121. Six sixty one
Mike Schultz’s presentation began with Zeno’s paradox.
The paradox of Zeno, which the major older sister briefly mentioned at a restaurant a month ago, is correct.
There are two representative methods for breaking Zeno’s paradox, one is a mathematical method using the concept of limit, and the other is a physical method.
Contrary to my expectations, the method Mike used was a physics method using the concept of velocity.
If the speed of the arrow leaving the bow does not change with time, the time it takes for the arrow to reach the target is the distance divided by the speed.
In this case, if the distance to the target is finite, dividing this finite distance by the velocity gives a finite time.
In other words, the arrow will reach the target, and Zeno’s paradox is broken.
Mike continued the explanation.
“(I have proven by a physical way that Zeno’s paradox is false, with one prerequisite.)”
Mike continued, pointing to one side of the blackboard.
“(This is the distance between the arrow and the target, assuming ‘x is finite.’)”
Watching Mike Schultz giving a presentation from the pulpit like this… The fact that he was alive and healthy became real, and I felt proud in a corner of my heart.
The first discovery of David McLean’s thesis in Professor Park’s lab 13 years ago, the writing of a thesis after finding errors in McLean’s theory with the major’s sister, and the fact that David McLean did not receive a doctorate by searching the Pennsylvania State University library website The fact that the truth was confirmed, and the fact that the major’s older sister was appointed as a professor at Texas State University… .
A lot of the things that happened to save Mike this life flashed through my mind.
A smile spread across my face without realizing it, and in the meantime, Mike’s presentation continued.
“(However, if the distance to the target is infinitely far, Zeno’s paradox is established that the arrow cannot reach the target.)”
The people in the classroom nodded, and Mike continued.
“(And we mathematicians call this a singularity, just like the singularity of manifolds in topology.)”
In topological mathematics, the singularity of a manifold is a point with infinite curvature, such as a pointed needle or an extremely thin thread.
And these singularities are the last remaining pieces of the puzzle to reach the end of the Poincaré conjecture proof.
“(At the singularity of a three-dimensional manifold, the curvature is infinite, so no matter how much rich flow you apply (botox injection in topology), this manifold cannot be transformed into a sphere.)”
Mike took a deep breath and continued.
“(And this situation has a lot of similarities to the situation where… if the distance to the target is infinity, no matter how many arrows fly, the target cannot be reached. So we tried to find a solution to the problem using this resemblance.)”
“(Let’s get back to Zeno’s paradox. Let’s say the distance to the target is x, and this time let’s assume that this value of x can be either finite or infinite.)”
Mike continued explaining by writing ＜S(x) = a/x> on the board.
“I defined a simple function called S(x) like this, and this S-function plays a role of extending and decreasing the distance to the target like a rubber band and converting it. That is, if we multiply the distance x by S(x), the transformed distance is always a finite value of a.”
Mike continued the explanation.
“Now let’s return to the three-dimensional manifold. Let the volume of the manifold be V, and the curvature at the surface of each of these manifolds is x, then the function S(x) can be defined as
＜S(x) = (4pi/3V)^(1/3)/x>
ah… ! i get it!
If this function S(x) is applied to the curvature values of all surfaces of the manifold, the manifold is transformed into a sphere of volume V.
In other words, Poincare’s conjecture that ＜a closed, single-connected three-dimensional manifold is topologically homomorphic with a sphere> is proved.
However, this method had one important limitation.
First, the problem that Mike’s S-function can be applied only to manifolds in which the curvature changes smoothly, that is, the curvature values are continuous and differentiable was the problem.
For example, since there are cases where the curvature values are not continuous, such as the corners of a cuboid, several assumptions are needed to generalize this method, and the process of proving each of these assumptions must be overcome.
So Mike’s presentation was over, and discussion began with questions/answers in the classroom.
As expected, when the curvature value is a non-differentiable function, various opinions were exchanged on how to finalize the proof.
After the discussion, Dr. Hamilton’s presentation followed, but his presentation only showed the direction of future research to solve the limitations of Mike’s method.
With the presentation of such a little principled content, all schedules of today’s seminar have come to an end.
Although it was very disappointing, I had to be content with hearing the seminars of my advisor in the past life.
I got out of the classroom with my bag and went down the stairs to the lobby of the College of Science.
The clock on the front of the lobby indicated 12:15 PM.
My steps toward the outside of the College of Science building are really light.
What… ?
I felt like I had just finished an arduous exam, probably because Mike made sure he was alive and well.
When I came out of the College of Science building like that, the phone in my pocket started ringing.
When I pressed the call button, I heard my sister’s voice.
– Jungho, where are you?
“It’s in front of the Faculty of Science building.”
“okay? Do you have any plans for lunch?
“no.”
– Then, would you like to have lunch with us? Dr. Hamilton said he wanted to talk with you.
“With me? that… he made me… Do you know?”
-no. Not that, Dr. When Hamilton was presenting, you heard that you were paying too much attention in the front row, so I guess I’d like to talk to you. So I’m thinking of having lunch together, are you okay?
I’m not the kind of person who meets strangers so spontaneously… .
I opened my mouth out of curiosity rather than gladness.
“Yeah, that’s good.”
On-campus guest dining room.
At the round table, Major Noona, Professor Donghyeong Kim, Mike, Dr. Hamilton and me… Five people took their seats and sat down.
After ordering the meal, Dr. Hamilton told me.
“(Have you ever been to New Haven, where Yale is?)”
I shook my head, and he asked me again.
“(So… have you ever been to the eastern part of the United States?)”
“(No. I haven’t been to America yet.)”
He tilted his head in response to my answer.
“(I must have seen it somewhere… Hmm—. Maybe I was mistaken. I’m sorry. Hehe—!)”
I am Dr. I looked at Hamilton, and thought that maybe the memories of his past life were left in his subconscious mind.
In this way, Dr. Looking at Hamilton… A question that I’ve always wanted to ask him in the past life came to my mind.
Maybe this isn’t a question, I’m talking about Dr. It was more like a small complaint I had with Hamilton.
Choose the one that bothers you most.
(Choose the one that bothers you the most.)
Past Life When I first started my PhD, Dr. This is what Hamilton said.
In other words, my advice was to choose the research topic that bothered me the most.
However, out of more than 20 of his Ph.D. students, I was the only one who decided on a research topic in this way.
Even when a master’s student was choosing a research topic, he was known for giving careful advice.
The salad I ordered as an appetizer came out, and I spread the sauce in the salad bowl and Dr. told Hamilton.
“(How many graduate students are you teaching at Yale right now?)”
“(Six PhD students and two Master’s students)”
“(Then, how do you help Ph.D. graduate students choose research topics?)”
He said with a serious expression.
“(At the beginning of my PhD studies, the research topic is really important, so I tend to pay a lot of attention to specifically identify the student’s strengths and weaknesses.)”
He dipped a fork into the salad and put it in his mouth, swallowed the food and continued.
“(Personally… I think that the most important thing for a professor to guide graduate students is to decide on a research topic that suits them. It’s a matter of one person’s future, and we have to be very careful and help out. Heh heh. —!.)”
But why am I… !
His words were a bit off-putting.
Also… Was it just that you didn’t know about it?
While I was taking care of my expressions, he put the fork down on the table and said with a smile.
“(But there is one exception.)”
“(exception…?)”
“(These are geniuses who are born with math, but I’m not just talking about smart students, there are some really overwhelming geniuses.)”
“(…?)”
He smiled slightly and continued.
“(I’m not that kind of genius, but I don’t know… In the case of such a student, I heard that the student’s instinct is to choose a research topic.)”
“(What do you mean by instinct?”)
At my question, he wet his mouth with water and said:
“(Choose the research topic that bothers the student the most. Heh heh heh—!)”
* * *
Jung Ho and Dr. While Hamilton was talking, Mike and the major were talking across the round table.
“(Dr. Yoon, this is what I discovered today, why do people call Dr. Yoon ‘So-ryong’?)”
At Mike’s question, the major smiled, and Professor Donghyeong Kim, who was sitting next to the major, spoke to Mike.
“(Dr. Yoon doesn’t seem to tell me his Korean name. ‘Major’ is Sonia’s original name.)”
At Professor Donghyung Kim’s words, Mike nodded and asked Professor Kim.
“(By the way, when Dr. Kim calls Dr. Yoon, he calls him ‘Sunbae’, is ‘Sunbae’ another name for Dr. Yoon?)”
At Mike’s question, a burst of laughter erupted between the major and Professor Donghyeong Kim, and the major explained to Mike the meaning of the word ‘senior’ and the culture of seniors and juniors in Korea in detail.
When the major finished explaining, Professor Donghyeong Kim pointed to the major and said to Mike.
“(In the past, Dr. Yoon was a really scary ‘senpai’ to the juniors, but how are you these days?)”
Mike smiled at his question.
“(Haha–! Did you? Now, Dr. Yoon is not afraid, and please treat all students kindly)”
The major spoke in Korean to Professor Dong-hyung Kim with a short sigh.
“under—! Do you keep nagging?”
“haha—-! Senior, I’m really going to stop now.”
The meal began in earnest, and Mike and Dr. While Hamilton was talking with Jeong-ho, the major spoke to Professor Dong-hyung Kim.
“Donghyung, there was a student who was sitting at the back of the classroom during the seminar earlier.”
“Are you behind? Who are you talking about?”
“what is it… The kid who was wearing colored glasses on his eyeglasses.”
“ah… ! Geunseok?”
“Geun-seok? what kind of stone?”
“This is Kim Geun-seok.”
“okay? Where is her school?”
“It’s our school. I… But why Geunseok? Did something happen?”
“no. I was just curious.”
Professor Donghyeong Kim, noticing the serious change in the Major’s expression, cautiously opened his mouth.
“I like Geun-seok to meddle here and there, but… The kid is good.”