u/LaoTzunami

There are about 12.37 lunar cycles per year. For cultures that use one lunar cycle for each month, this creates making a regular calendar a challenge. Some years have 12 lunar months, while the leap years have 13 lunar months. However, many ancient cultures, from Babylon, to Greece and China noticed that the 235 lunar cycle repeats every 19 years. This is called the Metonic cycle. With this regularity, you can create rules of what years to add the 13th leap month, and keep a decentralized kingdom's calendars synchronized.

The first picture shows the whole Metonic cycle as a torus. Each yearly turning creates a spoke, with the winter solstice in the center and the summer solstice on the outside. Then within each year is a helix of the moon phases, with the new moon as a black dot and the full moon as a white dot. Then a tighter helix is wound around the moon phases to show the day night cycle. I set the sunrise and sunset times based on Denver Colorado, the nearest big city to me. If you go further from the equator, the winter to summer day and night ratios in the summer and winter become more extreme.

The second image is a cross section of the torus, showing +/- 1 year.

This is a continuation of my Spiral Calendar post. Like the original, this is a supercoiling of the yearly , lunar and daily cycle. Each of the tiny loops is a single day.

u/SonOfDyeus asked why I made a spiral segment instead of a circle. The reason is, unlike our 12 months, the 12-13 lunar months don't line up perfectly, so there will be a jump in the lunar helix where the circle connects. BUT, the lunar cycle does repeat almost exactly every 19 years, which is called the Metonic cycle. If you graph 19 yearly spiral turns, you can loop the cycle back onto itself as a torus. I've posted 2 ways of wrapping the 19 years around the torus. The first wraps the seasonal cycle around the small radius, making 19 spokes, each a year. The second keeps the seasonal cycle on the main circle, and slowly moves the circle around the torus.

The first one especially would be cool to create when a baby is born, to show how much of their adolescence they've lived. You wouldn't want to put too much pressure on people, but I wonder if having a 19 year calendar on your wall (Birth through 18th year) would encourage patience, but also cherishing each day since you can see how big it is in the larger scheme.

I'm trying to transition to using natural time keeping: seasonal cycle, lunar month and 24hr daylight cycle. I had an idea to show all 3 cycles on a supercoiled spiral.

The overall spiral turn is a whole year with the 8 sabbats labeled on the outside

Then the first helix is the lunar cycle: outward = full moon, inward = new moon.

The tightest cycle is the daylight. The top days have more daylight and the bottom days have more nighttime.

I'm trying to transition to using natural time keeping: seasonal cycle, lunar month and 24hr daylight cycle. I had an idea to show all 3 cycles on a supercoiled spiral.

The overall spiral turn is a whole year with the 8 sabbats labeled on the outside

Then the first helix is the lunar cycle: outward = full moon, inward = new moon.

The tightest cycle is the daylight. The summer days have more daylight and the winter days have more nighttime.

Hexagrams are symbols with 6 yin (dark) or yang (light) lines. Evolution is a process that takes the top line, flips it, and then puts it at the bottom. If you apply evolution to all 64 hexagrams, you get 6 cycles. Since hexagrams change one line at a time, you can color each by its yin and yang bit, and then each hexagram is a window of 6 bits. The first image shows these necklaces, and then the later images show how this is related to a hypercube projection of the 64 hexagrams.

The 12 sovereign/tidal hexagrams (white) are a classic arrangement use to represent the turning of the seasons, or any cycle of energy in nature. Starting at all yin, ䷁ 2, yang lines grow from the bottom until all lines are yang, ䷀ 1, and then yin lines grow from the bottom until it has returned to all yin. This is the white outer cycle in the diagram:

>䷁ 2, ䷗ 24, ䷒ 19, ䷊ 11, ䷡ 34, ䷪ 43, ䷀ 1, ䷫ 44, ䷠ 33, ䷋ 12, ䷓ 20, ䷖ 23

This sequence can be generated by taking to top line, flipping it, and putting it at the bottom. The iching360 website calls this "evolution."

When you apply evolution to all 64 hexagrams, you get 5 cycles of 12 hexagrams, and 1 cycle of 4 hexagrams. These are the remaining cycles generated via evolution:

>䷚ 27, ䷆ 7, ䷣ 36, ䷵ 54, ䷄ 5, ䷍ 14, ䷛ 28, ䷌ 13, ䷅ 6, ䷴ 53, ䷢ 35, ䷇ 8

>䷏ 16, ䷂ 3, ䷨ 41, ䷭ 46, ䷶ 55, ䷹ 58, ䷈ 9, ䷱ 50, ䷞ 31, ䷘ 25, ䷺ 59, ䷳ 52

>䷎ 15, ䷲ 51, ䷻ 60, ䷙ 26, ䷟ 32, ䷰ 49, ䷉ 10, ䷸ 57, ䷷ 56, ䷬ 45, ䷩ 42, ䷃ 4

>䷜ 29, ䷕ 22, ䷧ 40, ䷾ 63, ䷥ 38, ䷯ 48, ䷝ 30, ䷮ 47, ䷤ 37, ䷿ 64, ䷦ 39, ䷔ 21

>䷽ 62, ䷐ 17, ䷼ 61, ䷑ 18

The picture is an orthographic projection of the 6-cube, also called the hexeract. Each of the 64 corners of the hexeract is a hexagram, and the edges connect 2 hexagrams that have 5 lines in common, and 1 line different. A popular way of projecting hypecubes to a 2D shadow is the Petrie polygon projection. This is the most symmetric projection and naturally places the 12 sovereign hexagrams on the outside. However, it overlaps some of the hexagrams, so my picture nudges the rotation so you can see all hexagrams. Normally, the green and aqua cycles would overlap, and the gold cycle of 4 would collapse to a point in the center.

In addition, this diagram has 2 important symmetries:

• Reverse pairs of hexagrams, which is how the King Wen sequence is arranged when it can, are reflected across the horizontal axis.
• Diametric opposite hexagrams have all 6 lines opposite

I wanted to share this dashboard I'm working on to explore the Jones Act data release by MARAD. You can filter by cargo, loading date, discharge date, state and port.

Dashboard: https://www.cato.org/jones-act-waiver-tracker

Notebook: https://observablehq.com/d/3a87558830e6537f

Data: https://www.maritime.dot.gov/ports/domestic-shipping/domestic-shipping

Any feedback about the chart welcome.

The images are just a preview of an interactive dashboard. This is really made to filter and sort voyages to read the MARD descriptions. Please visit these links for up to date numbers:

Landing page: https://www.cato.org/jones-act-waiver-tracker

Observable notebook: https://observablehq.com/d/3a87558830e6537f

Quick history:
After WWI, the US decided it was a national security risk to depend too much on foreign vessels to serve domestic shipping, because if we went to war and shipping suddenly stopped, it could crash our economy. To protect those supply lines, only vessels that meet these requiremetns can participate in US domestic shipping:

• Ship must be built in US
• Ship must sail under US flag
• Ship must be US owned
• Crew must be at least 75% US citizens

Instead of fostering a domestic shipping economy, this has made it much cheaper to import foreign goods than ship between two US ports. For example, the petroleum products California imports from Asia dwarf the products shipped from the Gulf Coast.

Due to the Iran war, Trump has signed a temporary waiver to the Jones Act to help lower gas prices. This dashboard tracks the shipping data published by MARAD. After a little over 100 days, we can see 141 voyages carrying a total of 34 million barrels across 16 cargo types. All of these shipments would not normally occur, so these numbers are in addition to the expected annual shipping volumes. Most notably, Jones Act waiver shipments for the west coast (PADD 5) and Puerto Rico are reaching their normal annual volumes! This indicates there is unmet demand that is artificially suppressed due to the Jones Act.

This has been soft launched, but I'd always appreciate feedback. If you have any ideas, please post them!

Try it out yourself: https://observablehq.com/d/e3ad3d0060994d0e

The second image are the orbit of the 64 6-bit vectors under the action of the Klein four group, created by reversing the bit order, and negating each bit.

Does this count?

Hope you enjoy this interactive diagram:
https://observablehq.com/d/e3ad3d0060994d0e

This is an intersection between data visualization, UI, mathematical art and Chinese culture. I understand this isn't exactly a typical bar graph, and the data is mathematical relationships and names of symbols. I had a lot of fun making this, and if you can have an open mind, this can be a bridge to a deeper understanding of binary mathematics, symbolism and philosophy.

I love, the Daodejing and the Zhuangzi, so following the advice of Confucius 😉I've decided to finally study the Yijing.

Like the Yili (meaning and principle) tradition that began in the 3rd century, I am only approaching this as philosophy, symbolism and poetry, not as an oracle.

In Taoist philosophy, we can only be aware of something by contrast with its opposite:

From chapter 2 Daodejing:
Being and non-being create each other
Difficulty is defined by the easy,
The long by the short,
The high by the low,
Before and after go along together

These are examples of the contrast of yin and yang. Most people know this concept from the yin-yang symbol , formally known as the taijitu ☯. Yin and yang can be represented as a broken and solid line:

⚊ yang (white, active)
⚋ yin (black, passive)

More complex dynamics are depicted by stacking lines together. The simplest example is how two lines represent the 4 seasons. The bottom line is the temperature of the earth, and the top line is the intensity of the sun:

⚎ spring: A hot sun warms a cold earth
⚌ summer: The earth and sun are hot
⚍ fall: A cold sun cools a hot earth
⚏ winter: the earth and sun are cold

Adding a third line creates 8 trigrams, commonly seen in martial arts movies, and also as the symbols on the South Korean flag 🇰🇷

Stacking 6 lines creates 64 hexagrams. From the bottom to top, these are some ways to understand the line ordering:

Levels: physical, biological, mental
Nature: earth, vegetation, sky
Stages: beginning, growth, culmination
Society: workers, managers, rulers
Self: inner world, outer role

The general pattern is hierarchical: upper lines build on the lower lines.

In the 18th century, the mathematician Leibniz encountered the 64 hexagrams, and directly connected them to binary numbers.

⚊ = 1
⚋ = 0

This diagram is an embodied way of representing the hexagrams and their relations to each other.

Each of the 6 hexagram lines are represented by an angled plane lit from above.

Slopes = white light
Overhangs = black shadows

These are physical forms that can rotate 180° about the x, y and z axes to create related hexagrams

The back side of a slope is an overhang and vice versa, so looking at the back side of a hexagram flips all 6 bits, creating a negative hexagram.
䷓䷡

If you rotate a plane about its horizontal axis, it will stay a slope, or stay an overhang. However, when 6 planes are connected as a hexagram, a horizontal rotation will move the segments on the top to the bottom, and the bottom to the top. Since this does not flip each bit, but it does switch the order of the 6 lines, this creates a reverse hexagram.
䷓䷒

You can also combine both of these into a negative reverse operation, that flips and reverse the bits. I call this isocline.
䷓䷠

Together, these 3 actions create a Klein 4 symmetry group.

Historically, the most important ordering of the hexagrams is the King Wen sequence that pairs each hexagram with its reverse when possible. However, there are 8 hexagrams that are palindromes, meaning they are their own reverses. For these 8, they are paired with their negative hexagram.
䷀ ䷁ ䷚ ䷛ ䷜ ䷝ ䷼ ䷽

Similarly, there are 8 anti-palindromes, which are their own isoclines:
䷊ ䷋ ䷐ ䷑ ䷴ ䷵ ䷾ ䷿

All 64 hexagram have a negative pair.

Putting all of this together, the 64 hexagrams exist as vertices on a 6-cube hypercube. The edges from each hexagram connects it to 6 similar hexagrams that are only 1 line different.

The diagram is a 2D shadow of the hypercube. It is projected in a way so when you rotate the entire hypercube 180° around the x, y and z axes, all hexagrams get mapped to their negative, reverse or isocline hexagrams. The left/right axis are the 8 hexagrams that are self-reverse, and the forward/back axis are the 8 hexagrams that are self-isocline. The negative pairs are diametrically opposed around the center.

In addition, the outside is a 12 sided Petrie polygon with the 12 sovereign/tidal hexagrams, that add yin or yang lines from the bottom up, and traditionally represent 12 months of the year.
䷗ ䷒ ䷊ ䷡ ䷪ ䷀ ䷫ ䷠ ䷋ ䷓ ䷖ ䷁

Hope you enjoy this interactive diagram:
https://observablehq.com/d/e3ad3d0060994d0e

I love, the Daodejing and the Zhuangzi, so following the advice of Confucius ;D I've decided to finally study the Yijing.

Like the Yili (meaning and principle) tradition that began in the 3rd century, I am only approaching this as philosophy, symbolism and poetry, not as an oracle.

In Taoist philosophy, we can only be aware of something by contrast with its opposite:

Chapter 2 Daodejing:
Being and non-being create each other
Difficulty is defined by the easy,
The long by the short,
The high by the low,
Before and after go along together

These are examples of the contrast of yin and yang. Most people know this concept from the yin-yang symbol , formally known as the taijitu. Yin and yang can be represented as a broken and solid line:

⚋ yin (black, passive), ⚊ yang (white, active)

More complex dynamics are depicted by stacking lines together. The simplest example is how two lines represent the 4 seasons. The bottom line is the temperature of the earth, and the top line is the intensity of the sun:

⚎ spring: A hot sun warms a cold earth
⚌ summer: The earth and sun are hot
⚍ fall: A cold sun cools a hot earth
⚏ winter: the earth and sun are cold

Adding a third line creates 8 trigrams, commonly seen in martial arts movies, and also as the symbols on the South Korean flag

Stacking 6 lines creates 64 hexagrams. From the bottom to top, these are some ways to understand the line ordering:

Levels: physical, biological, mental
Nature: earth, vegetation, sky
Stages: beginning, growth, culmination
Society: workers, managers, rulers
Self: inner world, outer role

The general pattern is hierarchical: upper lines build on the lower lines.

In the 18th century, the mathematician Leibniz encountered the 64 hexagrams, and directly connected them to binary numbers.

⚋ = 0 ⚊ = 1

This diagram is an embodied way of representing the hexagrams and their relations to each other.

Each of the 6 hexagram lines are represented by an angled plane lit from above.

Slopes = white light
Overhangs = black shadows

These are physical forms that can rotate 180° about the x, y and z axes to create related hexagrams

The back side of a slope is an overhang and vice versa, so looking at the back side of a hexagram flips all 6 bits, creating a negative hexagram.
䷓䷡

If you rotate a plane about its horizontal axis, it will stay a slope, or stay an overhang. However, when 6 planes are connected as a hexagram, a horizontal rotation will move the segments on the top to the bottom, and the bottom to the top. Since this does not flip each bit, but it does switch the order of the 6 lines, this creates a reverse hexagram.
䷓䷒

You can also combine both of these into a negative reverse operation, that flips and reverse the bits. I call this isocline.
䷓䷠

Together, these 3 actions create a Klein 4 symmetry group.

Historically, the most important ordering of the hexagrams is the King Wen sequence that pairs each hexagram with its reverse when possible. However, there are 8 hexagrams that are palindromes, meaning they are their own reverses. For these 8, they are paired with their negative hexagram.
䷀ ䷁ ䷚ ䷛ ䷜ ䷝ ䷼ ䷽

Similarly, there are 8 anti-palindromes, which are their own isoclines:
䷊ ䷋ ䷐ ䷑ ䷴ ䷵ ䷾ ䷿

All 64 hexagram have a negative pair.

Putting all of this together, the 64 hexagrams exist as vertices on a 6-cube hypercube. The edges from each hexagram connects it to 6 similar hexagrams that are only 1 line different.

The diagram is a 2D shadow of the hypercube. It is projected in a way so when you rotate the entire hypercube 180° around the x, y and z axes, all hexagrams get mapped to their negative, reverse or isocline hexagrams. The left/right axis are the 8 hexagrams that are self-reverse, and the forward/back axis are the 8 hexagrams that are self-isocline. The negative pairs are diametrically opposed around the center.

In addition, the outside is a 12 sided Petrie polygon with the 12 sovereign/tidal hexagrams, that add yin or yang lines from the bottom up, and traditionally represent 12 months of the year.
䷗ ䷒ ䷊ ䷡ ䷪ ䷀ ䷫ ䷠ ䷋ ䷓ ䷖ ䷁

All together, this creates a mandala that synthesizes most important relationships between hexagrams. There are some degrees of freedom that maintain all of these properties but arrange the hexagrams in the middle differently, but this is my favorite so far. Now I have a map for learning the meaning of each hexagram!

Please feel free to share any suggestions. This is a complex chart and I've done my best to make it manageable, but I'm always open to improvements.

I've always thought that mountains and tree are dual images symbolically. They both relate the one to the many. For mountains, the many starting places at the base converge towards the peak at the top as you climb. For trees, the trunk branches into a wide canopy. Both embody unity and diversity at the same time, but in opposite ways.

3D model: https://observablehq.com/d/1f1e526de8158cce

Stellated octahedron made of a fractal tree and fractal mountain. As a mountain is climbed, the many starting positions around the base of the mountain converge toward the peak at the top. As a tree grows, its branches differentiate from a trunk into a wider canopy. Both are relationships between the one and the many: hierarchical embodiments of unity and diversity.

3D model: https://observablehq.com/d/1f1e526de8158cce