From childhood, we are taught to think linearly about things. However, this approach does not prepare us for life in the modern world, which is changing rapidly and can adversely affect our finances, as well as cause difficulties in interaction with artificial intelligence, according to Future Eates Citure Cit.
"If Zhenya pays 50 UAH for 10 apples, how many apples she gets for 500 UAH?" - A familiar task, isn't it?
From the answer to this question, it follows that the idealized world of mathematics is not the only area where people buy 100 apples, and this is not admirable.
To solve this problem, we were taught to use linear thinking - to assume that for 10 times more money, Zhenya will receive 10 times more apples.
The term "linear" indicates a specific type of relationship between two variables - input and initial data. In the case of linear dependence, the change of one value always leads to a fixed change in another value.
This approach is used in various aspects of real life. For example, at a constant exchange rate, if the dollar costs 40 UAH, then two dollars will cost 80 UAH, and $ 10 - $ 400. As the amount of exchanged dollars increases, the amount of hryvnia received increases in proportion - by double the entrance, the weekends will also double.
For example, if I can buy three chocolate tiles for 100 UAH, then apparently, for 200 UAH, I will be able to buy six tiles. The number of chocolate tiles purchased linearly depends on the money I am ready to spend.
Note that linearity does not always mean direct proportionality. For example, to convert Celsius to Celsius into Fahrenheit Celsius, you need to multiply the Celsius Celsius by 1.8 and add 32.
In this case, the doubling of the input does not lead to doubling the output result, but due to linearity, the fixed change of input data always corresponds to fixed changes at the output. For example, an increase in a temperature of 5 degrees Celsius always leads to a fever -9 -degree increase, regardless of the initial temperature. These connections can be illustrated with straight lines, which led to their name "linear".
Linear relationships are familiar to most of us, but here's the main problem: we are so used to the concept of linearity that we often try to apply it in everything we see in the real world.
This phenomenon, known as "linear bias" in its simplest form, can be problematic, since many systems do not follow these simple linear dependencies.
For example, if I leave money in a bank account or forget to pay debt, this amount of money will increase non -linear, namely exponentially, since interest will be charged. The more money I have (or have to pay), the faster the amount will increase.
Given the trend of many of us to think linearly, we can underestimate how fast these amounts of money can increase by making the idea of saving less attractive, and loans, on the contrary, more attractive.
Scientists have found that people with higher level of linear bias have higher debt to income (the amount of money they borrow, relative to their income).
Pseudolinity
Also an important aspect is "pseudolinity". Studies have shown that the tendency to think is formed long before graduation. The students were offered tasks that needed to use a nonlinear approach, but most preferred a linear solution without paying attention to the realism of their assumptions.
For example, students were asked questions about the time that Lori needed to run 1 km, using its time by 100 meters. Most students simply multiply the time by 100 meters by 10, receiving a answer in 130 seconds. This assumption, though unrealistic, reflects our tendency to consider problems linearly.
Pseudolinity also explains the lack of explanations in mathematical lessons that the real world is usually not as simple as a mathematical task. Even artificial intelligence, such as Chatgpt, learned the same bias. For example, answering the question of drying time of towels, the model uses a linear approach that does not always reflect the real scenario.
Non -linear world
If you are preparing something with your kids and dreaming to do twice as much cupcakes as a recipe, you will have to take twice as much of each of the ingredients.
However, to assume that this rule is applied to every phenomenon in our world, would mean to reject the existence and charm of more complex phenomena. For example, the notion that each H20 molecule itself is not moist, or that unique fractals, forming snowflakes, do not occur by adding individual crystals, but as a result of a complex structure.
Even our own life is much larger than the simple sum of atoms and molecules that make up our bodies. Most of the world around us operates in the principles of nonlinearity, where the influence of one element can have a disproportionate effect on the common system.
The steady nature of nonlinear interactions
Despite the fact that many of the most significant daily interactions are nonlinear, we usually do not think about it. However, the concept of linearity is so early and so deeply rooted in our perception that sometimes we miss the possibility of existence of other types of interactions. Therefore, when there is any nonlinear situation, it can cause unexpected reactions and distort our expectations.
Assuming that the output data automatically scales linearly relative to the input, we can find ourselves in a situation where our forecasts do not come true and plans are destroyed.
We exist in a world where many things are obeyed by nonlinear laws, but we have died so much in linearly that sometimes we don't even notice it.
