Have you ever wondered what numbers come after trillions? Some are too big to fit into the mind of the known universe.
What’s the most significant number you can think of? This is a question that many people may have asked themselves in their childhood. A child might say the number one billion billion billion, and another child knows about trillions, squillions, or kajillions.

Finally, a child remembers that he knows the winning answer: “infinity”; But this arrogance is short-lived. Another child soon beats him with the solution, “infinity plus one”. Trying to imagine and understand huge numbers is beyond child’s play. Instead, it is a problem that has occupied the minds of mathematicians for centuries. They mentioned huge numbers that no human could even imagine in their mind. There is more than one infinity, and some infinities are more significant than others.

Let’s start with the obvious. No particular number can be considered the most significant number because natural numbers are infinite; Therefore, it is impossible to win in the children’s game of guessing the most considerable number.

However, computers still have imagined, expressed, written, or even represented all large numbers. First, go directly up the numbers ladder and reach numbers beyond everyday life. For example, in news headlines, the most significant digits of national debts are usually expressed in trillions. Still, again, there are numbers with a higher hierarchy that are rarely mentioned by name. These numbers start from quadrillion, quintillion, and sextillion and continue in that order. A quadrillion (US version) has 15 zeros, a quintillion has 18 zeros, and a sextillion has 21 zeros.

The mentioned numbers are significant. The human body has approximately 30 trillion cells, So to reach a quadrillion cells in a room, you need 34 people. A quintillion can be imagined by the number of insects on earth, which runs ten quintillions. Still, the sextillion number is so significant that a sextillion tower can be 180,000 light-years high, which is bigger than the diameter of the Milky Way galaxy.

You can even go up to a centillion, which has 303 zeros based on the American version. Beyond this number, there are two-centillion and three-centillion numbers, but they need a precise standard. Usually, only physicists and mathematicians use centillion, and even then, only experts in fields such as string theory use these numbers. If Elon Musk wanted to become a centillionaire, he would have to maintain his current earnings per millisecond for 1.7 times 10 to the power of 282 years, a number with 283 digits.

Google and Google Plex
Gogol is another considerable number, not as significant as an American centillion, but more famous. This number with one hundred zeros equals ten to the power of 100 and inspired the name of the well-known search engine, Google. The reason for choosing this number by the founders of Google was to provide a vast sea of online information to the audience. However, the Internet has yet to expand to this number: according to the Wayback Machine, the Internet Archive has only reached 801 billion indexed web pages since the 1990s.

Google Plex is a much larger version of Google (the name of the Google office in California), equal to ten to the power of one Google or ten to the power of ten to the hundredth power. Google Plex is a number with several zero Google, But how long does it take to write such a number? Even if you have held a pencil since childhood and started writing this number, you will not be able to finish it in your lifetime. To get a proper understanding of the number of digits in this number, Hamkins suggests this experiment:

Suppose you have a printer with these specifications. A super-fast printer that prints a million digits per second. This printer started working from the beginning of the world about 13.8 billion years ago. Even if such a printer has published a million digits per second since the Big Bang, it has only been able to print a small fraction of the Google Plex number.

Hamkins also makes an interesting point. Some big numbers smaller than Google Plex cannot be described with a more straightforward concept or word and are beyond our understanding. These numbers have never been imagined or described.

Hamkins believes that the only way to describe these numbers is to express their digits, But even if you print a million digits every second from the beginning of the world, you cannot say all these digits. It is an interesting situation because it shows that we have a simple definition of large numbers, but it isn’t easy to describe many intermediate numbers. There are milestone numbers that are easier to explain, but there is an ocean of complexity between them.

However, mathematicians defined numbers as even more significant than Google Plex, one of the most famous is “Graham’s number”. Ronald Graham used this number in the 1970s as part of a mathematical proof. He came up with this number to solve a problem in a branch of mathematics called Ramsey theory, which deals with how to find order in disorder. Graham’s natural number has about ten thousand zeros. Understanding the mathematics of this number is a bit complicated.

If you ever tried to write such a number on paper, there is not enough space in the visible world to accommodate such a number.

But what about infinity? To the average person, infinity seems like an obvious concept. In fact, from this point of view, infinity is not a number but something that continues forever; But whether the human mind can understand it is another question.

The author and philosopher Edmund Burke wrote in the 1700s that “infinity” tends to fill the brain with a kind of pleasant dread, which is the purest work and the most accurate test of the sublime. For Burke, infinity combined fear and wonder, pleasure and pain simultaneously. In the fantasy world, one can rarely face such a feeling in reality.

However, a century later, the logician Georg Cantor turned the concept of infinity into something confusing. He showed that some infinities are more significant than others, but how? To understand why, think of numbers as sets. If you want to compare all natural numbers (1, 2, 3, 4, etc.) in one scene and all even numbers are in another location, then every natural number can be paired with a similar even number. This pair shows that two infinite groups have the same size or so-called “countable infinity”.

However, Cantor shows that this cannot be done for natural and real numbers; Because real numbers have an infinity of intermediate decimal digits (for example, 0.123, 0.1234, 0.12345, and so on).

If you try to pair numbers with any set, you will always find an actual number not paired with a natural number. Real numbers are “infinitely uncountable”; Therefore, the infinities differ. In general, it isn’t easy to accept the above concepts. Just imagine what happens to the mind when it tries to imagine such large numbers.

By Pooyatp

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