On Cats, Part 7: The Fischer Projection
Last updated: March 27th, 2019 |
Last weekend while parts of North America and Europe were getting buried in snow, my wife and I went to Tel Aviv to pick up some gifts and dip our feet in the sea one last time.
There are worse ways to spend a weekend than to hang out by the Mediterranean. These cats seemed to agree.
As we were walking along the promenade, we passed this man he was pulling up a small, flat, oval-shaped fish from the waters. “Col a cavod!” we said, (congratulations). He smiled and waved.
As the fisherman unhooked his prize and placed it down with the others, we had the odd sensation of being watched. We turned around to find a sickly old white cat hungrily watching the fisherman’s every move.
“My wife’s cat”, said the man, whose name, naturally enough, was Ehud Fischer. “To her, when I am done, I will feed the scraps”.
I’m glad my wife was around to continue the conversation because it was at this point where I lost the thread of whatever we were talking about. Looking at Fischer’s cat from this angle reminded me of how easy it is to tell at a glance whether any stereocenters are present for a given cat. The Tummy View is helpful in being able to see this (much more so than the Newman projection, for instance, which is more helpful for examining conformations).
Now because we are all lazy, it would save us some drawing effort if we could just adopt the Tummy View as a convention. If we remember that the arms come out at the sides and the head/tail go back, then we can draw the cat like this (thanks to Charlie Kufs of Stats With Cats for the second photo)
This is a powerful new way of looking at cats if I don’t say so myself. In honor of our angling friend, let’s call it the “Fischer Projection”.
Now it’s important to realize that this is just a different way of representing a 3-dimentional cat on a two-dimensional page. So you can do certain things with the projection – like rotate it in the plane of the page and also do rotations, because these preserve the cat’s configuration. However, the one major rule is that you can’t flip the drawing outside the plane of the page. That’s the equivalent of breaking limbs and putting them back on different spots. You should be hearing a little pained “Meow!” sound in your mind every time you try to do this. Here are some guidelines.
Let’s have a look at the Fischer projections of all the cats we’ve looked at so far. The Fischer projection makes it easy to see planes of symmetry, stereocenters, and to compare the relationships between different isocats. You should be able to see the mirror plane in Sawhorse Cat and also to see the enantiomeric relationships between Freaky Sawhorse Cat/ent-Freaky Sawhorse Cat and Larry/Doug.