Chapter 5, Perimeter

Luo Qi is the youngest among those present; he is a network engineer at Cassini Station, responsible for the maintenance of the server room and systems. He excels at coding, and while he is not particularly skilled in mathematics and physics, he is familiar with natural logarithms and knows that it is an irrational number

Director Hu slowly widened his eyes

Unable to understand

The four of them were taken aback

31.4 centimeters

"Alright, please do not touch the samples any further, take a step back," came the voice of the technician from the loudspeaker. "I am currently calibrating the optical pressure quality testing instrument..."

It is truly astonishing

What about neutron stars?

If it is indeed the natural constant e, what does this imply

31.41593 centimeters

No matter how precise you are, regardless of how many decimal places you achieve, you will ultimately find that it completely matches the standard answer

a black ball with a mass of e

If this black ball is a sphere, then humanity may not be able to locate its position on the number line and in the coordinate system

Liang Jing, Lou Qi, and Hu Donghai exchanged glances; none of them dared to make a casual judgment. However, this string of numbers is indeed too famous. Not to mention Jiang Zi, even a student who has just graduated from high school standing here would be able to recognize it at a glance. The number on the screen is the base of the natural logarithm, e

"Is there anything in this world that is absolutely indivisible and cannot lose mass?" Liang Jing asked

Among the four people present, he has the lowest educational background. As the repairman and stationmaster of the Cassini station, he primarily engages in physical labor and is unable to contribute to academic discussions.

The natural constant has practical significance, but it is used to represent the limit of growth. Liang Jing continued, "It can appear in calculations, but it cannot appear in actual engineering measurement results"

How closely does it fit

31.41592653589793 centimeters

Debugging completed, weighing completed, the result values align with e

"Thus, the macroscopic world does not exist," replied Director Hu Donghai. "At the microscopic scale, there are indivisible entities; protons and other fundamental particles can be considered indivisible, or rather, they cannot exist stably once divided. This is because quark confinement does not allow for the existence of a single quark, so there is no such thing as a single quark or half a proton. Additionally, a quantum is the most fundamental unit of energy, which is also indivisible, but it is clearly unrelated to this black sphere, as it is not a proton.

A strong sense of incongruity and disorientation

"Dabai, be more precise!" Lou Qi shouted

I do not know

In mathematical terms, this calculation is certainly correct, but in practical engineering measurements, it is impossible to truly draw a square with a side length of 1 centimeter. The square root of 2 is an infinite non-repeating decimal; no matter how high your precision is, you can only approach it infinitely, but cannot completely match it. Liang Jing explained, "If your tool's precision is at the millimeter level, then the square root of 2 you draw will be 1.41 centimeters. If the precision is at the micrometer level, then the square root of 2 you can draw will be 1.41421 centimeters. You can continue to be precise indefinitely, but there will be no end to it."

Dabai's voice is very steady, as it is ultimately an emotionless artificial intelligence that can only faithfully complete tasks

The three of them hurriedly intervened, what kind of joke is this

Jiang Zi fell silent, and he also faintly sensed the strangeness within.

I said to the brothers, let’s dig it out from the permafrost, touch it here and there, and after all this time, is there really no loss in quality at all? Jiangzi suddenly realized another issue, even if its quality is indeed 2.7182818, an infinite non-repeating decimal, how could it still perfectly match up to the eighteenth decimal place? If I just tap it casually, it should at least lose even 0.0000000001 grams of quality, right?

Completely conforming within the range of measurement

"Let's put this issue aside for now," Lou Qi sighed. "Let's take a look at the other data... Next, let's measure the diameter and circumference, shall we, Bai? What is the circumference of this object?"

"Coincidence?" Lou Qi said, "Director Hu, is this a coincidence?"

Yes, it is completely consistent within the range of the precision optical pressure scale

Indeed, what Jiangzi said is reasonable. The precision optical pressure mass detector can measure mass with an accuracy of up to several decimal places, down to one-thousandth of a microgram, one ten-thousandth of a microgram, or even one hundred-thousandth of a microgram. At this level of precision, even a breath can cause significant fluctuations in the readings. Moreover, the black balls are excavated from underground, where the working environment is rough and harsh. This reckless man, Jiangzi, with a single strike of his pickaxe, can crack granite.

Director Hu Donghai gazed at the black sphere, a long period of scientific research had endowed him with a certain keen intuition, which often allowed him to find answers to problems more quickly than others. However, this time his intuition had failed him. Hu Donghai vaguely sensed that this sphere was unusual, and this unusualness was not only physical but also mathematical; it seemed to be a completely closed entity, inherently closed, both physically and mathematically, with no exchange of information with the outside world.

A square with a diagonal of √2

"Why does it not exist?" Jiang Zi interjected, "If I draw a square with a side length of 1 centimeter, its diagonal length would be √2 centimeters, right?"

Shall I give it a try? Jiang Zidong looked around, his gaze landing on the hammer on the laboratory table. "Give it a strike and see if there is any change in quality"

Do your utmost, precise to the limit

Director Hu Haiyang raised his stubbled chin and pointed to the black ball in the glove compartment, implying that if this object were a neutron star, it would likely weigh as much as half of Titan.

Luo Qi turned his head to look at Director Hu Donghai, who was the physicist

Why has its quality not suffered in the slightest

It seems as if someone has plucked the number e out of thin air and forcibly inserted it into mass

Perfectly matched, no errors?

The four individuals took a deep breath

Disorder

Big White, be more precise! Be a little more precise!

I am very sorry, Director, but I have already achieved an accuracy of 10^{-18} kilograms, and the current hardware conditions are unable to measure any further.

Although the limit of Da Bai's calculations can only extend to eighteen decimal places, Director Hu instinctively feels that if the precision were to continue to increase, the answer would still be e

Director, how many more decimal places do you need

Jiang Zinian was so tongue-tied that he couldn't pronounce the words clearly

The four individuals gazed at each other, each able to see the astonishment and incredulity in the eyes of the others

The large white debugging measurement instrument adjusts the range, and two green lasers emerge from the small holes at the bottom of the glove box, gradually approaching the black sphere as it begins to further refine its accuracy, and then the results are released

The prolonged silence in the laboratory

"Impossible, absolutely impossible." Lou Qi shook his head, "e is an irrational number; it only has significance in mathematics. How could it possibly be measured in real life?"

"Damn!" Jiang Zi blurted out instinctively

Electronic degenerate states ... or neutron degenerate state celestial bodies, where the self-gravity exceeds the neutron degeneracy pressure, tightly compressing atomic nuclei together. Such celestial bodies are nearly indivisible, commonly referred to as neutron stars, but the density of neutron stars exceeds one hundred million tons per cubic centimeter

It is truly astonishing that even the unit of kilogram itself is a human-defined concept, and there is no natural concept of a kilogram in the natural world

incongruity

However, this idea was too outrageous, and he did not dare to voice it directly

They were subtly uneasy

Can it be more precise

Can it be more precise?" Chairman Hu raised his head and asked, "Dabai, can this number be made a bit more precise?"

The natural constant e, this irrational number, this transcendental number, which frequently appears in the work of mathematicians on paper and blackboards, surprisingly appears in front of the unit kilogram

A few minutes later

Jiang Zi hesitated for a moment, "I think this number seems to be ... the natural logarithm?"

The other three individuals shook their heads in unison