The Greek adverb eike means 'in vain' or 'to no purpose' — doing something with no result, without reason, or thoughtlessly. It describes wasted effort or ungrounded action.
Paul uses eike to cut through religious externalism and point to what genuinely transforms. 'Are you so foolish? Having begun by the Spirit, are you now being perfected by the flesh? Did you suffer so many things in vain?' (Galatians 3:3–4). The Galatians' defection to law-keeping threatens to make all their Spirit-begun experience meaningless. In Romans 13:4, the governing authority does not bear the sword eike — 'in vain' — God has given it real, purposeful authority. In Colossians 2:18, false humility and angel worship are condemned as inflating pride 'without reason.' Real Christianity is neither thoughtless nor purposeless.