Being a good dad

Helped my son, Joseph Waksman, get his second "buck" of the season:

My Birthday Present

Was being with my son, finding his first arrowhead.

That is Joseph Waksman.

How do we love those stone blades?

I am struggling to understand my different aesthetic/emotional reactions to the different stone blades and arrowhead(s) I have been finding.

In the last three posts, I showed a badly weathered knife that must have once been an impressive blade:

Another blade made from a pretty, red jasper but water worn and slightly damaged (see here). And a "real" arrowhead: a the little, quartz "Squinocket stemmed point" from Raynham (see here).

I have been thinking about how one values an arrowhead, in terms of its design, execution, material, condition (damage and weathering), and anything peculiar to the arrowhead. Let's see how it applies to these finds. 

First the quartz point is a fine simple, design; well done, made from the noble material: quartz, and in good condition.

Next, the jasper blade is an ok design, the execution is fine, the material is a noble red rhyolite or jasper, the weathering is a bit severe and the chipped tip is a bit of a spoiler.

For the slate blade, the design is very fine - more exiting than either of the other two example. We cannot say much about the execution. The material is an un-inspiring slate and it is undamaged but severely weathered. 

So the aesthetic 'score' of each one varies according to how it ranks in these sorts of category. And it does somewhat match the aesthetics I experience looking at the three examples, sitting on my desk. But something else is going on, having to do with what I am learning finding these points. The title "The beaches begin to give up their secrets" represents the wishful thought that I am finding these beach arrowheads at the mouths of old rivers. and that I have figured something out. Certainly, two blades in two days suggests the theory might work.

But what I am struggling with is my desire to see these pieces in their original beauty and how, since it is not likely to be something other people appreciate: overly weathered items, like damaged ones, just don't quite make it. But you wish they did. My eyes keep tracking back towards the large dark blade. Is it only because of what I imagine its original beauty was? Or is the beauty still there? How important is it to me that I had these thoughts while finding it:

I will go back to that beach near Fay Rd where I believe there may be a few more stone tools in the gravel than other spots.[Then when getting there] Actually, I should go down to the beach with black sands, below the dune-blocked pond just north of Nobska lighthouse. That is where the river mouth was.

Latest on Elements of Narrative and Truisms

From notes:

Truism and Sequitur

Narrative Elements

Thing                          X
Thing with attribute    X_/A
Event                           X-v->Y (here, X is the "actor" and Y is the "target")
Sequence                     X,Y
Dependent sequence   X::Y
Exclusion                    X*
Subnarrative               (X)
Implicit Subnarrative  [X]
 
An attribute is something appearing after '_/'. If an attribute name is used in a different position in a narrative, it is cast as a 'thing'. If a non-attribute is used after '_/' it is cast as an attribute.
 
We build up more complicated expressions by taking these elements and substituting them for single letters in the above expressions, i.e. by assuming entire narrative elements can be substituted for 'thing' or 'attribute'. The results are called 'narratives'. A substitution requires use of '()'. These may be removed whenever operators inside are higher or equal priority to operators outside the parens, according to these priorities:
 
Priority of operation
'*', '[]', '()'  (unary before binary operators) 
'_/' , '->' , '::' , ','
 
Virtue
The notation is extended with "virtue" attributes GOOD/BAD, that may apply to any element or narrative. An event that is GOOD is called "efficient". 
 
Thing, person, place, idea
Recognize these subtypes of 'thing'. The differences between legal expressions and meaningful ones is that words are defined in a context with respect to these types of 'thing'. EG a person has feelings and a place has settings (my usage). An event with a person as the actor is called an "action".
 
Nar() notation
Given a narrative with fixed things and attributes A, B, C, ... This can be shorthanded with notation
Nar(A,B,C,...). These parens and commas are not those of the narrative notation. This allows using a narrative as a template with replaceable variables. The trusisms below using Nar(), assume that Nar() is given.
 
 
TRUISMS
(X->Y)_/[place, time, manner] (events have implicit localizers)
 X_/A :: X_/[A]                  (attributes remain constant)
X_/A_/GOOD :: X_/B_/[GOOD]      (virtue is transferred between attributes of an object)
(X->Y)_/GOOD :: Y_/GOOD         (efficient actions have virtue)
 X->person::person_/feeling     (affects cause feelings)
person_/feeling::person->Y     (feelings cause actions)
(person->Y)_/[GOOD]            (actions are efficient)
X*::X                                            (contrast is resolved)
                        
JUST-IN-TIME TRUISMS
Nar([Z]),Z                      (the implicit MAY become explicit)
Nar([Z]*)::Z                    (the blocked implicit MUST become explicit, eg "ready")
 Nar(X),Nar(Y),[Nar(Z)]         (lists - patterns are expected to continue)
A, B, [Nar(A,B)]               (tropes - familiar pattern are expected)
 
Comments
what is a category? EG "colors" vs "a color". Answer might be given
in terms of a standard model of a thing, having attribute slots with
allowed values. Similarly, the special properties of person and place
may be derivable from a model of standard attributes for these.
Thus maybe assume: person_/[GOOD]              
 
Formal equivalences
ASSUMING USE OF EQUALITY based on SUBSTITUTION and PAREN REMOVAL.
The use of equality is a meta statement, not a narrative structure.
Equality allows things like:
(X)=X
[Z]*=[Z*]
X->Y = Y_/[dY]         (Newton's 2nd: event is reflected in change)

In each case, a transition of notation occurs that replaces the left hand side with the right hand side.

 
There may be a law of narrative evolution that says:
if A::B then Nar(A)::Nar(B). This is not a truism.
Another law of evolution might say:
Y_/dY evolves to Y.
 
We might use this to derive something like this
1. (X->Y)_/GOOD = (Y_/[dY])_/GOOD (by Newton)
2. Y_/dY evolves to Y (or Y_/dY = Y)
3. Therefore (1) equals Y_/dY_/GOOD which evolves to Y_/GOOD
Thus "efficient actions have virtue" is derived. Not from other
truisms but from generative rules expressed with '='.
 
The actual laws of truism derivation, according to me, stem from general principles of the thesaurus and ledger. EG, [PLACE]_/raining comes from the requirement of making the object explicit, when setting an attribute.

Dear Bertrand Russell...what kind of "Foundations of Mathematics" were you looking for?

I was thinking about how set theory and what Russell et al call the "Foundations of Mathematics" is actually the most abstract type of math. It devolves into questions about infinite collections. Why would that be foundational? Did we really need transfinite arithmetic to understand the use of small whole numbers? Of course we didn't. But they were not really looking for foundations so much as gleaming golden spires, that could stand high above all other math as its parent in logic,  dependent on nothing more "basic" - rather - nothing more lofty.

There appears to have been a recent blossoming of homotopy theory around revisions of Russell's failed "Type Theory" attempt at defining foundations. Good luck with that! Rather than providing a deeper understanding of any sort of "foundation" these guys are off to the races doing a kind of math (Category Theory) that we called "abstract nonsense" in graduate school. As far as I am concerned, if you are going to skip ahead to the "For all"s, "There exists"s, "Not"s, etc., then you have already jumped the shark.

Rather than looking in the most abstract direction to find the foundations, why not look in the opposite direction with the most concrete realities possible, namely psychology and human behavior?

I think they were still (maybe also to this day) striving to understand Plato's idealized world. I am sure mathematicians are most comfortable believing that their work stems from something eternal and perfect, rather than something messy like Piaget's stages of cognitive development. I have no doubt whatsoever that mathematicians have no interest in psychology. 

But, as it turns out, psychologists [me] have an interest in mathematics. For what it is worth, I think you need to start with the name relation, persistence of meaning of letter and other symbols. And move from their into the definitions of "topic" data structures, thesaurus's, and ledgers. That leads to a kind of math that I remain interested in - the theory of patterns. But I do agree with those better mathematicians (than me) that it is important to get to a place where 1-1 or 1-many correspondences can be discussed.

Tartine Raspberry Turnovers

This is a croissant dough filled with raspberry jam but you could make croissant - which is what I started out to do. The original version is from a Tartine croissant recipe. I made mistakes but here it is. The result was stunningly fluffy:

Starter: I bought new organic rye flour. Mix 50-50 with water. Next day: discard 1/2 and re-fill, repeatedly, for several days until, when you check the brew, it is good and foamy. 

Leaven: mix a tablespoon of the foamy starter with a cup of water and a cup of flour. Rest in fridge overnight.

Poolish: mix one tsp of (freshly purchased) active dry yeast, one cup water, one cup flour. Rest in fridge the same night.

Dough: Mix Levin, Poolish and one cup of room temp milk, 3 tablespoons of sugar, one more tsp of yeast, one tsp of salt. Now stir in three cups of flour. If you can get a bit more flour in, go for it, but do not make the dough too tough and dry. At this point I kneaded it for five or so minutes. It should be a little silken. 

Rest dough for an hour, then fold it in on itself in each of four directions. Repeat this in-folding two more times after 1/2 hour intervals. Then put dough in fridge for at least three hours.

Folding in the butter: Soften 1 3/4 sticks of unsalted butter. Fold into an envelope of the dough - following standard croissant techniques: a flattened disk of dough + a rectangle of butter inside the circle of the disk. Fold disk edges in from each of four directions and pinch together to envelope the butter....you know. Then do TWO turns. Rest in fridge for an hour and do TWO more turns. [A TURN is rolling it out three times longer than wide, and folding it in three so it is a bit more back to being a square except in reality it is a rectangle in the perpendicular direction. Then you "turn" this ninety degree and do it again. That is TWO turns.] The original layer of butter has been tripled twice and then twice more, so 81 layers. 

Important note: you want the dough and the butter to be cool during folding. You do not want the butter to be softer than the dough or harder. I re-cooled the butter slightly after forming it into a rectangle. For this purpose, I put it between sheets of parchment paper and put in fridge. Then I rolled the dough out into a disk, then I took the butter out of the fridge and unwrapped it onto the disk.

After the "turns" and the final resting of the dough you are (almost) ready to use it and store it. The above recipe makes five cups of flour - worth of dough and after it becomes a butter layered wonder, I cut into three pieces and and froze two of them is separate saran-warp coverings. But then I made a mistake and went directly to  rolling out and rolling up some croissant. The error was that after the butter folding, the dough and butter were near room temperature. One key is that you need to cool it down one more time after that. Then roll the croissant or, in this case:

Making the turnovers: Roll out the layered dough/butter into <1/4 inch thick layer. Cut up into three inch square pieces. For each, put a tsp of raspberry jam in the middle of the square, fold one corner up and over to its opposite side, then use a fork to try to pinch together seams along the outer edge leaving a little pocket with the jam. It probably won't work, as the pastries tend to split back open during the next step but don't agonize. Place each finished pastry on a baking pan with parchment paper.

Rest the pastries at room temp, covered, for about three hours. Here the dough should really puff up. 

Bake at 425 F for 22 minutes. I was not able to wait for them to cool.

Quartz in Cape Cod Sands

Me telling a story about fragments of quartz stone tools, in search of arrowheads on the cape. 

Includes comments about this "heartbreaker":

Optimization can be a bad reflex

At my age (I'll be 70 in three weeks) I even try to optimize when I reach out for a glass of orange juice. I am faintly disappointed in anticipation of being inefficient and wonder if I am doing things in the right order. That is my interpretation of why I get slightly impatient reaching out for the glass.

Navigating the world increasingly becomes a matter of recognizing the circumstances, rather than experiencing them.

I saw a hummingbird

On December third

I saw a hummingbird

It knew its way around the yard

It's supposed to be long gone