User blog comment:B1mb0w/From omega to epsilon nought summary/@comment-1605058-20150630121014

If instead of adding $$\omega$$'s you started with adding 1's, then you would notice that you need $$3^{27}=3^{3^3}=3\uparrow\uparrow 3$$ steps. This is related to the fact that $$\varepsilon_0$$ can be seen to be equal to $$\omega\uparrow\uparrow\omega$$.