User blog comment:Nayuta Ito/Trying to Make a Continuous Psi Level/@comment-30754445-20171226045826/@comment-30754445-20171228061010

Yes, you need some form of continuous tetration, that's true.

But the whole point of Psi Levels is to have smoothly increasing scale. So we would probably want a continuous version to be more than just "continuous". We would want it to be smoothly increasing, and Letter Notation doesn't fit this bill very well.

Ideally, we would want to use the Psi Levels system itself to define our continuous tetration. Actually you've already done a very similar thing with your formula for levels 2.0-5.0. So 10^^7.3 will simply be 10^10^10^psi(4.3).

Of-course, this will only be as smooth as your interpolation formulas at level 1.0-2.0 are.