Doppelgängion

Doppelgängion is a number defined as \(10^{10^{68}}\). Antonio Padilla coined this number in his book Fantastic numbers and where to find them.Antonio Padilla (2023) "Fantastic numbers and where to find them: A journey to the edge of physics" Penguin Books. ISBN 978-0141992822p.55 Padilla calculated that this is the largest number of microstates you will ever need to describe a cubic metre of space. It is equal to a 1 with 100 unvigintillion (1068) zeros, and it's 1068+1 digits long. Writing down the full decimal expansion would take 100 novemdecillion (1062) books of 400 pages each, with 2,500 digits on each page (except for the first, which would have 2,501). It is slightly smaller than a duovigintillionplex (101069).
== Names in -illion systems ==
In Conway-Wechsler system,Conway and Guy (1995) "The book of Numbers" Copernicus. pp.14-15. doppelgängion is expressed in short scale as follows by using Fish's result.Fish Illion name of 10^10^x in Conway-Wechsler system 2021-12-25
According to Landon Curt Noll's The English name of a number, doppelgängion is also known as:
Using Jonathan Bowers -illions, doppelgängion is also known as:AR Googol - List of Bowers' illions Retrieved 2024-08-02. 
== How it was calculated ==
Padilla utilized for the calculations. and showed that a black hole with an event horizon area \(A_H\) has an entropy \(S\) expressed in the formula:
\[S = \frac{A_H}{4l_p^2}\]
Here, \(l_p\) represents the , approximately 1.6 x 10-35 meters.p.54 Padilla applied this formula in his calculations.p.55
Let's return to the cubic metre of space that you happen to occupy, or indeed any cubic metre of space. How many microstates do you need to be absolutely certain of capturing all its physics? To answer this, we need to touch upon all possible microstates and push things to the entropic limit. In other words, we need to consider the largest black hole that could fit inside the space. Such a black hole would have an event horizon with a surface area of around a square metre and therefore, according to Bekenstein and Hawking's formula, an entropy of around \(10^{69}\). That equates to around \(10^{10^{68}}\) microstates.
The value of \(10^{69}\) was derived by substituting \(A_H = 1 \mathrm{m}^2\) into the formula developed by Bekenstein and Hawking's, as shown above. The value \(10^{10^{68}}\) seems to approximate \(2^{10^{69}}\).p.54
== Sources ==
Category:Numbers
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Category:Numbers with peer-reviewed source