nonmechanistically

The story

1. Proto-Indo-European*né
2. Proto-Germanic*ne
3. Proto-Indo-European*ís?
4. Proto-Indo-European*h₁óynos
5. Proto-Germanic*ainaz
6. Proto-Germanic*nainaz
7. Proto-West Germanic*nain
8. Old Englishnān
9. Middle Englishnon
10. Old Englishnān
11. Old Englishnān-
12. Middle Englishnon-
13. Englishnon-
14. Proto-Indo-European*megʰ-der.?
15. Ancient Greekμηχᾰνή (mēkhănḗ)
16. New Latinmechanismu
17. Englishmechan(ism)
18. Englishmechanistic
19. Englishnonmechanistic
20. Proto-Indo-European*h₂el-
21. Proto-Indo-European*h₂élisder.?
22. Proto-Indo-European*leyg-
23. Proto-Germanic*līką
24. English todaynonmechanistically

From nonmechanistic + -ally.