"Alright, let’s first assu that the modal path you designed can accurately describe the evolution of a single quantum state in this space. But a quantum field consists of nurous quantum states. How can a single modal path be extended to state distribution in field theory?"
"I’ve considered two thods for this problem and ultimately chose the approach of spatial superposition. Constructing a structure of high-dinsional superposition directly."
...
And so the morning passed with questions and presentations. By twelve o’clock, whether Peter Schultz was hungry, Qiao Yu didn’t know, but he was indeed hungry.
No way, young people simply can’t resist hunger as much as these older folks.
So taking advantage of having just finished discussing a technical point, before Peter Schultz could continue with his questions, Qiao Yu suggested, "It’s past twelve, why don’t we go have lunch first?"
"Huh? It’s already twelve? So fast?" Peter Schultz, coming back to his senses, asked sowhat surprised and absent-minded.
Qiao Yu nodded and then pointed to the clock hanging behind him.
Peter Schultz glanced at it and sure enough, it was already five minutes past twelve.
"I have soone scheduled for lunch at noon." Peter Schultz suddenly rembered, taking out his phone, only to find several missed calls.
He had planned to just have a quick chat with Qiao Yu about a few recent research problems, giving him so pointers. Thinking it wouldn’t take long, he had put his phone on silent.
To avoid disturbing their discussion.
Who would have thought he would be led into a lecture by Qiao Yu, completely forgetting the ti.
"Forget it, let make a call first, I won’t be going. Maybe we can have lunch together, there are still so questions about your Qiao Yu Modal Quantum Space I’d like to discuss."
"It’s the Qiao Yu Modal Space. In fact, it can describe not only quantum states but has many other uses on different levels."
Qiao Yu corrected Peter Schultz’s statent.
Peter Schultz shrugged and didn’t comnt on Qiao Yu’s precision, standing up to find a place to return a call, while Qiao Yu looked for his student card in his bag.
Inviting soone for a al naturally ant going to the nearby Class A Restaurant. Not only was it close, but it was also upscale and allowed card paynts. Most importantly, he no longer needed Elder Yuan to have his back; his face alone was recognized.
But Qiao Yu realized he had made a miscalculation.
Although he indeed could use face recognition, Class A Restaurant was exceptionally lively that day.
Especially when two young Fields dal winners arrived together, it unsurprisingly attracted a lot of attention.
People cannot live isolated from society, and under such circumstances, it’s nearly impossible to find complete peace without disturbance. Soone will always co over to chat for a bit.
Fortunately, everyone was well-educated, recognizing that the two had things to discuss, they would chat for a bit and then leave.
Even so, the two couldn’t communicate as freely as in an office environnt. Not everyone could get used to having their train of thought interrupted.
But during the course of the al, even though Qiao Yu didn’t explicitly say it, Peter Schultz sharply understood the troubles Qiao Yu was currently facing and developed a strong interest.
It naturally led to Peter Schultz being pulled in, pushing back his afternoon commitnts, and obediently following Qiao Yu back to Qiuzhai.
In the afternoon, Elder Yuan was also around, and Qiao Yu took Peter Schultz to Elder Yuan’s office for a brief greeting before returning to his own office at Peter Schultz’s urging.
Peter Schultz couldn’t wait to share his conclusions after so thought.
"Your ideas are great, but the unification problem of local versus global states is difficult to solve. Once elevated to a global level, it’s impossible to ensure the uniqueness of the modal path for each mapping in the ultra-high-dinsional structure!"
Qiao Yu looked at Peter Schultz with appreciation. To be honest, that gaze made Peter Schultz sowhat uncomfortable.
It had been a long ti since soone looked at him this way. The last ti soone looked at him with such eyes was when he graduated with his PhD.
As for Qiao Yu, it was evident he wasn’t bothered by this. He just felt that discussing such academic problems with bright minds like Peter Schultz was indeed a relief. With just a slight lead, Peter Schultz could quickly grasp the main points.
This was much more comfortable than discussing problems with those folks at the computing institute, where often there was a lack of understanding.
However, when Qiao Yu spoke, it was not in those terms.
"Indeed, it is a hassle, but I already have solutions, and more than one in fact. Actually, this problem is not too difficult.
You can use the topological constraints of modal paths to reduce the possibility of paths, or perform consistency correction for each introduced path. Both thods can solve this problem."
As he spoke, Qiao Yu conveniently pulled out the solutions he had previously considered.
Although he wasn’t satisfied with either of these solutions, he couldn’t appear weak in montum.
He couldn’t let Peter Schultz think he couldn’t solve this problem temporarily and thus wanted to chat about it to possibly gain so inspiration.
Sorry, before solving this problem, he couldn’t let these foreigners have the slightest taste of success, not even ntal bliss.
After all, for mathematicians like Peter Schultz who didn’t lack money much anymore, ntal accomplishnts were often more satisfying than material gains.
Peter Schultz once more fell into a state of contemplation. Qiao Yu, anwhile, picked up the glass of water by his hand and also began pondering.
The issue indeed wasn’t easy to resolve.
Much later, no one knew how long the office had been silent, Peter Schultz finally frowned and said, "The combination of these two thods involves too much computation! I think it’s not suitable."
Qiao Yu imdiately countered, "But it allows for precise simulation."
"No, no, no, the principle of uncertainty dictates that the quantum world doesn’t actually require such precision. Personally, I think you should leverage this uncertainty rather than thinking about how to eliminate it."
Peter Schultz’s voice interrupted Qiao Yu’s thoughts.
Qiao Yu quickly ran through Peter Schultz’s aning in his mind, then confidently said, "Actually, I’ve also thought deeply about your approach.
It’s about finding a pattern from the inherent properties of high-dinsional mapping, making the branches of modal paths statistically controllable."
Peter Schultz pondered and asked, "Are you suggesting introducing an optimal path selection chanism from a probabilistic perspective? For example, constructing a path weighting function to unify paths with distribution probabilities globally?"
"Exactly!" Qiao Yu confidently nodded and then began to infer by analogy.
"The key is to let the system choose the optimal path rather than artificially imposing constraints. This needs to be defined by the fundantal rules of weight construction. My previous intention was to use the stability index of a path as the initial condition."
He hadn’t realized that this was sothing Qiao Yu had only thought of just recently. Based on his understanding, at least his thoughts wouldn’t move this quickly.
In fact, Peter Schultz was still marveling at the efficiency Qiao Yu demonstrated in scholarly research.
He couldn’t figure out how Qiao Yu managed to do it. While the occasional flash of inspiration solving a global mathematical issue isn’t unheard of, it can’t be that inspiration would keep flashing, right?
Can a person have no bottlenecks? It should be known that Qiao Yu had just resolved the Riemann Conjecture not long ago.
When everyone thought he would continue to delve deeply into Number Theory, he ca up with the Qiao Yu Modal Space...
Peter Schultz considers himself a genius, and indeed most of the world thinks so too.
But today, Qiao Yu had given him a solid lesson, making his life feel sowhat uninspiring.
To be honest, he even felt laziness creeping into his condensed state mathematics project. It seed to have less future potential compared to Qiao Yu’s Generalized Modal Axiomatic System.
To put it plainly, if Qiao Yu continues to expand this system, it could potentially replace his condensed state mathematics entirely.
After all, his ultimate goal was to provide simpler tools and verify complex theorems for research in fields such as algebraic geotry, algebraic topology, and high-dinsional category theory.
Clearly, his ultimate goal could be achieved by Qiao Yu’s Generalized Modal Axiomatic System, so why bother?
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