Island Universes

We have seen with astonishment shapes in the heavens that are nothing other than systems of such fixed stars limited to a common plane, such milky ways, if I may express myself in this way, that exhibit elliptical shapes in different positions in relation to the eye with a weakened shimmering as is appropriate to their infinite distance; they are systems of, so to speak, infinity times infinity greater diameter than that of our solar system,h but that, without doubt, are generated in the same way, ordered and arranged by the same causes, and that maintain themselves by the same mechanismi as this one in its constitution.

Immanuel Kant

Immanuel Kant wasn’t the first to posit that the “spiral nebulae” observed by many astronomers, such as Charles Messier, were actually galaxies like to the Milky Way. Theologians, such as Emanuel Swedenborg, had proposed that a limitless God wouldn’t limit creation to a single galaxy. The British astronomers William and Caroline Herschel had discussed the possibility, and their hypothetical proposals influenced Kant. Kant was the most prestigious philosopher of his time, and his endorsement gave the idea heft.

Copernicus and Kepler had shifted the view of the universe from geocentrism to heliocentrism, but up until Kant’s argument it was accepted that the universe was little larger than the Milky Way. Kant created room for the possibility that nature contained many galaxies equivalent to the Milky Way.

165 years later, in the early 1920s, the question was still being debated. Those who believed the Milky Way way the only galaxy argued that spin had been observed in the spiral nebulae. That spin would be impossible to observe if they were as vast as the Milky Way since the outer stars would have to be moving faster than the speed of light. They also argued that novae that had been observed in them were so bright that they outshone the rest of the nebulae. That would put the energy output from the novae so high as to be incomprehensible. Another problem with the novae was that more had been observed in the spiral nebulae than in the Milky Way, implying that the Milky Way had a different composition than the distant nebulae.

On the other side were those who took Kant’s position. Their most powerful argument was that of homogeneity–that the Milky Way wasn’t special, and that the rest of the universe would be very much like the part of it we can observe. They also argued that dark regions in the spiral nebulae strongly resembled regions of darkness in the Milky Way caused by vast expanses of dust hundreds of light years across.

The Milky Way is immense, estimated at 100,000 light years across, but visually it doesn’t fill the night sky. In fact, the band of stars, clusters, and dust doesn’t even cross the sky completely. Despite it’s enormity, is visible. It’s imaginable. It can be held in the mind. If the entire universe consisted mainly of the Milky Way and a few thousand nebulae caught in it’s orbit, then it’s still small enough and simple enough to be grasped in the human mind. On the other hand, if there are thousands or millions of island universes like the Milky Way, then the universe is so large it’s beyond comprehension.

The question was answered in 1924 by Edwin Hubble, through the use of a giant telescope, and a spectrometer. But before discussing the answer to the question, we need to discuss how it was answered–with a little thing known as a universal candle.

We Are Our Own Heroes

“We are the Universe experiencing Itself.”

Neil deGrasse Tyson

Dr Tyson wasn’t the first to express this sentiment; in fact, philosophers and prophets have been saying it for thousands of years. It’s similar to the statement in Genesis that man was given dominion over the Earth (Genesis 1:28). Humanity is placed within the universe, but at the intellectual apex of it. It’s as if all the components of the cosmos were the base and walls of a pyramid, with thinking human beings were at the top. At the same time, those human beings are constantly looking outward, to absorb and comprehend all that is.

It’s a statement of what it is be a human. To be human is to be an unerasable piece of the vast and mysterious cosmos. Learning, discovering, analyzing, imagining–all these things change us, and in changing ourselves we change the universe of which we are part. Beliefs form the basis of knowledge, and by extension, conscious choice. In the modern world, we’re presented with an array of beliefs–a buffet of thoughts and paradigms to select from. It’s bewildering and requires us to choose with imperfect knowledge. Many delay those choices until deep into adulthood. But beliefs become the basis from which one’s intellect is built, so an initial set of beliefs must be chosen. Trees need roots to become anything more than a thin twigs jutting from the ground. In the same way, a person needs a set of beliefs to grow from. Then, through experience and experimentation, our beliefs evolve.

Many books that are about an area of science–whether it’s cosmology, medicine, or chemistry–tell a narrative of the development of knowledge in that area. I think it’s not just because narrative is so important to people, but also because learning about the world around us changes us. And by changing ourselves, we change our world. We change the universe. Stories about the growth of knowledge become stories about the growth of the universe itself.

The first people to develop cities were the Sumerians. They dug canals in Mesopotamia, between the Tigris and Euphrates rivers, growing wheat and barley. In their fallow fields they herded sheep, goats, and cattle. They built cities and towers from clay brick and pitch. They invented writing, mathematics, and constructed the first wheels. They created the first piece of written literature, the Epic of Gilgamesh, a tale of a bad king who tries to defeat death. As Paul Cooper points out, their civilization had begun, reached its zenith, and collapsed before the last woolly mammoth died.

The Sumerian Model of the universe. This model spread geographically and is the basic model used in most Old World religions.

For the Sumerians the world was a round plate of land floating atop a vast ocean of bitter water, the sea. The sea surrounded the land, while sweet water filled the heavens. The sky was a dome that held the waters in the heavens high above the land. Clouds and rain were courses of water that passed through the ephemeral fabric of the sky. Sweet water from the mountains filled the rivers that nourished the people and their crops. In the Babylonian mythos, which was adapted from the Sumerian, the universe was not created from nothing. Instead, it sprang into existence when the god Marduk slayed Tiamat, the chaotic dragon-goddess of the sea. The Sumerian model spread throughout the old world, and is the basis of many religious texts.

Our understanding of the universe has changed, but many of those changes are more superficial than they appear at first glance. Untamable Tiamat has been replaced with a hot, roiling instanton. The god Marduk has been replaced with the unfractured pressure of the four fundamental forces. The symbolism of myth has been replaced with the abstract language of mathematics. The death-defying hero, Gilgamesh, has been replaced with millions of researchers, students, writers, and spectators. In short, all of us.

To discover, learn, and grow, is to change the universe. We are beings looking outward, searching the heavens. And there among the galaxies, we discover ourselves.

Views of Rolling Clouds

I bring fresh showers for the thirsting flowers,
From the seas and the streams;
I bear light shade for the leaves when laid
In their noonday dreams.
From my wings are shaken the dews that waken
The sweet buds every one,
When rocked to rest on their mother’s breast,
As she dances about the sun.
I wield the flail of the lashing hail,
And whiten the green plains under,
And then again I dissolve it in rain,
And laugh as I pass in thunder.

The Cloud, Percy Bysshe Shelley

As a child I spent what seemed like hours at a time watching clouds move across the sky, shifting shapes as they went. Seeing dragons, devils, ships, and castles moving and morphing across a blue canvas. I can’t be the only one. Rain clouds rolled in this morning and I found myself watching as a few low-lying, dark gray ones trundled along beneath the overcast sky.

Lower clouds appear to be moving faster than higher ones, but this is an illusion. In reality, wind speed increases with altitude. But when a low cloud bears down in its dark and shadow and immensity, it’s nearly impossible not to tremble at one’s own insignificance.

So, what creates the illusion of faster movement? The answer lies in the changing angle of an observer’s eye as it tracks a cloud. The observation angle changes faster when a cloud moves faster or when it’s closer to the observer. Closer can mean altitude–the cloud is lower in the sky, or it can mean distance over the ground–the cloud is closer to being directly above the observer.

So how much difference does it make?

Start with the sky, and a cloud, and it’s a sunny day, and there’s a guy standing on the ground looking at the cloud. The cloud’s altitude is a, and the distance over ground is d. Take a line straight into the sky and another that goes from the guy’s eyes to the cloud. Those two lines make an angle, θ. A breeze blows on the cloud, pushing it horizontally with velocity H, and vertically with velocity V.

So now for the nerdy stuff. When the cloud’s to the right of the dude, d and θ are positive, and to the left they’re negative. a is always positive. H is positive when going right and negative when going left. V is positive when the cloud moves up and negative when it moves down. The tangent of θ is d divided by a, and can be calculated if their lengths are known.

The total change of the angle θ with time is found by adding the change in angle due to horizontal movement to the change due to vertical movement:

Gad, that’s ugly to work with. It basically says when the cloud flies left, the angle changes in the negative direction. When the cloud is to the right of the observer, the angle changes in the positive direction when the cloud moves down, and in the negative direction when it moves up. And when the cloud is to the left, vertical movement causes changes in the opposite direction. How does it look when calculated?

I started with altitude and horizontal distances of 200 feet, and since they’re equal, the angle is 45 degrees. The cloud flies by at 10 feet per second, and the observers eyes track it across the sky. Here’s what the angle, θ looks like over time. It starts out at postive 45 degrees, reaches zero when the cloud is directly overhead, and goes negative as it flies to the right of our guy on the ground.

So what happens if the cloud is now 20 feet off the ground instead of 200, and still whizzing by at 10 feet per second? Well, at first it’s just a cloud on the horizon, getting bigger and bigger, and our guy’s head doesn’t even have to move. It takes 15 seconds for the angle of observation to go from 85 to 70 degrees. Then the cloud flies over in a tear, going to an angle of -70 degrees in only 13 seconds, before shrinking into the horizon.

This reminds me of something:
“How did you go bankrupt,” Bill asked.
“Two ways,” Mike said. “Gradually and then suddenly.”
Ernest Hemingway, The Sun Also Rises

A shot of the excel sheet and the formulas are below. Happy cloud watching.

B3 = A2 + E2 and copy down
C3 = C2 + D2 and copy down
F2 = DEGREES(ATAN(C2/B2)) and copy down
G2 = F2 – F3

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