Some find it very difficult to see the importance of mathematics and how it influences our world and the things around us. Daniel Tammet, a mathematician, and author presents us with a new insight into numbers throughout the book. Understand how mathematics is unlimited and how it is part of your life and your day to day life, even if you do not work directly with numbers. From the varied format of the snowflakes to even paying a bill in a bar, the numbers are always present! Learn the importance of numbers and how mathematics relates to many areas, such as nature and art!
People often think of mathematics as a rigid, structured thing, and as a tool bounded by innumerable rules. In fact, mathematics can show us how to break limits and can also teach us how some boundaries are not even real. For example, and if someone asked you how to describe an apple, you could use words like "red, fruit, tasty, small," but you could also say things like "it's not round, organic, unable to move by itself, multicolored. "
In mathematics, a collection of values such as these is called a "set" and defining sets can be an inexact science. It's easy to define a set as "number of donuts in a box of a dozen donuts," but when you think of sets such as "qualities of a plant" or "large objects," things are not so simple. We can start by using abstract terms to define things, and the list can be infinite as long as your imagination can feed it!
Numbers are infinite, and multipliers show us this. No matter how far we think numbers can reach, we can go even further by doubling the value. And we can double the total endless times. In our daily lives, we do not need numbers like "quadrillions" or "cribs," but their existence shows us an unlimited potential that no mind could ever imagine.
Probability is very much used in our lives. Bosses, family members, teachers, and others describe the chance that something might happen in abstract terms like "could be ..." and "probably ...". And sometimes even in specific terms, as estimated percentages. If the probability of something is very low, we as humans sometimes assume that this thing will not happen and we prepare for possible failures. Optimists and dreamers, however, like to stick to these small odds, remembering that it is still possible to happen.
Mathematicians often do the same thing. When we look at the odds, any chance other than zero is still a chance. For example, if there is a 0.0001% chance that unicorns exist, a more rational, fact-based person can use this data to discard this idea. A mathematical thinker, on the other hand, can hold onto this small fraction of chance and turn against the evidence.
Even if you are not planning to pick up on a unicorn horn, you can enjoy the beauty of non-zero probability. To think that the fantastic and the abnormal can have a tiny chance of being real is enough to fuel the imagination!
One of the most beautiful things about art is how it can be interpreted in different ways. Where a person sees a mixture of random colors in a painting, another person can see trees, buildings, and rivers. Another may not see anything tangible, but it feels lively, sad, hopeful or with any other emotion as you look at the painting. Beauty is in subjectivity and in how one piece can mean many different things to many people.
Believe it or not, the same thing is true for numbers! Numbers are not just collections of random digits; they are meaningful representations of quantities, expressions of shapes and angles, descriptions of possible and impossible things, and more.
For example, let's look at pi. For some, it is just a set of numbers. Nothing more than "3.1415..." onwards. But for some others, he is an example of the wonders of the infinite, a constant with no real end, so long that it can never be described. For others, pi is very tangible, a representation of a perfect circle; a representation of perfection that can not be seen in reality; a number so perfect in its infinity that putting an end to it would completely change its meaning. Still, others see pi as a challenge for memory and as a challenge for every part of their brains.
Part of the reason our minds love patterns, in numbers and art, comes from our natural tendency to repeat and to order. Regular repetitions in music, poetry, art, and math create calm, balanced, and easy patterns. When done right, these intentional balances can create feelings of anticipation or anxiety, as our mind knows the next part of the patterns that are not yet there, but they should be.
The masters of the arts know how to use these facts to draw us. Poets fill their descriptions of the world with patterns that attract us. Composers use sticky rhythms to leave their lyrics even more glued to our heads. And mathematicians find a natural rhythm in numerical patterns.
You could find math when you admire light asymmetry on the faces of a model, knowing that its beauty would be less if it possessed perfectly balanced characteristics. The math is there when you watch sports cars on races. And when you relax listening to your favorite music, you're enjoying rhythms that would be impossible without math.
Why do we sometimes have trouble remembering multiplication tables? Why can we easily remember phrases, slogans, and languages every day, but multiplying by eight is difficult? Possibly this is because we can not memorize as easy as the rhythms and patterns. Tables for the 5x or 10x can be easy because they have simple patterns (5,10,15,20,25 ...), but the others can be more complicated.
This is the same problem we face with spoken language. People often have trouble remembering complex statements until you organize them as memorable phrases or short presentations. You would have a hard time remembering the saying "saving resources allow for provisions for a future need, which you would not have if you did not save," but "not to waste, not to scarcity" is much simpler. It's fast, easy and has a sound that sticks to memory.
The Portuguese language and the mathematical language aren't very different and are even more similar when we give the individual numbers a meaning, associating them with familiar objects.
If you wanted to multiply by 6, imagine random numbers floating around there may not be efficient, but imagine numerous crates (they usually contain six packs each) of your favorite drink can help your brain make the necessary connection. Fractions become easier when you imagine them as well. You may have difficulty understanding 5/8 on a math problem, but visualizing a hot pizza cut into eight pieces is simple and helps you connect abstract ideas to the real world.
And that's the way we learn words too! Since we are very young, we associate each word with one thing, and our mind creates the connections between the two. The simplified way of learning languages is much more natural than decorating the meanings of words in our minds. It's the same with math.
We use mathematical, logical reasoning daily. We see milk in our refrigerator that is smelling bad and then we assume that it is sour, based on our past experiences. Young students who wake up one morning and see it's snowing think "normally I do not need to go to school when it snows and it's snowing now!"
We use ideas and discourses that we know are true to work with the unknown - as a mathematical proof.
A mathematician working with the "2x + 3 =?" The problem needs to use what he knows to be true to find the answer. If someone says that x is equal to 2, they can calculate that the sum is equal to 7. It is a matter of finding out what is true based on what is known, which is the same logic we use every day.
We reasoned to discover values as well. Using simple math, we can figure out the cost of an object's parts to understand whether buying them is a good idea. When we compare closed products, we sometimes weigh them in our hands to see if the most expensive choice really is worth the extra cost. We find out how much our time is worth by dividing our wages by the hour. Whenever we need to put value into something, we use mathematical logic to find the right way to do it.
From when you wake up to when you go to sleep, the numbers are influencing the way things are done.
When going to work every day, you should thank the numbers for helping a transportation engineer calculate the distances and angles in your city. You can thank math for helping law enforcement figure out speed limits and distances from mandatory stops. And if you live in a big city, you must have seen numbers sorting the streets too!
Math and numbers have also influenced the calendar you use to make appointments! For many years, scholars try to figure out the perfect way to measure the days, from sunrise to sunset, week after week, year after year. Unfortunately, for them, days do not have a fixed size, and any attempt to create a fixed calendar will end up unusable by the rotations of the sun.
Knowing the kinds of problems caused by these irregular days, it is no wonder that mathematicians were so sought after. Scholars were recruited to measure the movements of the sun, to find patterns at sunrise and sunset, and to create a system of days that would guarantee that society would always be in sync with the cycle. We should thank mathematicians for our current system of leap years because without them we would be in the dark all of a sudden.
The concepts of mathematics are even in nature. Have you ever noticed how nature affects the shapes of snowflakes? In a temperature-controlled vacuum, they might look perfectly symmetrical, but variations in temperature, winds, and other factors in our world mean that flakes have different shape patterns. This is why snowflakes have infinite variations.
Just as unpredictable variables can affect the formation of snowflakes, mathematical variables can affect a formula. We think mathematics is very rigid, but the reality is not this: things that seem random are a combination of effects that happen for a reason. Just as the perfect symmetry of snowflakes can be a special thing, a complete formula can become a completely different thing with the introduction of new variables, turning into a whole new thing.
Although our world is not unlimited, we as human beings still love exploring nature. Although our minds are captivated by infinity, the boundaries still give us a sense of wonder and joy. These boundaries do not make things less interesting, and the chance to discover or document an entire planet is a great attraction to curious minds.
The same is true for mathematicians. Just because there is a finite limit on something, it does not make it less valuable. Different permutations in a formula or changes of states in a chessboard generate fascinating studies. Exploring these studies is very encouraging for some people, just as exploring our world is as well.
You will find mathematical principles shaping events around the world, but they may be too small for you to see. In mathematics, an equation can change radically if you change a variable by even a tenth. Sums and products change, other variables are affected and what you thought to be just an imperceptible difference produces great results and drastic differences.
Turn on the news or read the newspaper and you will find the same truths around the world. Small variables do not make the news, but we see their eventual effects daily. Things as small as a lost phone call or traffic on the way to a meeting seem irrelevant, but they can change the world events entirely.
Small changes transform the world, but many times we do not even notice them. We assume that large occurrences are the most important when changes and small factors may have caused the big ones in the first place. Any mathematician will confirm that this is true also in your area and for the formulas and equations used daily. Looking at how the world works and how the formulas work, it is easy to see how a mathematical thought can be applied in our daily lives!
Although mathematics is a powerful tool for exploring and shaping our world, there are dangers in its misuse. For example, the idea of a "middle person" can be misinterpreted.
The idea of "average" is a highly mathematical thought. In mathematics, a mean is a statistical norm, a point in the middle of the die. We use it to find things like "the average person" or "the average diet." We have seen everything our samples offer us, and we have found their midpoint. It's a great way to get information about the cultures around us. But there is also a downside to that.
When compared to the average, a different person may find it unacceptable. She may want to change to fit what is revealed by statistics as normal. But people are not percentages. Our variety is what makes us human beings unique, and this is a characteristic to be valued. Just because a person does not fit the pattern does not mean that it is less valid. The differences are perfectly normal and positive!
Another danger may come from predictions of future events. Sometimes we treat the world as a great formula. We try to find out the variables and factors to predict the results. "How will my boss's mood be today?" "Will the lunch line be big?" "Will there be any traffic jam this afternoon?" People who are very good at it may seem almost psychic.
However, this is a dangerous area, because the more you try to anticipate the facts, the further you will get from the truth. If you go too far, you will find that your guesses were purely based on other guesses rather than concrete facts. Be careful and base your thoughts on the real world!
Some people see math as a strange thing. For them, math is a tool to be used only when needed. Phrases such as "When will I use this?" Echo in schools and people begin to get the impression that math is not important to them. They could not be more wrong.
Mathematics is all around us. From an early age, we are taught that mathematics will be an important part of our lives and we use it daily even without realizing it. The language of numbers affects all of us and has also affected how we travel, plan, think and live for centuries.
Many would consider Daniel Tammet a genius. And not for less, since his intellectual abilities are impressive and diverse. If you're still not convinced, take a look at his TED Talks on The Different Forms of Knowledge.
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