Abstract thinking is different from image thinking. It does not start from people's feelings or imagination, but from concepts, and then rises from abstract concepts to concrete concepts-only in this way can rich, diverse, vivid and concrete things be reproduced, and "warmth" replaces "cold". It can be seen that abstract thinking and concrete thinking are relative and mutually transformed. Only by penetrating behind things, temporarily putting aside accidental, concrete, complex and scattered things, extracting the essence of things and forming concepts in places invisible to the senses, can there be conditions for further reasoning and judgment. Without abstract thinking, there is no scientific theory and scientific research. However, abstract thinking cannot go to extremes, and it must be combined with concrete thinking, from abstract to concrete.
In the face of colorful apples, oranges, bananas and pineapples, we say "fruit" or even "fruit of plants". Facing all kinds of geese, petrels, cranes and swans, we say "birds" or even "birds". Isn't this a bit boring and blunt? Russian writer Chernyshevski said: "Theory is cold, but it can make people warm." When we face the word "abstraction", it seems that there is also a feeling of "cold", as if it transcends the reality we see in front of us, runs behind them, and even "leaves" them. This feeling is normal. Abstract thinking, as an important type of thinking, has the characteristics of generality, indirectness and detachment. It is a thinking activity that extracts the most essential characteristics of things to form concepts when analyzing things, and uses concepts for reasoning and judgment.
What is thinking in images? Simply put, "thinking in images is thinking that can be understood through conscious understanding of image materials." From the perspective of information processing, it can be understood that the subject processes (analyzes, compares, integrates and transforms) the relevant image information of the research object and the image information stored in the brain, and understands and grasps the essence and laws of the research object from the images.
Imagery thinking and abstract (logical) thinking are two basic forms of thinking. In the past, people divided them into different categories and thought that "... scientists think with concepts and artists think with images." This is a misunderstanding. In fact, thinking in images is not only the thinking of artists, but also an important thinking form for scientists to make scientific discoveries and creations. For example, all the image models in physics, such as Thomson jujube cake model or Rutherford small solar system model, such as power lines, magnetic lines and atomic structure, are the products of physicists' abstract thinking and image thinking. Einstein was a master with profound logical thinking ability, but he opposed logical method as the only scientific method. He is very good at exerting the free creativity of thinking in images. All kinds of idealized experiments he conceived are typical examples of using image thinking. These idealized experiments, instead of abandoning phenomena in an abstract way and extracting essence from concrete cases, use image thinking to preserve, condense and strengthen those universal and essential phenomena. For example, the establishment of Einstein's famous general theory of relativity actually stems from a free imagination. One day, Einstein was sitting in a chair in the Berne Patent Office, and it suddenly occurred to him that if a person fell freely, he would not feel his own weight. Einstein said that this simple ideal experiment "had a far-reaching impact on me, which gave me the theory of gravity".
The basic characteristics of thinking in images are:
(A) Image
Image is the most basic feature of thinking in images. The object of thinking in images is the image of things, and the form of thinking is vivid concepts such as image, intuition and imagination. The tools and means of expression are graphics, images, schemas and vivid symbols that can be perceived by the senses. The visualization of thinking in images makes it vivid, intuitive and holistic.
illogic
Different from abstract (logical) thinking, thinking in images deals with information step by step, end to end and linearly. Instead, you can call many image materials, which can be combined together at once to form a new image, or jump from one image to another. Its information processing process is not a series of processing, but parallel processing, which is single-sided or three-dimensional. It can make the thinking subject grasp the problem quickly as a whole. Thinking in images is possible.
(3) Roughness
Imagery thinking reflects problems with thick lines, grasps problems as a whole, and analyzes problems qualitatively or semi-quantitatively. Therefore, thinking in images is usually used for qualitative analysis of problems. Abstract thinking can give an accurate quantitative relationship, so in practical thinking activities, it is often necessary to skillfully combine abstract thinking and image thinking and use them together.
(4) Imagination
Imagination is a process in which the thinking subject uses the existing image to form a new image. Image thinking is not satisfied with the reproduction of the existing image, but more committed to the pursuit of the processing of the existing image and the output of new image products. Therefore, thinking in images has creative advantages, which also illustrates a truth; Creative people usually have a strong imagination.
Second, the role of thinking in images in solving physical problems
As mentioned above, abstract thinking and image thinking are two basic ways of thinking. When people are engaged in various activities, they often need to coordinate the use of these two ways of thinking. The same is true for physics problem-solving activities. Experts have a wealth of images in their brains. When solving physical problems, they always construct clear physical images according to the problem scenarios. As far as possible, use graphics to reflect the relationship between physical state, physical process and related physical quantities; Be good at analyzing, comparing, analogizing and integrating relevant images in your mind; Imagine what will happen. Therefore, experts often have a strong awareness of the image of the problem. However, the average person's brain is relatively poor in storing images and is not good at grasping problems from images when solving physical problems. As soon as you come into contact with the problem, you try to establish the relevant solving equation immediately, and the result is often haste makes waste. So, what positive role can image thinking play in solving physical problems?
(a) Qualitative
Cognitive psychologists refer to the presentation of information in the mind as representation, and think that representation is an important factor affecting problem solving. In solving physical problems, thinking in images is an important way of thinking to form representations. Because of the image and integrity of thinking in images, the subject is easy to directly feel the essence of the problem and the key to solving the problem, thus triggering creative problem solutions. For example:
Example 1A is 60km away from bilibili. A station goes to Miley Miley at a speed of 60km/h 10 minute. At present, a car is going from Miley Miley to a station at a speed of 60 km/h. Will the car coming from Miley Miley meet several cars coming from a station on the way? (suppose there is a bus leaving at Station A when the bus is going.)
For this problem, we can use the displacement diagram shown in figure 1 to express it intuitively. According to the diagram (intersection point), the car that goes by miles and miles will meet the car that goes by station A. We can also use the diagram shown in Figure 2 to show that when the car that goes by miles and miles just leaves, there are already five cars between A and B, and another car A has just left. In the first half, car B will meet six cars from Station A. Similarly, in the second half, car B will meet six cars from Station A. Except one car from Station A, car B will meet 1 1 cars from Station A on the way.
(2) Leading role
When solving physical problems, this topic uses image thinking to make extensive associations with various scenarios related to the problem, and puts forward meaningful guesses, which can roughly point out the direction for the analysis and reasoning of the problem and avoid falling into a blind position when solving problems, such as:
Example 2. There is a stack of circular metal sheets on the horizontal desktop, and the arrangement shape is shown in Figure 3. The lower piece weighs g and has an area of S/2, while the adjacent upper piece weighs G/2 and has an area of S/2. By analogy, the weight and area of the metal sheet are gradually halved until it is stacked. Then, for three metal plates from bottom to top, the pressure ratio on the upper surface of each metal plate is P 1: P2. What is the pressure on the desktop?
At first glance, this problem seems difficult to solve. Therefore, we consider the following from the image: transform the shape of each metal sheet into a series of rectangles, and number them from bottom to top according to 1, 2,3, as shown in Figure 4. As can be seen from the figure, the total area of each block above 1 is equal to the area of 1; The total area of the blocks above the second block is equal to the area of the second block ... and so on. According to the meaning of the question, so is the relationship between gravity. Therefore, the ratio of the pressure on the upper surface of 1, 2 and 3 metal sheets is 1: 1: 1. The pressure on the desktop is p = f/s =
(3) Supporting role
Solving physical problems requires rigorous reasoning, and thinking in images can provide strong support for this logical reasoning. Using imagery thinking, a vivid and clear physical image can be established in the subject's mind, which is the basis for the smooth progress of abstract thinking. For example, ask a question: "Can the resultant force of three * * * points be zero?"
Third, the basic form of thinking in images in solving physical problems.
(A) Image
An image is a freehand image of something reproduced by the human brain. It can be a conceptual image summarized from the images of several similar things, or a basic image of something that has been modeled. All kinds of image information obtained from perceptual knowledge, after generalization and typification, can become images and be stored in the subject's brain for further processing. Image is equivalent to a concept in abstract thinking. This is the basic element of thinking in images. Einstein said: "in my thinking mechanism, written or oral words seem to have no effect." As a thinking element, psychological things are symbols and images with certain clarity, which can be regenerated and combined by me at will ... This combination activity seems to be the main form of creative thinking. It is carried out before any logical structure established by words or other symbols that can be passed on to others. These elements are me.
For solving physical problems, the perfect image system of the object is an extremely important factor. For example, as shown in Figure 5, two small balls with radii of 1 and 2 are hung on the semi-circular bracket. Now the A end is fixed, and the B end gradually slides upward along the circular bracket, so that the line 2 gradually changes from the horizontal state to the vertical state. Variation of tension between two thin threads. What appears in our mind is a vector diagram related to the problem. As shown in fig. 6, the sliding of the end of line B is indicated by the clockwise rotation of vector T2 in the figure. As can be seen from the figure, in this process, the tension T2 of the thin thread 1 will gradually decrease, and the tension T2 of the thin thread 2 will first decrease and then increase. When two wires are perpendicular to each other, the tension T2 is minimum. When the thin thread 2 is in a vertical state, the pulling force T2=G 。
In addition to graphic images, physical images also include schematic images, such as mathematical symbols, formulas, charts and other visual materials, which can be the carriers of schematic images. For example:
Example 3 A long train runs by inertia to a hillside with an inclination angle of A. When the train comes to a complete stop, part of the train is on the hillside (as shown in Figure 7). Try to find out the time it takes for the train to stop up the hill. The total length of the train is l, excluding friction.
For this problem, let the mass of the whole train be M, the length of the train on the mountain be X and the mass be MX/L, and choose the mountain base as the origin of the X-axis coordinate, and the direction is upward along the hillside. According to Newton's second law, the resultant force on the train can be obtained by the following formula
When the above formula is obtained, if the schematic image of the discriminant F-X of simple harmonic vibration can appear in the minds of the subjects, it can be confirmed that it is a simple harmonic vibration equation with a period of, so that it is realized that the time from the start of the train climbing to the stop is equal to 1/4 of the vibration period, that is.
(2) direct perception
Intuition is the direct judgment and perception of specific images by using images. The essence of intuition is to compare the concrete images of related things in the current problem with images with universal and typical significance, so that the subject can judge the mode of the current problem and quickly determine the direction and way of thinking in solving problems. For example:
Example 4 as shown in fig. 8, the focused beam passes through the circular hole of the light shielding plate and then converges at the position a of 10 cm behind the plate. If a convex lens is embedded in the circular hole, the beam will converge at the position B 5 cm behind the plate, and the focal length of the convex lens can be obtained.
In fig. 8, if the light source is placed at point B, it can be seen that it will form a virtual image at point A according to the reversible optical path. From this, we can directly feel that the subject is essentially a problem of finding the focal length of convex lens with known object distance U = 5cm and image distance V =- 10cm. So according to the lens imaging formula, we can get.
This kind of thinking form, which compares the characteristics of a specific object's image (called an image) with those of a general image (called an image-like image) and judges whether the image and the image-like image are homogeneous or not according to the similarity of image feature integration, is called image recognition intuition, which is mainly manifested in the re-recognition of various images under the condition of variation and the decomposition and recognition under the compound and comprehensive forms.
Example 5: as shown in fig. 9a, at the height h from the ground and the horizontal distance between the mountain and the vertical wall, an elastic ball is horizontally thrown to the wall at the initial velocity V0, and then it elastically collides with the wall and lands. Try to find the distance S2 between the impact point and the wall (assuming that there is no kinetic energy loss when the ball collides with the wall).
In this question, the movement process of the ball can be divided into two sections, namely AB section and BC section. The trajectory of AB is a flat throwing motion, and BC is an oblique downward throwing motion. After the flat throwing, we can get a complete trajectory ABD (Figure B). This has always inspired us that turning BC around the wall 180o may just coincide with BD. We can easily prove this with the law of elastic collision.
As mentioned above, filling new images with existing image patterns and incorporating local images into the whole image is called pattern filling intuition, which is of great significance in image thinking. As American philosophers Lu Shoufu and arnheim wrote in the book Visual Thinking, "making up for incomplete things is one of the most basic skills of rational ability."
There are two ships in the river, A and B, sailing in opposite directions. A downlink, speed v 1, b uplink, speed v2, speed V 1 >: V2. When the two boats met, there was a bamboo raft downstream beside them. After driving for a period of time, the two ships turn around and return to driving at the same time, while the speed of the two ships relative to the current remains unchanged. Which ship met the bamboo raft first?
For this problem, we think of another similar scene: two people walking opposite each other in the aisle where the train is running. The two people walk at different speeds and meet at the edge of a seat. After walking for a while, they will return to walk at the same speed, so they will meet at the edge of their original seats. We can make an analogy between these two scenes: people are equivalent to ships, trains are equivalent to water, and seats are equivalent to bamboo rafts.
By comparing the similarity between the new image and the existing image, the thinking mode of linking the new image with the existing image system is called image similarity intuition, which often depends on the change and transformation of problems in physics problem solving.
(3) Imagination
Imagination is the thinking process of combining the existing images in the mind and transforming them into new images. It is the most creative form of thinking in images. Einstein said: "Imagination is more important than knowledge, because knowledge is limited, and imagination summarizes everything in the world, promotes progress and is the source of knowledge evolution. Strictly speaking, imagination is a real factor in scientific research. " Scientific imagination is a direct connection of a series of existing images. Imagination of spatial image, physical image, special state and ideal state, hypothetical situation, etc. when solving physical problems. Are extremely important factors in problem-solving thinking. For example:
Example 7 scatter a handful of marbles in all directions from a certain height at the same speed V0. Try to explain that all the marbles are in the air at any time, and on what surface are all the marbles located? (excluding air resistance)
For this problem, first imagine that if the initial velocity of all marbles is zero, they will fall freely along the same straight line at the same time; Imagine that when the marbles are thrown, the gravity suddenly loses, so the marbles will move in different directions in a straight line at a uniform speed, and each marbles is on the same sphere with a uniform radius. As you can imagine, in this problem, the marble will be on a spherical surface with a radius of R=V0t (increasing evenly with time), and the center of the ball will be in free fall.
Fourthly, how to cultivate the ability of thinking in images.
Modern science shows that the human brain can be divided into two hemispheres: the left hemisphere is responsible for the operation and processing of language and logical numbers, and the right hemisphere is responsible for the perceptual recognition of music, art and space. From the perspective of thinking, the left hemisphere is in charge of abstract thinking and the right brain is in charge of image thinking. People's thinking activities are often completed through the "resonance" of left and right brain functions. The fundamental purpose of education is to maximize the development of students' brain function. The ability mentioned here should include both abstract thinking ability and image thinking ability. In the past middle school physics teaching, we attached great importance to the cultivation of basic concepts, basic laws and logical reasoning ability, which is completely correct. However, we should see that, relatively speaking, we do not pay enough attention to the cultivation of thinking ability in images. This not only makes students' thinking structure imperfect, but also makes abstract thinking lack of strong "support" of images, so it is also true to some extent.
(A) increase the image reserve
Marxist epistemology holds that human thinking (that is, rational knowledge) is based on perceptual knowledge, so is abstract thinking, and so is image thinking. As a vivid image of thinking in images, it is not invented out of thin air in the subject's mind. It is rooted in real things. Without perceptual knowledge, thinking in images will become passive water and rootless wood. Therefore, we should pay attention to presenting students with rich perceptual materials and experiments.
(B) to strengthen imagination training
Imagination is the most meaningful form of thinking in images, and students should consciously strengthen their training. For example, after gravity is taught, students can imagine the scene after "if gravity suddenly loses"; After teaching friction, let the students imagine "a world without friction"; After teaching circular motion and gravity, let students imagine "if the earth suddenly stops rotating" or "if the rotation speed of the earth increases"; Wait a minute.
(C) focus on qualitative analysis
Thinking in images is to grasp the whole, outline and direction of the problem, and attaching importance to qualitative analysis of the problem is helpful to cultivate the ability of thinking in images. When asking questions, we should guide students to construct typical images and infer the trend of physical changes through their perception of the information of the questions. At the same time, they should draw schematic diagram, stress diagram, light path diagram and circuit diagram on paper, so that students can establish clear physical images in their minds, and then use physical laws to make reasoning calculations and draw quantitative conclusions.
(D) advocate the combination of numbers and shapes
When solving physical problems, we should advocate the cooperation of numbers and shapes, be good at transforming literal information into graphic information, express the law of physical change with images, reveal the corresponding relationship between numbers and shapes, and regard images as an intuitive tool to solve abstract physical problems.
What is thinking in images? Simply put, "thinking in images is thinking that can be understood through conscious understanding of image materials." From the perspective of information processing, it can be understood as subject processing (analysis, comparison, integration, transformation, etc. The related image information of the research object and the image information stored in the brain by means of representation, intuition and imagination, so as to understand and grasp the essence and law of the research object from the images.
Imagery thinking and abstract (logical) thinking are two basic forms of thinking. In the past, people divided them into different categories and thought that "... scientists think with concepts and artists think with images." This is a misunderstanding. In fact, thinking in images is not only the thinking of artists, but also an important thinking form for scientists to make scientific discoveries and creations. For example, all image models in physics, such as Thomson jujube cake model of electric power lines, magnetic lines and atomic structure or Rutherford small solar system model, are the products of the combination of abstract thinking and image thinking of physicists. Einstein was a master with profound logical thinking ability, but he opposed logical method as the only scientific method. He is very good at exerting the free creativity of thinking in images, and all kinds of idealized experiments he conceived are typical examples of using thinking in images. These idealized experiments are not abstracting concrete cases, abandoning phenomena and extracting essence, but retaining universal and essential phenomena through image thinking and concentrating and strengthening them. For example, Einstein's famous general theory of relativity actually stems from a free imagination. One day, Einstein was sitting in a chair in the Berne Patent Office, and it suddenly occurred to him that if a person fell freely, he would not feel his own weight. Einstein said that this simple ideal experiment "deeply influenced me and led me to the theory of universal gravitation".
The basic characteristics of thinking in images are:
(A) Image
Image is the most basic feature of thinking in images. The object of thinking in images is the image of things, and the form of thinking is vivid concepts such as image, intuition and imagination. The tools and means of expression are graphics, images, schemas and vivid symbols that can be perceived by the senses. The visualization of thinking in images makes it vivid, intuitive and holistic.