alt Hacker News> few of the computable numbers that are not algebraic are interesting, the main exceptions being the numbers that are algebraic expressions containing "2*Pi" and/or "ln 2".
I don’t think this is true at all. For example: the solution to a generic PDE that has no closed form solution at some point of import is likely transcendental, not algebraic, but definitely computable. (Think, say, Navier-Stokes being used for weather predictions in some specific place.)
True, but with such numbers you will normally not do anything else except computing an approximate value of them.
They are not comparable with numbers like 2*Pi or various irrational nth roots that can appear in a lot of relationships and formulae in symbolic computations.
That is what I meant by "interesting", i.e. the necessity of using symbols of such numbers, obviously for use in symbolic computations, since in numeric computations you would never use the actual numbers, but only some approximations of them.
What I have said is equivalent to saying that there are only a few transcendental numbers for which you need symbols.
The number of symbols that are really needed is much less than the number of symbols that happened to be used during the history. For instance a single symbol related to Pi is needed, and it would have been much better if it was a symbol for 2*Pi, not for Pi. When using decimal numbers, one may want to use the value of the decimal logarithm of "e", or of its inverse, but there exists no need whatsoever to use decimal numbers anywhere, this is just a historical accident. Etc., there are various other examples of superfluous constants, which are not needed in any practical application, unlike "2*Pi" and "ln 2", which are ubiquitous (because they appear in the derivation formulae for the trigonometric and exponential functions).