Between storms


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The late Yang stylist Fong Ha used to distinguish Xing Yi Chuan versus Tai Chi Chuan as ‘tearing cotton’ versus ‘spinning silk’.

There was a pause between storms here in Northern California and some photos were needed so …

The first challenge was not to exhale while the camera was shooting lest a small fog or cloud be visible.

No need to worry about perspiration or about hair being in disarray,

The second challenge was the intermittent breezes moving tassels, flags and, in the case of Judge’s pens (判官笔), spinning the entire weapon. There are at least two styles of Judge’s pens

While the latter, which is what I have, provide an interesting propeller effect when the rings are worn on various fingers for purposes of photographic clarity the former are to be preferred in situations where there are breezes, winds, tornadoes and so on.

The third challenge is not shivering in silks. Wearing long underwear provides two advantages: the wearer is, or at least should be, warmer AND the silks do not move as much. However, one does tend to look pear-shaped.

Triangles in triangles

Something of a continuation of the previous post about squares within squares. Just as a square is an equilateral quadrangle with equal angles (apologies to most rhomb-o-philes) the focus will be on equilateral triangles (which are equiangular) .

triangle with a side length of 1 – 1 triangle
triangle with a side length of 2 – 5 triangles
triangle with a side length of 3 – 13 triangles
triangle with a side length of 4 – 27 triangles
triangle with a side length of 5 – 48 triangles
triangle with a side length of 6 – 78 triangles
triangle with a side length of 7 – 118 triangles
triangle with a side length of 8 – 170 triangles
triangle with a side length of 9 – 235 triangles
triangle with a side length of 10 – 315 triangles
triangle with a side length of 11 – 411 triangles
triangle with a side length of 12 – 525 triangles
triangle with a side length of 13 – 658 triangles
triangle with a side length of 14 – 812 triangles
triangle with a side length of 15 – 988 triangles
triangle with a side length of 16 – 1188 triangles

(n(n+2) (2n+1))/8 – round down

or ((6n((n) + 16n + 9)/8 for the next term – make sure to round. For n= 8 (384+ 128 + 9)/8 = 65 = the difference to n = 9

Squares in squares



Sometimes in static space planning (for example for lockers and shelves) and in dynamic space planning (for example. choreography) it is useful to know how many squares are contained by a square. For a square with a side length of 1 the answer is just one. For a square with a side length of 2 the answer is five: one 2 x 2 square and four 1 x 1 squares.

For square with a side length of 3 the answer is 14: 1 3×3 square; 4 2×2 squares and nine 1×1 squares.

For a square with a side length of 4 the answer is 30: 1 4×4 square, 4 3×3 squares, 9 2×2 squares and 16 1×1 squares.

For a square with a side length of 5 the answer is 55: 1 5×5 square; 4 4×4 squares; 9 3×3 squares, 16 2×2 squares and 25 1×1 squares.

For a square with a side length of 6 the answer is 91: 1 6×6 square; 4 5×5 squares; 9 4×4 squares; 16 3×3 squares, 25 2×2 squares and 36 1×1 squares.

For a square with a side length of 7 the answer is 140: 1 7x 7 square; 4 6×6 squares ; 9 5×5 squares; 16 4×4 squares; 25 3×3 squares, 36 2×2 squares and 49 1×1 squares.

For a square with a side length of 8 (a chess or checkerboard) the answer is 204: 1 8×8 square; 4 7×7 squares; 9 6×6 squares; 16 5×5 squares; 25 4×4 squares; 36 3×3 squares, 49 2×2 squares and 64 1×1 squares.

What we have is the sum of a series of squares of consecutive integers – given by ((n)(n+1) (2n+1))/6 for n = 1, 2, 3 …

So for a square with a side length of 9 the answer is 285 – note you might choose to add 9 squared (81) to the answer for side length of 8.

For a square with a side length of 10 the answer is 385.

For my purposes a square with a side length of 16 has 1496 squares – more than enough.

Human heart valve diseases

Most of the time the human heart is built with four chambers that are separated by valves (yellow circles) whose purpose is to allow blood to be pumped from one chamber to the next. Each valve can have one of at least three challenges:

/1/ stenosis – the valve loses flexibility so it does not open fully, limiting how much blood flows onward

/2/ regurgitation – the valve does not close completely so some blood leaks into the previous chamber

/3/ atresia – usually the valve was not constructed correctly so it does not open completely or is blocked

Of the 12 combinations aortic valve stenosis is the most common (about 1 person in 8 for people 75 or older) and the most dangerous.

There are at least six symptoms (not all of which need be present) which are often arranged as the English language mnemonic LISTEN:

Lightheaded, faint, or dizzy

Irregular heartbeat, heart flutter, or chest pains

Shortness of breath – sometimes while lying down

Tiredness even after enough sleep

Edema (swelling of the ankles and feet)

Not Normal skipping or missing daily activities, avoiding exercise, not enjoying hobbies

What to do if a Tai Chi Chuan student or potential student has one of the heart valve conditions and cannot practice at the pace encountered in class?

NASA Artemis mission

The view from the UNCREWED spacecraft about 16 minutes from separation and 36 minutes from landing.

Normally, we would wish Godspeed, a word that holds the intention of a personal blessing for another to accomplish a difficult or journey. Orion is arriving at 25,000 miles per hour (about 50% faster than astronauts might return from the space station) so there will be a separation of the command and service modules and a quick burn to turn the module so the heat shield is at the bottom. There’s a long series of parachute openings – seems like a lot of moving parts. Here the desired Godspeed is a velocity of nearly zero.

Missouri COVID


This is a plot of reported COVID deaths in the US state of Missouri from the first reported death in March 2020 to present. Note that Missouri, like many US states, no longer reports deaths or cases on a daily bases, but rather reports weekly usually with a lag. Of interest here is the surge in cases from about 13,119 on January 1 2022 to 20,169 in April 10 2022 as contained in the green rectangle. Normally, one expects to see a series of stacked s-curves to the abrupt rocket upwards is probably some sort of artifact as opposed to the disease suddenly running wild. Sometimes radically vertical changes indicate someone cleaning up a backlog of old cases (or a component such as a county in the state resuming reporting) or a new testing lab coming online. In the early stages of COVID the disease swept through nursing homes and was catastrophic. In the absence of a footnote or some other explanation one might be tempted to conclude some new variant of COVID had erupted OR that hospital capacity was overwhelmed.

Unfortunately, both cases and deaths are chronically under-reported usually due to inadequate testing, poor diagnostic skills or political reasons. Even if Missouri’s refined coronavirus deaths more closely approximated the blue line a dispassionate comparison to other political entities with similar populations (Missouri’s population is about 6.17 million), inland (as opposed to coastal), not mountainous and reasonably urbanized would indicate Missouri did substantially worse that similar entities. . .analysis

Anatoly Yevgenyevich Karpov (Анато́лий Евге́ньевич Ка́рпов)


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I am not clear what events led to the former World Champion’s hospitalization but wish him a speedy and complete recovery.

He will always be linked with the late Viktor Lvovich Korchnoi (3/23/1931 – 6/6/2016) and with Garry Kimovich Kasparov – epic

matches with both. Somewhat unusually for a World Champion he regularly played strong tournaments and was very successful.



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The Meltwater Chess Tour is progressing and the third to last event is being played. The Julius Baer Generation Cup has two stages: the preliminaries which are a round-robin and then the knockouts which are head to head. The top eight finishers in the preliminaries advance to the knockouts. Both Magnus Carlsen and Hans Moke Niemann are playing in the preliminaries and they did meet over the board during round six (on the second day – there are multiple rounds per day). Magnus played one move and resigned. After considerable effort he is now back in first place after the 12th round (played on the third day). There will be three more rounds played tomorrow.

Personally, if I suspected cheating, I would have played in order to gather evidence of that cheating, but Magnus felt otherwise.

I don’t have a clear idea what will happen if Magnus and Hans meet in a knockout. It is not given that Hans will necessarily qualify: he has 5 wins, 3 draws and 4 losses. These very up and down results have him in 7th place. We’ll see how tomorrow’s three rounds play out.