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By James Ashenhurst

On Cats, Part 2: Cat Line Diagrams

Last updated: March 27th, 2019 |

When this blog was about organic chemistry, I’d never stoop so low as to put cute pictures of cats on my website to drive traffic. Now that it’s all about cat science, I’ve lost any compunctions I might have had earlier.  Want gratuitous cat pictures? You bet.

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Introducing the Cat Line Diagram

But this blog is really about breaking new ground in cat science and cat analysis.

Last time we defined “conformations” as “the shapes a cat can make by moving its limbs around, thus providing differing levels of comfort.”

Today I want to study cat conformations in more detail and introduce a valuable tool that you can use for their further study and enjoyment: the Cat Line Diagram.

See, if we want to analyze cats in general, we need to ignore all the extra details that make individual cats unique, like fur color, cuteness, girth – and instead focus on their common features. If we do that, we’d be left with a Cat Line Diagram.

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The advantage of the Cat Line Diagram is that it provides us with a means to take cats of different size, shape and age and analyze them. In this picture, for instance, you can see how these 4 different cats are drastically different but all share the same conformation as the cat in our first picture.

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How to Depict 3-D Cats on a 2-D Page

Now there’s one complication with doing this. The picture above kind of shows how tricky it can get. Cats are 3-dimensional creatures and it’s difficult to show the 3-dimensional nature of cats on a 2-dimensional page.

Thankfully there’s a solution for this. Here’s how we can do it. Take the “flat” part of the cat (that’s in the plane of the page) and use normal lines. But take the parts that project “out” of the page (the two feet, in our example below) and use dark wedges to make lines to the feet. With the parts that are pointing behind the page, use dashed lines. Like this:

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You can do anything with a Cat Line Diagram you can do with a normal cat, except you don’t run the risk of getting scratched. So just as Tabby Jr. in the picture below remains the same when we rotate him 180° in the plane of the page or along the the central axis, we can do the exact same things with a Cat Line Diagram. Notewe can only do this because this cat has a mirror plane (plane of symmetry) down the central axis. More on that later.

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Using Cat Line Diagrams to Show Rotations

So far, we’ve just been drawing cats in one conformation. But what makes cat line diagrams really shine is that we can use them to show how the orientations of the limbs change as we rotate about the central axis. For instance here’s the same cat, but the drawing on the right shows a 60° rotation of the back end:

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Here’s the best part: what we’ve really done here is make an abstract model of a cat and now we can manipulate it as we wish. We can even go further and rotate the cat’s rear end another 30°, even without a picture to guide us. So In the picture below, this represents it lifting its rear leg up until it is completely level with the head.  It takes a bit of time to see how these rotations work but if you’re really keen on studying this phenomenon you can pick up the skill rather quickly.

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It’s All About Cats People

My answer all of those skeptics out there who think that I’m basically using cats as an excuse to talk about concepts in organic chemistry – specifically, skeletal formulae – is the following: if you can’t see the difference here between molecules and cats, something’s seriously wrong with you. If they look the same, it’s just a coincidence.

Next post: On Cats, Part 3: Newman Projections

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Comments

Comment section

21 thoughts on “On Cats, Part 2: Cat Line Diagrams

  1. When “flipping” you are only flipping the images. If you were to rotate a real cat the foremost leg would move from the reader side of the image to the paper side. Your flipping only works because it’s just an image not a real cat. Unless you’re trying to show that the flip process involves changing the cat’s arrangement?

    If Schrodinger can teach quantum with cats, why not Organic Chemistry too?

  2. Very clever! And maybe we could use this method to represent various CATalytic transformations, particularly involving CATionic intermediates, such as (assuming H is a good leaving group)…

    F T
    |
    + ——-
    / /
    F F F

    (and I sure hope wysiwyg works…)

    1. Yes – although I saw 3-legged cats in Jerusalem regrettably I did not get any pictures – otherwise I’d use your idea. I do have a picture of a 3-legged dog, but somehow that doesn’t seem appropriate.

  3. Being a cat lover and chemistry educator, I love this idea! So easy to introduce the 3-D reality in a 2-D drawing.

  4. You are right on the money James ! Were you high when you made this connection. So beautifully it fits and answers most of the concepts !! :) I should have stumbled on this blog in high school !

  5. These blogs have really helped me understand all of the concepts being taught in my organic chemistry lecture this semester. Hearing it in lecture and seeing it written as a bunch of lines connected to a one-or-two letter abbreviation didn’t really make sense…but add in cute pictures of cats and I understand the concept immediately. THANK YOU!

  6. This is great.
    Its so much easier to understand than organic chemistry.
    I think I will abandon chemistry and just become a professional cat observer.

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