Section 326: Mathematical Theory of Error Checking
Qian Yuzhi's eyes began to be trance-like for the first time, and Li Janai also started to lose focus after persisting until this point. Only Feng Shan was still listening.
"Binary search searches for specific values in an ordered list. It is essentially a divide-and-conquer strategy, which means dividing a large problem into several similar sub-problems, and then either solving it directly or continuing to divide it. Why does it require an ordered list?
? is to ensure that each operation can solve all sub-problems at the same time. For example, if the median value of the ascending list is less than the value being searched, I can ensure two conclusions at the same time. One, the value being searched is not in the first half of the ordered list.
In, two, the value being looked up is in the second half of the ordered list - then I just repeat the above operation in the second half of the ordered list."
"Our problem is similar. In terms of probability, first we can reasonably assume that there is and only 1 card is wrong. Then, we count half of all the cards that are known to contain wrong cards each time. If we count
The results showed that the wrong card was not in this half, so it must be in the other half, and vice versa. So I narrowed down the "suspect range" of half of the wrong cards. I repeatedly performed the half operation to narrow the suspect range. When narrowed to a certain extent, the problem
It won’t be a problem anymore.”
"I told you before that the actual capabilities of the punched card computer we are making are not limited to what we see in front of us. My half-folding operation just now was very mechanical - I always cut out half, input it, and then check the result.
Take the stack containing the wrong card and repeat."
"So if one day, we design a machine to replace the repetitive mechanical operations I just did, and combined with the tabulation machine, more things can be done. Many big problems will be broken down into small ones, and then the same operating process will be used
solve."
"The idea of decomposing a seemingly complex problem into smaller problems that are similar to the original problem and repeatedly using a similar series of mechanical operations to solve it so that a computer can complete it is called 'recursion'. This is what we
You should think carefully about using computers, which is an essential idea. In particular, when thinking about this kind of problem, don't take into account the running speed of existing mechanical computers, which are not as fast as human power. The key is to think about it.
Without intervention, what kind of problems can a computer solve by just running according to the rules? That is, what kind of problems can be solved by a computer? We call them 'computable problems'. As for speed, that is not a problem - bread will have it.
.”
Feng Nuo stopped and asked Feng Shan to chew on this passage carefully. For her, this kind of thinking mode is similar to mathematics, but it is quite different from the mathematics she studied before. The mathematics of Li Janai and Qian Yuzhi is also four
It was really difficult for them to understand the level of calculation. Because they didn't sleep well last night, they were already very confused. These words were nothing more than a lullaby - Qian Yuzhi was still wondering what this had to do with bread.
relation.
"Okay, you two go to bed. Let me see what's going on with this card." Feng Nuo left Feng Shan aside who was still thinking blankly, and said to Qian Yuzhi and Li Janai, he pointed
In the back room, "You can sleep on that bed." After saying that, he picked up the card with the wrong hole on the table.
Li Janai woke up from the bed and found that Qian Yuzhi was still sitting on the chair, sleeping soundly against the wall. She looked around and saw that Feng Shan was reading a book and calculating something at the workbench, but Feng Yuanlao was not in the room.
Where are you going to have a meeting again?
She yawned and got out of bed, poked Qian Yuzhi, and said: "Go to bed and sleep." Unexpectedly, he just snorted and stopped moving. Li Janai dragged him to the bed with force and said
They were working in shifts. In fact, Qian Yuzhi stayed up late last night and was on duty much longer than she did.
Probably feeling the residual body temperature on the bed, Qian Yuzhi turned over, as if he wanted to curl up into the depression where Li Janai had just slept, and continue to sleep soundly.
Li Janai walked to the workbench and poured a glass of water. At this time, she saw Feng Shan put down her book and rubbed her eyes, as if she was planning to take a rest, so she started chatting with her. After a while, they made an agreement.
On Monday, I will go to a gathering of Li Janai and his classmates from the School of Arts and Sciences - it is said that several seniors will also attend.
In the next few days, the research team repeatedly improved and tested the duplicating machine. At Feng Nuo's request, a card reading mechanism was added to the row of the duplicating machine's punching mechanism. This change is not big, but it can make the duplicating machine more efficient.
The machine also has the function of part of the verification machine (Verifier). After the copy is completed, a small amount of wiring can be changed to make the machine function automatically check whether the perforations of the two stacks of cards are consistent, and stop and light up the alarm when the perforations are inconsistent.
No matter how fast the binary search is, it is still faster than having to go through the machine directly.
In addition, the improved version can also fix a mother card in the card reading mechanism, punch holes and verify a stack of cards. In practical applications, this function can pre-punch the common holes of a batch of cards, reducing manual printing.
Hole workload.
However, although the copying machine has been improved and the problem of punching wrong holes has been fixed, the phenomenon of missing holes still occasionally occurs. Finally, the research team reduced the card transmission and processing speed and found that the problem disappeared.
"It seems that the problem is the reaction speed of the relay." Sun Li threw the pen in his hand on the table, "Slow down the speed and run it."
Everyone looked at Feng Nuo with a "shua", and Feng Nuo could only nod wordlessly. But the elders are now very shameless - everyone is about the same level, no one should laugh at anyone. The embarrassment quickly recovered,
He also proposed a plan to develop a decoder.
According to the plan, the tabulating machine should have integrated printing and summary punching functions. In order to simplify the complexity of a single machine, the tabulating machine does not include these parts at this stage. Therefore, Fonnuo plans to make the most basic digital decoding first.
The machine, because it does not consider the printing of Latin letters, can no longer even be called "decoding". It is simply printing. Its mechanical structure is similar to that of a copying machine. It is nothing more than activating a relay after inspecting the hole to drive the arc-shaped typesetting 0-9.
The numbers are printed on the top of the card. Now that the replicator has been developed, the decoder is just a matter of course.
The elders of the machine shop felt that the problem was not a big one and promised to build a prototype and send it over as soon as possible.
The meeting ended here, and Feng Nuo returned to the office: He thought that he would have to prepare lessons again today - with the development of mechanical computers, he felt that he had to teach some mathematical issues related to software engineering in depth - first
Most modern programmers are mathematicians.
He processed the daily official documents of the data center in the office, walked around the computer room as usual, and did daily equipment maintenance. He also browsed the "to-be-repaired catalog" and used a red pencil to mark several "urgent" level projects.
After finishing the class, he had to sacrifice his sleep time to repair these things. Since he started the mechanical computer project, his original work has been reduced a lot. Now Xu Laowu has done most of the work for him.
It's unreasonable for me to continue to neglect my clerical work.
After finally finishing the things at hand one by one, he got up and went to the workroom.
Now the "workshop" is full. Various "engineering prototypes" manufactured from the machinery factory are filling the workshop. Some of them are not the products of "technical meetings" at all, but some hands-on abilities.
The product of the powerful veteran's imagination - it is not necessarily true to say that it is entirely a imagination, because these things are roughly the different technical ideas in the development process of mechanical computers at that time.
Naturally, engineering prototypes are not very sophisticated. Because of the tight time, and mostly just to verify whether the design idea has engineering feasibility, there is no optimization in design and manufacturing. Adhering to the usual silly, black and rough appearance of the products of the machinery factory,
Many equipment parts are also exposed, which saves manufacturing time and facilitates troubleshooting and debugging at any time.
The workshop is full of machines with iron mouths and teeth, and there are also many materials and parts scattered on the ground. Therefore, Feng Nuo has always taken care of his three helpers and must take protective measures when entering the workshop. He sets an example by wearing a rattan safety helmet.
, wearing coarse cloth work clothes and protective leather shoes.
Passing through the equipment area, at the other end of the workshop is the research area. A heavy and large "Holy Ship" 12-person conference table stands in the middle. The table is filled with drawings, documents and draft calculation papers, and seven or eight sheets are placed around it.
Folding chair. In the corner is a huge blackboard shelf, which is full of formulas and numbers written in chalk. Against the wall is a row of open bookshelves, filled with various technical information and reference materials - just a few
In just one month, so much paperwork has been accumulated. In accordance with the regulations of the Planning Institute, these materials were sorted and bound by categories by Feng Shan and Li Janai - they must be archived to provide reference for future technical workers.
.
However, without a set of efficient retrieval equipment, these technical materials would probably just lie dormant in a corner of the large library and eventually be slowly forgotten. Thinking of this, Feng Nuo felt more and more that he had a heavy responsibility on his shoulders.
The floor of the research area was covered with scattered calculation drafts, making it look like the scene in the old movie when the gangsters were defeated. The research team spent the whole day forgetting to sleep and eat, so they naturally didn't bother to clean up. Finally, everyone washed their lunch boxes and took them away.
Yes, otherwise it would be so sloppy that it would attract rats.
Feng Nuo sat down on the chair and took out a professional textbook on discrete mathematics - it was reprinted locally in Lingao and reviewed by the Office of Truth, so no confidentiality measures were required and it could be inserted directly on the bookshelf.
Just as I was about to open it, I suddenly saw that the wastebasket under the table was filled with scraps of paper - not ordinary scraps of paper, but torn and shredded scraps of paper. This was not the calculation paper they commonly used, but letter paper. Above