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However, mathematicians have described numbers even bigger than a googol plex. The most famous is Graham’s number.
Conceived of in the 1970s, the mathematician Ronald Graham used it as part of a mathematical proof. He proposed it to solve a problem in a branch of mathematics called Ramsey theory, which deals with how to find order in chaos.
Understanding the maths behind it is a little involved, but the main thing to know is that creating it involves exponentiation to a truly brain-shattering degree. Graham himself explains why in this video for the mathematics YouTube channel Numberphile.
Oh, and you should also know that even if you did try to write it down on paper, there wouldn’t be enough room in the visible Universe to fit it in.
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What about infinity though? For the average person, infinity seems a straightforward concept – it’s not a number, rather something that goes on forever. Whether the human mind is capable of truly understanding it, however, is another question.
In the 1700s, the writer and philosopher Edmund Burke wrote that “infinity has a tendency to fill the mind with that sort of delightful horror which is the most genuine effect and truest test of the sublime”. For Burke, the concept evoked a mixture of astonishment and fear; pleasure and pain, both at the same time. And there were few times that people would ever encounter it in the world, apart from in the imagination, and even then they could not truly know it.
However, the following century, the logician Georg Cantor took the concept of infinity and made it even more mind-bending. Some infinities, he showed, are bigger than others.
How so? One of the simplest ways to understand why is to imagine the set of all the even numbers. This would be infinite, right? But it must be smaller than the set of all whole numbers, because it does not contain the odd numbers. Cantor proved that when you compare such sets, they contain numbers that do not match up, therefore there must be multiple sizes of infinity.
This is hard to accept, let alone picture, but that’s what happens to the mind when it tries to grapple with mathematical enormity. Such enormous numbers are a great deal more difficult to understand than a 10-year-old me could ever have imagined.
*Richard Fisher is a senior journalist for BBC Future. Twitter: @rifish
The author used ChatGPT to research trusted sources and calculate parts of this story.
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