Hot Wavelength

Chapter 46 (Short History 2): Symmetric Ternary

August 22, 2031, Liangguo Rocket City

Today is a special day, the day designated by the legendary Captain Mirov to open the Mayan notebook envelope, exactly 52 years since 1979.

Eileen, who had given the Mayan notebook to Michael, had also been thinking about it, but she called too early; Michael and Daphne were still asleep.

“Eileen, thank you for reminding us. We remember the date; we’ll be opening the envelopes today. Could you come and see them with us?” Michael asked Eileen.

“No, I’m in country B, and we’re separated by the Atlantic Ocean. My return trip is uncertain and depends on my husband Andre’s health.”

Daphne, who was listening to the phone call next to Michael, said anxiously, "How is Mr. Andre's condition? I wish him a speedy recovery."

Rocket City is located in the low latitude region of Liang Kingdom. It is early autumn, and the temperature is still very high. The sun has just peeked out, and the hot and humid air rolls in from the southeast sea along the endless mudflats.

After washing up and having breakfast, Michael and Daphne, filled with curiosity and excitement, faced the large, dusty but well-sealed envelope. Both were eager to know what secrets Captain Mirov's Mayan notebook held.

Daphne tiptoed to the bedroom door and, through the crack, saw little Vito sleeping soundly in his crib.

When Daphne returned to the workbench, Michael had already opened the envelope with a paper cutter. Inside was a red notebook and another sealed small envelope. The notebook cover had Russian writing on it, and Daphne recognized that the writing meant Mayan notes.

Michael brought out an external device and connected it to the computer. It looked like a desk lamp, but it was actually a high-speed overhead scanner.

Daphne opened the notebook and placed it under the scanner, quickly flipping through the pages. After the scanned document was automatically translated and archived, the two began reading it on the computer.

"Hello, friend from the future! I am Mirov. This year is 1979. When you see this, it will be 52 years from now in 2031."

"You must be wondering why I asked to open this envelope 52 years from now. It's not just because I believe that human technology will make a leap forward in a few decades. If that were the only reason, I could have set it at 50 or 53 years."

"The year 52 has special significance. It comes from the Mayan calendar, specifically 52 cycles of 365 days, totaling 18980 days. You might find it hard to believe, but the Mayans marked each of these 18980 days with a different and specific symbol, making it a unique calendar that the Mayans called the Short Count."

Upon seeing this, Daphne said to Michael, "I know a little about the Mayan short calendar. 365 days is called the Hab calendar, and 260 days is called the Tzolkin calendar. The least common multiple of these two numbers is 18980 days, which is 52 times 365 and 73 times 260."

Michael said, "365 days obviously refers to the Earth's orbital period, but what about 260 days?"

As if sensing Michael's question, the notebook continued: "Almost all civilizations in the world have calendars based on astronomical cycles, and the Maya are no exception. Their calendars vary in length, but they all correspond to astronomical cycles."

"In addition to 365 days and 260 days, the Maya also used 584 days, which is the synodic period of Venus and Earth. This makes it easy to explain what 260 days means. The synodic period of Mars and Earth is 780 days, and 260 days is one-third of that synodic period."

"The Earth's orbital period is 365 days. The conjunction periods of Venus and Mars with Earth are 584 days and 780 days, respectively. The least common multiple of these three periods is 113880 days, which is 312 sets of 365 days. The Maya may have thought that 312 years was too long as a short calendar, so they took half of Venus' conjunction period and one-third of Mars' conjunction period, which gives them 52 sets of 365 days, or 18980 days."

Daphne said, "Yes, 18980 multiplied by 1 is divisible by 365, multiplied by 2 is divisible by 584, and multiplied by 3 is divisible by 780."

“我发现，18980天这个地球年和内外两颗行星的会合周期的最小公倍数好像很特殊，可以被写成一个对称的数学形式，18980=3^9-3^6+3^3-3^0。”

Daphne said, "This is ternary. The number 18980 is represented in ternary. 18980 = (22200222)3, and the 3 outside the parentheses indicates ternary. It's so symmetrical. The Maya used a base-20 system, so how come there's a ternary system here?"

The notes seem to answer: "Did the Maya consider symmetrical numbers represented by a ternary system to be beautiful? I found confirmation at the Mayan pyramid ruins in Chichen Itza, Mexico."

"This pyramid has four sides, each with 91 steps, for a total of 364 steps. In ternary notation, 364 = (111111)³. Six ones, how symmetrical!"

“金字塔台阶两侧分别有九层，91*9=819，玛雅的历法就是这么神奇，819天也是他们历法中的一个重要的日期。819=3^6+3^4+3^2=(1010100)3。”

"The Mayan astronomical observations are breathtaking. They measured Earth's orbital period to be 365.242 days. Although their observed synodic period of Mercury (117 days) differs from the actual period by 1 days, their measurements of the synodic periods of Venus, Mars, Jupiter, and Saturn with Earth are extremely accurate." "As mentioned earlier, the synodic periods of the two planets closest to Earth, Venus and Mars, are 584 days and 780 days respectively. The least common multiple of these periods with 365 days is 113880 days. If we also consider Mercury's synodic period of 117 days and Saturn's 378 days, the least common multiple of these five periods is no longer 113880 days."

“神奇的是，金字塔蕴含的819天和113880天的最小公倍数是7174440天，这个数字刚好是水星117天、金星584天、地球365天、火星780天和土星378天这五个天数的最小公倍数。”

“更令人难以置信的是，7174440用三进制表示，可被写成12个1和3个0，即，7174440=(111111111111000)3。”

"If you think the numbers above are too big, the Maya actually derived two numbers, 8 and 13, from the conjunction cycles of Venus and Mars. They discovered a coincidence: the common divisor of the Earth year (365 days) and the Venus conjunction cycle (584 days) is 73. 365 = 73 * 5, 584 = 73 * 8. Therefore, they believed that 8 was the contribution number of Venus and inscribed this coincidence on a stone tablet."

"Mars' synodic period is 780 days. 780 = 20 * 3 * 13. The Maya used a base-20 system, and in both their short and long calendars, 13 was considered a magical number. They believed that 13 was the number of Mars' contribution."

“在三进制中，8和13也恰恰是具有对称美的数字，8=(22)3，13=(111)3。数学上，在三进制中，只有0、1、2三个数字，如果把2记作-1，用1、0、-1表示三进制，就称为对称三进制。习惯上，也可以把-1记作字母T，则8=(10T)3。”

Michael was completely confused, but when he read "1, 0, -1", he seemed to understand Mirov's meaning. He said, "Ternary computer: In 2024, researchers at the University of California, Berkeley simplified the binary calculation of artificial large models using 1, 0, and -1, which increased the calculation speed by 5 times and reduced the energy consumption to 13 watts, close to the human brain."

The notes seemed to follow Michael's train of thought, and then popped up: "The study of the Mayan calendar and the various numerical coincidences of planetary conjunction cycles made me realize the simplicity and elegance of the ternary system. Binary only has two judgments, 'yes' and 'no,' while ternary adds a state, that is, it includes three judgments: 'yes,' 'no,' and 'uncertain,' which is obviously more in line with the logic of the human brain."

"In 1955, countries began to develop computers. The hardware for computing was based on vacuum tubes in circuits. The mainstream design used diodes to represent 0 and 1 respectively for binary calculations. At my suggestion, Soviet scientists used transistors, with positive charge representing 1, negative charge representing -1, and no charge representing 0, to develop a ternary computer."

Daphne exclaimed, "I know! The Soviet Union produced ternary computers and sold nearly a hundred to Europe. They were fast and energy-efficient. Why did they abandon them later?"

The notes answered Daphne's question: "In 1979, when I wrote these notes, the Soviet Union's ternary computer project was officially canceled. There were three reasons: first, the country didn't have enough money; second, the country didn't have a complete industrial chain; and third, and most importantly, neither the Soviet Union nor Europe sanctioned us, so we could buy their binary-based computing devices at any time. Compared to starting from scratch and independently developing a ternary computer, it was both cheaper and more convenient."

"The reason I wrote this note and gave it to Erin, asking her not to open it for another 52 years, is because I believe that by then, binary-based computers will encounter huge bottlenecks as computing speed increases exponentially. One bottleneck is the conflict with power supply, and another bottleneck is that binary does not conform to the human brain's thinking habits when computers try to imitate the human brain."

"I suspect that after seeing my notes, even if you realize that ternary computers have obvious advantages over binary, you may not be willing to abandon your long-accumulated hardware and software achievements and start from scratch to use ternary. So please take my notes as a friendly reminder."

Michael Max fell into deep thought. Although ternary computers are theoretically faster and less energy-consuming than binary computers, who among the vested interests in the entire industrial chain of the Western world, led by Liang Guo, would be willing to start over?

The clever Daphne smiled and said to Michael, "You bigwigs in the electronics and information field should unite to resist ternary, right?"

“Kim Sungju University has significantly improved computing speed and reduced energy consumption simply by using a symmetric ternary algorithm. What’s more, the underlying computing architecture has been changed to ternary. If ternary computers are a complete revolution, it is inevitable that they will threaten vested interests.”

Michael laughed and said, "I don't know what others think, but I won't resist any advanced technology. In fact, as far as I know, many companies, including ours, have already started researching ternary components and algorithms. After reading these notes, I will accelerate the development of a ternary computer and apply it to my brain-computer interface project."

Daphne picked up a smaller, unopened envelope and scanned the text on it, which read "Jupiter and the Long Count Calendar" and a line of small print: "If you think a ternary computer is unnecessary, then you don't need to open this small envelope, because a more complex positional system is even less necessary for you."

Daphne was very curious and was about to open it when Michael stopped her, saying, "We've already had enough information today. Let's digest it first and look at this later."

Daphne stopped, then couldn't help but ask curiously, "Jupiter? The short calendar doesn't include the conjunction period between Jupiter and Earth, which has 399 days. Let's guess what kind of thoughts the number 399 will inspire in Mirov?"

迈克尔分析说：“玛雅人采用二十进位制，399=19*21，二十进位制中‘21’表示为11，而‘19’表示为1T。”

达芙妮似有所悟，脱口说道：“399=20^2-1=(19.19)20=(10T)20，正是二十进位制中的1、0、-1。”

&
The poem composed of collected verses at the end of the chapter:
The short stele has deeply engraved characters; it is attributed to Shen Zhou of the Ming Dynasty.
This was once the proof of his past life. (Song Dynasty, Shi Shu)

The ingenuity of the calendar is beyond calculation; Song Dynasty, Chao Gongsu

To learn from the ancients by reading books. (Song Dynasty, Qiangzhi)

(End of this chapter)