Technology related to Super-distance Communication was developing at a rapid pace.
At the same time, as Li Qingsong’s understanding of the quantum entanglement phenomenon deepened, he also became aware of a problem.
Super-distance Communication technology, based on quantum entanglement, actually had its limits.
This limitation was related to distance.
Of course, it wasn’t that quantum entanglement itself was affected by distance—even if on opposite sides of the Cosmos, quantum entanglement remained instantaneous, taking zero time.
But Li Qingsong observed that the farther the distance, the greater the "interference" that quantum entanglement itself was subjected to.
Li Qingsong was not yet clear on where this interference originated, but for now, he suspected it might be related to dark matter and dark energy.
This interference made data interpretation extremely difficult. In other words, although the information was transmitted, the data became unreadable if the distance was too great.
And improving this interpretive ability was related to another extremely important discipline.
Mathematics.
’Perhaps, with the birth of Super-distance Communication technology, I’ll have to pioneer a whole new branch of mathematics. Hmm... I could probably call it quantum mathematics?’
Li Qingsong discovered that the level of development in quantum mathematics was closely related to the sophistication of his overall scientific system, as well as to the data interpretation capability for quantum communications.
At Li Qingsong’s current level of mathematics, the maximum communication distance he could support was approximately one billion kilometers.
Any farther, and the error and data loss rates would become so high that it would be fundamentally impossible to interpret a complete message.
Of course, Li Qingsong could also extend the communication distance via relays, that is, by deploying a Super-distance Communication relay station every one billion kilometers.
But even with a relay model, the error and loss rates would accumulate. After a maximum of nine relays, the information would become completely unreadable.
Thus, at Li Qingsong’s current level of mathematics, the absolute limit for Super-distance Communication was about 10 billion kilometers.
’Ten billion kilometers? That’s enough for now. After all, more than 99.9999% of an Interstellar System’s mass is concentrated within a radius of 10 billion kilometers.’
Li Qingsong thought to himself, ’No wonder I saw that the Intelligent Mechanical Calamity Fleet couldn’t communicate between Interstellar Systems back then.’
’Their mathematical level is likely much higher than mine, but they could probably only handle a communication distance of two or three hundred billion kilometers at most. The distance between Interstellar Systems, on the other hand, is easily in the tens of trillions of kilometers.’
’But developing mathematics, especially pioneering quantum mathematics... it’s so damn hard.’
Faced with the great mountain that was mathematics, Li Qingsong couldn’t help but feel a sense of dread and let out a curse.
Mathematics is an abstract science.
The simplest is using numbers to describe nature—for example, two apples, three oranges, and so on. This is the first level of abstraction. At this level, people replace physical objects with numbers.
The second level of abstraction is that of symbolic algebra. At this level, mathematicians use symbols to replace numbers, entering the stage of equations.
The third level of abstraction is that of operational laws. Mathematicians realized that symbols were not essential; the laws of operation were paramount. They abstracted these laws into universal axioms, laying the foundation for more advanced mathematics like groups, rings, and fields.
Then comes the fourth level of abstraction, where mathematicians further generalize operational laws into mathematical structures with common properties. They satisfy closure, associativity, identity, inverse, linear structure, continuity abstraction, and so on, no longer focusing on specific objects but defining systems that satisfy specific axioms.
Building upon the fourth level is the fifth level of abstraction, which begins to study the interactions and mappings between different mathematical structures. This developed into concepts like category theory and number theory, which would make an ordinary person’s head spin just hearing them.
And the quantum mathematics Li Qingsong was now pioneering, according to this pattern, was probably at the seventh level of abstraction.
At this level, Li Qingsong couldn’t even describe what he was researching in relatively simple terms.
It was like a problem where, regardless of the answer, Li Qingsong was unable to even describe the problem itself in simple terms.
It was a whole set of highly abstract and complex concepts. Although the Blutuk People had undergone several rounds of genetic modification, and their brains’ various capabilities had improved significantly compared to before, at this moment, there were fewer than 100 Blutuk mathematicians among the roughly 700 million Blutuk People who could even comprehend this problem.
The number of Blutuk mathematicians who could, on the premise of understanding the problem, actually research the answer, dwindled to a mere 20.
"Sigh..."
Li Qingsong heaved a deep sigh.
’Fortunately, my computer technology has also made great strides these past few years. The performance of the Quantum Supercomputer has been greatly enhanced again, so at least I have a suitable tool for researching quantum mathematics.’
’Otherwise, even if I could simultaneously control 10 billion Clones and think until their brains exploded, I wouldn’t be able to make a shred of progress.’
Due to the importance of Super-distance Communication technology, Li Qingsong had allocated the brainpower of a full 100 million Clones, having them either operate the Quantum Supercomputer or do nothing but think all day, dedicated solely to the study of quantum mathematics.
Li Qingsong invested the remaining 1.4 billion consciousness link shares into several other extremely important research projects, continuously maintaining the rapid advancement and development of his overall technology.
Time continued to flow by quietly. As the great pack of "dry rations" that was Flying Star continued to shrink, Li Qingsong finally made another massive technological leap on this day.
On Test Platform One, Li Qingsong had several Mercury-class Warships bombard it with their Electromagnetic Cannons at full power.
Normally, Test Platform One would have been torn to shreds instantly. But now, before the high-speed projectiles arrived, a pale yellow shield of light materialized around the test platform, completely encasing it without a single blind spot.
Gluon plasma, controlled by a magnetic field and bound by the Strong Core Force!
It was incredibly thin, only a few micrometers thick, yet extremely tough. Even though each Electromagnetic Cannon Projectile Li Qingsong was firing had a velocity of over a hundred kilometers per second, and each one was powerful enough to shatter mountains and crack stone...
...they could only cause ripples to spread across the surface of the few-micrometer-thick gluon plasma shield, completely unable to penetrate it!
Li Qingsong had finally mastered Energy Shield Technology. Although its performance was still far inferior to that of the Intelligent Mechanical Calamity Fleet, it didn’t matter. He just needed to continue iterating and optimizing!
At this moment, the fleet’s main energy source, deuterium gas, was running low.
The current supply was not even enough to support the fleet’s deceleration to enter an Interstellar System for resupply.
But this was not due to an oversight or error on Li Qingsong’s part during the resource gathering phase.
It was a deliberate arrangement by Li Qingsong. He had allocated a larger share of his reserves to ordinary hydrogen, also known as protium.
And now, following the breakthrough in Energy Shield Technology, there was also a breakthrough in protium fusion reactor technology!