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Join the ServerThe chimes for the end of the lesson were still echoing in the Grand Auditorium, but not a single mage rose to leave.
Every gaze was focused on the two small “tables” on the blackboard.
This seemingly simple “apprentice-level” math problem now felt like an abyss stretching between classical physics and the quantum world.
Masters Albin and Lorentz spoke in hushed tones, their faces etched with solemnity.
They had realized that Lia Farrien was not just playing around.
She was attempting to reconstruct the underlying logic of every mage.
If she succeeded, all their previous criticisms of Heisenberg would become a laughingstock.
“This makes no sense at all!” Albin whispered to Lorentz beside him.
“Numbers are numbers, tables are tables. To conflate them is simply insane!”
Lorentz didn’t reply immediately; he took out a pen and paper and began to try the calculation.
He tried multiplying the numbers in corresponding positions of the two tables, but quickly realized that it was nonsensical.
He tried several other operations he could think of, but none yielded a self-consistent logic.
Not just him—hundreds of mages in the auditorium were doing the same.
Some calculated in their magical notebooks, while others used mental power to construct virtual numbers in the air, trying to find the key to the puzzle.
Heisenberg did not move.
He knew the answer.
For he was the one who had spent countless sleepless nights laboring to learn and master this set of operational rules.
But he was more curious about how Professor Lia would imbue this bizarre set of rules with a vivid physical meaning that everyone could understand.
***
The ten-minute break passed quickly.
Lia stepped onto the podium once more.
“It seems everyone has made their own attempts,” she said with a smile.
“Now, who is willing to tell me: what is the result of Matrix I times Matrix II?”
Silence fell over the audience again.
No one dared to raise their hand.
‘Well, it seems this problem is indeed a bit beyond the apprentice level.’
Lia picked up the chalk and walked to the blackboard.
“Matrix multiplication follows a specific rule, which we call ‘row by column’.”
Using different colored chalk, she circled the first row of Matrix I (1, 7) and the first column of Matrix II (2, 6).
“We use the first row of Matrix I to perform a dot product with the first column of Matrix II.”
“In other words, the first number times the first number, and the second number times the second number, then we add the results.”
“1 times 2 equals 2. 7 times 6 equals 42.”
“2 plus 42 equals 44.”
“This number, 44, is the value in the upper-left corner of our result matrix.”
Lia drew a new two-by-two matrix on the blackboard and wrote “44” in the top-left corner.
“Next, we take the first row of I (1, 7) and multiply it by the second column of II (5, 4).”
“1 times 5 equals 5. 7 times 4 equals 28.”
“5 plus 28 equals 33.”
“This 33 is the value in the top-right corner of the result matrix.”
Lia filled “33” into the new matrix.
“Then, the second row of I (3, 8) multiplied by the first column of II (2, 6). 3 times 2 is 6, 8 times 6 is 48, added together is 54.”
“Finally, the second row of I (3, 8) multiplied by the second column of II (5, 4). 3 times 5 is 15, 8 times 4 is 32, added together is 47.”
Eventually, a brand-new matrix appeared on the blackboard.
“Now, let’s calculate II times I.”
Without pausing, Lia quickly used the same rule to perform the calculation.
When the two results were placed side-by-side on the blackboard, the entire auditorium fell into a deathly silence.
This conclusion, which had been repeatedly mentioned in Heisenberg’s paper but had remained difficult to accept, was now presented before everyone once again.
It was no longer a philosophical speculation, but a cold, calculated fact.
“Why?”
A young apprentice couldn’t help but stand up and ask loudly.
“Professor Lia, why is it like this? What does this represent physically?”
This question echoed the voice of everyone present.
Lia looked at the apprentice with approval.
“A good question. Mathematics is just a tool, a language to describe the world. If a grammar does not correspond to reality, then it is meaningless.”
“So, what is the physical meaning of matrix multiplication? It represents the sequence of operations.”
She pointed at the “p” and “q” on the blackboard.
“Let’s return to the electron’s position ‘q’ and momentum ‘p’.”
“The matrix ‘q’ represents the operation of ‘measuring the electron’s position.’ The matrix ‘p’ represents the operation of ‘measuring the electron’s momentum’.”
“Therefore, the matrix multiplication ‘p times q’ represents the sequence of ‘performing operation q first, then performing operation p’.”
“In other words, we first measure the electron’s position, and immediately after, we measure its momentum.”
“And ‘q times p’ represents the reverse order: we measure the momentum first, then the position.”
“Now, please look at the results on the blackboard again. p times q does not equal q times p.”
“Translated into physics, this means: measuring position first then momentum yields a different result than measuring momentum first then position!”
“Boom!”
The mages in the auditorium felt as if their brains had been struck by an invisible hammer.
This explanation was too subversive, yet too logical!
It perfectly linked an abstract mathematical inequality with an imaginable physical process.
“This… this is impossible!” Master Albin stood up abruptly.
He seemed extremely agitated, his voice trembling slightly, “To measure is to change the thing being measured? If I use a ruler to measure the length of a table, does the table change just because I measured its length before its width?”
“That is because,” Lia’s voice was calm and powerful, “your table is a macroscopic object composed of billions upon billions of atoms.”
“But what we are discussing is a microscopic, solitary electron.”
“If you want to see—to see the position of an electron—what do you need? You need to strike it with a photon, and then receive the photon that bounces back.”
“The moment you strike it with a photon, you inevitably change its momentum.”
“Similarly, when you measure its momentum in some way, you will inevitably disturb its position.”
“In the microscopic world, observation itself is a form of interference! We are no longer detached observers; we are part of the process!”
Lia’s words were like claps of thunder exploding in the minds of every mage.
The faces of those with rigid mindsets turned pale; they felt the edifice of physics they had spent their lives building crumbling inch by inch.
Meanwhile, the eyes of the more active-minded mages shone with the light of excitement and a thirst for knowledge.
A brand-new, more wondrous, and more profound worldview was unfolding before them.
Heisenberg, sitting in the corner, found his eyes becoming moist.
‘So that’s why! So that’s how it is!’
“Therefore, Mister Heisenberg’s theory is not some grotesque mathematical witchcraft.”
Lia’s gaze swept across the hall, finally landing on Albin and Lorentz.
“It is precisely the inevitable result of physics moving towards a deeper level. It tells us that we must abandon those outdated notions from the macroscopic world and use a brand-new grammar to describe that microscopic universe which we cannot see, but which truly exists.”
“And matrices are the cornerstone of this new grammar.”
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Read : I Possessed the Obsessive-Captive Dominant Top
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