An unusual day in the place of Quartz Triangles

Here was a heartbreaker, but I expected it.

It was an unusual day. I was picking up bits of quartz with both hands and stuffing nice arrowheads in my pocket without even realizing. Depending on how damaged a specimen is to be counted as an "arrowhead" I found between 10 and 15. The larger items, in the bottom row of the middle picture above, are hatchets - I think. They were comfortable knapping quartz in triangles.

Rhododendrons at entrance to Devil's Lane, Woods Hole

The Moving Topic - The Thesaurus as analog of Euclidean Space

I find the idea increasingly compelling, that a properly constructed thesaurus supports some of the same geometric ideas as are applied to Euclidean and related spaces. Specifically the moving point in space is analogous to the topic moving in the thesaurus. The final curve that was traced by the point is analogous to the story information, told one word at a time. 

This analogy continues at the local level, where different narrative structures are "best fit" to the adjacent verbiage, and used to fill in topic specific information. This mechanism is analogous to the derivatives at a point on a curve corresponding to "best fit" idealized line, circle, helix. Thus the moving frame of Frenet, Darboux, Cartan, Chern, [Pohl], ... becomes a moving local narrative for transforming local words into defined topic structures. It may seem awkward but, in this formulation, the words are parameters of the moving topic.

To round out the theory (literally) I hope to state some basic principles about connectivity and completeness of stories [Also the negatives: non-sequitur and irrelevance]. Details are coming into view.

Script in Utah

I tell you, those great basin petroglyphs with shadowy figures looming in every picture: those are a writing system - you can tell from the way the pictures are embellished with bits of other symbols. 

There was one with a picture of a person's intestines. To the left a cactus, to the right a hornet. Seems like a good place to start trying to understand. It seems obvious that it is a medical instruction. 

Asparagus

 

Chert is NOT quartz

Recently in an arrowhead video comment, I chastised another commenter for confusing chalceonoy with quartz. According to Britannica quartz is - pretty much - anything containing SiO2. So he was right and I was wrong.

However, in consideration of the difference in knapping properties of -say- chalcedony and quartz, the first is a smooth conchoidal fracture material and the second is an un-predictable and brittle material - these two should in no way be considered the same thing. Because in arrowhead commenting society the knapping properties are significant. I do not think the community uses the word "quartz" the way Britannica does.

Math is really the study of Z^n and R^n

They have had two or more thousand years to work on the counting numbers and the real number spaces. Math has been and remains about the "stuff" of R^n, Z^n, and abstract sets.

R^n is a mathematical object that lies very close to how we think about the material universe. So our thinking about the "stuff" of the one is like thinking about the "stuff" of the other. Now I want to study a new kind of "stuff" and I am afraid it might take quite a few years to understand this. The stuff is the thesaurus, ledger, and narrative structures that define the moving topic in my theory.

"a dog" versus "the dog"

I thought I understood the difference between "a" and "the" as a difference in assumptions about the set the dog belongs to. I now have a better explanation in terms of my current ideas of topics, thesaurus's, and ledgers: 

When we begin a discussion we put a topic instance into a ledger. If we say "a dog" we are putting it into the ledger without a context. When we say "the dog" an empty context structure is created or assumed to be pre-existing.

Proposing an origin of the Pythagorean Theorem

My grandparents left me several Arabic/Persian inlay boxes: made from mosaics of many small wooden tiles; triangular, square, and other shapes. It occurred to me that if you were constructing one of these boxes and needed to fill in a larger triangular or square area, then it would not take you long to know how many small tiles it was going to take. Knowing that a^2 and b^2 added up to c^2 would be empirical knowledge for a box maker. Easy to re-discover.

Osprey Sketch

I have been working on it. This version is a "that's what I'm talking about":

Now I have to try and execute this as a scrimshaw:

The advantages of slow cooking meat

A basic cooking technique for meat (beef, poultry, pork) is to use a baking dish and

• A bed of carrots and onions (with other flavors added as desired; like garlic, parsley, apples)
• A foil cover, stretched tight
• Meat that has been rubbed with salt and pepper, possibly other spices
• Cook at below 300 F for a few hours, remove foil and keep cooking for another hour. Basting as desired.

So, this is a recommended way to cook brisket or pork tenderloin. When I do it with turkey thighs or chicken breasts I get extremely flavorful and tender meat. After about four hours, pork and beef pull apart easily. You might not want that. One variation is to leave off the foil from the start- you get a dry result. You might just want to roast and baste. But for flavor and tenderness, this covered method is the way to go. You get accumulated moisture in the pan, which makes a good gravy. 

Here is a recipe: Use chicken breasts with garlic, paprika, parsley, salt, and pepper. Make a gravy from the juice. Serve with mashed potatoes and peas. The house smells good the next day.