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

Old favorite pictures of Barb Waksman

Black Canyon of the Gunnison 

Before we were married.

Organizing without leadership

It is too bad a leader is chosen to help organize a union (or other) who, so often, ends up becoming corrupt and, minimally, loses track of the values of the organization. 

I dream of software for a social medium that automatically guides a group towards its organizational goals, without any need for a corruptible person to lead the effort or any need to compromise the identity of its users. If it functioned smoothly and simply, it could revolutionize politics.

An alternative to immortality

The idea of immortality sounds like torture. Same for heaven, where - paraphrasing Mark Twain - you are stuck with smarmy people.

What would be nice would be to pass into a state of pleasure that persists infinitely. For me: surrounded by the smell of hay-scented ferns and the sound of blue jays crying in the woods nearby. 

Perhaps this could be accomplished if at the moment of death ( or what appears from the outside to be a single passing moment ) I am like Achilles approaching the tortoise - getting half way there in each of my internal moments, taking an infinite amount of time to enjoy each one. Let's hope something like that happens.

Fried Shrimp

I just cooked a surprisingly good dinner. Probably the best fried shrimp I ever had. How is that? You ask. 

Well, I had some frozen shrimp, in the shell, and took 4 of them out of the freezer, put them in the fridge for the day, then finished defrosting them on the counter, at the end of the afternoon. I dried them out, dusted them thoroughly in flour (salt and pepper too) and fried them in avocado oil for a few minutes on each side. I timed it so I could eat the shrimp with rice and boiled arugula, with a little soy sauce.

Now I want to tell you that something happened with the flour on the outer surface of the shrimp shells. It turned the shells into something like potato chips. Although I peeled off the shell while dripping soy sauce on each shrimp, it had retained enough of the cooking oil along with the soy sauce that the whole bite was still delightfully greasy. Also there were bits of the crispy shell still un-removed that I did not mind being in the bites. I had discarded the shells on a side dish but I enjoyed them so much, I ended by eating all of those shells as well, except for the little tail flippers. 

So I am telling you, there is something special about frying flour outside the shell. The little, fried legs were particularly good. Or maybe it was the avocado oil,

Waiting for Barb to get a Covid test

Waiting in the parking lot of "Convenient MD" in Falmouth:

A proposed Twitter algorithm

Instead of suppressing hate speech, how about promoting consistent and complex subjects- as expressed through a series of posts - or - threads. For example it should not be too hard to detect grossly off topic comments once the "subject" has been detected.

Quissett In October

 

The math I didn't do

I was watching a YouTube of Zagier talking about partitions and modular forms and was reminded of a summer project I worked on in graduate school. At the heart of the Zagier's talk was a discussion of simple singularities ("branch points") in [I think] some kind of covering map. My thought was: why go to the bother of creating a modular form when there is a direct route into studying the global properties of the mapping based on analyzing the singularities?

So, for whatever it is worth claiming you thought about something but took it nowhere, here is a little info about that summer project. At the time, a professor named Charlie McArthy approved the project and I got a little grant. I hate to regret the past, since it got me to where I am in the present, but it would have probably been better to have him as a thesis advisor than William Pohl. Pohl promised me that we would do differential geometry using probabilistic "forms" but ended up assigning me a problem from integral geometry that, to be honest, was a dead end in terms of what most people are interested in. Of course I did like the Buffon needle problem but resolution of singularities and the impact on PDE's would probably been a wiser course. Sadly, at that time I wouldn't have dreamed of asking a Functional Analysis guy to be my advisor.

It starts like this: I was intrigued with the exponential mapping and the logarithm. The exp{i*t} mapping a line into a circle really appealed to me and especially the way you could invert the mapping using cutting and pasting with a little algebra. In particular, consider the following general construction: 

Suppose a manifold M with a nicely embedded submanifold S, such that the topology of the boundary of M\S is a Lie group G. We consider (M\S)xG. Now, away from the boundary of M\S, we have (manifold)x(group). But along the boundary we have GxG, so can this can be pasted onto a single copy of G using the group operation (g1,g2)-->(g1*g2).

One variation is when the group is the quotient group of another group. Then (g1,g2) can map to one g1*g2 in the super group or to the quotient via the quotient mapping applied to  g1*g2.

Claim: The result is a manifold, we'll call M'. So M'=M\SxG + G

Proof: just define the neighborhoods along the pasted in copy of G.

Claim: The mapping defined on the boundary of M\SxG extends naturally to a mapping from all of M' back to M. This covering map is the exponential when M is a circle and S is a point and we use Z (so M' is the real line) or Z2 (where this resolves the singularity of a "figure 8").

More interestingly, then M is the 2-sphere and S is a point, G is a circle, and the covering map is the Hopf fibration. I like the notation

S1 = e^R1

S2 ₌ e^S3

I guess of some interest is the fact that the exponential map and the Hopf fibration are the lowest dimension examples of something general. For example, when the construction involves a 3D manifold with an embedded circle. The boundary of what is left is a torus, with its usual group structure. I would be surprised if there were not some nice theorems relating possible group structures to coverings of a manifold - based on homology of geodesics. 

But then, I expect many of us have stories about the big fish that got away. I was high enough to see these possibilities but too stoned to do the heavy lifting of real mathematics.

I went for a little row.

I went for a little row. I was having problems with my cheap fishing rod. The upper section didn't fit smoothly into the top of the lower section and, twisting it, I broke off one of the eyes. So the rod was not too functional but there was a large flock of gulls in the air and cormorants on the water before I got there and they moved off, but I knew there were fish. So I was trawling with my rod leaning against the side and suddenly the whole rig was snatched overboard - too fast to stop it. The rod sank promptly.

I was thinking about how this solved the problem of what to do with the junk fishing rod. Saw a guy casting from a Penzance boat-house deck and asked him what kind of fish he thought they were. He said Bonito. Note to self: get a rod that floats or start keeping a firm grip on the road -somehow- when there are fish around.

Anyway, I went over to Ram Island and found what looks like an arrowhead made from green bottle glass.

I am particularly suspicious of the serrations on each edge of the point, but not present on the other edges.

Chappaquoit and Stoney, Beginning of October

 

Pink granite Merrimack Point

From Ram Island:

Deprivation Dieting

I have been dieting hard. I was thinking of starting a YouTube channel to explain my "Deprivation Dieting" but, for now, here were the main thoughts:

Dieting is a way of life. You have to commit to it and figure out how to embrace the discomfort. So -yes- it involves discipline but not so much on a day-to-day basis as with an overall discipline to "enjoy" the dieting. You can do this if you feel lighter on your feet and physically healthier; but you do it primarily by planning some nice low calorie meals. Get ready to de-prioritize everything else because dieting will be your main activity.

After 3 years of Covid pandemic, I was seriously overweight at 200lbs. I knew well that I had to start getting my life together as the pandemic started to fade. Currently I am at 165lbs and hoping to lose another 15lbs. Then I'll worry about how to get back to "normal" eating. 

After Covid, I went to the Doctor and was told I had Type II diabetes and needed to start taking lots of pills. I am now taking a few, notably Berberine, but I refused to buy into the diabetes framing and by blood glucose and blood pressure have dropped back closer to "normal" range because of the dieting [and also blood pressure pills]. My initial problem was too much glucose. So the essential premise of my dieting has been eliminate carbohydrates - or replace them with carbohydrates (like graham crackers) that also have a lot of fiber. I am supposed to be eating more vegetables but fat and protein are OK. 

The feeling of losing weight is precisely the feeling of being hungry. So get used to being hungry all the time. Going to bed hungry, waking up hungry, and waiting for lunch. This is how a nice meal can become a delicious meal.

Supposedly a body my size and age needs 1,500 to 2,000 calories per day. So my goal was to eat fewer than 1,000 calories per day until I lost the weight. I also try to have an occasional "austerity" day, where I try to stay below 700 calories for the day. I am estimating calories and surely kidding myself more than a little. I was losing weight quickly two months ago. Now it is getting slower and I am having trouble keeping the discipline. Gosh I want a croissant!

So the fun part of dieting is discovering new foods. When you are hungry, things taste better. For example I am enjoying cod-liver oil. Awful as it is, it is giving me some good "Omega 3" fat. 

Standard foods are: 

 - a bit of protein on a bed of seared arugula.

Salmon:

Hard-boiled egg, with side of homemade tomato soup:

 - small bowl of oatmeal

 - soups (tomato and beef)

Ingredients of beef soup:

 - salads

Tuna and salad - a bit of hummus makes it all worthwhile.

Stuffed Turkey Breast with coleslaw and cherry tomatoes

 - walnuts and prunes for desert

 - kefir and kefir/fruit shakes

 - sauerkraut (just started)

 - protein with other fancy vegetables:

Chicken and ratatouille

Salmon and eggplant (with tomato and mozzarella) [and a tbs of rice]

Another favorite meal is a friend egg with cheese and ham, inside a "carb-balanced" tortilla which as only 80 calories and lots of fibre.

Typically I will have one of these meals, and follow it with desert consisting of a small portion of yogurt with agave syrup, or a 1/3 glass of almond-milk with 1/2 tsp of agave syrup. I usually follow this with a small handful of walnuts and two prunes. I also have a couple hundred calories of alcohol after 3PM. 

"Intensity" as a standard attribute of any verb

I have been toying with the idea that verbs are represented by nodes in the thesaurus of words, with their own peculiar attributes. Intensity seems like a reasonable candidate. Just like efficiency [the verb's version of THE GOOD]. 

I just made an error, the kind that gives you insight into cognitive processing (which I am purporting to understand in terms of narrative). I was going across the room to widen the opening of the living room sliding door and forgot what I was doing - to some extent. So I found myself across the room trying to open the slider but forgot how wide I needed to open the door. I forgot the intensity in my plan for "Peter crosses the room and opens the door".

Some pictures from a recent (ongoing) trip

Things started out normally, with the sorts of Fauvist scenes you would expect.

I was trying to draw actual things:

And of course things got a little weird, after I fell in love with the turquoise/lead-pencil combination. Not sure where I was going with this:

This is what happens when you don't know what to draw and are sitting there with your heart in your mouth.

[Note I am starting to look a bit like Selman.]

I started to calm down after an hour or so and went back to trying to draw real things. The flowers in the garden seemed inviting and a challenge to handle the details. I failed but was still enjoying playing with the colored pencils.

And now I am having some tea.

Fish Freeding Frenzy

 

September Shrooms

 Don't hurt:

For reference, here is a non-trip effort from a few weeks later:

An approach to systematizing Truisms.

 The latest list of Truisms is as follows:

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)

***************************************************************

I have been trying to figure out some kind of logic that would reduce these to a fewer number of more fundamental parts, with little progress. I was saying to Barb: "I would like to understand how these Truisms are interrelated".

So here is an approach that should have been obvious:

Truisms are relations between narrative structures that relate topics in a "topic tree" to each other. The Truisms can be analyzed as behaviors between topics in the context of their position in the tree.

Not sure how this may work out but I can come back with at least one fruit from this tree approach (ha ha pun). 

The first Truism says: events have context. We have that events 'X-v>Y' are the simplest connection between two topics 'X' and 'Y'. First, the event name 'v' has some presence in the tree, with the typical attributes (and parts?) of any topic. But second, it connects 'X' and 'Y'. So the Truism takes the form of activating the common denominators between 'X' and 'Y' in the tree. For 'X' to act on 'Y' they must share enough context for the verb to make sense. Bob cannot slap Mary if they are in different places.

This dingy little piece of "fruit", incomplete as it is, shows the possibility of using a tree structure to explain the Truisms.  But it is an awkward formalism because other Truisms seem to corresponds to quite different tree mechanisms and principles of tree modification. It would be surprising if such quite different mechanisms would manifest as similar usages of the word "but".

The Mystery of Beta Decay

A fellow named Unzicker on YouTube has been explaining that "beta decay" is not well explained by postulating a "beta" particle that nobody can detect. He says the theorists are replacing something they do not understand (the loss of mass of the neutron when it decays into an electron and a proton) with something they cannot observe. 

Listening to another video from the same guy he pins a nobel prize winner to the wall when that person says he can ignore gravity because it is too small to detect in the situations he is measuring. 

So, here on my own blog, I am allowed to make a fool of myself and suggest that physicists should consider that the so-called weak forces holding a neutron together, are losing out to gravity when the particles get far enough apart. Perhaps it is during the conversion of weak force into gravity that mass is lost.

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.

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.

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.

Deriving the total length of segments from the glance function

Theorem:

For glance function

H = ∑ c_a*h_a

where the c_a are constants and the h_a are Heaviside functions, with impulse at a.

Then we have

(*)          ∑ c_a*a = sum of lengths of the segments

The proof is a generalization of brute force calculation, which is always of the same form. So for example, if we have:

With segments of lengths a, c, and e; separated by gaps of lengths b and d, then the left hand side of (*) is:

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

Here, everything in the second row cancels most of what is above it, leaving alternating +/- a's. Being odd in number, the final sum is +a.

Now the second row was used up completely, in those cancelations. So the third row starts with c and because  of cancelations from the fourth row, result in a final value of +c. The fourth row was used up canceling things in the third row. Now the fifth row simply adds +e. In total we get a+c+e. This is the sum we wanted.

It follows that if two domains in the 2D plane have the same glance functions over all lines, then they have the same Radon transforms. So the domains are the same, up to the sorts of details usually assumed away.

Note: (sum of the gaps) = D - (sum of length of segments)

Evolution of a picture of Hollyhocks

A simple theorem of glance functions

THIS IS NAIVELY WRONG BUT MAY CONTAIN AN IDEA

A little Theorem about glance functions [described in my Hypothesis Testing... article].

Let h_a be the glance function of a simple interval of length a.

If H is the glance function for a collections of intervals separated by gaps, and a new interval of length a is added after a gap of length b, then the glance function of the new collection of intervals is

(*)                                      H -> H – H^b  + H^a + h_b + h_a  - h_a+b

Where the superscript on a function H indicates a term-wise shift of the independent variable by adding that amount, so  H^a(x)= H(a+x).

Corollary: the value of the glance function after the last step equals the number of intervals being glanced.

Proof: It is true for one interval, since h_a equals 1 at it's last step. If true for H, with N final steps, then we note the terms in the above (*) has final step values: +N , -N, +N,  +1, +1, -1. This totals to N+1. Hence the corollary is true by induction.

Update: The correct formula is

(**)                     H à H – H^b  + H^a+b + (h_a + h_b – h_a+b)

The induction argument is the same. We can name the first part the "shifted H" part. The rest is the "self-contained" info about the added segment.

Note: this encourages thinking about re-constructing the original segments, starting from their glance function. Because we know how many segments are involved and the maximum length from first to last end points of the segments.

Compare me to a paremecium

I was reading Feynman about his observing paramecium behavior to be quite diverse and unpredictable versus what the textbook said about paramecium moving and bouncing off of obstructions.

As I sit here, doing what I always did on a happy Saturday morning [except it is Thursday] - sitting with a piece of paper and thinking about abstractions, I realize that sitting at my desk is what I spend almost the entirety of my time doing. I move around a bit. I eat and sleep. But from the pov of an alien observer, they would conclude that my sitting with a piece of paper is what I do. Everything else in my life would be reduced to something not mentioned in the observer's textbook.

June Hollyhocks

Somsas, Camcas, Samosas... you know the Uzbeck one

Around the world and back again, trying different dough wrapped around meat/vegetables. Seems like the Uzbeck "camca", a croissant like layered butter/dough, is the best. Cobbling together various recipes:

Dough

2 cups flour, <1 cup water, salt, tbs of olive oil - Mix as a dry dough. Make ball, rest. Kneed. Rest, etc.

Later, roll out as thin as possible, make layers of butter and dough, roll up as a tight roll, make little cylinders, flatten, rest. Later, roll out one per somsa.

[NOTE: the larger diameter cylinder will allow thinner sections and less rolling out. This seems better for preserving the butter/dough spirals and a flakier pastry.]

Filling

Meat: I tried the minced beef (+ a bit of lard) + onion + spices. 

Veggies: 3 small potatoes, 3/4 cups peas, 1/4 cups carrots, 1 small onion.

Boil potatoes, soften the carrots and peas (with a little cooking or defrosting). Mash potatoes and mix with other vegetables. (Do not use too much potato or the result will be bland). Add diced, uncooked onion. 

Spices:

1 tsp salt, 1/2 tsp cumin, 1/2 tsp turmeric, 1 big tsp of Massala, 1 tsp of minced garlic, 2 tbs lemon juice, 1 tbs olive oil, 4 tbs of chopped coriander (or parsely).

Mix it up, fill-em up, bake 25-30 minutes at 420F.

Children of a lesser god

Took some acid

Not much fun. Physically unpleasant but no question you have more artistic freedom.

Johannes Raatz:

Spring nectarine flowers: