Hot Wavelength

Chapter 62 (Long Epoch II): The Landon Ants
In November 2033, Liangguo Rocket City

Michael Max and Dr. James led a team to develop a spacecraft that would fly to the edge of the solar system. They named this spacecraft VESSEL, which means "big ship" in this context.

Creating a second "business card" for human civilization, following the one in 1977, is still an exciting undertaking, though it cannot compare to restarting Mars.

Things are different now; everything has been digitized. This second version of the "business card" will certainly not be just a metal plate with nearly primitive pictographic patterns engraved on it like before.

Michael was considering what material to use for the data and what number system to use. The reason for discussing the number system is that Michael's computer used both binary and ternary systems.

But he had a vague feeling that there must be other possibilities.

Daphne reminded Michael, "There's still a small envelope in Mirov's Mayan notebook that hasn't been opened yet. Isn't it time?"

Michael has an indescribable feeling toward the Mayan notebooks, a mixture of admiration for Captain Mirov's work in deciphering the Mayan script and a sense of surprise and even awe at the convergence of the mysterious Mayan calendar with the logic of modern computer calculations.

Michael wanted to open the small envelope with a sense of ceremony, witnessed by Erin. He also invited Erin's daughter, Mandy, and Dr. James.

Eileen was very pleased to hear that Michael, inspired by the Mayan notebooks, had successfully developed a ternary computer that was faster and consumed less energy.

Mandy coughed lightly to attract everyone's attention, picked up two pens and six Vito candies from the table, and said:

“I visit Mayan villages every year, and I am very familiar with the Mayan counting system. Now I will show you how amazing it is.”

Mandy picked up a candy bean in one hand and a pen in the other, and said, "A candy bean (pebble) is a dot, which represents 1, and a pen (twig) is a line, which represents 5. The Maya used a base-20 system."

Mandy took out three candies and arranged them in a row, representing 3. She held up a pen, representing 5, and placed the pen under the candies. 3 + 5 = 8. She then placed another pen under the pen, and 8 + 5 = 13. She then placed three more candies in a row on top of the three candies and asked everyone:
"The top two rows each have three dots, and the bottom two rows have two horizontal bars. What is this number?"

Everyone was speechless. To avoid embarrassment, the clever Daphne took the lead and said, "The Mayan numerals use a base-20 system, unlike our current base-10 system, which is read from left to right. The way you arranged them, you read from top to bottom. The three dots in the first row are the tens digit, 3 * 20 = 60. The three rows below are the units digit, representing 13. The sum of the two numbers is 73."

The Maya discovered that 73 is a special number, as it is the common divisor of Earth's orbital period of 365 days and Venus's conjunction period of 584 days. When 73 is arranged in a symmetrical pattern using a base-20 system, with two rows of three dots on top and two rows of one horizontal line on the bottom, something truly remarkable happens.

Take the value 73 from all four rows, multiply it by the 5 represented by the horizontal line in the bottom row, and you get 365, which is the Earth's revolution period.

Take the value 73 corresponding to all four rows, multiply it by the 8 represented by the three dots and the horizontal line in the middle two rows, and you get 584, which is the Venus conjunction cycle.

Take the value 13 from the three rows below, multiply it by the 60 represented by the three dots in the top row, and you get 780, which is the Mars conjunction cycle.

取下面三行对应的数值13，乘以上面两行各3个圆点代表的63等于819，玛雅历法中的特殊数，其中暗含着土星会合周期378天对于最小公倍数7174440天的贡献数63。

Dr. James exclaimed in amazement, "It's unbelievable how the Mayans could have created 73 using a base-20 system!" With that, the doctor opened his laptop and showed everyone a similarly amazing computer number game.

In 1986, Christopher Langton designed a computer growth game consisting of black and white squares and an "ant".

The rule is to make the blank squares all the same color initially (all white or all black). Place an ant in any square. If the ant lands in a white square, it turns 90 degrees to the right and moves one square, turning the original white square into a black square. The opposite is also true.

The ants begin to "walk" according to the rules. The first 10,000 steps form a chaotic and irregular trajectory. Then a miracle happens: the ants' trajectory begins to cycle, with each row consisting of 11 squares. Each square records the cumulative number of steps the ants have taken. Each row has a total of 52 steps, and every two rows form a cycle of 104 steps. This cycle continues indefinitely, forming a "highway".

This game is called "Landon's Ants," and similar gameplay based on it is called "cellular automata," pioneering a new direction in the research of artificial intelligence and even "silicon-based life."

"52 steps? 104 steps?" Eileen exclaimed in surprise, "Grandma Vanita's playing cards?"

Although the rules of Langton's ants are simple, the mathematical proof of how they evolved from chaos to regularity has yet to be provided. Mathematicians believe that it involves a complex plane and a mixed base system of non-binary numbers in black and white and four directions (up, down, left, and right).

比如，基础循环数104=8*13=(10T)3*(111)3。熟悉玛雅历法的众人一下联想到8是金星贡献数，13是火星贡献数，这两个数又是三进制中的最特别的。

Is it really that amazing?
Grandma Vanita's 104 fortune-telling playing cards, the conjunction cycle of Venus, Mars and Earth, the Mayan mystical numbers 8 and 13, 8=(10T) and 13=(111) in ternary system, two symmetrical forms, etc.

Could it be that carbon-based and silicon-based life forms have some inexplicable coincidence and connection with the stars in the sky?
迈克尔又注意到，每11个104步组成一个“组循环”，即8*13*11=1144=(10T)3*(10T)12。他觉得不可思议地摇着头说道：“这好像是3进制和12进制的混合进位制。”

Dr. James said with a hint of pride, "I found the exact step to enter the loop by comparing the horizontal and vertical lines in the 'highway', which appears at step 10283 of the nine 1144-step large loops."

9*1144=10296=72^2+72*71=2*72^2-72=(2T0)72，兰顿蚂蚁中似乎除了3、12进位制还隐含了72进位制！而10296-10283=13，又是13！13在3进位制中是111，在12进位制中是11。

Under the eager gaze of everyone, Michael opened Captain Mirov's Mayan notebook envelope. The first thing he saw on the yellowed paper was a question:
How many sides does a pyramid have?

Mandy blurted out, "Four sides, facing east, west, south, and north respectively."

Mirov then abruptly shifted the topic: "Which number system should computers use to best suit humans?" This question requires consideration of two factors: how the human brain calculates and makes judgments, and whether the hardware materials possess the physical states required to satisfy the corresponding number system, such as in binary, where the on and off states of a circuit correspond to 1 and 0.

As we all know, the human brain uses a decimal system for calculations. But what system does the human brain use for judgments? The answer without hesitation is binary, with yes and no represented by 1 and 0.

Further reflection reveals that ternary system aligns better with human thinking habits, as yes, no, and uncertainty are represented by 1, -1, and 0.

Mirov's letter continued:

“玛雅神庙的石板上刻着8是个特殊数，因为金星汇合周期584天除以与地球365天的公约数73等于8，但我突然意识到365除以73等于5，真正特殊的数是地球贡献数，也就是5。”

The pyramid has 5 faces! In addition to the four sloping faces that face east, west, south, and north respectively, there is also a base that does not point to any horizontal direction.

In the Mayan counting system, one pebble (dot) represents 1, four pebbles represent 4, but 5 is not five pebbles, but a tree branch (line), following the rule of "carrying over one when reaching five".

Daphne immediately thought of the Roman numerals, which also have the same meaning: the number of "I"s corresponds to 1-4, but 5 is not five "I"s, but "V", which is also "carry over one when it reaches five".

迈克尔继续读信：“逢五进一不代表计算使用5进位制，玛雅采用了20进位制而其他的古老文明采用的是10进制，它们都是5的倍数，可以理解为是2和5的复合进位制。”

When computers develop to the stage of artificial intelligence, what number system should be used for large models to learn from and imitate the human brain in a way that is more efficient and closer to the thinking habits of the human brain?

"Of course, it's base 10! Using the same base system for both the human brain and computers not only saves the trouble of conversion, but more importantly, intelligent computing can better understand humans by using base 10, and it's faster and more energy-efficient."

"In terms of logic, a decimal computer does not use 0-9, but rather a mixed base system of 2 and 5, divided into two groups of five. When it reaches five, it carries over to get 5, and when it reaches two fives, it carries over to get 10. I named it 'five-state decimal system'."

“五态是考虑到半导体材料的物理可能性，既然三种金属或者化合物可以稳定输出高中低三个电压用以表示1、0、-1，那么稳定输出五个不同电压的材料就一定能够找到，对应表示0、1、2、3、4。”

“电路分为两层，第一层只有0、1，各自对应第二层五态，得到00、01、02、03、04和10、11、12、13、14分别对应0-9共10个状态。”

“五大行星和地球相关周期的最小公倍数136314360乘以169，玛雅长纪历表示为19.19.19.0.0.19.0.0=1.0.0.T.0.1.T.0.0=23037126840。这么大一个数字在玛雅历法中，每一位都能用1、0、T（19）表示，不只是为了简单优美。”

"More importantly, 1, 0, and T can be associated with the physical states of materials. Imagine if 17 appears in a base-20 system, the chip material would need to have 17 physical states. Therefore, a simple numerical value in mathematical counting that is easy to correspond to the physical state of materials can be called the 'state number'."

"Besides 1, 0, and -1, are there any other simple states of matter? In the Standard Model of quantum mechanics, the spin of a fermion is 1/2 and the spin of a boson is 1. If we define right-handed spin as positive and left-handed spin as negative, then we have 1/2, 1, -1, and -1/2. Adding the non-spinning 0, we have 5 states."

Dr. James said, "A half-integer! 1/2 is a half-integer. If the number of digits in a positional numeral system is allowed to be written as a half-integer, then the Langton's ant threshold can be written as 10296 = (1/2, 0, T/2, 0, 0)12. 1/2, 0, -1/2 is another simple and elegant symmetrical form."

Quantum spin has five states, a pyramid has five faces, and the Cartesian coordinate system also has five axial vector directions (the direction of 0 is directionless): positive and negative X, positive and negative Y, and 0.

The abacus, invented in China, calculates addition by carrying over one unit when the number of fives is increased and carrying over one unit when the number of nines is decreased. The formula is expressed as: 9 = (1T)10.

When the human brain makes judgments, it uses both mathematical reasoning (deductive reasoning) and perceptual reasoning (inductive reasoning).

The detour taken by artificial intelligence is precisely because it blindly relied on mathematics and logic while neglecting perception.

A typical example is that when the human brain receives a beam of light, it judges its color, whether it is red or blue, while a computer judges whether it is a long wave or a short wave.

The leap in artificial intelligence is precisely because it has abandoned "mathematical determinism." When a computer "sees" a beam of light, it no longer analyzes the spectrum of the light wave, but simply uses a video camera to distinguish whether it is red light or blue light, just like a human.

A five-state decimal computer can define 1 as "mathematical yes" or "public yes", -1 as "public no", 1/2 as "perceptual yes" or "private yes", -1/2 as "private no", and 0 as the indeterminate state, for a total of five states.

After reading the letter, Michael felt greatly inspired and his spirits lifted. He said:

"Both the human brain and computers use decimal, so there's no need for conversion. More efficient and lower-power computers will be a better match for the human brain."

“Just like a pyramid has five faces, including four opposite faces facing north and south, east and west, plus a base that has no direction,” Daphne said thoughtfully.

Eileen exclaimed, "Michael, the five-state decimal computer combines rational judgment with perceptual judgment; that's the way the human brain thinks!"

Mandy stretched out her hands and joked, "I never expected that after going through all this trouble, the computing engine that best matches the human brain is right between the ten fingers of each of our hands."

&
The poem composed of collected verses at the end of the chapter:
Two or three clouds beyond the mountain, Song Dynasty, Yang Jie
Such calculations are beyond comprehension. — Hu Yinglin, Ming Dynasty
The extraordinary power is in your hands, Qing Dynasty, Jiang Shiquan

The icy touch between ten fingers. (Ming Dynasty, Zhu Chengyong)
(End of this chapter)