Into Unscientific

  Chapter 32 Germination of Infinite Level (Part 2)

  In the house.

  Looking at the annoyed Maverick, Xu Yun couldn't help but be filled with emotion:

  Although this person's character is really hip, but his brain is really too good!

   Check out what he mentioned:

  Not to mention calculus, but also mentioned the concept of normal vector, the concept of potential energy, the concept of net torque and the assumption of the assumption of small deformation.

   One of the above concepts counts as one, and they were formally made public as a theory, and they all had to be after 1807 at the earliest.

  This kind of thinking span of 150 to 200 years dare to ask who can do it?

   True.

  The problem raised by Hooker is actually very simple. It is so simple that Xu Yun immediately thought of nearly 20 solutions. The fastest method can be solved by setting a covariant derivative on a non-Cartesian coordinate system.

   But don’t forget that Xu Yun’s knowledge was obtained through the learning of later generations, and the basic theory at that time had already been summed up quite well.

   It's like mastering the era of controllable nuclear fusion, and you can make a 200cc engine with your eyes closed.

   But what about the calf?

  He belongs to the era of drilling wood to make fire, but he saw that the cetane number calculation formula of the internal combustion engine is so outrageous!

  Thinking of this, Xu Yun inexplicably wanted to laugh:

  He once wrote a novel, but in the end, not to mention Newton, even Maxwell was dissed by some comments as ‘I looked it up, it’s just a system of equations’.

   Then he took a deep breath and turned his mind back to the scene:

   "Mr. Newton, I very much agree with your idea, but there are a lot of unknown mathematical tools that need to be used, and the current research progress in the mathematics field seems a bit weak."

   Mavericks nodded, and generously admitted this:

   "That's right, but other than that, you must use the Han Li expansion you mentioned."

   After speaking, Maverick continued to lower his head, and quickly listed another line of formula:

V(r)=V(re)+V'(re)(r-e)+[V''(re)/2!](r-re)^2+[V'''(re)/3!] (r-re)^3

  Then Mavericks drew a line under the formula, frowned and said:

   "If Han Li is used to expand, what should be the properties of the pinball near the stable position? This should be a series, but it is another problem to divide."

  Xu Yun looked up at him and said:

  "Mr. Newton, what if the stable position is calculated as a minimum value?

  We assume a mathematical approximation pose, ie. infinitely approaching 0?"

   "Infinitely approaching 0?"

  For some reason, Maverick suddenly had a strange emotion in his heart, as if he saw Lisa coming out of the bedroom arm in arm with someone else.

  But soon he put this emotion behind him, thought for a while and said:

   "Isn't that the principle of cutting circles?"

  Circle cutting method, that is, the early idea of ​​​​calculating pi, should be known to those who have attended elementary school.

  It actually implies such an idea:

  Although there is a gap between the two quantities, as long as the gap can be narrowed infinitely, it can be considered that the two quantities will eventually be equal.

  The method of cutting circles has been regarded as an abandoned mathematical tool in this era. Xu Yun can casually describe Han Li's mathematical attainments. Theoretically, this kind of backward thinking mistake should not be made.

   Facing Maverick’s question, Xu Yun shook his head lightly and said:

  "Mr. Newton, the concept you mentioned is a non-series variable, but what if you take it a step further and understand it as a series variable?

   Even a step further, consider it as a constant beyond the framework of real numbers? "

   "Tends to 0, series variable? Constant?"

  Hearing Xu Yun's words, Maverick was stunned.

  The concept of infinitesimals, this is a problem that has caused countless university fishing parties to hang on the tree.

  Generally speaking.

  From a college student to a Ph.D., the understanding of infinitesimals has to go through three stages.

  The infinitesimals in the first stage and the second stage are all variables. When the third stage is recognized, all the infinitesimals become constants, and each infinitesimal corresponds to a constant.

  These constants are not in the framework of real numbers, and are all generated by the axioms of non-standard analytical models.

  The first stage is the cognition when studying mathematical analysis or advanced mathematics in college, that is, how small the infinitesimal is.

   That is, the absolute value of positive and negative infinitesimals, which is less than any given positive real number.

  The second stage is when learning non-standard analysis. Many calculus formulas introduce infinitesimal quantities, and concepts such as order appear.

  The third stage is the time to understand the mathematical model theory, at this time the infinitesimal quantity can become a constant.

Once the infinitesimal quantity is recognized as a constant, it will be found that there is a broader mathematical world, which is wider, deeper and more complex than the known mathematical world today, and the second type of limit thinking and its geometric structure appear. The idea of ​​class limit is given by the infinite space, and the limit idea of ​​standard analysis is given by the infinitesimal space.

   Then there is a phenomenon of compatibility between Euclidean geometry and non-Euclidean geometry, and the coordinates of parallel intersection points can be accurately expressed.

  The above situation has derived a lot of unconventional geometry, they are neither Euclidean geometry nor non-Euclidean geometry, they belong to the third type of geometry (Chinese geometry) and so on.

  And what is the practical significance of the understanding of infinitesimal in the third stage?

  The most direct way is that you can go to a supercomputer.

  At present, the most in-depth research on the third stage in China is the University of Science and Technology of China. The quantum computer of Academician Pan Jianwei and Professor Lu Chaoyang is also one of the convenient and intuitive manifestations.

   Those who have participated in interviews for research and development of supercomputer algorithms should know that the third-order cognition of infinitesimals is a compulsory question in the interview.

  At this time, Maverick’s theoretical knowledge is not so perfect, but as the proposer and founder of calculus—especially the concept of infinitesimal, he can vaguely give feedback on this information.

   Then Xu Yun took the pen and continued to write:

  Assuming that the coefficient of the first-order term is zero at the equilibrium position, then the minimum can only be retained to the quadratic approximation, and naturally the form of the quadratic correlation between the potential energy and the balance deviation is obtained:

  V(r)≈[V’’(re)/2!](r-re)^2

  V(r)≈k/2(r-re)^2.

   Write here.

  Xu Yun stopped writing, glanced at the dazed calf, and quietly turned and left.

Before going out, he took from the table a small bag of white sugar, a little salt, a small half spoonful of butter, an unused crucible, and two potatoes—the first few are commonly used seasonings for breakfast and dinner, and the latter two are emergency reserves grain.

  Then tiptoed, and gently closed the door.

   Mavericks didn't say anything about it, he just stared blankly at Xu Yun's formula, especially the equal sign.

   A few minutes passed.

  His Adam's apple suddenly slid up and down a few times, and several gurgling sounds came out of his mouth.

  A moment later, he dashed back to his seat, and quickly started to write.

   Three hours later.

  Just hearing a bang, the Maverick rushed out of the door.

  Well, in a physical sense, he rushed out of the door—he slammed the door down and held it in his hands.

  No way, the house is too old.

   It was just after eight o'clock in the evening, so Maverick saw a cluster of fire not far away at first sight, and Xu Yun's face reflected by the fire.

   Maverick walked up to him quickly, and said excitedly:

   "Fat fish, I figured it out, it's a force that varies linearly with distance, an elastic force!

   There is no requirement for its specific form. In other words, any system near the steady state will exhibit elastic behavior!

   This is a formula that has not been discovered, a theorem in a steady state, I bet that Hooke himself did not derive it, because the function he gave actually has a 0th-order term! "

   Maverick ran and murmured to Xu Yun. When he came to the edge of the fire, he found that Xu Yun was lowering his head at this time, tinkering with something:

   "Fat fish, what is this.?"

   "Mr. Newton, you came just in time."

  Looking at the calf in front of him, Xu Yun picked up a dinner plate and smiled brightly:

  “The baked potatoes just out of the oven are delicious when dipped in sauce.”

   "Sauce? What kind of sauce?"

"ketchup."

Note:

   Do you still remember the tomato mentioned in the tableware introduction, hehehe

   Xuezhong started broadcasting yesterday, has anyone watched it, and is hesitating whether to subscribe to watch it

  (end of this chapter)