Alex Carson
Most people are familiar with millions and billions. We can relate to these numbers because there are quite a number of millionaires and billionaires on planet earth. However, a trillion, a centillion and a googol are numbers many people cannot fathom.
Now, if your field is physics, math or engineering, you are likely to encounter these huge numbers in your profession. Some of these numbers also pop up in quantum physics and other related courses. However, many people outside these fields have no notion that these huge numbers even exist. According to experts, many people are not even intuitively equipped to understand these numbers. Some of these numbers are so huge that you cannot even write them down in full. This is why different notations are used to indicate these numbers. Try to imagine these numbers the way you imagine a number like fifty, for instance, and you will find out this is impossible. In some cases, merely thinking about these numbers is enough to give you a headache. Some mathematicians even have a theory that storing these ginormous numbers in your head could create a black hole.
Huge Numbers in Ancient Times
The fascination with huge numbers is not a recent phenomenon. According to texts from ancient Babylon, people in this great city mentioned and contemplated some incredibly large numbers. Archimedes, the Greek philosopher allegedly calculated the number of grains of sand that would fit in to the universe. Clearly, it is almost impossible to express this number in Roman or Arabic numerals. This huge number was represented by 10 raised to the 63. This means the grains of sand we are talking about is approximately 1 with 63 zeroes after it. Now, try writing this number and you can understand how these numbers can lead to a splitting headache.
Tiny Numbers Are Just As Mysterious
Now, the black hole theory is not applicable to only huge numbers. This is also applicable to tiny numbers. This is easy to understand because tiny numbers are just the inverse of huge numbers. For instance, experts describe the “mysterious acceleration of the universe due to dark energy” as a cosmological constant. According to an expert who has written about very large numbers, the figure we are talking about here is 10 to the minus 122. You should not blame yourself if this whole thing sounds like a different language to you. Most people on planet earth have no idea of what the cosmological constant is.
Using Images Instead of Numbers
Even experts in huge numbers sometimes run out of numbers when things get too large or too tiny for that matter. For instance, trying to get exact numbers for the size of the universe is a bit like talking about the number of cells in the human body. Another breathtaking comparison is the one that has to do with the tiniest of sizes. One expert talked about viewing a tiny flake of paint on a wall from the top of the highest tower in the USA (without binoculars or a telescope).
An Explosion of Probabilities
Huge and tiny numbers are not limited to the physical world. Sometimes, these numbers are used to quantify all the possible worlds that could ever exist. In quantum theory, the experts go beyond a specific time or place. Instead, they use a wave of probabilities. The experts in this field speak about each object in a particular system being in a wave state or a particle. Supposing an expert tells you that 1,000 particles create 2 to the 1,000 possible configurations, will this make any sense to you? Chances are you as much in the dark as most people out there. However, you are not blame worthy because you are not an expert in quantum theory.
Beyond Scientific Notation
Even the experts know that some numbers cannot be captured using the old scientific notations. This is why when some numbers get big enough; the experts have to come up with entirely new ways of writing them. For instance, the great Archimedes had to create a new notation to express the size of the universe. He did this by compounding a Roman unit called a myriad and this is why English speakers talk about a myriad of problems or issues.
Graham’s Number
In 1971, the mathematician Ronald Graham conceived the Graham’s number. This number required the performance of 65 steps but after the first few steps, it became impossible to express the size of the number in scientific notation. If you think Graham’s number takes the biscuit, another number called TREE(3) put Graham’s number in the shade. It is impossible to capture the size of the tower of exponents involved in this number. However, you can always trust experts to have a solution to every mathematical problem. Using Ackerman functions, even this number can be expressed in a compact manner.
Final Word
Next time you are confronted with numbers you cannot fathom, do not give yourself a headache and do not fall into a black hole. Call in a mathematical physicist or an expert in quantum theory. These experts have the facilities to cope with mind-boggling numbers.
