## Archive for Turing machine

## Alain Turing cash!

Posted in pictures, Travel with tags ACE computer, Alan Turing, Bank of England, bills, Bletchley Park, British history, code breaking, England, Enigma code machine, The British Bomb, Turing machine, WW II on April 8, 2021 by xi'an## how large is 9!!!!!!!!!?

Posted in Statistics with tags big numbers, cellphone, coding, cross validated, factorial, mathematical puzzle, pocket calculator, Rado's numbers, The Riddler, Turing machine on March 17, 2017 by xi'an**T**his may sound like an absurd question [and in some sense it is!], but this came out of a recent mathematical riddle on The Riddler, asking for the largest number one could write with ten symbols. The difficulty with this riddle is the definition of a symbol, as the collection of available symbols is a very relative concept. For instance, if one takes the symbols available on a basic pocket calculator, besides the 10 digits and the decimal point, there should be the four basic operations plus square root and square,which means that presumably 999999999² is the largest one can on a cell phone, there are already many more operations, for instance my phone includes the factorial operator and hence 9!!!!!!!!! is a good guess. While moving to a computer the problem becomes somewhat meaningless, both because there are very few software that handle infinite precision computing and hence very large numbers are not achievable without additional coding, and because it very much depends on the environment and on which numbers and symbols are already coded in the local language. As illustrated by this X validated answer, this link from The Riddler, and the xkcd entry below. (The solution provided by The Riddler itself is not particularly relevant as it relies on a particular collection of symbols, which mean Rado’s number BB(9999!) is also a solution within the right referential.)