The shape of time

More and more acorns are dropping from the bur oaks, and being joined on the ground by ripened fruits and berries. Signs of impending autumn increase by the week. “And the seasons they go round and round,” as Joni Mitchell tells us in her wonderful lyrics to The Circle Game. Six months from now, some of us will be praying for a prompt end to winter, but first we have to harvest and store the products of the current growing season. Those who make it through the winter will be able to plant again next spring. The circle continues, though we age as it does. Is our passage through time a straight line? Do we pass through our own seasons as we age? Is there another universe to which we will pass at the end of our time on earth?

bur oak acorn

Photo by J. Harrington

Einstein tells us that space-time is a continuum. I have as much trouble picturing what that means as I do picturing an oak when I look at an acorn or a butterfly when I look at a chrysalis. If a continuum never ends, what was there before the big bang? If the universe is all that exists, into what is it expanding? Can we ask “how big is a light-year?” Or, do we need to stick with how far light travels in a year? Got a headache yet?

I got pulled into thinking about these kinds of questions when I tried to follow a simple direction this morning, “travel sunwise.” My first thought was: Is that clockwise or counterclockwise? Then, I was on to the sun rises in the east and sets in the west, but that’s not actually the sun moving, that’s the earth spinning on her axis. The seasons are caused by the earth’s orbit around the sun, neither days nor seasons are clockwise or counter. See how all of this circles around like a game?

By now you may be feeling as I did the first time I realized that Joni Mitchell’s lyrics from Woodstock aren't simply a metaphor, they're also literally true.

We are stardust
We are golden
And we've got to get ourselves
Back to the garden

I hope you’ve enjoyed this brief excursion through space-time as much as I have. Now, let’s put on our gloves and get back to work. We have a garden (earth) to tend. It’s time to shape up.

Squaring the Circle

By Philip Fried

It’s a little-known fact that God’s headgear — 

A magician’s collapsible silk top hat,

When viewed from Earth, from the bottom up — 

Is, sub specie aeternitatis,

A pluperfect halo, both circle and square,

And a premonition of this truth

Spurred on an ancient philosopher,

Anaxagoras, to make numerous vain

Attempts to approximate the circle

Of his concerns with the square of the cell

He was jailed in for impiety.

Doomed calculations which God acknowledged

By doffing then pancaking his topper.

He was still bareheaded millennia later,

When he learned of von Lindemann’s proof that pi

Is not the root of a polynomial

With rational coefficients, hence

Squaring the circle’s impossible.

God un-collapsed, re-donned his hat!

But — it was 1882,

Progress was a juggernaut

And the public had no patience for “proof.”

From below, God’s gesture looked like a signal

For all hat- and cap-wearing men,

Proper in their headgear, for nations,

Well-stocked with helmets for delicate brainwork,

To take up “the compass and straightedge”

And prepare for a singular all-out attack

On this seductive conundrum, so men 

Enlisted en masse in Geometry’s army,

Tossing up and away all hats

Of cloth, opaque haloes, hurray!

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