law of the Restoration of the Civil Service" forbidding those of Jewish background to teach in Germany, unless they had been World War I veterans (a concession made to placate Hindenburg). Noether fled Germany and obtained a position at Bryn Mawr College in the US. She died two years later.

Einstein wrote a beautiful obituary about her in the New York Times:

"In the judgment of the most competent living mathematicians, Fräulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began. In the realm of algebra, in which the most gifted mathematicians have been busy for centuries, she discovered methods which have proved of enormous importance in the development of the present-day younger generation of mathematicians. Pure mathematics is, in its way, the poetry of logical ideas." (Albert Einstein, New York Times, May 1, 1935)

Today I visited the site of her grave for the first time. It is in a quiet, monastery-like part of Bryn Mawr campus, known as The Cloisters. At first I didn't see the grave marker, as it is very plain and right in the pavement. Here are photos of The Cloisters and Emmy Noether's grave:

Quantum Horror in the Tales of H.P. Lovecraft

In his day H.P. Lovecraft was known purely as a pulp fantasy and horror writer, and only in recent years has the quality of his writing come to be respected. Though he was largely self-educated, it is remarkable how often this American writer of otherworldly horror instills genuine science into his prose.

Take for example his chilling 1933 tale "The Dreams in the Witch House" about a physics student living in an ancient house that used to be inhabited by a witch familiar with higher dimensions and non-Euclidean geometry.

The story has wonderful lines connected with modern physics:

“Non-Euclidean calculus and quantum physics are enough to stretch any brain; and when one mixes them with folklore, and tries to trace a strange background of multi-dimensional reality behind the ghoulish hints of the Gothic tales and the wild-whispers of the chimney corner, one can hardly expect to be wholly free from mental tension.”

"some circumstance had given a mediocre old woman of the seventeenth century an insight into mathematical depths perhaps beyond the utmost modern delvings of Planck, Heisenberg, Einstein, and de Sitter."

I used the first as the opening quote for my book The Great Beyond, a study of the scientific and cultural history of higher dimensions.

Einstein and Borges

A recent conference in Buenos Aires commemorated Einstein's miracle year of 1905. Interestingly the meeting focused on some of the cultural aspects of Einstein's work, including his influence on Borges. Recordings of some of the conference sessions (in Spanish) can be found at:

El Universo de Einstein

Wellsian Prophecies

From childhood, one of my favorite books has been "Seven Science Fiction Novels," a collection of some of the greatest and most imaginative novellas by H.G. Wells (and indeed some of the best science fiction of all time). The copy I have was published in 1934, bought by a school library, discarded and then brought home by my dad. When I was old enough to read it, it became a source of endless wonder. Each novella was a glimpse of eerie spectres of things to come: Martian invasion. A man who is utterly transparent. Journeys through time to the last days of Earth. Moon creatures living beneath its surface. The collision of a comet. It's all in there, written in a uniquely intelligent style, as if from the vantage point of someone who has stepped out of time and encompassed the past, present and future of all things.

As I delved further into Wells' career, I discovered that his books seem to alternate between prophecies of doom and predictions of an utopia beyond imagination. Sometimes, as in the Time Machine, what seems at first glance to be paradise reveals itself to be an utter nightmare. Other times, it takes complete devastation to clear the ground for a brave new order, as in one of Wells' lesser known works, "The World Set Free." That 1914 tale of destriction and restoration is notable for its prediction of atomic warfare and the first use of the term "atomic bomb"

What I didn't know until recently was that reading that frightening story helped inspire physicist Leo Szilard to work out the details of the concept of a chain reaction himself, become avidly interested in the possibilities and ramifications of nuclear weaponry in the 1930s, and contribute to the theory behind the development of the first atomic bombs in the Manhattan project. Szilard and Einstein wrote a famous letter to Roosevelt about the dangers of the Nazis developing the bomb first, and this led to the Allied effort and ultimately to the horrors of Hiroshima and Nagasaki (which the theorists had emphatically absolutely nothing to do with--it was strictly a presidential and military decision under Truman).

I'm currently reading a fascinating and important book, called Doomsday Men, written by the historian of science, reviewer, Einstein biographer, photographer and blogger PD Smith. I've been delighted to discover in his new work ample references to Wells and science fiction, woven into a riveting chronicle of how superweapons capable of mass destruction were pondered, developed and justified. Talk to any child about the idea behind nuclear weapons and he or she is likely to recoil in horror, and seriously wonder why any madman would consider building such devices. Yet in the 20th century the concept of a "war to end all wars" stimulated thoughts amongst serious-minded people that the existence of weapons too horrifying to use would bring about world peace. And at least some of this, as Smith writes, can be traced back to Wells and other writers who imagined that a world after devastation would be one of wise leaders guiding the masses to peace.

For those of you who recall the tumultous days of the 20th century that preceded the current Golden Age (as so we're told by the rock band U2, at any rate, who go on to say that "gold is the reason for the wars we wage), or even for those of you too young (or busy) to remember the 20th century at all, I suggest that you familiarize yourself with the past so that we're not doomed to repeat it. As you can probably tell, I highly recommend Doomsday Men, now available in the UK (through Amazon.co.uk. for example):

Doomsday Men

It will also be published by St. Martin's Press in December.

Either/Or

Written more than a century and a half ago, but possessing an honest and direct style more characteristic of modern works, Soren Kierkegaard's Either/Or is for me one of the best expressed statements of the stark choices in life. For those of you unfamiliar with the work, it is written in two parts, with each half purportedly written by a different author (but both actually penned by Kierkegaard himself). The first half, the "Either," beautifully describes the pleasures and anguish of the "aesthetic life:" a world of music, drama, art, and seduction, but also of chronic boredom and depression. The second part, "the Or," supposedly written by a married physician, succinctly argues for the pious and virtuous life of good clean hard work. It's written in the form of letters to the first chap.

The most famous sections of the book are the Diary of a Seducer (a chronicle of his meticulous wooing and subsequent abandonment of a young woman) and the Diapsalmata, a collection of fragmented thoughts about the boredom and restlessness in life -- what continuously drives the aesthetic appreciator to seek new forms of entertainment and stimulation. We realize what a futile quest the poor fellow is going through as nothing seems to satisfy him: "I do not care for anything," he writes. "I do not care to ride, for the exercise is too violent. I do not care to walk, walking is too strenuous. I do not care to lie down, for I should either have to remain lying, and I do not care to do that, or I should have to get up again, and I do not care to do that either. Summa summarum: I do not care at all."

So if the aesthetic side seems painful, then what about the ethical? Less stressful and easier on the heart, one surmises. However, while the second half seems the epitome of common sense it seems to lack color somehow.

Perhaps this dichotomy is a bit artificial, but in my mind Kierkegaard well depicts the sense of wonder about the roads not taken in life.