Interesting math facts for those who want to know more about the world around

2024 Author: Malcolm Clapton | [email protected]. Last modified: 2023-12-17 03:44

If you think that logarithms, linear programming and cryptography have nothing to do with your life, you are deeply mistaken.

The life hacker wondered what significance mathematics has in our daily life. Does anyone else need her at all? The answer to this question was found in the book by Nelly Litvak and Andrey Raigorodsky “Who Needs Mathematics? A clear book about how the digital world works."

What is this book about?

About mathematics.:) More precisely, about those sections that are most in demand in logistics, transport schedules, encryption and data coding. The authors use the available examples to show how math can help you save time and money, keep your data protected and choose the queue in the store.

What is linear programming

In this case, we are not talking about programming as such. It's more of an optimization process. Why linear? Because we are only talking about linear equations: when variables are added, subtracted, or multiplied by a number. No exponentiation or multiplication. Such programming helps to minimize the cost of goods or services (if we are talking about trade) or increase income.

Linear programming is used in the oil industry, as well as in the field of logistics, planning, scheduling.

In short, the example looks like this.

This is where the linear equation comes into play. We will not describe in detail how this problem is solved in the book, but after several stages of calculations, the most optimal option is found, which allows you to save 12% of the shipping cost in comparison with the costs that would have to be incurred if you did not use a mathematical approach.

Now imagine that we are not talking about the delivery of several sheets of tin, but about heavy trucks and the timetable of railway transport of the whole country. And here 12% is already a number with several zeros at the end.

Why are the best solutions not always the most comfortable ones?

Mathematics is an exact and beautiful science. However, the solution of problems does not always seem suitable for us. This happened with the timetable for rail transport in the Netherlands. In this small country, trains and electric trains are very popular. At the same time, the transport schedule was so outdated that a real collapse was about to occur.

Therefore, in 2002, it was decided to draw up a new schedule. The experts needed to think perfectly about the number of wagons, the time of stops, arrivals and departures, not to mention the schedule of drivers and conductors for 5,500 trains per day.

As a result, a mathematically ideal schedule was drawn up. And it seems that everyone should be happy. But not the passengers: the stops are too short, the cars are too loaded, and there is no comfort. This is because mathematicians can only solve mathematical problems. And who is to blame for the lameness of the management?

Can anything be encoded?

It is difficult for an ordinary computer user to imagine that all pictures, videos, texts, songs are not pictures, videos, texts and songs, but zeros and ones, ones and zeros.

It is easiest to encode text: for each letter, number or punctuation mark, come up with your own sequence of ones and zeros. But what about color? Fortunately, physicists have learned that each color is a combination of red, blue, and green. This means that colors can be turned into numbers.

Each color has 255 shades. For example, orange is 255 red and 128 green, blue is 191 green and 255 blue. And since color can be represented in numbers, it means that it can be placed in any computer, TV or phone.

Video is even more difficult - there is too much information. However, mathematicians found a way out of this situation and learned how to compress data. The first frame of the movie is encoded in full, and then only the changes are encoded.

The only problems remained with the music. Scientists have not yet learned how to code music so that it sounds as clear as in life. Because music cannot be decomposed into "shades" that could be recorded digitally.

Why does the internet never break down?

No, now it's not about the work of your providers, which could sometimes be better. It's about why, for example, Google always answers our queries, why we can always access the sites we need, and why interference (and there are actually many of them) does not cut off our access to the World Wide Web.

The short answer to this question is this: in the middle of the last century, two mathematicians Paul Erdös and Alfred Renyi discovered random graphs to the world. Graphs are representations of nodes connected by lines. So, let's imagine that nodes are computers, and lines are communication channels. If we take a graph for 100 computers, it will look like this:

And so Renyi and Erdash, through calculations that are difficult for the humanities and simple for techies, came to a stunning conclusion. The more computers in the network, the more connections between them, the less the probability of critical interference, that is, one that will tear us away from the world of unlimited communication and endless information.

If you don't believe me, here's a table.

That is, if a channel is broken, there is almost always an opportunity to go through another channel and contact the required server.

What is a queue on the Internet and how to avoid it?

Did you know that every time you ask Google a question or go to a site, you end up in a queue? Of course, it moves much faster than at the checkout in a supermarket, and you hardly notice any downtime, but nevertheless, if someone has made a request that is too global, it will take longer to process it.

Therefore, you need to choose the server in which the queue is the smallest, or the one in the queue to which there is no heavy request.

And then the rule of choice comes into force. In 1986, computer scientists Derek Yeager, Edward Lazowska and John Zahorjan proposed and proved the theory that if you limit the choice of servers to which your request will be sent to two, then the probability of slipping through the queue will increase significantly.

Let's take a look at the example of a supermarket. There are many ticket offices in front of you with different queue lengths. You have options: randomly choose the first one that comes across, or stop at two and choose the one in which there is less queue. This will make you more likely to complete your purchases faster.

The four handshake theory

Many have heard that all people in the world know each other through six handshakes. The sociologist Stanley Milgram proved this theory back in the 1960s by asking people from different states to send a letter to one person. The letter had to first be sent to his friend, who, in turn, sent it to his own - and so on, until the letter reached the addressee. As a result, the chain was only six people.

This was until the time when Facebook employees turned to scientists to once again confirm or refute this theory. Having processed all possible pairs of acquaintances between all Internet users, it turned out that this chain is even shorter. And it is only 4, 7! Can you imagine it? There are only 4, 7 handshakes between any person on Earth and you!

Should you read this book?

Yes, if you also want to know how data encryption works, who broke the Enigma cipher, how Google and Yandex advertisements are held, and dive deeper into the world of mathematical problems and equations.

Lifehacker told you not all interesting facts from entertaining mathematics, therefore, if you want to supplement your knowledge in this area, the book "Who Needs Mathematics" will certainly be useful for you.

Despite the simplicity of presentation, if you are a humanist, you may need a mathematical reference while reading.