Presumably everyone is familiar with QR codes. Because this coding method used on mobile devices has already penetrated into every aspect of production and life. According to incomplete statistics, as a brand-new information storage, transmission and identification technology, QR codes are currently widely used in public security, diplomacy, military, customs, taxation, commerce, transportation, postal and other departments in information acquisition and website redirection. , Advertising push, mobile e-commerce, anti-counterfeiting traceability, preferential promotion, member management, account management, etc. play an important role.

Take WeChat as an example. Login, payment, management and other operations will generate a large number of QR codes. Every day, the number of QR codes required is very large. Therefore, it is inevitable that some people are worried: Will the QR code be scanned? To answer this question, we must first start with the structure of the QR code.

More advanced barcode format

The so-called two-dimensional code refers to a black-and-white graphic that records data symbol information and is distributed on a plane (two-dimensional direction) with a certain geometric graphic according to a certain rule. Generally speaking, the information storage method of the two-dimensional code is binary, but 0 and 1 are represented by black and white respectively. Therefore, as long as you pay attention to observation, you will understand the mathematical meaning of the two-dimensional code composed of black and white squares: using several geometric shapes corresponding to binary to represent text and numerical information, which can be automatically read and processed by related equipment.

Compared with one-dimensional bar codes, two-dimensional codes have the characteristics of wide coding range, strong error correction ability, high decoding level, low cost, and easy production. The most obvious advantages are high-density coding, large information capacity, and generation. The number is almost unlimited.

There are currently 40 official versions of the QR code, numbered from Version1 to Version40, of which Version1 is a 21×21 matrix, followed by Version2 is a 25×25 matrix, and Version3 is a 29×29 matrix… Each version is 4 more than the previous version. , And so on, Version40 is a 177×177 (21+4×39=177) matrix.

For example, if you take the Version 4 version or the 33×33 matrix from it, there are 1,000 small squares in rough statistics. Paint these 1000 squares arbitrarily black and white. Each square has two kinds of painting methods: black and white. Then there are [2×2×…21000 pieces]=21000 kinds of painting methods for 1000 squares. This is the number of QR codes that Version4 can generate in a theoretical sense.

Considering that in practical applications, some small squares for positioning and redundant error correction are needed, even if the most conservative estimate is adopted, the information storage space required for these other uses is 50%, that is, it takes up 500 squares. Grid, then there are 500 more as data codes. According to the calculation method above, there are 2500 coating methods for 500 squares, that is, at least 2500 different QR codes can be generated by Version4. So, how big is this data? Here, allow me to make a point and introduce you to “Gugol” first.

“Maximum” count unit

”Gugol” means 10 100 , this number is a realistic limit, because no actual quantity in the universe can exceed it.

For example, the area of the earth is about 510 million square kilometers. If expressed in square millimeters, it is only 5×10 20 square millimeters. The volume of the earth is about 10,83 billion cubic kilometers. If we use cubic millimeters to express it, it is only 10 30 cubic millimeters. 1 cubic millimeter is equivalent to the size of the needle of a pin, and it can hold up to 10 grains of fine sand, so the number of fine sand that can be contained in the entire volume of the earth is 10 31 grains. These figures are obviously far smaller than “Gugol”.

For another example, the interstellar distance is generally measured in light years. One light-year is the distance that light travels in one year, about 9,460,730,472,580 kilometers. Assuming that the range of space that humans can observe is about 20 billion light years (1 light year ≈ 10 19 millimeters), if it is represented by the smallest unit of length “angstrom” (1 millimeter = 10 7 angstroms), it is only 1036 angstroms.

None of these counts can surpass “Gugol”. It is precisely because of this that Sergey Brin, one of the co-founders of Google, named the search engine “Google” (Google). The similar pronunciation metaphors the founder’s expectation of “Google”, that is, all-encompassing, Nothing can be done.

With the “Gugol” foreshadowing, let’s look at 2 500 again . It is not difficult to judge. 2 500 = (2 5 ) 100 = 32 100 is far greater than 10 100, To be sure, this number is so big that you can’t read it at all, you can only describe it as endless.

In order to further clarify the almost “endless” characteristics of the QR code, take the familiar mobile phone WeChat payment code as an example: it is a 25×25 matrix, except for the squares for positioning and redundant error correction. There are 478 squares used, which can form 2478 two-dimensional codes. Assuming that WeChat scans 600 billion QR codes in a year, it will take 1.301×10132 years to use up a 25×25 matrix of QR codes, which is far more than the 5 billion years of the earth’s lifespan that scientists have analyzed. Therefore, there is no need to worry about the “end of the world” when the QR code runs out.