Wednesday, August 17, 2022

Great trick for removing scum on top of beef soup

So I took the recipe for Taiwanese beef soup and swapped out the spices and replaced them with carrots, celery, onion, and parsley. A few flavors like tomato paste (and a few tomatoes if available) and soy sauce; salt and pepper. No garlic, although I was not sure about that. I thought I would just make it straight.

Whenever you make beef soup you get a scum on the surface of the liquid. I usually try to spoon it out, or catch it in some way. So I read a great trick here Beef Consomme - Craving Tasty about using brown paper to sop up the surface gunk. It really works.

Thursday, August 11, 2022

Wasp with Cicada

I just witnessed something unusual, so I might as well record it. I was bending close to the ground and a huge wasp landed with a buzz at my feet. Before I could barely register that it was carrying an entire cicada underneath it, it rushed into a nearby hole and disappeared underground. The tailings from the hole had looked like an anthill.

Monday, August 8, 2022

Number of segments derived from the glance function

For glance function H, with last jump at diameter, we have 

H(diameter)=number of segments

Several ways to see this is true without the (lost) argument by induction based on the (false) analysis of adding a new (segment+gap) at one end of the collection of (one fewer) segments. One is to simply examine the form of the glance function for these segments (N=3, diam=a+b+c+d+e):

With segments of lengths a, c, and e; separated by gaps of lengths b and d, then the glance function has rows with +/- jumps at these places (sorry about the shitty notation, inserting the "h" is awkward):

+a - (a+b) + (a+b+c) - (a+b+c+d) + (a+b+c+d)
       +b      -   (b+c)    + (b+c+d) - (b+c+d+e)
                       +c      -   (c+d)   + (c+d+e)
                                    +d     -    (d+e)
                                              + e
For each segment row: the row ends with + and all other +/- cancel. For a gap: all the +/- cancel. Hence the height of the glance function at (diam) is the same as the number of rows that start with a segment length - one per segment.