No matter what data the computer saves, it is actually stored in a one-dimensional manner. No matter what the physical form of the memory is, for the convenience of processing, all the data of the computer is stored in a long string. So why can it save and display various three-dimensional data and even express n-dimensional data, whether audio or video can be saved and reproduced? In fact, this is just a phenomenon of mechanical dimensionality reduction and dimensionality increase.
Approximate digitization and dimensionality reduction of objects :
Let's see how three-dimensional objects become one-dimensional data stored on a computer?
We can imagine this to understand. First of all, suppose there is a three-dimensional irregular object, such as a stone, how to express it as a bunch of data? You can first use a 1 cubic millimeter translucent cube to form a cube that is just larger than it, and then make the two overlap, record 1 where the substance can fill the cube more than or equal to 1 half, and record 0 if it is insufficient. When the object is taken out, it is found that its shape is recorded by approximate 0 and 1. This is sampling and quantization so that a continuous object becomes a discrete model with the desired accuracy but not too much data.
After digitization, it is a dimensionality reduction operation. We can divide this binary cube into pieces with a thickness of 1 cubic millimeter, and such a three-dimensional object directly becomes multiple discrete two-dimensional tables. Then, for each two-dimensional table, add a head mark before the head of each row, and add a tail mark after the tail, so that each two-dimensional table becomes a one-dimensional binary string. Then, the header of each string of binary strings is added with a mark of which table it belongs to, and then the first bit is connected to form a large string. The shape of the three-dimensional object can be stored in the computer in a black and white (binary) form in an approximate one-dimensional manner.
Then, we know that the colors we can see are composed of different ratios of red, green and blue, so when we want to save the color of the object, we can record the color of the object with the color depth value of each grid. For example, using 256 kinds of color depth types (2^8 power, exactly 8bit one byte) to record red, also uses the method of more retreat and less complement, the original infinite color depth of the grid may be approximately recorded with 256 depths , and then reduce the dimensionality into one-dimensional data, the red distribution of the entire object can be saved in the one-dimensional logical storage structure of the computer. Then the same operation is done for green and blue.
Dimensional output of data :
According to multiple one-dimensional data strings, according to the various marks at the beginning and the end, it can be re-split into a two-dimensional table, and then spelled into a three-dimensional object. Then it is presented in 3D large-scale and other occasions, or displayed on a two-dimensional screen by "projection" calculation.
In fact, this is the inexact mechanical version of differentiation and integration. But because the process is simple and mechanical enough to be easily implemented by computers, one can reduce the scale of quantification to continuously improve the accuracy to an acceptable level.
A similar idea is the process of digitizing audio and then recording it to a computer:
sound is originally a much simpler thing than recording objects and images, because after the sound passes through the microphone, it gets only a continuous voltage change, and we can record it every 1. A microsecond is an interval as a unit, and 65536 possibilities (2 bytes 16bit, 2 to the 16th power) are used to approximate the infinite voltage change, making it a discrete sound size string. (Of course, you can also use the Fourier transform algorithm to remove some tiny waveforms to perform lossy compression on the data that does not remain the same). Of course, you can add a few more sensors and microphones to record a few more copies.
Exactly like sound recordings, there are various types of waves, such as pressure waves, voltage and current changes, and so on. The smaller the quantization scale, the more accurate it is, but the higher the requirements for computer performance and storage space.
Dimensionality reduction output of abstraction and logical structure :
For example, in the storage of an n-ary tree, each layer of nodes can be uniquely marked, and then the parent-child connections and weights can be recorded with the mark. Stored in memory as a bunch of tagged one-dimensional byte strings. If there is any difficulty in storing logical structures, it should be the writing of a traversal algorithm that can find out the connections and contents of all nodes and record them.
The above is how the roughest and original objects and images are stored in the computer. It is only recorded here as a review. If there is anything wrong, please point out.
Finally :
say something very scary, if we are actually part of a program running in a computer, and the principle of this computer is similar to that of our electronic computer, then our nature is also one-dimensional, but we will never Oh, you will feel this.
Approximate digitization and dimensionality reduction of objects :
Let's see how three-dimensional objects become one-dimensional data stored on a computer?
We can imagine this to understand. First of all, suppose there is a three-dimensional irregular object, such as a stone, how to express it as a bunch of data? You can first use a 1 cubic millimeter translucent cube to form a cube that is just larger than it, and then make the two overlap, record 1 where the substance can fill the cube more than or equal to 1 half, and record 0 if it is insufficient. When the object is taken out, it is found that its shape is recorded by approximate 0 and 1. This is sampling and quantization so that a continuous object becomes a discrete model with the desired accuracy but not too much data.
After digitization, it is a dimensionality reduction operation. We can divide this binary cube into pieces with a thickness of 1 cubic millimeter, and such a three-dimensional object directly becomes multiple discrete two-dimensional tables. Then, for each two-dimensional table, add a head mark before the head of each row, and add a tail mark after the tail, so that each two-dimensional table becomes a one-dimensional binary string. Then, the header of each string of binary strings is added with a mark of which table it belongs to, and then the first bit is connected to form a large string. The shape of the three-dimensional object can be stored in the computer in a black and white (binary) form in an approximate one-dimensional manner.
Then, we know that the colors we can see are composed of different ratios of red, green and blue, so when we want to save the color of the object, we can record the color of the object with the color depth value of each grid. For example, using 256 kinds of color depth types (2^8 power, exactly 8bit one byte) to record red, also uses the method of more retreat and less complement, the original infinite color depth of the grid may be approximately recorded with 256 depths , and then reduce the dimensionality into one-dimensional data, the red distribution of the entire object can be saved in the one-dimensional logical storage structure of the computer. Then the same operation is done for green and blue.
Dimensional output of data :
According to multiple one-dimensional data strings, according to the various marks at the beginning and the end, it can be re-split into a two-dimensional table, and then spelled into a three-dimensional object. Then it is presented in 3D large-scale and other occasions, or displayed on a two-dimensional screen by "projection" calculation.
In fact, this is the inexact mechanical version of differentiation and integration. But because the process is simple and mechanical enough to be easily implemented by computers, one can reduce the scale of quantification to continuously improve the accuracy to an acceptable level.
A similar idea is the process of digitizing audio and then recording it to a computer:
sound is originally a much simpler thing than recording objects and images, because after the sound passes through the microphone, it gets only a continuous voltage change, and we can record it every 1. A microsecond is an interval as a unit, and 65536 possibilities (2 bytes 16bit, 2 to the 16th power) are used to approximate the infinite voltage change, making it a discrete sound size string. (Of course, you can also use the Fourier transform algorithm to remove some tiny waveforms to perform lossy compression on the data that does not remain the same). Of course, you can add a few more sensors and microphones to record a few more copies.
Exactly like sound recordings, there are various types of waves, such as pressure waves, voltage and current changes, and so on. The smaller the quantization scale, the more accurate it is, but the higher the requirements for computer performance and storage space.
Dimensionality reduction output of abstraction and logical structure :
For example, in the storage of an n-ary tree, each layer of nodes can be uniquely marked, and then the parent-child connections and weights can be recorded with the mark. Stored in memory as a bunch of tagged one-dimensional byte strings. If there is any difficulty in storing logical structures, it should be the writing of a traversal algorithm that can find out the connections and contents of all nodes and record them.
The above is how the roughest and original objects and images are stored in the computer. It is only recorded here as a review. If there is anything wrong, please point out.
Finally :
say something very scary, if we are actually part of a program running in a computer, and the principle of this computer is similar to that of our electronic computer, then our nature is also one-dimensional, but we will never Oh, you will feel this.