Prediction equation for winter solstice

A few weeks ago, I posted here a drawing of my prediction of the apparent place of sunrise on the winter solstice, based on my observations of the summer solstice and the spring equinox.

There was a request from the post: “how did you figure that out?”

I post photos of my notebook page of my original calculations. Let me explain.

I had three observations of distance and time. The velocity is a constant. d/t=v.
For distance, I used my outspread hands to measure along the mountain range at the east side of Kyoto. The northernmost point of sunrise was summer equinox, north of Mt. Heie, the tallest mountain in the range. The equinox point was a little south of Mt. Heie.

On November 29, the dawn was clear, and my observation of the sunrise point measure three hands (fingers outspread) from the sunrise point of the summer solstice. I had made observations by photograph.

I realized I could use algebra. The unknown, x, would be the sunrise point of winter solstice.

Summer solstice-------------Equinox----------------November 29----Winter solstice

/\/\ *---------------------/\ *----------------------------/\* --------------- ?????????
pair of hills Mt. Heie hill

[three hands with fingers outstretched ][ x ]
[six months ]
[six months minus three weeks ] [three weeks ]


d/t=v
EQUATION ONE 3 handwidths + x/6 months = v
EQUATION TWO 3 handwidths/6 months – three weeks = v

EQUATION ONE = EQUATION TWO
3 handwidths + x/6 months=3 handwidths/6 months – three weeks

I set up equation below and solved for x.

Let x = distance (hand widths with fingers outstretched) of sunrise from Nov. 29 to December 21
H = hand with stretched fingers , including thumb

Line one (3H + xH)/24 weeks = 3H/21 weeks

Line two 3H(24 weeks)=21 weeks(3H+xH)
Line three 3H (24 weeks)=3H(21 weeks) + xH(21 weeks)
Line four 3H(24 weeks) – 3H(21 weeks)= xH(21 weeks)
Line five 3H(8 weeks) – 3H (7 weeks) = xH(7 weeks)
Line six 3H(one week)=xH(7 weeks)
Line seven 3H ( one week)/7weeks=xH
Line eight 3/7H=xH
Line nine 3/7=x



x equaled 3/7 HAND. I could look at the mountain range and measure 3 and 3/7 HAND to predict the point of sunrise on the winter solstice.

Winter solstice prediction

Three weeks remain to the winter solstice. My calculations predict the point (pen cartridge center) of apparent sunrise. Check back in December!

Murder, snakes, gambling--in the garden!

A volunteer at the Kyoto Botanical Garden last week pointed out local lore. The thorn on the Ninja Star Tree recalls--in shape and size-- a weapon thrown by a ferocious deadly band of warriors.
The gourd on a vine seems to snake along the ground.
Finally, the so-called gambling tree drops bark in large pieces, its exterior wealth peeling like throwing away money. If I understood correctly.

Forgotten parasol

Hanging parasol
Forgotten with kiwi vines
Afternoon arbor

Fall Equinox

The autumn equinox at sunrise

and the summer solstic sunrise


photos made easy by sleeping on the rooftop.
The precession of the equinoxes joined, too, by dedicated digital camera (canon powershop A590) which was preceded by a cell phone camera (Vodafone 802SE).

Mt. Hiei is the tallest in the range of eastern Kyoto at 848.1 metres (2,782 ft).

Brain glue

Lunch in the garden of a restaurant in a Kyoto temple, Daitoku-ji. Something rectangular, deep fried, served on sticks like long thick pine needles.

“What is it?”

The Zen vegetarian waitress returns. “Gu ru ten.”

I expect a Japanese word, and the conversational part of my brain won’t compute. But quietly I see another part of my brain spelling out “gluten”.

She tries another word. “Fu.”

“Barley? Rice?”

“No,” she answers clearly. “Ofu.”

This is definitely a Japanese word and I can remember a few hours.

At home, I consult Japanese dictionaries without success.

But “vegetarian zen” search of the internet brings up “wheat gluten,” “macrobiotic,” “fu (not to be found in Japanese dictionaries),” and so forth. Success.

By the way, the three sticks of gluten sustained me well past my usual dinner time.

Jazz in Japan

A duo perform jazz on September 5 in Kyoto. Above the restaurant, the proprietor has a third floor music room. A dozen folding chairs are set up. Armadillo guitars hang on the wall; lessons take place once a week.

Today, the musicians are a female Japanese vocalist and a male guitarist.

The singer explains in Japanese the two meanings of MEAN in “Mean to Me.”
“You're mean to me…
You shouldn't, for can't you see
What you mean to me.”

For another tune, she first explains that there are three sets of answers “Whatever will be, will be” in “Que Sera, Sera.”

A guest singer from the audience belts out Route 66, later asking my opinion of her pronunciation. The pronunciation and swing beat were great, and I would have liked to extend my compliment by saying that we Americans often riddle ourselves with the lyrics.

“Well it goes through St. Louis, Joplin, Missouri.
Oklahoma City looks mighty pretty.
See Amarillo, Gallup, New Mexico.
Flagstaff Arizona, don't forget Winona.
Kingman, Barstow, San Bernardino….”

Encore request. “Got any more Billie Holiday?”
The vocalist calls out chords—in English—to the guitarist. They play an inspired, “Lover man, where can you be?”