The idea is that the calligraphy brush would change its thickness depending on the direction of the drawing. So, for example, a stroke down [↓] would give additional thickness of 7 pixels, a stroke up [↑] wouldn't give any additional thickness. A stroke sideways [← → ] would add 3.5 pixels to the line, and for example a line to the bottom left corner [↙] would increase thickness by 1.75 pixels, and so on, proportionally to the angle of the line. 

It could have parameters such as: 
1. Direction: what is the main direction, which would add maximum thickness (in terms of 360 degrees). I.e. in the above example if we replace up and down (180 degress difference), a stroke down wouldn't add any thickness, and a stroke up would add 7 pixels.
2. How much does the width increase: how much thickness will be added to the stroke.
3. Area: this means that if the area is set to 0.5, the area would be 180 degrees, which means that everything which is further than 90 degrees from the main direction wouldn't receive any additional thickness, and starting from 90 degrees away, the thickness would increase smoothly, from 1 pixel to the value of the width parameter.

This option could add more stability to calligraphy drawing (because often in calligraphy strokes up are thin and strokes down are thick, so it would automate this process), and it would also allow users, who don't have a tablet with pressure sensitivity, to experiment with calligraphy. 

Here is a rough example of what I mean (the main parameters: 'Width', 'Angle' [direction], 'Area'):  https://ultrabullet.com/calligraphy/

And this is a video demonstration: https://youtu.be/gjkWYtzGt08

Thanks for taking the time to discuss this.  Feature requests need to be formally documented in the bug tracker.  This message tells how to do that:  https://inkscape.org/forums/beyond/how-to-report-bugs-or-request-new-features/  (Fyi, you can delete the pre-formated text in the message field.  You don't have to use it for a feature request.)  

I don't use the Calligraphy tool much, but that sounds like something that should be optional, right?  It would make me crazy if it worked like that by default. Ooh, or what about if the user could define those things?  That would be very cool, I would think, for illustrators?

Anyway, please do make the official request!