A couple of geometric details about the Queen’s House
which I described a couple of days ago. The building is square but too wide to be cubic; its central salon, however, is said to be a cube of 40 feet on a side. And its Tulip Stair
was England’s first spiral stairway without a central support. Such a support consists either of a pillar or of the inner ends of the steps stacked on each other, or both. Instead, these steps support each other at their outer ends and are cantilevered from the wall. Cantilevering is where a piece sticks out from on, or in, a wall and is supported only at that end.
Of old, I would have pulled out a sketchbook and made a quick drawing of this jaggedly-flowing shape. Now I could scarcely do that, even if there hadn’t been people going up and down and stepping on my toes.
(British, “treading on”. There’s much vagueness in this little area of vocabulary. The whole assemblage can be “a stair” or “a stairs”. One of its pieces can be “a stair” or “a step”. The horizontal surface of one of those is its “tread”, the vertical its “riser”. You can take a “step” or a “pace”.)
Once, cycling through Italy, I came past a place in the Alban Hills called Monte Porzio Catone, “Mount Porcius Cato.” (It is near the site of ancient Tusculum, from which came a Roman family of which at least seven were named Marcus Porcius Cato. We remember mostly the patriarch, Cato the Elder or “Cato the Censor,” the stern senator who tried to scold Rome back into its old ways and who ended every speech, about whatever subject, with: “Furthermore, I judge that Carthago delenda est – Carthage should be destroyed.” All troublesome foreigners should be dealt with by force, not negotiation. Carthage was eventually conquered and razed, its surviving people sold into slavery, and its site sown with salt.)
Along the road near Monte Porzio Catone I noticed the gateway to the Astronomical Observatory of Rome, so I went in, and up the driveway, and entered the building. There was nobody about. I walked up stairs and along corridors past open doors, but found nobody. I waited a while, passing the time by drawing the stairway, but I had to leave without meeting an astronomer.
(The sketch is only a little over 8 inches high and 5 wide, and I’ve just noticed that in the scan, which I made some time ago, the marks down the left are not features of the building but holes with the sketchbook’s spiral wire going through them.)
Such stairways are often called “spiral,” but they’re really helical. A spiral is a curve in one plane, like a groove in an old record or like my spiral library.
A three-dimensional curve that slopes around the sides of a cylinder or cone is a helix. The Monte Porzio Catone stairway looks to be a helix that reverses direction, like the many hairpin-bend roads up Italian hillsides. The Tulip Stair is a right-handed helix, which means one that curves rightward as it goes onward.
Why do we call the two kinds of helix, curving in opposite directions, left-handed and right-handed? Look at your hand, or a larger one:
This is the four-and-a-half-ton bronze sculpture that gets to be on the “Fourth Plinth” in London’s Trafalgar Square for the next few months. It’s called “Really Good,” and sculptor David Shrigley hopes it will make the world cheer up. The original thumbs-up gesture was pleasant only by contrast with its opposite: made by a Roman emperor, it meant “Let him [the fallen gladiator] live.” I think it’s about the only gesture I often make, such as to a driver who lets me cross a road.
If you think of your curved fingers as coils of a helix, the thumb points the way it is going. So this directionality of the helix, and of lopsided molecules and other forms that can have mirror-images of themselves, is called chirality, “handedness.” (Kheir is Greek for “hand.” Chiron, Kheirôn, was the wise and “handy” Centaur to whom young heroes were sent for their education.)
The threads on screws are all right-handed helix curves, so that you drive them in by turning your screwdriver clockwise. (The only exception is on the shaft holding the left pedal of a bicycle, which otherwise would come unscrewed as you ride.) Every wire twist that holds something should be twisted on clockwise, forming a right-handed double helix, so that you know to untwist with the same motion as unscrewing a screw. Anyone who puts one of these twists on the other way should be – shot. Thumb down.
There has been scientific excitement recently about chirality. Amino acids, from which proteins are built, are almost all left-handed molecules; DNA, the double helix that programs proteins, is all right-handed. No reason is known why they chose to be this way and not the other.
Now for the first time a molecule showing chirality, propylene oxide, has been detected, from its radio signature, in outer space: in a dusty cloud, Sagittarius B2, near the center of the Milky Way galaxy. The scientists don’t yet know whether the molecules are left- or right-handed or both and are hoping to find out.
Perhaps Earth was seeded by local abundances in the cloud from which it formed.
Our bodies of course are chiral and our guts wind in one direction. Many shells and other forms coil, as they grow outward, into plane spirals, but if they are asymmetric in the other dimension they can become helix-like. I “borrowed” this beautiful shell from shell-collecting Miranda, meaning to paint it. That was so long ago that its sheen and all its exquisite markings have faded.
It seems to have grown outward with left-handed chirality – if you hold it this way up.