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Join the ServerAs Lia finished speaking, the auditorium fell into a long, deathly silence.
“Observation, in itself, is a form of interference…”
This short phrase contained a subversive power.
It negated the detached status mages had held since ancient times as onlookers of the world, pulling them down from their divine pedestals and transforming them into indispensable participants in the microscopic universe.
Master Albin’s face shifted between green and white.
He opened his mouth, only to find that the common sense of macroscopic physics he took such pride in seemed pale and powerless at this moment.
The ruler he used to measure a table indeed wouldn’t change the table’s dimensions.
But the “ruler” used to “measure” an electron was a photon.
How could an object being measured via impact remain entirely unchanged?
This logic was so simple, yet so fatal.
Master Lorentz was completely lost in thought.
The quill in his hand hovered in mid-air; a drop of ink fell quietly, blooming into a black dot on his notebook, yet he was entirely unaware.
He tried to construct a model of a microscopic particle undisturbed by observation in his mind, but failed time and time again.
Henry and Victor, the two former protagonists of the debate, also bore complex expressions.
One saw the strange scenery extending from particle theory, while the other felt the unavoidable reality of wave theory.
Sitting in the corner, Heisenberg clenched his fists tightly, his knuckles turning white from the force.
He was shaking with excitement, his vision blurred by tears.
Every word from Professor Lia struck the core of his theory with precision, imbuing his abstract mathematics—which the world could not understand—with an incredibly solid physical foundation.
‘She understands. She truly understands!’
Amidst this silence, a trembling but clear voice rang out from the student section.
“Professor… Professor Lia!”
Everyone looked toward the source of the sound.
A young apprentice, appearing no more than fifteen or sixteen years old, stood up, his face flushed red with nervousness.
“I… I still don’t understand,” he said loudly, summoning every ounce of his courage.
“I understand the interference caused by measurement that you mentioned, but… but that ‘row times column’ calculation you wrote on the blackboard, I still don’t get it.”
“Why… why is it like that?”
“Is… is quantum mechanics the only rational explanation behind so many inconceivable phenomena? Is the world really just an illusion composed of probabilities?”
For the vast majority of mages present, Professor Lia’s explanation regarding “observation” was a shock at the philosophical level, while that peculiar matrix multiplication was an unintelligible tome at the mathematical level.
A fleeting sense of satisfaction flashed in Master Albin’s eyes.
He felt he had caught a loophole.
Yes, you can interpret the physical meaning however you like, but mathematical laws are cold; you cannot simply invent a set of operational rules out of thin air.
Lia looked at the brave apprentice, a gentle smile appearing on her face.
“Please, have a seat. You have asked a very good question. I moved a bit too fast.”
She turned around and used her magic to erase the two multiplication results on the blackboard, leaving only the original two matrices.
“Let us temporarily forget about momentum, forget about position, and forget that complex multiplication,” Lia’s voice carried a soothing power.
“Let’s talk about something more practical—for instance, the public carriages in the capital.”
This transition left everyone stunned.
“Let us assume the capital has two carriage companies, operating Carriage Line 1 and Carriage Line 2, respectively,” Lia said while using chalk to draw two points on the blackboard, labeling them the ‘Tower of Truth’ and the ‘Magic Association’.
“Coincidentally, both lines only travel back and forth between these two stations.”
Lia pointed to the matrix on the left.
“This is the price list for Carriage Line 1—a table recording the fares between all starting points and destinations.”
Her explanation revitalized everyone; this metaphor was very intuitive.
“Let us agree that the rows of the table represent the departure station and the columns represent the destination station.”
Lia used the chalk to circle the first row of the matrix.
“The first row represents departing from the Tower of Truth.”
“The first number in the first row is 1.”
She tapped the number heavily with the chalk.
“It means you board at the Tower of Truth and also get off at the Tower of Truth. This sightseeing journey costs 1 copper coin.”
This simple and easy-to-understand explanation allowed everyone to grasp the concept easily.
“The second number in the first row is 7.”
Lia’s chalk moved to the number ‘7’.
“This represents you departing from the ‘Tower of Truth’ with the ‘Magic Association’ as your destination. This trip costs 7 copper coins.”
“Now look at the second row.”
Lia’s chalk moved to the (3, 8) part of the matrix.
“The second row represents departing from the ‘Magic Association’.”
“So, who can tell me what the first number in the second row, ‘3’, represents?” Lia asked with a smile.
“It represents departing from the Magic Association and getting off at the Tower of Truth; the fare is 3 copper coins!” an apprentice in the front row answered immediately, his tone laced with excitement.
“Exactly right!” Lia nodded in approval.
“Then, naturally, the last one is the price for ‘sightseeing’ at the Magic Association after departing from the Magic Association.”
After this deconstruction, the originally abstract two-dimensional array immediately became vivid and concrete.
It was no longer a pile of unrelated numbers, but an organized price list with clear information.
“The same principle applies,” Lia pointed to Matrix II on the right, “this is the price list for Carriage Line 2.”
Depart from the Tower of Truth, sightsee at the Tower of Truth: costs 2 copper coins.
Depart from the Tower of Truth, head to the Magic Association: costs 5 copper coins.
Depart from the Magic Association, head to the Tower of Truth: costs 6 copper coins.
Depart from the Magic Association, sightsee at the Magic Association: costs 4 copper coins.
With every explanation from Lia, the mages below nodded in unison.
They one after another began to map these two matrices to ‘Line 1’, ‘Line 2’, and the two location names in their notebooks.
The sense of alienation they felt toward these unknown mathematical symbols was rapidly fading.
“Now, we all understand these two ‘price lists’, correct?” Lia asked.
A chorus of affirmative answers rose from the audience.
“Very good.” Lia’s smile deepened.
“We have already completed the first and most important step in understanding this new grammar; we have learned how to read ‘words’.”
“Every matrix is a word; it contains a complete set of information.”
“Mister Heisenberg’s work is to tell us that in the microscopic world, physical quantities are no longer single numbers—like the length of a table being three meters—but are sets of information, just like these two price lists.”
Her words reached everyone’s ears clearly.
Master Albin’s brow was furrowed; he had to admit that the metaphor was ingenious.
It bypassed the baffling mathematical operations and clarified the meaning of a matrix directly from the concept itself.
He could find nothing to refute.
Master Lorentz wrote the words ‘set of information’ in his notebook and drew a heavy line beneath them.
A glimmer of contemplation shone in his eyes as he seemed to be comparing this concept with the physical phenomena he knew.
“Professor,” the young apprentice who had initially asked the question stood up once more, his face no longer nervous but filled with a thirst for knowledge.
“We understand the price list, but… but how do we multiply one price list by another? And what does that represent?”
This question struck the nail on the head once again.
All eyes in the auditorium were fixed on Lia.
They had just learned how to read words; now, they were desperate to know how these words formed a sentence.
Lia looked at the apprentice, and at the hundreds of pairs of inquisitive eyes below.
“The journey has only just begun,” she said softly.
“Learning to read words is only the first step. Next, we shall learn how to use these words to describe a more complex journey.”
“For example,” she paused, creating a bit of suspense, “a passenger who wants to first take Line 1 to complete a segment of travel, and immediately after, transfer to Line 2 to begin another segment.”
“What is the total cost of these two consecutive journeys? That is exactly what matrix multiplication seeks to tell us.”
The adventure continues! If you loved this chapter, I Possessed the Obsessive-Captive Dominant Top is a must-read. Click here to start!
Read : I Possessed the Obsessive-Captive Dominant Top
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