What is "Question?

What is "problem "?
Translated by Liu Jianwen (http://www.semi-translate.com/blog
)

Key: Methodology of question science and philosophy

What is "Question?

What is "Question? The "problem" is not a loaf of bread, not a car, but it does exist and has its own nature or objectivity. I pulled it out for research today.
Let's take a look at the definition of the modern Chinese Dictionary:

Problem

1. ① Question to be answered or explained: There are five questions for this test ~ │ I would like to reply to this kind ~.
2. ② Contradictions and difficulties that need to be discussed and resolved: Thoughts ~ │ This kind of medicine is very helpful to cure colds ~.
3. ③ Key; important: Important ~ Be good at learning.
4. ④ Accident or trouble: the lathe goes out again ~ .

From this definition, we can see that "Question" is a very high-level abstract concept, similar to "ordinary" concepts such as science, methods, and theories, it has penetrated into our discourse system and thinking structure. This also shows that the "problem" is of great value as other high-level abstract category concepts. Let's take a look at Wikipedia's definition:

A problem is an obstacle which makes it difficult to achieve a desired goal, objective or purpose. it refers to a situation, condition, or issue that is yet unresolved. in a broad sense, a problem exists when an individual becomes aware of a significant difference between what actually is and what is desired.

A "problem" is an obstacle for achieving the intended goal, purpose, or purpose to enter the predicament. It involves an unsolved situation, condition, or event. In a broader sense, the problem arises when individuals begin to realize that there is enough difference between what they desire and what they actually do.

From this definition, we understand that the "problem" is indeed not a specific intuitive "thing" like watermelon. It is an abstract concept like "computing; the problem is related to [a procedural concept]-"achieving a goal", which hinders the relationship. The problem hinders the realization of the goal. The problem is different from the calculation. The problem is a situation and a relatively static abstract concept; "computing" and "Achieving one goal" are both procedural abstract concepts with time. Take a look at some common problems:

• "How can we catch that girl ?"
• "I'm hungry. What can I eat ?"
• What is my birthday?
• How much salt should I put in fried vegetables?
• 1515X34-443 =?
• How to design a traffic signal to use the largest traffic flow?

Definition 1

It is difficult to have a definite and non-objectionable definition of the problem. However, generally, the problem includes the following three basic components:

• Context: A scenario related to a problem. It refers to a set of conditions that are clearly known and relevant to the problem.
• Objective: Refers to a clear description of the conclusion about the problem.
• Obstacle: the correct solution to the problem is not obvious. The answer can be found only through certain thinking activities.

In general, the problem is caused by some obstacles to achieving or achieving the goal. It means that the status quo is not resolved or unexpected.

Definition 2 (from "Mathematical methodology and problem solving research")

Generally, a problem is a situation where certain obstacles need to be overcome between the given information and the target. All problems have three basic components:

• Given (Givens), that is, a group of information given;
• Objective (goals), The State of the request or end of the problem, that is, the conclusion description about the problem;
• Barrier cannot immediately find the correct answer, and must change the given state in a certain way to gradually reach the target State.

Definition 3 mathematical discovery-understanding of solving problems and teaching of research volume 1

"Problematic" refers to the conscious pursuit of an appropriate action to achieve a purpose that is clearly known but cannot be achieved immediately. Solving a problem refers to looking for such activities.

The purpose of "solving" the problem is to require a definite object-the unknown number of the problem, which requires an unknown number that meets the conditions for the problem. This condition associates the unknown number with the known number of the problem. An unknown number may belong to any possible type. A clear problem must specify the type (SET) of its unknown quantity and the conditions that the unknown quantity should meet. In the object set specified by the problem (the unknown number must belong to this set), a subset of the objects that meet the conditions is defined, and any object that belongs to this subset is called a solution.

We call unknown quantities, conditions, and known quantities the main part of the "solving" problem.

The goal of our exploration can be any type of unknown or truth that discovers any type of problem: Our problem may be theoretical or practical, important or insignificant. To solve our problems, we must develop a well-thought-out and rational action plan (logical reasoning, mathematical operations, or specific work ), draw what we lack from what we already have-draw a conclusion from the premise, and draw an unknown number from the known amount.

What kind of "problems" does the computer handle "?

An example is taken from <algorithms and data structures: the Science of computing>

1.1.1 Problems

Some people (including one of the authors) Chill bottles or cans of soft drinks or fruit juice by putting them in a freezer for a short while before drinking them. this is a nice way to get an extra-cold drink, but it risks disaster: a drink left too long in the freezer begins to freeze, at which point it starts to expand, ultimately bursting its container and spilling whatever liquid isn' t already frozen all over the freezer. people who chill drinks in freezers may thus be interested in knowing the longest time that they can safely leave a drink in the freezer, in other words, the time that gives them the coldest drink with no mess to clean up afterwards. but since neither drinks nor freezers come with the longest safe chilling times stamped on them by the manufacturer, people face the problem of finding those times for themselves. this problem makes an excellent example of the kinds of problems and problem solving that exist in computer science. in particle, it shares two key features with all other problems of interest to computer science.

The above "frozen drinks" shows an excellent example of Computer Science's concerns and solutions. In particular, these problems have two common characteristics:

First, the problem is general enough to appear over and over in slightly different forms, or instances. in particle, different freezers May chill drinks at different speeds, and larger drinks will generally have longer safe chilling times than smaller drinks. furthermore, there will be some margin of error on Chilling times, within which more or less chilling really doesn't matter-for example, chilling a drink for a second more or a second less than planned is unlikely to change it from unacceptably warm to messily frozen. but the exact margin of error varies from one instance of the problem to the next (depending, for example, on how fast the freezer freezes things and how willing the person chilling the drink is to risk freezing it ). different instances of the longest safe chilling time problem are therefore distinguished by how powerful the freezer is, the size of the drink, and what margin of error the drinker will accept. things that distinguish one problem instance from another are called parameters or inputs to the problem.

First, these problems are common enough. You only need to make a slight modification (change one of the conditions) to evolve into many similar problems (instances ). For example, the refrigerator (skill) and beverage (volume) in the "frozen drinks" question can be different, so there is a different answer-the longest freezing time. In addition, there may be some errors in the freezing time, and some errors are irrelevant due to problems. The instance of the "frozen drinks" problem is determined by the refrigerator's power, beverage volume, and acceptable error values. The conditions for distinguishing problematic instances are called parameters or question inputs.

Also note that different instances of a problem generally have different answers. for example, the longest safe chilling time for a two-liter bottle in a kitchenette freezer is different from the longest safe chilling time for a half-liter in an unsupported cial deep freeze. it is therefore important to distinguish between an answer to a single instance of a problem and a process that can solve any instance of the problem. it is far more useful to know a process with which to solve a problem whenever it arises than to know the answer to only one instance-as an old proverb puts it, "Give a man a fish and you feed him dinner, but teach him to fish and you feed him for life."

(Similar) different question instances have different answers. Therefore, findSpecific problem instance

There is a big difference between the answer and the process of finding answers to all questions (that is, the problem-solving algorithm. The latter has greater value, just like the old saying: it is better to teach fish to fish.

The second important feature of any computer science problem is that you can tell whether a potential answer is right or not. for example, if someone tells you that a participant drink can be chilled in a participant freezer for up to 17 minutes, you can easily find out if this is right. chill the drink for 17 minutes and see if it comes out not quite frozen; then chill a similar container of the same drink for 17 minutes plus the margin of error and see if it starts to freeze. put another way, a time must meet certain requirements in order to solve a given instance of the problem, and it is possible to say exactly what those requirements are: the drink in question, chilled for that time in the freezer in question, shouldn't quite freeze, whereas the drink in question, chilled for that time plus the margin of error in the freezer in question, wocould start to freeze. that you need to know what constitutes a correct answer seems like a trivial point, but it bears an important moral nonetheless: before trying to find a process to solve a problem, make sure you understand exactly what answers you will accept.

Second, the answers to these questions must be fixed and cannot be ambiguous. For example, someone tells you that a refrigerator has a maximum of 17 minutes to freeze a drink of a specific size. You can directly test whether the answer is correct several times. Here, the answer-time-must satisfy certain prerequisites, such as the amount of drinks, the drinks cannot be too frozen or the refrigerator's skill. Therefore, you must know exactly what a correct answer is. This seems simple and insignificant, but actually plays a key role in solving the problem. When you try to find a solution (algorithm) to solve a problem, you must first specify the answer.

Not every problem has these two features. problems that lack one or the other are generally outside the scope of computer science. for example, consider the problem, "In what year did people first walk on the moon? "This problem lacks the first feature of being likely to appear in your different instances. it is so specific that it only has one instance, and so it's easier to just remember that the answer is "1969" than to find a process for finding that answer. as another example, consider the problem, "shocould I pay parking fines that I think are unfair? "This problem lacks the second feature of being able to say exactly what makes an answer right. different people will have different "right" answers to any instance of this problem, depending on their individual notions of fairness, the relative values they place on obeying the law versus challenging unfair actions, etc.